Subgroups — C₁₀₁×#10932 #38793083

Order 25856.

1138 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#103×C₁₀₁	C₂	1	2	yes	maximal
2	C₂×#391×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#340×C₁₀₁	C₂	1	2	yes	maximal
5	C₂×#336×C₁₀₁	C₂	1	1	yes	maximal, characteristic
6	C₂³×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₀₁	C₂²	1	2	yes	—
8	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
10	C₂²×C₄²×C₁₀₁	—	2	1	no	—
11	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
12	C₂×#103×C₁₀₁	—	2	4	no	—
13	C₂×#103×C₁₀₁	—	2	4	no	—
14	C₂×#103×C₁₀₁	C₄	1	8	yes	complemented
15	#391×C₁₀₁	—	2	2	no	—
16	#391×C₁₀₁	C₄	1	4	yes	complemented
17	C₄×C₄⋊C₄×C₁₀₁	—	2	4	no	—
18	C₂×#95×C₁₀₁	—	2	1	no	—
19	C₂×#95×C₁₀₁	—	2	1	no	—
20	C₂×#95×C₁₀₁	—	2	1	no	—
21	#340×C₁₀₁	—	2	4	no	—
22	#336×C₁₀₁	—	2	2	no	—
23	C₂²×Q₈×C₁₀₁	—	2	1	no	—
24	C₂²×Q₈×C₁₀₁	—	2	2	no	—
25	C₂²×Q₈×C₁₀₁	—	2	2	no	—
26	C₂²×Q₈×C₁₀₁	—	2	2	no	—
27	C₂²×Q₈×C₁₀₁	—	2	2	no	—
28	C₂²×Q₈×C₁₀₁	—	2	2	no	—
29	C₂²×Q₈×C₁₀₁	C₂×C₄	1	4	yes	—
30	C₂²×Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₁₀₁	—	2	2	no	—
32	C₂³×C₄×C₁₀₁	—	2	1	no	—
33	C₂³×C₄×C₁₀₁	—	2	1	no	—
34	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₀₁	—	2	2	no	—
38	C₂²×C₈×C₁₀₁	—	2	2	no	—
39	C₂²×C₈×C₁₀₁	—	2	2	no	—
40	C₂²×C₈×C₁₀₁	—	2	2	no	—
41	C₂²×C₈×C₁₀₁	—	2	2	no	—
42	C₂²×C₈×C₁₀₁	—	2	2	no	—
43	C₂²×C₈×C₁₀₁	C₂×C₄	1	4	yes	—
44	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
45	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
52	C₂×C₄⋊C₄×C₁₀₁	D₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₁₀₁	D₄	1	4	yes	—
54	C₂×C₄²×C₁₀₁	—	2	2	no	—
55	C₂×C₄²×C₁₀₁	—	2	2	no	—
56	C₂×C₄²×C₁₀₁	—	2	4	no	—
57	C₂×C₄²×C₁₀₁	—	4	2	no	—
58	C₂×C₄²×C₁₀₁	—	4	2	no	—
59	C₂×C₄²×C₁₀₁	C₂×C₄	1	2	yes	—
60	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
61	#103×C₁₀₁	—	2	16	no	—
62	#95×C₁₀₁	—	2	4	no	—
63	#95×C₁₀₁	—	2	4	no	—
64	#95×C₁₀₁	—	2	4	no	—
65	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
66	C₂×Q₈×C₁₀₁	—	2	2	no	—
67	C₂×Q₈×C₁₀₁	—	2	4	no	—
68	C₂×Q₈×C₁₀₁	—	2	4	no	—
69	C₂×Q₈×C₁₀₁	—	2	4	no	—
70	C₂×Q₈×C₁₀₁	—	2	4	no	—
71	C₂×Q₈×C₁₀₁	—	2	4	no	—
72	C₂×Q₈×C₁₀₁	—	2	4	no	—
73	C₂×Q₈×C₁₀₁	—	2	4	no	—
74	C₂×Q₈×C₁₀₁	—	4	2	no	—
75	C₂×Q₈×C₁₀₁	—	4	2	no	—
76	C₂×Q₈×C₁₀₁	—	4	2	no	—
77	C₂×Q₈×C₁₀₁	—	4	2	no	—
78	C₂×Q₈×C₁₀₁	—	4	1	no	—
79	C₂×Q₈×C₁₀₁	—	4	2	no	—
80	C₂×Q₈×C₁₀₁	—	4	1	no	—
81	C₂×Q₈×C₁₀₁	C₄²	1	4	yes	complemented
