Subgroups — C₁₀₁×#10922 #38793073

Order 25856.

1286 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊C₈×C₁₀₁	C₂	1	2	yes	maximal
2	C₂²×#97×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₂²⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#336×C₁₀₁	C₂	1	2	yes	maximal, complemented
5	C₂×#336×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₀₁	C₂²	1	2	yes	—
8	C₂³×C₈×C₁₀₁	C₂²	1	2	yes	—
9	C₂²×C₂²⋊C₄×C₁₀₁	C₄	1	2	yes	—
10	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊C₈×C₁₀₁	—	2	4	no	—
13	C₂×C₂²⋊C₈×C₁₀₁	—	2	4	no	—
14	C₂×C₂²⋊C₈×C₁₀₁	C₄	1	8	yes	complemented
15	C₂×#97×C₁₀₁	—	2	4	no	—
16	C₂×#97×C₁₀₁	—	2	2	no	—
17	C₄×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
18	C₄×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
19	C₂×#95×C₁₀₁	C₄	1	2	yes	—
20	#336×C₁₀₁	—	2	4	no	—
21	#336×C₁₀₁	—	2	2	no	—
22	C₂⁵×C₁₀₁	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₀₁	—	2	2	no	—
24	C₂³×C₄×C₁₀₁	—	2	2	no	—
25	C₂³×C₄×C₁₀₁	—	2	1	no	—
26	C₂³×C₄×C₁₀₁	—	2	1	no	—
27	C₂³×C₄×C₁₀₁	—	2	2	no	—
28	C₂³×C₄×C₁₀₁	—	2	2	no	—
29	C₂³×C₄×C₁₀₁	—	2	2	no	—
30	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₀₁	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
35	C₂²×C₈×C₁₀₁	—	2	2	no	—
36	C₂²×C₈×C₁₀₁	—	2	2	no	—
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	—	2	2	no	—
44	C₂²×C₈×C₁₀₁	—	2	2	no	—
45	C₂²×C₈×C₁₀₁	C₂×C₄	1	4	yes	—
46	C₂²×C₈×C₁₀₁	C₂×C₄	1	4	yes	—
47	C₂²×C₈×C₁₀₁	D₄	1	4	yes	—
48	C₂²×C₈×C₁₀₁	D₄	1	4	yes	—
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×C₄²×C₁₀₁	—	2	2	no	—
53	C₂×C₄²×C₁₀₁	—	2	2	no	—
54	C₂×C₄²×C₁₀₁	—	2	2	no	—
55	C₂×C₄²×C₁₀₁	—	2	1	no	—
56	C₂×C₄²×C₁₀₁	—	2	1	no	—
57	C₂×C₄²×C₁₀₁	—	2	2	no	—
58	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
59	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
60	C₂²⋊C₈×C₁₀₁	—	2	16	no	—
61	#97×C₁₀₁	—	2	8	no	—
62	#95×C₁₀₁	—	2	4	no	—
63	C₂⁴×C₁₀₁	—	2	1	no	—
64	C₂⁴×C₁₀₁	—	2	1	no	—
65	C₂⁴×C₁₀₁	—	2	2	no	—
66	C₂⁴×C₁₀₁	—	2	2	no	—
67	C₂⁴×C₁₀₁	—	2	2	no	—
68	C₂⁴×C₁₀₁	—	2	4	no	—
69	C₂⁴×C₁₀₁	C₄²	1	2	yes	—
70	C₂⁴×C₁₀₁	M₁₆	1	4	yes	—
71	C₂⁴×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₀₁	—	2	1	no	—
73	C₂²×C₄×C₁₀₁	—	2	2	no	—
74	C₂²×C₄×C₁₀₁	—	2	1	no	—
75	C₂²×C₄×C₁₀₁	—	2	4	no	—
