Subgroups — #37548301

Order 23168.

1050 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042026	C₂	1	2	yes	maximal, complemented
2	#26042019	C₂	1	2	yes	maximal, complemented
3	#26042012	C₂	1	1	yes	maximal, characteristic, complemented
4	#26042001	C₂	1	1	yes	maximal, characteristic, complemented
5	#26041973	C₂	1	2	yes	maximal, complemented
6	#26041953	C₂	1	2	yes	maximal, complemented
7	#26041947	C₂	1	1	yes	maximal, characteristic, complemented
8	#26041941	C₂	1	1	yes	maximal, characteristic, complemented
9	#26041939	C₂	1	1	yes	maximal, characteristic, complemented
10	#26041931	C₂	1	1	yes	maximal, characteristic, complemented
11	#26041926	C₂	1	1	yes	maximal, characteristic, complemented
12	#26041924	C₂	1	1	yes	maximal, characteristic, complemented
13	#26041892	C₂	1	1	yes	maximal, characteristic, complemented
14	#26041885	C₂	1	1	yes	maximal, characteristic, complemented
15	#26041880	C₂	1	2	yes	maximal, complemented
16	#26041870	C₂	1	2	yes	maximal, complemented
17	#26041868	C₂	1	2	yes	maximal, complemented
18	#26041862	C₂	1	2	yes	maximal, complemented
19	#26041849	C₂	1	1	yes	maximal, characteristic, complemented
20	#26041847	C₂	1	1	yes	maximal, characteristic, complemented
21	#26041829	C₂	1	1	yes	maximal, characteristic, complemented
22	#26041813	C₂	1	1	yes	maximal, characteristic, complemented
23	#529×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#15668450	C₂²	1	1	yes	characteristic
25	C₂×#15668449	C₂²	1	1	yes	characteristic
26	C₂×#15668449	C₂²	1	1	yes	characteristic, complemented
27	C₂×#15668448	C₂²	1	1	yes	characteristic
28	C₂×Q₈×D₁₈₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₁₈₁	C₂²	1	1	yes	characteristic
30	#19153816	C₂²	1	1	yes	characteristic, complemented
31	#19153814	C₂²	1	1	yes	characteristic, complemented
32	#19153813	C₂²	1	1	yes	characteristic
33	#19153812	C₂²	1	1	yes	characteristic
34	#19153812	C₂²	1	2	yes	complemented
35	#19153811	C₂²	1	2	yes	—
36	#19153811	C₂²	1	2	yes	—
37	#19153811	C₂²	1	2	yes	complemented
38	#19153810	C₂²	1	1	yes	characteristic
39	#19153810	C₂²	1	2	yes	complemented
40	#19153810	C₂²	1	1	yes	characteristic, complemented
41	#19153808	C₂²	1	1	yes	characteristic, complemented
42	#19153807	C₂²	1	2	yes	complemented
43	#19153807	C₂²	1	2	yes	complemented
44	#19153805	C₂²	1	1	yes	characteristic
45	#19153804	C₂²	1	2	yes	—
46	#19153804	C₂²	1	1	yes	characteristic
47	#19153804	C₂²	1	1	yes	characteristic
48	#19153804	C₂²	1	1	yes	characteristic, complemented
49	#19153803	C₂²	1	1	yes	characteristic
50	#19153802	C₂²	1	2	yes	complemented
51	#19153802	C₂²	1	2	yes	complemented
52	#19153801	C₂²	1	2	yes	—
53	#19153801	C₂²	1	2	yes	complemented
54	#19153801	C₂²	1	2	yes	complemented
55	#19153800	C₂²	1	2	yes	—
56	#19153799	C₂²	1	1	yes	characteristic
57	#19153799	C₂²	1	1	yes	characteristic, complemented
58	#19153799	C₂²	1	2	yes	complemented
