Subgroups — C₂×C₅₃×#3541 #27270232

Order 13568.

7258 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3541	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₅₃×#563	C₂	1	2	yes	maximal, complemented
3	C₂×C₅₃×#562	C₂	1	2	yes	maximal, complemented
4	C₂×C₅₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅₃×#554	C₂	1	2	yes	maximal, complemented
7	C₂×C₅₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₃×#553	C₂	1	2	yes	maximal, complemented
9	C₂×C₅₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×D₄×Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅₃×#542	C₂	1	2	yes	maximal, complemented
16	C₂×C₅₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅₃×#539	C₂	1	2	yes	maximal, complemented
18	C₂×C₅₃×#538	C₂	1	2	yes	maximal, complemented
19	C₂×C₅₃×#538	C₂	1	2	yes	maximal, complemented
20	C₂×C₅₃×#537	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₅₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₅₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₅₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₂²⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
26	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
27	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂³×Q₈×C₅₃	C₂²	1	1	yes	characteristic
29	C₂³×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
30	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
31	C₅₃×#563	C₂²	1	32	yes	complemented
32	C₅₃×#562	C₂²	1	32	yes	complemented
33	C₅₃×#556	C₂²	1	16	yes	complemented
34	C₅₃×#554	C₂²	1	16	yes	complemented
35	C₅₃×#554	C₂²	1	32	yes	complemented
36	C₅₃×#553	C₂²	1	16	yes	complemented
37	C₅₃×#553	C₂²	1	32	yes	complemented
38	C₅₃×#552	C₂²	1	16	yes	complemented
39	D₄×Q₈×C₅₃	C₂²	1	16	yes	complemented
40	C₅₃×#548	C₂²	1	16	yes	complemented
41	C₅₃×#548	C₂²	1	16	yes	complemented
42	C₅₃×#547	C₂²	1	16	yes	complemented
43	C₅₃×#542	C₂²	1	16	yes	complemented
44	C₅₃×#542	C₂²	1	32	yes	complemented
45	C₅₃×#541	C₂²	1	16	yes	complemented
46	C₅₃×#539	C₂²	1	32	yes	complemented
47	C₅₃×#538	C₂²	1	32	yes	complemented
48	C₅₃×#538	C₂²	1	32	yes	complemented
49	C₅₃×#537	C₂²	1	16	yes	complemented
50	C₅₃×#536	C₂²	1	16	yes	complemented
51	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
52	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
54	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×#126×C₅₃	C₂²	1	2	yes	—
56	C₂×#126×C₅₃	C₂²	1	2	yes	—
57	C₂×#126×C₅₃	C₂²	1	2	yes	—
58	C₂×#126×C₅₃	C₂²	1	2	yes	—
59	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
60	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
61	C₂×#126×C₅₃	C₂²	1	2	yes	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	1	yes	characteristic, complemented
65	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
66	C₂×#125×C₅₃	C₂²	1	2	yes	complemented
67	C₂×#124×C₅₃	C₂²	1	2	yes	—
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×#124×C₅₃	C₂²	1	2	yes	complemented
73	C₅₃×#525	C₂²	1	16	yes	complemented
74	C₅₃×#525	C₂²	1	16	yes	complemented
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	1	yes	characteristic
80	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
81	C₂×#123×C₅₃	C₂²	1	2	yes	—
82	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
83	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
84	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
85	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
86	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
87	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
92	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
93	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
94	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
95	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
96	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
97	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	16	yes	complemented
98	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
99	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
102	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
103	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
104	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
105	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
107	C₂×#121×C₅₃	C₂²	1	2	yes	—
108	C₂×#121×C₅₃	C₂²	1	2	yes	—
109	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
110	C₂×#121×C₅₃	C₂²	1	2	yes	—
111	C₂×#121×C₅₃	C₂²	1	2	yes	—
112	C₂×#121×C₅₃	C₂²	1	2	yes	—
113	C₂×#121×C₅₃	C₂²	1	2	yes	—
114	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
115	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
116	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
117	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
118	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
119	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
120	C₂×#120×C₅₃	C₂²	1	2	yes	—
121	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
122	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
125	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
126	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
127	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
128	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
129	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
130	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
131	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
132	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
133	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
134	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
135	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
136	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
137	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
138	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
139	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
140	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
141	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
142	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
143	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
144	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
145	C₂²×C₄⋊C₄×C₅₃	C₂²	1	2	yes	complemented
146	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
147	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
148	C₂×#41×C₅₃	—	4	4	no	—
149	C₂×#41×C₅₃	—	4	4	no	—
150	C₂×#41×C₅₃	—	4	4	no	—
151	C₂×#41×C₅₃	C₂³	1	8	yes	—
152	C₂×#41×C₅₃	C₂³	1	8	yes	—
153	C₂×#41×C₅₃	C₂³	1	8	yes	complemented
154	C₂²×Q₈×C₅₃	—	4	4	no	—
155	C₂²×Q₈×C₅₃	—	4	4	no	—
156	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
157	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
158	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
159	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
160	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
161	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
162	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
163	C₂²×Q₈×C₅₃	C₂³	1	8	yes	—
164	C₂²×Q₈×C₅₃	C₂³	1	8	yes	complemented
165	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
166	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
167	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
168	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
169	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
170	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
171	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
172	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
173	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
174	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
175	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
176	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
177	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
178	C₂³×C₄×C₅₃	—	4	4	no	—
179	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
180	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
181	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
182	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
183	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
184	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
185	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
186	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
187	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
188	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
