Subgroups — #28293200

Order 13568.

11618 conjugacy classes of subgroups.

The subgroup lattice has 1262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811459	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13133263	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288504	C₂	1	4	yes	maximal, complemented
4	#20288502	C₂	1	4	yes	maximal, complemented
5	#20288490	C₂	1	4	yes	maximal, complemented
6	#20288488	C₂	1	4	yes	maximal, complemented
7	#20288379	C₂	1	8	yes	maximal, complemented
8	#20288376	C₂	1	8	yes	maximal, complemented
9	#20288369	C₂	1	4	yes	maximal, complemented
10	#20288348	C₂	1	4	yes	maximal, complemented
11	#20288347	C₂	1	8	yes	maximal, complemented
12	#20288047	C₂	1	4	yes	maximal, complemented
13	#20288044	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16811192	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#16811187	C₂	1	1	yes	maximal, characteristic, complemented
16	#535×D₅₃	C₂	1	4	yes	maximal, complemented
17	#20287916	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
19	#16811459	—	2	16	no	—
20	C₂×#13133265	C₂²	1	2	yes	complemented
21	C₂×#13133264	C₂²	1	2	yes	complemented
22	C₂×#13133264	C₂²	1	2	yes	complemented
23	C₂×#13133263	—	2	16	no	—
24	C₂×#13133263	C₂²	1	4	yes	complemented
25	C₂×#13133263	C₂²	1	4	yes	complemented
26	C₂×#13133263	C₂²	1	4	yes	complemented
27	C₂×#13133263	C₂²	1	4	yes	complemented
28	C₂×#13133263	C₂²	1	2	yes	complemented
29	C₂×#13133263	C₂²	1	2	yes	complemented
30	C₂×#13133262	C₂²	1	4	yes	complemented
31	C₂×#13133262	C₂²	1	2	yes	complemented
32	C₂²×#11719949	C₂²	1	2	yes	complemented
33	C₂²×#11719945	C₂²	1	1	yes	characteristic
34	C₂²×#11719945	C₂²	1	2	yes	complemented
35	C₂²×#11719945	C₂²	1	1	yes	characteristic, complemented
36	C₂²×#11719945	C₂²	1	4	yes	complemented
37	C₂×#41×D₅₃	C₂²	1	4	yes	complemented
38	C₂×#41×D₅₃	C₂²	1	4	yes	complemented
39	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
40	C₂³×D₂₁₂	C₂²	1	2	yes	complemented
41	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
42	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
43	#16811294	C₂²	1	16	yes	complemented
44	#16811291	C₂²	1	16	yes	complemented
45	#16811283	C₂²	1	16	yes	complemented
46	#16811282	C₂²	1	16	yes	complemented
47	#16811269	C₂²	1	16	yes	complemented
48	#16811265	C₂²	1	32	yes	complemented
49	#16811264	C₂²	1	16	yes	complemented
50	#16811262	C₂²	1	32	yes	complemented
51	D₄×D₂₁₂	C₂²	1	16	yes	complemented
52	#16811257	C₂²	1	32	yes	complemented
53	#16811257	C₂²	1	16	yes	complemented
54	#16811255	C₂²	1	32	yes	complemented
55	#16811203	C₂²	1	16	yes	complemented
56	#16811201	C₂²	1	4	yes	complemented
57	#16811198	C₂²	1	8	yes	complemented
58	#16811197	C₂²	1	2	yes	complemented
59	#16811194	C₂²	1	2	yes	complemented
60	#16811192	C₂²	1	4	yes	complemented
61	#16811192	C₂²	1	4	yes	complemented
62	#16811192	C₂²	1	4	yes	complemented
63	#16811192	C₂²	1	4	yes	complemented
64	#16811191	C₂²	1	8	yes	complemented
65	#16811191	C₂²	1	8	yes	complemented
66	#16811190	C₂²	1	2	yes	complemented
67	#16811189	C₂²	1	16	yes	complemented
68	#16811188	C₂²	1	16	yes	complemented
69	#16811187	C₂²	1	4	yes	complemented
70	#16811187	C₂²	1	4	yes	complemented
71	#16811187	C₂²	1	2	yes	complemented
72	#16811187	C₂²	1	4	yes	complemented
73	#16811187	C₂²	1	4	yes	complemented
74	#16811186	C₂²	1	8	yes	complemented
75	#16811184	C₂²	1	16	yes	complemented
76	#16811182	C₂²	1	4	yes	complemented
77	#16811174	C₂²	1	8	yes	complemented
78	#16811172	C₂²	1	8	yes	complemented
79	#16811169	C₂²	1	4	yes	complemented
80	C₂×#13133214	C₂²	1	2	yes	complemented
81	C₂×#13133213	C₂²	1	2	yes	complemented
82	#127×D₅₃	C₂²	1	8	yes	complemented
83	C₂×#13133206	C₂²	1	2	yes	complemented
84	C₂×#13133205	C₂²	1	2	yes	complemented
85	#124×D₅₃	C₂²	1	8	yes	complemented
86	#16811136	C₂²	1	16	yes	complemented
87	#16811134	C₂²	1	4	yes	complemented
88	#16811131	C₂²	1	16	yes	complemented
89	#16811130	C₂²	1	4	yes	complemented
90	C₂×#13133192	C₂²	1	4	yes	complemented
91	C₂×#13133191	C₂²	1	4	yes	complemented
92	#121×D₅₃	C₂²	1	16	yes	complemented
93	C₂×#13133187	C₂²	1	4	yes	complemented
94	C₂×#13133185	C₂²	1	4	yes	complemented
95	#120×D₅₃	C₂²	1	16	yes	complemented
96	#16811104	C₂²	1	4	yes	complemented
97	#16811103	C₂²	1	4	yes	complemented
98	#16811100	C₂²	1	2	yes	complemented
99	#16811097	C₂²	1	2	yes	complemented
100	#16811096	C₂²	1	4	yes	complemented
101	C₄×#11719945	C₂²	1	4	yes	complemented
102	#16811091	C₂²	1	4	yes	complemented
103	C₂×#13133176	C₂²	1	1	yes	characteristic, complemented
104	#117×D₅₃	C₂²	1	4	yes	complemented
105	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
106	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#537	C₂²	1	4	yes	complemented
108	C₅₃×#536	C₂²	1	2	yes	complemented
109	C₅₃×#536	C₂²	1	2	yes	complemented
110	C₅₃×#535	C₂²	1	2	yes	complemented
111	C₅₃×#535	C₂²	1	2	yes	complemented
112	C₅₃×#534	C₂²	1	4	yes	complemented
113	C₅₃×#532	C₂²	1	4	yes	complemented
114	C₅₃×#525	C₂²	1	4	yes	complemented
115	C₅₃×#525	C₂²	1	4	yes	complemented
116	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
117	C₂⁴×D₅₃	C₂³	1	4	yes	—
118	C₂⁴×D₅₃	C₂³	1	2	yes	—
119	#13133265	—	2	16	no	—
120	#13133264	—	2	16	no	—
121	#13133264	—	2	16	no	—
122	#13133263	—	2	32	no	—
123	#13133263	—	2	32	no	—
124	#13133263	—	2	32	no	—
125	#13133263	—	2	32	no	—
126	#13133263	—	2	16	no	—
127	#13133263	—	2	16	no	—
128	#13133262	—	2	32	no	—
129	#13133262	—	2	16	no	—
130	C₂×#11719949	—	2	16	no	—
131	C₂×#11719949	C₂³	1	8	yes	—
132	C₂×#11719949	C₂³	1	8	yes	—
133	C₂×#11719949	C₂³	1	4	yes	complemented
134	C₂×#11719949	C₂³	1	4	yes	complemented
135	C₂×#11719945	—	2	8	no	—
136	C₂×#11719945	—	2	32	no	—
137	C₂×#11719945	—	2	16	no	—
138	C₂×#11719945	D₄	1	16	yes	complemented
139	C₂×#11719945	C₂³	1	8	yes	—
140	C₂×#11719945	C₂³	1	8	yes	—
141	C₂×#11719945	C₂³	1	2	yes	—
142	C₂×#11719945	C₂³	1	2	yes	—
143	C₂×#11719945	C₂³	1	2	yes	—
144	C₂×#11719945	C₂³	1	2	yes	—
145	C₂×#11719945	C₂³	1	2	yes	—
146	C₂×#11719945	C₂³	1	2	yes	—
147	C₂×#11719945	C₂³	1	8	yes	complemented
148	C₂×#11719945	C₂³	1	4	yes	complemented
149	C₂×#11719945	C₂³	1	4	yes	complemented
150	C₂×#11719945	C₂³	1	2	yes	complemented
151	C₂×#11719945	C₂³	1	8	yes	complemented
