Subgroups — C₁₀₁×#11201 #38793352

Order 25856.

1146 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#407×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#2280	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₂²⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#339×C₁₀₁	C₂	1	2	yes	maximal, complemented
5	C₂×#339×C₁₀₁	C₂	1	2	yes	maximal, complemented
6	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₀₁	C₂²	1	2	yes	—
8	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
9	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂²×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
11	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
12	#407×C₁₀₁	—	2	4	no	—
13	C₂×C₂²⋊C₈×C₁₀₁	—	2	2	no	—
14	#381×C₁₀₁	—	2	1	no	—
15	#380×C₁₀₁	C₄	1	2	yes	complemented
16	#380×C₁₀₁	C₄	1	2	yes	complemented
17	#379×C₁₀₁	—	2	1	no	—
18	C₄×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
19	C₄×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
20	C₂×#95×C₁₀₁	—	2	1	no	—
21	#339×C₁₀₁	—	2	4	no	—
22	#339×C₁₀₁	—	2	4	no	—
23	C₂⁵×C₁₀₁	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₀₁	—	2	2	no	—
25	C₂³×C₄×C₁₀₁	—	2	2	no	—
26	C₂³×C₄×C₁₀₁	—	2	2	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	—	2	2	no	—
31	C₂³×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
34	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
35	C₂×M₁₆×C₁₀₁	—	2	2	no	—
36	C₂×M₁₆×C₁₀₁	—	2	2	no	—
37	C₂×M₁₆×C₁₀₁	—	2	2	no	—
38	C₂×M₁₆×C₁₀₁	—	2	2	no	—
39	C₂×M₁₆×C₁₀₁	—	2	2	no	—
40	C₂×M₁₆×C₁₀₁	D₄	1	4	yes	—
41	C₂²×C₈×C₁₀₁	—	2	2	no	—
42	#117×C₁₀₁	—	2	2	no	—
43	#117×C₁₀₁	—	2	2	no	—
44	#117×C₁₀₁	—	2	2	no	—
45	#117×C₁₀₁	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
50	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
51	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
52	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
54	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
55	C₂×C₄²×C₁₀₁	—	2	2	no	—
56	C₂×C₄²×C₁₀₁	—	2	2	no	—
57	C₂×C₄²×C₁₀₁	—	2	2	no	—
58	C₂×C₄²×C₁₀₁	—	2	2	no	—
59	C₂×C₄²×C₁₀₁	—	2	2	no	—
60	C₂×C₄²×C₁₀₁	—	2	1	no	—
61	C₂×C₄²×C₁₀₁	—	2	1	no	—
62	C₂×C₄²×C₁₀₁	D₄	1	4	yes	—
63	C₂²⋊C₈×C₁₀₁	—	2	8	no	—
64	#95×C₁₀₁	—	2	4	no	—
65	#95×C₁₀₁	—	2	2	no	—
66	#95×C₁₀₁	—	2	2	no	—
67	C₂⁴×C₁₀₁	—	2	4	no	—
68	C₂⁴×C₁₀₁	—	2	1	no	—
69	C₂⁴×C₁₀₁	—	2	1	no	—
70	C₂⁴×C₁₀₁	—	2	2	no	—
71	C₂⁴×C₁₀₁	—	2	2	no	—
72	C₂⁴×C₁₀₁	—	4	2	no	—
73	C₂⁴×C₁₀₁	C₂²⋊C₄	1	2	yes	—
74	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₀₁	—	2	8	no	—
76	C₂²×C₄×C₁₀₁	—	2	1	no	—
77	C₂²×C₄×C₁₀₁	—	2	4	no	—
