Subgroups — #72262947

Order 2048.

At least 6931 conjugacy classes of subgroups; only the 2492 normal subgroups are shown.

The subgroup lattice has 551 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262885	C₂	1	4	yes	maximal, complemented
2	#72262872	C₂	1	4	yes	maximal, complemented
3	#72262701	C₂	1	1	yes	maximal, characteristic, complemented
4	#72262671	C₂	1	1	yes	maximal, characteristic, complemented
5	#72262637	C₂	1	1	yes	maximal, characteristic, complemented
6	#72262540	C₂	1	1	yes	maximal, characteristic, complemented
7	#72256426	C₂	1	2	yes	maximal, complemented
8	#72256156	C₂	1	2	yes	maximal, complemented
9	#72255928	C₂	1	2	yes	maximal, complemented
10	#72237446	C₂	1	1	yes	maximal, characteristic, complemented
11	#72235932	C₂	1	4	yes	maximal, complemented
12	#72218180	C₂	1	2	yes	maximal, complemented
13	#72217789	C₂	1	1	yes	maximal, characteristic, complemented
14	#72217511	C₂	1	1	yes	maximal, characteristic
15	C₂×#115690	C₂	1	4	yes	maximal, complemented
16	C₂×#62817	C₂²	1	1	yes	characteristic
17	C₂⁴×#120	C₂²	1	1	yes	characteristic
18	#7670206	C₄	1	8	yes	complemented
19	#7670203	C₄	1	8	yes	complemented
20	#7642273	C₂²	1	2	yes	—
21	#7642244	C₂²	1	2	yes	—
22	#7641845	C₂²	1	2	yes	—
23	C₂²×#2846	C₂²	1	2	yes	—
24	#7630944	C₂²	1	2	yes	—
25	#7630939	C₂²	1	2	yes	—
26	#7626202	C₂²	1	1	yes	characteristic
27	C₂×#34356	C₂²	1	2	yes	complemented
28	C₂×#21746	C₂²	1	1	yes	characteristic
29	C₂×#21746	C₂²	1	1	yes	characteristic
30	C₂×#21746	C₂²	1	4	yes	complemented
31	C₂×#21746	C₂²	1	4	yes	complemented
32	C₂×#21746	C₂²	1	2	yes	complemented
33	C₂×#14679	C₂²	1	2	yes	complemented
34	C₂×#14679	C₂²	1	2	yes	complemented
35	#556752	C₂²	1	1	yes	characteristic
36	#556752	C₂²	1	1	yes	characteristic
37	#555899	C₂²	1	1	yes	characteristic, complemented
38	#555899	C₂²	1	1	yes	characteristic, complemented
39	#555894	C₂²	1	2	yes	complemented
40	#517441	C₂²	1	2	yes	complemented
41	#517415	C₂²	1	1	yes	characteristic, complemented
42	#517411	C₂²	1	1	yes	characteristic, complemented
43	#392207	C₂²	1	2	yes	complemented
44	#392109	C₂²	1	2	yes	complemented
45	#382422	C₂²	1	2	yes	complemented
46	#382422	C₂²	1	2	yes	complemented
47	#201691	C₂²	1	8	yes	complemented
48	#201690	C₂²	1	8	yes	complemented
49	#201688	C₂²	1	8	yes	complemented
50	#201687	C₂²	1	8	yes	complemented
51	#187945	C₂²	1	4	yes	complemented
52	#187945	C₂²	1	4	yes	complemented
53	#187944	C₂²	1	2	yes	complemented
54	#187944	C₂²	1	2	yes	complemented
55	#187944	C₂²	1	2	yes	complemented
56	#187944	C₂²	1	2	yes	complemented
57	C₂×#8101	C₂²	1	4	yes	complemented
58	C₂×#8101	C₂²	1	4	yes	complemented
59	#115690	C₂²	1	8	yes	complemented
60	#115690	C₂²	1	8	yes	complemented
61	#115690	C₂²	1	8	yes	complemented
62	#115690	C₂²	1	8	yes	complemented
63	#107115	C₂²	1	4	yes	complemented
64	#107115	C₂²	1	4	yes	complemented
65	#107114	C₂²	1	2	yes	complemented
66	#107114	C₂²	1	2	yes	complemented
