Subgroups — #72334998

Order 1024.

At least 6263 conjugacy classes of subgroups; only the 1725 normal subgroups are shown.

The subgroup lattice has 652 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15315	C₂	1	2	yes	maximal, complemented
3	C₂×#15267	C₂	1	2	yes	maximal, complemented
4	C₂×#14762	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14732	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14724	C₂	1	2	yes	maximal, complemented
7	C₂×#14715	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14715	C₂	1	2	yes	maximal, complemented
9	C₂×#14715	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13902	C₂	1	1	yes	maximal, characteristic, complemented
11	#158327	C₂	1	1	yes	maximal, characteristic, complemented
12	#158314	C₂	1	1	yes	maximal, characteristic, complemented
13	#156824	C₂	1	1	yes	maximal, characteristic, complemented
14	#156706	C₂	1	1	yes	maximal, characteristic, complemented
15	#156688	C₂	1	2	yes	maximal, complemented
16	#156684	C₂	1	2	yes	maximal, complemented
17	#155625	C₂	1	1	yes	maximal, characteristic, complemented
18	#154729	C₂	1	2	yes	maximal, complemented
19	#154671	C₂	1	2	yes	maximal, complemented
20	#154634	C₂	1	1	yes	maximal, characteristic, complemented
21	#154446	C₂	1	1	yes	maximal, characteristic, complemented
22	#154094	C₂	1	1	yes	maximal, characteristic, complemented
23	#153868	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂⁵×D₄	C₂²	1	2	yes	—
25	C₂⁵×D₄	C₂²	1	1	yes	characteristic
26	C₂⁵×D₄	C₂²	1	1	yes	characteristic
27	C₂³×#127	C₂²	1	1	yes	characteristic
28	C₂³×#121	C₂²	1	1	yes	characteristic
29	C₂³×#121	C₂²	1	2	yes	—
30	C₂³×#121	C₂²	1	1	yes	characteristic
31	C₂³×#120	C₂²	1	2	yes	—
32	C₂³×#120	C₂²	1	2	yes	—
33	C₂³×#120	C₂²	1	2	yes	complemented
34	C₂³×#120	C₂²	1	2	yes	complemented
35	C₂³×C₄×D₄	C₂²	1	1	yes	characteristic
36	C₂³×C₄×D₄	C₂²	1	1	yes	characteristic
37	C₂²×#396	C₂²	1	1	yes	characteristic, complemented
38	C₂²×#394	C₂²	1	1	yes	characteristic
39	C₂²×#394	C₂²	1	1	yes	characteristic, complemented
40	C₂²×#394	C₂²	1	2	yes	complemented
41	C₂²×#394	C₂²	1	2	yes	complemented
42	C₂²×#394	C₂²	1	2	yes	complemented
43	C₂²×#392	C₂²	1	1	yes	characteristic
44	C₂²×#392	C₂²	1	1	yes	characteristic
45	C₂²×#392	C₂²	1	2	yes	complemented
46	C₂²×#392	C₂²	1	2	yes	complemented
47	C₂²×#392	C₂²	1	2	yes	complemented
48	C₂²×#392	C₂²	1	2	yes	complemented
49	C₂²×#392	C₂²	1	2	yes	complemented
50	C₂²×#392	C₂²	1	1	yes	characteristic, complemented
51	C₂²×#392	C₂²	1	2	yes	complemented
52	C₂²×#392	C₂²	1	1	yes	characteristic, complemented
53	C₂²×#390	C₂²	1	2	yes	complemented
54	C₂²×#390	C₂²	1	2	yes	complemented
55	C₂²×#390	C₂²	1	2	yes	complemented
56	C₂²×#386	C₂²	1	1	yes	characteristic, complemented
57	C₂²×#386	C₂²	1	2	yes	complemented
58	C₂²×#386	C₂²	1	1	yes	characteristic, complemented
59	C₂²×#385	C₂²	1	2	yes	complemented
60	C₂²×#380	C₂²	1	1	yes	characteristic, complemented
61	C₂²×#379	C₂²	1	2	yes	complemented
62	C₂²×#379	C₂²	1	2	yes	complemented
63	C₂²×#379	C₂²	1	2	yes	complemented
64	C₂²×#379	C₂²	1	2	yes	complemented
65	C₂²×#379	C₂²	1	2	yes	complemented
