Subgroups — C₂×#30632503 #44565131

Order 32128.

1408 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22548763	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#22548762	C₂	1	1	yes	maximal, characteristic, complemented
3	#30632503	C₂	1	16	yes	maximal, direct product factor
4	C₂×#22548748	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#22548747	C₂	1	2	yes	maximal, complemented
6	C₂×#22548744	C₂	1	2	yes	maximal, complemented
7	C₂×#22548736	C₂	1	2	yes	maximal, complemented
8	C₂×#22548735	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#16860800	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×Q₁₆×D₂₅₁	C₂	1	2	yes	maximal, complemented
11	C₂×#22548723	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#22548763	—	2	4	no	—
14	#22548763	C₂²	1	8	yes	complemented
15	#22548762	—	2	4	no	—
16	#22548762	C₂²	1	8	yes	complemented
17	C₂×#16860811	—	2	1	no	—
18	C₂×#16860811	C₂²	1	2	yes	—
19	C₂×#16860810	—	2	1	no	—
20	C₂×#16860810	—	2	2	no	—
21	C₂×#16860810	C₂²	1	1	yes	characteristic
22	C₂×#16860810	C₂²	1	1	yes	characteristic
23	C₂×#16860809	—	2	2	no	—
24	C₂×#16860809	C₂²	1	2	yes	—
25	C₂²×Dic₅₀₂	—	2	1	no	—
26	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₂₅₁	—	2	1	no	—
28	C₂×Q₈×D₂₅₁	C₂²	1	2	yes	—
29	C₂×Q₈×D₂₅₁	C₂²	1	2	yes	—
30	#22548748	C₂²	1	8	yes	complemented
31	#22548747	C₂²	1	16	yes	complemented
32	#22548744	C₂²	1	16	yes	complemented
33	#22548736	C₂²	1	16	yes	complemented
34	#22548735	C₂²	1	8	yes	complemented
35	C₂×Dic₁₀₀₄	C₂²	1	2	yes	—
36	C₂×#16860800	C₂²	1	1	yes	characteristic
37	C₂×#16860800	C₂²	1	2	yes	—
38	C₂×#16860800	C₂²	1	2	yes	—
39	C₂×#16860800	C₂²	1	8	yes	complemented
40	Q₁₆×D₂₅₁	C₂²	1	16	yes	complemented
41	C₂×#16860799	C₂²	1	2	yes	—
42	C₂×#16860798	C₂²	1	1	yes	characteristic
43	C₂×#16860797	C₂²	1	1	yes	characteristic
44	C₂×#16860795	C₂²	1	1	yes	characteristic
45	#22548723	C₂²	1	8	yes	complemented
46	C₂×#16860793	C₂²	1	2	yes	—
47	C₂²×C₂₅₁⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₈×D₂₅₁	C₂²	1	2	yes	—
49	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic
50	C₂²×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
