Subgroups — #72266344

Order 8192.

Only the 1382 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 553 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72266342	C₂	1	1	yes	maximal, characteristic, complemented
2	#72266341	C₂	1	1	yes	maximal, characteristic, complemented
3	#72266340	C₂	1	4	yes	maximal, complemented
4	#72266339	C₂	1	1	yes	maximal, characteristic, complemented
5	#72266336	C₂	1	4	yes	maximal, complemented
6	#72266335	C₂	1	4	yes	maximal, complemented
7	#72266334	C₂²	1	4	yes	complemented
8	#72266333	C₂²	1	4	yes	complemented
9	#72266332	C₂	1	4	yes	maximal, complemented
10	#72266331	C₂²	1	4	yes	complemented
11	#72266330	C₂²	1	4	yes	complemented
12	#72266321	C₂	1	1	yes	maximal, characteristic, complemented
13	#72266320	C₂²	1	4	yes	complemented
14	#72266319	C₂²	1	4	yes	complemented
15	#72266317	C₂	1	1	yes	maximal, characteristic, complemented
16	#72266316	C₂²	1	4	yes	complemented
17	#72266315	C₂²	1	4	yes	complemented
18	#72266303	C₂	1	1	yes	maximal, characteristic, complemented
19	#72266302	C₂²	1	4	yes	complemented
20	#72266301	C₂²	1	4	yes	complemented
21	#72266293	C₂²	1	1	yes	characteristic, complemented
22	#72266289	C₂²	1	1	yes	characteristic, complemented
23	#72266288	C₂³	1	4	yes	complemented
24	#72266272	C₂	1	1	yes	maximal, characteristic, complemented
25	#72266246	C₂	1	1	yes	maximal, characteristic, complemented
26	#72266245	C₂²	1	4	yes	complemented
27	#72266244	C₂²	1	4	yes	complemented
28	#72266242	C₂²	1	1	yes	characteristic, complemented
29	#72266235	C₂	1	1	yes	maximal, characteristic, complemented
30	#72266234	C₂²	1	4	yes	complemented
31	#72266233	C₂²	1	4	yes	complemented
32	#72266218	C₂	1	1	yes	maximal, characteristic, complemented
33	#72266215	C₂²	1	2	yes	complemented
34	#72266214	C₂²	1	2	yes	complemented
35	#72266211	C₂²	1	2	yes	complemented
36	#72266202	C₂²	1	1	yes	characteristic, complemented
37	#72266201	C₂³	1	4	yes	complemented
38	#72266197	C₂²	1	1	yes	characteristic, complemented
39	#72266194	C₂³	1	2	yes	complemented
40	#72266180	C₂	1	1	yes	maximal, characteristic, complemented
41	#72266178	C₂²	1	4	yes	complemented
42	#72266177	C₂²	1	4	yes	complemented
43	#72266154	C₂²	1	1	yes	characteristic, complemented
44	#72266145	C₂	1	1	yes	maximal, characteristic, complemented
45	#72266143	C₂²	1	2	yes	complemented
46	#72266142	C₂²	1	2	yes	complemented
47	#72266140	C₂²	1	2	yes	complemented
48	#72266138	C₂²	1	2	yes	complemented
49	#72266134	C₂²	1	1	yes	characteristic, complemented
50	#72266133	C₂²	1	1	yes	characteristic, complemented
51	#72266072	C₂	1	1	yes	maximal, characteristic, complemented
52	#72266071	C₂²	1	1	yes	characteristic, complemented
53	#72266068	C₂²	1	1	yes	characteristic, complemented
54	#72266064	C₂²	1	4	yes	—
55	#72266064	C₂²	1	4	yes	complemented
56	#72266058	D₄	1	8	yes	complemented
57	#72266053	D₄	1	8	yes	complemented
58	#72265775	C₂²	1	4	yes	complemented
59	#72265767	C₂²	1	4	yes	complemented
60	#72265766	C₂³	1	4	yes	complemented
61	C₂×#72233689	C₂²	1	1	yes	characteristic
62	#72259040	C₂²	1	1	yes	characteristic, complemented
63	#72259019	C₂³	1	2	yes	complemented
64	#72259016	C₂³	1	2	yes	complemented
65	#72258946	C₂²	1	1	yes	characteristic, complemented
66	#72258752	C₂³	1	2	yes	complemented
67	#72258375	C₂²	1	1	yes	characteristic, complemented
68	#72255646	C₂²	1	1	yes	characteristic
69	#72255646	C₂²	1	1	yes	characteristic, complemented
70	#72255646	C₂²	1	1	yes	characteristic, complemented
71	#72255642	D₄	1	2	yes	complemented
72	#72255642	C₂³	1	2	yes	complemented
73	#72251570	C₂³	1	2	yes	—
74	#72251570	C₂³	1	2	yes	complemented
75	#72251492	D₄	1	2	yes	complemented
76	C₂×#6628900	D₄	1	2	yes	complemented