59	#19153798	C₂²	1	2	yes	—
60	#19153798	C₂²	1	2	yes	complemented
61	#19153798	C₂²	1	2	yes	complemented
62	#19153798	C₂²	1	2	yes	complemented
63	#19153798	C₂²	1	2	yes	complemented
64	#19153796	C₂²	1	1	yes	characteristic
65	#19153796	C₂²	1	1	yes	characteristic
66	#19153796	C₂²	1	2	yes	complemented
67	#19153795	C₂²	1	1	yes	characteristic, complemented
68	#19153794	C₂²	1	2	yes	complemented
69	#19153794	C₂²	1	2	yes	complemented
70	#19153793	C₂²	1	2	yes	complemented
71	#19153793	C₂²	1	2	yes	complemented
72	#19153791	C₂²	1	2	yes	—
73	#19153791	C₂²	1	1	yes	characteristic
74	#19153791	C₂²	1	2	yes	complemented
75	#19153791	C₂²	1	1	yes	characteristic, complemented
76	#19153791	C₂²	1	2	yes	complemented
77	#19153790	C₂²	1	2	yes	—
78	#19153790	C₂²	1	1	yes	characteristic
79	#19153790	C₂²	1	2	yes	complemented
80	#19153790	C₂²	1	2	yes	complemented
81	#19153789	C₂²	1	2	yes	—
82	#19153789	C₂²	1	2	yes	—
83	#19153789	C₂²	1	2	yes	—
84	#19153789	C₂²	1	2	yes	complemented
85	#19153789	C₂²	1	2	yes	complemented
86	#19153788	C₂²	1	2	yes	complemented
87	#19153787	C₂²	1	2	yes	—
88	#19153786	C₂²	1	2	yes	—
89	#19153786	C₂²	1	2	yes	—
90	#19153786	C₂²	1	2	yes	—
91	#19153784	C₂²	1	2	yes	—
92	C₄×Dic₃₆₂	C₂²	1	1	yes	characteristic, complemented
93	#19153781	C₂²	1	1	yes	characteristic, complemented
94	#19153781	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₇₂₄	C₂²	1	1	yes	characteristic
96	C₄×D₇₂₄	C₂²	1	2	yes	complemented
97	C₄×D₇₂₄	C₂²	1	2	yes	complemented
98	C₄×D₇₂₄	C₂²	1	2	yes	complemented
99	#19153778	C₂²	1	1	yes	characteristic
100	#19153778	C₂²	1	2	yes	complemented
101	#19153778	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₂²⋊D₁₈₁	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊D₁₈₁	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊D₁₈₁	C₂²	1	1	yes	characteristic, complemented
105	#19153776	C₂²	1	2	yes	complemented
106	#19153773	C₂²	1	1	yes	characteristic
107	#19153773	C₂²	1	2	yes	complemented
108	#19153773	C₂²	1	1	yes	characteristic, complemented
109	C₄⋊C₄×D₁₈₁	C₂²	1	2	yes	complemented
110	C₂×#15668426	C₂²	1	2	yes	—
111	C₂²⋊C₄×D₁₈₁	C₂²	1	2	yes	—
112	#126×C₁₈₁	C₂²	1	2	yes	complemented
113	#125×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
114	#124×C₁₈₁	C₂²	1	1	yes	characteristic
115	#123×C₁₈₁	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
117	#121×C₁₈₁	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₈₁	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₁₈₁	C₂²	1	2	yes	complemented
121	#117×C₁₈₁	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₈₁	C₂³	1	2	yes	—
124	#15668450	—	4	2	no	—
125	#15668449	—	4	2	no	—
126	#15668449	—	4	2	no	—
127	#15668448	—	4	2	no	—
128	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
129	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
130	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
