Subgroups — C₂×C₅₃×#3566 #27270254

Order 13568.

6694 conjugacy classes of subgroups.

The subgroup lattice has 1904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3566	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₅₃×#563	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₃×#562	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₃×#562	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₃×#560	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅₃×#551	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₃×#551	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅₃×#551	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₅₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₅₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₅₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₅₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₅₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₅₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂×C₅₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×C₅₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
27	C₂×C₅₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
28	C₂×C₅₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂×C₅₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
33	C₅₃×#563	C₂²	1	16	yes	complemented
34	C₅₃×#562	C₂²	1	16	yes	complemented
35	C₅₃×#562	C₂²	1	16	yes	complemented
36	C₅₃×#560	C₂²	1	16	yes	complemented
37	C₅₃×#559	C₂²	1	16	yes	complemented
38	C₅₃×#556	C₂²	1	16	yes	complemented
39	C₅₃×#555	C₂²	1	16	yes	complemented
40	C₅₃×#553	C₂²	1	16	yes	complemented
41	C₅₃×#553	C₂²	1	16	yes	complemented
42	C₅₃×#553	C₂²	1	16	yes	complemented
43	C₅₃×#552	C₂²	1	16	yes	complemented
44	C₅₃×#552	C₂²	1	16	yes	complemented
45	C₅₃×#552	C₂²	1	16	yes	complemented
46	C₅₃×#551	C₂²	1	16	yes	complemented
47	C₅₃×#551	C₂²	1	16	yes	complemented
48	C₅₃×#551	C₂²	1	16	yes	complemented
49	C₅₃×#542	C₂²	1	16	yes	complemented
50	C₅₃×#542	C₂²	1	16	yes	complemented
51	C₅₃×#542	C₂²	1	16	yes	complemented
52	C₅₃×#541	C₂²	1	16	yes	complemented
53	C₅₃×#541	C₂²	1	16	yes	complemented
54	C₅₃×#540	C₂²	1	16	yes	complemented
55	C₅₃×#539	C₂²	1	16	yes	complemented
56	C₅₃×#539	C₂²	1	16	yes	complemented
57	C₅₃×#539	C₂²	1	16	yes	complemented
58	C₅₃×#538	C₂²	1	16	yes	complemented
59	C₅₃×#538	C₂²	1	16	yes	complemented
60	C₅₃×#538	C₂²	1	16	yes	complemented
61	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
64	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
65	C₅₃×#529	C₂²	1	16	yes	complemented
66	C₅₃×#529	C₂²	1	16	yes	complemented
67	C₅₃×#529	C₂²	1	16	yes	complemented
68	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
69	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
70	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
71	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
72	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
73	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
74	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
75	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
76	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
77	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
78	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
79	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
80	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
81	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
82	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
83	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
84	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
85	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
86	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
87	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
88	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
89	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
90	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
91	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
92	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
93	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
94	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
95	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
96	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
97	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
98	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
99	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
100	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
101	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
102	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
103	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
104	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
105	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
106	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
107	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
108	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
109	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
110	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
111	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
112	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
113	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
114	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
115	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
116	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
117	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
118	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
119	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
120	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
121	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
122	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
123	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
124	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
125	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
126	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
127	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
128	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
129	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
130	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
131	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
132	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
133	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
134	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
136	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
137	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
138	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
139	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
140	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
141	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
142	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
143	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
144	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
145	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
146	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
147	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
148	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
149	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
150	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
151	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
152	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
153	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
154	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
155	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
156	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
157	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
158	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
159	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
160	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
161	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
162	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
163	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
164	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
165	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
166	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
167	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
168	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
169	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
170	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
171	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
172	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
173	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
174	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
175	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
176	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
177	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
178	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
179	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
180	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
181	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
182	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
183	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
184	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
185	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
186	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
187	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
188	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
189	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
190	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
191	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
192	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
193	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
194	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
195	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
196	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
197	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
198	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
199	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
200	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
201	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
202	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
203	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
204	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
205	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
206	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
207	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
208	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
209	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
210	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
211	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
212	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
213	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
214	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
215	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
216	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
217	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
218	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
219	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
220	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
221	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
222	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
223	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
224	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
225	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
227	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
228	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
229	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
230	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
231	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
232	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
233	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
234	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
235	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
244	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
248	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
249	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
