Subgroups — #72261078

Order 2048.

At least 10575 conjugacy classes of subgroups; only the 1246 normal subgroups are shown.

The subgroup lattice has 508 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72261070	C₂	1	1	yes	maximal, characteristic, complemented
2	#72261068	C₂	1	1	yes	maximal, characteristic, complemented
3	#72261063	C₂	1	1	yes	maximal, characteristic, complemented
4	#72261051	C₂	1	1	yes	maximal, characteristic, complemented
5	#72261045	C₂	1	2	yes	maximal, complemented
6	#72261041	C₂	1	2	yes	maximal, complemented
7	#72261039	C₂	1	2	yes	maximal, complemented
8	#72261031	C₂	1	2	yes	maximal, complemented
9	#72261029	C₂	1	4	yes	maximal, complemented
10	#72261023	C₂	1	4	yes	maximal, complemented
11	#72234968	C₂	1	1	yes	maximal, characteristic, complemented
12	#72234135	C₂	1	1	yes	maximal, characteristic, complemented
13	#72233910	C₂	1	1	yes	maximal, characteristic, complemented
14	#72233314	C₂	1	2	yes	maximal, complemented
15	#72233299	C₂	1	2	yes	maximal, complemented
16	#72233137	C₂	1	2	yes	maximal, complemented
17	#72232727	C₂	1	2	yes	maximal, complemented
18	C₂×#62905	C₂²	1	1	yes	characteristic, complemented
19	C₂×D₄×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
20	#7805069	C₂²	1	2	yes	complemented
21	#7759611	C₂²	1	2	yes	complemented
22	#7733603	C₂²	1	2	yes	—
23	#7677051	C₂²	1	2	yes	—
24	#7645255	C₂²	1	1	yes	characteristic
25	C₂×#38080	C₂²	1	1	yes	characteristic
26	#7631719	C₂²	1	1	yes	characteristic, complemented
27	#7631286	C₂²	1	2	yes	complemented
28	#7631286	C₂²	1	1	yes	characteristic, complemented
29	#7628721	C₂²	1	1	yes	characteristic, complemented
30	#7626245	C₂²	1	1	yes	characteristic, complemented
31	#6629386	C₂²	1	2	yes	complemented
32	#6628867	C₂²	1	2	yes	complemented
33	C₂×#32888	C₂²	1	1	yes	characteristic, complemented
34	#6487644	C₂²	1	2	yes	—
35	#6487644	C₂²	1	4	yes	complemented
36	#6451827	C₂²	1	2	yes	complemented
37	#6451765	C₂²	1	4	yes	complemented
38	#6385971	C₂²	1	2	yes	complemented
39	#6385971	C₂²	1	1	yes	characteristic, complemented
40	C₂×#20616	C₂²	1	1	yes	characteristic, complemented
41	#6346649	C₂²	1	4	yes	complemented
42	#6346377	C₂²	1	2	yes	complemented
43	#405108	C₂²	1	4	yes	complemented
44	#405096	C₂²	1	2	yes	complemented
45	#394261	C₂²	1	4	yes	complemented
46	#394257	C₂²	1	2	yes	complemented
47	#374052	C₂²	1	1	yes	characteristic, complemented
48	#374045	C₂²	1	2	yes	complemented
49	#364422	C₂²	1	4	yes	complemented
50	#364391	C₂²	1	2	yes	complemented
51	#359869	C₂²	1	2	yes	complemented
52	#359829	C₂²	1	1	yes	characteristic, complemented
53	#359583	C₂²	1	2	yes	complemented
54	#359583	C₂²	1	1	yes	characteristic, complemented
55	#234946	C₂²	1	4	yes	complemented
56	#234936	C₂²	1	4	yes	complemented
57	#234923	C₂²	1	4	yes	complemented
58	#201475	C₂²	1	4	yes	complemented
59	#201464	C₂²	1	2	yes	complemented
60	#201336	C₂²	1	2	yes	complemented
61	#201336	C₂²	1	2	yes	complemented
62	#201293	C₂²	1	2	yes	complemented
63	#188087	C₂²	1	2	yes	complemented
64	#188087	C₂²	1	1	yes	characteristic, complemented