131	C₂×Dic₃₆₂	C₂³	1	2	yes	—
132	Q₈×D₁₈₁	—	4	2	no	—
133	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
134	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
135	C₂×D₇₂₄	C₂³	1	2	yes	—
136	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
137	C₂×D₇₂₄	C₂³	1	2	yes	—
138	C₂×D₇₂₄	C₂³	1	2	yes	—
139	C₂×D₇₂₄	C₂³	1	2	yes	—
140	C₂×D₇₂₄	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
149	D₄×D₁₈₁	—	4	2	no	—
150	C₂²×Dic₁₈₁	C₂³	1	2	yes	—
151	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
154	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
155	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
156	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
157	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
158	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
159	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
160	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
162	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
163	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
164	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
165	#15668428	C₂³	1	1	yes	characteristic
166	#15668428	C₂³	1	2	yes	—
167	#15668428	C₂³	1	1	yes	characteristic
168	#15668428	C₂³	1	1	yes	characteristic
169	#15668428	C₂³	1	1	yes	characteristic
170	#15668428	C₂³	1	1	yes	characteristic
171	#15668428	C₂³	1	1	yes	characteristic
172	#15668428	C₂³	1	2	yes	—
173	#15668428	C₂³	1	1	yes	characteristic
174	#15668428	C₂³	1	1	yes	characteristic
175	#15668428	C₂³	1	2	yes	—
176	#15668428	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
181	#15668426	C₂³	1	1	yes	characteristic
182	#15668426	C₂³	1	2	yes	—
183	#15668426	C₂³	1	1	yes	characteristic
184	#15668426	C₂³	1	2	yes	—
185	#15668426	C₂³	1	2	yes	—
186	#15668426	C₂³	1	2	yes	—
187	#15668426	C₂³	1	1	yes	characteristic
188	#15668426	C₂³	1	1	yes	characteristic
189	#15668426	C₂³	1	2	yes	—
190	#15668426	C₂³	1	1	yes	characteristic
191	#15668426	C₂³	1	1	yes	characteristic
192	#15668426	C₂³	1	2	yes	—
193	#15668426	C₂³	1	1	yes	characteristic
194	#15668426	C₂³	1	2	yes	—
195	#15668426	C₂³	1	2	yes	—
196	#15668426	C₂³	1	2	yes	—
197	#15668426	C₂³	1	2	yes	—
198	#15668426	C₂³	1	1	yes	characteristic
199	#15668426	C₂³	1	2	yes	—
200	#15668426	C₂³	1	2	yes	—
201	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
202	C₄×Dic₁₈₁	C₂³	1	2	yes	—
203	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
204	C₄×Dic₁₈₁	C₂³	1	2	yes	—
205	C₂×Q₈×C₁₈₁	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₁₈₁	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₁₈₁	C₂³	1	2	yes	—
208	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
212	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
213	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
223	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
