Subgroups — C₂×C₁₀₁×#1460 #38799498

Order 25856.

1714 conjugacy classes of subgroups.

The subgroup lattice has 368 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×#431×C₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#1460	C₂	1	8	yes	maximal, direct product factor
4	C₂×#323×C₁₀₁	C₂	1	4	yes	maximal, complemented
5	C₂³×D₄×C₁₀₁	C₄	1	1	yes	characteristic
6	C₂⁴×C₄×C₁₀₁	C₄	1	2	yes	—
7	C₂×C₄×D₄×C₁₀₁	—	2	2	no	—
8	C₂×C₄×D₄×C₁₀₁	—	2	4	no	—
9	C₂×C₄×D₄×C₁₀₁	—	2	2	no	—
10	C₂×C₄×D₄×C₁₀₁	C₄	1	4	yes	—
11	C₂×C₄×D₄×C₁₀₁	C₂²	1	4	yes	—
12	C₂²×C₄⋊C₄×C₁₀₁	C₄	1	1	yes	characteristic
13	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
14	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
15	#431×C₁₀₁	—	2	4	no	—
16	#431×C₁₀₁	C₂²	1	8	yes	complemented
17	C₂×C₄⋊C₈×C₁₀₁	—	2	2	no	—
18	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	4	yes	—
19	C₂×C₄×C₈×C₁₀₁	—	2	2	no	—
20	#323×C₁₀₁	C₂²	1	16	yes	complemented
21	C₂⁵×C₁₀₁	C₂×C₄	1	2	yes	—
22	C₂²×D₄×C₁₀₁	—	2	2	no	—
23	C₂²×D₄×C₁₀₁	—	2	2	no	—
24	C₂²×D₄×C₁₀₁	—	2	4	no	—
25	C₂²×D₄×C₁₀₁	C₈	1	8	yes	complemented
26	C₂²×D₄×C₁₀₁	C₂×C₄	1	4	yes	—
27	C₂³×C₄×C₁₀₁	—	2	4	no	—
28	C₂³×C₄×C₁₀₁	—	2	2	no	—
29	C₂³×C₄×C₁₀₁	—	2	2	no	—
30	C₂³×C₄×C₁₀₁	—	4	8	no	—
31	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₁₀₁	C₂×C₄	1	8	yes	—
34	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₁₀₁	—	2	4	no	—
37	C₄×D₄×C₁₀₁	—	2	8	no	—
38	C₄×D₄×C₁₀₁	—	2	8	no	—
39	C₄×D₄×C₁₀₁	—	2	8	no	—
40	C₄×D₄×C₁₀₁	—	2	8	no	—
41	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
44	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
45	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
46	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
47	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
48	C₂×C₄²×C₁₀₁	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
50	C₂×C₄²×C₁₀₁	D₄	1	4	yes	—
51	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
52	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
53	C₄⋊C₈×C₁₀₁	—	2	8	no	—
54	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
55	C₂²⋊C₈×C₁₀₁	C₂³	1	8	yes	—
56	C₄×C₈×C₁₀₁	—	2	8	no	—
57	C₂⁴×C₁₀₁	—	2	2	no	—
58	C₂⁴×C₁₀₁	—	2	2	no	—
59	C₂⁴×C₁₀₁	—	2	4	no	—
60	C₂⁴×C₁₀₁	—	4	4	no	—
61	C₂⁴×C₁₀₁	—	4	4	no	—
62	C₂⁴×C₁₀₁	C₂×C₈	1	8	yes	—
63	C₂⁴×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
64	C₂⁴×C₁₀₁	C₂²×C₄	1	4	yes	—
65	C₂×D₄×C₁₀₁	—	2	16	no	—
66	C₂×D₄×C₁₀₁	—	2	16	no	—
67	C₂×D₄×C₁₀₁	—	2	8	no	—
68	C₂×D₄×C₁₀₁	—	2	8	no	—
69	C₂×D₄×C₁₀₁	C₂×C₈	1	16	yes	complemented