67	#107114	C₂²	1	2	yes	complemented
68	#107114	C₂²	1	2	yes	complemented
69	C₂⁸	C₂³	1	1	yes	characteristic
70	C₂⁵×D₄	D₄	1	2	yes	—
71	C₂⁵×D₄	C₂³	1	1	yes	characteristic
72	C₂×#3490	C₂×C₄	1	4	yes	complemented
73	C₂×#3490	C₂³	1	2	yes	—
74	C₂×#3484	C₂×C₄	1	4	yes	complemented
75	C₂×#3484	C₂×C₄	1	4	yes	complemented
76	C₂×#3484	C₂³	1	2	yes	—
77	C₂³×#120	C₂×C₄	1	8	yes	—
78	C₂³×#120	C₂×C₄	1	4	yes	complemented
79	C₂³×#120	D₄	1	8	yes	—
80	C₂³×#120	D₄	1	2	yes	—
81	C₂³×#120	D₄	1	2	yes	—
82	C₂³×#120	C₂³	1	2	yes	—
83	C₂³×#120	C₂³	1	1	yes	characteristic
84	C₂³×#120	C₂³	1	1	yes	characteristic
85	C₂³×#120	C₂³	1	1	yes	characteristic
86	C₂³×#120	C₂³	1	1	yes	characteristic
87	C₂⁴×C₂²⋊C₄	D₄	1	2	yes	—
88	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
89	#37436	D₄	1	16	yes	—
90	C₂×#2846	C₂×C₄	1	8	yes	complemented
91	C₂×#2846	C₂³	1	4	yes	—
92	C₂×#2846	C₂³	1	4	yes	—
93	#35390	C₂×C₄	1	4	yes	complemented
94	#35367	C₂×C₄	1	4	yes	complemented
95	#35350	C₂×C₄	1	4	yes	complemented
96	#35348	C₂×C₄	1	8	yes	complemented
97	#35348	C₂×C₄	1	8	yes	complemented
98	#35346	C₂×C₄	1	4	yes	complemented
99	#34992	C₂×C₄	1	4	yes	—
100	#34992	D₄	1	8	yes	—
101	#34992	C₂³	1	4	yes	—
102	#34982	C₂×C₄	1	4	yes	complemented
103	#34981	C₂×C₄	1	8	yes	—
104	#34981	C₂×C₄	1	4	yes	complemented
105	#34980	C₂×C₄	1	4	yes	—
106	#34980	C₂×C₄	1	8	yes	complemented
107	#34980	D₄	1	8	yes	—
108	#34980	C₂³	1	4	yes	—
109	#34198	C₂×C₄	1	8	yes	complemented
110	#34198	C₂×C₄	1	8	yes	complemented
111	#34176	C₂³	1	2	yes	—
112	#34171	C₂×C₄	1	4	yes	complemented
113	#34171	C₂³	1	2	yes	—
114	C₂×#2312	C₂³	1	2	yes	—
115	C₂×#2312	C₂³	1	2	yes	—
116	C₂×#2309	C₂³	1	2	yes	—
117	C₂×#2308	C₂³	1	2	yes	—
118	C₂²×#379	C₂×C₄	1	4	yes	complemented
119	C₂²×#379	C₂³	1	2	yes	—
120	C₂²×#379	C₂³	1	2	yes	—
121	C₂²×#379	C₂³	1	2	yes	—
122	C₂²×#379	C₂³	1	2	yes	—
123	C₂²×#379	C₂³	1	2	yes	—
124	#21746	C₂³	1	8	yes	—
125	#21746	C₂³	1	8	yes	—
126	#21746	C₂³	1	8	yes	—
127	#21746	C₂³	1	8	yes	—
128	C₂×#1819	C₂³	1	2	yes	—
129	C₂×#1819	C₂³	1	2	yes	—
130	C₂×#1819	C₂³	1	4	yes	—
131	C₂×#1781	C₂³	1	2	yes	—
132	C₂×#1781	C₂³	1	2	yes	—
133	C₂×#1781	C₂³	1	4	yes	—
134	#14679	C₂³	1	2	yes	—
135	#14679	C₂³	1	2	yes	—
136	#14679	C₂³	1	2	yes	—
137	#14679	C₂³	1	2	yes	—
138	#14679	C₂³	1	4	yes	—
139	#14679	C₂³	1	4	yes	—
140	#14657	D₄	1	4	yes	complemented
141	#14341	C₂³	1	2	yes	—
142	#14341	C₂³	1	2	yes	—
143	#14335	C₂³	1	1	yes	characteristic
144	#14335	C₂³	1	1	yes	characteristic
145	#14335	C₂³	1	1	yes	characteristic
146	#14335	C₂³	1	1	yes	characteristic
147	#14255	D₄	1	8	yes	complemented
148	#14134	D₄	1	4	yes	complemented
149	#8101	C₂³	1	8	yes	—
150	#8101	C₂³	1	8	yes	—
151	#8101	C₂³	1	8	yes	—
152	#8101	C₂³	1	8	yes	—
153	C₂⁷	C₂²×C₄	1	4	yes	—
154	C₂⁷	C₂×D₄	1	2	yes	—
155	C₂⁷	C₂×D₄	1	2	yes	—
156	C₂⁷	C₂×D₄	1	4	yes	—
157	C₂⁷	C₂×D₄	1	1	yes	characteristic
158	C₂⁷	C₂⁴	1	1	yes	characteristic
159	C₂⁷	C₂⁴	1	1	yes	characteristic
160	C₂⁷	C₂⁴	1	1	yes	characteristic