224	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
225	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
226	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
227	C₄²×C₁₈₁	C₂³	1	2	yes	—
228	C₂²×D₁₈₁	—	4	2	no	—
229	C₂²×D₁₈₁	—	4	2	no	—
230	C₂²×D₁₈₁	—	4	2	no	—
231	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₈₁	C₂⁴	1	2	yes	—
233	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
234	C₂²×D₁₈₁	C₂⁴	1	2	yes	—
235	Dic₃₆₂	—	2	2	no	—
236	Dic₃₆₂	—	2	2	no	—
237	Dic₃₆₂	—	4	2	no	—
238	Dic₃₆₂	—	4	1	no	—
239	D₇₂₄	—	2	2	no	—
240	D₇₂₄	—	2	2	no	—
241	D₇₂₄	—	4	2	no	—
242	D₇₂₄	—	4	2	no	—
243	D₇₂₄	—	4	2	no	—
244	D₇₂₄	—	4	1	no	—
245	D₇₂₄	—	4	2	no	—
246	D₇₂₄	—	4	2	no	—
247	C₂²⋊D₁₈₁	—	4	2	no	—
248	C₂²⋊D₁₈₁	—	4	1	no	—
249	C₂²⋊D₁₈₁	—	4	2	no	—
250	C₂²⋊D₁₈₁	—	4	1	no	—
251	C₂²⋊D₁₈₁	—	4	2	no	—
252	C₂²⋊D₁₈₁	—	4	2	no	—
253	C₂²⋊D₁₈₁	—	4	2	no	—
254	C₂²⋊D₁₈₁	—	4	2	no	—
255	C₂×Dic₁₈₁	—	4	2	no	—
256	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
261	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
262	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
264	C₄×D₁₈₁	—	2	2	no	—
265	C₄×D₁₈₁	—	2	2	no	—
266	C₄×D₁₈₁	—	4	2	no	—
267	C₄×D₁₈₁	—	4	2	no	—
268	C₄×D₁₈₁	—	4	2	no	—
269	C₄×D₁₈₁	—	4	2	no	—
270	C₄×D₁₈₁	—	4	2	no	—
271	C₄×D₁₈₁	—	4	2	no	—
272	C₂³×C₁₈₁	C₂⁴	1	2	yes	—
273	C₂³×C₁₈₁	C₂⁴	1	1	yes	characteristic
274	Q₈×C₁₈₁	—	2	2	no	—
275	D₄×C₁₈₁	—	2	2	no	—
276	D₄×C₁₈₁	—	4	2	no	—
277	C₂×C₄×C₁₈₁	—	2	2	no	—
278	C₂×C₄×C₁₈₁	—	4	2	no	—
279	C₂×C₄×C₁₈₁	—	4	1	no	—
280	C₂×C₄×C₁₈₁	—	4	1	no	—
281	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
286	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
287	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
288	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
289	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
290	C₂²×C₁₈₁	—	2	1	no	—
291	C₂²×C₁₈₁	—	2	2	no	—
292	C₂²×C₁₈₁	—	2	1	no	—
293	C₂²×C₁₈₁	—	2	1	no	—
294	C₂²×C₁₈₁	—	2	2	no	—
295	C₂²×C₁₈₁	—	2	2	no	—
296	C₂²×C₁₈₁	C₂⁵	1	1	yes	characteristic
297	C₂×D₁₈₁	—	2	1	no	—
298	C₂×D₁₈₁	—	2	1	no	—
299	C₂×D₁₈₁	—	2	2	no	—
300	C₂×D₁₈₁	—	2	2	no	—
301	C₂×D₁₈₁	—	2	2	no	—
302	C₂×D₁₈₁	—	2	2	no	—
303	C₂×D₁₈₁	—	2	1	no	—
304	C₂×D₁₈₁	—	2	2	no	—
305	C₂×D₁₈₁	—	2	1	no	—
306	C₂×D₁₈₁	—	2	1	no	—
307	C₂×D₁₈₁	—	2	2	no	—
308	C₂×D₁₈₁	—	2	1	no	—
309	C₂×D₁₈₁	—	8	4	no	—
310	C₄×C₁₈₁	—	2	1	no	—
311	C₄×C₁₈₁	—	2	2	no	—
312	C₄×C₁₈₁	—	2	1	no	—
313	C₄×C₁₈₁	—	2	2	no	—
314	C₄×C₁₈₁	—	2	1	no	—
315	C₄×C₁₈₁	—	2	1	no	—
316	C₄×C₁₈₁	—	2	1	no	—
317	C₄×C₁₈₁	—	2	2	no	—
318	C₄×C₁₈₁	H(5,𝔽₂)	1	2	yes	—
319	Dic₁₈₁	—	2	1	no	—
320	Dic₁₈₁	—	2	1	no	—
321	Dic₁₈₁	—	2	2	no	—
322	Dic₁₈₁	—	2	2	no	—
323	Dic₁₈₁	—	2	1	no	—
324	Dic₁₈₁	—	2	1	no	—
325	Dic₁₈₁	—	2	1	no	—
326	Dic₁₈₁	—	2	1	no	—
327	C₂×C₁₈₁	—	4	2	no	—
328	C₂×C₁₈₁	—	4	1	no	—
329	C₂×C₁₈₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
330	C₂×C₁₈₁	#585	1	1	yes	characteristic
