Subgroups — #72266080

Order 2048.

At least 11636 conjugacy classes of subgroups; only the 932 normal subgroups are shown.

The subgroup lattice has 613 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72266079	C₂	1	1	yes	maximal, characteristic, complemented
2	#72266073	C₂	1	1	yes	maximal, characteristic, complemented
3	#72266035	C₂	1	1	yes	maximal, characteristic, complemented
4	#72266035	C₂	1	1	yes	maximal, characteristic, complemented
5	#72266029	C₂	1	1	yes	maximal, characteristic, complemented
6	#72266028	C₂	1	1	yes	maximal, characteristic, complemented
7	#72240619	C₂	1	1	yes	maximal, characteristic, complemented
8	#72240617	C₂	1	1	yes	maximal, characteristic, complemented
9	#72240568	C₂	1	1	yes	maximal, characteristic, complemented
10	#72238531	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#201664	C₂	1	1	yes	maximal, characteristic, complemented
12	#72225796	C₂	1	1	yes	maximal, characteristic, complemented
13	#72225796	C₂	1	1	yes	maximal, characteristic, complemented
14	#72225783	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#32898	C₂	1	1	yes	maximal, characteristic
16	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
17	C₂²×#2403	C₂²	1	1	yes	characteristic
18	C₂²×#2403	C₂²	1	1	yes	characteristic
19	C₂²×#2403	C₂²	1	1	yes	characteristic
20	C₂×#34171	C₂²	1	1	yes	characteristic, complemented
21	C₂×#32898	C₄	1	8	yes	complemented
22	C₂²×#1781	C₂²	1	1	yes	characteristic
23	C₂²×#1781	C₂²	1	1	yes	characteristic
24	C₂²×#1781	C₂²	1	1	yes	characteristic
25	C₂²×#1781	C₂²	1	1	yes	characteristic
26	C₂²×#1781	C₂²	1	1	yes	characteristic
27	C₂²×#1781	C₂²	1	1	yes	characteristic
28	C₂²×#1781	C₂²	1	1	yes	characteristic
29	C₂²×#1781	C₂²	1	1	yes	characteristic
30	C₂²×#1781	C₂²	1	1	yes	characteristic
31	C₂²×#1781	C₂²	1	1	yes	characteristic
32	C₂²×#1781	C₂²	1	1	yes	characteristic, complemented
33	C₂²×#1781	C₂²	1	1	yes	characteristic, complemented
34	#517411	C₂²	1	1	yes	characteristic
35	#517411	C₂²	1	1	yes	characteristic
36	#517411	C₂²	1	1	yes	characteristic
37	#517411	C₂²	1	1	yes	characteristic
38	#517411	C₂²	1	1	yes	characteristic
39	#517411	C₂²	1	1	yes	characteristic, complemented
40	#355913	C₂²	1	1	yes	characteristic, complemented
41	#355913	C₂²	1	1	yes	characteristic, complemented
42	#355913	C₂²	1	1	yes	characteristic, complemented
43	#355913	C₂²	1	1	yes	characteristic, complemented
44	#355913	C₂²	1	1	yes	characteristic, complemented
45	#355913	C₂²	1	1	yes	characteristic, complemented
46	C₂×#8101	C₂²	1	1	yes	characteristic, complemented
47	C₂×#8101	C₂²	1	1	yes	characteristic, complemented
48	C₂×#8101	C₂²	1	1	yes	characteristic, complemented
49	C₂×#8101	C₂²	1	1	yes	characteristic, complemented
50	C₂×#8101	C₂²	1	1	yes	characteristic, complemented
51	C₂×#8101	C₂²	1	1	yes	characteristic, complemented
52	C₂³×H(5,𝔽₂)	C₂×C₄	1	4	yes	complemented
53	C₂⁵×D₄	C₂³	1	1	yes	characteristic
54	C₂⁵×D₄	C₂³	1	1	yes	characteristic
55	C₂⁵×D₄	C₂³	1	1	yes	characteristic
56	C₂⁵×D₄	C₂³	1	1	yes	characteristic
57	C₂³×#120	D₄	1	2	yes	—
58	C₂³×#99	D₄	1	4	yes	complemented
59	C₂³×#99	D₄	1	4	yes	complemented
60	C₂×#2403	C₂×C₄	1	4	yes	—
61	C₂×#2403	C₂×C₄	1	4	yes	—
