Subgroups — #72335599

Order 1024.

At least 6464 conjugacy classes of subgroups; only the 1857 normal subgroups are shown.

The subgroup lattice has 704 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#2410	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#2403	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×#390	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15267	C₂	1	2	yes	maximal, complemented
5	C₂×#14725	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14719	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#14716	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14716	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14715	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14698	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#13867	C₂	1	1	yes	maximal, characteristic, complemented
12	#158362	C₂	1	2	yes	maximal, complemented
13	#158361	C₂	1	2	yes	maximal, complemented
14	#158317	C₂	1	2	yes	maximal, complemented
15	#156831	C₂	1	2	yes	maximal, complemented
16	#155066	C₂	1	2	yes	maximal, complemented
17	#154688	C₂	1	2	yes	maximal, complemented
18	#154671	C₂	1	2	yes	maximal, complemented
19	#154248	C₂	1	1	yes	maximal, characteristic, complemented
20	#154195	C₂	1	1	yes	maximal, characteristic, complemented
21	#154195	C₂	1	1	yes	maximal, characteristic, complemented
22	#154095	C₂	1	1	yes	maximal, characteristic, complemented
23	#154088	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂⁵×D₄	C₂²	1	1	yes	characteristic
25	C₂⁵×D₄	C₂²	1	1	yes	characteristic
26	C₂³×#121	C₂²	1	1	yes	characteristic
27	C₂³×#121	C₂²	1	1	yes	characteristic
28	C₂³×#120	C₂²	1	2	yes	—
29	C₂³×#120	C₂²	1	1	yes	characteristic
30	C₂³×#120	C₂²	1	1	yes	characteristic
31	C₂³×#120	C₂²	1	1	yes	characteristic
32	C₂³×#120	C₂²	1	1	yes	characteristic, complemented
33	C₂³×#120	C₂²	1	1	yes	characteristic, complemented
34	C₂⁴×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
35	C₂⁴×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂⁴×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂⁴×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	C₂⁴×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₂⁴×C₄²	C₂²	1	1	yes	characteristic, complemented
40	C₂²×#394	C₂²	1	1	yes	characteristic, complemented
41	C₂²×#394	C₂²	1	1	yes	characteristic, complemented
42	C₂²×#394	C₂²	1	2	yes	complemented
43	C₂²×#394	C₂²	1	2	yes	complemented
44	C₂²×#392	C₂²	1	2	yes	—
45	C₂²×#392	C₂²	1	2	yes	—
46	C₂²×#392	C₂²	1	2	yes	—
47	C₂²×#392	C₂²	1	1	yes	characteristic, complemented
48	C₂²×#392	C₂²	1	1	yes	characteristic, complemented
49	C₂²×#392	C₂²	1	2	yes	complemented
50	C₂²×#392	C₂²	1	2	yes	complemented
51	C₂²×#392	C₂²	1	2	yes	complemented
52	C₂²×#390	C₂²	1	2	yes	—
53	C₂²×#390	C₂²	1	2	yes	—
54	C₂²×#390	C₂²	1	2	yes	complemented
55	C₂²×#390	C₂²	1	2	yes	complemented
56	C₂²×#390	C₂²	1	2	yes	complemented
57	C₂²×#386	C₂²	1	2	yes	—
58	C₂²×#386	C₂²	1	1	yes	characteristic
59	C₂²×#386	C₂²	1	1	yes	characteristic
60	C₂²×#386	C₂²	1	1	yes	characteristic
61	C₂²×#386	C₂²	1	1	yes	characteristic
62	C₂²×#386	C₂²	1	1	yes	characteristic
63	C₂²×#386	C₂²	1	1	yes	characteristic
64	C₂²×#386	C₂²	1	1	yes	characteristic
65	C₂²×#386	C₂²	1	1	yes	characteristic
66	C₂²×#386	C₂²	1	1	yes	characteristic, complemented
67	C₂²×#386	C₂²	1	1	yes	characteristic, complemented
68	C₂²×#386	C₂²	1	1	yes	characteristic, complemented
