Subgroups — #72330250

Order 1024.

At least 6028 conjugacy classes of subgroups; only the 1345 normal subgroups are shown.

The subgroup lattice has 586 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×#2433	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#2403	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16508	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16500	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16249	C₂	1	2	yes	maximal, complemented
6	C₂×#15283	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15258	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14715	C₂	1	2	yes	maximal, complemented
9	#158823	C₂	1	2	yes	maximal, complemented
10	#158818	C₂	1	2	yes	maximal, complemented
11	#158420	C₂	1	1	yes	maximal, characteristic, complemented
12	#158418	C₂	1	1	yes	maximal, characteristic, complemented
13	#158314	C₂	1	1	yes	maximal, characteristic, complemented
14	#158314	C₂	1	1	yes	maximal, characteristic, complemented
15	#156826	C₂	1	2	yes	maximal, complemented
16	#156688	C₂	1	2	yes	maximal, complemented
17	#156684	C₂	1	2	yes	maximal, complemented
18	#156684	C₂	1	2	yes	maximal, complemented
19	#154775	C₂	1	1	yes	maximal, characteristic, complemented
20	#154763	C₂	1	1	yes	maximal, characteristic, complemented
21	#154408	C₂	1	1	yes	maximal, characteristic, complemented
22	#154094	C₂	1	1	yes	maximal, characteristic, complemented
23	#153913	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×#127	C₂²	1	1	yes	characteristic
27	C₂³×#127	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	2	yes	—
32	C₂³×#120	C₂²	1	1	yes	characteristic
33	C₂³×#120	C₂²	1	1	yes	characteristic
34	C₂³×#120	C₂²	1	2	yes	complemented
35	C₂³×#120	C₂²	1	2	yes	complemented
36	C₂²×#399	C₂²	1	1	yes	characteristic, complemented
37	C₂²×#397	C₂²	1	1	yes	characteristic, complemented
38	C₂²×#394	C₂²	1	2	yes	complemented
39	C₂²×#394	C₂²	1	2	yes	complemented
40	C₂²×#392	C₂²	1	2	yes	—
41	C₂²×#392	C₂²	1	1	yes	characteristic
42	C₂²×#392	C₂²	1	1	yes	characteristic
43	C₂²×#392	C₂²	1	1	yes	characteristic
44	C₂²×#392	C₂²	1	1	yes	characteristic
45	C₂²×#392	C₂²	1	2	yes	—
46	C₂²×#392	C₂²	1	2	yes	—
47	C₂²×#392	C₂²	1	2	yes	complemented
48	C₂²×#392	C₂²	1	2	yes	complemented
49	C₂²×#392	C₂²	1	1	yes	characteristic, complemented
50	C₂²×#392	C₂²	1	1	yes	characteristic, complemented
51	C₂²×#392	C₂²	1	2	yes	complemented
52	C₂²×#392	C₂²	1	2	yes	complemented
53	C₂²×#392	C₂²	1	2	yes	complemented
54	C₂²×#392	C₂²	1	2	yes	complemented
55	C₂²×#392	C₂²	1	2	yes	complemented
56	C₂²×#390	C₂²	1	1	yes	characteristic
57	C₂²×#390	C₂²	1	1	yes	characteristic, complemented
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	2	yes	complemented
