Subgroups — #72251188

Order 2048.

Only the 11864 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 722 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72251160	C₂	1	8	yes	maximal, complemented
2	#72251158	C₂	1	1	yes	maximal, characteristic, complemented
3	#72251154	C₂	1	2	yes	maximal, complemented
4	C₂×#6371551	C₂	1	1	yes	maximal, characteristic, complemented
5	#72251147	C₂	1	1	yes	maximal, characteristic, complemented
6	#72251136	C₂	1	2	yes	maximal, complemented
7	#72251134	C₂	1	16	yes	maximal, complemented
8	#72249537	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#10574873	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#6370693	C₂	1	1	yes	maximal, characteristic, complemented
11	#72238117	C₂	1	8	yes	maximal, complemented
12	C₂×#394064	C₂	1	16	yes	maximal, complemented
13	#72235904	C₂	1	2	yes	maximal, complemented
14	C₂×#6431795	C₂	1	2	yes	maximal, complemented
15	C₂×#10586066	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×H(7,𝔽₂)	C₂²	1	1	yes	characteristic
17	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
18	C₂×#62852	C₂²	1	4	yes	complemented
19	C₂×#62842	C₂²	1	2	yes	—
20	C₂×#62842	C₂²	1	1	yes	characteristic
21	C₂×#62842	C₂²	1	8	yes	complemented
22	C₂×#62842	C₂²	1	1	yes	characteristic, complemented
23	C₂×#62842	C₂²	1	2	yes	complemented
24	C₂×#62811	C₂²	1	4	yes	complemented
25	C₂²×#3484	C₂²	1	2	yes	—
26	C₂²×#3484	C₂²	1	8	yes	complemented
27	C₂²×#3484	C₂²	1	1	yes	characteristic, complemented
28	C₂×#62652	C₂²	1	1	yes	characteristic
29	C₂×#60398	C₂²	1	8	yes	complemented
30	C₂²×#3026	C₂²	1	16	yes	complemented
31	C₂²×#2883	C₂²	1	1	yes	characteristic
32	C₂²×#2883	C₂²	1	1	yes	characteristic
33	C₂²×#2883	C₂²	1	2	yes	complemented
34	C₂²×#2883	C₂²	1	2	yes	complemented
35	C₂²×#2883	C₂²	1	2	yes	complemented
36	C₂²×#2883	C₂²	1	2	yes	complemented
37	#7630502	C₂²	1	4	yes	complemented
38	#7630442	C₂²	1	8	yes	complemented
39	#7628649	C₂²	1	4	yes	complemented
40	C₂×#34980	C₂²	1	8	yes	complemented
41	#7625680	C₂²	1	1	yes	characteristic
42	#7625680	C₂²	1	1	yes	characteristic, complemented
43	#7625680	C₂²	1	2	yes	complemented
44	C₂×#34171	C₂²	1	2	yes	complemented
45	C₂×#34171	C₂²	1	1	yes	characteristic, complemented
46	#6431794	C₂²	1	16	yes	complemented
47	C₂×#23445	C₂²	1	8	yes	complemented
48	C₂×#23444	C₂²	1	16	yes	complemented
49	C₂×#23444	C₂²	1	32	yes	complemented
50	C₂×#23443	C₂²	1	8	yes	complemented
51	C₂²×#2021	C₂²	1	16	yes	complemented
52	C₂×#21014	C₂²	1	8	yes	complemented
53	C₂²×#1913	C₂²	1	16	yes	complemented
54	#6370734	C₂²	1	8	yes	complemented
55	C₂×#20609	C₂²	1	16	yes	complemented
56	C₂×#20586	C₂²	1	4	yes	complemented
57	C₂×#20585	C₂²	1	8	yes	complemented
58	C₂×#20584	C₂²	1	4	yes	complemented
59	C₂²×#1781	C₂²	1	8	yes	complemented
60	C₂×#20354	C₂²	1	2	yes	complemented
61	C₂×#20354	C₂²	1	2	yes	complemented
62	C₂×#20354	C₂²	1	2	yes	complemented
63	#394065	C₂²	1	64	yes	complemented
64	#394064	C₂²	1	128	yes	complemented
65	#394064	C₂²	1	64	yes	complemented
66	#357531	C₂²	1	8	yes	complemented
67	#357530	C₂²	1	16	yes	complemented
68	#357529	C₂²	1	8	yes	complemented
69	C₂×#10991	C₂²	1	16	yes	complemented
70	#357443	C₂²	1	16	yes	complemented
71	C₂×#10972	C₂²	1	32	yes	complemented
72	#353448	C₂²	1	8	yes	complemented
73	C₂×#10754	C₂²	1	16	yes	complemented
74	C₂×H(7,𝔽₂)	D₄	1	16	yes	complemented
75	C₂²×#585	C₂³	1	4	yes	—
76	C₂³×H(5,𝔽₂)	D₄	1	4	yes	complemented
77	C₂³×H(5,𝔽₂)	D₄	1	4	yes	complemented
78	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
79	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
80	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
81	C₂³×H(5,𝔽₂)	C₂³	1	4	yes	—
82	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
83	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
84	C₂³×H(5,𝔽₂)	C₂³	1	8	yes	—
85	C₂⁴×#41	D₄	1	4	yes	complemented
86	C₂⁴×#41	C₂³	1	2	yes	—
87	C₂⁵×D₄	D₄	1	4	yes	complemented
88	C₂⁵×D₄	C₂³	1	4	yes	—
89	C₂⁵×D₄	C₂³	1	1	yes	characteristic
90	C₂×#3485	D₄	1	16	yes	complemented
91	C₂×#3485	D₄	1	8	yes	complemented
92	C₂×#3485	C₂³	1	16	yes	—
93	C₂×#3484	D₄	1	32	yes	complemented
