Subgroups — C₁₀₁×#18904 #38801055

Order 25856.

946 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3501	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#3229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₁×#3229	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#461×C₁₀₁	C₂	1	1	yes	maximal, characteristic
5	C₁₀₁×#1651	C₂	1	4	yes	maximal, complemented
6	C₁₀₁×#1643	C₂	1	4	yes	maximal, complemented
7	C₁₀₁×#1542	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₁×#1481	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₁×#1478	C₂	1	1	yes	maximal, characteristic
10	C₂²×SD₁₆×C₁₀₁	—	2	1	no	—
11	#554×C₁₀₁	—	2	1	no	—
12	#554×C₁₀₁	—	2	2	no	—
13	#554×C₁₀₁	—	2	2	no	—
14	#554×C₁₀₁	C₂²	1	2	yes	—
15	D₄×Q₈×C₁₀₁	—	2	1	no	—
16	D₄×Q₈×C₁₀₁	C₂²	1	2	yes	—
17	#544×C₁₀₁	—	2	1	no	—
18	#543×C₁₀₁	—	2	2	no	—
19	#533×C₁₀₁	C₂²	1	1	yes	characteristic
20	#533×C₁₀₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
23	#518×C₁₀₁	—	2	1	no	—
24	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
25	#498×C₁₀₁	—	2	1	no	—
26	#498×C₁₀₁	C₂²	1	2	yes	complemented
27	#487×C₁₀₁	—	2	1	no	—
28	#487×C₁₀₁	C₂²	1	2	yes	complemented
29	#483×C₁₀₁	—	2	2	no	—
30	#483×C₁₀₁	—	2	2	no	—
31	#475×C₁₀₁	—	2	2	no	—
32	#475×C₁₀₁	C₂²	1	4	yes	complemented
33	#461×C₁₀₁	—	2	2	no	—
34	#461×C₁₀₁	C₂²	1	4	yes	—
35	#431×C₁₀₁	C₂²	1	1	yes	characteristic
36	#431×C₁₀₁	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
38	C₂×#103×C₁₀₁	—	2	1	no	—
39	#333×C₁₀₁	C₂²	1	2	yes	complemented
40	#332×C₁₀₁	C₂²	1	2	yes	complemented
41	Q₈⋊C₈×C₁₀₁	C₂²	1	4	yes	complemented
42	D₄⋊C₈×C₁₀₁	C₂²	1	4	yes	—
43	C₂²×Q₈×C₁₀₁	—	2	2	no	—
44	C₂²×Q₈×C₁₀₁	—	2	1	no	—
45	C₂²×D₄×C₁₀₁	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₀₁	—	2	1	no	—
47	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
48	C₂×SD₁₆×C₁₀₁	—	4	4	no	—
49	C₂²×C₈×C₁₀₁	—	2	1	no	—
50	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
51	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
52	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
53	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
54	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
55	C₄⋊Q₈×C₁₀₁	D₄	1	1	yes	characteristic
56	C₄⋊Q₈×C₁₀₁	D₄	1	1	yes	characteristic
57	C₄⋊Q₈×C₁₀₁	C₂³	1	2	yes	—
58	C₄⋊Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
59	C₄⋊Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
60	#125×C₁₀₁	—	2	2	no	—
61	#125×C₁₀₁	—	2	2	no	—
62	#125×C₁₀₁	—	2	1	no	—
63	#125×C₁₀₁	—	2	1	no	—
