Subgroups — C₂×C₁₀₁×#2060 #38805709

Order 25856.

1218 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#544×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#428×C₁₀₁	C₂	1	2	yes	maximal
3	C₂×#384×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#2060	C₂	1	8	yes	maximal, direct product factor
5	C₂×#343×C₁₀₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#339×C₁₀₁	C₂	1	2	yes	maximal
7	C₂²×M₁₆×C₁₀₁	C₂²	1	2	yes	—
8	#544×C₁₀₁	—	2	4	no	—
9	#544×C₁₀₁	—	2	2	no	—
10	#544×C₁₀₁	C₂²	1	4	yes	—
11	C₂×C₄⋊Q₈×C₁₀₁	—	2	2	no	—
12	C₂×#125×C₁₀₁	—	2	2	no	—
13	C₂×C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
14	C₂×#117×C₁₀₁	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₁₀₁	—	2	2	no	—
16	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
19	#428×C₁₀₁	—	2	4	no	—
20	#428×C₁₀₁	C₂²	1	8	yes	—
21	C₂×#107×C₁₀₁	—	2	2	no	—
22	C₂×#106×C₁₀₁	—	2	2	no	—
23	#384×C₁₀₁	—	2	2	no	—
24	#384×C₁₀₁	C₂²	1	4	yes	—
25	#343×C₁₀₁	C₂²	1	4	yes	—
26	#339×C₁₀₁	C₂²	1	8	yes	—
27	C₂²×Q₈×C₁₀₁	—	2	2	no	—
28	C₂³×C₄×C₁₀₁	—	2	1	no	—
29	C₂³×C₄×C₁₀₁	—	2	1	no	—
30	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
31	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
32	C₂×M₁₆×C₁₀₁	—	2	2	no	—
33	C₂×M₁₆×C₁₀₁	—	2	4	no	—
34	C₂×M₁₆×C₁₀₁	Q₈	1	8	yes	complemented
35	C₂×M₁₆×C₁₀₁	C₂³	1	4	yes	—
36	C₂²×C₈×C₁₀₁	—	2	2	no	—
37	C₄⋊Q₈×C₁₀₁	—	2	8	no	—
38	C₄⋊Q₈×C₁₀₁	—	2	8	no	—
39	#125×C₁₀₁	—	2	8	no	—
40	#125×C₁₀₁	—	2	8	no	—
41	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
42	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
43	#117×C₁₀₁	—	2	2	no	—
44	#117×C₁₀₁	—	2	2	no	—
45	#117×C₁₀₁	D₄	1	4	yes	—
46	#117×C₁₀₁	C₂³	1	4	yes	—
47	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₀₁	—	2	8	no	—
54	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₀₁	—	4	8	no	—
56	C₂×C₄⋊C₄×C₁₀₁	D₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₀₁	D₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₀₁	D₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
62	C₂×C₄²×C₁₀₁	—	2	1	no	—
63	C₂×C₄²×C₁₀₁	—	2	2	no	—
64	C₂×C₄²×C₁₀₁	—	2	2	no	—
65	C₂×C₄²×C₁₀₁	Q₈	1	4	yes	complemented
66	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
67	#107×C₁₀₁	—	2	8	no	—
68	#106×C₁₀₁	—	2	8	no	—
69	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
70	C₂×Q₈×C₁₀₁	—	2	8	no	—
71	C₂×Q₈×C₁₀₁	—	8	4	no	—
72	C₂²×C₄×C₁₀₁	—	2	4	no	—