161	C₂²×H(5,𝔽₂)	C₂²×C₄	1	2	yes	—
162	C₂⁴×D₄	C₂²⋊C₄	1	16	yes	—
163	C₂⁴×D₄	C₂²×C₄	1	4	yes	—
164	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
165	C₂⁴×D₄	C₂×D₄	1	4	yes	—
166	C₂⁴×D₄	C₂×D₄	1	4	yes	—
167	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
168	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
169	C₂⁴×D₄	C₂×D₄	1	2	yes	—
170	C₂⁴×D₄	C₂×D₄	1	2	yes	—
171	C₂⁴×D₄	C₂×D₄	1	2	yes	—
172	C₂⁴×D₄	C₂×D₄	1	2	yes	—
173	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
174	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
175	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
176	C₂⁵×C₄	C₂×D₄	1	2	yes	—
177	C₂×#543	C₂²×C₄	1	2	yes	—
178	C₂×#534	C₂²×C₄	1	4	yes	—
179	C₂×#534	C₂²×C₄	1	2	yes	—
180	C₂×#534	C₂²×C₄	1	8	yes	—
181	C₂²×#120	C₂²⋊C₄	1	16	yes	—
182	C₂²×#120	C₂²⋊C₄	1	16	yes	—
183	C₂²×#120	C₂²×C₄	1	8	yes	—
184	C₂²×#120	C₂²×C₄	1	8	yes	—
185	C₂²×#120	C₂²×C₄	1	4	yes	—
186	C₂²×#120	C₂²×C₄	1	4	yes	—
187	C₂²×#120	C₂²×C₄	1	4	yes	—
188	C₂²×#120	C₂²×C₄	1	4	yes	—
189	C₂²×#120	C₂²×C₄	1	4	yes	—
190	C₂²×#120	C₂×D₄	1	4	yes	—
191	C₂²×#120	C₂×D₄	1	4	yes	—
192	C₂²×#120	C₂×D₄	1	4	yes	—
193	C₂²×#120	C₂×D₄	1	4	yes	—
194	C₂²×#120	C₂×D₄	1	8	yes	—
195	C₂²×#120	C₂×D₄	1	8	yes	—
196	C₂²×#120	C₂×D₄	1	8	yes	—
197	C₂²×#120	C₂×D₄	1	2	yes	—
198	C₂²×#120	C₂×D₄	1	2	yes	—
199	C₂²×#120	C₂×D₄	1	4	yes	—
200	C₂²×#120	#41	1	4	yes	—
201	C₂²×#120	#41	1	4	yes	—
202	C₂²×#120	C₂⁴	1	4	yes	—
203	C₂×#518	C₂²×C₄	1	4	yes	—
204	C₂×#518	C₂²×C₄	1	2	yes	—
205	C₂×#518	C₂²×C₄	1	4	yes	—
206	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	16	yes	—
207	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
208	C₂³×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
209	C₂³×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
210	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
211	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
212	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
213	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
214	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
215	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
216	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
217	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
218	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
219	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
220	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
221	#2849	C₂²⋊C₄	1	16	yes	complemented
222	#2849	C₂²⋊C₄	1	8	yes	complemented
223	#2846	C₂²⋊C₄	1	8	yes	complemented
224	#2622	C₂²⋊C₄	1	16	yes	complemented
225	#2613	C₂²⋊C₄	1	16	yes	complemented
226	#2483	C₂×D₄	1	16	yes	—
227	#2412	C₂²⋊C₄	1	32	yes	complemented
228	#2410	C₂²⋊C₄	1	32	yes	complemented
229	#2405	C₂×D₄	1	16	yes	—
230	#2405	C₂×D₄	1	16	yes	—
231	#2403	C₂×D₄	1	16	yes	—
232	#2315	C₂²×C₄	1	4	yes	—
233	#2315	C₂²×C₄	1	8	yes	—
234	#2308	C₂²×C₄	1	4	yes	—
235	#2308	C₂²×C₄	1	8	yes	—
236	#2308	C₂²×C₄	1	8	yes	—