70	C₂²×C₄×C₁₀₁	—	2	4	no	—
71	C₂²×C₄×C₁₀₁	—	2	2	no	—
72	C₂²×C₄×C₁₀₁	—	2	2	no	—
73	C₂²×C₄×C₁₀₁	—	2	8	no	—
74	C₂²×C₄×C₁₀₁	—	2	8	no	—
75	C₂²×C₄×C₁₀₁	—	4	2	no	—
76	C₂²×C₄×C₁₀₁	—	4	8	no	—
77	C₂²×C₄×C₁₀₁	—	4	16	no	—
78	C₂²×C₄×C₁₀₁	—	4	16	no	—
79	C₂²×C₄×C₁₀₁	—	4	8	no	—
80	C₂²×C₄×C₁₀₁	—	4	4	no	—
81	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
83	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
84	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
85	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₀₁	C₂×C₈	1	4	yes	—
87	C₂²×C₄×C₁₀₁	M₁₆	1	4	yes	—
88	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
95	C₂×C₈×C₁₀₁	—	2	8	no	—
96	C₂×C₈×C₁₀₁	—	4	8	no	—
97	C₄⋊C₄×C₁₀₁	—	2	8	no	—
98	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
99	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
100	C₄²×C₁₀₁	C₂²⋊C₄	1	4	yes	—
101	C₄²×C₁₀₁	C₂²⋊C₄	1	4	yes	—
102	C₄²×C₁₀₁	C₂×D₄	1	4	yes	—
103	C₄²×C₁₀₁	C₂×D₄	1	4	yes	—
104	C₂³×C₁₀₁	—	2	2	no	—
105	C₂³×C₁₀₁	—	2	2	no	—
106	C₂³×C₁₀₁	—	2	4	no	—
107	C₂³×C₁₀₁	—	2	4	no	—
108	C₂³×C₁₀₁	—	2	8	no	—
109	C₂³×C₁₀₁	—	2	8	no	—
110	C₂³×C₁₀₁	—	4	4	no	—
111	C₂³×C₁₀₁	—	4	16	no	—
112	C₂³×C₁₀₁	—	4	4	no	—
113	C₂³×C₁₀₁	—	4	4	no	—
114	C₂³×C₁₀₁	—	4	4	no	—
115	C₂³×C₁₀₁	—	4	16	no	—
116	C₂³×C₁₀₁	—	4	4	no	—
117	C₂³×C₁₀₁	—	4	4	no	—
118	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂³×C₁₀₁	C₂²×C₈	1	2	yes	—
121	C₂³×C₁₀₁	C₂²×C₈	1	8	yes	—
122	C₂³×C₁₀₁	C₂×M₁₆	1	2	yes	—
123	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
124	D₄×C₁₀₁	—	2	32	no	—
125	C₂×C₄×C₁₀₁	—	2	4	no	—
126	C₂×C₄×C₁₀₁	—	2	2	no	—
127	C₂×C₄×C₁₀₁	—	2	4	no	—
128	C₂×C₄×C₁₀₁	—	2	4	no	—
129	C₂×C₄×C₁₀₁	—	2	4	no	—
130	C₂×C₄×C₁₀₁	—	4	1	no	—
131	C₂×C₄×C₁₀₁	—	4	2	no	—
132	C₂×C₄×C₁₀₁	—	4	1	no	—
133	C₂×C₄×C₁₀₁	—	4	16	no	—
134	C₂×C₄×C₁₀₁	—	4	4	no	—
135	C₂×C₄×C₁₀₁	—	4	4	no	—
136	C₂×C₄×C₁₀₁	—	4	16	no	—
137	C₂×C₄×C₁₀₁	—	4	4	no	—
138	C₂×C₄×C₁₀₁	C₂²⋊C₈	1	8	yes	—
139	C₂×C₄×C₁₀₁	C₂²⋊C₈	1	8	yes	—
140	C₂×C₄×C₁₀₁	#100	1	4	yes	—
141	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
142	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
143	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
144	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂×C₄×C₁₀₁	C₂²×C₈	1	4	yes	—
146	C₂×C₄×C₁₀₁	C₂×M₁₆	1	4	yes	—
147	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
148	C₈×C₁₀₁	—	4	8	no	—
149	C₂²×C₁₀₁	—	2	1	no	—
150	C₂²×C₁₀₁	—	2	1	no	—
151	C₂²×C₁₀₁	—	2	1	no	—
152	C₂²×C₁₀₁	—	2	1	no	—
153	C₂²×C₁₀₁	—	2	4	no	—
154	C₂²×C₁₀₁	—	2	4	no	—
155	C₂²×C₁₀₁	—	2	8	no	—