251	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
252	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
263	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
264	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
265	#127×C₅₃	C₂³	1	8	yes	—
266	#126×C₅₃	C₂³	1	8	yes	—
267	#126×C₅₃	C₂³	1	8	yes	—
268	#126×C₅₃	C₂³	1	8	yes	—
269	#126×C₅₃	C₂³	1	8	yes	—
270	#126×C₅₃	C₂³	1	8	yes	—
271	#126×C₅₃	C₂³	1	8	yes	—
272	#126×C₅₃	C₂³	1	8	yes	—
273	#126×C₅₃	C₂³	1	8	yes	—
274	#126×C₅₃	C₂³	1	8	yes	—
275	#126×C₅₃	C₂³	1	8	yes	—
276	#126×C₅₃	C₂³	1	8	yes	—
277	#126×C₅₃	C₂³	1	8	yes	—
278	#126×C₅₃	C₂³	1	8	yes	—
279	#126×C₅₃	C₂³	1	8	yes	—
280	#126×C₅₃	C₂³	1	8	yes	complemented
281	#126×C₅₃	C₂³	1	8	yes	complemented
282	#126×C₅₃	C₂³	1	8	yes	complemented
283	#126×C₅₃	C₂³	1	8	yes	complemented
284	#126×C₅₃	C₂³	1	8	yes	complemented
285	#126×C₅₃	C₂³	1	8	yes	complemented
286	#125×C₅₃	C₂³	1	8	yes	complemented
287	#125×C₅₃	C₂³	1	8	yes	complemented
288	#125×C₅₃	C₂³	1	8	yes	complemented
289	#125×C₅₃	C₂³	1	8	yes	complemented
290	#125×C₅₃	C₂³	1	8	yes	complemented
291	#125×C₅₃	C₂³	1	8	yes	complemented
292	#125×C₅₃	C₂³	1	8	yes	complemented
293	#125×C₅₃	C₂³	1	8	yes	complemented
294	#125×C₅₃	C₂³	1	8	yes	complemented
295	#125×C₅₃	C₂³	1	8	yes	complemented
296	#125×C₅₃	C₂³	1	8	yes	complemented
297	#125×C₅₃	C₂³	1	8	yes	complemented
298	#124×C₅₃	C₂³	1	8	yes	—
299	#124×C₅₃	C₂³	1	8	yes	—
300	#124×C₅₃	C₂³	1	8	yes	—
301	#124×C₅₃	C₂³	1	8	yes	—
302	#124×C₅₃	C₂³	1	8	yes	—
303	#124×C₅₃	C₂³	1	8	yes	—
304	#124×C₅₃	C₂³	1	8	yes	—
305	#124×C₅₃	C₂³	1	8	yes	—
306	#124×C₅₃	C₂³	1	8	yes	—
307	#124×C₅₃	C₂³	1	8	yes	complemented
308	#124×C₅₃	C₂³	1	8	yes	complemented
309	#124×C₅₃	C₂³	1	8	yes	complemented
310	#123×C₅₃	C₂³	1	8	yes	—
311	#123×C₅₃	C₂³	1	8	yes	—
312	#123×C₅₃	C₂³	1	8	yes	—
313	#123×C₅₃	C₂³	1	8	yes	—
314	#123×C₅₃	C₂³	1	8	yes	—
315	#123×C₅₃	C₂³	1	8	yes	—
316	#123×C₅₃	C₂³	1	8	yes	—
317	#123×C₅₃	C₂³	1	8	yes	—
318	#123×C₅₃	C₂³	1	8	yes	—
319	#123×C₅₃	C₂³	1	8	yes	—
320	#123×C₅₃	C₂³	1	8	yes	—
321	#123×C₅₃	C₂³	1	8	yes	—
322	#123×C₅₃	C₂³	1	8	yes	—
323	#123×C₅₃	C₂³	1	8	yes	—
324	#123×C₅₃	C₂³	1	8	yes	—
325	#123×C₅₃	C₂³	1	8	yes	—
326	#123×C₅₃	C₂³	1	8	yes	—
327	#123×C₅₃	C₂³	1	8	yes	—
328	#123×C₅₃	C₂³	1	8	yes	complemented
329	#123×C₅₃	C₂³	1	8	yes	complemented
330	#123×C₅₃	C₂³	1	8	yes	complemented
331	#123×C₅₃	C₂³	1	8	yes	complemented
332	#123×C₅₃	C₂³	1	8	yes	complemented
333	#123×C₅₃	C₂³	1	8	yes	complemented
334	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
335	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
336	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
337	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
338	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
339	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
340	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
341	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
342	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
343	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
344	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
345	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
346	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
347	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
348	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
349	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
350	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
351	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
352	#121×C₅₃	C₂³	1	8	yes	—
353	#121×C₅₃	C₂³	1	8	yes	—
354	#121×C₅₃	C₂³	1	8	yes	—
355	#121×C₅₃	C₂³	1	8	yes	—
356	#121×C₅₃	C₂³	1	8	yes	—
357	#121×C₅₃	C₂³	1	8	yes	—
358	#121×C₅₃	C₂³	1	8	yes	—
359	#121×C₅₃	C₂³	1	8	yes	—
360	#121×C₅₃	C₂³	1	8	yes	—
361	#121×C₅₃	C₂³	1	8	yes	—
362	#121×C₅₃	C₂³	1	8	yes	—
363	#121×C₅₃	C₂³	1	8	yes	—
364	#121×C₅₃	C₂³	1	8	yes	—
365	#121×C₅₃	C₂³	1	8	yes	—
366	#121×C₅₃	C₂³	1	8	yes	—
367	#121×C₅₃	C₂³	1	8	yes	complemented
368	#121×C₅₃	C₂³	1	8	yes	complemented
369	#121×C₅₃	C₂³	1	8	yes	complemented
370	#120×C₅₃	C₂³	1	8	yes	—
371	#120×C₅₃	C₂³	1	8	yes	—
372	#120×C₅₃	C₂³	1	8	yes	—
373	#120×C₅₃	C₂³	1	8	yes	—
374	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
375	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
376	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
377	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
378	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
379	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
380	C₄×D₄×C₅₃	C₂³	1	8	yes	—
381	C₄×D₄×C₅₃	C₂³	1	8	yes	—
382	C₄×D₄×C₅₃	C₂³	1	8	yes	—
383	C₄×D₄×C₅₃	C₂³	1	8	yes	—
384	C₄×D₄×C₅₃	C₂³	1	8	yes	—
385	C₄×D₄×C₅₃	C₂³	1	8	yes	—
386	C₄×D₄×C₅₃	C₂³	1	8	yes	—
387	C₄×D₄×C₅₃	C₂³	1	8	yes	—
388	C₄×D₄×C₅₃	C₂³	1	8	yes	—
389	C₄×D₄×C₅₃	C₂³	1	8	yes	—
390	C₄×D₄×C₅₃	C₂³	1	8	yes	—
391	C₄×D₄×C₅₃	C₂³	1	8	yes	—
392	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
393	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
394	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
395	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
396	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
397	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
398	#117×C₅₃	C₂³	1	8	yes	—
399	#117×C₅₃	C₂³	1	8	yes	—
400	#117×C₅₃	C₂³	1	8	yes	—
401	#117×C₅₃	C₂³	1	8	yes	—
402	#117×C₅₃	C₂³	1	8	yes	—
403	#117×C₅₃	C₂³	1	8	yes	—
404	#117×C₅₃	C₂³	1	8	yes	complemented
405	#117×C₅₃	C₂³	1	8	yes	complemented
406	#117×C₅₃	C₂³	1	8	yes	complemented
407	#117×C₅₃	C₂³	1	8	yes	complemented
408	#117×C₅₃	C₂³	1	8	yes	complemented
409	#117×C₅₃	C₂³	1	8	yes	complemented
410	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
411	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
412	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
413	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
414	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
415	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
416	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
417	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
418	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
419	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
420	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
421	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
422	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
423	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
424	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
425	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
426	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
427	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
428	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
429	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
430	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
431	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
432	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
433	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
434	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
435	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
436	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
437	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
438	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
439	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
440	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
441	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
442	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
443	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
444	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
445	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
446	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
447	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
448	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
449	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
450	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
451	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
452	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
453	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
454	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
455	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
456	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
457	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
458	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
459	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
460	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
461	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
462	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
463	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
464	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
465	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
466	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
467	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
468	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
469	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
470	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
471	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
472	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
473	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
474	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
475	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
476	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
477	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
478	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
479	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
480	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
481	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
482	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
483	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
484	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
485	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
486	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
487	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
488	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
489	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
490	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
491	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
492	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
493	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
494	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
495	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
496	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
497	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
498	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
499	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
500	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
501	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
502	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
503	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
504	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
505	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
506	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
507	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
508	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
509	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
510	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
511	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
512	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
513	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
514	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
515	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
516	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
517	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
518	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
519	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
520	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
521	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
522	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
523	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
524	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
525	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
526	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
527	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
528	C₂×C₄²×C₅₃	C₂³	1	8	yes	complemented