77	C₂×#6628900	D₄	1	2	yes	complemented
78	#72241156	C₂³	1	4	yes	—
79	C₂×#72216396	C₂²	1	2	yes	complemented
80	C₂×#213828	C₂³	1	2	yes	complemented
81	#72240620	C₂²	1	1	yes	characteristic
82	#72240620	C₂²	1	1	yes	characteristic, complemented
83	#72240619	D₄	1	2	yes	complemented
84	#72240423	C₂²	1	4	yes	complemented
85	#72240423	C₂²	1	4	yes	complemented
86	C₂×#133278	C₂³	1	4	yes	—
87	C₂×#6370693	D₄	1	1	yes	characteristic, complemented
88	C₂×#6370693	D₄	1	1	yes	characteristic, complemented
89	C₂×#6370693	D₄	1	1	yes	characteristic, complemented
90	#72238594	D₄	1	2	yes	complemented
91	#72238594	C₂³	1	2	yes	—
92	#72238594	C₂³	1	2	yes	—
93	#72238594	C₂³	1	4	yes	—
94	#72238594	C₂³	1	2	yes	complemented
95	#72237720	C₂	1	1	yes	maximal, characteristic, complemented
96	#72237718	C₂²	1	1	yes	characteristic, complemented
97	#72237575	C₂	1	1	yes	maximal, characteristic, complemented
98	C₂×#6628896	C₂³	1	2	yes	—
99	C₂×#6628896	C₂³	1	2	yes	—
100	C₂³×H(7,𝔽₂)	D₄	1	1	yes	characteristic, complemented
101	#72237035	C₂³	1	4	yes	complemented
102	#72236921	C₂²	1	4	yes	complemented
103	#72236915	C₂²	1	4	yes	complemented
104	#72236906	C₂²	1	1	yes	characteristic, complemented
105	#72236901	C₂³	1	4	yes	complemented
106	#72236899	C₂²	1	1	yes	characteristic, complemented
107	#72236870	C₂²	1	1	yes	characteristic, complemented
108	#72236847	C₂²	1	1	yes	characteristic, complemented
109	#72236837	C₂³	1	4	yes	complemented
110	#72236821	C₂²	1	1	yes	characteristic, complemented
111	#72236816	C₂³	1	2	yes	complemented
112	#72236812	C₂³	1	2	yes	complemented
113	#72236800	C₂²	1	1	yes	characteristic
114	#72236800	C₂²	1	1	yes	characteristic, complemented
115	#72236754	C₂³	1	2	yes	—
116	#72236754	C₂³	1	2	yes	complemented
117	#72236742	D₄	1	2	yes	complemented
118	C₂×#245229	D₄	1	2	yes	complemented
119	#72236110	C₂²	1	1	yes	characteristic, complemented
120	#72236034	C₂²	1	1	yes	characteristic, complemented
121	#72236003	C₂²	1	1	yes	characteristic, complemented
122	#72235963	C₂²	1	1	yes	characteristic, complemented
123	#72235937	C₂³	1	1	yes	characteristic
124	#72235930	C₂³	1	1	yes	characteristic
125	#72235909	C₂²	1	2	yes	complemented
126	#72235881	C₂³	1	1	yes	characteristic, complemented
127	#72235872	C₂²	1	2	yes	complemented
128	#72235865	C₂³	1	2	yes	complemented
129	#72235859	C₂²	1	2	yes	complemented
130	#72235854	C₂³	1	2	yes	complemented
131	#72235850	C₂³	1	1	yes	characteristic, complemented
132	#72235848	C₂³	1	2	yes	complemented
133	C₂×#245233	D₄	1	2	yes	complemented
134	#72235054	C₂³	1	2	yes	complemented
135	#72235054	C₂³	1	2	yes	complemented
136	#72235054	C₂³	1	2	yes	complemented
137	#72234825	C₂³	1	1	yes	characteristic, complemented
138	#72234749	C₂²	1	1	yes	characteristic
139	#72234749	C₂²	1	1	yes	characteristic, complemented
140	#72234675	C₂³	1	1	yes	characteristic
141	#72234668	D₄	1	2	yes	complemented
142	#72234625	D₄	1	2	yes	complemented
143	#72234586	D₄	1	4	yes	complemented
144	#72233780	D₄	1	2	yes	complemented
145	#72231951	C₂²	1	2	yes	complemented
146	#72231822	C₂³	1	2	yes	complemented
147	#72231822	C₂³	1	2	yes	complemented
148	#72231822	C₂³	1	4	yes	complemented
149	C₂×#8932885	C₂³	1	1	yes	characteristic, complemented
150	#72231810	C₂³	1	2	yes	complemented
151	#72231810	C₂³	1	2	yes	complemented
152	#72226161	C₂²	1	1	yes	characteristic, complemented
153	#72226161	C₂²	1	1	yes	characteristic, complemented
154	#72226038	C₂³	1	4	yes	—
155	#72225994	C₂³	1	4	yes	complemented
156	#72225881	C₂³	1	1	yes	characteristic
157	#72225873	C₂³	1	2	yes	complemented
158	#72225873	C₂³	1	2	yes	complemented
159	#72225737	C₂³	1	1	yes	characteristic
160	#72225733	C₂³	1	2	yes	—
161	#72225733	C₂³	1	2	yes	—
162	#72225733	C₂³	1	4	yes	—