76	C₂²×C₄×C₁₀₁	—	2	4	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	—	2	2	no	—
82	C₂²×C₄×C₁₀₁	—	2	4	no	—
83	C₂²×C₄×C₁₀₁	—	2	4	no	—
84	C₂²×C₄×C₁₀₁	—	2	4	no	—
85	C₂²×C₄×C₁₀₁	—	2	4	no	—
86	C₂²×C₄×C₁₀₁	—	2	4	no	—
87	C₂²×C₄×C₁₀₁	—	2	4	no	—
88	C₂²×C₄×C₁₀₁	—	2	4	no	—
89	C₂²×C₄×C₁₀₁	—	2	4	no	—
90	C₂²×C₄×C₁₀₁	—	4	1	no	—
91	C₂²×C₄×C₁₀₁	—	4	2	no	—
92	C₂²×C₄×C₁₀₁	—	4	2	no	—
93	C₂²×C₄×C₁₀₁	—	4	2	no	—
94	C₂²×C₄×C₁₀₁	—	4	1	no	—
95	C₂²×C₄×C₁₀₁	—	4	2	no	—
96	C₂²×C₄×C₁₀₁	—	4	2	no	—
97	C₂²×C₄×C₁₀₁	—	4	1	no	—
98	C₂²×C₄×C₁₀₁	—	4	2	no	—
99	C₂²×C₄×C₁₀₁	—	4	1	no	—
100	C₂²×C₄×C₁₀₁	C₄²	1	2	yes	—
101	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	4	yes	—
102	C₂²×C₄×C₁₀₁	M₁₆	1	4	yes	—
103	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
109	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
110	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
111	C₂×C₈×C₁₀₁	—	2	4	no	—
112	C₂×C₈×C₁₀₁	—	2	4	no	—
113	C₂×C₈×C₁₀₁	—	2	4	no	—
114	C₂×C₈×C₁₀₁	—	2	4	no	—
115	C₂×C₈×C₁₀₁	—	2	4	no	—
116	C₂×C₈×C₁₀₁	—	2	4	no	—
117	C₂×C₈×C₁₀₁	—	2	4	no	—
118	C₂×C₈×C₁₀₁	—	2	4	no	—
119	C₂×C₈×C₁₀₁	—	2	4	no	—
120	C₂×C₈×C₁₀₁	—	4	2	no	—
121	C₂×C₈×C₁₀₁	—	4	2	no	—
122	C₂×C₈×C₁₀₁	—	4	2	no	—
123	C₂×C₈×C₁₀₁	—	4	2	no	—
124	C₂×C₈×C₁₀₁	C₂²⋊C₄	1	8	yes	complemented
125	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
126	C₄²×C₁₀₁	—	2	2	no	—
127	C₄²×C₁₀₁	—	2	4	no	—
128	C₄²×C₁₀₁	—	2	2	no	—
129	C₄²×C₁₀₁	—	4	2	no	—
130	C₄²×C₁₀₁	—	4	1	no	—
131	C₄²×C₁₀₁	—	4	1	no	—
132	C₂³×C₁₀₁	—	2	2	no	—
133	C₂³×C₁₀₁	—	2	4	no	—
134	C₂³×C₁₀₁	—	2	2	no	—
135	C₂³×C₁₀₁	—	2	4	no	—
136	C₂³×C₁₀₁	—	2	4	no	—
137	C₂³×C₁₀₁	—	2	4	no	—
138	C₂³×C₁₀₁	—	2	8	no	—
139	C₂³×C₁₀₁	—	2	8	no	—
140	C₂³×C₁₀₁	—	4	1	no	—
141	C₂³×C₁₀₁	—	4	2	no	—
142	C₂³×C₁₀₁	—	4	1	no	—
143	C₂³×C₁₀₁	—	4	2	no	—
144	C₂³×C₁₀₁	—	4	2	no	—
145	C₂³×C₁₀₁	—	4	4	no	—
146	C₂³×C₁₀₁	—	4	4	no	—
147	C₂³×C₁₀₁	#97	1	4	yes	complemented
148	C₂³×C₁₀₁	C₂×C₄²	1	1	yes	characteristic
149	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂³×C₁₀₁	#117	1	1	yes	characteristic
151	C₂³×C₁₀₁	C₄×D₄	1	2	yes	—
152	C₂³×C₁₀₁	C₄×D₄	1	2	yes	—
153	C₂³×C₁₀₁	C₂×M₁₆	1	2	yes	—
154	C₂³×C₁₀₁	C₂×M₁₆	1	2	yes	—
155	C₂³×C₁₀₁	#131	1	4	yes	—
156	C₂×C₄×C₁₀₁	—	2	2	no	—
157	C₂×C₄×C₁₀₁	—	2	4	no	—
158	C₂×C₄×C₁₀₁	—	2	4	no	—