529	C₂⁴×C₅₃	—	4	2	no	—
530	C₂⁴×C₅₃	—	4	2	no	—
531	C₂⁴×C₅₃	—	4	2	no	—
532	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
533	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
534	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
535	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
536	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
537	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
538	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
539	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
540	C₂×Q₈×C₅₃	—	4	2	no	—
541	C₂×Q₈×C₅₃	—	4	2	no	—
542	C₂×Q₈×C₅₃	—	4	2	no	—
543	C₂×Q₈×C₅₃	—	4	2	no	—
544	C₂×Q₈×C₅₃	—	4	2	no	—
545	C₂×Q₈×C₅₃	—	4	2	no	—
546	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
547	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
548	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
549	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
550	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
551	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
552	C₂×D₄×C₅₃	—	4	2	no	—
553	C₂×D₄×C₅₃	—	4	2	no	—
554	C₂×D₄×C₅₃	—	4	2	no	—
555	C₂×D₄×C₅₃	—	4	2	no	—
556	C₂×D₄×C₅₃	—	4	2	no	—
557	C₂×D₄×C₅₃	—	4	2	no	—
558	C₂×D₄×C₅₃	—	4	2	no	—
559	C₂×D₄×C₅₃	—	4	2	no	—
560	C₂×D₄×C₅₃	—	4	2	no	—
561	C₂×D₄×C₅₃	—	4	2	no	—
562	C₂×D₄×C₅₃	—	4	2	no	—
563	C₂×D₄×C₅₃	—	4	2	no	—
564	C₂×D₄×C₅₃	—	4	2	no	—
565	C₂×D₄×C₅₃	—	4	2	no	—
566	C₂×D₄×C₅₃	—	4	2	no	—
567	C₂×D₄×C₅₃	—	4	2	no	—
568	C₂×D₄×C₅₃	—	4	2	no	—
569	C₂×D₄×C₅₃	—	4	2	no	—
570	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
571	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
572	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
573	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
574	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
575	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
576	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
577	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
578	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
579	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
580	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
581	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
582	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
583	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
584	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
585	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
586	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
587	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
588	C₂²×C₄×C₅₃	—	4	2	no	—
589	C₂²×C₄×C₅₃	—	4	2	no	—
590	C₂²×C₄×C₅₃	—	4	2	no	—
591	C₂²×C₄×C₅₃	—	4	2	no	—
592	C₂²×C₄×C₅₃	—	4	2	no	—
593	C₂²×C₄×C₅₃	—	4	2	no	—
594	C₂²×C₄×C₅₃	—	4	2	no	—
595	C₂²×C₄×C₅₃	—	4	2	no	—
596	C₂²×C₄×C₅₃	—	4	2	no	—
597	C₂²×C₄×C₅₃	—	4	2	no	—
598	C₂²×C₄×C₅₃	—	4	2	no	—
599	C₂²×C₄×C₅₃	—	4	2	no	—
600	C₂²×C₄×C₅₃	—	4	2	no	—
601	C₂²×C₄×C₅₃	—	4	2	no	—
602	C₂²×C₄×C₅₃	—	4	2	no	—
603	C₂²×C₄×C₅₃	—	4	2	no	—
604	C₂²×C₄×C₅₃	—	4	2	no	—
605	C₂²×C₄×C₅₃	—	4	2	no	—
606	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
607	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
608	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
609	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
610	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
611	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
612	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
613	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
614	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
615	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
616	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
617	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
618	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
619	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
620	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
621	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
622	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
623	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
624	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
625	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
626	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
627	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
628	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
629	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
630	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
631	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
632	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
633	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
634	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
635	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
636	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
637	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
638	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
639	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
640	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
641	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
642	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
643	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
644	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
645	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
646	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
647	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
648	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
649	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
650	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
651	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
652	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
653	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
654	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
655	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
656	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
657	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
658	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
659	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
660	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
661	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
662	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
663	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
664	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
665	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
666	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
667	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
668	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
669	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
670	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
671	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
672	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
673	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
674	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
675	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
676	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
677	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
678	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
679	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
680	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
681	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
682	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
683	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
684	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
685	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
686	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
687	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
688	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
689	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
690	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
691	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
692	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
693	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
694	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
695	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
696	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
697	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
698	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
699	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
700	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
701	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
702	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
703	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
704	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
705	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
706	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
707	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
708	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
709	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
710	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
711	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
712	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
713	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
714	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
715	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
716	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
717	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
718	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
719	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
720	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
721	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
722	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
723	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
724	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
725	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
726	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
727	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
728	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
729	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
730	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
731	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
732	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
733	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
734	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
735	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
736	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
737	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
738	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
739	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
740	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
741	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
742	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
743	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
744	C₄²×C₅₃	C₂⁴	1	4	yes	—
745	C₄²×C₅₃	C₂⁴	1	4	yes	—
746	C₄²×C₅₃	C₂⁴	1	4	yes	—
747	C₄²×C₅₃	C₂⁴	1	4	yes	—
748	C₄²×C₅₃	C₂⁴	1	4	yes	—
749	C₄²×C₅₃	C₂⁴	1	4	yes	—
750	C₄²×C₅₃	C₂⁴	1	4	yes	—
751	C₄²×C₅₃	C₂⁴	1	4	yes	—
752	C₄²×C₅₃	C₂⁴	1	4	yes	—
753	C₄²×C₅₃	C₂⁴	1	4	yes	—
754	C₄²×C₅₃	C₂⁴	1	4	yes	—
755	C₄²×C₅₃	C₂⁴	1	4	yes	—
756	C₄²×C₅₃	C₂⁴	1	4	yes	—
757	C₄²×C₅₃	C₂⁴	1	4	yes	—
758	C₄²×C₅₃	C₂⁴	1	4	yes	—
759	C₄²×C₅₃	C₂⁴	1	4	yes	—
760	C₂³×C₅₃	—	2	2	no	—
761	C₂³×C₅₃	—	2	2	no	—
762	C₂³×C₅₃	—	2	2	no	—
763	C₂³×C₅₃	—	2	2	no	—
764	C₂³×C₅₃	—	2	2	no	—
765	C₂³×C₅₃	—	2	2	no	—
766	C₂³×C₅₃	—	2	2	no	—
767	C₂³×C₅₃	—	2	2	no	—
768	C₂³×C₅₃	—	2	2	no	—
769	C₂³×C₅₃	—	2	2	no	—
770	C₂³×C₅₃	—	2	2	no	—
771	C₂³×C₅₃	—	2	2	no	—
772	C₂³×C₅₃	—	2	2	no	—
773	C₂³×C₅₃	—	2	2	no	—
774	C₂³×C₅₃	—	2	2	no	—
775	C₂³×C₅₃	—	2	2	no	—
776	C₂³×C₅₃	—	2	2	no	—
777	C₂³×C₅₃	—	2	2	no	—
778	C₂³×C₅₃	—	2	2	no	—
779	C₂³×C₅₃	—	2	2	no	—
780	C₂³×C₅₃	—	2	2	no	—
781	C₂³×C₅₃	—	4	4	no	—
782	C₂³×C₅₃	—	4	4	no	—
783	C₂³×C₅₃	—	4	4	no	—
784	C₂³×C₅₃	—	8	8	no	—
785	C₂³×C₅₃	C₂⁵	1	2	yes	—
786	C₂³×C₅₃	C₂⁵	1	2	yes	—
787	C₂³×C₅₃	C₂⁵	1	2	yes	—
788	C₂³×C₅₃	C₂⁵	1	2	yes	—
789	C₂³×C₅₃	C₂⁵	1	2	yes	—
790	C₂³×C₅₃	C₂⁵	1	2	yes	—
791	C₂³×C₅₃	C₂⁵	1	2	yes	—
792	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
793	Q₈×C₅₃	—	4	4	no	—
794	Q₈×C₅₃	—	4	4	no	—
795	Q₈×C₅₃	—	4	4	no	—
796	Q₈×C₅₃	—	4	4	no	—
797	Q₈×C₅₃	—	4	4	no	—
798	Q₈×C₅₃	—	4	4	no	—
