Subgroups — C₂×#72264992 #72296466

Order 2048.

At least 6860 conjugacy classes of subgroups; only the 10104 normal subgroups are shown.

The subgroup lattice has 732 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#155632	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#157600	C₂	1	2	yes	maximal, complemented
3	C₂×#156826	C₂	1	4	yes	maximal, complemented
4	C₂×#155065	C₂	1	4	yes	maximal, complemented
5	C₂×#155941	C₂	1	2	yes	maximal, complemented
6	C₂²×#15257	C₂	1	4	yes	maximal, complemented
7	#72264992	C₂	1	32	yes	maximal, direct product factor
8	C₂²×#14716	C₂	1	2	yes	maximal, complemented
9	C₂×#154094	C₂	1	2	yes	maximal, complemented
10	C₂×#156684	C₂	1	4	yes	maximal, complemented
11	C₂×#156684	C₂	1	2	yes	maximal, complemented
12	C₂²×#13867	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×#2403	C₂	1	2	yes	maximal, complemented
14	C₂³×#2403	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂⁶×D₄	C₂²	1	2	yes	—
16	C₂⁶×D₄	C₂²	1	1	yes	characteristic
17	C₂⁴×#121	C₂²	1	2	yes	complemented
18	C₂⁴×#120	C₂²	1	2	yes	complemented
19	C₂⁴×#120	C₂²	1	4	yes	complemented
20	C₂⁴×#120	C₂²	1	4	yes	complemented
21	C₂⁴×#120	C₂²	1	2	yes	complemented
22	C₂⁵×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
23	C₂²×#2403	C₂²	1	16	yes	complemented
24	C₂²×#2403	C₂²	1	32	yes	complemented
25	C₂³×#392	C₂²	1	2	yes	—
26	C₂³×#392	C₂²	1	4	yes	—
27	C₂³×#392	C₂²	1	2	yes	—
28	C₂³×#392	C₂²	1	4	yes	—
29	C₂³×#392	C₂²	1	2	yes	complemented
30	C₂³×#392	C₂²	1	2	yes	complemented
31	C₂³×#392	C₂²	1	2	yes	complemented
32	C₂³×#386	C₂²	1	4	yes	complemented
33	C₂³×#386	C₂²	1	2	yes	complemented
34	C₂³×#386	C₂²	1	4	yes	complemented
35	C₂³×#386	C₂²	1	2	yes	complemented
36	C₂³×#386	C₂²	1	4	yes	complemented
37	C₂³×#386	C₂²	1	4	yes	complemented
38	C₂³×#379	C₂²	1	2	yes	—
39	C₂³×#379	C₂²	1	1	yes	characteristic
40	C₂³×#379	C₂²	1	1	yes	characteristic
41	C₂³×#379	C₂²	1	4	yes	complemented
42	C₂³×#379	C₂²	1	1	yes	characteristic, complemented
43	C₂×#15257	C₂²	1	64	yes	complemented
44	C₂×#14716	C₂²	1	32	yes	complemented
45	C₂×#13867	C₂²	1	16	yes	complemented
46	C₂²×#1440	C₂²	1	4	yes	complemented
47	C₂²×#1439	C₂²	1	2	yes	complemented
48	C₂²×#1439	C₂²	1	2	yes	complemented
49	C₂²×#1439	C₂²	1	4	yes	complemented
50	C₂²×#1439	C₂²	1	4	yes	complemented
51	C₂²×#1438	C₂²	1	4	yes	complemented
52	C₂²×#1438	C₂²	1	4	yes	complemented
53	C₂²×#1438	C₂²	1	4	yes	complemented
54	C₂²×#1438	C₂²	1	4	yes	complemented
55	C₂²×#1438	C₂²	1	4	yes	complemented
56	C₂²×#1438	C₂²	1	4	yes	complemented
57	C₂²×#1438	C₂²	1	4	yes	complemented
58	C₂²×#1438	C₂²	1	4	yes	complemented
59	C₂²×#1438	C₂²	1	4	yes	complemented
60	C₂²×#1438	C₂²	1	4	yes	complemented
61	C₂²×C₂²⋊#95	C₂²	1	2	yes	complemented
62	C₂²×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
63	C₂²×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
64	C₂²×C₂²⋊#95	C₂²	1	4	yes	complemented
65	#157600	C₂²	1	32	yes	complemented
66	#156826	C₂²	1	64	yes	complemented
67	#156684	C₂²	1	64	yes	complemented
68	#156684	C₂²	1	32	yes	complemented
69	#155941	C₂²	1	32	yes	complemented
70	#155632	C₂²	1	16	yes	complemented
71	#155065	C₂²	1	64	yes	complemented
72	#154094	C₂²	1	32	yes	complemented
73	C₂×#7556	C₂²	1	4	yes	complemented
74	C₂×#7556	C₂²	1	4	yes	complemented
75	C₂×#7555	C₂²	1	2	yes	complemented
76	C₂×#7555	C₂²	1	4	yes	complemented
77	C₂×#7555	C₂²	1	4	yes	complemented
78	C₂×#7555	C₂²	1	4	yes	complemented
79	C₂×#7555	C₂²	1	2	yes	complemented
80	C₂×#7555	C₂²	1	2	yes	complemented
81	C₂⁸	C₂³	1	1	yes	characteristic
82	C₂⁸	C₂³	1	2	yes	—
83	C₂⁸	C₂³	1	1	yes	characteristic
84	C₂⁵×D₄	D₄	1	16	yes	complemented
85	C₂⁵×D₄	C₂³	1	2	yes	—
86	C₂⁵×D₄	C₂³	1	4	yes	—