152	C₂×#11719945	C₂³	1	2	yes	complemented
153	C₂×#11719947	C₂³	1	8	yes	—
154	C₂×#11719947	C₂³	1	4	yes	complemented
155	C₂×#11719947	C₂³	1	4	yes	complemented
156	C₂×#11719947	C₂³	1	8	yes	complemented
157	#41×D₅₃	—	2	32	no	—
158	#41×D₅₃	—	2	32	no	—
159	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
160	C₂²×Dic₁₀₆	C₂³	1	4	yes	complemented
161	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
162	C₂×Q₈×D₅₃	C₂³	1	4	yes	complemented
163	C₂×Q₈×D₅₃	C₂³	1	4	yes	complemented
164	C₂²×D₂₁₂	—	2	8	no	—
165	C₂²×D₂₁₂	—	2	16	no	—
166	C₂²×D₂₁₂	C₂³	1	8	yes	—
167	C₂²×D₂₁₂	C₂³	1	8	yes	—
168	C₂²×D₂₁₂	C₂³	1	2	yes	—
169	C₂²×D₂₁₂	C₂³	1	2	yes	—
170	C₂²×D₂₁₂	C₂³	1	2	yes	—
171	C₂²×D₂₁₂	C₂³	1	2	yes	—
172	C₂²×D₂₁₂	C₂³	1	4	yes	—
173	C₂²×D₂₁₂	C₂³	1	2	yes	—
174	C₂²×D₂₁₂	C₂³	1	2	yes	—
175	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
176	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic, complemented
177	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
178	C₂²×D₂₁₂	C₂³	1	8	yes	complemented
179	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
180	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
181	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
182	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
183	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
184	C₂×D₄×D₅₃	—	2	32	no	—
185	C₂×D₄×D₅₃	—	2	16	no	—
186	C₂×D₄×D₅₃	C₂³	1	16	yes	—
187	C₂×D₄×D₅₃	C₂³	1	8	yes	—
188	C₂×D₄×D₅₃	C₂³	1	8	yes	—
189	C₂×D₄×D₅₃	C₂³	1	8	yes	—
190	C₂×D₄×D₅₃	C₂³	1	16	yes	—
191	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
192	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
193	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
194	C₂×D₄×D₅₃	C₂³	1	32	yes	complemented
195	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
196	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
197	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
198	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
199	#13133215	C₂³	1	4	yes	complemented
200	#13133214	C₂³	1	8	yes	complemented
201	#13133214	C₂³	1	8	yes	complemented
202	#13133213	C₂³	1	8	yes	complemented
203	#13133213	C₂³	1	32	yes	complemented
204	#13133213	C₂³	1	4	yes	complemented
205	#13133213	C₂³	1	8	yes	complemented
206	#13133206	C₂³	1	8	yes	complemented
207	#13133206	C₂³	1	8	yes	complemented
208	#13133206	C₂³	1	4	yes	complemented
209	#13133205	C₂³	1	8	yes	complemented
210	#13133205	C₂³	1	8	yes	complemented
211	#13133204	C₂³	1	4	yes	complemented
212	#13133203	C₂³	1	32	yes	complemented
213	#13133202	C₂³	1	32	yes	complemented
214	#13133200	C₂³	1	8	yes	—
215	#13133198	C₂³	1	8	yes	complemented
216	#13133196	C₂³	1	8	yes	complemented
217	#13133195	C₂³	1	32	yes	complemented
218	#13133193	C₂³	1	8	yes	complemented
219	#13133192	C₂³	1	32	yes	complemented
220	#13133192	C₂³	1	16	yes	complemented
221	#13133192	C₂³	1	16	yes	complemented
222	#13133191	C₂³	1	16	yes	complemented
223	#13133191	C₂³	1	8	yes	complemented
224	#13133191	C₂³	1	16	yes	complemented
225	#13133190	C₂³	1	32	yes	complemented
226	#13133190	C₂³	1	32	yes	complemented
227	#13133190	C₂³	1	32	yes	complemented
228	#13133189	C₂³	1	16	yes	complemented
229	#13133189	C₂³	1	32	yes	complemented
230	#13133188	C₂³	1	8	yes	complemented
231	#13133187	C₂³	1	16	yes	—
232	#13133187	C₂³	1	32	yes	complemented
233	#13133187	C₂³	1	16	yes	complemented
234	#13133187	C₂³	1	32	yes	complemented
235	#13133186	C₂³	1	8	yes	—
236	#13133185	C₂³	1	16	yes	—
237	#13133185	C₂³	1	32	yes	complemented
238	#13133185	C₂³	1	16	yes	complemented
239	#13133185	C₂³	1	8	yes	complemented
240	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
241	#13133182	C₂³	1	8	yes	complemented
242	C₄×D₂₁₂	C₂³	1	8	yes	complemented
243	#13133179	C₂³	1	8	yes	complemented
244	#13133179	C₂³	1	32	yes	complemented
245	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
246	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
247	#13133177	C₂³	1	16	yes	complemented
248	#13133177	C₂³	1	32	yes	complemented
249	#13133176	C₂³	1	2	yes	—
250	#13133176	C₂³	1	2	yes	—
251	#13133176	C₂³	1	2	yes	complemented
252	#13133176	C₂³	1	2	yes	complemented
253	#13133175	C₂³	1	8	yes	complemented
254	#13133174	C₂³	1	8	yes	complemented
255	#13133173	C₂³	1	8	yes	—
256	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
257	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
258	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
259	C₂×#11719921	C₂³	1	8	yes	complemented
260	C₂×#11719921	C₂³	1	8	yes	complemented
261	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
262	C₂²⋊C₄×D₅₃	C₂³	1	32	yes	complemented
263	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
264	C₄²×D₅₃	C₂³	1	8	yes	complemented
265	C₂×#41×C₅₃	—	2	8	no	—
266	C₂×#41×C₅₃	—	2	8	no	—
267	C₂×#41×C₅₃	C₂³	1	2	yes	—
268	C₂×#41×C₅₃	C₂³	1	2	yes	—
269	C₂×#41×C₅₃	C₂³	1	2	yes	—
270	C₂×#41×C₅₃	C₂³	1	2	yes	—
271	C₂×#41×C₅₃	C₂³	1	2	yes	—
272	C₂×#41×C₅₃	C₂³	1	2	yes	—
273	C₂×#41×C₅₃	C₂³	1	2	yes	complemented
274	C₂×#41×C₅₃	C₂³	1	2	yes	complemented
275	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
276	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
277	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
278	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
279	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
280	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
281	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
282	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
283	C₂³×C₄×C₅₃	C₂³	1	2	yes	complemented
284	C₄⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
285	#127×C₅₃	C₂³	1	4	yes	complemented
286	#124×C₅₃	C₂³	1	4	yes	complemented
287	#124×C₅₃	C₂³	1	4	yes	complemented
288	#123×C₅₃	C₂³	1	8	yes	—
289	#123×C₅₃	C₂³	1	8	yes	complemented
290	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
291	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
292	#121×C₅₃	C₂³	1	8	yes	complemented
293	#121×C₅₃	C₂³	1	8	yes	complemented
294	#121×C₅₃	C₂³	1	16	yes	complemented
295	#120×C₅₃	C₂³	1	8	yes	—
296	#120×C₅₃	C₂³	1	8	yes	complemented
297	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
298	#117×C₅₃	C₂³	1	2	yes	—
299	#117×C₅₃	C₂³	1	2	yes	—
