Subgroups — C₂×C₅₃×#3564 #27270246

Order 13568.

6598 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3564	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₅₃×#563	C₂	1	2	yes	maximal, complemented
3	C₂×C₅₃×#563	C₂	1	2	yes	maximal, complemented
4	C₂×C₅₃×#556	C₂	1	2	yes	maximal, complemented
5	C₂×C₅₃×#554	C₂	1	2	yes	maximal, complemented
6	C₂×C₅₃×#552	C₂	1	2	yes	maximal, complemented
7	C₂×C₅₃×#552	C₂	1	2	yes	maximal, complemented
8	C₂×C₅₃×#551	C₂	1	2	yes	maximal, complemented
9	C₂×C₅₃×#551	C₂	1	2	yes	maximal, complemented
10	C₂×C₅₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#543	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅₃×#542	C₂	1	2	yes	maximal, complemented
13	C₂×C₅₃×#541	C₂	1	2	yes	maximal, complemented
14	C₂×C₅₃×#541	C₂	1	2	yes	maximal, complemented
15	C₂×C₅₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅₃×#539	C₂	1	2	yes	maximal, complemented
17	C₂×C₅₃×#538	C₂	1	1	yes	maximal, characteristic
18	C₂×C₅₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#126×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#563	C₂²	1	32	yes	complemented
22	C₅₃×#563	C₂²	1	32	yes	complemented
23	C₅₃×#556	C₂²	1	32	yes	complemented
24	C₅₃×#554	C₂²	1	32	yes	complemented
25	C₅₃×#552	C₂²	1	32	yes	complemented
26	C₅₃×#552	C₂²	1	32	yes	complemented
27	C₅₃×#551	C₂²	1	32	yes	complemented
28	C₅₃×#551	C₂²	1	32	yes	complemented
29	C₅₃×#544	C₂²	1	16	yes	complemented
30	C₅₃×#543	C₂²	1	16	yes	complemented
31	C₅₃×#542	C₂²	1	32	yes	complemented
32	C₅₃×#541	C₂²	1	32	yes	complemented
33	C₅₃×#541	C₂²	1	32	yes	complemented
34	C₅₃×#539	C₂²	1	16	yes	complemented
35	C₅₃×#539	C₂²	1	32	yes	complemented
36	C₅₃×#538	C₂²	1	16	yes	—
37	C₅₃×#533	C₂²	1	16	yes	complemented
38	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
39	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
40	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
41	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#529	C₂²	1	16	yes	complemented
44	C₂×#126×C₅₃	C₂²	1	2	yes	—
45	C₂×#126×C₅₃	C₂²	1	2	yes	—
46	C₂×#126×C₅₃	C₂²	1	2	yes	—
47	C₂×#126×C₅₃	C₂²	1	2	yes	—
48	C₂×#126×C₅₃	C₂²	1	2	yes	—
49	C₂×#126×C₅₃	C₂²	1	2	yes	—
50	C₂×#126×C₅₃	C₂²	1	2	yes	—
51	C₂×#126×C₅₃	C₂²	1	2	yes	—
52	C₂×#126×C₅₃	C₂²	1	2	yes	—
53	C₂×#126×C₅₃	C₂²	1	16	yes	complemented
54	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
55	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
56	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
57	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
58	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
59	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
60	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
61	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
63	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
64	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
65	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
66	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
67	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
68	C₂×#124×C₅₃	C₂²	1	2	yes	—
69	C₂×#124×C₅₃	C₂²	1	2	yes	—
70	C₂×#124×C₅₃	C₂²	1	2	yes	—
71	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
72	C₂×#123×C₅₃	C₂²	1	2	yes	—
73	C₂×#123×C₅₃	C₂²	1	2	yes	—
74	C₂×#123×C₅₃	C₂²	1	2	yes	—
75	C₂×#123×C₅₃	C₂²	1	2	yes	—
76	C₂×#123×C₅₃	C₂²	1	2	yes	—
77	C₂×#123×C₅₃	C₂²	1	2	yes	—
78	C₂×#123×C₅₃	C₂²	1	2	yes	—
79	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
80	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
81	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
82	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
83	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
84	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
85	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
86	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
87	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
88	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
89	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
90	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
91	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
92	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
93	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
94	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
95	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
96	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
97	C₂×#121×C₅₃	C₂²	1	2	yes	—
98	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
99	C₂×#120×C₅₃	C₂²	1	2	yes	—
100	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
102	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
103	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
104	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
107	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
108	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
109	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
110	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
111	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
112	C₂×#117×C₅₃	C₂²	1	2	yes	—
113	C₂×#117×C₅₃	C₂²	1	2	yes	—
114	C₂×#117×C₅₃	C₂²	1	2	yes	—
115	C₂×#117×C₅₃	C₂²	1	2	yes	—
116	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
117	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
118	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
119	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
120	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
121	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
122	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
123	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
124	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
125	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
126	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
127	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
128	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
129	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
130	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
132	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
133	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
135	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
136	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
137	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
145	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
146	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
147	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
148	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
149	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
150	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
151	C₄⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
152	C₄⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
153	C₄⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