78	C₂²×C₄×C₁₀₁	—	2	2	no	—
79	C₂²×C₄×C₁₀₁	—	2	2	no	—
80	C₂²×C₄×C₁₀₁	—	2	1	no	—
81	C₂²×C₄×C₁₀₁	—	2	2	no	—
82	C₂²×C₄×C₁₀₁	—	2	2	no	—
83	C₂²×C₄×C₁₀₁	—	2	4	no	—
84	C₂²×C₄×C₁₀₁	—	2	4	no	—
85	C₂²×C₄×C₁₀₁	—	2	2	no	—
86	C₂²×C₄×C₁₀₁	—	2	4	no	—
87	C₂²×C₄×C₁₀₁	—	2	4	no	—
88	C₂²×C₄×C₁₀₁	—	2	2	no	—
89	C₂²×C₄×C₁₀₁	—	2	1	no	—
90	C₂²×C₄×C₁₀₁	—	2	2	no	—
91	C₂²×C₄×C₁₀₁	—	2	1	no	—
92	C₂²×C₄×C₁₀₁	—	4	4	no	—
93	C₂²×C₄×C₁₀₁	—	4	2	no	—
94	C₂²×C₄×C₁₀₁	—	4	2	no	—
95	C₂²×C₄×C₁₀₁	—	4	2	no	—
96	C₂²×C₄×C₁₀₁	—	4	2	no	—
97	C₂²×C₄×C₁₀₁	—	4	2	no	—
98	C₂²×C₄×C₁₀₁	—	4	2	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	C₂²⋊C₄	1	2	yes	—
104	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
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	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
112	M₁₆×C₁₀₁	—	2	4	no	—
113	M₁₆×C₁₀₁	—	2	4	no	—
114	M₁₆×C₁₀₁	—	4	2	no	—
115	M₁₆×C₁₀₁	—	4	2	no	—
116	C₂×C₈×C₁₀₁	—	2	4	no	—
117	C₂×C₈×C₁₀₁	—	4	2	no	—
118	C₂×C₈×C₁₀₁	—	4	2	no	—
119	C₄⋊C₄×C₁₀₁	—	2	4	no	—
120	C₄⋊C₄×C₁₀₁	—	2	2	no	—
121	C₄⋊C₄×C₁₀₁	—	2	2	no	—
122	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
123	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
124	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
125	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
126	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
127	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
128	C₄²×C₁₀₁	—	2	4	no	—
129	C₄²×C₁₀₁	—	2	4	no	—
130	C₄²×C₁₀₁	—	4	1	no	—
131	C₄²×C₁₀₁	—	4	2	no	—
132	C₄²×C₁₀₁	—	4	2	no	—
133	C₄²×C₁₀₁	—	4	1	no	—
134	C₄²×C₁₀₁	—	4	2	no	—
135	C₂³×C₁₀₁	—	2	2	no	—
136	C₂³×C₁₀₁	—	2	2	no	—
137	C₂³×C₁₀₁	—	2	4	no	—
138	C₂³×C₁₀₁	—	2	4	no	—
139	C₂³×C₁₀₁	—	2	2	no	—
140	C₂³×C₁₀₁	—	2	2	no	—
141	C₂³×C₁₀₁	—	2	2	no	—
142	C₂³×C₁₀₁	—	2	2	no	—
143	C₂³×C₁₀₁	—	2	2	no	—
144	C₂³×C₁₀₁	—	2	2	no	—
145	C₂³×C₁₀₁	—	4	8	no	—
146	C₂³×C₁₀₁	—	4	8	no	—
147	C₂³×C₁₀₁	—	4	2	no	—
148	C₂³×C₁₀₁	—	4	2	no	—
149	C₂³×C₁₀₁	—	4	2	no	—
150	C₂³×C₁₀₁	—	4	2	no	—
151	C₂³×C₁₀₁	#104	1	4	yes	—
152	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂³×C₁₀₁	#120	1	1	yes	characteristic
154	C₂³×C₁₀₁	#121	1	2	yes	—
155	C₂³×C₁₀₁	#123	1	2	yes	—
156	C₂³×C₁₀₁	#123	1	1	yes	characteristic
157	C₂×C₄×C₁₀₁	—	2	8	no	—
158	C₂×C₄×C₁₀₁	—	2	2	no	—
159	C₂×C₄×C₁₀₁	—	2	2	no	—
160	C₂×C₄×C₁₀₁	—	2	2	no	—
161	C₂×C₄×C₁₀₁	—	4	8	no	—
162	C₂×C₄×C₁₀₁	—	4	8	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	2	no	—
167	C₂×C₄×C₁₀₁	—	4	4	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	2	no	—
172	C₂×C₄×C₁₀₁	—	4	1	no	—
