Subgroups — C₁₀₁×#17690 #38799841

Order 25856.

898 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	C₁₀₁×#3512	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#2970	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#1535	C₂	1	2	yes	maximal, complemented
4	C₁₀₁×#1534	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#1532	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1530	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1529	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#1524	C₂	1	2	yes	maximal, complemented
9	C₂×#330×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#553×C₁₀₁	—	2	2	no	—
11	#553×C₁₀₁	—	2	2	no	—
12	#553×C₁₀₁	—	2	2	no	—
13	#552×C₁₀₁	—	2	2	no	—
14	#541×C₁₀₁	C₄	1	2	yes	—
15	#540×C₁₀₁	C₄	1	2	yes	—
16	#537×C₁₀₁	C₄	1	2	yes	—
17	#532×C₁₀₁	C₂²	1	1	yes	characteristic
18	#529×C₁₀₁	C₂²	1	2	yes	—
19	#529×C₁₀₁	C₂²	1	2	yes	—
20	C₂×#125×C₁₀₁	C₂²	1	1	yes	characteristic
21	#520×C₁₀₁	C₄	1	2	yes	—
22	C₄×#41×C₁₀₁	C₂²	1	1	yes	characteristic
23	#446×C₁₀₁	—	2	2	no	—
24	#435×C₁₀₁	—	2	2	no	—
25	#435×C₁₀₁	—	2	2	no	—
26	C₈×D₄×C₁₀₁	—	2	2	no	—
27	#432×C₁₀₁	C₂²	1	2	yes	—
28	#432×C₁₀₁	C₂²	1	2	yes	—
29	#432×C₁₀₁	C₂²	1	2	yes	—
30	C₄×M₁₆×C₁₀₁	C₂²	1	2	yes	—
31	C₂×#97×C₁₀₁	C₂²	1	2	yes	—
32	C₂×#97×C₁₀₁	C₂²	1	2	yes	—
33	#330×C₁₀₁	C₂²	1	1	yes	characteristic
34	#330×C₁₀₁	C₂²	1	2	yes	—
35	#330×C₁₀₁	C₂²	1	1	yes	characteristic
36	#330×C₁₀₁	C₂²	1	2	yes	—
37	#330×C₁₀₁	C₂²	1	1	yes	characteristic
38	#330×C₁₀₁	C₂²	1	1	yes	characteristic
39	#329×C₁₀₁	C₂²	1	2	yes	—
40	#329×C₁₀₁	C₂²	1	2	yes	—
41	#329×C₁₀₁	C₂²	1	2	yes	—
42	#329×C₁₀₁	C₂²	1	2	yes	—
43	C₂×#41×C₁₀₁	C₂×C₄	1	2	yes	—
44	C₂×#41×C₁₀₁	C₂×C₄	1	1	yes	characteristic
45	C₂×M₁₆×C₁₀₁	—	2	2	no	—
46	C₂²×C₈×C₁₀₁	—	2	2	no	—
47	C₂²×C₈×C₁₀₁	—	2	2	no	—
48	C₄⋊Q₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
49	#127×C₁₀₁	C₂×C₄	1	1	yes	characteristic
50	#126×C₁₀₁	—	2	2	no	—
51	#126×C₁₀₁	—	2	2	no	—
52	#126×C₁₀₁	—	2	2	no	—
53	#126×C₁₀₁	—	2	2	no	—
54	#125×C₁₀₁	—	2	2	no	—
55	#125×C₁₀₁	—	2	2	no	—
56	#125×C₁₀₁	—	2	2	no	—
57	#125×C₁₀₁	C₂×C₄	1	2	yes	—
58	#125×C₁₀₁	C₂³	1	1	yes	characteristic
59	#125×C₁₀₁	C₂³	1	1	yes	characteristic
60	#124×C₁₀₁	C₂³	1	2	yes	—
61	#123×C₁₀₁	—	2	2	no	—
62	#123×C₁₀₁	—	2	2	no	—
63	#123×C₁₀₁	—	2	2	no	—
64	#123×C₁₀₁	—	2	2	no	—
65	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
66	C₂²⋊Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
67	C₂²⋊Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
68	#121×C₁₀₁	—	2	2	no	—
69	#121×C₁₀₁	—	2	2	no	—
70	#121×C₁₀₁	—	2	2	no	—
71	#121×C₁₀₁	—	2	2	no	—
72	#121×C₁₀₁	—	2	2	no	—
73	#121×C₁₀₁	—	2	2	no	—
74	#121×C₁₀₁	C₂×C₄	1	2	yes	—
75	#121×C₁₀₁	C₂×C₄	1	2	yes	—
76	C₄×Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
77	C₄×Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
78	C₄×Q₈×C₁₀₁	D₄	1	2	yes	—
79	C₄×D₄×C₁₀₁	—	2	2	no	—
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	C₂×C₄	1	2	yes	—
85	C₄×D₄×C₁₀₁	C₂×C₄	1	2	yes	—