66	C₂²×#379	C₂²	1	2	yes	complemented
67	C₂²×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
68	C₂×#1444	C₂²	1	1	yes	characteristic, complemented
69	C₂×#1441	C₂²	1	1	yes	characteristic, complemented
70	C₂×#1440	C₂²	1	1	yes	characteristic, complemented
71	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
72	C₂×#1439	C₂²	1	2	yes	complemented
73	C₂×#1439	C₂²	1	2	yes	complemented
74	C₂×#1439	C₂²	1	2	yes	complemented
75	C₂×#1439	C₂²	1	1	yes	characteristic, complemented
76	C₂×#1439	C₂²	1	2	yes	complemented
77	C₂×#1438	C₂²	1	1	yes	characteristic
78	C₂×#1438	C₂²	1	1	yes	characteristic
79	C₂×#1438	C₂²	1	2	yes	—
80	C₂×#1438	C₂²	1	1	yes	characteristic
81	C₂×#1438	C₂²	1	2	yes	complemented
82	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
83	C₂×#1438	C₂²	1	2	yes	complemented
84	C₂×#1438	C₂²	1	2	yes	complemented
85	C₂×#1438	C₂²	1	2	yes	complemented
86	C₂×#1438	C₂²	1	2	yes	complemented
87	C₂×#1438	C₂²	1	2	yes	complemented
88	C₂×#1438	C₂²	1	2	yes	complemented
89	C₂×#1438	C₂²	1	2	yes	complemented
90	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
91	C₂×#1438	C₂²	1	2	yes	complemented
92	C₂×#1438	C₂²	1	2	yes	complemented
93	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
94	C₂×#1438	C₂²	1	2	yes	complemented
95	C₂×#1438	C₂²	1	2	yes	complemented
96	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
97	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
98	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
99	C₂×#1438	C₂²	1	2	yes	complemented
100	C₂×#1438	C₂²	1	2	yes	complemented
101	C₂×#1438	C₂²	1	2	yes	complemented
102	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
103	C₂×#1437	C₂²	1	1	yes	characteristic, complemented
104	C₂×#1437	C₂²	1	2	yes	complemented
105	C₂×#1437	C₂²	1	2	yes	complemented
106	C₂×#1436	C₂²	1	2	yes	complemented
107	C₂×#1436	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₂²⋊#95	C₂²	1	2	yes	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	2	yes	complemented
112	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic, complemented
114	#7557	C₂²	1	1	yes	characteristic, complemented
115	#7557	C₂²	1	1	yes	characteristic, 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	1	yes	characteristic, complemented
122	#7554	C₂²	1	1	yes	characteristic, complemented
123	C₂⁷	C₂³	1	2	yes	—
124	C₂⁷	C₂³	1	2	yes	—
125	C₂⁴×D₄	D₄	1	8	yes	complemented
126	C₂⁴×D₄	C₂³	1	1	yes	characteristic
127	C₂⁴×D₄	C₂³	1	1	yes	characteristic
128	C₂⁴×D₄	C₂³	1	2	yes	—
129	C₂⁴×D₄	C₂³	1	1	yes	characteristic
130	C₂⁴×D₄	C₂³	1	1	yes	characteristic
131	C₂⁴×D₄	C₂³	1	2	yes	—
132	C₂⁴×D₄	C₂³	1	2	yes	—
133	C₂⁴×D₄	C₂³	1	2	yes	—
134	C₂⁴×D₄	C₂³	1	2	yes	—
135	C₂⁴×D₄	C₂³	1	1	yes	characteristic
136	C₂⁴×D₄	C₂³	1	1	yes	characteristic
137	C₂⁴×D₄	C₂³	1	2	yes	—
138	C₂⁴×D₄	C₂³	1	2	yes	—
139	C₂⁴×D₄	C₂³	1	2	yes	—
140	C₂⁴×D₄	C₂³	1	2	yes	—
141	C₂⁵×C₄	C₂³	1	1	yes	characteristic
142	C₂⁵×C₄	C₂³	1	2	yes	—
143	C₂⁵×C₄	C₂³	1	1	yes	characteristic
144	C₂²×#121	D₄	1	8	yes	complemented
145	C₂²×#121	D₄	1	16	yes	complemented
146	C₂²×#120	D₄	1	16	yes	complemented
147	C₂²×C₄×D₄	D₄	1	8	yes	complemented