87	C₂⁵×D₄	C₂³	1	4	yes	—
88	C₂⁵×D₄	C₂³	1	4	yes	—
89	C₂⁵×D₄	C₂³	1	2	yes	—
90	C₂⁵×D₄	C₂³	1	2	yes	—
91	C₂⁵×D₄	C₂³	1	4	yes	—
92	C₂⁵×D₄	C₂³	1	16	yes	—
93	C₂⁵×D₄	C₂³	1	2	yes	—
94	C₂⁵×D₄	C₂³	1	8	yes	—
95	C₂⁶×C₄	C₂³	1	2	yes	—
96	C₂⁶×C₄	C₂³	1	2	yes	—
97	C₂⁶×C₄	C₂³	1	1	yes	characteristic
98	C₂³×#121	C₂³	1	16	yes	complemented
99	C₂³×#120	C₂³	1	16	yes	complemented
100	C₂³×#120	C₂³	1	32	yes	complemented
101	C₂³×#120	C₂³	1	32	yes	complemented
102	C₂³×#120	C₂³	1	16	yes	complemented
103	C₂⁴×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
105	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
106	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
107	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
108	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
110	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
113	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
114	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
115	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
116	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
117	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
118	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
119	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
124	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
127	C₂⁴×C₂²⋊C₄	C₂³	1	8	yes	complemented
128	C₂²×#392	D₄	1	64	yes	complemented
129	C₂²×#392	D₄	1	32	yes	complemented
130	C₂²×#392	C₂³	1	32	yes	—
131	C₂²×#392	C₂³	1	16	yes	—
132	C₂²×#392	C₂³	1	32	yes	—
133	C₂²×#392	C₂³	1	16	yes	—
134	C₂²×#392	C₂³	1	16	yes	complemented
135	C₂²×#392	C₂³	1	16	yes	complemented
136	C₂²×#392	C₂³	1	16	yes	complemented
137	C₂²×#386	C₂³	1	32	yes	complemented
138	C₂²×#386	C₂³	1	16	yes	complemented
139	C₂²×#386	C₂³	1	32	yes	complemented
140	C₂²×#386	C₂³	1	16	yes	complemented
141	C₂²×#386	C₂³	1	32	yes	complemented
142	C₂²×#386	C₂³	1	32	yes	complemented
143	C₂²×#379	D₄	1	16	yes	complemented
144	C₂²×#379	C₂³	1	16	yes	—
145	C₂²×#379	C₂³	1	8	yes	—
146	C₂²×#379	C₂³	1	8	yes	—
147	C₂²×#379	C₂³	1	8	yes	complemented
148	C₂²×#379	C₂³	1	32	yes	complemented
149	C₂³×#95	C₂³	1	4	yes	—
150	C₂³×#95	C₂³	1	2	yes	—
151	C₂³×#95	C₂³	1	4	yes	—
152	C₂³×#95	C₂³	1	4	yes	—
153	C₂³×#95	C₂³	1	4	yes	—
154	C₂³×#95	C₂³	1	4	yes	—
155	C₂³×#95	C₂³	1	2	yes	—
156	C₂³×#95	C₂³	1	2	yes	—
157	C₂³×#95	C₂³	1	4	yes	—
158	C₂³×#95	C₂³	1	4	yes	—
159	C₂³×#95	C₂³	1	2	yes	—
160	C₂³×#95	C₂³	1	4	yes	—
161	C₂³×#95	C₂³	1	4	yes	—
162	C₂³×#95	C₂³	1	4	yes	—
163	C₂³×#95	C₂³	1	2	yes	—
164	C₂×#1440	C₂³	1	32	yes	complemented
165	C₂×#1439	C₂³	1	32	yes	complemented
166	C₂×#1439	C₂³	1	32	yes	complemented
167	C₂×#1439	C₂³	1	16	yes	complemented
168	C₂×#1439	C₂³	1	16	yes	complemented
169	C₂×#1438	C₂³	1	32	yes	complemented
170	C₂×#1438	C₂³	1	32	yes	complemented
171	C₂×#1438	C₂³	1	32	yes	complemented
172	C₂×#1438	C₂³	1	32	yes	complemented
173	C₂×#1438	C₂³	1	32	yes	complemented
174	C₂×#1438	C₂³	1	32	yes	complemented
175	C₂×#1438	C₂³	1	32	yes	complemented
176	C₂×#1438	C₂³	1	32	yes	complemented
177	C₂×#1438	C₂³	1	32	yes	complemented
178	C₂×#1438	C₂³	1	32	yes	complemented
179	C₂×C₂²⋊#95	C₂³	1	8	yes	complemented
180	C₂×C₂²⋊#95	C₂³	1	16	yes	complemented
181	C₂×C₂²⋊#95	C₂³	1	8	yes	complemented
182	C₂×C₂²⋊#95	C₂³	1	32	yes	complemented
183	#7556	C₂³	1	32	yes	complemented
184	#7556	C₂³	1	32	yes	complemented
185	#7555	C₂³	1	32	yes	complemented
186	#7555	C₂³	1	16	yes	complemented
187	#7555	C₂³	1	32	yes	complemented
188	#7555	C₂³	1	16	yes	complemented
189	#7555	C₂³	1	16	yes	complemented
190	#7555	C₂³	1	32	yes	complemented
191	C₂⁷	C₂×D₄	1	8	yes	—
192	C₂⁷	C₂×D₄	1	8	yes	—
193	C₂⁷	C₂×D₄	1	8	yes	—
194	C₂⁷	#41	1	8	yes	—
195	C₂⁷	C₂⁴	1	4	yes	—
