Subgroups — C₂×C₁₀₁×#1666 #38801262

Order 25856.

786 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#492×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#475×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#460×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×Q₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#1666	C₂	1	8	yes	maximal, direct product factor
6	C₂×#334×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#332×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#331×C₁₀₁	C₂	1	1	yes	maximal, characteristic
9	C₂²×SD₁₆×C₁₀₁	—	2	1	no	—
10	C₂²×SD₁₆×C₁₀₁	—	2	1	no	—
11	C₂²×SD₁₆×C₁₀₁	—	2	1	no	—
12	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂×#127×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
15	#492×C₁₀₁	—	2	2	no	—
16	#492×C₁₀₁	C₂²	1	4	yes	—
17	#475×C₁₀₁	—	2	2	no	—
18	#475×C₁₀₁	C₂²	1	4	yes	complemented
19	#460×C₁₀₁	—	2	2	no	—
20	#460×C₁₀₁	C₂²	1	4	yes	—
21	C₈×Q₈×C₁₀₁	—	2	2	no	—
22	C₈×Q₈×C₁₀₁	C₂²	1	4	yes	complemented
23	C₂×#106×C₁₀₁	—	2	1	no	—
24	C₂×C₄⋊C₈×C₁₀₁	—	2	1	no	—
25	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
28	C₂×#103×C₁₀₁	—	2	1	no	—
29	C₂×#102×C₁₀₁	—	2	1	no	—
30	C₂×C₄×C₈×C₁₀₁	—	2	1	no	—
31	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
32	#334×C₁₀₁	C₂²	1	4	yes	complemented
33	#332×C₁₀₁	C₂²	1	4	yes	complemented
34	#331×C₁₀₁	C₂²	1	4	yes	—
35	C₂²×Q₈×C₁₀₁	—	2	1	no	—
36	C₂²×Q₈×C₁₀₁	D₄	1	1	yes	characteristic
37	C₂²×D₄×C₁₀₁	—	2	1	no	—
38	C₂²×D₄×C₁₀₁	—	2	1	no	—
39	C₂²×D₄×C₁₀₁	—	2	1	no	—
40	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
41	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
42	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
43	C₂×SD₁₆×C₁₀₁	—	4	4	no	—
44	C₂×SD₁₆×C₁₀₁	—	4	4	no	—
45	C₂×SD₁₆×C₁₀₁	—	4	4	no	—
46	C₂²×C₈×C₁₀₁	—	2	1	no	—
47	C₂²×C₈×C₁₀₁	—	2	1	no	—
48	C₂²×C₈×C₁₀₁	—	2	1	no	—
49	C₂²×C₈×C₁₀₁	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₀₁	D₄	1	1	yes	characteristic
51	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
52	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
53	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
54	C₄⋊Q₈×C₁₀₁	C₂³	1	2	yes	—
55	#127×C₁₀₁	—	2	1	no	—
56	#127×C₁₀₁	—	2	1	no	—
57	#127×C₁₀₁	—	2	1	no	—
58	#127×C₁₀₁	C₂³	1	2	yes	—
59	C₄×Q₈×C₁₀₁	—	2	1	no	—
60	C₄×Q₈×C₁₀₁	—	2	1	no	—
61	C₄×Q₈×C₁₀₁	D₄	1	2	yes	—
62	C₄×Q₈×C₁₀₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₀₁	—	2	1	no	—
68	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
69	#106×C₁₀₁	—	2	4	no	—
70	C₄⋊C₈×C₁₀₁	—	2	4	no	—
71	C₄⋊C₈×C₁₀₁	—	2	1	no	—