237	C₂×#379	C₂²×C₄	1	8	yes	—
238	C₂×#379	C₂²×C₄	1	8	yes	—
239	C₂×#379	C₂²×C₄	1	4	yes	—
240	C₂×#379	C₂×D₄	1	8	yes	—
241	C₂×#379	C₂×D₄	1	8	yes	—
242	C₂×#379	C₂×D₄	1	4	yes	complemented
243	C₂×#379	C₂×D₄	1	4	yes	complemented
244	C₂×#379	C₂⁴	1	4	yes	—
245	C₂×#379	C₂⁴	1	4	yes	—
246	C₂×#379	C₂⁴	1	4	yes	—
247	C₂×#379	C₂⁴	1	2	yes	—
248	C₂×#379	C₂⁴	1	2	yes	—
249	C₂×#379	C₂⁴	1	2	yes	—
250	C₂×#379	C₂⁴	1	2	yes	—
251	#2273	C₂²×C₄	1	4	yes	—
252	#1440	C₂×D₄	1	8	yes	complemented
253	#1440	C₂×D₄	1	8	yes	complemented
254	#1438	C₂×D₄	1	4	yes	complemented
255	#1438	C₂×D₄	1	4	yes	complemented
256	#1438	C₂×D₄	1	4	yes	complemented
257	#1438	C₂×D₄	1	4	yes	complemented
258	C₂⁶	C₂×C₂²⋊C₄	1	8	yes	—
259	C₂⁶	C₂×C₂²⋊C₄	1	8	yes	—
260	C₂⁶	C₂×C₂²⋊C₄	1	4	yes	—
261	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	complemented
262	C₂⁶	C₂³×C₄	1	2	yes	—
263	C₂⁶	C₂³×C₄	1	2	yes	—
264	C₂⁶	C₂³×C₄	1	2	yes	—
265	C₂⁶	C₂²×D₄	1	1	yes	characteristic
266	C₂⁶	C₂²×D₄	1	1	yes	characteristic
267	C₂⁶	C₂²×D₄	1	2	yes	—
268	C₂⁶	C₂²×D₄	1	2	yes	—
269	C₂⁶	C₂²×D₄	1	2	yes	—
270	C₂⁶	C₂²×D₄	1	1	yes	characteristic
271	C₂⁶	C₂²×D₄	1	1	yes	characteristic
272	C₂⁶	C₂²×D₄	1	2	yes	—
273	C₂⁶	C₂²×D₄	1	1	yes	characteristic
274	C₂⁶	C₂²×D₄	1	2	yes	—
275	C₂⁶	C₂²×D₄	1	4	yes	—
276	C₂⁶	C₂²×D₄	1	2	yes	—
277	C₂⁶	C₂²×D₄	1	4	yes	—
278	C₂⁶	C₂²×D₄	1	1	yes	characteristic
279	C₂⁶	C₂×#41	1	2	yes	—
280	C₂⁶	C₂×#41	1	2	yes	—
281	C₂⁶	H(5,𝔽₂)	1	4	yes	—
282	C₂⁶	H(5,𝔽₂)	1	4	yes	—
283	C₂⁶	C₂⁵	1	1	yes	characteristic
284	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
285	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
286	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
287	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
288	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
289	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
290	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	complemented
291	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	complemented
292	C₂³×D₄	#120	1	4	yes	—
293	C₂³×D₄	#120	1	4	yes	—
294	C₂³×D₄	#120	1	4	yes	—
295	C₂³×D₄	#120	1	8	yes	—
296	C₂³×D₄	#120	1	4	yes	—
297	C₂³×D₄	#123	1	8	yes	—
298	C₂³×D₄	C₂³×C₄	1	4	yes	—
299	C₂³×D₄	C₂³×C₄	1	2	yes	—
300	C₂³×D₄	C₂³×C₄	1	2	yes	—
301	C₂³×D₄	C₂²×D₄	1	8	yes	—
302	C₂³×D₄	C₂²×D₄	1	2	yes	—
303	C₂³×D₄	C₂²×D₄	1	2	yes	—
304	C₂³×D₄	C₂²×D₄	1	8	yes	—
305	C₂³×D₄	C₂²×D₄	1	2	yes	—
306	C₂³×D₄	C₂²×D₄	1	2	yes	—
307	C₂³×D₄	C₂×#41	1	2	yes	—
308	C₂³×D₄	C₂×#41	1	2	yes	—
309	C₂⁴×C₄	C₂×C₂²⋊C₄	1	4	yes	—
310	C₂⁴×C₄	C₂×C₂²⋊C₄	1	8	yes	—
311	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	complemented
312	C₂⁴×C₄	C₂×C₂²⋊C₄	1	4	yes	complemented
313	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
314	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
315	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
316	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
317	C₂×#123	C₂×C₂²⋊C₄	1	16	yes	complemented
318	C₂×#120	C₂×C₂²⋊C₄	1	8	yes	—
