Subgroups — C₁₀₁×#22539 #38804690

Order 25856.

1066 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	Q₈×M₁₆×C₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#1967	C₂	1	4	yes	maximal, complemented
4	C₁₀₁×#1965	C₂	1	2	yes	maximal
5	C₁₀₁×#1801	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₁×#1800	C₂	1	2	yes	maximal, complemented
7	C₄×#101×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#100×C₁₀₁	C₂	1	2	yes	maximal, complemented
9	#559×C₁₀₁	—	2	2	no	—
10	#559×C₁₀₁	—	2	4	no	—
11	#559×C₁₀₁	—	2	2	no	—
12	C₂×#127×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂×#124×C₁₀₁	C₄	1	2	yes	—
14	C₂×#124×C₁₀₁	C₂²	1	2	yes	—
15	C₂×#123×C₁₀₁	C₄	1	4	yes	—
16	C₂×C₄×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₀₁	C₄	1	2	yes	—
19	C₂×C₄×D₄×C₁₀₁	C₂²	1	2	yes	—
20	#446×C₁₀₁	—	2	4	no	—
21	#446×C₁₀₁	—	2	2	no	—
22	C₈×Q₈×C₁₀₁	—	2	2	no	—
23	#423×C₁₀₁	C₂²	1	2	yes	—
24	#423×C₁₀₁	C₂²	1	4	yes	—
25	C₂×#101×C₁₀₁	C₂²	1	2	yes	—
26	C₂×#101×C₁₀₁	C₂²	1	2	yes	—
27	C₂×#100×C₁₀₁	C₂²	1	4	yes	—
28	C₂×#100×C₁₀₁	C₂²	1	4	yes	—
29	C₄×M₁₆×C₁₀₁	C₂²	1	2	yes	—
30	C₄×M₁₆×C₁₀₁	C₂²	1	4	yes	—
31	#343×C₁₀₁	C₂²	1	1	yes	characteristic
32	#343×C₁₀₁	C₂²	1	2	yes	—
33	#343×C₁₀₁	C₂²	1	1	yes	characteristic
34	C₂²×Q₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
35	C₂²×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
36	C₂²×D₄×C₁₀₁	C₂×C₄	1	2	yes	—
37	C₂²×D₄×C₁₀₁	C₂×C₄	1	2	yes	—
38	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₀₁	C₂×C₄	1	4	yes	—
40	C₂×M₁₆×C₁₀₁	C₂³	1	4	yes	—
41	C₂×M₁₆×C₁₀₁	C₂³	1	2	yes	—
42	C₂×M₁₆×C₁₀₁	C₂³	1	2	yes	—
43	#127×C₁₀₁	—	2	2	no	—
44	#127×C₁₀₁	—	2	2	no	—
45	#124×C₁₀₁	—	2	4	no	—
46	#124×C₁₀₁	—	2	4	no	—
47	#124×C₁₀₁	—	2	4	no	—
48	#124×C₁₀₁	—	2	4	no	—
49	#123×C₁₀₁	—	2	8	no	—
50	#123×C₁₀₁	—	2	8	no	—
51	C₄×Q₈×C₁₀₁	—	2	2	no	—
52	C₄×Q₈×C₁₀₁	—	2	2	no	—
53	C₄×Q₈×C₁₀₁	D₄	1	2	yes	—
54	C₄×Q₈×C₁₀₁	D₄	1	4	yes	—
55	C₄×Q₈×C₁₀₁	D₄	1	2	yes	—
56	C₄×D₄×C₁₀₁	—	2	4	no	—
57	C₄×D₄×C₁₀₁	—	2	2	no	—
58	C₄×D₄×C₁₀₁	—	2	2	no	—
59	C₄×D₄×C₁₀₁	—	2	4	no	—
60	C₄×D₄×C₁₀₁	—	2	4	no	—
61	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
66	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
67	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
68	C₂×C₄²×C₁₀₁	C₂×C₄	1	2	yes	—
69	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₁₀₁	—	2	4	no	—
72	C₄⋊C₈×C₁₀₁	—	2	2	no	—
73	C₄⋊C₈×C₁₀₁	—	2	4	no	—
74	C₄⋊C₈×C₁₀₁	—	2	2	no	—
75	#101×C₁₀₁	—	2	4	no	—
76	#101×C₁₀₁	—	4	2	no	—
77	#100×C₁₀₁	—	2	8	no	—
78	#100×C₁₀₁	—	4	4	no	—
79	#97×C₁₀₁	—	2	4	no	—
80	#97×C₁₀₁	—	2	2	no	—
81	C₄×C₈×C₁₀₁	—	2	4	no	—
