Subgroups — #72335722

Order 1024.

At least 6241 conjugacy classes of subgroups; only the 1633 normal subgroups are shown.

The subgroup lattice has 675 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	C₂³×#392	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15320	C₂	1	2	yes	maximal, complemented
4	C₂×#14725	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14715	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14715	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#13971	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13902	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#13867	C₂	1	1	yes	maximal, characteristic, complemented
10	#158997	C₂	1	2	yes	maximal, complemented
11	#158818	C₂	1	2	yes	maximal, complemented
12	#158317	C₂	1	2	yes	maximal, complemented
13	#158142	C₂	1	2	yes	maximal, complemented
14	#156706	C₂	1	2	yes	maximal, complemented
15	#156694	C₂	1	2	yes	maximal, complemented
16	#155066	C₂	1	2	yes	maximal, complemented
17	#154214	C₂	1	1	yes	maximal, characteristic, complemented
18	#154195	C₂	1	1	yes	maximal, characteristic, complemented
19	#154195	C₂	1	1	yes	maximal, characteristic, complemented
20	#154096	C₂	1	1	yes	maximal, characteristic, complemented
21	#154094	C₂	1	1	yes	maximal, characteristic, complemented
22	#153851	C₂	1	1	yes	maximal, characteristic, complemented
23	#153775	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂⁵×D₄	C₂²	1	1	yes	characteristic
25	C₂⁵×D₄	C₂²	1	1	yes	characteristic
26	C₂⁵×D₄	C₂²	1	1	yes	characteristic
27	C₂³×#121	C₂²	1	1	yes	characteristic, complemented
28	C₂³×#121	C₂²	1	1	yes	characteristic, complemented
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	C₂⁴×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂⁴×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂⁴×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂⁴×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×#394	C₂²	1	1	yes	characteristic, complemented
37	C₂²×#394	C₂²	1	1	yes	characteristic, complemented
38	C₂²×#394	C₂²	1	2	yes	complemented
39	C₂²×#392	C₂²	1	2	yes	—
40	C₂²×#392	C₂²	1	2	yes	—
41	C₂²×#392	C₂²	1	2	yes	—
42	C₂²×#392	C₂²	1	2	yes	—
43	C₂²×#392	C₂²	1	1	yes	characteristic, complemented
44	C₂²×#392	C₂²	1	1	yes	characteristic, complemented
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×#390	C₂²	1	2	yes	complemented
50	C₂²×#390	C₂²	1	2	yes	complemented
51	C₂²×#388	C₂²	1	2	yes	complemented
52	C₂²×#386	C₂²	1	1	yes	characteristic
53	C₂²×#386	C₂²	1	1	yes	characteristic
54	C₂²×#386	C₂²	1	1	yes	characteristic
55	C₂²×#386	C₂²	1	1	yes	characteristic
56	C₂²×#386	C₂²	1	1	yes	characteristic, complemented
57	C₂²×#386	C₂²	1	1	yes	characteristic, complemented
58	C₂²×#386	C₂²	1	2	yes	complemented
59	C₂²×#386	C₂²	1	2	yes	complemented
60	C₂²×#385	C₂²	1	1	yes	characteristic
61	C₂²×#380	C₂²	1	1	yes	characteristic
62	C₂²×#379	C₂²	1	1	yes	characteristic