319	C₂×#120	C₂×C₂²⋊C₄	1	8	yes	—
320	C₂×#120	C₂×C₂²⋊C₄	1	16	yes	—
321	C₂×#120	C₂×C₂²⋊C₄	1	16	yes	complemented
322	C₂×#120	C₄×D₄	1	8	yes	—
323	C₂×#120	C₄×D₄	1	16	yes	—
324	C₂×#120	C₄×D₄	1	8	yes	—
325	C₂×#120	#120	1	16	yes	—
326	C₂×#120	#120	1	8	yes	—
327	C₂×#120	#120	1	8	yes	—
328	C₂×#120	#121	1	8	yes	—
329	C₂×#120	#121	1	16	yes	—
330	C₂×#120	#121	1	8	yes	—
331	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	8	yes	—
332	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	8	yes	—
333	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	8	yes	—
334	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	8	yes	—
335	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	8	yes	—
336	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	complemented
337	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	8	yes	complemented
338	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	16	yes	complemented
339	C₂²×C₂²⋊C₄	#120	1	4	yes	—
340	C₂²×C₂²⋊C₄	#120	1	4	yes	—
341	C₂²×C₂²⋊C₄	#120	1	8	yes	—
342	C₂²×C₂²⋊C₄	#120	1	4	yes	—
343	C₂²×C₂²⋊C₄	#120	1	4	yes	—
344	C₂²×C₂²⋊C₄	#123	1	8	yes	—
345	C₂²×C₂²⋊C₄	C₂³×C₄	1	4	yes	—
346	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
347	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
348	C₂²×C₂²⋊C₄	C₂³×C₄	1	8	yes	—
349	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
350	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
351	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
352	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
353	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
354	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
355	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
356	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
357	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
358	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
359	C₂²×C₂²⋊C₄	C₂×#41	1	2	yes	—
360	C₂²×C₂²⋊C₄	C₂×#41	1	2	yes	—
361	#386	C₂×C₂²⋊C₄	1	32	yes	complemented
362	#385	C₂×C₂²⋊C₄	1	32	yes	complemented
363	#381	C₂×C₂²⋊C₄	1	16	yes	complemented
364	#379	C₂×C₂²⋊C₄	1	16	yes	complemented
365	#379	C₂×C₂²⋊C₄	1	8	yes	complemented
366	#379	C₂×C₂²⋊C₄	1	8	yes	complemented
367	#379	C₂²×D₄	1	16	yes	—
368	C₂⁵	C₂²×C₂²⋊C₄	1	4	yes	—
369	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
370	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
371	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
372	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
373	C₂⁵	C₂²×C₂²⋊C₄	1	4	yes	—
374	C₂⁵	C₂²×C₂²⋊C₄	1	4	yes	—
375	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
376	C₂⁵	C₂²×C₂²⋊C₄	1	4	yes	—
377	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
378	C₂⁵	C₂×C₄×D₄	1	2	yes	—
379	C₂⁵	C₂×C₄×D₄	1	4	yes	—
380	C₂⁵	C₂×C₄×D₄	1	2	yes	—
381	C₂⁵	#518	1	2	yes	—
382	C₂⁵	#518	1	4	yes	—
383	C₂⁵	#518	1	2	yes	—
384	C₂⁵	C₂×#120	1	2	yes	—
385	C₂⁵	C₂×#120	1	2	yes	—