189	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
190	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
191	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
192	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
193	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
194	C₂³×C₄×C₅₃	C₂³	1	8	yes	—
195	C₄⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
196	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
197	C₄⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
198	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
199	#126×C₅₃	C₂³	1	16	yes	—
200	#126×C₅₃	C₂³	1	16	yes	—
201	#126×C₅₃	C₂³	1	16	yes	—
202	#126×C₅₃	C₂³	1	16	yes	—
203	#126×C₅₃	C₂³	1	16	yes	complemented
204	#126×C₅₃	C₂³	1	16	yes	complemented
205	#126×C₅₃	C₂³	1	16	yes	complemented
206	#125×C₅₃	C₂³	1	16	yes	complemented
207	#125×C₅₃	C₂³	1	16	yes	complemented
208	#125×C₅₃	C₂³	1	8	yes	complemented
209	#125×C₅₃	C₂³	1	16	yes	complemented
210	#125×C₅₃	C₂³	1	16	yes	complemented
211	#124×C₅₃	C₂³	1	16	yes	—
212	#124×C₅₃	C₂³	1	16	yes	—
213	#124×C₅₃	C₂³	1	16	yes	—
214	#124×C₅₃	C₂³	1	16	yes	—
215	#124×C₅₃	C₂³	1	8	yes	complemented
216	#124×C₅₃	C₂³	1	16	yes	complemented
217	#123×C₅₃	C₂³	1	8	yes	—
218	#123×C₅₃	C₂³	1	8	yes	—
219	#123×C₅₃	C₂³	1	16	yes	—
220	#123×C₅₃	C₂³	1	16	yes	—
221	#123×C₅₃	C₂³	1	16	yes	—
222	#123×C₅₃	C₂³	1	16	yes	—
223	#123×C₅₃	C₂³	1	16	yes	—
224	#123×C₅₃	C₂³	1	16	yes	complemented
225	#123×C₅₃	C₂³	1	16	yes	complemented
226	#123×C₅₃	C₂³	1	16	yes	complemented
227	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
228	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
229	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
230	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
231	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
232	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
233	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
234	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
235	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
236	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
237	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
238	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	—
239	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
240	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
241	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
242	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
243	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
244	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
245	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
246	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
247	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
248	#121×C₅₃	C₂³	1	8	yes	—
249	#121×C₅₃	C₂³	1	8	yes	—
250	#121×C₅₃	C₂³	1	8	yes	—
251	#121×C₅₃	C₂³	1	8	yes	—
252	#121×C₅₃	C₂³	1	16	yes	—
253	#121×C₅₃	C₂³	1	16	yes	—
254	#121×C₅₃	C₂³	1	16	yes	—
255	#121×C₅₃	C₂³	1	16	yes	—
256	#121×C₅₃	C₂³	1	16	yes	—
257	#121×C₅₃	C₂³	1	16	yes	—
258	#121×C₅₃	C₂³	1	8	yes	complemented
259	#121×C₅₃	C₂³	1	16	yes	complemented
260	#120×C₅₃	C₂³	1	8	yes	—
261	#120×C₅₃	C₂³	1	16	yes	—
262	#120×C₅₃	C₂³	1	8	yes	—
263	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
264	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
265	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
266	C₄×Q₈×C₅₃	C₂³	1	16	yes	complemented
267	C₄×D₄×C₅₃	C₂³	1	16	yes	—
268	C₄×D₄×C₅₃	C₂³	1	8	yes	—
269	C₄×D₄×C₅₃	C₂³	1	8	yes	—
270	C₄×D₄×C₅₃	C₂³	1	8	yes	—
271	C₄×D₄×C₅₃	C₂³	1	8	yes	—
272	C₄×D₄×C₅₃	C₂³	1	16	yes	—
273	C₄×D₄×C₅₃	C₂³	1	16	yes	—
274	C₄×D₄×C₅₃	C₂³	1	16	yes	—
275	C₄×D₄×C₅₃	C₂³	1	16	yes	—
276	C₄×D₄×C₅₃	C₂³	1	16	yes	—
277	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
278	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
279	#117×C₅₃	C₂³	1	8	yes	—
280	#117×C₅₃	C₂³	1	8	yes	—
281	#117×C₅₃	C₂³	1	8	yes	complemented
282	#117×C₅₃	C₂³	1	16	yes	complemented
283	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
285	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
286	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
288	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
289	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
290	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	—
291	C₂×C₄⋊C₄×C₅₃	C₂³	1	16	yes	—
292	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
295	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
296	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
297	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
299	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
300	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
301	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
302	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
303	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
304	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
305	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
306	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
307	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
308	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
309	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
310	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
311	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
312	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
313	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
314	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
315	C₂×C₄⋊C₄×C₅₃	C₂³	1	16	yes	complemented
316	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
317	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
318	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
319	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
320	C₂×C₂²⋊C₄×C₅₃	C₂³	1	16	yes	—
321	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
322	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
323	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
324	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
325	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
326	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
327	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
328	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
329	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
330	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
331	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
332	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
333	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
334	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
335	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
336	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
337	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
340	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
341	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
342	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
343	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
344	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
345	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
346	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
347	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
348	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
349	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
350	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
351	C₂⁴×C₅₃	—	2	4	no	—
352	C₂⁴×C₅₃	—	4	2	no	—
353	C₂⁴×C₅₃	—	4	2	no	—
354	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
355	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
357	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
359	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
361	#41×C₅₃	—	4	16	no	—
362	#41×C₅₃	—	4	16	no	—
363	#41×C₅₃	—	4	16	no	—
364	C₂×Q₈×C₅₃	—	2	4	no	—
365	C₂×Q₈×C₅₃	—	2	4	no	—
366	C₂×Q₈×C₅₃	—	2	4	no	—
367	C₂×Q₈×C₅₃	—	4	4	no	—
368	C₂×Q₈×C₅₃	—	4	4	no	—
369	C₂×Q₈×C₅₃	—	4	4	no	—
370	C₂×Q₈×C₅₃	—	4	2	no	—
371	C₂×Q₈×C₅₃	—	4	16	no	—
372	C₂×Q₈×C₅₃	—	4	16	no	—
373	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
374	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
375	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
376	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
