Subgroups — #72265206

Order 2048.

At least 15044 conjugacy classes of subgroups; only the 1086 normal subgroups are shown.

The subgroup lattice has 584 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72265195	C₂	1	1	yes	maximal, characteristic, complemented
2	#72265188	C₂	1	1	yes	maximal, characteristic, complemented
3	#72265184	C₂	1	2	yes	maximal, complemented
4	#72241329	C₂	1	1	yes	maximal, characteristic, complemented
5	#72234960	C₂	1	2	yes	maximal, complemented
6	#72234958	C₂	1	4	yes	maximal, complemented
7	#72234644	C₂	1	2	yes	maximal, complemented
8	#72234596	C₂	1	2	yes	maximal, complemented
9	#72234150	C₂	1	2	yes	maximal, complemented
10	#72233348	C₂	1	1	yes	maximal, characteristic, complemented
11	#72233199	C₂	1	2	yes	maximal, complemented
12	#72233156	C₂	1	2	yes	maximal, complemented
13	#72232934	C₂	1	4	yes	maximal, complemented
14	#72232787	C₂	1	1	yes	maximal, characteristic, complemented
15	#72225689	C₂	1	1	yes	maximal, characteristic, complemented
16	#72225609	C₂	1	2	yes	maximal, complemented
17	#72219461	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#3026	C₂²	1	1	yes	characteristic, complemented
19	#7804411	C₂²	1	2	yes	—
20	#7752093	C₂²	1	2	yes	complemented
21	#7733089	C₂²	1	2	yes	complemented
22	#7675392	C₂²	1	2	yes	—
23	#7644631	C₂²	1	1	yes	characteristic, complemented
24	C₂×#37644	C₂²	1	1	yes	characteristic
25	#7631286	C₂²	1	1	yes	characteristic
26	#7631286	C₂²	1	1	yes	characteristic
27	C₂×#35346	C₂²	1	1	yes	characteristic, complemented
28	#7626568	C₂²	1	1	yes	characteristic
29	#7626202	C₂²	1	1	yes	characteristic, complemented
30	C₂²⋊C₄×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
31	C₂×#32898	C₂²	1	2	yes	—
32	C₂×#32898	C₂²	1	2	yes	complemented
33	C₂×#32898	C₂²	1	1	yes	characteristic, complemented
34	#6385971	C₂²	1	1	yes	characteristic
35	#6370693	C₂²	1	2	yes	complemented
36	#616960	C₂²	1	2	yes	—
37	#394470	C₂²	1	4	yes	complemented
38	#394267	C₂²	1	2	yes	complemented
39	#394061	C₂²	1	2	yes	complemented
40	#393929	C₂²	1	4	yes	complemented
41	#392125	C₂²	1	2	yes	complemented
42	#374038	C₂²	1	2	yes	complemented
43	#374038	C₂²	1	1	yes	characteristic, complemented
44	#364471	C₂²	1	2	yes	—
45	#364471	C₂²	1	4	yes	complemented
46	#359892	C₂²	1	2	yes	complemented
47	#359579	C₂²	1	1	yes	characteristic
48	#359504	C₂²	1	1	yes	characteristic, complemented
49	#359442	C₂²	1	2	yes	complemented
50	#359442	C₂²	1	4	yes	complemented
51	#238082	C₂²	1	4	yes	complemented
52	#233541	C₂²	1	4	yes	complemented
53	C₂×#10336	C₂²	1	4	yes	complemented
54	#201678	C₂²	1	4	yes	complemented
55	#201664	C₂²	1	2	yes	—
56	#201664	C₂²	1	2	yes	—
57	#201664	C₂²	1	2	yes	complemented
58	#201664	C₂²	1	2	yes	complemented
59	#201664	C₂²	1	4	yes	complemented
60	#201664	C₂²	1	2	yes	complemented
61	#201664	C₂²	1	4	yes	complemented
62	C₂×#9495	C₂²	1	2	yes	—
63	#190107	C₂²	1	2	yes	complemented
64	#188035	C₂²	1	1	yes	characteristic
65	C₂×#8541	C₂²	1	2	yes	complemented
66	#181344	C₂²	1	2	yes	complemented
67	#122191	C₂²	1	4	yes	complemented
68	#122187	C₂²	1	4	yes	complemented
69	#115631	C₂²	1	2	yes	complemented
70	#115204	C₂²	1	4	yes	complemented
71	#115163	C₂²	1	2	yes	complemented
72	#115133	C₂²	1	4	yes	complemented
73	#111458	C₂²	1	4	yes	complemented
74	#107194	C₂²	1	4	yes	complemented
75	#107114	C₂²	1	4	yes	complemented
76	#106766	C₂²	1	2	yes	complemented
77	#106766	C₂²	1	2	yes	complemented