156	C₂²×C₁₀₁	—	4	8	no	—
157	C₂²×C₁₀₁	—	4	8	no	—
158	C₂²×C₁₀₁	—	4	16	no	—
159	C₂²×C₁₀₁	—	4	4	no	—
160	C₂²×C₁₀₁	—	4	4	no	—
161	C₂²×C₁₀₁	—	4	16	no	—
162	C₂²×C₁₀₁	C₂×C₂²⋊C₈	1	2	yes	—
163	C₂²×C₁₀₁	C₂×C₂²⋊C₈	1	2	yes	—
164	C₂²×C₁₀₁	#410	1	2	yes	—
165	C₂²×C₁₀₁	C₂×#100	1	2	yes	—
166	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₁₀₁	C₂³×C₈	1	1	yes	characteristic
168	C₂²×C₁₀₁	C₂²×M₁₆	1	1	yes	characteristic
169	C₄×C₁₀₁	—	2	2	no	—
170	C₄×C₁₀₁	—	2	2	no	—
171	C₄×C₁₀₁	—	2	2	no	—
172	C₄×C₁₀₁	—	4	4	no	—
173	C₄×C₁₀₁	C₂×C₂²⋊C₈	1	8	yes	—
174	C₄×C₁₀₁	C₂×#100	1	4	yes	—
175	C₂×#1460	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂×C₁₀₁	—	2	1	no	—
177	C₂×C₁₀₁	—	2	1	no	—
178	C₂×C₁₀₁	—	2	2	no	—
179	C₂×C₁₀₁	—	4	8	no	—
180	C₂×C₁₀₁	#1460	1	4	yes	direct product factor
181	C₂×C₁₀₁	C₂²×C₂²⋊C₈	1	1	yes	characteristic
182	C₂×C₁₀₁	C₂×#410	1	1	yes	characteristic
183	C₂×C₁₀₁	C₂²×#100	1	1	yes	characteristic
184	C₂²×C₄×D₄	C₂×C₁₀₁	1	1	yes	characteristic
185	C₂×#431	C₂×C₁₀₁	1	2	yes	complemented
186	#1460	C₂×C₁₀₁	1	8	yes	direct product factor
187	C₂×#323	C₂×C₁₀₁	1	4	yes	complemented
188	C₁₀₁	C₂×#1460	1	1	yes	characteristic, direct product factor, Sylow
189	C₂³×D₄	C₄×C₁₀₁	1	1	yes	characteristic
190	C₂⁴×C₄	C₄×C₁₀₁	1	2	yes	—
191	C₂×C₄×D₄	—	2	2	no	—
192	C₂×C₄×D₄	—	2	2	no	—
193	C₂×C₄×D₄	—	2	4	no	—
194	C₂×C₄×D₄	C₄×C₁₀₁	1	4	yes	—
195	C₂×C₄×D₄	C₂²×C₁₀₁	1	4	yes	—
196	C₂²×C₄⋊C₄	C₄×C₁₀₁	1	1	yes	characteristic
197	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
198	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
199	#431	—	2	4	no	—
200	#431	C₂²×C₁₀₁	1	8	yes	complemented
201	C₂×C₄⋊C₈	—	2	2	no	—
202	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	4	yes	—
203	C₂×C₄×C₈	—	2	2	no	—
204	#323	C₂²×C₁₀₁	1	16	yes	complemented
205	C₂⁵	C₂×C₄×C₁₀₁	1	2	yes	—
206	C₂²×D₄	—	2	2	no	—
207	C₂²×D₄	—	2	2	no	—
208	C₂²×D₄	—	2	4	no	—
209	C₂²×D₄	C₈×C₁₀₁	1	8	yes	complemented
210	C₂²×D₄	C₂×C₄×C₁₀₁	1	4	yes	—
211	C₂³×C₄	—	2	4	no	—
212	C₂³×C₄	—	2	2	no	—
213	C₂³×C₄	—	2	2	no	—
214	C₂³×C₄	—	4	8	no	—
215	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
216	C₂³×C₄	C₂×C₄×C₁₀₁	1	2	yes	—
217	C₂³×C₄	C₂×C₄×C₁₀₁	1	8	yes	—
218	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
219	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
220	C₂²×C₈	—	2	4	no	—
221	C₄×D₄	—	2	8	no	—
222	C₄×D₄	—	2	8	no	—
223	C₄×D₄	—	2	8	no	—
224	C₄×D₄	—	2	8	no	—
225	C₂×C₄⋊C₄	—	2	2	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
228	C₂×C₂²⋊C₄	—	2	4	no	—
229	C₂×C₂²⋊C₄	—	2	4	no	—