69	C₂²×#386	C₂²	1	1	yes	characteristic, complemented
70	C₂²×#385	C₂²	1	1	yes	characteristic, complemented
71	C₂²×#380	C₂²	1	1	yes	characteristic, complemented
72	C₂²×#379	C₂²	1	1	yes	characteristic
73	C₂²×#379	C₂²	1	1	yes	characteristic
74	C₂²×#379	C₂²	1	1	yes	characteristic, complemented
75	C₂²×#379	C₂²	1	2	yes	complemented
76	C₂²×#379	C₂²	1	1	yes	characteristic, complemented
77	C₂×#1441	C₂²	1	2	yes	complemented
78	C₂×#1440	C₂²	1	2	yes	complemented
79	C₂×#1439	C₂²	1	2	yes	complemented
80	C₂×#1439	C₂²	1	2	yes	complemented
81	C₂×#1439	C₂²	1	2	yes	complemented
82	C₂×#1439	C₂²	1	2	yes	complemented
83	C₂×#1439	C₂²	1	2	yes	complemented
84	C₂×#1439	C₂²	1	2	yes	complemented
85	C₂×#1439	C₂²	1	2	yes	complemented
86	C₂×#1439	C₂²	1	2	yes	complemented
87	C₂×#1439	C₂²	1	2	yes	complemented
88	C₂×#1438	C₂²	1	2	yes	—
89	C₂×#1438	C₂²	1	2	yes	complemented
90	C₂×#1438	C₂²	1	2	yes	complemented
91	C₂×#1438	C₂²	1	2	yes	complemented
92	C₂×#1438	C₂²	1	2	yes	complemented
93	C₂×#1438	C₂²	1	2	yes	complemented
94	C₂×#1438	C₂²	1	2	yes	complemented
95	C₂×#1438	C₂²	1	2	yes	complemented
96	C₂×#1438	C₂²	1	2	yes	complemented
97	C₂×#1438	C₂²	1	2	yes	complemented
98	C₂×#1438	C₂²	1	2	yes	complemented
99	C₂×#1438	C₂²	1	2	yes	complemented
100	C₂×#1438	C₂²	1	2	yes	complemented
101	C₂×#1437	C₂²	1	2	yes	complemented
102	C₂×#1437	C₂²	1	2	yes	complemented
103	C₂×#1437	C₂²	1	2	yes	complemented
104	C₂×#1437	C₂²	1	2	yes	complemented
105	C₂×C₄⋊#95	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊#95	C₂²	1	2	yes	complemented
107	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
109	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
112	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
113	#7557	C₂²	1	2	yes	complemented
114	#7557	C₂²	1	2	yes	complemented
115	#7555	C₂²	1	2	yes	complemented
116	#7555	C₂²	1	2	yes	complemented
117	#7555	C₂²	1	2	yes	complemented
118	#7555	C₂²	1	2	yes	complemented
119	#7555	C₂²	1	2	yes	complemented
120	#7555	C₂²	1	2	yes	complemented
121	#7554	C₂²	1	2	yes	complemented
122	#7554	C₂²	1	2	yes	complemented
123	C₂⁷	C₂³	1	1	yes	characteristic
124	C₂⁷	C₂³	1	1	yes	characteristic
125	C₂⁷	C₂³	1	1	yes	characteristic
126	C₂⁴×D₄	D₄	1	8	yes	complemented
127	C₂⁴×D₄	C₂³	1	1	yes	characteristic
128	C₂⁴×D₄	C₂³	1	1	yes	characteristic
129	C₂⁴×D₄	C₂³	1	1	yes	characteristic
130	C₂⁴×D₄	C₂³	1	2	yes	—
131	C₂⁴×D₄	C₂³	1	1	yes	characteristic
132	C₂⁴×D₄	C₂³	1	1	yes	characteristic
133	C₂⁴×D₄	C₂³	1	1	yes	characteristic
134	C₂⁴×D₄	C₂³	1	1	yes	characteristic
135	C₂⁴×D₄	C₂³	1	2	yes	—
136	C₂⁴×D₄	C₂³	1	2	yes	—
137	C₂⁴×D₄	C₂³	1	2	yes	—
138	C₂⁴×D₄	C₂³	1	1	yes	characteristic
139	C₂⁴×D₄	C₂³	1	1	yes	characteristic
140	C₂⁴×D₄	C₂³	1	2	yes	—
141	C₂⁵×C₄	C₂³	1	1	yes	characteristic
142	C₂⁵×C₄	C₂³	1	1	yes	characteristic
143	C₂⁵×C₄	C₂³	1	1	yes	characteristic
144	C₂⁵×C₄	C₂³	1	1	yes	characteristic
145	C₂⁵×C₄	C₂³	1	1	yes	characteristic
146	C₂⁵×C₄	C₂³	1	1	yes	characteristic
147	C₂²×#121	D₄	1	8	yes	complemented
148	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂³×C₂²⋊C₄	D₄	1	8	yes	complemented
154	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
156	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
157	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
160	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
161	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
162	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