78	#106766	C₂²	1	4	yes	complemented
79	#106766	C₂²	1	4	yes	complemented
80	#106654	C₂²	1	2	yes	complemented
81	#106654	C₂²	1	4	yes	complemented
82	#106542	C₂²	1	2	yes	complemented
83	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
84	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
85	C₂×#3490	D₄	1	2	yes	complemented
86	C₂²×D₄²	C₂³	1	1	yes	characteristic
87	C₂²×#534	C₂³	1	2	yes	—
88	C₂²×#534	C₂³	1	1	yes	characteristic
89	C₂³×#120	D₄	1	1	yes	characteristic, complemented
90	C₂³×#120	C₂³	1	1	yes	characteristic
91	C₂³×#99	C₂³	1	1	yes	characteristic
92	C₂³×#99	C₂³	1	2	yes	—
93	#47563	D₄	1	2	yes	complemented
94	#46996	D₄	1	2	yes	complemented
95	#46387	D₄	1	2	yes	complemented
96	#46387	D₄	1	2	yes	complemented
97	#46387	D₄	1	2	yes	complemented
98	#46384	D₄	1	2	yes	complemented
99	#46384	D₄	1	2	yes	complemented
100	#46384	D₄	1	2	yes	complemented
101	#37475	C₂³	1	2	yes	—
102	C₂×#2846	D₄	1	1	yes	characteristic, complemented
103	#35527	D₄	1	2	yes	complemented
104	#35512	D₄	1	2	yes	complemented
105	#35360	D₄	1	2	yes	complemented
106	#35360	D₄	1	2	yes	complemented
107	#35348	D₄	1	2	yes	complemented
108	#35348	D₄	1	2	yes	complemented
109	#35347	D₄	1	1	yes	characteristic, complemented
110	#35347	D₄	1	1	yes	characteristic, complemented
111	#35346	D₄	1	1	yes	characteristic, complemented
112	#35346	D₄	1	1	yes	characteristic, complemented
113	#34993	D₄	1	2	yes	complemented
114	#34982	C₂³	1	2	yes	—
115	#34981	D₄	1	2	yes	complemented
116	#34980	C₂³	1	2	yes	—
117	#34980	C₂³	1	2	yes	—
118	C₂×#2539	D₄	1	1	yes	characteristic, complemented
119	C₂×#2534	D₄	1	1	yes	characteristic, complemented
120	C₂×#2412	D₄	1	1	yes	characteristic, complemented
121	C₂×#2405	D₄	1	1	yes	characteristic, complemented
122	C₂×#2410	C₂³	1	1	yes	characteristic
123	C₂×#2403	C₂³	1	2	yes	—
124	C₂×#2403	C₂³	1	2	yes	—
125	C₂×#2403	C₂³	1	2	yes	—
126	C₂×#2403	C₂³	1	2	yes	—
127	C₂×#2403	C₂³	1	1	yes	characteristic
128	C₂×#2403	C₂³	1	2	yes	—
129	C₂×#2403	C₂³	1	4	yes	—
130	C₂×#2617	D₄	1	1	yes	characteristic, complemented
131	C₂×#2613	C₂³	1	1	yes	characteristic
132	#34363	D₄	1	2	yes	complemented
133	#34356	D₄	1	2	yes	complemented
134	#34356	C₂³	1	2	yes	—
135	#34273	D₄	1	2	yes	complemented
136	#34185	D₄	1	1	yes	characteristic, complemented
137	#34171	D₄	1	1	yes	characteristic, complemented
138	#34171	C₂³	1	1	yes	characteristic
139	#34171	C₂³	1	2	yes	—
140	#34171	C₂³	1	1	yes	characteristic
141	#34171	C₂³	1	1	yes	characteristic
142	#34171	C₂³	1	2	yes	—
143	#34171	C₂³	1	2	yes	—
144	#34171	C₂³	1	2	yes	—
145	#34171	C₂³	1	2	yes	—
146	C₂×D₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×D₄×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂×#2321	D₄	1	1	yes	characteristic, complemented
149	#34057	D₄	1	1	yes	characteristic, complemented
150	C₂×#2308	D₄	1	1	yes	characteristic, complemented
151	C₂×#2308	C₂³	1	1	yes	characteristic
152	#21746	C₂³	1	2	yes	—
153	#21746	C₂³	1	2	yes	—
154	C₂×#1898	C₂³	1	2	yes	—
155	C₂×#1781	C₂³	1	2	yes	—
156	C₂×#1781	C₂³	1	4	yes	—
157	C₂×#1781	C₂³	1	4	yes	—
158	C₂×#1781	C₂³	1	2	yes	—
159	C₂×#1781	C₂³	1	2	yes	—
160	C₂×#1781	C₂³	1	2	yes	—
161	C₂×#1781	C₂³	1	4	yes	—
162	C₂×#1781	C₂³	1	1	yes	characteristic
163	C₂×#1781	C₂³	1	4	yes	—
164	C₂×#1781	C₂³	1	4	yes	—
165	C₂×#1781	C₂³	1	4	yes	—
166	C₂×#1781	C₂³	1	4	yes	—
167	#14335	C₂³	1	2	yes	—
168	#13867	C₂³	1	2	yes	—
169	#13867	C₂³	1	2	yes	—