154	#126×C₅₃	C₂³	1	16	yes	—
155	#126×C₅₃	C₂³	1	16	yes	—
156	#126×C₅₃	C₂³	1	16	yes	—
157	#126×C₅₃	C₂³	1	16	yes	—
158	#126×C₅₃	C₂³	1	16	yes	—
159	#126×C₅₃	C₂³	1	16	yes	—
160	#126×C₅₃	C₂³	1	16	yes	—
161	#126×C₅₃	C₂³	1	16	yes	—
162	#126×C₅₃	C₂³	1	16	yes	—
163	#126×C₅₃	C₂³	1	16	yes	complemented
164	#126×C₅₃	C₂³	1	16	yes	complemented
165	#126×C₅₃	C₂³	1	16	yes	complemented
166	#126×C₅₃	C₂³	1	16	yes	complemented
167	#125×C₅₃	C₂³	1	8	yes	complemented
168	#125×C₅₃	C₂³	1	16	yes	complemented
169	#125×C₅₃	C₂³	1	16	yes	complemented
170	#125×C₅₃	C₂³	1	16	yes	complemented
171	#125×C₅₃	C₂³	1	16	yes	complemented
172	#125×C₅₃	C₂³	1	16	yes	complemented
173	#125×C₅₃	C₂³	1	16	yes	complemented
174	#125×C₅₃	C₂³	1	16	yes	complemented
175	#125×C₅₃	C₂³	1	16	yes	complemented
176	#125×C₅₃	C₂³	1	16	yes	complemented
177	#124×C₅₃	C₂³	1	16	yes	—
178	#124×C₅₃	C₂³	1	16	yes	—
179	#124×C₅₃	C₂³	1	16	yes	—
180	#124×C₅₃	C₂³	1	8	yes	complemented
181	#123×C₅₃	C₂³	1	16	yes	—
182	#123×C₅₃	C₂³	1	16	yes	—
183	#123×C₅₃	C₂³	1	16	yes	—
184	#123×C₅₃	C₂³	1	16	yes	—
185	#123×C₅₃	C₂³	1	16	yes	—
186	#123×C₅₃	C₂³	1	16	yes	—
187	#123×C₅₃	C₂³	1	16	yes	—
188	#123×C₅₃	C₂³	1	16	yes	complemented
189	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
190	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
191	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
192	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
193	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
194	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
195	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
196	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
197	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
198	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
199	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
200	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
201	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
202	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
203	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
204	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
205	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
206	#121×C₅₃	C₂³	1	8	yes	—
207	#121×C₅₃	C₂³	1	16	yes	—
208	#120×C₅₃	C₂³	1	16	yes	—
209	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
210	C₄×Q₈×C₅₃	C₂³	1	16	yes	complemented
211	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
212	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
213	C₄×Q₈×C₅₃	C₂³	1	16	yes	complemented
214	C₄×Q₈×C₅₃	C₂³	1	16	yes	complemented
215	C₄×D₄×C₅₃	C₂³	1	16	yes	—
216	C₄×D₄×C₅₃	C₂³	1	16	yes	—
217	C₄×D₄×C₅₃	C₂³	1	16	yes	—
218	C₄×D₄×C₅₃	C₂³	1	16	yes	—
219	C₄×D₄×C₅₃	C₂³	1	16	yes	—
220	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
221	#117×C₅₃	C₂³	1	16	yes	—
222	#117×C₅₃	C₂³	1	16	yes	—
223	#117×C₅₃	C₂³	1	16	yes	—
224	#117×C₅₃	C₂³	1	16	yes	—
225	#117×C₅₃	C₂³	1	16	yes	complemented
226	#117×C₅₃	C₂³	1	16	yes	complemented
227	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
228	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
229	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
230	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
231	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
232	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
233	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	—
234	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	—
235	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	—
236	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
237	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
238	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
239	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
240	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
241	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
242	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
243	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
244	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
245	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
246	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
247	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
248	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
249	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
250	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
251	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
252	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₅₃	C₂³	1	16	yes	complemented
264	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
265	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
266	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
267	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
268	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
269	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
270	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
271	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
272	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
273	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
274	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
275	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
276	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
277	C₂×C₂²⋊C₄×C₅₃	C₂³	1	16	yes	—
278	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
279	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
280	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
281	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
282	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
283	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
284	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
285	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
286	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
287	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
288	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
289	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
290	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
291	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
292	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
293	C₂×C₄²×C₅₃	C₂³	1	8	yes	—
294	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
295	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
296	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
297	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
298	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
299	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
300	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
301	C₂⁴×C₅₃	—	2	4	no	—
302	C₂⁴×C₅₃	—	4	2	no	—
303	C₂⁴×C₅₃	—	4	2	no	—
304	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
305	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