64	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
65	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
66	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
67	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
68	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
69	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
70	C₂²⋊Q₈×C₁₀₁	—	2	1	no	—
71	C₂²⋊Q₈×C₁₀₁	—	2	1	no	—
72	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
73	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
74	C₂²⋊Q₈×C₁₀₁	D₄	1	2	yes	—
75	C₂²⋊Q₈×C₁₀₁	D₄	1	2	yes	—
76	C₄×Q₈×C₁₀₁	—	2	1	no	—
77	C₄×Q₈×C₁₀₁	—	2	1	no	—
78	C₄×Q₈×C₁₀₁	D₄	1	2	yes	—
79	C₄×Q₈×C₁₀₁	C₂³	1	2	yes	—
80	C₄×D₄×C₁₀₁	—	2	2	no	—
81	C₄×D₄×C₁₀₁	—	2	2	no	—
82	C₄×D₄×C₁₀₁	—	2	2	no	—
83	C₄×D₄×C₁₀₁	—	2	2	no	—
84	C₄×D₄×C₁₀₁	—	2	1	no	—
85	C₄×D₄×C₁₀₁	—	2	1	no	—
86	C₄×D₄×C₁₀₁	D₄	1	2	yes	—
87	C₄×D₄×C₁₀₁	C₂³	1	2	yes	—
88	#117×C₁₀₁	—	2	1	no	—
89	#117×C₁₀₁	—	2	1	no	—
90	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
91	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
92	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
96	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
97	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
98	#106×C₁₀₁	—	2	4	no	—
99	#106×C₁₀₁	—	2	4	no	—
100	C₄⋊C₈×C₁₀₁	—	2	1	no	—
101	C₄⋊C₈×C₁₀₁	—	2	1	no	—
102	C₄⋊C₈×C₁₀₁	C₂³	1	2	yes	—
103	C₄⋊C₈×C₁₀₁	C₂³	1	2	yes	—
104	#103×C₁₀₁	—	2	4	no	—
105	#103×C₁₀₁	—	2	4	no	—
106	#103×C₁₀₁	—	2	4	no	—
107	C₂²⋊C₈×C₁₀₁	—	2	1	no	—
108	C₂²⋊C₈×C₁₀₁	—	2	1	no	—
109	C₄×C₈×C₁₀₁	—	2	1	no	—
110	C₄×C₈×C₁₀₁	C₂³	1	2	yes	—
111	C₂⁴×C₁₀₁	—	2	1	no	—
112	C₂×Q₈×C₁₀₁	—	2	4	no	—
113	C₂×Q₈×C₁₀₁	—	2	1	no	—
114	C₂×Q₈×C₁₀₁	—	2	1	no	—
115	C₂×Q₈×C₁₀₁	—	2	2	no	—
116	C₂×Q₈×C₁₀₁	—	4	1	no	—
117	C₂×Q₈×C₁₀₁	—	4	2	no	—
118	C₂×Q₈×C₁₀₁	—	4	2	no	—
119	C₂×Q₈×C₁₀₁	—	8	4	no	—
120	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
121	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
122	C₂×D₄×C₁₀₁	—	2	1	no	—
123	C₂×D₄×C₁₀₁	—	2	2	no	—
124	C₂×D₄×C₁₀₁	SD₁₆	1	4	yes	—
125	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₀₁	—	2	4	no	—
127	C₂²×C₄×C₁₀₁	—	2	4	no	—
128	C₂²×C₄×C₁₀₁	—	2	1	no	—
129	C₂²×C₄×C₁₀₁	—	2	2	no	—
130	C₂²×C₄×C₁₀₁	—	2	2	no	—
131	C₂²×C₄×C₁₀₁	—	4	1	no	—
132	C₂²×C₄×C₁₀₁	—	8	2	no	—
133	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
136	SD₁₆×C₁₀₁	—	4	8	no	—
137	C₂×C₈×C₁₀₁	—	2	2	no	—
138	C₂×C₈×C₁₀₁	—	2	2	no	—
139	C₂×C₈×C₁₀₁	—	2	2	no	—
140	C₂×C₈×C₁₀₁	—	4	2	no	—
141	C₄⋊C₄×C₁₀₁	—	2	4	no	—
142	C₄⋊C₄×C₁₀₁	—	2	4	no	—