159	C₂×C₄×C₁₀₁	—	2	4	no	—
160	C₂×C₄×C₁₀₁	—	2	4	no	—
161	C₂×C₄×C₁₀₁	—	2	4	no	—
162	C₂×C₄×C₁₀₁	—	2	8	no	—
163	C₂×C₄×C₁₀₁	—	4	1	no	—
164	C₂×C₄×C₁₀₁	—	4	2	no	—
165	C₂×C₄×C₁₀₁	—	4	2	no	—
166	C₂×C₄×C₁₀₁	—	4	1	no	—
167	C₂×C₄×C₁₀₁	—	4	2	no	—
168	C₂×C₄×C₁₀₁	—	4	4	no	—
169	C₂×C₄×C₁₀₁	—	4	4	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	4	no	—
174	C₂×C₄×C₁₀₁	—	4	4	no	—
175	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
176	C₂×C₄×C₁₀₁	#117	1	2	yes	—
177	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
180	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
182	C₂×C₄×C₁₀₁	#121	1	2	yes	—
183	C₂×C₄×C₁₀₁	#121	1	2	yes	—
184	C₂×C₄×C₁₀₁	#121	1	2	yes	—
185	C₂×C₄×C₁₀₁	#123	1	2	yes	—
186	C₂×C₄×C₁₀₁	#123	1	1	yes	characteristic
187	C₂×C₄×C₁₀₁	#124	1	1	yes	characteristic
188	C₂×C₄×C₁₀₁	#124	1	2	yes	—
189	C₂×C₄×C₁₀₁	#126	1	2	yes	—
190	C₂×C₄×C₁₀₁	#127	1	1	yes	characteristic
191	C₈×C₁₀₁	—	2	8	no	—
192	C₈×C₁₀₁	—	4	4	no	—
193	C₂²×C₁₀₁	—	2	4	no	—
194	C₂²×C₁₀₁	—	2	8	no	—
195	C₂²×C₁₀₁	—	4	4	no	—
196	C₂²×C₁₀₁	—	4	8	no	—
197	C₂²×C₁₀₁	—	4	2	no	—
198	C₂²×C₁₀₁	—	4	4	no	—
199	C₂²×C₁₀₁	—	4	2	no	—
200	C₂²×C₁₀₁	—	4	4	no	—
201	C₂²×C₁₀₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
202	C₂²×C₁₀₁	C₄×C₂²⋊C₄	1	2	yes	—
203	C₂²×C₁₀₁	#386	1	1	yes	characteristic
204	C₂²×C₁₀₁	#388	1	2	yes	—
205	C₂²×C₁₀₁	#390	1	1	yes	characteristic
206	C₂²×C₁₀₁	C₂×#97	1	1	yes	characteristic
207	C₂²×C₁₀₁	C₄×M₁₆	1	1	yes	characteristic
208	C₂²×C₁₀₁	#405	1	2	yes	—
209	C₂²×C₁₀₁	#407	1	2	yes	—
210	C₂²×C₁₀₁	#408	1	2	yes	—
211	C₂²×C₁₀₁	#432	1	2	yes	—
212	C₂²×C₁₀₁	#433	1	2	yes	—
213	C₂²×C₁₀₁	#435	1	4	yes	—
214	C₂²×C₁₀₁	#435	1	4	yes	—
215	C₂²×C₁₀₁	#435	1	4	yes	—
216	C₂²×C₁₀₁	#436	1	4	yes	—
217	C₄×C₁₀₁	—	4	4	no	—
218	C₄×C₁₀₁	—	4	2	no	—
219	C₄×C₁₀₁	—	4	4	no	—
220	C₄×C₁₀₁	#386	1	2	yes	—
221	C₄×C₁₀₁	#388	1	2	yes	—
222	C₄×C₁₀₁	#388	1	2	yes	—
223	C₄×C₁₀₁	#390	1	2	yes	—
224	#10922	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂×C₁₀₁	—	4	4	no	—
226	C₂×C₁₀₁	#1437	1	1	yes	characteristic
227	C₂×C₁₀₁	#1749	1	1	yes	characteristic
228	C₂×C₁₀₁	#1750	1	1	yes	characteristic
229	C₂×C₁₀₁	#1752	1	2	yes	—
230	C₂×C₁₀₁	#1753	1	2	yes	—
231	C₂×C₁₀₁	#1870	1	2	yes	—
232	C₂×C₁₀₁	#1924	1	4	yes	—
