Subgroups — C₁₀₁×#17413 #38799564

Order 25856.

944 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#2924	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#1472	C₂	1	2	yes	maximal, complemented
4	C₁₀₁×#1470	C₂	1	4	yes	maximal, complemented
5	C₁₀₁×#1465	C₂	1	1	yes	maximal, characteristic
6	C₁₀₁×#1464	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1459	C₂	1	1	yes	maximal, characteristic
8	C₁₀₁×#1458	C₂	1	2	yes	maximal, complemented
9	#552×C₁₀₁	—	2	2	no	—
10	#552×C₁₀₁	—	2	2	no	—
11	#552×C₁₀₁	—	2	4	no	—
12	C₂×#126×C₁₀₁	C₄	1	2	yes	—
13	C₂×#125×C₁₀₁	C₄	1	1	yes	characteristic
14	C₂×#125×C₁₀₁	C₂²	1	2	yes	—
15	C₂×#123×C₁₀₁	C₄	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₁₀₁	C₄	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₀₁	C₄	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂×#117×C₁₀₁	C₂²	1	2	yes	—
21	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₀₁	C₄	1	1	yes	characteristic
23	#433×C₁₀₁	—	2	4	no	—
24	#432×C₁₀₁	C₂²	1	4	yes	—
25	#431×C₁₀₁	C₂²	1	4	yes	—
26	#424×C₁₀₁	—	2	2	no	—
27	#407×C₁₀₁	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	2	yes	—
29	#405×C₁₀₁	—	2	2	no	—
30	#324×C₁₀₁	C₂²	1	4	yes	—
31	#324×C₁₀₁	C₂²	1	2	yes	—
32	#324×C₁₀₁	C₂²	1	4	yes	—
33	#324×C₁₀₁	C₂²	1	2	yes	—
34	#323×C₁₀₁	C₂²	1	1	yes	characteristic
35	#323×C₁₀₁	C₂²	1	2	yes	—
36	#323×C₁₀₁	C₂²	1	1	yes	characteristic
37	C₂²×Q₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×D₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
42	C₂×M₁₆×C₁₀₁	—	2	2	no	—
43	C₂²×C₈×C₁₀₁	—	2	2	no	—
44	#126×C₁₀₁	—	2	4	no	—
45	#126×C₁₀₁	—	2	4	no	—
46	#125×C₁₀₁	—	2	2	no	—
47	#125×C₁₀₁	—	2	2	no	—
48	#125×C₁₀₁	—	2	4	no	—
49	#125×C₁₀₁	—	2	4	no	—
50	#123×C₁₀₁	—	2	4	no	—
51	#123×C₁₀₁	—	2	4	no	—
52	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
53	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
54	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
55	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
56	C₄×Q₈×C₁₀₁	—	2	2	no	—
57	C₄×Q₈×C₁₀₁	—	2	1	no	—
58	C₄×Q₈×C₁₀₁	—	2	1	no	—
59	C₄×D₄×C₁₀₁	—	2	2	no	—
60	C₄×D₄×C₁₀₁	—	2	2	no	—
61	#117×C₁₀₁	—	2	4	no	—
62	#117×C₁₀₁	—	2	4	no	—
63	#117×C₁₀₁	D₄	1	2	yes	—
64	#117×C₁₀₁	D₄	1	2	yes	—
65	#117×C₁₀₁	D₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
75	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
80	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
83	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₁₀₁	C₂×C₄	1	2	yes	—
85	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
87	C₄⋊C₈×C₁₀₁	—	2	4	no	—
88	C₄⋊C₈×C₁₀₁	—	2	4	no	—
89	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
90	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
91	C₂²⋊C₈×C₁₀₁	C₂³	1	2	yes	—
92	C₂²⋊C₈×C₁₀₁	C₂³	1	2	yes	—
93	C₂²⋊C₈×C₁₀₁	C₂³	1	4	yes	—
94	#97×C₁₀₁	—	2	4	no	—
95	C₄×C₈×C₁₀₁	—	2	4	no	—
96	C₂⁴×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
97	C₂⁴×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
98	C₂×Q₈×C₁₀₁	—	2	1	no	—
99	C₂×Q₈×C₁₀₁	—	2	1	no	—
100	C₂×Q₈×C₁₀₁	—	4	2	no	—
101	C₂×D₄×C₁₀₁	—	2	2	no	—
102	C₂×D₄×C₁₀₁	—	2	2	no	—
103	C₂×D₄×C₁₀₁	—	4	1	no	—
104	C₂²×C₄×C₁₀₁	—	2	4	no	—
105	C₂²×C₄×C₁₀₁	—	2	2	no	—
106	C₂²×C₄×C₁₀₁	—	2	2	no	—
107	C₂²×C₄×C₁₀₁	—	2	1	no	—
108	C₂²×C₄×C₁₀₁	—	2	1	no	—
