Subgroups — C₁₀₁×#17362 #38799513

Order 25856.

1738 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#407×C₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#1465	C₂	1	4	yes	maximal, complemented
4	C₁₀₁×#1463	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1462	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1459	C₂	1	4	yes	maximal, complemented
7	C₂³×D₄×C₁₀₁	C₄	1	1	yes	characteristic
8	C₂⁴×C₄×C₁₀₁	C₄	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₀₁	—	2	2	no	—
11	C₂×C₄×D₄×C₁₀₁	—	2	2	no	—
12	C₂×C₄×D₄×C₁₀₁	—	2	2	no	—
13	C₂×C₄×D₄×C₁₀₁	—	2	2	no	—
14	C₂×C₄×D₄×C₁₀₁	—	2	2	no	—
15	C₂×C₄×D₄×C₁₀₁	C₄	1	2	yes	—
16	C₂×C₄×D₄×C₁₀₁	C₄	1	2	yes	—
17	C₂×C₄×D₄×C₁₀₁	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₁₀₁	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₁₀₁	C₄	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₀₁	C₄	1	1	yes	characteristic
23	#407×C₁₀₁	—	2	2	no	—
24	#407×C₁₀₁	—	2	2	no	—
25	#407×C₁₀₁	C₂²	1	4	yes	—
26	#407×C₁₀₁	C₂²	1	4	yes	complemented
27	C₂×C₂²⋊C₈×C₁₀₁	—	2	2	no	—
28	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	4	yes	complemented
29	#324×C₁₀₁	C₂²	1	8	yes	complemented
30	#323×C₁₀₁	C₂²	1	8	yes	complemented
31	C₂⁵×C₁₀₁	C₂×C₄	1	1	yes	characteristic
32	C₂⁵×C₁₀₁	C₂×C₄	1	1	yes	characteristic
33	C₂²×D₄×C₁₀₁	—	2	2	no	—
34	C₂²×D₄×C₁₀₁	—	2	2	no	—
35	C₂²×D₄×C₁₀₁	—	2	8	no	—
36	C₂²×D₄×C₁₀₁	C₂×C₄	1	2	yes	—
37	C₂²×D₄×C₁₀₁	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₁₀₁	—	2	1	no	—
39	C₂³×C₄×C₁₀₁	—	2	1	no	—
40	C₂³×C₄×C₁₀₁	—	2	1	no	—
41	C₂³×C₄×C₁₀₁	—	2	1	no	—
42	C₂³×C₄×C₁₀₁	—	4	4	no	—
43	C₂³×C₄×C₁₀₁	—	4	4	no	—
44	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
49	C₂³×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
50	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
53	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
54	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
55	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
56	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
59	C₂×M₁₆×C₁₀₁	—	2	4	no	—
60	C₂×M₁₆×C₁₀₁	—	2	4	no	—
61	C₂×M₁₆×C₁₀₁	—	4	8	no	—
62	C₂²×C₈×C₁₀₁	—	2	4	no	—
63	C₄×D₄×C₁₀₁	—	2	4	no	—
64	C₄×D₄×C₁₀₁	—	2	4	no	—
65	C₄×D₄×C₁₀₁	—	2	4	no	—
66	C₄×D₄×C₁₀₁	—	2	4	no	—
67	C₄×D₄×C₁₀₁	—	2	4	no	—
68	C₄×D₄×C₁₀₁	—	2	4	no	—
69	C₄×D₄×C₁₀₁	—	2	4	no	—
70	C₄×D₄×C₁₀₁	—	2	4	no	—
71	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
72	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
80	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
81	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
83	C₂×C₄²×C₁₀₁	—	2	1	no	—
84	C₂×C₄²×C₁₀₁	—	2	1	no	—
85	C₂×C₄²×C₁₀₁	—	2	1	no	—
86	C₂×C₄²×C₁₀₁	—	2	1	no	—
87	C₂×C₄²×C₁₀₁	C₂×C₄	1	2	yes	—
88	C₂×C₄²×C₁₀₁	C₂×C₄	1	2	yes	—
89	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
90	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
91	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
92	C₂²⋊C₈×C₁₀₁	C₂³	1	8	yes	—
93	C₂⁴×C₁₀₁	—	2	1	no	—
94	C₂⁴×C₁₀₁	—	2	1	no	—
