Subgroups — C₁₀₁×#10735 #38792886

Order 25856.

3062 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂²⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#379×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#379×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#342×C₁₀₁	C₂	1	4	yes	maximal, complemented
5	C₂⁶×C₁₀₁	C₂²	1	1	yes	characteristic
6	C₂⁴×C₄×C₁₀₁	—	2	1	no	—
7	C₂²×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
8	C₂²×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
9	C₂²×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
10	C₂²×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
11	C₂²×C₂²⋊C₄×C₁₀₁	C₄	1	4	yes	complemented
12	C₂²×C₂²⋊C₄×C₁₀₁	C₄	1	4	yes	complemented
13	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
14	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
16	#379×C₁₀₁	—	2	2	no	—
17	#379×C₁₀₁	—	2	1	no	—
18	#379×C₁₀₁	—	2	2	no	—
19	#379×C₁₀₁	—	2	1	no	—
20	#379×C₁₀₁	C₄	1	4	yes	complemented
21	#342×C₁₀₁	—	2	8	no	—
22	C₂⁵×C₁₀₁	—	2	4	no	—
23	C₂⁵×C₁₀₁	—	2	4	no	—
24	C₂⁵×C₁₀₁	—	4	8	no	—
25	C₂⁵×C₁₀₁	C₂×C₄	1	2	yes	—
26	C₂⁵×C₁₀₁	C₂×C₄	1	2	yes	—
27	C₂⁵×C₁₀₁	C₂×C₄	1	2	yes	—
28	C₂⁵×C₁₀₁	D₄	1	1	yes	characteristic
29	C₂⁵×C₁₀₁	D₄	1	2	yes	—
30	C₂⁵×C₁₀₁	D₄	1	2	yes	—
31	C₂⁵×C₁₀₁	D₄	1	1	yes	characteristic
32	C₂⁵×C₁₀₁	Q₈	1	2	yes	—
33	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
34	C₂³×C₄×C₁₀₁	—	2	8	no	—
35	C₂³×C₄×C₁₀₁	—	2	4	no	—
36	C₂³×C₄×C₁₀₁	—	2	2	no	—
37	C₂³×C₄×C₁₀₁	—	2	2	no	—
38	C₂³×C₄×C₁₀₁	—	4	8	no	—
39	C₂³×C₄×C₁₀₁	C₂×C₄	1	4	yes	complemented
40	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
41	C₂×C₂²⋊C₄×C₁₀₁	—	2	16	no	—
42	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
43	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
44	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
45	C₂×C₂²⋊C₄×C₁₀₁	—	2	16	no	—
46	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
47	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
48	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
49	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
50	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
51	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
52	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
54	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₁₀₁	—	4	8	no	—
57	C₂×C₂²⋊C₄×C₁₀₁	—	4	8	no	—
58	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
