Subgroups — C₂×#30632253 #44563673

Order 32128.

1896 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#16860810	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#30632253	C₂	1	16	yes	maximal, direct product factor
4	C₂×#22548711	C₂	1	2	yes	maximal, complemented
5	C₂×#22548701	C₂	1	2	yes	maximal, complemented
6	C₂×#22548690	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#22548689	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#22548686	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#22548685	C₂	1	2	yes	maximal, complemented
10	C₂×#22548683	C₂	1	2	yes	maximal, complemented
11	C₂×#22548673	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#121×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₂₅₁	C₂²	1	2	yes	—
14	C₂×#16860810	—	2	8	no	—
15	C₂×#16860810	C₂²	1	8	yes	complemented
16	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
17	C₂²×D₁₀₀₄	C₂²	1	1	yes	characteristic
18	C₂²×D₁₀₀₄	C₂²	1	1	yes	characteristic
19	C₂²×D₁₀₀₄	C₂²	1	2	yes	complemented
20	C₂²×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
21	C₂²×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
24	C₂²×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
25	C₂×D₄×D₂₅₁	—	2	8	no	—
26	C₂×D₄×D₂₅₁	C₂²	1	8	yes	complemented
27	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
29	#22548711	C₂²	1	16	yes	complemented
30	#22548701	C₂²	1	16	yes	complemented
31	#22548690	C₂²	1	8	yes	complemented
32	#22548689	C₂²	1	8	yes	complemented
33	#22548686	C₂²	1	8	yes	complemented
34	#22548685	C₂²	1	16	yes	complemented
35	#22548683	C₂²	1	16	yes	complemented
36	#22548673	C₂²	1	8	yes	complemented
37	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂²⋊Dic₂₅₁	C₂²	1	2	yes	complemented
39	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	2	yes	—
40	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
41	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
42	C₂×C₄×Dic₂₅₁	C₂²	1	2	yes	complemented
43	C₂²×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
44	C₂²×D₄×C₂₅₁	C₂²	1	2	yes	complemented
45	C₂³×C₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
46	#121×C₂₅₁	C₂²	1	8	yes	complemented
47	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	2	yes	complemented
49	C₂³×D₂₅₁	—	2	8	no	—
50	C₂³×D₂₅₁	—	4	4	no	—
51	C₂³×D₂₅₁	—	4	4	no	—
52	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
53	C₂³×D₂₅₁	C₂³	1	2	yes	—
54	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
55	C₂³×D₂₅₁	C₂³	1	8	yes	—