86	C₄×D₄×C₁₀₁	D₄	1	2	yes	—
87	C₄×D₄×C₁₀₁	D₄	1	2	yes	—
88	C₄×D₄×C₁₀₁	D₄	1	2	yes	—
89	#117×C₁₀₁	—	2	2	no	—
90	#117×C₁₀₁	—	2	2	no	—
91	#117×C₁₀₁	—	2	2	no	—
92	#117×C₁₀₁	C₂×C₄	1	1	yes	characteristic
93	#117×C₁₀₁	C₂×C₄	1	2	yes	—
94	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
95	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
96	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
97	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
99	C₄⋊C₈×C₁₀₁	—	2	2	no	—
100	C₄⋊C₈×C₁₀₁	—	2	2	no	—
101	C₄⋊C₈×C₁₀₁	—	2	2	no	—
102	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
103	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
104	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
105	#97×C₁₀₁	—	2	2	no	—
106	#97×C₁₀₁	—	2	2	no	—
107	#97×C₁₀₁	C₂³	1	2	yes	—
108	#97×C₁₀₁	C₂³	1	2	yes	—
109	#97×C₁₀₁	C₂³	1	2	yes	—
110	#97×C₁₀₁	C₂³	1	2	yes	—
111	C₄×C₈×C₁₀₁	—	2	2	no	—
112	#41×C₁₀₁	—	4	2	no	—
113	#41×C₁₀₁	—	4	4	no	—
114	C₂×Q₈×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×Q₈×C₁₀₁	C₂²×C₄	1	2	yes	—
116	C₂×D₄×C₁₀₁	—	2	2	no	—
117	C₂×D₄×C₁₀₁	—	2	2	no	—
118	C₂×D₄×C₁₀₁	—	2	2	no	—
119	C₂×D₄×C₁₀₁	—	2	2	no	—
120	C₂×D₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
121	C₂×D₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
122	C₂×D₄×C₁₀₁	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₁₀₁	—	2	2	no	—
124	C₂²×C₄×C₁₀₁	—	2	2	no	—
125	C₂²×C₄×C₁₀₁	—	2	2	no	—
126	C₂²×C₄×C₁₀₁	—	2	2	no	—
127	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
132	M₁₆×C₁₀₁	—	4	4	no	—
133	C₂×C₈×C₁₀₁	—	2	2	no	—
134	C₂×C₈×C₁₀₁	—	2	2	no	—
135	C₂×C₈×C₁₀₁	—	2	2	no	—
136	C₂×C₈×C₁₀₁	—	2	2	no	—
137	C₂×C₈×C₁₀₁	—	4	4	no	—
138	C₂×C₈×C₁₀₁	—	4	4	no	—
139	C₄⋊C₄×C₁₀₁	—	2	2	no	—
140	C₄⋊C₄×C₁₀₁	—	2	2	no	—
141	C₄⋊C₄×C₁₀₁	—	2	2	no	—
142	C₄⋊C₄×C₁₀₁	—	2	2	no	—
143	C₄⋊C₄×C₁₀₁	—	2	2	no	—
144	C₄⋊C₄×C₁₀₁	—	2	2	no	—
145	C₄⋊C₄×C₁₀₁	—	2	2	no	—
146	C₄⋊C₄×C₁₀₁	—	2	2	no	—
147	C₄⋊C₄×C₁₀₁	—	2	2	no	—
148	C₄⋊C₄×C₁₀₁	—	2	2	no	—
149	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
150	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
151	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
152	C₄⋊C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
153	C₄⋊C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
154	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
155	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
156	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
157	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
158	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
159	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
160	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
161	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
162	C₂²⋊C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
163	C₂²⋊C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
164	C₂²⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
165	C₂²⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