59	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	complemented
60	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	8	yes	—
61	C₂⁴×C₁₀₁	—	2	8	no	—
62	C₂⁴×C₁₀₁	—	2	2	no	—
63	C₂⁴×C₁₀₁	—	2	2	no	—
64	C₂⁴×C₁₀₁	—	2	8	no	—
65	C₂⁴×C₁₀₁	—	2	8	no	—
66	C₂⁴×C₁₀₁	—	2	4	no	—
67	C₂⁴×C₁₀₁	—	2	4	no	—
68	C₂⁴×C₁₀₁	—	2	8	no	—
69	C₂⁴×C₁₀₁	—	2	8	no	—
70	C₂⁴×C₁₀₁	—	2	4	no	—
71	C₂⁴×C₁₀₁	—	2	2	no	—
72	C₂⁴×C₁₀₁	—	2	8	no	—
73	C₂⁴×C₁₀₁	—	2	8	no	—
74	C₂⁴×C₁₀₁	—	2	4	no	—
75	C₂⁴×C₁₀₁	—	2	2	no	—
76	C₂⁴×C₁₀₁	—	4	8	no	—
77	C₂⁴×C₁₀₁	—	4	8	no	—
78	C₂⁴×C₁₀₁	—	4	4	no	—
79	C₂⁴×C₁₀₁	—	4	8	no	—
80	C₂⁴×C₁₀₁	—	4	4	no	—
81	C₂⁴×C₁₀₁	—	4	4	no	—
82	C₂⁴×C₁₀₁	—	4	8	no	—
83	C₂⁴×C₁₀₁	—	4	4	no	—
84	C₂⁴×C₁₀₁	—	4	32	no	—
85	C₂⁴×C₁₀₁	—	4	32	no	—
86	C₂⁴×C₁₀₁	C₄²	1	4	yes	—
87	C₂⁴×C₁₀₁	C₂²⋊C₄	1	2	yes	—
88	C₂⁴×C₁₀₁	C₂²⋊C₄	1	2	yes	—
89	C₂⁴×C₁₀₁	C₂²⋊C₄	1	4	yes	—
90	C₂⁴×C₁₀₁	C₂²⋊C₄	1	2	yes	—
91	C₂⁴×C₁₀₁	C₂²⋊C₄	1	2	yes	—
92	C₂⁴×C₁₀₁	C₄⋊C₄	1	2	yes	—
93	C₂⁴×C₁₀₁	C₄⋊C₄	1	4	yes	—
94	C₂⁴×C₁₀₁	C₄⋊C₄	1	4	yes	—
95	C₂⁴×C₁₀₁	C₄⋊C₄	1	2	yes	—
96	C₂⁴×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
97	C₂⁴×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
98	C₂⁴×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
99	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
100	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
101	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
102	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	—
103	C₂⁴×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
104	C₂⁴×C₁₀₁	#41	1	4	yes	—
105	C₂²×C₄×C₁₀₁	—	2	16	no	—
106	C₂²×C₄×C₁₀₁	—	2	4	no	—
107	C₂²×C₄×C₁₀₁	—	2	8	no	—
108	C₂²×C₄×C₁₀₁	—	2	4	no	—
109	C₂²×C₄×C₁₀₁	—	2	4	no	—
110	C₂²×C₄×C₁₀₁	—	2	8	no	—
111	C₂²×C₄×C₁₀₁	—	4	32	no	—
112	C₂²×C₄×C₁₀₁	—	4	16	no	—
113	C₂²×C₄×C₁₀₁	—	4	8	no	—
114	C₂²×C₄×C₁₀₁	—	4	8	no	—
115	C₂²×C₄×C₁₀₁	—	4	4	no	—
116	C₂²×C₄×C₁₀₁	—	4	8	no	—
117	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
118	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
119	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
120	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
121	C₂²⋊C₄×C₁₀₁	—	4	16	no	—
122	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
123	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
124	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
125	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
126	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
127	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