56	#16860810	—	2	32	no	—
57	C₂×Dic₅₀₂	—	2	4	no	—
58	C₂×Dic₅₀₂	C₂³	1	4	yes	complemented
59	C₂×D₁₀₀₄	—	2	4	no	—
60	C₂×D₁₀₀₄	—	2	4	no	—
61	C₂×D₁₀₀₄	—	4	4	no	—
62	C₂×D₁₀₀₄	C₂³	1	4	yes	—
63	C₂×D₁₀₀₄	C₂³	1	4	yes	—
64	C₂×D₁₀₀₄	C₂³	1	8	yes	complemented
65	C₂×C₂²⋊D₂₅₁	—	2	4	no	—
66	C₂×C₂²⋊D₂₅₁	—	2	8	no	—
67	C₂×C₂²⋊D₂₅₁	—	2	4	no	—
68	C₂×C₂²⋊D₂₅₁	—	4	4	no	—
69	C₂×C₂²⋊D₂₅₁	—	4	4	no	—
70	C₂×C₂²⋊D₂₅₁	C₂³	1	8	yes	—
71	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
72	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	complemented
73	C₂×C₂²⋊D₂₅₁	C₂³	1	8	yes	complemented
74	C₂×C₂²⋊D₂₅₁	C₂³	1	8	yes	complemented
75	D₄×D₂₅₁	—	2	32	no	—
76	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
77	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
78	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
79	C₂×C₄×D₂₅₁	—	2	4	no	—
80	C₂×C₄×D₂₅₁	D₄	1	8	yes	complemented
81	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
82	C₂×C₄×D₂₅₁	C₂³	1	4	yes	complemented
83	C₄⋊Dic₂₅₁	C₂³	1	4	yes	complemented
84	C₂²⋊Dic₂₅₁	C₂³	1	8	yes	complemented
85	(C₂×D₂₅₁)⋊C₄	C₂³	1	8	yes	—
86	(C₂×D₂₅₁)⋊C₄	C₂³	1	8	yes	complemented
87	(C₂×D₂₅₁)⋊C₄	C₂³	1	8	yes	complemented
88	C₄×Dic₂₅₁	C₂³	1	8	yes	complemented
89	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
90	C₂⁴×C₂₅₁	C₂³	1	2	yes	—
91	C₂×D₄×C₂₅₁	—	2	4	no	—
92	C₂×D₄×C₂₅₁	—	4	4	no	—
93	C₂×D₄×C₂₅₁	C₂³	1	4	yes	—
94	C₂×D₄×C₂₅₁	C₂³	1	8	yes	complemented
95	C₂²×C₄×C₂₅₁	—	2	4	no	—
96	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
98	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₂₅₁	C₂³	1	4	yes	complemented
100	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	complemented
101	C₂²⋊C₄×C₂₅₁	C₂³	1	8	yes	complemented
102	C₂²×D₂₅₁	—	2	2	no	—
103	C₂²×D₂₅₁	—	2	2	no	—
104	C₂²×D₂₅₁	—	2	2	no	—
105	C₂²×D₂₅₁	—	2	4	no	—
106	C₂²×D₂₅₁	—	2	2	no	—
107	C₂²×D₂₅₁	—	2	4	no	—
108	C₂²×D₂₅₁	—	2	2	no	—
109	C₂²×D₂₅₁	—	2	4	no	—
110	C₂²×D₂₅₁	—	2	16	no	—
111	C₂²×D₂₅₁	—	4	8	no	—
112	C₂²×D₂₅₁	—	4	8	no	—
113	C₂²×D₂₅₁	—	4	32	no	—
114	C₂²×D₂₅₁	C₂×D₄	1	4	yes	—
115	C₂²×D₂₅₁	C₂⁴	1	4	yes	—
116	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
117	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
118	Dic₅₀₂	—	2	8	no	—
119	D₁₀₀₄	—	2	8	no	—
120	D₁₀₀₄	—	2	8	no	—
121	D₁₀₀₄	—	4	8	no	—
122	C₂²⋊D₂₅₁	—	2	8	no	—
123	C₂²⋊D₂₅₁	—	2	16	no	—
124	C₂²⋊D₂₅₁	—	2	8	no	—
125	C₂²⋊D₂₅₁	—	4	8	no	—
126	C₂²⋊D₂₅₁	—	4	8	no	—
127	C₂×Dic₂₅₁	—	2	2	no	—
128	C₂×Dic₂₅₁	—	2	4	no	—
129	C₂×Dic₂₅₁	C₂×D₄	1	4	yes	—