377	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
378	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
379	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
380	C₂×D₄×C₅₃	—	2	8	no	—
381	C₂×D₄×C₅₃	—	2	4	no	—
382	C₂×D₄×C₅₃	—	2	4	no	—
383	C₂×D₄×C₅₃	—	2	4	no	—
384	C₂×D₄×C₅₃	—	4	2	no	—
385	C₂×D₄×C₅₃	—	4	4	no	—
386	C₂×D₄×C₅₃	—	4	4	no	—
387	C₂×D₄×C₅₃	—	4	2	no	—
388	C₂×D₄×C₅₃	—	4	2	no	—
389	C₂×D₄×C₅₃	—	4	2	no	—
390	C₂×D₄×C₅₃	—	4	2	no	—
391	C₂×D₄×C₅₃	—	4	4	no	—
392	C₂×D₄×C₅₃	—	4	4	no	—
393	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
394	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
395	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
396	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
397	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
398	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
399	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
400	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
401	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
402	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
403	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
404	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
405	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
406	C₂²×C₄×C₅₃	—	2	4	no	—
407	C₂²×C₄×C₅₃	—	2	4	no	—
408	C₂²×C₄×C₅₃	—	2	4	no	—
409	C₂²×C₄×C₅₃	—	2	4	no	—
410	C₂²×C₄×C₅₃	—	2	4	no	—
411	C₂²×C₄×C₅₃	—	4	16	no	—
412	C₂²×C₄×C₅₃	—	4	2	no	—
413	C₂²×C₄×C₅₃	—	4	2	no	—
414	C₂²×C₄×C₅₃	—	4	2	no	—
415	C₂²×C₄×C₅₃	—	4	4	no	—
416	C₂²×C₄×C₅₃	—	4	4	no	—
417	C₂²×C₄×C₅₃	—	4	4	no	—
418	C₂²×C₄×C₅₃	—	4	4	no	—
419	C₂²×C₄×C₅₃	—	4	4	no	—
420	C₂²×C₄×C₅₃	—	4	4	no	—
421	C₂²×C₄×C₅₃	—	4	4	no	—
422	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
423	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
424	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
425	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
426	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
427	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
428	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
429	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
430	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
431	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
432	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
433	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
434	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
435	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
436	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
437	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
438	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
439	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
440	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
441	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
442	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
443	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
444	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
445	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
446	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
447	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
448	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
449	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
450	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
451	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
452	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
453	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
455	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
456	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
457	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
458	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
459	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
460	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
461	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
462	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
463	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
464	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
465	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
466	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
467	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
468	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
469	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
470	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
471	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
472	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
473	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
474	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
475	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
476	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
477	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
478	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
479	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
480	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
481	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
482	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
483	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
484	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
485	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
486	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
487	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
488	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
489	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
490	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
491	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
492	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
493	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
494	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
495	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
496	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
497	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
498	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
499	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
500	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
501	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
502	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
503	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
504	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
505	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
506	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
507	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
508	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
509	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
510	C₄²×C₅₃	C₂⁴	1	8	yes	—
511	C₄²×C₅₃	C₂⁴	1	4	yes	—
512	C₄²×C₅₃	C₂⁴	1	4	yes	—
513	C₄²×C₅₃	C₂⁴	1	8	yes	—
514	C₄²×C₅₃	C₂⁴	1	8	yes	—
515	C₄²×C₅₃	C₂⁴	1	8	yes	—
516	C₄²×C₅₃	C₂⁴	1	8	yes	—
517	C₂³×C₅₃	—	2	2	no	—
518	C₂³×C₅₃	—	2	2	no	—
519	C₂³×C₅₃	—	2	2	no	—
520	C₂³×C₅₃	—	2	2	no	—
521	C₂³×C₅₃	—	2	2	no	—
522	C₂³×C₅₃	—	2	2	no	—
523	C₂³×C₅₃	—	2	4	no	—
524	C₂³×C₅₃	—	2	2	no	—
525	C₂³×C₅₃	—	2	2	no	—
526	C₂³×C₅₃	—	2	4	no	—
527	C₂³×C₅₃	—	2	8	no	—
528	C₂³×C₅₃	—	2	2	no	—
529	C₂³×C₅₃	—	2	2	no	—
530	C₂³×C₅₃	—	2	2	no	—
531	C₂³×C₅₃	—	2	4	no	—
532	C₂³×C₅₃	—	2	2	no	—
533	C₂³×C₅₃	—	2	2	no	—
534	C₂³×C₅₃	—	2	2	no	—
535	C₂³×C₅₃	—	4	4	no	—
536	C₂³×C₅₃	—	4	4	no	—
537	C₂³×C₅₃	—	4	16	no	—
538	C₂³×C₅₃	2₋¹⁺⁴	1	4	yes	—
539	C₂³×C₅₃	C₂⁵	1	2	yes	—
540	C₂³×C₅₃	C₂⁵	1	2	yes	—
541	C₂³×C₅₃	C₂⁵	1	4	yes	—
542	C₂³×C₅₃	C₂⁵	1	2	yes	—
543	C₂³×C₅₃	C₂⁵	1	2	yes	—
544	C₂³×C₅₃	C₂⁵	1	2	yes	—
545	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
546	Q₈×C₅₃	—	2	8	no	—
547	Q₈×C₅₃	—	2	8	no	—
548	Q₈×C₅₃	—	2	8	no	—
549	Q₈×C₅₃	—	4	8	no	—
550	Q₈×C₅₃	—	4	8	no	—
551	Q₈×C₅₃	—	4	8	no	—
552	Q₈×C₅₃	—	4	4	no	—
553	D₄×C₅₃	—	2	8	no	—
554	D₄×C₅₃	—	2	8	no	—
555	D₄×C₅₃	—	2	16	no	—
556	D₄×C₅₃	—	2	8	no	—
557	D₄×C₅₃	—	4	4	no	—
558	D₄×C₅₃	—	4	8	no	—
559	D₄×C₅₃	—	4	8	no	—
560	D₄×C₅₃	—	4	4	no	—
561	D₄×C₅₃	—	4	4	no	—
562	D₄×C₅₃	—	4	4	no	—
563	D₄×C₅₃	—	4	4	no	—
564	D₄×C₅₃	—	4	8	no	—
565	D₄×C₅₃	—	4	8	no	—
566	C₂×C₄×C₅₃	—	2	2	no	—
567	C₂×C₄×C₅₃	—	2	2	no	—
568	C₂×C₄×C₅₃	—	2	2	no	—
569	C₂×C₄×C₅₃	—	2	2	no	—
570	C₂×C₄×C₅₃	—	2	2	no	—
571	C₂×C₄×C₅₃	—	2	4	no	—
572	C₂×C₄×C₅₃	—	2	4	no	—
573	C₂×C₄×C₅₃	—	2	4	no	—