72	C₄⋊C₈×C₁₀₁	—	2	1	no	—
73	C₄⋊C₈×C₁₀₁	—	2	1	no	—
74	C₄⋊C₈×C₁₀₁	C₂³	1	2	yes	—
75	C₄⋊C₈×C₁₀₁	C₂³	1	2	yes	—
76	C₄⋊C₈×C₁₀₁	C₂³	1	2	yes	—
77	#103×C₁₀₁	—	2	4	no	—
78	#102×C₁₀₁	—	2	4	no	—
79	C₄×C₈×C₁₀₁	—	2	4	no	—
80	C₄×C₈×C₁₀₁	D₄	1	2	yes	—
81	C₄×C₈×C₁₀₁	C₂³	1	2	yes	—
82	C₂⁴×C₁₀₁	—	4	1	no	—
83	C₂×Q₈×C₁₀₁	—	2	1	no	—
84	C₂×Q₈×C₁₀₁	—	2	2	no	—
85	C₂×Q₈×C₁₀₁	—	2	2	no	—
86	C₂×Q₈×C₁₀₁	—	4	1	no	—
87	C₂×Q₈×C₁₀₁	—	4	2	no	—
88	C₂×Q₈×C₁₀₁	—	4	2	no	—
89	C₂×Q₈×C₁₀₁	SD₁₆	1	4	yes	complemented
90	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
91	C₂×D₄×C₁₀₁	—	2	2	no	—
92	C₂×D₄×C₁₀₁	—	2	2	no	—
93	C₂×D₄×C₁₀₁	—	2	2	no	—
94	C₂×D₄×C₁₀₁	—	4	1	no	—
95	C₂×D₄×C₁₀₁	—	4	1	no	—
96	C₂×D₄×C₁₀₁	—	4	1	no	—
97	C₂×D₄×C₁₀₁	—	4	2	no	—
98	C₂×D₄×C₁₀₁	—	4	2	no	—
99	C₂×D₄×C₁₀₁	—	4	2	no	—
100	C₂×D₄×C₁₀₁	—	4	2	no	—
101	C₂×D₄×C₁₀₁	—	8	2	no	—
102	C₂²×C₄×C₁₀₁	—	2	1	no	—
103	C₂²×C₄×C₁₀₁	—	2	1	no	—
104	C₂²×C₄×C₁₀₁	—	4	1	no	—
105	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₀₁	#41	1	1	yes	characteristic
108	SD₁₆×C₁₀₁	—	4	8	no	—
109	SD₁₆×C₁₀₁	—	4	8	no	—
110	SD₁₆×C₁₀₁	—	4	8	no	—
111	C₂×C₈×C₁₀₁	—	2	2	no	—
112	C₂×C₈×C₁₀₁	—	2	2	no	—
113	C₂×C₈×C₁₀₁	—	2	2	no	—
114	C₂×C₈×C₁₀₁	—	2	2	no	—
115	C₂×C₈×C₁₀₁	—	4	2	no	—
116	C₂×C₈×C₁₀₁	—	4	2	no	—
117	C₂×C₈×C₁₀₁	—	4	2	no	—
118	C₂×C₈×C₁₀₁	SD₁₆	1	4	yes	complemented
119	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
121	C₄⋊C₄×C₁₀₁	—	2	2	no	—
122	C₄⋊C₄×C₁₀₁	—	2	1	no	—
123	C₄⋊C₄×C₁₀₁	—	2	2	no	—
124	C₄⋊C₄×C₁₀₁	—	2	2	no	—
125	C₄⋊C₄×C₁₀₁	—	2	2	no	—
126	C₄⋊C₄×C₁₀₁	—	4	1	no	—
127	C₄⋊C₄×C₁₀₁	—	4	1	no	—
128	C₄⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	—
129	C₄²×C₁₀₁	—	2	2	no	—
130	C₄²×C₁₀₁	—	2	2	no	—
131	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₀₁	#41	1	1	yes	characteristic
134	C₄²×C₁₀₁	C₂⁴	1	1	yes	characteristic
135	C₂³×C₁₀₁	—	4	2	no	—
136	C₂³×C₁₀₁	—	8	2	no	—
137	C₂³×C₁₀₁	—	8	2	no	—
138	C₂³×C₁₀₁	—	8	2	no	—
139	C₂³×C₁₀₁	#121	1	1	yes	characteristic
140	Q₈×C₁₀₁	—	2	2	no	—
141	Q₈×C₁₀₁	—	2	4	no	—
142	Q₈×C₁₀₁	—	4	2	no	—
143	Q₈×C₁₀₁	—	4	2	no	—
144	Q₈×C₁₀₁	—	8	2	no	—
145	Q₈×C₁₀₁	C₂×SD₁₆	1	4	yes	complemented
146	D₄×C₁₀₁	—	4	2	no	—
147	D₄×C₁₀₁	—	4	2	no	—
148	D₄×C₁₀₁	—	4	2	no	—
149	D₄×C₁₀₁	—	4	2	no	—
150	D₄×C₁₀₁	—	8	2	no	—
151	D₄×C₁₀₁	—	8	2	no	—
152	D₄×C₁₀₁	—	8	2	no	—
153	D₄×C₁₀₁	—	8	2	no	—
154	C₂×C₄×C₁₀₁	—	2	2	no	—
155	C₂×C₄×C₁₀₁	—	2	4	no	—
156	C₂×C₄×C₁₀₁	—	2	2	no	—
157	C₂×C₄×C₁₀₁	—	2	2	no	—
158	C₂×C₄×C₁₀₁	—	4	2	no	—
159	C₂×C₄×C₁₀₁	—	4	2	no	—
160	C₂×C₄×C₁₀₁	—	8	2	no	—
161	C₂×C₄×C₁₀₁	#121	1	1	yes	characteristic
162	C₂×C₄×C₁₀₁	#121	1	1	yes	characteristic