62	C₂×#2403	C₂×C₄	1	4	yes	—
63	C₂×#2403	D₄	1	4	yes	—
64	C₂×#2403	D₄	1	4	yes	—
65	C₂×#2403	D₄	1	4	yes	—
66	C₂×#2403	D₄	1	2	yes	—
67	C₂×#2403	D₄	1	2	yes	—
68	C₂×#2403	D₄	1	2	yes	—
69	C₂×#2403	D₄	1	2	yes	—
70	C₂²×#386	D₄	1	2	yes	—
71	C₂²×#379	C₂³	1	1	yes	characteristic
72	C₂²×#379	C₂³	1	1	yes	characteristic
73	C₂²×#379	C₂³	1	1	yes	characteristic
74	C₂²×#379	C₂³	1	1	yes	characteristic
75	C₂²×#379	C₂³	1	1	yes	characteristic
76	C₂²×#379	C₂³	1	1	yes	characteristic
77	C₂²×#379	C₂³	1	1	yes	characteristic
78	C₂²×#379	C₂³	1	1	yes	characteristic
79	C₂²×#379	C₂³	1	1	yes	characteristic
80	C₂²×#379	C₂³	1	1	yes	characteristic
81	C₂²×#379	C₂³	1	1	yes	characteristic
82	C₂×#1781	C₂×C₄	1	4	yes	complemented
83	C₂×#1781	C₂×C₄	1	4	yes	complemented
84	C₂×#1781	C₂×C₄	1	4	yes	complemented
85	C₂×#1781	D₄	1	4	yes	complemented
86	C₂×#1781	D₄	1	4	yes	complemented
87	#14681	D₄	1	2	yes	complemented
88	#14679	D₄	1	2	yes	complemented
89	#13867	D₄	1	4	yes	complemented
90	C₂⁷	C₂×D₄	1	1	yes	characteristic
91	C₂⁷	C₂×D₄	1	1	yes	characteristic
92	C₂⁷	#41	1	1	yes	characteristic
93	C₂⁷	#41	1	1	yes	characteristic
94	C₂⁷	C₂⁴	1	1	yes	characteristic
95	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
96	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
97	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
98	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
99	C₂⁴×D₄	C₂×D₄	1	2	yes	—
100	C₂⁴×D₄	C₂×D₄	1	2	yes	—
101	C₂⁴×D₄	C₂×D₄	1	2	yes	—
102	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
103	C₂⁴×D₄	C₂×D₄	1	2	yes	—
104	C₂⁴×D₄	C₂×D₄	1	2	yes	—
105	C₂⁴×D₄	C₂×D₄	1	2	yes	—
106	C₂⁴×D₄	C₂×D₄	1	2	yes	—
107	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
108	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
109	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
110	C₂⁴×D₄	C₂×D₄	1	2	yes	—
111	C₂⁴×D₄	C₂×D₄	1	2	yes	—
112	C₂⁴×D₄	C₂×D₄	1	2	yes	—
113	C₂⁴×D₄	C₂×D₄	1	2	yes	—
114	C₂⁴×D₄	C₂×D₄	1	2	yes	—
115	C₂⁴×D₄	C₂×D₄	1	2	yes	—
116	C₂⁴×D₄	C₂×D₄	1	2	yes	—
117	C₂⁴×D₄	#41	1	2	yes	—
118	C₂⁴×D₄	#41	1	2	yes	—
119	C₂⁴×D₄	#41	1	2	yes	—
120	C₂⁴×D₄	#41	1	2	yes	—
121	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
122	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
123	C₂⁵×C₄	#41	1	1	yes	characteristic
124	C₂⁵×C₄	#41	1	1	yes	characteristic
125	C₂²×#120	C₂²⋊C₄	1	8	yes	complemented
126	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
127	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
128	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
129	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
130	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
131	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
132	#2403	C₂²⋊C₄	1	8	yes	complemented
133	#2403	C₂²⋊C₄	1	8	yes	complemented
134	#2403	C₂²⋊C₄	1	8	yes	complemented
135	#2403	C₂²⋊C₄	1	8	yes	complemented
136	C₂×#386	C₂²⋊C₄	1	8	yes	complemented
137	C₂×#379	C₂²×C₄	1	2	yes	—
138	C₂×#379	C₂²×C₄	1	2	yes	—
139	C₂×#379	C₂²×C₄	1	2	yes	—
140	C₂×#379	C₂×D₄	1	2	yes	—
141	C₂×#379	C₂×D₄	1	2	yes	—
142	C₂×#379	C₂×D₄	1	2	yes	—
143	C₂×#379	C₂×D₄	1	2	yes	—
144	C₂×#379	C₂×D₄	1	2	yes	—
145	C₂×#379	C₂×D₄	1	2	yes	—