163	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
183	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
188	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₂³×C₄²	C₂³	1	2	yes	—
198	C₂³×C₄²	C₂³	1	2	yes	—
199	C₂×#390	D₄	1	16	yes	complemented
200	C₂×#386	D₄	1	8	yes	complemented
201	C₂×#386	D₄	1	8	yes	complemented
202	C₂×#386	D₄	1	8	yes	complemented
203	C₂×#386	D₄	1	8	yes	complemented
204	C₂²×#95	C₂³	1	2	yes	—
205	C₂²×#95	C₂³	1	2	yes	—
206	C₂²×#95	C₂³	1	2	yes	—
207	C₂²×#95	C₂³	1	2	yes	—
208	C₂²×#95	C₂³	1	2	yes	—
209	C₂²×#95	C₂³	1	1	yes	characteristic
210	C₂²×#95	C₂³	1	1	yes	characteristic
211	C₂²×#95	C₂³	1	2	yes	—
212	C₂²×#95	C₂³	1	2	yes	—
213	C₂²×#95	C₂³	1	2	yes	—
214	C₂²×#95	C₂³	1	2	yes	—
215	C₂²×#95	C₂³	1	2	yes	—
216	C₂²×#95	C₂³	1	2	yes	—
217	C₂²×#95	C₂³	1	2	yes	—
218	C₂²×#95	C₂³	1	2	yes	—
219	C₂²×#95	C₂³	1	2	yes	—
220	C₂²×#95	C₂³	1	2	yes	—
221	C₂²×#95	C₂³	1	1	yes	characteristic
222	C₂²×#95	C₂³	1	1	yes	characteristic
223	C₂²×#95	C₂³	1	2	yes	—
224	C₂²×#95	C₂³	1	2	yes	—
225	C₂²×#95	C₂³	1	2	yes	—
226	C₂²×#95	C₂³	1	2	yes	—
227	C₂²×#95	C₂³	1	2	yes	—
228	C₂²×#95	C₂³	1	2	yes	—
229	C₂²×#95	C₂³	1	2	yes	—
230	C₂⁶	C₂×D₄	1	4	yes	—
231	C₂⁶	C₂×D₄	1	4	yes	—
232	C₂⁶	C₂×D₄	1	4	yes	—
233	C₂⁶	#41	1	4	yes	—
234	C₂⁶	C₂⁴	1	1	yes	characteristic
235	C₂⁶	C₂⁴	1	1	yes	characteristic
236	C₂⁶	C₂⁴	1	2	yes	—
237	C₂⁶	C₂⁴	1	1	yes	characteristic
238	C₂⁶	C₂⁴	1	1	yes	characteristic
239	C₂⁶	C₂⁴	1	1	yes	characteristic
240	C₂⁶	C₂⁴	1	1	yes	characteristic
241	C₂³×D₄	C₂×D₄	1	4	yes	—
242	C₂³×D₄	C₂×D₄	1	4	yes	—
243	C₂³×D₄	C₂×D₄	1	4	yes	—
244	C₂³×D₄	C₂×D₄	1	4	yes	—
245	C₂³×D₄	C₂×D₄	1	4	yes	—
246	C₂³×D₄	C₂×D₄	1	4	yes	—
247	C₂³×D₄	C₂×D₄	1	8	yes	—
248	C₂³×D₄	C₂×D₄	1	8	yes	—
249	C₂³×D₄	C₂×D₄	1	8	yes	—
250	C₂³×D₄	C₂×D₄	1	4	yes	complemented
251	C₂³×D₄	#41	1	4	yes	—
252	C₂³×D₄	#41	1	8	yes	—
253	C₂⁴×C₄	C₂×D₄	1	4	yes	—
254	C₂⁴×C₄	C₂×D₄	1	4	yes	—
255	C₂⁴×C₄	C₂×D₄	1	4	yes	—
256	C₂⁴×C₄	C₂×D₄	1	4	yes	—
257	C₂⁴×C₄	C₂×D₄	1	4	yes	—
258	C₂⁴×C₄	C₂×D₄	1	4	yes	—
259	C₂⁴×C₄	C₂×D₄	1	4	yes	—
260	C₂⁴×C₄	C₂×D₄	1	4	yes	—
261	C₂⁴×C₄	C₂⁴	1	2	yes	—
262	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
263	C₂⁴×C₄	C₂⁴	1	2	yes	—
264	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
265	C₂⁴×C₄	C₂⁴	1	2	yes	—
266	C₂⁴×C₄	C₂⁴	1	2	yes	—
267	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
268	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
269	C₂⁴×C₄	C₂⁴	1	2	yes	—
270	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
271	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
272	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
273	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
274	C₂⁴×C₄	C₂⁴	1	2	yes	—
275	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
276	C₂⁴×C₄	C₂⁴	1	2	yes	—
277	C₂²×C₄⋊C₄	C₂×D₄	1	8	yes	complemented
278	C₂²×C₄⋊C₄	C₂×D₄	1	4	yes	complemented
279	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
280	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
281	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
282	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
283	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
284	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
285	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
286	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
287	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
