Subgroups — C₁₀₁×#20726 #38802877

Order 25856.

1694 conjugacy classes of subgroups.

The subgroup lattice has 446 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	C₁₀₁×#2920	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#1821	C₂	1	2	yes	maximal, complemented
4	C₁₀₁×#1800	C₂	1	4	yes	maximal, complemented
5	C₁₀₁×#1783	C₂	1	2	yes	maximal
6	C₄×#100×C₁₀₁	C₂	1	4	yes	maximal, complemented
7	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₁₀₁	C₄	1	2	yes	—
9	C₂×C₄×D₄×C₁₀₁	—	2	2	no	—
10	C₂×C₄×D₄×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	C₄	1	2	yes	—
14	C₂×C₄×D₄×C₁₀₁	C₄	1	2	yes	—
15	C₂×C₄×D₄×C₁₀₁	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₀₁	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₁₀₁	C₄	1	2	yes	—
19	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
20	#432×C₁₀₁	—	2	2	no	—
21	#432×C₁₀₁	—	2	2	no	—
22	#431×C₁₀₁	—	2	2	no	—
23	#431×C₁₀₁	—	2	2	no	—
24	#423×C₁₀₁	C₂²	1	4	yes	complemented
25	C₂×#100×C₁₀₁	C₂²	1	8	yes	—
26	#407×C₁₀₁	C₂²	1	4	yes	—
27	C₄×M₁₆×C₁₀₁	C₂²	1	4	yes	complemented
28	#343×C₁₀₁	C₂²	1	8	yes	complemented
29	C₂⁵×C₁₀₁	C₂×C₄	1	2	yes	—
30	C₂²×D₄×C₁₀₁	—	2	8	no	—
31	C₂²×D₄×C₁₀₁	—	2	2	no	—
32	C₂²×D₄×C₁₀₁	—	2	2	no	—
33	C₂²×D₄×C₁₀₁	C₂×C₄	1	2	yes	—
34	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
35	C₂³×C₄×C₁₀₁	—	2	2	no	—
36	C₂³×C₄×C₁₀₁	—	2	2	no	—
37	C₂³×C₄×C₁₀₁	—	2	2	no	—
38	C₂³×C₄×C₁₀₁	—	2	2	no	—
39	C₂³×C₄×C₁₀₁	—	4	8	no	—
40	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
42	C₂³×C₄×C₁₀₁	C₂×C₄	1	4	yes	—
43	C₂³×C₄×C₁₀₁	C₂×C₄	1	4	yes	—
44	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₁₀₁	C₂³	1	8	yes	—
47	C₄×D₄×C₁₀₁	—	2	4	no	—
48	C₄×D₄×C₁₀₁	—	2	4	no	—
49	C₄×D₄×C₁₀₁	—	2	4	no	—
50	C₄×D₄×C₁₀₁	—	2	4	no	—
51	C₄×D₄×C₁₀₁	—	2	4	no	—
52	C₄×D₄×C₁₀₁	—	2	4	no	—
53	C₄×D₄×C₁₀₁	—	2	4	no	—
54	C₄×D₄×C₁₀₁	—	2	4	no	—
55	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
59	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
60	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
61	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
62	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
63	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
66	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
67	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
68	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
69	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₁₀₁	—	2	4	no	—
72	C₄⋊C₈×C₁₀₁	—	2	4	no	—
73	#100×C₁₀₁	—	2	16	no	—
74	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
75	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
76	#97×C₁₀₁	—	2	4	no	—
77	C₄×C₈×C₁₀₁	—	2	4	no	—
78	C₂⁴×C₁₀₁	—	2	2	no	—
79	C₂⁴×C₁₀₁	—	2	2	no	—
80	C₂⁴×C₁₀₁	—	2	8	no	—
81	C₂⁴×C₁₀₁	—	4	4	no	—
82	C₂⁴×C₁₀₁	—	4	4	no	—
83	C₂⁴×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