51	#137×C₂₅₁	C₂²	1	8	yes	complemented
52	C₂×Q₁₆×C₂₅₁	C₂²	1	2	yes	—
53	C₂×SD₁₆×C₂₅₁	C₂²	1	2	yes	—
54	C₂×M₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
55	#16860811	—	2	8	no	—
56	#16860811	—	2	4	no	—
57	#16860811	C₂³	1	8	yes	—
58	#16860810	—	2	8	no	—
59	#16860810	—	2	16	no	—
60	#16860810	—	2	2	no	—
61	#16860810	D₄	1	4	yes	—
62	#16860810	C₂³	1	4	yes	—
63	#16860810	C₂³	1	4	yes	—
64	#16860809	—	2	16	no	—
65	#16860809	—	2	4	no	—
66	#16860809	C₂³	1	8	yes	—
67	C₂×Dic₅₀₂	—	2	8	no	—
68	C₂×Dic₅₀₂	—	2	2	no	—
69	C₂×Dic₅₀₂	—	2	2	no	—
70	C₂×Dic₅₀₂	—	2	1	no	—
71	C₂×Dic₅₀₂	—	2	2	no	—
72	C₂×Dic₅₀₂	D₄	1	1	yes	characteristic
73	C₂×Dic₅₀₂	C₂³	1	4	yes	—
74	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
75	C₂×Dic₅₀₂	C₂³	1	2	yes	—
76	Q₈×D₂₅₁	—	2	8	no	—
77	Q₈×D₂₅₁	—	2	4	no	—
78	Q₈×D₂₅₁	—	2	4	no	—
79	Q₈×D₂₅₁	C₂³	1	8	yes	—
80	Q₈×D₂₅₁	C₂³	1	8	yes	—
81	C₂×D₁₀₀₄	—	2	2	no	—
82	C₂×D₁₀₀₄	D₄	1	1	yes	characteristic
83	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊D₂₅₁	—	2	2	no	—
85	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
86	C₂×C₂²⋊D₂₅₁	D₄	1	2	yes	—
87	C₂²×Dic₂₅₁	—	2	2	no	—
88	C₂²×Dic₂₅₁	—	2	1	no	—
89	C₂×C₄×D₂₅₁	—	2	2	no	—
90	C₂×C₄×D₂₅₁	—	2	2	no	—
91	C₂×C₄×D₂₅₁	—	2	2	no	—
92	C₂×C₄×D₂₅₁	—	2	1	no	—
93	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
94	Dic₁₀₀₄	C₂³	1	8	yes	—
95	#16860800	C₂³	1	8	yes	—
96	#16860800	C₂³	1	8	yes	—
97	#16860800	C₂³	1	4	yes	—
98	#16860799	C₂³	1	8	yes	—
99	#16860798	C₂³	1	4	yes	—
100	#16860797	C₂³	1	4	yes	—
101	#16860795	C₂³	1	4	yes	—
102	#16860793	C₂³	1	8	yes	—
103	C₂×C₂₅₁⋊C₈	C₂³	1	1	yes	characteristic
104	C₂×C₂₅₁⋊C₈	C₂³	1	1	yes	characteristic
105	C₂×C₂₅₁⋊C₈	C₂³	1	4	yes	—
106	C₈×D₂₅₁	C₂³	1	8	yes	—
107	#41×C₂₅₁	—	2	2	no	—
108	#41×C₂₅₁	C₂³	1	4	yes	—
109	C₂×Q₈×C₂₅₁	—	2	1	no	—
110	C₂×Q₈×C₂₅₁	—	2	2	no	—
111	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
112	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
113	C₂×Q₈×C₂₅₁	C₂³	1	4	yes	—
114	C₂×D₄×C₂₅₁	—	2	1	no	—
115	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₂₅₁	—	2	1	no	—
117	C₂²×C₄×C₂₅₁	—	2	1	no	—
118	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