230	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
231	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	4	yes	—
232	C₂×C₄²	C₂×C₄×C₁₀₁	1	2	yes	—
233	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
234	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
235	C₂×C₄²	D₄×C₁₀₁	1	4	yes	—
236	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
237	C₄⋊C₈	—	2	8	no	—
238	C₂²⋊C₈	—	2	4	no	—
239	C₂²⋊C₈	C₂³×C₁₀₁	1	8	yes	—
240	C₄×C₈	—	2	8	no	—
241	C₂⁴	—	2	2	no	—
242	C₂⁴	—	2	2	no	—
243	C₂⁴	—	2	4	no	—
244	C₂⁴	—	4	4	no	—
245	C₂⁴	—	4	4	no	—
246	C₂⁴	C₂×C₈×C₁₀₁	1	8	yes	—
247	C₂⁴	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
248	C₂⁴	C₂²×C₄×C₁₀₁	1	4	yes	—
249	C₂×D₄	—	2	16	no	—
250	C₂×D₄	—	2	16	no	—
251	C₂×D₄	—	2	8	no	—
252	C₂×D₄	—	2	8	no	—
253	C₂×D₄	C₂×C₈×C₁₀₁	1	16	yes	complemented
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	—	2	8	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	4	8	no	—
261	C₂²×C₄	—	4	16	no	—
262	C₂²×C₄	—	4	16	no	—
263	C₂²×C₄	—	4	8	no	—
264	C₂²×C₄	—	4	4	no	—
265	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
266	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
267	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
268	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
269	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₈×C₁₀₁	1	4	yes	—
271	C₂²×C₄	M₁₆×C₁₀₁	1	4	yes	—
272	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
273	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
274	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
275	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
277	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
278	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
279	C₂×C₈	—	2	8	no	—
280	C₂×C₈	—	4	8	no	—
281	C₄⋊C₄	—	2	8	no	—
282	C₂²⋊C₄	—	2	8	no	—
283	C₂²⋊C₄	—	2	8	no	—
284	C₄²	C₂²⋊C₄×C₁₀₁	1	4	yes	—
285	C₄²	C₂²⋊C₄×C₁₀₁	1	4	yes	—
286	C₄²	C₂×D₄×C₁₀₁	1	4	yes	—
287	C₄²	C₂×D₄×C₁₀₁	1	4	yes	—
288	C₂³	—	2	2	no	—
289	C₂³	—	2	2	no	—
290	C₂³	—	2	8	no	—
291	C₂³	—	2	8	no	—
292	C₂³	—	2	4	no	—
293	C₂³	—	2	4	no	—
294	C₂³	—	4	4	no	—
295	C₂³	—	4	16	no	—
296	C₂³	—	4	4	no	—
297	C₂³	—	4	4	no	—
298	C₂³	—	4	16	no	—
299	C₂³	—	4	4	no	—
300	C₂³	—	4	4	no	—
301	C₂³	—	4	4	no	—
302	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
303	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
304	C₂³	C₂²×C₈×C₁₀₁	1	2	yes	—
305	C₂³	C₂²×C₈×C₁₀₁	1	8	yes	—
306	C₂³	C₂×M₁₆×C₁₀₁	1	2	yes	—
307	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