799	D₄×C₅₃	—	4	4	no	—
800	D₄×C₅₃	—	4	4	no	—
801	D₄×C₅₃	—	4	4	no	—
802	D₄×C₅₃	—	4	4	no	—
803	D₄×C₅₃	—	4	4	no	—
804	D₄×C₅₃	—	4	4	no	—
805	D₄×C₅₃	—	4	4	no	—
806	D₄×C₅₃	—	4	4	no	—
807	D₄×C₅₃	—	4	4	no	—
808	D₄×C₅₃	—	4	4	no	—
809	D₄×C₅₃	—	4	4	no	—
810	D₄×C₅₃	—	4	4	no	—
811	D₄×C₅₃	—	4	4	no	—
812	D₄×C₅₃	—	4	4	no	—
813	D₄×C₅₃	—	4	4	no	—
814	D₄×C₅₃	—	4	4	no	—
815	D₄×C₅₃	—	4	4	no	—
816	D₄×C₅₃	—	4	4	no	—
817	C₂×C₄×C₅₃	—	2	2	no	—
818	C₂×C₄×C₅₃	—	2	2	no	—
819	C₂×C₄×C₅₃	—	2	2	no	—
820	C₂×C₄×C₅₃	—	2	2	no	—
821	C₂×C₄×C₅₃	—	2	2	no	—
822	C₂×C₄×C₅₃	—	2	2	no	—
823	C₂×C₄×C₅₃	—	2	2	no	—
824	C₂×C₄×C₅₃	—	2	2	no	—
825	C₂×C₄×C₅₃	—	2	2	no	—
826	C₂×C₄×C₅₃	—	2	2	no	—
827	C₂×C₄×C₅₃	—	2	2	no	—
828	C₂×C₄×C₅₃	—	2	2	no	—
829	C₂×C₄×C₅₃	—	2	2	no	—
830	C₂×C₄×C₅₃	—	2	2	no	—
831	C₂×C₄×C₅₃	—	2	2	no	—
832	C₂×C₄×C₅₃	—	2	2	no	—
833	C₂×C₄×C₅₃	—	2	2	no	—
834	C₂×C₄×C₅₃	—	2	2	no	—
835	C₂×C₄×C₅₃	—	2	2	no	—
836	C₂×C₄×C₅₃	—	2	2	no	—
837	C₂×C₄×C₅₃	—	2	2	no	—
838	C₂×C₄×C₅₃	—	2	2	no	—
839	C₂×C₄×C₅₃	—	2	2	no	—
840	C₂×C₄×C₅₃	—	2	2	no	—
841	C₂×C₄×C₅₃	—	4	4	no	—
842	C₂×C₄×C₅₃	—	4	4	no	—
843	C₂×C₄×C₅₃	—	4	4	no	—
844	C₂×C₄×C₅₃	—	4	4	no	—
845	C₂×C₄×C₅₃	—	4	4	no	—
846	C₂×C₄×C₅₃	—	4	4	no	—
847	C₂×C₄×C₅₃	—	4	4	no	—
848	C₂×C₄×C₅₃	—	4	4	no	—
849	C₂×C₄×C₅₃	—	4	4	no	—
850	C₂×C₄×C₅₃	—	4	4	no	—
851	C₂×C₄×C₅₃	—	4	4	no	—
852	C₂×C₄×C₅₃	—	4	4	no	—
853	C₂×C₄×C₅₃	—	4	4	no	—
854	C₂×C₄×C₅₃	—	4	4	no	—
855	C₂×C₄×C₅₃	—	4	4	no	—
856	C₂×C₄×C₅₃	—	4	4	no	—
857	C₂×C₄×C₅₃	—	4	4	no	—
858	C₂×C₄×C₅₃	—	4	4	no	—
859	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
860	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
861	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
862	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
863	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
864	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
865	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
866	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
867	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
868	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
869	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
870	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
871	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
872	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
873	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
874	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
875	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
876	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
877	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
878	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
879	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
880	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
881	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
882	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
883	C₂×#3566	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
884	C₂²×C₅₃	—	2	2	no	—
885	C₂²×C₅₃	—	2	2	no	—
886	C₂²×C₅₃	—	2	2	no	—
887	C₂²×C₅₃	—	2	2	no	—
888	C₂²×C₅₃	—	2	2	no	—
889	C₂²×C₅₃	—	2	2	no	—
890	C₂²×C₅₃	—	2	2	no	—
891	C₂²×C₅₃	—	2	2	no	—
892	C₂²×C₅₃	—	2	2	no	—
893	C₂²×C₅₃	—	2	2	no	—
894	C₂²×C₅₃	—	2	2	no	—
895	C₂²×C₅₃	—	2	2	no	—
896	C₂²×C₅₃	—	2	2	no	—
897	C₂²×C₅₃	—	2	2	no	—
898	C₂²×C₅₃	—	2	2	no	—
899	C₂²×C₅₃	—	2	2	no	—
900	C₂²×C₅₃	—	2	2	no	—
901	C₂²×C₅₃	—	2	2	no	—
902	C₂²×C₅₃	—	2	2	no	—
903	C₂²×C₅₃	—	2	2	no	—
904	C₂²×C₅₃	—	2	2	no	—
905	C₂²×C₅₃	—	4	4	no	—
906	C₂²×C₅₃	—	4	4	no	—
907	C₂²×C₅₃	—	4	4	no	—
908	C₂²×C₅₃	—	4	4	no	—
909	C₂²×C₅₃	—	4	4	no	—
910	C₂²×C₅₃	—	4	4	no	—
911	C₂²×C₅₃	—	4	4	no	—
912	C₂²×C₅₃	—	8	8	no	—
913	C₂²×C₅₃	#585	1	2	yes	—
914	C₂²×C₅₃	#585	1	2	yes	—
915	C₂²×C₅₃	#585	1	2	yes	—
916	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
917	C₄×C₅₃	—	2	2	no	—
918	C₄×C₅₃	—	2	2	no	—
919	C₄×C₅₃	—	2	2	no	—
920	C₄×C₅₃	—	2	2	no	—
921	C₄×C₅₃	—	2	2	no	—
922	C₄×C₅₃	—	2	2	no	—
923	C₄×C₅₃	—	2	2	no	—
924	C₄×C₅₃	—	2	2	no	—
925	C₄×C₅₃	—	2	2	no	—
926	C₄×C₅₃	—	2	2	no	—
927	C₄×C₅₃	—	2	2	no	—
928	C₄×C₅₃	—	2	2	no	—
929	C₄×C₅₃	—	2	2	no	—
930	C₄×C₅₃	—	2	2	no	—
931	C₄×C₅₃	—	2	2	no	—
932	C₄×C₅₃	—	2	2	no	—
933	C₄×C₅₃	—	2	2	no	—
934	C₄×C₅₃	—	2	2	no	—
935	C₄×C₅₃	—	2	2	no	—
936	C₄×C₅₃	—	2	2	no	—
937	C₄×C₅₃	—	2	2	no	—
938	C₄×C₅₃	—	2	2	no	—
939	C₄×C₅₃	—	2	2	no	—
940	C₄×C₅₃	—	2	2	no	—
941	#3566	C₂×C₅₃	1	32	yes	direct product factor
942	C₂×#563	C₂×C₅₃	1	1	yes	characteristic, complemented
943	C₂×#562	C₂×C₅₃	1	1	yes	characteristic, complemented
944	C₂×#562	C₂×C₅₃	1	1	yes	characteristic, complemented
945	C₂×#560	C₂×C₅₃	1	1	yes	characteristic, complemented
946	C₂×#559	C₂×C₅₃	1	1	yes	characteristic, complemented
947	C₂×#556	C₂×C₅₃	1	1	yes	characteristic, complemented
948	C₂×#555	C₂×C₅₃	1	1	yes	characteristic, complemented
949	C₂×#553	C₂×C₅₃	1	1	yes	characteristic, complemented
950	C₂×#553	C₂×C₅₃	1	1	yes	characteristic, complemented
951	C₂×#553	C₂×C₅₃	1	1	yes	characteristic, complemented
952	C₂×#552	C₂×C₅₃	1	1	yes	characteristic, complemented
953	C₂×#552	C₂×C₅₃	1	1	yes	characteristic, complemented
954	C₂×#552	C₂×C₅₃	1	1	yes	characteristic, complemented
955	C₂×#551	C₂×C₅₃	1	1	yes	characteristic, complemented
956	C₂×#551	C₂×C₅₃	1	1	yes	characteristic, complemented
957	C₂×#551	C₂×C₅₃	1	1	yes	characteristic, complemented
958	C₂×#542	C₂×C₅₃	1	1	yes	characteristic, complemented
959	C₂×#542	C₂×C₅₃	1	1	yes	characteristic, complemented
960	C₂×#542	C₂×C₅₃	1	1	yes	characteristic, complemented
961	C₂×#541	C₂×C₅₃	1	1	yes	characteristic, complemented
962	C₂×#541	C₂×C₅₃	1	1	yes	characteristic, complemented
963	C₂×#540	C₂×C₅₃	1	1	yes	characteristic, complemented
964	C₂×#539	C₂×C₅₃	1	1	yes	characteristic, complemented
965	C₂×#539	C₂×C₅₃	1	1	yes	characteristic, complemented
966	C₂×#539	C₂×C₅₃	1	1	yes	characteristic, complemented
967	C₂×#538	C₂×C₅₃	1	1	yes	characteristic, complemented
968	C₂×#538	C₂×C₅₃	1	1	yes	characteristic, complemented
969	C₂×#538	C₂×C₅₃	1	1	yes	characteristic, complemented
970	C₂×#529	C₂×C₅₃	1	1	yes	characteristic, complemented
971	C₂×#529	C₂×C₅₃	1	1	yes	characteristic, complemented
972	C₂×#529	C₂×C₅₃	1	1	yes	characteristic, complemented
973	C₂×C₅₃	—	4	2	no	—
974	C₂×C₅₃	—	4	2	no	—
975	C₂×C₅₃	—	4	2	no	—
976	C₂×C₅₃	—	4	2	no	—
977	C₂×C₅₃	—	4	2	no	—
978	C₂×C₅₃	—	4	2	no	—
979	C₂×C₅₃	—	4	2	no	—
980	C₂×C₅₃	#3566	1	4	yes	direct product factor
981	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
982	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
983	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
984	#563	C₂²×C₅₃	1	16	yes	complemented
985	#562	C₂²×C₅₃	1	16	yes	complemented
986	#562	C₂²×C₅₃	1	16	yes	complemented
987	#560	C₂²×C₅₃	1	16	yes	complemented
988	#559	C₂²×C₅₃	1	16	yes	complemented
989	#556	C₂²×C₅₃	1	16	yes	complemented
990	#555	C₂²×C₅₃	1	16	yes	complemented
991	#553	C₂²×C₅₃	1	16	yes	complemented
992	#553	C₂²×C₅₃	1	16	yes	complemented
993	#553	C₂²×C₅₃	1	16	yes	complemented
994	#552	C₂²×C₅₃	1	16	yes	complemented
995	#552	C₂²×C₅₃	1	16	yes	complemented
996	#552	C₂²×C₅₃	1	16	yes	complemented
997	#551	C₂²×C₅₃	1	16	yes	complemented
998	#551	C₂²×C₅₃	1	16	yes	complemented
999	#551	C₂²×C₅₃	1	16	yes	complemented
1000	#542	C₂²×C₅₃	1	16	yes	complemented
1001	#542	C₂²×C₅₃	1	16	yes	complemented
1002	#542	C₂²×C₅₃	1	16	yes	complemented
1003	#541	C₂²×C₅₃	1	16	yes	complemented
1004	#541	C₂²×C₅₃	1	16	yes	complemented
1005	#540	C₂²×C₅₃	1	16	yes	complemented
1006	#539	C₂²×C₅₃	1	16	yes	complemented
1007	#539	C₂²×C₅₃	1	16	yes	complemented
1008	#539	C₂²×C₅₃	1	16	yes	complemented
1009	#538	C₂²×C₅₃	1	16	yes	complemented
1010	#538	C₂²×C₅₃	1	16	yes	complemented
1011	#538	C₂²×C₅₃	1	16	yes	complemented
1012	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1013	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1014	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1015	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
1016	#529	C₂²×C₅₃	1	16	yes	complemented
1017	#529	C₂²×C₅₃	1	16	yes	complemented
1018	#529	C₂²×C₅₃	1	16	yes	complemented
1019	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
1020	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
1021	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
1022	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
1023	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
1024	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
1025	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
1026	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
1027	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
1028	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
1029	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
1030	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
1031	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
1032	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
1033	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic, complemented
1035	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic, complemented
1037	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic, complemented
1038	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic, complemented
1039	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
1040	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
1041	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
1042	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
1043	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
1044	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
1045	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
1046	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
1047	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
1048	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
1051	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
1052	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
1053	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
1054	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
1055	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
1056	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
1057	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
1058	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
1059	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
1060	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
1061	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
1062	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
1063	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
1064	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
1065	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
1066	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
1067	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
1068	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
1069	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
1070	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
1071	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
1072	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
1073	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
1074	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
1075	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
1076	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
1077	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
1078	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
1079	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
1080	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
1081	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
1082	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
1083	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
1084	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
1085	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
1086	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
1087	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
1088	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
1089	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
1090	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
1091	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
1092	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
1093	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
1094	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
1095	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