288	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
289	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
290	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
291	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
292	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
293	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
294	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
295	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
296	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
297	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
298	C₂²×C₄²	C₂×D₄	1	8	yes	complemented
299	C₂×#95	C₂×D₄	1	8	yes	—
300	C₂×#95	C₂×D₄	1	8	yes	—
301	C₂×#95	C₂×D₄	1	4	yes	complemented
302	C₂×#95	C₂×D₄	1	4	yes	complemented
303	C₂×#95	C₂×D₄	1	8	yes	complemented
304	C₂⁵	#121	1	16	yes	—
305	C₂⁵	C₂²×D₄	1	2	yes	—
306	C₂⁵	C₂²×D₄	1	2	yes	—
307	C₂⁵	C₂²×D₄	1	4	yes	—
308	C₂⁵	C₂²×D₄	1	2	yes	—
309	C₂⁵	C₂²×D₄	1	2	yes	—
310	C₂⁵	C₂²×D₄	1	2	yes	—
311	C₂⁵	C₂²×D₄	1	4	yes	—
312	C₂⁵	C₂²×D₄	1	2	yes	—
313	C₂⁵	C₂²×D₄	1	2	yes	—
314	C₂⁵	C₂²×D₄	1	2	yes	—
315	C₂⁵	C₂²×D₄	1	4	yes	—
316	C₂⁵	C₂²×D₄	1	2	yes	—
317	C₂⁵	C₂²×D₄	1	2	yes	—
318	C₂⁵	C₂²×D₄	1	2	yes	—
319	C₂⁵	C₂²×D₄	1	2	yes	—
320	C₂⁵	C₂²×D₄	1	2	yes	—
321	C₂⁵	C₂²×D₄	1	2	yes	—
322	C₂⁵	C₂²×D₄	1	2	yes	—
323	C₂⁵	C₂²×D₄	1	2	yes	—
324	C₂⁵	C₂²×D₄	1	2	yes	—
325	C₂⁵	C₂×#41	1	2	yes	—
326	C₂⁵	C₂×#41	1	4	yes	—
327	C₂⁵	C₂×#41	1	2	yes	—
328	C₂⁵	C₂×#41	1	4	yes	—
329	C₂⁵	C₂×#41	1	2	yes	—
330	C₂⁵	C₂×#41	1	2	yes	—
331	C₂⁵	C₂×#41	1	2	yes	—
332	C₂⁵	H(5,𝔽₂)	1	2	yes	—
333	C₂⁵	H(5,𝔽₂)	1	2	yes	—
334	C₂⁵	H(5,𝔽₂)	1	2	yes	—
335	C₂⁵	H(5,𝔽₂)	1	2	yes	—
336	C₂⁵	H(5,𝔽₂)	1	2	yes	—
337	C₂⁵	H(5,𝔽₂)	1	2	yes	—
338	C₂⁵	C₂⁵	1	1	yes	characteristic
339	C₂²×D₄	#121	1	16	yes	—
340	C₂²×D₄	#121	1	32	yes	complemented
341	C₂²×D₄	#127	1	16	yes	—
342	C₂³×C₄	#120	1	16	yes	complemented
343	C₂³×C₄	#120	1	16	yes	complemented
344	C₂³×C₄	C₂²×D₄	1	2	yes	—
345	C₂³×C₄	C₂²×D₄	1	4	yes	—
346	C₂³×C₄	C₂²×D₄	1	2	yes	—
347	C₂³×C₄	C₂²×D₄	1	4	yes	—
348	C₂³×C₄	C₂²×D₄	1	4	yes	—
349	C₂³×C₄	C₂²×D₄	1	2	yes	—
350	C₂³×C₄	C₂²×D₄	1	2	yes	—
351	C₂³×C₄	C₂²×D₄	1	4	yes	—
352	C₂³×C₄	C₂²×D₄	1	2	yes	—
353	C₂³×C₄	C₂²×D₄	1	2	yes	—
354	C₂³×C₄	C₂²×D₄	1	2	yes	—
355	C₂³×C₄	C₂²×D₄	1	2	yes	—
356	C₂³×C₄	C₂²×D₄	1	4	yes	—
357	C₂³×C₄	C₂²×D₄	1	2	yes	—
358	C₂³×C₄	C₂²×D₄	1	2	yes	—
359	C₂³×C₄	C₂²×D₄	1	2	yes	—
360	C₂³×C₄	C₂²×D₄	1	2	yes	—
361	C₂³×C₄	C₂²×D₄	1	2	yes	—
362	C₂³×C₄	C₂²×D₄	1	4	yes	—
363	C₂³×C₄	C₂²×D₄	1	4	yes	—
364	C₂³×C₄	C₂²×D₄	1	2	yes	—
365	C₂³×C₄	C₂²×D₄	1	4	yes	—
366	C₂³×C₄	C₂²×D₄	1	2	yes	—
367	C₂³×C₄	C₂²×D₄	1	2	yes	—
368	C₂³×C₄	C₂²×D₄	1	4	yes	—
369	C₂³×C₄	C₂²×D₄	1	4	yes	—
370	C₂³×C₄	C₂²×D₄	1	4	yes	—
371	C₂³×C₄	C₂²×D₄	1	4	yes	—
372	C₂³×C₄	C₂×#41	1	2	yes	—
373	C₂³×C₄	C₂×#41	1	4	yes	—
374	C₂³×C₄	H(5,𝔽₂)	1	4	yes	—
375	C₂³×C₄	H(5,𝔽₂)	1	4	yes	—
376	C₂³×C₄	H(5,𝔽₂)	1	4	yes	—
377	C₂³×C₄	H(5,𝔽₂)	1	4	yes	—
378	C₂×C₂²⋊C₄	#120	1	16	yes	complemented
379	C₂⁴	C₂×#120	1	4	yes	—
380	C₂⁴	C₂×#120	1	4	yes	—
381	C₂⁴	C₂×#120	1	4	yes	—
382	C₂⁴	C₂×#121	1	4	yes	—
383	C₂⁴	C₂×#121	1	4	yes	—
384	C₂⁴	C₂×#121	1	8	yes	—
385	C₂⁴	C₂×#121	1	8	yes	—
386	C₂⁴	C₂×#121	1	4	yes	—
387	C₂⁴	C₂×#121	1	4	yes	—
388	C₂⁴	C₂×#121	1	4	yes	—
389	C₂⁴	#525	1	8	yes	—
390	C₂⁴	#525	1	4	yes	—
391	C₂⁴	#525	1	4	yes	—
392	C₂⁴	C₂×#127	1	4	yes	—
393	C₂⁴	C₂×#127	1	4	yes	—
394	C₂⁴	#534	1	4	yes	—
395	C₂⁴	#534	1	4	yes	—
396	C₂⁴	#534	1	4	yes	—
397	C₂⁴	#535	1	4	yes	—
398	C₂⁴	#535	1	4	yes	—