300	#117×C₅₃	C₂³	1	2	yes	complemented
301	#117×C₅₃	C₂³	1	2	yes	complemented
302	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
303	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
304	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
305	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
306	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
307	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
308	C₂³×D₅₃	—	2	8	no	—
309	C₂³×D₅₃	—	2	16	no	—
310	C₂³×D₅₃	—	8	4	no	—
311	C₂³×D₅₃	—	8	8	no	—
312	C₂³×D₅₃	C₂⁴	1	16	yes	—
313	C₂³×D₅₃	C₂⁴	1	4	yes	—
314	C₂³×D₅₃	C₂⁴	1	4	yes	—
315	C₂³×D₅₃	C₂⁴	1	4	yes	—
316	C₂³×D₅₃	C₂⁴	1	2	yes	—
317	C₂³×D₅₃	C₂⁴	1	8	yes	—
318	C₂³×D₅₃	C₂⁴	1	2	yes	—
319	#41×C₅₃	—	2	8	no	—
320	#41×C₅₃	—	2	8	no	—
321	#41×C₅₃	—	2	8	no	—
322	#41×C₅₃	—	2	8	no	—
323	#41×C₅₃	—	2	8	no	—
324	#41×C₅₃	—	2	8	no	—
325	#41×C₅₃	—	2	8	no	—
326	#41×C₅₃	—	2	8	no	—
327	C₂×Q₈×C₅₃	—	2	4	no	—
328	C₂×Q₈×C₅₃	—	2	4	no	—
329	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
333	C₂×D₄×C₅₃	—	2	8	no	—
334	C₂×D₄×C₅₃	—	2	8	no	—
335	C₂×D₄×C₅₃	—	2	4	no	—
336	C₂×D₄×C₅₃	—	2	4	no	—
337	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
338	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
339	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
340	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
341	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
342	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
343	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
344	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
345	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
346	C₂²×C₄×C₅₃	—	2	8	no	—
347	C₂²×C₄×C₅₃	—	2	8	no	—
348	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	complemented
349	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
350	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
351	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
352	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
353	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
356	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
362	C₂×C₂²⋊D₅₃	—	2	8	no	—
363	C₂×C₂²⋊D₅₃	—	2	32	no	—
364	C₂×C₂²⋊D₅₃	—	2	16	no	—
365	C₂×C₂²⋊D₅₃	—	8	8	no	—
366	C₂×C₂²⋊D₅₃	C₂×D₄	1	16	yes	complemented
367	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
368	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
369	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
370	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
371	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
372	C₂×C₂²⋊D₅₃	C₂⁴	1	32	yes	—
373	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
374	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
375	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
376	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
377	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
378	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
379	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
380	#11719949	—	2	16	no	—
381	#11719949	—	2	16	no	—
382	#11719949	—	2	32	no	—
383	#11719949	—	2	32	no	—
384	Q₈×D₅₃	—	2	16	no	—
385	Q₈×D₅₃	—	2	16	no	—
386	#11719947	—	2	32	no	—
387	#11719947	—	2	32	no	—
388	#11719947	—	2	16	no	—
389	#11719947	—	2	16	no	—
390	D₄×D₅₃	—	2	32	no	—
391	D₄×D₅₃	—	2	64	no	—
392	D₄×D₅₃	—	2	64	no	—
393	D₄×D₅₃	—	2	32	no	—
394	D₄×D₅₃	—	2	16	no	—
395	D₄×D₅₃	—	2	32	no	—
396	D₄×D₅₃	—	2	32	no	—
397	D₄×D₅₃	—	2	16	no	—
398	D₄×D₅₃	—	8	32	no	—
399	#11719945	—	2	8	no	—
400	#11719945	—	2	8	no	—
401	#11719945	—	2	8	no	—
402	#11719945	—	2	8	no	—
403	#11719945	—	2	32	no	—
404	#11719945	—	2	16	no	—
405	#11719945	—	2	32	no	—
406	#11719945	—	2	32	no	—
407	#11719945	—	2	32	no	—
408	#11719945	—	2	16	no	—
409	#11719945	C₂×D₄	1	16	yes	complemented
410	#11719945	C₂×D₄	1	16	yes	complemented
411	#11719945	C₂×D₄	1	16	yes	complemented
412	#11719945	C₂×D₄	1	16	yes	complemented
413	C₂×D₂₁₂	—	2	16	no	—
414	C₂×D₂₁₂	—	2	8	no	—
415	C₂×D₂₁₂	—	2	8	no	—
416	C₂×D₂₁₂	—	2	8	no	—
417	C₂×D₂₁₂	—	2	8	no	—
418	C₂×D₂₁₂	—	2	8	no	—
419	C₂×D₂₁₂	—	2	8	no	—
420	C₂×D₂₁₂	—	2	4	no	—
421	C₂×D₂₁₂	—	2	32	no	—
422	C₂×D₂₁₂	—	2	32	no	—
423	C₂×D₂₁₂	—	2	16	no	—
424	C₂×D₂₁₂	—	8	8	no	—
425	C₂×D₂₁₂	C₂×D₄	1	8	yes	complemented
426	C₂×D₂₁₂	C₂⁴	1	8	yes	—
427	C₂×D₂₁₂	C₂⁴	1	16	yes	—
428	C₂×D₂₁₂	C₂⁴	1	4	yes	—
429	C₂×D₂₁₂	C₂⁴	1	4	yes	—
430	C₂×D₂₁₂	C₂⁴	1	2	yes	—
431	C₂×D₂₁₂	C₂⁴	1	4	yes	—
432	C₂×D₂₁₂	C₂⁴	1	4	yes	—
433	C₂×D₂₁₂	C₂⁴	1	2	yes	—
434	C₂×D₂₁₂	C₂⁴	1	32	yes	—
435	C₂×D₂₁₂	C₂⁴	1	2	yes	—
436	C₂×D₂₁₂	C₂⁴	1	2	yes	—
437	C₂×C₄×D₅₃	—	2	8	no	—
438	C₂×C₄×D₅₃	—	2	16	no	—
439	C₂×C₄×D₅₃	—	2	32	no	—
440	C₂×C₄×D₅₃	C₂×D₄	1	16	yes	complemented
441	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
442	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
443	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
444	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
445	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
446	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
447	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
448	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
449	C₂×Dic₁₀₆	—	2	4	no	—
450	C₂×Dic₁₀₆	—	2	16	no	—
451	C₂×Dic₁₀₆	C₂×D₄	1	8	yes	complemented
452	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
453	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
454	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
455	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
456	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
457	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
458	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
459	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
460	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
461	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
462	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
463	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
464	C₄²×C₅₃	C₂⁴	1	4	yes	—
465	C₄²×C₅₃	C₂⁴	1	4	yes	—
466	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
467	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
468	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
469	#11719921	C₂⁴	1	16	yes	—