146	C₂×#379	C₂×D₄	1	2	yes	—
147	C₂×#379	C₂×D₄	1	2	yes	—
148	C₂×#379	C₂×D₄	1	2	yes	—
149	C₂×#379	C₂×D₄	1	2	yes	—
150	C₂×#379	C₂×D₄	1	2	yes	—
151	C₂×#379	C₂×D₄	1	2	yes	—
152	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂⁶	C₄×D₄	1	2	yes	—
154	C₂⁶	C₄×D₄	1	2	yes	—
155	C₂⁶	C₄×D₄	1	2	yes	—
156	C₂⁶	#120	1	1	yes	characteristic
157	C₂⁶	#120	1	2	yes	—
158	C₂⁶	#120	1	2	yes	—
159	C₂⁶	#120	1	1	yes	characteristic
160	C₂⁶	#121	1	2	yes	—
161	C₂⁶	#121	1	2	yes	—
162	C₂⁶	#121	1	2	yes	—
163	C₂⁶	#123	1	2	yes	—
164	C₂⁶	#123	1	2	yes	—
165	C₂⁶	C₂³×C₄	1	1	yes	characteristic
166	C₂⁶	C₂²×D₄	1	1	yes	characteristic
167	C₂⁶	C₂²×D₄	1	1	yes	characteristic
168	C₂⁶	C₂²×D₄	1	1	yes	characteristic
169	C₂⁶	C₂²×D₄	1	1	yes	characteristic
170	C₂⁶	C₂²×D₄	1	1	yes	characteristic
171	C₂⁶	C₂²×D₄	1	1	yes	characteristic
172	C₂⁶	C₂²×D₄	1	1	yes	characteristic
173	C₂⁶	C₂²×D₄	1	1	yes	characteristic
174	C₂⁶	C₂²×D₄	1	1	yes	characteristic
175	C₂⁶	C₂²×D₄	1	1	yes	characteristic
176	C₂⁶	C₂²×D₄	1	1	yes	characteristic
177	C₂⁶	C₂²×D₄	1	1	yes	characteristic
178	C₂⁶	C₂×#41	1	1	yes	characteristic
179	C₂⁶	C₂×#41	1	1	yes	characteristic
180	C₂⁶	C₂×#41	1	1	yes	characteristic
181	C₂⁶	C₂×#41	1	1	yes	characteristic
182	C₂⁶	C₂×#41	1	1	yes	characteristic
183	C₂⁶	C₂×#41	1	1	yes	characteristic
184	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
185	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
189	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
190	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
193	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
196	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
197	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
198	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
199	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
200	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
201	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
202	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
203	C₂³×D₄	C₄×D₄	1	4	yes	—
204	C₂³×D₄	C₄×D₄	1	4	yes	—
205	C₂³×D₄	C₄×D₄	1	4	yes	—
206	C₂³×D₄	#120	1	2	yes	—
207	C₂³×D₄	#120	1	2	yes	—
208	C₂³×D₄	#120	1	2	yes	—
209	C₂³×D₄	#120	1	2	yes	—
210	C₂³×D₄	#120	1	4	yes	—
211	C₂³×D₄	#120	1	4	yes	—
212	C₂³×D₄	#121	1	4	yes	—
213	C₂³×D₄	#121	1	4	yes	—
214	C₂³×D₄	#121	1	4	yes	—
215	C₂³×D₄	#123	1	4	yes	—
216	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
217	C₂⁴×C₄	C₄×D₄	1	2	yes	—
218	C₂⁴×C₄	C₄×D₄	1	2	yes	—
219	C₂⁴×C₄	C₄×D₄	1	2	yes	—
220	C₂⁴×C₄	#120	1	1	yes	characteristic
221	C₂⁴×C₄	#120	1	2	yes	—
222	C₂⁴×C₄	#120	1	2	yes	—
223	C₂⁴×C₄	#120	1	1	yes	characteristic
224	C₂⁴×C₄	#121	1	2	yes	—
225	C₂⁴×C₄	#121	1	2	yes	—
226	C₂⁴×C₄	#121	1	2	yes	—
227	C₂⁴×C₄	#123	1	2	yes	—
228	C₂⁴×C₄	#123	1	2	yes	—
229	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
230	C₂²×C₂²⋊C₄	#120	1	4	yes	—
231	C₂²×C₂²⋊C₄	#120	1	4	yes	—
232	#379	C₂×C₂²⋊C₄	1	4	yes	—
233	#379	C₂×C₂²⋊C₄	1	4	yes	—
234	C₂⁵	#379	1	2	yes	—
235	C₂⁵	#379	1	2	yes	—
236	C₂⁵	#386	1	4	yes	—
237	C₂⁵	#386	1	4	yes	—
238	C₂⁵	#386	1	4	yes	—
239	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
240	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
