Subgroups — C₁₀₁×#13901 #38796052

Order 25856.

1818 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#383×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₂²⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×#95×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#1443	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1443	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1434	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₁×#1434	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₁×#1434	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₁×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic
10	C₁₀₁×C₂²⋊#95	C₂	1	2	yes	maximal
11	C₁₀₁×C₂²⋊#95	C₂	1	2	yes	maximal
12	C₂⁴×C₄×C₁₀₁	C₂²	1	2	yes	—
13	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
19	#383×C₁₀₁	—	2	4	no	—
20	C₄×C₂²⋊C₄×C₁₀₁	C₄	1	8	yes	complemented
21	C₂×#95×C₁₀₁	—	2	4	no	—
22	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
23	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
24	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
25	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
26	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
27	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
28	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
29	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
30	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
31	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
32	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
33	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
34	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
35	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
36	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
37	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
38	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₀₁	—	2	4	no	—
40	C₂³×C₄×C₁₀₁	—	2	4	no	—
41	C₂³×C₄×C₁₀₁	—	2	4	no	—
42	C₂³×C₄×C₁₀₁	—	2	2	no	—
43	C₂³×C₄×C₁₀₁	—	2	4	no	—
44	C₂³×C₄×C₁₀₁	—	2	2	no	—
45	C₂³×C₄×C₁₀₁	—	2	4	no	—
46	C₂³×C₄×C₁₀₁	—	2	4	no	—
47	C₂³×C₄×C₁₀₁	—	4	2	no	—
48	C₂³×C₄×C₁₀₁	—	4	2	no	—
49	C₂³×C₄×C₁₀₁	—	4	2	no	—
50	C₂³×C₄×C₁₀₁	C₂×C₄	1	4	yes	—
51	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
61	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
63	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
68	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
69	C₂×C₄²×C₁₀₁	—	2	2	no	—
70	C₂×C₄²×C₁₀₁	—	2	2	no	—
71	C₂×C₄²×C₁₀₁	—	4	2	no	—
72	C₂×C₄²×C₁₀₁	C₂×C₄	1	4	yes	complemented
73	C₂×C₄²×C₁₀₁	C₂×C₄	1	4	yes	complemented
74	#95×C₁₀₁	—	2	4	no	—
75	#95×C₁₀₁	—	2	2	no	—
76	#95×C₁₀₁	—	2	4	no	—
77	#95×C₁₀₁	—	2	4	no	—
78	#95×C₁₀₁	—	2	2	no	—
79	#95×C₁₀₁	—	2	4	no	—
80	#95×C₁₀₁	—	2	4	no	—
81	#95×C₁₀₁	—	2	2	no	—
82	#95×C₁₀₁	—	4	2	no	—
83	#95×C₁₀₁	—	4	2	no	—
84	#95×C₁₀₁	—	4	2	no	—
85	#95×C₁₀₁	—	4	2	no	—
86	#95×C₁₀₁	—	4	2	no	—
87	#95×C₁₀₁	C₂×C₄	1	4	yes	complemented