119	Q₁₆×C₂₅₁	C₂³	1	8	yes	—
120	SD₁₆×C₂₅₁	C₂³	1	8	yes	—
121	M₁₆×C₂₅₁	C₂³	1	4	yes	—
122	C₂×C₈×C₂₅₁	C₂³	1	2	yes	—
123	C₂²×D₂₅₁	—	2	1	no	—
124	C₂²×D₂₅₁	C₂×D₄	1	2	yes	—
125	Dic₅₀₂	—	2	1	no	—
126	Dic₅₀₂	—	2	2	no	—
127	Dic₅₀₂	—	2	4	no	—
128	Dic₅₀₂	—	2	8	no	—
129	Dic₅₀₂	—	2	8	no	—
130	Dic₅₀₂	C₂×D₄	1	4	yes	—
131	Dic₅₀₂	C₂⁴	1	2	yes	—
132	Dic₅₀₂	C₂⁴	1	4	yes	—
133	D₁₀₀₄	—	2	8	no	—
134	D₁₀₀₄	—	2	1	no	—
135	D₁₀₀₄	C₂×D₄	1	4	yes	—
136	D₁₀₀₄	C₂⁴	1	2	yes	—
137	C₂²⋊D₂₅₁	—	2	4	no	—
138	C₂²⋊D₂₅₁	—	2	8	no	—
139	C₂²⋊D₂₅₁	C₂×D₄	1	8	yes	—
140	C₂×Dic₂₅₁	—	2	1	no	—
141	C₂×Dic₂₅₁	—	2	2	no	—
142	C₂×Dic₂₅₁	—	2	4	no	—
143	C₂×Dic₂₅₁	—	2	8	no	—
144	C₂×Dic₂₅₁	C₂×D₄	1	2	yes	—
145	C₄×D₂₅₁	—	2	8	no	—
146	C₄×D₂₅₁	—	2	8	no	—
147	C₄×D₂₅₁	—	2	4	no	—
148	C₄×D₂₅₁	—	2	8	no	—
149	C₄×D₂₅₁	C₂×D₄	1	4	yes	—
150	C₄×D₂₅₁	C₂⁴	1	4	yes	—
151	C₂₅₁⋊C₈	C₂⁴	1	2	yes	—
152	C₂₅₁⋊C₈	C₂⁴	1	2	yes	—
153	C₂³×C₂₅₁	—	2	1	no	—
154	C₂³×C₂₅₁	C₂×D₄	1	1	yes	characteristic
155	Q₈×C₂₅₁	—	2	4	no	—
156	Q₈×C₂₅₁	—	2	2	no	—
157	Q₈×C₂₅₁	—	2	1	no	—
158	Q₈×C₂₅₁	C₂⁴	1	4	yes	—
159	Q₈×C₂₅₁	C₂⁴	1	2	yes	—
160	D₄×C₂₅₁	—	2	4	no	—
161	D₄×C₂₅₁	—	2	1	no	—
162	D₄×C₂₅₁	C₂⁴	1	2	yes	—
163	C₂×C₄×C₂₅₁	—	2	1	no	—
164	C₂×C₄×C₂₅₁	—	2	2	no	—
165	C₂×C₄×C₂₅₁	—	2	4	no	—
166	C₂×C₄×C₂₅₁	—	2	4	no	—
167	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
168	C₂×C₄×C₂₅₁	C₂×D₄	1	2	yes	—
169	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
171	C₈×C₂₅₁	C₂⁴	1	4	yes	—
172	C₂²×C₂₅₁	—	2	2	no	—
173	C₂²×C₂₅₁	—	2	2	no	—
174	C₂²×C₂₅₁	—	4	2	no	—
175	C₂²×C₂₅₁	C₂²×D₄	1	2	yes	—
176	C₂²×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
177	C₂×D₂₅₁	—	2	4	no	—
178	C₂×D₂₅₁	—	2	2	no	—
179	C₂×D₂₅₁	—	4	2	no	—
180	C₂×D₂₅₁	C₂²×D₄	1	4	yes	—
181	C₄×C₂₅₁	—	2	2	no	—
182	C₄×C₂₅₁	—	2	4	no	—
183	C₄×C₂₅₁	C₂²×D₄	1	2	yes	—
184	C₄×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
185	C₄×C₂₅₁	C₂⁵	1	1	yes	characteristic
186	Dic₂₅₁	—	2	2	no	—
187	Dic₂₅₁	—	2	4	no	—
188	Dic₂₅₁	C₂²×D₄	1	4	yes	—
189	C₂×C₂₅₁	—	2	2	no	—
190	C₂×C₂₅₁	—	4	2	no	—
191	C₂×C₂₅₁	#578	1	2	yes	complemented
192	C₂×C₂₅₁	C₂³×D₄	1	1	yes	characteristic
193	D₂₅₁	—	2	4	no	—
194	D₂₅₁	—	4	2	no	—
195	C₂₅₁	C₂×#578	1	1	yes	characteristic, complemented, Sylow