163	C₂×C₄×C₁₀₁	#121	1	1	yes	characteristic
164	C₂×C₄×C₁₀₁	C₂×SD₁₆	1	2	yes	—
165	C₂×C₄×C₁₀₁	C₂×SD₁₆	1	2	yes	—
166	C₂×C₄×C₁₀₁	#135	1	2	yes	—
167	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
168	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
171	C₈×C₁₀₁	—	2	2	no	—
172	C₈×C₁₀₁	—	4	2	no	—
173	C₈×C₁₀₁	—	4	2	no	—
174	C₈×C₁₀₁	—	4	2	no	—
175	C₈×C₁₀₁	C₂×SD₁₆	1	4	yes	complemented
176	C₂²×C₁₀₁	—	8	2	no	—
177	C₂²×C₁₀₁	—	8	2	no	—
178	C₂²×C₁₀₁	—	8	2	no	—
179	C₂²×C₁₀₁	—	16	4	no	—
180	C₂²×C₁₀₁	#460	1	2	yes	—
181	C₂²×C₁₀₁	#465	1	2	yes	—
182	C₂²×C₁₀₁	#471	1	2	yes	—
183	C₂²×C₁₀₁	C₂×#121	1	1	yes	characteristic
184	C₄×C₁₀₁	—	2	4	no	—
185	C₄×C₁₀₁	—	2	1	no	—
186	C₄×C₁₀₁	—	2	1	no	—
187	C₄×C₁₀₁	—	4	2	no	—
188	C₄×C₁₀₁	—	8	2	no	—
189	C₄×C₁₀₁	#460	1	2	yes	—
190	C₄×C₁₀₁	#465	1	2	yes	—
191	C₄×C₁₀₁	C₂²×SD₁₆	1	1	yes	characteristic
192	C₄×C₁₀₁	C₂²×SD₁₆	1	1	yes	characteristic
193	C₄×C₁₀₁	C₂×#135	1	1	yes	characteristic
194	C₄×C₁₀₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₂×#1666	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂×C₁₀₁	—	16	2	no	—
197	C₂×C₁₀₁	#1666	1	4	yes	direct product factor
198	C₂×C₁₀₁	C₂×#460	1	1	yes	characteristic
199	C₂×C₁₀₁	C₂×#465	1	1	yes	characteristic
200	C₂×C₁₀₁	C₂×#471	1	1	yes	characteristic
201	C₂×#492	C₂×C₁₀₁	1	1	yes	characteristic
202	C₂×#475	C₂×C₁₀₁	1	1	yes	characteristic, complemented
203	C₂×#460	C₂×C₁₀₁	1	1	yes	characteristic
204	C₂×C₈×Q₈	C₂×C₁₀₁	1	1	yes	characteristic, complemented
205	#1666	C₂×C₁₀₁	1	8	yes	direct product factor
206	C₂×#334	C₂×C₁₀₁	1	1	yes	characteristic, complemented
207	C₂×#332	C₂×C₁₀₁	1	1	yes	characteristic, complemented
208	C₂×#331	C₂×C₁₀₁	1	1	yes	characteristic
209	C₁₀₁	C₂×#1666	1	1	yes	characteristic, direct product factor, Sylow
210	C₂²×SD₁₆	—	2	1	no	—
211	C₂²×SD₁₆	—	2	1	no	—
212	C₂²×SD₁₆	—	2	1	no	—
213	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
214	C₂×#127	C₂²×C₁₀₁	1	1	yes	characteristic
215	C₂×C₄×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
216	#492	—	2	2	no	—
217	#492	C₂²×C₁₀₁	1	4	yes	—
218	#475	—	2	2	no	—
219	#475	C₂²×C₁₀₁	1	4	yes	complemented
220	#460	—	2	2	no	—
221	#460	C₂²×C₁₀₁	1	4	yes	—
222	C₈×Q₈	—	2	2	no	—
223	C₈×Q₈	C₂²×C₁₀₁	1	4	yes	complemented
224	C₂×#106	—	2	1	no	—
225	C₂×C₄⋊C₈	—	2	1	no	—
226	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
227	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
228	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
229	C₂×#103	—	2	1	no	—
230	C₂×#102	—	2	1	no	—
231	C₂×C₄×C₈	—	2	1	no	—
232	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
