Subgroups — #72315225

Order 4096.

Only the 939 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 543 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72315164	C₂	1	1	yes	maximal, characteristic, complemented
2	#72315149	C₂	1	1	yes	maximal, characteristic, complemented
3	#72315059	C₂	1	2	yes	maximal, complemented
4	#72315031	C₂	1	2	yes	maximal, complemented
5	#72314996	C₂	1	2	yes	maximal, complemented
6	#72314884	C₂	1	2	yes	maximal, complemented
7	#72314879	C₂	1	2	yes	maximal, complemented
8	#72314855	C₂²	1	2	yes	complemented
9	#72314760	C₂	1	2	yes	maximal, complemented
10	#72314748	C₂²	1	2	yes	complemented
11	#72314748	C₂²	1	2	yes	complemented
12	#72314746	C₂	1	2	yes	maximal, complemented
13	#72314739	C₂²	1	2	yes	complemented
14	#72314734	C₂²	1	2	yes	complemented
15	#72314729	C₂²	1	2	yes	complemented
16	#72314671	C₂	1	2	yes	maximal, complemented
17	#72314665	C₂²	1	2	yes	complemented
18	#72312328	C₂	1	1	yes	maximal, characteristic, complemented
19	#72312312	C₂²	1	2	yes	complemented
20	#72312258	C₂	1	1	yes	maximal, characteristic, complemented
21	#72310327	C₂	1	1	yes	maximal, characteristic, complemented
22	#72310322	C₂²	1	2	yes	complemented
23	#72310319	C₂²	1	2	yes	complemented
24	#72309483	C₂	1	1	yes	maximal, characteristic, complemented
25	#72309478	C₂²	1	2	yes	complemented
26	#72309478	C₂²	1	2	yes	complemented
27	#72266873	C₂	1	1	yes	maximal, characteristic, complemented
28	#72266836	C₂	1	1	yes	maximal, characteristic, complemented
29	#72266835	C₂²	1	2	yes	—
30	#72266835	C₂²	1	2	yes	—
31	#72266834	C₂²	1	2	yes	—
32	#72266834	C₂²	1	2	yes	—
33	#72266378	C₂²	1	2	yes	complemented
34	#72264793	C₂	1	1	yes	maximal, characteristic, complemented
35	#72264784	C₂	1	1	yes	maximal, characteristic, complemented
36	#72264765	C₂²	1	2	yes	complemented
37	#72264754	C₂²	1	2	yes	complemented
38	#72263490	C₂²	1	2	yes	complemented
39	#72260584	C₂²	1	2	yes	complemented
40	#72260562	C₂²	1	2	yes	complemented
41	#72259117	C₂²	1	2	yes	complemented
42	C₂×#135516	C₂²	1	2	yes	complemented
43	#72258334	C₂²	1	2	yes	complemented
44	C₂×#144639	C₂²	1	2	yes	complemented
45	#72258094	C₂²	1	2	yes	—
46	#72258094	C₂²	1	2	yes	—
47	#72258019	C₂²	1	2	yes	—
48	#72258019	C₂²	1	2	yes	—
49	#72255980	C₂²	1	2	yes	complemented
50	#72255874	C₂²	1	2	yes	complemented
51	#72251547	C₂	1	1	yes	maximal, characteristic, complemented
52	#72251533	C₂²	1	2	yes	complemented
53	#72251530	C₂²	1	2	yes	complemented
54	#72251528	C₂²	1	2	yes	complemented
55	#72251527	C₂²	1	2	yes	complemented
56	#72251291	C₂	1	1	yes	maximal, characteristic, complemented
57	#72251157	C₂²	1	1	yes	characteristic, complemented
58	#72251143	C₂²	1	1	yes	characteristic, complemented
59	#72251140	C₂²	1	1	yes	characteristic, complemented
60	#72251140	C₂²	1	1	yes	characteristic, complemented
61	#72246287	C₂²	1	2	yes	complemented
62	#72246286	C₂²	1	2	yes	complemented
63	#72238613	C₂²	1	1	yes	characteristic, complemented
64	#72238352	C₂	1	1	yes	maximal, characteristic, complemented
65	#72238351	C₂²	1	2	yes	complemented
66	#72238350	C₂²	1	2	yes	complemented
67	#72238349	C₂²	1	2	yes	complemented
68	#72238345	C₂	1	1	yes	maximal, characteristic, complemented
69	#72238344	C₂	1	1	yes	maximal, characteristic, complemented
70	#72238343	C₂²	1	2	yes	—
71	#72238343	C₂²	1	2	yes	—