109	C₂²×C₄×C₁₀₁	—	4	2	no	—
110	C₂²×C₄×C₁₀₁	—	4	2	no	—
111	C₂²×C₄×C₁₀₁	—	4	2	no	—
112	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
123	M₁₆×C₁₀₁	—	4	4	no	—
124	C₂×C₈×C₁₀₁	—	2	2	no	—
125	C₂×C₈×C₁₀₁	—	2	4	no	—
126	C₂×C₈×C₁₀₁	—	2	2	no	—
127	C₂×C₈×C₁₀₁	—	4	4	no	—
128	C₄⋊C₄×C₁₀₁	—	2	1	no	—
129	C₄⋊C₄×C₁₀₁	—	2	1	no	—
130	C₄⋊C₄×C₁₀₁	—	2	2	no	—
131	C₄⋊C₄×C₁₀₁	—	2	2	no	—
132	C₄⋊C₄×C₁₀₁	—	2	4	no	—
133	C₄⋊C₄×C₁₀₁	—	2	2	no	—
134	C₄⋊C₄×C₁₀₁	—	2	2	no	—
135	C₄⋊C₄×C₁₀₁	—	2	4	no	—
136	C₄⋊C₄×C₁₀₁	—	2	4	no	—
137	C₄⋊C₄×C₁₀₁	—	2	4	no	—
138	C₄⋊C₄×C₁₀₁	—	2	2	no	—
139	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
140	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
141	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
142	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
143	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
144	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
145	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
146	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
147	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
148	C₂²⋊C₄×C₁₀₁	C₂²⋊C₄	1	4	yes	—
149	C₂²⋊C₄×C₁₀₁	C₂²⋊C₄	1	4	yes	—
150	C₄²×C₁₀₁	—	2	2	no	—
151	C₄²×C₁₀₁	—	2	2	no	—
152	C₄²×C₁₀₁	—	2	1	no	—
153	C₄²×C₁₀₁	—	2	1	no	—
154	C₄²×C₁₀₁	C₂×D₄	1	4	yes	—
155	C₄²×C₁₀₁	C₂×D₄	1	4	yes	—
156	C₂³×C₁₀₁	—	2	1	no	—
157	C₂³×C₁₀₁	—	2	1	no	—
158	C₂³×C₁₀₁	—	2	1	no	—
159	C₂³×C₁₀₁	—	2	1	no	—
160	C₂³×C₁₀₁	—	4	1	no	—
161	C₂³×C₁₀₁	—	4	1	no	—
162	C₂³×C₁₀₁	—	4	1	no	—
163	C₂³×C₁₀₁	—	4	1	no	—
164	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂³×C₁₀₁	#131	1	2	yes	—
166	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
167	Q₈×C₁₀₁	—	4	2	no	—
168	Q₈×C₁₀₁	—	4	2	no	—
169	D₄×C₁₀₁	—	4	4	no	—
170	C₂×C₄×C₁₀₁	—	2	2	no	—
171	C₂×C₄×C₁₀₁	—	2	2	no	—
172	C₂×C₄×C₁₀₁	—	2	4	no	—
173	C₂×C₄×C₁₀₁	—	2	2	no	—
174	C₂×C₄×C₁₀₁	—	2	1	no	—
175	C₂×C₄×C₁₀₁	—	2	2	no	—
176	C₂×C₄×C₁₀₁	—	2	1	no	—
177	C₂×C₄×C₁₀₁	—	2	2	no	—
178	C₂×C₄×C₁₀₁	—	2	1	no	—
179	C₂×C₄×C₁₀₁	—	2	2	no	—
180	C₂×C₄×C₁₀₁	—	2	1	no	—
181	C₂×C₄×C₁₀₁	—	2	2	no	—
182	C₂×C₄×C₁₀₁	—	2	1	no	—
183	C₂×C₄×C₁₀₁	—	4	2	no	—
184	C₂×C₄×C₁₀₁	—	4	1	no	—
185	C₂×C₄×C₁₀₁	—	4	2	no	—
186	C₂×C₄×C₁₀₁	—	4	4	no	—
187	C₂×C₄×C₁₀₁	—	4	4	no	—
188	C₂×C₄×C₁₀₁	—	4	2	no	—
189	C₂×C₄×C₁₀₁	—	4	2	no	—
190	C₂×C₄×C₁₀₁	—	4	1	no	—
191	C₂×C₄×C₁₀₁	—	4	1	no	—
192	C₂×C₄×C₁₀₁	—	4	2	no	—
193	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
194	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
195	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
197	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
199	C₈×C₁₀₁	—	4	2	no	—
200	C₈×C₁₀₁	—	4	2	no	—
201	C₈×C₁₀₁	—	4	4	no	—
202	C₂²×C₁₀₁	—	2	1	no	—
203	C₂²×C₁₀₁	—	2	1	no	—
204	C₂²×C₁₀₁	—	2	2	no	—
205	C₂²×C₁₀₁	—	2	2	no	—
206	C₂²×C₁₀₁	—	2	2	no	—
207	C₂²×C₁₀₁	—	2	2	no	—
208	C₂²×C₁₀₁	—	4	2	no	—
209	C₂²×C₁₀₁	—	4	2	no	—
210	C₂²×C₁₀₁	—	4	1	no	—
211	C₂²×C₁₀₁	—	4	1	no	—
212	C₂²×C₁₀₁	—	8	1	no	—
213	C₂²×C₁₀₁	—	8	1	no	—
214	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
215	C₂²×C₁₀₁	C₂×#131	1	1	yes	characteristic
216	C₂²×C₁₀₁	#568	1	1	yes	characteristic
217	C₄×C₁₀₁	—	2	2	no	—
218	C₄×C₁₀₁	—	2	2	no	—
219	C₄×C₁₀₁	—	2	2	no	—
220	C₄×C₁₀₁	—	2	1	no	—
221	C₄×C₁₀₁	—	2	4	no	—
222	C₄×C₁₀₁	—	4	2	no	—