331	C₂×C₁₈₁	#585	1	1	yes	characteristic
332	D₁₈₁	—	4	1	no	—
333	D₁₈₁	—	4	2	no	—
334	D₁₈₁	—	4	2	no	—
335	D₁₈₁	—	4	1	no	—
336	C₁₈₁	#3562	1	1	yes	characteristic, complemented, Sylow
337	#3562	—	181	1	no	maximal, Sylow
338	#562	—	181	2	no	—
339	#560	—	181	2	no	—
340	#559	—	181	1	no	—
341	#556	—	181	1	no	—
342	#553	—	181	2	no	—
343	#551	—	181	2	no	—
344	#550	—	181	1	no	—
345	#548	—	181	1	no	—
346	#548	—	181	1	no	—
347	#547	—	181	1	no	—
348	#546	—	181	1	no	—
349	#546	—	181	1	no	—
350	#541	—	181	1	no	—
351	#540	—	181	1	no	—
352	#540	—	181	2	no	—
353	#539	—	181	2	no	—
354	#538	—	181	2	no	—
355	#538	—	181	2	no	—
356	#536	—	181	1	no	—
357	#535	—	181	1	no	—
358	#532	—	181	1	no	—
359	#529	—	181	1	no	—
360	#529	D₁₈₁	1	1	yes	characteristic, complemented
361	C₂×#41	—	181	1	no	—
362	C₂×#41	—	181	1	no	—
363	C₂×#41	—	181	1	no	—
364	C₂×#41	—	181	1	no	—
365	C₂²×Q₈	—	181	1	no	—
366	C₂²×D₄	—	181	1	no	—
367	C₄⋊Q₈	—	181	1	no	—
368	C₄⋊Q₈	—	181	1	no	—
369	#127	—	181	1	no	—
370	#127	—	181	2	no	—
371	#127	—	181	1	no	—
372	#126	—	181	2	no	—
373	#126	—	181	2	no	—
374	#126	—	181	2	no	—
375	#126	—	181	1	no	—
376	#126	—	181	1	no	—
377	#126	—	181	2	no	—
378	#126	C₂×D₁₈₁	1	2	yes	complemented
379	#125	—	181	2	no	—
380	#125	—	181	2	no	—
381	#125	—	181	1	no	—
382	#125	C₂×D₁₈₁	1	1	yes	characteristic, complemented
383	#124	—	181	1	no	—
384	#124	—	181	1	no	—
385	#124	—	181	2	no	—
386	#124	—	181	2	no	—
387	#124	—	181	1	no	—
388	#124	—	181	1	no	—
389	#124	—	181	1	no	—
390	#124	—	181	2	no	—
391	#124	C₂×D₁₈₁	1	1	yes	characteristic
392	#123	—	181	1	no	—
393	#123	—	181	1	no	—
394	#123	—	181	2	no	—
395	#123	—	181	2	no	—
396	#123	—	181	2	no	—
397	#123	—	181	2	no	—
398	#123	—	181	2	no	—
399	#123	—	181	2	no	—
400	#123	—	181	2	no	—
401	#123	—	181	2	no	—
402	#123	—	181	2	no	—
403	#123	—	181	2	no	—
404	#123	C₂×D₁₈₁	1	2	yes	complemented
405	C₂²⋊Q₈	—	181	1	no	—
406	C₂²⋊Q₈	—	181	2	no	—
407	C₂²⋊Q₈	—	181	2	no	—
408	C₂²⋊Q₈	—	181	2	no	—
409	C₂²⋊Q₈	—	181	1	no	—
410	C₂²⋊Q₈	—	181	1	no	—
411	C₂²⋊Q₈	—	181	2	no	—
412	C₂²⋊Q₈	—	181	2	no	—
413	C₂²⋊Q₈	C₂×D₁₈₁	1	1	yes	characteristic, complemented
414	#121	—	181	2	no	—
415	#121	—	181	2	no	—
416	#121	—	181	1	no	—
417	#121	—	181	2	no	—
418	#121	—	181	2	no	—
419	#121	—	181	2	no	—
420	#121	—	181	2	no	—
421	#121	—	181	2	no	—
422	#121	—	181	1	no	—
423	#121	—	181	1	no	—
424	#121	—	181	2	no	—
425	#121	—	181	2	no	—
426	#121	—	181	2	no	—
427	#121	—	181	2	no	—
428	#121	—	181	2	no	—
429	#121	—	181	2	no	—
430	#121	C₂×D₁₈₁	1	1	yes	characteristic
431	#120	—	181	2	no	—
432	#120	—	181	2	no	—
433	#120	—	181	2	no	—
434	#120	—	181	2	no	—
435	C₄×Q₈	—	181	1	no	—
436	C₄×Q₈	—	181	1	no	—
437	C₄×Q₈	—	181	1	no	—
438	C₄×Q₈	C₂×D₁₈₁	1	1	yes	characteristic, complemented
439	C₄×D₄	—	181	1	no	—
440	C₄×D₄	—	181	1	no	—
441	C₄×D₄	—	181	2	no	—
442	C₄×D₄	—	181	2	no	—
443	C₄×D₄	—	181	1	no	—
444	C₄×D₄	—	181	1	no	—