72	#72238342	C₂²	1	2	yes	—
73	#72238342	C₂²	1	2	yes	—
74	#72237900	C₂²	1	1	yes	characteristic, complemented
75	#72237899	C₂²	1	1	yes	characteristic, complemented
76	#72237829	C₂²	1	1	yes	characteristic, complemented
77	#72237638	C₂²	1	2	yes	complemented
78	#72237633	C₂²	1	2	yes	complemented
79	#72237632	C₂²	1	2	yes	complemented
80	#72237473	C₂²	1	2	yes	complemented
81	#72237400	C₂²	1	1	yes	characteristic
82	#72237374	C₂²	1	2	yes	complemented
83	#72236508	C₂²	1	2	yes	complemented
84	#72234661	C₂²	1	1	yes	characteristic
85	#72234661	C₂²	1	1	yes	characteristic
86	#72232884	C₂²	1	1	yes	characteristic
87	#72226366	C₂²	1	2	yes	complemented
88	#72225713	C₂²	1	1	yes	characteristic, complemented
89	#72225667	C₂²	1	1	yes	characteristic, complemented
90	#72225650	C₂²	1	1	yes	characteristic, complemented
91	#72225617	C₂²	1	1	yes	characteristic, complemented
92	#72219418	C₂²	1	1	yes	characteristic, complemented
93	#72219414	C₂²	1	1	yes	characteristic, complemented
94	#72219311	C₂²	1	1	yes	characteristic, complemented
95	#72219301	C₂²	1	1	yes	characteristic
96	#72219301	C₂²	1	1	yes	characteristic
97	#72219300	C₂²	1	1	yes	characteristic, complemented
98	#72219257	C₂²	1	1	yes	characteristic
99	#72219251	C₂²	1	1	yes	characteristic, complemented
100	#72219248	C₂²	1	1	yes	characteristic, complemented
101	#72219248	C₂²	1	1	yes	characteristic, complemented
102	#72219237	C₂²	1	1	yes	characteristic, complemented
103	C₂²×#8534	C₂²	1	1	yes	characteristic
104	C₂²×#8534	C₂²	1	1	yes	characteristic
105	#72219160	C₂²	1	2	yes	complemented
106	#72219160	C₂²	1	2	yes	complemented
107	#72218381	C₂²	1	1	yes	characteristic, complemented
108	#72218381	C₂²	1	1	yes	characteristic, complemented
109	#72218313	C₂²	1	1	yes	characteristic, complemented
110	#72218306	C₂²	1	1	yes	characteristic
111	#72218306	C₂²	1	1	yes	characteristic
112	C₂×#139743	C₂²	1	2	yes	complemented
113	C₂×#139743	C₂²	1	2	yes	complemented
114	#72218057	C₂²	1	1	yes	characteristic, complemented
115	#72213862	C₂²	1	1	yes	characteristic
116	#72213862	C₂²	1	1	yes	characteristic
117	#72210555	C₂²	1	1	yes	characteristic
118	#72210555	C₂²	1	1	yes	characteristic
119	#72210555	C₂²	1	1	yes	characteristic
120	#72210555	C₂²	1	1	yes	characteristic
121	#72210555	C₂²	1	1	yes	characteristic
122	#72210511	C₂²	1	1	yes	characteristic
123	#10586422	C₂³	1	2	yes	—
124	#10586422	C₂³	1	2	yes	—
125	C₂²×#3484	C₂³	1	1	yes	characteristic
126	C₂²×#3484	C₂³	1	1	yes	characteristic
127	C₂²×#3484	C₂³	1	1	yes	characteristic
128	#7641845	D₄	1	2	yes	complemented
129	#7630939	C₂³	1	1	yes	characteristic
130	C₂×#34980	C₂³	1	1	yes	characteristic
131	C₂×#32873	C₂³	1	1	yes	characteristic, complemented
132	#6440460	D₄	1	2	yes	complemented
133	#6440460	C₂³	1	1	yes	characteristic
134	#6440460	C₂³	1	1	yes	characteristic
135	#6440460	C₂³	1	2	yes	—
136	#6440460	C₂³	1	1	yes	characteristic, complemented
137	C₂×#23895	D₄	1	2	yes	complemented
138	C₂×#23895	C₂³	1	1	yes	characteristic
139	C₂×#23895	C₂³	1	1	yes	characteristic
140	C₂×#23895	C₂³	1	2	yes	—
141	#6437621	D₄	1	2	yes	complemented
142	#6437621	D₄	1	2	yes	complemented
143	#6437621	C₂³	1	1	yes	characteristic
144	#6437621	C₂³	1	2	yes	—
145	#6437621	C₂³	1	1	yes	characteristic
146	#6437621	C₂³	1	1	yes	characteristic, complemented
147	#6437445	C₂³	1	2	yes	—