65	#187961	C₂²	1	2	yes	complemented
66	#187961	C₂²	1	4	yes	complemented
67	#187186	C₂²	1	4	yes	complemented
68	#186995	C₂²	1	4	yes	complemented
69	#185863	C₂²	1	2	yes	complemented
70	#185481	C₂²	1	2	yes	complemented
71	#184911	C₂²	1	2	yes	complemented
72	#115650	C₂²	1	2	yes	complemented
73	#115378	C₂²	1	4	yes	complemented
74	#112870	C₂²	1	4	yes	complemented
75	#112581	C₂²	1	4	yes	complemented
76	#111981	C₂²	1	4	yes	complemented
77	#111963	C₂²	1	4	yes	complemented
78	#111915	C₂²	1	2	yes	complemented
79	#108266	C₂²	1	4	yes	complemented
80	#106344	C₂²	1	2	yes	complemented
81	#106089	C₂²	1	4	yes	complemented
82	#105580	C₂²	1	2	yes	complemented
83	C₂³×H(5,𝔽₂)	D₄	1	2	yes	—
84	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
85	C₂×#3494	C₂³	1	2	yes	—
86	C₂×#3496	C₂³	1	1	yes	characteristic
87	C₂×#3496	C₂³	1	2	yes	—
88	C₂×#3484	D₄	1	4	yes	—
89	C₂×#3484	D₄	1	2	yes	—
90	C₂×#3537	C₂³	1	2	yes	—
91	C₂²×#553	C₂³	1	1	yes	characteristic
92	C₂²×D₄²	C₂³	1	1	yes	characteristic
93	C₂²×D₄²	C₂³	1	2	yes	—
94	C₂×#3459	C₂³	1	1	yes	characteristic
95	C₂×C₄×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
96	#60359	C₂³	1	4	yes	complemented
97	C₂×#3006	C₂³	1	2	yes	complemented
98	C₂²×#421	C₂³	1	2	yes	complemented
99	C₂×#2896	C₂³	1	2	yes	complemented
100	C₂³×#100	C₂³	1	1	yes	characteristic
101	#37437	C₂³	1	2	yes	—
102	#37185	D₄	1	4	yes	complemented
103	#36717	D₄	1	4	yes	complemented
104	#36703	D₄	1	4	yes	complemented
105	C₂×#2856	D₄	1	1	yes	characteristic, complemented
106	#35584	D₄	1	2	yes	complemented
107	#35563	D₄	1	2	yes	complemented
108	#35554	D₄	1	2	yes	complemented
109	#35528	D₄	1	2	yes	complemented
110	#35395	D₄	1	4	yes	complemented
111	#35390	D₄	1	2	yes	complemented
112	#35390	D₄	1	4	yes	complemented
113	#35367	D₄	1	2	yes	complemented
114	#35250	C₂³	1	4	yes	—
115	#35250	C₂³	1	2	yes	—
116	#35222	D₄	1	2	yes	complemented
117	#35222	C₂³	1	2	yes	—
118	#35174	D₄	1	2	yes	complemented
119	#35076	C₂³	1	2	yes	—
120	#34957	C₂³	1	2	yes	—
121	C₂×#2541	D₄	1	1	yes	characteristic, complemented
122	C₂×#2566	D₄	1	1	yes	characteristic, complemented
123	#34809	C₂³	1	2	yes	—
124	C₂×#2500	C₂³	1	1	yes	characteristic
125	C₂×#2504	D₄	1	1	yes	characteristic, complemented
126	#34737	C₂³	1	2	yes	—
127	#34736	C₂³	1	2	yes	—
128	#34736	C₂³	1	4	yes	—
129	C₂×#2433	D₄	1	1	yes	characteristic, complemented
130	C₂×#2433	C₂³	1	1	yes	characteristic
131	C₂×#2641	D₄	1	1	yes	characteristic, complemented
132	C₂×#2619	C₂³	1	1	yes	characteristic
133	#34265	D₄	1	2	yes	complemented
134	#34246	C₂³	1	2	yes	—
135	#34204	C₂³	1	2	yes	—
136	#34185	C₂³	1	1	yes	characteristic
137	#34171	D₄	1	2	yes	complemented
138	#34171	C₂³	1	2	yes	—
139	#34171	C₂³	1	1	yes	characteristic
140	C₂×#2328	D₄	1	1	yes	characteristic, complemented
141	C₂×#2309	C₂³	1	1	yes	characteristic
142	C₂²×#390	D₄	1	1	yes	characteristic, complemented
143	C₂×#2290	C₂³	1	1	yes	characteristic
144	#25899	D₄	1	8	yes	complemented
145	#25771	D₄	1	8	yes	complemented
146	#21793	C₂³	1	2	yes	—
147	#21793	C₂³	1	4	yes	—
148	C₂×#1900	C₂³	1	4	yes	—
149	C₂×#1900	C₂³	1	2	yes	—