173	C₂×C₄×C₁₀₁	—	4	1	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	—	4	2	no	—
178	C₂×C₄×C₁₀₁	#117	1	1	yes	characteristic
179	C₂×C₄×C₁₀₁	#117	1	1	yes	characteristic
180	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
183	C₂×C₄×C₁₀₁	#121	1	2	yes	—
184	C₂×C₄×C₁₀₁	#121	1	2	yes	—
185	C₂×C₄×C₁₀₁	#121	1	2	yes	—
186	C₂×C₄×C₁₀₁	#123	1	2	yes	—
187	C₂×C₄×C₁₀₁	#123	1	2	yes	—
188	C₂×C₄×C₁₀₁	#123	1	2	yes	—
189	C₂×C₄×C₁₀₁	#123	1	1	yes	characteristic
190	C₂×C₄×C₁₀₁	#124	1	2	yes	—
191	C₂×C₄×C₁₀₁	#124	1	2	yes	—
192	C₂×C₄×C₁₀₁	#126	1	2	yes	—
193	C₂×C₄×C₁₀₁	#126	1	2	yes	—
194	C₈×C₁₀₁	—	4	4	no	—
195	C₂²×C₁₀₁	—	2	4	no	—
196	C₂²×C₁₀₁	—	2	4	no	—
197	C₂²×C₁₀₁	—	2	1	no	—
198	C₂²×C₁₀₁	—	2	1	no	—
199	C₂²×C₁₀₁	—	2	1	no	—
200	C₂²×C₁₀₁	—	2	1	no	—
201	C₂²×C₁₀₁	—	2	4	no	—
202	C₂²×C₁₀₁	—	2	4	no	—
203	C₂²×C₁₀₁	—	2	4	no	—
204	C₂²×C₁₀₁	—	4	8	no	—
205	C₂²×C₁₀₁	—	4	8	no	—
206	C₂²×C₁₀₁	—	4	2	no	—
207	C₂²×C₁₀₁	—	4	2	no	—
208	C₂²×C₁₀₁	—	4	2	no	—
209	C₂²×C₁₀₁	—	4	2	no	—
210	C₂²×C₁₀₁	#381	1	1	yes	characteristic
211	C₂²×C₁₀₁	#386	1	1	yes	characteristic
212	C₂²×C₁₀₁	#386	1	1	yes	characteristic
213	C₂²×C₁₀₁	#394	1	2	yes	—
214	C₂²×C₁₀₁	#397	1	2	yes	—
215	C₂²×C₁₀₁	C₂×#104	1	2	yes	—
216	C₂²×C₁₀₁	#421	1	2	yes	—
217	C₄×C₁₀₁	—	4	8	no	—
218	C₄×C₁₀₁	—	4	2	no	—
219	C₄×C₁₀₁	—	8	2	no	—
220	C₄×C₁₀₁	—	8	1	no	—
221	C₄×C₁₀₁	—	8	1	no	—
222	C₄×C₁₀₁	#388	1	2	yes	—
223	C₄×C₁₀₁	#388	1	2	yes	—
224	C₄×C₁₀₁	#394	1	2	yes	—
225	C₄×C₁₀₁	#397	1	2	yes	—
226	#11201	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂×C₁₀₁	—	2	2	no	—
228	C₂×C₁₀₁	—	2	2	no	—
229	C₂×C₁₀₁	—	4	4	no	—
230	C₂×C₁₀₁	#1440	1	1	yes	characteristic
231	C₂×C₁₀₁	#1826	1	2	yes	—
232	C₂×C₁₀₁	#1871	1	2	yes	—
233	C₂×C₁₀₁	#1896	1	1	yes	characteristic
234	C₂×C₁₀₁	#1897	1	1	yes	characteristic
235	C₂×#407	C₂×C₁₀₁	1	1	yes	characteristic
236	#2280	C₂×C₁₀₁	1	1	yes	characteristic
237	C₂×C₄×C₂²⋊C₄	C₂×C₁₀₁	1	1	yes	characteristic
238	C₂×#339	C₂×C₁₀₁	1	2	yes	complemented
239	C₂×#339	C₂×C₁₀₁	1	2	yes	complemented
240	C₁₀₁	#11201	1	1	yes	characteristic, direct product factor, Sylow
241	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
242	C₂²×M₁₆	C₂²×C₁₀₁	1	2	yes	—
243	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
244	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
245	C₂²×C₂²⋊C₄	—	2	1	no	—
246	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
247	#407	—	2	4	no	—
248	C₂×C₂²⋊C₈	—	2	2	no	—
249	#381	—	2	1	no	—
250	#380	C₄×C₁₀₁	1	2	yes	complemented
251	#380	C₄×C₁₀₁	1	2	yes	complemented
252	#379	—	2	1	no	—
253	C₄×C₂²⋊C₄	—	2	2	no	—
254	C₄×C₂²⋊C₄	—	2	4	no	—
255	C₂×#95	—	2	1	no	—