306	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
307	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
308	C₂×Q₈×C₅₃	—	4	4	no	—
309	C₂×Q₈×C₅₃	—	4	2	no	—
310	C₂×Q₈×C₅₃	—	4	4	no	—
311	C₂×Q₈×C₅₃	—	4	2	no	—
312	C₂×Q₈×C₅₃	—	4	4	no	—
313	C₂×Q₈×C₅₃	—	4	2	no	—
314	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
315	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
316	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
317	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
318	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
319	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
320	C₂×D₄×C₅₃	—	2	8	no	—
321	C₂×D₄×C₅₃	—	4	4	no	—
322	C₂×D₄×C₅₃	—	4	2	no	—
323	C₂×D₄×C₅₃	—	4	4	no	—
324	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
325	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
326	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
327	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
328	C₂²×C₄×C₅₃	—	2	4	no	—
329	C₂²×C₄×C₅₃	—	2	4	no	—
330	C₂²×C₄×C₅₃	—	4	4	no	—
331	C₂²×C₄×C₅₃	—	4	2	no	—
332	C₂²×C₄×C₅₃	—	4	2	no	—
333	C₂²×C₄×C₅₃	—	4	2	no	—
334	C₂²×C₄×C₅₃	—	4	4	no	—
335	C₂²×C₄×C₅₃	—	4	4	no	—
336	C₂²×C₄×C₅₃	—	4	4	no	—
337	C₂²×C₄×C₅₃	—	4	4	no	—
338	C₂²×C₄×C₅₃	—	4	2	no	—
339	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
340	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
341	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
347	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
357	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
358	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
359	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
360	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
361	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
362	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
363	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
364	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
365	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
366	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
367	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
368	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
369	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
370	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
371	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
372	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
373	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
374	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
375	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
376	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
377	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
378	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
379	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
380	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
381	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
382	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
383	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
384	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
385	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
386	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
387	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
388	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
389	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
390	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
391	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
392	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
393	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
394	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
395	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
396	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
397	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
398	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
399	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
400	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
401	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
402	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
403	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
404	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
405	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
406	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
407	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
408	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
409	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
410	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
411	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
412	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
413	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
414	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
415	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
416	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
417	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
418	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
419	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
420	C₄²×C₅₃	C₂⁴	1	4	yes	—
421	C₄²×C₅₃	C₂⁴	1	4	yes	—
422	C₄²×C₅₃	C₂⁴	1	4	yes	—
423	C₄²×C₅₃	C₂⁴	1	4	yes	—
424	C₄²×C₅₃	C₂⁴	1	8	yes	—
425	C₄²×C₅₃	C₂⁴	1	8	yes	—
426	C₄²×C₅₃	C₂⁴	1	8	yes	—
427	C₄²×C₅₃	C₂⁴	1	8	yes	—
428	C₄²×C₅₃	C₂⁴	1	8	yes	—
429	C₄²×C₅₃	C₂⁴	1	8	yes	—
430	C₄²×C₅₃	C₂⁴	1	8	yes	—
431	C₂³×C₅₃	—	2	2	no	—
432	C₂³×C₅₃	—	2	2	no	—
433	C₂³×C₅₃	—	2	4	no	—
434	C₂³×C₅₃	—	2	4	no	—
435	C₂³×C₅₃	—	2	4	no	—
436	C₂³×C₅₃	—	2	4	no	—
437	C₂³×C₅₃	—	2	4	no	—
438	C₂³×C₅₃	—	2	4	no	—
439	C₂³×C₅₃	—	2	8	no	—
440	C₂³×C₅₃	—	4	4	no	—
441	C₂³×C₅₃	—	4	4	no	—
442	C₂³×C₅₃	—	8	8	no	—
443	C₂³×C₅₃	2₋¹⁺⁴	1	4	yes	—
444	C₂³×C₅₃	C₂⁵	1	4	yes	—
445	C₂³×C₅₃	C₂⁵	1	4	yes	—
446	C₂³×C₅₃	C₂⁵	1	2	yes	—
447	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
448	Q₈×C₅₃	—	4	4	no	—
449	Q₈×C₅₃	—	4	8	no	—
450	Q₈×C₅₃	—	4	8	no	—
451	Q₈×C₅₃	—	4	4	no	—
452	Q₈×C₅₃	—	4	8	no	—
453	Q₈×C₅₃	—	4	4	no	—
454	D₄×C₅₃	—	2	16	no	—
455	D₄×C₅₃	—	4	8	no	—
456	D₄×C₅₃	—	4	4	no	—
457	D₄×C₅₃	—	4	8	no	—
458	C₂×C₄×C₅₃	—	2	8	no	—
459	C₂×C₄×C₅₃	—	2	8	no	—
460	C₂×C₄×C₅₃	—	2	2	no	—
461	C₂×C₄×C₅₃	—	2	2	no	—
462	C₂×C₄×C₅₃	—	2	4	no	—
463	C₂×C₄×C₅₃	—	2	4	no	—
464	C₂×C₄×C₅₃	—	2	2	no	—
465	C₂×C₄×C₅₃	—	2	4	no	—
466	C₂×C₄×C₅₃	—	2	4	no	—
467	C₂×C₄×C₅₃	—	2	4	no	—
468	C₂×C₄×C₅₃	—	2	4	no	—
469	C₂×C₄×C₅₃	—	2	4	no	—
470	C₂×C₄×C₅₃	—	2	2	no	—
471	C₂×C₄×C₅₃	—	2	2	no	—
472	C₂×C₄×C₅₃	—	2	4	no	—
473	C₂×C₄×C₅₃	—	2	4	no	—
474	C₂×C₄×C₅₃	—	2	2	no	—
475	C₂×C₄×C₅₃	—	2	4	no	—
476	C₂×C₄×C₅₃	—	4	8	no	—
477	C₂×C₄×C₅₃	—	4	4	no	—
478	C₂×C₄×C₅₃	—	4	4	no	—
479	C₂×C₄×C₅₃	—	4	4	no	—
480	C₂×C₄×C₅₃	—	4	8	no	—
481	C₂×C₄×C₅₃	—	4	8	no	—
482	C₂×C₄×C₅₃	—	4	8	no	—
483	C₂×C₄×C₅₃	—	4	8	no	—
484	C₂×C₄×C₅₃	—	4	4	no	—
485	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