233	#334	C₂²×C₁₀₁	1	4	yes	complemented
234	#332	C₂²×C₁₀₁	1	4	yes	complemented
235	#331	C₂²×C₁₀₁	1	4	yes	—
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×Q₈	D₄×C₁₀₁	1	1	yes	characteristic
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂×SD₁₆	—	2	4	no	—
242	C₂×SD₁₆	—	2	4	no	—
243	C₂×SD₁₆	—	2	4	no	—
244	C₂×SD₁₆	—	4	4	no	—
245	C₂×SD₁₆	—	4	4	no	—
246	C₂×SD₁₆	—	4	4	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	2	1	no	—
249	C₂²×C₈	—	2	1	no	—
250	C₂²×C₈	D₄×C₁₀₁	1	1	yes	characteristic
251	C₂²×C₈	D₄×C₁₀₁	1	1	yes	characteristic
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	C₂³×C₁₀₁	1	2	yes	—
256	#127	—	2	1	no	—
257	#127	—	2	1	no	—
258	#127	—	2	1	no	—
259	#127	C₂³×C₁₀₁	1	2	yes	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×Q₈	D₄×C₁₀₁	1	2	yes	—
263	C₄×Q₈	C₂³×C₁₀₁	1	2	yes	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
270	#106	—	2	4	no	—
271	C₄⋊C₈	—	2	4	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	C₂³×C₁₀₁	1	2	yes	—
276	C₄⋊C₈	C₂³×C₁₀₁	1	2	yes	—
277	C₄⋊C₈	C₂³×C₁₀₁	1	2	yes	—
278	#103	—	2	4	no	—
279	#102	—	2	4	no	—
280	C₄×C₈	—	2	4	no	—
281	C₄×C₈	D₄×C₁₀₁	1	2	yes	—
282	C₄×C₈	C₂³×C₁₀₁	1	2	yes	—
283	C₂⁴	—	4	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×Q₈	—	4	2	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	SD₁₆×C₁₀₁	1	4	yes	complemented
291	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	8	2	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
308	C₂²×C₄	#41×C₁₀₁	1	1	yes	characteristic
309	SD₁₆	—	4	8	no	—
310	SD₁₆	—	4	8	no	—
311	SD₁₆	—	4	8	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	—	4	2	no	—
318	C₂×C₈	—	4	2	no	—
319	C₂×C₈	SD₁₆×C₁₀₁	1	4	yes	complemented
320	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
321	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
333	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
334	C₄²	#41×C₁₀₁	1	1	yes	characteristic
335	C₄²	C₂⁴×C₁₀₁	1	1	yes	characteristic
336	C₂³	—	4	2	no	—
337	C₂³	—	8	2	no	—
338	C₂³	—	8	2	no	—
339	C₂³	—	8	2	no	—
340	C₂³	#121×C₁₀₁	1	1	yes	characteristic
341	Q₈	—	2	4	no	—
342	Q₈	—	2	2	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	4	2	no	—
345	Q₈	—	8	2	no	—
346	Q₈	C₂×SD₁₆×C₁₀₁	1	4	yes	complemented
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	8	2	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	2	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	8	2	no	—
362	C₂×C₄	#121×C₁₀₁	1	1	yes	characteristic
363	C₂×C₄	#121×C₁₀₁	1	1	yes	characteristic
364	C₂×C₄	#121×C₁₀₁	1	1	yes	characteristic