196	C₂⁷	C₂⁴	1	1	yes	characteristic
197	C₂⁷	C₂⁴	1	1	yes	characteristic
198	C₂⁷	C₂⁴	1	2	yes	—
199	C₂⁷	C₂⁴	1	1	yes	characteristic
200	C₂⁷	C₂⁴	1	4	yes	—
201	C₂⁷	C₂⁴	1	8	yes	—
202	C₂⁷	C₂⁴	1	4	yes	—
203	C₂⁴×D₄	C₂×D₄	1	32	yes	—
204	C₂⁴×D₄	C₂×D₄	1	32	yes	—
205	C₂⁴×D₄	C₂×D₄	1	16	yes	—
206	C₂⁴×D₄	C₂×D₄	1	32	yes	—
207	C₂⁴×D₄	C₂×D₄	1	16	yes	—
208	C₂⁴×D₄	C₂×D₄	1	32	yes	complemented
209	C₂⁴×D₄	C₂×D₄	1	64	yes	complemented
210	C₂⁴×D₄	C₂×D₄	1	16	yes	complemented
211	C₂⁴×D₄	C₂⁴	1	8	yes	—
212	C₂⁴×D₄	C₂⁴	1	16	yes	—
213	C₂⁴×D₄	C₂⁴	1	16	yes	—
214	C₂⁴×D₄	C₂⁴	1	16	yes	—
215	C₂⁴×D₄	C₂⁴	1	8	yes	—
216	C₂⁴×D₄	C₂⁴	1	8	yes	—
217	C₂⁴×D₄	C₂⁴	1	16	yes	—
218	C₂⁴×D₄	C₂⁴	1	8	yes	—
219	C₂⁵×C₄	C₂×D₄	1	8	yes	—
220	C₂⁵×C₄	C₂⁴	1	2	yes	—
221	C₂⁵×C₄	C₂⁴	1	4	yes	—
222	C₂⁵×C₄	C₂⁴	1	2	yes	—
223	C₂⁵×C₄	C₂⁴	1	4	yes	—
224	C₂⁵×C₄	C₂⁴	1	2	yes	—
225	C₂⁵×C₄	C₂⁴	1	2	yes	—
226	C₂⁵×C₄	C₂⁴	1	2	yes	—
227	C₂⁵×C₄	C₂⁴	1	4	yes	—
228	C₂⁵×C₄	C₂⁴	1	8	yes	—
229	C₂⁵×C₄	C₂⁴	1	8	yes	—
230	C₂⁵×C₄	C₂⁴	1	4	yes	—
231	C₂³×C₄⋊C₄	C₂⁴	1	8	yes	—
232	C₂³×C₂²⋊C₄	C₂×D₄	1	32	yes	—
233	C₂³×C₂²⋊C₄	C₂×D₄	1	32	yes	—
234	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
235	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	—
236	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
237	C₂³×C₂²⋊C₄	C₂×D₄	1	32	yes	complemented
238	C₂³×C₂²⋊C₄	C₂×D₄	1	32	yes	complemented
239	C₂³×C₂²⋊C₄	C₂×D₄	1	32	yes	complemented
240	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
241	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
242	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
243	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
244	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
245	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
246	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
247	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
248	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
249	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
250	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
251	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
252	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
253	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
254	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
255	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
256	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
257	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
258	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
259	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
260	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
261	C₂³×C₂²⋊C₄	C₂⁴	1	16	yes	—
262	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
263	C₂×#392	C₂×D₄	1	128	yes	complemented
264	C₂×#392	C₂×D₄	1	256	yes	complemented
265	C₂×#379	C₂×D₄	1	64	yes	complemented
266	C₂²×#95	C₂×D₄	1	32	yes	complemented
267	C₂²×#95	C₂×D₄	1	16	yes	complemented
268	C₂²×#95	C₂⁴	1	16	yes	—
269	C₂²×#95	C₂⁴	1	16	yes	—
270	C₂²×#95	C₂⁴	1	8	yes	—
271	C₂²×#95	C₂⁴	1	16	yes	—
272	C₂²×#95	C₂⁴	1	16	yes	—
273	C₂²×#95	C₂⁴	1	16	yes	—
274	C₂²×#95	C₂⁴	1	8	yes	—
275	C₂²×#95	C₂⁴	1	16	yes	—
276	C₂²×#95	C₂⁴	1	8	yes	—
277	C₂²×#95	C₂⁴	1	16	yes	—
278	C₂²×#95	C₂⁴	1	16	yes	—
279	C₂²×#95	C₂⁴	1	16	yes	—
280	C₂²×#95	C₂⁴	1	16	yes	—
281	C₂²×#95	C₂⁴	1	8	yes	—
282	C₂²×#95	C₂⁴	1	8	yes	—
283	C₂⁶	#121	1	64	yes	complemented
284	C₂⁶	C₂²×D₄	1	4	yes	—
285	C₂⁶	C₂²×D₄	1	16	yes	—
286	C₂⁶	C₂²×D₄	1	16	yes	—
287	C₂⁶	C₂²×D₄	1	4	yes	—
288	C₂⁶	C₂²×D₄	1	8	yes	—
289	C₂⁶	C₂²×D₄	1	4	yes	—
290	C₂⁶	C₂²×D₄	1	16	yes	—
291	C₂⁶	C₂²×D₄	1	8	yes	—
292	C₂⁶	C₂²×D₄	1	16	yes	—
293	C₂⁶	C₂²×D₄	1	8	yes	—
294	C₂⁶	C₂²×D₄	1	4	yes	—
295	C₂⁶	C₂²×D₄	1	16	yes	—
