Subgroups — C₂×#30632325 #44563808

Order 32128.

1900 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#30632325	C₂	1	16	yes	maximal, direct product factor
3	C₂×#22548704	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#22548698	C₂	1	2	yes	maximal, complemented
5	C₂×#22548691	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#22548689	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#22548687	C₂	1	2	yes	maximal, complemented
8	C₂×#22548683	C₂	1	2	yes	maximal, complemented
9	C₂×D₄×Dic₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×C₂²⋊D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×(C₂×D₂₅₁)⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₂₅₁	C₂²	1	2	yes	—
14	C₂²×D₁₀₀₄	C₂²	1	1	yes	characteristic
15	C₂²×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
16	C₂²×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
18	C₂×D₄×D₂₅₁	—	2	8	no	—
19	C₂×D₄×D₂₅₁	C₂²	1	8	yes	complemented
20	C₂³×Dic₂₅₁	C₂²	1	2	yes	complemented
21	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
22	#22548704	C₂²	1	8	yes	complemented
23	#22548698	C₂²	1	16	yes	complemented
24	#22548691	C₂²	1	8	yes	complemented
25	#22548689	C₂²	1	8	yes	complemented
26	#22548687	C₂²	1	16	yes	complemented
27	#22548683	C₂²	1	16	yes	complemented
28	D₄×Dic₂₅₁	C₂²	1	8	yes	complemented
29	C₄×C₂²⋊D₂₅₁	C₂²	1	8	yes	complemented
30	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
31	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	C₂×Dic₂₅₁⋊C₄	C₂²	1	2	yes	complemented
33	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₂²⋊Dic₂₅₁	C₂²	1	2	yes	complemented
35	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	2	yes	—
37	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
38	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
39	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
40	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	16	yes	complemented
41	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
42	C₂×#41×C₂₅₁	—	2	8	no	—
43	C₂×#41×C₂₅₁	C₂²	1	8	yes	complemented
44	C₂²×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
45	C₂²×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
46	C₂²×D₄×C₂₅₁	C₂²	1	2	yes	complemented
47	C₂³×C₄×C₂₅₁	C₂²	1	2	yes	complemented
48	C₂³×C₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
49	C₂³×D₂₅₁	—	2	8	no	—
50	C₂³×D₂₅₁	—	2	8	no	—
51	C₂³×D₂₅₁	—	4	4	no	—
52	C₂³×D₂₅₁	C₂³	1	2	yes	—
53	C₂³×D₂₅₁	C₂³	1	8	yes	—