163	#72225658	C₂³	1	4	yes	—
164	#72225621	C₂³	1	1	yes	characteristic
165	#72219377	C₂³	1	1	yes	characteristic
166	#72219377	C₂³	1	1	yes	characteristic
167	#72219377	C₂³	1	1	yes	characteristic
168	#72219307	C₂³	1	1	yes	characteristic
169	#72219307	C₂³	1	1	yes	characteristic
170	C₂×#7631286	C₂³	1	1	yes	characteristic
171	C₂×#7631286	C₂³	1	1	yes	characteristic
172	C₂×#7631286	C₂³	1	1	yes	characteristic
173	C₂×#7631286	C₂³	1	1	yes	characteristic
174	#72219034	C₂³	1	2	yes	complemented
175	#72219022	C₂³	1	4	yes	complemented
176	#72218846	D₄	1	2	yes	complemented
177	C₂×#131967	C₂³	1	4	yes	complemented
178	C₂×#245225	C₂³	1	2	yes	—
179	C₂×#245225	C₂³	1	2	yes	—
180	C₂×#245225	C₂³	1	2	yes	complemented
181	C₂×#245225	C₂³	1	2	yes	complemented
182	#72216646	D₄	1	8	yes	complemented
183	#72214832	D₄	1	4	yes	complemented
184	#72214832	D₄	1	2	yes	complemented
185	#72210024	D₄	1	8	yes	complemented
186	C₂²×H(7,𝔽₂)	C₂×D₄	1	2	yes	—
187	C₂²×H(7,𝔽₂)	C₂×D₄	1	2	yes	—
188	C₂⁴×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
189	C₂⁴×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
190	C₂⁴×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
191	C₂⁴×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
192	C₂×#62817	C₂×D₄	1	1	yes	characteristic, complemented
193	C₂²×#3484	C₂×D₄	1	2	yes	—
194	C₂²×#3484	C₂×D₄	1	1	yes	characteristic, complemented
195	C₂³×D₄²	C₂⁴	1	1	yes	characteristic
196	#8093110	C₂×D₄	1	4	yes	complemented
197	#8093108	C₂×D₄	1	4	yes	complemented
198	#7670333	C₂×D₄	1	4	yes	complemented
199	#7670203	C₂×D₄	1	4	yes	complemented
200	#7642273	C₂⁴	1	2	yes	—
201	#7630945	C₂×D₄	1	2	yes	complemented
202	C₂×#35527	C₂×D₄	1	2	yes	—
203	C₂×#35527	C₂×D₄	1	1	yes	characteristic, complemented
204	C₂×#35512	C₂×D₄	1	2	yes	—
205	C₂×#35347	C₂×D₄	1	2	yes	—
206	C₂×#35347	C₂×D₄	1	1	yes	characteristic
207	C₂×#35347	C₂×D₄	1	1	yes	characteristic
208	C₂×#35347	C₂×D₄	1	2	yes	—
209	C₂×#35347	C₂×D₄	1	1	yes	characteristic, complemented
210	C₂×#35346	C₂×D₄	1	1	yes	characteristic, complemented
211	C₂×#35346	C₂⁴	1	1	yes	characteristic
212	C₂×#35346	C₂⁴	1	2	yes	—
213	C₂×#35346	C₂⁴	1	2	yes	—
214	C₂×#35346	C₂⁴	1	1	yes	characteristic
215	C₂×#35346	C₂⁴	1	1	yes	characteristic
216	C₂×#35346	C₂⁴	1	1	yes	characteristic
217	C₂×#34980	C₂×D₄	1	2	yes	—
218	C₂×#34980	C₂×D₄	1	2	yes	—
219	C₂×#34980	C₂⁴	1	2	yes	—
220	C₂²×#2403	C₂×D₄	1	2	yes	—
221	C₂²×#2403	C₂×D₄	1	2	yes	—
222	C₂²×#2403	C₂×D₄	1	2	yes	complemented
223	#7626202	C₂×D₄	1	1	yes	characteristic, complemented
224	C₂×#34256	C₂×D₄	1	2	yes	—
225	C₂×#34171	C₂×D₄	1	1	yes	characteristic
226	C₂×#34171	C₂×D₄	1	1	yes	characteristic
227	C₂×#34171	C₂×D₄	1	1	yes	characteristic
228	C₂×#34171	C₂×D₄	1	1	yes	characteristic, complemented
229	#6628896	C₂×D₄	1	8	yes	—
230	#6628896	C₂×D₄	1	8	yes	—
231	C₂×#32898	C₂×D₄	1	4	yes	complemented
232	C₂×#32898	C₂×D₄	1	4	yes	complemented
233	#6451874	C₂×D₄	1	4	yes	—
234	#6451874	C₂×D₄	1	4	yes	complemented
235	C₂×#21746	C₂×D₄	1	2	yes	complemented
236	C₂×#20585	C₂×D₄	1	2	yes	—
237	C₂×#20585	C₂×D₄	1	2	yes	—
238	C₂×#20585	C₂×D₄	1	2	yes	—
239	C₂×#20585	C₂×D₄	1	2	yes	—
240	C₂×#20585	C₂×D₄	1	2	yes	—
241	C₂×#20585	C₂×D₄	1	2	yes	—
242	#612424	C₂×D₄	1	4	yes	—
243	#612424	C₂×D₄	1	4	yes	complemented
244	#555905	C₂×D₄	1	1	yes	characteristic, complemented
245	#555894	C₂×D₄	1	1	yes	characteristic, complemented
246	#555894	C₂⁴	1	1	yes	characteristic
247	#517411	C₂×D₄	1	2	yes	complemented
248	#517411	C₂×D₄	1	1	yes	characteristic, complemented
249	#515362	C₂×D₄	1	1	yes	characteristic, complemented
250	#515285	C₂⁴	1	1	yes	characteristic
251	#449501	C₂×D₄	1	8	yes	—
252	#449501	C₂×D₄	1	8	yes	complemented
253	#449475	C₂×D₄	1	8	yes	—