148	#6374251	C₂³	1	1	yes	characteristic, complemented
149	C₂×#21776	D₄	1	2	yes	complemented
150	C₂×#21776	C₂³	1	2	yes	—
151	C₂×#21776	C₂³	1	1	yes	characteristic
152	C₂×#21776	C₂³	1	1	yes	characteristic
153	C₂×#21776	C₂³	1	1	yes	characteristic, complemented
154	#6374128	C₂³	1	1	yes	characteristic, complemented
155	C₂×#21746	D₄	1	2	yes	complemented
156	#6370693	D₄	1	2	yes	complemented
157	C₂²×#1781	C₂³	1	1	yes	characteristic
158	C₂²×#1781	C₂³	1	1	yes	characteristic
159	#763514	C₂³	1	2	yes	—
160	#763333	C₂³	1	2	yes	—
161	C₂²×#1438	C₂³	1	1	yes	characteristic
162	#493879	C₂³	1	2	yes	complemented
163	C₂×#12707	C₂³	1	2	yes	—
164	C₂×#12707	C₂³	1	2	yes	—
165	C₂×#12707	C₂³	1	2	yes	—
166	C₂×#12707	C₂³	1	2	yes	—
167	C₂×#12707	C₂³	1	2	yes	complemented
168	C₂×#12705	C₂³	1	2	yes	—
169	C₂×#12705	C₂³	1	2	yes	—
170	C₂×#12705	C₂³	1	2	yes	—
171	C₂×#12705	C₂³	1	2	yes	—
172	#493370	C₂³	1	2	yes	—
173	#493370	C₂³	1	2	yes	—
174	#493370	C₂³	1	2	yes	—
175	#493370	C₂³	1	2	yes	—
176	#493370	C₂³	1	2	yes	—
177	#493370	C₂³	1	2	yes	—
178	#493357	C₂³	1	2	yes	complemented
179	#392231	D₄	1	2	yes	complemented
180	#392113	C₂³	1	1	yes	characteristic
181	#392109	C₂³	1	1	yes	characteristic
182	#392109	C₂³	1	1	yes	characteristic
183	#392109	C₂³	1	1	yes	characteristic
184	#392109	C₂³	1	1	yes	characteristic
185	#392109	C₂³	1	1	yes	characteristic
186	#392109	C₂³	1	1	yes	characteristic
187	#392030	C₂³	1	1	yes	characteristic, complemented
188	#392030	C₂³	1	1	yes	characteristic, complemented
189	#392030	C₂³	1	1	yes	characteristic, complemented
190	#382707	C₂³	1	1	yes	characteristic, complemented
191	#382707	C₂³	1	1	yes	characteristic, complemented
192	#382544	C₂³	1	1	yes	characteristic, complemented
193	#382434	D₄	1	2	yes	complemented
194	#382434	C₂³	1	2	yes	—
195	#382434	C₂³	1	1	yes	characteristic
196	#382434	C₂³	1	1	yes	characteristic
197	#382434	C₂³	1	1	yes	characteristic, complemented
198	#359811	C₂³	1	1	yes	characteristic, complemented
199	#359549	D₄	1	2	yes	complemented
200	#359549	C₂³	1	1	yes	characteristic
201	#359549	C₂³	1	1	yes	characteristic
202	#359549	C₂³	1	2	yes	—
203	#359509	C₂³	1	2	yes	—
204	#359442	D₄	1	2	yes	complemented
205	#359442	C₂³	1	1	yes	characteristic, complemented
206	#355096	C₂³	1	1	yes	characteristic, complemented
207	#347057	D₄	1	4	yes	complemented
208	#347056	D₄	1	4	yes	complemented
209	#347047	D₄	1	4	yes	complemented
210	#347045	D₄	1	4	yes	complemented
211	#190116	C₂³	1	2	yes	complemented
212	#188050	C₂³	1	2	yes	—
213	#188050	C₂³	1	2	yes	—
214	#188049	C₂³	1	2	yes	complemented
215	C₂×#8534	C₂³	1	2	yes	—
216	C₂×#8534	C₂³	1	2	yes	—
217	C₂×#8534	C₂³	1	2	yes	—
218	C₂×#8534	C₂³	1	2	yes	—
219	C₂×#8534	C₂³	1	2	yes	complemented
220	#146479	C₂³	1	2	yes	complemented
221	C₂×#7304	C₂³	1	2	yes	complemented
222	C₂×#7304	C₂³	1	2	yes	complemented
223	C₂×#7316	C₂³	1	2	yes	complemented
224	C₂×#7316	C₂³	1	2	yes	complemented
225	C₂×#7314	C₂³	1	2	yes	complemented
226	C₂×#7314	C₂³	1	2	yes	complemented
227	C₂×#7310	C₂³	1	2	yes	complemented
228	C₂×#7310	C₂³	1	2	yes	complemented
229	C₂×#7310	C₂³	1	2	yes	complemented
230	C₂×#7310	C₂³	1	2	yes	complemented
231	C₂×#7310	C₂³	1	2	yes	complemented
232	C₂×#7310	C₂³	1	2	yes	complemented
233	C₂×#7307	C₂³	1	2	yes	complemented
234	C₂×#7307	C₂³	1	2	yes	complemented
235	C₂×#7307	C₂³	1	2	yes	complemented