574	C₂×C₄×C₅₃	—	2	4	no	—
575	C₂×C₄×C₅₃	—	2	2	no	—
576	C₂×C₄×C₅₃	—	2	2	no	—
577	C₂×C₄×C₅₃	—	2	4	no	—
578	C₂×C₄×C₅₃	—	2	2	no	—
579	C₂×C₄×C₅₃	—	2	4	no	—
580	C₂×C₄×C₅₃	—	2	4	no	—
581	C₂×C₄×C₅₃	—	2	2	no	—
582	C₂×C₄×C₅₃	—	2	8	no	—
583	C₂×C₄×C₅₃	—	2	8	no	—
584	C₂×C₄×C₅₃	—	2	8	no	—
585	C₂×C₄×C₅₃	—	2	8	no	—
586	C₂×C₄×C₅₃	—	2	8	no	—
587	C₂×C₄×C₅₃	—	4	4	no	—
588	C₂×C₄×C₅₃	—	4	4	no	—
589	C₂×C₄×C₅₃	—	4	4	no	—
590	C₂×C₄×C₅₃	—	4	8	no	—
591	C₂×C₄×C₅₃	—	4	8	no	—
592	C₂×C₄×C₅₃	—	4	8	no	—
593	C₂×C₄×C₅₃	—	4	8	no	—
594	C₂×C₄×C₅₃	—	4	8	no	—
595	C₂×C₄×C₅₃	—	4	8	no	—
596	C₂×C₄×C₅₃	—	4	8	no	—
597	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
598	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
599	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
600	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
601	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
602	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
603	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
604	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
605	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
606	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
607	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
608	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
609	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
610	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
611	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
612	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
613	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
614	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
615	C₂×#3541	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
616	C₂²×C₅₃	—	2	2	no	—
617	C₂²×C₅₃	—	2	2	no	—
618	C₂²×C₅₃	—	2	8	no	—
619	C₂²×C₅₃	—	2	2	no	—
620	C₂²×C₅₃	—	2	2	no	—
621	C₂²×C₅₃	—	2	2	no	—
622	C₂²×C₅₃	—	2	2	no	—
623	C₂²×C₅₃	—	2	4	no	—
624	C₂²×C₅₃	—	2	2	no	—
625	C₂²×C₅₃	—	2	2	no	—
626	C₂²×C₅₃	—	2	4	no	—
627	C₂²×C₅₃	—	2	2	no	—
628	C₂²×C₅₃	—	2	2	no	—
629	C₂²×C₅₃	—	2	2	no	—
630	C₂²×C₅₃	—	2	4	no	—
631	C₂²×C₅₃	—	2	2	no	—
632	C₂²×C₅₃	—	2	2	no	—
633	C₂²×C₅₃	—	2	2	no	—
634	C₂²×C₅₃	—	4	16	no	—
635	C₂²×C₅₃	—	4	4	no	—
636	C₂²×C₅₃	—	4	4	no	—
637	C₂²×C₅₃	—	4	8	no	—
638	C₂²×C₅₃	—	4	4	no	—
639	C₂²×C₅₃	—	4	4	no	—
640	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
641	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	4	yes	—
642	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	2	yes	—
643	C₂²×C₅₃	#585	1	2	yes	—
644	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
645	C₄×C₅₃	—	2	2	no	—
646	C₄×C₅₃	—	2	2	no	—
647	C₄×C₅₃	—	2	2	no	—
648	C₄×C₅₃	—	2	2	no	—
649	C₄×C₅₃	—	2	2	no	—
650	C₄×C₅₃	—	2	4	no	—
651	C₄×C₅₃	—	2	4	no	—
652	C₄×C₅₃	—	2	4	no	—
653	C₄×C₅₃	—	2	4	no	—
654	C₄×C₅₃	—	2	2	no	—
655	C₄×C₅₃	—	2	2	no	—
656	C₄×C₅₃	—	2	4	no	—
657	C₄×C₅₃	—	2	2	no	—
658	C₄×C₅₃	—	2	4	no	—
659	C₄×C₅₃	—	2	4	no	—
660	C₄×C₅₃	—	2	2	no	—
661	C₄×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
662	#3541	C₂×C₅₃	1	32	yes	direct product factor
663	C₂×#563	C₂×C₅₃	1	2	yes	complemented
664	C₂×#562	C₂×C₅₃	1	2	yes	complemented
665	C₂×#556	C₂×C₅₃	1	1	yes	characteristic, complemented
666	C₂×#554	C₂×C₅₃	1	1	yes	characteristic, complemented
667	C₂×#554	C₂×C₅₃	1	2	yes	complemented
668	C₂×#553	C₂×C₅₃	1	1	yes	characteristic, complemented
669	C₂×#553	C₂×C₅₃	1	2	yes	complemented
670	C₂×#552	C₂×C₅₃	1	1	yes	characteristic, complemented
671	C₂×D₄×Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
672	C₂×#548	C₂×C₅₃	1	1	yes	characteristic, complemented
673	C₂×#548	C₂×C₅₃	1	1	yes	characteristic, complemented
674	C₂×#547	C₂×C₅₃	1	1	yes	characteristic, complemented
675	C₂×#542	C₂×C₅₃	1	1	yes	characteristic, complemented
676	C₂×#542	C₂×C₅₃	1	2	yes	complemented
677	C₂×#541	C₂×C₅₃	1	1	yes	characteristic, complemented
678	C₂×#539	C₂×C₅₃	1	2	yes	complemented
679	C₂×#538	C₂×C₅₃	1	2	yes	complemented
680	C₂×#538	C₂×C₅₃	1	2	yes	complemented
681	C₂×#537	C₂×C₅₃	1	1	yes	characteristic, complemented
682	C₂×#536	C₂×C₅₃	1	1	yes	characteristic, complemented
683	C₂×#525	C₂×C₅₃	1	1	yes	characteristic, complemented
684	C₂×#525	C₂×C₅₃	1	1	yes	characteristic, complemented
685	C₂²×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
686	C₂×C₅₃	—	2	4	no	—
687	C₂×C₅₃	—	4	2	no	—
688	C₂×C₅₃	—	4	2	no	—
689	C₂×C₅₃	—	4	4	no	—
690	C₂×C₅₃	—	4	2	no	—
691	C₂×C₅₃	—	4	2	no	—
692	C₂×C₅₃	#3541	1	4	yes	direct product factor
693	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
694	C₂×C₅₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
695	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
696	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
697	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
698	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
699	C₂³×Q₈	C₂²×C₅₃	1	1	yes	characteristic
700	C₂³×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
701	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
702	#563	C₂²×C₅₃	1	32	yes	complemented
703	#562	C₂²×C₅₃	1	32	yes	complemented
704	#556	C₂²×C₅₃	1	16	yes	complemented
705	#554	C₂²×C₅₃	1	16	yes	complemented
706	#554	C₂²×C₅₃	1	32	yes	complemented
707	#553	C₂²×C₅₃	1	16	yes	complemented
708	#553	C₂²×C₅₃	1	32	yes	complemented
709	#552	C₂²×C₅₃	1	16	yes	complemented
710	D₄×Q₈	C₂²×C₅₃	1	16	yes	complemented
711	#548	C₂²×C₅₃	1	16	yes	complemented
712	#548	C₂²×C₅₃	1	16	yes	complemented
713	#547	C₂²×C₅₃	1	16	yes	complemented
714	#542	C₂²×C₅₃	1	16	yes	complemented
715	#542	C₂²×C₅₃	1	32	yes	complemented
716	#541	C₂²×C₅₃	1	16	yes	complemented
717	#539	C₂²×C₅₃	1	32	yes	complemented
718	#538	C₂²×C₅₃	1	32	yes	complemented
719	#538	C₂²×C₅₃	1	32	yes	complemented
720	#537	C₂²×C₅₃	1	16	yes	complemented
721	#536	C₂²×C₅₃	1	16	yes	complemented
722	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
723	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
724	C₂×C₄⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
725	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
726	C₂×#126	C₂²×C₅₃	1	2	yes	—
727	C₂×#126	C₂²×C₅₃	1	2	yes	—
728	C₂×#126	C₂²×C₅₃	1	2	yes	—
729	C₂×#126	C₂²×C₅₃	1	2	yes	—
730	C₂×#126	C₂²×C₅₃	1	2	yes	complemented
731	C₂×#126	C₂²×C₅₃	1	2	yes	complemented
732	C₂×#126	C₂²×C₅₃	1	2	yes	complemented
733	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
734	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
735	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
736	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
737	C₂×#125	C₂²×C₅₃	1	2	yes	complemented
738	C₂×#124	C₂²×C₅₃	1	2	yes	—
739	C₂×#124	C₂²×C₅₃	1	2	yes	—
740	C₂×#124	C₂²×C₅₃	1	2	yes	—
741	C₂×#124	C₂²×C₅₃	1	2	yes	—
742	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
743	C₂×#124	C₂²×C₅₃	1	2	yes	complemented
744	#525	C₂²×C₅₃	1	16	yes	complemented
745	#525	C₂²×C₅₃	1	16	yes	complemented
746	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
747	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
748	C₂×#123	C₂²×C₅₃	1	2	yes	—
749	C₂×#123	C₂²×C₅₃	1	2	yes	—
750	C₂×#123	C₂²×C₅₃	1	2	yes	—
751	C₂×#123	C₂²×C₅₃	1	2	yes	—
752	C₂×#123	C₂²×C₅₃	1	2	yes	—
753	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
754	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
755	C₂×#123	C₂²×C₅₃	1	2	yes	complemented
756	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
757	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
758	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
759	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
760	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
761	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
762	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
763	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
764	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
765	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
766	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
767	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	—
768	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	16	yes	complemented
769	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
770	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
771	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
772	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
773	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
774	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