470	#11719921	C₂⁴	1	32	yes	—
471	#11719921	C₂⁴	1	32	yes	—
472	#11719921	C₂⁴	1	16	yes	—
473	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
474	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
475	#11719919	C₂⁴	1	16	yes	—
476	#11719919	C₂⁴	1	16	yes	—
477	C₄×Dic₅₃	C₂⁴	1	4	yes	—
478	C₄×Dic₅₃	C₂⁴	1	16	yes	—
479	C₄×Dic₅₃	C₂⁴	1	4	yes	—
480	C₂³×C₅₃	—	2	4	no	—
481	C₂³×C₅₃	—	2	4	no	—
482	C₂³×C₅₃	—	4	2	no	—
483	C₂³×C₅₃	—	4	4	no	—
484	C₂³×C₅₃	—	4	4	no	—
485	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
486	C₂³×C₅₃	C₂⁵	1	4	yes	—
487	C₂³×C₅₃	C₂⁵	1	4	yes	—
488	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
489	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
490	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
491	C₂²×D₅₃	—	2	8	no	—
492	C₂²×D₅₃	—	2	4	no	—
493	C₂²×D₅₃	—	2	8	no	—
494	C₂²×D₅₃	—	2	8	no	—
495	C₂²×D₅₃	—	2	16	no	—
496	C₂²×D₅₃	—	2	32	no	—
497	C₂²×D₅₃	—	4	4	no	—
498	C₂²×D₅₃	—	4	8	no	—
499	C₂²×D₅₃	—	4	4	no	—
500	C₂²×D₅₃	—	4	8	no	—
501	C₂²×D₅₃	—	4	16	no	—
502	C₂²×D₅₃	—	4	32	no	—
503	C₂²×D₅₃	—	4	8	no	—
504	C₂²×D₅₃	—	8	32	no	—
505	C₂²×D₅₃	—	8	16	no	—
506	C₂²×D₅₃	C₂²×D₄	1	8	yes	—
507	C₂²×D₅₃	C₂⁵	1	4	yes	—
508	C₂²×D₅₃	C₂⁵	1	8	yes	—
509	C₂²×D₅₃	C₂⁵	1	4	yes	—
510	Q₈×C₅₃	—	2	4	no	—
511	Q₈×C₅₃	—	2	4	no	—
512	Q₈×C₅₃	—	2	4	no	—
513	Q₈×C₅₃	—	2	4	no	—
514	D₄×C₅₃	—	2	8	no	—
515	D₄×C₅₃	—	2	8	no	—
516	D₄×C₅₃	—	2	8	no	—
517	D₄×C₅₃	—	2	8	no	—
518	D₄×C₅₃	—	2	4	no	—
519	D₄×C₅₃	—	2	4	no	—
520	D₄×C₅₃	—	2	4	no	—
521	D₄×C₅₃	—	2	4	no	—
522	D₄×C₅₃	—	4	16	no	—
523	C₂×C₄×C₅₃	—	2	4	no	—
524	C₂×C₄×C₅₃	—	2	4	no	—
525	C₂×C₄×C₅₃	—	2	8	no	—
526	C₂×C₄×C₅₃	—	2	8	no	—
527	C₂×C₄×C₅₃	—	2	8	no	—
528	C₂×C₄×C₅₃	—	2	8	no	—
529	C₂×C₄×C₅₃	—	4	4	no	—
530	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
531	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
532	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
533	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
534	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
535	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
536	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
537	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
538	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
539	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
540	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
541	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
542	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
543	C₂²⋊D₅₃	—	2	8	no	—
544	C₂²⋊D₅₃	—	2	8	no	—
545	C₂²⋊D₅₃	—	2	16	no	—
546	C₂²⋊D₅₃	—	2	32	no	—
547	C₂²⋊D₅₃	—	2	16	no	—
548	C₂²⋊D₅₃	—	4	16	no	—
549	C₂²⋊D₅₃	—	4	32	no	—
550	C₂²⋊D₅₃	C₂²×D₄	1	16	yes	—
551	C₂²⋊D₅₃	C₂²×D₄	1	16	yes	—
552	C₂×Dic₅₃	—	2	4	no	—
553	C₂×Dic₅₃	—	2	16	no	—
554	C₂×Dic₅₃	—	4	4	no	—
555	C₂×Dic₅₃	C₂²×D₄	1	8	yes	—
556	C₂×Dic₅₃	C₂⁵	1	4	yes	—
557	C₂×Dic₅₃	C₂⁵	1	8	yes	—
558	C₂×Dic₅₃	C₂⁵	1	4	yes	—
559	D₂₁₂	—	2	32	no	—
560	D₂₁₂	—	2	16	no	—
561	D₂₁₂	—	2	8	no	—
562	D₂₁₂	—	2	8	no	—
563	D₂₁₂	—	2	4	no	—
564	D₂₁₂	—	2	8	no	—
565	D₂₁₂	—	2	8	no	—
566	D₂₁₂	—	2	4	no	—
567	D₂₁₂	—	4	32	no	—
568	D₂₁₂	C₂²×D₄	1	8	yes	—
569	D₂₁₂	C₂²×D₄	1	8	yes	—
570	C₄×D₅₃	—	2	16	no	—
571	C₄×D₅₃	—	2	8	no	—
572	C₄×D₅₃	—	2	8	no	—
573	C₄×D₅₃	—	2	32	no	—
574	C₄×D₅₃	—	2	16	no	—
575	C₄×D₅₃	—	4	16	no	—
576	C₄×D₅₃	C₂²×D₄	1	16	yes	—
577	C₄×D₅₃	C₂²×D₄	1	16	yes	—
578	Dic₁₀₆	—	2	4	no	—
579	Dic₁₀₆	—	2	4	no	—
580	Dic₁₀₆	—	2	16	no	—
581	Dic₁₀₆	C₂²×D₄	1	8	yes	—
582	Dic₁₀₆	C₂²×D₄	1	8	yes	—
583	#62852	—	53	1	no	maximal, Sylow
584	C₂²×C₅₃	—	2	2	no	—
585	C₂²×C₅₃	—	2	2	no	—
586	C₂²×C₅₃	—	2	2	no	—
587	C₂²×C₅₃	—	2	4	no	—
588	C₂²×C₅₃	—	2	4	no	—
589	C₂²×C₅₃	—	2	8	no	—
590	C₂²×C₅₃	—	2	8	no	—
591	C₂²×C₅₃	—	4	4	no	—
592	C₂²×C₅₃	—	4	8	no	—
593	C₂²×C₅₃	—	8	4	no	—
594	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
595	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
596	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
597	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
598	C₂×D₅₃	—	2	8	no	—
599	C₂×D₅₃	—	2	4	no	—
600	C₂×D₅₃	—	2	8	no	—
601	C₂×D₅₃	—	2	8	no	—
602	C₂×D₅₃	—	2	16	no	—
603	C₂×D₅₃	—	4	8	no	—
604	C₂×D₅₃	—	4	16	no	—
605	C₂×D₅₃	—	8	16	no	—
606	C₂×D₅₃	—	8	32	no	—
607	C₂×D₅₃	—	8	4	no	—
608	C₂×D₅₃	—	8	8	no	—
609	C₂×D₅₃	—	8	8	no	—
610	C₂×D₅₃	C₂³×D₄	1	8	yes	—
611	C₄×C₅₃	—	2	4	no	—
612	C₄×C₅₃	—	2	4	no	—
613	C₄×C₅₃	—	2	8	no	—
614	C₄×C₅₃	C₂³×D₄	1	2	yes	—
615	C₄×C₅₃	C₂³×D₄	1	2	yes	—
616	C₄×C₅₃	C₂³×D₄	1	2	yes	—
617	C₄×C₅₃	C₂³×D₄	1	2	yes	—
618	Dic₅₃	—	2	4	no	—
619	Dic₅₃	—	2	8	no	—
620	Dic₅₃	C₂³×D₄	1	8	yes	—
621	C₂×#585	—	53	1	no	—
622	C₂²×H(5,𝔽₂)	—	53	1	no	—
623	#3500	—	53	4	no	—
624	#3500	—	53	4	no	—
625	#3498	—	53	4	no	—
626	#3498	—	53	4	no	—
627	#3488	—	53	8	no	—
628	#3488	—	53	8	no	—
629	#3487	—	53	4	no	—
630	#3484	—	53	8	no	—
631	#3484	—	53	4	no	—
632	#3449	—	53	1	no	—
633	#3449	—	53	4	no	—
634	#3449	D₅₃	1	1	yes	characteristic, complemented
635	C₂×#535	—	53	1	no	—
636	C₂×#535	—	53	4	no	—
637	C₂×#535	—	53	1	no	—
638	#3428	—	53	1	no	—
639	C₂×C₅₃	—	2	2	no	—
640	C₂×C₅₃	—	2	2	no	—
641	C₂×C₅₃	—	2	2	no	—
642	C₂×C₅₃	—	4	4	no	—
643	C₂×C₅₃	—	4	4	no	—
644	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
645	C₂×C₅₃	H(7,𝔽₂)	1	2	yes	—
646	D₅₃	—	2	8	no	—
647	D₅₃	—	4	8	no	—
648	D₅₃	—	4	4	no	—
649	#585	—	106	16	no	—
650	C₂×2₋¹⁺⁴	—	53	2	no	—
651	C₂×2₋¹⁺⁴	—	53	2	no	—
652	C₂×2₋¹⁺⁴	—	53	2	no	—
653	C₂×H(5,𝔽₂)	—	53	4	no	—
654	C₂×H(5,𝔽₂)	—	53	4	no	—
655	C₂×H(5,𝔽₂)	—	53	4	no	—
656	C₂×H(5,𝔽₂)	—	53	4	no	—
657	C₂×H(5,𝔽₂)	—	53	2	no	—
658	C₂×H(5,𝔽₂)	—	53	2	no	—
659	C₂×H(5,𝔽₂)	—	53	4	no	—
660	C₂×H(5,𝔽₂)	—	53	2	no	—
661	C₂×H(5,𝔽₂)	—	106	16	no	—
662	C₂²×#41	—	53	4	no	—
663	C₂²×#41	—	53	4	no	—
664	C₂²×#41	—	53	2	no	—
665	C₂²×#41	—	53	1	no	—
666	C₂²×#41	—	53	2	no	—
667	C₂²×#41	—	53	1	no	—
668	C₂²×#41	—	53	4	no	—
669	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
670	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
671	C₂³×D₄	—	53	2	no	—
672	C₂³×D₄	—	53	4	no	—
673	C₂³×D₄	—	53	1	no	—
674	C₂³×D₄	—	53	2	no	—
675	#550	—	53	16	no	—
676	#550	—	53	16	no	—
677	#548	—	53	16	no	—
678	#548	—	53	16	no	—
679	#546	—	53	32	no	—
680	#546	—	53	16	no	—
681	#546	—	53	32	no	—
682	#546	—	53	16	no	—
683	D₄²	—	53	32	no	—
684	D₄²	—	53	16	no	—
685	D₄²	—	53	32	no	—