386	C₂⁵	C₂×#120	1	2	yes	—
387	C₂⁵	C₂×#120	1	4	yes	—
388	C₂⁵	C₂×#120	1	2	yes	—
389	C₂⁵	C₂×#120	1	4	yes	—
390	C₂⁵	C₂×#120	1	2	yes	—
391	C₂⁵	C₂×#120	1	2	yes	—
392	C₂⁵	C₂×#120	1	4	yes	—
393	C₂⁵	C₂×#120	1	2	yes	—
394	C₂⁵	C₂×#121	1	2	yes	—
395	C₂⁵	C₂×#121	1	4	yes	—
396	C₂⁵	C₂×#121	1	2	yes	—
397	C₂⁵	C₂×#123	1	2	yes	—
398	C₂⁵	C₂×#123	1	4	yes	—
399	C₂⁵	#534	1	2	yes	—
400	C₂⁵	#534	1	4	yes	—
401	C₂⁵	#534	1	2	yes	—
402	C₂⁵	#534	1	2	yes	—
403	C₂⁵	#534	1	4	yes	—
404	C₂⁵	#534	1	2	yes	—
405	C₂⁵	D₄²	1	4	yes	—
406	C₂⁵	D₄²	1	4	yes	—
407	C₂⁵	D₄²	1	4	yes	—
408	C₂⁵	D₄²	1	4	yes	—
409	C₂⁵	D₄²	1	4	yes	—
410	C₂⁵	D₄²	1	4	yes	—
411	C₂⁵	D₄²	1	4	yes	—
412	C₂⁵	D₄²	1	4	yes	—
413	C₂⁵	#546	1	4	yes	—
414	C₂⁵	#546	1	4	yes	—
415	C₂⁵	#546	1	4	yes	—
416	C₂⁵	#546	1	4	yes	—
417	C₂⁵	#546	1	4	yes	—
418	C₂⁵	#546	1	4	yes	—
419	C₂⁵	#546	1	4	yes	—
420	C₂⁵	#546	1	4	yes	—
421	C₂⁵	C₂⁴×C₄	1	1	yes	characteristic
422	C₂⁵	C₂³×D₄	1	1	yes	characteristic
423	C₂⁵	C₂³×D₄	1	1	yes	characteristic
424	C₂⁵	C₂³×D₄	1	1	yes	characteristic
425	C₂⁵	C₂³×D₄	1	1	yes	characteristic
426	C₂⁵	C₂³×D₄	1	4	yes	—
427	C₂⁵	C₂²×#41	1	1	yes	characteristic
428	C₂⁵	C₂²×#41	1	1	yes	characteristic
429	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
430	C₂²×D₄	#379	1	16	yes	—
431	C₂²×D₄	#379	1	16	yes	—
432	C₂²×D₄	#386	1	16	yes	—
433	C₂²×D₄	#386	1	16	yes	—
434	C₂²×D₄	C₂²×C₂²⋊C₄	1	8	yes	—
435	C₂²×D₄	C₂×C₄×D₄	1	4	yes	—
436	C₂²×D₄	C₂×C₄×D₄	1	4	yes	—
437	C₂²×D₄	C₂×#120	1	8	yes	—
438	C₂²×D₄	C₂×#121	1	4	yes	—
439	C₂²×D₄	C₂×#121	1	4	yes	—
440	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
441	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
442	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
443	C₂³×C₄	C₂²×C₂²⋊C₄	1	8	yes	—
444	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
445	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
446	C₂³×C₄	C₂×#120	1	4	yes	—
447	C₂³×C₄	C₂×#120	1	4	yes	—
448	C₂³×C₄	C₂×#120	1	2	yes	—
449	C₂³×C₄	C₂×#120	1	4	yes	—
450	C₂³×C₄	C₂×#120	1	4	yes	—
451	C₂³×C₄	C₂×#123	1	2	yes	—
452	C₂³×C₄	C₂×#123	1	4	yes	—
453	C₂×C₂²⋊C₄	#379	1	16	yes	—
454	C₂×C₂²⋊C₄	#379	1	16	yes	—
455	C₂×C₂²⋊C₄	#386	1	16	yes	—
456	C₂×C₂²⋊C₄	#386	1	16	yes	—
457	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	8	yes	—
458	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	16	yes	—
459	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	4	yes	—
460	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
462	C₂×C₂²⋊C₄	C₂×#121	1	4	yes	—
463	C₂×C₂²⋊C₄	C₂×#121	1	4	yes	—
464	C₂⁴	C₂×#379	1	4	yes	—
465	C₂⁴	C₂×#379	1	4	yes	—
466	C₂⁴	C₂×#379	1	4	yes	—
467	C₂⁴	C₂×#386	1	4	yes	—
468	C₂⁴	C₂×#386	1	4	yes	—
469	C₂⁴	C₂×#386	1	4	yes	—
470	C₂⁴	#2308	1	4	yes	—
471	C₂⁴	#2308	1	4	yes	—
472	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
473	C₂⁴	D₄×C₂²⋊C₄	1	4	yes	—
474	C₂⁴	D₄×C₂²⋊C₄	1	4	yes	—
475	C₂⁴	D₄×C₂²⋊C₄	1	4	yes	—
476	C₂⁴	D₄×C₂²⋊C₄	1	4	yes	—
477	C₂⁴	D₄×C₂²⋊C₄	1	4	yes	—
478	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