128	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
129	C₂²⋊C₄×C₁₀₁	C₂²⋊C₄	1	8	yes	complemented
130	C₂³×C₁₀₁	—	2	16	no	—
131	C₂³×C₁₀₁	—	2	16	no	—
132	C₂³×C₁₀₁	—	2	8	no	—
133	C₂³×C₁₀₁	—	2	8	no	—
134	C₂³×C₁₀₁	—	2	2	no	—
135	C₂³×C₁₀₁	—	2	2	no	—
136	C₂³×C₁₀₁	—	2	4	no	—
137	C₂³×C₁₀₁	—	2	4	no	—
138	C₂³×C₁₀₁	—	2	4	no	—
139	C₂³×C₁₀₁	—	2	4	no	—
140	C₂³×C₁₀₁	—	2	4	no	—
141	C₂³×C₁₀₁	—	2	4	no	—
142	C₂³×C₁₀₁	—	2	8	no	—
143	C₂³×C₁₀₁	—	2	8	no	—
144	C₂³×C₁₀₁	—	2	8	no	—
145	C₂³×C₁₀₁	—	2	8	no	—
146	C₂³×C₁₀₁	—	2	8	no	—
147	C₂³×C₁₀₁	—	2	2	no	—
148	C₂³×C₁₀₁	—	2	8	no	—
149	C₂³×C₁₀₁	—	2	2	no	—
150	C₂³×C₁₀₁	—	2	8	no	—
151	C₂³×C₁₀₁	—	2	4	no	—
152	C₂³×C₁₀₁	—	2	8	no	—
153	C₂³×C₁₀₁	—	2	4	no	—
154	C₂³×C₁₀₁	—	2	4	no	—
155	C₂³×C₁₀₁	—	2	4	no	—
156	C₂³×C₁₀₁	—	4	4	no	—
157	C₂³×C₁₀₁	—	4	4	no	—
158	C₂³×C₁₀₁	—	4	4	no	—
159	C₂³×C₁₀₁	—	4	4	no	—
160	C₂³×C₁₀₁	—	4	4	no	—
161	C₂³×C₁₀₁	—	4	4	no	—
162	C₂³×C₁₀₁	—	4	2	no	—
163	C₂³×C₁₀₁	—	4	2	no	—
164	C₂³×C₁₀₁	—	4	8	no	—
165	C₂³×C₁₀₁	—	4	2	no	—
166	C₂³×C₁₀₁	—	4	2	no	—
167	C₂³×C₁₀₁	—	4	8	no	—
168	C₂³×C₁₀₁	—	4	32	no	—
169	C₂³×C₁₀₁	—	4	32	no	—
170	C₂³×C₁₀₁	—	4	16	no	—
171	C₂³×C₁₀₁	—	4	16	no	—
172	C₂³×C₁₀₁	—	4	16	no	—
173	C₂³×C₁₀₁	—	4	32	no	—
174	C₂³×C₁₀₁	—	4	32	no	—
175	C₂³×C₁₀₁	—	4	16	no	—
176	C₂³×C₁₀₁	—	4	8	no	—
177	C₂³×C₁₀₁	—	4	8	no	—
178	C₂³×C₁₀₁	#95	1	4	yes	—
179	C₂³×C₁₀₁	#95	1	4	yes	—
180	C₂³×C₁₀₁	#99	1	8	yes	—
181	C₂³×C₁₀₁	C₂×C₄²	1	1	yes	characteristic
182	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
185	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂³×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂³×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂³×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂³×C₁₀₁	#117	1	2	yes	—
190	C₂³×C₁₀₁	C₄×D₄	1	4	yes	—
191	C₂³×C₁₀₁	C₄×D₄	1	4	yes	—
192	C₂³×C₁₀₁	#120	1	2	yes	—
193	C₂³×C₁₀₁	#120	1	2	yes	—
194	C₂³×C₁₀₁	#121	1	4	yes	—
195	C₂³×C₁₀₁	C₂²⋊Q₈	1	4	yes	—
196	C₂³×C₁₀₁	#123	1	2	yes	—
197	C₂³×C₁₀₁	#123	1	2	yes	—
198	C₂×C₄×C₁₀₁	—	2	8	no	—
199	C₂×C₄×C₁₀₁	—	4	32	no	—
200	C₂×C₄×C₁₀₁	—	4	16	no	—
201	C₂×C₄×C₁₀₁	—	4	8	no	—
202	C₂×C₄×C₁₀₁	—	4	8	no	—
203	C₂×C₄×C₁₀₁	—	4	4	no	—
204	C₂×C₄×C₁₀₁	—	4	4	no	—
205	C₂×C₄×C₁₀₁	—	4	8	no	—
206	C₂×C₄×C₁₀₁	—	8	8	no	—
207	C₂×C₄×C₁₀₁	—	8	8	no	—
208	C₂²×C₁₀₁	—	2	8	no	—
209	C₂²×C₁₀₁	—	2	8	no	—
210	C₂²×C₁₀₁	—	2	16	no	—
211	C₂²×C₁₀₁	—	2	4	no	—
212	C₂²×C₁₀₁	—	2	8	no	—
213	C₂²×C₁₀₁	—	2	8	no	—
214	C₂²×C₁₀₁	—	2	16	no	—
215	C₂²×C₁₀₁	—	2	4	no	—