686	D₄²	—	53	16	no	—
687	#537	—	53	4	no	—
688	#537	—	53	16	no	—
689	#537	C₂×D₅₃	1	4	yes	complemented
690	#536	—	53	2	no	—
691	#536	—	53	2	no	—
692	#536	—	53	8	no	—
693	#536	C₂×D₅₃	1	2	yes	complemented
694	#536	C₂×D₅₃	1	2	yes	complemented
695	#535	—	53	4	no	—
696	#535	—	53	4	no	—
697	#535	—	53	2	no	—
698	#535	—	53	4	no	—
699	#535	—	53	4	no	—
700	#535	—	53	2	no	—
701	#535	—	53	8	no	—
702	#535	—	53	8	no	—
703	#535	—	53	8	no	—
704	#535	—	53	16	no	—
705	#535	—	53	16	no	—
706	#535	—	53	4	no	—
707	#535	—	53	4	no	—
708	#535	—	53	4	no	—
709	#535	—	53	4	no	—
710	#535	C₂×D₅₃	1	2	yes	complemented
711	#535	C₂×D₅₃	1	2	yes	complemented
712	#534	—	53	4	no	—
713	#534	—	53	16	no	—
714	#534	C₂×D₅₃	1	4	yes	complemented
715	#532	—	53	4	no	—
716	#532	—	53	8	no	—
717	#532	—	53	8	no	—
718	#532	C₂×D₅₃	1	4	yes	complemented
719	C₂×#127	—	53	2	no	—
720	C₂×#127	—	53	8	no	—
721	C₂×#127	—	53	2	no	—
722	C₂×#124	—	53	2	no	—
723	C₂×#124	—	53	8	no	—
724	C₂×#124	—	53	2	no	—
725	#525	—	53	4	no	—
726	#525	—	53	4	no	—
727	#525	—	53	16	no	—
728	#525	—	53	16	no	—
729	#525	C₂×D₅₃	1	4	yes	complemented
730	#525	C₂×D₅₃	1	4	yes	complemented
731	C₂×#121	—	53	4	no	—
732	C₂×#121	—	53	16	no	—
733	C₂×#121	—	53	4	no	—
734	C₂×#120	—	53	4	no	—
735	C₂×#120	—	53	16	no	—
736	C₂×#120	—	53	4	no	—
737	#520	—	53	4	no	—
738	#520	—	53	4	no	—
739	#519	—	53	2	no	—
740	#518	—	53	2	no	—
741	#518	—	53	4	no	—
742	C₄×#41	—	53	4	no	—
743	C₄×#41	—	53	4	no	—
744	C₂×#117	—	53	1	no	—
745	C₂×#117	—	53	4	no	—
746	C₂×#117	C₂×D₅₃	1	1	yes	characteristic, complemented
747	C₅₃	#62852	1	1	yes	characteristic, complemented, Sylow
748	C₂⁵	—	53	4	no	—
749	C₂⁵	—	53	2	no	—
750	2₋¹⁺⁴	—	106	16	no	—
751	2₋¹⁺⁴	—	106	16	no	—
752	2₋¹⁺⁴	—	106	16	no	—
753	H(5,𝔽₂)	—	106	32	no	—
754	H(5,𝔽₂)	—	106	16	no	—
755	H(5,𝔽₂)	—	106	16	no	—
756	H(5,𝔽₂)	—	106	32	no	—
757	H(5,𝔽₂)	—	106	32	no	—
758	H(5,𝔽₂)	—	106	32	no	—
759	H(5,𝔽₂)	—	106	32	no	—
760	H(5,𝔽₂)	—	106	16	no	—
761	C₂×#41	—	2	8	no	—
762	C₂×#41	—	2	8	no	—
763	C₂×#41	—	53	8	no	—
764	C₂×#41	—	53	4	no	—
765	C₂×#41	—	53	8	no	—
766	C₂×#41	—	53	4	no	—
767	C₂×#41	—	53	8	no	—
768	C₂×#41	—	53	4	no	—
769	C₂×#41	—	53	8	no	—
770	C₂×#41	—	53	4	no	—
771	C₂×#41	—	53	16	no	—
772	C₂×#41	—	53	2	no	—
773	C₂×#41	—	53	2	no	—
774	C₂×#41	—	53	2	no	—
775	C₂×#41	—	53	2	no	—
776	C₂×#41	—	53	2	no	—
777	C₂×#41	—	53	2	no	—
778	C₂×#41	—	53	2	no	—
779	C₂×#41	—	53	8	no	—
780	C₂×#41	—	53	2	no	—
781	C₂×#41	—	53	4	no	—
782	C₂×#41	—	53	8	no	—
783	C₂×#41	—	53	8	no	—
784	C₂×#41	—	53	8	no	—
785	C₂×#41	—	53	4	no	—
786	C₂×#41	—	106	16	no	—
787	C₂×#41	—	106	32	no	—
788	C₂×#41	—	106	16	no	—
789	C₂×#41	—	106	32	no	—
790	C₂×#41	—	106	32	no	—
791	C₂×#41	—	106	8	no	—
792	C₂×#41	C₂²×D₅₃	1	2	yes	—
793	C₂×#41	C₂²×D₅₃	1	2	yes	—
794	C₂×#41	C₂²×D₅₃	1	2	yes	—
795	C₂×#41	C₂²×D₅₃	1	2	yes	—
796	C₂×#41	C₂²×D₅₃	1	2	yes	—
797	C₂×#41	C₂²×D₅₃	1	2	yes	—
798	C₂×#41	C₂²×D₅₃	1	2	yes	complemented
799	C₂×#41	C₂²×D₅₃	1	2	yes	complemented
800	C₂²×Q₈	—	53	4	no	—
801	C₂²×Q₈	—	53	4	no	—
802	C₂²×Q₈	—	53	1	no	—
803	C₂²×Q₈	—	53	1	no	—
804	C₂²×Q₈	—	53	4	no	—
805	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
806	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
807	C₂²×D₄	—	53	2	no	—
808	C₂²×D₄	—	53	2	no	—
809	C₂²×D₄	—	53	4	no	—
810	C₂²×D₄	—	53	8	no	—
811	C₂²×D₄	—	53	8	no	—
812	C₂²×D₄	—	53	8	no	—
813	C₂²×D₄	—	53	8	no	—
814	C₂²×D₄	—	53	8	no	—
815	C₂²×D₄	—	53	4	no	—
816	C₂²×D₄	—	53	8	no	—
817	C₂²×D₄	—	53	4	no	—
818	C₂²×D₄	—	53	16	no	—
819	C₂²×D₄	—	53	16	no	—
820	C₂²×D₄	—	53	32	no	—
821	C₂²×D₄	—	53	1	no	—
822	C₂²×D₄	—	53	2	no	—
823	C₂²×D₄	—	53	2	no	—
824	C₂²×D₄	—	53	2	no	—
825	C₂²×D₄	—	53	2	no	—
826	C₂²×D₄	—	53	1	no	—
827	C₂²×D₄	—	53	4	no	—
828	C₂²×D₄	—	53	2	no	—
829	C₂²×D₄	—	53	2	no	—
830	C₂²×D₄	—	53	4	no	—
831	C₂²×D₄	—	53	8	no	—
832	C₂²×D₄	—	53	8	no	—
833	C₂²×D₄	—	53	8	no	—
834	C₂²×D₄	—	106	16	no	—
835	C₂²×D₄	—	106	16	no	—
836	C₂²×D₄	—	106	32	no	—
837	C₂²×D₄	—	106	8	no	—
838	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
839	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
840	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
841	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
842	C₂³×C₄	—	53	2	no	—
843	C₂³×C₄	—	53	8	no	—
844	C₂³×C₄	—	53	2	no	—
845	C₂³×C₄	—	53	4	no	—
846	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
847	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
848	C₂³×C₄	C₂²×D₅₃	1	2	yes	complemented
849	C₄⋊Q₈	—	53	4	no	—
850	C₄⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
851	#127	—	53	8	no	—
852	#127	—	53	4	no	—
853	#127	—	53	32	no	—
854	#127	—	53	8	no	—
855	#127	—	53	8	no	—
856	#127	—	53	8	no	—
857	#127	C₂²×D₅₃	1	4	yes	complemented
858	#124	—	53	8	no	—
859	#124	—	53	8	no	—
860	#124	—	53	4	no	—
861	#124	—	53	4	no	—
862	#124	—	53	32	no	—
863	#124	—	53	8	no	—
864	#124	—	53	8	no	—
865	#124	C₂²×D₅₃	1	4	yes	complemented
866	#124	C₂²×D₅₃	1	4	yes	complemented
867	#123	—	53	8	no	—
868	#123	—	53	8	no	—
869	#123	—	53	32	no	—
870	#123	C₂²×D₅₃	1	8	yes	—
871	#123	C₂²×D₅₃	1	8	yes	complemented
872	C₂²⋊Q₈	—	53	8	no	—
873	C₂²⋊Q₈	—	53	8	no	—
874	C₂²⋊Q₈	—	53	32	no	—
875	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
876	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
877	#121	—	53	8	no	—
878	#121	—	53	32	no	—
879	#121	—	53	16	no	—
880	#121	—	53	16	no	—
881	#121	—	53	16	no	—
882	#121	—	53	8	no	—
883	#121	—	53	16	no	—
884	#121	—	53	16	no	—
885	#121	—	53	32	no	—
886	#121	—	53	32	no	—
887	#121	—	53	32	no	—
888	#121	—	53	32	no	—
889	#121	C₂²×D₅₃	1	8	yes	complemented
890	#121	C₂²×D₅₃	1	8	yes	complemented
891	#121	C₂²×D₅₃	1	16	yes	complemented
892	#120	—	53	8	no	—
893	#120	—	53	16	no	—
894	#120	—	53	32	no	—
895	#120	—	53	16	no	—
896	#120	—	53	8	no	—
897	#120	—	53	16	no	—
898	#120	—	53	16	no	—
899	#120	—	53	32	no	—
900	#120	—	53	32	no	—
901	#120	C₂²×D₅₃	1	8	yes	—
902	#120	C₂²×D₅₃	1	8	yes	complemented
903	C₄×Q₈	—	53	8	no	—
904	C₄×Q₈	—	53	8	no	—
905	C₄×D₄	—	53	16	no	—
906	C₄×D₄	—	53	16	no	—
907	C₄×D₄	—	53	8	no	—
908	C₄×D₄	—	53	32	no	—
909	C₄×D₄	—	53	16	no	—
910	C₄×D₄	—	53	32	no	—
911	C₄×D₄	—	53	8	no	—
912	C₄×D₄	C₂²×D₅₃	1	16	yes	complemented
913	#117	—	53	2	no	—
914	#117	—	53	2	no	—
915	#117	—	53	2	no	—
916	#117	—	53	2	no	—
917	#117	—	53	8	no	—