150	#20973	C₂³	1	2	yes	complemented
151	#20902	C₂³	1	4	yes	complemented
152	#20898	C₂³	1	2	yes	—
153	#20898	C₂³	1	4	yes	—
154	#20722	C₂³	1	4	yes	—
155	#20722	C₂³	1	2	yes	—
156	#20705	C₂³	1	4	yes	complemented
157	#20701	C₂³	1	2	yes	complemented
158	#20605	C₂³	1	4	yes	complemented
159	C₂×#1789	C₂³	1	2	yes	complemented
160	C₂×#1783	C₂³	1	2	yes	—
161	C₂×#1783	C₂³	1	1	yes	characteristic
162	#17577	C₂³	1	4	yes	complemented
163	#17559	C₂³	1	4	yes	complemented
164	#17559	C₂³	1	4	yes	complemented
165	#17396	C₂³	1	4	yes	—
166	#17396	C₂³	1	2	yes	—
167	#17362	C₂³	1	2	yes	—
168	#17362	C₂³	1	4	yes	—
169	#10732	C₂³	1	2	yes	complemented
170	#10720	C₂³	1	2	yes	complemented
171	#10717	C₂³	1	4	yes	complemented
172	#10716	C₂³	1	4	yes	complemented
173	#7946	C₂³	1	4	yes	complemented
174	#7946	C₂³	1	4	yes	complemented
175	#7942	C₂³	1	4	yes	complemented
176	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
177	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
178	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
179	C₂³×#41	C₂⁴	1	2	yes	—
180	C₂⁴×D₄	C₂×D₄	1	4	yes	—
181	C₂⁴×D₄	C₂×D₄	1	2	yes	—
182	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
183	C₂⁴×D₄	C₂×D₄	1	2	yes	—
184	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
185	C₂³×M₁₆	C₂⁴	1	2	yes	—
186	#3496	C₂×D₄	1	8	yes	—
187	C₂×#544	C₂×D₄	1	2	yes	complemented
188	C₂×#543	C₂×D₄	1	1	yes	characteristic, complemented
189	C₂×#539	C₂×D₄	1	2	yes	complemented
190	C₂×#538	C₂×D₄	1	4	yes	complemented
191	C₂×#535	C₂×D₄	1	2	yes	—
192	C₂×#535	C₂×D₄	1	2	yes	—
193	C₂×#535	C₂×D₄	1	2	yes	complemented
194	C₂×#534	C₂×D₄	1	2	yes	—
195	C₂×#534	C₂×D₄	1	4	yes	—
196	C₂×#534	C₂×D₄	1	4	yes	complemented
197	C₂×#534	C₂×D₄	1	1	yes	characteristic, complemented
198	C₂²×#127	C₂×D₄	1	1	yes	characteristic
199	C₂²×#127	C₂×D₄	1	2	yes	—
200	C₂²×#127	C₂×D₄	1	1	yes	characteristic
201	C₂²×#127	C₂×D₄	1	1	yes	characteristic
202	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
203	C₂²×#125	C₂×D₄	1	1	yes	characteristic, complemented
204	C₂×#525	C₂×D₄	1	2	yes	complemented
205	C₂×#525	C₂⁴	1	2	yes	—
206	C₂²×#121	C₂×D₄	1	2	yes	—
207	C₂²×#121	C₂×D₄	1	1	yes	characteristic
208	C₂²×#121	C₂×D₄	1	4	yes	—
209	C₂²×#121	C₂×D₄	1	2	yes	—
210	C₂²×#121	C₂×D₄	1	1	yes	characteristic, complemented
211	C₂²×#121	C₂⁴	1	1	yes	characteristic
212	C₂²×#121	C₂⁴	1	1	yes	characteristic
213	C₂²×#121	C₂⁴	1	2	yes	—
214	C₂²×#120	C₂×D₄	1	4	yes	—
215	C₂²×#120	C₂×D₄	1	2	yes	—
216	C₂²×#120	C₂×D₄	1	2	yes	—
217	C₂²×#120	C₂×D₄	1	4	yes	—
218	C₂×#520	C₂×D₄	1	2	yes	complemented
219	C₂×#518	C₂×D₄	1	1	yes	characteristic
220	C₂×#518	C₂×D₄	1	2	yes	—
221	C₂×#518	C₂×D₄	1	2	yes	complemented
222	C₂×#518	C₂×D₄	1	2	yes	complemented
223	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
225	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic, complemented
226	C₂²×C₄×D₄	C₂⁴	1	2	yes	—
227	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
228	C₂²×#117	C₂⁴	1	1	yes	characteristic
229	C₂²×#117	C₂⁴	1	1	yes	characteristic
230	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
231	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