73	C₂²×C₄×C₁₀₁	—	2	4	no	—
74	C₂²×C₄×C₁₀₁	—	2	4	no	—
75	C₂²×C₄×C₁₀₁	—	2	2	no	—
76	C₂²×C₄×C₁₀₁	—	2	2	no	—
77	C₂²×C₄×C₁₀₁	—	2	2	no	—
78	C₂²×C₄×C₁₀₁	—	2	2	no	—
79	C₂²×C₄×C₁₀₁	—	2	2	no	—
80	C₂²×C₄×C₁₀₁	—	2	2	no	—
81	C₂²×C₄×C₁₀₁	—	4	4	no	—
82	C₂²×C₄×C₁₀₁	—	4	4	no	—
83	C₂²×C₄×C₁₀₁	—	4	1	no	—
84	C₂²×C₄×C₁₀₁	—	4	1	no	—
85	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
86	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₁₀₁	C₂×Q₈	1	4	yes	—
90	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
92	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
93	M₁₆×C₁₀₁	—	2	8	no	—
94	M₁₆×C₁₀₁	—	2	4	no	—
95	M₁₆×C₁₀₁	C₂×Q₈	1	8	yes	complemented
96	C₂×C₈×C₁₀₁	—	2	8	no	—
97	C₂×C₈×C₁₀₁	—	2	4	no	—
98	C₄⋊C₄×C₁₀₁	—	2	8	no	—
99	C₄⋊C₄×C₁₀₁	—	2	16	no	—
100	C₄⋊C₄×C₁₀₁	—	2	4	no	—
101	C₄⋊C₄×C₁₀₁	—	2	2	no	—
102	C₄⋊C₄×C₁₀₁	—	2	2	no	—
103	C₄⋊C₄×C₁₀₁	—	2	4	no	—
104	C₄⋊C₄×C₁₀₁	—	2	4	no	—
105	C₄⋊C₄×C₁₀₁	—	4	16	no	—
106	C₄⋊C₄×C₁₀₁	—	4	2	no	—
107	C₄⋊C₄×C₁₀₁	C₂×D₄	1	4	yes	—
108	C₄⋊C₄×C₁₀₁	C₂×D₄	1	4	yes	—
109	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
110	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
111	C₄²×C₁₀₁	—	2	4	no	—
112	C₄²×C₁₀₁	—	2	4	no	—
113	C₄²×C₁₀₁	—	2	4	no	—
114	C₄²×C₁₀₁	—	2	2	no	—
115	C₄²×C₁₀₁	C₂×Q₈	1	4	yes	complemented
116	C₂³×C₁₀₁	—	2	2	no	—
117	C₂³×C₁₀₁	—	2	2	no	—
118	C₂³×C₁₀₁	#120	1	1	yes	characteristic
119	C₂³×C₁₀₁	#120	1	1	yes	characteristic
120	C₂³×C₁₀₁	C₂²⋊Q₈	1	2	yes	—
121	C₂³×C₁₀₁	C₄⋊Q₈	1	2	yes	—
122	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
123	Q₈×C₁₀₁	—	8	8	no	—
124	C₂×C₄×C₁₀₁	—	2	4	no	—
125	C₂×C₄×C₁₀₁	—	2	16	no	—
126	C₂×C₄×C₁₀₁	—	2	4	no	—
127	C₂×C₄×C₁₀₁	—	2	4	no	—
128	C₂×C₄×C₁₀₁	—	2	4	no	—
129	C₂×C₄×C₁₀₁	—	2	4	no	—
130	C₂×C₄×C₁₀₁	—	2	4	no	—
131	C₂×C₄×C₁₀₁	—	4	4	no	—
132	C₂×C₄×C₁₀₁	—	4	4	no	—
133	C₂×C₄×C₁₀₁	—	4	4	no	—
134	C₂×C₄×C₁₀₁	—	4	4	no	—
135	C₂×C₄×C₁₀₁	—	4	4	no	—
136	C₂×C₄×C₁₀₁	—	4	2	no	—
137	C₂×C₄×C₁₀₁	—	8	2	no	—
138	C₂×C₄×C₁₀₁	—	8	2	no	—
139	C₂×C₄×C₁₀₁	—	8	2	no	—
140	C₂×C₄×C₁₀₁	#120	1	2	yes	—
141	C₂×C₄×C₁₀₁	C₂²⋊Q₈	1	4	yes	—
142	C₂×C₄×C₁₀₁	C₂²⋊Q₈	1	4	yes	—
143	C₂×C₄×C₁₀₁	C₂²⋊Q₈	1	2	yes	—
144	C₂×C₄×C₁₀₁	C₄⋊Q₈	1	4	yes	—
145	C₂×C₄×C₁₀₁	C₄⋊Q₈	1	4	yes	—
146	C₂×C₄×C₁₀₁	C₄⋊Q₈	1	2	yes	—
147	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
148	C₂×C₄×C₁₀₁	C₂²×Q₈	1	2	yes	—
149	C₂×C₄×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