95	C₂⁴×C₁₀₁	—	2	4	no	—
96	C₂⁴×C₁₀₁	—	2	4	no	—
97	C₂⁴×C₁₀₁	—	4	2	no	—
98	C₂⁴×C₁₀₁	—	4	2	no	—
99	C₂⁴×C₁₀₁	—	4	2	no	—
100	C₂⁴×C₁₀₁	—	4	2	no	—
101	C₂⁴×C₁₀₁	C₂²⋊C₄	1	2	yes	—
102	C₂⁴×C₁₀₁	C₂²⋊C₄	1	2	yes	—
103	C₂⁴×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
104	C₂⁴×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
105	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
106	C₂⁴×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
107	C₂×D₄×C₁₀₁	—	2	16	no	—
108	C₂×D₄×C₁₀₁	—	2	16	no	—
109	C₂×D₄×C₁₀₁	—	2	4	no	—
110	C₂×D₄×C₁₀₁	—	2	4	no	—
111	C₂×D₄×C₁₀₁	—	2	4	no	—
112	C₂×D₄×C₁₀₁	—	2	4	no	—
113	C₂×D₄×C₁₀₁	—	2	4	no	—
114	C₂×D₄×C₁₀₁	M₁₆	1	8	yes	complemented
115	C₂²×C₄×C₁₀₁	—	2	1	no	—
116	C₂²×C₄×C₁₀₁	—	2	1	no	—
117	C₂²×C₄×C₁₀₁	—	2	8	no	—
118	C₂²×C₄×C₁₀₁	—	2	4	no	—
119	C₂²×C₄×C₁₀₁	—	2	4	no	—
120	C₂²×C₄×C₁₀₁	—	2	1	no	—
121	C₂²×C₄×C₁₀₁	—	2	1	no	—
122	C₂²×C₄×C₁₀₁	—	2	1	no	—
123	C₂²×C₄×C₁₀₁	—	2	1	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	—	2	2	no	—
128	C₂²×C₄×C₁₀₁	—	4	2	no	—
129	C₂²×C₄×C₁₀₁	—	4	2	no	—
130	C₂²×C₄×C₁₀₁	—	4	4	no	—
131	C₂²×C₄×C₁₀₁	—	4	4	no	—
132	C₂²×C₄×C₁₀₁	—	4	2	no	—
133	C₂²×C₄×C₁₀₁	—	4	2	no	—
134	C₂²×C₄×C₁₀₁	—	4	4	no	—
135	C₂²×C₄×C₁₀₁	—	4	2	no	—
136	C₂²×C₄×C₁₀₁	—	4	4	no	—
137	C₂²×C₄×C₁₀₁	—	4	4	no	—
138	C₂²×C₄×C₁₀₁	—	4	4	no	—
139	C₂²×C₄×C₁₀₁	—	4	4	no	—
140	C₂²×C₄×C₁₀₁	—	4	4	no	—
141	C₂²×C₄×C₁₀₁	—	4	4	no	—
142	C₂²×C₄×C₁₀₁	—	4	2	no	—
143	C₂²×C₄×C₁₀₁	—	4	2	no	—
144	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
147	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
149	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
150	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
151	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
155	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
156	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
165	M₁₆×C₁₀₁	—	4	8	no	—
166	M₁₆×C₁₀₁	—	4	8	no	—
167	C₂×C₈×C₁₀₁	—	2	8	no	—
168	C₂×C₈×C₁₀₁	—	4	8	no	—
169	C₄⋊C₄×C₁₀₁	—	2	4	no	—
170	C₄⋊C₄×C₁₀₁	—	2	4	no	—
171	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
172	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
173	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
174	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
175	C₄²×C₁₀₁	—	2	2	no	—
176	C₄²×C₁₀₁	—	2	2	no	—
177	C₄²×C₁₀₁	—	2	2	no	—
178	C₄²×C₁₀₁	—	2	2	no	—
179	C₂³×C₁₀₁	—	2	2	no	—
180	C₂³×C₁₀₁	—	2	2	no	—
181	C₂³×C₁₀₁	—	2	2	no	—
182	C₂³×C₁₀₁	—	2	4	no	—
183	C₂³×C₁₀₁	—	2	4	no	—
184	C₂³×C₁₀₁	—	2	2	no	—
185	C₂³×C₁₀₁	—	2	2	no	—
186	C₂³×C₁₀₁	—	2	2	no	—
187	C₂³×C₁₀₁	—	2	4	no	—
188	C₂³×C₁₀₁	—	2	4	no	—
189	C₂³×C₁₀₁	—	2	4	no	—
190	C₂³×C₁₀₁	—	2	4	no	—
191	C₂³×C₁₀₁	—	4	2	no	—
192	C₂³×C₁₀₁	—	4	1	no	—
193	C₂³×C₁₀₁	—	4	1	no	—
194	C₂³×C₁₀₁	—	4	2	no	—
195	C₂³×C₁₀₁	—	4	1	no	—
196	C₂³×C₁₀₁	—	4	1	no	—
197	C₂³×C₁₀₁	—	4	2	no	—
198	C₂³×C₁₀₁	—	4	2	no	—
199	C₂³×C₁₀₁	—	4	2	no	—
200	C₂³×C₁₀₁	—	4	16	no	—
201	C₂³×C₁₀₁	—	4	16	no	—
202	C₂³×C₁₀₁	—	4	2	no	—
203	C₂³×C₁₀₁	—	4	2	no	—
204	C₂³×C₁₀₁	—	4	2	no	—