63	C₂²×#379	C₂²	1	1	yes	characteristic
64	C₂²×#379	C₂²	1	1	yes	characteristic
65	C₂²×#379	C₂²	1	1	yes	characteristic
66	C₂²×#379	C₂²	1	1	yes	characteristic
67	C₂²×#379	C₂²	1	1	yes	characteristic
68	C₂²×#379	C₂²	1	1	yes	characteristic
69	C₂²×#379	C₂²	1	1	yes	characteristic
70	C₂²×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
71	C₂³×#95	C₂²	1	1	yes	characteristic
72	C₂×#1441	C₂²	1	2	yes	complemented
73	C₂×#1440	C₂²	1	2	yes	complemented
74	C₂×#1440	C₂²	1	2	yes	complemented
75	C₂×#1440	C₂²	1	2	yes	complemented
76	C₂×#1440	C₂²	1	2	yes	complemented
77	C₂×#1439	C₂²	1	2	yes	complemented
78	C₂×#1439	C₂²	1	2	yes	complemented
79	C₂×#1438	C₂²	1	2	yes	complemented
80	C₂×#1438	C₂²	1	2	yes	complemented
81	C₂×#1438	C₂²	1	2	yes	complemented
82	C₂×#1438	C₂²	1	2	yes	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	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×#1437	C₂²	1	2	yes	complemented
97	C₂×#1437	C₂²	1	2	yes	complemented
98	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
99	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
100	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
101	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
102	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
103	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
104	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
105	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
106	C₂×C₂²⋊#95	C₂²	1	1	yes	characteristic
107	C₂×C₂²⋊#95	C₂²	1	2	yes	complemented
108	C₂×C₂²⋊#95	C₂²	1	2	yes	complemented
109	#7557	C₂²	1	2	yes	complemented
110	#7557	C₂²	1	2	yes	complemented
111	#7556	C₂²	1	2	yes	complemented
112	#7556	C₂²	1	2	yes	complemented
113	#7555	C₂²	1	2	yes	complemented
114	#7555	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	#7555	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	2	yes	—
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	1	yes	characteristic
134	C₂⁴×D₄	C₂³	1	1	yes	characteristic
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	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	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
151	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
153	C₂³×C₂²⋊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	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	1	yes	characteristic
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	2	yes	—
170	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
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	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	1	yes	characteristic
181	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
183	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
191	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂³×C₄²	C₂³	1	2	yes	—
194	C₂×#392	D₄	1	16	yes	complemented
195	C₂×#386	D₄	1	8	yes	complemented
196	C₂×#385	D₄	1	8	yes	complemented