63	C₂²×#379	C₂²	1	1	yes	characteristic
64	C₂²×#379	C₂²	1	2	yes	—
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×#1445	C₂²	1	1	yes	characteristic, complemented
69	C₂×#1445	C₂²	1	1	yes	characteristic, complemented
70	C₂×#1440	C₂²	1	2	yes	complemented
71	C₂×#1440	C₂²	1	2	yes	complemented
72	C₂×#1440	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	2	yes	complemented
76	C₂×#1439	C₂²	1	2	yes	complemented
77	C₂×#1438	C₂²	1	2	yes	—
78	C₂×#1438	C₂²	1	1	yes	characteristic
79	C₂×#1438	C₂²	1	1	yes	characteristic
80	C₂×#1438	C₂²	1	2	yes	—
81	C₂×#1438	C₂²	1	2	yes	—
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	1	yes	characteristic, complemented
92	C₂×#1438	C₂²	1	1	yes	characteristic, 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×#1438	C₂²	1	1	yes	characteristic, complemented
102	C₂×#1438	C₂²	1	1	yes	characteristic, complemented
103	C₂×#1437	C₂²	1	1	yes	characteristic, complemented
104	C₂×#1437	C₂²	1	1	yes	characteristic, complemented
105	C₂×#1437	C₂²	1	1	yes	characteristic, complemented
106	C₂×#1437	C₂²	1	1	yes	characteristic, 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	2	yes	complemented
110	#7556	C₂²	1	2	yes	complemented
111	#7556	C₂²	1	2	yes	complemented
112	#7555	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	#7554	C₂²	1	1	yes	characteristic, complemented
120	#7554	C₂²	1	1	yes	characteristic, complemented
121	#7554	C₂²	1	1	yes	characteristic, complemented
122	#7554	C₂²	1	1	yes	characteristic, 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	1	yes	characteristic
131	C₂⁴×D₄	C₂³	1	1	yes	characteristic
132	C₂⁴×D₄	C₂³	1	2	yes	—
133	C₂⁴×D₄	C₂³	1	2	yes	—
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	1	yes	characteristic
138	C₂⁴×D₄	C₂³	1	2	yes	—
139	C₂⁴×D₄	C₂³	1	2	yes	—
140	C₂⁴×D₄	C₂³	1	1	yes	characteristic
141	C₂⁴×D₄	C₂³	1	1	yes	characteristic
142	C₂⁴×D₄	C₂³	1	1	yes	characteristic
143	C₂⁴×D₄	C₂³	1	2	yes	—
144	C₂⁴×D₄	C₂³	1	2	yes	—
145	C₂⁴×D₄	C₂³	1	2	yes	—
146	C₂⁴×D₄	C₂³	1	1	yes	characteristic
147	C₂⁵×C₄	C₂³	1	1	yes	characteristic
148	C₂⁵×C₄	C₂³	1	1	yes	characteristic
149	C₂²×#127	D₄	1	8	yes	complemented
150	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
157	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
159	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
160	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	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	1	yes	characteristic
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	1	yes	characteristic
189	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²	C₂³	1	1	yes	characteristic
195	C₂³×C₄²	C₂³	1	1	yes	characteristic
196	C₂×#390	D₄	1	8	yes	complemented