205	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
206	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
207	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂³×C₁₀₁	C₂×M₁₆	1	4	yes	—
210	C₂³×C₁₀₁	C₂×M₁₆	1	4	yes	complemented
211	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
212	D₄×C₁₀₁	—	2	16	no	—
213	D₄×C₁₀₁	—	2	16	no	—
214	C₂×C₄×C₁₀₁	—	2	4	no	—
215	C₂×C₄×C₁₀₁	—	2	4	no	—
216	C₂×C₄×C₁₀₁	—	2	2	no	—
217	C₂×C₄×C₁₀₁	—	2	2	no	—
218	C₂×C₄×C₁₀₁	—	2	4	no	—
219	C₂×C₄×C₁₀₁	—	2	2	no	—
220	C₂×C₄×C₁₀₁	—	2	4	no	—
221	C₂×C₄×C₁₀₁	—	2	4	no	—
222	C₂×C₄×C₁₀₁	—	2	2	no	—
223	C₂×C₄×C₁₀₁	—	2	2	no	—
224	C₂×C₄×C₁₀₁	—	2	2	no	—
225	C₂×C₄×C₁₀₁	—	2	2	no	—
226	C₂×C₄×C₁₀₁	—	2	4	no	—
227	C₂×C₄×C₁₀₁	—	2	4	no	—
228	C₂×C₄×C₁₀₁	—	2	2	no	—
229	C₂×C₄×C₁₀₁	—	2	2	no	—
230	C₂×C₄×C₁₀₁	—	4	2	no	—
231	C₂×C₄×C₁₀₁	—	4	2	no	—
232	C₂×C₄×C₁₀₁	—	4	1	no	—
233	C₂×C₄×C₁₀₁	—	4	2	no	—
234	C₂×C₄×C₁₀₁	—	4	2	no	—
235	C₂×C₄×C₁₀₁	—	4	2	no	—
236	C₂×C₄×C₁₀₁	—	4	1	no	—
237	C₂×C₄×C₁₀₁	—	4	4	no	—
238	C₂×C₄×C₁₀₁	—	4	4	no	—
239	C₂×C₄×C₁₀₁	—	4	2	no	—
240	C₂×C₄×C₁₀₁	—	4	2	no	—
241	C₂×C₄×C₁₀₁	—	4	2	no	—
242	C₂×C₄×C₁₀₁	—	4	2	no	—
243	C₂×C₄×C₁₀₁	—	4	4	no	—
244	C₂×C₄×C₁₀₁	—	4	4	no	—
245	C₂×C₄×C₁₀₁	—	4	2	no	—
246	C₂×C₄×C₁₀₁	—	4	2	no	—
247	C₂×C₄×C₁₀₁	#99	1	4	yes	—
248	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
251	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×C₄×C₁₀₁	C₂×M₁₆	1	4	yes	complemented
254	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
255	C₈×C₁₀₁	—	4	8	no	—
256	C₂²×C₁₀₁	—	2	8	no	—
257	C₂²×C₁₀₁	—	2	1	no	—
258	C₂²×C₁₀₁	—	2	1	no	—
259	C₂²×C₁₀₁	—	2	1	no	—
260	C₂²×C₁₀₁	—	2	1	no	—
261	C₂²×C₁₀₁	—	2	2	no	—
262	C₂²×C₁₀₁	—	2	1	no	—
263	C₂²×C₁₀₁	—	2	1	no	—
264	C₂²×C₁₀₁	—	2	2	no	—
265	C₂²×C₁₀₁	—	2	2	no	—
266	C₂²×C₁₀₁	—	2	4	no	—
267	C₂²×C₁₀₁	—	2	2	no	—
268	C₂²×C₁₀₁	—	2	2	no	—
269	C₂²×C₁₀₁	—	4	4	no	—
270	C₂²×C₁₀₁	—	4	8	no	—
271	C₂²×C₁₀₁	—	4	8	no	—
272	C₂²×C₁₀₁	—	4	4	no	—
273	C₂²×C₁₀₁	—	4	4	no	—
274	C₂²×C₁₀₁	—	4	4	no	—
275	C₂²×C₁₀₁	—	4	8	no	—
276	C₂²×C₁₀₁	—	4	8	no	—
277	C₂²×C₁₀₁	—	4	2	no	—
278	C₂²×C₁₀₁	—	4	2	no	—
279	C₂²×C₁₀₁	#407	1	4	yes	—
280	C₂²×C₁₀₁	C₂×#99	1	2	yes	—
281	C₂²×C₁₀₁	#413	1	2	yes	—
282	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
283	C₂²×C₁₀₁	C₂²×M₁₆	1	2	yes	—
284	C₄×C₁₀₁	—	2	4	no	—
285	C₄×C₁₀₁	—	2	2	no	—
286	C₄×C₁₀₁	—	2	1	no	—
287	C₄×C₁₀₁	—	2	1	no	—
288	C₄×C₁₀₁	—	2	2	no	—
289	C₄×C₁₀₁	—	4	2	no	—
290	C₄×C₁₀₁	—	4	2	no	—
291	C₄×C₁₀₁	C₂×#99	1	2	yes	—
292	C₄×C₁₀₁	C₂×#99	1	2	yes	—
293	#17362	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
294	C₂×C₁₀₁	—	2	2	no	—
295	C₂×C₁₀₁	—	2	2	no	—
296	C₂×C₁₀₁	—	2	2	no	—
297	C₂×C₁₀₁	—	2	4	no	—
298	C₂×C₁₀₁	—	4	2	no	—
299	C₂×C₁₀₁	—	4	4	no	—
300	C₂×C₁₀₁	C₂×#407	1	1	yes	characteristic
301	C₂×C₁₀₁	C₂²×#99	1	1	yes	characteristic
302	C₂×C₁₀₁	C₂×#413	1	1	yes	characteristic
303	C₂²×C₄×D₄	C₂×C₁₀₁	1	1	yes	characteristic
304	C₂×#407	C₂×C₁₀₁	1	2	yes	complemented
305	#1465	C₂×C₁₀₁	1	4	yes	complemented
306	#1463	C₂×C₁₀₁	1	2	yes	complemented
307	#1462	C₂×C₁₀₁	1	2	yes	complemented