216	C₂²×C₁₀₁	—	2	4	no	—
217	C₂²×C₁₀₁	—	2	2	no	—
218	C₂²×C₁₀₁	—	2	2	no	—
219	C₂²×C₁₀₁	—	2	4	no	—
220	C₂²×C₁₀₁	—	2	2	no	—
221	C₂²×C₁₀₁	—	2	2	no	—
222	C₂²×C₁₀₁	—	2	2	no	—
223	C₂²×C₁₀₁	—	2	2	no	—
224	C₂²×C₁₀₁	—	2	4	no	—
225	C₂²×C₁₀₁	—	2	4	no	—
226	C₂²×C₁₀₁	—	2	4	no	—
227	C₂²×C₁₀₁	—	4	2	no	—
228	C₂²×C₁₀₁	—	4	2	no	—
229	C₂²×C₁₀₁	—	4	4	no	—
230	C₂²×C₁₀₁	—	4	2	no	—
231	C₂²×C₁₀₁	—	4	4	no	—
232	C₂²×C₁₀₁	—	4	2	no	—
233	C₂²×C₁₀₁	—	4	16	no	—
234	C₂²×C₁₀₁	—	4	16	no	—
235	C₂²×C₁₀₁	—	4	16	no	—
236	C₂²×C₁₀₁	—	4	16	no	—
237	C₂²×C₁₀₁	—	4	4	no	—
238	C₂²×C₁₀₁	—	4	4	no	—
239	C₂²×C₁₀₁	—	4	8	no	—
240	C₂²×C₁₀₁	—	4	8	no	—
241	C₂²×C₁₀₁	#342	1	8	yes	complemented
242	C₂²×C₁₀₁	C₂×#95	1	1	yes	characteristic
243	C₂²×C₁₀₁	C₄×C₂²⋊C₄	1	2	yes	—
244	C₂²×C₁₀₁	#379	1	1	yes	characteristic
245	C₂²×C₁₀₁	#380	1	2	yes	—
246	C₂²×C₁₀₁	#381	1	1	yes	characteristic
247	C₂²×C₁₀₁	#385	1	2	yes	—
248	C₂²×C₁₀₁	#385	1	2	yes	—
249	C₂²×C₁₀₁	#386	1	2	yes	—
250	C₂²×C₁₀₁	#386	1	2	yes	—
251	C₂²×C₁₀₁	C₂×#99	1	4	yes	—
252	C₄×C₁₀₁	—	4	8	no	—
253	C₄×C₁₀₁	—	8	4	no	—
254	C₄×C₁₀₁	—	8	4	no	—
255	#10735	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂×C₁₀₁	—	2	1	no	—
257	C₂×C₁₀₁	—	2	2	no	—
258	C₂×C₁₀₁	—	2	8	no	—
259	C₂×C₁₀₁	—	2	1	no	—
260	C₂×C₁₀₁	—	2	2	no	—
261	C₂×C₁₀₁	—	2	2	no	—
262	C₂×C₁₀₁	—	2	2	no	—
263	C₂×C₁₀₁	—	2	2	no	—
264	C₂×C₁₀₁	—	4	4	no	—
265	C₂×C₁₀₁	C₂²⋊#95	1	1	yes	characteristic
266	C₂×C₁₀₁	C₂×#342	1	2	yes	—
267	C₂×C₁₀₁	#1898	1	4	yes	—
268	C₂³×C₂²⋊C₄	C₂×C₁₀₁	1	1	yes	characteristic
269	C₂×#379	C₂×C₁₀₁	1	1	yes	characteristic
270	C₂×#379	C₂×C₁₀₁	1	1	yes	characteristic
271	C₂×#342	C₂×C₁₀₁	1	4	yes	complemented
272	C₁₀₁	#10735	1	1	yes	characteristic, direct product factor, Sylow
273	C₂⁶	C₂²×C₁₀₁	1	1	yes	characteristic
274	C₂⁴×C₄	—	2	1	no	—
275	C₂²×C₂²⋊C₄	—	2	1	no	—
276	C₂²×C₂²⋊C₄	—	2	2	no	—
277	C₂²×C₂²⋊C₄	—	2	8	no	—
278	C₂²×C₂²⋊C₄	—	2	2	no	—
279	C₂²×C₂²⋊C₄	C₄×C₁₀₁	1	4	yes	complemented
280	C₂²×C₂²⋊C₄	C₄×C₁₀₁	1	4	yes	complemented
281	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
282	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
283	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
284	#379	—	2	2	no	—
285	#379	—	2	1	no	—
286	#379	—	2	2	no	—
287	#379	—	2	1	no	—
288	#379	C₄×C₁₀₁	1	4	yes	complemented
289	#342	—	2	8	no	—
290	C₂⁵	—	2	4	no	—
291	C₂⁵	—	2	4	no	—
292	C₂⁵	—	4	8	no	—
293	C₂⁵	C₂×C₄×C₁₀₁	1	2	yes	—
294	C₂⁵	C₂×C₄×C₁₀₁	1	2	yes	—
295	C₂⁵	C₂×C₄×C₁₀₁	1	2	yes	—
296	C₂⁵	D₄×C₁₀₁	1	1	yes	characteristic