399	C₂⁴	#535	1	4	yes	—
400	C₂⁴	#535	1	4	yes	—
401	C₂⁴	#538	1	4	yes	—
402	C₂⁴	#538	1	4	yes	—
403	C₂⁴	D₄²	1	4	yes	—
404	C₂⁴	D₄²	1	4	yes	—
405	C₂⁴	D₄²	1	4	yes	—
406	C₂⁴	D₄²	1	4	yes	—
407	C₂⁴	D₄²	1	4	yes	—
408	C₂⁴	D₄²	1	4	yes	—
409	C₂⁴	D₄²	1	4	yes	—
410	C₂⁴	D₄²	1	4	yes	—
411	C₂⁴	D₄²	1	4	yes	—
412	C₂⁴	D₄²	1	4	yes	—
413	C₂⁴	#546	1	4	yes	—
414	C₂⁴	#546	1	4	yes	—
415	C₂⁴	#546	1	4	yes	—
416	C₂⁴	#546	1	4	yes	—
417	C₂⁴	#546	1	4	yes	—
418	C₂⁴	#546	1	4	yes	—
419	C₂⁴	#546	1	4	yes	—
420	C₂⁴	#546	1	4	yes	—
421	C₂⁴	#560	1	4	yes	—
422	C₂⁴	H(3,𝔽₄)	1	4	yes	—
423	C₂⁴	C₂³×D₄	1	1	yes	characteristic
424	C₂⁴	C₂³×D₄	1	1	yes	characteristic
425	C₂⁴	C₂³×D₄	1	2	yes	—
426	C₂⁴	C₂³×D₄	1	1	yes	characteristic
427	C₂⁴	C₂³×D₄	1	1	yes	characteristic
428	C₂⁴	C₂³×D₄	1	1	yes	characteristic
429	C₂⁴	C₂³×D₄	1	1	yes	characteristic
430	C₂⁴	C₂³×D₄	1	1	yes	characteristic
431	C₂⁴	C₂²×#41	1	1	yes	characteristic
432	C₂⁴	C₂²×#41	1	2	yes	—
433	C₂⁴	C₂²×#41	1	1	yes	characteristic
434	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
435	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
436	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
437	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
439	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
440	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
441	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
442	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
443	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
444	C₂⁴	#585	1	2	yes	—
445	C₂⁴	#585	1	2	yes	—
446	C₂²×C₄	C₂×#120	1	4	yes	—
447	C₂²×C₄	C₂×#120	1	4	yes	—
448	C₂²×C₄	C₂×#120	1	4	yes	—
449	C₂²×C₄	C₂×#120	1	4	yes	—
450	C₂²×C₄	C₂×#120	1	8	yes	—
451	C₂²×C₄	C₂×#121	1	4	yes	—
452	C₂²×C₄	C₂×#121	1	8	yes	—
453	C₂²×C₄	C₂×#127	1	4	yes	—
454	C₂²×C₄	#534	1	4	yes	—
455	C₂²×C₄	#534	1	8	yes	—
456	C₂²×C₄	D₄²	1	8	yes	—
457	C₂²×C₄	D₄²	1	8	yes	—
458	C₂²×C₄	D₄²	1	8	yes	—
459	C₂²×C₄	D₄²	1	8	yes	—
460	C₂²×C₄	D₄²	1	8	yes	—
461	C₂²×C₄	#546	1	8	yes	—
462	C₂²×C₄	#546	1	8	yes	—
463	C₂³	#2408	1	8	yes	—
464	C₂³	#2408	1	8	yes	—
465	C₂³	#2410	1	8	yes	—
466	C₂³	#2410	1	8	yes	—
467	C₂³	#2424	1	8	yes	—
468	C₂³	#2424	1	8	yes	—
469	C₂³	#2433	1	8	yes	—
470	C₂³	#2433	1	8	yes	—
471	C₂³	#2539	1	8	yes	—
472	C₂³	#2669	1	8	yes	—
473	C₂³	#2670	1	8	yes	—
474	C₂³	#2670	1	8	yes	—
475	C₂³	#2678	1	8	yes	—
476	C₂³	#2678	1	8	yes	—
477	C₂³	#2679	1	8	yes	—
478	C₂³	#2847	1	8	yes	—
479	C₂³	C₂²×#120	1	1	yes	characteristic
480	C₂³	C₂²×#120	1	1	yes	characteristic
481	C₂³	C₂²×#120	1	1	yes	characteristic
482	C₂³	C₂²×#121	1	1	yes	characteristic
483	C₂³	C₂²×#121	1	2	yes	—
484	C₂³	C₂²×#121	1	1	yes	characteristic
485	C₂³	C₂×#525	1	2	yes	—
486	C₂³	C₂×#525	1	1	yes	characteristic
487	C₂³	C₂×#525	1	1	yes	characteristic
488	C₂³	C₂²×#127	1	1	yes	characteristic
489	C₂³	C₂×#534	1	1	yes	characteristic
490	C₂³	C₂×#534	1	1	yes	characteristic
491	C₂³	C₂×#534	1	1	yes	characteristic
492	C₂³	C₂×#534	1	1	yes	characteristic
493	C₂³	C₂×#534	1	2	yes	—
494	C₂³	C₂×#535	1	1	yes	characteristic
495	C₂³	C₂×#535	1	1	yes	characteristic
496	C₂³	C₂×#535	1	1	yes	characteristic
497	C₂³	C₂×#535	1	1	yes	characteristic
498	C₂³	#3449	1	1	yes	characteristic
499	C₂³	C₂×#538	1	1	yes	characteristic
500	C₂³	C₂×#538	1	1	yes	characteristic
501	C₂³	#3459	1	2	yes	—
502	C₂³	C₂×D₄²	1	2	yes	—
503	C₂³	C₂×D₄²	1	2	yes	—
504	C₂³	C₂×D₄²	1	1	yes	characteristic
505	C₂³	C₂×D₄²	1	2	yes	—
506	C₂³	C₂×D₄²	1	2	yes	—