197	C₂×#379	D₄	1	8	yes	complemented
198	C₂×#379	D₄	1	8	yes	complemented
199	C₂²×#95	C₂³	1	2	yes	—
200	C₂²×#95	C₂³	1	2	yes	—
201	C₂²×#95	C₂³	1	2	yes	—
202	C₂²×#95	C₂³	1	2	yes	—
203	C₂²×#95	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
214	C₂²×#95	C₂³	1	2	yes	—
215	C₂²×#95	C₂³	1	2	yes	—
216	C₂²×#95	C₂³	1	1	yes	characteristic
217	C₂²×#95	C₂³	1	1	yes	characteristic
218	C₂²×#95	C₂³	1	1	yes	characteristic
219	C₂²×#95	C₂³	1	1	yes	characteristic
220	C₂²×#95	C₂³	1	2	yes	—
221	C₂²×#95	C₂³	1	2	yes	—
222	C₂²×#95	C₂³	1	2	yes	—
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	C₂⁶	C₂×D₄	1	4	yes	—
229	C₂⁶	C₂×D₄	1	4	yes	—
230	C₂⁶	C₂×D₄	1	4	yes	—
231	C₂⁶	C₂×D₄	1	4	yes	—
232	C₂⁶	#41	1	4	yes	—
233	C₂⁶	C₂⁴	1	1	yes	characteristic
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	C₂³×D₄	C₂×D₄	1	4	yes	—
241	C₂³×D₄	C₂×D₄	1	8	yes	—
242	C₂³×D₄	C₂×D₄	1	4	yes	—
243	C₂³×D₄	C₂×D₄	1	4	yes	—
244	C₂³×D₄	C₂×D₄	1	8	yes	—
245	C₂³×D₄	C₂×D₄	1	4	yes	—
246	C₂³×D₄	C₂×D₄	1	8	yes	—
247	C₂³×D₄	C₂×D₄	1	4	yes	—
248	C₂⁴×C₄	C₂×D₄	1	4	yes	—
249	C₂⁴×C₄	C₂×D₄	1	4	yes	—
250	C₂⁴×C₄	C₂×D₄	1	4	yes	—
251	C₂⁴×C₄	#41	1	4	yes	—
252	C₂⁴×C₄	#41	1	4	yes	—
253	C₂⁴×C₄	C₂⁴	1	2	yes	—
254	C₂⁴×C₄	C₂⁴	1	2	yes	—
255	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
256	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
257	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
258	C₂⁴×C₄	C₂⁴	1	2	yes	—
259	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
260	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
261	C₂⁴×C₄	C₂⁴	1	2	yes	—
262	C₂⁴×C₄	C₂⁴	1	2	yes	—
263	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
264	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
265	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
266	C₂⁴×C₄	C₂⁴	1	2	yes	—
267	C₂⁴×C₄	C₂⁴	1	2	yes	—
268	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄⋊C₄	C₂×D₄	1	4	yes	complemented
270	C₂²×C₄⋊C₄	C₂×D₄	1	4	yes	complemented
271	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
272	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
273	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
274	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
275	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
276	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
277	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
278	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
279	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
280	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
281	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
282	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
283	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
284	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
285	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
286	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
287	C₂²×C₂²⋊C₄	#41	1	4	yes	—