88	#95×C₁₀₁	C₂×C₄	1	4	yes	complemented
89	#95×C₁₀₁	D₄	1	4	yes	—
90	C₂⁴×C₁₀₁	—	2	1	no	—
91	C₂⁴×C₁₀₁	—	2	1	no	—
92	C₂⁴×C₁₀₁	—	2	2	no	—
93	C₂⁴×C₁₀₁	—	2	2	no	—
94	C₂⁴×C₁₀₁	—	2	1	no	—
95	C₂⁴×C₁₀₁	—	2	1	no	—
96	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
97	C₂⁴×C₁₀₁	#41	1	2	yes	—
98	C₂⁴×C₁₀₁	#41	1	4	yes	—
99	C₂⁴×C₁₀₁	#41	1	2	yes	—
100	C₂⁴×C₁₀₁	#41	1	4	yes	—
101	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
102	C₂²×C₄×C₁₀₁	—	2	2	no	—
103	C₂²×C₄×C₁₀₁	—	2	2	no	—
104	C₂²×C₄×C₁₀₁	—	2	16	no	—
105	C₂²×C₄×C₁₀₁	—	2	8	no	—
106	C₂²×C₄×C₁₀₁	—	2	1	no	—
107	C₂²×C₄×C₁₀₁	—	2	1	no	—
108	C₂²×C₄×C₁₀₁	—	2	1	no	—
109	C₂²×C₄×C₁₀₁	—	2	2	no	—
110	C₂²×C₄×C₁₀₁	—	2	2	no	—
111	C₂²×C₄×C₁₀₁	—	2	2	no	—
112	C₂²×C₄×C₁₀₁	—	2	1	no	—
113	C₂²×C₄×C₁₀₁	—	2	1	no	—
114	C₂²×C₄×C₁₀₁	—	2	2	no	—
115	C₂²×C₄×C₁₀₁	—	2	2	no	—
116	C₂²×C₄×C₁₀₁	—	2	1	no	—
117	C₂²×C₄×C₁₀₁	—	2	1	no	—
118	C₂²×C₄×C₁₀₁	—	2	1	no	—
119	C₂²×C₄×C₁₀₁	—	2	1	no	—
120	C₂²×C₄×C₁₀₁	—	2	2	no	—
121	C₂²×C₄×C₁₀₁	—	2	1	no	—
122	C₂²×C₄×C₁₀₁	—	2	2	no	—
123	C₂²×C₄×C₁₀₁	—	2	2	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	—	2	2	no	—
129	C₂²×C₄×C₁₀₁	—	2	1	no	—
130	C₂²×C₄×C₁₀₁	—	2	1	no	—
131	C₂²×C₄×C₁₀₁	—	2	2	no	—
132	C₂²×C₄×C₁₀₁	—	2	2	no	—
133	C₂²×C₄×C₁₀₁	—	2	2	no	—
134	C₂²×C₄×C₁₀₁	—	2	2	no	—
135	C₂²×C₄×C₁₀₁	—	2	2	no	—
136	C₂²×C₄×C₁₀₁	—	2	2	no	—
137	C₂²×C₄×C₁₀₁	—	2	2	no	—
138	C₂²×C₄×C₁₀₁	—	2	1	no	—
139	C₂²×C₄×C₁₀₁	—	2	1	no	—
140	C₂²×C₄×C₁₀₁	—	2	8	no	—
141	C₂²×C₄×C₁₀₁	—	2	2	no	—
142	C₂²×C₄×C₁₀₁	—	2	2	no	—
143	C₂²×C₄×C₁₀₁	—	2	2	no	—
144	C₂²×C₄×C₁₀₁	—	2	2	no	—
145	C₂²×C₄×C₁₀₁	—	2	2	no	—
146	C₂²×C₄×C₁₀₁	—	2	2	no	—
147	C₂²×C₄×C₁₀₁	—	2	2	no	—
148	C₂²×C₄×C₁₀₁	—	2	2	no	—
149	C₂²×C₄×C₁₀₁	—	2	2	no	—
150	C₂²×C₄×C₁₀₁	—	2	2	no	—
151	C₂²×C₄×C₁₀₁	—	2	2	no	—
152	C₂²×C₄×C₁₀₁	—	2	2	no	—
153	C₂²×C₄×C₁₀₁	—	2	2	no	—
154	C₂²×C₄×C₁₀₁	—	2	2	no	—
155	C₂²×C₄×C₁₀₁	—	4	4	no	—
156	C₂²×C₄×C₁₀₁	—	4	8	no	—
157	C₂²×C₄×C₁₀₁	—	4	8	no	—
158	C₂²×C₄×C₁₀₁	—	4	8	no	—
159	C₂²×C₄×C₁₀₁	—	4	8	no	—
160	C₂²×C₄×C₁₀₁	—	4	8	no	—
161	C₂²×C₄×C₁₀₁	—	4	8	no	—
162	C₂²×C₄×C₁₀₁	—	4	8	no	—
163	C₂²×C₄×C₁₀₁	—	4	8	no	—
164	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
165	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
166	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
167	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
168	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
169	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
170	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
171	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
173	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
174	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
175	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
176	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
177	C₄²×C₁₀₁	—	2	8	no	—
178	C₄²×C₁₀₁	—	4	4	no	—
179	C₂³×C₁₀₁	—	2	2	no	—
180	C₂³×C₁₀₁	—	2	2	no	—
181	C₂³×C₁₀₁	—	2	2	no	—
182	C₂³×C₁₀₁	—	2	2	no	—
183	C₂³×C₁₀₁	—	2	4	no	—
184	C₂³×C₁₀₁	—	2	4	no	—