296	C₂⁶	C₂²×D₄	1	16	yes	—
297	C₂⁶	C₂²×D₄	1	16	yes	—
298	C₂⁶	C₂×#41	1	8	yes	—
299	C₂⁶	C₂×#41	1	4	yes	—
300	C₂⁶	C₂×#41	1	16	yes	—
301	C₂⁶	H(5,𝔽₂)	1	4	yes	—
302	C₂⁶	H(5,𝔽₂)	1	4	yes	—
303	C₂⁶	H(5,𝔽₂)	1	16	yes	—
304	C₂⁶	H(5,𝔽₂)	1	4	yes	—
305	C₂⁶	H(5,𝔽₂)	1	4	yes	—
306	C₂⁶	H(5,𝔽₂)	1	16	yes	—
307	C₂⁶	H(5,𝔽₂)	1	8	yes	—
308	C₂⁶	C₂⁵	1	8	yes	—
309	C₂⁶	C₂⁵	1	2	yes	—
310	C₂⁶	C₂⁵	1	2	yes	—
311	C₂⁶	C₂⁵	1	4	yes	—
312	C₂⁶	C₂⁵	1	2	yes	—
313	C₂⁶	C₂⁵	1	1	yes	characteristic
314	C₂³×D₄	#120	1	128	yes	complemented
315	C₂³×D₄	C₂²×D₄	1	64	yes	—
316	C₂³×D₄	C₂²×D₄	1	64	yes	—
317	C₂³×D₄	C₂²×D₄	1	32	yes	—
318	C₂³×D₄	C₂²×D₄	1	64	yes	—
319	C₂³×D₄	C₂²×D₄	1	32	yes	—
320	C₂³×D₄	C₂²×D₄	1	64	yes	complemented
321	C₂³×D₄	C₂²×D₄	1	32	yes	complemented
322	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
323	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
324	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
325	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
326	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
327	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
328	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
329	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
330	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
331	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
332	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
333	C₂⁴×C₄	H(5,𝔽₂)	1	8	yes	—
334	C₂⁴×C₄	H(5,𝔽₂)	1	16	yes	—
335	C₂⁴×C₄	C₂⁵	1	4	yes	—
336	C₂⁴×C₄	C₂⁵	1	8	yes	—
337	C₂⁴×C₄	C₂⁵	1	4	yes	—
338	C₂⁴×C₄	C₂⁵	1	8	yes	—
339	C₂⁴×C₄	C₂⁵	1	4	yes	—
340	C₂⁴×C₄	C₂⁵	1	4	yes	—
341	C₂⁴×C₄	C₂⁵	1	4	yes	—
342	C₂⁴×C₄	C₂⁵	1	8	yes	—
343	C₂²×C₂²⋊C₄	#120	1	64	yes	complemented
344	C₂²×C₂²⋊C₄	C₂²×D₄	1	64	yes	—
345	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
346	C₂²×C₂²⋊C₄	C₂²×D₄	1	64	yes	—
347	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
348	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
349	C₂²×C₂²⋊C₄	C₂²×D₄	1	64	yes	complemented
350	C₂²×C₂²⋊C₄	C₂²×D₄	1	64	yes	complemented
351	C₂²×C₂²⋊C₄	C₂²×D₄	1	64	yes	complemented
352	C₂×#95	C₂²×D₄	1	32	yes	complemented
353	C₂×#95	C₂²×D₄	1	64	yes	complemented
354	C₂⁵	C₂×#120	1	32	yes	—
355	C₂⁵	C₂×#120	1	16	yes	—
356	C₂⁵	C₂×#120	1	32	yes	—
357	C₂⁵	C₂×#121	1	16	yes	—
358	C₂⁵	C₂×#121	1	32	yes	—
359	C₂⁵	C₂×#121	1	64	yes	complemented
360	C₂⁵	#534	1	16	yes	—
361	C₂⁵	#534	1	16	yes	—
362	C₂⁵	#534	1	32	yes	—
363	C₂⁵	#535	1	16	yes	—
364	C₂⁵	D₄²	1	64	yes	—
365	C₂⁵	D₄²	1	32	yes	—
366	C₂⁵	D₄²	1	32	yes	—
367	C₂⁵	D₄²	1	32	yes	—
368	C₂⁵	D₄²	1	64	yes	—
369	C₂⁵	#546	1	32	yes	—
370	C₂⁵	#546	1	64	yes	—
371	C₂⁵	C₂³×D₄	1	4	yes	—
372	C₂⁵	C₂³×D₄	1	16	yes	—
373	C₂⁵	C₂³×D₄	1	16	yes	—
374	C₂⁵	C₂³×D₄	1	4	yes	—
375	C₂⁵	C₂³×D₄	1	8	yes	—
376	C₂⁵	C₂³×D₄	1	4	yes	—
377	C₂⁵	C₂³×D₄	1	16	yes	—
378	C₂⁵	C₂³×D₄	1	8	yes	—
379	C₂⁵	C₂³×D₄	1	16	yes	—
380	C₂⁵	C₂³×D₄	1	4	yes	—
381	C₂⁵	C₂³×D₄	1	8	yes	—
382	C₂⁵	C₂³×D₄	1	2	yes	—
383	C₂⁵	C₂³×D₄	1	2	yes	—
384	C₂⁵	C₂³×D₄	1	4	yes	—
385	C₂⁵	C₂³×D₄	1	8	yes	—
386	C₂⁵	C₂²×#41	1	8	yes	—
387	C₂⁵	C₂²×#41	1	4	yes	—
388	C₂⁵	C₂²×#41	1	2	yes	—
389	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
390	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
391	C₂⁵	C₂×H(5,𝔽₂)	1	16	yes	—
392	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
393	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
394	C₂⁵	C₂×H(5,𝔽₂)	1	16	yes	—
395	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
396	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
397	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
398	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
399	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