232	C₂×#407	C₂⁴	1	4	yes	—
233	C₂×#407	C₂⁴	1	2	yes	—
234	#2591	C₂×D₄	1	4	yes	complemented
235	#2591	C₂×D₄	1	2	yes	complemented
236	#2583	C₂×D₄	1	2	yes	complemented
237	#2561	C₂×D₄	1	2	yes	complemented
238	#2561	C₂×D₄	1	4	yes	complemented
239	#2539	C₂×D₄	1	4	yes	complemented
240	#2539	C₂×D₄	1	4	yes	complemented
241	#2539	C₂×D₄	1	2	yes	complemented
242	#2436	C₂×D₄	1	8	yes	complemented
243	#2435	C₂×D₄	1	4	yes	—
244	#2435	C₂×D₄	1	4	yes	—
245	#2433	C₂×D₄	1	4	yes	—
246	#2433	C₂×D₄	1	4	yes	—
247	#2433	C₂×D₄	1	4	yes	—
248	#2433	C₂×D₄	1	4	yes	—
249	#2433	C₂×D₄	1	8	yes	complemented
250	#2409	C₂×D₄	1	4	yes	complemented
251	#2408	C₂×D₄	1	4	yes	complemented
252	#2316	C₂×D₄	1	2	yes	complemented
253	#2313	C₂×D₄	1	2	yes	complemented
254	#2312	C₂×D₄	1	4	yes	complemented
255	#2309	C₂×D₄	1	2	yes	—
256	#2309	C₂×D₄	1	2	yes	—
257	#2309	C₂×D₄	1	2	yes	—
258	#2309	C₂×D₄	1	2	yes	—
259	#2309	C₂×D₄	1	2	yes	—
260	#2309	C₂×D₄	1	2	yes	—
261	#2309	C₂×D₄	1	2	yes	complemented
262	#2297	C₂×D₄	1	2	yes	complemented
263	#2296	C₂×D₄	1	2	yes	complemented
264	#2296	C₂×D₄	1	2	yes	complemented
265	#2296	C₂×D₄	1	2	yes	complemented
266	C₂×#390	C₂×D₄	1	1	yes	characteristic
267	C₂×#390	C₂×D₄	1	1	yes	characteristic
268	C₂×#390	C₂×D₄	1	1	yes	characteristic
269	C₂×#390	C₂×D₄	1	1	yes	characteristic
270	C₂×#390	C₂×D₄	1	1	yes	characteristic
271	C₂×#390	C₂×D₄	1	1	yes	characteristic
272	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
273	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
274	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
275	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
276	C₂×#384	C₂×D₄	1	1	yes	characteristic, complemented
277	C₂×#382	C₂×D₄	1	1	yes	characteristic, complemented
278	C₂×#382	C₂×D₄	1	1	yes	characteristic, complemented
279	#2280	C₂×D₄	1	2	yes	complemented
280	#2280	C₂×D₄	1	2	yes	complemented
281	#2280	C₂×D₄	1	2	yes	complemented
282	#2280	C₂⁴	1	2	yes	—
283	#2280	C₂⁴	1	4	yes	—
284	#2280	C₂⁴	1	2	yes	—
285	#2274	C₂×D₄	1	2	yes	complemented
286	#2273	C₂×D₄	1	2	yes	complemented
287	#2273	C₂×D₄	1	4	yes	complemented
288	C₂×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
289	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
290	C₂×C₄×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
291	C₂×#376	C₂×D₄	1	1	yes	characteristic, complemented
292	#1964	C₂×D₄	1	16	yes	complemented
293	C₄×#99	C₂×D₄	1	8	yes	complemented
294	C₂⁶	#120	1	2	yes	—
295	C₂⁶	#120	1	4	yes	—
296	C₂⁶	C₂²×D₄	1	2	yes	—
297	C₂×H(5,𝔽₂)	#120	1	8	yes	—
298	C₂²×#41	C₂²×D₄	1	2	yes	—
299	C₂³×Q₈	C₂²×D₄	1	2	yes	—
300	C₂³×D₄	#120	1	2	yes	—
301	C₂³×D₄	#120	1	4	yes	—
302	C₂³×D₄	#120	1	2	yes	—
303	C₂³×D₄	#120	1	2	yes	—
304	C₂³×D₄	#120	1	4	yes	—
305	C₂³×D₄	#120	1	4	yes	—
306	C₂³×D₄	#120	1	4	yes	—
307	C₂³×D₄	#120	1	2	yes	—
308	C₂³×D₄	C₂²×D₄	1	2	yes	—
309	C₂³×D₄	C₂²×D₄	1	2	yes	—
310	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
311	C₂³×D₄	C₂²×D₄	1	4	yes	—
312	C₂³×D₄	C₂²×D₄	1	2	yes	—
313	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
314	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