148	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
155	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
156	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
157	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
158	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
159	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
162	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
169	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
174	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
183	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
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×C₄²	C₂³	1	1	yes	characteristic
197	C₂³×C₄²	C₂³	1	2	yes	—
198	C₂²×#95	C₂³	1	1	yes	characteristic
199	C₂²×#95	C₂³	1	1	yes	characteristic
200	C₂²×#95	C₂³	1	1	yes	characteristic
201	C₂²×#95	C₂³	1	1	yes	characteristic
202	C₂²×#95	C₂³	1	1	yes	characteristic
203	C₂²×#95	C₂³	1	1	yes	characteristic
204	C₂²×#95	C₂³	1	1	yes	characteristic
205	C₂²×#95	C₂³	1	1	yes	characteristic
206	C₂²×#95	C₂³	1	1	yes	characteristic
207	C₂²×#95	C₂³	1	1	yes	characteristic
208	C₂²×#95	C₂³	1	2	yes	—
209	C₂²×#95	C₂³	1	1	yes	characteristic
210	C₂²×#95	C₂³	1	2	yes	—
211	C₂²×#95	C₂³	1	2	yes	—
212	C₂²×#95	C₂³	1	2	yes	—
213	C₂²×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
220	C₂²×#95	C₂³	1	1	yes	characteristic
221	C₂²×#95	C₂³	1	2	yes	—
222	C₂²×#95	C₂³	1	2	yes	—
223	C₂²×#95	C₂³	1	1	yes	characteristic
224	C₂²×#95	C₂³	1	2	yes	—
225	C₂²×#95	C₂³	1	2	yes	—
226	C₂²×#95	C₂³	1	1	yes	characteristic
227	#1438	D₄	1	8	yes	complemented
228	#1438	D₄	1	16	yes	complemented
229	C₂⁶	C₂×D₄	1	8	yes	—
230	C₂⁶	C₂×D₄	1	8	yes	—
231	C₂⁶	C₂⁴	1	1	yes	characteristic
232	C₂⁶	C₂⁴	1	2	yes	—
233	C₂⁶	C₂⁴	1	2	yes	—
234	C₂⁶	C₂⁴	1	1	yes	characteristic
235	C₂⁶	C₂⁴	1	1	yes	characteristic
236	C₂⁶	C₂⁴	1	2	yes	—
237	C₂³×D₄	C₂×D₄	1	4	yes	—
238	C₂³×D₄	C₂×D₄	1	4	yes	—
239	C₂³×D₄	C₂×D₄	1	4	yes	—
240	C₂³×D₄	C₂×D₄	1	8	yes	—
241	C₂³×D₄	C₂×D₄	1	8	yes	—
242	C₂³×D₄	C₂×D₄	1	8	yes	—
243	C₂³×D₄	C₂×D₄	1	8	yes	—
244	C₂³×D₄	C₂×D₄	1	8	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	8	yes	—
251	C₂³×D₄	#41	1	4	yes	—
252	C₂⁴×C₄	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
258	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
259	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
260	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
261	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
262	C₂⁴×C₄	C₂⁴	1	2	yes	—
263	C₂⁴×C₄	C₂⁴	1	2	yes	—
264	C₂⁴×C₄	C₂⁴	1	2	yes	—
265	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
266	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
267	C₂⁴×C₄	C₂⁴	1	2	yes	—
268	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
269	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
270	C₂⁴×C₄	C₂⁴	1	2	yes	—
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	C₂²×C₄⋊C₄	C₂×D₄	1	4	yes	—
275	C₂²×C₄⋊C₄	C₂×D₄	1	8	yes	—
276	C₂²×C₄⋊C₄	C₂×D₄	1	4	yes	—
277	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
278	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
279	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