143	C₄⋊C₄×C₁₀₁	—	2	4	no	—
144	C₄⋊C₄×C₁₀₁	—	2	2	no	—
145	C₄⋊C₄×C₁₀₁	—	2	2	no	—
146	C₄⋊C₄×C₁₀₁	—	2	1	no	—
147	C₄⋊C₄×C₁₀₁	—	2	1	no	—
148	C₄⋊C₄×C₁₀₁	—	2	1	no	—
149	C₄⋊C₄×C₁₀₁	—	2	1	no	—
150	C₄⋊C₄×C₁₀₁	—	2	2	no	—
151	C₄⋊C₄×C₁₀₁	—	2	1	no	—
152	C₄⋊C₄×C₁₀₁	—	2	1	no	—
153	C₄⋊C₄×C₁₀₁	—	2	1	no	—
154	C₄⋊C₄×C₁₀₁	—	2	2	no	—
155	C₄⋊C₄×C₁₀₁	—	2	2	no	—
156	C₄⋊C₄×C₁₀₁	—	2	2	no	—
157	C₄⋊C₄×C₁₀₁	—	4	1	no	—
158	C₄⋊C₄×C₁₀₁	—	4	1	no	—
159	C₄⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	—
160	C₄⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	—
161	C₄⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	—
162	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
163	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
164	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
165	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
166	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
167	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
168	C₄²×C₁₀₁	—	2	2	no	—
169	C₄²×C₁₀₁	—	2	2	no	—
170	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₀₁	C₂⁴	1	1	yes	characteristic
174	C₂³×C₁₀₁	—	2	2	no	—
175	C₂³×C₁₀₁	—	2	4	no	—
176	C₂³×C₁₀₁	—	8	1	no	—
177	C₂³×C₁₀₁	—	8	1	no	—
178	C₂³×C₁₀₁	#120	1	1	yes	characteristic
179	Q₈×C₁₀₁	—	2	4	no	—
180	Q₈×C₁₀₁	—	4	2	no	—
181	Q₈×C₁₀₁	—	4	2	no	—
182	Q₈×C₁₀₁	—	4	2	no	—
183	Q₈×C₁₀₁	—	4	2	no	—
184	Q₈×C₁₀₁	—	8	1	no	—
185	Q₈×C₁₀₁	—	8	4	no	—
186	Q₈×C₁₀₁	—	8	2	no	—
187	D₄×C₁₀₁	—	2	2	no	—
188	D₄×C₁₀₁	—	2	4	no	—
189	D₄×C₁₀₁	C₂×SD₁₆	1	4	yes	—
190	C₂×C₄×C₁₀₁	—	2	2	no	—
191	C₂×C₄×C₁₀₁	—	2	2	no	—
192	C₂×C₄×C₁₀₁	—	2	2	no	—
193	C₂×C₄×C₁₀₁	—	2	2	no	—
194	C₂×C₄×C₁₀₁	—	2	2	no	—
195	C₂×C₄×C₁₀₁	—	2	2	no	—
196	C₂×C₄×C₁₀₁	—	4	1	no	—
197	C₂×C₄×C₁₀₁	—	4	4	no	—
198	C₂×C₄×C₁₀₁	—	4	2	no	—
199	C₂×C₄×C₁₀₁	—	8	2	no	—
200	C₂×C₄×C₁₀₁	—	8	1	no	—
201	C₂×C₄×C₁₀₁	—	8	4	no	—
202	C₂×C₄×C₁₀₁	—	8	4	no	—
203	C₂×C₄×C₁₀₁	—	8	2	no	—
204	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
205	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
206	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
207	C₂×C₄×C₁₀₁	C₂×SD₁₆	1	2	yes	—
208	C₂×C₄×C₁₀₁	#137	1	2	yes	—
209	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
212	C₈×C₁₀₁	—	4	2	no	—
213	C₈×C₁₀₁	—	4	2	no	—
214	C₈×C₁₀₁	—	4	2	no	—
215	C₂²×C₁₀₁	—	2	1	no	—
216	C₂²×C₁₀₁	—	2	1	no	—
217	C₂²×C₁₀₁	—	2	4	no	—
218	C₂²×C₁₀₁	—	4	2	no	—
219	C₂²×C₁₀₁	—	4	2	no	—
220	C₂²×C₁₀₁	—	8	4	no	—
221	C₂²×C₁₀₁	#448	1	2	yes	—
222	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