241	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
242	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
243	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
244	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
245	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
246	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
247	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
248	C₂⁵	#518	1	1	yes	characteristic
249	C₂⁵	#518	1	1	yes	characteristic
250	C₂⁵	#518	1	1	yes	characteristic
251	C₂⁵	#518	1	1	yes	characteristic
252	C₂⁵	#518	1	1	yes	characteristic
253	C₂⁵	#518	1	1	yes	characteristic
254	C₂⁵	C₂×#120	1	1	yes	characteristic
255	C₂⁵	C₂×#120	1	1	yes	characteristic
256	C₂⁵	C₂×#120	1	1	yes	characteristic
257	C₂⁵	C₂×#120	1	1	yes	characteristic
258	C₂⁵	C₂×#120	1	1	yes	characteristic
259	C₂⁵	C₂×#120	1	1	yes	characteristic
260	C₂⁵	C₂×#120	1	1	yes	characteristic
261	C₂⁵	C₂×#120	1	1	yes	characteristic
262	C₂⁵	C₂×#120	1	1	yes	characteristic
263	C₂⁵	C₂×#121	1	1	yes	characteristic
264	C₂⁵	C₂×#121	1	1	yes	characteristic
265	C₂⁵	C₂×#121	1	1	yes	characteristic
266	C₂⁵	C₂×#121	1	1	yes	characteristic
267	C₂⁵	C₂×#121	1	1	yes	characteristic
268	C₂⁵	C₂×#121	1	1	yes	characteristic
269	C₂⁵	C₂×#123	1	1	yes	characteristic
270	C₂⁵	C₂×#123	1	1	yes	characteristic
271	C₂⁵	C₂×#123	1	1	yes	characteristic
272	C₂⁵	#525	1	1	yes	characteristic
273	C₂⁵	#525	1	1	yes	characteristic
274	C₂⁵	#525	1	1	yes	characteristic
275	C₂⁵	#525	1	1	yes	characteristic
276	C₂⁵	#525	1	1	yes	characteristic
277	C₂⁵	#525	1	1	yes	characteristic
278	C₂⁵	#534	1	1	yes	characteristic
279	C₂⁵	#534	1	1	yes	characteristic
280	C₂⁵	#534	1	1	yes	characteristic
281	C₂⁵	#534	1	1	yes	characteristic
282	C₂⁵	#534	1	1	yes	characteristic
283	C₂⁵	#534	1	1	yes	characteristic
284	C₂⁵	#534	1	1	yes	characteristic
285	C₂⁵	#534	1	1	yes	characteristic
286	C₂⁵	#534	1	1	yes	characteristic
287	C₂⁵	#534	1	1	yes	characteristic
288	C₂⁵	#534	1	1	yes	characteristic
289	C₂⁵	#534	1	1	yes	characteristic
290	C₂⁵	#534	1	1	yes	characteristic
291	C₂⁵	#534	1	1	yes	characteristic
292	C₂⁵	#534	1	1	yes	characteristic
293	C₂⁵	#534	1	1	yes	characteristic
294	C₂⁵	#534	1	1	yes	characteristic
295	C₂⁵	#534	1	1	yes	characteristic
296	C₂⁵	#535	1	1	yes	characteristic
297	C₂⁵	#535	1	1	yes	characteristic
298	C₂⁵	#535	1	1	yes	characteristic
299	C₂⁵	#535	1	1	yes	characteristic
300	C₂⁵	#535	1	1	yes	characteristic
301	C₂⁵	#535	1	1	yes	characteristic
302	C₂⁵	#538	1	1	yes	characteristic
303	C₂⁵	#538	1	1	yes	characteristic
304	C₂⁵	#538	1	1	yes	characteristic
305	C₂⁵	#538	1	1	yes	characteristic
306	C₂⁵	#538	1	1	yes	characteristic
307	C₂⁵	#538	1	1	yes	characteristic
308	C₂⁵	#538	1	1	yes	characteristic
309	C₂⁵	#538	1	1	yes	characteristic
310	C₂⁵	#538	1	1	yes	characteristic
311	C₂⁵	#538	1	1	yes	characteristic
312	C₂⁵	#538	1	1	yes	characteristic
313	C₂⁵	#538	1	1	yes	characteristic
314	C₂⁵	D₄²	1	1	yes	characteristic
315	C₂⁵	D₄²	1	1	yes	characteristic
316	C₂⁵	D₄²	1	1	yes	characteristic
317	C₂⁵	D₄²	1	1	yes	characteristic
318	C₂⁵	D₄²	1	1	yes	characteristic
319	C₂⁵	D₄²	1	1	yes	characteristic
320	C₂⁵	D₄²	1	1	yes	characteristic