236	C₂×#7307	C₂³	1	2	yes	complemented
237	#108222	C₂³	1	2	yes	complemented
238	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
239	C₂³×H(5,𝔽₂)	#41	1	1	yes	characteristic, complemented
240	C₂³×H(5,𝔽₂)	#41	1	1	yes	characteristic, complemented
241	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
242	#62832	C₂×D₄	1	4	yes	—
243	#62824	C₂×D₄	1	4	yes	—
244	C₂×#3484	C₂×D₄	1	2	yes	—
245	C₂×#3484	C₂×D₄	1	2	yes	—
246	C₂×#3484	C₂×D₄	1	1	yes	characteristic
247	C₂×#3484	C₂×D₄	1	1	yes	characteristic
248	C₂×#3484	C₂×D₄	1	1	yes	characteristic
249	C₂×#3484	C₂×D₄	1	1	yes	characteristic
250	C₂×#3484	#41	1	2	yes	complemented
251	C₂×#3484	C₂⁴	1	1	yes	characteristic
252	C₂×#3484	C₂⁴	1	1	yes	characteristic
253	C₂×#3484	C₂⁴	1	1	yes	characteristic
254	C₂×#3484	C₂⁴	1	2	yes	—
255	C₂²×#535	C₂⁴	1	2	yes	—
256	C₂²×#534	C₂×D₄	1	2	yes	—
257	C₂²×#534	C₂×D₄	1	1	yes	characteristic
258	C₂²×#534	C₂⁴	1	1	yes	characteristic
259	C₂²×#525	#41	1	2	yes	complemented
260	C₂³×#120	C₂×D₄	1	2	yes	—
261	C₂³×#120	C₂×D₄	1	1	yes	characteristic
262	C₂²×#518	C₂×D₄	1	1	yes	characteristic
263	C₂²×#518	#41	1	1	yes	characteristic, complemented
264	C₂²×#518	#41	1	1	yes	characteristic, complemented
265	C₂×#3026	C₂×D₄	1	2	yes	—
266	C₂×#3026	C₂×D₄	1	2	yes	—
267	C₂×#2883	C₂×D₄	1	2	yes	—
268	C₂×#2883	C₂×D₄	1	2	yes	—
269	#34992	C₂×D₄	1	2	yes	—
270	#34992	C₂×D₄	1	2	yes	—
271	#34980	C₂×D₄	1	2	yes	—
272	#34980	C₂×D₄	1	2	yes	—
273	#34171	C₂×D₄	1	1	yes	characteristic
274	#34171	C₂×D₄	1	1	yes	characteristic
275	#34171	C₂⁴	1	1	yes	characteristic
276	C₂×#2308	C₂×D₄	1	1	yes	characteristic
277	C₂×#2308	C₂⁴	1	1	yes	characteristic
278	C₂²×#379	C₂×D₄	1	1	yes	characteristic
279	C₂²×#379	C₂×D₄	1	2	yes	—
280	#23901	C₂×D₄	1	4	yes	—
281	#23901	C₂×D₄	1	4	yes	—
282	#23900	C₂×D₄	1	4	yes	—
283	#23900	C₂×D₄	1	4	yes	—
284	C₂×#1913	C₂×D₄	1	2	yes	—
285	C₂×#1913	C₂×D₄	1	2	yes	—
286	C₂×#1913	C₂×D₄	1	2	yes	—
287	C₂×#1913	C₂×D₄	1	2	yes	—
288	C₂×#1898	C₂×D₄	1	2	yes	—
289	C₂×#1898	C₂×D₄	1	2	yes	—
290	C₂×#1898	C₂×D₄	1	2	yes	—
291	C₂×#1898	C₂×D₄	1	2	yes	—
292	#20960	C₂×D₄	1	2	yes	—
293	#20960	C₂×D₄	1	2	yes	—
294	C₂×#1828	C₂×D₄	1	2	yes	—
295	C₂×#1828	C₂×D₄	1	2	yes	—
296	C₂×#1828	C₂×D₄	1	2	yes	—
297	C₂×#1828	C₂×D₄	1	2	yes	—
298	C₂×#1783	C₂⁴	1	2	yes	—
299	#20585	C₂×D₄	1	2	yes	—
300	#20585	C₂×D₄	1	2	yes	—
301	C₂×#1781	C₂×D₄	1	2	yes	—
302	C₂×#1781	C₂×D₄	1	2	yes	—
303	C₂×#1781	C₂×D₄	1	2	yes	—
304	C₂×#1781	C₂×D₄	1	2	yes	—
305	C₂×#1781	C₂×D₄	1	2	yes	—
306	C₂×#1781	C₂×D₄	1	2	yes	—
307	C₂×#1781	C₂×D₄	1	2	yes	—
308	C₂×#1781	C₂⁴	1	2	yes	—
309	C₂×#1781	C₂⁴	1	2	yes	—
310	C₂×#1781	C₂⁴	1	2	yes	—
311	C₂×#1781	C₂⁴	1	1	yes	characteristic
312	C₂×#1781	C₂⁴	1	1	yes	characteristic
313	C₂×#1781	C₂⁴	1	1	yes	characteristic
314	C₂×#1781	C₂⁴	1	1	yes	characteristic
315	C₂×#1781	C₂⁴	1	1	yes	characteristic
316	C₂×#1781	C₂⁴	1	1	yes	characteristic
317	C₂×#1781	C₂⁴	1	1	yes	characteristic
318	C₂×#1781	C₂⁴	1	1	yes	characteristic
319	C₂×#1781	C₂⁴	1	2	yes	—
320	#15262	C₂×D₄	1	2	yes	—
321	#15261	C₂×D₄	1	2	yes	—
322	#15259	C₂×D₄	1	2	yes	—
323	#15258	C₂×D₄	1	2	yes	—
324	C₂×#1438	C₂⁴	1	2	yes	—
325	#8546	C₂×D₄	1	4	yes	—
326	#8544	C₂×D₄	1	4	yes	—
327	#8534	C₂×D₄	1	4	yes	—
328	#8534	C₂×D₄	1	4	yes	—
329	#8534	C₂×D₄	1	4	yes	—
330	#8534	C₂×D₄	1	4	yes	—
331	C₂⁷	C₂²×D₄	1	1	yes	characteristic
332	C₂⁷	H(5,𝔽₂)	1	1	yes	characteristic