486	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
487	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
488	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
489	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
490	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
491	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
492	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
493	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
494	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
495	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
496	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
497	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
498	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
499	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
500	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
501	C₂×#3564	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
502	C₂²×C₅₃	—	2	2	no	—
503	C₂²×C₅₃	—	2	2	no	—
504	C₂²×C₅₃	—	2	8	no	—
505	C₂²×C₅₃	—	2	4	no	—
506	C₂²×C₅₃	—	2	4	no	—
507	C₂²×C₅₃	—	2	4	no	—
508	C₂²×C₅₃	—	2	4	no	—
509	C₂²×C₅₃	—	2	4	no	—
510	C₂²×C₅₃	—	2	4	no	—
511	C₂²×C₅₃	—	4	8	no	—
512	C₂²×C₅₃	—	4	8	no	—
513	C₂²×C₅₃	—	8	8	no	—
514	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	4	yes	—
515	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	2	yes	—
516	C₂²×C₅₃	#585	1	2	yes	—
517	C₂²×C₅₃	#585	1	2	yes	—
518	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
519	C₄×C₅₃	—	2	2	no	—
520	C₄×C₅₃	—	2	2	no	—
521	C₄×C₅₃	—	2	4	no	—
522	C₄×C₅₃	—	2	4	no	—
523	C₄×C₅₃	—	2	2	no	—
524	C₄×C₅₃	—	2	4	no	—
525	C₄×C₅₃	—	2	4	no	—
526	C₄×C₅₃	—	2	4	no	—
527	C₄×C₅₃	—	2	4	no	—
528	C₄×C₅₃	—	2	4	no	—
529	C₄×C₅₃	—	2	2	no	—
530	C₄×C₅₃	—	2	2	no	—
531	C₄×C₅₃	—	2	4	no	—
532	C₄×C₅₃	—	2	4	no	—
533	C₄×C₅₃	—	2	2	no	—
534	C₄×C₅₃	—	2	4	no	—
535	#3564	C₂×C₅₃	1	32	yes	direct product factor
536	C₂×#563	C₂×C₅₃	1	2	yes	complemented
537	C₂×#563	C₂×C₅₃	1	2	yes	complemented
538	C₂×#556	C₂×C₅₃	1	2	yes	complemented
539	C₂×#554	C₂×C₅₃	1	2	yes	complemented
540	C₂×#552	C₂×C₅₃	1	2	yes	complemented
541	C₂×#552	C₂×C₅₃	1	2	yes	complemented
542	C₂×#551	C₂×C₅₃	1	2	yes	complemented
543	C₂×#551	C₂×C₅₃	1	2	yes	complemented
544	C₂×#544	C₂×C₅₃	1	1	yes	characteristic, complemented
545	C₂×#543	C₂×C₅₃	1	1	yes	characteristic, complemented
546	C₂×#542	C₂×C₅₃	1	2	yes	complemented
547	C₂×#541	C₂×C₅₃	1	2	yes	complemented
548	C₂×#541	C₂×C₅₃	1	2	yes	complemented
549	C₂×#539	C₂×C₅₃	1	1	yes	characteristic, complemented
550	C₂×#539	C₂×C₅₃	1	2	yes	complemented
551	C₂×#538	C₂×C₅₃	1	1	yes	characteristic
552	C₂×#533	C₂×C₅₃	1	1	yes	characteristic, complemented
553	C₂×#529	C₂×C₅₃	1	1	yes	characteristic, complemented
554	C₂²×#126	C₂×C₅₃	1	1	yes	characteristic, complemented
555	C₂×C₅₃	—	2	4	no	—
556	C₂×C₅₃	—	4	4	no	—
557	C₂×C₅₃	—	4	4	no	—
558	C₂×C₅₃	#3564	1	4	yes	direct product factor
559	C₂×C₅₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
560	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
561	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
562	#563	C₂²×C₅₃	1	32	yes	complemented
563	#563	C₂²×C₅₃	1	32	yes	complemented
564	#556	C₂²×C₅₃	1	32	yes	complemented
565	#554	C₂²×C₅₃	1	32	yes	complemented
566	#552	C₂²×C₅₃	1	32	yes	complemented
567	#552	C₂²×C₅₃	1	32	yes	complemented
568	#551	C₂²×C₅₃	1	32	yes	complemented
569	#551	C₂²×C₅₃	1	32	yes	complemented
570	#544	C₂²×C₅₃	1	16	yes	complemented
571	#543	C₂²×C₅₃	1	16	yes	complemented
572	#542	C₂²×C₅₃	1	32	yes	complemented
573	#541	C₂²×C₅₃	1	32	yes	complemented
574	#541	C₂²×C₅₃	1	32	yes	complemented
575	#539	C₂²×C₅₃	1	16	yes	complemented
576	#539	C₂²×C₅₃	1	32	yes	complemented
577	#538	C₂²×C₅₃	1	16	yes	—
578	#533	C₂²×C₅₃	1	16	yes	complemented
579	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
580	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
581	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
582	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
583	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
584	#529	C₂²×C₅₃	1	16	yes	complemented
585	C₂×#126	C₂²×C₅₃	1	2	yes	—
586	C₂×#126	C₂²×C₅₃	1	2	yes	—
587	C₂×#126	C₂²×C₅₃	1	2	yes	—
588	C₂×#126	C₂²×C₅₃	1	2	yes	—
589	C₂×#126	C₂²×C₅₃	1	2	yes	—
590	C₂×#126	C₂²×C₅₃	1	2	yes	—
591	C₂×#126	C₂²×C₅₃	1	2	yes	—
592	C₂×#126	C₂²×C₅₃	1	2	yes	—
593	C₂×#126	C₂²×C₅₃	1	2	yes	—
594	C₂×#126	C₂²×C₅₃	1	16	yes	complemented
595	C₂×#126	C₂²×C₅₃	1	2	yes	complemented
596	C₂×#126	C₂²×C₅₃	1	2	yes	complemented
597	C₂×#126	C₂²×C₅₃	1	2	yes	complemented
598	C₂×#126	C₂²×C₅₃	1	2	yes	complemented
599	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
600	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
601	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
602	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
603	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
604	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
605	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
606	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
607	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
608	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
609	C₂×#124	C₂²×C₅₃	1	2	yes	—
610	C₂×#124	C₂²×C₅₃	1	2	yes	—
611	C₂×#124	C₂²×C₅₃	1	2	yes	—
612	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
613	C₂×#123	C₂²×C₅₃	1	2	yes	—
614	C₂×#123	C₂²×C₅₃	1	2	yes	—
615	C₂×#123	C₂²×C₅₃	1	2	yes	—
616	C₂×#123	C₂²×C₅₃	1	2	yes	—
617	C₂×#123	C₂²×C₅₃	1	2	yes	—
618	C₂×#123	C₂²×C₅₃	1	2	yes	—
619	C₂×#123	C₂²×C₅₃	1	2	yes	—
620	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
621	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
622	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
623	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
624	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
625	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
626	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
627	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
628	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
629	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
630	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
631	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
632	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
633	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
634	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
635	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
636	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
637	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
638	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
639	C₂×#121	C₂²×C₅₃	1	2	yes	—
640	C₂×#120	C₂²×C₅₃	1	2	yes	—
641	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
642	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
643	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
644	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