196	C₂×#578	—	251	1	no	maximal, Sylow
197	C₂×2₋¹⁺⁴	—	251	1	no	—
198	C₂×2₋¹⁺⁴	—	251	1	no	—
199	#578	—	251	16	no	—
200	C₂×#137	—	251	2	no	—
201	C₂×#137	—	251	2	no	—
202	C₂×#137	—	251	1	no	—
203	C₂×#137	D₂₅₁	1	1	yes	characteristic, complemented
204	C₂×#135	—	251	1	no	—
205	C₂×#135	—	251	2	no	—
206	C₂²×Q₁₆	—	251	1	no	—
207	C₂²×Q₁₆	—	251	2	no	—
208	C₂×#131	—	251	1	no	—
209	2₋¹⁺⁴	—	502	4	no	—
210	2₋¹⁺⁴	—	502	4	no	—
211	2₋¹⁺⁴	—	251	8	no	—
212	2₋¹⁺⁴	—	251	8	no	—
213	C₂×#41	—	502	2	no	—
214	C₂×#41	—	502	1	no	—
215	C₂×#41	—	502	2	no	—
216	C₂×#41	—	502	1	no	—
217	C₂×#41	—	251	2	no	—
218	C₂×#41	—	251	2	no	—
219	C₂×#41	—	251	1	no	—
220	C₂×#41	—	251	1	no	—
221	C₂×#41	C₂×D₂₅₁	1	1	yes	characteristic
222	C₂²×Q₈	—	502	1	no	—
223	C₂²×Q₈	—	502	1	no	—
224	C₂²×Q₈	—	251	2	no	—
225	C₂²×Q₈	—	251	2	no	—
226	C₂²×Q₈	—	251	1	no	—
227	C₂²×Q₈	C₂×D₂₅₁	1	1	yes	characteristic
228	#137	—	251	16	no	—
229	#137	—	251	16	no	—
230	#137	—	251	8	no	—
231	#137	C₂×D₂₅₁	1	8	yes	complemented
232	#135	—	251	8	no	—
233	#135	—	251	16	no	—
234	C₂×Q₁₆	—	251	1	no	—
235	C₂×Q₁₆	—	251	2	no	—
236	C₂×Q₁₆	—	251	2	no	—
237	C₂×Q₁₆	—	251	8	no	—
238	C₂×Q₁₆	—	251	16	no	—
239	C₂×Q₁₆	—	251	2	no	—
240	C₂×Q₁₆	C₂×D₂₅₁	1	2	yes	—
241	C₂×SD₁₆	—	251	1	no	—
242	C₂×SD₁₆	—	251	1	no	—
243	C₂×SD₁₆	—	251	2	no	—
244	C₂×SD₁₆	C₂×D₂₅₁	1	2	yes	—
245	C₂×D₈	—	251	1	no	—
246	#131	—	251	8	no	—
247	C₂×M₁₆	—	251	2	no	—
248	C₂×M₁₆	C₂×D₂₅₁	1	1	yes	characteristic
249	C₂²×C₈	—	251	1	no	—
250	C₂²×C₈	—	251	2	no	—
251	#41	—	2	2	no	—
252	#41	—	502	16	no	—
253	#41	—	502	8	no	—
254	#41	—	502	16	no	—
255	#41	—	502	8	no	—
256	#41	—	502	4	no	—
257	#41	—	502	4	no	—
258	#41	—	502	2	no	—
259	#41	—	251	8	no	—
260	#41	—	251	8	no	—
261	#41	—	251	4	no	—
262	#41	—	251	4	no	—
263	#41	—	251	4	no	—
264	#41	C₂²×D₂₅₁	1	4	yes	—
265	C₂×Q₈	—	2	1	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	502	8	no	—
268	C₂×Q₈	—	502	2	no	—
269	C₂×Q₈	—	502	2	no	—
270	C₂×Q₈	—	502	8	no	—
271	C₂×Q₈	—	502	4	no	—
272	C₂×Q₈	—	502	4	no	—
273	C₂×Q₈	—	502	1	no	—
274	C₂×Q₈	—	502	2	no	—
275	C₂×Q₈	—	251	8	no	—
276	C₂×Q₈	—	251	8	no	—
277	C₂×Q₈	—	251	1	no	—
278	C₂×Q₈	—	251	2	no	—