321	C₂⁵	D₄²	1	1	yes	characteristic
322	C₂⁵	D₄²	1	1	yes	characteristic
323	C₂⁵	D₄²	1	1	yes	characteristic
324	C₂⁵	D₄²	1	1	yes	characteristic
325	C₂⁵	D₄²	1	1	yes	characteristic
326	C₂⁵	D₄²	1	1	yes	characteristic
327	C₂⁵	D₄²	1	1	yes	characteristic
328	C₂⁵	D₄²	1	1	yes	characteristic
329	C₂⁵	D₄²	1	1	yes	characteristic
330	C₂⁵	D₄²	1	1	yes	characteristic
331	C₂⁵	D₄²	1	1	yes	characteristic
332	C₂⁵	D₄²	1	1	yes	characteristic
333	C₂⁵	D₄²	1	1	yes	characteristic
334	C₂⁵	D₄²	1	1	yes	characteristic
335	C₂⁵	D₄²	1	1	yes	characteristic
336	C₂⁵	D₄²	1	1	yes	characteristic
337	C₂⁵	D₄²	1	1	yes	characteristic
338	C₂⁵	D₄²	1	1	yes	characteristic
339	C₂⁵	D₄²	1	1	yes	characteristic
340	C₂⁵	D₄²	1	1	yes	characteristic
341	C₂⁵	D₄²	1	1	yes	characteristic
342	C₂⁵	D₄²	1	1	yes	characteristic
343	C₂⁵	D₄²	1	1	yes	characteristic
344	C₂⁵	#546	1	1	yes	characteristic
345	C₂⁵	#546	1	1	yes	characteristic
346	C₂⁵	#546	1	1	yes	characteristic
347	C₂⁵	#546	1	1	yes	characteristic
348	C₂⁵	#546	1	1	yes	characteristic
349	C₂⁵	#546	1	1	yes	characteristic
350	C₂⁵	#546	1	1	yes	characteristic
351	C₂⁵	#546	1	1	yes	characteristic
352	C₂⁵	#546	1	1	yes	characteristic
353	C₂⁵	#546	1	1	yes	characteristic
354	C₂⁵	#546	1	1	yes	characteristic
355	C₂⁵	#546	1	1	yes	characteristic
356	C₂⁵	#546	1	1	yes	characteristic
357	C₂⁵	#546	1	1	yes	characteristic
358	C₂⁵	#546	1	1	yes	characteristic
359	C₂⁵	#546	1	1	yes	characteristic
360	C₂⁵	#546	1	1	yes	characteristic
361	C₂⁵	#546	1	1	yes	characteristic
362	C₂⁵	#546	1	1	yes	characteristic
363	C₂⁵	#546	1	1	yes	characteristic
364	C₂⁵	#546	1	1	yes	characteristic
365	C₂⁵	#546	1	1	yes	characteristic
366	C₂⁵	#546	1	1	yes	characteristic
367	C₂⁵	#546	1	1	yes	characteristic
368	C₂⁵	#546	1	1	yes	characteristic
369	C₂⁵	#546	1	1	yes	characteristic
370	C₂⁵	#546	1	1	yes	characteristic
371	C₂⁵	#546	1	1	yes	characteristic
372	C₂⁵	#546	1	1	yes	characteristic
373	C₂⁵	#546	1	1	yes	characteristic
374	C₂⁵	#546	1	1	yes	characteristic
375	C₂⁵	#546	1	1	yes	characteristic
376	C₂⁵	#546	1	1	yes	characteristic
377	C₂⁵	#546	1	1	yes	characteristic
378	C₂⁵	#546	1	1	yes	characteristic
379	C₂⁵	#546	1	1	yes	characteristic
380	C₂⁵	#551	1	1	yes	characteristic
381	C₂⁵	#551	1	1	yes	characteristic
382	C₂⁵	#551	1	1	yes	characteristic
383	C₂⁵	#551	1	1	yes	characteristic
384	C₂⁵	#551	1	1	yes	characteristic
385	C₂⁵	#551	1	1	yes	characteristic
386	C₂⁵	#560	1	1	yes	characteristic
387	C₂⁵	#560	1	1	yes	characteristic
388	C₂⁵	#560	1	1	yes	characteristic
389	C₂⁵	#560	1	1	yes	characteristic
390	C₂⁵	#560	1	1	yes	characteristic
391	C₂⁵	#560	1	1	yes	characteristic
392	C₂⁵	H(3,𝔽₄)	1	1	yes	characteristic
393	C₂⁵	H(3,𝔽₄)	1	1	yes	characteristic
394	C₂²×D₄	B(4,𝔽₂)	1	16	yes	—
395	C₂³×C₄	#379	1	2	yes	—
396	C₂³×C₄	#379	1	2	yes	—
397	C₂³×C₄	#386	1	4	yes	—
398	C₂³×C₄	#386	1	4	yes	—
399	C₂³×C₄	#386	1	4	yes	—
400	C₂⁴	#1889	1	8	yes	complemented
401	C₂⁴	C₂×#379	1	1	yes	characteristic
402	C₂⁴	C₂×#386	1	1	yes	characteristic
403	C₂⁴	C₂×#386	1	1	yes	characteristic
404	C₂⁴	C₂×#386	1	1	yes	characteristic
405	C₂⁴	C₄×#120	1	1	yes	characteristic
406	C₂⁴	C₄×#120	1	1	yes	characteristic
407	C₂⁴	#2308	1	1	yes	characteristic