297	C₂⁵	D₄×C₁₀₁	1	2	yes	—
298	C₂⁵	D₄×C₁₀₁	1	1	yes	characteristic
299	C₂⁵	D₄×C₁₀₁	1	2	yes	—
300	C₂⁵	Q₈×C₁₀₁	1	2	yes	—
301	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
302	C₂³×C₄	—	2	8	no	—
303	C₂³×C₄	—	2	4	no	—
304	C₂³×C₄	—	2	2	no	—
305	C₂³×C₄	—	2	2	no	—
306	C₂³×C₄	—	4	8	no	—
307	C₂³×C₄	C₂×C₄×C₁₀₁	1	4	yes	complemented
308	C₂×C₂²⋊C₄	—	2	8	no	—
309	C₂×C₂²⋊C₄	—	2	16	no	—
310	C₂×C₂²⋊C₄	—	2	4	no	—
311	C₂×C₂²⋊C₄	—	2	4	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	16	no	—
314	C₂×C₂²⋊C₄	—	2	4	no	—
315	C₂×C₂²⋊C₄	—	2	4	no	—
316	C₂×C₂²⋊C₄	—	2	8	no	—
317	C₂×C₂²⋊C₄	—	2	4	no	—
318	C₂×C₂²⋊C₄	—	2	4	no	—
319	C₂×C₂²⋊C₄	—	2	4	no	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	4	no	—
324	C₂×C₂²⋊C₄	—	4	8	no	—
325	C₂×C₂²⋊C₄	—	4	8	no	—
326	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
327	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	complemented
328	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	8	yes	—
329	C₂⁴	—	2	8	no	—
330	C₂⁴	—	2	2	no	—
331	C₂⁴	—	2	2	no	—
332	C₂⁴	—	2	8	no	—
333	C₂⁴	—	2	8	no	—
334	C₂⁴	—	2	4	no	—
335	C₂⁴	—	2	4	no	—
336	C₂⁴	—	2	8	no	—
337	C₂⁴	—	2	8	no	—
338	C₂⁴	—	2	4	no	—
339	C₂⁴	—	2	2	no	—
340	C₂⁴	—	2	8	no	—
341	C₂⁴	—	2	8	no	—
342	C₂⁴	—	2	4	no	—
343	C₂⁴	—	2	2	no	—
344	C₂⁴	—	4	4	no	—
345	C₂⁴	—	4	8	no	—
346	C₂⁴	—	4	8	no	—
347	C₂⁴	—	4	4	no	—
348	C₂⁴	—	4	4	no	—
349	C₂⁴	—	4	8	no	—
350	C₂⁴	—	4	8	no	—
351	C₂⁴	—	4	4	no	—
352	C₂⁴	—	4	32	no	—
353	C₂⁴	—	4	32	no	—
354	C₂⁴	C₄²×C₁₀₁	1	4	yes	—
355	C₂⁴	C₂²⋊C₄×C₁₀₁	1	2	yes	—
356	C₂⁴	C₂²⋊C₄×C₁₀₁	1	2	yes	—
357	C₂⁴	C₂²⋊C₄×C₁₀₁	1	4	yes	—
358	C₂⁴	C₂²⋊C₄×C₁₀₁	1	2	yes	—
359	C₂⁴	C₂²⋊C₄×C₁₀₁	1	2	yes	—
360	C₂⁴	C₄⋊C₄×C₁₀₁	1	2	yes	—
361	C₂⁴	C₄⋊C₄×C₁₀₁	1	4	yes	—
362	C₂⁴	C₄⋊C₄×C₁₀₁	1	4	yes	—
363	C₂⁴	C₄⋊C₄×C₁₀₁	1	2	yes	—
364	C₂⁴	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
365	C₂⁴	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
366	C₂⁴	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
367	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
368	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
369	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
370	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	—
371	C₂⁴	C₂×Q₈×C₁₀₁	1	1	yes	characteristic
372	C₂⁴	#41×C₁₀₁	1	4	yes	—
373	C₂²×C₄	—	2	16	no	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	8	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	8	no	—
379	C₂²×C₄	—	4	32	no	—
380	C₂²×C₄	—	4	8	no	—
381	C₂²×C₄	—	4	16	no	—