256	#339	—	2	4	no	—
257	#339	—	2	4	no	—
258	C₂⁵	D₄×C₁₀₁	1	1	yes	characteristic
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	—	2	2	no	—
265	C₂³×C₄	—	2	2	no	—
266	C₂³×C₄	C₂×C₄×C₁₀₁	1	2	yes	—
267	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
268	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
269	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
270	C₂×M₁₆	—	2	2	no	—
271	C₂×M₁₆	—	2	2	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	—	2	2	no	—
275	C₂×M₁₆	D₄×C₁₀₁	1	4	yes	—
276	C₂²×C₈	—	2	2	no	—
277	#117	—	2	2	no	—
278	#117	—	2	2	no	—
279	#117	—	2	2	no	—
280	#117	—	2	2	no	—
281	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
283	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	—	2	8	no	—
285	C₂×C₂²⋊C₄	—	2	4	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	1	no	—
289	C₂×C₂²⋊C₄	—	2	1	no	—
290	C₂×C₄²	—	2	2	no	—
291	C₂×C₄²	—	2	2	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	—	2	2	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	D₄×C₁₀₁	1	4	yes	—
298	C₂²⋊C₈	—	2	8	no	—
299	#95	—	2	4	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	C₂⁴	—	2	4	no	—
303	C₂⁴	—	2	1	no	—
304	C₂⁴	—	2	1	no	—
305	C₂⁴	—	2	2	no	—
306	C₂⁴	—	2	2	no	—
307	C₂⁴	—	4	2	no	—
308	C₂⁴	C₂²⋊C₄×C₁₀₁	1	2	yes	—
309	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	4	4	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
339	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
343	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
344	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
345	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
346	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
347	M₁₆	—	2	4	no	—
348	M₁₆	—	2	4	no	—
349	M₁₆	—	4	2	no	—
350	M₁₆	—	4	2	no	—
351	C₂×C₈	—	2	4	no	—
352	C₂×C₈	—	4	2	no	—
353	C₂×C₈	—	4	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₂²⋊C₄	—	2	16	no	—
358	C₂²⋊C₄	—	4	4	no	—
359	C₂²⋊C₄	—	4	4	no	—
360	C₂²⋊C₄	—	4	1	no	—
361	C₂²⋊C₄	—	4	2	no	—
362	C₂²⋊C₄	—	4	1	no	—
363	C₄²	—	2	4	no	—
364	C₄²	—	2	4	no	—
365	C₄²	—	4	1	no	—
366	C₄²	—	4	2	no	—
367	C₄²	—	4	2	no	—
368	C₄²	—	4	1	no	—
369	C₄²	—	4	2	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	4	no	—
373	C₂³	—	2	4	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	4	8	no	—
381	C₂³	—	4	8	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	2	no	—
386	C₂³	#104×C₁₀₁	1	4	yes	—
387	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
388	C₂³	#120×C₁₀₁	1	1	yes	characteristic
389	C₂³	#121×C₁₀₁	1	2	yes	—
390	C₂³	#123×C₁₀₁	1	1	yes	characteristic