288	C₂×#95	C₂×D₄	1	8	yes	—
289	C₂×#95	C₂×D₄	1	4	yes	complemented
290	C₂×#95	C₂×D₄	1	4	yes	complemented
291	C₂×#95	C₂×D₄	1	4	yes	complemented
292	C₂×#95	C₂×D₄	1	4	yes	complemented
293	C₂⁵	#121	1	16	yes	—
294	C₂⁵	C₂²×D₄	1	2	yes	—
295	C₂⁵	C₂²×D₄	1	2	yes	—
296	C₂⁵	C₂²×D₄	1	4	yes	—
297	C₂⁵	C₂²×D₄	1	2	yes	—
298	C₂⁵	C₂²×D₄	1	2	yes	—
299	C₂⁵	C₂²×D₄	1	2	yes	—
300	C₂⁵	C₂²×D₄	1	4	yes	—
301	C₂⁵	C₂²×D₄	1	4	yes	—
302	C₂⁵	C₂²×D₄	1	2	yes	—
303	C₂⁵	C₂²×D₄	1	4	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	2	yes	—
308	C₂⁵	C₂²×D₄	1	2	yes	—
309	C₂⁵	C₂²×D₄	1	2	yes	—
310	C₂⁵	C₂×#41	1	2	yes	—
311	C₂⁵	C₂×#41	1	2	yes	—
312	C₂⁵	C₂×#41	1	2	yes	—
313	C₂⁵	C₂×#41	1	2	yes	—
314	C₂⁵	C₂×#41	1	2	yes	—
315	C₂⁵	C₂×#41	1	2	yes	—
316	C₂⁵	H(5,𝔽₂)	1	4	yes	—
317	C₂⁵	H(5,𝔽₂)	1	4	yes	—
318	C₂⁵	H(5,𝔽₂)	1	4	yes	—
319	C₂⁵	H(5,𝔽₂)	1	2	yes	—
320	C₂⁵	H(5,𝔽₂)	1	2	yes	—
321	C₂⁵	H(5,𝔽₂)	1	2	yes	—
322	C₂⁵	H(5,𝔽₂)	1	2	yes	—
323	C₂⁵	H(5,𝔽₂)	1	2	yes	—
324	C₂⁵	H(5,𝔽₂)	1	2	yes	—
325	C₂⁵	C₂⁵	1	1	yes	characteristic
326	C₂²×D₄	#120	1	16	yes	complemented
327	C₂³×C₄	#120	1	16	yes	—
328	C₂³×C₄	C₂²×D₄	1	2	yes	—
329	C₂³×C₄	C₂²×D₄	1	4	yes	—
330	C₂³×C₄	C₂²×D₄	1	4	yes	—
331	C₂³×C₄	C₂²×D₄	1	2	yes	—
332	C₂³×C₄	C₂²×D₄	1	2	yes	—
333	C₂³×C₄	C₂²×D₄	1	2	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	2	yes	—
338	C₂³×C₄	C₂²×D₄	1	2	yes	—
339	C₂³×C₄	C₂²×D₄	1	2	yes	—
340	C₂³×C₄	C₂²×D₄	1	2	yes	—
341	C₂³×C₄	C₂²×D₄	1	2	yes	—
342	C₂³×C₄	C₂²×D₄	1	2	yes	—
343	C₂³×C₄	C₂²×D₄	1	2	yes	—
344	C₂³×C₄	C₂²×D₄	1	4	yes	—
345	C₂³×C₄	C₂²×D₄	1	4	yes	—
346	C₂³×C₄	C₂²×D₄	1	2	yes	—
347	C₂³×C₄	C₂²×D₄	1	2	yes	—
348	C₂³×C₄	C₂²×D₄	1	4	yes	—
349	C₂³×C₄	C₂²×D₄	1	2	yes	—
350	C₂³×C₄	C₂×#41	1	2	yes	—
351	C₂³×C₄	C₂×#41	1	2	yes	—
352	C₂³×C₄	C₂×#41	1	4	yes	—
353	C₂³×C₄	C₂×#41	1	4	yes	—
354	C₂³×C₄	H(5,𝔽₂)	1	4	yes	—
355	C₂³×C₄	H(5,𝔽₂)	1	4	yes	—
356	C₂³×C₄	H(5,𝔽₂)	1	4	yes	—
357	C₂×C₂²⋊C₄	#121	1	16	yes	—
358	C₂⁴	C₂×#120	1	4	yes	—
359	C₂⁴	C₂×#120	1	4	yes	—
360	C₂⁴	C₂×#120	1	4	yes	—
361	C₂⁴	C₂×#121	1	4	yes	—
362	C₂⁴	C₂×#121	1	4	yes	—
363	C₂⁴	C₂×#121	1	4	yes	—
364	C₂⁴	C₂×#121	1	4	yes	—
365	C₂⁴	#525	1	4	yes	—
366	C₂⁴	#532	1	4	yes	—
367	C₂⁴	#532	1	4	yes	—
368	C₂⁴	#534	1	4	yes	—
369	C₂⁴	#534	1	4	yes	—
370	C₂⁴	#534	1	4	yes	—
371	C₂⁴	#534	1	4	yes	—
372	C₂⁴	#535	1	4	yes	—
373	C₂⁴	#535	1	4	yes	—
374	C₂⁴	#535	1	4	yes	—
375	C₂⁴	#538	1	4	yes	—
376	C₂⁴	#538	1	4	yes	—
377	C₂⁴	#540	1	4	yes	—
378	C₂⁴	#540	1	4	yes	—
379	C₂⁴	D₄²	1	8	yes	—
380	C₂⁴	D₄²	1	8	yes	—
381	C₂⁴	D₄²	1	4	yes	—
382	C₂⁴	D₄²	1	4	yes	—
383	C₂⁴	D₄²	1	4	yes	—
384	C₂⁴	D₄²	1	4	yes	—
385	C₂⁴	D₄²	1	4	yes	—
386	C₂⁴	#546	1	8	yes	—
387	C₂⁴	#546	1	4	yes	—
388	C₂⁴	#546	1	4	yes	—
389	C₂⁴	#546	1	4	yes	—
390	C₂⁴	#546	1	4	yes	—
391	C₂⁴	#546	1	4	yes	—
392	C₂⁴	#546	1	4	yes	—
393	C₂⁴	#546	1	4	yes	—
394	C₂⁴	#546	1	4	yes	—
395	C₂⁴	#550	1	4	yes	—
396	C₂⁴	#550	1	4	yes	—
397	C₂⁴	#553	1	4	yes	—
398	C₂⁴	#553	1	4	yes	—
399	C₂⁴	#555	1	4	yes	—
400	C₂⁴	#560	1	4	yes	—