197	C₂×#386	D₄	1	8	yes	complemented
198	C₂×#386	D₄	1	8	yes	complemented
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	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	1	yes	characteristic
214	C₂²×#95	C₂³	1	1	yes	characteristic
215	C₂²×#95	C₂³	1	1	yes	characteristic
216	C₂²×#95	C₂³	1	1	yes	characteristic
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	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	#1438	D₄	1	16	yes	complemented
228	C₂⁶	C₂×D₄	1	4	yes	—
229	C₂⁶	C₂×D₄	1	4	yes	—
230	C₂⁶	C₂⁴	1	2	yes	—
231	C₂⁶	C₂⁴	1	1	yes	characteristic
232	C₂⁶	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
237	C₂⁶	C₂⁴	1	1	yes	characteristic
238	C₂³×D₄	C₂×D₄	1	4	yes	—
239	C₂³×D₄	C₂×D₄	1	4	yes	—
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	4	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	C₂³×D₄	C₂×D₄	1	4	yes	complemented
249	C₂³×D₄	C₂×D₄	1	8	yes	complemented
250	C₂⁴×C₄	C₂×D₄	1	4	yes	—
251	C₂⁴×C₄	C₂×D₄	1	4	yes	—
252	C₂⁴×C₄	C₂×D₄	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	1	yes	characteristic
259	C₂⁴×C₄	C₂⁴	1	2	yes	—
260	C₂⁴×C₄	C₂⁴	1	2	yes	—
261	C₂⁴×C₄	C₂⁴	1	2	yes	—
262	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
263	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
264	C₂⁴×C₄	C₂⁴	1	2	yes	—
265	C₂⁴×C₄	C₂⁴	1	2	yes	—
266	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
267	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄⋊C₄	C₂×D₄	1	4	yes	complemented
269	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
270	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
271	C₂²×C₂²⋊C₄	C₂×D₄	1	4	yes	—
272	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
273	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	—
274	C₂²×C₂²⋊C₄	C₂×D₄	1	8	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	4	yes	—
278	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
279	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
280	C₂²×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
281	C₂²×C₄²	C₂×D₄	1	4	yes	complemented
282	C₂²×C₄²	C₂×D₄	1	4	yes	complemented
283	C₂×#95	C₂×D₄	1	4	yes	—
284	C₂×#95	C₂×D₄	1	4	yes	—
285	C₂×#95	C₂×D₄	1	4	yes	—
286	C₂×#95	C₂×D₄	1	4	yes	—
287	C₂×#95	C₂×D₄	1	8	yes	complemented
288	C₂×#95	C₂×D₄	1	8	yes	complemented
289	C₂⁵	C₂²×D₄	1	4	yes	—
290	C₂⁵	C₂²×D₄	1	2	yes	—
291	C₂⁵	C₂²×D₄	1	2	yes	—
292	C₂⁵	C₂²×D₄	1	2	yes	—
293	C₂⁵	C₂²×D₄	1	2	yes	—
294	C₂⁵	C₂²×D₄	1	4	yes	—
295	C₂⁵	C₂²×D₄	1	2	yes	—
296	C₂⁵	C₂²×D₄	1	2	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	2	yes	—
301	C₂⁵	C₂²×D₄	1	2	yes	—
302	C₂⁵	C₂²×D₄	1	2	yes	—
303	C₂⁵	C₂²×D₄	1	2	yes	—
304	C₂⁵	C₂²×D₄	1	4	yes	—
305	C₂⁵	H(5,𝔽₂)	1	4	yes	—
306	C₂⁵	H(5,𝔽₂)	1	4	yes	—