82	C₄×C₈×C₁₀₁	—	2	2	no	—
83	C₂⁴×C₁₀₁	C₂²×C₄	1	4	yes	—
84	C₂×Q₈×C₁₀₁	—	2	2	no	—
85	C₂×Q₈×C₁₀₁	—	2	2	no	—
86	C₂×Q₈×C₁₀₁	—	2	1	no	—
87	C₂×Q₈×C₁₀₁	—	2	1	no	—
88	C₂×Q₈×C₁₀₁	—	4	2	no	—
89	C₂×Q₈×C₁₀₁	C₂²⋊C₄	1	2	yes	—
90	C₂×Q₈×C₁₀₁	C₂²⋊C₄	1	2	yes	—
91	C₂×D₄×C₁₀₁	—	2	2	no	—
92	C₂×D₄×C₁₀₁	—	2	2	no	—
93	C₂×D₄×C₁₀₁	—	2	4	no	—
94	C₂×D₄×C₁₀₁	—	2	4	no	—
95	C₂×D₄×C₁₀₁	—	2	4	no	—
96	C₂×D₄×C₁₀₁	—	2	2	no	—
97	C₂×D₄×C₁₀₁	—	2	2	no	—
98	C₂×D₄×C₁₀₁	—	4	4	no	—
99	C₂×D₄×C₁₀₁	—	8	2	no	—
100	C₂²×C₄×C₁₀₁	—	2	4	no	—
101	C₂²×C₄×C₁₀₁	—	2	4	no	—
102	C₂²×C₄×C₁₀₁	—	8	4	no	—
103	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
110	M₁₆×C₁₀₁	—	2	2	no	—
111	M₁₆×C₁₀₁	—	2	4	no	—
112	M₁₆×C₁₀₁	—	2	2	no	—
113	M₁₆×C₁₀₁	—	2	2	no	—
114	M₁₆×C₁₀₁	—	2	4	no	—
115	M₁₆×C₁₀₁	#41	1	4	yes	—
116	C₂×C₈×C₁₀₁	—	2	2	no	—
117	C₂×C₈×C₁₀₁	—	2	4	no	—
118	C₂×C₈×C₁₀₁	—	2	2	no	—
119	C₄⋊C₄×C₁₀₁	—	2	4	no	—
120	C₄⋊C₄×C₁₀₁	—	2	2	no	—
121	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
122	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
123	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
124	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	4	yes	—
125	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	4	yes	—
126	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
127	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
128	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
129	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
130	C₄²×C₁₀₁	—	2	2	no	—
131	C₄²×C₁₀₁	—	2	2	no	—
132	C₄²×C₁₀₁	C₂×D₄	1	4	yes	—
133	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
134	C₄²×C₁₀₁	C₂×D₄	1	4	yes	—
135	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
136	C₂³×C₁₀₁	—	2	4	no	—
137	C₂³×C₁₀₁	—	2	4	no	—
138	C₂³×C₁₀₁	—	2	4	no	—
139	C₂³×C₁₀₁	—	4	4	no	—
140	C₂³×C₁₀₁	—	4	4	no	—
141	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
142	Q₈×C₁₀₁	—	2	4	no	—
143	Q₈×C₁₀₁	—	4	2	no	—
144	Q₈×C₁₀₁	—	4	2	no	—
145	Q₈×C₁₀₁	—	4	2	no	—
146	D₄×C₁₀₁	—	4	4	no	—
147	D₄×C₁₀₁	—	4	4	no	—
148	D₄×C₁₀₁	—	4	4	no	—
149	D₄×C₁₀₁	—	4	4	no	—
150	D₄×C₁₀₁	—	8	4	no	—
151	C₂×C₄×C₁₀₁	—	2	2	no	—
152	C₂×C₄×C₁₀₁	—	2	2	no	—
153	C₂×C₄×C₁₀₁	—	2	2	no	—
154	C₂×C₄×C₁₀₁	—	2	2	no	—
155	C₂×C₄×C₁₀₁	—	2	2	no	—
156	C₂×C₄×C₁₀₁	—	4	2	no	—
157	C₂×C₄×C₁₀₁	—	4	1	no	—
158	C₂×C₄×C₁₀₁	—	4	2	no	—
159	C₂×C₄×C₁₀₁	—	4	2	no	—
160	C₂×C₄×C₁₀₁	—	8	4	no	—
161	C₂×C₄×C₁₀₁	—	8	4	no	—
162	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
164	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
169	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