84	C₂⁴×C₁₀₁	C₂²×C₄	1	4	yes	—
85	C₂×D₄×C₁₀₁	—	2	16	no	—
86	C₂×D₄×C₁₀₁	—	2	16	no	—
87	C₂×D₄×C₁₀₁	—	2	8	no	—
88	C₂×D₄×C₁₀₁	—	2	4	no	—
89	C₂×D₄×C₁₀₁	—	2	4	no	—
90	C₂×D₄×C₁₀₁	—	2	4	no	—
91	C₂×D₄×C₁₀₁	#41	1	8	yes	—
92	C₂²×C₄×C₁₀₁	—	2	4	no	—
93	C₂²×C₄×C₁₀₁	—	2	4	no	—
94	C₂²×C₄×C₁₀₁	—	2	2	no	—
95	C₂²×C₄×C₁₀₁	—	2	2	no	—
96	C₂²×C₄×C₁₀₁	—	2	4	no	—
97	C₂²×C₄×C₁₀₁	—	2	4	no	—
98	C₂²×C₄×C₁₀₁	—	2	4	no	—
99	C₂²×C₄×C₁₀₁	—	2	4	no	—
100	C₂²×C₄×C₁₀₁	—	4	2	no	—
101	C₂²×C₄×C₁₀₁	—	4	8	no	—
102	C₂²×C₄×C₁₀₁	—	4	8	no	—
103	C₂²×C₄×C₁₀₁	—	4	8	no	—
104	C₂²×C₄×C₁₀₁	—	4	8	no	—
105	C₂²×C₄×C₁₀₁	—	4	8	no	—
106	C₂²×C₄×C₁₀₁	—	4	8	no	—
107	C₂²×C₄×C₁₀₁	—	4	4	no	—
108	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
109	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
113	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
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	4	yes	—
118	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
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	—	2	16	no	—
124	C₂×C₈×C₁₀₁	—	2	8	no	—
125	C₄⋊C₄×C₁₀₁	—	2	4	no	—
126	C₄⋊C₄×C₁₀₁	—	2	4	no	—
127	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
128	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
129	C₄²×C₁₀₁	C₂²⋊C₄	1	2	yes	—
130	C₄²×C₁₀₁	C₂²⋊C₄	1	2	yes	—
131	C₄²×C₁₀₁	C₂²⋊C₄	1	2	yes	—
132	C₄²×C₁₀₁	C₂²⋊C₄	1	2	yes	—
133	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
134	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
135	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
136	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
137	C₂³×C₁₀₁	—	2	2	no	—
138	C₂³×C₁₀₁	—	2	2	no	—
139	C₂³×C₁₀₁	—	2	2	no	—
140	C₂³×C₁₀₁	—	2	8	no	—
141	C₂³×C₁₀₁	—	2	8	no	—
142	C₂³×C₁₀₁	—	2	4	no	—
143	C₂³×C₁₀₁	—	2	4	no	—
144	C₂³×C₁₀₁	—	4	4	no	—
145	C₂³×C₁₀₁	—	4	4	no	—
146	C₂³×C₁₀₁	—	4	4	no	—
147	C₂³×C₁₀₁	—	4	32	no	—
148	C₂³×C₁₀₁	—	4	4	no	—
149	C₂³×C₁₀₁	—	4	4	no	—
150	C₂³×C₁₀₁	—	4	4	no	—
151	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂³×C₁₀₁	#117	1	8	yes	—
154	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
155	D₄×C₁₀₁	—	2	16	no	—
156	D₄×C₁₀₁	—	2	16	no	—
157	C₂×C₄×C₁₀₁	—	2	2	no	—
158	C₂×C₄×C₁₀₁	—	2	2	no	—
159	C₂×C₄×C₁₀₁	—	2	4	no	—
160	C₂×C₄×C₁₀₁	—	2	4	no	—
161	C₂×C₄×C₁₀₁	—	2	4	no	—
162	C₂×C₄×C₁₀₁	—	2	2	no	—
163	C₂×C₄×C₁₀₁	—	2	2	no	—
164	C₂×C₄×C₁₀₁	—	2	2	no	—
165	C₂×C₄×C₁₀₁	—	2	2	no	—
166	C₂×C₄×C₁₀₁	—	2	4	no	—
167	C₂×C₄×C₁₀₁	—	4	2	no	—
168	C₂×C₄×C₁₀₁	—	4	1	no	—
169	C₂×C₄×C₁₀₁	—	4	1	no	—
170	C₂×C₄×C₁₀₁	—	4	8	no	—
171	C₂×C₄×C₁₀₁	—	4	8	no	—
172	C₂×C₄×C₁₀₁	—	4	4	no	—
173	C₂×C₄×C₁₀₁	—	4	4	no	—
174	C₂×C₄×C₁₀₁	—	4	8	no	—
175	C₂×C₄×C₁₀₁	—	4	8	no	—
176	C₂×C₄×C₁₀₁	—	4	4	no	—
177	C₂×C₄×C₁₀₁	#100	1	4	yes	complemented
178	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
186	C₂×C₄×C₁₀₁	C₂×#41	1	4	yes	—