185	C₂³×C₁₀₁	—	2	4	no	—
186	C₂³×C₁₀₁	—	2	4	no	—
187	C₂³×C₁₀₁	—	2	4	no	—
188	C₂³×C₁₀₁	—	2	2	no	—
189	C₂³×C₁₀₁	—	2	2	no	—
190	C₂³×C₁₀₁	—	2	4	no	—
191	C₂³×C₁₀₁	—	2	4	no	—
192	C₂³×C₁₀₁	—	2	4	no	—
193	C₂³×C₁₀₁	—	2	4	no	—
194	C₂³×C₁₀₁	—	2	2	no	—
195	C₂³×C₁₀₁	—	2	2	no	—
196	C₂³×C₁₀₁	—	2	4	no	—
197	C₂³×C₁₀₁	#117	1	4	yes	—
198	C₂³×C₁₀₁	#117	1	4	yes	—
199	C₂³×C₁₀₁	#117	1	4	yes	—
200	C₂³×C₁₀₁	#126	1	8	yes	—
201	C₂³×C₁₀₁	#126	1	8	yes	—
202	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
203	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
204	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
205	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
206	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
207	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
208	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
209	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
210	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
211	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂³×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
213	C₂×C₄×C₁₀₁	—	2	2	no	—
214	C₂×C₄×C₁₀₁	—	2	2	no	—
215	C₂×C₄×C₁₀₁	—	2	4	no	—
216	C₂×C₄×C₁₀₁	—	2	4	no	—
217	C₂×C₄×C₁₀₁	—	2	2	no	—
218	C₂×C₄×C₁₀₁	—	2	2	no	—
219	C₂×C₄×C₁₀₁	—	2	2	no	—
220	C₂×C₄×C₁₀₁	—	2	2	no	—
221	C₂×C₄×C₁₀₁	—	2	2	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	2	no	—
227	C₂×C₄×C₁₀₁	—	2	2	no	—
228	C₂×C₄×C₁₀₁	—	2	2	no	—
229	C₂×C₄×C₁₀₁	—	2	2	no	—
230	C₂×C₄×C₁₀₁	—	2	2	no	—
231	C₂×C₄×C₁₀₁	—	2	2	no	—
232	C₂×C₄×C₁₀₁	—	2	4	no	—
233	C₂×C₄×C₁₀₁	—	2	4	no	—
234	C₂×C₄×C₁₀₁	—	2	4	no	—
235	C₂×C₄×C₁₀₁	—	2	4	no	—
236	C₂×C₄×C₁₀₁	—	2	4	no	—
237	C₂×C₄×C₁₀₁	—	2	4	no	—
238	C₂×C₄×C₁₀₁	—	4	16	no	—
239	C₂×C₄×C₁₀₁	—	4	32	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	2	no	—
244	C₂×C₄×C₁₀₁	—	4	2	no	—
245	C₂×C₄×C₁₀₁	—	4	2	no	—
246	C₂×C₄×C₁₀₁	—	4	2	no	—
247	C₂×C₄×C₁₀₁	—	4	2	no	—
248	C₂×C₄×C₁₀₁	—	4	1	no	—
249	C₂×C₄×C₁₀₁	—	4	2	no	—
250	C₂×C₄×C₁₀₁	—	4	2	no	—
251	C₂×C₄×C₁₀₁	—	4	2	no	—
252	C₂×C₄×C₁₀₁	—	4	1	no	—
253	C₂×C₄×C₁₀₁	—	4	2	no	—
254	C₂×C₄×C₁₀₁	—	4	2	no	—
255	C₂×C₄×C₁₀₁	—	4	2	no	—
256	C₂×C₄×C₁₀₁	—	4	2	no	—
257	C₂×C₄×C₁₀₁	—	4	1	no	—
258	C₂×C₄×C₁₀₁	—	4	1	no	—
259	C₂×C₄×C₁₀₁	—	4	2	no	—
260	C₂×C₄×C₁₀₁	—	4	2	no	—
261	C₂×C₄×C₁₀₁	—	4	2	no	—
262	C₂×C₄×C₁₀₁	—	4	2	no	—
263	C₂×C₄×C₁₀₁	—	4	2	no	—
264	C₂×C₄×C₁₀₁	—	4	2	no	—
265	C₂×C₄×C₁₀₁	—	4	2	no	—
266	C₂×C₄×C₁₀₁	—	4	2	no	—
267	C₂×C₄×C₁₀₁	—	4	2	no	—
268	C₂×C₄×C₁₀₁	—	4	2	no	—
269	C₂×C₄×C₁₀₁	—	4	2	no	—
270	C₂×C₄×C₁₀₁	—	4	2	no	—
271	C₂×C₄×C₁₀₁	—	4	2	no	—
272	C₂×C₄×C₁₀₁	—	4	2	no	—
273	C₂×C₄×C₁₀₁	—	4	2	no	—
274	C₂×C₄×C₁₀₁	C₄×D₄	1	4	yes	—
275	C₂²×C₁₀₁	—	2	4	no	—
276	C₂²×C₁₀₁	—	2	4	no	—
277	C₂²×C₁₀₁	—	2	4	no	—
278	C₂²×C₁₀₁	—	2	4	no	—
279	C₂²×C₁₀₁	—	2	4	no	—
280	C₂²×C₁₀₁	—	2	8	no	—
281	C₂²×C₁₀₁	—	2	8	no	—
282	C₂²×C₁₀₁	—	2	8	no	—
283	C₂²×C₁₀₁	—	2	8	no	—
284	C₂²×C₁₀₁	—	2	4	no	—
285	C₂²×C₁₀₁	#383	1	8	yes	complemented
286	C₂²×C₁₀₁	C₂×#117	1	1	yes	characteristic