82	C₂²×C₄×C₁₀₁	—	2	1	no	—
83	C₂²×C₄×C₁₀₁	—	2	1	no	—
84	C₂²×C₄×C₁₀₁	—	2	1	no	—
85	C₂²×C₄×C₁₀₁	—	2	1	no	—
86	C₂²×C₄×C₁₀₁	—	2	2	no	—
87	C₂²×C₄×C₁₀₁	—	2	4	no	—
88	C₂²×C₄×C₁₀₁	—	2	4	no	—
89	C₂²×C₄×C₁₀₁	—	2	1	no	—
90	C₂²×C₄×C₁₀₁	—	2	4	no	—
91	C₂²×C₄×C₁₀₁	—	2	4	no	—
92	C₂²×C₄×C₁₀₁	—	2	1	no	—
93	C₂²×C₄×C₁₀₁	—	2	2	no	—
94	C₂²×C₄×C₁₀₁	—	2	2	no	—
95	C₂²×C₄×C₁₀₁	—	2	2	no	—
96	C₂²×C₄×C₁₀₁	—	4	1	no	—
97	C₂²×C₄×C₁₀₁	—	4	2	no	—
98	C₂²×C₄×C₁₀₁	—	4	1	no	—
99	C₂²×C₄×C₁₀₁	—	4	2	no	—
100	C₂²×C₄×C₁₀₁	—	4	2	no	—
101	C₂²×C₄×C₁₀₁	—	4	2	no	—
102	C₂²×C₄×C₁₀₁	—	4	2	no	—
103	C₂²×C₄×C₁₀₁	—	4	2	no	—
104	C₂²×C₄×C₁₀₁	—	4	2	no	—
105	C₂²×C₄×C₁₀₁	—	4	1	no	—
106	C₂²×C₄×C₁₀₁	—	4	1	no	—
107	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
108	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
109	C₂²×C₄×C₁₀₁	SD₁₆	1	2	yes	—
110	C₂²×C₄×C₁₀₁	Q₁₆	1	2	yes	—
111	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
117	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
118	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
119	C₂×C₈×C₁₀₁	—	2	4	no	—
120	C₂×C₈×C₁₀₁	—	2	4	no	—
121	C₂×C₈×C₁₀₁	—	2	4	no	—
122	C₂×C₈×C₁₀₁	—	4	2	no	—
123	C₂×C₈×C₁₀₁	—	4	2	no	—
124	C₂×C₈×C₁₀₁	—	4	2	no	—
125	C₂×C₈×C₁₀₁	—	4	2	no	—
126	C₄⋊C₄×C₁₀₁	—	2	4	no	—
127	C₄⋊C₄×C₁₀₁	—	2	4	no	—
128	C₄⋊C₄×C₁₀₁	—	2	4	no	—
129	C₄⋊C₄×C₁₀₁	—	2	4	no	—
130	C₄⋊C₄×C₁₀₁	—	4	1	no	—
131	C₄⋊C₄×C₁₀₁	—	4	1	no	—
132	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	8	yes	—
133	C₄²×C₁₀₁	—	2	4	no	—
134	C₄²×C₁₀₁	—	2	4	no	—
135	C₄²×C₁₀₁	—	4	8	no	—
136	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂³×C₁₀₁	C₄×D₄	1	2	yes	—
138	C₂³×C₁₀₁	#120	1	1	yes	characteristic
139	C₂³×C₁₀₁	#121	1	2	yes	—
140	C₂³×C₁₀₁	#123	1	1	yes	characteristic
141	C₂³×C₁₀₁	C₂×SD₁₆	1	1	yes	characteristic
142	C₂³×C₁₀₁	C₂×Q₁₆	1	1	yes	characteristic
143	C₂³×C₁₀₁	#135	1	2	yes	—
144	C₂³×C₁₀₁	AGL(1,ℤ/8)	1	1	yes	characteristic
145	C₂³×C₁₀₁	#137	1	1	yes	characteristic
146	C₂³×C₁₀₁	#137	1	2	yes	—
147	Q₈×C₁₀₁	—	2	8	no	—
148	Q₈×C₁₀₁	—	4	4	no	—
149	Q₈×C₁₀₁	—	4	4	no	—
150	Q₈×C₁₀₁	—	4	4	no	—
151	C₂×C₄×C₁₀₁	—	2	2	no	—
152	C₂×C₄×C₁₀₁	—	2	2	no	—
153	C₂×C₄×C₁₀₁	—	2	2	no	—
154	C₂×C₄×C₁₀₁	—	2	2	no	—
155	C₂×C₄×C₁₀₁	—	2	2	no	—
156	C₂×C₄×C₁₀₁	—	2	2	no	—
157	C₂×C₄×C₁₀₁	—	2	4	no	—
158	C₂×C₄×C₁₀₁	—	2	2	no	—
159	C₂×C₄×C₁₀₁	—	2	8	no	—
160	C₂×C₄×C₁₀₁	—	2	2	no	—
161	C₂×C₄×C₁₀₁	—	2	2	no	—
162	C₂×C₄×C₁₀₁	—	4	2	no	—
163	C₂×C₄×C₁₀₁	—	4	4	no	—