223	C₄×C₁₀₁	—	4	1	no	—
224	C₄×C₁₀₁	—	4	1	no	—
225	C₄×C₁₀₁	—	4	2	no	—
226	C₄×C₁₀₁	—	4	1	no	—
227	C₄×C₁₀₁	#410	1	2	yes	—
228	#17413	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂×C₁₀₁	—	2	1	no	—
230	C₂×C₁₀₁	—	2	1	no	—
231	C₂×C₁₀₁	—	4	2	no	—
232	C₂×C₁₀₁	—	4	2	no	—
233	C₂×C₁₀₁	#2880	1	1	yes	characteristic
234	C₂×C₁₀₁	C₂×#410	1	1	yes	characteristic
235	C₂×C₁₀₁	#2889	1	1	yes	characteristic
236	C₂×#552	C₂×C₁₀₁	1	1	yes	characteristic
237	#2924	C₂×C₁₀₁	1	2	yes	complemented
238	#1472	C₂×C₁₀₁	1	2	yes	complemented
239	#1470	C₂×C₁₀₁	1	4	yes	complemented
240	#1465	C₂×C₁₀₁	1	1	yes	characteristic
241	#1464	C₂×C₁₀₁	1	2	yes	complemented
242	#1459	C₂×C₁₀₁	1	1	yes	characteristic
243	#1458	C₂×C₁₀₁	1	2	yes	complemented
244	C₁₀₁	#17413	1	1	yes	characteristic, direct product factor, Sylow
245	#552	—	2	2	no	—
246	#552	—	2	2	no	—
247	#552	—	2	4	no	—
248	C₂×#126	C₄×C₁₀₁	1	2	yes	—
249	C₂×#125	C₄×C₁₀₁	1	1	yes	characteristic
250	C₂×#125	C₂²×C₁₀₁	1	2	yes	—
251	C₂×#123	C₄×C₁₀₁	1	2	yes	—
252	C₂×C₂²⋊Q₈	C₄×C₁₀₁	1	1	yes	characteristic
253	C₂×C₂²⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
254	C₂×C₄×Q₈	C₄×C₁₀₁	1	1	yes	characteristic
255	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
256	C₂×#117	C₂²×C₁₀₁	1	2	yes	—
257	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
258	C₂²×C₄⋊C₄	C₄×C₁₀₁	1	1	yes	characteristic
259	#433	—	2	4	no	—
260	#432	C₂²×C₁₀₁	1	4	yes	—
261	#431	C₂²×C₁₀₁	1	4	yes	—
262	#424	—	2	2	no	—
263	#407	C₂²×C₁₀₁	1	2	yes	—
264	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	2	yes	—
265	#405	—	2	2	no	—
266	#324	C₂²×C₁₀₁	1	4	yes	—
267	#324	C₂²×C₁₀₁	1	2	yes	—
268	#324	C₂²×C₁₀₁	1	4	yes	—
269	#324	C₂²×C₁₀₁	1	2	yes	—
270	#323	C₂²×C₁₀₁	1	1	yes	characteristic
271	#323	C₂²×C₁₀₁	1	2	yes	—
272	#323	C₂²×C₁₀₁	1	1	yes	characteristic
273	C₂²×Q₈	C₂×C₄×C₁₀₁	1	1	yes	characteristic
274	C₂²×D₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
275	C₂³×C₄	C₂×C₄×C₁₀₁	1	2	yes	—
276	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
277	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
278	C₂×M₁₆	—	2	2	no	—
279	C₂²×C₈	—	2	2	no	—
280	#126	—	2	4	no	—
281	#126	—	2	4	no	—
282	#125	—	2	2	no	—
283	#125	—	2	2	no	—
284	#125	—	2	4	no	—
285	#125	—	2	4	no	—
286	#123	—	2	4	no	—
287	#123	—	2	4	no	—
288	C₂²⋊Q₈	—	2	2	no	—
289	C₂²⋊Q₈	—	2	2	no	—
290	C₂²⋊Q₈	—	2	2	no	—
291	C₂²⋊Q₈	—	2	2	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	—	2	2	no	—
297	#117	—	2	4	no	—
298	#117	—	2	4	no	—
299	#117	D₄×C₁₀₁	1	2	yes	—
300	#117	D₄×C₁₀₁	1	2	yes	—
301	#117	D₄×C₁₀₁	1	4	yes	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
307	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
308	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
309	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
310	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
311	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
316	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
318	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
319	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
320	C₂×C₄²	C₂×C₄×C₁₀₁	1	2	yes	—
321	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
323	C₄⋊C₈	—	2	4	no	—
324	C₄⋊C₈	—	2	4	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	C₂²⋊C₈	C₂³×C₁₀₁	1	2	yes	—