918	#117	—	53	8	no	—
919	#117	—	53	8	no	—
920	#117	C₂²×D₅₃	1	2	yes	—
921	#117	C₂²×D₅₃	1	2	yes	—
922	#117	C₂²×D₅₃	1	2	yes	complemented
923	#117	C₂²×D₅₃	1	2	yes	complemented
924	C₂×C₄⋊C₄	—	53	2	no	—
925	C₂×C₄⋊C₄	—	53	8	no	—
926	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
927	C₂×C₂²⋊C₄	—	53	2	no	—
928	C₂×C₂²⋊C₄	—	53	8	no	—
929	C₂×C₂²⋊C₄	—	53	8	no	—
930	C₂×C₂²⋊C₄	—	53	8	no	—
931	C₂×C₂²⋊C₄	—	53	32	no	—
932	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
933	C₂×C₄²	—	53	2	no	—
934	C₂×C₄²	—	53	8	no	—
935	C₂×C₄²	C₂²×D₅₃	1	2	yes	complemented
936	C₂⁴	—	53	2	no	—
937	C₂⁴	—	53	16	no	—
938	C₂⁴	—	53	4	no	—
939	C₂⁴	—	53	4	no	—
940	C₂⁴	—	53	4	no	—
941	C₂⁴	—	53	8	no	—
942	C₂⁴	—	53	2	no	—
943	C₂⁴	—	106	16	no	—
944	C₂⁴	—	106	8	no	—
945	C₂⁴	—	424	4	no	—
946	C₂⁴	—	424	8	no	—
947	C₂⁴	C₂³×D₅₃	1	2	yes	—
948	C₂⁴	C₂³×D₅₃	1	2	yes	—
949	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
950	#41	—	2	8	no	—
951	#41	—	2	8	no	—
952	#41	—	2	8	no	—
953	#41	—	2	8	no	—
954	#41	—	2	8	no	—
955	#41	—	2	8	no	—
956	#41	—	2	8	no	—
957	#41	—	2	8	no	—
958	#41	—	53	16	no	—
959	#41	—	53	16	no	—
960	#41	—	53	16	no	—
961	#41	—	53	16	no	—
962	#41	—	106	32	no	—
963	#41	—	106	32	no	—
964	#41	—	106	16	no	—
965	#41	—	106	32	no	—
966	#41	—	106	32	no	—
967	#41	—	106	16	no	—
968	#41	—	106	32	no	—
969	#41	—	106	16	no	—
970	#41	—	106	32	no	—
971	#41	—	106	32	no	—
972	#41	—	106	16	no	—
973	#41	—	106	32	no	—
974	#41	—	106	16	no	—
975	#41	—	106	16	no	—
976	#41	—	106	8	no	—
977	#41	—	106	8	no	—
978	#41	—	106	8	no	—
979	#41	—	106	8	no	—
980	C₂×Q₈	—	2	4	no	—
981	C₂×Q₈	—	2	4	no	—
982	C₂×Q₈	—	53	8	no	—
983	C₂×Q₈	—	53	2	no	—
984	C₂×Q₈	—	53	2	no	—
985	C₂×Q₈	—	53	8	no	—
986	C₂×Q₈	—	53	2	no	—
987	C₂×Q₈	—	53	2	no	—
988	C₂×Q₈	—	106	16	no	—
989	C₂×Q₈	—	106	16	no	—
990	C₂×Q₈	—	106	16	no	—
991	C₂×Q₈	—	106	4	no	—
992	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
993	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
994	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
995	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
996	C₂×D₄	—	2	8	no	—
997	C₂×D₄	—	2	8	no	—
998	C₂×D₄	—	2	4	no	—
999	C₂×D₄	—	2	4	no	—
1000	C₂×D₄	—	53	16	no	—
1001	C₂×D₄	—	53	4	no	—
1002	C₂×D₄	—	53	4	no	—
1003	C₂×D₄	—	53	4	no	—
1004	C₂×D₄	—	53	8	no	—
1005	C₂×D₄	—	53	4	no	—
1006	C₂×D₄	—	53	16	no	—
1007	C₂×D₄	—	53	8	no	—
1008	C₂×D₄	—	53	32	no	—
1009	C₂×D₄	—	53	16	no	—
1010	C₂×D₄	—	53	8	no	—
1011	C₂×D₄	—	53	2	no	—
1012	C₂×D₄	—	53	2	no	—
1013	C₂×D₄	—	53	8	no	—
1014	C₂×D₄	—	53	16	no	—
1015	C₂×D₄	—	53	4	no	—
1016	C₂×D₄	—	53	4	no	—
1017	C₂×D₄	—	53	4	no	—
1018	C₂×D₄	—	53	2	no	—
1019	C₂×D₄	—	53	4	no	—
1020	C₂×D₄	—	53	2	no	—
1021	C₂×D₄	—	53	32	no	—
1022	C₂×D₄	—	106	32	no	—
1023	C₂×D₄	—	106	32	no	—
1024	C₂×D₄	—	106	16	no	—
1025	C₂×D₄	—	106	16	no	—
1026	C₂×D₄	—	106	32	no	—
1027	C₂×D₄	—	106	32	no	—
1028	C₂×D₄	—	106	16	no	—
1029	C₂×D₄	—	106	16	no	—
1030	C₂×D₄	—	106	64	no	—
1031	C₂×D₄	—	106	64	no	—
1032	C₂×D₄	—	106	32	no	—
1033	C₂×D₄	—	106	16	no	—
1034	C₂×D₄	—	106	32	no	—
1035	C₂×D₄	—	106	32	no	—
1036	C₂×D₄	—	106	8	no	—
1037	C₂×D₄	—	106	8	no	—
1038	C₂×D₄	—	106	8	no	—
1039	C₂×D₄	—	106	8	no	—
1040	C₂×D₄	—	106	8	no	—
1041	C₂×D₄	—	106	8	no	—
1042	C₂×D₄	—	106	8	no	—
1043	C₂×D₄	—	106	4	no	—
1044	C₂×D₄	—	424	8	no	—
1045	C₂×D₄	—	424	32	no	—
1046	C₂×D₄	—	424	8	no	—
1047	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1048	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1049	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1050	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1051	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1052	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1053	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1054	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1055	C₂×D₄	C₂³×D₅₃	1	16	yes	—
1056	C₂²×C₄	—	2	8	no	—
1057	C₂²×C₄	—	2	8	no	—
1058	C₂²×C₄	—	53	2	no	—
1059	C₂²×C₄	—	53	16	no	—
1060	C₂²×C₄	—	53	4	no	—
1061	C₂²×C₄	—	53	4	no	—
1062	C₂²×C₄	—	53	2	no	—
1063	C₂²×C₄	—	53	8	no	—
1064	C₂²×C₄	—	53	4	no	—
1065	C₂²×C₄	—	53	8	no	—
1066	C₂²×C₄	—	53	8	no	—
1067	C₂²×C₄	—	53	4	no	—
1068	C₂²×C₄	—	53	16	no	—
1069	C₂²×C₄	—	53	4	no	—
1070	C₂²×C₄	—	53	16	no	—
1071	C₂²×C₄	—	106	16	no	—
1072	C₂²×C₄	—	106	32	no	—
1073	C₂²×C₄	—	106	8	no	—
1074	C₂²×C₄	D₄×D₅₃	1	8	yes	complemented
1075	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1076	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1077	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1078	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1079	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1080	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1081	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1082	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1083	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1084	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1085	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1086	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1087	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1088	C₄⋊C₄	—	53	4	no	—
1089	C₄⋊C₄	—	53	16	no	—
1090	C₄⋊C₄	—	53	4	no	—
1091	C₄⋊C₄	—	53	16	no	—
1092	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1093	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1094	C₄⋊C₄	C₂³×D₅₃	1	16	yes	—
1095	C₂²⋊C₄	—	53	4	no	—
1096	C₂²⋊C₄	—	53	16	no	—
1097	C₂²⋊C₄	—	53	4	no	—
1098	C₂²⋊C₄	—	53	32	no	—
1099	C₂²⋊C₄	—	53	32	no	—
1100	C₂²⋊C₄	—	53	16	no	—
1101	C₂²⋊C₄	—	53	16	no	—
1102	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1103	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
1104	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1105	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
1106	C₄²	—	53	4	no	—
1107	C₄²	—	53	16	no	—
1108	C₄²	—	53	4	no	—
1109	C₄²	C₂³×D₅₃	1	4	yes	—
1110	C₄²	C₂³×D₅₃	1	4	yes	—
1111	C₂³	—	2	4	no	—
1112	C₂³	—	2	4	no	—
1113	C₂³	—	4	2	no	—
1114	C₂³	—	4	4	no	—
1115	C₂³	—	4	4	no	—
1116	C₂³	—	53	4	no	—
1117	C₂³	—	53	8	no	—
1118	C₂³	—	53	8	no	—
1119	C₂³	—	53	4	no	—
1120	C₂³	—	106	16	no	—
1121	C₂³	—	106	32	no	—
1122	C₂³	—	106	4	no	—
1123	C₂³	—	106	8	no	—
1124	C₂³	—	106	8	no	—
1125	C₂³	—	106	8	no	—
1126	C₂³	—	424	16	no	—