445	C₄×D₄	—	181	2	no	—
446	C₄×D₄	—	181	1	no	—
447	C₄×D₄	—	181	2	no	—
448	C₄×D₄	—	181	2	no	—
449	C₄×D₄	—	181	2	no	—
450	C₄×D₄	C₂×D₁₈₁	1	1	yes	characteristic
451	C₄×D₄	C₂×D₁₈₁	1	2	yes	complemented
452	#117	—	181	1	no	—
453	#117	—	181	1	no	—
454	#117	—	181	2	no	—
455	#117	C₂×D₁₈₁	1	2	yes	complemented
456	C₂×C₄⋊C₄	—	181	2	no	—
457	C₂×C₂²⋊C₄	—	181	2	no	—
458	C₂×C₂²⋊C₄	—	181	2	no	—
459	C₂×C₄²	C₂×D₁₈₁	1	1	yes	characteristic, complemented
460	C₂⁴	—	181	2	no	—
461	#41	—	724	2	no	—
462	#41	—	724	2	no	—
463	#41	—	724	2	no	—
464	#41	—	724	2	no	—
465	C₂×Q₈	—	181	1	no	—
466	C₂×Q₈	—	181	1	no	—
467	C₂×Q₈	—	181	1	no	—
468	C₂×Q₈	—	181	2	no	—
469	C₂×Q₈	—	724	2	no	—
470	C₂×Q₈	C₂²×D₁₈₁	1	1	yes	characteristic
471	C₂×D₄	—	181	1	no	—
472	C₂×D₄	—	181	2	no	—
473	C₂×D₄	—	181	2	no	—
474	C₂×D₄	—	181	1	no	—
475	C₂×D₄	—	181	2	no	—
476	C₂×D₄	—	181	2	no	—
477	C₂×D₄	—	181	2	no	—
478	C₂×D₄	—	181	2	no	—
479	C₂×D₄	—	181	1	no	—
480	C₂×D₄	—	181	1	no	—
481	C₂×D₄	—	181	1	no	—
482	C₂×D₄	—	181	2	no	—
483	C₂×D₄	—	181	2	no	—
484	C₂×D₄	—	181	2	no	—
485	C₂×D₄	—	181	2	no	—
486	C₂×D₄	—	181	2	no	—
487	C₂×D₄	—	724	2	no	—
488	C₂×D₄	C₂²×D₁₈₁	1	1	yes	characteristic
489	C₂×D₄	C₂²×D₁₈₁	1	2	yes	—
490	C₂²×C₄	—	181	1	no	—
491	C₂²×C₄	—	181	1	no	—
492	C₂²×C₄	—	181	2	no	—
493	C₂²×C₄	—	181	2	no	—
494	C₂²×C₄	—	181	2	no	—
495	C₂²×C₄	—	181	2	no	—
496	C₂²×C₄	—	181	2	no	—
497	C₂²×C₄	—	181	2	no	—
498	C₂²×C₄	—	181	2	no	—
499	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
503	C₄⋊C₄	—	181	1	no	—
504	C₄⋊C₄	—	181	2	no	—
505	C₄⋊C₄	—	181	2	no	—
506	C₄⋊C₄	—	181	1	no	—
507	C₄⋊C₄	—	181	1	no	—
508	C₄⋊C₄	—	181	1	no	—
509	C₄⋊C₄	—	181	1	no	—
510	C₄⋊C₄	—	181	1	no	—
511	C₄⋊C₄	—	181	2	no	—
512	C₄⋊C₄	—	181	1	no	—
513	C₄⋊C₄	—	181	1	no	—
514	C₄⋊C₄	—	181	2	no	—
515	C₄⋊C₄	—	181	2	no	—
516	C₄⋊C₄	—	181	2	no	—
517	C₄⋊C₄	—	181	1	no	—
518	C₄⋊C₄	—	181	2	no	—
519	C₄⋊C₄	—	181	2	no	—
520	C₄⋊C₄	—	181	1	no	—
521	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
522	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
523	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
526	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
527	C₂²⋊C₄	—	181	2	no	—
528	C₂²⋊C₄	—	181	2	no	—
529	C₂²⋊C₄	—	181	1	no	—
530	C₂²⋊C₄	—	181	1	no	—
531	C₂²⋊C₄	—	181	1	no	—
532	C₂²⋊C₄	—	181	1	no	—
533	C₂²⋊C₄	—	181	2	no	—
534	C₂²⋊C₄	—	181	2	no	—
535	C₂²⋊C₄	—	181	2	no	—
536	C₂²⋊C₄	—	181	2	no	—
537	C₂²⋊C₄	—	181	1	no	—
538	C₂²⋊C₄	—	181	1	no	—
539	C₂²⋊C₄	—	181	2	no	—
540	C₂²⋊C₄	—	181	1	no	—
541	C₂²⋊C₄	—	181	1	no	—
542	C₂²⋊C₄	—	181	1	no	—
543	C₂²⋊C₄	—	181	1	no	—
544	C₂²⋊C₄	—	181	2	no	—
545	C₂²⋊C₄	—	181	2	no	—
546	C₂²⋊C₄	—	181	2	no	—
547	C₂²⋊C₄	—	181	2	no	—
548	C₂²⋊C₄	—	181	2	no	—
549	C₂²⋊C₄	—	181	2	no	—
550	C₂²⋊C₄	—	181	2	no	—
551	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
556	C₄²	—	181	1	no	—
557	C₄²	—	181	1	no	—
558	C₄²	—	181	2	no	—
559	C₄²	—	181	2	no	—