401	C₂⁴	#560	1	4	yes	—
402	C₂⁴	C₂³×D₄	1	1	yes	characteristic
403	C₂⁴	C₂³×D₄	1	1	yes	characteristic
404	C₂⁴	C₂³×D₄	1	1	yes	characteristic
405	C₂⁴	C₂³×D₄	1	2	yes	—
406	C₂⁴	C₂³×D₄	1	1	yes	characteristic
407	C₂⁴	C₂³×D₄	1	1	yes	characteristic
408	C₂⁴	C₂²×#41	1	1	yes	characteristic
409	C₂⁴	C₂²×#41	1	1	yes	characteristic
410	C₂⁴	C₂²×#41	1	1	yes	characteristic
411	C₂⁴	C₂²×#41	1	1	yes	characteristic
412	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
413	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
415	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
416	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
417	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
418	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
419	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
420	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
421	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
422	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
423	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
424	C₂⁴	#585	1	2	yes	—
425	C₂²×C₄	C₂×#120	1	4	yes	—
426	C₂²×C₄	C₂×#120	1	4	yes	—
427	C₂²×C₄	C₂×#120	1	4	yes	—
428	C₂²×C₄	C₂×#121	1	4	yes	—
429	C₂²×C₄	C₂×#121	1	4	yes	—
430	C₂²×C₄	#534	1	4	yes	—
431	C₂²×C₄	D₄²	1	8	yes	—
432	C₂²×C₄	D₄²	1	8	yes	—
433	C₂²×C₄	#546	1	8	yes	—
434	C₂²×C₄	#546	1	8	yes	—
435	C₂³	#2408	1	8	yes	—
436	C₂³	#2410	1	8	yes	—
437	C₂³	#2410	1	8	yes	—
438	C₂³	#2414	1	8	yes	—
439	C₂³	#2424	1	8	yes	—
440	C₂³	#2428	1	8	yes	—
441	C₂³	#2431	1	8	yes	—
442	C₂³	#2464	1	8	yes	—
443	C₂³	#2543	1	8	yes	—
444	C₂³	#2555	1	8	yes	—
445	C₂³	#2669	1	8	yes	—
446	C₂³	#2673	1	8	yes	—
447	C₂³	#2678	1	8	yes	—
448	C₂³	#2699	1	8	yes	—
449	C₂³	#2703	1	8	yes	—
450	C₂³	#2714	1	8	yes	—
451	C₂³	C₂²×#120	1	1	yes	characteristic
452	C₂³	C₂²×#120	1	1	yes	characteristic
453	C₂³	C₂²×#121	1	1	yes	characteristic
454	C₂³	C₂²×#121	1	1	yes	characteristic
455	C₂³	C₂×#525	1	1	yes	characteristic
456	C₂³	C₂×#532	1	1	yes	characteristic
457	C₂³	C₂×#532	1	1	yes	characteristic
458	C₂³	C₂×#534	1	1	yes	characteristic
459	C₂³	C₂×#534	1	1	yes	characteristic
460	C₂³	C₂×#534	1	1	yes	characteristic
461	C₂³	C₂×#534	1	1	yes	characteristic
462	C₂³	C₂×#534	1	1	yes	characteristic
463	C₂³	C₂×#535	1	1	yes	characteristic
464	C₂³	C₂×#535	1	1	yes	characteristic
465	C₂³	C₂×#535	1	1	yes	characteristic
466	C₂³	C₂×#538	1	1	yes	characteristic
467	C₂³	C₂×#538	1	1	yes	characteristic
468	C₂³	C₂×#540	1	1	yes	characteristic
469	C₂³	C₂×#540	1	1	yes	characteristic
470	C₂³	C₂×D₄²	1	2	yes	—
471	C₂³	C₂×D₄²	1	1	yes	characteristic
472	C₂³	C₂×D₄²	1	1	yes	characteristic
473	C₂³	C₂×D₄²	1	2	yes	—
474	C₂³	C₂×D₄²	1	2	yes	—
475	C₂³	C₂×D₄²	1	2	yes	—
476	C₂³	C₂×D₄²	1	1	yes	characteristic
477	C₂³	C₂×D₄²	1	1	yes	characteristic
478	C₂³	C₂×D₄²	1	1	yes	characteristic
479	C₂³	C₂×#546	1	1	yes	characteristic
480	C₂³	C₂×#546	1	1	yes	characteristic
481	C₂³	C₂×#546	1	2	yes	—