54	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
55	C₂×D₁₀₀₄	—	2	4	no	—
56	C₂×D₁₀₀₄	C₂³	1	4	yes	—
57	C₂×C₂²⋊D₂₅₁	—	2	4	no	—
58	C₂×C₂²⋊D₂₅₁	—	2	8	no	—
59	C₂×C₂²⋊D₂₅₁	—	4	4	no	—
60	C₂×C₂²⋊D₂₅₁	C₂³	1	8	yes	—
61	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
62	C₂×C₂²⋊D₂₅₁	C₂³	1	8	yes	complemented
63	D₄×D₂₅₁	—	2	32	no	—
64	C₂²×Dic₂₅₁	—	4	4	no	—
65	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
66	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
67	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
68	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
69	C₂²×Dic₂₅₁	C₂³	1	8	yes	complemented
70	C₂×C₄×D₂₅₁	—	2	4	no	—
71	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
72	C₄⋊Dic₂₅₁	C₂³	1	4	yes	complemented
73	Dic₂₅₁⋊C₄	C₂³	1	4	yes	complemented
74	Dic₂₅₁⋊C₄	C₂³	1	8	yes	complemented
75	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	complemented
76	C₂²⋊Dic₂₅₁	C₂³	1	8	yes	complemented
77	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
78	(C₂×D₂₅₁)⋊C₄	C₂³	1	8	yes	—
79	(C₂×D₂₅₁)⋊C₄	C₂³	1	8	yes	complemented
80	(C₂×D₂₅₁)⋊C₄	C₂³	1	8	yes	complemented
81	(C₂×D₂₅₁)⋊C₄	C₂³	1	8	yes	complemented
82	C₄×Dic₂₅₁	C₂³	1	4	yes	complemented
83	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
84	C₂⁴×C₂₅₁	C₂³	1	2	yes	—
85	#41×C₂₅₁	—	2	32	no	—
86	C₂×Q₈×C₂₅₁	—	2	4	no	—
87	C₂×Q₈×C₂₅₁	C₂³	1	4	yes	complemented
88	C₂×D₄×C₂₅₁	—	2	8	no	—
89	C₂×D₄×C₂₅₁	D₄	1	8	yes	complemented
90	C₂×D₄×C₂₅₁	C₂³	1	4	yes	—
91	C₂×D₄×C₂₅₁	C₂³	1	8	yes	complemented
92	C₂²×C₄×C₂₅₁	—	2	8	no	—
93	C₂²×C₄×C₂₅₁	—	2	4	no	—
94	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
96	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₂₅₁	C₂³	1	8	yes	complemented
98	C₂²×C₄×C₂₅₁	C₂³	1	4	yes	complemented
99	C₂²×D₂₅₁	—	2	2	no	—
100	C₂²×D₂₅₁	—	2	2	no	—
101	C₂²×D₂₅₁	—	2	16	no	—
102	C₂²×D₂₅₁	—	2	4	no	—
103	C₂²×D₂₅₁	—	2	4	no	—
104	C₂²×D₂₅₁	—	2	4	no	—
105	C₂²×D₂₅₁	—	2	16	no	—
106	C₂²×D₂₅₁	—	4	8	no	—
107	C₂²×D₂₅₁	—	4	32	no	—
108	C₂²×D₂₅₁	#41	1	4	yes	complemented
109	C₂²×D₂₅₁	C₂⁴	1	4	yes	—
110	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
111	D₁₀₀₄	—	2	8	no	—
112	C₂²⋊D₂₅₁	—	2	16	no	—
113	C₂²⋊D₂₅₁	—	2	8	no	—
114	C₂²⋊D₂₅₁	—	4	8	no	—
115	C₂×Dic₂₅₁	—	2	2	no	—
116	C₂×Dic₂₅₁	—	2	2	no	—
117	C₂×Dic₂₅₁	—	2	2	no	—
118	C₂×Dic₂₅₁	—	2	4	no	—
119	C₂×Dic₂₅₁	—	4	8	no	—
120	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
121	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
122	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