223	C₄×C₁₀₁	—	2	1	no	—
224	C₄×C₁₀₁	—	2	1	no	—
225	C₄×C₁₀₁	—	2	1	no	—
226	C₄×C₁₀₁	—	4	2	no	—
227	C₄×C₁₀₁	—	4	2	no	—
228	C₄×C₁₀₁	—	4	2	no	—
229	C₄×C₁₀₁	—	4	2	no	—
230	C₄×C₁₀₁	—	4	2	no	—
231	C₄×C₁₀₁	—	8	2	no	—
232	C₄×C₁₀₁	#448	1	2	yes	—
233	C₄×C₁₀₁	C₂²×SD₁₆	1	1	yes	characteristic
234	C₄×C₁₀₁	C₂×#137	1	1	yes	characteristic
235	C₄×C₁₀₁	#577	1	2	yes	—
236	#18904	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂×C₁₀₁	—	2	2	no	—
238	C₂×C₁₀₁	—	4	4	no	—
239	C₂×C₁₀₁	C₂×#448	1	1	yes	characteristic
240	C₂×C₁₀₁	#3009	1	1	yes	characteristic
241	C₂×C₁₀₁	#3022	1	1	yes	characteristic
242	#3501	C₂×C₁₀₁	1	1	yes	characteristic
243	#3229	C₂×C₁₀₁	1	1	yes	characteristic, complemented
244	#3229	C₂×C₁₀₁	1	1	yes	characteristic, complemented
245	C₂×#461	C₂×C₁₀₁	1	1	yes	characteristic
246	#1651	C₂×C₁₀₁	1	4	yes	complemented
247	#1643	C₂×C₁₀₁	1	4	yes	complemented
248	#1542	C₂×C₁₀₁	1	1	yes	characteristic, complemented
249	#1481	C₂×C₁₀₁	1	1	yes	characteristic, complemented
250	#1478	C₂×C₁₀₁	1	1	yes	characteristic
251	C₁₀₁	#18904	1	1	yes	characteristic, direct product factor, Sylow
252	C₂²×SD₁₆	—	2	1	no	—
253	#554	—	2	1	no	—
254	#554	—	2	2	no	—
255	#554	—	2	2	no	—
256	#554	C₂²×C₁₀₁	1	2	yes	—
257	D₄×Q₈	—	2	1	no	—
258	D₄×Q₈	C₂²×C₁₀₁	1	2	yes	—
259	#544	—	2	1	no	—
260	#543	—	2	2	no	—
261	#533	C₂²×C₁₀₁	1	1	yes	characteristic
262	#533	C₂²×C₁₀₁	1	1	yes	characteristic
263	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
264	C₂×C₂²⋊Q₈	—	2	2	no	—
265	#518	—	2	1	no	—
266	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
267	#498	—	2	1	no	—
268	#498	C₂²×C₁₀₁	1	2	yes	complemented
269	#487	—	2	1	no	—
270	#487	C₂²×C₁₀₁	1	2	yes	complemented
271	#483	—	2	2	no	—
272	#483	—	2	2	no	—
273	#475	—	2	2	no	—
274	#475	C₂²×C₁₀₁	1	4	yes	complemented
275	#461	—	2	2	no	—
276	#461	C₂²×C₁₀₁	1	4	yes	—
277	#431	C₂²×C₁₀₁	1	1	yes	characteristic
278	#431	C₂²×C₁₀₁	1	1	yes	characteristic
279	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
280	C₂×#103	—	2	1	no	—
281	#333	C₂²×C₁₀₁	1	2	yes	complemented
282	#332	C₂²×C₁₀₁	1	2	yes	complemented
283	Q₈⋊C₈	C₂²×C₁₀₁	1	4	yes	complemented
284	D₄⋊C₈	C₂²×C₁₀₁	1	4	yes	—
285	C₂²×Q₈	—	2	2	no	—
286	C₂²×Q₈	—	2	1	no	—
287	C₂²×D₄	D₄×C₁₀₁	1	1	yes	characteristic
288	C₂³×C₄	—	2	1	no	—
289	C₂×SD₁₆	—	2	4	no	—
290	C₂×SD₁₆	—	4	4	no	—
291	C₂²×C₈	—	2	1	no	—
292	C₄⋊Q₈	—	2	2	no	—
293	C₄⋊Q₈	—	2	2	no	—
294	C₄⋊Q₈	—	2	1	no	—
295	C₄⋊Q₈	—	2	1	no	—
296	C₄⋊Q₈	—	2	1	no	—
297	C₄⋊Q₈	D₄×C₁₀₁	1	1	yes	characteristic