151	C₈×C₁₀₁	—	2	8	no	—
152	C₂²×C₁₀₁	—	2	4	no	—
153	C₂²×C₁₀₁	—	2	4	no	—
154	C₂²×C₁₀₁	—	2	1	no	—
155	C₂²×C₁₀₁	—	2	1	no	—
156	C₂²×C₁₀₁	—	2	1	no	—
157	C₂²×C₁₀₁	—	2	1	no	—
158	C₂²×C₁₀₁	#395	1	2	yes	—
159	C₂²×C₁₀₁	#395	1	2	yes	—
160	C₂²×C₁₀₁	#453	1	2	yes	—
161	C₂²×C₁₀₁	#456	1	2	yes	—
162	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
163	C₂²×C₁₀₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
164	C₂²×C₁₀₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
165	C₄×C₁₀₁	—	2	8	no	—
166	C₄×C₁₀₁	—	4	4	no	—
167	C₄×C₁₀₁	—	4	4	no	—
168	C₄×C₁₀₁	—	4	4	no	—
169	C₄×C₁₀₁	—	8	2	no	—
170	C₄×C₁₀₁	#395	1	4	yes	—
171	C₄×C₁₀₁	C₂×C₂²⋊Q₈	1	2	yes	—
172	C₄×C₁₀₁	C₂×C₄⋊Q₈	1	2	yes	—
173	C₂×#2060	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂×C₁₀₁	—	2	1	no	—
175	C₂×C₁₀₁	—	2	1	no	—
176	C₂×C₁₀₁	—	2	2	no	—
177	C₂×C₁₀₁	#2060	1	4	yes	direct product factor
178	C₂×C₁₀₁	C₂×#395	1	1	yes	characteristic
179	C₂×C₁₀₁	C₂×#453	1	1	yes	characteristic
180	C₂×C₁₀₁	C₂×#456	1	1	yes	characteristic
181	C₂×#544	C₂×C₁₀₁	1	1	yes	characteristic
182	C₂×#428	C₂×C₁₀₁	1	2	yes	—
183	C₂×#384	C₂×C₁₀₁	1	1	yes	characteristic
184	#2060	C₂×C₁₀₁	1	8	yes	direct product factor
185	C₂×#343	C₂×C₁₀₁	1	1	yes	characteristic
186	C₂×#339	C₂×C₁₀₁	1	2	yes	—
187	C₁₀₁	C₂×#2060	1	1	yes	characteristic, direct product factor, Sylow
188	C₂²×M₁₆	C₂²×C₁₀₁	1	2	yes	—
189	#544	—	2	4	no	—
190	#544	—	2	2	no	—
191	#544	C₂²×C₁₀₁	1	4	yes	—
192	C₂×C₄⋊Q₈	—	2	2	no	—
193	C₂×#125	—	2	2	no	—
194	C₂×C₂²⋊Q₈	—	2	2	no	—
195	C₂×#117	C₂²×C₁₀₁	1	2	yes	—
196	C₂²×C₄⋊C₄	—	2	2	no	—
197	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
198	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
199	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
200	#428	—	2	4	no	—
201	#428	C₂²×C₁₀₁	1	8	yes	—
202	C₂×#107	—	2	2	no	—
203	C₂×#106	—	2	2	no	—
204	#384	—	2	2	no	—
205	#384	C₂²×C₁₀₁	1	4	yes	—
206	#343	C₂²×C₁₀₁	1	4	yes	—
207	#339	C₂²×C₁₀₁	1	8	yes	—
208	C₂²×Q₈	—	2	2	no	—
209	C₂³×C₄	—	2	1	no	—
210	C₂³×C₄	—	2	1	no	—
211	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
212	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
213	C₂×M₁₆	—	2	2	no	—
214	C₂×M₁₆	—	2	4	no	—
215	C₂×M₁₆	Q₈×C₁₀₁	1	8	yes	complemented
216	C₂×M₁₆	C₂³×C₁₀₁	1	4	yes	—
217	C₂²×C₈	—	2	2	no	—
218	C₄⋊Q₈	—	2	8	no	—
219	C₄⋊Q₈	—	2	8	no	—
220	#125	—	2	8	no	—
221	#125	—	2	8	no	—