645	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
646	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
647	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
648	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
649	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
650	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
651	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
652	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
653	C₂×#117	C₂²×C₅₃	1	2	yes	—
654	C₂×#117	C₂²×C₅₃	1	2	yes	—
655	C₂×#117	C₂²×C₅₃	1	2	yes	—
656	C₂×#117	C₂²×C₅₃	1	2	yes	—
657	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
658	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
659	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
660	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
661	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
662	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
663	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
664	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
665	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
666	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
667	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
668	C₅₃	C₂×#3564	1	1	yes	characteristic, direct product factor, Sylow
669	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
670	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
671	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
672	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
673	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
674	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
675	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
676	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
677	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
678	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
679	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
680	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
681	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
682	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
683	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
684	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
685	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
686	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
687	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
688	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
689	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
690	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
691	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
692	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
693	C₄⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
694	C₄⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
695	C₄⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
696	#126	C₂³×C₅₃	1	16	yes	—
697	#126	C₂³×C₅₃	1	16	yes	—
698	#126	C₂³×C₅₃	1	16	yes	—
699	#126	C₂³×C₅₃	1	16	yes	—
700	#126	C₂³×C₅₃	1	16	yes	—
701	#126	C₂³×C₅₃	1	16	yes	—
702	#126	C₂³×C₅₃	1	16	yes	—
703	#126	C₂³×C₅₃	1	16	yes	—
704	#126	C₂³×C₅₃	1	16	yes	—
705	#126	C₂³×C₅₃	1	16	yes	complemented
706	#126	C₂³×C₅₃	1	16	yes	complemented
707	#126	C₂³×C₅₃	1	16	yes	complemented
708	#126	C₂³×C₅₃	1	16	yes	complemented
709	#125	C₂³×C₅₃	1	8	yes	complemented
710	#125	C₂³×C₅₃	1	16	yes	complemented
711	#125	C₂³×C₅₃	1	16	yes	complemented
712	#125	C₂³×C₅₃	1	16	yes	complemented
713	#125	C₂³×C₅₃	1	16	yes	complemented
714	#125	C₂³×C₅₃	1	16	yes	complemented
715	#125	C₂³×C₅₃	1	16	yes	complemented
716	#125	C₂³×C₅₃	1	16	yes	complemented
717	#125	C₂³×C₅₃	1	16	yes	complemented
718	#125	C₂³×C₅₃	1	16	yes	complemented
719	#124	C₂³×C₅₃	1	16	yes	—
720	#124	C₂³×C₅₃	1	16	yes	—
721	#124	C₂³×C₅₃	1	16	yes	—
722	#124	C₂³×C₅₃	1	8	yes	complemented
723	#123	C₂³×C₅₃	1	16	yes	—
724	#123	C₂³×C₅₃	1	16	yes	—
725	#123	C₂³×C₅₃	1	16	yes	—
726	#123	C₂³×C₅₃	1	16	yes	—
727	#123	C₂³×C₅₃	1	16	yes	—
728	#123	C₂³×C₅₃	1	16	yes	—
729	#123	C₂³×C₅₃	1	16	yes	—
730	#123	C₂³×C₅₃	1	16	yes	complemented
731	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
732	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
733	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
734	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
735	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
736	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
737	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
738	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
739	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
740	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
741	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
742	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
743	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
744	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
745	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
746	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
747	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
748	#121	C₂³×C₅₃	1	8	yes	—
749	#121	C₂³×C₅₃	1	16	yes	—
750	#120	C₂³×C₅₃	1	16	yes	—
751	C₄×Q₈	C₂³×C₅₃	1	8	yes	complemented
752	C₄×Q₈	C₂³×C₅₃	1	16	yes	complemented
753	C₄×Q₈	C₂³×C₅₃	1	8	yes	complemented
754	C₄×Q₈	C₂³×C₅₃	1	8	yes	complemented
755	C₄×Q₈	C₂³×C₅₃	1	16	yes	complemented
756	C₄×Q₈	C₂³×C₅₃	1	16	yes	complemented
757	C₄×D₄	C₂³×C₅₃	1	16	yes	—
758	C₄×D₄	C₂³×C₅₃	1	16	yes	—
759	C₄×D₄	C₂³×C₅₃	1	16	yes	—
760	C₄×D₄	C₂³×C₅₃	1	16	yes	—
761	C₄×D₄	C₂³×C₅₃	1	16	yes	—
762	C₄×D₄	C₂³×C₅₃	1	8	yes	complemented
763	#117	C₂³×C₅₃	1	16	yes	—
764	#117	C₂³×C₅₃	1	16	yes	—
765	#117	C₂³×C₅₃	1	16	yes	—
766	#117	C₂³×C₅₃	1	16	yes	—
767	#117	C₂³×C₅₃	1	16	yes	complemented
768	#117	C₂³×C₅₃	1	16	yes	complemented
769	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
770	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
771	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
772	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
773	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
774	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
775	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	—
776	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	—
777	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	—
778	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
779	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
780	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
781	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
782	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
783	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
784	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
785	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
786	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
787	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