94	C₂×#3484	D₄	1	16	yes	complemented
95	C₂×#3484	D₄	1	8	yes	complemented
96	C₂×#3484	C₂³	1	16	yes	—
97	C₂×#3484	C₂³	1	32	yes	—
98	C₂×#3449	C₂³	1	4	yes	—
99	C₂×#3449	C₂³	1	8	yes	—
100	C₂×#3449	C₂³	1	8	yes	complemented
101	C₂×#3449	C₂³	1	4	yes	complemented
102	C₂²×#535	C₂³	1	4	yes	—
103	C₂²×#535	C₂³	1	2	yes	complemented
104	C₂²×#534	C₂³	1	8	yes	—
105	C₂²×#534	C₂³	1	16	yes	—
106	C₂²×#534	C₂³	1	8	yes	—
107	C₂²×#534	C₂³	1	4	yes	complemented
108	C₂²×#534	C₂³	1	16	yes	complemented
109	C₂²×#534	C₂³	1	8	yes	complemented
110	C₂²×#525	C₂³	1	4	yes	—
111	C₂²×#525	C₂³	1	2	yes	complemented
112	C₂³×#120	C₂³	1	8	yes	—
113	C₂³×#120	C₂³	1	4	yes	complemented
114	#62652	D₄	1	16	yes	complemented
115	C₂×#3428	C₂³	1	4	yes	—
116	C₂²×#518	C₂³	1	8	yes	—
117	C₂²×#518	C₂³	1	2	yes	—
118	C₂²×#518	C₂³	1	1	yes	characteristic
119	C₂²×#518	C₂³	1	2	yes	—
120	C₂²×#518	C₂³	1	1	yes	characteristic
121	C₂²×#518	C₂³	1	1	yes	characteristic
122	C₂²×#518	C₂³	1	2	yes	—
123	C₂×#3026	C₂³	1	64	yes	complemented
124	C₂×#2883	D₄	1	16	yes	complemented
125	C₂²×#410	C₂³	1	4	yes	—
126	C₂²×#410	C₂³	1	4	yes	—
127	C₂²×#410	C₂³	1	8	yes	complemented
128	C₂²×#410	C₂³	1	8	yes	complemented
129	C₂²×#410	C₂³	1	8	yes	complemented
130	C₂²×#410	C₂³	1	8	yes	complemented
131	C₂³×#99	C₂³	1	8	yes	—
132	C₂³×#99	C₂³	1	8	yes	—
133	C₂³×#99	C₂³	1	16	yes	complemented
134	C₂³×#99	C₂³	1	16	yes	complemented
135	C₂³×#99	C₂³	1	16	yes	complemented
136	C₂³×#99	C₂³	1	16	yes	complemented
137	#35088	C₂³	1	16	yes	complemented
138	#34980	C₂³	1	16	yes	complemented
139	#34980	C₂³	1	32	yes	complemented
140	#34256	D₄	1	16	yes	complemented
141	#34044	C₂³	1	4	yes	—
142	#34044	C₂³	1	8	yes	complemented
143	#34044	C₂³	1	4	yes	complemented
144	C₂×#2309	C₂³	1	4	yes	complemented
145	C₂×#2309	C₂³	1	2	yes	complemented
146	C₂×#2308	C₂³	1	8	yes	—
147	C₂×#2308	C₂³	1	16	yes	complemented
148	C₂×#2308	C₂³	1	8	yes	complemented
149	C₂×#2308	C₂³	1	8	yes	complemented
150	C₂×#2308	C₂³	1	4	yes	complemented
151	C₂×#2280	C₂³	1	4	yes	complemented
152	C₂×#2280	C₂³	1	2	yes	complemented
153	C₂²×#379	C₂³	1	8	yes	complemented
154	C₂²×#379	C₂³	1	4	yes	complemented
155	#23444	C₂³	1	128	yes	complemented
156	C₂×#2022	C₂³	1	32	yes	complemented
157	C₂×#2021	C₂³	1	32	yes	complemented
158	C₂×#2021	C₂³	1	64	yes	complemented
159	C₂×#1913	C₂³	1	64	yes	complemented
160	#20609	C₂³	1	64	yes	complemented
161	C₂×#1782	C₂³	1	16	yes	complemented
162	C₂×#1781	C₂³	1	16	yes	complemented
163	C₂×#1781	C₂³	1	32	yes	complemented
164	C₂×#1740	C₂³	1	8	yes	complemented
165	C₂×#1740	C₂³	1	8	yes	complemented
166	C₂×#1740	C₂³	1	8	yes	complemented
167	C₂²×#342	C₂³	1	16	yes	complemented
168	C₂²×#342	C₂³	1	16	yes	complemented
169	C₂²×#342	C₂³	1	16	yes	complemented
170	#10992	C₂³	1	32	yes	complemented
171	#10991	C₂³	1	32	yes	complemented
172	#10991	C₂³	1	64	yes	complemented
173	#10972	C₂³	1	128	yes	complemented
174	#10754	C₂³	1	64	yes	complemented
175	C₂⁷	C₂×D₄	1	4	yes	complemented
176	C₂⁷	C₂⁴	1	2	yes	—
177	C₂×#585	C₂×D₄	1	32	yes	complemented
178	C₂²×H(5,𝔽₂)	C₂×D₄	1	16	yes	—
179	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
180	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
181	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
182	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
183	C₂²×H(5,𝔽₂)	C₂×D₄	1	16	yes	—
184	C₂²×H(5,𝔽₂)	C₂×D₄	1	16	yes	—
185	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
186	C₂²×H(5,𝔽₂)	C₂×D₄	1	64	yes	complemented
187	C₂²×H(5,𝔽₂)	#41	1	8	yes	—
188	C₂²×H(5,𝔽₂)	C₂⁴	1	16	yes	—
189	C₂³×#41	C₂×D₄	1	4	yes	—
190	C₂³×#41	C₂×D₄	1	4	yes	—
191	C₂³×#41	C₂×D₄	1	8	yes	—
192	C₂³×#41	C₂×D₄	1	4	yes	complemented
193	C₂³×#41	C₂×D₄	1	8	yes	complemented
194	C₂³×#41	C₂×D₄	1	4	yes	complemented
195	C₂³×#41	C₂×D₄	1	8	yes	complemented
196	C₂³×#41	C₂×D₄	1	4	yes	complemented
197	C₂³×#41	C₂×D₄	1	2	yes	complemented
198	C₂³×#41	C₂×D₄	1	2	yes	complemented
199	C₂³×#41	C₂×D₄	1	4	yes	complemented
200	C₂³×#41	C₂⁴	1	4	yes	—
201	C₂³×#41	C₂⁴	1	2	yes	—
202	C₂³×#41	C₂⁴	1	4	yes	—
203	C₂³×#41	C₂⁴	1	2	yes	—
204	C₂³×#41	C₂⁴	1	2	yes	—
205	C₂⁴×Q₈	C₂×D₄	1	2	yes	complemented
206	C₂⁴×D₄	C₂×D₄	1	4	yes	—