164	C₂×C₄×C₁₀₁	—	4	4	no	—
165	C₂×C₄×C₁₀₁	—	4	2	no	—
166	C₂×C₄×C₁₀₁	—	4	4	no	—
167	C₂×C₄×C₁₀₁	—	4	4	no	—
168	C₂×C₄×C₁₀₁	—	4	4	no	—
169	C₂×C₄×C₁₀₁	—	4	2	no	—
170	C₂×C₄×C₁₀₁	—	4	4	no	—
171	C₂×C₄×C₁₀₁	—	4	4	no	—
172	C₂×C₄×C₁₀₁	—	4	4	no	—
173	C₂×C₄×C₁₀₁	—	4	2	no	—
174	C₂×C₄×C₁₀₁	—	4	2	no	—
175	C₂×C₄×C₁₀₁	—	4	2	no	—
176	C₂×C₄×C₁₀₁	—	4	2	no	—
177	C₂×C₄×C₁₀₁	—	8	2	no	—
178	C₂×C₄×C₁₀₁	—	8	2	no	—
179	C₂×C₄×C₁₀₁	#103	1	4	yes	complemented
180	C₂×C₄×C₁₀₁	C₂×C₄²	1	1	yes	characteristic
181	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
182	C₂×C₄×C₁₀₁	#117	1	2	yes	—
183	C₂×C₄×C₁₀₁	#117	1	1	yes	characteristic
184	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
185	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
187	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
188	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
189	C₂×C₄×C₁₀₁	#121	1	2	yes	—
190	C₂×C₄×C₁₀₁	#121	1	2	yes	—
191	C₂×C₄×C₁₀₁	#123	1	2	yes	—
192	C₂×C₄×C₁₀₁	#124	1	1	yes	characteristic
193	C₂×C₄×C₁₀₁	#124	1	2	yes	—
194	C₂×C₄×C₁₀₁	#126	1	2	yes	—
195	C₂×C₄×C₁₀₁	#127	1	1	yes	characteristic
196	C₈×C₁₀₁	—	4	4	no	—
197	C₂²×C₁₀₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
198	C₂²×C₁₀₁	#386	1	1	yes	characteristic
199	C₂²×C₁₀₁	#386	1	2	yes	—
200	C₂²×C₁₀₁	#388	1	2	yes	—
201	C₂²×C₁₀₁	#390	1	1	yes	characteristic
202	C₂²×C₁₀₁	C₂×#103	1	1	yes	characteristic
203	C₂²×C₁₀₁	#416	1	1	yes	characteristic
204	C₂²×C₁₀₁	#417	1	1	yes	characteristic
205	C₂²×C₁₀₁	#419	1	1	yes	characteristic
206	C₂²×C₁₀₁	C₄×SD₁₆	1	2	yes	—
207	C₂²×C₁₀₁	C₄×Q₁₆	1	2	yes	—
208	C₂²×C₁₀₁	#440	1	2	yes	—
209	C₂²×C₁₀₁	#441	1	2	yes	—
210	C₂²×C₁₀₁	#450	1	1	yes	characteristic
211	C₂²×C₁₀₁	#451	1	1	yes	characteristic
212	C₂²×C₁₀₁	#452	1	2	yes	—
213	C₂²×C₁₀₁	#461	1	2	yes	—
214	C₂²×C₁₀₁	#462	1	2	yes	—
215	C₂²×C₁₀₁	#463	1	2	yes	—
216	C₂²×C₁₀₁	#464	1	2	yes	—
217	C₂²×C₁₀₁	#483	1	1	yes	characteristic
218	C₂²×C₁₀₁	#484	1	1	yes	characteristic
219	C₂²×C₁₀₁	#485	1	2	yes	—
220	C₄×C₁₀₁	—	2	4	no	—
221	C₄×C₁₀₁	—	4	2	no	—
222	C₄×C₁₀₁	—	4	8	no	—
223	C₄×C₁₀₁	—	4	4	no	—
224	C₄×C₁₀₁	—	8	2	no	—
225	C₄×C₁₀₁	C₄×C₂²⋊C₄	1	2	yes	—
226	C₄×C₁₀₁	#388	1	2	yes	—
227	C₄×C₁₀₁	#388	1	2	yes	—
228	C₄×C₁₀₁	#390	1	2	yes	—
229	#10932	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂×C₁₀₁	#1437	1	1	yes	characteristic
231	C₂×C₁₀₁	C₄×#103	1	1	yes	characteristic
232	C₂×C₁₀₁	#1763	1	1	yes	characteristic