560	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
561	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
562	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
563	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
564	C₄²	C₂²×D₁₈₁	1	2	yes	—
565	C₂³	—	181	1	no	—
566	C₂³	—	181	2	no	—
567	C₂³	—	181	2	no	—
568	C₂³	—	181	1	no	—
569	C₂³	—	724	2	no	—
570	C₂³	—	724	2	no	—
571	C₂³	—	724	2	no	—
572	C₂³	C₂³×D₁₈₁	1	2	yes	—
573	C₂³	C₂³×D₁₈₁	1	1	yes	characteristic
574	Q₈	—	2	2	no	—
575	Q₈	—	362	2	no	—
576	Q₈	—	362	2	no	—
577	Q₈	—	724	2	no	—
578	Q₈	—	724	1	no	—
579	D₄	—	2	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	362	2	no	—
582	D₄	—	362	2	no	—
583	D₄	—	724	2	no	—
584	D₄	—	724	2	no	—
585	D₄	—	724	2	no	—
586	D₄	—	724	2	no	—
587	D₄	—	724	1	no	—
588	D₄	—	724	2	no	—
589	D₄	—	724	2	no	—
590	D₄	—	724	2	no	—
591	D₄	—	724	2	no	—
592	D₄	—	724	2	no	—
593	D₄	—	724	1	no	—
594	D₄	—	724	1	no	—
595	D₄	—	724	2	no	—
596	D₄	—	724	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	362	2	no	—
602	C₂×C₄	—	362	2	no	—
603	C₂×C₄	—	181	1	no	—
604	C₂×C₄	—	181	1	no	—
605	C₂×C₄	—	181	1	no	—
606	C₂×C₄	—	181	1	no	—
607	C₂×C₄	—	181	2	no	—
608	C₂×C₄	—	181	2	no	—
609	C₂×C₄	—	181	1	no	—
610	C₂×C₄	—	181	1	no	—
611	C₂×C₄	—	724	2	no	—
612	C₂×C₄	—	724	2	no	—
613	C₂×C₄	—	724	2	no	—
614	C₂×C₄	—	724	2	no	—
615	C₂×C₄	—	724	2	no	—
616	C₂×C₄	—	724	2	no	—
617	C₂×C₄	—	724	2	no	—
618	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
619	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
620	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
626	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	362	2	no	—
634	C₂²	—	362	2	no	—
635	C₂²	—	362	1	no	—
636	C₂²	—	362	2	no	—
637	C₂²	—	362	1	no	—
638	C₂²	—	362	2	no	—
639	C₂²	—	362	1	no	—
640	C₂²	—	362	1	no	—
641	C₂²	—	362	1	no	—
642	C₂²	—	362	1	no	—
643	C₂²	—	362	2	no	—
644	C₂²	—	362	2	no	—
645	C₂²	—	1448	4	no	—
646	C₂²	C₂⁴×D₁₈₁	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	362	1	no	—
656	C₄	—	362	1	no	—
657	C₄	—	362	1	no	—
658	C₄	—	362	1	no	—
659	C₄	—	362	1	no	—
660	C₄	—	362	1	no	—
661	C₄	—	362	2	no	—
662	C₄	—	362	2	no	—
663	C₄	#19153862	1	2	yes	—
664	C₂	—	4	2	no	—
665	C₂	—	4	1	no	—
666	C₂	—	724	1	no	—
667	C₂	—	724	2	no	—
668	C₂	—	724	2	no	—
669	C₂	—	724	1	no	—
670	C₂	C₂×#19153862	1	1	yes	characteristic
671	C₂	#26042115	1	1	yes	characteristic
672	C₂	#26042115	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₈₁
commutator, socle, cosocle	C₂²×C₁₈₁	C₂⁵
Fitting	#529×C₁₈₁	C₂
hypercenter	#529	D₁₈₁
hypocenter	C₁₈₁	#3562
LCS	G ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #26042026	C₂	semidirect
2. #26042019	C₂	semidirect
3. #26042012	C₂	semidirect
4. #26042001	C₂	semidirect
5. #26041973	C₂	semidirect
6. #26041953	C₂	semidirect
7. #26041947	C₂	semidirect
8. #26041941	C₂	semidirect
9. #26041939	C₂	semidirect
10. #26041931	C₂	semidirect