207	C₂⁴×D₄	C₂×D₄	1	16	yes	—
208	C₂⁴×D₄	C₂×D₄	1	4	yes	—
209	C₂⁴×D₄	C₂×D₄	1	4	yes	—
210	C₂⁴×D₄	C₂×D₄	1	4	yes	—
211	C₂⁴×D₄	C₂×D₄	1	8	yes	—
212	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
213	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
214	C₂⁴×D₄	C₂×D₄	1	4	yes	complemented
215	C₂⁴×D₄	C₂×D₄	1	4	yes	complemented
216	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
217	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
218	C₂⁴×D₄	C₂×D₄	1	4	yes	complemented
219	C₂⁴×D₄	C₂×D₄	1	4	yes	complemented
220	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
221	C₂⁴×D₄	C₂×D₄	1	4	yes	complemented
222	C₂⁴×D₄	C₂⁴	1	4	yes	—
223	C₂⁴×D₄	C₂⁴	1	4	yes	—
224	C₂⁴×D₄	C₂⁴	1	8	yes	—
225	C₂⁴×D₄	C₂⁴	1	4	yes	—
226	C₂⁴×D₄	C₂⁴	1	8	yes	—
227	C₂⁴×D₄	C₂⁴	1	4	yes	—
228	C₂⁴×D₄	C₂⁴	1	2	yes	—
229	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
230	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
231	C₂⁵×C₄	C₂×D₄	1	4	yes	complemented
232	C₂⁵×C₄	C₂×D₄	1	4	yes	complemented
233	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
234	C₂×#536	C₂×D₄	1	16	yes	complemented
235	C₂×#536	C₂×D₄	1	8	yes	complemented
236	C₂×#535	C₂×D₄	1	32	yes	complemented
237	C₂×#535	C₂×D₄	1	16	yes	complemented
238	C₂×#535	C₂×D₄	1	8	yes	complemented
239	C₂×#534	C₂×D₄	1	64	yes	complemented
240	C₂×#534	C₂×D₄	1	64	yes	complemented
241	C₂×#534	C₂×D₄	1	32	yes	complemented
242	C₂×#534	C₂⁴	1	32	yes	—
243	C₂×#534	C₂⁴	1	16	yes	—
244	C₂×#534	C₂⁴	1	16	yes	—
245	C₂×#534	C₂⁴	1	32	yes	—
246	C₂×#525	C₂×D₄	1	32	yes	complemented
247	C₂×#525	C₂×D₄	1	32	yes	complemented
248	C₂×#525	C₂×D₄	1	16	yes	complemented
249	C₂²×#123	C₂×D₄	1	32	yes	complemented
250	C₂²×#123	C₂×D₄	1	16	yes	complemented
251	C₂²×#123	C₂⁴	1	8	yes	—
252	C₂²×#123	C₂⁴	1	4	yes	—
253	C₂²×#120	C₂×D₄	1	64	yes	complemented
254	C₂²×#120	C₂×D₄	1	32	yes	complemented
255	C₂²×#120	C₂×D₄	1	16	yes	complemented
256	C₂²×#120	C₂⁴	1	8	yes	—
257	C₂²×#120	C₂⁴	1	16	yes	—
258	C₂²×#120	C₂⁴	1	4	yes	—
259	C₂²×#120	C₂⁴	1	8	yes	—
260	#3428	C₂×D₄	1	32	yes	complemented
261	C₂×#518	C₂×D₄	1	16	yes	—
262	C₂×#518	C₂×D₄	1	16	yes	—
263	C₂×#518	C₂×D₄	1	16	yes	—
264	C₂×#518	C₂×D₄	1	64	yes	complemented
265	C₂×#518	C₂×D₄	1	8	yes	complemented
266	C₂×#518	C₂×D₄	1	16	yes	complemented
267	C₂×#518	C₂×D₄	1	8	yes	complemented
268	C₂×#518	C₂⁴	1	16	yes	—
269	C₂²×C₄×D₄	C₂×D₄	1	8	yes	complemented
270	C₂²×#117	C₂⁴	1	2	yes	—
271	C₂²×#117	C₂⁴	1	4	yes	—
272	C₂²×#117	C₂⁴	1	4	yes	—
273	C₂²×#117	C₂⁴	1	2	yes	—
274	C₂²×#117	C₂⁴	1	2	yes	—
275	C₂²×#117	C₂⁴	1	4	yes	—
276	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
277	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
278	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
279	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
280	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
281	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
282	C₂×#410	C₂×D₄	1	32	yes	complemented
283	C₂²×#99	C₂×D₄	1	64	yes	complemented
284	C₂²×#99	C₂⁴	1	16	yes	—
285	C₂²×#99	C₂⁴	1	32	yes	—
286	C₂²×#99	C₂⁴	1	32	yes	—
287	C₂²×#99	C₂⁴	1	32	yes	—
288	C₂²×#99	C₂⁴	1	32	yes	—
289	C₂²×#99	C₂⁴	1	16	yes	—
290	#2311	C₂×D₄	1	16	yes	complemented
291	#2308	C₂×D₄	1	32	yes	complemented
292	#2308	C₂⁴	1	16	yes	—
293	#2308	C₂⁴	1	32	yes	—
294	#2308	C₂⁴	1	16	yes	—
295	#2297	C₂×D₄	1	16	yes	complemented
296	C₂×#386	C₂×D₄	1	32	yes	complemented
297	C₂×#381	C₂⁴	1	4	yes	—
298	C₂×#381	C₂⁴	1	8	yes	—
299	C₂×#379	C₂⁴	1	8	yes	—
300	C₂×#379	C₂⁴	1	16	yes	—
301	C₂×#379	C₂⁴	1	4	yes	—
302	C₂×#379	C₂⁴	1	8	yes	—
303	C₂×#342	C₂⁴	1	32	yes	—
304	C₂×#342	C₂⁴	1	32	yes	—
305	C₂×#342	C₂⁴	1	32	yes	—
306	C₂⁶	C₂²×D₄	1	4	yes	—
307	C₂⁶	C₂²×D₄	1	4	yes	—
308	C₂⁶	C₂²×D₄	1	4	yes	—
309	C₂⁶	C₂²×D₄	1	4	yes	—
310	C₂⁶	C₂²×D₄	1	16	yes	—
311	C₂⁶	C₂²×D₄	1	8	yes	—
312	C₂⁶	C₂²×D₄	1	4	yes	—
313	C₂⁶	C₂²×D₄	1	8	yes	—
314	C₂⁶	C₂²×D₄	1	4	yes	complemented
315	C₂⁶	C₂⁵	1	2	yes	—
316	C₂⁶	C₂⁵	1	1	yes	characteristic
317	C₂⁶	C₂⁵	1	2	yes	—
318	C₂×H(5,𝔽₂)	#120	1	64	yes	—
319	C₂×H(5,𝔽₂)	#121	1	64	yes	—
320	C₂×H(5,𝔽₂)	#121	1	64	yes	—
321	C₂×H(5,𝔽₂)	#127	1	64	yes	—
322	C₂×H(5,𝔽₂)	C₂²×D₄	1	64	yes	—