130	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
131	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
132	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
133	C₄×D₂₅₁	—	2	8	no	—
134	C₄×D₂₅₁	C₂×D₄	1	16	yes	complemented
135	C₂³×C₂₅₁	—	2	2	no	—
136	C₂³×C₂₅₁	—	2	4	no	—
137	C₂³×C₂₅₁	—	2	2	no	—
138	C₂³×C₂₅₁	—	2	4	no	—
139	C₂³×C₂₅₁	—	2	2	no	—
140	C₂³×C₂₅₁	—	2	4	no	—
141	C₂³×C₂₅₁	C₂⁴	1	4	yes	—
142	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
143	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
144	D₄×C₂₅₁	—	2	8	no	—
145	D₄×C₂₅₁	—	4	8	no	—
146	C₂×C₄×C₂₅₁	—	2	2	no	—
147	C₂×C₄×C₂₅₁	—	2	4	no	—
148	C₂×C₄×C₂₅₁	—	2	8	no	—
149	C₂×C₄×C₂₅₁	C₂×D₄	1	4	yes	—
150	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
151	C₂×C₄×C₂₅₁	C₂⁴	1	4	yes	—
152	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
153	C₂²×C₂₅₁	—	2	2	no	—
154	C₂²×C₂₅₁	—	2	4	no	—
155	C₂²×C₂₅₁	—	2	2	no	—
156	C₂²×C₂₅₁	—	2	4	no	—
157	C₂²×C₂₅₁	—	2	2	no	—
158	C₂²×C₂₅₁	—	2	4	no	—
159	C₂²×C₂₅₁	—	4	4	no	—
160	C₂²×C₂₅₁	—	4	8	no	—
161	C₂²×C₂₅₁	C₂²×D₄	1	2	yes	—
162	C₂²×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
163	C₂²×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
164	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
165	C₂×D₂₅₁	—	2	8	no	—
166	C₂×D₂₅₁	—	2	2	no	—
167	C₂×D₂₅₁	—	2	2	no	—
168	C₂×D₂₅₁	—	2	2	no	—
169	C₂×D₂₅₁	—	2	4	no	—
170	C₂×D₂₅₁	—	2	2	no	—
171	C₂×D₂₅₁	—	2	4	no	—
172	C₂×D₂₅₁	—	2	2	no	—
173	C₂×D₂₅₁	—	2	4	no	—
174	C₂×D₂₅₁	—	4	32	no	—
175	C₂×D₂₅₁	—	4	4	no	—
176	C₂×D₂₅₁	—	4	8	no	—
177	C₂×D₂₅₁	C₂²×D₄	1	4	yes	—
178	C₄×C₂₅₁	—	2	2	no	—
179	C₄×C₂₅₁	—	2	4	no	—
180	C₄×C₂₅₁	C₂²×D₄	1	4	yes	—
181	Dic₂₅₁	—	2	2	no	—
182	Dic₂₅₁	—	2	4	no	—
183	Dic₂₅₁	C₂²×D₄	1	4	yes	—
184	C₂×C₂₅₁	—	4	4	no	—
185	C₂×C₂₅₁	—	4	2	no	—
186	C₂×C₂₅₁	#535	1	4	yes	complemented
187	C₂×C₂₅₁	C₂³×D₄	1	1	yes	characteristic
188	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
189	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
190	D₂₅₁	—	2	4	no	—
191	D₂₅₁	—	4	2	no	—
192	D₂₅₁	—	4	4	no	—
193	C₂₅₁	C₂×#535	1	1	yes	characteristic, complemented, Sylow
194	C₂×#535	—	251	1	no	maximal, Sylow
195	C₂²×#41	—	251	1	no	—
196	C₂³×D₄	—	251	1	no	—
197	#535	—	251	16	no	—
198	C₂×#127	—	251	2	no	—
199	C₂×#124	—	251	2	no	—
200	C₂×#121	—	251	1	no	—
201	C₂×#121	—	251	1	no	—
202	C₂×#121	—	251	1	no	—
203	C₂×#121	D₂₅₁	1	1	yes	characteristic, complemented
204	C₂×#120	—	251	2	no	—
205	C₂×#120	—	251	2	no	—
206	C₂×#117	—	251	1	no	—
207	C₂⁵	—	251	2	no	—