333	C₂²×H(5,𝔽₂)	#120	1	2	yes	—
334	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
335	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
336	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
337	C₂²×H(5,𝔽₂)	C₂×#41	1	2	yes	—
338	C₂³×#41	C₂×#41	1	2	yes	—
339	C₂⁴×D₄	#120	1	2	yes	—
340	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
341	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
342	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
343	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
344	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
345	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
346	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
347	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
348	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
349	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
350	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
351	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
352	C₂⁴×D₄	C₂⁵	1	1	yes	characteristic
353	C₂⁵×C₄	C₂×#41	1	1	yes	characteristic
354	#3484	C₂²×D₄	1	4	yes	—
355	#3484	C₂²×D₄	1	4	yes	—
356	#3484	H(5,𝔽₂)	1	4	yes	—
357	#3484	H(5,𝔽₂)	1	4	yes	—
358	C₂×#534	#120	1	2	yes	—
359	C₂×#534	#120	1	2	yes	—
360	C₂×#534	C₂²×D₄	1	2	yes	—
361	C₂×#534	C₂²×D₄	1	2	yes	—
362	C₂²×#127	C₂²×D₄	1	2	yes	—
363	C₂²×#127	H(5,𝔽₂)	1	2	yes	—
364	C₂²×#124	C₂²×D₄	1	2	yes	—
365	C₂²×#124	H(5,𝔽₂)	1	2	yes	—
366	C₂²×#123	C₂²×D₄	1	2	yes	—
367	C₂²×#120	#120	1	2	yes	—
368	C₂²×#120	#120	1	2	yes	—
369	C₂²×#120	C₂²×D₄	1	2	yes	—
370	C₂²×#120	C₂²×D₄	1	2	yes	—
371	C₂²×#120	C₂²×D₄	1	2	yes	—
372	C₂×#518	#120	1	2	yes	—
373	C₂×#518	C₂²×D₄	1	1	yes	characteristic
374	C₂×#518	C₂²×D₄	1	1	yes	characteristic
375	C₂×#518	C₂²×D₄	1	1	yes	characteristic
376	C₂×#518	C₂²×D₄	1	1	yes	characteristic
377	C₂×#518	C₂²×D₄	1	1	yes	characteristic
378	C₂×#518	C₂×#41	1	2	yes	—
379	C₂²×#117	C₂×#41	1	2	yes	—
380	C₂³×C₂²⋊C₄	#120	1	2	yes	—
381	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
382	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
383	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
384	C₂²×#99	C₂²×D₄	1	2	yes	—
385	C₂²×#99	C₂²×D₄	1	2	yes	—
386	C₂²×#99	C₂²×D₄	1	2	yes	—
387	C₂²×#99	C₂²×D₄	1	2	yes	—
388	C₂²×#99	C₂²×D₄	1	2	yes	—
389	C₂²×#99	C₂²×D₄	1	2	yes	—
390	#2849	#120	1	4	yes	complemented
391	#2846	#120	1	4	yes	complemented
392	C₂×#379	C₂²×D₄	1	2	yes	—
393	C₂×#379	C₂²×D₄	1	2	yes	—
394	#1898	#120	1	8	yes	complemented
395	#1781	C₂²×D₄	1	4	yes	—
396	#1781	C₂²×D₄	1	4	yes	—
397	#1438	C₂²×D₄	1	2	yes	—
398	#1438	C₂²×D₄	1	2	yes	—
399	C₂⁶	B(4,𝔽₂)	1	2	yes	—
400	C₂⁶	C₂×#120	1	1	yes	characteristic
401	C₂⁶	C₂×#120	1	1	yes	characteristic
402	C₂⁶	C₂×#120	1	1	yes	characteristic
403	C₂⁶	#535	1	1	yes	characteristic
404	C₂⁶	#535	1	1	yes	characteristic
405	C₂⁶	#546	1	1	yes	characteristic
406	C₂⁶	#546	1	1	yes	characteristic
407	C₂⁶	#546	1	1	yes	characteristic
408	C₂⁶	#546	1	1	yes	characteristic
409	C₂⁶	#546	1	1	yes	characteristic
410	C₂⁶	#546	1	1	yes	characteristic
411	C₂⁶	#546	1	1	yes	characteristic
412	C₂⁶	C₂³×D₄	1	1	yes	characteristic
413	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂×H(5,𝔽₂)	D₄²	1	4	yes	—
415	C₂×H(5,𝔽₂)	#546	1	4	yes	—
416	C₂³×Q₈	#546	1	2	yes	—
417	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