287	C₂²×C₁₀₁	C₂×#117	1	1	yes	characteristic
288	C₂²×C₁₀₁	C₂×#117	1	1	yes	characteristic
289	C₂²×C₁₀₁	C₂×C₄×D₄	1	1	yes	characteristic
290	C₂²×C₁₀₁	C₄×#41	1	1	yes	characteristic
291	C₂²×C₁₀₁	#518	1	1	yes	characteristic
292	C₂²×C₁₀₁	#520	1	1	yes	characteristic
293	C₂²×C₁₀₁	#525	1	2	yes	—
294	C₂²×C₁₀₁	C₂×#126	1	2	yes	—
295	C₂²×C₁₀₁	C₂×#126	1	2	yes	—
296	C₂²×C₁₀₁	#529	1	2	yes	—
297	C₂²×C₁₀₁	#538	1	2	yes	—
298	C₂²×C₁₀₁	#539	1	2	yes	—
299	C₂²×C₁₀₁	#546	1	2	yes	—
300	C₂²×C₁₀₁	#546	1	1	yes	characteristic
301	C₂²×C₁₀₁	#548	1	1	yes	characteristic
302	C₂²×C₁₀₁	#551	1	2	yes	—
303	C₂²×C₁₀₁	#551	1	2	yes	—
304	C₂²×C₁₀₁	#551	1	2	yes	—
305	C₂²×C₁₀₁	#552	1	2	yes	—
306	C₂²×C₁₀₁	#552	1	1	yes	characteristic
307	C₂²×C₁₀₁	#553	1	1	yes	characteristic
308	C₂²×C₁₀₁	#553	1	2	yes	—
309	C₄×C₁₀₁	—	2	4	no	—
310	C₄×C₁₀₁	—	4	2	no	—
311	C₄×C₁₀₁	—	4	2	no	—
312	C₄×C₁₀₁	—	4	2	no	—
313	C₄×C₁₀₁	—	4	2	no	—
314	C₄×C₁₀₁	—	4	4	no	—
315	C₄×C₁₀₁	—	4	4	no	—
316	C₄×C₁₀₁	—	4	2	no	—
317	C₄×C₁₀₁	—	8	2	no	—
318	C₄×C₁₀₁	—	8	2	no	—
319	#13901	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
320	C₂×C₁₀₁	—	2	8	no	—
321	C₂×C₁₀₁	C₂×#383	1	1	yes	characteristic
322	C₂×C₁₀₁	#2290	1	1	yes	characteristic
323	C₂×C₁₀₁	#2318	1	1	yes	characteristic
324	C₂×C₁₀₁	#2342	1	1	yes	characteristic
325	C₂×C₁₀₁	#2343	1	1	yes	characteristic
326	C₂×C₁₀₁	#2352	1	1	yes	characteristic
327	C₂×C₁₀₁	#2353	1	1	yes	characteristic
328	C₂×C₁₀₁	#2480	1	2	yes	—
329	C₂×C₁₀₁	#2481	1	2	yes	—
330	C₂×C₁₀₁	#2493	1	2	yes	—
331	C₂×C₁₀₁	#2510	1	2	yes	—
332	C₂×#383	C₂×C₁₀₁	1	1	yes	characteristic, complemented
333	C₂×C₄×C₂²⋊C₄	C₂×C₁₀₁	1	1	yes	characteristic
334	C₂²×#95	C₂×C₁₀₁	1	1	yes	characteristic
335	#1443	C₂×C₁₀₁	1	2	yes	complemented
336	#1443	C₂×C₁₀₁	1	2	yes	complemented
337	#1434	C₂×C₁₀₁	1	1	yes	characteristic, complemented
338	#1434	C₂×C₁₀₁	1	1	yes	characteristic, complemented
339	#1434	C₂×C₁₀₁	1	1	yes	characteristic, complemented
340	C₂²⋊#95	C₂×C₁₀₁	1	1	yes	characteristic
341	C₂²⋊#95	C₂×C₁₀₁	1	2	yes	—
342	C₂²⋊#95	C₂×C₁₀₁	1	2	yes	—
343	C₁₀₁	#13901	1	1	yes	characteristic, direct product factor, Sylow
344	C₂⁴×C₄	C₂²×C₁₀₁	1	2	yes	—
345	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
346	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
347	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
348	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
349	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
350	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
351	#383	—	2	4	no	—
352	C₄×C₂²⋊C₄	C₄×C₁₀₁	1	8	yes	complemented
353	C₂×#95	—	2	4	no	—
354	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
355	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
356	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
357	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
358	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
359	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
360	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