280	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
281	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
282	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
283	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
284	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
285	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
286	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
287	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
288	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
289	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
290	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
291	C₂²×C₄²	C₂×D₄	1	4	yes	—
292	C₂×#95	C₂×D₄	1	4	yes	complemented
293	C₂×#95	C₂×D₄	1	8	yes	complemented
294	C₂×#95	C₂×D₄	1	8	yes	complemented
295	C₂×#95	C₂×D₄	1	4	yes	complemented
296	C₂⁵	C₂²×D₄	1	4	yes	—
297	C₂⁵	C₂²×D₄	1	4	yes	—
298	C₂⁵	C₂²×D₄	1	4	yes	—
299	C₂⁵	C₂²×D₄	1	4	yes	—
300	C₂⁵	C₂²×D₄	1	4	yes	—
301	C₂⁵	C₂²×D₄	1	4	yes	—
302	C₂⁵	C₂²×D₄	1	4	yes	—
303	C₂⁵	C₂²×D₄	1	2	yes	—
304	C₂⁵	C₂²×D₄	1	2	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	4	yes	—
309	C₂⁵	C₂²×D₄	1	4	yes	—
310	C₂⁵	C₂²×D₄	1	4	yes	—
311	C₂⁵	C₂²×D₄	1	4	yes	—
312	C₂⁵	C₂²×D₄	1	4	yes	—
313	C₂⁵	C₂×#41	1	4	yes	—
314	C₂⁵	H(5,𝔽₂)	1	2	yes	—
315	C₂⁵	H(5,𝔽₂)	1	4	yes	—
316	C₂⁵	H(5,𝔽₂)	1	4	yes	—
317	C₂⁵	H(5,𝔽₂)	1	2	yes	—
318	C₂⁵	H(5,𝔽₂)	1	4	yes	—
319	C₂⁵	H(5,𝔽₂)	1	2	yes	—
320	C₂⁵	C₂⁵	1	1	yes	characteristic
321	C₂²×D₄	#120	1	32	yes	complemented
322	C₂²×D₄	#121	1	16	yes	—
323	C₂²×D₄	#127	1	16	yes	—
324	C₂³×C₄	#120	1	16	yes	complemented
325	C₂³×C₄	C₂²×D₄	1	2	yes	—
326	C₂³×C₄	C₂²×D₄	1	4	yes	—
327	C₂³×C₄	C₂²×D₄	1	2	yes	—
328	C₂³×C₄	C₂²×D₄	1	4	yes	—
329	C₂³×C₄	C₂²×D₄	1	4	yes	—
330	C₂³×C₄	C₂²×D₄	1	2	yes	—
331	C₂³×C₄	C₂²×D₄	1	4	yes	—
332	C₂³×C₄	C₂²×D₄	1	4	yes	—
333	C₂³×C₄	C₂²×D₄	1	4	yes	—
334	C₂³×C₄	C₂²×D₄	1	2	yes	—
335	C₂³×C₄	C₂²×D₄	1	4	yes	—
336	C₂³×C₄	C₂²×D₄	1	4	yes	—
337	C₂³×C₄	C₂²×D₄	1	4	yes	—
338	C₂³×C₄	C₂²×D₄	1	4	yes	—
339	C₂³×C₄	C₂²×D₄	1	2	yes	—
340	C₂³×C₄	C₂²×D₄	1	2	yes	—
341	C₂³×C₄	C₂²×D₄	1	4	yes	—
342	C₂³×C₄	C₂²×D₄	1	4	yes	—
343	C₂³×C₄	C₂²×D₄	1	2	yes	—
344	C₂³×C₄	C₂²×D₄	1	2	yes	—
345	C₂³×C₄	C₂²×D₄	1	2	yes	—
346	C₂³×C₄	C₂²×D₄	1	4	yes	—
347	C₂³×C₄	C₂²×D₄	1	2	yes	—
348	C₂³×C₄	C₂²×D₄	1	2	yes	—
349	C₂³×C₄	C₂²×D₄	1	2	yes	—
350	C₂³×C₄	C₂²×D₄	1	4	yes	—
351	C₂³×C₄	C₂×#41	1	2	yes	—
352	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
353	C₂³×C₄	H(5,𝔽₂)	1	4	yes	—
354	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
355	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
356	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
357	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
358	C₂×C₄⋊C₄	#120	1	16	yes	complemented
359	C₂×C₂²⋊C₄	#120	1	16	yes	complemented
360	C₂×C₂²⋊C₄	#120	1	32	yes	complemented
361	C₂⁴	C₂×#120	1	8	yes	—
362	C₂⁴	C₂×#120	1	8	yes	—
363	C₂⁴	C₂×#120	1	8	yes	—
364	C₂⁴	C₂×#120	1	4	yes	—
365	C₂⁴	C₂×#120	1	4	yes	—
366	C₂⁴	C₂×#121	1	8	yes	—
367	C₂⁴	C₂×#127	1	4	yes	—
368	C₂⁴	C₂×#127	1	4	yes	—
369	C₂⁴	#534	1	8	yes	—
370	C₂⁴	#535	1	4	yes	—
371	C₂⁴	#535	1	4	yes	—
372	C₂⁴	D₄²	1	8	yes	—
373	C₂⁴	D₄²	1	8	yes	—