254	#449475	C₂×D₄	1	8	yes	complemented
255	#417896	C₂×D₄	1	8	yes	—
256	#417896	C₂×D₄	1	8	yes	complemented
257	#417824	C₂×D₄	1	8	yes	—
258	#417824	C₂×D₄	1	8	yes	complemented
259	#392658	C₂×D₄	1	4	yes	complemented
260	#392245	C₂×D₄	1	2	yes	complemented
261	#392109	C₂×D₄	1	2	yes	complemented
262	#392109	C₂×D₄	1	2	yes	complemented
263	#391709	C₂×D₄	1	8	yes	complemented
264	#382422	C₂×D₄	1	2	yes	complemented
265	#382422	C₂⁴	1	2	yes	—
266	#382422	C₂⁴	1	2	yes	—
267	#382422	C₂⁴	1	2	yes	—
268	#379754	C₂×D₄	1	4	yes	complemented
269	#374004	C₂×D₄	1	8	yes	complemented
270	#359705	C₂×D₄	1	4	yes	—
271	#359705	C₂×D₄	1	4	yes	complemented
272	#359428	C₂×D₄	1	4	yes	—
273	#359428	C₂×D₄	1	4	yes	complemented
274	C₂×#10965	C₂⁴	1	2	yes	—
275	C₂×#9497	C₂×D₄	1	4	yes	complemented
276	C₂×#9495	C₂×D₄	1	4	yes	complemented
277	C₂×#9495	C₂×D₄	1	4	yes	complemented
278	C₂×#9495	C₂×D₄	1	4	yes	complemented
279	C₂×#8547	C₂⁴	1	2	yes	—
280	C₂×#8547	C₂⁴	1	2	yes	—
281	C₂×#8546	C₂×D₄	1	2	yes	complemented
282	C₂×#8542	C₂×D₄	1	2	yes	complemented
283	C₂×#8541	C₂⁴	1	2	yes	—
284	C₂×#8541	C₂⁴	1	2	yes	—
285	C₂×H(7,𝔽₂)	#120	1	4	yes	—
286	C₂×H(7,𝔽₂)	#120	1	4	yes	—
287	C₂³×H(5,𝔽₂)	#120	1	2	yes	—
288	C₂³×H(5,𝔽₂)	#120	1	2	yes	—
289	C₂³×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
290	C₂³×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
291	C₂³×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
292	C₂³×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
293	C₂³×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic, complemented
294	C₂³×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic, complemented
295	C₂⁵×D₄	#120	1	2	yes	—
296	C₂⁵×D₄	#120	1	2	yes	—
297	C₂⁵×D₄	C₂²×D₄	1	1	yes	characteristic
298	C₂⁵×D₄	C₂²×D₄	1	2	yes	—
299	C₂⁵×D₄	C₂²×D₄	1	1	yes	characteristic
300	C₂⁵×D₄	C₂²×D₄	1	1	yes	characteristic
301	C₂⁵×D₄	C₂²×D₄	1	1	yes	characteristic
302	C₂×#3490	C₂²×D₄	1	2	yes	—
303	C₂²×#534	#120	1	2	yes	—
304	C₂²×#534	#120	1	2	yes	—
305	C₂³×#127	C₂²×D₄	1	1	yes	characteristic
306	C₂³×#121	C₂²×D₄	1	1	yes	characteristic
307	C₂³×#121	C₂²×D₄	1	1	yes	characteristic
308	C₂³×#121	H(5,𝔽₂)	1	1	yes	characteristic
309	C₂³×#121	H(5,𝔽₂)	1	1	yes	characteristic
310	C₂³×#120	C₂²×D₄	1	1	yes	characteristic
311	C₂³×#120	C₂²×D₄	1	2	yes	—
312	C₂³×#120	C₂²×D₄	1	2	yes	—
313	C₂³×#120	C₂²×D₄	1	1	yes	characteristic
314	C₂³×#120	H(5,𝔽₂)	1	1	yes	characteristic
315	C₂³×#120	C₂⁵	1	1	yes	characteristic
316	C₂²×#518	#120	1	2	yes	—
317	C₂²×#518	C₂²×D₄	1	1	yes	characteristic, complemented
318	C₂³×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
319	C₂³×C₄×D₄	H(5,𝔽₂)	1	1	yes	characteristic
320	C₂×#2849	C₂²×D₄	1	4	yes	—
321	C₂×#2846	#120	1	8	yes	complemented
322	C₂×#2846	C₂²×D₄	1	4	yes	—
323	#35390	C₂²×D₄	1	4	yes	—
324	#35367	C₂²×D₄	1	4	yes	—
325	#35346	C₂²×D₄	1	8	yes	—
326	#35346	C₂²×D₄	1	4	yes	—
327	#35346	C₂²×D₄	1	4	yes	—
328	#35346	C₂²×D₄	1	8	yes	—
329	#35346	H(5,𝔽₂)	1	8	yes	—
330	C₂×#2405	#120	1	4	yes	—
331	C₂×#2403	#120	1	4	yes	—
332	C₂×#2403	C₂²×D₄	1	4	yes	—
333	C₂×#2403	C₂²×D₄	1	4	yes	—
334	#34176	C₂²×D₄	1	2	yes	—
335	C₂×#2309	#120	1	2	yes	—
336	C₂×#2309	C₂²×D₄	1	1	yes	characteristic, complemented
337	C₂×#2308	C₂²×D₄	1	2	yes	—
338	C₂×#2308	C₂²×D₄	1	1	yes	characteristic
339	C₂×#2308	C₂²×D₄	1	2	yes	—
340	C₂×#2308	C₂²×D₄	1	2	yes	—
341	C₂×#2308	C₂²×D₄	1	2	yes	—
342	C₂×#2308	C₂²×D₄	1	1	yes	characteristic
343	C₂×#2308	C₂²×D₄	1	1	yes	characteristic, complemented
344	C₂×#2308	C₂²×D₄	1	1	yes	characteristic, complemented
345	C₂×#2308	C₂²×D₄	1	1	yes	characteristic, complemented
346	C₂×#2308	C₂²×D₄	1	1	yes	characteristic, complemented
347	C₂²×#386	#120	1	2	yes	—
348	C₂²×#386	#120	1	2	yes	—
349	C₂²×#379	#120	1	2	yes	—