323	C₂²×#41	#120	1	32	yes	—
324	C₂²×#41	#120	1	32	yes	—
325	C₂²×#41	#120	1	32	yes	—
326	C₂²×#41	#120	1	64	yes	complemented
327	C₂²×#41	#121	1	32	yes	—
328	C₂²×#41	C₂²×D₄	1	16	yes	—
329	C₂²×#41	C₂²×D₄	1	8	yes	—
330	C₂²×#41	C₂²×D₄	1	8	yes	—
331	C₂²×#41	C₂²×D₄	1	8	yes	—
332	C₂²×#41	C₂²×D₄	1	8	yes	—
333	C₂²×#41	C₂²×D₄	1	16	yes	—
334	C₂²×#41	C₂²×D₄	1	16	yes	—
335	C₂²×#41	C₂²×D₄	1	8	yes	—
336	C₂²×#41	C₂×#41	1	8	yes	—
337	C₂³×Q₈	C₂²×D₄	1	4	yes	—
338	C₂³×Q₈	C₂²×D₄	1	2	yes	—
339	C₂³×Q₈	C₂²×D₄	1	2	yes	—
340	C₂³×Q₈	C₂²×D₄	1	4	yes	—
341	C₂³×Q₈	C₂²×D₄	1	2	yes	complemented
342	C₂³×D₄	#120	1	32	yes	—
343	C₂³×D₄	#120	1	32	yes	—
344	C₂³×D₄	#120	1	32	yes	—
345	C₂³×D₄	#120	1	32	yes	—
346	C₂³×D₄	#120	1	32	yes	—
347	C₂³×D₄	#120	1	64	yes	complemented
348	C₂³×D₄	#121	1	32	yes	—
349	C₂³×D₄	C₂²×D₄	1	16	yes	—
350	C₂³×D₄	C₂²×D₄	1	16	yes	—
351	C₂³×D₄	C₂²×D₄	1	16	yes	—
352	C₂³×D₄	C₂²×D₄	1	16	yes	—
353	C₂³×D₄	C₂²×D₄	1	32	yes	—
354	C₂³×D₄	C₂²×D₄	1	32	yes	—
355	C₂³×D₄	C₂²×D₄	1	32	yes	—
356	C₂³×D₄	C₂²×D₄	1	16	yes	—
357	C₂³×D₄	C₂²×D₄	1	4	yes	—
358	C₂³×D₄	C₂²×D₄	1	4	yes	—
359	C₂³×D₄	C₂²×D₄	1	4	yes	—
360	C₂³×D₄	C₂²×D₄	1	8	yes	—
361	C₂³×D₄	C₂²×D₄	1	8	yes	—
362	C₂³×D₄	C₂²×D₄	1	4	yes	—
363	C₂³×D₄	C₂²×D₄	1	2	yes	—
364	C₂³×D₄	C₂²×D₄	1	8	yes	—
365	C₂³×D₄	C₂²×D₄	1	4	yes	—
366	C₂³×D₄	C₂²×D₄	1	4	yes	—
367	C₂³×D₄	C₂²×D₄	1	2	yes	—
368	C₂³×D₄	C₂²×D₄	1	4	yes	—
369	C₂³×D₄	C₂²×D₄	1	8	yes	—
370	C₂³×D₄	C₂²×D₄	1	16	yes	—
371	C₂³×D₄	C₂²×D₄	1	8	yes	—
372	C₂³×D₄	C₂²×D₄	1	8	yes	—
373	C₂³×D₄	C₂²×D₄	1	4	yes	—
374	C₂³×D₄	C₂²×D₄	1	16	yes	—
375	C₂³×D₄	C₂²×D₄	1	4	yes	—
376	C₂³×D₄	C₂²×D₄	1	8	yes	—
377	C₂³×D₄	C₂²×D₄	1	4	yes	—
378	C₂³×D₄	C₂²×D₄	1	8	yes	—
379	C₂³×D₄	C₂²×D₄	1	4	yes	—
380	C₂³×D₄	C₂²×D₄	1	2	yes	complemented
381	C₂³×D₄	C₂²×D₄	1	8	yes	complemented
382	C₂³×D₄	C₂×#41	1	16	yes	—
383	C₂³×D₄	C₂×#41	1	4	yes	—
384	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
385	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
386	C₂³×D₄	C₂⁵	1	4	yes	—
387	C₂³×D₄	C₂⁵	1	4	yes	—
388	C₂³×D₄	C₂⁵	1	8	yes	—
389	C₂³×D₄	C₂⁵	1	4	yes	—
390	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
391	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
392	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
393	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
394	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
395	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
396	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
397	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
398	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
399	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
400	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
401	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
402	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
403	C₂⁴×C₄	C₂²×D₄	1	4	yes	complemented
404	C₂⁴×C₄	C₂²×D₄	1	4	yes	complemented
405	C₂⁴×C₄	C₂²×D₄	1	8	yes	complemented
406	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
407	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
408	C₂×#123	C₂²×D₄	1	64	yes	—
409	C₂×#123	C₂²×D₄	1	32	yes	—
410	C₂×#123	C₂²×D₄	1	32	yes	complemented
411	C₂×#120	C₂²×D₄	1	32	yes	—
412	C₂×#120	C₂²×D₄	1	64	yes	—
413	C₂×#120	C₂²×D₄	1	64	yes	—
414	C₂×#120	C₂²×D₄	1	32	yes	complemented
415	#518	#120	1	128	yes	complemented
416	#518	C₂²×D₄	1	64	yes	—
417	C₂×#117	C₂²×D₄	1	16	yes	—
418	C₂×#117	C₂²×D₄	1	16	yes	—
419	C₂×#117	C₂²×D₄	1	16	yes	—
420	C₂×#117	C₂²×D₄	1	8	yes	complemented
421	C₂×#117	C₂²×D₄	1	16	yes	complemented
422	C₂×#117	C₂²×D₄	1	8	yes	complemented
423	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	complemented
424	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
425	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
426	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
427	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	complemented
428	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	complemented
429	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	complemented
430	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	complemented