374	C₂⁴	D₄²	1	8	yes	—
375	C₂⁴	D₄²	1	8	yes	—
376	C₂⁴	D₄²	1	8	yes	—
377	C₂⁴	D₄²	1	8	yes	—
378	C₂⁴	#546	1	8	yes	—
379	C₂⁴	#546	1	8	yes	—
380	C₂⁴	C₂³×D₄	1	1	yes	characteristic
381	C₂⁴	C₂³×D₄	1	1	yes	characteristic
382	C₂⁴	C₂³×D₄	1	2	yes	—
383	C₂⁴	C₂³×D₄	1	1	yes	characteristic
384	C₂⁴	C₂³×D₄	1	2	yes	—
385	C₂⁴	C₂³×D₄	1	1	yes	characteristic
386	C₂⁴	C₂³×D₄	1	2	yes	—
387	C₂⁴	C₂²×#41	1	1	yes	characteristic
388	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
389	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
390	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
391	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
392	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
393	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
394	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
395	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
396	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
397	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
398	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
399	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
400	C₂⁴	#585	1	2	yes	—
401	C₂⁴	#585	1	1	yes	characteristic
402	C₂⁴	#585	1	1	yes	characteristic
403	C₂²×C₄	C₂×#120	1	4	yes	—
404	C₂²×C₄	C₂×#120	1	4	yes	—
405	C₂²×C₄	C₂×#120	1	8	yes	—
406	C₂²×C₄	C₂×#120	1	8	yes	—
407	C₂²×C₄	C₂×#120	1	4	yes	—
408	C₂²×C₄	C₂×#120	1	8	yes	—
409	C₂²×C₄	C₂×#120	1	4	yes	—
410	C₂²×C₄	C₂×#120	1	4	yes	—
411	C₂²×C₄	C₂×#120	1	4	yes	—
412	C₂²×C₄	C₂×#120	1	4	yes	—
413	C₂²×C₄	C₂×#121	1	4	yes	—
414	C₂²×C₄	C₂×#127	1	4	yes	—
415	C₂²×C₄	#534	1	4	yes	—
416	C₂²×C₄	#535	1	4	yes	—
417	C₂²×C₄	D₄²	1	4	yes	—
418	C₂²×C₄	D₄²	1	4	yes	—
419	C₂²×C₄	D₄²	1	8	yes	—
420	C₂²×C₄	D₄²	1	8	yes	—
421	C₂²×C₄	D₄²	1	8	yes	complemented
422	C₂²×C₄	#546	1	4	yes	—
423	C₂²×C₄	#546	1	4	yes	—
424	C₂³	#2410	1	16	yes	—
425	C₂³	#2433	1	8	yes	—
426	C₂³	#2433	1	8	yes	—
427	C₂³	C₂²×#120	1	1	yes	characteristic
428	C₂³	C₂²×#120	1	1	yes	characteristic
429	C₂³	C₂²×#120	1	2	yes	—
430	C₂³	C₂²×#120	1	2	yes	—
431	C₂³	C₂²×#120	1	1	yes	characteristic
432	C₂³	C₂²×#121	1	1	yes	characteristic
433	C₂³	C₂²×#127	1	1	yes	characteristic
434	C₂³	C₂×#534	1	2	yes	—
435	C₂³	C₂×#534	1	1	yes	characteristic
436	C₂³	C₂×#535	1	1	yes	characteristic
437	C₂³	C₂×#535	1	1	yes	characteristic
438	C₂³	C₂×#535	1	1	yes	characteristic
439	C₂³	C₂×D₄²	1	2	yes	—
440	C₂³	C₂×D₄²	1	2	yes	—
441	C₂³	C₂×D₄²	1	2	yes	—
442	C₂³	C₂×D₄²	1	1	yes	characteristic
443	C₂³	C₂×D₄²	1	2	yes	—
444	C₂³	C₂×D₄²	1	2	yes	—
445	C₂³	C₂×D₄²	1	2	yes	—
446	C₂³	C₂×D₄²	1	1	yes	characteristic
447	C₂³	C₂×D₄²	1	2	yes	—
448	C₂³	C₂×D₄²	1	2	yes	—
449	C₂³	C₂×D₄²	1	2	yes	—
450	C₂³	C₂×#546	1	2	yes	—
451	C₂³	C₂×#546	1	1	yes	characteristic
452	C₂³	C₂×#546	1	2	yes	—
453	C₂³	C₂×#546	1	1	yes	characteristic
454	C₂³	D₄×#41	1	2	yes	—
455	C₂³	#3484	1	2	yes	—
456	C₂³	#3484	1	1	yes	characteristic
457	C₂³	#3484	1	2	yes	—
458	C₂³	#3484	1	2	yes	—
459	C₂³	#3484	1	2	yes	—
460	C₂³	#3484	1	1	yes	characteristic
461	C₂³	#3484	1	1	yes	characteristic
462	C₂³	#3484	1	1	yes	characteristic
463	C₂³	#3484	1	1	yes	characteristic