11. #26041926	C₂	semidirect
12. #26041924	C₂	semidirect
13. #26041892	C₂	semidirect
14. #26041885	C₂	semidirect
15. #26041880	C₂	semidirect
16. #26041870	C₂	semidirect
17. #26041868	C₂	semidirect
18. #26041862	C₂	semidirect
19. #26041849	C₂	semidirect
20. #26041847	C₂	semidirect
21. #26041829	C₂	semidirect
22. #26041813	C₂	semidirect
23. #529×C₁₈₁	C₂	semidirect
26. C₂×#15668449	C₂²	semidirect
28. C₂×Q₈×D₁₈₁	C₂²	semidirect
30. #19153816	C₂²	semidirect
31. #19153814	C₂²	semidirect
34. #19153812	C₂²	semidirect
37. #19153811	C₂²	semidirect
39. #19153810	C₂²	semidirect
40. #19153810	C₂²	semidirect
41. #19153808	C₂²	semidirect
42. #19153807	C₂²	semidirect
43. #19153807	C₂²	semidirect
48. #19153804	C₂²	semidirect
50. #19153802	C₂²	semidirect
51. #19153802	C₂²	semidirect
53. #19153801	C₂²	semidirect
54. #19153801	C₂²	semidirect
57. #19153799	C₂²	semidirect
58. #19153799	C₂²	semidirect
60. #19153798	C₂²	semidirect
61. #19153798	C₂²	semidirect
62. #19153798	C₂²	semidirect
63. #19153798	C₂²	semidirect
66. #19153796	C₂²	semidirect
67. #19153795	C₂²	semidirect
68. #19153794	C₂²	semidirect
69. #19153794	C₂²	semidirect
70. #19153793	C₂²	semidirect
71. #19153793	C₂²	semidirect
74. #19153791	C₂²	semidirect
75. #19153791	C₂²	semidirect
76. #19153791	C₂²	semidirect
79. #19153790	C₂²	semidirect
80. #19153790	C₂²	semidirect
84. #19153789	C₂²	semidirect
85. #19153789	C₂²	semidirect
86. #19153788	C₂²	semidirect
92. C₄×Dic₃₆₂	C₂²	semidirect
93. #19153781	C₂²	semidirect
94. #19153781	C₂²	semidirect
96. C₄×D₇₂₄	C₂²	semidirect
97. C₄×D₇₂₄	C₂²	semidirect
98. C₄×D₇₂₄	C₂²	semidirect
100. #19153778	C₂²	semidirect
101. #19153778	C₂²	semidirect
103. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
104. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
105. #19153776	C₂²	semidirect
107. #19153773	C₂²	semidirect
108. #19153773	C₂²	semidirect
109. C₄⋊C₄×D₁₈₁	C₂²	semidirect
112. #126×C₁₈₁	C₂²	semidirect
113. #125×C₁₈₁	C₂²	semidirect
115. #123×C₁₈₁	C₂²	semidirect
116. C₂²⋊Q₈×C₁₈₁	C₂²	semidirect
118. C₄×Q₈×C₁₈₁	C₂²	semidirect
120. C₄×D₄×C₁₈₁	C₂²	semidirect
121. #117×C₁₈₁	C₂²	semidirect
122. C₂×C₄²×C₁₈₁	C₂²	semidirect
336. C₁₈₁	#3562	semidirect
360. #529	D₁₈₁	semidirect
378. #126	C₂×D₁₈₁	semidirect
382. #125	C₂×D₁₈₁	semidirect
404. #123	C₂×D₁₈₁	semidirect
413. C₂²⋊Q₈	C₂×D₁₈₁	semidirect
438. C₄×Q₈	C₂×D₁₈₁	semidirect
451. C₄×D₄	C₂×D₁₈₁	semidirect
455. #117	C₂×D₁₈₁	semidirect
459. C₂×C₄²	C₂×D₁₈₁	semidirect

Maximal subgroups

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

subgroup	index
#26042026	2
#26042019	2
#26042012	2
#26042001	2
#26041973	2
#26041953	2
#26041947	2
#26041941	2
#26041939	2
#26041931	2
#26041926	2
#26041924	2
#26041892	2
#26041885	2
#26041880	2
#26041870	2
#26041868	2
#26041862	2
#26041849	2
#26041847	2
#26041829	2
#26041813	2
#529×C₁₈₁	2
#3562	181