400	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
401	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
402	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
403	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
404	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
405	C₂⁵	#585	1	4	yes	—
406	C₂⁵	C₂⁶	1	1	yes	characteristic
407	C₂²×D₄	C₂×#120	1	128	yes	complemented
408	C₂³×C₄	C₂×#120	1	32	yes	—
409	C₂³×C₄	C₂×#120	1	32	yes	—
410	C₂³×C₄	D₄²	1	64	yes	—
411	C₂³×C₄	C₂³×D₄	1	16	yes	—
412	C₂³×C₄	C₂³×D₄	1	8	yes	—
413	C₂³×C₄	C₂³×D₄	1	16	yes	—
414	C₂³×C₄	C₂³×D₄	1	8	yes	—
415	C₂³×C₄	C₂³×D₄	1	8	yes	—
416	C₂³×C₄	C₂³×D₄	1	8	yes	—
417	C₂³×C₄	C₂³×D₄	1	8	yes	—
418	C₂³×C₄	C₂³×D₄	1	16	yes	—
419	C₂³×C₄	C₂³×D₄	1	16	yes	—
420	C₂³×C₄	C₂³×D₄	1	16	yes	—
421	C₂³×C₄	C₂×H(5,𝔽₂)	1	8	yes	—
422	C₂³×C₄	C₂×H(5,𝔽₂)	1	16	yes	—
423	C₂×C₂²⋊C₄	C₂×#120	1	64	yes	complemented
424	C₂⁴	#2403	1	64	yes	complemented
425	C₂⁴	#2408	1	64	yes	—
426	C₂⁴	#2410	1	128	yes	—
427	C₂⁴	C₂²×#120	1	16	yes	—
428	C₂⁴	C₂²×#120	1	16	yes	—
429	C₂⁴	C₂²×#120	1	8	yes	—
430	C₂⁴	C₂²×#120	1	4	yes	—
431	C₂⁴	C₂²×#120	1	8	yes	—
432	C₂⁴	C₂²×#121	1	16	yes	—
433	C₂⁴	C₂²×#121	1	8	yes	—
434	C₂⁴	C₂²×#121	1	4	yes	—
435	C₂⁴	C₂×#534	1	8	yes	—
436	C₂⁴	C₂×#534	1	8	yes	—
437	C₂⁴	C₂×#534	1	16	yes	—
438	C₂⁴	C₂×#534	1	8	yes	—
439	C₂⁴	C₂×#534	1	4	yes	—
440	C₂⁴	C₂×#534	1	4	yes	—
441	C₂⁴	C₂×#535	1	8	yes	—
442	C₂⁴	C₂×#535	1	4	yes	—
443	C₂⁴	#3459	1	8	yes	—
444	C₂⁴	C₂×D₄²	1	32	yes	—
445	C₂⁴	C₂×D₄²	1	16	yes	—
446	C₂⁴	C₂×D₄²	1	16	yes	—
447	C₂⁴	C₂×D₄²	1	32	yes	—
448	C₂⁴	C₂×D₄²	1	16	yes	—
449	C₂⁴	C₂×D₄²	1	8	yes	—
450	C₂⁴	C₂×D₄²	1	16	yes	—
451	C₂⁴	C₂×D₄²	1	16	yes	—
452	C₂⁴	C₂×D₄²	1	8	yes	—
453	C₂⁴	C₂×D₄²	1	8	yes	—
454	C₂⁴	C₂×D₄²	1	16	yes	—
455	C₂⁴	C₂×#546	1	32	yes	—
456	C₂⁴	C₂×#546	1	16	yes	—
457	C₂⁴	C₂×#546	1	16	yes	—
458	C₂⁴	C₂×#546	1	8	yes	—
459	C₂⁴	#3484	1	16	yes	—
460	C₂⁴	#3484	1	16	yes	—
461	C₂⁴	#3484	1	16	yes	—
462	C₂⁴	#3484	1	16	yes	—
463	C₂⁴	#3484	1	16	yes	—
464	C₂⁴	#3484	1	16	yes	—
465	C₂⁴	#3484	1	8	yes	—
466	C₂⁴	#3484	1	8	yes	—
467	C₂⁴	#3484	1	4	yes	—
468	C₂⁴	#3484	1	4	yes	—
469	C₂⁴	#3484	1	16	yes	—
470	C₂⁴	#3484	1	16	yes	—
471	C₂⁴	#3484	1	16	yes	—
472	C₂⁴	#3484	1	4	yes	—
473	C₂⁴	#3485	1	4	yes	—
474	C₂⁴	#3488	1	16	yes	—
475	C₂⁴	#3488	1	8	yes	—
476	C₂⁴	#3488	1	8	yes	—
477	C₂⁴	#3490	1	8	yes	—
478	C₂⁴	#3490	1	8	yes	—
479	C₂⁴	#3490	1	4	yes	—
480	C₂⁴	#3490	1	4	yes	—
481	C₂⁴	#3496	1	16	yes	—
482	C₂⁴	#3496	1	8	yes	—
483	C₂⁴	#3498	1	16	yes	—
484	C₂⁴	#3532	1	16	yes	—
485	C₂⁴	#3532	1	16	yes	—
486	C₂⁴	#3532	1	8	yes	—
487	C₂⁴	#3532	1	8	yes	—
488	C₂⁴	#3532	1	8	yes	—
489	C₂⁴	#3532	1	8	yes	—
490	C₂⁴	#3534	1	16	yes	—
491	C₂⁴	#3534	1	8	yes	—
492	C₂⁴	#3534	1	8	yes	—
493	C₂⁴	#3537	1	8	yes	—
494	C₂⁴	#3537	1	16	yes	—
495	C₂⁴	#3537	1	16	yes	—
496	C₂⁴	#3537	1	16	yes	—
497	C₂⁴	#3537	1	8	yes	—
498	C₂⁴	#3537	1	16	yes	—
499	C₂⁴	#3543	1	8	yes	—
500	C₂⁴	#3543	1	8	yes	—
501	C₂⁴	#3558	1	16	yes	—
502	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
503	C₂⁴	C₂⁴×D₄	1	2	yes	—
504	C₂⁴	C₂⁴×D₄	1	4	yes	—
505	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
506	C₂⁴	C₂³×#41	1	1	yes	characteristic
507	C₂⁴	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
508	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
509	C₂⁴	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
510	C₂⁴	C₂²×H(5,𝔽₂)	1	4	yes	—
511	C₂⁴	C₂²×H(5,𝔽₂)	1	4	yes	—
512	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
513	C₂⁴	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
514	C₂⁴	C₂²×H(5,𝔽₂)	1	4	yes	—
515	C₂⁴	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
516	C₂⁴	C₂×#585	1	2	yes	—
517	C₂²×C₄	C₂²×#120	1	16	yes	—
518	C₂²×C₄	C₂²×#120	1	16	yes	—
519	C₂²×C₄	C₂×D₄²	1	32	yes	—