1096	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1097	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1098	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1099	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1100	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1101	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1102	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1103	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1104	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1105	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
1106	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
1107	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
1108	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
1109	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
1110	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
1111	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
1112	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
1113	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
1114	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
1115	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
1116	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
1117	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
1118	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
1119	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
1120	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
1121	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
1122	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
1123	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
1124	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
1125	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
1126	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
1127	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1128	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1129	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1130	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1131	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1132	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1133	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
1134	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
1135	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
1136	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
1137	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
1138	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
1139	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
1140	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
1141	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
1142	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
1143	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
1144	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
1145	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1146	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1147	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1148	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1149	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1150	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1151	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
1152	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
1153	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
1154	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
1155	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
1156	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
1157	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
1158	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
1159	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
1160	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
1161	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
1162	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
1163	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1164	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1165	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1166	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
1167	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
1168	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
1169	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
1170	C₅₃	C₂×#3566	1	1	yes	characteristic, direct product factor, Sylow
1171	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
1172	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1173	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1174	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1175	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1176	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1177	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1178	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1179	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1180	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1181	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1182	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1183	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1184	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1185	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1186	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1187	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1188	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1189	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1190	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1191	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1192	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1193	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1194	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1195	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1196	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1197	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1198	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1199	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1200	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1201	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1202	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1203	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1204	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1205	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1206	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1207	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1208	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1209	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1210	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1211	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1212	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1213	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1214	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1215	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1216	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1217	#127	C₂³×C₅₃	1	8	yes	—
1218	#126	C₂³×C₅₃	1	8	yes	—
1219	#126	C₂³×C₅₃	1	8	yes	—
1220	#126	C₂³×C₅₃	1	8	yes	—
1221	#126	C₂³×C₅₃	1	8	yes	—
1222	#126	C₂³×C₅₃	1	8	yes	—
1223	#126	C₂³×C₅₃	1	8	yes	—
1224	#126	C₂³×C₅₃	1	8	yes	—
1225	#126	C₂³×C₅₃	1	8	yes	—
1226	#126	C₂³×C₅₃	1	8	yes	—
1227	#126	C₂³×C₅₃	1	8	yes	—
1228	#126	C₂³×C₅₃	1	8	yes	—
1229	#126	C₂³×C₅₃	1	8	yes	—
1230	#126	C₂³×C₅₃	1	8	yes	—
1231	#126	C₂³×C₅₃	1	8	yes	—
1232	#126	C₂³×C₅₃	1	8	yes	complemented
1233	#126	C₂³×C₅₃	1	8	yes	complemented
1234	#126	C₂³×C₅₃	1	8	yes	complemented
1235	#126	C₂³×C₅₃	1	8	yes	complemented
1236	#126	C₂³×C₅₃	1	8	yes	complemented
1237	#126	C₂³×C₅₃	1	8	yes	complemented
1238	#125	C₂³×C₅₃	1	8	yes	complemented
1239	#125	C₂³×C₅₃	1	8	yes	complemented
1240	#125	C₂³×C₅₃	1	8	yes	complemented
1241	#125	C₂³×C₅₃	1	8	yes	complemented
1242	#125	C₂³×C₅₃	1	8	yes	complemented
1243	#125	C₂³×C₅₃	1	8	yes	complemented
1244	#125	C₂³×C₅₃	1	8	yes	complemented
1245	#125	C₂³×C₅₃	1	8	yes	complemented
1246	#125	C₂³×C₅₃	1	8	yes	complemented
1247	#125	C₂³×C₅₃	1	8	yes	complemented
1248	#125	C₂³×C₅₃	1	8	yes	complemented
1249	#125	C₂³×C₅₃	1	8	yes	complemented
1250	#124	C₂³×C₅₃	1	8	yes	—
1251	#124	C₂³×C₅₃	1	8	yes	—
1252	#124	C₂³×C₅₃	1	8	yes	—
1253	#124	C₂³×C₅₃	1	8	yes	—
1254	#124	C₂³×C₅₃	1	8	yes	—
1255	#124	C₂³×C₅₃	1	8	yes	—
1256	#124	C₂³×C₅₃	1	8	yes	—
1257	#124	C₂³×C₅₃	1	8	yes	—
1258	#124	C₂³×C₅₃	1	8	yes	—
1259	#124	C₂³×C₅₃	1	8	yes	complemented
1260	#124	C₂³×C₅₃	1	8	yes	complemented
1261	#124	C₂³×C₅₃	1	8	yes	complemented
1262	#123	C₂³×C₅₃	1	8	yes	—
1263	#123	C₂³×C₅₃	1	8	yes	—
1264	#123	C₂³×C₅₃	1	8	yes	—
1265	#123	C₂³×C₅₃	1	8	yes	—
1266	#123	C₂³×C₅₃	1	8	yes	—
1267	#123	C₂³×C₅₃	1	8	yes	—
1268	#123	C₂³×C₅₃	1	8	yes	—
1269	#123	C₂³×C₅₃	1	8	yes	—
1270	#123	C₂³×C₅₃	1	8	yes	—
1271	#123	C₂³×C₅₃	1	8	yes	—
1272	#123	C₂³×C₅₃	1	8	yes	—
1273	#123	C₂³×C₅₃	1	8	yes	—
1274	#123	C₂³×C₅₃	1	8	yes	—
1275	#123	C₂³×C₅₃	1	8	yes	—
1276	#123	C₂³×C₅₃	1	8	yes	—
1277	#123	C₂³×C₅₃	1	8	yes	—
1278	#123	C₂³×C₅₃	1	8	yes	—
1279	#123	C₂³×C₅₃	1	8	yes	—
1280	#123	C₂³×C₅₃	1	8	yes	complemented
1281	#123	C₂³×C₅₃	1	8	yes	complemented
1282	#123	C₂³×C₅₃	1	8	yes	complemented
1283	#123	C₂³×C₅₃	1	8	yes	complemented
1284	#123	C₂³×C₅₃	1	8	yes	complemented
1285	#123	C₂³×C₅₃	1	8	yes	complemented
1286	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1287	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1288	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1289	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1290	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1291	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1292	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1293	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1294	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
1295	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1296	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1297	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1298	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1299	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1300	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1301	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1302	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1303	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
1304	#121	C₂³×C₅₃	1	8	yes	—
1305	#121	C₂³×C₅₃	1	8	yes	—
1306	#121	C₂³×C₅₃	1	8	yes	—
1307	#121	C₂³×C₅₃	1	8	yes	—
1308	#121	C₂³×C₅₃	1	8	yes	—
1309	#121	C₂³×C₅₃	1	8	yes	—
1310	#121	C₂³×C₅₃	1	8	yes	—
1311	#121	C₂³×C₅₃	1	8	yes	—
1312	#121	C₂³×C₅₃	1	8	yes	—
1313	#121	C₂³×C₅₃	1	8	yes	—
1314	#121	C₂³×C₅₃	1	8	yes	—
1315	#121	C₂³×C₅₃	1	8	yes	—
1316	#121	C₂³×C₅₃	1	8	yes	—
1317	#121	C₂³×C₅₃	1	8	yes	—
1318	#121	C₂³×C₅₃	1	8	yes	—
1319	#121	C₂³×C₅₃	1	8	yes	complemented
1320	#121	C₂³×C₅₃	1	8	yes	complemented
1321	#121	C₂³×C₅₃	1	8	yes	complemented
1322	#120	C₂³×C₅₃	1	8	yes	—
1323	#120	C₂³×C₅₃	1	8	yes	—
1324	#120	C₂³×C₅₃	1	8	yes	—
1325	#120	C₂³×C₅₃	1	8	yes	—
1326	C₄×Q₈	C₂³×C₅₃	1	8	yes	complemented
1327	C₄×Q₈	C₂³×C₅₃	1	8	yes	complemented
1328	C₄×Q₈	C₂³×C₅₃	1	8	yes	complemented
1329	C₄×Q₈	C₂³×C₅₃	1	8	yes	complemented
1330	C₄×Q₈	C₂³×C₅₃	1	8	yes	complemented
1331	C₄×Q₈	C₂³×C₅₃	1	8	yes	complemented
1332	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1333	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1334	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1335	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1336	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1337	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1338	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1339	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1340	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1341	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1342	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1343	C₄×D₄	C₂³×C₅₃	1	8	yes	—
1344	C₄×D₄	C₂³×C₅₃	1	8	yes	complemented
1345	C₄×D₄	C₂³×C₅₃	1	8	yes	complemented
1346	C₄×D₄	C₂³×C₅₃	1	8	yes	complemented
1347	C₄×D₄	C₂³×C₅₃	1	8	yes	complemented
1348	C₄×D₄	C₂³×C₅₃	1	8	yes	complemented
1349	C₄×D₄	C₂³×C₅₃	1	8	yes	complemented
1350	#117	C₂³×C₅₃	1	8	yes	—
1351	#117	C₂³×C₅₃	1	8	yes	—
1352	#117	C₂³×C₅₃	1	8	yes	—
1353	#117	C₂³×C₅₃	1	8	yes	—
1354	#117	C₂³×C₅₃	1	8	yes	—
1355	#117	C₂³×C₅₃	1	8	yes	—
1356	#117	C₂³×C₅₃	1	8	yes	complemented
1357	#117	C₂³×C₅₃	1	8	yes	complemented
1358	#117	C₂³×C₅₃	1	8	yes	complemented
1359	#117	C₂³×C₅₃	1	8	yes	complemented