315	C₂³×D₄	C₂²×D₄	1	2	yes	—
316	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
317	C₂³×D₄	C₂²×D₄	1	2	yes	—
318	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
319	C₂³×D₄	C₂²×D₄	1	2	yes	—
320	C₂³×D₄	C₂²×D₄	1	4	yes	—
321	C₂³×D₄	C₂²×D₄	1	2	yes	—
322	C₂⁴×C₄	#120	1	4	yes	—
323	C₂⁴×C₄	#120	1	2	yes	—
324	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
325	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
326	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
327	#534	#120	1	8	yes	—
328	C₂×#127	#120	1	4	yes	—
329	C₂×#127	#120	1	4	yes	—
330	C₂×#127	#120	1	2	yes	—
331	C₂×#127	#120	1	2	yes	—
332	C₂×#127	#120	1	4	yes	—
333	C₂×#124	#120	1	4	yes	—
334	C₂×#124	#120	1	4	yes	—
335	C₂×C₂²⋊Q₈	C₂²×D₄	1	2	yes	—
336	C₂×C₂²⋊Q₈	C₂²×D₄	1	2	yes	—
337	C₂×#121	C₂²×D₄	1	4	yes	—
338	C₂×#121	C₂²×D₄	1	2	yes	—
339	C₂×#121	C₂²×D₄	1	2	yes	—
340	C₂×#121	C₂²×D₄	1	8	yes	—
341	C₂×#121	H(5,𝔽₂)	1	8	yes	—
342	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
343	C₂×C₄×D₄	H(5,𝔽₂)	1	4	yes	—
344	C₂×#117	C₂²×D₄	1	2	yes	—
345	C₂×#117	C₂²×D₄	1	2	yes	—
346	C₂×#117	C₂²×D₄	1	2	yes	—
347	C₂×#117	C₂²×D₄	1	2	yes	—
348	C₂×#117	C₂²×D₄	1	2	yes	—
349	C₂×#117	C₂²×D₄	1	2	yes	—
350	C₂×#117	C₂²×D₄	1	2	yes	—
351	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
352	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
353	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
354	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
355	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
356	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
357	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
358	C₂²×C₂²⋊C₄	#120	1	2	yes	—
359	C₂²×C₂²⋊C₄	#120	1	4	yes	—
360	C₂²×C₂²⋊C₄	#120	1	4	yes	—
361	C₂²×C₂²⋊C₄	#120	1	2	yes	—
362	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
363	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
364	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
365	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
366	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
367	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
368	C₂²×C₄²	C₂²×D₄	1	2	yes	—
369	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
370	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
371	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
372	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
373	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
374	#390	#120	1	2	yes	—
375	#390	#120	1	2	yes	—
376	#390	#120	1	1	yes	characteristic
377	#390	#120	1	1	yes	characteristic
378	#390	#120	1	1	yes	characteristic
379	#390	#120	1	1	yes	characteristic
380	#390	#120	1	2	yes	—
381	#390	#120	1	2	yes	—
382	#390	#120	1	2	yes	—
383	#390	#120	1	2	yes	—
384	#390	#120	1	4	yes	—
385	#390	#120	1	4	yes	—
386	#390	#120	1	4	yes	—
387	#390	#120	1	4	yes	—
388	#390	#120	1	2	yes	—
389	#390	#120	1	2	yes	—
390	#390	#120	1	4	yes	—
391	#380	C₂²×D₄	1	4	yes	—
392	C₄×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
393	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