170	#13867	C₂³	1	4	yes	—
171	#10735	C₂³	1	4	yes	—
172	#10735	C₂³	1	4	yes	—
173	#10735	C₂³	1	2	yes	—
174	#10735	C₂³	1	4	yes	—
175	#10735	C₂³	1	2	yes	—
176	#10725	C₂³	1	4	yes	—
177	#8101	C₂³	1	4	yes	—
178	#8101	C₂³	1	4	yes	—
179	#8101	C₂³	1	4	yes	—
180	#8101	C₂³	1	4	yes	—
181	#8101	C₂³	1	4	yes	—
182	C₂×#1304	C₂³	1	4	yes	—
183	C₂×#1304	C₂³	1	4	yes	—
184	C₂⁷	C₂×D₄	1	1	yes	characteristic
185	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
186	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
187	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
188	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
189	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
190	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
191	C₂⁴×D₄	C₂⁴	1	2	yes	—
192	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
193	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
194	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
195	C₂⁴×D₄	C₂⁴	1	2	yes	—
196	C₂×#543	C₂×D₄	1	2	yes	complemented
197	C₂×#534	C₂×D₄	1	2	yes	—
198	C₂×#534	C₂×D₄	1	2	yes	—
199	C₂×#534	C₂×D₄	1	2	yes	—
200	C₂×#534	C₂×D₄	1	2	yes	—
201	C₂²×#127	C₂×D₄	1	1	yes	characteristic
202	C₂²×#123	C₂×D₄	1	1	yes	characteristic
203	C₂²×#123	C₂×D₄	1	1	yes	characteristic
204	C₂²×#123	C₂×D₄	1	1	yes	characteristic
205	C₂²×#121	C₂×D₄	1	1	yes	characteristic
206	C₂²×#121	C₂×D₄	1	1	yes	characteristic
207	C₂²×#121	C₂×D₄	1	1	yes	characteristic
208	C₂²×#121	C₂×D₄	1	1	yes	characteristic
209	C₂²×#120	C₂×D₄	1	1	yes	characteristic
210	C₂²×#120	C₂×D₄	1	1	yes	characteristic
211	C₂²×#120	C₂×D₄	1	1	yes	characteristic
212	C₂²×#120	C₂×D₄	1	1	yes	characteristic
213	C₂²×#120	C₂×D₄	1	2	yes	—
214	C₂²×#120	C₂×D₄	1	1	yes	characteristic
215	C₂²×#120	C₂×D₄	1	1	yes	characteristic
216	C₂²×#120	C₂×D₄	1	2	yes	—
217	C₂²×#120	C₂×D₄	1	1	yes	characteristic
218	C₂²×#120	C₂×D₄	1	1	yes	characteristic
219	C₂²×#120	C₂×D₄	1	1	yes	characteristic
220	C₂²×#120	C₂×D₄	1	2	yes	complemented
221	C₂²×#120	C₂×D₄	1	2	yes	complemented
222	C₂²×#120	#41	1	4	yes	complemented
223	C₂²×#120	C₂⁴	1	1	yes	characteristic
224	C₂×#518	C₂×D₄	1	2	yes	—
225	C₂×#518	C₂×D₄	1	2	yes	—
226	C₂×#518	C₂×D₄	1	2	yes	complemented
227	C₂×#518	C₂×D₄	1	2	yes	complemented
228	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
230	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
231	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
232	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
233	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
234	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
235	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
236	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
237	#2842	C₂×D₄	1	2	yes	complemented
238	#2842	C₂×D₄	1	2	yes	complemented
239	#2842	C₂×D₄	1	2	yes	complemented
240	#2840	C₂×D₄	1	2	yes	complemented
241	#2405	C₂×D₄	1	2	yes	—
242	#2405	C₂×D₄	1	2	yes	—
243	#2403	C₂×D₄	1	2	yes	—
244	#2403	C₂×D₄	1	2	yes	—
245	#2403	C₂×D₄	1	2	yes	—
246	#2403	C₂×D₄	1	2	yes	—
247	#2403	C₂×D₄	1	2	yes	—
248	#2403	C₂×D₄	1	2	yes	—
249	#2403	C₂×D₄	1	2	yes	—
250	#2403	C₂×D₄	1	2	yes	—
251	#2403	C₂×D₄	1	2	yes	—
252	#2403	C₂×D₄	1	2	yes	—
253	#2403	C₂×D₄	1	2	yes	—
254	#2403	C₂×D₄	1	2	yes	—
255	#2403	C₂×D₄	1	2	yes	—
256	#2403	C₂×D₄	1	2	yes	—
257	#2403	C₂×D₄	1	2	yes	complemented
258	#2403	C₂×D₄	1	2	yes	complemented
259	#2403	C₂×D₄	1	2	yes	complemented
260	#2403	C₂×D₄	1	2	yes	complemented