365	C₂×C₄	C₂×SD₁₆×C₁₀₁	1	2	yes	—
366	C₂×C₄	C₂×SD₁₆×C₁₀₁	1	2	yes	—
367	C₂×C₄	#135×C₁₀₁	1	2	yes	—
368	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
369	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
370	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
372	C₈	—	2	2	no	—
373	C₈	—	4	2	no	—
374	C₈	—	4	2	no	—
375	C₈	—	4	2	no	—
376	C₈	C₂×SD₁₆×C₁₀₁	1	4	yes	complemented
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	16	4	no	—
381	C₂²	#460×C₁₀₁	1	2	yes	—
382	C₂²	#465×C₁₀₁	1	2	yes	—
383	C₂²	#471×C₁₀₁	1	2	yes	—
384	C₂²	C₂×#121×C₁₀₁	1	1	yes	characteristic
385	C₄	—	2	4	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	4	2	no	—
389	C₄	—	8	2	no	—
390	C₄	#460×C₁₀₁	1	2	yes	—
391	C₄	#465×C₁₀₁	1	2	yes	—
392	C₄	C₂²×SD₁₆×C₁₀₁	1	1	yes	characteristic
393	C₄	C₂²×SD₁₆×C₁₀₁	1	1	yes	characteristic
394	C₄	C₂×#135×C₁₀₁	1	1	yes	characteristic
395	C₄	C₂×AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
396	C₂	—	16	2	no	—
397	C₂	C₁₀₁×#1666	1	4	yes	direct product factor
398	C₂	C₂×#460×C₁₀₁	1	1	yes	characteristic
399	C₂	C₂×#465×C₁₀₁	1	1	yes	characteristic
400	C₂	C₂×#471×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₁	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₁
prime radical	C₂×#127×C₁₀₁	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#475×C₁₀₁	C₂	semidirect
4. C₂×C₈×Q₈×C₁₀₁	C₂	semidirect
5. C₁₀₁×#1666	C₂	direct (N × H)
6. C₂×#334×C₁₀₁	C₂	semidirect
7. C₂×#332×C₁₀₁	C₂	semidirect
18. #475×C₁₀₁	C₂²	semidirect
22. C₈×Q₈×C₁₀₁	C₂²	semidirect
32. #334×C₁₀₁	C₂²	semidirect
33. #332×C₁₀₁	C₂²	semidirect
89. C₂×Q₈×C₁₀₁	SD₁₆	semidirect
118. C₂×C₈×C₁₀₁	SD₁₆	semidirect
145. Q₈×C₁₀₁	C₂×SD₁₆	semidirect
175. C₈×C₁₀₁	C₂×SD₁₆	semidirect
195. C₂×#1666	C₁₀₁	direct (N × H)
197. C₂×C₁₀₁	#1666	direct (N × H)
202. C₂×#475	C₂×C₁₀₁	semidirect
204. C₂×C₈×Q₈	C₂×C₁₀₁	semidirect
205. #1666	C₂×C₁₀₁	direct (N × H)
206. C₂×#334	C₂×C₁₀₁	semidirect
207. C₂×#332	C₂×C₁₀₁	semidirect
209. C₁₀₁	C₂×#1666	direct (N × H)
219. #475	C₂²×C₁₀₁	semidirect
223. C₈×Q₈	C₂²×C₁₀₁	semidirect
233. #334	C₂²×C₁₀₁	semidirect
234. #332	C₂²×C₁₀₁	semidirect
290. C₂×Q₈	SD₁₆×C₁₀₁	semidirect
319. C₂×C₈	SD₁₆×C₁₀₁	semidirect
346. Q₈	C₂×SD₁₆×C₁₀₁	semidirect
376. C₈	C₂×SD₁₆×C₁₀₁	semidirect
397. C₂	C₁₀₁×#1666	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×#492×C₁₀₁	2
C₂×#475×C₁₀₁	2
C₂×#460×C₁₀₁	2
C₂×C₈×Q₈×C₁₀₁	2
C₁₀₁×#1666	2
C₂×#334×C₁₀₁	2
C₂×#332×C₁₀₁	2
C₂×#331×C₁₀₁	2
C₂×#1666	101

Subgroups — C2×C101×#1666 #38801262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₁×#1666 #38801262