233	C₂×C₁₀₁	#1955	1	2	yes	—
234	C₂²×C₂²⋊C₈	C₂×C₁₀₁	1	2	yes	—
235	C₂²×#97	C₂×C₁₀₁	1	1	yes	characteristic, complemented
236	C₂×C₄×C₂²⋊C₄	C₂×C₁₀₁	1	1	yes	characteristic
237	C₂×#336	C₂×C₁₀₁	1	1	yes	characteristic, complemented
238	C₂×#336	C₂×C₁₀₁	1	2	yes	complemented
239	C₁₀₁	#10922	1	1	yes	characteristic, direct product factor, Sylow
240	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
241	C₂³×C₈	C₂²×C₁₀₁	1	2	yes	—
242	C₂³×C₈	C₂²×C₁₀₁	1	2	yes	—
243	C₂²×C₂²⋊C₄	C₄×C₁₀₁	1	2	yes	—
244	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
245	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
246	C₂×C₂²⋊C₈	—	2	4	no	—
247	C₂×C₂²⋊C₈	—	2	4	no	—
248	C₂×C₂²⋊C₈	C₄×C₁₀₁	1	8	yes	complemented
249	C₂×#97	—	2	4	no	—
250	C₂×#97	—	2	2	no	—
251	C₄×C₂²⋊C₄	—	2	2	no	—
252	C₄×C₂²⋊C₄	—	2	2	no	—
253	C₂×#95	C₄×C₁₀₁	1	2	yes	—
254	#336	—	2	4	no	—
255	#336	—	2	2	no	—
256	C₂⁵	C₂×C₄×C₁₀₁	1	1	yes	characteristic
257	C₂³×C₄	—	2	1	no	—
258	C₂³×C₄	—	2	1	no	—
259	C₂³×C₄	—	2	2	no	—
260	C₂³×C₄	—	2	2	no	—
261	C₂³×C₄	—	2	2	no	—
262	C₂³×C₄	—	2	2	no	—
263	C₂³×C₄	—	2	2	no	—
264	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
265	C₂³×C₄	C₂×C₄×C₁₀₁	1	4	yes	—
266	C₂³×C₄	C₂×C₄×C₁₀₁	1	2	yes	—
267	C₂³×C₄	C₂×C₄×C₁₀₁	1	2	yes	—
268	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	—	2	2	no	—
273	C₂²×C₈	—	2	2	no	—
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	—	2	2	no	—
276	C₂²×C₈	—	2	2	no	—
277	C₂²×C₈	—	2	2	no	—
278	C₂²×C₈	—	2	2	no	—
279	C₂²×C₈	C₂×C₄×C₁₀₁	1	4	yes	—
280	C₂²×C₈	C₂×C₄×C₁₀₁	1	4	yes	—
281	C₂²×C₈	D₄×C₁₀₁	1	4	yes	—
282	C₂²×C₈	D₄×C₁₀₁	1	4	yes	—
283	C₂×C₂²⋊C₄	—	2	4	no	—
284	C₂×C₂²⋊C₄	—	2	4	no	—
285	C₂×C₂²⋊C₄	—	2	4	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	—	2	2	no	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	—	2	2	no	—
292	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
293	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
294	C₂²⋊C₈	—	2	16	no	—
295	#97	—	2	8	no	—
296	#95	—	2	4	no	—
297	C₂⁴	—	2	1	no	—
298	C₂⁴	—	2	1	no	—
299	C₂⁴	—	2	2	no	—
300	C₂⁴	—	2	2	no	—
301	C₂⁴	—	2	2	no	—
302	C₂⁴	—	2	4	no	—
303	C₂⁴	C₄²×C₁₀₁	1	2	yes	—
304	C₂⁴	M₁₆×C₁₀₁	1	4	yes	—
305	C₂⁴	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	4	2	no	—