479	C₂⁴	D₄×C₂²⋊C₄	1	4	yes	—
480	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
481	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
482	C₂⁴	#2403	1	4	yes	—
483	C₂⁴	#2403	1	2	yes	—
484	C₂⁴	#2403	1	4	yes	—
485	C₂⁴	#2403	1	2	yes	—
486	C₂⁴	#2403	1	2	yes	—
487	C₂⁴	#2403	1	2	yes	—
488	C₂⁴	#2405	1	4	yes	—
489	C₂⁴	#2405	1	4	yes	—
490	C₂⁴	#2405	1	4	yes	—
491	C₂⁴	#2405	1	4	yes	—
492	C₂⁴	#2410	1	2	yes	—
493	C₂⁴	#2410	1	4	yes	—
494	C₂⁴	#2410	1	4	yes	—
495	C₂⁴	#2410	1	4	yes	—
496	C₂⁴	#2410	1	2	yes	—
497	C₂⁴	#2410	1	4	yes	—
498	C₂⁴	#2410	1	4	yes	—
499	C₂⁴	#2410	1	2	yes	—
500	C₂⁴	#2410	1	4	yes	—
501	C₂⁴	#2410	1	2	yes	—
502	C₂⁴	#2883	1	4	yes	—
503	C₂⁴	#2883	1	4	yes	—
504	C₂⁴	C₂³×C₂²⋊C₄	1	2	yes	—
505	C₂⁴	C₂³×C₂²⋊C₄	1	1	yes	characteristic
506	C₂⁴	C₂²×C₄×D₄	1	1	yes	characteristic
507	C₂⁴	C₂²×C₄×D₄	1	1	yes	characteristic
508	C₂⁴	C₂×#518	1	2	yes	—
509	C₂⁴	C₂²×#120	1	1	yes	characteristic
510	C₂⁴	C₂²×#120	1	2	yes	—
511	C₂⁴	C₂²×#120	1	2	yes	—
512	C₂⁴	C₂²×#121	1	1	yes	characteristic
513	C₂⁴	C₂²×#121	1	1	yes	characteristic
514	C₂⁴	C₂²×#123	1	1	yes	characteristic
515	C₂⁴	C₂×#534	1	2	yes	—
516	C₂⁴	C₂×#534	1	2	yes	—
517	C₂⁴	C₂×D₄²	1	4	yes	—
518	C₂⁴	C₂×D₄²	1	4	yes	—
519	C₂⁴	C₂×#546	1	4	yes	—
520	C₂⁴	C₂×#546	1	4	yes	—
521	C₂²×C₄	C₂×#379	1	4	yes	—
522	C₂²×C₄	C₂×#379	1	8	yes	—
523	C₂²×C₄	C₂×#386	1	4	yes	—
524	C₂²×C₄	C₂×#386	1	8	yes	—
525	C₂³	#13867	1	4	yes	—
526	C₂³	#13867	1	4	yes	—
527	C₂³	#13867	1	4	yes	—
528	C₂³	#13867	1	4	yes	—
529	C₂³	#23895	1	8	yes	—
530	C₂³	C₂²×#379	1	1	yes	characteristic
531	C₂³	C₂²×#386	1	1	yes	characteristic
532	C₂³	C₂×#2308	1	1	yes	characteristic
533	C₂³	C₂×D₄×C₂²⋊C₄	1	2	yes	—
534	C₂³	C₂×D₄×C₂²⋊C₄	1	2	yes	—
535	C₂³	C₂×#2403	1	2	yes	—
536	C₂³	C₂×#2410	1	2	yes	—
537	C₂³	C₂×#2410	1	2	yes	—
538	C₂³	C₂×#2405	1	2	yes	—
539	C₂³	C₂×#2883	1	2	yes	—
540	C₂³	C₂×#2883	1	2	yes	—
541	C₂²	#359549	1	8	yes	—
542	C₂²	C₂×#13867	1	1	yes	characteristic
543	C₂²	#6370693	1	2	yes	—
544	C₂²	#6371504	1	1	yes	characteristic
545	C₂²	#6371504	1	1	yes	characteristic
546	C₂²	#6374210	1	2	yes	—
547	C₂²	C₂×#23895	1	4	yes	—
548	C₂	C₂×#359549	1	2	yes	—
549	C₂	#72251739	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#13867
commutator	C₂⁵	C₂⁴×C₄
Frattini, cosocle	C₂⁶	C₂⁵
prime radical	#72217511	C₂
LCS	G ▷ C₂⁵ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72262885	C₂	semidirect
2. #72262872	C₂	semidirect
3. #72262701	C₂	semidirect
4. #72262671	C₂	semidirect
5. #72262637	C₂	semidirect
6. #72262540	C₂	semidirect
7. #72256426	C₂	semidirect
8. #72256156	C₂	semidirect
9. #72255928	C₂	semidirect
10. #72237446	C₂	semidirect
11. #72235932	C₂	semidirect
12. #72218180	C₂	semidirect
13. #72217789	C₂	semidirect
15. C₂×#115690	C₂	semidirect
18. #7670206	C₄	semidirect
19. #7670203	C₄	semidirect
27. C₂×#34356	C₂²	semidirect
30. C₂×#21746	C₂²	semidirect
31. C₂×#21746	C₂²	semidirect
32. C₂×#21746	C₂²	semidirect