233	C₂×C₁₀₁	#1872	1	1	yes	characteristic
234	C₂×C₁₀₁	#1873	1	1	yes	characteristic
235	C₂×C₁₀₁	#1877	1	2	yes	—
236	C₂×C₁₀₁	#1878	1	2	yes	—
237	C₂×C₁₀₁	#1927	1	2	yes	—
238	C₂×C₁₀₁	#1928	1	2	yes	—
239	C₂×C₁₀₁	#1981	1	1	yes	characteristic
240	C₂×C₁₀₁	#1983	1	1	yes	characteristic
241	C₂²×#103	C₂×C₁₀₁	1	2	yes	—
242	C₂×#391	C₂×C₁₀₁	1	1	yes	characteristic
243	C₂×C₄×C₄⋊C₄	C₂×C₁₀₁	1	1	yes	characteristic
244	C₂×#340	C₂×C₁₀₁	1	2	yes	—
245	C₂×#336	C₂×C₁₀₁	1	1	yes	characteristic
246	C₁₀₁	#10932	1	1	yes	characteristic, direct product factor, Sylow
247	C₂³×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
248	C₂³×C₈	C₂²×C₁₀₁	1	2	yes	—
249	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
250	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
251	C₂²×C₄²	—	2	1	no	—
252	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
253	C₂×#103	—	2	4	no	—
254	C₂×#103	—	2	4	no	—
255	C₂×#103	C₄×C₁₀₁	1	8	yes	complemented
256	#391	—	2	2	no	—
257	#391	C₄×C₁₀₁	1	4	yes	complemented
258	C₄×C₄⋊C₄	—	2	4	no	—
259	C₂×#95	—	2	1	no	—
260	C₂×#95	—	2	1	no	—
261	C₂×#95	—	2	1	no	—
262	#340	—	2	4	no	—
263	#336	—	2	2	no	—
264	C₂²×Q₈	—	2	1	no	—
265	C₂²×Q₈	—	2	2	no	—
266	C₂²×Q₈	—	2	2	no	—
267	C₂²×Q₈	—	2	2	no	—
268	C₂²×Q₈	—	2	2	no	—
269	C₂²×Q₈	—	2	2	no	—
270	C₂²×Q₈	C₂×C₄×C₁₀₁	1	2	yes	—
271	C₂²×Q₈	C₂×C₄×C₁₀₁	1	4	yes	—
272	C₂³×C₄	—	2	2	no	—
273	C₂³×C₄	—	2	1	no	—
274	C₂³×C₄	—	2	1	no	—
275	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
276	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
277	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
278	C₂²×C₈	—	2	2	no	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	—	2	2	no	—
283	C₂²×C₈	—	2	2	no	—
284	C₂²×C₈	C₂×C₄×C₁₀₁	1	4	yes	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
292	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
293	C₂×C₄⋊C₄	D₄×C₁₀₁	1	4	yes	—
294	C₂×C₄⋊C₄	D₄×C₁₀₁	1	4	yes	—
295	C₂×C₄²	—	2	2	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	2	4	no	—
298	C₂×C₄²	—	4	2	no	—
299	C₂×C₄²	—	4	2	no	—
300	C₂×C₄²	C₂×C₄×C₁₀₁	1	2	yes	—
301	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
302	#103	—	2	16	no	—
303	#95	—	2	4	no	—
304	#95	—	2	4	no	—
305	#95	—	2	4	no	—
306	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	4	no	—
309	C₂×Q₈	—	2	4	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	2	4	no	—
313	C₂×Q₈	—	2	4	no	—
314	C₂×Q₈	—	2	4	no	—
315	C₂×Q₈	—	4	2	no	—