408	C₂⁴	#2308	1	1	yes	characteristic
409	C₂⁴	#2308	1	1	yes	characteristic
410	C₂⁴	#2321	1	1	yes	characteristic
411	C₂⁴	#2321	1	1	yes	characteristic
412	C₂⁴	#2321	1	1	yes	characteristic
413	C₂⁴	#2321	1	1	yes	characteristic
414	C₂⁴	#2321	1	1	yes	characteristic
415	C₂⁴	#2321	1	1	yes	characteristic
416	C₂⁴	D₄×C₂²⋊C₄	1	1	yes	characteristic
417	C₂⁴	D₄×C₂²⋊C₄	1	1	yes	characteristic
418	C₂⁴	D₄×C₂²⋊C₄	1	1	yes	characteristic
419	C₂⁴	D₄×C₂²⋊C₄	1	1	yes	characteristic
420	C₂⁴	D₄×C₂²⋊C₄	1	1	yes	characteristic
421	C₂⁴	D₄×C₂²⋊C₄	1	1	yes	characteristic
422	C₂⁴	D₄×C₂²⋊C₄	1	1	yes	characteristic
423	C₂⁴	D₄×C₂²⋊C₄	1	1	yes	characteristic
424	C₂⁴	D₄×C₂²⋊C₄	1	1	yes	characteristic
425	C₂⁴	D₄×C₂²⋊C₄	1	1	yes	characteristic
426	C₂⁴	D₄×C₂²⋊C₄	1	1	yes	characteristic
427	C₂⁴	D₄×C₂²⋊C₄	1	1	yes	characteristic
428	C₂⁴	#2358	1	1	yes	characteristic
429	C₂⁴	#2358	1	1	yes	characteristic
430	C₂⁴	#2358	1	1	yes	characteristic
431	C₂⁴	#2358	1	1	yes	characteristic
432	C₂⁴	#2358	1	1	yes	characteristic
433	C₂⁴	#2358	1	1	yes	characteristic
434	C₂⁴	#2375	1	1	yes	characteristic
435	C₂⁴	#2375	1	1	yes	characteristic
436	C₂⁴	#2403	1	1	yes	characteristic
437	C₂⁴	#2403	1	1	yes	characteristic
438	C₂⁴	#2403	1	1	yes	characteristic
439	C₂⁴	#2403	1	1	yes	characteristic
440	C₂⁴	#2403	1	1	yes	characteristic
441	C₂⁴	#2403	1	1	yes	characteristic
442	C₂⁴	#2403	1	1	yes	characteristic
443	C₂⁴	#2403	1	1	yes	characteristic
444	C₂⁴	#2403	1	1	yes	characteristic
445	C₂⁴	#2403	1	1	yes	characteristic
446	C₂⁴	#2403	1	1	yes	characteristic
447	C₂⁴	#2403	1	1	yes	characteristic
448	C₂⁴	#2404	1	1	yes	characteristic
449	C₂⁴	#2404	1	1	yes	characteristic
450	C₂⁴	#2404	1	1	yes	characteristic
451	C₂⁴	#2404	1	1	yes	characteristic
452	C₂⁴	#2404	1	1	yes	characteristic
453	C₂⁴	#2404	1	1	yes	characteristic
454	C₂⁴	#2405	1	1	yes	characteristic
455	C₂⁴	#2405	1	1	yes	characteristic
456	C₂⁴	#2405	1	1	yes	characteristic
457	C₂⁴	#2405	1	1	yes	characteristic
458	C₂⁴	#2405	1	1	yes	characteristic
459	C₂⁴	#2405	1	1	yes	characteristic
460	C₂⁴	#2408	1	1	yes	characteristic
461	C₂⁴	#2408	1	1	yes	characteristic
462	C₂⁴	#2408	1	1	yes	characteristic
463	C₂⁴	#2408	1	1	yes	characteristic
464	C₂⁴	#2408	1	1	yes	characteristic
465	C₂⁴	#2408	1	1	yes	characteristic
466	C₂⁴	#2410	1	1	yes	characteristic
467	C₂⁴	#2410	1	1	yes	characteristic
468	C₂⁴	#2410	1	1	yes	characteristic
469	C₂⁴	#2410	1	1	yes	characteristic
470	C₂⁴	#2410	1	1	yes	characteristic
471	C₂⁴	#2410	1	1	yes	characteristic
472	C₂⁴	#2410	1	1	yes	characteristic
473	C₂⁴	#2410	1	1	yes	characteristic
474	C₂⁴	#2410	1	1	yes	characteristic
475	C₂⁴	#2410	1	1	yes	characteristic
476	C₂⁴	#2410	1	1	yes	characteristic
477	C₂⁴	#2410	1	1	yes	characteristic
478	C₂⁴	#2418	1	1	yes	characteristic
479	C₂⁴	#2418	1	1	yes	characteristic
480	C₂⁴	#2418	1	1	yes	characteristic
481	C₂⁴	#2418	1	1	yes	characteristic
482	C₂⁴	#2418	1	1	yes	characteristic
483	C₂⁴	#2418	1	1	yes	characteristic
484	C₂⁴	#2418	1	1	yes	characteristic
485	C₂⁴	#2418	1	1	yes	characteristic
486	C₂⁴	#2418	1	1	yes	characteristic
487	C₂⁴	#2418	1	1	yes	characteristic
488	C₂⁴	#2418	1	1	yes	characteristic
489	C₂⁴	#2418	1	1	yes	characteristic