350	C₂²×#379	#120	1	2	yes	—
351	C₂²×#379	C₂²×D₄	1	2	yes	—
352	#23468	#120	1	8	yes	complemented
353	#23444	#120	1	8	yes	complemented
354	C₂×#1819	C₂²×D₄	1	4	yes	—
355	#20585	#120	1	4	yes	—
356	#20585	#120	1	4	yes	—
357	#20585	#120	1	8	yes	—
358	#20585	#120	1	8	yes	—
359	C₂×#1781	C₂²×D₄	1	4	yes	complemented
360	C₂×#1781	C₂²×D₄	1	4	yes	complemented
361	#14694	#120	1	8	yes	complemented
362	#14679	C₂²×D₄	1	4	yes	—
363	#10965	#120	1	16	yes	complemented
364	#10965	C₂²×D₄	1	8	yes	—
365	#10965	C₂²×D₄	1	8	yes	—
366	#10938	#120	1	16	yes	complemented
367	C₂⁷	B(4,𝔽₂)	1	2	yes	—
368	C₂⁷	B(4,𝔽₂)	1	2	yes	complemented
369	C₂⁷	C₂×#120	1	1	yes	characteristic
370	C₂⁷	C₂×#120	1	1	yes	characteristic
371	C₂⁷	C₂×#120	1	2	yes	complemented
372	C₂⁷	D₄²	1	1	yes	characteristic
373	C₂⁷	C₂³×D₄	1	1	yes	characteristic
374	C₂²×H(5,𝔽₂)	B(4,𝔽₂)	1	2	yes	complemented
375	C₂²×H(5,𝔽₂)	B(4,𝔽₂)	1	4	yes	complemented
376	C₂²×H(5,𝔽₂)	B(4,𝔽₂)	1	2	yes	complemented
377	C₂²×H(5,𝔽₂)	C₂×#120	1	4	yes	—
378	C₂²×H(5,𝔽₂)	C₂×#120	1	2	yes	—
379	C₂²×H(5,𝔽₂)	C₂×#120	1	2	yes	—
380	C₂²×H(5,𝔽₂)	C₂×#120	1	4	yes	—
381	C₂²×H(5,𝔽₂)	#534	1	4	yes	—
382	C₂⁴×D₄	B(4,𝔽₂)	1	2	yes	—
383	C₂⁴×D₄	B(4,𝔽₂)	1	2	yes	—
384	C₂⁴×D₄	B(4,𝔽₂)	1	4	yes	complemented
385	C₂⁴×D₄	C₂×#120	1	1	yes	characteristic
386	C₂⁴×D₄	C₂×#120	1	1	yes	characteristic
387	C₂⁴×D₄	C₂×#120	1	1	yes	characteristic
388	C₂⁴×D₄	C₂×#120	1	1	yes	characteristic
389	C₂⁴×D₄	C₂×#120	1	2	yes	—
390	C₂⁴×D₄	C₂×#120	1	4	yes	—
391	C₂⁴×D₄	C₂×#120	1	2	yes	—
392	C₂⁴×D₄	#534	1	1	yes	characteristic
393	C₂⁴×D₄	D₄²	1	1	yes	characteristic
394	C₂⁴×D₄	D₄²	1	1	yes	characteristic
395	C₂⁴×D₄	D₄²	1	1	yes	characteristic
396	C₂⁴×D₄	D₄²	1	1	yes	characteristic
397	C₂⁴×D₄	D₄²	1	1	yes	characteristic
398	C₂⁴×D₄	D₄²	1	1	yes	characteristic
399	C₂⁴×D₄	D₄²	1	1	yes	characteristic
400	C₂⁴×D₄	D₄²	1	1	yes	characteristic
401	C₂⁴×D₄	C₂³×D₄	1	1	yes	characteristic
402	C₂⁴×D₄	C₂³×D₄	1	1	yes	characteristic
403	C₂⁴×D₄	C₂³×D₄	1	1	yes	characteristic
404	C₂⁵×C₄	B(4,𝔽₂)	1	2	yes	—
405	C₂⁵×C₄	B(4,𝔽₂)	1	2	yes	complemented
406	C₂⁵×C₄	C₂×#120	1	1	yes	characteristic
407	C₂⁵×C₄	C₂×#120	1	2	yes	complemented
408	C₂⁵×C₄	#534	1	1	yes	characteristic
409	C₂⁵×C₄	D₄²	1	1	yes	characteristic
410	C₂⁵×C₄	D₄²	1	1	yes	characteristic
411	C₂×#543	C₂×#120	1	2	yes	complemented
412	C₂×#534	C₂×#120	1	2	yes	complemented
413	C₂²×#120	C₂×#120	1	8	yes	—
414	C₂²×#120	C₂³×D₄	1	4	yes	—
415	C₂²×#120	C₂×H(5,𝔽₂)	1	4	yes	—
416	C₂³×C₄⋊C₄	#534	1	1	yes	characteristic
417	C₂³×C₄⋊C₄	D₄²	1	1	yes	characteristic
418	C₂³×C₂²⋊C₄	C₂×#120	1	2	yes	—
419	C₂³×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
420	C₂³×C₂²⋊C₄	C₂×#120	1	2	yes	—
421	C₂³×C₂²⋊C₄	#534	1	1	yes	characteristic
422	C₂³×C₂²⋊C₄	D₄²	1	1	yes	characteristic
423	C₂³×C₂²⋊C₄	D₄²	1	1	yes	characteristic
424	C₂³×C₂²⋊C₄	D₄²	1	1	yes	characteristic
425	C₂³×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
426	C₂³×C₂²⋊C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂³×C₂²⋊C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
428	C₂³×C₄²	D₄²	1	1	yes	characteristic
429	#2403	D₄²	1	8	yes	—
430	#2403	D₄²	1	8	yes	—
431	#2403	D₄²	1	8	yes	—
432	#2403	D₄²	1	8	yes	—
433	#2308	C₂×#120	1	4	yes	—
434	#2308	C₂×#120	1	8	yes	—
435	#2308	C₂×#120	1	4	yes	—
436	#2308	C₂×#120	1	4	yes	—
437	#2308	#534	1	4	yes	—
438	C₂×#379	C₂×#120	1	4	yes	—
439	C₂×#379	C₂×#120	1	8	yes	complemented
440	C₂×#379	C₂×#120	1	4	yes	complemented
441	#2273	C₂×#120	1	4	yes	complemented
442	C₂×#342	C₂×#120	1	8	yes	complemented
443	C₂⁶	#2403	1	1	yes	characteristic
444	C₂⁶	#2403	1	1	yes	characteristic
445	C₂⁶	#2403	1	1	yes	characteristic
446	C₂⁶	#2403	1	1	yes	characteristic
447	C₂⁶	C₂×B(4,𝔽₂)	1	2	yes	—
448	C₂⁶	C₂×B(4,𝔽₂)	1	2	yes	—
449	C₂⁶	C₂×B(4,𝔽₂)	1	4	yes	—