520	C₂³	C₂×#2403	1	8	yes	—
521	C₂³	C₂×#2403	1	16	yes	complemented
522	C₂³	C₂×#2410	1	32	yes	—
523	C₂³	C₂×#2410	1	16	yes	—
524	C₂³	C₂×#2408	1	16	yes	—
525	C₂³	C₂×#2408	1	8	yes	—
526	C₂³	#34980	1	16	yes	—
527	C₂³	#34981	1	8	yes	—
528	C₂³	#34984	1	8	yes	—
529	C₂³	#35346	1	8	yes	—
530	C₂³	#35348	1	16	yes	—
531	C₂³	#35512	1	8	yes	—
532	C₂³	#35680	1	32	yes	—
533	C₂³	D₄×#120	1	32	yes	—
534	C₂³	D₄×#120	1	32	yes	—
535	C₂³	#36717	1	8	yes	—
536	C₂³	#36721	1	8	yes	—
537	C₂³	#37436	1	8	yes	—
538	C₂³	#37644	1	32	yes	—
539	C₂³	#37645	1	32	yes	—
540	C₂³	#37672	1	16	yes	—
541	C₂³	#37672	1	16	yes	—
542	C₂³	#37744	1	16	yes	—
543	C₂³	#37744	1	32	yes	—
544	C₂³	#37744	1	16	yes	—
545	C₂³	#39412	1	32	yes	—
546	C₂³	#40486	1	32	yes	—
547	C₂³	#40584	1	16	yes	—
548	C₂³	#40584	1	16	yes	—
549	C₂³	#42996	1	16	yes	—
550	C₂³	#43001	1	32	yes	—
551	C₂³	#43001	1	32	yes	—
552	C₂³	#43001	1	32	yes	—
553	C₂³	#43023	1	32	yes	—
554	C₂³	#43098	1	32	yes	—
555	C₂³	#43098	1	16	yes	—
556	C₂³	#44877	1	32	yes	—
557	C₂³	#45355	1	32	yes	—
558	C₂³	#46384	1	16	yes	—
559	C₂³	#46387	1	8	yes	—
560	C₂³	#46996	1	8	yes	—
561	C₂³	#47827	1	16	yes	—
562	C₂³	#47827	1	16	yes	—
563	C₂³	#47827	1	16	yes	—
564	C₂³	#47838	1	32	yes	—
565	C₂³	#47838	1	32	yes	—
566	C₂³	#47942	1	32	yes	—
567	C₂³	#52004	1	32	yes	—
568	C₂³	#52004	1	16	yes	—
569	C₂³	#52031	1	32	yes	—
570	C₂³	#56344	1	16	yes	—
571	C₂³	#56346	1	32	yes	—
572	C₂³	#56413	1	16	yes	—
573	C₂³	#58990	1	16	yes	—
574	C₂³	#58990	1	16	yes	—
575	C₂³	#58990	1	16	yes	—
576	C₂³	#58991	1	16	yes	—
577	C₂³	#58991	1	32	yes	—
578	C₂³	#58991	1	32	yes	—
579	C₂³	#58991	1	16	yes	—
580	C₂³	#58997	1	32	yes	—
581	C₂³	#59126	1	16	yes	—
582	C₂³	C₂³×#120	1	2	yes	—
583	C₂³	C₂³×#120	1	1	yes	characteristic
584	C₂³	C₂³×#121	1	1	yes	characteristic
585	C₂³	C₂²×#534	1	1	yes	characteristic
586	C₂³	C₂²×#534	1	2	yes	—
587	C₂³	C₂²×#534	1	1	yes	characteristic
588	C₂³	C₂×#3459	1	2	yes	—
589	C₂³	C₂²×#535	1	1	yes	characteristic
590	C₂³	C₂²×D₄²	1	2	yes	—
591	C₂³	C₂²×D₄²	1	4	yes	—
592	C₂³	C₂²×D₄²	1	4	yes	—
593	C₂³	C₂²×D₄²	1	2	yes	—
594	C₂³	C₂²×D₄²	1	2	yes	—
595	C₂³	C₂²×D₄²	1	4	yes	—
596	C₂³	C₂²×#546	1	4	yes	—
597	C₂³	C₂²×#546	1	2	yes	—
598	C₂³	C₂×#3532	1	4	yes	—
599	C₂³	C₂×#3532	1	4	yes	—
600	C₂³	C₂×#3532	1	2	yes	—
601	C₂³	C₂×#3532	1	2	yes	—
602	C₂³	C₂×#3532	1	2	yes	—
603	C₂³	C₂×#3532	1	2	yes	—
604	C₂³	C₂×#3534	1	4	yes	—
605	C₂³	C₂×#3534	1	2	yes	—
606	C₂³	C₂×#3534	1	2	yes	—
607	C₂³	C₂×#3537	1	4	yes	—
608	C₂³	C₂×#3537	1	4	yes	—
609	C₂³	C₂×#3537	1	2	yes	—
610	C₂³	C₂×#3537	1	4	yes	—
611	C₂³	C₂×#3537	1	2	yes	—
612	C₂³	C₂×#3537	1	4	yes	—
613	C₂³	C₂×#3558	1	4	yes	—
614	C₂³	C₂×#3543	1	2	yes	—
615	C₂³	C₂×#3543	1	2	yes	—
616	C₂³	C₂×#3484	1	2	yes	—
617	C₂³	C₂×#3484	1	4	yes	—
618	C₂³	C₂×#3484	1	4	yes	—
619	C₂³	C₂×#3484	1	4	yes	—
620	C₂³	C₂×#3484	1	4	yes	—
621	C₂³	C₂×#3484	1	4	yes	—
622	C₂³	C₂×#3484	1	4	yes	—
623	C₂³	C₂×#3484	1	4	yes	—
624	C₂³	C₂×#3484	1	2	yes	—
625	C₂³	C₂×#3484	1	4	yes	—
626	C₂³	C₂×#3484	1	1	yes	characteristic
627	C₂³	C₂×#3484	1	1	yes	characteristic
628	C₂³	C₂×#3484	1	4	yes	—
629	C₂³	C₂×#3484	1	1	yes	characteristic
630	C₂³	C₂×#3496	1	4	yes	—
631	C₂³	C₂×#3496	1	2	yes	—
632	C₂³	C₂×#3490	1	2	yes	—
633	C₂³	C₂×#3490	1	1	yes	characteristic
634	C₂³	C₂×#3490	1	1	yes	characteristic
635	C₂³	C₂×#3490	1	2	yes	—
636	C₂³	C₂×#3485	1	1	yes	characteristic
637	C₂³	C₂×#3488	1	4	yes	—
638	C₂³	C₂×#3488	1	2	yes	—
639	C₂³	C₂×#3488	1	2	yes	—
640	C₂³	C₂×#3498	1	4	yes	—
641	C₂²	#625760	1	16	yes	—
642	C₂²	#647670	1	32	yes	—
643	C₂²	#688032	1	32	yes	—
644	C₂²	#759288	1	16	yes	—
645	C₂²	#772778	1	32	yes	—
646	C₂²	#1259281	1	64	yes	—
647	C₂²	#1418385	1	32	yes	—
648	C₂²	#1418393	1	32	yes	—