490	C₂⁴	#2424	1	1	yes	characteristic
491	C₂⁴	#2424	1	1	yes	characteristic
492	C₂⁴	#2424	1	1	yes	characteristic
493	C₂⁴	#2424	1	1	yes	characteristic
494	C₂⁴	#2424	1	1	yes	characteristic
495	C₂⁴	#2424	1	1	yes	characteristic
496	C₂⁴	#2424	1	1	yes	characteristic
497	C₂⁴	#2424	1	1	yes	characteristic
498	C₂⁴	#2424	1	1	yes	characteristic
499	C₂⁴	#2424	1	1	yes	characteristic
500	C₂⁴	#2424	1	1	yes	characteristic
501	C₂⁴	#2424	1	1	yes	characteristic
502	C₂⁴	#2534	1	1	yes	characteristic
503	C₂⁴	#2534	1	1	yes	characteristic
504	C₂⁴	#2534	1	1	yes	characteristic
505	C₂⁴	#2534	1	1	yes	characteristic
506	C₂⁴	#2534	1	1	yes	characteristic
507	C₂⁴	#2534	1	1	yes	characteristic
508	C₂⁴	#2668	1	1	yes	characteristic
509	C₂⁴	#2668	1	1	yes	characteristic
510	C₂⁴	#2668	1	1	yes	characteristic
511	C₂⁴	#2668	1	1	yes	characteristic
512	C₂⁴	#2668	1	1	yes	characteristic
513	C₂⁴	#2668	1	1	yes	characteristic
514	C₂⁴	#2668	1	1	yes	characteristic
515	C₂⁴	#2668	1	1	yes	characteristic
516	C₂⁴	#2668	1	1	yes	characteristic
517	C₂⁴	#2668	1	1	yes	characteristic
518	C₂⁴	#2668	1	1	yes	characteristic
519	C₂⁴	#2668	1	1	yes	characteristic
520	C₂⁴	#2669	1	1	yes	characteristic
521	C₂⁴	#2669	1	1	yes	characteristic
522	C₂⁴	#2669	1	1	yes	characteristic
523	C₂⁴	#2669	1	1	yes	characteristic
524	C₂⁴	#2669	1	1	yes	characteristic
525	C₂⁴	#2669	1	1	yes	characteristic
526	C₂⁴	#2678	1	1	yes	characteristic
527	C₂⁴	#2678	1	1	yes	characteristic
528	C₂⁴	#2678	1	1	yes	characteristic
529	C₂⁴	#2678	1	1	yes	characteristic
530	C₂⁴	#2678	1	1	yes	characteristic
531	C₂⁴	#2678	1	1	yes	characteristic
532	C₂⁴	#2678	1	1	yes	characteristic
533	C₂⁴	#2678	1	1	yes	characteristic
534	C₂⁴	#2678	1	1	yes	characteristic
535	C₂⁴	#2678	1	1	yes	characteristic
536	C₂⁴	#2678	1	1	yes	characteristic
537	C₂⁴	#2678	1	1	yes	characteristic
538	C₂⁴	#2679	1	1	yes	characteristic
539	C₂⁴	#2679	1	1	yes	characteristic
540	C₂⁴	#2679	1	1	yes	characteristic
541	C₂⁴	#2679	1	1	yes	characteristic
542	C₂⁴	#2679	1	1	yes	characteristic
543	C₂⁴	#2679	1	1	yes	characteristic
544	C₂⁴	#2684	1	1	yes	characteristic
545	C₂⁴	#2684	1	1	yes	characteristic
546	C₂⁴	#2684	1	1	yes	characteristic
547	C₂⁴	#2684	1	1	yes	characteristic
548	C₂⁴	#2684	1	1	yes	characteristic
549	C₂⁴	#2684	1	1	yes	characteristic
550	C₂⁴	#2697	1	1	yes	characteristic
551	C₂⁴	#2697	1	1	yes	characteristic
552	C₂⁴	#2697	1	1	yes	characteristic
553	C₂⁴	#2697	1	1	yes	characteristic
554	C₂⁴	#2697	1	1	yes	characteristic
555	C₂⁴	#2697	1	1	yes	characteristic
556	C₂⁴	C₂×B(4,𝔽₂)	1	8	yes	—
557	C₂²×C₄	#1889	1	8	yes	complemented
558	C₂³	#13867	1	1	yes	characteristic
559	C₂³	#13867	1	1	yes	characteristic
560	C₂³	#13867	1	1	yes	characteristic
561	C₂³	#13967	1	1	yes	characteristic
562	C₂³	#13967	1	1	yes	characteristic
563	C₂³	#13967	1	1	yes	characteristic
564	C₂³	#13967	1	1	yes	characteristic
565	C₂³	#13967	1	1	yes	characteristic
566	C₂³	#13967	1	1	yes	characteristic
567	C₂³	#14357	1	1	yes	characteristic
568	C₂³	#14357	1	1	yes	characteristic
569	C₂³	#14357	1	1	yes	characteristic
570	C₂³	#14357	1	1	yes	characteristic
571	C₂³	#14357	1	1	yes	characteristic
572	C₂³	#14357	1	1	yes	characteristic
573	C₂³	#15257	1	1	yes	characteristic