775	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
776	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
777	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	2	yes	complemented
778	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
779	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
780	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
781	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
782	C₂×#121	C₂²×C₅₃	1	2	yes	—
783	C₂×#121	C₂²×C₅₃	1	2	yes	—
784	C₂×#121	C₂²×C₅₃	1	2	yes	—
785	C₂×#121	C₂²×C₅₃	1	2	yes	—
786	C₂×#121	C₂²×C₅₃	1	2	yes	—
787	C₂×#121	C₂²×C₅₃	1	2	yes	—
788	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
789	C₂×#121	C₂²×C₅₃	1	2	yes	complemented
790	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
791	C₂×#120	C₂²×C₅₃	1	2	yes	—
792	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
793	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
794	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
795	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
796	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
797	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
798	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
799	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
800	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
801	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
802	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
803	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
804	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
805	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
806	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
807	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	complemented
808	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
809	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
810	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
811	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
812	C₂×#117	C₂²×C₅₃	1	2	yes	complemented
813	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
814	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
815	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
816	C₂²×C₄⋊C₄	C₂²×C₅₃	1	2	yes	complemented
817	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
818	C₅₃	C₂×#3541	1	1	yes	characteristic, direct product factor, Sylow
819	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
820	C₂×#41	—	4	4	no	—
821	C₂×#41	—	4	4	no	—
822	C₂×#41	—	4	4	no	—
823	C₂×#41	C₂³×C₅₃	1	8	yes	—
824	C₂×#41	C₂³×C₅₃	1	8	yes	—
825	C₂×#41	C₂³×C₅₃	1	8	yes	complemented
826	C₂²×Q₈	—	4	4	no	—
827	C₂²×Q₈	—	4	4	no	—
828	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
829	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
830	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
831	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
832	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
833	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
834	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
835	C₂²×Q₈	C₂³×C₅₃	1	8	yes	—
836	C₂²×Q₈	C₂³×C₅₃	1	8	yes	complemented
837	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
838	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
839	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
840	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
841	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
842	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
843	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
844	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
845	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
846	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
847	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
848	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
849	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
850	C₂³×C₄	—	4	4	no	—
851	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
852	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
853	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
854	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
855	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
856	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
857	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
858	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
859	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
860	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
861	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
862	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
863	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
864	C₂³×C₄	C₂³×C₅₃	1	2	yes	—
865	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
866	C₂³×C₄	C₂³×C₅₃	1	8	yes	—
867	C₄⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
868	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
869	C₄⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
870	C₄⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
871	#126	C₂³×C₅₃	1	16	yes	—
872	#126	C₂³×C₅₃	1	16	yes	—
873	#126	C₂³×C₅₃	1	16	yes	—
874	#126	C₂³×C₅₃	1	16	yes	—
875	#126	C₂³×C₅₃	1	16	yes	complemented
876	#126	C₂³×C₅₃	1	16	yes	complemented
877	#126	C₂³×C₅₃	1	16	yes	complemented
878	#125	C₂³×C₅₃	1	16	yes	complemented
879	#125	C₂³×C₅₃	1	16	yes	complemented
880	#125	C₂³×C₅₃	1	8	yes	complemented
881	#125	C₂³×C₅₃	1	16	yes	complemented
882	#125	C₂³×C₅₃	1	16	yes	complemented
883	#124	C₂³×C₅₃	1	16	yes	—
884	#124	C₂³×C₅₃	1	16	yes	—
885	#124	C₂³×C₅₃	1	16	yes	—
886	#124	C₂³×C₅₃	1	16	yes	—
887	#124	C₂³×C₅₃	1	8	yes	complemented
888	#124	C₂³×C₅₃	1	16	yes	complemented
889	#123	C₂³×C₅₃	1	8	yes	—
890	#123	C₂³×C₅₃	1	8	yes	—
891	#123	C₂³×C₅₃	1	16	yes	—
892	#123	C₂³×C₅₃	1	16	yes	—
893	#123	C₂³×C₅₃	1	16	yes	—
894	#123	C₂³×C₅₃	1	16	yes	—
895	#123	C₂³×C₅₃	1	16	yes	—
896	#123	C₂³×C₅₃	1	16	yes	complemented
897	#123	C₂³×C₅₃	1	16	yes	complemented
898	#123	C₂³×C₅₃	1	16	yes	complemented
899	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
900	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
901	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
902	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
903	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
904	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
905	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
906	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
907	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
908	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	—
909	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
910	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	—
911	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
912	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
913	C₂²⋊Q₈	C₂³×C₅₃	1	8	yes	complemented
914	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
915	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
916	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
917	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
918	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
919	C₂²⋊Q₈	C₂³×C₅₃	1	16	yes	complemented
920	#121	C₂³×C₅₃	1	8	yes	—
921	#121	C₂³×C₅₃	1	8	yes	—
922	#121	C₂³×C₅₃	1	8	yes	—
923	#121	C₂³×C₅₃	1	8	yes	—
924	#121	C₂³×C₅₃	1	16	yes	—
925	#121	C₂³×C₅₃	1	16	yes	—
926	#121	C₂³×C₅₃	1	16	yes	—
927	#121	C₂³×C₅₃	1	16	yes	—
928	#121	C₂³×C₅₃	1	16	yes	—
929	#121	C₂³×C₅₃	1	16	yes	—
930	#121	C₂³×C₅₃	1	8	yes	complemented
931	#121	C₂³×C₅₃	1	16	yes	complemented
932	#120	C₂³×C₅₃	1	8	yes	—
933	#120	C₂³×C₅₃	1	16	yes	—
934	#120	C₂³×C₅₃	1	8	yes	—
935	C₄×Q₈	C₂³×C₅₃	1	8	yes	complemented
936	C₄×Q₈	C₂³×C₅₃	1	8	yes	complemented
937	C₄×Q₈	C₂³×C₅₃	1	8	yes	complemented
938	C₄×Q₈	C₂³×C₅₃	1	16	yes	complemented
939	C₄×D₄	C₂³×C₅₃	1	16	yes	—
940	C₄×D₄	C₂³×C₅₃	1	8	yes	—
941	C₄×D₄	C₂³×C₅₃	1	8	yes	—
942	C₄×D₄	C₂³×C₅₃	1	8	yes	—
943	C₄×D₄	C₂³×C₅₃	1	8	yes	—
944	C₄×D₄	C₂³×C₅₃	1	16	yes	—
945	C₄×D₄	C₂³×C₅₃	1	16	yes	—
946	C₄×D₄	C₂³×C₅₃	1	16	yes	—
947	C₄×D₄	C₂³×C₅₃	1	16	yes	—
948	C₄×D₄	C₂³×C₅₃	1	16	yes	—
949	C₄×D₄	C₂³×C₅₃	1	16	yes	complemented
950	C₄×D₄	C₂³×C₅₃	1	8	yes	complemented
951	#117	C₂³×C₅₃	1	8	yes	—
952	#117	C₂³×C₅₃	1	8	yes	—
953	#117	C₂³×C₅₃	1	8	yes	complemented
954	#117	C₂³×C₅₃	1	16	yes	complemented
955	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