307	C₂⁵	H(5,𝔽₂)	1	4	yes	—
308	C₂⁵	H(5,𝔽₂)	1	4	yes	—
309	C₂⁵	H(5,𝔽₂)	1	4	yes	—
310	C₂⁵	H(5,𝔽₂)	1	4	yes	—
311	C₂⁵	C₂⁵	1	1	yes	characteristic
312	C₂²×D₄	#120	1	16	yes	—
313	C₂²×D₄	#127	1	16	yes	complemented
314	C₂³×C₄	#120	1	16	yes	complemented
315	C₂³×C₄	C₂²×D₄	1	4	yes	—
316	C₂³×C₄	C₂²×D₄	1	2	yes	—
317	C₂³×C₄	C₂²×D₄	1	2	yes	—
318	C₂³×C₄	C₂²×D₄	1	2	yes	—
319	C₂³×C₄	C₂²×D₄	1	2	yes	—
320	C₂³×C₄	C₂²×D₄	1	4	yes	—
321	C₂³×C₄	C₂²×D₄	1	4	yes	—
322	C₂³×C₄	C₂²×D₄	1	2	yes	—
323	C₂³×C₄	C₂²×D₄	1	2	yes	—
324	C₂³×C₄	C₂²×D₄	1	2	yes	—
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	4	yes	—
331	C₂³×C₄	C₂²×D₄	1	4	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	2	yes	—
336	C₂³×C₄	C₂²×D₄	1	2	yes	—
337	C₂³×C₄	H(5,𝔽₂)	1	4	yes	—
338	C₂³×C₄	H(5,𝔽₂)	1	4	yes	—
339	C₂³×C₄	H(5,𝔽₂)	1	4	yes	—
340	C₂³×C₄	H(5,𝔽₂)	1	4	yes	—
341	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
342	C₂³×C₄	H(5,𝔽₂)	1	2	yes	—
343	C₂⁴	C₂×#120	1	4	yes	—
344	C₂⁴	C₂×#120	1	4	yes	—
345	C₂⁴	C₂×#120	1	4	yes	—
346	C₂⁴	C₂×#127	1	4	yes	—
347	C₂⁴	C₂×#127	1	4	yes	—
348	C₂⁴	#534	1	4	yes	—
349	C₂⁴	#534	1	4	yes	—
350	C₂⁴	#534	1	8	yes	—
351	C₂⁴	#534	1	4	yes	—
352	C₂⁴	#534	1	4	yes	—
353	C₂⁴	#535	1	4	yes	—
354	C₂⁴	#535	1	8	yes	—
355	C₂⁴	#535	1	4	yes	—
356	C₂⁴	D₄²	1	8	yes	—
357	C₂⁴	D₄²	1	8	yes	—
358	C₂⁴	C₂³×D₄	1	1	yes	characteristic
359	C₂⁴	C₂³×D₄	1	1	yes	characteristic
360	C₂⁴	C₂³×D₄	1	1	yes	characteristic
361	C₂⁴	C₂³×D₄	1	1	yes	characteristic
362	C₂⁴	C₂³×D₄	1	1	yes	characteristic
363	C₂⁴	C₂³×D₄	1	2	yes	—
364	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
365	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
366	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
367	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
368	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
369	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
370	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
371	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
372	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
373	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
374	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
375	C₂⁴	C₂×H(5,𝔽₂)	1	2	yes	—
376	C₂⁴	#585	1	2	yes	—
377	C₂²×C₄	C₂×#120	1	4	yes	—
378	C₂²×C₄	C₂×#120	1	4	yes	—
379	C₂²×C₄	C₂×#120	1	4	yes	—
380	C₂²×C₄	C₂×#127	1	4	yes	—
381	C₂²×C₄	#534	1	4	yes	—
382	C₂²×C₄	#535	1	4	yes	—
383	C₂²×C₄	D₄²	1	8	yes	—
384	C₂²×C₄	D₄²	1	8	yes	—
385	C₂²×C₄	D₄²	1	4	yes	—
386	C₂²×C₄	D₄²	1	4	yes	—
387	C₂²×C₄	D₄²	1	4	yes	—
388	C₂²×C₄	D₄²	1	4	yes	—
389	C₂³	#2433	1	8	yes	—
390	C₂³	#2613	1	8	yes	—
391	C₂³	C₂²×#120	1	1	yes	characteristic
392	C₂³	C₂²×#120	1	1	yes	characteristic
393	C₂³	C₂²×#127	1	1	yes	characteristic