298	C₄⋊Q₈	D₄×C₁₀₁	1	1	yes	characteristic
299	C₄⋊Q₈	C₂³×C₁₀₁	1	2	yes	—
300	C₄⋊Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
301	C₄⋊Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
302	#125	—	2	2	no	—
303	#125	—	2	2	no	—
304	#125	—	2	1	no	—
305	#125	—	2	1	no	—
306	C₂²⋊Q₈	—	2	4	no	—
307	C₂²⋊Q₈	—	2	4	no	—
308	C₂²⋊Q₈	—	2	4	no	—
309	C₂²⋊Q₈	—	2	4	no	—
310	C₂²⋊Q₈	—	2	2	no	—
311	C₂²⋊Q₈	—	2	4	no	—
312	C₂²⋊Q₈	—	2	1	no	—
313	C₂²⋊Q₈	—	2	1	no	—
314	C₂²⋊Q₈	—	2	2	no	—
315	C₂²⋊Q₈	—	2	4	no	—
316	C₂²⋊Q₈	D₄×C₁₀₁	1	2	yes	—
317	C₂²⋊Q₈	D₄×C₁₀₁	1	2	yes	—
318	C₄×Q₈	—	2	1	no	—
319	C₄×Q₈	—	2	1	no	—
320	C₄×Q₈	D₄×C₁₀₁	1	2	yes	—
321	C₄×Q₈	C₂³×C₁₀₁	1	2	yes	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	—	2	2	no	—
325	C₄×D₄	—	2	2	no	—
326	C₄×D₄	—	2	1	no	—
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	D₄×C₁₀₁	1	2	yes	—
329	C₄×D₄	C₂³×C₁₀₁	1	2	yes	—
330	#117	—	2	1	no	—
331	#117	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	4	no	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	—	2	4	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
340	#106	—	2	4	no	—
341	#106	—	2	4	no	—
342	C₄⋊C₈	—	2	1	no	—
343	C₄⋊C₈	—	2	1	no	—
344	C₄⋊C₈	C₂³×C₁₀₁	1	2	yes	—
345	C₄⋊C₈	C₂³×C₁₀₁	1	2	yes	—
346	#103	—	2	4	no	—
347	#103	—	2	4	no	—
348	#103	—	2	4	no	—
349	C₂²⋊C₈	—	2	1	no	—
350	C₂²⋊C₈	—	2	1	no	—
351	C₄×C₈	—	2	1	no	—
352	C₄×C₈	C₂³×C₁₀₁	1	2	yes	—
353	C₂⁴	—	2	1	no	—
354	C₂×Q₈	—	2	4	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	4	1	no	—
359	C₂×Q₈	—	4	2	no	—
360	C₂×Q₈	—	4	2	no	—
361	C₂×Q₈	—	8	4	no	—
362	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
363	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	SD₁₆×C₁₀₁	1	4	yes	—
367	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	4	1	no	—
374	C₂²×C₄	—	8	2	no	—
375	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
378	SD₁₆	—	4	8	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	4	2	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	4	1	no	—
400	C₄⋊C₄	—	4	1	no	—
401	C₄⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	—
402	C₄⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	—
403	C₄⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	2	4	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	2	no	—
412	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
413	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
414	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
415	C₄²	C₂⁴×C₁₀₁	1	1	yes	characteristic