394	C₄×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
395	C₄×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
396	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
397	C₂⁵	C₂×#120	1	1	yes	characteristic
398	C₂⁵	C₂×#120	1	2	yes	—
399	C₂⁵	C₂×#120	1	4	yes	—
400	C₂⁵	C₂×#120	1	2	yes	—
401	C₂⁵	C₂×#120	1	2	yes	—
402	C₂⁵	C₂×#120	1	2	yes	—
403	C₂⁵	C₂×#120	1	4	yes	—
404	C₂⁵	C₂×#120	1	4	yes	—
405	C₂⁵	C₂³×D₄	1	1	yes	characteristic
406	C₂²×Q₈	C₂×#120	1	2	yes	—
407	C₂²×D₄	C₂×#120	1	2	yes	—
408	C₂²×D₄	C₂×#120	1	8	yes	—
409	C₂²×D₄	C₂×#120	1	2	yes	—
410	C₂²×D₄	C₂×#120	1	1	yes	characteristic
411	C₂²×D₄	C₂×#120	1	4	yes	—
412	C₂²×D₄	C₂×#120	1	2	yes	—
413	C₂²×D₄	C₂×#120	1	1	yes	characteristic
414	C₂²×D₄	C₂×#120	1	2	yes	—
415	C₂²×D₄	C₂×#120	1	2	yes	—
416	C₂²×D₄	C₂×#120	1	4	yes	—
417	C₂²×D₄	C₂×#120	1	2	yes	—
418	C₂²×D₄	#534	1	2	yes	—
419	C₂²×D₄	#534	1	8	yes	—
420	C₂²×D₄	D₄²	1	8	yes	—
421	C₂³×C₄	C₂×#120	1	2	yes	—
422	C₂³×C₄	C₂×#120	1	2	yes	—
423	C₂³×C₄	C₂×#120	1	2	yes	—
424	C₂³×C₄	C₂×#120	1	2	yes	—
425	C₂³×C₄	C₂×#120	1	1	yes	characteristic
426	C₂³×C₄	C₂×#120	1	1	yes	characteristic
427	C₂³×C₄	C₂×#120	1	1	yes	characteristic
428	C₂³×C₄	C₂×#120	1	4	yes	—
429	C₂³×C₄	D₄²	1	4	yes	—
430	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
431	C₂³×C₄	C₂³×D₄	1	2	yes	—
432	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
433	C₂³×C₄	C₂³×D₄	1	2	yes	—
434	C₂³×C₄	C₂³×D₄	1	2	yes	—
435	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
436	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
437	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
440	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
441	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
442	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
443	C₂×C₄⋊C₄	D₄²	1	8	yes	—
444	C₂×C₄⋊C₄	D₄²	1	4	yes	—
445	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
446	C₂×C₂²⋊C₄	#534	1	2	yes	—
447	C₂×C₂²⋊C₄	D₄²	1	4	yes	—
448	C₂×C₂²⋊C₄	D₄²	1	16	yes	—
449	C₂×C₄²	C₂×#120	1	2	yes	—
450	C₂×C₄²	C₂×#120	1	1	yes	characteristic
451	C₂×C₄²	C₂×#120	1	1	yes	characteristic
452	C₂×C₄²	C₂×#120	1	4	yes	—
453	C₂×C₄²	C₂×#120	1	4	yes	—
454	C₂×C₄²	C₂×#120	1	2	yes	—
455	C₂×C₄²	C₂×#120	1	1	yes	characteristic
456	C₂×C₄²	C₂×#120	1	1	yes	characteristic
457	C₂×C₄²	D₄²	1	4	yes	—
458	C₂⁴	#2403	1	2	yes	—
459	C₂⁴	#2403	1	8	yes	—
460	C₂⁴	#2846	1	4	yes	—
461	C₂⁴	#2846	1	2	yes	—
462	C₂⁴	#2846	1	2	yes	—
463	C₂⁴	C₂²×#120	1	1	yes	characteristic
464	C₂⁴	C₂²×#120	1	2	yes	—
465	C₂⁴	C₂²×#120	1	1	yes	characteristic
466	C₂⁴	C₂×#534	1	1	yes	characteristic
467	C₂⁴	C₂×#534	1	2	yes	—
468	C₂×D₄	#3025	1	2	yes	—
469	C₂×D₄	#3027	1	2	yes	—
470	C₂²×C₄	#2403	1	2	yes	—
471	C₂²×C₄	#2403	1	2	yes	—
472	C₂²×C₄	#2403	1	8	yes	—
473	C₂²×C₄	#2403	1	2	yes	—
474	C₂²×C₄	C₂²×#120	1	2	yes	—
475	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
476	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄²	1	4	yes	—
478	C₂²×C₄	C₂×D₄²	1	2	yes	—
479	C₂²×C₄	C₂×D₄²	1	2	yes	—
480	C₂²×C₄	C₂×D₄²	1	4	yes	—
481	C₂²×C₄	#3484	1	2	yes	—
482	C₂²×C₄	#3484	1	4	yes	—
483	C₂²×C₄	#3484	1	2	yes	—
484	C₂²×C₄	#3484	1	4	yes	—
