Subgroups — C₁₀₁×#8320 #38790471

Order 25856.

794 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	C₁₀₁×#3460	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#1954	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₁×#1477	C₂	1	2	yes	maximal, complemented
4	C₁₀₁×#1476	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1460	C₂	1	1	yes	maximal, characteristic, complemented
6	#544×C₁₀₁	C₄	1	1	yes	characteristic
7	#542×C₁₀₁	—	2	2	no	—
8	#540×C₁₀₁	—	2	2	no	—
9	#538×C₁₀₁	—	2	2	no	—
10	#537×C₁₀₁	C₄	1	1	yes	characteristic
11	#535×C₁₀₁	C₄	1	2	yes	—
12	#532×C₁₀₁	—	2	2	no	—
13	#529×C₁₀₁	—	2	2	no	—
14	#525×C₁₀₁	—	2	2	no	—
15	C₄×#41×C₁₀₁	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
17	#431×C₁₀₁	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊C₈×C₁₀₁	—	2	2	no	—
20	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
21	Q₈⋊C₈×C₁₀₁	—	2	2	no	—
22	Q₈⋊C₈×C₁₀₁	—	2	2	no	—
23	D₄⋊C₈×C₁₀₁	—	2	2	no	—
24	D₄⋊C₈×C₁₀₁	—	2	2	no	—
25	#323×C₁₀₁	—	2	2	no	—
26	C₂×#41×C₁₀₁	—	2	2	no	—
27	C₂×#41×C₁₀₁	C₂×C₄	1	2	yes	—
28	C₂²×D₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
30	C₂²×C₈×C₁₀₁	—	2	1	no	—
31	C₂²×C₈×C₁₀₁	—	2	1	no	—
32	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
33	#127×C₁₀₁	—	2	2	no	—
34	#126×C₁₀₁	—	2	4	no	—
35	#125×C₁₀₁	—	2	2	no	—
36	#124×C₁₀₁	—	2	4	no	—
37	#124×C₁₀₁	—	2	2	no	—
38	#123×C₁₀₁	—	2	4	no	—
39	#123×C₁₀₁	—	2	4	no	—
40	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
41	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
42	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
43	#121×C₁₀₁	—	2	2	no	—
44	#121×C₁₀₁	—	2	4	no	—
45	#121×C₁₀₁	—	2	2	no	—
46	#121×C₁₀₁	—	2	2	no	—
47	#121×C₁₀₁	—	2	2	no	—
48	#121×C₁₀₁	—	2	2	no	—
49	#120×C₁₀₁	—	2	4	no	—
50	C₄×Q₈×C₁₀₁	D₄	1	2	yes	—
51	C₄×Q₈×C₁₀₁	D₄	1	2	yes	—
52	C₄×D₄×C₁₀₁	—	2	4	no	—
53	C₄×D₄×C₁₀₁	—	2	2	no	—
54	C₄×D₄×C₁₀₁	—	2	2	no	—
55	C₄×D₄×C₁₀₁	—	2	2	no	—
56	C₄×D₄×C₁₀₁	—	2	2	no	—
57	C₄×D₄×C₁₀₁	D₄	1	2	yes	—
58	C₄×D₄×C₁₀₁	D₄	1	2	yes	—
59	#117×C₁₀₁	—	2	2	no	—
60	#117×C₁₀₁	—	2	2	no	—
61	#117×C₁₀₁	C₂×C₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	2	yes	—
64	C₂×C₄²×C₁₀₁	—	2	2	no	—
65	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₁₀₁	—	2	2	no	—
67	C₄⋊C₈×C₁₀₁	—	2	2	no	—
68	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
69	C₂²⋊C₈×C₁₀₁	—	4	4	no	—
70	C₄×C₈×C₁₀₁	—	2	2	no	—
71	C₄×C₈×C₁₀₁	—	2	2	no	—
72	C₂⁴×C₁₀₁	C₂²⋊C₄	1	2	yes	—
73	#41×C₁₀₁	—	2	4	no	—
74	#41×C₁₀₁	—	2	4	no	—
75	#41×C₁₀₁	—	8	2	no	—
76	#41×C₁₀₁	—	8	2	no	—
77	C₂×Q₈×C₁₀₁	—	2	2	no	—
78	C₂×Q₈×C₁₀₁	C₂²⋊C₄	1	2	yes	—
79	C₂×D₄×C₁₀₁	—	2	2	no	—
80	C₂×D₄×C₁₀₁	—	2	4	no	—
81	C₂×D₄×C₁₀₁	—	2	4	no	—
82	C₂×D₄×C₁₀₁	—	2	2	no	—
83	C₂×D₄×C₁₀₁	—	2	2	no	—
84	C₂×D₄×C₁₀₁	—	2	2	no	—
85	C₂×D₄×C₁₀₁	—	2	2	no	—
86	C₂×D₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