1360	#117	C₂³×C₅₃	1	8	yes	complemented
1361	#117	C₂³×C₅₃	1	8	yes	complemented
1362	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1363	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1364	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1365	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1366	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1367	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1368	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1369	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1370	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1371	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1372	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1373	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1374	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1375	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1376	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1377	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1378	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1379	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1380	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1381	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1382	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1383	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1384	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1385	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1386	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1387	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1388	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1389	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1390	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1391	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1392	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1393	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1394	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1395	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1396	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1397	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1398	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1399	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1400	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1401	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1402	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1403	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1404	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1405	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1406	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1407	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1408	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1409	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1410	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	complemented
1411	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	complemented
1412	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	complemented
1413	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1414	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1415	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1416	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1417	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1418	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1419	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1420	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1421	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1422	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1423	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1424	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1425	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
1426	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
1427	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
1428	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1429	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1430	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1431	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1432	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1433	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1434	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1435	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1436	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1437	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1438	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1439	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1440	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1441	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1442	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1443	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1444	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1445	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1446	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1447	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1448	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1449	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1450	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1451	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1452	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1453	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1454	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1455	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1456	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1457	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1458	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1459	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1460	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1461	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1462	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1463	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1464	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1465	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1466	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1467	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1468	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1469	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1470	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1471	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1472	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1473	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1474	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1475	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1476	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1477	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1478	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1479	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1480	C₂×C₄²	C₂³×C₅₃	1	8	yes	complemented
1481	C₂⁴	—	4	2	no	—
1482	C₂⁴	—	4	2	no	—
1483	C₂⁴	—	4	2	no	—
1484	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1485	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1486	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1487	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1488	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1489	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1490	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1491	C₂⁴	C₂⁴×C₅₃	1	4	yes	—
1492	C₂×Q₈	—	4	2	no	—
1493	C₂×Q₈	—	4	2	no	—
1494	C₂×Q₈	—	4	2	no	—
1495	C₂×Q₈	—	4	2	no	—
1496	C₂×Q₈	—	4	2	no	—
1497	C₂×Q₈	—	4	2	no	—
1498	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
1499	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
1500	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
1501	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
1502	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
1503	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
1504	C₂×D₄	—	4	2	no	—
1505	C₂×D₄	—	4	2	no	—
1506	C₂×D₄	—	4	2	no	—
1507	C₂×D₄	—	4	2	no	—
1508	C₂×D₄	—	4	2	no	—
1509	C₂×D₄	—	4	2	no	—
1510	C₂×D₄	—	4	2	no	—
1511	C₂×D₄	—	4	2	no	—
1512	C₂×D₄	—	4	2	no	—
1513	C₂×D₄	—	4	2	no	—
1514	C₂×D₄	—	4	2	no	—
1515	C₂×D₄	—	4	2	no	—
1516	C₂×D₄	—	4	2	no	—
1517	C₂×D₄	—	4	2	no	—
1518	C₂×D₄	—	4	2	no	—
1519	C₂×D₄	—	4	2	no	—
1520	C₂×D₄	—	4	2	no	—
1521	C₂×D₄	—	4	2	no	—
1522	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1523	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1524	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1525	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1526	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1527	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1528	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1529	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1530	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1531	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1532	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1533	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1534	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1535	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1536	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1537	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1538	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1539	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1540	C₂²×C₄	—	4	2	no	—
1541	C₂²×C₄	—	4	2	no	—
1542	C₂²×C₄	—	4	2	no	—
1543	C₂²×C₄	—	4	2	no	—
1544	C₂²×C₄	—	4	2	no	—
1545	C₂²×C₄	—	4	2	no	—
1546	C₂²×C₄	—	4	2	no	—
1547	C₂²×C₄	—	4	2	no	—
1548	C₂²×C₄	—	4	2	no	—
1549	C₂²×C₄	—	4	2	no	—
1550	C₂²×C₄	—	4	2	no	—
1551	C₂²×C₄	—	4	2	no	—
1552	C₂²×C₄	—	4	2	no	—
1553	C₂²×C₄	—	4	2	no	—
1554	C₂²×C₄	—	4	2	no	—
1555	C₂²×C₄	—	4	2	no	—
1556	C₂²×C₄	—	4	2	no	—
1557	C₂²×C₄	—	4	2	no	—
1558	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1559	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1560	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1561	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1562	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1563	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1564	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1565	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1566	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1567	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1568	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1569	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1570	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1571	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1572	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1573	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1574	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1575	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1576	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1577	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1578	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1579	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1580	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1581	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1582	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1583	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1584	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1585	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1586	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1587	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1588	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1589	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1590	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1591	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1592	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1593	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1594	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1595	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1596	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1597	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1598	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1599	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1600	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1601	