431	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
432	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
433	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
434	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
435	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
436	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
437	C₂²×C₄²	C₂²×D₄	1	4	yes	complemented
438	C₂×#99	C₂²×D₄	1	64	yes	complemented
439	#386	C₂²×D₄	1	64	yes	complemented
440	C₂⁵	C₂×#120	1	16	yes	—
441	C₂⁵	C₂×#120	1	16	yes	—
442	C₂⁵	C₂×#120	1	16	yes	—
443	C₂⁵	C₂×#120	1	16	yes	—
444	C₂⁵	C₂×#120	1	16	yes	—
445	C₂⁵	C₂×#120	1	32	yes	complemented
446	C₂⁵	C₂×#121	1	16	yes	—
447	C₂⁵	C₂³×D₄	1	4	yes	—
448	C₂⁵	C₂³×D₄	1	4	yes	—
449	C₂⁵	C₂³×D₄	1	8	yes	—
450	C₂⁵	C₂³×D₄	1	8	yes	—
451	C₂⁵	C₂³×D₄	1	1	yes	characteristic
452	C₂⁵	C₂³×D₄	1	1	yes	characteristic
453	C₂⁵	C₂³×D₄	1	4	yes	—
454	C₂⁵	C₂³×D₄	1	4	yes	—
455	C₂⁵	C₂³×D₄	1	4	yes	—
456	C₂⁵	C₂³×D₄	1	4	yes	—
457	C₂⁵	C₂³×D₄	1	4	yes	—
458	C₂⁵	C₂³×D₄	1	8	yes	—
459	C₂⁵	C₂³×D₄	1	8	yes	—
460	C₂⁵	C₂³×D₄	1	4	yes	—
461	C₂⁵	C₂³×D₄	1	4	yes	—
462	C₂⁵	C₂³×D₄	1	4	yes	—
463	C₂⁵	C₂³×D₄	1	4	yes	—
464	C₂⁵	C₂²×#41	1	4	yes	—
465	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
466	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
467	C₂⁵	C₂⁶	1	1	yes	characteristic
468	C₂×#41	#392	1	256	yes	—
469	C₂×#41	C₂×#120	1	32	yes	—
470	C₂×#41	C₂×#121	1	32	yes	—
471	C₂×#41	C₂×#121	1	32	yes	—
472	C₂×#41	C₂×#127	1	32	yes	—
473	C₂²×Q₈	C₂×#120	1	8	yes	—
474	C₂²×Q₈	C₂×#120	1	8	yes	—
475	C₂²×Q₈	C₂×#120	1	8	yes	—
476	C₂²×Q₈	C₂×#120	1	16	yes	complemented
477	C₂²×Q₈	C₂×#121	1	8	yes	—
478	C₂²×D₄	#392	1	256	yes	—
479	C₂²×D₄	C₂×#120	1	64	yes	—
480	C₂²×D₄	C₂×#120	1	16	yes	—
481	C₂²×D₄	C₂×#120	1	16	yes	—
482	C₂²×D₄	C₂×#120	1	16	yes	—
483	C₂²×D₄	C₂×#120	1	32	yes	—
484	C₂²×D₄	C₂×#120	1	32	yes	—
485	C₂²×D₄	C₂×#120	1	16	yes	—
486	C₂²×D₄	C₂×#120	1	16	yes	—
487	C₂²×D₄	C₂×#120	1	8	yes	—
488	C₂²×D₄	C₂×#120	1	8	yes	—
489	C₂²×D₄	C₂×#120	1	32	yes	—
490	C₂²×D₄	C₂×#120	1	32	yes	—
491	C₂²×D₄	C₂×#120	1	16	yes	—
492	C₂²×D₄	C₂×#120	1	32	yes	—
493	C₂²×D₄	C₂×#120	1	8	yes	—
494	C₂²×D₄	C₂×#120	1	32	yes	—
495	C₂²×D₄	C₂×#120	1	16	yes	complemented
496	C₂²×D₄	C₂×#120	1	64	yes	complemented
497	C₂²×D₄	C₂×#121	1	64	yes	—
498	C₂²×D₄	C₂×#121	1	64	yes	—
499	C₂²×D₄	C₂×#121	1	16	yes	—
500	C₂²×D₄	C₂×#121	1	16	yes	—
501	C₂²×D₄	C₂×#121	1	16	yes	—
502	C₂²×D₄	C₂×#121	1	8	yes	—
503	C₂²×D₄	C₂×#121	1	32	yes	—
504	C₂²×D₄	C₂×#127	1	64	yes	—
505	C₂²×D₄	C₂×#127	1	16	yes	—
506	C₂²×D₄	#534	1	16	yes	—
507	C₂²×D₄	#534	1	16	yes	—
508	C₂²×D₄	#534	1	32	yes	—
509	C₂²×D₄	#535	1	32	yes	—
510	C₂²×D₄	D₄²	1	32	yes	—
511	C₂²×D₄	D₄²	1	32	yes	—
512	C₂²×D₄	D₄²	1	32	yes	—
513	C₂²×D₄	D₄²	1	32	yes	—
514	C₂²×D₄	D₄²	1	32	yes	—
515	C₂²×D₄	D₄²	1	32	yes	—
516	C₂²×D₄	#546	1	32	yes	—
517	C₂²×D₄	#546	1	32	yes	—
518	C₂²×D₄	C₂³×D₄	1	8	yes	—
519	C₂²×D₄	C₂³×D₄	1	8	yes	—
520	C₂²×D₄	C₂³×D₄	1	8	yes	—
521	C₂²×D₄	C₂³×D₄	1	8	yes	—
522	C₂²×D₄	C₂³×D₄	1	16	yes	—
523	C₂²×D₄	C₂³×D₄	1	16	yes	—
524	C₂²×D₄	C₂³×D₄	1	16	yes	—
525	C₂²×D₄	C₂³×D₄	1	8	yes	—
526	C₂²×D₄	C₂²×#41	1	8	yes	—
527	C₂³×C₄	C₂×#120	1	16	yes	—
528	C₂³×C₄	C₂×#120	1	16	yes	—
529	C₂³×C₄	C₂×#120	1	16	yes	—
530	C₂³×C₄	C₂×#120	1	16	yes	—
531	C₂³×C₄	C₂×#120	1	8	yes	—
532	C₂³×C₄	C₂×#120	1	8	yes	—
533	C₂³×C₄	C₂×#120	1	16	yes	—
534	C₂³×C₄	C₂×#120	1	16	yes	—
535	C₂³×C₄	C₂×#120	1	32	yes	complemented
536	C₂³×C₄	C₂×#120	1	32	yes	complemented
537	C₂³×C₄	C₂×#121	1	16	yes	—
538	C₂³×C₄	C₂×#121	1	16	yes	—
539	C₂³×C₄	C₂³×D₄	1	2	yes	—
540	C₂³×C₄	C₂³×D₄	1	2	yes	—
541	C₂³×C₄	C₂³×D₄	1	2	yes	—
542	C₂³×C₄	C₂³×D₄	1	4	yes	—
543	C₂³×C₄	C₂³×D₄	1	4	yes	—
544	C₂³×C₄	C₂³×D₄	1	2	yes	—
545	C₂³×C₄	C₂³×D₄	1	4	yes	—
546	C₂³×C₄	C₂³×D₄	1	2	yes	—
547	C₂³×C₄	C₂³×D₄	1	2	yes	—
548	C₂³×C₄	C₂³×D₄	1	8	yes	—
549	C₂³×C₄	C₂³×D₄	1	4	yes	—
550	C₂³×C₄	C₂³×D₄	1	4	yes	—
551	C₂³×C₄	C₂³×D₄	1	2	yes	—
552	C₂³×C₄	C₂³×D₄	1	8	yes	—
553	C₂³×C₄	C₂³×D₄	1	4	yes	—
554	C₂³×C₄	C₂²×#41	1	2	yes	—
555	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
556	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
557	#117	C₂×#120	1	64	yes	complemented