482	C₂³	C₂×#546	1	2	yes	—
483	C₂³	C₂×#546	1	1	yes	characteristic
484	C₂³	C₂×#546	1	1	yes	characteristic
485	C₂³	C₂×#546	1	2	yes	—
486	C₂³	C₂×#546	1	1	yes	characteristic
487	C₂³	C₂×#546	1	1	yes	characteristic
488	C₂³	C₂×#546	1	1	yes	characteristic
489	C₂³	C₂×#546	1	1	yes	characteristic
490	C₂³	C₂×#550	1	1	yes	characteristic
491	C₂³	C₂×#550	1	1	yes	characteristic
492	C₂³	D₄×#41	1	2	yes	—
493	C₂³	C₂×#553	1	1	yes	characteristic
494	C₂³	C₂×#553	1	1	yes	characteristic
495	C₂³	C₂×#555	1	1	yes	characteristic
496	C₂³	#3484	1	2	yes	—
497	C₂³	#3484	1	2	yes	—
498	C₂³	#3484	1	2	yes	—
499	C₂³	#3484	1	1	yes	characteristic
500	C₂³	#3484	1	1	yes	characteristic
501	C₂³	#3484	1	2	yes	—
502	C₂³	#3484	1	2	yes	—
503	C₂³	#3484	1	1	yes	characteristic
504	C₂³	#3484	1	2	yes	—
505	C₂³	#3484	1	2	yes	—
506	C₂³	#3484	1	2	yes	—
507	C₂³	#3484	1	2	yes	—
508	C₂³	#3484	1	2	yes	—
509	C₂³	#3484	1	2	yes	—
510	C₂³	#3485	1	1	yes	characteristic
511	C₂³	#3488	1	2	yes	—
512	C₂³	#3488	1	2	yes	—
513	C₂³	#3488	1	2	yes	—
514	C₂³	#3490	1	2	yes	—
515	C₂³	#3490	1	2	yes	—
516	C₂³	#3490	1	2	yes	—
517	C₂³	#3490	1	2	yes	—
518	C₂³	#3494	1	2	yes	—
519	C₂³	#3494	1	2	yes	—
520	C₂³	#3496	1	2	yes	—
521	C₂³	#3496	1	2	yes	—
522	C₂³	#3498	1	2	yes	—
523	C₂³	#3498	1	2	yes	—
524	C₂³	#3505	1	2	yes	—
525	C₂³	#3508	1	2	yes	—
526	C₂³	#3508	1	2	yes	—
527	C₂³	#3519	1	2	yes	—
528	C₂³	#3519	1	2	yes	—
529	C₂³	#3519	1	2	yes	—
530	C₂³	C₂×#560	1	1	yes	characteristic
531	C₂³	C₂×#560	1	1	yes	characteristic
532	C₂³	#3532	1	2	yes	—
533	C₂³	#3532	1	2	yes	—
534	C₂³	#3532	1	2	yes	—
535	C₂³	#3532	1	2	yes	—
536	C₂³	#3532	1	2	yes	—
537	C₂³	#3532	1	2	yes	—
538	C₂³	#3532	1	2	yes	—
539	C₂³	#3532	1	2	yes	—
540	C₂³	#3534	1	2	yes	—
541	C₂³	#3534	1	2	yes	—
542	C₂³	#3537	1	2	yes	—
543	C₂³	#3537	1	2	yes	—
544	C₂³	#3537	1	2	yes	—
545	C₂³	#3542	1	2	yes	—
546	C₂³	#3542	1	2	yes	—
547	C₂³	#3542	1	2	yes	—
548	C₂³	#3543	1	2	yes	—
549	C₂³	#3543	1	2	yes	—
550	C₂×C₄	#2403	1	8	yes	—
551	C₂²	#15320	1	16	yes	complemented
552	C₂²	C₂×#2403	1	1	yes	characteristic
553	C₂²	C₂×#2410	1	1	yes	characteristic
554	C₂²	C₂×#2410	1	1	yes	characteristic
555	C₂²	C₂×#2424	1	1	yes	characteristic
556	C₂²	C₂×#2408	1	1	yes	characteristic
557	C₂²	C₂×#2464	1	1	yes	characteristic
558	C₂²	C₂×#2428	1	1	yes	characteristic
559	C₂²	C₂×#2414	1	1	yes	characteristic
560	C₂²	C₂×#2431	1	1	yes	characteristic
561	C₂²	C₂×#2543	1	1	yes	characteristic
562	C₂²	C₂×#2555	1	1	yes	characteristic
563	C₂²	#34980	1	1	yes	characteristic
564	C₂²	#34980	1	1	yes	characteristic
565	C₂²	#34981	1	1	yes	characteristic
566	C₂²	#35348	1	1	yes	characteristic
567	C₂²	#35358	1	1	yes	characteristic
568	C₂²	#35512	1	1	yes	characteristic
569	C₂²	#35527	1	1	yes	characteristic
570	C₂²	#35681	1	2	yes	—
571	C₂²	#35691	1	2	yes	—
572	C₂²	#35694	1	2	yes	—
573	C₂²	#35922	1	2	yes	—
574	C₂²	D₄×#120	1	1	yes	characteristic
575	C₂²	D₄×#121	1	2	yes	—
576	C₂²	#36098	1	2	yes	—
577	C₂²	#36121	1	2	yes	—