261	#2315	C₂×D₄	1	2	yes	complemented
262	#2315	C₂×D₄	1	2	yes	complemented
263	#2315	C₂×D₄	1	2	yes	complemented
264	#2312	C₂×D₄	1	2	yes	—
265	#2312	C₂×D₄	1	2	yes	—
266	#2309	C₂×D₄	1	2	yes	—
267	#2309	C₂×D₄	1	2	yes	—
268	#2309	C₂×D₄	1	2	yes	—
269	#2309	C₂×D₄	1	2	yes	—
270	#2309	C₂×D₄	1	2	yes	—
271	#2309	C₂×D₄	1	2	yes	complemented
272	#2309	C₂×D₄	1	2	yes	complemented
273	#2309	C₂×D₄	1	2	yes	complemented
274	#2309	C₂×D₄	1	2	yes	complemented
275	#2308	C₂×D₄	1	1	yes	characteristic
276	#2308	C₂×D₄	1	1	yes	characteristic
277	#2308	C₂×D₄	1	2	yes	—
278	#2308	C₂×D₄	1	1	yes	characteristic
279	#2308	C₂×D₄	1	1	yes	characteristic
280	#2308	C₂×D₄	1	1	yes	characteristic
281	#2308	C₂×D₄	1	2	yes	—
282	#2308	C₂×D₄	1	1	yes	characteristic
283	#2308	C₂×D₄	1	2	yes	—
284	#2308	C₂×D₄	1	2	yes	—
285	#2308	C₂×D₄	1	2	yes	—
286	#2308	C₂×D₄	1	2	yes	—
287	#2308	C₂×D₄	1	2	yes	complemented
288	#2308	C₂×D₄	1	2	yes	complemented
289	#2308	C₂×D₄	1	2	yes	complemented
290	#2308	C₂×D₄	1	2	yes	complemented
291	#2308	C₂×D₄	1	2	yes	complemented
292	#2308	C₂×D₄	1	2	yes	complemented
293	C₂×#386	C₂×D₄	1	1	yes	characteristic
294	C₂×#386	C₂×D₄	1	1	yes	characteristic
295	C₂×#386	C₂×D₄	1	1	yes	characteristic
296	C₂×#386	C₂×D₄	1	2	yes	—
297	C₂×#386	C₂×D₄	1	2	yes	—
298	C₂×#386	C₂×D₄	1	2	yes	complemented
299	C₂×#386	C₂×D₄	1	2	yes	complemented
300	C₂×#386	#41	1	4	yes	complemented
301	C₂×#385	C₂×D₄	1	1	yes	characteristic
302	#2280	C₂×D₄	1	2	yes	—
303	#2280	C₂×D₄	1	2	yes	—
304	C₂×#381	C₂×D₄	1	1	yes	characteristic
305	C₂×#380	C₂×D₄	1	1	yes	characteristic
306	C₂×#380	C₂×D₄	1	2	yes	complemented
307	C₂×#379	C₂×D₄	1	2	yes	—
308	C₂×#379	C₂×D₄	1	2	yes	—
309	C₂×#379	C₂×D₄	1	1	yes	characteristic
310	C₂×#379	C₂×D₄	1	1	yes	characteristic
311	C₂×#379	C₂×D₄	1	1	yes	characteristic
312	C₂×#379	C₂×D₄	1	2	yes	complemented
313	C₂×#379	C₂⁴	1	2	yes	—
314	C₂×#379	C₂⁴	1	4	yes	—
315	C₂×#379	C₂⁴	1	4	yes	—
316	C₂×#379	C₂⁴	1	2	yes	—
317	C₂×#379	C₂⁴	1	1	yes	characteristic
318	C₂×#379	C₂⁴	1	2	yes	—
319	C₂×#379	C₂⁴	1	2	yes	—
320	C₂×#379	C₂⁴	1	2	yes	—
321	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
322	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
323	C₂⁶	#120	1	1	yes	characteristic
324	C₂⁶	C₂²×D₄	1	1	yes	characteristic
325	C₂⁶	C₂²×D₄	1	1	yes	characteristic
326	C₂⁶	C₂²×D₄	1	2	yes	—
327	C₂⁶	C₂²×D₄	1	1	yes	characteristic
328	C₂⁶	C₂²×D₄	1	1	yes	characteristic
329	C₂⁶	C₂×#41	1	2	yes	complemented
330	C₂⁶	C₂⁵	1	1	yes	characteristic
331	C₂³×D₄	#120	1	1	yes	characteristic
332	C₂³×D₄	#120	1	1	yes	characteristic
333	C₂³×D₄	#120	1	1	yes	characteristic
334	C₂³×D₄	#120	1	1	yes	characteristic
335	C₂³×D₄	#120	1	1	yes	characteristic
336	C₂³×D₄	C₂²×D₄	1	2	yes	—
337	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
338	C₂³×D₄	C₂²×D₄	1	2	yes	—
339	C₂³×D₄	C₂²×D₄	1	2	yes	—
340	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
341	C₂³×D₄	C₂²×D₄	1	2	yes	—
342	C₂³×D₄	C₂²×D₄	1	2	yes	—
343	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
344	C₂³×D₄	C₂²×D₄	1	2	yes	—
345	C₂³×D₄	C₂²×D₄	1	2	yes	—
346	C₂³×D₄	C₂²×D₄	1	2	yes	—
347	C₂³×D₄	C₂²×D₄	1	2	yes	—
348	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
349	C₂³×D₄	C₂²×D₄	1	2	yes	—
350	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
351	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
352	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
353	C₂³×D₄	C₂²×D₄	1	2	yes	—