418	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
419	C₂³×D₄	C₂×#120	1	1	yes	characteristic
420	C₂³×D₄	C₂×#120	1	1	yes	characteristic
421	C₂³×D₄	C₂×#120	1	2	yes	—
422	C₂³×D₄	C₂×#120	1	2	yes	—
423	C₂³×D₄	#525	1	1	yes	characteristic
424	C₂³×D₄	#525	1	1	yes	characteristic
425	C₂³×D₄	#535	1	1	yes	characteristic
426	C₂³×D₄	#535	1	1	yes	characteristic
427	C₂³×D₄	#546	1	1	yes	characteristic
428	C₂³×D₄	#546	1	1	yes	characteristic
429	C₂³×D₄	#546	1	1	yes	characteristic
430	C₂³×D₄	#546	1	1	yes	characteristic
431	C₂³×D₄	#546	1	2	yes	—
432	C₂³×D₄	#546	1	1	yes	characteristic
433	C₂³×D₄	#546	1	1	yes	characteristic
434	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
435	C₂³×D₄	C₂³×D₄	1	2	yes	—
436	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
437	C₂³×D₄	C₂²×#41	1	1	yes	characteristic
438	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
439	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
440	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
441	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
442	C₂⁴×C₄	B(4,𝔽₂)	1	2	yes	—
443	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
444	C₂⁴×C₄	#525	1	1	yes	characteristic
445	C₂⁴×C₄	#525	1	1	yes	characteristic
446	C₂⁴×C₄	#546	1	1	yes	characteristic
447	C₂⁴×C₄	#546	1	1	yes	characteristic
448	C₂⁴×C₄	#546	1	1	yes	characteristic
449	C₂⁴×C₄	C₂²×#41	1	1	yes	characteristic
450	#534	D₄²	1	8	yes	—
451	C₂×#120	B(4,𝔽₂)	1	8	yes	—
452	C₂×#120	C₂×#120	1	4	yes	—
453	C₂×#120	#534	1	4	yes	—
454	#518	D₄²	1	4	yes	—
455	#518	#546	1	4	yes	—
456	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
457	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
458	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
459	C₂²×C₄²	#546	1	2	yes	—
460	C₂²×C₄²	#546	1	2	yes	—
461	#379	C₂×#120	1	4	yes	—
462	C₂⁵	#2404	1	1	yes	characteristic
463	C₂⁵	#2404	1	1	yes	characteristic
464	C₂⁵	#2404	1	1	yes	characteristic
465	C₂⁵	#2404	1	1	yes	characteristic
466	C₂⁵	#2404	1	1	yes	characteristic
467	C₂⁵	#2404	1	1	yes	characteristic
468	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
469	C₂⁵	C₂×B(4,𝔽₂)	1	4	yes	—
470	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
471	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
472	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
473	C₂⁵	C₂²×#120	1	1	yes	characteristic
474	C₂⁵	C₂²×#120	1	1	yes	characteristic
475	C₂⁵	C₂×#534	1	1	yes	characteristic
476	C₂⁵	C₂×#535	1	1	yes	characteristic
477	C₂⁵	C₂×#546	1	1	yes	characteristic
478	C₂⁵	C₂×#546	1	1	yes	characteristic
479	C₂⁵	C₂×#546	1	1	yes	characteristic
480	C₂⁵	#3484	1	2	yes	—
481	C₂⁵	#3484	1	1	yes	characteristic
482	C₂⁵	#3484	1	1	yes	characteristic
483	C₂⁵	#3532	1	2	yes	—
484	C₂²×D₄	#2403	1	4	yes	—
485	C₂²×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
486	C₂²×D₄	C₂×D₄²	1	2	yes	—
487	C₂²×D₄	C₂×D₄²	1	2	yes	—
488	C₂²×D₄	C₂×#546	1	2	yes	—
489	C₂²×D₄	#3484	1	2	yes	—
490	C₂²×D₄	#3484	1	2	yes	—
491	C₂²×D₄	#3484	1	2	yes	—
492	C₂²×D₄	#3490	1	2	yes	—
493	C₂²×D₄	#3532	1	2	yes	—
494	C₂³×C₄	#2404	1	1	yes	characteristic
495	C₂³×C₄	#2404	1	1	yes	characteristic
496	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
497	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
498	C₂³×C₄	C₂×#525	1	1	yes	characteristic
499	C₂³×C₄	C₂×#546	1	2	yes	—
500	C₂³×C₄	C₂×#546	1	1	yes	characteristic