649	C₂²	#2601293	1	32	yes	—
650	C₂²	#2805709	1	32	yes	—
651	C₂²	#2805719	1	32	yes	—
652	C₂²	#4029237	1	64	yes	—
653	C₂²	#4029441	1	32	yes	—
654	C₂²	#4029469	1	32	yes	—
655	C₂²	#4387614	1	16	yes	—
656	C₂²	C₂²×#2403	1	1	yes	characteristic
657	C₂²	C₂²×#2410	1	2	yes	—
658	C₂²	C₂²×#2408	1	1	yes	characteristic
659	C₂²	C₂×#34980	1	2	yes	—
660	C₂²	C₂×#34981	1	1	yes	characteristic
661	C₂²	C₂×#34984	1	1	yes	characteristic
662	C₂²	C₂×#35346	1	1	yes	characteristic
663	C₂²	C₂×#35348	1	2	yes	—
664	C₂²	C₂×#35512	1	1	yes	characteristic
665	C₂²	C₂×#35680	1	4	yes	—
666	C₂²	C₂×D₄×#120	1	4	yes	—
667	C₂²	C₂×D₄×#120	1	4	yes	—
668	C₂²	C₂×#37436	1	1	yes	characteristic
669	C₂²	C₂×#36717	1	1	yes	characteristic
670	C₂²	C₂×#36721	1	1	yes	characteristic
671	C₂²	C₂×#37644	1	4	yes	—
672	C₂²	C₂×#37672	1	2	yes	—
673	C₂²	C₂×#37672	1	2	yes	—
674	C₂²	C₂×#37744	1	2	yes	—
675	C₂²	C₂×#37744	1	4	yes	—
676	C₂²	C₂×#37744	1	2	yes	—
677	C₂²	C₂×#37645	1	4	yes	—
678	C₂²	C₂×#39412	1	4	yes	—
679	C₂²	C₂×#40584	1	2	yes	—
680	C₂²	C₂×#40584	1	2	yes	—
681	C₂²	C₂×#40486	1	4	yes	—
682	C₂²	C₂×#58990	1	2	yes	—
683	C₂²	C₂×#58990	1	2	yes	—
684	C₂²	C₂×#58990	1	2	yes	—
685	C₂²	C₂×#58991	1	2	yes	—
686	C₂²	C₂×#58991	1	4	yes	—
687	C₂²	C₂×#58991	1	2	yes	—
688	C₂²	C₂×#58991	1	4	yes	—
689	C₂²	C₂×#58997	1	4	yes	—
690	C₂²	C₂×#59126	1	2	yes	—
691	C₂²	C₂×#42996	1	2	yes	—
692	C₂²	C₂×#43001	1	4	yes	—
693	C₂²	C₂×#43001	1	4	yes	—
694	C₂²	C₂×#43001	1	4	yes	—
695	C₂²	C₂×#43023	1	4	yes	—
696	C₂²	C₂×#43098	1	4	yes	—
697	C₂²	C₂×#43098	1	2	yes	—
698	C₂²	C₂×#44877	1	4	yes	—
699	C₂²	C₂×#45355	1	4	yes	—
700	C₂²	C₂×#46384	1	2	yes	—
701	C₂²	C₂×#46387	1	1	yes	characteristic
702	C₂²	C₂×#46996	1	1	yes	characteristic
703	C₂²	C₂×#47827	1	2	yes	—
704	C₂²	C₂×#47827	1	2	yes	—
705	C₂²	C₂×#47827	1	2	yes	—
706	C₂²	C₂×#47838	1	4	yes	—
707	C₂²	C₂×#47838	1	4	yes	—
708	C₂²	C₂×#47942	1	4	yes	—
709	C₂²	C₂×#52004	1	4	yes	—
710	C₂²	C₂×#52004	1	2	yes	—
711	C₂²	C₂×#52031	1	4	yes	—
712	C₂²	C₂×#56344	1	2	yes	—
713	C₂²	C₂×#56346	1	4	yes	—
714	C₂²	C₂×#56413	1	2	yes	—
715	C₂	C₂×#1259281	1	4	yes	—
716	C₂	C₂×#772778	1	2	yes	—
717	C₂	C₂×#1418385	1	2	yes	—
718	C₂	#72264992	1	32	yes	direct product factor
719	C₂	C₂×#647670	1	2	yes	—
720	C₂	C₂×#625760	1	1	yes	characteristic
721	C₂	C₂×#4029469	1	2	yes	—
722	C₂	C₂×#1418393	1	2	yes	—
723	C₂	C₂×#688032	1	2	yes	—
724	C₂	C₂×#4387614	1	1	yes	characteristic
725	C₂	C₂×#759288	1	1	yes	characteristic
726	C₂	C₂×#4029237	1	4	yes	—
727	C₂	C₂×#2601293	1	2	yes	—
728	C₂	C₂×#2805719	1	2	yes	—
729	C₂	C₂×#2805709	1	2	yes	—
730	C₂	C₂×#4029441	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×#155632	C₂	semidirect
2. C₂×#157600	C₂	semidirect
3. C₂×#156826	C₂	semidirect
4. C₂×#155065	C₂	semidirect
5. C₂×#155941	C₂	semidirect
6. C₂²×#15257	C₂	semidirect
7. #72264992	C₂	direct (N × H)
8. C₂²×#14716	C₂	semidirect
9. C₂×#154094	C₂	semidirect
10. C₂×#156684	C₂	semidirect
11. C₂×#156684	C₂	semidirect
12. C₂²×#13867	C₂	semidirect
13. C₂³×#2403	C₂	semidirect
14. C₂³×#2403	C₂	semidirect
17. C₂⁴×#121	C₂²	semidirect
18. C₂⁴×#120	C₂²	semidirect
19. C₂⁴×#120	C₂²	semidirect
20. C₂⁴×#120	C₂²	semidirect
21. C₂⁴×#120	C₂²	semidirect
22. C₂⁵×C₂²⋊C₄	C₂²	semidirect
23. C₂²×#2403	C₂²	semidirect
24. C₂²×#2403	C₂²	semidirect
29. C₂³×#392	C₂²	semidirect
30. C₂³×#392	C₂²	semidirect
31. C₂³×#392	C₂²	semidirect
32. C₂³×#386	C₂²	semidirect
33. C₂³×#386	C₂²	semidirect
34. C₂³×#386	C₂²	semidirect
35. C₂³×#386	C₂²	semidirect
36. C₂³×#386	C₂²	semidirect
37. C₂³×#386	C₂²	semidirect
41. C₂³×#379	C₂²	semidirect
42. C₂³×#379	C₂²	semidirect
43. C₂×#15257	C₂²	semidirect
44. C₂×#14716	C₂²	semidirect
45. C₂×#13867	C₂²	semidirect
46. C₂²×#1440	C₂²	semidirect