354	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
355	C₂³×D₄	C₂²×D₄	1	2	yes	—
356	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
357	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
358	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
359	C₂³×D₄	C₂×#41	1	4	yes	—
360	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
361	C₂⁴×C₄	#120	1	1	yes	characteristic
362	C₂⁴×C₄	#120	1	1	yes	characteristic
363	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
364	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
365	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
366	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
367	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
368	C₂⁴×C₄	C₂×#41	1	2	yes	complemented
369	C₂×#123	#120	1	2	yes	—
370	C₂×#123	#120	1	2	yes	—
371	C₂×#123	#120	1	2	yes	—
372	C₂×#123	#120	1	2	yes	—
373	C₂×#120	#120	1	1	yes	characteristic
374	C₂×#120	#120	1	1	yes	characteristic
375	C₂×#120	#120	1	1	yes	characteristic
376	C₂×#120	#120	1	2	yes	—
377	C₂×#120	#120	1	1	yes	characteristic
378	C₂×#120	#120	1	2	yes	—
379	C₂×#120	#120	1	1	yes	characteristic
380	C₂×#120	#120	1	1	yes	characteristic
381	C₂×#120	#120	1	1	yes	characteristic
382	C₂×#120	#120	1	1	yes	characteristic
383	C₂×#120	#120	1	2	yes	—
384	C₂×#120	#120	1	2	yes	—
385	C₂×#120	#120	1	2	yes	complemented
386	C₂×#120	#120	1	2	yes	complemented
387	C₂×#120	#120	1	2	yes	complemented
388	C₂×#120	#120	1	2	yes	complemented
389	C₂×#120	#120	1	2	yes	complemented
390	C₂×#120	#120	1	2	yes	complemented
391	C₂×#120	#120	1	2	yes	complemented
392	C₂×#120	#120	1	2	yes	complemented
393	C₂×#117	#120	1	2	yes	complemented
394	C₂×#117	#120	1	2	yes	complemented
395	C₂×#117	#120	1	2	yes	complemented
396	C₂×#117	#120	1	2	yes	complemented
397	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
398	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
399	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
400	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
401	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
402	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
403	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
404	C₂²×C₂²⋊C₄	#120	1	2	yes	complemented
405	C₂²×C₂²⋊C₄	#120	1	2	yes	complemented
406	C₂²×C₂²⋊C₄	#120	1	2	yes	complemented
407	C₂²×C₂²⋊C₄	#120	1	2	yes	complemented
408	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
409	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
410	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
411	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
412	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
413	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
414	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
415	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
416	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
417	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
418	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
419	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
420	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
421	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
422	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
423	C₂²×C₂²⋊C₄	C₂×#41	1	4	yes	complemented
424	C₂²×C₄²	#120	1	1	yes	characteristic
425	#386	#120	1	2	yes	—
426	#386	#120	1	2	yes	—
427	#386	#120	1	2	yes	—