507	C₂³	C₂×D₄²	1	1	yes	characteristic
508	C₂³	C₂×D₄²	1	1	yes	characteristic
509	C₂³	C₂×D₄²	1	2	yes	—
510	C₂³	C₂×D₄²	1	1	yes	characteristic
511	C₂³	C₂×D₄²	1	1	yes	characteristic
512	C₂³	C₂×D₄²	1	1	yes	characteristic
513	C₂³	C₂×D₄²	1	1	yes	characteristic
514	C₂³	C₂×D₄²	1	1	yes	characteristic
515	C₂³	C₂×D₄²	1	1	yes	characteristic
516	C₂³	C₂×D₄²	1	1	yes	characteristic
517	C₂³	C₂×#546	1	1	yes	characteristic
518	C₂³	C₂×#546	1	1	yes	characteristic
519	C₂³	C₂×#546	1	1	yes	characteristic
520	C₂³	C₂×#546	1	2	yes	—
521	C₂³	C₂×#546	1	1	yes	characteristic
522	C₂³	C₂×#546	1	2	yes	—
523	C₂³	C₂×#546	1	1	yes	characteristic
524	C₂³	C₂×#546	1	1	yes	characteristic
525	C₂³	C₂×#546	1	1	yes	characteristic
526	C₂³	C₂×#546	1	1	yes	characteristic
527	C₂³	D₄×#41	1	2	yes	—
528	C₂³	D₄×#41	1	2	yes	—
529	C₂³	D₄×#41	1	2	yes	—
530	C₂³	D₄×#41	1	2	yes	—
531	C₂³	#3481	1	2	yes	—
532	C₂³	#3484	1	1	yes	characteristic
533	C₂³	#3484	1	2	yes	—
534	C₂³	#3484	1	2	yes	—
535	C₂³	#3484	1	1	yes	characteristic
536	C₂³	#3484	1	2	yes	—
537	C₂³	#3484	1	1	yes	characteristic
538	C₂³	#3485	1	1	yes	characteristic
539	C₂³	#3488	1	2	yes	—
540	C₂³	#3488	1	2	yes	—
541	C₂³	#3488	1	2	yes	—
542	C₂³	#3488	1	2	yes	—
543	C₂³	#3488	1	2	yes	—
544	C₂³	#3490	1	2	yes	—
545	C₂³	#3490	1	2	yes	—
546	C₂³	#3490	1	2	yes	—
547	C₂³	#3496	1	2	yes	—
548	C₂³	#3496	1	2	yes	—
549	C₂³	#3496	1	2	yes	—
550	C₂³	#3496	1	2	yes	—
551	C₂³	#3496	1	2	yes	—
552	C₂³	#3498	1	2	yes	—
553	C₂³	#3498	1	2	yes	—
554	C₂³	#3498	1	2	yes	—
555	C₂³	#3498	1	2	yes	—
556	C₂³	#3500	1	2	yes	—
557	C₂³	#3505	1	2	yes	—
558	C₂³	#3513	1	2	yes	—
559	C₂³	#3514	1	2	yes	—
560	C₂³	#3519	1	2	yes	—
561	C₂³	#3519	1	2	yes	—
562	C₂³	#3519	1	2	yes	—
563	C₂³	#3519	1	2	yes	—
564	C₂³	C₂×#560	1	1	yes	characteristic
565	C₂³	C₂×H(3,𝔽₄)	1	1	yes	characteristic
566	C₂³	#3534	1	2	yes	—
567	C₂³	#3534	1	2	yes	—
568	C₂³	#3537	1	2	yes	—
569	C₂³	#3537	1	2	yes	—
570	C₂³	#3537	1	2	yes	—
571	C₂³	#3542	1	2	yes	—
572	C₂³	#3543	1	2	yes	—
573	C₂³	#3543	1	2	yes	—
574	C₂³	#3545	1	2	yes	—
575	C₂³	#3558	1	2	yes	—
576	C₂³	#3558	1	2	yes	—
577	C₂³	#3558	1	2	yes	—
578	C₂×C₄	#2403	1	8	yes	complemented
579	C₂×C₄	#2410	1	16	yes	complemented
580	C₂²	#15267	1	16	yes	complemented
581	C₂²	C₂×#2403	1	1	yes	characteristic
582	C₂²	C₂×#2410	1	1	yes	characteristic
583	C₂²	C₂×#2410	1	1	yes	characteristic
584	C₂²	C₂×#2410	1	2	yes	—
585	C₂²	C₂×#2424	1	1	yes	characteristic
586	C₂²	C₂×#2424	1	1	yes	characteristic
587	C₂²	#34655	1	2	yes	—
588	C₂²	C₂×#2408	1	1	yes	characteristic
589	C₂²	C₂×#2408	1	1	yes	characteristic
590	C₂²	C₂×#2433	1	1	yes	characteristic
591	C₂²	C₂×#2433	1	1	yes	characteristic
592	C₂²	#34736	1	1	yes	characteristic
593	C₂²	C₂×#2539	1	1	yes	characteristic
594	C₂²	#34981	1	1	yes	characteristic
595	C₂²	#34981	1	2	yes	—
596	C₂²	#34984	1	1	yes	characteristic
597	C₂²	#34990	1	2	yes	—
598	C₂²	#35000	1	1	yes	characteristic
599	C₂²	#35076	1	1	yes	characteristic
600	C₂²	#35250	1	1	yes	characteristic
601	C₂²	#35347	1	1	yes	characteristic
602	C₂²	#35361	1	2	yes	—
603	C₂²	#35513	1	2	yes	—
604	C₂²	#35527	1	1	yes	characteristic
605	C₂²	D₄×#120	1	1	yes	characteristic
606	C₂²	D₄×#120	1	1	yes	characteristic
607	C₂²	D₄×#120	1	1	yes	characteristic
608	C₂²	D₄×#121	1	2	yes	—
609	C₂²	D₄×#121	1	2	yes	—
610	C₂²	D₄×#121	1	2	yes	—
611	C₂²	D₄×#121	1	2	yes	—
612	C₂²	#36096	1	2	yes	—
613	C₂²	#36096	1	2	yes	—
614	C₂²	#36098	1	2	yes	—