166	C₄²×C₁₀₁	—	2	2	no	—
167	C₄²×C₁₀₁	—	2	2	no	—
168	C₄²×C₁₀₁	C₂²×C₄	1	2	yes	—
169	C₄²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
171	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
172	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
173	C₄²×C₁₀₁	C₂⁴	1	1	yes	characteristic
174	C₂³×C₁₀₁	—	2	2	no	—
175	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
176	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	Q₈×C₁₀₁	—	4	1	no	—
178	Q₈×C₁₀₁	—	4	2	no	—
179	D₄×C₁₀₁	—	2	4	no	—
180	D₄×C₁₀₁	—	4	1	no	—
181	D₄×C₁₀₁	—	4	2	no	—
182	D₄×C₁₀₁	—	4	4	no	—
183	D₄×C₁₀₁	—	8	2	no	—
184	D₄×C₁₀₁	—	8	2	no	—
185	D₄×C₁₀₁	—	8	2	no	—
186	C₂×C₄×C₁₀₁	—	2	2	no	—
187	C₂×C₄×C₁₀₁	—	2	2	no	—
188	C₂×C₄×C₁₀₁	—	2	2	no	—
189	C₂×C₄×C₁₀₁	—	2	2	no	—
190	C₂×C₄×C₁₀₁	—	4	2	no	—
191	C₂×C₄×C₁₀₁	—	4	2	no	—
192	C₂×C₄×C₁₀₁	—	4	2	no	—
193	C₂×C₄×C₁₀₁	—	4	2	no	—
194	C₂×C₄×C₁₀₁	—	4	4	no	—
195	C₂×C₄×C₁₀₁	—	8	2	no	—
196	C₂×C₄×C₁₀₁	—	8	2	no	—
197	C₂×C₄×C₁₀₁	—	8	2	no	—
198	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
199	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
200	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
201	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
202	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
205	C₈×C₁₀₁	—	2	4	no	—
206	C₈×C₁₀₁	—	4	2	no	—
207	C₈×C₁₀₁	—	4	2	no	—
208	C₈×C₁₀₁	—	4	2	no	—
209	C₂²×C₁₀₁	—	2	2	no	—
210	C₂²×C₁₀₁	—	2	2	no	—
211	C₂²×C₁₀₁	—	2	2	no	—
212	C₂²×C₁₀₁	—	2	2	no	—
213	C₂²×C₁₀₁	—	4	2	no	—
214	C₂²×C₁₀₁	—	4	2	no	—
215	C₂²×C₁₀₁	—	4	2	no	—
216	C₂²×C₁₀₁	#413	1	2	yes	—
217	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
218	C₄×C₁₀₁	—	2	1	no	—
219	C₄×C₁₀₁	—	2	1	no	—
220	C₄×C₁₀₁	—	2	2	no	—
221	C₄×C₁₀₁	—	2	2	no	—
222	C₄×C₁₀₁	—	2	2	no	—
223	C₄×C₁₀₁	—	2	2	no	—
224	C₄×C₁₀₁	—	2	2	no	—
225	C₄×C₁₀₁	—	4	2	no	—
226	C₄×C₁₀₁	—	4	2	no	—
227	C₄×C₁₀₁	—	4	2	no	—
228	#17690	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂×C₁₀₁	—	2	2	no	—
230	C₂×C₁₀₁	—	4	2	no	—
231	C₂×C₁₀₁	—	8	2	no	—
232	C₂×C₁₀₁	C₂×#413	1	1	yes	characteristic
233	C₂×C₁₀₁	#2901	1	2	yes	—
234	#3512	C₂×C₁₀₁	1	1	yes	characteristic
235	#2970	C₂×C₁₀₁	1	2	yes	complemented
236	#1535	C₂×C₁₀₁	1	2	yes	complemented
237	#1534	C₂×C₁₀₁	1	1	yes	characteristic, complemented
238	#1532	C₂×C₁₀₁	1	2	yes	complemented
239	#1530	C₂×C₁₀₁	1	2	yes	complemented
240	#1529	C₂×C₁₀₁	1	2	yes	complemented
241	#1524	C₂×C₁₀₁	1	2	yes	complemented
242	C₂×#330	C₂×C₁₀₁	1	1	yes	characteristic, complemented
243	C₁₀₁	#17690	1	1	yes	characteristic, direct product factor, Sylow
244	#553	—	2	2	no	—
245	#553	—	2	2	no	—
246	#553	—	2	2	no	—
247	#552	—	2	2	no	—
248	#541	C₄×C₁₀₁	1	2	yes	—
249	#540	C₄×C₁₀₁	1	2	yes	—
250	#537	C₄×C₁₀₁	1	2	yes	—
251	#532	C₂²×C₁₀₁	1	1	yes	characteristic
252	#529	C₂²×C₁₀₁	1	2	yes	—
253	#529	C₂²×C₁₀₁	1	2	yes	—
254	C₂×#125	C₂²×C₁₀₁	1	1	yes	characteristic
255	#520	C₄×C₁₀₁	1	2	yes	—
256	C₄×#41	C₂²×C₁₀₁	1	1	yes	characteristic
257	#446	—	2	2	no	—