558	C₂×C₂²⋊C₄	C₂×#120	1	128	yes	complemented
559	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	—
560	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	—
561	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	—
562	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
563	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
564	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	—
565	C₂⁴	C₂×#392	1	64	yes	—
566	C₂⁴	C₂²×#120	1	8	yes	—
567	C₂⁴	C₂²×#120	1	16	yes	—
568	C₂⁴	C₂²×#120	1	8	yes	—
569	C₂⁴	C₂²×#120	1	16	yes	—
570	C₂⁴	C₂²×#120	1	8	yes	—
571	C₂⁴	C₂²×#120	1	8	yes	—
572	C₂⁴	C₂²×#120	1	8	yes	—
573	C₂⁴	C₂²×#120	1	2	yes	—
574	C₂⁴	C₂²×#120	1	2	yes	—
575	C₂⁴	C₂²×#120	1	8	yes	—
576	C₂⁴	C₂²×#120	1	16	yes	—
577	C₂⁴	C₂²×#120	1	8	yes	—
578	C₂⁴	C₂²×#120	1	8	yes	—
579	C₂⁴	C₂²×#120	1	8	yes	—
580	C₂⁴	C₂²×#121	1	8	yes	—
581	C₂⁴	C₂²×#121	1	8	yes	—
582	C₂⁴	C₂²×#121	1	8	yes	—
583	C₂⁴	C₂²×#121	1	8	yes	—
584	C₂⁴	C₂²×#127	1	8	yes	—
585	C₂⁴	C₂×#534	1	8	yes	—
586	C₂⁴	C₂×#534	1	16	yes	—
587	C₂⁴	C₂×#534	1	8	yes	—
588	C₂⁴	C₂×#535	1	16	yes	—
589	C₂⁴	C₂×D₄²	1	16	yes	—
590	C₂⁴	C₂×D₄²	1	16	yes	—
591	C₂⁴	C₂×D₄²	1	16	yes	—
592	C₂⁴	C₂×D₄²	1	16	yes	—
593	C₂⁴	C₂×D₄²	1	16	yes	—
594	C₂⁴	C₂×D₄²	1	16	yes	—
595	C₂⁴	C₂×#546	1	16	yes	—
596	C₂⁴	C₂×#546	1	16	yes	—
597	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
598	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
599	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
600	C₂⁴	C₂⁴×D₄	1	2	yes	—
601	C₂⁴	C₂⁴×D₄	1	2	yes	—
602	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
603	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
604	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
605	C₂⁴	C₂³×#41	1	1	yes	characteristic
606	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
607	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
608	C₂×Q₈	C₂×#392	1	32	yes	—
609	C₂×D₄	C₂×#392	1	64	yes	—
610	C₂×D₄	C₂×#392	1	128	yes	—
611	C₂×D₄	C₂×#392	1	32	yes	—
612	C₂×D₄	#2403	1	64	yes	—
613	C₂×D₄	#2403	1	128	yes	—
614	C₂×D₄	#2403	1	64	yes	—
615	C₂×D₄	#2408	1	128	yes	—
616	C₂×D₄	#2410	1	64	yes	—
617	C₂×D₄	#2410	1	64	yes	—
618	C₂×D₄	#2410	1	128	yes	—
619	C₂×D₄	#2433	1	128	yes	—
620	C₂×D₄	#2613	1	64	yes	—
621	C₂×D₄	#2846	1	64	yes	—
622	C₂×D₄	C₂²×#120	1	16	yes	—
623	C₂×D₄	C₂²×#121	1	16	yes	—
624	C₂×D₄	C₂²×#121	1	16	yes	—
625	C₂×D₄	C₂²×#127	1	16	yes	—
626	C₂²×C₄	C₂×#392	1	64	yes	—
627	C₂²×C₄	C₂×#392	1	64	yes	—
628	C₂²×C₄	C₂²×#120	1	4	yes	—
629	C₂²×C₄	C₂²×#120	1	4	yes	—
630	C₂²×C₄	C₂²×#120	1	8	yes	—
631	C₂²×C₄	C₂²×#120	1	8	yes	—
632	C₂²×C₄	C₂²×#120	1	4	yes	—
633	C₂²×C₄	C₂²×#120	1	4	yes	—
634	C₂²×C₄	C₂²×#120	1	4	yes	—
635	C₂²×C₄	C₂²×#120	1	8	yes	—
636	C₂²×C₄	C₂²×#120	1	8	yes	—
637	C₂²×C₄	C₂²×#120	1	8	yes	—
638	C₂²×C₄	C₂²×#120	1	4	yes	—
639	C₂²×C₄	C₂²×#120	1	16	yes	—
640	C₂²×C₄	C₂²×#121	1	4	yes	—
641	C₂²×C₄	C₂²×#121	1	4	yes	—
642	C₂²×C₄	C₂²×#121	1	4	yes	—
643	C₂²×C₄	C₂²×#121	1	8	yes	—
644	C₂²×C₄	C₂²×#127	1	4	yes	—
645	C₂²×C₄	C₂×#534	1	4	yes	—
646	C₂²×C₄	C₂×#534	1	8	yes	—
647	C₂²×C₄	C₂×#534	1	4	yes	—
648	C₂²×C₄	C₂×#535	1	8	yes	—
649	C₂²×C₄	C₂×D₄²	1	8	yes	—
650	C₂²×C₄	C₂×D₄²	1	8	yes	—
651	C₂²×C₄	C₂×D₄²	1	8	yes	—
652	C₂²×C₄	C₂×D₄²	1	8	yes	—
653	C₂²×C₄	C₂×D₄²	1	8	yes	—
654	C₂²×C₄	C₂×D₄²	1	8	yes	—
655	C₂²×C₄	C₂×#546	1	8	yes	—
656	C₂²×C₄	C₂×#546	1	8	yes	—
657	C₂²⋊C₄	C₂²×#120	1	32	yes	—
658	C₂³	C₂²×#392	1	16	yes	—
659	C₂³	C₂²×#392	1	16	yes	—
660	C₂³	C₂×#2613	1	16	yes	—
661	C₂³	C₂×#2403	1	32	yes	—
662	C₂³	C₂×#2403	1	16	yes	—
663	C₂³	C₂×#2403	1	16	yes	—
664	C₂³	C₂×#2410	1	16	yes	—
665	C₂³	C₂×#2410	1	32	yes	—
666	C₂³	C₂×#2410	1	16	yes	—
667	C₂³	C₂×#2408	1	32	yes	—
668	C₂³	C₂×#2433	1	32	yes	—
669	C₂³	C₂×#2846	1	16	yes	—
670	C₂³	C₂³×#120	1	1	yes	characteristic
671	C₂³	C₂³×#120	1	1	yes	characteristic
672	C₂³	C₂³×#120	1	2	yes	—
673	C₂³	C₂³×#120	1	1	yes	characteristic
674	C₂³	C₂³×#120	1	1	yes	characteristic
675	C₂³	C₂³×#120	1	2	yes	—
676	C₂³	C₂³×#120	1	1	yes	characteristic
677	C₂³	C₂³×#121	1	1	yes	characteristic
678	C₂³	C₂³×#121	1	1	yes	characteristic
679	C₂³	C₂³×#121	1	1	yes	characteristic
680	C₂³	C₂³×#127	1	1	yes	characteristic