788	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
789	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
790	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
791	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
792	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
793	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
794	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
795	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
796	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
797	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
798	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
799	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
800	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
801	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
802	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
803	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
804	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
805	C₂×C₄⋊C₄	C₂³×C₅₃	1	16	yes	complemented
806	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
807	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
808	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
809	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
811	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
812	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
813	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
814	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
815	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
816	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
817	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
818	C₂×C₂²⋊C₄	C₂³×C₅₃	1	8	yes	—
819	C₂×C₂²⋊C₄	C₂³×C₅₃	1	16	yes	—
820	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
821	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
822	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
823	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
824	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
825	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
826	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
827	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
828	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
829	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
830	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
831	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
832	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
833	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
834	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
835	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
836	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
837	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
838	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
839	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
840	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
841	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
842	C₂×C₄²	C₂³×C₅₃	1	8	yes	—
843	C₂⁴	—	2	4	no	—
844	C₂⁴	—	4	2	no	—
845	C₂⁴	—	4	2	no	—
846	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
847	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
848	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
849	C₂⁴	C₂⁴×C₅₃	1	4	yes	—
850	C₂×Q₈	—	4	2	no	—
851	C₂×Q₈	—	4	4	no	—
852	C₂×Q₈	—	4	4	no	—
853	C₂×Q₈	—	4	2	no	—
854	C₂×Q₈	—	4	4	no	—
855	C₂×Q₈	—	4	2	no	—
856	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
857	C₂×Q₈	C₂⁴×C₅₃	1	8	yes	—
858	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
859	C₂×Q₈	C₂⁴×C₅₃	1	8	yes	—
860	C₂×Q₈	C₂⁴×C₅₃	1	8	yes	—
861	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
862	C₂×D₄	—	2	8	no	—
863	C₂×D₄	—	4	4	no	—
864	C₂×D₄	—	4	2	no	—
865	C₂×D₄	—	4	4	no	—
866	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
867	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
868	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
869	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
870	C₂²×C₄	—	2	4	no	—
871	C₂²×C₄	—	2	4	no	—
872	C₂²×C₄	—	4	4	no	—
873	C₂²×C₄	—	4	2	no	—
874	C₂²×C₄	—	4	2	no	—
875	C₂²×C₄	—	4	2	no	—
876	C₂²×C₄	—	4	4	no	—
877	C₂²×C₄	—	4	4	no	—
878	C₂²×C₄	—	4	4	no	—
879	C₂²×C₄	—	4	4	no	—
880	C₂²×C₄	—	4	2	no	—
881	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
884	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
885	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
886	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
888	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
889	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
890	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
892	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
893	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
894	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
895	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
896	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
897	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
898	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
899	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
900	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
901	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
902	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
903	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
904	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
905	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
906	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
907	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
908	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
909	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
910	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
911	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
912	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
913	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
914	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
915	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
916	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
917	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
918	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
919	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
920	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
921	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
922	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
923	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
924	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
925	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
926	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
927	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
928	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