416	C₂³	—	2	2	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	8	1	no	—
419	C₂³	—	8	1	no	—
420	C₂³	#120×C₁₀₁	1	1	yes	characteristic
421	Q₈	—	2	4	no	—
422	Q₈	—	4	2	no	—
423	Q₈	—	4	2	no	—
424	Q₈	—	4	2	no	—
425	Q₈	—	4	2	no	—
426	Q₈	—	8	1	no	—
427	Q₈	—	8	4	no	—
428	Q₈	—	8	2	no	—
429	D₄	—	2	4	no	—
430	D₄	—	2	2	no	—
431	D₄	C₂×SD₁₆×C₁₀₁	1	4	yes	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	8	2	no	—
442	C₂×C₄	—	8	1	no	—
443	C₂×C₄	—	8	4	no	—
444	C₂×C₄	—	8	4	no	—
445	C₂×C₄	—	8	2	no	—
446	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
447	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
448	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
449	C₂×C₄	C₂×SD₁₆×C₁₀₁	1	2	yes	—
450	C₂×C₄	#137×C₁₀₁	1	2	yes	—
451	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
454	C₈	—	4	2	no	—
455	C₈	—	4	2	no	—
456	C₈	—	4	2	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	4	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	8	4	no	—
463	C₂²	#448×C₁₀₁	1	2	yes	—
464	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	8	2	no	—
474	C₄	#448×C₁₀₁	1	2	yes	—
475	C₄	C₂²×SD₁₆×C₁₀₁	1	1	yes	characteristic
476	C₄	C₂×#137×C₁₀₁	1	1	yes	characteristic
477	C₄	#577×C₁₀₁	1	2	yes	—
478	C₂	—	2	2	no	—
479	C₂	—	4	4	no	—
480	C₂	C₂×#448×C₁₀₁	1	1	yes	characteristic
481	C₂	C₁₀₁×#3009	1	1	yes	characteristic
482	C₂	C₁₀₁×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₁
prime radical	C₂²×D₄×C₁₀₁	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₁×#3229	C₂	semidirect
3. C₁₀₁×#3229	C₂	semidirect
5. C₁₀₁×#1651	C₂	semidirect
6. C₁₀₁×#1643	C₂	semidirect
7. C₁₀₁×#1542	C₂	semidirect
8. C₁₀₁×#1481	C₂	semidirect
26. #498×C₁₀₁	C₂²	semidirect
28. #487×C₁₀₁	C₂²	semidirect
32. #475×C₁₀₁	C₂²	semidirect
39. #333×C₁₀₁	C₂²	semidirect
40. #332×C₁₀₁	C₂²	semidirect
41. Q₈⋊C₈×C₁₀₁	C₂²	semidirect
236. #18904	C₁₀₁	direct (N × H)
243. #3229	C₂×C₁₀₁	semidirect
244. #3229	C₂×C₁₀₁	semidirect
246. #1651	C₂×C₁₀₁	semidirect
247. #1643	C₂×C₁₀₁	semidirect
248. #1542	C₂×C₁₀₁	semidirect
249. #1481	C₂×C₁₀₁	semidirect
251. C₁₀₁	#18904	direct (N × H)
268. #498	C₂²×C₁₀₁	semidirect
270. #487	C₂²×C₁₀₁	semidirect
274. #475	C₂²×C₁₀₁	semidirect
281. #333	C₂²×C₁₀₁	semidirect
282. #332	C₂²×C₁₀₁	semidirect
283. Q₈⋊C₈	C₂²×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₁×#3501	2
C₁₀₁×#3229	2
C₂×#461×C₁₀₁	2
C₁₀₁×#1651	2
C₁₀₁×#1643	2
C₁₀₁×#1542	2
C₁₀₁×#1481	2
C₁₀₁×#1478	2
#18904	101

Subgroups — C101×#18904 #38801055

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#18904 #38801055