464	C₂³	#3484	1	1	yes	characteristic
465	C₂³	#3484	1	1	yes	characteristic
466	C₂³	#3484	1	2	yes	—
467	C₂³	#3484	1	2	yes	—
468	C₂³	#3484	1	2	yes	—
469	C₂³	#3484	1	2	yes	—
470	C₂³	#3484	1	2	yes	—
471	C₂³	#3484	1	2	yes	—
472	C₂³	#3484	1	2	yes	—
473	C₂³	#3484	1	1	yes	characteristic
474	C₂³	#3484	1	2	yes	—
475	C₂³	#3485	1	1	yes	characteristic
476	C₂³	#3485	1	2	yes	—
477	C₂³	#3488	1	2	yes	—
478	C₂³	#3488	1	2	yes	—
479	C₂³	#3488	1	2	yes	—
480	C₂³	#3488	1	1	yes	characteristic
481	C₂³	#3488	1	1	yes	characteristic
482	C₂³	#3488	1	1	yes	characteristic
483	C₂³	#3488	1	2	yes	—
484	C₂³	#3488	1	1	yes	characteristic
485	C₂³	#3488	1	1	yes	characteristic
486	C₂³	#3488	1	2	yes	—
487	C₂³	#3488	1	2	yes	—
488	C₂³	#3496	1	2	yes	—
489	C₂³	#3496	1	1	yes	characteristic
490	C₂³	#3496	1	2	yes	—
491	C₂³	#3496	1	2	yes	—
492	C₂³	#3496	1	2	yes	—
493	C₂³	#3498	1	1	yes	characteristic
494	C₂³	#3498	1	2	yes	—
495	C₂³	#3498	1	2	yes	—
496	C₂³	#3498	1	1	yes	characteristic
497	C₂³	#3500	1	1	yes	characteristic
498	C₂³	#3500	1	2	yes	—
499	C₂³	#3513	1	1	yes	characteristic
500	C₂³	#3514	1	1	yes	characteristic
501	C₂³	#3519	1	2	yes	—
502	C₂³	#3519	1	1	yes	characteristic
503	C₂³	#3519	1	1	yes	characteristic
504	C₂³	#3532	1	2	yes	—
505	C₂³	#3532	1	2	yes	—
506	C₂³	#3532	1	2	yes	—
507	C₂³	#3534	1	2	yes	—
508	C₂³	#3534	1	2	yes	—
509	C₂³	#3534	1	2	yes	—
510	C₂³	#3534	1	2	yes	—
511	C₂³	#3537	1	2	yes	—
512	C₂³	#3537	1	1	yes	characteristic
513	C₂³	#3537	1	2	yes	—
514	C₂³	#3537	1	2	yes	—
515	C₂³	#3542	1	1	yes	characteristic
516	C₂³	#3542	1	2	yes	—
517	C₂³	#3543	1	2	yes	—
518	C₂³	#3543	1	1	yes	characteristic
519	C₂³	#3543	1	1	yes	characteristic
520	C₂³	#3546	1	1	yes	characteristic
521	C₂³	#3546	1	1	yes	characteristic
522	C₂³	#3549	1	1	yes	characteristic
523	C₂³	#3558	1	1	yes	characteristic
524	C₂³	#3558	1	2	yes	—
525	C₂³	#3558	1	2	yes	—
526	C₂×C₄	#2410	1	8	yes	—
527	C₂×C₄	#2433	1	8	yes	—
528	C₂×C₄	#2846	1	8	yes	—
529	C₂²	C₂×#2410	1	2	yes	—
530	C₂²	C₂×#2410	1	1	yes	characteristic
531	C₂²	C₂×#2433	1	1	yes	characteristic
532	C₂²	C₂×#2433	1	1	yes	characteristic
533	C₂²	C₂×#2433	1	1	yes	characteristic
534	C₂²	#34980	1	2	yes	—
535	C₂²	#34980	1	1	yes	characteristic
536	C₂²	#35222	1	1	yes	characteristic
537	C₂²	#35222	1	1	yes	characteristic
538	C₂²	#35222	1	1	yes	characteristic
539	C₂²	#35512	1	1	yes	characteristic
540	C₂²	#35512	1	2	yes	—
541	C₂²	#35513	1	1	yes	characteristic
542	C₂²	#35513	1	2	yes	—
543	C₂²	#35680	1	2	yes	—
544	C₂²	#35680	1	1	yes	characteristic
545	C₂²	#35691	1	1	yes	characteristic
546	C₂²	#35750	1	2	yes	—
547	C₂²	#35750	1	1	yes	characteristic
548	C₂²	#35761	1	1	yes	characteristic
549	C₂²	#35921	1	1	yes	characteristic
550	C₂²	#35921	1	1	yes	characteristic
551	C₂²	#36082	1	1	yes	characteristic
552	C₂²	#36091	1	1	yes	characteristic
553	C₂²	D₄×#120	1	2	yes	—
554	C₂²	D₄×#120	1	2	yes	—
555	C₂²	D₄×#120	1	1	yes	characteristic
556	C₂²	D₄×#120	1	1	yes	characteristic
557	C₂²	D₄×#120	1	2	yes	—
558	C₂²	D₄×#120	1	2	yes	—
559	C₂²	D₄×#120	1	2	yes	—
560	C₂²	D₄×#121	1	2	yes	—
561	C₂²	D₄×#127	1	1	yes	characteristic
562	C₂²	#36152	1	2	yes	—
563	C₂²	#36152	1	1	yes	characteristic