123	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
124	C₄×D₂₅₁	—	2	8	no	—
125	C₂³×C₂₅₁	—	2	4	no	—
126	C₂³×C₂₅₁	—	2	4	no	—
127	C₂³×C₂₅₁	—	2	2	no	—
128	C₂³×C₂₅₁	—	2	2	no	—
129	C₂³×C₂₅₁	—	2	2	no	—
130	C₂³×C₂₅₁	C₂×D₄	1	8	yes	—
131	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
132	C₂³×C₂₅₁	C₂⁴	1	4	yes	—
133	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
134	Q₈×C₂₅₁	—	2	8	no	—
135	D₄×C₂₅₁	—	2	16	no	—
136	D₄×C₂₅₁	C₂×D₄	1	16	yes	complemented
137	C₂×C₄×C₂₅₁	—	2	2	no	—
138	C₂×C₄×C₂₅₁	—	2	4	no	—
139	C₂×C₄×C₂₅₁	—	2	16	no	—
140	C₂×C₄×C₂₅₁	—	2	8	no	—
141	C₂×C₄×C₂₅₁	C₂×D₄	1	4	yes	—
142	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
143	C₂×C₄×C₂₅₁	C₂⁴	1	4	yes	—
144	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
145	C₂²×C₂₅₁	—	2	16	no	—
146	C₂²×C₂₅₁	—	2	4	no	—
147	C₂²×C₂₅₁	—	2	4	no	—
148	C₂²×C₂₅₁	—	2	2	no	—
149	C₂²×C₂₅₁	—	2	2	no	—
150	C₂²×C₂₅₁	—	2	2	no	—
151	C₂²×C₂₅₁	—	4	4	no	—
152	C₂²×C₂₅₁	C₂²×D₄	1	8	yes	—
153	C₂²×C₂₅₁	C₂²×D₄	1	2	yes	—
154	C₂²×C₂₅₁	C₂×#41	1	2	yes	—
155	C₂²×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
156	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
157	C₂×D₂₅₁	—	2	8	no	—
158	C₂×D₂₅₁	—	2	2	no	—
159	C₂×D₂₅₁	—	2	2	no	—
160	C₂×D₂₅₁	—	2	4	no	—
161	C₂×D₂₅₁	—	2	4	no	—
162	C₂×D₂₅₁	—	2	4	no	—
163	C₂×D₂₅₁	—	4	32	no	—
164	C₂×D₂₅₁	—	4	8	no	—
165	C₂×D₂₅₁	C₂×#41	1	4	yes	complemented
166	C₄×C₂₅₁	—	2	2	no	—
167	C₄×C₂₅₁	—	2	4	no	—
168	C₄×C₂₅₁	C₂²×D₄	1	4	yes	—
169	Dic₂₅₁	—	2	2	no	—
170	Dic₂₅₁	—	2	2	no	—
171	Dic₂₅₁	—	2	2	no	—
172	Dic₂₅₁	—	2	4	no	—
173	C₂×C₂₅₁	—	2	8	no	—
174	C₂×C₂₅₁	—	4	2	no	—
175	C₂×C₂₅₁	#546	1	4	yes	complemented
176	C₂×C₂₅₁	C₂³×D₄	1	1	yes	characteristic
177	C₂×C₂₅₁	C₂²×#41	1	1	yes	characteristic
178	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
179	D₂₅₁	—	2	4	no	—
180	D₂₅₁	—	4	4	no	—
181	C₂₅₁	C₂×#546	1	1	yes	characteristic, complemented, Sylow
182	C₂×#546	—	251	1	no	maximal, Sylow
183	C₂²×#41	D₂₅₁	1	1	yes	characteristic, complemented
184	C₂³×D₄	—	251	1	no	—
185	#546	—	251	16	no	—
186	C₂×#124	—	251	1	no	—
187	C₂×#123	—	251	2	no	—
188	C₂×C₂²⋊Q₈	—	251	1	no	—
189	C₂×#121	—	251	2	no	—
190	C₂×#121	—	251	1	no	—
191	C₂×#120	—	251	2	no	—
192	C₂×C₄×D₄	—	251	1	no	—
193	C₂×C₄×D₄	—	251	1	no	—
194	C₂²×C₂²⋊C₄	—	251	2	no	—
195	C₂⁵	—	251	2	no	—
196	C₂×#41	—	2	8	no	—
197	C₂×#41	C₂×D₂₅₁	1	8	yes	complemented
198	C₂²×Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
199	C₂²×D₄	—	502	8	no	—
200	C₂²×D₄	—	251	2	no	—