208	C₂×#41	—	502	8	no	—
209	C₂×#41	—	251	8	no	—
210	C₂²×Q₈	—	251	1	no	—
211	C₂²×D₄	—	502	8	no	—
212	C₂²×D₄	—	251	2	no	—
213	C₂²×D₄	—	251	2	no	—
214	C₂²×D₄	—	251	1	no	—
215	C₂²×D₄	—	251	2	no	—
216	C₂²×D₄	—	251	1	no	—
217	C₂²×D₄	—	251	8	no	—
218	C₂²×D₄	—	251	2	no	—
219	C₂²×D₄	—	251	1	no	—
220	C₂²×D₄	—	251	1	no	—
221	C₂²×D₄	C₂×D₂₅₁	1	1	yes	characteristic
222	C₂²×D₄	C₂×D₂₅₁	1	2	yes	complemented
223	C₂³×C₄	—	251	1	no	—
224	C₂³×C₄	—	251	1	no	—
225	C₂³×C₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
226	#127	—	251	16	no	—
227	#124	—	251	16	no	—
228	#121	—	251	8	no	—
229	#121	—	251	8	no	—
230	#121	—	251	8	no	—
231	#121	C₂×D₂₅₁	1	8	yes	complemented
232	#120	—	251	16	no	—
233	#120	—	251	16	no	—
234	#117	—	251	8	no	—
235	C₂×C₄⋊C₄	—	251	1	no	—
236	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
237	C₂×C₂²⋊C₄	—	251	2	no	—
238	C₂×C₂²⋊C₄	—	251	2	no	—
239	C₂×C₂²⋊C₄	—	251	2	no	—
240	C₂×C₂²⋊C₄	—	251	2	no	—
241	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	2	yes	complemented
242	C₂×C₄²	—	251	2	no	—
243	C₂⁴	—	1004	4	no	—
244	C₂⁴	—	1004	4	no	—
245	C₂⁴	—	502	8	no	—
246	C₂⁴	—	251	8	no	—
247	C₂⁴	—	251	2	no	—
248	C₂⁴	—	251	1	no	—
249	C₂⁴	—	251	1	no	—
250	C₂⁴	C₂²×D₂₅₁	1	2	yes	—
251	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
252	#41	—	502	32	no	—
253	C₂×Q₈	—	502	4	no	—
254	C₂×Q₈	—	251	4	no	—
255	C₂×D₄	—	2	4	no	—
256	C₂×D₄	—	4	4	no	—
257	C₂×D₄	—	1004	4	no	—
258	C₂×D₄	—	1004	4	no	—
259	C₂×D₄	—	1004	4	no	—
260	C₂×D₄	—	502	4	no	—
261	C₂×D₄	—	502	4	no	—
262	C₂×D₄	—	502	32	no	—
263	C₂×D₄	—	502	8	no	—
264	C₂×D₄	—	502	4	no	—
265	C₂×D₄	—	502	4	no	—
266	C₂×D₄	—	251	8	no	—
267	C₂×D₄	—	251	8	no	—
268	C₂×D₄	—	251	4	no	—
269	C₂×D₄	—	251	8	no	—
270	C₂×D₄	—	251	4	no	—
271	C₂×D₄	—	251	8	no	—
272	C₂×D₄	—	251	4	no	—
273	C₂×D₄	—	251	4	no	—
274	C₂×D₄	C₂²×D₂₅₁	1	4	yes	—
275	C₂×D₄	C₂²×D₂₅₁	1	8	yes	complemented
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	502	4	no	—
278	C₂²×C₄	—	251	2	no	—
279	C₂²×C₄	—	251	1	no	—
280	C₂²×C₄	—	251	4	no	—
281	C₂²×C₄	—	251	1	no	—
282	C₂²×C₄	—	251	8	no	—
283	C₂²×C₄	—	251	4	no	—
284	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
285	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
286	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
287	C₂²×C₄	C₂²×D₂₅₁	1	4	yes	complemented
288	C₄⋊C₄	—	251	4	no	—
289	C₄⋊C₄	C₂²×D₂₅₁	1	4	yes	complemented
290	C₂²⋊C₄	—	251	8	no	—
291	C₂²⋊C₄	—	251	8	no	—
292	C₂²⋊C₄	—	251	8	no	—
293	C₂²⋊C₄	—	251	8	no	—