956	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
957	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
958	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
959	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
960	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
961	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
962	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	—
963	C₂×C₄⋊C₄	C₂³×C₅₃	1	16	yes	—
964	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
965	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
966	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
967	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
968	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
969	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
970	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
971	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
972	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
973	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
974	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
975	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
976	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
977	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
978	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
979	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
980	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
981	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
982	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
983	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
984	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
985	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
986	C₂×C₄⋊C₄	C₂³×C₅₃	1	8	yes	complemented
987	C₂×C₄⋊C₄	C₂³×C₅₃	1	16	yes	complemented
988	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
989	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
990	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
991	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
992	C₂×C₂²⋊C₄	C₂³×C₅₃	1	16	yes	—
993	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
994	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
995	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
996	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
997	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
998	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
999	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1000	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
1001	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1002	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1003	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1004	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
1005	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1006	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
1007	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
1008	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
1009	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1010	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1011	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
1012	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
1013	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
1014	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
1015	C₂×C₂²⋊C₄	C₂³×C₅₃	1	2	yes	—
1016	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
1017	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1018	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1019	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
1020	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
1021	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
1022	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
1023	C₂⁴	—	2	4	no	—
1024	C₂⁴	—	4	2	no	—
1025	C₂⁴	—	4	2	no	—
1026	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1027	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1028	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1029	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1030	C₂⁴	C₂⁴×C₅₃	1	2	yes	—
1031	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1032	C₂⁴	C₂⁴×C₅₃	1	4	yes	—
1033	#41	—	4	16	no	—
1034	#41	—	4	16	no	—
1035	#41	—	4	16	no	—
1036	C₂×Q₈	—	2	4	no	—
1037	C₂×Q₈	—	2	4	no	—
1038	C₂×Q₈	—	2	4	no	—
1039	C₂×Q₈	—	4	4	no	—
1040	C₂×Q₈	—	4	4	no	—
1041	C₂×Q₈	—	4	4	no	—
1042	C₂×Q₈	—	4	2	no	—
1043	C₂×Q₈	—	4	16	no	—
1044	C₂×Q₈	—	4	16	no	—
1045	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
1046	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
1047	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
1048	C₂×Q₈	C₂⁴×C₅₃	1	8	yes	—
1049	C₂×Q₈	C₂⁴×C₅₃	1	8	yes	—
1050	C₂×Q₈	C₂⁴×C₅₃	1	4	yes	—
1051	C₂×Q₈	C₂⁴×C₅₃	1	8	yes	—
1052	C₂×D₄	—	2	4	no	—
1053	C₂×D₄	—	2	4	no	—
1054	C₂×D₄	—	2	8	no	—
1055	C₂×D₄	—	2	4	no	—
1056	C₂×D₄	—	4	2	no	—
1057	C₂×D₄	—	4	4	no	—
1058	C₂×D₄	—	4	4	no	—
1059	C₂×D₄	—	4	2	no	—
1060	C₂×D₄	—	4	2	no	—
1061	C₂×D₄	—	4	2	no	—
1062	C₂×D₄	—	4	2	no	—
1063	C₂×D₄	—	4	4	no	—
1064	C₂×D₄	—	4	4	no	—
1065	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1066	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1067	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1068	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1069	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1070	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1071	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1072	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1073	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1074	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1075	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1076	C₂×D₄	C₂⁴×C₅₃	1	8	yes	—
1077	C₂×D₄	C₂⁴×C₅₃	1	4	yes	—
1078	C₂²×C₄	—	2	4	no	—
1079	C₂²×C₄	—	2	4	no	—
1080	C₂²×C₄	—	2	4	no	—
1081	C₂²×C₄	—	2	4	no	—
1082	C₂²×C₄	—	2	4	no	—
1083	C₂²×C₄	—	4	16	no	—
1084	C₂²×C₄	—	4	2	no	—
1085	C₂²×C₄	—	4	2	no	—
1086	C₂²×C₄	—	4	2	no	—
1087	C₂²×C₄	—	4	4	no	—
1088	C₂²×C₄	—	4	4	no	—
1089	C₂²×C₄	—	4	4	no	—
1090	C₂²×C₄	—	4	4	no	—
1091	C₂²×C₄	—	4	4	no	—
1092	C₂²×C₄	—	4	4	no	—
1093	C₂²×C₄	—	4	4	no	—
1094	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1095	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1096	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1097	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1098	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1099	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1100	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1101	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1102	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1103	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1104	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1105	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1106	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1107	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1108	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1109	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1110	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1111	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1112	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1113	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1114	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1115	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1116	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1117	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1118	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1119	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1120	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1121	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1122	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1123	C₂²×C₄	C₂⁴×C₅₃	1	8	yes	—
1124	C₂²×C₄	C₂⁴×C₅₃	1	4	yes	—