316	C₂×Q₈	—	4	2	no	—
317	C₂×Q₈	—	4	2	no	—
318	C₂×Q₈	—	4	2	no	—
319	C₂×Q₈	—	4	1	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×Q₈	—	4	1	no	—
322	C₂×Q₈	C₄²×C₁₀₁	1	4	yes	complemented
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	—	4	1	no	—
348	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
349	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
350	C₂²×C₄	SD₁₆×C₁₀₁	1	2	yes	—
351	C₂²×C₄	Q₁₆×C₁₀₁	1	2	yes	—
352	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
353	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
357	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
358	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
359	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
360	C₂×C₈	—	2	4	no	—
361	C₂×C₈	—	2	4	no	—
362	C₂×C₈	—	2	4	no	—
363	C₂×C₈	—	4	2	no	—
364	C₂×C₈	—	4	2	no	—
365	C₂×C₈	—	4	2	no	—
366	C₂×C₈	—	4	2	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	4	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	8	yes	—
374	C₄²	—	2	4	no	—
375	C₄²	—	2	4	no	—
376	C₄²	—	4	8	no	—
377	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
378	C₂³	C₄×D₄×C₁₀₁	1	2	yes	—
379	C₂³	#120×C₁₀₁	1	1	yes	characteristic
380	C₂³	#121×C₁₀₁	1	2	yes	—
381	C₂³	#123×C₁₀₁	1	1	yes	characteristic
382	C₂³	C₂×SD₁₆×C₁₀₁	1	1	yes	characteristic
383	C₂³	C₂×Q₁₆×C₁₀₁	1	1	yes	characteristic
384	C₂³	#135×C₁₀₁	1	2	yes	—
385	C₂³	AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
386	C₂³	#137×C₁₀₁	1	1	yes	characteristic
387	C₂³	#137×C₁₀₁	1	2	yes	—
388	Q₈	—	2	8	no	—
389	Q₈	—	4	4	no	—
390	Q₈	—	4	4	no	—
391	Q₈	—	4	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	8	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	8	2	no	—
419	C₂×C₄	—	8	2	no	—
420	C₂×C₄	#103×C₁₀₁	1	4	yes	complemented
421	C₂×C₄	C₂×C₄²×C₁₀₁	1	1	yes	characteristic
422	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
423	C₂×C₄	#117×C₁₀₁	1	2	yes	—
424	C₂×C₄	#117×C₁₀₁	1	1	yes	characteristic
425	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
426	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
427	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
428	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
429	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
430	C₂×C₄	#121×C₁₀₁	1	2	yes	—
431	C₂×C₄	#121×C₁₀₁	1	2	yes	—
432	C₂×C₄	#123×C₁₀₁	1	2	yes	—
433	C₂×C₄	#124×C₁₀₁	1	1	yes	characteristic
434	C₂×C₄	#124×C₁₀₁	1	2	yes	—