578	C₂²	#36123	1	2	yes	—
579	C₂²	#36152	1	1	yes	characteristic
580	C₂²	#36152	1	1	yes	characteristic
581	C₂²	#36212	1	1	yes	characteristic
582	C₂²	#36714	1	1	yes	characteristic
583	C₂²	#36715	1	1	yes	characteristic
584	C₂²	#37436	1	1	yes	characteristic
585	C₂²	#37644	1	1	yes	characteristic
586	C₂²	#37644	1	1	yes	characteristic
587	C₂²	#37645	1	2	yes	—
588	C₂²	#37650	1	2	yes	—
589	C₂²	#37660	1	2	yes	—
590	C₂²	#37660	1	2	yes	—
591	C₂²	#37662	1	2	yes	—
592	C₂²	#37672	1	2	yes	—
593	C₂²	#37674	1	2	yes	—
594	C₂²	#37722	1	2	yes	—
595	C₂²	#37832	1	1	yes	characteristic
596	C₂²	#37832	1	1	yes	characteristic
597	C₂²	#37834	1	1	yes	characteristic
598	C₂²	#37834	1	1	yes	characteristic
599	C₂²	#38020	1	1	yes	characteristic
600	C₂²	#38020	1	1	yes	characteristic
601	C₂²	#38904	1	1	yes	characteristic
602	C₂²	#39338	1	1	yes	characteristic
603	C₂²	#39464	1	1	yes	characteristic
604	C₂²	#39464	1	1	yes	characteristic
605	C₂²	#40485	1	2	yes	—
606	C₂²	#40490	1	2	yes	—
607	C₂²	#40537	1	2	yes	—
608	C₂²	#40540	1	2	yes	—
609	C₂²	#40584	1	2	yes	—
610	C₂²	#40588	1	2	yes	—
611	C₂²	#40730	1	2	yes	—
612	C₂²	#41962	1	2	yes	—
613	C₂²	#42996	1	2	yes	—
614	C₂²	#43001	1	2	yes	—
615	C₂²	#43080	1	2	yes	—
616	C₂²	#43099	1	2	yes	—
617	C₂²	#43099	1	2	yes	—
618	C₂²	#43173	1	2	yes	—
619	C₂²	#43886	1	2	yes	—
620	C₂²	#43886	1	2	yes	—
621	C₂²	#43887	1	2	yes	—
622	C₂²	#43887	1	2	yes	—
623	C₂²	#43893	1	2	yes	—
624	C₂²	#43932	1	2	yes	—
625	C₂²	#43932	1	2	yes	—
626	C₂²	#43963	1	2	yes	—
627	C₂²	#45438	1	2	yes	—
628	C₂²	#45444	1	2	yes	—
629	C₂²	C₂×#2669	1	1	yes	characteristic
630	C₂²	C₂×#2673	1	1	yes	characteristic
631	C₂²	C₂×#2678	1	1	yes	characteristic
632	C₂²	C₂×#2699	1	1	yes	characteristic
633	C₂²	C₂×#2703	1	1	yes	characteristic
634	C₂²	C₂×#2714	1	1	yes	characteristic
635	C₂²	#52308	1	2	yes	—
636	C₂²	#52315	1	2	yes	—
637	C₂²	#58990	1	2	yes	—
638	C₂²	#58990	1	2	yes	—
639	C₂²	#58990	1	2	yes	—
640	C₂²	#58991	1	2	yes	—
641	C₂²	#58991	1	2	yes	—
642	C₂²	#58991	1	2	yes	—
643	C₂²	#58991	1	2	yes	—
644	C₂²	#58997	1	2	yes	—
645	C₂²	#59004	1	2	yes	—
646	C₂²	#59013	1	2	yes	—
647	C₂²	#59026	1	2	yes	—
648	C₂²	#59124	1	2	yes	—
649	C₂²	#59124	1	2	yes	—
650	C₂²	#59142	1	2	yes	—
651	C₂	C₂×#15320	1	1	yes	characteristic
652	C₂	#647663	1	1	yes	characteristic
653	C₂	#648042	1	1	yes	characteristic
654	C₂	#649037	1	1	yes	characteristic
655	C₂	#649049	1	1	yes	characteristic
656	C₂	#686918	1	1	yes	characteristic
657	C₂	#696094	1	1	yes	characteristic
658	C₂	#719096	1	1	yes	characteristic
659	C₂	#725988	1	1	yes	characteristic
660	C₂	#759288	1	1	yes	characteristic
661	C₂	#763343	1	1	yes	characteristic
662	C₂	#774038	1	2	yes	—
663	C₂	#777542	1	2	yes	—
664	C₂	#778570	1	2	yes	—
665	C₂	#790380	1	2	yes	—
666	C₂	#845309	1	1	yes	characteristic
667	C₂	#845801	1	1	yes	characteristic
668	C₂	#917181	1	1	yes	characteristic
669	C₂	#917673	1	1	yes	characteristic
670	C₂	#991006	1	2	yes	—