1125	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1126	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1127	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1128	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1129	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1130	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1131	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1132	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1133	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1134	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1135	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1136	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1137	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1138	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1139	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1140	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1141	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1142	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1143	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1144	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1145	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1146	C₄⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1147	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1148	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1149	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1150	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1151	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1152	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1153	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1154	C₄⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1155	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1156	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1157	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1158	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1159	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1160	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1161	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1162	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1163	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1164	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1165	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1166	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1167	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1168	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1169	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1170	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1171	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1172	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1173	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1174	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1175	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1176	C₂²⋊C₄	C₂⁴×C₅₃	1	4	yes	—
1177	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1178	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1179	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1180	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1181	C₂²⋊C₄	C₂⁴×C₅₃	1	8	yes	—
1182	C₄²	C₂⁴×C₅₃	1	8	yes	—
1183	C₄²	C₂⁴×C₅₃	1	4	yes	—
1184	C₄²	C₂⁴×C₅₃	1	4	yes	—
1185	C₄²	C₂⁴×C₅₃	1	8	yes	—
1186	C₄²	C₂⁴×C₅₃	1	8	yes	—
1187	C₄²	C₂⁴×C₅₃	1	8	yes	—
1188	C₄²	C₂⁴×C₅₃	1	8	yes	—
1189	C₂³	—	2	2	no	—
1190	C₂³	—	2	2	no	—
1191	C₂³	—	2	2	no	—
1192	C₂³	—	2	2	no	—
1193	C₂³	—	2	2	no	—
1194	C₂³	—	2	2	no	—
1195	C₂³	—	2	4	no	—
1196	C₂³	—	2	2	no	—
1197	C₂³	—	2	2	no	—
1198	C₂³	—	2	4	no	—
1199	C₂³	—	2	8	no	—
1200	C₂³	—	2	2	no	—
1201	C₂³	—	2	2	no	—
1202	C₂³	—	2	2	no	—
1203	C₂³	—	2	4	no	—
1204	C₂³	—	2	2	no	—
1205	C₂³	—	2	2	no	—
1206	C₂³	—	2	2	no	—
1207	C₂³	—	4	4	no	—
1208	C₂³	—	4	4	no	—
1209	C₂³	—	4	16	no	—
1210	C₂³	2₋¹⁺⁴×C₅₃	1	4	yes	—
1211	C₂³	C₂⁵×C₅₃	1	2	yes	—
1212	C₂³	C₂⁵×C₅₃	1	2	yes	—
1213	C₂³	C₂⁵×C₅₃	1	2	yes	—
1214	C₂³	C₂⁵×C₅₃	1	2	yes	—
1215	C₂³	C₂⁵×C₅₃	1	4	yes	—
1216	C₂³	C₂⁵×C₅₃	1	2	yes	—
1217	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1218	Q₈	—	2	8	no	—
1219	Q₈	—	2	8	no	—
1220	Q₈	—	2	8	no	—
1221	Q₈	—	4	8	no	—
1222	Q₈	—	4	8	no	—
1223	Q₈	—	4	8	no	—
1224	Q₈	—	4	4	no	—
1225	D₄	—	2	8	no	—
1226	D₄	—	2	8	no	—
1227	D₄	—	2	16	no	—
1228	D₄	—	2	8	no	—
1229	D₄	—	4	4	no	—
1230	D₄	—	4	8	no	—
1231	D₄	—	4	8	no	—
1232	D₄	—	4	4	no	—
1233	D₄	—	4	4	no	—
1234	D₄	—	4	4	no	—
1235	D₄	—	4	4	no	—
1236	D₄	—	4	8	no	—
1237	D₄	—	4	8	no	—
1238	C₂×C₄	—	2	2	no	—
1239	C₂×C₄	—	2	2	no	—
1240	C₂×C₄	—	2	2	no	—
1241	C₂×C₄	—	2	2	no	—
1242	C₂×C₄	—	2	2	no	—
1243	C₂×C₄	—	2	4	no	—
1244	C₂×C₄	—	2	4	no	—
1245	C₂×C₄	—	2	4	no	—
1246	C₂×C₄	—	2	4	no	—
1247	C₂×C₄	—	2	2	no	—
1248	C₂×C₄	—	2	2	no	—
1249	C₂×C₄	—	2	4	no	—
1250	C₂×C₄	—	2	2	no	—
1251	C₂×C₄	—	2	4	no	—
1252	C₂×C₄	—	2	4	no	—
1253	C₂×C₄	—	2	2	no	—
1254	C₂×C₄	—	2	8	no	—
1255	C₂×C₄	—	2	8	no	—
1256	C₂×C₄	—	2	8	no	—
1257	C₂×C₄	—	2	8	no	—
1258	C₂×C₄	—	2	8	no	—
1259	C₂×C₄	—	4	4	no	—
1260	C₂×C₄	—	4	4	no	—
1261	C₂×C₄	—	4	4	no	—
1262	C₂×C₄	—	4	8	no	—
1263	C₂×C₄	—	4	8	no	—
1264	C₂×C₄	—	4	8	no	—
1265	C₂×C₄	—	4	8	no	—
1266	C₂×C₄	—	4	8	no	—
1267	C₂×C₄	—	4	8	no	—
1268	C₂×C₄	—	4	8	no	—
1269	C₂×C₄	H(5,𝔽₂)×C₅₃	1	4	yes	—
1270	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1271	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1272	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1273	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1274	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1275	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1276	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1277	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1278	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1279	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1280	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1281	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1282	C₂×C₄	C₂⁵×C₅₃	1	4	yes	—
1283	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1284	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1285	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1286	C₂×C₄	C₂⁵×C₅₃	1	2	yes	—
1287	C₂²	—	2	8	no	—
1288	C₂²	—	2	2	no	—
1289	C₂²	—	2	2	no	—
1290	C₂²	—	2	2	no	—
1291	C₂²	—	2	2	no	—
1292	C₂²	—	2	2	no	—
1293	C₂²	—	2	2	no	—
1294	C₂²	—	2	4	no	—
1295	C₂²	—	2	2	no	—
1296	C₂²	—	2	2	no	—
1297	C₂²	—	2	4	no	—
1298	C₂²	—	2	2	no	—
1299	C₂²	—	2	2	no	—
1300	C₂²	—	2	2	no	—
1301	C₂²	—	2	4	no	—
1302	C₂²	—	2	2	no	—
1303	C₂²	—	2	2	no	—
1304	C₂²	—	2	2	no	—
1305	C₂²	—	4	16	no	—
1306	C₂²	—	4	4	no	—
1307	C₂²	—	4	4	no	—
1308	C₂²	—	4	4	no	—
1309	C₂²	—	4	4	no	—
1310	C₂²	—	4	8	no	—
1311	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	2	yes	—
1312	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	4	yes	—
1313	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	2	yes	—
1314	C₂²	C₅₃×#585	1	2	yes	—
1315	C₂²	C₂⁶×C₅₃	1	1	yes	characteristic
1316	C₄	—	2	2	no	—
1317	C₄	—	2	2	no	—
1318	C₄	—	2	2	no	—
1319	C₄	—	2	2	no	—
1320	C₄	—	2	2	no	—
1321	C₄	—	2	4	no	—
1322	C₄	—	2	4	no	—
1323	C₄	—	2	4	no	—
1324	C₄	—	2	4	no	—
1325	C₄	—	2	2	no	—
1326	C₄	—	2	2	no	—
1327	C₄	—	2	4	no	—
1328	C₄	—	2	2	no	—
1329	C₄	—	2	4	no	—
1330	C₄	—	2	4	no	—
1331	C₄	—	2	2	no	—
1332	C₄	C₂×H(5,𝔽₂)×C₅₃	1	4	yes	—
1333	C₂	—	2	4	no	—
1334	C₂	—	4	2	no	—
1335	C₂	—	4	2	no	—
1336	C₂	—	4	2	no	—
1337	C₂	—	4	2	no	—
1338	C₂	—	4	4	no	—
1339	C₂	C₅₃×#3541	1	4	yes	direct product factor
1340	C₂	C₂²×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1341	C₂	C₂²×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1342	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×#3541	C₂	direct (N × H)
2. C₂×C₅₃×#563	C₂	semidirect
3. C₂×C₅₃×#562	C₂	semidirect
4. C₂×C₅₃×#556	C₂	semidirect
5. C₂×C₅₃×#554	C₂	semidirect
6. C₂×C₅₃×#554	C₂	semidirect
7. C₂×C₅₃×#553	C₂	semidirect
8. C₂×C₅₃×#553	C₂	semidirect
9. C₂×C₅₃×#552	C₂	semidirect
10. C₂×D₄×Q₈×C₅₃	C₂	semidirect
11. C₂×C₅₃×#548	C₂	semidirect
12. C₂×C₅₃×#548	C₂	semidirect
13. C₂×C₅₃×#547	C₂	semidirect
14. C₂×C₅₃×#542	C₂	semidirect
15. C₂×C₅₃×#542	C₂	semidirect
16. C₂×C₅₃×#541	C₂	semidirect
17. C₂×C₅₃×#539	C₂	semidirect
18. C₂×C₅₃×#538	C₂	semidirect
19. C₂×C₅₃×#538	C₂	semidirect
20. C₂×C₅₃×#537	C₂	semidirect
21. C₂×C₅₃×#536	C₂	semidirect
22. C₂×C₅₃×#525	C₂	semidirect
23. C₂×C₅₃×#525	C₂	semidirect
24. C₂²×C₂²⋊Q₈×C₅₃	C₂	semidirect
27. C₂²×#41×C₅₃	C₂²	semidirect
29. C₂³×Q₈×C₅₃	C₂²	semidirect
31. C₅₃×#563	C₂²	semidirect
32. C₅₃×#562	C₂²	semidirect
33. C₅₃×#556	C₂²	semidirect
34. C₅₃×#554	C₂²	semidirect
35. C₅₃×#554	C₂²	semidirect
36. C₅₃×#553	C₂²	semidirect
37. C₅₃×#553	C₂²	semidirect
38. C₅₃×#552	C₂²	semidirect
39. D₄×Q₈×C₅₃	C₂²	semidirect
40. C₅₃×#548	C₂²	semidirect