681	C₂³	C₂²×#534	1	1	yes	characteristic
682	C₂³	C₂²×#534	1	2	yes	—
683	C₂³	C₂²×#534	1	1	yes	characteristic
684	C₂³	C₂²×#535	1	2	yes	—
685	C₂³	C₂²×D₄²	1	2	yes	—
686	C₂³	C₂²×D₄²	1	2	yes	—
687	C₂³	C₂²×D₄²	1	2	yes	—
688	C₂³	C₂²×D₄²	1	2	yes	—
689	C₂³	C₂²×D₄²	1	2	yes	—
690	C₂³	C₂²×D₄²	1	2	yes	—
691	C₂³	C₂²×#546	1	2	yes	—
692	C₂³	C₂²×#546	1	2	yes	—
693	D₄	#14715	1	256	yes	—
694	C₂×C₄	C₂²×#392	1	8	yes	—
695	C₂×C₄	C₂²×#392	1	16	yes	—
696	C₂×C₄	C₂×#2613	1	8	yes	—
697	C₂×C₄	C₂×#2403	1	8	yes	—
698	C₂×C₄	C₂×#2403	1	16	yes	—
699	C₂×C₄	C₂×#2403	1	8	yes	—
700	C₂×C₄	C₂×#2410	1	8	yes	—
701	C₂×C₄	C₂×#2410	1	8	yes	—
702	C₂×C₄	C₂×#2410	1	16	yes	—
703	C₂×C₄	C₂×#2408	1	16	yes	—
704	C₂×C₄	C₂×#2433	1	16	yes	—
705	C₂×C₄	C₂×#2846	1	8	yes	—
706	C₂²	C₂×#14715	1	32	yes	—
707	C₂²	C₂³×#392	1	1	yes	characteristic
708	C₂²	C₂²×#2613	1	1	yes	characteristic
709	C₂²	C₂²×#2403	1	2	yes	—
710	C₂²	C₂²×#2403	1	1	yes	characteristic
711	C₂²	C₂²×#2403	1	1	yes	characteristic
712	C₂²	C₂²×#2410	1	2	yes	—
713	C₂²	C₂²×#2410	1	1	yes	characteristic
714	C₂²	C₂²×#2410	1	1	yes	characteristic
715	C₂²	C₂²×#2408	1	2	yes	—
716	C₂²	C₂²×#2433	1	2	yes	—
717	C₂²	C₂²×#2846	1	1	yes	characteristic
718	C₄	C₂×#14715	1	16	yes	—
719	C₂	#72240522	1	2	yes	—
720	C₂	C₂²×#14715	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#2403
commutator, Frattini, cosocle	C₂⁵	C₂⁶
LCS	G ▷ C₂⁵ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴×D₄ ◁ G
LECS	G ▷ C₂⁵ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72251160	C₂	semidirect
2. #72251158	C₂	semidirect
3. #72251154	C₂	semidirect
4. C₂×#6371551	C₂	semidirect
5. #72251147	C₂	semidirect
6. #72251136	C₂	semidirect
7. #72251134	C₂	semidirect
8. #72249537	C₂	semidirect
9. C₂×#10574873	C₂	semidirect
10. C₂×#6370693	C₂	semidirect
11. #72238117	C₂	semidirect
12. C₂×#394064	C₂	semidirect
13. #72235904	C₂	semidirect
14. C₂×#6431795	C₂	semidirect
15. C₂×#10586066	C₂	semidirect
18. C₂×#62852	C₂²	semidirect
21. C₂×#62842	C₂²	semidirect
22. C₂×#62842	C₂²	semidirect
23. C₂×#62842	C₂²	semidirect
24. C₂×#62811	C₂²	semidirect
26. C₂²×#3484	C₂²	semidirect
27. C₂²×#3484	C₂²	semidirect
29. C₂×#60398	C₂²	semidirect
30. C₂²×#3026	C₂²	semidirect
33. C₂²×#2883	C₂²	semidirect
34. C₂²×#2883	C₂²	semidirect
35. C₂²×#2883	C₂²	semidirect
36. C₂²×#2883	C₂²	semidirect
37. #7630502	C₂²	semidirect
38. #7630442	C₂²	semidirect
39. #7628649	C₂²	semidirect
40. C₂×#34980	C₂²	semidirect
42. #7625680	C₂²	semidirect
43. #7625680	C₂²	semidirect
44. C₂×#34171	C₂²	semidirect
45. C₂×#34171	C₂²	semidirect
46. #6431794	C₂²	semidirect
47. C₂×#23445	C₂²	semidirect
48. C₂×#23444	C₂²	semidirect
49. C₂×#23444	C₂²	semidirect
50. C₂×#23443	C₂²	semidirect
51. C₂²×#2021	C₂²	semidirect
52. C₂×#21014	C₂²	semidirect
53. C₂²×#1913	C₂²	semidirect
54. #6370734	C₂²	semidirect
55. C₂×#20609	C₂²	semidirect
56. C₂×#20586	C₂²	semidirect
57. C₂×#20585	C₂²	semidirect
58. C₂×#20584	C₂²	semidirect
59. C₂²×#1781	C₂²	semidirect
60. C₂×#20354	C₂²	semidirect
61. C₂×#20354	C₂²	semidirect
62. C₂×#20354	C₂²	semidirect
63. #394065	C₂²	semidirect
64. #394064	C₂²	semidirect
65. #394064	C₂²	semidirect
66. #357531	C₂²	semidirect
67. #357530	C₂²	semidirect
68. #357529	C₂²	semidirect
69. C₂×#10991	C₂²	semidirect
70. #357443	C₂²	semidirect
71. C₂×#10972	C₂²	semidirect
72. #353448	C₂²	semidirect
73. C₂×#10754	C₂²	semidirect
74. C₂×H(7,𝔽₂)	D₄	semidirect
76. C₂³×H(5,𝔽₂)	D₄	semidirect
77. C₂³×H(5,𝔽₂)	D₄	semidirect
85. C₂⁴×#41	D₄	semidirect
87. C₂⁵×D₄	D₄	semidirect
90. C₂×#3485	D₄	semidirect
91. C₂×#3485	D₄	semidirect
93. C₂×#3484	D₄	semidirect
94. C₂×#3484	D₄	semidirect
95. C₂×#3484	D₄	semidirect
100. C₂×#3449	C₂³	semidirect
101. C₂×#3449	C₂³	semidirect
103. C₂²×#535	C₂³	semidirect
107. C₂²×#534	C₂³	semidirect
108. C₂²×#534	C₂³	semidirect
109. C₂²×#534	C₂³	semidirect
111. C₂²×#525	C₂³	semidirect
113. C₂³×#120	C₂³	semidirect
114. #62652	D₄	semidirect
123. C₂×#3026	C₂³	semidirect
124. C₂×#2883	D₄	semidirect
127. C₂²×#410	C₂³	semidirect
128. C₂²×#410	C₂³	semidirect
129. C₂²×#410	C₂³	semidirect
130. C₂²×#410	C₂³	semidirect
133. C₂³×#99	C₂³	semidirect