671	C₂	#991054	1	2	yes	—
672	C₂	#991637	1	2	yes	—
673	C₂	#1007551	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. C₂³×#392	C₂	semidirect
3. C₂×#15320	C₂	semidirect
4. C₂×#14725	C₂	semidirect
5. C₂×#14715	C₂	semidirect
6. C₂×#14715	C₂	semidirect
7. C₂×#13971	C₂	semidirect
8. C₂×#13902	C₂	semidirect
9. C₂×#13867	C₂	semidirect
10. #158997	C₂	semidirect
11. #158818	C₂	semidirect
12. #158317	C₂	semidirect
13. #158142	C₂	semidirect
14. #156706	C₂	semidirect
15. #156694	C₂	semidirect
16. #155066	C₂	semidirect
17. #154214	C₂	semidirect
18. #154195	C₂	semidirect
19. #154195	C₂	semidirect
20. #154096	C₂	semidirect
21. #154094	C₂	semidirect
22. #153851	C₂	semidirect
23. #153775	C₂	semidirect
27. C₂³×#121	C₂²	semidirect
28. C₂³×#121	C₂²	semidirect
36. C₂²×#394	C₂²	semidirect
37. C₂²×#394	C₂²	semidirect
38. C₂²×#394	C₂²	semidirect
43. C₂²×#392	C₂²	semidirect
44. C₂²×#392	C₂²	semidirect
45. C₂²×#392	C₂²	semidirect
46. C₂²×#392	C₂²	semidirect
47. C₂²×#392	C₂²	semidirect
48. C₂²×#392	C₂²	semidirect
49. C₂²×#390	C₂²	semidirect
50. C₂²×#390	C₂²	semidirect
51. C₂²×#388	C₂²	semidirect
56. C₂²×#386	C₂²	semidirect
57. C₂²×#386	C₂²	semidirect
58. C₂²×#386	C₂²	semidirect
59. C₂²×#386	C₂²	semidirect
72. C₂×#1441	C₂²	semidirect
73. C₂×#1440	C₂²	semidirect
74. C₂×#1440	C₂²	semidirect
75. C₂×#1440	C₂²	semidirect
76. C₂×#1440	C₂²	semidirect
77. C₂×#1439	C₂²	semidirect
78. C₂×#1439	C₂²	semidirect
79. C₂×#1438	C₂²	semidirect
80. C₂×#1438	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×#1437	C₂²	semidirect
97. C₂×#1437	C₂²	semidirect
107. C₂×C₂²⋊#95	C₂²	semidirect
108. C₂×C₂²⋊#95	C₂²	semidirect
109. #7557	C₂²	semidirect
110. #7557	C₂²	semidirect
111. #7556	C₂²	semidirect
112. #7556	C₂²	semidirect
113. #7555	C₂²	semidirect
114. #7555	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. #7555	C₂²	semidirect
122. #7554	C₂²	semidirect
126. C₂⁴×D₄	D₄	semidirect
194. C₂×#392	D₄	semidirect
195. C₂×#386	D₄	semidirect
196. C₂×#385	D₄	semidirect
197. C₂×#379	D₄	semidirect
198. C₂×#379	D₄	semidirect
269. C₂²×C₄⋊C₄	C₂×D₄	semidirect
270. C₂²×C₄⋊C₄	C₂×D₄	semidirect
281. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
282. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
283. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
284. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
285. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
286. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
289. C₂×#95	C₂×D₄	semidirect
290. C₂×#95	C₂×D₄	semidirect
291. C₂×#95	C₂×D₄	semidirect
292. C₂×#95	C₂×D₄	semidirect
326. C₂²×D₄	#120	semidirect
551. C₂²	#15320	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
C₂³×#392	2
C₂×#15320	2
C₂×#14725	2
C₂×#14715	2
C₂×#13971	2
C₂×#13902	2
C₂×#13867	2
#158997	2
#158818	2
#158317	2
#158142	2
#156706	2
#156694	2
#155066	2
#154214	2
#154195	2
#154096	2
#154094	2
#153851	2
#153775	2