450	C₂⁶	C₂×B(4,𝔽₂)	1	2	yes	—
451	C₂⁶	C₂×B(4,𝔽₂)	1	2	yes	—
452	C₂⁶	C₂×B(4,𝔽₂)	1	2	yes	—
453	C₂⁶	C₂×B(4,𝔽₂)	1	2	yes	—
454	C₂⁶	C₂²×#120	1	1	yes	characteristic
455	C₂⁶	C₂²×#120	1	2	yes	—
456	C₂⁶	C₂²×#120	1	1	yes	characteristic
457	C₂⁶	C₂×D₄²	1	1	yes	characteristic
458	C₂⁶	C₂×D₄²	1	1	yes	characteristic
459	C₂⁶	#3484	1	2	yes	—
460	C₂³×D₄	#2403	1	4	yes	—
461	C₂³×D₄	#2403	1	4	yes	—
462	C₂³×D₄	#2846	1	4	yes	—
463	C₂³×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
464	C₂³×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
465	C₂³×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
466	C₂³×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
467	C₂³×D₄	#3026	1	4	yes	—
468	C₂³×D₄	C₂²×#120	1	2	yes	—
469	C₂³×D₄	C₂×#534	1	2	yes	—
470	C₂³×D₄	C₂×D₄²	1	4	yes	—
471	C₂³×D₄	C₂×D₄²	1	4	yes	—
472	C₂⁴×C₄	#2403	1	1	yes	characteristic
473	C₂⁴×C₄	#2403	1	1	yes	characteristic
474	C₂⁴×C₄	#2403	1	1	yes	characteristic
475	C₂⁴×C₄	#2403	1	1	yes	characteristic
476	C₂⁴×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
477	C₂⁴×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
478	C₂⁴×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
479	C₂⁴×C₄	C₂×#534	1	1	yes	characteristic
480	C₂⁴×C₄	C₂×D₄²	1	1	yes	characteristic
481	C₂⁴×C₄	C₂×D₄²	1	1	yes	characteristic
482	C₂²×C₂²⋊C₄	#2846	1	4	yes	—
483	C₂²×C₂²⋊C₄	C₂²×#120	1	2	yes	—
484	C₂²×C₂²⋊C₄	#3484	1	4	yes	—
485	C₂²×C₂²⋊C₄	#3484	1	4	yes	—
486	C₂²×C₂²⋊C₄	#3484	1	2	yes	—
487	#379	#2403	1	8	yes	—
488	C₂⁵	#23895	1	1	yes	characteristic
489	C₂⁵	#23895	1	1	yes	characteristic
490	C₂⁵	#23895	1	2	yes	—
491	C₂⁵	#23900	1	1	yes	characteristic
492	C₂⁵	#23900	1	1	yes	characteristic
493	C₂⁵	#23900	1	1	yes	characteristic
494	C₂⁵	#23900	1	1	yes	characteristic
495	C₂⁵	#23900	1	1	yes	characteristic
496	C₂⁵	#23900	1	2	yes	—
497	C₂⁵	#23900	1	1	yes	characteristic
498	C₂⁵	#23900	1	4	yes	—
499	C₂⁵	#23900	1	4	yes	—
500	C₂⁵	#23900	1	2	yes	—
501	C₂⁵	#32898	1	4	yes	—
502	C₂⁵	C₂×#2403	1	2	yes	—
503	C₂⁵	C₂×#2403	1	1	yes	characteristic
504	C₂⁵	#34980	1	1	yes	characteristic
505	C₂⁵	D₄×#120	1	2	yes	—
506	C₂⁵	D₄×#120	1	2	yes	—
507	C₂⁵	C₂×#2846	1	1	yes	characteristic
508	C₂⁵	C₂²×B(4,𝔽₂)	1	2	yes	—
509	C₂⁵	C₂²×B(4,𝔽₂)	1	2	yes	—
510	C₂⁵	C₂²×B(4,𝔽₂)	1	2	yes	—
511	C₂⁵	C₂×#3026	1	2	yes	—
512	C₂³×C₄	#23900	1	2	yes	—
513	C₂³×C₄	#23900	1	4	yes	—
514	C₂³×C₄	#23900	1	4	yes	—
515	C₂³×C₄	#32898	1	4	yes	—
516	C₂³×C₄	#34980	1	2	yes	—
517	C₂³×C₄	D₄×#120	1	2	yes	—
518	C₂³×C₄	D₄×#120	1	2	yes	—
519	C₂⁴	#245225	1	1	yes	characteristic
520	C₂⁴	#245225	1	2	yes	—
521	C₂⁴	#245225	1	2	yes	—
522	C₂⁴	#245225	1	1	yes	characteristic
523	C₂⁴	#245225	1	1	yes	characteristic
524	C₂⁴	#245225	1	1	yes	characteristic
525	C₂⁴	#511790	1	8	yes	complemented
526	C₂⁴	#612424	1	1	yes	characteristic
527	C₂⁴	C₂×#23900	1	1	yes	characteristic
528	C₂⁴	C₂×#23900	1	4	yes	—
529	C₂⁴	C₂×#23900	1	1	yes	characteristic
530	C₂⁴	C₂×#23900	1	1	yes	characteristic
531	C₂⁴	#6437621	1	1	yes	characteristic
532	C₂⁴	C₂×#23895	1	1	yes	characteristic
533	C₂⁴	C₂×#23895	1	1	yes	characteristic
534	C₂⁴	#6470225	1	2	yes	—
535	C₂⁴	C₂×#32898	1	2	yes	—
536	C₂³	B(5,𝔽₂)	1	2	yes	—
537	C₂³	#72213862	1	1	yes	characteristic
538	C₂³	C₂×#511790	1	4	yes	—
539	C₂³	#72214832	1	1	yes	characteristic
540	C₂³	#72215858	1	1	yes	characteristic
541	C₂³	C₂×#245225	1	1	yes	characteristic
542	C₂³	C₂×#245225	1	1	yes	characteristic
543	C₂³	#72233065	1	1	yes	characteristic
544	C₂³	#72233065	1	1	yes	characteristic
545	C₂²	C₂×B(5,𝔽₂)	1	1	yes	characteristic
546	C₂²	#72218133	1	2	yes	—
547	C₂²	#72256243	1	1	yes	characteristic
548	C₂²	#72258059	1	1	yes	characteristic
549	C₂	#72258932	1	1	yes	characteristic
550	C₂	#72265839	1	1	yes	characteristic