485	C₂³	#23897	1	4	yes	—
486	C₂³	#32899	1	4	yes	—
487	C₂³	C₂×#2403	1	2	yes	—
488	C₂³	C₂×#2403	1	1	yes	characteristic
489	C₂³	#34980	1	2	yes	—
490	C₂³	#34980	1	1	yes	characteristic
491	C₂³	C₂×#2846	1	1	yes	characteristic
492	C₂×C₄	D₄×#120	1	2	yes	—
493	C₂×C₄	D₄×#120	1	4	yes	—
494	C₂×C₄	D₄×#120	1	2	yes	—
495	C₂×C₄	C₂×#3025	1	1	yes	characteristic
496	C₂×C₄	C₂×#3027	1	1	yes	characteristic
497	C₂×C₄	#60399	1	2	yes	—
498	C₂²	#612424	1	1	yes	characteristic
499	C₂²	C₂×#23897	1	2	yes	—
500	C₂²	C₂×#32899	1	1	yes	characteristic
501	C₂²	#6628896	1	1	yes	characteristic
502	C₄	#6573710	1	2	yes	—
503	C₄	#6573716	1	2	yes	—
504	C₂	#72210511	1	1	yes	characteristic
505	C₂	#72240574	1	1	yes	characteristic
506	C₂	#72260694	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#612424
commutator, Frattini, cosocle	C₂⁴×C₄	C₂⁵
LCS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72261070	C₂	semidirect
2. #72261068	C₂	semidirect
3. #72261063	C₂	semidirect
4. #72261051	C₂	semidirect
5. #72261045	C₂	semidirect
6. #72261041	C₂	semidirect
7. #72261039	C₂	semidirect
8. #72261031	C₂	semidirect
9. #72261029	C₂	semidirect
10. #72261023	C₂	semidirect
11. #72234968	C₂	semidirect
12. #72234135	C₂	semidirect
13. #72233910	C₂	semidirect
14. #72233314	C₂	semidirect
15. #72233299	C₂	semidirect
16. #72233137	C₂	semidirect
17. #72232727	C₂	semidirect
18. C₂×#62905	C₂²	semidirect
20. #7805069	C₂²	semidirect
21. #7759611	C₂²	semidirect
26. #7631719	C₂²	semidirect
27. #7631286	C₂²	semidirect
28. #7631286	C₂²	semidirect
29. #7628721	C₂²	semidirect
30. #7626245	C₂²	semidirect
31. #6629386	C₂²	semidirect
32. #6628867	C₂²	semidirect
33. C₂×#32888	C₂²	semidirect
35. #6487644	C₂²	semidirect
36. #6451827	C₂²	semidirect
37. #6451765	C₂²	semidirect
38. #6385971	C₂²	semidirect
39. #6385971	C₂²	semidirect
40. C₂×#20616	C₂²	semidirect
41. #6346649	C₂²	semidirect
42. #6346377	C₂²	semidirect
43. #405108	C₂²	semidirect
44. #405096	C₂²	semidirect
45. #394261	C₂²	semidirect
46. #394257	C₂²	semidirect
47. #374052	C₂²	semidirect
48. #374045	C₂²	semidirect
49. #364422	C₂²	semidirect
50. #364391	C₂²	semidirect
51. #359869	C₂²	semidirect
52. #359829	C₂²	semidirect
53. #359583	C₂²	semidirect
54. #359583	C₂²	semidirect
55. #234946	C₂²	semidirect
56. #234936	C₂²	semidirect
57. #234923	C₂²	semidirect
58. #201475	C₂²	semidirect
59. #201464	C₂²	semidirect
60. #201336	C₂²	semidirect
61. #201336	C₂²	semidirect
62. #201293	C₂²	semidirect
63. #188087	C₂²	semidirect
64. #188087	C₂²	semidirect
65. #187961	C₂²	semidirect
66. #187961	C₂²	semidirect
67. #187186	C₂²	semidirect
68. #186995	C₂²	semidirect
69. #185863	C₂²	semidirect
70. #185481	C₂²	semidirect
71. #184911	C₂²	semidirect
72. #115650	C₂²	semidirect
73. #115378	C₂²	semidirect
74. #112870	C₂²	semidirect
75. #112581	C₂²	semidirect
76. #111981	C₂²	semidirect
77. #111963	C₂²	semidirect
78. #111915	C₂²	semidirect
79. #108266	C₂²	semidirect
80. #106344	C₂²	semidirect
81. #106089	C₂²	semidirect
82. #105580	C₂²	semidirect
96. #60359	C₂³	semidirect
97. C₂×#3006	C₂³	semidirect