222	C₂²⋊Q₈	—	2	8	no	—
223	C₂²⋊Q₈	—	2	8	no	—
224	#117	—	2	2	no	—
225	#117	—	2	2	no	—
226	#117	D₄×C₁₀₁	1	4	yes	—
227	#117	C₂³×C₁₀₁	1	4	yes	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	4	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	8	no	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₄⋊C₄	—	4	8	no	—
237	C₂×C₄⋊C₄	D₄×C₁₀₁	1	2	yes	—
238	C₂×C₄⋊C₄	D₄×C₁₀₁	1	2	yes	—
239	C₂×C₄⋊C₄	D₄×C₁₀₁	1	2	yes	—
240	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
241	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
242	C₂×C₂²⋊C₄	—	2	2	no	—
243	C₂×C₄²	—	2	2	no	—
244	C₂×C₄²	—	2	1	no	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	Q₈×C₁₀₁	1	4	yes	complemented
247	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
248	#107	—	2	8	no	—
249	#106	—	2	8	no	—
250	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
251	C₂×Q₈	—	2	8	no	—
252	C₂×Q₈	—	8	4	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	4	4	no	—
263	C₂²×C₄	—	4	4	no	—
264	C₂²×C₄	—	4	1	no	—
265	C₂²×C₄	—	4	1	no	—
266	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
267	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
268	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
269	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
270	C₂²×C₄	C₂×Q₈×C₁₀₁	1	4	yes	—
271	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
272	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
273	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
274	M₁₆	—	2	8	no	—
275	M₁₆	—	2	4	no	—
276	M₁₆	C₂×Q₈×C₁₀₁	1	8	yes	complemented
277	C₂×C₈	—	2	8	no	—
278	C₂×C₈	—	2	4	no	—
279	C₄⋊C₄	—	2	8	no	—
280	C₄⋊C₄	—	2	16	no	—
281	C₄⋊C₄	—	2	4	no	—
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	4	16	no	—
287	C₄⋊C₄	—	4	2	no	—
288	C₄⋊C₄	C₂×D₄×C₁₀₁	1	4	yes	—
289	C₄⋊C₄	C₂×D₄×C₁₀₁	1	4	yes	—
290	C₂²⋊C₄	—	2	4	no	—
291	C₂²⋊C₄	—	2	4	no	—
292	C₄²	—	2	4	no	—
293	C₄²	—	2	4	no	—
294	C₄²	—	2	4	no	—
295	C₄²	—	2	2	no	—
296	C₄²	C₂×Q₈×C₁₀₁	1	4	yes	complemented
297	C₂³	—	2	2	no	—
298	C₂³	—	2	2	no	—
299	C₂³	#120×C₁₀₁	1	1	yes	characteristic
300	C₂³	#120×C₁₀₁	1	1	yes	characteristic
301	C₂³	C₂²⋊Q₈×C₁₀₁	1	2	yes	—
302	C₂³	C₄⋊Q₈×C₁₀₁	1	2	yes	—
303	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
304	Q₈	—	8	8	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	16	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	4	4	no	—