428	#386	#120	1	2	yes	—
429	#386	#120	1	2	yes	complemented
430	#386	#120	1	2	yes	complemented
431	#386	#120	1	2	yes	complemented
432	#386	#120	1	2	yes	complemented
433	#386	#120	1	2	yes	complemented
434	#386	#120	1	2	yes	complemented
435	#386	#120	1	2	yes	complemented
436	#386	#120	1	2	yes	complemented
437	#381	#120	1	2	yes	complemented
438	#381	#120	1	2	yes	complemented
439	#381	#120	1	2	yes	complemented
440	#381	#120	1	2	yes	complemented
441	#379	#120	1	2	yes	complemented
442	#379	#120	1	2	yes	complemented
443	#379	#120	1	2	yes	complemented
444	#379	#120	1	2	yes	complemented
445	#379	C₂²×D₄	1	2	yes	—
446	#379	C₂²×D₄	1	2	yes	—
447	#379	C₂²×D₄	1	2	yes	—
448	#379	C₂²×D₄	1	2	yes	—
449	#379	C₂²×D₄	1	2	yes	—
450	#379	C₂²×D₄	1	2	yes	—
451	#379	C₂²×D₄	1	2	yes	—
452	#379	C₂²×D₄	1	2	yes	—
453	#379	C₂²×D₄	1	2	yes	—
454	#379	C₂²×D₄	1	2	yes	—
455	#379	C₂²×D₄	1	2	yes	—
456	#379	C₂²×D₄	1	2	yes	—
457	#379	C₂²×D₄	1	2	yes	—
458	#379	C₂²×D₄	1	2	yes	—
459	C₂⁵	C₂×#120	1	1	yes	characteristic
460	C₂⁵	C₂×#120	1	1	yes	characteristic
461	C₂⁵	C₂×#120	1	1	yes	characteristic
462	C₂⁵	C₂×#120	1	1	yes	characteristic
463	C₂⁵	C₂×#120	1	2	yes	—
464	C₂⁵	C₂×#120	1	1	yes	characteristic
465	C₂⁵	C₂×#120	1	1	yes	characteristic
466	C₂⁵	C₂×#120	1	2	yes	—
467	C₂⁵	C₂×#120	1	2	yes	—
468	C₂⁵	C₂×#120	1	1	yes	characteristic
469	C₂⁵	C₂×#120	1	1	yes	characteristic
470	C₂⁵	C₂×#120	1	1	yes	characteristic
471	C₂⁵	C₂×#120	1	2	yes	—
472	C₂⁵	#546	1	4	yes	—
473	C₂⁵	C₂³×D₄	1	1	yes	characteristic
474	C₂⁵	C₂³×D₄	1	2	yes	—
475	C₂⁵	C₂³×D₄	1	1	yes	characteristic
476	C₂⁵	C₂³×D₄	1	1	yes	characteristic
477	C₂⁵	C₂³×D₄	1	2	yes	—
478	C₂⁵	C₂²×#41	1	2	yes	—
479	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
480	C₂⁵	#585	1	4	yes	—
481	C₂²×D₄	C₂×#120	1	2	yes	—
482	C₂²×D₄	C₂×#120	1	1	yes	characteristic
483	C₂²×D₄	C₂×#120	1	2	yes	—
484	C₂²×D₄	C₂×#120	1	2	yes	—
485	C₂²×D₄	C₂×#120	1	1	yes	characteristic
486	C₂²×D₄	C₂×#120	1	1	yes	characteristic
487	C₂²×D₄	C₂×#120	1	1	yes	characteristic
488	C₂²×D₄	C₂×#120	1	2	yes	—
489	C₂²×D₄	C₂×#120	1	2	yes	—
490	C₂²×D₄	C₂×#120	1	2	yes	—
491	C₂²×D₄	#525	1	2	yes	—
492	C₂²×D₄	#525	1	2	yes	—
493	C₂²×D₄	#535	1	2	yes	—
494	C₂²×D₄	#535	1	2	yes	—
495	C₂²×D₄	#546	1	4	yes	—
496	C₂²×D₄	#546	1	4	yes	—
497	C₂³×C₄	C₂×#120	1	2	yes	—
498	C₂³×C₄	C₂×#120	1	1	yes	characteristic
499	C₂³×C₄	C₂×#120	1	2	yes	—
500	C₂³×C₄	C₂×#120	1	1	yes	characteristic
501	C₂³×C₄	C₂×#120	1	1	yes	characteristic
502	C₂³×C₄	C₂×#120	1	2	yes	—
503	C₂³×C₄	C₂×#120	1	1	yes	characteristic
504	C₂³×C₄	C₂×#120	1	2	yes	—
505	C₂³×C₄	C₂×#120	1	2	yes	—
506	C₂³×C₄	C₂×#120	1	1	yes	characteristic
507	C₂³×C₄	C₂×#120	1	2	yes	—
508	C₂³×C₄	C₂×#120	1	1	yes	characteristic
509	C₂³×C₄	C₂×#120	1	1	yes	characteristic
510	C₂³×C₄	#546	1	4	yes	—
511	#120	B(4,𝔽₂)	1	4	yes	complemented
512	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
513	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
515	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
518	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
530	C₂⁴	#2404	1	2	yes	—
531	C₂⁴	#2404	1	2	yes	—
532	C₂⁴	#2846	1	1	yes	characteristic
533	C₂⁴	#2846	1	2	yes	—
534	C₂⁴	#2846	1	1	yes	characteristic
535	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
536	C₂⁴	C₂²×#120	1	1	yes	characteristic
537	C₂⁴	C₂²×#120	1	1	yes	characteristic
538	C₂⁴	C₂²×#120	1	2	yes	—
539	C₂⁴	C₂²×#120	1	2	yes	—
540	C₂⁴	C₂²×#120	1	1	yes	characteristic