187	C₈×C₁₀₁	—	4	8	no	—
188	C₂²×C₁₀₁	—	2	8	no	—
189	C₂²×C₁₀₁	—	2	1	no	—
190	C₂²×C₁₀₁	—	2	1	no	—
191	C₂²×C₁₀₁	—	2	1	no	—
192	C₂²×C₁₀₁	—	2	1	no	—
193	C₂²×C₁₀₁	—	2	1	no	—
194	C₂²×C₁₀₁	—	2	1	no	—
195	C₂²×C₁₀₁	—	2	8	no	—
196	C₂²×C₁₀₁	—	4	8	no	—
197	C₂²×C₁₀₁	—	4	8	no	—
198	C₂²×C₁₀₁	—	4	16	no	—
199	C₂²×C₁₀₁	—	4	16	no	—
200	C₂²×C₁₀₁	—	4	4	no	—
201	C₂²×C₁₀₁	—	4	4	no	—
202	C₂²×C₁₀₁	C₂×#100	1	2	yes	—
203	C₂²×C₁₀₁	#413	1	2	yes	—
204	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
205	C₂²×C₁₀₁	C₂×#117	1	2	yes	—
206	C₄×C₁₀₁	—	2	1	no	—
207	C₄×C₁₀₁	—	2	1	no	—
208	C₄×C₁₀₁	—	2	2	no	—
209	C₄×C₁₀₁	—	2	2	no	—
210	C₄×C₁₀₁	—	2	2	no	—
211	C₄×C₁₀₁	—	4	4	no	—
212	C₄×C₁₀₁	C₂×#100	1	2	yes	—
213	C₄×C₁₀₁	C₂×#100	1	2	yes	—
214	C₄×C₁₀₁	#525	1	4	yes	—
215	#20726	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂×C₁₀₁	—	2	2	no	—
217	C₂×C₁₀₁	—	2	2	no	—
218	C₂×C₁₀₁	—	2	2	no	—
219	C₂×C₁₀₁	—	4	8	no	—
220	C₂×C₁₀₁	#2280	1	1	yes	characteristic
221	C₂×C₁₀₁	C₂²×#100	1	1	yes	characteristic
222	C₂×C₁₀₁	C₂×#413	1	1	yes	characteristic
223	C₂²×C₄×D₄	C₂×C₁₀₁	1	1	yes	characteristic
224	#2920	C₂×C₁₀₁	1	2	yes	complemented
225	#1821	C₂×C₁₀₁	1	2	yes	complemented
226	#1800	C₂×C₁₀₁	1	4	yes	complemented
227	#1783	C₂×C₁₀₁	1	2	yes	—
228	C₄×#100	C₂×C₁₀₁	1	4	yes	complemented
229	C₁₀₁	#20726	1	1	yes	characteristic, direct product factor, Sylow
230	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
231	C₂⁴×C₄	C₄×C₁₀₁	1	2	yes	—
232	C₂×C₄×D₄	—	2	2	no	—
233	C₂×C₄×D₄	—	2	2	no	—
234	C₂×C₄×D₄	—	2	2	no	—
235	C₂×C₄×D₄	—	2	2	no	—
236	C₂×C₄×D₄	C₄×C₁₀₁	1	2	yes	—
237	C₂×C₄×D₄	C₄×C₁₀₁	1	2	yes	—
238	C₂×C₄×D₄	C₂²×C₁₀₁	1	2	yes	—
239	C₂×C₄×D₄	C₂²×C₁₀₁	1	2	yes	—
240	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
241	C₂²×C₂²⋊C₄	C₄×C₁₀₁	1	2	yes	—
242	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
243	#432	—	2	2	no	—
244	#432	—	2	2	no	—
245	#431	—	2	2	no	—
246	#431	—	2	2	no	—
247	#423	C₂²×C₁₀₁	1	4	yes	complemented
248	C₂×#100	C₂²×C₁₀₁	1	8	yes	—
249	#407	C₂²×C₁₀₁	1	4	yes	—
250	C₄×M₁₆	C₂²×C₁₀₁	1	4	yes	complemented
251	#343	C₂²×C₁₀₁	1	8	yes	complemented
252	C₂⁵	C₂×C₄×C₁₀₁	1	2	yes	—
253	C₂²×D₄	—	2	8	no	—
254	C₂²×D₄	—	2	2	no	—
255	C₂²×D₄	—	2	2	no	—
256	C₂²×D₄	C₂×C₄×C₁₀₁	1	2	yes	—
257	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
258	C₂³×C₄	—	2	2	no	—
259	C₂³×C₄	—	2	2	no	—
260	C₂³×C₄	—	2	2	no	—
261	C₂³×C₄	—	2	2	no	—
262	C₂³×C₄	—	4	8	no	—
263	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
264	C₂³×C₄	C₂×C₄×C₁₀₁	1	2	yes	—
265	C₂³×C₄	C₂×C₄×C₁₀₁	1	4	yes	—
266	C₂³×C₄	C₂×C₄×C₁₀₁	1	4	yes	—
267	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
268	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
269	C₂×M₁₆	C₂³×C₁₀₁	1	8	yes	—
270	C₄×D₄	—	2	4	no	—
271	C₄×D₄	—	2	4	no	—
272	C₄×D₄	—	2	4	no	—
273	C₄×D₄	—	2	4	no	—
274	C₄×D₄	—	2	4	no	—
275	C₄×D₄	—	2	4	no	—