501	C₂³×C₄	#3490	1	2	yes	—
502	C₂×C₂²⋊C₄	#2403	1	4	yes	—
503	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	4	yes	—
504	C₂⁴	#23900	1	4	yes	—
505	C₂⁴	#23984	1	1	yes	characteristic
506	C₂⁴	#23984	1	1	yes	characteristic
507	C₂⁴	#23984	1	2	yes	—
508	C₂⁴	#23984	1	2	yes	—
509	C₂⁴	#23984	1	2	yes	—
510	C₂⁴	#23996	1	2	yes	—
511	C₂⁴	C₂×#2403	1	1	yes	characteristic
512	C₂⁴	C₂×#2404	1	1	yes	characteristic
513	C₂⁴	#35346	1	1	yes	characteristic
514	C₂⁴	#36152	1	1	yes	characteristic
515	C₂⁴	#36152	1	1	yes	characteristic
516	C₂⁴	#37645	1	2	yes	—
517	C₂⁴	#37832	1	1	yes	characteristic
518	C₂⁴	#37832	1	1	yes	characteristic
519	C₂⁴	#58991	1	2	yes	—
520	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
521	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
522	C₂²×C₄	#23900	1	4	yes	—
523	C₂²×C₄	#36098	1	2	yes	—
524	C₂²×C₄	#58991	1	2	yes	—
525	C₂³	#647657	1	1	yes	characteristic
526	C₂³	C₂×#23900	1	2	yes	—
527	C₂³	C₂×#23996	1	1	yes	characteristic
528	C₂³	#6451863	1	1	yes	characteristic
529	C₂³	#6451863	1	1	yes	characteristic
530	C₂³	#6451863	1	1	yes	characteristic
531	C₂³	C₂×#23984	1	1	yes	characteristic
532	C₂³	C₂×#23984	1	1	yes	characteristic
533	C₂³	#6499867	1	2	yes	—
534	C₂²	#72217617	1	1	yes	characteristic
535	C₂²	#72234644	1	1	yes	characteristic
536	C₂²	#72234955	1	1	yes	characteristic
537	C₂²	#72240110	1	1	yes	characteristic
538	C₂²	#72252238	1	1	yes	characteristic
539	C₂²	#72258461	1	1	yes	characteristic
540	C₂²	#72265948	1	1	yes	characteristic
541	C₂	#72266216	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72266216
commutator, Frattini, cosocle	C₂⁴×D₄	C₂⁵
LCS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72315164	C₂	semidirect
2. #72315149	C₂	semidirect
3. #72315059	C₂	semidirect
4. #72315031	C₂	semidirect
5. #72314996	C₂	semidirect
6. #72314884	C₂	semidirect
7. #72314879	C₂	semidirect
8. #72314855	C₂²	semidirect
9. #72314760	C₂	semidirect
10. #72314748	C₂²	semidirect
11. #72314748	C₂²	semidirect
12. #72314746	C₂	semidirect
13. #72314739	C₂²	semidirect
14. #72314734	C₂²	semidirect
15. #72314729	C₂²	semidirect
16. #72314671	C₂	semidirect
17. #72314665	C₂²	semidirect
18. #72312328	C₂	semidirect
19. #72312312	C₂²	semidirect
20. #72312258	C₂	semidirect
21. #72310327	C₂	semidirect
22. #72310322	C₂²	semidirect
23. #72310319	C₂²	semidirect
24. #72309483	C₂	semidirect
25. #72309478	C₂²	semidirect
26. #72309478	C₂²	semidirect
27. #72266873	C₂	semidirect
28. #72266836	C₂	semidirect
33. #72266378	C₂²	semidirect
34. #72264793	C₂	semidirect
35. #72264784	C₂	semidirect
36. #72264765	C₂²	semidirect
37. #72264754	C₂²	semidirect
38. #72263490	C₂²	semidirect
39. #72260584	C₂²	semidirect
40. #72260562	C₂²	semidirect
41. #72259117	C₂²	semidirect
42. C₂×#135516	C₂²	semidirect
43. #72258334	C₂²	semidirect
44. C₂×#144639	C₂²	semidirect
49. #72255980	C₂²	semidirect
50. #72255874	C₂²	semidirect
51. #72251547	C₂	semidirect
52. #72251533	C₂²	semidirect
53. #72251530	C₂²	semidirect
54. #72251528	C₂²	semidirect
55. #72251527	C₂²	semidirect
56. #72251291	C₂	semidirect
57. #72251157	C₂²	semidirect
58. #72251143	C₂²	semidirect
59. #72251140	C₂²	semidirect
60. #72251140	C₂²	semidirect
61. #72246287	C₂²	semidirect
62. #72246286	C₂²	semidirect
63. #72238613	C₂²	semidirect
64. #72238352	C₂	semidirect