394	C₂³	C₂×#534	1	2	yes	—
395	C₂³	C₂×#534	1	1	yes	characteristic
396	C₂³	C₂×#534	1	1	yes	characteristic
397	C₂³	C₂×#534	1	1	yes	characteristic
398	C₂³	C₂×#534	1	1	yes	characteristic
399	C₂³	C₂×#534	1	1	yes	characteristic
400	C₂³	C₂×#535	1	2	yes	—
401	C₂³	C₂×#535	1	1	yes	characteristic
402	C₂³	C₂×#535	1	1	yes	characteristic
403	C₂³	C₂×#535	1	1	yes	characteristic
404	C₂³	C₂×D₄²	1	1	yes	characteristic
405	C₂³	C₂×D₄²	1	2	yes	—
406	C₂³	C₂×D₄²	1	1	yes	characteristic
407	C₂³	C₂×D₄²	1	2	yes	—
408	C₂³	C₂×D₄²	1	1	yes	characteristic
409	C₂³	C₂×D₄²	1	1	yes	characteristic
410	C₂³	C₂×D₄²	1	2	yes	—
411	C₂³	C₂×D₄²	1	2	yes	—
412	C₂³	#3484	1	2	yes	—
413	C₂³	#3484	1	2	yes	—
414	C₂³	#3484	1	2	yes	—
415	C₂³	#3484	1	2	yes	—
416	C₂³	#3484	1	2	yes	—
417	C₂³	#3484	1	2	yes	—
418	C₂³	#3484	1	2	yes	—
419	C₂³	#3484	1	2	yes	—
420	C₂³	#3484	1	2	yes	—
421	C₂³	#3484	1	2	yes	—
422	C₂³	#3484	1	2	yes	—
423	C₂³	#3484	1	2	yes	—
424	C₂³	#3484	1	2	yes	—
425	C₂³	#3484	1	2	yes	—
426	C₂³	#3484	1	2	yes	—
427	C₂³	#3484	1	2	yes	—
428	C₂³	#3484	1	2	yes	—
429	C₂³	#3484	1	2	yes	—
430	C₂³	#3488	1	2	yes	—
431	C₂³	#3488	1	2	yes	—
432	C₂³	#3488	1	2	yes	—
433	C₂³	#3488	1	2	yes	—
434	C₂³	#3496	1	2	yes	—
435	C₂³	#3496	1	2	yes	—
436	C₂³	#3498	1	2	yes	—
437	C₂³	#3498	1	2	yes	—
438	C₂³	#3498	1	1	yes	characteristic
439	C₂³	#3498	1	1	yes	characteristic
440	C₂³	#3498	1	2	yes	—
441	C₂³	#3498	1	1	yes	characteristic
442	C₂³	#3498	1	2	yes	—
443	C₂³	#3500	1	1	yes	characteristic
444	C₂³	#3532	1	2	yes	—
445	C₂³	#3532	1	2	yes	—
446	C₂³	#3532	1	2	yes	—
447	C₂³	#3532	1	2	yes	—
448	C₂³	#3532	1	2	yes	—
449	C₂³	#3532	1	2	yes	—
450	C₂³	#3532	1	2	yes	—
451	C₂³	#3532	1	2	yes	—
452	C₂³	#3532	1	2	yes	—
453	C₂³	#3532	1	2	yes	—
454	C₂³	#3532	1	2	yes	—
455	C₂³	#3534	1	2	yes	—
456	C₂³	#3534	1	2	yes	—
457	C₂³	#3534	1	2	yes	—
458	C₂³	#3534	1	2	yes	—
459	C₂³	#3537	1	2	yes	—
460	C₂³	#3537	1	2	yes	—
461	C₂³	#3537	1	2	yes	—
462	C₂³	#3537	1	2	yes	—
463	C₂³	#3537	1	2	yes	—
464	C₂³	#3537	1	2	yes	—
465	C₂³	#3537	1	2	yes	—
466	C₂³	#3537	1	2	yes	—
467	C₂³	#3542	1	2	yes	—
468	C₂³	#3543	1	2	yes	—
469	C₂³	#3543	1	2	yes	—
470	C₂³	#3543	1	2	yes	—
471	C₂³	#3543	1	2	yes	—
472	C₂³	#3543	1	2	yes	—
473	C₂³	#3543	1	2	yes	—
474	C₂³	#3543	1	2	yes	—
475	C₂³	#3546	1	2	yes	—
476	C₂³	#3558	1	2	yes	—
477	C₂³	#3558	1	2	yes	—
478	C₂×C₄	#2403	1	8	yes	—
479	C₂²	C₂×#2613	1	1	yes	characteristic
480	C₂²	C₂×#2403	1	1	yes	characteristic
481	C₂²	C₂×#2433	1	1	yes	characteristic
482	C₂²	#34980	1	1	yes	characteristic
483	C₂²	#34980	1	1	yes	characteristic
484	C₂²	#34980	1	1	yes	characteristic
485	C₂²	#35222	1	1	yes	characteristic
486	C₂²	#35390	1	2	yes	—
487	C₂²	#35513	1	1	yes	characteristic
488	C₂²	#35527	1	1	yes	characteristic