279	C₂×Q₈	—	251	4	no	—
280	C₂×Q₈	—	251	1	no	—
281	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
282	C₂×Q₈	C₂²×D₂₅₁	1	2	yes	—
283	C₂×Q₈	C₂²×D₂₅₁	1	4	yes	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	502	2	no	—
286	C₂×D₄	—	502	2	no	—
287	C₂×D₄	—	502	1	no	—
288	C₂×D₄	—	251	2	no	—
289	C₂×D₄	—	251	1	no	—
290	C₂×D₄	—	251	1	no	—
291	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	502	2	no	—
295	C₂²×C₄	—	502	2	no	—
296	C₂²×C₄	—	502	2	no	—
297	C₂²×C₄	—	502	1	no	—
298	C₂²×C₄	—	502	2	no	—
299	C₂²×C₄	—	502	1	no	—
300	C₂²×C₄	—	251	2	no	—
301	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
302	Q₁₆	—	251	4	no	—
303	Q₁₆	—	251	8	no	—
304	Q₁₆	—	251	8	no	—
305	Q₁₆	—	251	8	no	—
306	Q₁₆	C₂²×D₂₅₁	1	8	yes	—
307	SD₁₆	—	251	4	no	—
308	SD₁₆	—	251	4	no	—
309	SD₁₆	—	251	8	no	—
310	SD₁₆	C₂²×D₂₅₁	1	8	yes	—
311	D₈	—	251	4	no	—
312	M₁₆	—	251	8	no	—
313	M₁₆	C₂²×D₂₅₁	1	4	yes	—
314	C₂×C₈	—	251	1	no	—
315	C₂×C₈	—	251	1	no	—
316	C₂×C₈	—	251	4	no	—
317	C₂×C₈	—	251	8	no	—
318	C₂×C₈	C₂²×D₂₅₁	1	2	yes	—
319	C₂³	—	2	1	no	—
320	C₂³	—	502	1	no	—
321	C₂³	—	251	2	no	—
322	C₂³	D₄×D₂₅₁	1	1	yes	characteristic
323	Q₈	—	2	4	no	—
324	Q₈	—	2	2	no	—
325	Q₈	—	2	1	no	—
326	Q₈	—	502	8	no	—
327	Q₈	—	502	8	no	—
328	Q₈	—	502	4	no	—
329	Q₈	—	502	1	no	—
330	Q₈	—	502	2	no	—
331	Q₈	—	251	2	no	—
332	Q₈	—	251	4	no	—
333	Q₈	—	251	4	no	—
334	Q₈	C₂³×D₂₅₁	1	2	yes	—
335	Q₈	C₂³×D₂₅₁	1	4	yes	—
336	D₄	—	2	4	no	—
337	D₄	—	2	1	no	—
338	D₄	—	502	8	no	—
339	D₄	—	502	8	no	—
340	D₄	—	502	4	no	—
341	D₄	—	502	1	no	—
342	D₄	—	251	8	no	—
343	D₄	—	251	4	no	—
344	D₄	—	251	2	no	—
345	D₄	C₂³×D₂₅₁	1	2	yes	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	502	8	no	—
351	C₂×C₄	—	502	8	no	—
352	C₂×C₄	—	502	8	no	—
353	C₂×C₄	—	502	4	no	—
354	C₂×C₄	—	502	1	no	—
355	C₂×C₄	—	502	2	no	—
356	C₂×C₄	—	502	8	no	—
357	C₂×C₄	—	502	4	no	—
358	C₂×C₄	—	251	2	no	—
359	C₂×C₄	—	251	4	no	—
360	C₂×C₄	—	251	4	no	—
361	C₂×C₄	D₄×D₂₅₁	1	2	yes	—
362	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
363	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
364	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
365	C₈	—	251	2	no	—
366	C₈	—	251	2	no	—