328	C₂²⋊C₈	C₂³×C₁₀₁	1	2	yes	—
329	C₂²⋊C₈	C₂³×C₁₀₁	1	4	yes	—
330	#97	—	2	4	no	—
331	C₄×C₈	—	2	4	no	—
332	C₂⁴	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
333	C₂⁴	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	4	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
350	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
351	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
352	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
353	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
354	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
355	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
359	M₁₆	—	4	4	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	4	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	4	4	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
376	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
377	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
378	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
379	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	C₂²⋊C₄×C₁₀₁	1	4	yes	—
385	C₂²⋊C₄	C₂²⋊C₄×C₁₀₁	1	4	yes	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	C₂×D₄×C₁₀₁	1	4	yes	—
391	C₄²	C₂×D₄×C₁₀₁	1	4	yes	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
401	C₂³	#131×C₁₀₁	1	2	yes	—
402	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
403	Q₈	—	4	2	no	—
404	Q₈	—	4	2	no	—
405	D₄	—	4	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
430	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
431	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
432	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
433	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
434	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
435	C₈	—	4	2	no	—
436	C₈	—	4	2	no	—
437	C₈	—	4	4	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	1	no	—
450	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
451	C₂²	C₂×#131×C₁₀₁	1	1	yes	characteristic
452	C₂²	#568×C₁₀₁	1	1	yes	characteristic
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	4	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	1	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	1	no	—
463	C₄	#410×C₁₀₁	1	2	yes	—
464	C₂	—	2	1	no	—
465	C₂	—	2	1	no	—
466	C₂	—	4	2	no	—
467	C₂	—	4	2	no	—
468	C₂	C₁₀₁×#2880	1	1	yes	characteristic
469	C₂	C₂×#410×C₁₀₁	1	1	yes	characteristic
470	C₂	C₁₀₁×#2889	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂²×D₄×C₁₀₁	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂×#117×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₁×#2924	C₂	semidirect
3. C₁₀₁×#1472	C₂	semidirect
4. C₁₀₁×#1470	C₂	semidirect
6. C₁₀₁×#1464	C₂	semidirect
8. C₁₀₁×#1458	C₂	semidirect
228. #17413	C₁₀₁	direct (N × H)
237. #2924	C₂×C₁₀₁	semidirect
238. #1472	C₂×C₁₀₁	semidirect
239. #1470	C₂×C₁₀₁	semidirect
241. #1464	C₂×C₁₀₁	semidirect
243. #1458	C₂×C₁₀₁	semidirect
244. C₁₀₁	#17413	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#552×C₁₀₁	2
C₁₀₁×#2924	2
C₁₀₁×#1472	2
C₁₀₁×#1470	2
C₁₀₁×#1465	2
C₁₀₁×#1464	2
C₁₀₁×#1459	2
C₁₀₁×#1458	2
#17413	101

Subgroups — C101×#17413 #38799564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#17413 #38799564