47. C₂²×#1439	C₂²	semidirect
48. C₂²×#1439	C₂²	semidirect
49. C₂²×#1439	C₂²	semidirect
50. C₂²×#1439	C₂²	semidirect
51. C₂²×#1438	C₂²	semidirect
52. C₂²×#1438	C₂²	semidirect
53. C₂²×#1438	C₂²	semidirect
54. C₂²×#1438	C₂²	semidirect
55. C₂²×#1438	C₂²	semidirect
56. C₂²×#1438	C₂²	semidirect
57. C₂²×#1438	C₂²	semidirect
58. C₂²×#1438	C₂²	semidirect
59. C₂²×#1438	C₂²	semidirect
60. C₂²×#1438	C₂²	semidirect
61. C₂²×C₂²⋊#95	C₂²	semidirect
62. C₂²×C₂²⋊#95	C₂²	semidirect
63. C₂²×C₂²⋊#95	C₂²	semidirect
64. C₂²×C₂²⋊#95	C₂²	semidirect
65. #157600	C₂²	semidirect
66. #156826	C₂²	semidirect
67. #156684	C₂²	semidirect
68. #156684	C₂²	semidirect
69. #155941	C₂²	semidirect
70. #155632	C₂²	semidirect
71. #155065	C₂²	semidirect
72. #154094	C₂²	semidirect
73. C₂×#7556	C₂²	semidirect
74. C₂×#7556	C₂²	semidirect
75. C₂×#7555	C₂²	semidirect
76. C₂×#7555	C₂²	semidirect
77. C₂×#7555	C₂²	semidirect
78. C₂×#7555	C₂²	semidirect
79. C₂×#7555	C₂²	semidirect
80. C₂×#7555	C₂²	semidirect
84. C₂⁵×D₄	D₄	semidirect
98. C₂³×#121	C₂³	semidirect
99. C₂³×#120	C₂³	semidirect
100. C₂³×#120	C₂³	semidirect
101. C₂³×#120	C₂³	semidirect
102. C₂³×#120	C₂³	semidirect
127. C₂⁴×C₂²⋊C₄	C₂³	semidirect
128. C₂²×#392	D₄	semidirect
129. C₂²×#392	D₄	semidirect
134. C₂²×#392	C₂³	semidirect
135. C₂²×#392	C₂³	semidirect
136. C₂²×#392	C₂³	semidirect
137. C₂²×#386	C₂³	semidirect
138. C₂²×#386	C₂³	semidirect
139. C₂²×#386	C₂³	semidirect
140. C₂²×#386	C₂³	semidirect
141. C₂²×#386	C₂³	semidirect
142. C₂²×#386	C₂³	semidirect
143. C₂²×#379	D₄	semidirect
147. C₂²×#379	C₂³	semidirect
148. C₂²×#379	C₂³	semidirect
164. C₂×#1440	C₂³	semidirect
165. C₂×#1439	C₂³	semidirect
166. C₂×#1439	C₂³	semidirect
167. C₂×#1439	C₂³	semidirect
168. C₂×#1439	C₂³	semidirect
169. C₂×#1438	C₂³	semidirect
170. C₂×#1438	C₂³	semidirect
171. C₂×#1438	C₂³	semidirect
172. C₂×#1438	C₂³	semidirect
173. C₂×#1438	C₂³	semidirect
174. C₂×#1438	C₂³	semidirect
175. C₂×#1438	C₂³	semidirect
176. C₂×#1438	C₂³	semidirect
177. C₂×#1438	C₂³	semidirect
178. C₂×#1438	C₂³	semidirect
179. C₂×C₂²⋊#95	C₂³	semidirect
180. C₂×C₂²⋊#95	C₂³	semidirect
181. C₂×C₂²⋊#95	C₂³	semidirect
182. C₂×C₂²⋊#95	C₂³	semidirect
183. #7556	C₂³	semidirect
184. #7556	C₂³	semidirect
185. #7555	C₂³	semidirect
186. #7555	C₂³	semidirect
187. #7555	C₂³	semidirect
188. #7555	C₂³	semidirect
189. #7555	C₂³	semidirect
190. #7555	C₂³	semidirect
208. C₂⁴×D₄	C₂×D₄	semidirect
209. C₂⁴×D₄	C₂×D₄	semidirect
210. C₂⁴×D₄	C₂×D₄	semidirect
237. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
238. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
239. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
263. C₂×#392	C₂×D₄	semidirect
264. C₂×#392	C₂×D₄	semidirect
265. C₂×#379	C₂×D₄	semidirect
266. C₂²×#95	C₂×D₄	semidirect
267. C₂²×#95	C₂×D₄	semidirect
283. C₂⁶	#121	semidirect
314. C₂³×D₄	#120	semidirect
320. C₂³×D₄	C₂²×D₄	semidirect
321. C₂³×D₄	C₂²×D₄	semidirect
343. C₂²×C₂²⋊C₄	#120	semidirect
349. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
350. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
351. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
352. C₂×#95	C₂²×D₄	semidirect
353. C₂×#95	C₂²×D₄	semidirect
359. C₂⁵	C₂×#121	semidirect
407. C₂²×D₄	C₂×#120	semidirect
423. C₂×C₂²⋊C₄	C₂×#120	semidirect
424. C₂⁴	#2403	semidirect
521. C₂³	C₂×#2403	semidirect
718. C₂	#72264992	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#155632	2
C₂×#157600	2
C₂×#156826	2
C₂×#155065	2
C₂×#155941	2
C₂²×#15257	2
#72264992	2
C₂²×#14716	2
C₂×#154094	2
C₂×#156684	2
C₂²×#13867	2
C₂³×#2403	2

Subgroups — C2×#72264992 #72296466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72264992 #72296466