541	C₂⁴	C₂×#525	1	1	yes	characteristic
542	C₂⁴	C₂×#535	1	1	yes	characteristic
543	C₂⁴	#3449	1	2	yes	—
544	C₂⁴	C₂×#546	1	2	yes	—
545	C₂⁴	C₂×#546	1	2	yes	—
546	C₂⁴	D₄×#41	1	4	yes	—
547	C₂⁴	D₄×#41	1	4	yes	—
548	C₂⁴	#3485	1	2	yes	—
549	C₂⁴	#3485	1	2	yes	—
550	C₂⁴	#3488	1	4	yes	—
551	C₂⁴	#3488	1	4	yes	—
552	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
553	C₂×D₄	#3026	1	2	yes	—
554	C₂²×C₄	#2404	1	2	yes	—
555	C₂²×C₄	#2404	1	2	yes	—
556	C₂²×C₄	#2846	1	1	yes	characteristic
557	C₂²×C₄	#2846	1	2	yes	—
558	C₂²×C₄	#2846	1	1	yes	characteristic
559	C₂²⋊C₄	C₂×B(4,𝔽₂)	1	2	yes	—
560	C₂³	#23996	1	4	yes	complemented
561	C₂³	#32898	1	2	yes	—
562	C₂³	C₂×#2404	1	1	yes	characteristic
563	C₂³	#34736	1	2	yes	—
564	C₂³	#35088	1	1	yes	characteristic
565	C₂³	#35250	1	2	yes	—
566	C₂³	#36212	1	2	yes	—
567	C₂³	#36212	1	4	yes	—
568	C₂³	#36212	1	2	yes	—
569	C₂³	C₂×#2846	1	1	yes	characteristic
570	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
571	C₂³	C₂×#3026	1	1	yes	characteristic
572	C₂³	#60399	1	2	yes	—
573	C₂×C₄	#32898	1	2	yes	—
574	C₂²	#613188	1	1	yes	characteristic
575	C₂²	C₂×#23996	1	2	yes	—
576	C₂²	#6595772	1	2	yes	—
577	C₂²	#6595778	1	2	yes	—
578	C₂²	C₂×#32898	1	1	yes	characteristic
579	C₂²	#6628896	1	1	yes	characteristic
580	C₂	#72237562	1	1	yes	characteristic
581	C₂	#72237919	1	1	yes	characteristic
582	C₂	#72264896	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#613188
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁶ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72265195	C₂	semidirect
2. #72265188	C₂	semidirect
3. #72265184	C₂	semidirect
4. #72241329	C₂	semidirect
5. #72234960	C₂	semidirect
6. #72234958	C₂	semidirect
7. #72234644	C₂	semidirect
8. #72234596	C₂	semidirect
9. #72234150	C₂	semidirect
10. #72233348	C₂	semidirect
11. #72233199	C₂	semidirect
12. #72233156	C₂	semidirect
13. #72232934	C₂	semidirect
14. #72232787	C₂	semidirect
15. #72225689	C₂	semidirect
16. #72225609	C₂	semidirect
17. #72219461	C₂	semidirect
18. C₂²×#3026	C₂²	semidirect
20. #7752093	C₂²	semidirect
21. #7733089	C₂²	semidirect
23. #7644631	C₂²	semidirect
27. C₂×#35346	C₂²	semidirect
29. #7626202	C₂²	semidirect
30. C₂²⋊C₄×H(5,𝔽₂)	C₂²	semidirect
32. C₂×#32898	C₂²	semidirect
33. C₂×#32898	C₂²	semidirect
35. #6370693	C₂²	semidirect
37. #394470	C₂²	semidirect
38. #394267	C₂²	semidirect
39. #394061	C₂²	semidirect
40. #393929	C₂²	semidirect
41. #392125	C₂²	semidirect
42. #374038	C₂²	semidirect
43. #374038	C₂²	semidirect
45. #364471	C₂²	semidirect
46. #359892	C₂²	semidirect
48. #359504	C₂²	semidirect
49. #359442	C₂²	semidirect
50. #359442	C₂²	semidirect
51. #238082	C₂²	semidirect
52. #233541	C₂²	semidirect
53. C₂×#10336	C₂²	semidirect
54. #201678	C₂²	semidirect
57. #201664	C₂²	semidirect
58. #201664	C₂²	semidirect
59. #201664	C₂²	semidirect
60. #201664	C₂²	semidirect
61. #201664	C₂²	semidirect
63. #190107	C₂²	semidirect
65. C₂×#8541	C₂²	semidirect
66. #181344	C₂²	semidirect
67. #122191	C₂²	semidirect
68. #122187	C₂²	semidirect
69. #115631	C₂²	semidirect
70. #115204	C₂²	semidirect
71. #115163	C₂²	semidirect
72. #115133	C₂²	semidirect
73. #111458	C₂²	semidirect
74. #107194	C₂²	semidirect
75. #107114	C₂²	semidirect
76. #106766	C₂²	semidirect
77. #106766	C₂²	semidirect
78. #106766	C₂²	semidirect
79. #106766	C₂²	semidirect
80. #106654	C₂²	semidirect
81. #106654	C₂²	semidirect