170	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂×C₄×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
172	C₈×C₁₀₁	—	2	4	no	—
173	C₈×C₁₀₁	—	4	4	no	—
174	C₈×C₁₀₁	—	4	2	no	—
175	C₂²×C₁₀₁	—	2	1	no	—
176	C₂²×C₁₀₁	—	2	1	no	—
177	C₂²×C₁₀₁	—	4	4	no	—
178	C₂²×C₁₀₁	—	4	4	no	—
179	C₂²×C₁₀₁	—	4	4	no	—
180	C₂²×C₁₀₁	—	8	4	no	—
181	C₂²×C₁₀₁	—	8	4	no	—
182	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
183	C₂²×C₁₀₁	C₄×#41	1	1	yes	characteristic
184	C₂²×C₁₀₁	#520	1	1	yes	characteristic
185	C₄×C₁₀₁	—	2	1	no	—
186	C₄×C₁₀₁	—	2	4	no	—
187	C₄×C₁₀₁	—	2	2	no	—
188	C₄×C₁₀₁	—	2	2	no	—
189	C₄×C₁₀₁	—	2	2	no	—
190	C₄×C₁₀₁	—	4	2	no	—
191	C₄×C₁₀₁	—	4	2	no	—
192	C₄×C₁₀₁	#413	1	2	yes	—
193	C₄×C₁₀₁	#548	1	2	yes	—
194	C₄×C₁₀₁	#550	1	2	yes	—
195	#22539	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂×C₁₀₁	—	2	1	no	—
197	C₂×C₁₀₁	—	2	1	no	—
198	C₂×C₁₀₁	—	8	4	no	—
199	C₂×C₁₀₁	#2341	1	1	yes	characteristic
200	C₂×C₁₀₁	C₂×#413	1	1	yes	characteristic
201	C₂×C₁₀₁	#2888	1	1	yes	characteristic
202	C₂×#559	C₂×C₁₀₁	1	1	yes	characteristic
203	Q₈×M₁₆	C₂×C₁₀₁	1	2	yes	complemented
204	#1967	C₂×C₁₀₁	1	4	yes	complemented
205	#1965	C₂×C₁₀₁	1	2	yes	—
206	#1801	C₂×C₁₀₁	1	1	yes	characteristic, complemented
207	#1800	C₂×C₁₀₁	1	2	yes	complemented
208	C₄×#101	C₂×C₁₀₁	1	1	yes	characteristic, complemented
209	C₄×#100	C₂×C₁₀₁	1	2	yes	complemented
210	C₁₀₁	#22539	1	1	yes	characteristic, direct product factor, Sylow
211	#559	—	2	2	no	—
212	#559	—	2	4	no	—
213	#559	—	2	2	no	—
214	C₂×#127	C₂²×C₁₀₁	1	1	yes	characteristic
215	C₂×#124	C₄×C₁₀₁	1	2	yes	—
216	C₂×#124	C₂²×C₁₀₁	1	2	yes	—
217	C₂×#123	C₄×C₁₀₁	1	4	yes	—
218	C₂×C₄×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
219	C₂×C₄×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
220	C₂×C₄×D₄	C₄×C₁₀₁	1	2	yes	—
221	C₂×C₄×D₄	C₂²×C₁₀₁	1	2	yes	—
222	#446	—	2	4	no	—
223	#446	—	2	2	no	—
224	C₈×Q₈	—	2	2	no	—
225	#423	C₂²×C₁₀₁	1	4	yes	—
226	#423	C₂²×C₁₀₁	1	2	yes	—
227	C₂×#101	C₂²×C₁₀₁	1	2	yes	—
228	C₂×#101	C₂²×C₁₀₁	1	2	yes	—
229	C₂×#100	C₂²×C₁₀₁	1	4	yes	—
230	C₂×#100	C₂²×C₁₀₁	1	4	yes	—
231	C₄×M₁₆	C₂²×C₁₀₁	1	2	yes	—
232	C₄×M₁₆	C₂²×C₁₀₁	1	4	yes	—
233	#343	C₂²×C₁₀₁	1	1	yes	characteristic
234	#343	C₂²×C₁₀₁	1	2	yes	—
235	#343	C₂²×C₁₀₁	1	1	yes	characteristic
236	C₂²×Q₈	C₂×C₄×C₁₀₁	1	1	yes	characteristic
237	C₂²×Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
238	C₂²×D₄	C₂×C₄×C₁₀₁	1	2	yes	—
239	C₂²×D₄	C₂×C₄×C₁₀₁	1	2	yes	—
240	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
241	C₂³×C₄	C₂×C₄×C₁₀₁	1	4	yes	—
242	C₂×M₁₆	C₂³×C₁₀₁	1	4	yes	—
243	C₂×M₁₆	C₂³×C₁₀₁	1	2	yes	—