382	C₂²×C₄	—	4	8	no	—
383	C₂²×C₄	—	4	4	no	—
384	C₂²×C₄	—	4	8	no	—
385	C₂²⋊C₄	—	2	16	no	—
386	C₂²⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂²⋊C₄	—	4	16	no	—
390	C₂²⋊C₄	—	4	8	no	—
391	C₂²⋊C₄	—	4	8	no	—
392	C₂²⋊C₄	—	4	2	no	—
393	C₂²⋊C₄	—	4	2	no	—
394	C₂²⋊C₄	—	4	4	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₂²⋊C₄	—	4	2	no	—
397	C₂²⋊C₄	C₂²⋊C₄×C₁₀₁	1	8	yes	complemented
398	C₂³	—	2	16	no	—
399	C₂³	—	2	16	no	—
400	C₂³	—	2	4	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	2	4	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	2	8	no	—
405	C₂³	—	2	8	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	4	no	—
409	C₂³	—	2	4	no	—
410	C₂³	—	2	4	no	—
411	C₂³	—	2	4	no	—
412	C₂³	—	2	8	no	—
413	C₂³	—	2	8	no	—
414	C₂³	—	2	8	no	—
415	C₂³	—	2	8	no	—
416	C₂³	—	2	8	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	8	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	8	no	—
421	C₂³	—	2	4	no	—
422	C₂³	—	2	8	no	—
423	C₂³	—	2	4	no	—
424	C₂³	—	4	4	no	—
425	C₂³	—	4	4	no	—
426	C₂³	—	4	4	no	—
427	C₂³	—	4	4	no	—
428	C₂³	—	4	4	no	—
429	C₂³	—	4	4	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	8	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	8	no	—
436	C₂³	—	4	32	no	—
437	C₂³	—	4	32	no	—
438	C₂³	—	4	16	no	—
439	C₂³	—	4	16	no	—
440	C₂³	—	4	16	no	—
441	C₂³	—	4	32	no	—
442	C₂³	—	4	32	no	—
443	C₂³	—	4	16	no	—
444	C₂³	—	4	8	no	—
445	C₂³	—	4	8	no	—
446	C₂³	#95×C₁₀₁	1	4	yes	—
447	C₂³	#95×C₁₀₁	1	4	yes	—
448	C₂³	#99×C₁₀₁	1	8	yes	—
449	C₂³	C₂×C₄²×C₁₀₁	1	1	yes	characteristic
450	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
451	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
452	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
453	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
454	C₂³	C₂×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
455	C₂³	C₂×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
456	C₂³	C₂×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
457	C₂³	#117×C₁₀₁	1	2	yes	—
458	C₂³	C₄×D₄×C₁₀₁	1	4	yes	—
459	C₂³	C₄×D₄×C₁₀₁	1	4	yes	—
460	C₂³	#120×C₁₀₁	1	2	yes	—
461	C₂³	#120×C₁₀₁	1	2	yes	—
462	C₂³	#121×C₁₀₁	1	4	yes	—
463	C₂³	C₂²⋊Q₈×C₁₀₁	1	4	yes	—
464	C₂³	#123×C₁₀₁	1	2	yes	—
465	C₂³	#123×C₁₀₁	1	2	yes	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	4	32	no	—
468	C₂×C₄	—	4	16	no	—
469	C₂×C₄	—	4	8	no	—
470	C₂×C₄	—	4	8	no	—
471	C₂×C₄	—	4	8	no	—
472	C₂×C₄	—	4	4	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	8	8	no	—