615	C₂²	#36098	1	1	yes	characteristic
616	C₂²	#36098	1	2	yes	—
617	C₂²	#36098	1	1	yes	characteristic
618	C₂²	#36099	1	1	yes	characteristic
619	C₂²	D₄×#127	1	2	yes	—
620	C₂²	#36212	1	1	yes	characteristic
621	C₂²	#36214	1	2	yes	—
622	C₂²	#36258	1	2	yes	—
623	C₂²	#36260	1	2	yes	—
624	C₂²	#36316	1	1	yes	characteristic
625	C₂²	C₂×#2847	1	1	yes	characteristic
626	C₂²	#36717	1	1	yes	characteristic
627	C₂²	#36808	1	2	yes	—
628	C₂²	#36967	1	1	yes	characteristic
629	C₂²	#37129	1	2	yes	—
630	C₂²	#37646	1	1	yes	characteristic
631	C₂²	#37650	1	2	yes	—
632	C₂²	#37652	1	1	yes	characteristic
633	C₂²	#37672	1	2	yes	—
634	C₂²	#37672	1	2	yes	—
635	C₂²	#37674	1	2	yes	—
636	C₂²	#37677	1	2	yes	—
637	C₂²	#37716	1	2	yes	—
638	C₂²	#37778	1	2	yes	—
639	C₂²	#38020	1	1	yes	characteristic
640	C₂²	#38026	1	2	yes	—
641	C₂²	#38028	1	1	yes	characteristic
642	C₂²	#38080	1	2	yes	—
643	C₂²	#38420	1	2	yes	—
644	C₂²	#38424	1	2	yes	—
645	C₂²	#38424	1	2	yes	—
646	C₂²	#38564	1	2	yes	—
647	C₂²	#38949	1	2	yes	—
648	C₂²	#39332	1	1	yes	characteristic
649	C₂²	#39333	1	1	yes	characteristic
650	C₂²	#39336	1	1	yes	characteristic
651	C₂²	#39336	1	1	yes	characteristic
652	C₂²	#39358	1	2	yes	—
653	C₂²	#39358	1	2	yes	—
654	C₂²	#39358	1	2	yes	—
655	C₂²	#39412	1	2	yes	—
656	C₂²	#39412	1	2	yes	—
657	C₂²	#39430	1	2	yes	—
658	C₂²	#45444	1	2	yes	—
659	C₂²	#45732	1	2	yes	—
660	C₂²	#45977	1	2	yes	—
661	C₂²	#46089	1	2	yes	—
662	C₂²	C₂×#2669	1	1	yes	characteristic
663	C₂²	C₂×#2670	1	1	yes	characteristic
664	C₂²	C₂×#2670	1	1	yes	characteristic
665	C₂²	C₂×#2678	1	1	yes	characteristic
666	C₂²	C₂×#2678	1	1	yes	characteristic
667	C₂²	C₂×#2679	1	1	yes	characteristic
668	C₂²	#58997	1	2	yes	—
669	C₂²	#58997	1	2	yes	—
670	C₂²	#59095	1	2	yes	—
671	C₂²	#59095	1	2	yes	—
672	C₂²	#59123	1	2	yes	—
673	C₂²	#59126	1	2	yes	—
674	C₂²	#59126	1	2	yes	—
675	C₂²	#59131	1	2	yes	—
676	C₂²	#59408	1	2	yes	—
677	C₂²	#59800	1	2	yes	—
678	C₂²	#59808	1	2	yes	—
679	C₂²	#59814	1	2	yes	—
680	C₂	C₂×#15267	1	1	yes	characteristic
681	C₂	#612431	1	1	yes	characteristic
682	C₂	#612459	1	1	yes	characteristic
683	C₂	#612525	1	1	yes	characteristic
684	C₂	#616995	1	1	yes	characteristic
685	C₂	#617775	1	1	yes	characteristic
686	C₂	#626066	1	1	yes	characteristic
687	C₂	#647714	1	1	yes	characteristic
688	C₂	#647718	1	1	yes	characteristic
689	C₂	#647723	1	2	yes	—
690	C₂	#649038	1	1	yes	characteristic
691	C₂	#649106	1	2	yes	—
692	C₂	#649390	1	2	yes	—
693	C₂	#650532	1	2	yes	—
694	C₂	#674170	1	1	yes	characteristic
695	C₂	#845485	1	1	yes	characteristic
696	C₂	#845487	1	1	yes	characteristic
697	C₂	#846845	1	1	yes	characteristic
698	C₂	#846847	1	1	yes	characteristic
699	C₂	#855329	1	2	yes	—
700	C₂	#856657	1	2	yes	—
701	C₂	#874495	1	2	yes	—
702	C₂	#874584	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂²×#2410	C₂	semidirect
2. C₂²×#2403	C₂	semidirect
3. C₂³×#390	C₂	semidirect
4. C₂×#15267	C₂	semidirect
5. C₂×#14725	C₂	semidirect
6. C₂×#14719	C₂	semidirect
7. C₂×#14716	C₂	semidirect
8. C₂×#14716	C₂	semidirect
9. C₂×#14715	C₂	semidirect
10. C₂×#14698	C₂	semidirect
11. C₂×#13867	C₂	semidirect
12. #158362	C₂	semidirect
13. #158361	C₂	semidirect
14. #158317	C₂	semidirect
15. #156831	C₂	semidirect
16. #155066	C₂	semidirect
17. #154688	C₂	semidirect
18. #154671	C₂	semidirect
19. #154248	C₂	semidirect
20. #154195	C₂	semidirect
21. #154195	C₂	semidirect
22. #154095	C₂	semidirect
23. #154088	C₂	semidirect