87	C₂²×C₄×C₁₀₁	—	2	2	no	—
88	C₂²×C₄×C₁₀₁	—	2	2	no	—
89	C₂²×C₄×C₁₀₁	—	2	2	no	—
90	C₂²×C₄×C₁₀₁	—	2	2	no	—
91	C₂²×C₄×C₁₀₁	—	2	2	no	—
92	C₂²×C₄×C₁₀₁	—	4	2	no	—
93	C₂²×C₄×C₁₀₁	—	4	2	no	—
94	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
95	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
98	C₂×C₈×C₁₀₁	—	2	2	no	—
99	C₂×C₈×C₁₀₁	—	4	1	no	—
100	C₂×C₈×C₁₀₁	—	4	1	no	—
101	C₂×C₈×C₁₀₁	—	4	2	no	—
102	C₂×C₈×C₁₀₁	—	4	2	no	—
103	C₂×C₈×C₁₀₁	—	4	1	no	—
104	C₄⋊C₄×C₁₀₁	—	2	2	no	—
105	C₄⋊C₄×C₁₀₁	—	2	2	no	—
106	C₄⋊C₄×C₁₀₁	—	2	4	no	—
107	C₄⋊C₄×C₁₀₁	—	2	2	no	—
108	C₄⋊C₄×C₁₀₁	—	2	2	no	—
109	C₄⋊C₄×C₁₀₁	—	2	2	no	—
110	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
111	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
112	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
113	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
114	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
115	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
116	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
117	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
118	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
119	C₄²×C₁₀₁	—	2	2	no	—
120	C₄²×C₁₀₁	—	2	2	no	—
121	C₄²×C₁₀₁	—	2	2	no	—
122	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
123	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
124	C₂³×C₁₀₁	—	2	2	no	—
125	C₂³×C₁₀₁	—	2	2	no	—
126	C₂³×C₁₀₁	—	2	2	no	—
127	C₂³×C₁₀₁	—	2	2	no	—
128	C₂³×C₁₀₁	—	4	2	no	—
129	C₂³×C₁₀₁	—	4	2	no	—
130	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	Q₈×C₁₀₁	—	2	4	no	—
132	Q₈×C₁₀₁	—	8	2	no	—
133	D₄×C₁₀₁	—	2	4	no	—
134	D₄×C₁₀₁	—	4	2	no	—
135	D₄×C₁₀₁	—	4	2	no	—
136	D₄×C₁₀₁	—	4	4	no	—
137	D₄×C₁₀₁	—	8	4	no	—
138	D₄×C₁₀₁	—	8	2	no	—
139	D₄×C₁₀₁	—	8	4	no	—
140	C₂×C₄×C₁₀₁	—	2	1	no	—
141	C₂×C₄×C₁₀₁	—	2	1	no	—
142	C₂×C₄×C₁₀₁	—	2	2	no	—
143	C₂×C₄×C₁₀₁	—	2	2	no	—
144	C₂×C₄×C₁₀₁	—	2	2	no	—
145	C₂×C₄×C₁₀₁	—	2	2	no	—
146	C₂×C₄×C₁₀₁	—	4	1	no	—
147	C₂×C₄×C₁₀₁	—	4	4	no	—
148	C₂×C₄×C₁₀₁	—	4	2	no	—
149	C₂×C₄×C₁₀₁	—	4	2	no	—
150	C₂×C₄×C₁₀₁	—	4	2	no	—
151	C₂×C₄×C₁₀₁	—	4	2	no	—
152	C₂×C₄×C₁₀₁	—	4	2	no	—
153	C₂×C₄×C₁₀₁	—	8	2	no	—
154	C₂×C₄×C₁₀₁	—	8	2	no	—
155	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂×C₄×C₁₀₁	#120	1	2	yes	—
157	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
158	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
159	C₂×C₄×C₁₀₁	#131	1	2	yes	—
160	C₂×C₄×C₁₀₁	#131	1	2	yes	—
161	C₈×C₁₀₁	—	4	2	no	—
162	C₈×C₁₀₁	—	8	2	no	—
163	C₈×C₁₀₁	—	8	1	no	—
164	C₂²×C₁₀₁	—	2	1	no	—
165	C₂²×C₁₀₁	—	2	1	no	—
166	C₂²×C₁₀₁	—	4	4	no	—
167	C₂²×C₁₀₁	—	4	2	no	—
168	C₂²×C₁₀₁	—	4	2	no	—
169	C₂²×C₁₀₁	—	4	2	no	—
170	C₂²×C₁₀₁	—	4	2	no	—
171	C₂²×C₁₀₁	—	4	2	no	—
172	C₂²×C₁₀₁	—	4	2	no	—
173	C₂²×C₁₀₁	—	8	2	no	—
174	C₂²×C₁₀₁	#379	1	1	yes	characteristic