475	C₂×C₄	—	8	8	no	—
476	C₂²	—	2	8	no	—
477	C₂²	—	2	8	no	—
478	C₂²	—	2	16	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	2	8	no	—
481	C₂²	—	2	8	no	—
482	C₂²	—	2	16	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	4	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	4	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	2	4	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	4	4	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	16	no	—
502	C₂²	—	4	16	no	—
503	C₂²	—	4	16	no	—
504	C₂²	—	4	16	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	4	8	no	—
508	C₂²	—	4	8	no	—
509	C₂²	#342×C₁₀₁	1	8	yes	complemented
510	C₂²	C₂×#95×C₁₀₁	1	1	yes	characteristic
511	C₂²	C₄×C₂²⋊C₄×C₁₀₁	1	2	yes	—
512	C₂²	#379×C₁₀₁	1	1	yes	characteristic
513	C₂²	#380×C₁₀₁	1	2	yes	—
514	C₂²	#381×C₁₀₁	1	1	yes	characteristic
515	C₂²	#385×C₁₀₁	1	2	yes	—
516	C₂²	#385×C₁₀₁	1	2	yes	—
517	C₂²	#386×C₁₀₁	1	2	yes	—
518	C₂²	#386×C₁₀₁	1	2	yes	—
519	C₂²	C₂×#99×C₁₀₁	1	4	yes	—
520	C₄	—	4	8	no	—
521	C₄	—	8	4	no	—
522	C₄	—	8	4	no	—
523	C₂	—	2	1	no	—
524	C₂	—	2	2	no	—
525	C₂	—	2	8	no	—
526	C₂	—	2	1	no	—
527	C₂	—	2	2	no	—
528	C₂	—	2	2	no	—
529	C₂	—	2	2	no	—
530	C₂	—	2	2	no	—
531	C₂	—	4	4	no	—
532	C₂	C₁₀₁×C₂²⋊#95	1	1	yes	characteristic
533	C₂	C₂×#342×C₁₀₁	1	2	yes	—
534	C₂	C₁₀₁×#1898	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂×C₂²⋊C₄
commutator	C₂³	C₂×C₄²×C₁₀₁
Frattini, cosocle	C₂⁵	C₂³×C₁₀₁
prime radical	C₂⁶×C₁₀₁	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂⁶×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×#342×C₁₀₁	C₂	semidirect
11. C₂²×C₂²⋊C₄×C₁₀₁	C₄	semidirect
12. C₂²×C₂²⋊C₄×C₁₀₁	C₄	semidirect
20. #379×C₁₀₁	C₄	semidirect
39. C₂³×C₄×C₁₀₁	C₂×C₄	semidirect
59. C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	semidirect
129. C₂²⋊C₄×C₁₀₁	C₂²⋊C₄	semidirect
241. C₂²×C₁₀₁	#342	semidirect
255. #10735	C₁₀₁	direct (N × H)
271. C₂×#342	C₂×C₁₀₁	semidirect
272. C₁₀₁	#10735	direct (N × H)
279. C₂²×C₂²⋊C₄	C₄×C₁₀₁	semidirect
280. C₂²×C₂²⋊C₄	C₄×C₁₀₁	semidirect
288. #379	C₄×C₁₀₁	semidirect
307. C₂³×C₄	C₂×C₄×C₁₀₁	semidirect
327. C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	semidirect
397. C₂²⋊C₄	C₂²⋊C₄×C₁₀₁	semidirect
509. C₂²	#342×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₂²⋊C₄×C₁₀₁	2
C₂×#379×C₁₀₁	2
C₂×#342×C₁₀₁	2
#10735	101

Subgroups — C101×#10735 #38792886

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#10735 #38792886