564	C₂²	#36152	1	1	yes	characteristic
565	C₂²	#36260	1	1	yes	characteristic
566	C₂²	C₂×#2846	1	1	yes	characteristic
567	C₂²	#37644	1	2	yes	—
568	C₂²	#37646	1	2	yes	—
569	C₂²	#37650	1	1	yes	characteristic
570	C₂²	#37677	1	1	yes	characteristic
571	C₂²	#38026	1	1	yes	characteristic
572	C₂²	#38080	1	1	yes	characteristic
573	C₂²	#38910	1	1	yes	characteristic
574	C₂²	#39342	1	1	yes	characteristic
575	C₂²	#39358	1	2	yes	—
576	C₂²	#40484	1	2	yes	—
577	C₂²	#40486	1	2	yes	—
578	C₂²	#40490	1	1	yes	characteristic
579	C₂²	#40494	1	1	yes	characteristic
580	C₂²	#40590	1	1	yes	characteristic
581	C₂²	#40590	1	1	yes	characteristic
582	C₂²	#42426	1	1	yes	characteristic
583	C₂²	#42430	1	1	yes	characteristic
584	C₂²	#42474	1	1	yes	characteristic
585	C₂²	#42475	1	1	yes	characteristic
586	C₂²	#42996	1	2	yes	—
587	C₂²	#43001	1	2	yes	—
588	C₂²	#43019	1	2	yes	—
589	C₂²	#43023	1	2	yes	—
590	C₂²	#43023	1	2	yes	—
591	C₂²	#43095	1	2	yes	—
592	C₂²	#43098	1	2	yes	—
593	C₂²	#43098	1	2	yes	—
594	C₂²	#43098	1	2	yes	—
595	C₂²	#43102	1	2	yes	—
596	C₂²	#43886	1	2	yes	—
597	C₂²	#43886	1	2	yes	—
598	C₂²	#43889	1	2	yes	—
599	C₂²	#43893	1	2	yes	—
600	C₂²	#44868	1	2	yes	—
601	C₂²	#44870	1	2	yes	—
602	C₂²	#44877	1	2	yes	—
603	C₂²	#44877	1	1	yes	characteristic
604	C₂²	#44927	1	2	yes	—
605	C₂²	#44927	1	1	yes	characteristic
606	C₂²	#44929	1	1	yes	characteristic
607	C₂²	#45352	1	1	yes	characteristic
608	C₂²	#47827	1	2	yes	—
609	C₂²	#47829	1	2	yes	—
610	C₂²	#47838	1	2	yes	—
611	C₂²	#47838	1	2	yes	—
612	C₂²	#47838	1	2	yes	—
613	C₂²	#47928	1	2	yes	—
614	C₂²	#47929	1	2	yes	—
615	C₂²	#47942	1	2	yes	—
616	C₂²	#47946	1	2	yes	—
617	C₂²	#49554	1	2	yes	—
618	C₂²	#58990	1	2	yes	—
619	C₂²	#58994	1	2	yes	—
620	C₂²	#58997	1	2	yes	—
621	C₂²	#58997	1	2	yes	—
622	C₂²	#58997	1	2	yes	—
623	C₂²	#59004	1	2	yes	—
624	C₂²	#59095	1	2	yes	—
625	C₂²	#59123	1	2	yes	—
626	C₂²	#59126	1	2	yes	—
627	C₂²	#59131	1	2	yes	—
628	C₂	#612433	1	1	yes	characteristic
629	C₂	#612801	1	1	yes	characteristic
630	C₂	#649106	1	1	yes	characteristic
631	C₂	#686267	1	1	yes	characteristic
632	C₂	#719140	1	1	yes	characteristic
633	C₂	#772794	1	2	yes	—
634	C₂	#773154	1	2	yes	—
635	C₂	#773780	1	1	yes	characteristic
636	C₂	#773781	1	1	yes	characteristic
637	C₂	#773786	1	1	yes	characteristic
638	C₂	#773787	1	1	yes	characteristic
639	C₂	#1258513	1	2	yes	—
640	C₂	#1258514	1	2	yes	—
641	C₂	#1259290	1	1	yes	characteristic
642	C₂	#1259674	1	1	yes	characteristic
643	C₂	#1260058	1	1	yes	characteristic
644	C₂	#1260442	1	1	yes	characteristic
645	C₂	#1418370	1	2	yes	—
646	C₂	#1418393	1	2	yes	—
647	C₂	#1418394	1	2	yes	—
648	C₂	#1419356	1	2	yes	—
649	C₂	#4417868	1	1	yes	characteristic
650	C₂	#4929082	1	1	yes	characteristic

	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. C₂³×D₄²	C₂	semidirect
2. C₂×#15315	C₂	semidirect
3. C₂×#15267	C₂	semidirect
4. C₂×#14762	C₂	semidirect
5. C₂×#14732	C₂	semidirect
6. C₂×#14724	C₂	semidirect
7. C₂×#14715	C₂	semidirect
8. C₂×#14715	C₂	semidirect
9. C₂×#14715	C₂	semidirect
10. C₂×#13902	C₂	semidirect
11. #158327	C₂	semidirect
12. #158314	C₂	semidirect