258	#435	—	2	2	no	—
259	#435	—	2	2	no	—
260	C₈×D₄	—	2	2	no	—
261	#432	C₂²×C₁₀₁	1	2	yes	—
262	#432	C₂²×C₁₀₁	1	2	yes	—
263	#432	C₂²×C₁₀₁	1	2	yes	—
264	C₄×M₁₆	C₂²×C₁₀₁	1	2	yes	—
265	C₂×#97	C₂²×C₁₀₁	1	2	yes	—
266	C₂×#97	C₂²×C₁₀₁	1	2	yes	—
267	#330	C₂²×C₁₀₁	1	1	yes	characteristic
268	#330	C₂²×C₁₀₁	1	2	yes	—
269	#330	C₂²×C₁₀₁	1	1	yes	characteristic
270	#330	C₂²×C₁₀₁	1	2	yes	—
271	#330	C₂²×C₁₀₁	1	1	yes	characteristic
272	#330	C₂²×C₁₀₁	1	1	yes	characteristic
273	#329	C₂²×C₁₀₁	1	2	yes	—
274	#329	C₂²×C₁₀₁	1	2	yes	—
275	#329	C₂²×C₁₀₁	1	2	yes	—
276	#329	C₂²×C₁₀₁	1	2	yes	—
277	C₂×#41	C₂×C₄×C₁₀₁	1	2	yes	—
278	C₂×#41	C₂×C₄×C₁₀₁	1	1	yes	characteristic
279	C₂×M₁₆	—	2	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₄⋊Q₈	C₂×C₄×C₁₀₁	1	1	yes	characteristic
283	#127	C₂×C₄×C₁₀₁	1	1	yes	characteristic
284	#126	—	2	2	no	—
285	#126	—	2	2	no	—
286	#126	—	2	2	no	—
287	#126	—	2	2	no	—
288	#125	—	2	2	no	—
289	#125	—	2	2	no	—
290	#125	—	2	2	no	—
291	#125	C₂×C₄×C₁₀₁	1	2	yes	—
292	#125	C₂³×C₁₀₁	1	1	yes	characteristic
293	#125	C₂³×C₁₀₁	1	1	yes	characteristic
294	#124	C₂³×C₁₀₁	1	2	yes	—
295	#123	—	2	2	no	—
296	#123	—	2	2	no	—
297	#123	—	2	2	no	—
298	#123	—	2	2	no	—
299	C₂²⋊Q₈	—	2	2	no	—
300	C₂²⋊Q₈	C₂×C₄×C₁₀₁	1	2	yes	—
301	C₂²⋊Q₈	C₂×C₄×C₁₀₁	1	2	yes	—
302	#121	—	2	2	no	—
303	#121	—	2	2	no	—
304	#121	—	2	2	no	—
305	#121	—	2	2	no	—
306	#121	—	2	2	no	—
307	#121	—	2	2	no	—
308	#121	C₂×C₄×C₁₀₁	1	2	yes	—
309	#121	C₂×C₄×C₁₀₁	1	2	yes	—
310	C₄×Q₈	C₂×C₄×C₁₀₁	1	2	yes	—
311	C₄×Q₈	C₂×C₄×C₁₀₁	1	2	yes	—
312	C₄×Q₈	D₄×C₁₀₁	1	2	yes	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	—	2	2	no	—
315	C₄×D₄	—	2	2	no	—
316	C₄×D₄	—	2	2	no	—
317	C₄×D₄	—	2	2	no	—
318	C₄×D₄	C₂×C₄×C₁₀₁	1	2	yes	—
319	C₄×D₄	C₂×C₄×C₁₀₁	1	2	yes	—
320	C₄×D₄	D₄×C₁₀₁	1	2	yes	—
321	C₄×D₄	D₄×C₁₀₁	1	2	yes	—
322	C₄×D₄	D₄×C₁₀₁	1	2	yes	—
323	#117	—	2	2	no	—
324	#117	—	2	2	no	—
325	#117	—	2	2	no	—
326	#117	C₂×C₄×C₁₀₁	1	1	yes	characteristic
327	#117	C₂×C₄×C₁₀₁	1	2	yes	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
331	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
332	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
333	C₄⋊C₈	—	2	2	no	—
334	C₄⋊C₈	—	2	2	no	—
335	C₄⋊C₈	—	2	2	no	—
336	C₂²⋊C₈	—	2	2	no	—
337	C₂²⋊C₈	—	2	2	no	—
338	C₂²⋊C₈	—	2	2	no	—
339	#97	—	2	2	no	—
340	#97	—	2	2	no	—
341	#97	C₂³×C₁₀₁	1	2	yes	—
342	#97	C₂³×C₁₀₁	1	2	yes	—
343	#97	C₂³×C₁₀₁	1	2	yes	—
344	#97	C₂³×C₁₀₁	1	2	yes	—
345	C₄×C₈	—	2	2	no	—
346	#41	—	4	2	no	—
347	#41	—	4	4	no	—
348	C₂×Q₈	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
349	C₂×Q₈	C₂²×C₄×C₁₀₁	1	2	yes	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
355	C₂×D₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
356	C₂×D₄	C₂²×C₄×C₁₀₁	1	2	yes	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
362	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
366	M₁₆	—	4	4	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	4	4	no	—
372	C₂×C₈	—	4	4	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