313	C₂×C₄	—	4	4	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	—	4	4	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	8	2	no	—
319	C₂×C₄	—	8	2	no	—
320	C₂×C₄	—	8	2	no	—
321	C₂×C₄	#120×C₁₀₁	1	2	yes	—
322	C₂×C₄	C₂²⋊Q₈×C₁₀₁	1	2	yes	—
323	C₂×C₄	C₂²⋊Q₈×C₁₀₁	1	4	yes	—
324	C₂×C₄	C₂²⋊Q₈×C₁₀₁	1	4	yes	—
325	C₂×C₄	C₄⋊Q₈×C₁₀₁	1	2	yes	—
326	C₂×C₄	C₄⋊Q₈×C₁₀₁	1	4	yes	—
327	C₂×C₄	C₄⋊Q₈×C₁₀₁	1	4	yes	—
328	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
329	C₂×C₄	C₂²×Q₈×C₁₀₁	1	2	yes	—
330	C₂×C₄	C₂²×Q₈×C₁₀₁	1	1	yes	characteristic
331	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
332	C₈	—	2	8	no	—
333	C₂²	—	2	1	no	—
334	C₂²	—	2	1	no	—
335	C₂²	—	2	1	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	2	4	no	—
338	C₂²	—	2	4	no	—
339	C₂²	#395×C₁₀₁	1	2	yes	—
340	C₂²	#395×C₁₀₁	1	2	yes	—
341	C₂²	#453×C₁₀₁	1	2	yes	—
342	C₂²	#456×C₁₀₁	1	2	yes	—
343	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
344	C₂²	C₂×C₂²⋊Q₈×C₁₀₁	1	1	yes	characteristic
345	C₂²	C₂×C₄⋊Q₈×C₁₀₁	1	1	yes	characteristic
346	C₄	—	2	8	no	—
347	C₄	—	4	4	no	—
348	C₄	—	4	4	no	—
349	C₄	—	4	4	no	—
350	C₄	—	8	2	no	—
351	C₄	#395×C₁₀₁	1	4	yes	—
352	C₄	C₂×C₂²⋊Q₈×C₁₀₁	1	2	yes	—
353	C₄	C₂×C₄⋊Q₈×C₁₀₁	1	2	yes	—
354	C₂	—	2	1	no	—
355	C₂	—	2	2	no	—
356	C₂	—	2	1	no	—
357	C₂	C₁₀₁×#2060	1	4	yes	direct product factor
358	C₂	C₂×#395×C₁₀₁	1	1	yes	characteristic
359	C₂	C₂×#453×C₁₀₁	1	1	yes	characteristic
360	C₂	C₂×#456×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₁	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂⁴×C₁₀₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂³×C₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₀₁×#2060	C₂	direct (N × H)
34. C₂×M₁₆×C₁₀₁	Q₈	semidirect
65. C₂×C₄²×C₁₀₁	Q₈	semidirect
95. M₁₆×C₁₀₁	C₂×Q₈	semidirect
115. C₄²×C₁₀₁	C₂×Q₈	semidirect
173. C₂×#2060	C₁₀₁	direct (N × H)
177. C₂×C₁₀₁	#2060	direct (N × H)
184. #2060	C₂×C₁₀₁	direct (N × H)
187. C₁₀₁	C₂×#2060	direct (N × H)
215. C₂×M₁₆	Q₈×C₁₀₁	semidirect
246. C₂×C₄²	Q₈×C₁₀₁	semidirect
276. M₁₆	C₂×Q₈×C₁₀₁	semidirect
296. C₄²	C₂×Q₈×C₁₀₁	semidirect
357. C₂	C₁₀₁×#2060	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×#544×C₁₀₁	2
C₂×#428×C₁₀₁	2
C₂×#384×C₁₀₁	2
C₁₀₁×#2060	2
C₂×#343×C₁₀₁	2
C₂×#339×C₁₀₁	2
C₂×#2060	101

Subgroups — C2×C101×#2060 #38805709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₁×#2060 #38805709