308	#1459	C₂×C₁₀₁	1	4	yes	complemented
309	C₁₀₁	#17362	1	1	yes	characteristic, direct product factor, Sylow
310	C₂³×D₄	C₄×C₁₀₁	1	1	yes	characteristic
311	C₂⁴×C₄	C₄×C₁₀₁	1	1	yes	characteristic
312	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
313	C₂²×M₁₆	—	2	2	no	—
314	C₂×C₄×D₄	—	2	2	no	—
315	C₂×C₄×D₄	—	2	2	no	—
316	C₂×C₄×D₄	—	2	2	no	—
317	C₂×C₄×D₄	—	2	2	no	—
318	C₂×C₄×D₄	C₄×C₁₀₁	1	2	yes	—
319	C₂×C₄×D₄	C₄×C₁₀₁	1	2	yes	—
320	C₂×C₄×D₄	C₂²×C₁₀₁	1	2	yes	—
321	C₂×C₄×D₄	C₂²×C₁₀₁	1	2	yes	—
322	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
323	C₂²×C₂²⋊C₄	C₄×C₁₀₁	1	1	yes	characteristic
324	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
325	C₂²×C₄²	C₄×C₁₀₁	1	1	yes	characteristic
326	#407	—	2	2	no	—
327	#407	—	2	2	no	—
328	#407	C₂²×C₁₀₁	1	4	yes	—
329	#407	C₂²×C₁₀₁	1	4	yes	complemented
330	C₂×C₂²⋊C₈	—	2	2	no	—
331	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	4	yes	complemented
332	#324	C₂²×C₁₀₁	1	8	yes	complemented
333	#323	C₂²×C₁₀₁	1	8	yes	complemented
334	C₂⁵	C₂×C₄×C₁₀₁	1	1	yes	characteristic
335	C₂⁵	C₂×C₄×C₁₀₁	1	1	yes	characteristic
336	C₂²×D₄	—	2	2	no	—
337	C₂²×D₄	—	2	2	no	—
338	C₂²×D₄	—	2	8	no	—
339	C₂²×D₄	C₂×C₄×C₁₀₁	1	2	yes	—
340	C₂²×D₄	C₂×C₄×C₁₀₁	1	2	yes	—
341	C₂³×C₄	—	2	1	no	—
342	C₂³×C₄	—	2	1	no	—
343	C₂³×C₄	—	2	1	no	—
344	C₂³×C₄	—	2	1	no	—
345	C₂³×C₄	—	4	4	no	—
346	C₂³×C₄	—	4	4	no	—
347	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
348	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
349	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
350	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
351	C₂³×C₄	C₂×C₄×C₁₀₁	1	2	yes	—
352	C₂³×C₄	C₂×C₄×C₁₀₁	1	2	yes	—
353	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
354	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
355	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
356	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
357	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
358	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
359	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
360	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
361	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
362	C₂×M₁₆	—	2	4	no	—
363	C₂×M₁₆	—	2	4	no	—
364	C₂×M₁₆	—	4	8	no	—
365	C₂²×C₈	—	2	4	no	—
366	C₄×D₄	—	2	4	no	—
367	C₄×D₄	—	2	4	no	—
368	C₄×D₄	—	2	4	no	—
369	C₄×D₄	—	2	4	no	—
370	C₄×D₄	—	2	4	no	—
371	C₄×D₄	—	2	4	no	—
372	C₄×D₄	—	2	4	no	—
373	C₄×D₄	—	2	4	no	—
374	C₂×C₄⋊C₄	—	2	2	no	—
375	C₂×C₄⋊C₄	—	2	2	no	—
376	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
378	C₂×C₂²⋊C₄	—	2	2	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₂²⋊C₄	—	2	2	no	—
382	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
383	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
384	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	2	yes	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	—	2	1	no	—
388	C₂×C₄²	—	2	1	no	—
389	C₂×C₄²	—	2	1	no	—
390	C₂×C₄²	C₂×C₄×C₁₀₁	1	2	yes	—