13. #156824	C₂	semidirect
14. #156706	C₂	semidirect
15. #156688	C₂	semidirect
16. #156684	C₂	semidirect
17. #155625	C₂	semidirect
18. #154729	C₂	semidirect
19. #154671	C₂	semidirect
20. #154634	C₂	semidirect
21. #154446	C₂	semidirect
22. #154094	C₂	semidirect
23. #153868	C₂	semidirect
33. C₂³×#120	C₂²	semidirect
34. C₂³×#120	C₂²	semidirect
37. C₂²×#396	C₂²	semidirect
39. C₂²×#394	C₂²	semidirect
40. C₂²×#394	C₂²	semidirect
41. C₂²×#394	C₂²	semidirect
42. C₂²×#394	C₂²	semidirect
45. C₂²×#392	C₂²	semidirect
46. C₂²×#392	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
52. C₂²×#392	C₂²	semidirect
53. C₂²×#390	C₂²	semidirect
54. C₂²×#390	C₂²	semidirect
55. C₂²×#390	C₂²	semidirect
56. C₂²×#386	C₂²	semidirect
57. C₂²×#386	C₂²	semidirect
58. C₂²×#386	C₂²	semidirect
59. C₂²×#385	C₂²	semidirect
60. C₂²×#380	C₂²	semidirect
61. C₂²×#379	C₂²	semidirect
62. C₂²×#379	C₂²	semidirect
63. C₂²×#379	C₂²	semidirect
64. C₂²×#379	C₂²	semidirect
65. C₂²×#379	C₂²	semidirect
66. C₂²×#379	C₂²	semidirect
67. C₂²×C₄×C₂²⋊C₄	C₂²	semidirect
68. C₂×#1444	C₂²	semidirect
69. C₂×#1441	C₂²	semidirect
70. C₂×#1440	C₂²	semidirect
71. C₂×#1439	C₂²	semidirect
72. C₂×#1439	C₂²	semidirect
73. C₂×#1439	C₂²	semidirect
74. C₂×#1439	C₂²	semidirect
75. C₂×#1439	C₂²	semidirect
76. C₂×#1439	C₂²	semidirect
81. C₂×#1438	C₂²	semidirect
82. C₂×#1438	C₂²	semidirect
83. C₂×#1438	C₂²	semidirect
84. C₂×#1438	C₂²	semidirect
85. C₂×#1438	C₂²	semidirect
86. C₂×#1438	C₂²	semidirect
87. C₂×#1438	C₂²	semidirect
88. C₂×#1438	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×#1438	C₂²	semidirect
102. C₂×#1438	C₂²	semidirect
103. C₂×#1437	C₂²	semidirect
104. C₂×#1437	C₂²	semidirect
105. C₂×#1437	C₂²	semidirect
106. C₂×#1436	C₂²	semidirect
107. C₂×#1436	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. C₂×C₂²⋊#95	C₂²	semidirect
114. #7557	C₂²	semidirect
115. #7557	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
125. C₂⁴×D₄	D₄	semidirect
144. C₂²×#121	D₄	semidirect
145. C₂²×#121	D₄	semidirect
146. C₂²×#120	D₄	semidirect
147. C₂²×C₄×D₄	D₄	semidirect
227. #1438	D₄	semidirect
228. #1438	D₄	semidirect
285. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
286. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
287. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
288. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
289. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
290. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
292. C₂×#95	C₂×D₄	semidirect
293. C₂×#95	C₂×D₄	semidirect
294. C₂×#95	C₂×D₄	semidirect
295. C₂×#95	C₂×D₄	semidirect
321. C₂²×D₄	#120	semidirect
324. C₂³×C₄	#120	semidirect
358. C₂×C₄⋊C₄	#120	semidirect
359. C₂×C₂²⋊C₄	#120	semidirect
360. C₂×C₂²⋊C₄	#120	semidirect
421. C₂²×C₄	D₄²	semidirect

Maximal subgroups

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

subgroup	index
C₂³×D₄²	2
C₂×#15315	2
C₂×#15267	2
C₂×#14762	2
C₂×#14732	2
C₂×#14724	2
C₂×#14715	2
C₂×#13902	2
#158327	2
#158314	2
#156824	2
#156706	2
#156688	2
#156684	2
#155625	2
#154729	2
#154671	2
#154634	2
#154446	2
#154094	2
#153868	2