367	C₈	C₂³×D₂₅₁	1	4	yes	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	1004	2	no	—
372	C₂²	—	502	2	no	—
373	C₂²	—	502	4	no	—
374	C₂²	—	251	4	no	—
375	C₂²	C₂×D₄×D₂₅₁	1	2	yes	—
376	C₂²	C₂×D₄×D₂₅₁	1	1	yes	characteristic
377	C₄	—	2	2	no	—
378	C₄	—	2	4	no	—
379	C₄	—	502	2	no	—
380	C₄	—	502	4	no	—
381	C₄	—	251	4	no	—
382	C₄	C₂×D₄×D₂₅₁	1	2	yes	—
383	C₄	C₂×D₄×D₂₅₁	1	1	yes	characteristic
384	C₄	C₂⁴×D₂₅₁	1	1	yes	characteristic
385	C₂	—	2	2	no	—
386	C₂	—	4	2	no	—
387	C₂	—	1004	2	no	—
388	C₂	—	502	4	no	—
389	C₂	#30632503	1	2	yes	direct product factor
390	C₂	C₂²×D₄×D₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₂₅₁
commutator, cosocle	C₄×C₂₅₁	C₂⁵
Frattini	C₄	C₂⁴×D₂₅₁
Fitting	C₂×#137×C₂₅₁	C₂
socle	C₂²×C₂₅₁	C₂²×D₄
hypercenter	C₂×#137	D₂₅₁
hypocenter	C₂₅₁	C₂×#578
LCS	G ▷ C₄×C₂₅₁ ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#137

Complements

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

N	H ≅ G/N	type
1. C₂×#22548763	C₂	semidirect
2. C₂×#22548762	C₂	semidirect
3. #30632503	C₂	direct (N × H)
4. C₂×#22548748	C₂	semidirect
5. C₂×#22548747	C₂	semidirect
6. C₂×#22548744	C₂	semidirect
7. C₂×#22548736	C₂	semidirect
8. C₂×#22548735	C₂	semidirect
9. C₂²×#16860800	C₂	semidirect
10. C₂×Q₁₆×D₂₅₁	C₂	semidirect
11. C₂×#22548723	C₂	semidirect
12. C₂×#137×C₂₅₁	C₂	semidirect
14. #22548763	C₂²	semidirect
16. #22548762	C₂²	semidirect
30. #22548748	C₂²	semidirect
31. #22548747	C₂²	semidirect
32. #22548744	C₂²	semidirect
33. #22548736	C₂²	semidirect
34. #22548735	C₂²	semidirect
39. C₂×#16860800	C₂²	semidirect
40. Q₁₆×D₂₅₁	C₂²	semidirect
45. #22548723	C₂²	semidirect
51. #137×C₂₅₁	C₂²	semidirect
191. C₂×C₂₅₁	#578	semidirect
195. C₂₅₁	C₂×#578	semidirect
203. C₂×#137	D₂₅₁	semidirect
231. #137	C₂×D₂₅₁	semidirect
389. C₂	#30632503	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#22548763	2
C₂×#22548762	2
#30632503	2
C₂×#22548748	2
C₂×#22548747	2
C₂×#22548744	2
C₂×#22548736	2
C₂×#22548735	2
C₂²×#16860800	2
C₂×Q₁₆×D₂₅₁	2
C₂×#22548723	2
C₂×#137×C₂₅₁	2
C₂×#578	251

Subgroups — C2×#30632503 #44565131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#30632503 #44565131