175	C₂²×C₁₀₁	#408	1	1	yes	characteristic
176	C₂²×C₁₀₁	#408	1	1	yes	characteristic
177	C₄×C₁₀₁	—	2	1	no	—
178	C₄×C₁₀₁	—	2	2	no	—
179	C₄×C₁₀₁	—	4	2	no	—
180	C₄×C₁₀₁	—	4	2	no	—
181	C₄×C₁₀₁	—	4	2	no	—
182	C₄×C₁₀₁	—	4	2	no	—
183	C₄×C₁₀₁	#408	1	4	yes	—
184	C₄×C₁₀₁	#453	1	1	yes	characteristic
185	C₄×C₁₀₁	#455	1	1	yes	characteristic
186	#8320	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂×C₁₀₁	—	2	1	no	—
188	C₂×C₁₀₁	—	2	1	no	—
189	C₂×C₁₀₁	—	8	2	no	—
190	C₂×C₁₀₁	—	8	2	no	—
191	C₂×C₁₀₁	#1780	1	1	yes	characteristic
192	C₂×C₁₀₁	#1792	1	1	yes	characteristic
193	C₂×C₁₀₁	#1794	1	1	yes	characteristic
194	#3460	C₂×C₁₀₁	1	1	yes	characteristic
195	#1954	C₂×C₁₀₁	1	1	yes	characteristic, complemented
196	#1477	C₂×C₁₀₁	1	2	yes	complemented
197	#1476	C₂×C₁₀₁	1	2	yes	complemented
198	#1460	C₂×C₁₀₁	1	1	yes	characteristic, complemented
199	C₁₀₁	#8320	1	1	yes	characteristic, direct product factor, Sylow
200	#544	C₄×C₁₀₁	1	1	yes	characteristic
201	#542	—	2	2	no	—
202	#540	—	2	2	no	—
203	#538	—	2	2	no	—
204	#537	C₄×C₁₀₁	1	1	yes	characteristic
205	#535	C₄×C₁₀₁	1	2	yes	—
206	#532	—	2	2	no	—
207	#529	—	2	2	no	—
208	#525	—	2	2	no	—
209	C₄×#41	C₂²×C₁₀₁	1	2	yes	—
210	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
211	#431	C₂²×C₁₀₁	1	2	yes	—
212	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
213	C₂×C₂²⋊C₈	—	2	2	no	—
214	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
215	Q₈⋊C₈	—	2	2	no	—
216	Q₈⋊C₈	—	2	2	no	—
217	D₄⋊C₈	—	2	2	no	—
218	D₄⋊C₈	—	2	2	no	—
219	#323	—	2	2	no	—
220	C₂×#41	—	2	2	no	—
221	C₂×#41	C₂×C₄×C₁₀₁	1	2	yes	—
222	C₂²×D₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
223	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
224	C₂²×C₈	—	2	1	no	—
225	C₂²×C₈	—	2	1	no	—
226	C₄⋊Q₈	—	2	2	no	—
227	#127	—	2	2	no	—
228	#126	—	2	4	no	—
229	#125	—	2	2	no	—
230	#124	—	2	4	no	—
231	#124	—	2	2	no	—
232	#123	—	2	4	no	—
233	#123	—	2	4	no	—
234	C₂²⋊Q₈	—	2	2	no	—
235	C₂²⋊Q₈	—	2	2	no	—
236	C₂²⋊Q₈	—	2	2	no	—
237	#121	—	2	2	no	—
238	#121	—	2	4	no	—
239	#121	—	2	2	no	—
240	#121	—	2	2	no	—
241	#121	—	2	2	no	—
242	#121	—	2	2	no	—
243	#120	—	2	4	no	—
244	C₄×Q₈	D₄×C₁₀₁	1	2	yes	—
245	C₄×Q₈	D₄×C₁₀₁	1	2	yes	—
246	C₄×D₄	—	2	4	no	—
247	C₄×D₄	—	2	2	no	—
248	C₄×D₄	—	2	2	no	—
249	C₄×D₄	—	2	2	no	—
250	C₄×D₄	—	2	2	no	—
251	C₄×D₄	D₄×C₁₀₁	1	2	yes	—
252	C₄×D₄	D₄×C₁₀₁	1	2	yes	—
253	#117	—	2	2	no	—
254	#117	—	2	2	no	—
255	#117	C₂×C₄×C₁₀₁	1	2	yes	—
256	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	2	yes	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
260	C₄⋊C₈	—	2	2	no	—
261	C₄⋊C₈	—	2	2	no	—
262	C₂²⋊C₈	—	2	2	no	—
263	C₂²⋊C₈	—	4	4	no	—
264	C₄×C₈	—	2	2	no	—
265	C₄×C₈	—	2	2	no	—
266	C₂⁴	C₂²⋊C₄×C₁₀₁	1	2	yes	—
267	#41	—	2	4	no	—
268	#41	—	2	4	no	—
269	#41	—	8	2	no	—