551	C₂	#72265939	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#72258059
commutator, Frattini, cosocle	C₂³×#120	C₂⁵
LCS	G ▷ C₂³×#120 ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×D₄² ◁ G
LECS	G ▷ C₂³×#120 ▷ C₂⁴ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72266342	C₂	semidirect
2. #72266341	C₂	semidirect
3. #72266340	C₂	semidirect
4. #72266339	C₂	semidirect
5. #72266336	C₂	semidirect
6. #72266335	C₂	semidirect
7. #72266334	C₂²	semidirect
8. #72266333	C₂²	semidirect
9. #72266332	C₂	semidirect
10. #72266331	C₂²	semidirect
11. #72266330	C₂²	semidirect
12. #72266321	C₂	semidirect
13. #72266320	C₂²	semidirect
14. #72266319	C₂²	semidirect
15. #72266317	C₂	semidirect
16. #72266316	C₂²	semidirect
17. #72266315	C₂²	semidirect
18. #72266303	C₂	semidirect
19. #72266302	C₂²	semidirect
20. #72266301	C₂²	semidirect
21. #72266293	C₂²	semidirect
22. #72266289	C₂²	semidirect
23. #72266288	C₂³	semidirect
24. #72266272	C₂	semidirect
25. #72266246	C₂	semidirect
26. #72266245	C₂²	semidirect
27. #72266244	C₂²	semidirect
28. #72266242	C₂²	semidirect
29. #72266235	C₂	semidirect
30. #72266234	C₂²	semidirect
31. #72266233	C₂²	semidirect
32. #72266218	C₂	semidirect
33. #72266215	C₂²	semidirect
34. #72266214	C₂²	semidirect
35. #72266211	C₂²	semidirect
36. #72266202	C₂²	semidirect
37. #72266201	C₂³	semidirect
38. #72266197	C₂²	semidirect
39. #72266194	C₂³	semidirect
40. #72266180	C₂	semidirect
41. #72266178	C₂²	semidirect
42. #72266177	C₂²	semidirect
43. #72266154	C₂²	semidirect
44. #72266145	C₂	semidirect
45. #72266143	C₂²	semidirect
46. #72266142	C₂²	semidirect
47. #72266140	C₂²	semidirect
48. #72266138	C₂²	semidirect
49. #72266134	C₂²	semidirect
50. #72266133	C₂²	semidirect
51. #72266072	C₂	semidirect
52. #72266071	C₂²	semidirect
53. #72266068	C₂²	semidirect
55. #72266064	C₂²	semidirect
56. #72266058	D₄	semidirect
57. #72266053	D₄	semidirect
58. #72265775	C₂²	semidirect
59. #72265767	C₂²	semidirect
60. #72265766	C₂³	semidirect
62. #72259040	C₂²	semidirect
63. #72259019	C₂³	semidirect
64. #72259016	C₂³	semidirect
65. #72258946	C₂²	semidirect
66. #72258752	C₂³	semidirect
67. #72258375	C₂²	semidirect
69. #72255646	C₂²	semidirect
70. #72255646	C₂²	semidirect
71. #72255642	D₄	semidirect
72. #72255642	C₂³	semidirect
74. #72251570	C₂³	semidirect
75. #72251492	D₄	semidirect
76. C₂×#6628900	D₄	semidirect
77. C₂×#6628900	D₄	semidirect
79. C₂×#72216396	C₂²	semidirect
80. C₂×#213828	C₂³	semidirect
82. #72240620	C₂²	semidirect
83. #72240619	D₄	semidirect
84. #72240423	C₂²	semidirect
85. #72240423	C₂²	semidirect
87. C₂×#6370693	D₄	semidirect
88. C₂×#6370693	D₄	semidirect
89. C₂×#6370693	D₄	semidirect
90. #72238594	D₄	semidirect
94. #72238594	C₂³	semidirect
95. #72237720	C₂	semidirect
96. #72237718	C₂²	semidirect
97. #72237575	C₂	semidirect
100. C₂³×H(7,𝔽₂)	D₄	semidirect
101. #72237035	C₂³	semidirect
102. #72236921	C₂²	semidirect
103. #72236915	C₂²	semidirect
104. #72236906	C₂²	semidirect
105. #72236901	C₂³	semidirect
106. #72236899	C₂²	semidirect
107. #72236870	C₂²	semidirect
108. #72236847	C₂²	semidirect
109. #72236837	C₂³	semidirect
110. #72236821	C₂²	semidirect
111. #72236816	C₂³	semidirect
112. #72236812	C₂³	semidirect
114. #72236800	C₂²	semidirect
116. #72236754	C₂³	semidirect
117. #72236742	D₄	semidirect
118. C₂×#245229	D₄	semidirect
119. #72236110	C₂²	semidirect
120. #72236034	C₂²	semidirect
121. #72236003	C₂²	semidirect
122. #72235963	C₂²	semidirect
125. #72235909	C₂²	semidirect
126. #72235881	C₂³	semidirect
127. #72235872	C₂²	semidirect
128. #72235865	C₂³	semidirect
129. #72235859	C₂²	semidirect
130. #72235854	C₂³	semidirect
131. #72235850	C₂³	semidirect