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	1	no	—
334	C₂²×C₄	C₄²×C₁₀₁	1	2	yes	—
335	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	4	yes	—
336	C₂²×C₄	M₁₆×C₁₀₁	1	4	yes	—
337	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
339	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
342	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
343	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
344	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
345	C₂×C₈	—	2	4	no	—
346	C₂×C₈	—	2	4	no	—
347	C₂×C₈	—	2	4	no	—
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	2	4	no	—
350	C₂×C₈	—	2	4	no	—
351	C₂×C₈	—	2	4	no	—
352	C₂×C₈	—	2	4	no	—
353	C₂×C₈	—	2	4	no	—
354	C₂×C₈	—	4	2	no	—
355	C₂×C₈	—	4	2	no	—
356	C₂×C₈	—	4	2	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	C₂²⋊C₄×C₁₀₁	1	8	yes	complemented
359	C₂²⋊C₄	—	2	16	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	4	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	4	2	no	—
364	C₄²	—	4	1	no	—
365	C₄²	—	4	1	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	2	4	no	—
368	C₂³	—	2	4	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	2	8	no	—
371	C₂³	—	2	8	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	4	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	4	no	—
377	C₂³	—	4	4	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	1	no	—
381	C₂³	#97×C₁₀₁	1	4	yes	complemented
382	C₂³	C₂×C₄²×C₁₀₁	1	1	yes	characteristic
383	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
384	C₂³	#117×C₁₀₁	1	1	yes	characteristic
385	C₂³	C₄×D₄×C₁₀₁	1	2	yes	—
386	C₂³	C₄×D₄×C₁₀₁	1	2	yes	—
387	C₂³	C₂×M₁₆×C₁₀₁	1	2	yes	—
388	C₂³	C₂×M₁₆×C₁₀₁	1	2	yes	—
389	C₂³	#131×C₁₀₁	1	4	yes	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
410	C₂×C₄	#117×C₁₀₁	1	2	yes	—
411	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
412	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
413	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
414	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
415	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
416	C₂×C₄	#121×C₁₀₁	1	2	yes	—
417	C₂×C₄	#121×C₁₀₁	1	2	yes	—
418	C₂×C₄	#121×C₁₀₁	1	2	yes	—
419	C₂×C₄	#123×C₁₀₁	1	2	yes	—
420	C₂×C₄	#123×C₁₀₁	1	1	yes	characteristic