391	C₂×C₄²	C₂×C₄×C₁₀₁	1	2	yes	—
392	C₂²⋊C₈	—	2	4	no	—
393	C₂²⋊C₈	—	2	4	no	—
394	C₂²⋊C₈	—	2	4	no	—
395	C₂²⋊C₈	C₂³×C₁₀₁	1	8	yes	—
396	C₂⁴	—	2	1	no	—
397	C₂⁴	—	2	1	no	—
398	C₂⁴	—	2	4	no	—
399	C₂⁴	—	2	4	no	—
400	C₂⁴	—	4	2	no	—
401	C₂⁴	—	4	2	no	—
402	C₂⁴	—	4	2	no	—
403	C₂⁴	—	4	2	no	—
404	C₂⁴	C₂²⋊C₄×C₁₀₁	1	2	yes	—
405	C₂⁴	C₂²⋊C₄×C₁₀₁	1	2	yes	—
406	C₂⁴	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
407	C₂⁴	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
408	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
409	C₂⁴	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
410	C₂×D₄	—	2	16	no	—
411	C₂×D₄	—	2	16	no	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	M₁₆×C₁₀₁	1	8	yes	complemented
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	8	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	4	4	no	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	—	4	4	no	—
440	C₂²×C₄	—	4	4	no	—
441	C₂²×C₄	—	4	4	no	—
442	C₂²×C₄	—	4	4	no	—
443	C₂²×C₄	—	4	4	no	—
444	C₂²×C₄	—	4	4	no	—
445	C₂²×C₄	—	4	2	no	—
446	C₂²×C₄	—	4	2	no	—
447	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
448	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
449	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
450	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
451	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
452	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
453	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
454	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
455	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
456	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
457	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
458	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
459	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
460	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
462	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
463	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
464	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
465	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
466	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
467	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
468	M₁₆	—	4	8	no	—
469	M₁₆	—	4	8	no	—
470	C₂×C₈	—	2	8	no	—
471	C₂×C₈	—	4	8	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	—	2	4	no	—
476	C₂²⋊C₄	—	2	4	no	—
477	C₂²⋊C₄	—	2	4	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	2	2	no	—
485	C₂³	—	2	4	no	—
486	C₂³	—	2	4	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	4	1	no	—
496	C₂³	—	4	1	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	1	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	4	2	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	4	16	no	—
504	C₂³	—	4	16	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	2	no	—
507	C₂³	—	4	2	no	—
508	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
509	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