134. C₂³×#99	C₂³	semidirect
135. C₂³×#99	C₂³	semidirect
136. C₂³×#99	C₂³	semidirect
137. #35088	C₂³	semidirect
138. #34980	C₂³	semidirect
139. #34980	C₂³	semidirect
140. #34256	D₄	semidirect
142. #34044	C₂³	semidirect
143. #34044	C₂³	semidirect
144. C₂×#2309	C₂³	semidirect
145. C₂×#2309	C₂³	semidirect
147. C₂×#2308	C₂³	semidirect
148. C₂×#2308	C₂³	semidirect
149. C₂×#2308	C₂³	semidirect
150. C₂×#2308	C₂³	semidirect
151. C₂×#2280	C₂³	semidirect
152. C₂×#2280	C₂³	semidirect
153. C₂²×#379	C₂³	semidirect
154. C₂²×#379	C₂³	semidirect
155. #23444	C₂³	semidirect
156. C₂×#2022	C₂³	semidirect
157. C₂×#2021	C₂³	semidirect
158. C₂×#2021	C₂³	semidirect
159. C₂×#1913	C₂³	semidirect
160. #20609	C₂³	semidirect
161. C₂×#1782	C₂³	semidirect
162. C₂×#1781	C₂³	semidirect
163. C₂×#1781	C₂³	semidirect
164. C₂×#1740	C₂³	semidirect
165. C₂×#1740	C₂³	semidirect
166. C₂×#1740	C₂³	semidirect
167. C₂²×#342	C₂³	semidirect
168. C₂²×#342	C₂³	semidirect
169. C₂²×#342	C₂³	semidirect
170. #10992	C₂³	semidirect
171. #10991	C₂³	semidirect
172. #10991	C₂³	semidirect
173. #10972	C₂³	semidirect
174. #10754	C₂³	semidirect
175. C₂⁷	C₂×D₄	semidirect
177. C₂×#585	C₂×D₄	semidirect
186. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
192. C₂³×#41	C₂×D₄	semidirect
193. C₂³×#41	C₂×D₄	semidirect
194. C₂³×#41	C₂×D₄	semidirect
195. C₂³×#41	C₂×D₄	semidirect
196. C₂³×#41	C₂×D₄	semidirect
197. C₂³×#41	C₂×D₄	semidirect
198. C₂³×#41	C₂×D₄	semidirect
199. C₂³×#41	C₂×D₄	semidirect
205. C₂⁴×Q₈	C₂×D₄	semidirect
212. C₂⁴×D₄	C₂×D₄	semidirect
213. C₂⁴×D₄	C₂×D₄	semidirect
214. C₂⁴×D₄	C₂×D₄	semidirect
215. C₂⁴×D₄	C₂×D₄	semidirect
216. C₂⁴×D₄	C₂×D₄	semidirect
217. C₂⁴×D₄	C₂×D₄	semidirect
218. C₂⁴×D₄	C₂×D₄	semidirect
219. C₂⁴×D₄	C₂×D₄	semidirect
220. C₂⁴×D₄	C₂×D₄	semidirect
221. C₂⁴×D₄	C₂×D₄	semidirect
231. C₂⁵×C₄	C₂×D₄	semidirect
232. C₂⁵×C₄	C₂×D₄	semidirect
234. C₂×#536	C₂×D₄	semidirect
235. C₂×#536	C₂×D₄	semidirect
236. C₂×#535	C₂×D₄	semidirect
237. C₂×#535	C₂×D₄	semidirect
238. C₂×#535	C₂×D₄	semidirect
239. C₂×#534	C₂×D₄	semidirect
240. C₂×#534	C₂×D₄	semidirect
241. C₂×#534	C₂×D₄	semidirect
246. C₂×#525	C₂×D₄	semidirect
247. C₂×#525	C₂×D₄	semidirect
248. C₂×#525	C₂×D₄	semidirect
249. C₂²×#123	C₂×D₄	semidirect
250. C₂²×#123	C₂×D₄	semidirect
253. C₂²×#120	C₂×D₄	semidirect
254. C₂²×#120	C₂×D₄	semidirect
255. C₂²×#120	C₂×D₄	semidirect
260. #3428	C₂×D₄	semidirect
264. C₂×#518	C₂×D₄	semidirect
265. C₂×#518	C₂×D₄	semidirect
266. C₂×#518	C₂×D₄	semidirect
267. C₂×#518	C₂×D₄	semidirect
269. C₂²×C₄×D₄	C₂×D₄	semidirect
282. C₂×#410	C₂×D₄	semidirect
283. C₂²×#99	C₂×D₄	semidirect
290. #2311	C₂×D₄	semidirect
291. #2308	C₂×D₄	semidirect
295. #2297	C₂×D₄	semidirect
296. C₂×#386	C₂×D₄	semidirect
314. C₂⁶	C₂²×D₄	semidirect
326. C₂²×#41	#120	semidirect
341. C₂³×Q₈	C₂²×D₄	semidirect
347. C₂³×D₄	#120	semidirect
380. C₂³×D₄	C₂²×D₄	semidirect
381. C₂³×D₄	C₂²×D₄	semidirect
403. C₂⁴×C₄	C₂²×D₄	semidirect
404. C₂⁴×C₄	C₂²×D₄	semidirect
405. C₂⁴×C₄	C₂²×D₄	semidirect
410. C₂×#123	C₂²×D₄	semidirect
414. C₂×#120	C₂²×D₄	semidirect
415. #518	#120	semidirect
420. C₂×#117	C₂²×D₄	semidirect
421. C₂×#117	C₂²×D₄	semidirect
422. C₂×#117	C₂²×D₄	semidirect
423. C₂²×C₄⋊C₄	C₂²×D₄	semidirect
427. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
428. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
429. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
430. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
437. C₂²×C₄²	C₂²×D₄	semidirect
438. C₂×#99	C₂²×D₄	semidirect
439. #386	C₂²×D₄	semidirect
445. C₂⁵	C₂×#120	semidirect
476. C₂²×Q₈	C₂×#120	semidirect
495. C₂²×D₄	C₂×#120	semidirect
496. C₂²×D₄	C₂×#120	semidirect
535. C₂³×C₄	C₂×#120	semidirect
536. C₂³×C₄	C₂×#120	semidirect
557. #117	C₂×#120	semidirect
558. C₂×C₂²⋊C₄	C₂×#120	semidirect

Maximal subgroups

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

subgroup	index
#72251160	2
#72251158	2
#72251154	2
C₂×#6371551	2
#72251147	2
#72251136	2
#72251134	2
#72249537	2
C₂×#10574873	2
C₂×#6370693	2
#72238117	2
C₂×#394064	2
#72235904	2
C₂×#6431795	2
C₂×#10586066	2