276	C₄×D₄	—	2	4	no	—
277	C₄×D₄	—	2	4	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
282	C₂×C₂²⋊C₄	—	2	4	no	—
283	C₂×C₂²⋊C₄	—	2	4	no	—
284	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
285	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
286	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
287	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
288	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
289	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
290	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
291	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
292	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
293	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
294	C₄⋊C₈	—	2	4	no	—
295	C₄⋊C₈	—	2	4	no	—
296	#100	—	2	16	no	—
297	C₂²⋊C₈	—	2	4	no	—
298	C₂²⋊C₈	—	2	4	no	—
299	#97	—	2	4	no	—
300	C₄×C₈	—	2	4	no	—
301	C₂⁴	—	2	2	no	—
302	C₂⁴	—	2	2	no	—
303	C₂⁴	—	2	8	no	—
304	C₂⁴	—	4	4	no	—
305	C₂⁴	—	4	4	no	—
306	C₂⁴	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
307	C₂⁴	C₂²×C₄×C₁₀₁	1	4	yes	—
308	C₂×D₄	—	2	16	no	—
309	C₂×D₄	—	2	16	no	—
310	C₂×D₄	—	2	8	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	#41×C₁₀₁	1	8	yes	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	4	8	no	—
325	C₂²×C₄	—	4	8	no	—
326	C₂²×C₄	—	4	8	no	—
327	C₂²×C₄	—	4	8	no	—
328	C₂²×C₄	—	4	8	no	—
329	C₂²×C₄	—	4	8	no	—
330	C₂²×C₄	—	4	4	no	—
331	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
332	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
333	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
334	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
335	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
336	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
337	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
338	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
339	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
340	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
341	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
342	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
344	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
345	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
346	M₁₆	—	2	16	no	—
347	C₂×C₈	—	2	8	no	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	2	4	no	—
350	C₂²⋊C₄	—	2	8	no	—
351	C₂²⋊C₄	—	2	8	no	—
352	C₄²	C₂²⋊C₄×C₁₀₁	1	2	yes	—
353	C₄²	C₂²⋊C₄×C₁₀₁	1	2	yes	—
354	C₄²	C₂²⋊C₄×C₁₀₁	1	2	yes	—
355	C₄²	C₂²⋊C₄×C₁₀₁	1	2	yes	—
356	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
357	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
358	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
359	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	2	8	no	—
364	C₂³	—	2	8	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	2	4	no	—