65. #72238351	C₂²	semidirect
66. #72238350	C₂²	semidirect
67. #72238349	C₂²	semidirect
68. #72238345	C₂	semidirect
69. #72238344	C₂	semidirect
74. #72237900	C₂²	semidirect
75. #72237899	C₂²	semidirect
76. #72237829	C₂²	semidirect
77. #72237638	C₂²	semidirect
78. #72237633	C₂²	semidirect
79. #72237632	C₂²	semidirect
80. #72237473	C₂²	semidirect
82. #72237374	C₂²	semidirect
83. #72236508	C₂²	semidirect
87. #72226366	C₂²	semidirect
88. #72225713	C₂²	semidirect
89. #72225667	C₂²	semidirect
90. #72225650	C₂²	semidirect
91. #72225617	C₂²	semidirect
92. #72219418	C₂²	semidirect
93. #72219414	C₂²	semidirect
94. #72219311	C₂²	semidirect
97. #72219300	C₂²	semidirect
99. #72219251	C₂²	semidirect
100. #72219248	C₂²	semidirect
101. #72219248	C₂²	semidirect
102. #72219237	C₂²	semidirect
105. #72219160	C₂²	semidirect
106. #72219160	C₂²	semidirect
107. #72218381	C₂²	semidirect
108. #72218381	C₂²	semidirect
109. #72218313	C₂²	semidirect
112. C₂×#139743	C₂²	semidirect
113. C₂×#139743	C₂²	semidirect
114. #72218057	C₂²	semidirect
128. #7641845	D₄	semidirect
131. C₂×#32873	C₂³	semidirect
132. #6440460	D₄	semidirect
136. #6440460	C₂³	semidirect
137. C₂×#23895	D₄	semidirect
141. #6437621	D₄	semidirect
142. #6437621	D₄	semidirect
146. #6437621	C₂³	semidirect
148. #6374251	C₂³	semidirect
149. C₂×#21776	D₄	semidirect
153. C₂×#21776	C₂³	semidirect
154. #6374128	C₂³	semidirect
155. C₂×#21746	D₄	semidirect
156. #6370693	D₄	semidirect
162. #493879	C₂³	semidirect
167. C₂×#12707	C₂³	semidirect
178. #493357	C₂³	semidirect
179. #392231	D₄	semidirect
187. #392030	C₂³	semidirect
188. #392030	C₂³	semidirect
189. #392030	C₂³	semidirect
190. #382707	C₂³	semidirect
191. #382707	C₂³	semidirect
192. #382544	C₂³	semidirect
193. #382434	D₄	semidirect
197. #382434	C₂³	semidirect
198. #359811	C₂³	semidirect
199. #359549	D₄	semidirect
204. #359442	D₄	semidirect
205. #359442	C₂³	semidirect
206. #355096	C₂³	semidirect
207. #347057	D₄	semidirect
208. #347056	D₄	semidirect
209. #347047	D₄	semidirect
210. #347045	D₄	semidirect
211. #190116	C₂³	semidirect
214. #188049	C₂³	semidirect
219. C₂×#8534	C₂³	semidirect
220. #146479	C₂³	semidirect
221. C₂×#7304	C₂³	semidirect
222. C₂×#7304	C₂³	semidirect
223. C₂×#7316	C₂³	semidirect
224. C₂×#7316	C₂³	semidirect
225. C₂×#7314	C₂³	semidirect
226. C₂×#7314	C₂³	semidirect
227. C₂×#7310	C₂³	semidirect
228. C₂×#7310	C₂³	semidirect
229. C₂×#7310	C₂³	semidirect
230. C₂×#7310	C₂³	semidirect
231. C₂×#7310	C₂³	semidirect
232. C₂×#7310	C₂³	semidirect
233. C₂×#7307	C₂³	semidirect
234. C₂×#7307	C₂³	semidirect
235. C₂×#7307	C₂³	semidirect
236. C₂×#7307	C₂³	semidirect
237. #108222	C₂³	semidirect
239. C₂³×H(5,𝔽₂)	#41	semidirect
240. C₂³×H(5,𝔽₂)	#41	semidirect
250. C₂×#3484	#41	semidirect
259. C₂²×#525	#41	semidirect
263. C₂²×#518	#41	semidirect
264. C₂²×#518	#41	semidirect
390. #2849	#120	semidirect
391. #2846	#120	semidirect
394. #1898	#120	semidirect

Maximal subgroups

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

subgroup	index
#72315164	2
#72315149	2
#72315059	2
#72315031	2
#72314996	2
#72314884	2
#72314879	2
#72314760	2
#72314746	2
#72314671	2
#72312328	2
#72312258	2
#72310327	2
#72309483	2
#72266873	2
#72266836	2
#72264793	2
#72264784	2
#72251547	2
#72251291	2
#72238352	2
#72238345	2
#72238344	2