294	C₂²⋊C₄	C₂²×D₂₅₁	1	8	yes	complemented
295	C₄²	—	251	8	no	—
296	C₂³	—	2	2	no	—
297	C₂³	—	2	4	no	—
298	C₂³	—	2	2	no	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	4	no	—
302	C₂³	—	1004	8	no	—
303	C₂³	—	1004	8	no	—
304	C₂³	—	1004	32	no	—
305	C₂³	—	502	16	no	—
306	C₂³	—	502	2	no	—
307	C₂³	—	502	4	no	—
308	C₂³	—	502	2	no	—
309	C₂³	—	502	4	no	—
310	C₂³	—	502	2	no	—
311	C₂³	—	502	4	no	—
312	C₂³	—	502	2	no	—
313	C₂³	—	502	2	no	—
314	C₂³	—	251	4	no	—
315	C₂³	—	251	2	no	—
316	C₂³	—	251	4	no	—
317	C₂³	—	251	2	no	—
318	C₂³	C₂³×D₂₅₁	1	4	yes	—
319	C₂³	C₂³×D₂₅₁	1	2	yes	—
320	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
321	Q₈	—	502	8	no	—
322	D₄	—	2	8	no	—
323	D₄	—	4	8	no	—
324	D₄	—	1004	8	no	—
325	D₄	—	1004	8	no	—
326	D₄	—	1004	8	no	—
327	D₄	—	502	8	no	—
328	D₄	—	502	8	no	—
329	D₄	—	502	16	no	—
330	D₄	—	502	8	no	—
331	D₄	—	502	8	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	502	2	no	—
336	C₂×C₄	—	502	4	no	—
337	C₂×C₄	—	502	8	no	—
338	C₂×C₄	—	251	4	no	—
339	C₂×C₄	—	251	2	no	—
340	C₂×C₄	—	251	4	no	—
341	C₂×C₄	—	251	2	no	—
342	C₂×C₄	—	251	16	no	—
343	C₂×C₄	D₄×D₂₅₁	1	4	yes	—
344	C₂×C₄	C₂³×D₂₅₁	1	4	yes	—
345	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
346	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	4	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	4	8	no	—
354	C₂²	—	4	4	no	—
355	C₂²	—	1004	32	no	—
356	C₂²	—	1004	8	no	—
357	C₂²	—	1004	4	no	—
358	C₂²	—	502	2	no	—
359	C₂²	—	502	4	no	—
360	C₂²	—	502	2	no	—
361	C₂²	—	502	4	no	—
362	C₂²	—	502	2	no	—
363	C₂²	—	502	4	no	—
364	C₂²	—	502	8	no	—
365	C₂²	—	502	2	no	—
366	C₂²	—	502	2	no	—
367	C₂²	—	251	4	no	—
368	C₂²	C₂×D₄×D₂₅₁	1	2	yes	—
369	C₂²	#22548760	1	2	yes	—
370	C₂²	#22548761	1	2	yes	—
371	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	4	no	—
374	C₄	—	502	2	no	—
375	C₄	—	502	4	no	—
376	C₄	—	251	4	no	—
377	C₄	C₂×D₄×D₂₅₁	1	4	yes	—
378	C₂	—	4	4	no	—
379	C₂	—	4	2	no	—
380	C₂	—	1004	4	no	—
381	C₂	—	1004	2	no	—
382	C₂	—	502	4	no	—
383	C₂	#30632253	1	4	yes	direct product factor
384	C₂	C₂²×D₄×D₂₅₁	1	1	yes	characteristic
385	C₂	C₂×#22548760	1	1	yes	characteristic
386	C₂	C₂×#22548761	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₅₁
commutator, cosocle	C₂²×C₂₅₁	C₂⁵
Frattini	C₂²	C₂⁴×D₂₅₁
Fitting	C₂×#121×C₂₅₁	C₂
socle	C₂³×C₂₅₁	C₂⁴
hypercenter	C₂×#121	D₂₅₁
hypocenter	C₂₅₁	C₂×#535
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂³ ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. C₂²×#16860810	C₂	semidirect