201	C₂²×D₄	—	251	1	no	—
202	C₂²×D₄	—	251	2	no	—
203	C₂²×D₄	—	251	8	no	—
204	C₂²×D₄	—	251	1	no	—
205	C₂²×D₄	C₂×D₂₅₁	1	1	yes	characteristic
206	C₂²×D₄	C₂×D₂₅₁	1	2	yes	complemented
207	C₂³×C₄	—	251	2	no	—
208	C₂³×C₄	—	251	1	no	—
209	C₂³×C₄	C₂×D₂₅₁	1	2	yes	complemented
210	C₂³×C₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
211	#124	—	251	8	no	—
212	#123	—	251	16	no	—
213	C₂²⋊Q₈	—	251	8	no	—
214	#121	—	251	16	no	—
215	#121	—	251	8	no	—
216	#120	—	251	16	no	—
217	C₄×D₄	—	251	8	no	—
218	C₄×D₄	—	251	8	no	—
219	C₂×C₄⋊C₄	—	251	1	no	—
220	C₂×C₄⋊C₄	—	251	1	no	—
221	C₂×C₄⋊C₄	—	251	2	no	—
222	C₂×C₂²⋊C₄	—	251	2	no	—
223	C₂×C₂²⋊C₄	—	251	1	no	—
224	C₂×C₂²⋊C₄	—	251	1	no	—
225	C₂×C₂²⋊C₄	—	251	2	no	—
226	C₂×C₂²⋊C₄	—	251	2	no	—
227	C₂×C₂²⋊C₄	—	251	2	no	—
228	C₂×C₂²⋊C₄	—	251	2	no	—
229	C₂×C₂²⋊C₄	—	251	16	no	—
230	C₂×C₄²	—	251	1	no	—
231	C₂⁴	—	1004	4	no	—
232	C₂⁴	—	502	8	no	—
233	C₂⁴	—	502	8	no	—
234	C₂⁴	—	251	8	no	—
235	C₂⁴	—	251	2	no	—
236	C₂⁴	—	251	1	no	—
237	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
238	C₂⁴	C₂²×D₂₅₁	1	2	yes	—
239	#41	—	2	32	no	—
240	C₂×Q₈	—	2	4	no	—
241	C₂×Q₈	C₂²×D₂₅₁	1	4	yes	complemented
242	C₂×D₄	—	2	8	no	—
243	C₂×D₄	—	1004	4	no	—
244	C₂×D₄	—	502	4	no	—
245	C₂×D₄	—	502	8	no	—
246	C₂×D₄	—	502	32	no	—
247	C₂×D₄	—	502	4	no	—
248	C₂×D₄	—	251	8	no	—
249	C₂×D₄	—	251	4	no	—
250	C₂×D₄	—	251	8	no	—
251	C₂×D₄	—	251	4	no	—
252	C₂×D₄	C₂²⋊D₂₅₁	1	8	yes	complemented
253	C₂×D₄	C₂²×D₂₅₁	1	4	yes	—
254	C₂×D₄	C₂²×D₂₅₁	1	8	yes	complemented
255	C₂²×C₄	—	2	8	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	1004	4	no	—
258	C₂²×C₄	—	502	4	no	—
259	C₂²×C₄	—	251	8	no	—
260	C₂²×C₄	—	251	1	no	—
261	C₂²×C₄	—	251	1	no	—
262	C₂²×C₄	—	251	2	no	—
263	C₂²×C₄	—	251	1	no	—
264	C₂²×C₄	—	251	4	no	—
265	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
266	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
267	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
268	C₂²×C₄	C₂²×D₂₅₁	1	8	yes	complemented
269	C₂²×C₄	C₂²×D₂₅₁	1	4	yes	complemented
270	C₄⋊C₄	—	251	4	no	—
271	C₄⋊C₄	—	251	8	no	—
272	C₄⋊C₄	—	251	4	no	—
273	C₂²⋊C₄	—	251	8	no	—
274	C₂²⋊C₄	—	251	4	no	—
275	C₂²⋊C₄	—	251	4	no	—
276	C₂²⋊C₄	—	251	8	no	—
277	C₂²⋊C₄	—	251	8	no	—
278	C₂²⋊C₄	—	251	8	no	—
279	C₂²⋊C₄	—	251	8	no	—
280	C₄²	—	251	4	no	—
281	C₂³	—	2	4	no	—
282	C₂³	—	2	4	no	—
283	C₂³	—	2	2	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	1004	32	no	—
287	C₂³	—	1004	8	no	—
288	C₂³	—	502	16	no	—