574	C₂³	#15257	1	1	yes	characteristic
575	C₂³	#15257	1	1	yes	characteristic
576	C₂³	#15257	1	1	yes	characteristic
577	C₂³	#15257	1	1	yes	characteristic
578	C₂³	#15257	1	1	yes	characteristic
579	C₂³	#15266	1	1	yes	characteristic
580	C₂³	#15266	1	1	yes	characteristic
581	C₂³	#15266	1	1	yes	characteristic
582	C₂³	#15266	1	1	yes	characteristic
583	C₂³	#15266	1	1	yes	characteristic
584	C₂³	#15266	1	1	yes	characteristic
585	C₂³	#15947	1	1	yes	characteristic
586	C₂³	#15948	1	1	yes	characteristic
587	C₂³	#15948	1	1	yes	characteristic
588	C₂³	#15948	1	1	yes	characteristic
589	C₂³	C₂×#1889	1	4	yes	—
590	C₂³	#23900	1	4	yes	—
591	C₂³	#23900	1	4	yes	—
592	C₂³	#23900	1	4	yes	—
593	C₂³	#23900	1	4	yes	—
594	C₂³	#23984	1	4	yes	—
595	C₂³	#23984	1	4	yes	—
596	C₂³	#23996	1	4	yes	—
597	C₂²	#154670	1	1	yes	characteristic
598	C₂²	#359501	1	2	yes	—
599	C₂²	#364410	1	2	yes	—
600	C₂²	#364410	1	2	yes	—
601	C₂²	#364532	1	2	yes	—
602	C₂²	#417493	1	2	yes	—
603	C₂²	#417493	1	2	yes	—
604	C₂²	#417538	1	2	yes	—
605	C₂²	#418849	1	2	yes	—
606	C₂²	#449475	1	2	yes	—
607	C₂²	#449521	1	2	yes	—
608	C₂²	#449578	1	2	yes	—
609	C₂	#72218789	1	1	yes	characteristic
610	C₂	#72240550	1	1	yes	characteristic
611	C₂	#72240603	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#154670
commutator	C₂⁶	C₂³×C₄
Frattini, cosocle	C₂⁷	C₂⁴
prime radical	C₂²×#32898	C₂
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁷ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72266079	C₂	semidirect
2. #72266073	C₂	semidirect
3. #72266035	C₂	semidirect
4. #72266035	C₂	semidirect
5. #72266029	C₂	semidirect
6. #72266028	C₂	semidirect
7. #72240619	C₂	semidirect
8. #72240617	C₂	semidirect
9. #72240568	C₂	semidirect
10. #72238531	C₂	semidirect
11. C₂×#201664	C₂	semidirect
12. #72225796	C₂	semidirect
13. #72225796	C₂	semidirect
14. #72225783	C₂	semidirect
20. C₂×#34171	C₂²	semidirect
21. C₂×#32898	C₄	semidirect
32. C₂²×#1781	C₂²	semidirect
33. C₂²×#1781	C₂²	semidirect
39. #517411	C₂²	semidirect
40. #355913	C₂²	semidirect
41. #355913	C₂²	semidirect
42. #355913	C₂²	semidirect
43. #355913	C₂²	semidirect
44. #355913	C₂²	semidirect
45. #355913	C₂²	semidirect
46. C₂×#8101	C₂²	semidirect
47. C₂×#8101	C₂²	semidirect
48. C₂×#8101	C₂²	semidirect
49. C₂×#8101	C₂²	semidirect
50. C₂×#8101	C₂²	semidirect
51. C₂×#8101	C₂²	semidirect
52. C₂³×H(5,𝔽₂)	C₂×C₄	semidirect
58. C₂³×#99	D₄	semidirect
59. C₂³×#99	D₄	semidirect
82. C₂×#1781	C₂×C₄	semidirect
83. C₂×#1781	C₂×C₄	semidirect
84. C₂×#1781	C₂×C₄	semidirect
85. C₂×#1781	D₄	semidirect
86. C₂×#1781	D₄	semidirect
87. #14681	D₄	semidirect
88. #14679	D₄	semidirect
89. #13867	D₄	semidirect
125. C₂²×#120	C₂²⋊C₄	semidirect
132. #2403	C₂²⋊C₄	semidirect
133. #2403	C₂²⋊C₄	semidirect
134. #2403	C₂²⋊C₄	semidirect
135. #2403	C₂²⋊C₄	semidirect
136. C₂×#386	C₂²⋊C₄	semidirect
400. C₂⁴	#1889	semidirect
557. C₂²×C₄	#1889	semidirect

Maximal subgroups

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

subgroup	index
#72266079	2
#72266073	2
#72266035	2
#72266029	2
#72266028	2
#72240619	2
#72240617	2
#72240568	2
#72238531	2
C₂×#201664	2
#72225796	2
#72225783	2
C₂²×#32898	2