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1602	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1603	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1604	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1605	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1606	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1607	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1608	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1609	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1610	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1611	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1612	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1613	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1614	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1615	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1616	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1617	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1618	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1619	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1620	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1621	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1622	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1623	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1624	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1625	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1626	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1627	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1628	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1629	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1630	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1631	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1632	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1633	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1634	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1635	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1636	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1637	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1638	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1639	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1640	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1641	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1642	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1643	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1644	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1645	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1646	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1647	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1648	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1649	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1650	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1651	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1652	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1653	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1654	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1655	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1656	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1657	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1658	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1659	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1660	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1661	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1662	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1663	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1664	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1665	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1666	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1667	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1668	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1669	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1670	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1671	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1672	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1673	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1674	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1675	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1676	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1677	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1678	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1679	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1680	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1681	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1682	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1683	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1684	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1685	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1686	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1687	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1688	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1689	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1690	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1691	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1692	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1693	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1694	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1695	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1696	C₄²	C₂⁴×C₅₃	1	4	yes	—
1697	C₄²	C₂⁴×C₅₃	1	4	yes	—
1698	C₄²	C₂⁴×C₅₃	1	4	yes	—
1699	C₄²	C₂⁴×C₅₃	1	4	yes	—
1700	C₄²	C₂⁴×C₅₃	1	4	yes	—
1701	C₄²	C₂⁴×C₅₃	1	4	yes	—
1702	C₄²	C₂⁴×C₅₃	1	4	yes	—
1703	C₄²	C₂⁴×C₅₃	1	4	yes	—
1704	C₄²	C₂⁴×C₅₃	1	4	yes	—
1705	C₄²	C₂⁴×C₅₃	1	4	yes	—
1706	C₄²	C₂⁴×C₅₃	1	4	yes	—
1707	C₄²	C₂⁴×C₅₃	1	4	yes	—
1708	C₄²	C₂⁴×C₅₃	1	4	yes	—
1709	C₄²	C₂⁴×C₅₃	1	4	yes	—
1710	C₄²	C₂⁴×C₅₃	1	4	yes	—
1711	C₄²	C₂⁴×C₅₃	1	4	yes	—
1712	C₂³	—	2	2	no	—
1713	C₂³	—	2	2	no	—
1714	C₂³	—	2	2	no	—
1715	C₂³	—	2	2	no	—
1716	C₂³	—	2	2	no	—
1717	C₂³	—	2	2	no	—
1718	C₂³	—	2	2	no	—
1719	C₂³	—	2	2	no	—
1720	C₂³	—	2	2	no	—
1721	C₂³	—	2	2	no	—
1722	C₂³	—	2	2	no	—
1723	C₂³	—	2	2	no	—
1724	C₂³	—	2	2	no	—
1725	C₂³	—	2	2	no	—
1726	C₂³	—	2	2	no	—
1727	C₂³	—	2	2	no	—
1728	C₂³	—	2	2	no	—
1729	C₂³	—	2	2	no	—
1730	C₂³	—	2	2	no	—
1731	C₂³	—	2	2	no	—
1732	C₂³	—	2	2	no	—
1733	C₂³	—	4	4	no	—
1734	C₂³	—	4	4	no	—
1735	C₂³	—	4	4	no	—
1736	C₂³	—	8	8	no	—
1737	C₂³	C₂⁵×C₅₃	1	2	yes	—
1738	C₂³	C₂⁵×C₅₃	1	2	yes	—
1739	C₂³	C₂⁵×C₅₃	1	2	yes	—
1740	C₂³	C₂⁵×C₅₃	1	2	yes	—
1741	C₂³	C₂⁵×C₅₃	1	2	yes	—
1742	C₂³	C₂⁵×C₅₃	1	2	yes	—
1743	C₂³	C₂⁵×C₅₃	1	2	yes	—
1744	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1745	Q₈	—	4	4	no	—
1746	Q₈	—	4	4	no	—
1747	Q₈	—	4	4	no	—
1748	Q₈	—	4	4	no	—
1749	Q₈	—	4	4	no	—
1750	Q₈	—	4	4	no	—
1751	D₄	—	4	4	no	—
1752	D₄	—	4	4	no	—
1753	D₄	—	4	4	no	—
1754	D₄	—	4	4	no	—
1755	D₄	—	4	4	no	—
1756	D₄	—	4	4	no	—
1757	D₄	—	4	4	no	—
1758	D₄	—	4	4	no	—
1759	D₄	—	4	4	no	—
1760	D₄	—	4	4	no	—
1761	D₄	—	4	4	no	—
1762	D₄	—	4	4	no	—
1763	D₄	—	4	4	no	—
1764	D₄	—	4	4	no	—
1765	D₄	—	4	4	no	—
1766	D₄	—	4	4	no	—
1767	D₄	—	4	4	no	—
1768	D₄	—	4	4	no	—
1769	C₂×C₄	—	2	2	no	—
1770	C₂×C₄	—	2	2	no	—
1771	C₂×C₄	—	2	2	no	—
1772	C₂×C₄	—	2	2	no	—
1773	C₂×C₄	—	2	2	no	—
1774	C₂×C₄	—	2	2	no	—
1775	C₂×C₄	—	2	2	no	—
1776	C₂×C₄	—	2	2	no	—
1777	C₂×C₄	—	2	2	no	—
1778	C₂×C₄	—	2	2	no	—
1779	C₂×C₄	—	2	2	no	—
1780	C₂×C₄	—	2	2	no	—
1781	C₂×C₄	—	2	2	no	—
1782	C₂×C₄	—	2	2	no	—
1783	C₂×C₄	—	2	2	no	—
1784	C₂×C₄	—	2	2	no	—
1785	C₂×C₄	—	2	2	no	—
1786	C₂×C₄	—	2	2	no	—
1787	C₂×C₄	—	2	2	no	—
1788	C₂×C₄	—	2	2	no	—
1789	C₂×C₄	—	2	2	no	—
1790	C₂×C₄	—	2	2	no	—
1791	C₂×C₄	—	2	2	no	—
1792	C₂×C₄	—	2	2	no	—
1793	C₂×C₄	—	4	4	no	—
1794	C₂×C₄	—	4	4	no	—
1795	C₂×C₄	—	4	4	no	—
1796	C₂×C₄	—	4	4	no	—
1797	C₂×C₄	—	4	4	no	—
1798	C₂×C₄	—	4	4	no	—
1799	C₂×C₄	—	4	4	no	—
1800	C₂×C₄	—	4	4	no	—
1801	C₂×C₄	—	4	4	no	—
1802	C₂×C₄	—	4	4	no	—
1803	C₂×C₄	—	4	4	no	—
1804	C₂×C₄	—	4	4	no	—
1805	C₂×C₄	—	4	4	no	—
1806	C₂×C₄	—	4	4	no	—
1807	C₂×C₄	—	4	4	no	—
1808	C₂×C₄	—	4	4	no	—
1809	C₂×C₄	—	4	4	no	—
1810	C₂×C₄	—	4	4	no	—
1811	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1812	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1813	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1814	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1815	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1816	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1817	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1818	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1819	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1820	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1821	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1822	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1823	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1824	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1825	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1826	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1827	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1828	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1829	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1830	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1831	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1832	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1833	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1834	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1835	C₂²	—	2	2	no	—
1836	C₂²	—	2	2	no	—
1837	C₂²	—	2	2	no	—
1838	C₂²	—	2	2	no	—
1839	C₂²	—	2	2	no	—
1840	C₂²	—	2	2	no	—
1841	C₂²	—	2	2	no	—
1842	C₂²	—	2	2	no	—
1843	C₂²	—	2	2	no	—
1844	C₂²	—	2	2	no	—
1845	C₂²	—	2	2	no	—
1846	C₂²	—	2	2	no	—
1847	C₂²	—	2	2	no	—
1848	C₂²	—	2	2	no	—
1849	C₂²	—	2	2	no	—
1850	C₂²	—	2	2	no	—
1851	C₂²	—	2	2	no	—
1852	C₂²	—	2	2	no	—
1853	C₂²	—	2	2	no	—
1854	C₂²	—	2	2	no	—
1855	C₂²	—	2	2	no	—
1856	C₂²	—	4	4	no	—
1857	C₂²	—	4	4	no	—
1858	C₂²	—	4	4	no	—
1859	C₂²	—	4	4	no	—
1860	C₂²	—	4	4	no	—
1861	C₂²	—	4	4	no	—
1862	C₂²	—	4	4	no	—
1863	C₂²	—	8	8	no	—
1864	C₂²	C₅₃×#585	1	2	yes	—
1865	C₂²	C₅₃×#585	1	2	yes	—
1866	C₂²	C₅₃×#585	1	2	yes	—
1867	C₂²	C₂⁶×C₅₃	1	1	yes	characteristic
1868	C₄	—	2	2	no	—
1869	C₄	—	2	2	no	—
1870	C₄	—	2	2	no	—
1871	C₄	—	2	2	no	—
1872	C₄	—	2	2	no	—
1873	C₄	—	2	2	no	—
1874	C₄	—	2	2	no	—
1875	C₄	—	2	2	no	—
1876	C₄	—	2	2	no	—
1877	C₄	—	2	2	no	—
1878	C₄	—	2	2	no	—
1879	C₄	—	2	2	no	—
1880	C₄	—	2	2	no	—
1881	C₄	—	2	2	no	—
1882	C₄	—	2	2	no	—
1883	C₄	—	2	2	no	—
1884	C₄	—	2	2	no	—
1885	C₄	—	2	2	no	—
1886	C₄	—	2	2	no	—
1887	C₄	—	2	2	no	—
1888	C₄	—	2	2	no	—
1889	C₄	—	2	2	no	—
1890	C₄	—	2	2	no	—
1891	C₄	—	2	2	no	—
1892	C₂	—	4	2	no	—
1893	C₂	—	4	2	no	—
1894	C₂	—	4	2	no	—
1895	C₂	—	4	2	no	—
1896	C₂	—	4	2	no	—
1897	C₂	—	4	2	no	—
1898	C₂	—	4	2	no	—
1899	C₂	C₅₃×#3566	1	4	yes	direct product factor
1900	C₂	C₂×C₅₃×#585	1	1	yes	characteristic
1901	C₂	C₂×C₅₃×#585	1	1	yes	characteristic
1902	C₂	C₂×C₅₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₅₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅₃×#3566	C₂	direct (N × H)
2. C₂×C₅₃×#563	C₂	semidirect
3. C₂×C₅₃×#562	C₂	semidirect
4. C₂×C₅₃×#562	C₂	semidirect
5. C₂×C₅₃×#560	C₂	semidirect
6. C₂×C₅₃×#559	C₂	semidirect
7. C₂×C₅₃×#556	C₂	semidirect
8. C₂×C₅₃×#555	C₂	semidirect
9. C₂×C₅₃×#553	C₂	semidirect
10. C₂×C₅₃×#553	C₂	semidirect
11. C₂×C₅₃×#553	C₂	semidirect
12. C₂×C₅₃×#552	C₂	semidirect
13. C₂×C₅₃×#552	C₂	semidirect
14. C₂×C₅₃×#552	C₂	semidirect
15. C₂×C₅₃×#551	C₂	semidirect
16. C₂×C₅₃×#551	C₂	semidirect
17. C₂×C₅₃×#551	C₂	semidirect
18. C₂×C₅₃×#542	C₂	semidirect
19. C₂×C₅₃×#542	C₂	semidirect
20. C₂×C₅₃×#542	C₂	semidirect
21. C₂×C₅₃×#541	C₂	semidirect
22. C₂×C₅₃×#541	C₂	semidirect
23. C₂×C₅₃×#540	C₂	semidirect
24. C₂×C₅₃×#539	C₂	semidirect
25. C₂×C₅₃×#539	C₂	semidirect
26. C₂×C₅₃×#539	C₂	semidirect
27. C₂×C₅₃×#538	C₂	semidirect
28. C₂×C₅₃×#538	C₂	semidirect
29. C₂×C₅₃×#538	C₂	semidirect
30. C₂×C₅₃×#529	C₂	semidirect
31. C₂×C₅₃×#529	C₂	semidirect
32. C₂×C₅₃×#529	C₂	semidirect
33. C₅₃×#563	C₂²	semidirect
34. C₅₃×#562	C₂²	semidirect
35. C₅₃×#562	C₂²	semidirect
36. C₅₃×#560	C₂²	semidirect
37. C₅₃×#559	C₂²	semidirect
38. C₅₃×#556	C₂²	semidirect
39. C₅₃×#555	C₂²	semidirect
40. C₅₃×#553	C₂²	semidirect
41. C₅₃×#553	C₂²	semidirect
42. C₅₃×#553	C₂²	semidirect
43. C₅₃×#552	C₂²	semidirect
44. C₅₃×#552	C₂²	semidirect
45. C₅₃×#552	C₂²	semidirect
46. C₅₃×#551	C₂²	semidirect
47. C₅₃×#551	C₂²	semidirect