391	C₂³	#123×C₁₀₁	1	2	yes	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	—	4	8	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	4	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	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	#117×C₁₀₁	1	1	yes	characteristic
414	C₂×C₄	#117×C₁₀₁	1	1	yes	characteristic
415	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
416	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
417	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
418	C₂×C₄	#121×C₁₀₁	1	2	yes	—
419	C₂×C₄	#121×C₁₀₁	1	2	yes	—
420	C₂×C₄	#121×C₁₀₁	1	2	yes	—
421	C₂×C₄	#123×C₁₀₁	1	1	yes	characteristic
422	C₂×C₄	#123×C₁₀₁	1	2	yes	—
423	C₂×C₄	#123×C₁₀₁	1	2	yes	—
424	C₂×C₄	#123×C₁₀₁	1	2	yes	—
425	C₂×C₄	#124×C₁₀₁	1	2	yes	—
426	C₂×C₄	#124×C₁₀₁	1	2	yes	—
427	C₂×C₄	#126×C₁₀₁	1	2	yes	—
428	C₂×C₄	#126×C₁₀₁	1	2	yes	—
429	C₈	—	4	4	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	4	no	—
439	C₂²	—	4	8	no	—
440	C₂²	—	4	8	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	#381×C₁₀₁	1	1	yes	characteristic
446	C₂²	#386×C₁₀₁	1	1	yes	characteristic
447	C₂²	#386×C₁₀₁	1	1	yes	characteristic
448	C₂²	#394×C₁₀₁	1	2	yes	—
449	C₂²	#397×C₁₀₁	1	2	yes	—
450	C₂²	C₂×#104×C₁₀₁	1	2	yes	—
451	C₂²	#421×C₁₀₁	1	2	yes	—
452	C₄	—	4	8	no	—
453	C₄	—	4	2	no	—
454	C₄	—	8	1	no	—
455	C₄	—	8	1	no	—
456	C₄	—	8	2	no	—
457	C₄	#388×C₁₀₁	1	2	yes	—
458	C₄	#388×C₁₀₁	1	2	yes	—
459	C₄	#394×C₁₀₁	1	2	yes	—
460	C₄	#397×C₁₀₁	1	2	yes	—
461	C₂	—	2	2	no	—
462	C₂	—	2	2	no	—
463	C₂	—	4	4	no	—
464	C₂	C₁₀₁×#1440	1	1	yes	characteristic
465	C₂	C₁₀₁×#1826	1	2	yes	—
466	C₂	C₁₀₁×#1871	1	2	yes	—
467	C₂	C₁₀₁×#1896	1	1	yes	characteristic
468	C₂	C₁₀₁×#1897	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₀₁	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₀₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₀₁
socle	C₂³×C₁₀₁	C₂×C₂²⋊C₄
prime radical	C₂⁵×C₁₀₁	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₁ ◁ C₂⁴×C₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×#339×C₁₀₁	C₂	semidirect
5. C₂×#339×C₁₀₁	C₂	semidirect
15. #380×C₁₀₁	C₄	semidirect
16. #380×C₁₀₁	C₄	semidirect
226. #11201	C₁₀₁	direct (N × H)
238. C₂×#339	C₂×C₁₀₁	semidirect
239. C₂×#339	C₂×C₁₀₁	semidirect
240. C₁₀₁	#11201	direct (N × H)
250. #380	C₄×C₁₀₁	semidirect
251. #380	C₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#407×C₁₀₁	2
C₁₀₁×#2280	2
C₂×C₄×C₂²⋊C₄×C₁₀₁	2
C₂×#339×C₁₀₁	2
#11201	101

Subgroups — C101×#11201 #38793352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#11201 #38793352