33. C₂×#14679	C₂²	semidirect
34. C₂×#14679	C₂²	semidirect
37. #555899	C₂²	semidirect
38. #555899	C₂²	semidirect
39. #555894	C₂²	semidirect
40. #517441	C₂²	semidirect
41. #517415	C₂²	semidirect
42. #517411	C₂²	semidirect
43. #392207	C₂²	semidirect
44. #392109	C₂²	semidirect
45. #382422	C₂²	semidirect
46. #382422	C₂²	semidirect
47. #201691	C₂²	semidirect
48. #201690	C₂²	semidirect
49. #201688	C₂²	semidirect
50. #201687	C₂²	semidirect
51. #187945	C₂²	semidirect
52. #187945	C₂²	semidirect
53. #187944	C₂²	semidirect
54. #187944	C₂²	semidirect
55. #187944	C₂²	semidirect
56. #187944	C₂²	semidirect
57. C₂×#8101	C₂²	semidirect
58. C₂×#8101	C₂²	semidirect
59. #115690	C₂²	semidirect
60. #115690	C₂²	semidirect
61. #115690	C₂²	semidirect
62. #115690	C₂²	semidirect
63. #107115	C₂²	semidirect
64. #107115	C₂²	semidirect
65. #107114	C₂²	semidirect
66. #107114	C₂²	semidirect
67. #107114	C₂²	semidirect
68. #107114	C₂²	semidirect
72. C₂×#3490	C₂×C₄	semidirect
74. C₂×#3484	C₂×C₄	semidirect
75. C₂×#3484	C₂×C₄	semidirect
78. C₂³×#120	C₂×C₄	semidirect
90. C₂×#2846	C₂×C₄	semidirect
93. #35390	C₂×C₄	semidirect
94. #35367	C₂×C₄	semidirect
95. #35350	C₂×C₄	semidirect
96. #35348	C₂×C₄	semidirect
97. #35348	C₂×C₄	semidirect
98. #35346	C₂×C₄	semidirect
102. #34982	C₂×C₄	semidirect
104. #34981	C₂×C₄	semidirect
106. #34980	C₂×C₄	semidirect
109. #34198	C₂×C₄	semidirect
110. #34198	C₂×C₄	semidirect
112. #34171	C₂×C₄	semidirect
118. C₂²×#379	C₂×C₄	semidirect
140. #14657	D₄	semidirect
147. #14255	D₄	semidirect
148. #14134	D₄	semidirect
217. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
218. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
221. #2849	C₂²⋊C₄	semidirect
222. #2849	C₂²⋊C₄	semidirect
223. #2846	C₂²⋊C₄	semidirect
224. #2622	C₂²⋊C₄	semidirect
225. #2613	C₂²⋊C₄	semidirect
227. #2412	C₂²⋊C₄	semidirect
228. #2410	C₂²⋊C₄	semidirect
242. C₂×#379	C₂×D₄	semidirect
243. C₂×#379	C₂×D₄	semidirect
252. #1440	C₂×D₄	semidirect
253. #1440	C₂×D₄	semidirect
254. #1438	C₂×D₄	semidirect
255. #1438	C₂×D₄	semidirect
256. #1438	C₂×D₄	semidirect
257. #1438	C₂×D₄	semidirect
261. C₂⁶	C₂×C₂²⋊C₄	semidirect
290. C₂³×D₄	C₂×C₂²⋊C₄	semidirect
291. C₂³×D₄	C₂×C₂²⋊C₄	semidirect
311. C₂⁴×C₄	C₂×C₂²⋊C₄	semidirect
312. C₂⁴×C₄	C₂×C₂²⋊C₄	semidirect
317. C₂×#123	C₂×C₂²⋊C₄	semidirect
321. C₂×#120	C₂×C₂²⋊C₄	semidirect
336. C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
337. C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
338. C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
361. #386	C₂×C₂²⋊C₄	semidirect
362. #385	C₂×C₂²⋊C₄	semidirect
363. #381	C₂×C₂²⋊C₄	semidirect
364. #379	C₂×C₂²⋊C₄	semidirect
365. #379	C₂×C₂²⋊C₄	semidirect
366. #379	C₂×C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#72262885	2
#72262872	2
#72262701	2
#72262671	2
#72262637	2
#72262540	2
#72256426	2
#72256156	2
#72255928	2
#72237446	2
#72235932	2
#72218180	2
#72217789	2
#72217511	2
C₂×#115690	2