510	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
511	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
512	C₂³	C₂×M₁₆×C₁₀₁	1	4	yes	—
513	C₂³	C₂×M₁₆×C₁₀₁	1	4	yes	complemented
514	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
515	D₄	—	2	16	no	—
516	D₄	—	2	16	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	—	4	4	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	4	no	—
547	C₂×C₄	—	4	4	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	#99×C₁₀₁	1	4	yes	—
551	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
552	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
553	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
554	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
555	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
556	C₂×C₄	C₂×M₁₆×C₁₀₁	1	4	yes	complemented
557	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
558	C₈	—	4	8	no	—
559	C₂²	—	2	8	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	1	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	4	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	4	4	no	—
573	C₂²	—	4	8	no	—
574	C₂²	—	4	8	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	4	8	no	—
577	C₂²	—	4	8	no	—
578	C₂²	—	4	4	no	—
579	C₂²	—	4	4	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	#407×C₁₀₁	1	4	yes	—
583	C₂²	C₂×#99×C₁₀₁	1	2	yes	—
584	C₂²	#413×C₁₀₁	1	2	yes	—
585	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
586	C₂²	C₂²×M₁₆×C₁₀₁	1	2	yes	—
587	C₄	—	2	4	no	—
588	C₄	—	2	2	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	2	no	—
592	C₄	—	4	2	no	—
593	C₄	—	4	2	no	—
594	C₄	C₂×#99×C₁₀₁	1	2	yes	—
595	C₄	C₂×#99×C₁₀₁	1	2	yes	—
596	C₂	—	2	2	no	—
597	C₂	—	2	2	no	—
598	C₂	—	2	2	no	—
599	C₂	—	2	4	no	—
600	C₂	—	4	2	no	—
601	C₂	—	4	4	no	—
602	C₂	C₂×#407×C₁₀₁	1	1	yes	characteristic
603	C₂	C₂²×#99×C₁₀₁	1	1	yes	characteristic
604	C₂	C₂×#413×C₁₀₁	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×#407×C₁₀₁	C₂	semidirect
3. C₁₀₁×#1465	C₂	semidirect
4. C₁₀₁×#1463	C₂	semidirect
5. C₁₀₁×#1462	C₂	semidirect
6. C₁₀₁×#1459	C₂	semidirect
26. #407×C₁₀₁	C₂²	semidirect
28. C₂×C₂²⋊C₈×C₁₀₁	C₂²	semidirect
29. #324×C₁₀₁	C₂²	semidirect
30. #323×C₁₀₁	C₂²	semidirect
114. C₂×D₄×C₁₀₁	M₁₆	semidirect
210. C₂³×C₁₀₁	C₂×M₁₆	semidirect
253. C₂×C₄×C₁₀₁	C₂×M₁₆	semidirect
293. #17362	C₁₀₁	direct (N × H)
304. C₂×#407	C₂×C₁₀₁	semidirect
305. #1465	C₂×C₁₀₁	semidirect
306. #1463	C₂×C₁₀₁	semidirect
307. #1462	C₂×C₁₀₁	semidirect
308. #1459	C₂×C₁₀₁	semidirect
309. C₁₀₁	#17362	direct (N × H)
329. #407	C₂²×C₁₀₁	semidirect
331. C₂×C₂²⋊C₈	C₂²×C₁₀₁	semidirect
332. #324	C₂²×C₁₀₁	semidirect
333. #323	C₂²×C₁₀₁	semidirect
417. C₂×D₄	M₁₆×C₁₀₁	semidirect
513. C₂³	C₂×M₁₆×C₁₀₁	semidirect
556. C₂×C₄	C₂×M₁₆×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₁₀₁	2
C₂×#407×C₁₀₁	2
C₁₀₁×#1465	2
C₁₀₁×#1463	2
C₁₀₁×#1462	2
C₁₀₁×#1459	2
#17362	101

Subgroups — C101×#17362 #38799513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#17362 #38799513