289	C₂³	—	502	16	no	—
290	C₂³	—	502	4	no	—
291	C₂³	—	502	4	no	—
292	C₂³	—	502	4	no	—
293	C₂³	—	502	2	no	—
294	C₂³	—	502	2	no	—
295	C₂³	—	251	4	no	—
296	C₂³	—	251	4	no	—
297	C₂³	—	251	2	no	—
298	C₂³	C₂×C₂²⋊D₂₅₁	1	8	yes	—
299	C₂³	C₂³×D₂₅₁	1	2	yes	—
300	C₂³	C₂³×D₂₅₁	1	4	yes	—
301	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
302	Q₈	—	2	8	no	—
303	D₄	—	2	16	no	—
304	D₄	—	1004	8	no	—
305	D₄	—	502	8	no	—
306	D₄	—	502	16	no	—
307	D₄	—	502	8	no	—
308	D₄	C₂×C₂²⋊D₂₅₁	1	16	yes	complemented
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	16	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	1004	8	no	—
314	C₂×C₄	—	502	2	no	—
315	C₂×C₄	—	502	2	no	—
316	C₂×C₄	—	502	2	no	—
317	C₂×C₄	—	502	4	no	—
318	C₂×C₄	—	502	8	no	—
319	C₂×C₄	—	251	2	no	—
320	C₂×C₄	—	251	2	no	—
321	C₂×C₄	—	251	4	no	—
322	C₂×C₄	—	251	2	no	—
323	C₂×C₄	C₂×C₂²⋊D₂₅₁	1	4	yes	—
324	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
325	C₂×C₄	C₂³×D₂₅₁	1	4	yes	—
326	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
327	C₂²	—	2	4	no	—
328	C₂²	—	2	4	no	—
329	C₂²	—	2	16	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	4	4	no	—
334	C₂²	—	1004	32	no	—
335	C₂²	—	1004	8	no	—
336	C₂²	—	502	4	no	—
337	C₂²	—	502	4	no	—
338	C₂²	—	502	4	no	—
339	C₂²	—	502	2	no	—
340	C₂²	—	502	2	no	—
341	C₂²	—	502	8	no	—
342	C₂²	—	251	4	no	—
343	C₂²	C₂²×C₂²⋊D₂₅₁	1	8	yes	—
344	C₂²	C₂²×C₂²⋊D₂₅₁	1	2	yes	—
345	C₂²	#41×D₂₅₁	1	2	yes	—
346	C₂²	#22548761	1	2	yes	—
347	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
348	C₄	—	2	2	no	—
349	C₄	—	2	4	no	—
350	C₄	—	502	2	no	—
351	C₄	—	502	2	no	—
352	C₄	—	502	2	no	—
353	C₄	—	502	4	no	—
354	C₄	C₂²×C₂²⋊D₂₅₁	1	4	yes	—
355	C₂	—	2	8	no	—
356	C₂	—	4	2	no	—
357	C₂	—	1004	4	no	—
358	C₂	—	502	4	no	—
359	C₂	#30632325	1	4	yes	direct product factor
360	C₂	C₂³×C₂²⋊D₂₅₁	1	1	yes	characteristic
361	C₂	C₂×#41×D₂₅₁	1	1	yes	characteristic
362	C₂	C₂×#22548761	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₅₁
commutator, cosocle	C₂²×C₂₅₁	C₂⁵
Frattini	C₂²	C₂⁴×D₂₅₁
Fitting	C₂²×#41×C₂₅₁	C₂
socle	C₂³×C₂₅₁	C₂⁴
hypercenter	C₂²×#41	D₂₅₁
hypocenter	C₂₅₁	C₂×#546
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂³ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×D₄×D₂₅₁	C₂	semidirect
2. #30632325	C₂	direct (N × H)
3. C₂×#22548704	C₂	semidirect
4. C₂×#22548698	C₂	semidirect
5. C₂×#22548691	C₂	semidirect
6. C₂×#22548689	C₂	semidirect
7. C₂×#22548687	C₂	semidirect
8. C₂×#22548683	C₂	semidirect
9. C₂×D₄×Dic₂₅₁	C₂	semidirect