384	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
385	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
386	C₄⋊C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
387	C₄⋊C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
397	C₂²⋊C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
398	C₂²⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
399	C₂²⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	C₂²×C₄×C₁₀₁	1	2	yes	—
403	C₄²	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
404	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
405	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
406	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
407	C₄²	C₂⁴×C₁₀₁	1	1	yes	characteristic
408	C₂³	—	2	2	no	—
409	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
410	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
411	Q₈	—	4	1	no	—
412	Q₈	—	4	2	no	—
413	D₄	—	2	4	no	—
414	D₄	—	4	1	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	4	no	—
417	D₄	—	8	2	no	—
418	D₄	—	8	2	no	—
419	D₄	—	8	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	8	2	no	—
430	C₂×C₄	—	8	2	no	—
431	C₂×C₄	—	8	2	no	—
432	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
433	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
434	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
435	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
436	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
437	C₂×C₄	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
438	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
439	C₈	—	2	4	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	2	no	—
442	C₈	—	4	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	#413×C₁₀₁	1	2	yes	—
451	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₂	—	2	2	no	—
463	C₂	—	4	2	no	—
464	C₂	—	8	2	no	—
465	C₂	C₂×#413×C₁₀₁	1	1	yes	characteristic
466	C₂	C₁₀₁×#2901	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₄²	C₂⁴×C₁₀₁
prime radical	C₁₀₁×#3512	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₄×#41×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₁×#2970	C₂	semidirect
3. C₁₀₁×#1535	C₂	semidirect
4. C₁₀₁×#1534	C₂	semidirect
5. C₁₀₁×#1532	C₂	semidirect
6. C₁₀₁×#1530	C₂	semidirect
7. C₁₀₁×#1529	C₂	semidirect
8. C₁₀₁×#1524	C₂	semidirect
9. C₂×#330×C₁₀₁	C₂	semidirect
228. #17690	C₁₀₁	direct (N × H)
235. #2970	C₂×C₁₀₁	semidirect
236. #1535	C₂×C₁₀₁	semidirect
237. #1534	C₂×C₁₀₁	semidirect
238. #1532	C₂×C₁₀₁	semidirect
239. #1530	C₂×C₁₀₁	semidirect
240. #1529	C₂×C₁₀₁	semidirect
241. #1524	C₂×C₁₀₁	semidirect
242. C₂×#330	C₂×C₁₀₁	semidirect
243. C₁₀₁	#17690	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₀₁×#3512	2
C₁₀₁×#2970	2
C₁₀₁×#1535	2
C₁₀₁×#1534	2
C₁₀₁×#1532	2
C₁₀₁×#1530	2
C₁₀₁×#1529	2
C₁₀₁×#1524	2
C₂×#330×C₁₀₁	2
#17690	101

Subgroups — C101×#17690 #38799841

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#17690 #38799841