421	C₂×C₄	#124×C₁₀₁	1	1	yes	characteristic
422	C₂×C₄	#124×C₁₀₁	1	2	yes	—
423	C₂×C₄	#126×C₁₀₁	1	2	yes	—
424	C₂×C₄	#127×C₁₀₁	1	1	yes	characteristic
425	C₈	—	2	8	no	—
426	C₈	—	4	4	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	2	8	no	—
429	C₂²	—	4	8	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	C₄×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
436	C₂²	C₄×C₂²⋊C₄×C₁₀₁	1	2	yes	—
437	C₂²	#386×C₁₀₁	1	1	yes	characteristic
438	C₂²	#388×C₁₀₁	1	2	yes	—
439	C₂²	#390×C₁₀₁	1	1	yes	characteristic
440	C₂²	C₂×#97×C₁₀₁	1	1	yes	characteristic
441	C₂²	C₄×M₁₆×C₁₀₁	1	1	yes	characteristic
442	C₂²	#405×C₁₀₁	1	2	yes	—
443	C₂²	#407×C₁₀₁	1	2	yes	—
444	C₂²	#408×C₁₀₁	1	2	yes	—
445	C₂²	#432×C₁₀₁	1	2	yes	—
446	C₂²	#433×C₁₀₁	1	2	yes	—
447	C₂²	#435×C₁₀₁	1	4	yes	—
448	C₂²	#435×C₁₀₁	1	4	yes	—
449	C₂²	#435×C₁₀₁	1	4	yes	—
450	C₂²	#436×C₁₀₁	1	4	yes	—
451	C₄	—	4	2	no	—
452	C₄	—	4	4	no	—
453	C₄	—	4	4	no	—
454	C₄	#386×C₁₀₁	1	2	yes	—
455	C₄	#388×C₁₀₁	1	2	yes	—
456	C₄	#388×C₁₀₁	1	2	yes	—
457	C₄	#390×C₁₀₁	1	2	yes	—
458	C₂	—	4	4	no	—
459	C₂	C₁₀₁×#1437	1	1	yes	characteristic
460	C₂	C₁₀₁×#1749	1	1	yes	characteristic
461	C₂	C₁₀₁×#1750	1	1	yes	characteristic
462	C₂	C₁₀₁×#1752	1	2	yes	—
463	C₂	C₁₀₁×#1753	1	2	yes	—
464	C₂	C₁₀₁×#1870	1	2	yes	—
465	C₂	C₁₀₁×#1924	1	4	yes	—
466	C₂	C₁₀₁×#1955	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₀₁	C₂³
commutator	C₂³	C₂×C₄²×C₁₀₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₀₁
socle	C₂⁴×C₁₀₁	C₂²×C₄
prime radical	C₂⁵×C₁₀₁	C₂×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#97×C₁₀₁	C₂	semidirect
4. C₂×#336×C₁₀₁	C₂	semidirect
5. C₂×#336×C₁₀₁	C₂	semidirect
14. C₂×C₂²⋊C₈×C₁₀₁	C₄	semidirect
124. C₂×C₈×C₁₀₁	C₂²⋊C₄	semidirect
147. C₂³×C₁₀₁	#97	semidirect
224. #10922	C₁₀₁	direct (N × H)
235. C₂²×#97	C₂×C₁₀₁	semidirect
237. C₂×#336	C₂×C₁₀₁	semidirect
238. C₂×#336	C₂×C₁₀₁	semidirect
239. C₁₀₁	#10922	direct (N × H)
248. C₂×C₂²⋊C₈	C₄×C₁₀₁	semidirect
358. C₂×C₈	C₂²⋊C₄×C₁₀₁	semidirect
381. C₂³	#97×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊C₈×C₁₀₁	2
C₂²×#97×C₁₀₁	2
C₂×C₄×C₂²⋊C₄×C₁₀₁	2
C₂×#336×C₁₀₁	2
#10922	101

Subgroups — C101×#10922 #38793073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#10922 #38793073