132. #72235848	C₂³	semidirect
133. C₂×#245233	D₄	semidirect
134. #72235054	C₂³	semidirect
135. #72235054	C₂³	semidirect
136. #72235054	C₂³	semidirect
137. #72234825	C₂³	semidirect
139. #72234749	C₂²	semidirect
141. #72234668	D₄	semidirect
142. #72234625	D₄	semidirect
143. #72234586	D₄	semidirect
144. #72233780	D₄	semidirect
145. #72231951	C₂²	semidirect
146. #72231822	C₂³	semidirect
147. #72231822	C₂³	semidirect
148. #72231822	C₂³	semidirect
149. C₂×#8932885	C₂³	semidirect
150. #72231810	C₂³	semidirect
151. #72231810	C₂³	semidirect
152. #72226161	C₂²	semidirect
153. #72226161	C₂²	semidirect
155. #72225994	C₂³	semidirect
157. #72225873	C₂³	semidirect
158. #72225873	C₂³	semidirect
174. #72219034	C₂³	semidirect
175. #72219022	C₂³	semidirect
176. #72218846	D₄	semidirect
177. C₂×#131967	C₂³	semidirect
180. C₂×#245225	C₂³	semidirect
181. C₂×#245225	C₂³	semidirect
182. #72216646	D₄	semidirect
183. #72214832	D₄	semidirect
184. #72214832	D₄	semidirect
185. #72210024	D₄	semidirect
191. C₂⁴×H(5,𝔽₂)	C₂×D₄	semidirect
192. C₂×#62817	C₂×D₄	semidirect
194. C₂²×#3484	C₂×D₄	semidirect
196. #8093110	C₂×D₄	semidirect
197. #8093108	C₂×D₄	semidirect
198. #7670333	C₂×D₄	semidirect
199. #7670203	C₂×D₄	semidirect
201. #7630945	C₂×D₄	semidirect
203. C₂×#35527	C₂×D₄	semidirect
209. C₂×#35347	C₂×D₄	semidirect
210. C₂×#35346	C₂×D₄	semidirect
222. C₂²×#2403	C₂×D₄	semidirect
223. #7626202	C₂×D₄	semidirect
228. C₂×#34171	C₂×D₄	semidirect
231. C₂×#32898	C₂×D₄	semidirect
232. C₂×#32898	C₂×D₄	semidirect
234. #6451874	C₂×D₄	semidirect
235. C₂×#21746	C₂×D₄	semidirect
243. #612424	C₂×D₄	semidirect
244. #555905	C₂×D₄	semidirect
245. #555894	C₂×D₄	semidirect
247. #517411	C₂×D₄	semidirect
248. #517411	C₂×D₄	semidirect
249. #515362	C₂×D₄	semidirect
252. #449501	C₂×D₄	semidirect
254. #449475	C₂×D₄	semidirect
256. #417896	C₂×D₄	semidirect
258. #417824	C₂×D₄	semidirect
259. #392658	C₂×D₄	semidirect
260. #392245	C₂×D₄	semidirect
261. #392109	C₂×D₄	semidirect
262. #392109	C₂×D₄	semidirect
263. #391709	C₂×D₄	semidirect
264. #382422	C₂×D₄	semidirect
268. #379754	C₂×D₄	semidirect
269. #374004	C₂×D₄	semidirect
271. #359705	C₂×D₄	semidirect
273. #359428	C₂×D₄	semidirect
275. C₂×#9497	C₂×D₄	semidirect
276. C₂×#9495	C₂×D₄	semidirect
277. C₂×#9495	C₂×D₄	semidirect
278. C₂×#9495	C₂×D₄	semidirect
281. C₂×#8546	C₂×D₄	semidirect
282. C₂×#8542	C₂×D₄	semidirect
293. C₂³×H(5,𝔽₂)	C₂²×D₄	semidirect
294. C₂³×H(5,𝔽₂)	C₂²×D₄	semidirect
317. C₂²×#518	C₂²×D₄	semidirect
321. C₂×#2846	#120	semidirect
336. C₂×#2309	C₂²×D₄	semidirect
343. C₂×#2308	C₂²×D₄	semidirect
344. C₂×#2308	C₂²×D₄	semidirect
345. C₂×#2308	C₂²×D₄	semidirect
346. C₂×#2308	C₂²×D₄	semidirect
352. #23468	#120	semidirect
353. #23444	#120	semidirect
359. C₂×#1781	C₂²×D₄	semidirect
360. C₂×#1781	C₂²×D₄	semidirect
361. #14694	#120	semidirect
363. #10965	#120	semidirect
366. #10938	#120	semidirect
368. C₂⁷	B(4,𝔽₂)	semidirect
371. C₂⁷	C₂×#120	semidirect
374. C₂²×H(5,𝔽₂)	B(4,𝔽₂)	semidirect
375. C₂²×H(5,𝔽₂)	B(4,𝔽₂)	semidirect
376. C₂²×H(5,𝔽₂)	B(4,𝔽₂)	semidirect
384. C₂⁴×D₄	B(4,𝔽₂)	semidirect
405. C₂⁵×C₄	B(4,𝔽₂)	semidirect
407. C₂⁵×C₄	C₂×#120	semidirect
411. C₂×#543	C₂×#120	semidirect
412. C₂×#534	C₂×#120	semidirect
439. C₂×#379	C₂×#120	semidirect
440. C₂×#379	C₂×#120	semidirect
441. #2273	C₂×#120	semidirect
442. C₂×#342	C₂×#120	semidirect
525. C₂⁴	#511790	semidirect

Maximal subgroups

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

subgroup	index
#72266342	2
#72266341	2
#72266340	2
#72266339	2
#72266336	2
#72266335	2
#72266332	2
#72266321	2
#72266317	2
#72266303	2
#72266272	2
#72266246	2
#72266235	2
#72266218	2
#72266180	2
#72266145	2
#72266072	2
#72237720	2
#72237575	2