244	C₂×M₁₆	C₂³×C₁₀₁	1	2	yes	—
245	#127	—	2	2	no	—
246	#127	—	2	2	no	—
247	#124	—	2	4	no	—
248	#124	—	2	4	no	—
249	#124	—	2	4	no	—
250	#124	—	2	4	no	—
251	#123	—	2	8	no	—
252	#123	—	2	8	no	—
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	D₄×C₁₀₁	1	2	yes	—
256	C₄×Q₈	D₄×C₁₀₁	1	4	yes	—
257	C₄×Q₈	D₄×C₁₀₁	1	2	yes	—
258	C₄×D₄	—	2	4	no	—
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	—	2	2	no	—
261	C₄×D₄	—	2	4	no	—
262	C₄×D₄	—	2	4	no	—
263	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
264	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
268	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
269	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
270	C₂×C₄²	C₂×C₄×C₁₀₁	1	2	yes	—
271	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
272	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
273	C₄⋊C₈	—	2	4	no	—
274	C₄⋊C₈	—	2	2	no	—
275	C₄⋊C₈	—	2	4	no	—
276	C₄⋊C₈	—	2	2	no	—
277	#101	—	2	4	no	—
278	#101	—	4	2	no	—
279	#100	—	2	8	no	—
280	#100	—	4	4	no	—
281	#97	—	2	4	no	—
282	#97	—	2	2	no	—
283	C₄×C₈	—	2	4	no	—
284	C₄×C₈	—	2	2	no	—
285	C₂⁴	C₂²×C₄×C₁₀₁	1	4	yes	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×Q₈	C₂²⋊C₄×C₁₀₁	1	2	yes	—
292	C₂×Q₈	C₂²⋊C₄×C₁₀₁	1	2	yes	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	4	4	no	—
301	C₂×D₄	—	8	2	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	8	4	no	—
305	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
306	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
308	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
309	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
310	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
311	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
312	M₁₆	—	2	2	no	—
313	M₁₆	—	2	4	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	2	no	—
316	M₁₆	—	2	4	no	—
317	M₁₆	#41×C₁₀₁	1	4	yes	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	—	2	2	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
324	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
325	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
326	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	4	yes	—
327	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	4	yes	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₂²⋊C₄	—	2	8	no	—
331	C₂²⋊C₄	—	2	8	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	C₂×D₄×C₁₀₁	1	4	yes	—
335	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
336	C₄²	C₂×D₄×C₁₀₁	1	4	yes	—
337	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