48. C₅₃×#551	C₂²	semidirect
49. C₅₃×#542	C₂²	semidirect
50. C₅₃×#542	C₂²	semidirect
51. C₅₃×#542	C₂²	semidirect
52. C₅₃×#541	C₂²	semidirect
53. C₅₃×#541	C₂²	semidirect
54. C₅₃×#540	C₂²	semidirect
55. C₅₃×#539	C₂²	semidirect
56. C₅₃×#539	C₂²	semidirect
57. C₅₃×#539	C₂²	semidirect
58. C₅₃×#538	C₂²	semidirect
59. C₅₃×#538	C₂²	semidirect
60. C₅₃×#538	C₂²	semidirect
61. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
62. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
63. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
65. C₅₃×#529	C₂²	semidirect
66. C₅₃×#529	C₂²	semidirect
67. C₅₃×#529	C₂²	semidirect
82. C₂×#126×C₅₃	C₂²	semidirect
83. C₂×#126×C₅₃	C₂²	semidirect
84. C₂×#126×C₅₃	C₂²	semidirect
85. C₂×#126×C₅₃	C₂²	semidirect
86. C₂×#126×C₅₃	C₂²	semidirect
87. C₂×#126×C₅₃	C₂²	semidirect
88. C₂×#125×C₅₃	C₂²	semidirect
89. C₂×#125×C₅₃	C₂²	semidirect
90. C₂×#125×C₅₃	C₂²	semidirect
91. C₂×#125×C₅₃	C₂²	semidirect
92. C₂×#125×C₅₃	C₂²	semidirect
93. C₂×#125×C₅₃	C₂²	semidirect
94. C₂×#125×C₅₃	C₂²	semidirect
95. C₂×#125×C₅₃	C₂²	semidirect
96. C₂×#125×C₅₃	C₂²	semidirect
97. C₂×#125×C₅₃	C₂²	semidirect
98. C₂×#125×C₅₃	C₂²	semidirect
99. C₂×#125×C₅₃	C₂²	semidirect
109. C₂×#124×C₅₃	C₂²	semidirect
110. C₂×#124×C₅₃	C₂²	semidirect
111. C₂×#124×C₅₃	C₂²	semidirect
130. C₂×#123×C₅₃	C₂²	semidirect
131. C₂×#123×C₅₃	C₂²	semidirect
132. C₂×#123×C₅₃	C₂²	semidirect
133. C₂×#123×C₅₃	C₂²	semidirect
134. C₂×#123×C₅₃	C₂²	semidirect
135. C₂×#123×C₅₃	C₂²	semidirect
145. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
146. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
147. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
148. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
149. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
150. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
151. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
152. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
153. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
169. C₂×#121×C₅₃	C₂²	semidirect
170. C₂×#121×C₅₃	C₂²	semidirect
171. C₂×#121×C₅₃	C₂²	semidirect
176. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
177. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
178. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
179. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
180. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
181. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
194. C₂×C₄×D₄×C₅₃	C₂²	semidirect
195. C₂×C₄×D₄×C₅₃	C₂²	semidirect
196. C₂×C₄×D₄×C₅₃	C₂²	semidirect
197. C₂×C₄×D₄×C₅₃	C₂²	semidirect
198. C₂×C₄×D₄×C₅₃	C₂²	semidirect
199. C₂×C₄×D₄×C₅₃	C₂²	semidirect
206. C₂×#117×C₅₃	C₂²	semidirect
207. C₂×#117×C₅₃	C₂²	semidirect
208. C₂×#117×C₅₃	C₂²	semidirect
209. C₂×#117×C₅₃	C₂²	semidirect
210. C₂×#117×C₅₃	C₂²	semidirect
211. C₂×#117×C₅₃	C₂²	semidirect
212. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
213. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
214. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
218. C₂²×C₄²×C₅₃	C₂²	semidirect
262. C₄⋊Q₈×C₅₃	C₂³	semidirect
263. C₄⋊Q₈×C₅₃	C₂³	semidirect
264. C₄⋊Q₈×C₅₃	C₂³	semidirect
280. #126×C₅₃	C₂³	semidirect
281. #126×C₅₃	C₂³	semidirect
282. #126×C₅₃	C₂³	semidirect
283. #126×C₅₃	C₂³	semidirect
284. #126×C₅₃	C₂³	semidirect
285. #126×C₅₃	C₂³	semidirect
286. #125×C₅₃	C₂³	semidirect
287. #125×C₅₃	C₂³	semidirect
288. #125×C₅₃	C₂³	semidirect
289. #125×C₅₃	C₂³	semidirect
290. #125×C₅₃	C₂³	semidirect
291. #125×C₅₃	C₂³	semidirect
292. #125×C₅₃	C₂³	semidirect
293. #125×C₅₃	C₂³	semidirect
294. #125×C₅₃	C₂³	semidirect
295. #125×C₅₃	C₂³	semidirect
296. #125×C₅₃	C₂³	semidirect
297. #125×C₅₃	C₂³	semidirect
307. #124×C₅₃	C₂³	semidirect
308. #124×C₅₃	C₂³	semidirect
309. #124×C₅₃	C₂³	semidirect
328. #123×C₅₃	C₂³	semidirect
329. #123×C₅₃	C₂³	semidirect
330. #123×C₅₃	C₂³	semidirect
331. #123×C₅₃	C₂³	semidirect
332. #123×C₅₃	C₂³	semidirect
333. #123×C₅₃	C₂³	semidirect
343. C₂²⋊Q₈×C₅₃	C₂³	semidirect
344. C₂²⋊Q₈×C₅₃	C₂³	semidirect
345. C₂²⋊Q₈×C₅₃	C₂³	semidirect
346. C₂²⋊Q₈×C₅₃	C₂³	semidirect
347. C₂²⋊Q₈×C₅₃	C₂³	semidirect
348. C₂²⋊Q₈×C₅₃	C₂³	semidirect
349. C₂²⋊Q₈×C₅₃	C₂³	semidirect
350. C₂²⋊Q₈×C₅₃	C₂³	semidirect
351. C₂²⋊Q₈×C₅₃	C₂³	semidirect
367. #121×C₅₃	C₂³	semidirect
368. #121×C₅₃	C₂³	semidirect
369. #121×C₅₃	C₂³	semidirect
374. C₄×Q₈×C₅₃	C₂³	semidirect
375. C₄×Q₈×C₅₃	C₂³	semidirect
376. C₄×Q₈×C₅₃	C₂³	semidirect
377. C₄×Q₈×C₅₃	C₂³	semidirect
378. C₄×Q₈×C₅₃	C₂³	semidirect
379. C₄×Q₈×C₅₃	C₂³	semidirect
392. C₄×D₄×C₅₃	C₂³	semidirect
393. C₄×D₄×C₅₃	C₂³	semidirect
394. C₄×D₄×C₅₃	C₂³	semidirect
395. C₄×D₄×C₅₃	C₂³	semidirect
396. C₄×D₄×C₅₃	C₂³	semidirect
397. C₄×D₄×C₅₃	C₂³	semidirect
404. #117×C₅₃	C₂³	semidirect
405. #117×C₅₃	C₂³	semidirect
406. #117×C₅₃	C₂³	semidirect
407. #117×C₅₃	C₂³	semidirect
408. #117×C₅₃	C₂³	semidirect
409. #117×C₅₃	C₂³	semidirect
458. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
459. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
460. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
528. C₂×C₄²×C₅₃	C₂³	semidirect
883. C₂×#3566	C₅₃	direct (N × H)
941. #3566	C₂×C₅₃	direct (N × H)
942. C₂×#563	C₂×C₅₃	semidirect
943. C₂×#562	C₂×C₅₃	semidirect
944. C₂×#562	C₂×C₅₃	semidirect
945. C₂×#560	C₂×C₅₃	semidirect
946. C₂×#559	C₂×C₅₃	semidirect
947. C₂×#556	C₂×C₅₃	semidirect
948. C₂×#555	C₂×C₅₃	semidirect
949. C₂×#553	C₂×C₅₃	semidirect
950. C₂×#553	C₂×C₅₃	semidirect
951. C₂×#553	C₂×C₅₃	semidirect
952. C₂×#552	C₂×C₅₃	semidirect
953. C₂×#552	C₂×C₅₃	semidirect
954. C₂×#552	C₂×C₅₃	semidirect
955. C₂×#551	C₂×C₅₃	semidirect
956. C₂×#551	C₂×C₅₃	semidirect
957. C₂×#551	C₂×C₅₃	semidirect
958. C₂×#542	C₂×C₅₃	semidirect
959. C₂×#542	C₂×C₅₃	semidirect
960. C₂×#542	C₂×C₅₃	semidirect
961. C₂×#541	C₂×C₅₃	semidirect
962. C₂×#541	C₂×C₅₃	semidirect
963. C₂×#540	C₂×C₅₃	semidirect
964. C₂×#539	C₂×C₅₃	semidirect
965. C₂×#539	C₂×C₅₃	semidirect
966. C₂×#539	C₂×C₅₃	semidirect
967. C₂×#538	C₂×C₅₃	semidirect
968. C₂×#538	C₂×C₅₃	semidirect
969. C₂×#538	C₂×C₅₃	semidirect
970. C₂×#529	C₂×C₅₃	semidirect
971. C₂×#529	C₂×C₅₃	semidirect
972. C₂×#529	C₂×C₅₃	semidirect
980. C₂×C₅₃	#3566	direct (N × H)
984. #563	C₂²×C₅₃	semidirect
985. #562	C₂²×C₅₃	semidirect
986. #562	C₂²×C₅₃	semidirect
987. #560	C₂²×C₅₃	semidirect
988. #559	C₂²×C₅₃	semidirect
989. #556	C₂²×C₅₃	semidirect
990. #555	C₂²×C₅₃	semidirect
991. #553	C₂²×C₅₃	semidirect
992. #553	C₂²×C₅₃	semidirect
993. #553	C₂²×C₅₃	semidirect
994. #552	C₂²×C₅₃	semidirect
995. #552	C₂²×C₅₃	semidirect
996. #552	C₂²×C₅₃	semidirect
997. #551	C₂²×C₅₃	semidirect
998. #551	C₂²×C₅₃	semidirect
999. #551	C₂²×C₅₃	semidirect
1000. #542	C₂²×C₅₃	semidirect
1001. #542	C₂²×C₅₃	semidirect
1002. #542	C₂²×C₅₃	semidirect
1003. #541	C₂²×C₅₃	semidirect
1004. #541	C₂²×C₅₃	semidirect
1005. #540	C₂²×C₅₃	semidirect
1006. #539	C₂²×C₅₃	semidirect
1007. #539	C₂²×C₅₃	semidirect
1008. #539	C₂²×C₅₃	semidirect
1009. #538	C₂²×C₅₃	semidirect
1010. #538	C₂²×C₅₃	semidirect
1011. #538	C₂²×C₅₃	semidirect
1012. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
1013. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
1014. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
1016. #529	C₂²×C₅₃	semidirect
1017. #529	C₂²×C₅₃	semidirect
1018. #529	C₂²×C₅₃	semidirect
1033. C₂×#126	C₂²×C₅₃	semidirect
1034. C₂×#126	C₂²×C₅₃	semidirect
1035. C₂×#126	C₂²×C₅₃	semidirect
1036. C₂×#126	C₂²×C₅₃	semidirect
1037. C₂×#126	C₂²×C₅₃	semidirect
1038. C₂×#126	C₂²×C₅₃	semidirect
1039. C₂×#125	C₂²×C₅₃	semidirect
1040. C₂×#125	C₂²×C₅₃	semidirect
1041. C₂×#125	C₂²×C₅₃	semidirect
1042. C₂×#125	C₂²×C₅₃	semidirect
1043. C₂×#125	C₂²×C₅₃	semidirect
1044. C₂×#125	C₂²×C₅₃	semidirect
1045. C₂×#125	C₂²×C₅₃	semidirect
1046. C₂×#125	C₂²×C₅₃	semidirect
1047. C₂×#125	C₂²×C₅₃	semidirect
1048. C₂×#125	C₂²×C₅₃	semidirect
1049. C₂×#125	C₂²×C₅₃	semidirect
1050. C₂×#125	C₂²×C₅₃	semidirect
1060. C₂×#124	C₂²×C₅₃	semidirect
1061. C₂×#124	C₂²×C₅₃	semidirect
1062. C₂×#124	C₂²×C₅₃	semidirect
1081. C₂×#123	C₂²×C₅₃	semidirect
1082. C₂×#123	C₂²×C₅₃	semidirect
1083. C₂×#123	C₂²×C₅₃	semidirect
1084. C₂×#123	C₂²×C₅₃	semidirect
1085. C₂×#123	C₂²×C₅₃	semidirect
1086. C₂×#123	C₂²×C₅₃	semidirect
1096. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
1097. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
1098. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
1099. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
1100. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
1101. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
1102. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
1103. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
1104. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
1120. C₂×#121	C₂²×C₅₃	semidirect
1121. C₂×#121	C₂²×C₅₃	semidirect
1122. C₂×#121	C₂²×C₅₃	semidirect
1127. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
1128. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
1129. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
1130. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
1131. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
1132. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
1145. C₂×C₄×D₄	C₂²×C₅₃	semidirect
1146. C₂×C₄×D₄	C₂²×C₅₃	semidirect
1147. C₂×C₄×D₄	C₂²×C₅₃	semidirect
1148. C₂×C₄×D₄	C₂²×C₅₃	semidirect
1149. C₂×C₄×D₄	C₂²×C₅₃	semidirect
1150. C₂×C₄×D₄	C₂²×C₅₃	semidirect
1157. C₂×#117	C₂²×C₅₃	semidirect
1158. C₂×#117	C₂²×C₅₃	semidirect
1159. C₂×#117	C₂²×C₅₃	semidirect
1160. C₂×#117	C₂²×C₅₃	semidirect
1161. C₂×#117	C₂²×C₅₃	semidirect
1162. C₂×#117	C₂²×C₅₃	semidirect
1163. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
1164. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
1165. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
1169. C₂²×C₄²	C₂²×C₅₃	semidirect
1170. C₅₃	C₂×#3566	direct (N × H)
1214. C₄⋊Q₈	C₂³×C₅₃	semidirect
1215. C₄⋊Q₈	C₂³×C₅₃	semidirect
1216. C₄⋊Q₈	C₂³×C₅₃	semidirect
1232. #126	C₂³×C₅₃	semidirect
1233. #126	C₂³×C₅₃	semidirect
1234. #126	C₂³×C₅₃	semidirect
1235. #126	C₂³×C₅₃	semidirect
1236. #126	C₂³×C₅₃	semidirect
1237. #126	C₂³×C₅₃	semidirect
1238. #125	C₂³×C₅₃	semidirect
1239. #125	C₂³×C₅₃	semidirect
1240. #125	C₂³×C₅₃	semidirect
1241. #125	C₂³×C₅₃	semidirect
1242. #125	C₂³×C₅₃	semidirect
1243. #125	C₂³×C₅₃	semidirect
1244. #125	C₂³×C₅₃	semidirect
1245. #125	C₂³×C₅₃	semidirect
1246. #125	C₂³×C₅₃	semidirect
1247. #125	C₂³×C₅₃	semidirect
1248. #125	C₂³×C₅₃	semidirect
1249. #125	C₂³×C₅₃	semidirect
1259. #124	C₂³×C₅₃	semidirect
1260. #124	C₂³×C₅₃	semidirect
1261. #124	C₂³×C₅₃	semidirect
1280. #123	C₂³×C₅₃	semidirect
1281. #123	C₂³×C₅₃	semidirect
1282. #123	C₂³×C₅₃	semidirect
1283. #123	C₂³×C₅₃	semidirect
1284. #123	C₂³×C₅₃	semidirect
1285. #123	C₂³×C₅₃	semidirect
1295. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1296. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1297. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1298. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1299. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1300. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1301. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1302. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1303. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1319. #121	C₂³×C₅₃	semidirect
1320. #121	C₂³×C₅₃	semidirect
1321. #121	C₂³×C₅₃	semidirect
1326. C₄×Q₈	C₂³×C₅₃	semidirect
1327. C₄×Q₈	C₂³×C₅₃	semidirect
1328. C₄×Q₈	C₂³×C₅₃	semidirect
1329. C₄×Q₈	C₂³×C₅₃	semidirect
1330. C₄×Q₈	C₂³×C₅₃	semidirect
1331. C₄×Q₈	C₂³×C₅₃	semidirect
1344. C₄×D₄	C₂³×C₅₃	semidirect
1345. C₄×D₄	C₂³×C₅₃	semidirect
1346. C₄×D₄	C₂³×C₅₃	semidirect
1347. C₄×D₄	C₂³×C₅₃	semidirect
1348. C₄×D₄	C₂³×C₅₃	semidirect
1349. C₄×D₄	C₂³×C₅₃	semidirect
1356. #117	C₂³×C₅₃	semidirect
1357. #117	C₂³×C₅₃	semidirect
1358. #117	C₂³×C₅₃	semidirect
1359. #117	C₂³×C₅₃	semidirect
1360. #117	C₂³×C₅₃	semidirect
1361. #117	C₂³×C₅₃	semidirect
1410. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
1411. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
1412. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
1480. C₂×C₄²	C₂³×C₅₃	semidirect
1899. C₂	C₅₃×#3566	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅₃×#3566	2
C₂×C₅₃×#563	2
C₂×C₅₃×#562	2
C₂×C₅₃×#560	2
C₂×C₅₃×#559	2
C₂×C₅₃×#556	2
C₂×C₅₃×#555	2
C₂×C₅₃×#553	2
C₂×C₅₃×#552	2
C₂×C₅₃×#551	2
C₂×C₅₃×#542	2
C₂×C₅₃×#541	2
C₂×C₅₃×#540	2
C₂×C₅₃×#539	2
C₂×C₅₃×#538	2
C₂×C₅₃×#529	2
C₂×#3566	53

Subgroups — C2×C53×#3566 #27270254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3566 #27270254