32. C₂³×#120	C₂²	semidirect
33. C₂³×#120	C₂²	semidirect
34. C₂⁴×C₄⋊C₄	C₂²	semidirect
37. C₂⁴×C₂²⋊C₄	C₂²	semidirect
38. C₂⁴×C₂²⋊C₄	C₂²	semidirect
39. C₂⁴×C₄²	C₂²	semidirect
40. C₂²×#394	C₂²	semidirect
41. C₂²×#394	C₂²	semidirect
42. C₂²×#394	C₂²	semidirect
43. C₂²×#394	C₂²	semidirect
47. C₂²×#392	C₂²	semidirect
48. C₂²×#392	C₂²	semidirect
49. C₂²×#392	C₂²	semidirect
50. C₂²×#392	C₂²	semidirect
51. C₂²×#392	C₂²	semidirect
54. C₂²×#390	C₂²	semidirect
55. C₂²×#390	C₂²	semidirect
56. C₂²×#390	C₂²	semidirect
66. C₂²×#386	C₂²	semidirect
67. C₂²×#386	C₂²	semidirect
68. C₂²×#386	C₂²	semidirect
69. C₂²×#386	C₂²	semidirect
70. C₂²×#385	C₂²	semidirect
71. C₂²×#380	C₂²	semidirect
74. C₂²×#379	C₂²	semidirect
75. C₂²×#379	C₂²	semidirect
76. C₂²×#379	C₂²	semidirect
77. C₂×#1441	C₂²	semidirect
78. C₂×#1440	C₂²	semidirect
79. C₂×#1439	C₂²	semidirect
80. C₂×#1439	C₂²	semidirect
81. C₂×#1439	C₂²	semidirect
82. C₂×#1439	C₂²	semidirect
83. C₂×#1439	C₂²	semidirect
84. C₂×#1439	C₂²	semidirect
85. C₂×#1439	C₂²	semidirect
86. C₂×#1439	C₂²	semidirect
87. C₂×#1439	C₂²	semidirect
89. C₂×#1438	C₂²	semidirect
90. C₂×#1438	C₂²	semidirect
91. C₂×#1438	C₂²	semidirect
92. C₂×#1438	C₂²	semidirect
93. C₂×#1438	C₂²	semidirect
94. C₂×#1438	C₂²	semidirect
95. C₂×#1438	C₂²	semidirect
96. C₂×#1438	C₂²	semidirect
97. C₂×#1438	C₂²	semidirect
98. C₂×#1438	C₂²	semidirect
99. C₂×#1438	C₂²	semidirect
100. C₂×#1438	C₂²	semidirect
101. C₂×#1437	C₂²	semidirect
102. C₂×#1437	C₂²	semidirect
103. C₂×#1437	C₂²	semidirect
104. C₂×#1437	C₂²	semidirect
105. C₂×C₄⋊#95	C₂²	semidirect
106. C₂×C₂²⋊#95	C₂²	semidirect
107. C₂×C₂²⋊#95	C₂²	semidirect
108. C₂×C₂²⋊#95	C₂²	semidirect
109. C₂×C₂²⋊#95	C₂²	semidirect
110. C₂×C₂²⋊#95	C₂²	semidirect
111. C₂×C₂²⋊#95	C₂²	semidirect
112. C₂×C₂²⋊#95	C₂²	semidirect
113. #7557	C₂²	semidirect
114. #7557	C₂²	semidirect
115. #7555	C₂²	semidirect
116. #7555	C₂²	semidirect
117. #7555	C₂²	semidirect
118. #7555	C₂²	semidirect
119. #7555	C₂²	semidirect
120. #7555	C₂²	semidirect
121. #7554	C₂²	semidirect
122. #7554	C₂²	semidirect
126. C₂⁴×D₄	D₄	semidirect
147. C₂²×#121	D₄	semidirect
153. C₂³×C₂²⋊C₄	D₄	semidirect
199. C₂×#390	D₄	semidirect
200. C₂×#386	D₄	semidirect
201. C₂×#386	D₄	semidirect
202. C₂×#386	D₄	semidirect
203. C₂×#386	D₄	semidirect
250. C₂³×D₄	C₂×D₄	semidirect
277. C₂²×C₄⋊C₄	C₂×D₄	semidirect
278. C₂²×C₄⋊C₄	C₂×D₄	semidirect
291. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
292. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
293. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
294. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
295. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
296. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
297. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
298. C₂²×C₄²	C₂×D₄	semidirect
301. C₂×#95	C₂×D₄	semidirect
302. C₂×#95	C₂×D₄	semidirect
303. C₂×#95	C₂×D₄	semidirect
340. C₂²×D₄	#121	semidirect
342. C₂³×C₄	#120	semidirect
343. C₂³×C₄	#120	semidirect
378. C₂×C₂²⋊C₄	#120	semidirect
578. C₂×C₄	#2403	semidirect
579. C₂×C₄	#2410	semidirect
580. C₂²	#15267	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#2410	2
C₂²×#2403	2
C₂³×#390	2
C₂×#15267	2
C₂×#14725	2
C₂×#14719	2
C₂×#14716	2
C₂×#14715	2
C₂×#14698	2
C₂×#13867	2
#158362	2
#158361	2
#158317	2
#156831	2
#155066	2
#154688	2
#154671	2
#154248	2
#154195	2
#154095	2
#154088	2