338	C₂³	—	2	4	no	—
339	C₂³	—	2	4	no	—
340	C₂³	—	2	4	no	—
341	C₂³	—	4	4	no	—
342	C₂³	—	4	4	no	—
343	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
344	Q₈	—	2	4	no	—
345	Q₈	—	4	2	no	—
346	Q₈	—	4	2	no	—
347	Q₈	—	4	2	no	—
348	D₄	—	4	4	no	—
349	D₄	—	4	4	no	—
350	D₄	—	4	4	no	—
351	D₄	—	4	4	no	—
352	D₄	—	8	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	8	4	no	—
363	C₂×C₄	—	8	4	no	—
364	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
365	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
366	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
367	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
368	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
369	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
370	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
371	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
372	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
373	C₂×C₄	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
374	C₈	—	2	4	no	—
375	C₈	—	4	4	no	—
376	C₈	—	4	2	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	4	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	8	4	no	—
383	C₂²	—	8	4	no	—
384	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
385	C₂²	C₄×#41×C₁₀₁	1	1	yes	characteristic
386	C₂²	#520×C₁₀₁	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	4	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	2	no	—
394	C₄	#413×C₁₀₁	1	2	yes	—
395	C₄	#548×C₁₀₁	1	2	yes	—
396	C₄	#550×C₁₀₁	1	2	yes	—
397	C₂	—	2	1	no	—
398	C₂	—	2	1	no	—
399	C₂	—	8	4	no	—
400	C₂	C₁₀₁×#2341	1	1	yes	characteristic
401	C₂	C₂×#413×C₁₀₁	1	1	yes	characteristic
402	C₂	C₁₀₁×#2888	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	C₂×#127×C₁₀₁	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂×C₄×Q₈×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×M₁₆×C₁₀₁	C₂	semidirect
3. C₁₀₁×#1967	C₂	semidirect
5. C₁₀₁×#1801	C₂	semidirect
6. C₁₀₁×#1800	C₂	semidirect
7. C₄×#101×C₁₀₁	C₂	semidirect
8. C₄×#100×C₁₀₁	C₂	semidirect
195. #22539	C₁₀₁	direct (N × H)
203. Q₈×M₁₆	C₂×C₁₀₁	semidirect
204. #1967	C₂×C₁₀₁	semidirect
206. #1801	C₂×C₁₀₁	semidirect
207. #1800	C₂×C₁₀₁	semidirect
208. C₄×#101	C₂×C₁₀₁	semidirect
209. C₄×#100	C₂×C₁₀₁	semidirect
210. C₁₀₁	#22539	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×#559×C₁₀₁	2
Q₈×M₁₆×C₁₀₁	2
C₁₀₁×#1967	2
C₁₀₁×#1965	2
C₁₀₁×#1801	2
C₁₀₁×#1800	2
C₄×#101×C₁₀₁	2
C₄×#100×C₁₀₁	2
#22539	101

Subgroups — C101×#22539 #38804690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#22539 #38804690