1127	C₂³	—	424	32	no	—
1128	C₂³	—	212	4	no	—
1129	C₂³	—	212	16	no	—
1130	C₂³	—	212	8	no	—
1131	C₂³	—	212	8	no	—
1132	C₂³	—	212	32	no	—
1133	C₂³	—	212	4	no	—
1134	C₂³	—	212	8	no	—
1135	C₂³	C₂×D₄×D₅₃	1	4	yes	—
1136	C₂³	C₂⁴×D₅₃	1	4	yes	—
1137	C₂³	C₂⁴×D₅₃	1	4	yes	—
1138	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1139	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1140	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1141	Q₈	—	2	4	no	—
1142	Q₈	—	2	4	no	—
1143	Q₈	—	2	4	no	—
1144	Q₈	—	2	4	no	—
1145	Q₈	—	53	8	no	—
1146	Q₈	—	53	8	no	—
1147	Q₈	—	106	16	no	—
1148	Q₈	—	106	4	no	—
1149	Q₈	—	106	4	no	—
1150	D₄	—	2	8	no	—
1151	D₄	—	2	8	no	—
1152	D₄	—	2	8	no	—
1153	D₄	—	2	8	no	—
1154	D₄	—	2	4	no	—
1155	D₄	—	2	4	no	—
1156	D₄	—	2	4	no	—
1157	D₄	—	2	4	no	—
1158	D₄	—	4	16	no	—
1159	D₄	—	53	16	no	—
1160	D₄	—	53	16	no	—
1161	D₄	—	53	8	no	—
1162	D₄	—	53	8	no	—
1163	D₄	—	106	32	no	—
1164	D₄	—	106	16	no	—
1165	D₄	—	106	32	no	—
1166	D₄	—	106	16	no	—
1167	D₄	—	106	16	no	—
1168	D₄	—	106	8	no	—
1169	D₄	—	106	8	no	—
1170	D₄	—	106	8	no	—
1171	D₄	—	106	8	no	—
1172	D₄	—	106	8	no	—
1173	D₄	—	106	8	no	—
1174	D₄	—	106	4	no	—
1175	D₄	—	106	4	no	—
1176	D₄	—	212	32	no	—
1177	D₄	—	212	32	no	—
1178	D₄	—	212	16	no	—
1179	C₂×C₄	—	2	4	no	—
1180	C₂×C₄	—	2	4	no	—
1181	C₂×C₄	—	2	8	no	—
1182	C₂×C₄	—	2	8	no	—
1183	C₂×C₄	—	2	8	no	—
1184	C₂×C₄	—	2	8	no	—
1185	C₂×C₄	—	4	4	no	—
1186	C₂×C₄	—	53	8	no	—
1187	C₂×C₄	—	53	4	no	—
1188	C₂×C₄	—	53	16	no	—
1189	C₂×C₄	—	53	16	no	—
1190	C₂×C₄	—	53	8	no	—
1191	C₂×C₄	—	53	4	no	—
1192	C₂×C₄	—	106	32	no	—
1193	C₂×C₄	—	106	16	no	—
1194	C₂×C₄	—	106	16	no	—
1195	C₂×C₄	—	106	16	no	—
1196	C₂×C₄	—	106	4	no	—
1197	C₂×C₄	—	106	8	no	—
1198	C₂×C₄	—	106	8	no	—
1199	C₂×C₄	—	212	16	no	—
1200	C₂×C₄	—	212	4	no	—
1201	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
1202	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
1203	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
1204	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
1205	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
1206	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
1207	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1208	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1209	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1210	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1211	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1212	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1213	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1214	C₂²	—	2	2	no	—
1215	C₂²	—	2	2	no	—
1216	C₂²	—	2	2	no	—
1217	C₂²	—	2	4	no	—
1218	C₂²	—	2	4	no	—
1219	C₂²	—	2	8	no	—
1220	C₂²	—	2	8	no	—
1221	C₂²	—	4	4	no	—
1222	C₂²	—	4	8	no	—
1223	C₂²	—	8	4	no	—
1224	C₂²	—	53	8	no	—
1225	C₂²	—	106	8	no	—
1226	C₂²	—	106	4	no	—
1227	C₂²	—	106	8	no	—
1228	C₂²	—	106	8	no	—
1229	C₂²	—	106	16	no	—
1230	C₂²	—	424	8	no	—
1231	C₂²	—	424	8	no	—
1232	C₂²	—	424	4	no	—
1233	C₂²	—	424	32	no	—
1234	C₂²	—	424	16	no	—
1235	C₂²	—	212	8	no	—
1236	C₂²	—	212	16	no	—
1237	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
1238	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
1239	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
1240	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1241	C₄	—	2	4	no	—
1242	C₄	—	2	4	no	—
1243	C₄	—	2	8	no	—
1244	C₄	—	53	8	no	—
1245	C₄	—	106	4	no	—
1246	C₄	—	106	8	no	—
1247	C₄	C₂²×D₄×D₅₃	1	2	yes	—
1248	C₄	C₂²×D₄×D₅₃	1	2	yes	—
1249	C₄	C₂²×D₄×D₅₃	1	2	yes	—
1250	C₄	C₂²×D₄×D₅₃	1	2	yes	—
1251	C₂	—	2	2	no	—
1252	C₂	—	2	2	no	—
1253	C₂	—	2	2	no	—
1254	C₂	—	4	4	no	—
1255	C₂	—	4	4	no	—
1256	C₂	—	106	8	no	—
1257	C₂	—	212	8	no	—
1258	C₂	—	212	4	no	—
1259	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
1260	C₂	#20289526	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3449	C₂
hypercenter	#3449	D₅₃
hypocenter	C₅₃	#62852
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3449

Complements

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

N	H ≅ G/N	type
1. C₂×#16811459	C₂	semidirect
2. C₂²×#13133263	C₂	semidirect
3. #20288504	C₂	semidirect
4. #20288502	C₂	semidirect
5. #20288490	C₂	semidirect
6. #20288488	C₂	semidirect
7. #20288379	C₂	semidirect
8. #20288376	C₂	semidirect
9. #20288369	C₂	semidirect
10. #20288348	C₂	semidirect
11. #20288347	C₂	semidirect
12. #20288047	C₂	semidirect
13. #20288044	C₂	semidirect
14. C₂×#16811192	C₂	semidirect
15. C₂×#16811187	C₂	semidirect
16. #535×D₅₃	C₂	semidirect
17. #20287916	C₂	semidirect
18. C₅₃×#3449	C₂	semidirect
20. C₂×#13133265	C₂²	semidirect
21. C₂×#13133264	C₂²	semidirect
22. C₂×#13133264	C₂²	semidirect
24. C₂×#13133263	C₂²	semidirect
25. C₂×#13133263	C₂²	semidirect
26. C₂×#13133263	C₂²	semidirect
27. C₂×#13133263	C₂²	semidirect
28. C₂×#13133263	C₂²	semidirect
29. C₂×#13133263	C₂²	semidirect
30. C₂×#13133262	C₂²	semidirect
31. C₂×#13133262	C₂²	semidirect
32. C₂²×#11719949	C₂²	semidirect
34. C₂²×#11719945	C₂²	semidirect
35. C₂²×#11719945	C₂²	semidirect
36. C₂²×#11719945	C₂²	semidirect
37. C₂×#41×D₅₃	C₂²	semidirect
38. C₂×#41×D₅₃	C₂²	semidirect
39. C₂³×D₂₁₂	C₂²	semidirect
40. C₂³×D₂₁₂	C₂²	semidirect
41. C₂²×D₄×D₅₃	C₂²	semidirect
42. C₂²×D₄×D₅₃	C₂²	semidirect
43. #16811294	C₂²	semidirect
44. #16811291	C₂²	semidirect
45. #16811283	C₂²	semidirect
46. #16811282	C₂²	semidirect
47. #16811269	C₂²	semidirect
48. #16811265	C₂²	semidirect
49. #16811264	C₂²	semidirect
50. #16811262	C₂²	semidirect
51. D₄×D₂₁₂	C₂²	semidirect
52. #16811257	C₂²	semidirect
53. #16811257	C₂²	semidirect
54. #16811255	C₂²	semidirect
55. #16811203	C₂²	semidirect
56. #16811201	C₂²	semidirect
57. #16811198	C₂²	semidirect
58. #16811197	C₂²	semidirect
59. #16811194	C₂²	semidirect
60. #16811192	C₂²	semidirect
61. #16811192	C₂²	semidirect
62. #16811192	C₂²	semidirect
63. #16811192	C₂²	semidirect
64. #16811191	C₂²	semidirect
65. #16811191	C₂²	semidirect
66. #16811190	C₂²	semidirect
67. #16811189	C₂²	semidirect
68. #16811188	C₂²	semidirect
69. #16811187	C₂²	semidirect
70. #16811187	C₂²	semidirect
71. #16811187	C₂²	semidirect
72. #16811187	C₂²	semidirect
73. #16811187	C₂²	semidirect
74. #16811186	C₂²	semidirect
75. #16811184	C₂²	semidirect
76. #16811182	C₂²	semidirect