98. C₂²×#421	C₂³	semidirect
99. C₂×#2896	C₂³	semidirect
102. #37185	D₄	semidirect
103. #36717	D₄	semidirect
104. #36703	D₄	semidirect
105. C₂×#2856	D₄	semidirect
106. #35584	D₄	semidirect
107. #35563	D₄	semidirect
108. #35554	D₄	semidirect
109. #35528	D₄	semidirect
110. #35395	D₄	semidirect
111. #35390	D₄	semidirect
112. #35390	D₄	semidirect
113. #35367	D₄	semidirect
116. #35222	D₄	semidirect
118. #35174	D₄	semidirect
121. C₂×#2541	D₄	semidirect
122. C₂×#2566	D₄	semidirect
125. C₂×#2504	D₄	semidirect
129. C₂×#2433	D₄	semidirect
131. C₂×#2641	D₄	semidirect
133. #34265	D₄	semidirect
137. #34171	D₄	semidirect
140. C₂×#2328	D₄	semidirect
142. C₂²×#390	D₄	semidirect
144. #25899	D₄	semidirect
145. #25771	D₄	semidirect
150. #20973	C₂³	semidirect
151. #20902	C₂³	semidirect
156. #20705	C₂³	semidirect
157. #20701	C₂³	semidirect
158. #20605	C₂³	semidirect
159. C₂×#1789	C₂³	semidirect
162. #17577	C₂³	semidirect
163. #17559	C₂³	semidirect
164. #17559	C₂³	semidirect
169. #10732	C₂³	semidirect
170. #10720	C₂³	semidirect
171. #10717	C₂³	semidirect
172. #10716	C₂³	semidirect
173. #7946	C₂³	semidirect
174. #7946	C₂³	semidirect
175. #7942	C₂³	semidirect
187. C₂×#544	C₂×D₄	semidirect
188. C₂×#543	C₂×D₄	semidirect
189. C₂×#539	C₂×D₄	semidirect
190. C₂×#538	C₂×D₄	semidirect
193. C₂×#535	C₂×D₄	semidirect
196. C₂×#534	C₂×D₄	semidirect
197. C₂×#534	C₂×D₄	semidirect
202. C₂²×#127	C₂×D₄	semidirect
203. C₂²×#125	C₂×D₄	semidirect
204. C₂×#525	C₂×D₄	semidirect
210. C₂²×#121	C₂×D₄	semidirect
218. C₂×#520	C₂×D₄	semidirect
221. C₂×#518	C₂×D₄	semidirect
222. C₂×#518	C₂×D₄	semidirect
225. C₂²×C₄×D₄	C₂×D₄	semidirect
230. C₂³×C₄⋊C₄	C₂×D₄	semidirect
231. C₂³×C₄²	C₂×D₄	semidirect
234. #2591	C₂×D₄	semidirect
235. #2591	C₂×D₄	semidirect
236. #2583	C₂×D₄	semidirect
237. #2561	C₂×D₄	semidirect
238. #2561	C₂×D₄	semidirect
239. #2539	C₂×D₄	semidirect
240. #2539	C₂×D₄	semidirect
241. #2539	C₂×D₄	semidirect
242. #2436	C₂×D₄	semidirect
249. #2433	C₂×D₄	semidirect
250. #2409	C₂×D₄	semidirect
251. #2408	C₂×D₄	semidirect
252. #2316	C₂×D₄	semidirect
253. #2313	C₂×D₄	semidirect
254. #2312	C₂×D₄	semidirect
261. #2309	C₂×D₄	semidirect
262. #2297	C₂×D₄	semidirect
263. #2296	C₂×D₄	semidirect
264. #2296	C₂×D₄	semidirect
265. #2296	C₂×D₄	semidirect
272. C₂×#390	C₂×D₄	semidirect
273. C₂×#390	C₂×D₄	semidirect
274. C₂×#390	C₂×D₄	semidirect
275. C₂×#390	C₂×D₄	semidirect
276. C₂×#384	C₂×D₄	semidirect
277. C₂×#382	C₂×D₄	semidirect
278. C₂×#382	C₂×D₄	semidirect
279. #2280	C₂×D₄	semidirect
280. #2280	C₂×D₄	semidirect
281. #2280	C₂×D₄	semidirect
285. #2274	C₂×D₄	semidirect
286. #2273	C₂×D₄	semidirect
287. #2273	C₂×D₄	semidirect
288. C₂×C₄×C₄⋊C₄	C₂×D₄	semidirect
289. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
291. C₂×#376	C₂×D₄	semidirect
292. #1964	C₂×D₄	semidirect
293. C₄×#99	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72261070	2
#72261068	2
#72261063	2
#72261051	2
#72261045	2
#72261041	2
#72261039	2
#72261031	2
#72261029	2
#72261023	2
#72234968	2
#72234135	2
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