361	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
362	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
363	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
364	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
365	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
366	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
367	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
368	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
369	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
370	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
371	C₂³×C₄	—	2	4	no	—
372	C₂³×C₄	—	2	4	no	—
373	C₂³×C₄	—	2	4	no	—
374	C₂³×C₄	—	2	2	no	—
375	C₂³×C₄	—	2	4	no	—
376	C₂³×C₄	—	2	2	no	—
377	C₂³×C₄	—	2	4	no	—
378	C₂³×C₄	—	2	4	no	—
379	C₂³×C₄	—	4	2	no	—
380	C₂³×C₄	—	4	2	no	—
381	C₂³×C₄	—	4	2	no	—
382	C₂³×C₄	C₂×C₄×C₁₀₁	1	4	yes	—
383	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
384	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
385	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
387	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
388	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
389	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
391	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
392	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
393	C₂×C₂²⋊C₄	—	2	2	no	—
394	C₂×C₂²⋊C₄	—	2	4	no	—
395	C₂×C₂²⋊C₄	—	2	2	no	—
396	C₂×C₂²⋊C₄	—	2	4	no	—
397	C₂×C₂²⋊C₄	—	2	4	no	—
398	C₂×C₂²⋊C₄	—	2	4	no	—
399	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
400	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
401	C₂×C₄²	—	2	2	no	—
402	C₂×C₄²	—	2	2	no	—
403	C₂×C₄²	—	4	2	no	—
404	C₂×C₄²	C₂×C₄×C₁₀₁	1	4	yes	complemented
405	C₂×C₄²	C₂×C₄×C₁₀₁	1	4	yes	complemented
406	#95	—	2	4	no	—
407	#95	—	2	2	no	—
408	#95	—	2	4	no	—
409	#95	—	2	4	no	—
410	#95	—	2	2	no	—
411	#95	—	2	4	no	—
412	#95	—	2	4	no	—
413	#95	—	2	2	no	—
414	#95	—	4	2	no	—
415	#95	—	4	2	no	—
416	#95	—	4	2	no	—
417	#95	—	4	2	no	—
418	#95	—	4	2	no	—
419	#95	C₂×C₄×C₁₀₁	1	4	yes	complemented
420	#95	C₂×C₄×C₁₀₁	1	4	yes	complemented
421	#95	D₄×C₁₀₁	1	4	yes	—
422	C₂⁴	—	2	1	no	—
423	C₂⁴	—	2	1	no	—
424	C₂⁴	—	2	2	no	—
425	C₂⁴	—	2	2	no	—
426	C₂⁴	—	2	1	no	—
427	C₂⁴	—	2	1	no	—
428	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
429	C₂⁴	#41×C₁₀₁	1	2	yes	—
430	C₂⁴	#41×C₁₀₁	1	4	yes	—
431	C₂⁴	#41×C₁₀₁	1	2	yes	—
432	C₂⁴	#41×C₁₀₁	1	4	yes	—
433	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	16	no	—
437	C₂²×C₄	—	2	8	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	8	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	4	4	no	—
488	C₂²×C₄	—	4	8	no	—
489	C₂²×C₄	—	4	8	no	—
490	C₂²×C₄	—	4	8	no	—
491	C₂²×C₄	—	4	8	no	—
492	C₂²×C₄	—	4	8	no	—
493	C₂²×C₄	—	4	8	no	—
494	C₂²×C₄	—	4	8	no	—
495	C₂²×C₄	—	4	8	no	—
496	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
497	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