489	C₂²	#35680	1	2	yes	—
490	C₂²	#35921	1	2	yes	—
491	C₂²	D₄×#120	1	2	yes	—
492	C₂²	D₄×#127	1	1	yes	characteristic
493	C₂²	D₄×#127	1	1	yes	characteristic
494	C₂²	#36703	1	2	yes	—
495	C₂²	#37436	1	1	yes	characteristic
496	C₂²	#37436	1	1	yes	characteristic
497	C₂²	#37644	1	2	yes	—
498	C₂²	#37644	1	2	yes	—
499	C₂²	#37644	1	2	yes	—
500	C₂²	#37644	1	2	yes	—
501	C₂²	#37644	1	2	yes	—
502	C₂²	#37645	1	2	yes	—
503	C₂²	#37645	1	2	yes	—
504	C₂²	#37645	1	2	yes	—
505	C₂²	#37645	1	2	yes	—
506	C₂²	#37650	1	2	yes	—
507	C₂²	#37672	1	2	yes	—
508	C₂²	#37672	1	2	yes	—
509	C₂²	#37672	1	2	yes	—
510	C₂²	#37674	1	2	yes	—
511	C₂²	#37674	1	1	yes	characteristic
512	C₂²	#37674	1	1	yes	characteristic
513	C₂²	#37674	1	1	yes	characteristic
514	C₂²	#37677	1	1	yes	characteristic
515	C₂²	#39336	1	2	yes	—
516	C₂²	#39361	1	1	yes	characteristic
517	C₂²	#39362	1	1	yes	characteristic
518	C₂²	#40484	1	2	yes	—
519	C₂²	#40484	1	2	yes	—
520	C₂²	#40486	1	2	yes	—
521	C₂²	#40490	1	2	yes	—
522	C₂²	#40490	1	2	yes	—
523	C₂²	#40584	1	2	yes	—
524	C₂²	#40584	1	2	yes	—
525	C₂²	#40584	1	2	yes	—
526	C₂²	#40590	1	2	yes	—
527	C₂²	#40594	1	2	yes	—
528	C₂²	#42422	1	2	yes	—
529	C₂²	#42430	1	2	yes	—
530	C₂²	#43001	1	2	yes	—
531	C₂²	#43001	1	2	yes	—
532	C₂²	#43098	1	2	yes	—
533	C₂²	#43889	1	2	yes	—
534	C₂²	#44877	1	2	yes	—
535	C₂²	#44877	1	2	yes	—
536	C₂²	#44927	1	2	yes	—
537	C₂²	#45355	1	2	yes	—
538	C₂²	#46355	1	2	yes	—
539	C₂²	#46355	1	2	yes	—
540	C₂²	#46364	1	2	yes	—
541	C₂²	#46364	1	2	yes	—
542	C₂²	#46419	1	2	yes	—
543	C₂²	#47689	1	2	yes	—
544	C₂²	#47838	1	2	yes	—
545	C₂²	#47942	1	2	yes	—
546	C₂²	#47942	1	2	yes	—
547	C₂²	#47942	1	2	yes	—
548	C₂²	#47942	1	2	yes	—
549	C₂²	#47942	1	2	yes	—
550	C₂²	#47952	1	2	yes	—
551	C₂²	#50646	1	2	yes	—
552	C₂²	#50647	1	2	yes	—
553	C₂²	#51068	1	2	yes	—
554	C₂²	#52004	1	2	yes	—
555	C₂²	#52031	1	2	yes	—
556	C₂²	#53425	1	2	yes	—
557	C₂²	#53431	1	2	yes	—
558	C₂²	#55040	1	2	yes	—
559	C₂²	#56291	1	2	yes	—
560	C₂²	#56303	1	2	yes	—
561	C₂²	#56405	1	2	yes	—
562	C₂²	#57213	1	2	yes	—
563	C₂²	#57974	1	2	yes	—
564	C₂²	#59126	1	2	yes	—
565	C₂²	#59126	1	2	yes	—
566	C₂	#617359	1	1	yes	characteristic
567	C₂	#635984	1	1	yes	characteristic
568	C₂	#649038	1	1	yes	characteristic
569	C₂	#687589	1	1	yes	characteristic
570	C₂	#719692	1	1	yes	characteristic
571	C₂	#1192577	1	2	yes	—
572	C₂	#1192583	1	2	yes	—
573	C₂	#1259281	1	2	yes	—
574	C₂	#1393169	1	2	yes	—
575	C₂	#1515101	1	2	yes	—
576	C₂	#1515105	1	2	yes	—
577	C₂	#2078557	1	2	yes	—
578	C₂	#2078623	1	2	yes	—
579	C₂	#2110333	1	2	yes	—
580	C₂	#2110399	1	2	yes	—
581	C₂	#2607246	1	2	yes	—
582	C₂	#2760366	1	2	yes	—
583	C₂	#4379699	1	1	yes	characteristic