308	D₄	—	2	32	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	16	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	16	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	C₂²⋊C₈×C₁₀₁	1	8	yes	—
323	C₂×C₄	C₂²⋊C₈×C₁₀₁	1	8	yes	—
324	C₂×C₄	#100×C₁₀₁	1	4	yes	—
325	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
328	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
329	C₂×C₄	C₂²×C₈×C₁₀₁	1	4	yes	—
330	C₂×C₄	C₂×M₁₆×C₁₀₁	1	4	yes	—
331	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
332	C₈	—	4	8	no	—
333	C₂²	—	2	4	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	2	1	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	8	no	—
340	C₂²	—	4	8	no	—
341	C₂²	—	4	16	no	—
342	C₂²	—	4	8	no	—
343	C₂²	—	4	16	no	—
344	C₂²	—	4	4	no	—
345	C₂²	—	4	4	no	—
346	C₂²	C₂×C₂²⋊C₈×C₁₀₁	1	2	yes	—
347	C₂²	C₂×C₂²⋊C₈×C₁₀₁	1	2	yes	—
348	C₂²	#410×C₁₀₁	1	2	yes	—
349	C₂²	C₂×#100×C₁₀₁	1	2	yes	—
350	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
351	C₂²	C₂³×C₈×C₁₀₁	1	1	yes	characteristic
352	C₂²	C₂²×M₁₆×C₁₀₁	1	1	yes	characteristic
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	—	4	4	no	—
357	C₄	C₂×C₂²⋊C₈×C₁₀₁	1	8	yes	—
358	C₄	C₂×#100×C₁₀₁	1	4	yes	—
359	C₂	—	2	2	no	—
360	C₂	—	2	1	no	—
361	C₂	—	2	1	no	—
362	C₂	—	4	8	no	—
363	C₂	C₁₀₁×#1460	1	4	yes	direct product factor
364	C₂	C₂²×C₂²⋊C₈×C₁₀₁	1	1	yes	characteristic
365	C₂	C₂×#410×C₁₀₁	1	1	yes	characteristic
366	C₂	C₂²×#100×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₀₁	C₂²⋊C₄
commutator	C₂²	C₂³×C₈×C₁₀₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
socle	C₂³×C₁₀₁	C₂×C₂²⋊C₄
prime radical	C₂³×D₄×C₁₀₁	C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₁ ◁ C₂²×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#431×C₁₀₁	C₂	semidirect
3. C₁₀₁×#1460	C₂	direct (N × H)
4. C₂×#323×C₁₀₁	C₂	semidirect
16. #431×C₁₀₁	C₂²	semidirect
20. #323×C₁₀₁	C₂²	semidirect
25. C₂²×D₄×C₁₀₁	C₈	semidirect
69. C₂×D₄×C₁₀₁	C₂×C₈	semidirect
175. C₂×#1460	C₁₀₁	direct (N × H)
180. C₂×C₁₀₁	#1460	direct (N × H)
185. C₂×#431	C₂×C₁₀₁	semidirect
186. #1460	C₂×C₁₀₁	direct (N × H)
187. C₂×#323	C₂×C₁₀₁	semidirect
188. C₁₀₁	C₂×#1460	direct (N × H)
200. #431	C₂²×C₁₀₁	semidirect
204. #323	C₂²×C₁₀₁	semidirect
209. C₂²×D₄	C₈×C₁₀₁	semidirect
253. C₂×D₄	C₂×C₈×C₁₀₁	semidirect
363. C₂	C₁₀₁×#1460	direct (N × H)

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×#431×C₁₀₁	2
C₁₀₁×#1460	2
C₂×#323×C₁₀₁	2
C₂×#1460	101

Subgroups — C2×C101×#1460 #38799498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₁×#1460 #38799498