10. C₂×C₄×C₂²⋊D₂₅₁	C₂	semidirect
11. C₂²×(C₂×D₂₅₁)⋊C₄	C₂	semidirect
12. C₂²×#41×C₂₅₁	C₂	semidirect
17. C₂²×C₂²⋊D₂₅₁	C₂²	semidirect
19. C₂×D₄×D₂₅₁	C₂²	semidirect
20. C₂³×Dic₂₅₁	C₂²	semidirect
22. #22548704	C₂²	semidirect
23. #22548698	C₂²	semidirect
24. #22548691	C₂²	semidirect
25. #22548689	C₂²	semidirect
26. #22548687	C₂²	semidirect
27. #22548683	C₂²	semidirect
28. D₄×Dic₂₅₁	C₂²	semidirect
29. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
30. C₂×C₄⋊Dic₂₅₁	C₂²	semidirect
31. C₂×Dic₂₅₁⋊C₄	C₂²	semidirect
32. C₂×Dic₂₅₁⋊C₄	C₂²	semidirect
33. C₂×C₂²⋊Dic₂₅₁	C₂²	semidirect
34. C₂×C₂²⋊Dic₂₅₁	C₂²	semidirect
37. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
38. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
39. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
40. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
41. C₂×C₄×Dic₂₅₁	C₂²	semidirect
43. C₂×#41×C₂₅₁	C₂²	semidirect
44. C₂²×Q₈×C₂₅₁	C₂²	semidirect
46. C₂²×D₄×C₂₅₁	C₂²	semidirect
47. C₂³×C₄×C₂₅₁	C₂²	semidirect
48. C₂³×C₄×C₂₅₁	C₂²	semidirect
62. C₂×C₂²⋊D₂₅₁	C₂³	semidirect
69. C₂²×Dic₂₅₁	C₂³	semidirect
72. C₄⋊Dic₂₅₁	C₂³	semidirect
73. Dic₂₅₁⋊C₄	C₂³	semidirect
74. Dic₂₅₁⋊C₄	C₂³	semidirect
75. C₂²⋊Dic₂₅₁	C₂³	semidirect
76. C₂²⋊Dic₂₅₁	C₂³	semidirect
79. (C₂×D₂₅₁)⋊C₄	C₂³	semidirect
80. (C₂×D₂₅₁)⋊C₄	C₂³	semidirect
81. (C₂×D₂₅₁)⋊C₄	C₂³	semidirect
82. C₄×Dic₂₅₁	C₂³	semidirect
87. C₂×Q₈×C₂₅₁	C₂³	semidirect
89. C₂×D₄×C₂₅₁	D₄	semidirect
91. C₂×D₄×C₂₅₁	C₂³	semidirect
97. C₂²×C₄×C₂₅₁	C₂³	semidirect
98. C₂²×C₄×C₂₅₁	C₂³	semidirect
108. C₂²×D₂₅₁	#41	semidirect
136. D₄×C₂₅₁	C₂×D₄	semidirect
165. C₂×D₂₅₁	C₂×#41	semidirect
175. C₂×C₂₅₁	#546	semidirect
181. C₂₅₁	C₂×#546	semidirect
183. C₂²×#41	D₂₅₁	semidirect
197. C₂×#41	C₂×D₂₅₁	semidirect
198. C₂²×Q₈	C₂×D₂₅₁	semidirect
206. C₂²×D₄	C₂×D₂₅₁	semidirect
209. C₂³×C₄	C₂×D₂₅₁	semidirect
210. C₂³×C₄	C₂×D₂₅₁	semidirect
241. C₂×Q₈	C₂²×D₂₅₁	semidirect
252. C₂×D₄	C₂²⋊D₂₅₁	semidirect
254. C₂×D₄	C₂²×D₂₅₁	semidirect
268. C₂²×C₄	C₂²×D₂₅₁	semidirect
269. C₂²×C₄	C₂²×D₂₅₁	semidirect
308. D₄	C₂×C₂²⋊D₂₅₁	semidirect
359. C₂	#30632325	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₄×D₂₅₁	2
#30632325	2
C₂×#22548704	2
C₂×#22548698	2
C₂×#22548691	2
C₂×#22548689	2
C₂×#22548687	2
C₂×#22548683	2
C₂×D₄×Dic₂₅₁	2
C₂×C₄×C₂²⋊D₂₅₁	2
C₂²×(C₂×D₂₅₁)⋊C₄	2
C₂²×#41×C₂₅₁	2
C₂×#546	251

Subgroups — C2×#30632325 #44563808

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#30632325 #44563808