584	C₂	#4417886	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. C₂²×#2433	C₂	semidirect
2. C₂²×#2403	C₂	semidirect
3. C₂×#16508	C₂	semidirect
4. C₂×#16500	C₂	semidirect
5. C₂×#16249	C₂	semidirect
6. C₂×#15283	C₂	semidirect
7. C₂×#15258	C₂	semidirect
8. C₂×#14715	C₂	semidirect
9. #158823	C₂	semidirect
10. #158818	C₂	semidirect
11. #158420	C₂	semidirect
12. #158418	C₂	semidirect
13. #158314	C₂	semidirect
14. #158314	C₂	semidirect
15. #156826	C₂	semidirect
16. #156688	C₂	semidirect
17. #156684	C₂	semidirect
18. #156684	C₂	semidirect
19. #154775	C₂	semidirect
20. #154763	C₂	semidirect
21. #154408	C₂	semidirect
22. #154094	C₂	semidirect
23. #153913	C₂	semidirect
27. C₂³×#127	C₂²	semidirect
28. C₂³×#121	C₂²	semidirect
34. C₂³×#120	C₂²	semidirect
35. C₂³×#120	C₂²	semidirect
36. C₂²×#399	C₂²	semidirect
37. C₂²×#397	C₂²	semidirect
38. C₂²×#394	C₂²	semidirect
39. 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
52. C₂²×#392	C₂²	semidirect
53. C₂²×#392	C₂²	semidirect
54. C₂²×#392	C₂²	semidirect
55. C₂²×#392	C₂²	semidirect
57. C₂²×#390	C₂²	semidirect
62. C₂²×#386	C₂²	semidirect
65. C₂²×#379	C₂²	semidirect
66. C₂²×#379	C₂²	semidirect
67. C₂²×C₄×C₂²⋊C₄	C₂²	semidirect
68. C₂×#1445	C₂²	semidirect
69. C₂×#1445	C₂²	semidirect
70. C₂×#1440	C₂²	semidirect
71. C₂×#1440	C₂²	semidirect
72. C₂×#1440	C₂²	semidirect
73. C₂×#1439	C₂²	semidirect
74. C₂×#1439	C₂²	semidirect
75. C₂×#1439	C₂²	semidirect
76. C₂×#1439	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×#1437	C₂²	semidirect
107. C₂×C₂²⋊#95	C₂²	semidirect
108. C₂×C₂²⋊#95	C₂²	semidirect
109. C₂×C₂²⋊#95	C₂²	semidirect
110. #7556	C₂²	semidirect
111. #7556	C₂²	semidirect
112. #7555	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. #7554	C₂²	semidirect
120. #7554	C₂²	semidirect
121. #7554	C₂²	semidirect
122. #7554	C₂²	semidirect
126. C₂⁴×D₄	D₄	semidirect
149. C₂²×#127	D₄	semidirect
196. C₂×#390	D₄	semidirect
197. C₂×#386	D₄	semidirect
198. C₂×#386	D₄	semidirect
227. #1438	D₄	semidirect
248. C₂³×D₄	C₂×D₄	semidirect
249. C₂³×D₄	C₂×D₄	semidirect
268. C₂²×C₄⋊C₄	C₂×D₄	semidirect
278. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
279. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
280. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
281. C₂²×C₄²	C₂×D₄	semidirect
282. C₂²×C₄²	C₂×D₄	semidirect
287. C₂×#95	C₂×D₄	semidirect
288. C₂×#95	C₂×D₄	semidirect
313. C₂²×D₄	#127	semidirect
314. C₂³×C₄	#120	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#2433	2
C₂²×#2403	2
C₂×#16508	2
C₂×#16500	2
C₂×#16249	2
C₂×#15283	2
C₂×#15258	2
C₂×#14715	2
#158823	2
#158818	2
#158420	2
#158418	2
#158314	2
#156826	2
#156688	2
#156684	2
#154775	2
#154763	2
#154408	2
#154094	2
#153913	2