82. #106542	C₂²	semidirect
85. C₂×#3490	D₄	semidirect
89. C₂³×#120	D₄	semidirect
93. #47563	D₄	semidirect
94. #46996	D₄	semidirect
95. #46387	D₄	semidirect
96. #46387	D₄	semidirect
97. #46387	D₄	semidirect
98. #46384	D₄	semidirect
99. #46384	D₄	semidirect
100. #46384	D₄	semidirect
102. C₂×#2846	D₄	semidirect
103. #35527	D₄	semidirect
104. #35512	D₄	semidirect
105. #35360	D₄	semidirect
106. #35360	D₄	semidirect
107. #35348	D₄	semidirect
108. #35348	D₄	semidirect
109. #35347	D₄	semidirect
110. #35347	D₄	semidirect
111. #35346	D₄	semidirect
112. #35346	D₄	semidirect
113. #34993	D₄	semidirect
115. #34981	D₄	semidirect
118. C₂×#2539	D₄	semidirect
119. C₂×#2534	D₄	semidirect
120. C₂×#2412	D₄	semidirect
121. C₂×#2405	D₄	semidirect
130. C₂×#2617	D₄	semidirect
132. #34363	D₄	semidirect
133. #34356	D₄	semidirect
135. #34273	D₄	semidirect
136. #34185	D₄	semidirect
137. #34171	D₄	semidirect
148. C₂×#2321	D₄	semidirect
149. #34057	D₄	semidirect
150. C₂×#2308	D₄	semidirect
196. C₂×#543	C₂×D₄	semidirect
220. C₂²×#120	C₂×D₄	semidirect
221. C₂²×#120	C₂×D₄	semidirect
222. C₂²×#120	#41	semidirect
226. C₂×#518	C₂×D₄	semidirect
227. C₂×#518	C₂×D₄	semidirect
234. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
237. #2842	C₂×D₄	semidirect
238. #2842	C₂×D₄	semidirect
239. #2842	C₂×D₄	semidirect
240. #2840	C₂×D₄	semidirect
257. #2403	C₂×D₄	semidirect
258. #2403	C₂×D₄	semidirect
259. #2403	C₂×D₄	semidirect
260. #2403	C₂×D₄	semidirect
261. #2315	C₂×D₄	semidirect
262. #2315	C₂×D₄	semidirect
263. #2315	C₂×D₄	semidirect
271. #2309	C₂×D₄	semidirect
272. #2309	C₂×D₄	semidirect
273. #2309	C₂×D₄	semidirect
274. #2309	C₂×D₄	semidirect
287. #2308	C₂×D₄	semidirect
288. #2308	C₂×D₄	semidirect
289. #2308	C₂×D₄	semidirect
290. #2308	C₂×D₄	semidirect
291. #2308	C₂×D₄	semidirect
292. #2308	C₂×D₄	semidirect
298. C₂×#386	C₂×D₄	semidirect
299. C₂×#386	C₂×D₄	semidirect
300. C₂×#386	#41	semidirect
306. C₂×#380	C₂×D₄	semidirect
312. C₂×#379	C₂×D₄	semidirect
322. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
329. C₂⁶	C₂×#41	semidirect
368. C₂⁴×C₄	C₂×#41	semidirect
385. C₂×#120	#120	semidirect
386. C₂×#120	#120	semidirect
387. C₂×#120	#120	semidirect
388. C₂×#120	#120	semidirect
389. C₂×#120	#120	semidirect
390. C₂×#120	#120	semidirect
391. C₂×#120	#120	semidirect
392. C₂×#120	#120	semidirect
393. C₂×#117	#120	semidirect
394. C₂×#117	#120	semidirect
395. C₂×#117	#120	semidirect
396. C₂×#117	#120	semidirect
404. C₂²×C₂²⋊C₄	#120	semidirect
405. C₂²×C₂²⋊C₄	#120	semidirect
406. C₂²×C₂²⋊C₄	#120	semidirect
407. C₂²×C₂²⋊C₄	#120	semidirect
423. C₂²×C₂²⋊C₄	C₂×#41	semidirect
429. #386	#120	semidirect
430. #386	#120	semidirect
431. #386	#120	semidirect
432. #386	#120	semidirect
433. #386	#120	semidirect
434. #386	#120	semidirect
435. #386	#120	semidirect
436. #386	#120	semidirect
437. #381	#120	semidirect
438. #381	#120	semidirect
439. #381	#120	semidirect
440. #381	#120	semidirect
441. #379	#120	semidirect
442. #379	#120	semidirect
443. #379	#120	semidirect
444. #379	#120	semidirect
511. #120	B(4,𝔽₂)	semidirect
560. C₂³	#23996	semidirect

Maximal subgroups

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

subgroup	index
#72265195	2
#72265188	2
#72265184	2
#72241329	2
#72234960	2
#72234958	2
#72234644	2
#72234596	2
#72234150	2
#72233348	2
#72233199	2
#72233156	2
#72232934	2
#72232787	2
#72225689	2
#72225609	2
#72219461	2