77. #16811174	C₂²	semidirect
78. #16811172	C₂²	semidirect
79. #16811169	C₂²	semidirect
80. C₂×#13133214	C₂²	semidirect
81. C₂×#13133213	C₂²	semidirect
82. #127×D₅₃	C₂²	semidirect
83. C₂×#13133206	C₂²	semidirect
84. C₂×#13133205	C₂²	semidirect
85. #124×D₅₃	C₂²	semidirect
86. #16811136	C₂²	semidirect
87. #16811134	C₂²	semidirect
88. #16811131	C₂²	semidirect
89. #16811130	C₂²	semidirect
90. C₂×#13133192	C₂²	semidirect
91. C₂×#13133191	C₂²	semidirect
92. #121×D₅₃	C₂²	semidirect
93. C₂×#13133187	C₂²	semidirect
94. C₂×#13133185	C₂²	semidirect
95. #120×D₅₃	C₂²	semidirect
96. #16811104	C₂²	semidirect
97. #16811103	C₂²	semidirect
98. #16811100	C₂²	semidirect
99. #16811097	C₂²	semidirect
100. #16811096	C₂²	semidirect
101. C₄×#11719945	C₂²	semidirect
102. #16811091	C₂²	semidirect
103. C₂×#13133176	C₂²	semidirect
104. #117×D₅₃	C₂²	semidirect
105. C₂²×#41×C₅₃	C₂²	semidirect
106. C₂²×#41×C₅₃	C₂²	semidirect
107. C₅₃×#537	C₂²	semidirect
108. C₅₃×#536	C₂²	semidirect
109. C₅₃×#536	C₂²	semidirect
110. C₅₃×#535	C₂²	semidirect
111. C₅₃×#535	C₂²	semidirect
112. C₅₃×#534	C₂²	semidirect
113. C₅₃×#532	C₂²	semidirect
114. C₅₃×#525	C₂²	semidirect
115. C₅₃×#525	C₂²	semidirect
116. C₂×#117×C₅₃	C₂²	semidirect
133. C₂×#11719949	C₂³	semidirect
134. C₂×#11719949	C₂³	semidirect
138. C₂×#11719945	D₄	semidirect
147. C₂×#11719945	C₂³	semidirect
148. C₂×#11719945	C₂³	semidirect
149. C₂×#11719945	C₂³	semidirect
150. C₂×#11719945	C₂³	semidirect
151. C₂×#11719945	C₂³	semidirect
152. C₂×#11719945	C₂³	semidirect
154. C₂×#11719947	C₂³	semidirect
155. C₂×#11719947	C₂³	semidirect
156. C₂×#11719947	C₂³	semidirect
160. C₂²×Dic₁₀₆	C₂³	semidirect
161. C₂²×Dic₁₀₆	C₂³	semidirect
162. C₂×Q₈×D₅₃	C₂³	semidirect
163. C₂×Q₈×D₅₃	C₂³	semidirect
176. C₂²×D₂₁₂	C₂³	semidirect
177. C₂²×D₂₁₂	C₂³	semidirect
178. C₂²×D₂₁₂	C₂³	semidirect
182. C₂²×C₂²⋊D₅₃	C₂³	semidirect
183. C₂²×C₂²⋊D₅₃	C₂³	semidirect
191. C₂×D₄×D₅₃	C₂³	semidirect
192. C₂×D₄×D₅₃	C₂³	semidirect
193. C₂×D₄×D₅₃	C₂³	semidirect
194. C₂×D₄×D₅₃	C₂³	semidirect
197. C₂²×C₄×D₅₃	C₂³	semidirect
198. C₂²×C₄×D₅₃	C₂³	semidirect
199. #13133215	C₂³	semidirect
200. #13133214	C₂³	semidirect
201. #13133214	C₂³	semidirect
202. #13133213	C₂³	semidirect
203. #13133213	C₂³	semidirect
204. #13133213	C₂³	semidirect
205. #13133213	C₂³	semidirect
206. #13133206	C₂³	semidirect
207. #13133206	C₂³	semidirect
208. #13133206	C₂³	semidirect
209. #13133205	C₂³	semidirect
210. #13133205	C₂³	semidirect
211. #13133204	C₂³	semidirect
212. #13133203	C₂³	semidirect
213. #13133202	C₂³	semidirect
215. #13133198	C₂³	semidirect
216. #13133196	C₂³	semidirect
217. #13133195	C₂³	semidirect
218. #13133193	C₂³	semidirect
219. #13133192	C₂³	semidirect
220. #13133192	C₂³	semidirect
221. #13133192	C₂³	semidirect
222. #13133191	C₂³	semidirect
223. #13133191	C₂³	semidirect
224. #13133191	C₂³	semidirect
225. #13133190	C₂³	semidirect
226. #13133190	C₂³	semidirect
227. #13133190	C₂³	semidirect
228. #13133189	C₂³	semidirect
229. #13133189	C₂³	semidirect
230. #13133188	C₂³	semidirect
232. #13133187	C₂³	semidirect
233. #13133187	C₂³	semidirect
234. #13133187	C₂³	semidirect
237. #13133185	C₂³	semidirect
238. #13133185	C₂³	semidirect
239. #13133185	C₂³	semidirect
240. C₄×Dic₁₀₆	C₂³	semidirect
241. #13133182	C₂³	semidirect
242. C₄×D₂₁₂	C₂³	semidirect
243. #13133179	C₂³	semidirect
244. #13133179	C₂³	semidirect
245. C₄×C₂²⋊D₅₃	C₂³	semidirect
246. C₄×C₂²⋊D₅₃	C₂³	semidirect
247. #13133177	C₂³	semidirect
248. #13133177	C₂³	semidirect
251. #13133176	C₂³	semidirect
252. #13133176	C₂³	semidirect
253. #13133175	C₂³	semidirect
254. #13133174	C₂³	semidirect
256. C₂×C₄⋊Dic₅₃	C₂³	semidirect
257. C₄⋊C₄×D₅₃	C₂³	semidirect
259. C₂×#11719921	C₂³	semidirect
260. C₂×#11719921	C₂³	semidirect
262. C₂²⋊C₄×D₅₃	C₂³	semidirect
263. C₂×C₄×Dic₅₃	C₂³	semidirect
264. C₄²×D₅₃	C₂³	semidirect
273. C₂×#41×C₅₃	C₂³	semidirect
274. C₂×#41×C₅₃	C₂³	semidirect
276. C₂²×Q₈×C₅₃	C₂³	semidirect
280. C₂²×D₄×C₅₃	C₂³	semidirect
283. C₂³×C₄×C₅₃	C₂³	semidirect
284. C₄⋊Q₈×C₅₃	C₂³	semidirect
285. #127×C₅₃	C₂³	semidirect
286. #124×C₅₃	C₂³	semidirect
287. #124×C₅₃	C₂³	semidirect
289. #123×C₅₃	C₂³	semidirect
290. C₂²⋊Q₈×C₅₃	C₂³	semidirect
291. C₂²⋊Q₈×C₅₃	C₂³	semidirect
292. #121×C₅₃	C₂³	semidirect
293. #121×C₅₃	C₂³	semidirect
294. #121×C₅₃	C₂³	semidirect
296. #120×C₅₃	C₂³	semidirect
297. C₄×D₄×C₅₃	C₂³	semidirect
300. #117×C₅₃	C₂³	semidirect
301. #117×C₅₃	C₂³	semidirect
302. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
304. C₂×C₄²×C₅₃	C₂³	semidirect
348. C₂²×C₄×C₅₃	C₂×D₄	semidirect
366. C₂×C₂²⋊D₅₃	C₂×D₄	semidirect
409. #11719945	C₂×D₄	semidirect
410. #11719945	C₂×D₄	semidirect
411. #11719945	C₂×D₄	semidirect
412. #11719945	C₂×D₄	semidirect
425. C₂×D₂₁₂	C₂×D₄	semidirect
440. C₂×C₄×D₅₃	C₂×D₄	semidirect
451. C₂×Dic₁₀₆	C₂×D₄	semidirect
634. #3449	D₅₃	semidirect
669. C₂²×#41	C₂×D₅₃	semidirect
670. C₂²×#41	C₂×D₅₃	semidirect
689. #537	C₂×D₅₃	semidirect
693. #536	C₂×D₅₃	semidirect
694. #536	C₂×D₅₃	semidirect
710. #535	C₂×D₅₃	semidirect
711. #535	C₂×D₅₃	semidirect
714. #534	C₂×D₅₃	semidirect
718. #532	C₂×D₅₃	semidirect
729. #525	C₂×D₅₃	semidirect
730. #525	C₂×D₅₃	semidirect
746. C₂×#117	C₂×D₅₃	semidirect
747. C₅₃	#62852	semidirect
798. C₂×#41	C₂²×D₅₃	semidirect
799. C₂×#41	C₂²×D₅₃	semidirect
806. C₂²×Q₈	C₂²×D₅₃	semidirect
841. C₂²×D₄	C₂²×D₅₃	semidirect
848. C₂³×C₄	C₂²×D₅₃	semidirect
850. C₄⋊Q₈	C₂²×D₅₃	semidirect
857. #127	C₂²×D₅₃	semidirect
865. #124	C₂²×D₅₃	semidirect
866. #124	C₂²×D₅₃	semidirect
871. #123	C₂²×D₅₃	semidirect
875. C₂²⋊Q₈	C₂²×D₅₃	semidirect
876. C₂²⋊Q₈	C₂²×D₅₃	semidirect
889. #121	C₂²×D₅₃	semidirect
890. #121	C₂²×D₅₃	semidirect
891. #121	C₂²×D₅₃	semidirect
902. #120	C₂²×D₅₃	semidirect
912. C₄×D₄	C₂²×D₅₃	semidirect
922. #117	C₂²×D₅₃	semidirect
923. #117	C₂²×D₅₃	semidirect
926. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
935. C₂×C₄²	C₂²×D₅₃	semidirect
1074. C₂²×C₄	D₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811459	2
C₂²×#13133263	2
#20288504	2
#20288502	2
#20288490	2
#20288488	2
#20288379	2
#20288376	2
#20288369	2
#20288348	2
#20288347	2
#20288047	2
#20288044	2
C₂×#16811192	2
C₂×#16811187	2
#535×D₅₃	2
#20287916	2
C₅₃×#3449	2
#62852	53