41. C₅₃×#548	C₂²	semidirect
42. C₅₃×#547	C₂²	semidirect
43. C₅₃×#542	C₂²	semidirect
44. C₅₃×#542	C₂²	semidirect
45. C₅₃×#541	C₂²	semidirect
46. C₅₃×#539	C₂²	semidirect
47. C₅₃×#538	C₂²	semidirect
48. C₅₃×#538	C₂²	semidirect
49. C₅₃×#537	C₂²	semidirect
50. C₅₃×#536	C₂²	semidirect
51. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
52. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
53. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
54. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
59. C₂×#126×C₅₃	C₂²	semidirect
60. C₂×#126×C₅₃	C₂²	semidirect
61. C₂×#126×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
71. C₂×#124×C₅₃	C₂²	semidirect
72. C₂×#124×C₅₃	C₂²	semidirect
73. C₅₃×#525	C₂²	semidirect
74. C₅₃×#525	C₂²	semidirect
82. C₂×#123×C₅₃	C₂²	semidirect
83. C₂×#123×C₅₃	C₂²	semidirect
84. C₂×#123×C₅₃	C₂²	semidirect
97. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
98. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
99. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
100. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
101. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
102. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
103. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
104. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
105. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
106. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
117. C₂×#121×C₅₃	C₂²	semidirect
118. C₂×#121×C₅₃	C₂²	semidirect
122. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
123. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
124. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
125. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
136. C₂×C₄×D₄×C₅₃	C₂²	semidirect
137. C₂×C₄×D₄×C₅₃	C₂²	semidirect
140. C₂×#117×C₅₃	C₂²	semidirect
141. C₂×#117×C₅₃	C₂²	semidirect
144. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
145. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
153. C₂×#41×C₅₃	C₂³	semidirect
164. C₂²×Q₈×C₅₃	C₂³	semidirect
195. C₄⋊Q₈×C₅₃	C₂³	semidirect
196. C₄⋊Q₈×C₅₃	C₂³	semidirect
197. C₄⋊Q₈×C₅₃	C₂³	semidirect
198. C₄⋊Q₈×C₅₃	C₂³	semidirect
203. #126×C₅₃	C₂³	semidirect
204. #126×C₅₃	C₂³	semidirect
205. #126×C₅₃	C₂³	semidirect
206. #125×C₅₃	C₂³	semidirect
207. #125×C₅₃	C₂³	semidirect
208. #125×C₅₃	C₂³	semidirect
209. #125×C₅₃	C₂³	semidirect
210. #125×C₅₃	C₂³	semidirect
215. #124×C₅₃	C₂³	semidirect
216. #124×C₅₃	C₂³	semidirect
224. #123×C₅₃	C₂³	semidirect
225. #123×C₅₃	C₂³	semidirect
226. #123×C₅₃	C₂³	semidirect
239. C₂²⋊Q₈×C₅₃	C₂³	semidirect
240. C₂²⋊Q₈×C₅₃	C₂³	semidirect
241. C₂²⋊Q₈×C₅₃	C₂³	semidirect
242. C₂²⋊Q₈×C₅₃	C₂³	semidirect
243. C₂²⋊Q₈×C₅₃	C₂³	semidirect
244. C₂²⋊Q₈×C₅₃	C₂³	semidirect
245. C₂²⋊Q₈×C₅₃	C₂³	semidirect
246. C₂²⋊Q₈×C₅₃	C₂³	semidirect
247. C₂²⋊Q₈×C₅₃	C₂³	semidirect
258. #121×C₅₃	C₂³	semidirect
259. #121×C₅₃	C₂³	semidirect
263. C₄×Q₈×C₅₃	C₂³	semidirect
264. C₄×Q₈×C₅₃	C₂³	semidirect
265. C₄×Q₈×C₅₃	C₂³	semidirect
266. C₄×Q₈×C₅₃	C₂³	semidirect
277. C₄×D₄×C₅₃	C₂³	semidirect
278. C₄×D₄×C₅₃	C₂³	semidirect
281. #117×C₅₃	C₂³	semidirect
282. #117×C₅₃	C₂³	semidirect
314. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
315. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
615. C₂×#3541	C₅₃	direct (N × H)
662. #3541	C₂×C₅₃	direct (N × H)
663. C₂×#563	C₂×C₅₃	semidirect
664. C₂×#562	C₂×C₅₃	semidirect
665. C₂×#556	C₂×C₅₃	semidirect
666. C₂×#554	C₂×C₅₃	semidirect
667. C₂×#554	C₂×C₅₃	semidirect
668. C₂×#553	C₂×C₅₃	semidirect
669. C₂×#553	C₂×C₅₃	semidirect
670. C₂×#552	C₂×C₅₃	semidirect
671. C₂×D₄×Q₈	C₂×C₅₃	semidirect
672. C₂×#548	C₂×C₅₃	semidirect
673. C₂×#548	C₂×C₅₃	semidirect
674. C₂×#547	C₂×C₅₃	semidirect
675. C₂×#542	C₂×C₅₃	semidirect
676. C₂×#542	C₂×C₅₃	semidirect
677. C₂×#541	C₂×C₅₃	semidirect
678. C₂×#539	C₂×C₅₃	semidirect
679. C₂×#538	C₂×C₅₃	semidirect
680. C₂×#538	C₂×C₅₃	semidirect
681. C₂×#537	C₂×C₅₃	semidirect
682. C₂×#536	C₂×C₅₃	semidirect
683. C₂×#525	C₂×C₅₃	semidirect
684. C₂×#525	C₂×C₅₃	semidirect
685. C₂²×C₂²⋊Q₈	C₂×C₅₃	semidirect
692. C₂×C₅₃	#3541	direct (N × H)
698. C₂²×#41	C₂²×C₅₃	semidirect
700. C₂³×Q₈	C₂²×C₅₃	semidirect
702. #563	C₂²×C₅₃	semidirect
703. #562	C₂²×C₅₃	semidirect
704. #556	C₂²×C₅₃	semidirect
705. #554	C₂²×C₅₃	semidirect
706. #554	C₂²×C₅₃	semidirect
707. #553	C₂²×C₅₃	semidirect
708. #553	C₂²×C₅₃	semidirect
709. #552	C₂²×C₅₃	semidirect
710. D₄×Q₈	C₂²×C₅₃	semidirect
711. #548	C₂²×C₅₃	semidirect
712. #548	C₂²×C₅₃	semidirect
713. #547	C₂²×C₅₃	semidirect
714. #542	C₂²×C₅₃	semidirect
715. #542	C₂²×C₅₃	semidirect
716. #541	C₂²×C₅₃	semidirect
717. #539	C₂²×C₅₃	semidirect
718. #538	C₂²×C₅₃	semidirect
719. #538	C₂²×C₅₃	semidirect
720. #537	C₂²×C₅₃	semidirect
721. #536	C₂²×C₅₃	semidirect
722. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
723. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
724. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
725. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
730. C₂×#126	C₂²×C₅₃	semidirect
731. C₂×#126	C₂²×C₅₃	semidirect
732. C₂×#126	C₂²×C₅₃	semidirect
733. C₂×#125	C₂²×C₅₃	semidirect
734. C₂×#125	C₂²×C₅₃	semidirect
735. C₂×#125	C₂²×C₅₃	semidirect
736. C₂×#125	C₂²×C₅₃	semidirect
737. C₂×#125	C₂²×C₅₃	semidirect
742. C₂×#124	C₂²×C₅₃	semidirect
743. C₂×#124	C₂²×C₅₃	semidirect
744. #525	C₂²×C₅₃	semidirect
745. #525	C₂²×C₅₃	semidirect
753. C₂×#123	C₂²×C₅₃	semidirect
754. C₂×#123	C₂²×C₅₃	semidirect
755. C₂×#123	C₂²×C₅₃	semidirect
768. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
769. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
770. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
771. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
772. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
773. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
774. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
775. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
776. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
777. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
788. C₂×#121	C₂²×C₅₃	semidirect
789. C₂×#121	C₂²×C₅₃	semidirect
793. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
794. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
795. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
796. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
807. C₂×C₄×D₄	C₂²×C₅₃	semidirect
808. C₂×C₄×D₄	C₂²×C₅₃	semidirect
811. C₂×#117	C₂²×C₅₃	semidirect
812. C₂×#117	C₂²×C₅₃	semidirect
815. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
816. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
818. C₅₃	C₂×#3541	direct (N × H)
825. C₂×#41	C₂³×C₅₃	semidirect
836. C₂²×Q₈	C₂³×C₅₃	semidirect
867. C₄⋊Q₈	C₂³×C₅₃	semidirect
868. C₄⋊Q₈	C₂³×C₅₃	semidirect
869. C₄⋊Q₈	C₂³×C₅₃	semidirect
870. C₄⋊Q₈	C₂³×C₅₃	semidirect
875. #126	C₂³×C₅₃	semidirect
876. #126	C₂³×C₅₃	semidirect
877. #126	C₂³×C₅₃	semidirect
878. #125	C₂³×C₅₃	semidirect
879. #125	C₂³×C₅₃	semidirect
880. #125	C₂³×C₅₃	semidirect
881. #125	C₂³×C₅₃	semidirect
882. #125	C₂³×C₅₃	semidirect
887. #124	C₂³×C₅₃	semidirect
888. #124	C₂³×C₅₃	semidirect
896. #123	C₂³×C₅₃	semidirect
897. #123	C₂³×C₅₃	semidirect
898. #123	C₂³×C₅₃	semidirect
911. C₂²⋊Q₈	C₂³×C₅₃	semidirect
912. C₂²⋊Q₈	C₂³×C₅₃	semidirect
913. C₂²⋊Q₈	C₂³×C₅₃	semidirect
914. C₂²⋊Q₈	C₂³×C₅₃	semidirect
915. C₂²⋊Q₈	C₂³×C₅₃	semidirect
916. C₂²⋊Q₈	C₂³×C₅₃	semidirect
917. C₂²⋊Q₈	C₂³×C₅₃	semidirect
918. C₂²⋊Q₈	C₂³×C₅₃	semidirect
919. C₂²⋊Q₈	C₂³×C₅₃	semidirect
930. #121	C₂³×C₅₃	semidirect
931. #121	C₂³×C₅₃	semidirect
935. C₄×Q₈	C₂³×C₅₃	semidirect
936. C₄×Q₈	C₂³×C₅₃	semidirect
937. C₄×Q₈	C₂³×C₅₃	semidirect
938. C₄×Q₈	C₂³×C₅₃	semidirect
949. C₄×D₄	C₂³×C₅₃	semidirect
950. C₄×D₄	C₂³×C₅₃	semidirect
953. #117	C₂³×C₅₃	semidirect
954. #117	C₂³×C₅₃	semidirect
986. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
987. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
1339. C₂	C₅₃×#3541	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×#3541	2
C₂×C₅₃×#563	2
C₂×C₅₃×#562	2
C₂×C₅₃×#556	2
C₂×C₅₃×#554	2
C₂×C₅₃×#553	2
C₂×C₅₃×#552	2
C₂×D₄×Q₈×C₅₃	2
C₂×C₅₃×#548	2
C₂×C₅₃×#547	2
C₂×C₅₃×#542	2
C₂×C₅₃×#541	2
C₂×C₅₃×#539	2
C₂×C₅₃×#538	2
C₂×C₅₃×#537	2
C₂×C₅₃×#536	2
C₂×C₅₃×#525	2
C₂²×C₂²⋊Q₈×C₅₃	2
C₂×#3541	53

Subgroups — C2×C53×#3541 #27270232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×#3541 #27270232