2. C₂²×D₄×D₂₅₁	C₂	semidirect
3. #30632253	C₂	direct (N × H)
4. C₂×#22548711	C₂	semidirect
5. C₂×#22548701	C₂	semidirect
6. C₂×#22548690	C₂	semidirect
7. C₂×#22548689	C₂	semidirect
8. C₂×#22548686	C₂	semidirect
9. C₂×#22548685	C₂	semidirect
10. C₂×#22548683	C₂	semidirect
11. C₂×#22548673	C₂	semidirect
12. C₂×#121×C₂₅₁	C₂	semidirect
15. C₂×#16860810	C₂²	semidirect
16. C₂²×Dic₅₀₂	C₂²	semidirect
19. C₂²×D₁₀₀₄	C₂²	semidirect
22. C₂²×C₂²⋊D₂₅₁	C₂²	semidirect
23. C₂²×C₂²⋊D₂₅₁	C₂²	semidirect
24. C₂²×C₂²⋊D₂₅₁	C₂²	semidirect
26. C₂×D₄×D₂₅₁	C₂²	semidirect
28. C₂²×C₄×D₂₅₁	C₂²	semidirect
29. #22548711	C₂²	semidirect
30. #22548701	C₂²	semidirect
31. #22548690	C₂²	semidirect
32. #22548689	C₂²	semidirect
33. #22548686	C₂²	semidirect
34. #22548685	C₂²	semidirect
35. #22548683	C₂²	semidirect
36. #22548673	C₂²	semidirect
37. C₂×C₄⋊Dic₂₅₁	C₂²	semidirect
38. C₂×C₂²⋊Dic₂₅₁	C₂²	semidirect
40. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
41. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
42. C₂×C₄×Dic₂₅₁	C₂²	semidirect
44. C₂²×D₄×C₂₅₁	C₂²	semidirect
45. C₂³×C₄×C₂₅₁	C₂²	semidirect
46. #121×C₂₅₁	C₂²	semidirect
47. C₂×C₄⋊C₄×C₂₅₁	C₂²	semidirect
48. C₂×C₂²⋊C₄×C₂₅₁	C₂²	semidirect
58. C₂×Dic₅₀₂	C₂³	semidirect
64. C₂×D₁₀₀₄	C₂³	semidirect
72. C₂×C₂²⋊D₂₅₁	C₂³	semidirect
73. C₂×C₂²⋊D₂₅₁	C₂³	semidirect
74. C₂×C₂²⋊D₂₅₁	C₂³	semidirect
80. C₂×C₄×D₂₅₁	D₄	semidirect
82. C₂×C₄×D₂₅₁	C₂³	semidirect
83. C₄⋊Dic₂₅₁	C₂³	semidirect
84. C₂²⋊Dic₂₅₁	C₂³	semidirect
86. (C₂×D₂₅₁)⋊C₄	C₂³	semidirect
87. (C₂×D₂₅₁)⋊C₄	C₂³	semidirect
88. C₄×Dic₂₅₁	C₂³	semidirect
94. C₂×D₄×C₂₅₁	C₂³	semidirect
99. C₂²×C₄×C₂₅₁	C₂³	semidirect
100. C₄⋊C₄×C₂₅₁	C₂³	semidirect
101. C₂²⋊C₄×C₂₅₁	C₂³	semidirect
134. C₄×D₂₅₁	C₂×D₄	semidirect
186. C₂×C₂₅₁	#535	semidirect
193. C₂₅₁	C₂×#535	semidirect
203. C₂×#121	D₂₅₁	semidirect
222. C₂²×D₄	C₂×D₂₅₁	semidirect
225. C₂³×C₄	C₂×D₂₅₁	semidirect
231. #121	C₂×D₂₅₁	semidirect
236. C₂×C₄⋊C₄	C₂×D₂₅₁	semidirect
241. C₂×C₂²⋊C₄	C₂×D₂₅₁	semidirect
275. C₂×D₄	C₂²×D₂₅₁	semidirect
287. C₂²×C₄	C₂²×D₂₅₁	semidirect
289. C₄⋊C₄	C₂²×D₂₅₁	semidirect
294. C₂²⋊C₄	C₂²×D₂₅₁	semidirect
383. C₂	#30632253	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×#16860810	2
C₂²×D₄×D₂₅₁	2
#30632253	2
C₂×#22548711	2
C₂×#22548701	2
C₂×#22548690	2
C₂×#22548689	2
C₂×#22548686	2
C₂×#22548685	2
C₂×#22548683	2
C₂×#22548673	2
C₂×#121×C₂₅₁	2
C₂×#535	251

Subgroups — C2×#30632253 #44563673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#30632253 #44563673