435	C₂×C₄	#126×C₁₀₁	1	2	yes	—
436	C₂×C₄	#127×C₁₀₁	1	1	yes	characteristic
437	C₈	—	4	4	no	—
438	C₂²	C₄×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
439	C₂²	#386×C₁₀₁	1	2	yes	—
440	C₂²	#386×C₁₀₁	1	1	yes	characteristic
441	C₂²	#388×C₁₀₁	1	2	yes	—
442	C₂²	#390×C₁₀₁	1	1	yes	characteristic
443	C₂²	C₂×#103×C₁₀₁	1	1	yes	characteristic
444	C₂²	#416×C₁₀₁	1	1	yes	characteristic
445	C₂²	#417×C₁₀₁	1	1	yes	characteristic
446	C₂²	#419×C₁₀₁	1	1	yes	characteristic
447	C₂²	C₄×SD₁₆×C₁₀₁	1	2	yes	—
448	C₂²	C₄×Q₁₆×C₁₀₁	1	2	yes	—
449	C₂²	#440×C₁₀₁	1	2	yes	—
450	C₂²	#441×C₁₀₁	1	2	yes	—
451	C₂²	#450×C₁₀₁	1	1	yes	characteristic
452	C₂²	#451×C₁₀₁	1	1	yes	characteristic
453	C₂²	#452×C₁₀₁	1	2	yes	—
454	C₂²	#461×C₁₀₁	1	2	yes	—
455	C₂²	#462×C₁₀₁	1	2	yes	—
456	C₂²	#463×C₁₀₁	1	2	yes	—
457	C₂²	#464×C₁₀₁	1	2	yes	—
458	C₂²	#483×C₁₀₁	1	1	yes	characteristic
459	C₂²	#484×C₁₀₁	1	1	yes	characteristic
460	C₂²	#485×C₁₀₁	1	2	yes	—
461	C₄	—	2	4	no	—
462	C₄	—	4	4	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	8	no	—
465	C₄	—	8	2	no	—
466	C₄	C₄×C₂²⋊C₄×C₁₀₁	1	2	yes	—
467	C₄	#388×C₁₀₁	1	2	yes	—
468	C₄	#388×C₁₀₁	1	2	yes	—
469	C₄	#390×C₁₀₁	1	2	yes	—
470	C₂	C₁₀₁×#1437	1	1	yes	characteristic
471	C₂	C₄×#103×C₁₀₁	1	1	yes	characteristic
472	C₂	C₁₀₁×#1763	1	1	yes	characteristic
473	C₂	C₁₀₁×#1872	1	1	yes	characteristic
474	C₂	C₁₀₁×#1873	1	1	yes	characteristic
475	C₂	C₁₀₁×#1877	1	2	yes	—
476	C₂	C₁₀₁×#1878	1	2	yes	—
477	C₂	C₁₀₁×#1927	1	2	yes	—
478	C₂	C₁₀₁×#1928	1	2	yes	—
479	C₂	C₁₀₁×#1981	1	1	yes	characteristic
480	C₂	C₁₀₁×#1983	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₀₁	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₀₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₀₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₀₁ ◁ C₂²×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
14. C₂×#103×C₁₀₁	C₄	semidirect
16. #391×C₁₀₁	C₄	semidirect
81. C₂×Q₈×C₁₀₁	C₄²	semidirect
179. C₂×C₄×C₁₀₁	#103	semidirect
229. #10932	C₁₀₁	direct (N × H)
246. C₁₀₁	#10932	direct (N × H)
255. C₂×#103	C₄×C₁₀₁	semidirect
257. #391	C₄×C₁₀₁	semidirect
322. C₂×Q₈	C₄²×C₁₀₁	semidirect
420. C₂×C₄	#103×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#103×C₁₀₁	2
C₂×#391×C₁₀₁	2
C₂×C₄×C₄⋊C₄×C₁₀₁	2
C₂×#340×C₁₀₁	2
C₂×#336×C₁₀₁	2
#10932	101

Subgroups — C101×#10932 #38793083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#10932 #38793083