270	#41	—	8	2	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	C₂²⋊C₄×C₁₀₁	1	2	yes	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	2	4	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
289	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	—	4	2	no	—
296	C₂×C₈	—	4	2	no	—
297	C₂×C₈	—	4	1	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
305	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
306	C₂²⋊C₄	—	2	4	no	—
307	C₂²⋊C₄	—	2	4	no	—
308	C₂²⋊C₄	—	2	4	no	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	2	4	no	—
311	C₂²⋊C₄	—	2	2	no	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
317	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	4	2	no	—
323	C₂³	—	4	2	no	—
324	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
325	Q₈	—	2	4	no	—
326	Q₈	—	8	2	no	—
327	D₄	—	2	4	no	—
328	D₄	—	4	2	no	—
329	D₄	—	4	2	no	—
330	D₄	—	4	4	no	—
331	D₄	—	8	2	no	—
332	D₄	—	8	4	no	—
333	D₄	—	8	4	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	—	8	2	no	—
349	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
350	C₂×C₄	#120×C₁₀₁	1	2	yes	—
351	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
352	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
353	C₂×C₄	#131×C₁₀₁	1	2	yes	—
354	C₂×C₄	#131×C₁₀₁	1	2	yes	—
355	C₈	—	4	2	no	—
356	C₈	—	8	2	no	—
357	C₈	—	8	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	4	4	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	8	2	no	—
368	C₂²	#379×C₁₀₁	1	1	yes	characteristic
369	C₂²	#408×C₁₀₁	1	1	yes	characteristic
370	C₂²	#408×C₁₀₁	1	1	yes	characteristic
371	C₄	—	2	1	no	—
372	C₄	—	2	2	no	—
373	C₄	—	4	2	no	—
374	C₄	—	4	2	no	—
375	C₄	—	4	2	no	—
376	C₄	—	4	2	no	—
377	C₄	#408×C₁₀₁	1	4	yes	—
378	C₄	#453×C₁₀₁	1	1	yes	characteristic
379	C₄	#455×C₁₀₁	1	1	yes	characteristic
380	C₂	—	2	1	no	—
381	C₂	—	2	1	no	—
382	C₂	—	8	2	no	—
383	C₂	—	8	2	no	—
384	C₂	C₁₀₁×#1780	1	1	yes	characteristic
385	C₂	C₁₀₁×#1792	1	1	yes	characteristic
386	C₂	C₁₀₁×#1794	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₀₁	#120
commutator	C₂²×C₄	C₂²×C₄×C₁₀₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₀₁
socle	C₂²×C₁₀₁	#379
prime radical	C₁₀₁×#3460	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₁ ◁ C₂×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₁×#1954	C₂	semidirect
3. C₁₀₁×#1477	C₂	semidirect
4. C₁₀₁×#1476	C₂	semidirect
5. C₁₀₁×#1460	C₂	semidirect
186. #8320	C₁₀₁	direct (N × H)
195. #1954	C₂×C₁₀₁	semidirect
196. #1477	C₂×C₁₀₁	semidirect
197. #1476	C₂×C₁₀₁	semidirect
198. #1460	C₂×C₁₀₁	semidirect
199. C₁₀₁	#8320	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₀₁×#3460	2
C₁₀₁×#1954	2
C₁₀₁×#1477	2
C₁₀₁×#1476	2
C₁₀₁×#1460	2
#8320	101

Subgroups — C101×#8320 #38790471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#8320 #38790471