929	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
930	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
931	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
932	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
933	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
934	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
935	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
936	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
937	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
938	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
939	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
940	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
941	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
942	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
943	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
944	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
945	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
946	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
947	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
948	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
949	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
950	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
951	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
952	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
953	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
954	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
955	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
956	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
957	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
958	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
959	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
960	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
961	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
962	C₄²	C₂⁴×C₅₃	1	4	yes	—
963	C₄²	C₂⁴×C₅₃	1	4	yes	—
964	C₄²	C₂⁴×C₅₃	1	4	yes	—
965	C₄²	C₂⁴×C₅₃	1	4	yes	—
966	C₄²	C₂⁴×C₅₃	1	8	yes	—
967	C₄²	C₂⁴×C₅₃	1	8	yes	—
968	C₄²	C₂⁴×C₅₃	1	8	yes	—
969	C₄²	C₂⁴×C₅₃	1	8	yes	—
970	C₄²	C₂⁴×C₅₃	1	8	yes	—
971	C₄²	C₂⁴×C₅₃	1	8	yes	—
972	C₄²	C₂⁴×C₅₃	1	8	yes	—
973	C₂³	—	2	2	no	—
974	C₂³	—	2	2	no	—
975	C₂³	—	2	4	no	—
976	C₂³	—	2	4	no	—
977	C₂³	—	2	4	no	—
978	C₂³	—	2	4	no	—
979	C₂³	—	2	4	no	—
980	C₂³	—	2	4	no	—
981	C₂³	—	2	8	no	—
982	C₂³	—	4	4	no	—
983	C₂³	—	4	4	no	—
984	C₂³	—	8	8	no	—
985	C₂³	2₋¹⁺⁴×C₅₃	1	4	yes	—
986	C₂³	C₂⁵×C₅₃	1	4	yes	—
987	C₂³	C₂⁵×C₅₃	1	4	yes	—
988	C₂³	C₂⁵×C₅₃	1	2	yes	—
989	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
990	Q₈	—	4	4	no	—
991	Q₈	—	4	8	no	—
992	Q₈	—	4	8	no	—
993	Q₈	—	4	4	no	—
994	Q₈	—	4	8	no	—
995	Q₈	—	4	4	no	—
996	D₄	—	2	16	no	—
997	D₄	—	4	8	no	—
998	D₄	—	4	4	no	—
999	D₄	—	4	8	no	—
1000	C₂×C₄	—	2	8	no	—
1001	C₂×C₄	—	2	8	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	4	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	4	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	4	no	—
1008	C₂×C₄	—	2	4	no	—
1009	C₂×C₄	—	2	4	no	—
1010	C₂×C₄	—	2	4	no	—
1011	C₂×C₄	—	2	4	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	4	no	—
1015	C₂×C₄	—	2	4	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	4	no	—
1018	C₂×C₄	—	4	8	no	—
1019	C₂×C₄	—	4	4	no	—
1020	C₂×C₄	—	4	4	no	—
1021	C₂×C₄	—	4	4	no	—
1022	C₂×C₄	—	4	8	no	—
1023	C₂×C₄	—	4	8	no	—
1024	C₂×C₄	—	4	8	no	—
1025	C₂×C₄	—	4	8	no	—
1026	C₂×C₄	—	4	4	no	—
1027	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1028	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1029	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1030	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1031	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1032	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1033	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1034	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1035	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1036	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1037	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1038	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1039	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1040	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1041	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1042	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1043	C₂²	—	2	8	no	—
1044	C₂²	—	2	2	no	—
1045	C₂²	—	2	2	no	—
1046	C₂²	—	2	4	no	—
1047	C₂²	—	2	4	no	—
1048	C₂²	—	2	4	no	—
1049	C₂²	—	2	4	no	—
1050	C₂²	—	2	4	no	—
1051	C₂²	—	2	4	no	—
1052	C₂²	—	4	8	no	—
1053	C₂²	—	4	8	no	—
1054	C₂²	—	8	8	no	—
1055	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	4	yes	—
1056	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	2	yes	—
1057	C₂²	C₅₃×#585	1	2	yes	—
1058	C₂²	C₅₃×#585	1	2	yes	—
1059	C₂²	C₂⁶×C₅₃	1	1	yes	characteristic
1060	C₄	—	2	2	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	4	no	—
1063	C₄	—	2	4	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	2	4	no	—
1066	C₄	—	2	4	no	—
1067	C₄	—	2	4	no	—
1068	C₄	—	2	4	no	—
1069	C₄	—	2	4	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	4	no	—
1073	C₄	—	2	4	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	2	4	no	—
1076	C₂	—	2	4	no	—
1077	C₂	—	4	4	no	—
1078	C₂	—	4	4	no	—
1079	C₂	C₅₃×#3564	1	4	yes	direct product factor
1080	C₂	C₂²×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1081	C₂	C₂×C₅₃×#585	1	1	yes	characteristic
1082	C₂	C₂×C₅₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₅₃
prime radical	C₂×C₅₃×#538	C₂
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×#3564	C₂	direct (N × H)
2. C₂×C₅₃×#563	C₂	semidirect
3. C₂×C₅₃×#563	C₂	semidirect
4. C₂×C₅₃×#556	C₂	semidirect
5. C₂×C₅₃×#554	C₂	semidirect
6. C₂×C₅₃×#552	C₂	semidirect
7. C₂×C₅₃×#552	C₂	semidirect
8. C₂×C₅₃×#551	C₂	semidirect
9. C₂×C₅₃×#551	C₂	semidirect
10. C₂×C₅₃×#544	C₂	semidirect
11. C₂×C₅₃×#543	C₂	semidirect
12. C₂×C₅₃×#542	C₂	semidirect
13. C₂×C₅₃×#541	C₂	semidirect
14. C₂×C₅₃×#541	C₂	semidirect
15. C₂×C₅₃×#539	C₂	semidirect
16. C₂×C₅₃×#539	C₂	semidirect
18. C₂×C₅₃×#533	C₂	semidirect
19. C₂×C₅₃×#529	C₂	semidirect
20. C₂²×#126×C₅₃	C₂	semidirect
21. C₅₃×#563	C₂²	semidirect
22. C₅₃×#563	C₂²	semidirect
23. C₅₃×#556	C₂²	semidirect
24. C₅₃×#554	C₂²	semidirect
25. C₅₃×#552	C₂²	semidirect
26. C₅₃×#552	C₂²	semidirect
27. C₅₃×#551	C₂²	semidirect
28. C₅₃×#551	C₂²	semidirect
29. C₅₃×#544	C₂²	semidirect
30. C₅₃×#543	C₂²	semidirect
31. C₅₃×#542	C₂²	semidirect
32. C₅₃×#541	C₂²	semidirect
33. C₅₃×#541	C₂²	semidirect
34. C₅₃×#539	C₂²	semidirect
35. C₅₃×#539	C₂²	semidirect
37. C₅₃×#533	C₂²	semidirect
38. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
39. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
40. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
41. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
42. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
43. C₅₃×#529	C₂²	semidirect
53. C₂×#126×C₅₃	C₂²	semidirect
54. C₂×#126×C₅₃	C₂²	semidirect
55. C₂×#126×C₅₃	C₂²	semidirect
56. C₂×#126×C₅₃	C₂²	semidirect
57. C₂×#126×C₅₃	C₂²	semidirect
58. C₂×#125×C₅₃	C₂²	semidirect
59. C₂×#125×C₅₃	C₂²	semidirect
60. C₂×#125×C₅₃	C₂²	semidirect
61. C₂×#125×C₅₃	C₂²	semidirect
62. C₂×#125×C₅₃	C₂²	semidirect
63. C₂×#125×C₅₃	C₂²	semidirect
64. C₂×#125×C₅₃	C₂²	semidirect
65. C₂×#125×C₅₃	C₂²	semidirect
66. C₂×#125×C₅₃	C₂²	semidirect
67. C₂×#125×C₅₃	C₂²	semidirect
71. C₂×#124×C₅₃	C₂²	semidirect
79. C₂×#123×C₅₃	C₂²	semidirect
92. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
93. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
94. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
95. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
96. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
100. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
101. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
102. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
103. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
104. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
105. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
111. C₂×C₄×D₄×C₅₃	C₂²	semidirect
116. C₂×#117×C₅₃	C₂²	semidirect
117. C₂×#117×C₅₃	C₂²	semidirect
121. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
149. C₄⋊Q₈×C₅₃	C₂³	semidirect
150. C₄⋊Q₈×C₅₃	C₂³	semidirect
151. C₄⋊Q₈×C₅₃	C₂³	semidirect
152. C₄⋊Q₈×C₅₃	C₂³	semidirect
153. C₄⋊Q₈×C₅₃	C₂³	semidirect
163. #126×C₅₃	C₂³	semidirect
164. #126×C₅₃	C₂³	semidirect
165. #126×C₅₃	C₂³	semidirect
166. #126×C₅₃	C₂³	semidirect
167. #125×C₅₃	C₂³	semidirect
168. #125×C₅₃	C₂³	semidirect
169. #125×C₅₃	C₂³	semidirect
170. #125×C₅₃	C₂³	semidirect
171. #125×C₅₃	C₂³	semidirect
172. #125×C₅₃	C₂³	semidirect
173. #125×C₅₃	C₂³	semidirect
174. #125×C₅₃	C₂³	semidirect
175. #125×C₅₃	C₂³	semidirect
176. #125×C₅₃	C₂³	semidirect
180. #124×C₅₃	C₂³	semidirect
188. #123×C₅₃	C₂³	semidirect
201. C₂²⋊Q₈×C₅₃	C₂³	semidirect
202. C₂²⋊Q₈×C₅₃	C₂³	semidirect
203. C₂²⋊Q₈×C₅₃	C₂³	semidirect
204. C₂²⋊Q₈×C₅₃	C₂³	semidirect
205. C₂²⋊Q₈×C₅₃	C₂³	semidirect
209. C₄×Q₈×C₅₃	C₂³	semidirect
210. C₄×Q₈×C₅₃	C₂³	semidirect
211. C₄×Q₈×C₅₃	C₂³	semidirect
212. C₄×Q₈×C₅₃	C₂³	semidirect
213. C₄×Q₈×C₅₃	C₂³	semidirect
214. C₄×Q₈×C₅₃	C₂³	semidirect
220. C₄×D₄×C₅₃	C₂³	semidirect
225. #117×C₅₃	C₂³	semidirect
226. #117×C₅₃	C₂³	semidirect
263. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
501. C₂×#3564	C₅₃	direct (N × H)
535. #3564	C₂×C₅₃	direct (N × H)
536. C₂×#563	C₂×C₅₃	semidirect
537. C₂×#563	C₂×C₅₃	semidirect
538. C₂×#556	C₂×C₅₃	semidirect
539. C₂×#554	C₂×C₅₃	semidirect
540. C₂×#552	C₂×C₅₃	semidirect
541. C₂×#552	C₂×C₅₃	semidirect
542. C₂×#551	C₂×C₅₃	semidirect
543. C₂×#551	C₂×C₅₃	semidirect
544. C₂×#544	C₂×C₅₃	semidirect
545. C₂×#543	C₂×C₅₃	semidirect
546. C₂×#542	C₂×C₅₃	semidirect
547. C₂×#541	C₂×C₅₃	semidirect
548. C₂×#541	C₂×C₅₃	semidirect
549. C₂×#539	C₂×C₅₃	semidirect
550. C₂×#539	C₂×C₅₃	semidirect
552. C₂×#533	C₂×C₅₃	semidirect
553. C₂×#529	C₂×C₅₃	semidirect
554. C₂²×#126	C₂×C₅₃	semidirect
558. C₂×C₅₃	#3564	direct (N × H)
562. #563	C₂²×C₅₃	semidirect
563. #563	C₂²×C₅₃	semidirect
564. #556	C₂²×C₅₃	semidirect
565. #554	C₂²×C₅₃	semidirect
566. #552	C₂²×C₅₃	semidirect
567. #552	C₂²×C₅₃	semidirect
568. #551	C₂²×C₅₃	semidirect
569. #551	C₂²×C₅₃	semidirect
570. #544	C₂²×C₅₃	semidirect
571. #543	C₂²×C₅₃	semidirect
572. #542	C₂²×C₅₃	semidirect
573. #541	C₂²×C₅₃	semidirect
574. #541	C₂²×C₅₃	semidirect
575. #539	C₂²×C₅₃	semidirect
576. #539	C₂²×C₅₃	semidirect
578. #533	C₂²×C₅₃	semidirect
579. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
580. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
581. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
582. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
583. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
584. #529	C₂²×C₅₃	semidirect
594. C₂×#126	C₂²×C₅₃	semidirect
595. C₂×#126	C₂²×C₅₃	semidirect
596. C₂×#126	C₂²×C₅₃	semidirect
597. C₂×#126	C₂²×C₅₃	semidirect
598. C₂×#126	C₂²×C₅₃	semidirect
599. C₂×#125	C₂²×C₅₃	semidirect
600. C₂×#125	C₂²×C₅₃	semidirect
601. C₂×#125	C₂²×C₅₃	semidirect
602. C₂×#125	C₂²×C₅₃	semidirect
603. C₂×#125	C₂²×C₅₃	semidirect
604. C₂×#125	C₂²×C₅₃	semidirect
605. C₂×#125	C₂²×C₅₃	semidirect
606. C₂×#125	C₂²×C₅₃	semidirect
607. C₂×#125	C₂²×C₅₃	semidirect
608. C₂×#125	C₂²×C₅₃	semidirect
612. C₂×#124	C₂²×C₅₃	semidirect
620. C₂×#123	C₂²×C₅₃	semidirect
633. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
634. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
635. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
636. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
637. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
641. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
642. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
643. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
644. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
645. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
646. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
652. C₂×C₄×D₄	C₂²×C₅₃	semidirect
657. C₂×#117	C₂²×C₅₃	semidirect
658. C₂×#117	C₂²×C₅₃	semidirect
662. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
668. C₅₃	C₂×#3564	direct (N × H)
691. C₄⋊Q₈	C₂³×C₅₃	semidirect
692. C₄⋊Q₈	C₂³×C₅₃	semidirect
693. C₄⋊Q₈	C₂³×C₅₃	semidirect
694. C₄⋊Q₈	C₂³×C₅₃	semidirect
695. C₄⋊Q₈	C₂³×C₅₃	semidirect
705. #126	C₂³×C₅₃	semidirect
706. #126	C₂³×C₅₃	semidirect
707. #126	C₂³×C₅₃	semidirect
708. #126	C₂³×C₅₃	semidirect
709. #125	C₂³×C₅₃	semidirect
710. #125	C₂³×C₅₃	semidirect
711. #125	C₂³×C₅₃	semidirect
712. #125	C₂³×C₅₃	semidirect
713. #125	C₂³×C₅₃	semidirect
714. #125	C₂³×C₅₃	semidirect
715. #125	C₂³×C₅₃	semidirect
716. #125	C₂³×C₅₃	semidirect
717. #125	C₂³×C₅₃	semidirect
718. #125	C₂³×C₅₃	semidirect
722. #124	C₂³×C₅₃	semidirect
730. #123	C₂³×C₅₃	semidirect
743. C₂²⋊Q₈	C₂³×C₅₃	semidirect
744. C₂²⋊Q₈	C₂³×C₅₃	semidirect
745. C₂²⋊Q₈	C₂³×C₅₃	semidirect
746. C₂²⋊Q₈	C₂³×C₅₃	semidirect
747. C₂²⋊Q₈	C₂³×C₅₃	semidirect
751. C₄×Q₈	C₂³×C₅₃	semidirect
752. C₄×Q₈	C₂³×C₅₃	semidirect
753. C₄×Q₈	C₂³×C₅₃	semidirect
754. C₄×Q₈	C₂³×C₅₃	semidirect
755. C₄×Q₈	C₂³×C₅₃	semidirect
756. C₄×Q₈	C₂³×C₅₃	semidirect
762. C₄×D₄	C₂³×C₅₃	semidirect
767. #117	C₂³×C₅₃	semidirect
768. #117	C₂³×C₅₃	semidirect
805. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
1079. C₂	C₅₃×#3564	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×#3564	2
C₂×C₅₃×#563	2
C₂×C₅₃×#556	2
C₂×C₅₃×#554	2
C₂×C₅₃×#552	2
C₂×C₅₃×#551	2
C₂×C₅₃×#544	2
C₂×C₅₃×#543	2
C₂×C₅₃×#542	2
C₂×C₅₃×#541	2
C₂×C₅₃×#539	2
C₂×C₅₃×#538	2
C₂×C₅₃×#533	2
C₂×C₅₃×#529	2
C₂²×#126×C₅₃	2
C₂×#3564	53

Subgroups — C2×C53×#3564 #27270246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3564 #27270246