367	C₂³	—	4	4	no	—
368	C₂³	—	4	4	no	—
369	C₂³	—	4	4	no	—
370	C₂³	—	4	32	no	—
371	C₂³	—	4	4	no	—
372	C₂³	—	4	4	no	—
373	C₂³	—	4	4	no	—
374	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
375	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
376	C₂³	#117×C₁₀₁	1	8	yes	—
377	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
378	D₄	—	2	16	no	—
379	D₄	—	2	16	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	8	no	—
394	C₂×C₄	—	4	8	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	—	4	8	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	#100×C₁₀₁	1	4	yes	complemented
401	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
402	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
403	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
404	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
405	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
406	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
407	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
408	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
409	C₂×C₄	C₂×#41×C₁₀₁	1	4	yes	—
410	C₈	—	4	8	no	—
411	C₂²	—	2	8	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	8	no	—
419	C₂²	—	4	8	no	—
420	C₂²	—	4	16	no	—
421	C₂²	—	4	16	no	—
422	C₂²	—	4	8	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	4	no	—
425	C₂²	C₂×#100×C₁₀₁	1	2	yes	—
426	C₂²	#413×C₁₀₁	1	2	yes	—
427	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
428	C₂²	C₂×#117×C₁₀₁	1	2	yes	—
429	C₄	—	2	2	no	—
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	4	4	no	—
435	C₄	C₂×#100×C₁₀₁	1	2	yes	—
436	C₄	C₂×#100×C₁₀₁	1	2	yes	—
437	C₄	#525×C₁₀₁	1	4	yes	—
438	C₂	—	2	2	no	—
439	C₂	—	2	2	no	—
440	C₂	—	2	2	no	—
441	C₂	—	4	8	no	—
442	C₂	C₁₀₁×#2280	1	1	yes	characteristic
443	C₂	C₂²×#100×C₁₀₁	1	1	yes	characteristic
444	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	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₁ ◁ C₂²×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₁×#2920	C₂	semidirect
3. C₁₀₁×#1821	C₂	semidirect
4. C₁₀₁×#1800	C₂	semidirect
6. C₄×#100×C₁₀₁	C₂	semidirect
24. #423×C₁₀₁	C₂²	semidirect
27. C₄×M₁₆×C₁₀₁	C₂²	semidirect
28. #343×C₁₀₁	C₂²	semidirect
177. C₂×C₄×C₁₀₁	#100	semidirect
215. #20726	C₁₀₁	direct (N × H)
224. #2920	C₂×C₁₀₁	semidirect
225. #1821	C₂×C₁₀₁	semidirect
226. #1800	C₂×C₁₀₁	semidirect
228. C₄×#100	C₂×C₁₀₁	semidirect
229. C₁₀₁	#20726	direct (N × H)
247. #423	C₂²×C₁₀₁	semidirect
250. C₄×M₁₆	C₂²×C₁₀₁	semidirect
251. #343	C₂²×C₁₀₁	semidirect
400. C₂×C₄	#100×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
C₁₀₁×#2920	2
C₁₀₁×#1821	2
C₁₀₁×#1800	2
C₁₀₁×#1783	2
C₄×#100×C₁₀₁	2
#20726	101

Subgroups — C101×#20726 #38802877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#20726 #38802877