498	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
499	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
500	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
501	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
502	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
503	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
504	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
505	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
506	C₂²⋊C₄	—	2	8	no	—
507	C₂²⋊C₄	—	2	8	no	—
508	C₂²⋊C₄	—	4	8	no	—
509	C₄²	—	2	8	no	—
510	C₄²	—	4	4	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	2	2	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	2	no	—
515	C₂³	—	2	4	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	2	4	no	—
519	C₂³	—	2	2	no	—
520	C₂³	—	2	4	no	—
521	C₂³	—	2	2	no	—
522	C₂³	—	2	4	no	—
523	C₂³	—	2	4	no	—
524	C₂³	—	2	4	no	—
525	C₂³	—	2	4	no	—
526	C₂³	—	2	2	no	—
527	C₂³	—	2	4	no	—
528	C₂³	—	2	2	no	—
529	C₂³	#117×C₁₀₁	1	4	yes	—
530	C₂³	#117×C₁₀₁	1	4	yes	—
531	C₂³	#117×C₁₀₁	1	4	yes	—
532	C₂³	#126×C₁₀₁	1	8	yes	—
533	C₂³	#126×C₁₀₁	1	8	yes	—
534	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
535	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
536	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
537	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
538	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
539	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
540	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
541	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
542	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
543	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
544	C₂³	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	4	16	no	—
571	C₂×C₄	—	4	32	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	2	no	—
578	C₂×C₄	—	4	2	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	C₄×D₄×C₁₀₁	1	4	yes	—
607	C₂²	—	2	8	no	—
608	C₂²	—	2	8	no	—
609	C₂²	—	2	8	no	—
610	C₂²	—	2	8	no	—
611	C₂²	—	2	4	no	—
612	C₂²	—	2	4	no	—
613	C₂²	—	2	4	no	—
614	C₂²	—	2	4	no	—
615	C₂²	—	2	4	no	—
616	C₂²	—	2	4	no	—
617	C₂²	#383×C₁₀₁	1	8	yes	complemented
618	C₂²	C₂×#117×C₁₀₁	1	1	yes	characteristic
619	C₂²	C₂×#117×C₁₀₁	1	1	yes	characteristic
620	C₂²	C₂×#117×C₁₀₁	1	1	yes	characteristic
621	C₂²	C₂×C₄×D₄×C₁₀₁	1	1	yes	characteristic
622	C₂²	C₄×#41×C₁₀₁	1	1	yes	characteristic
623	C₂²	#518×C₁₀₁	1	1	yes	characteristic
624	C₂²	#520×C₁₀₁	1	1	yes	characteristic
625	C₂²	#525×C₁₀₁	1	2	yes	—
626	C₂²	C₂×#126×C₁₀₁	1	2	yes	—
627	C₂²	C₂×#126×C₁₀₁	1	2	yes	—
628	C₂²	#529×C₁₀₁	1	2	yes	—
629	C₂²	#538×C₁₀₁	1	2	yes	—
630	C₂²	#539×C₁₀₁	1	2	yes	—
631	C₂²	#546×C₁₀₁	1	1	yes	characteristic
632	C₂²	#546×C₁₀₁	1	2	yes	—
633	C₂²	#548×C₁₀₁	1	1	yes	characteristic
634	C₂²	#551×C₁₀₁	1	2	yes	—
635	C₂²	#551×C₁₀₁	1	2	yes	—
636	C₂²	#551×C₁₀₁	1	2	yes	—
637	C₂²	#552×C₁₀₁	1	2	yes	—
638	C₂²	#552×C₁₀₁	1	1	yes	characteristic
639	C₂²	#553×C₁₀₁	1	2	yes	—
640	C₂²	#553×C₁₀₁	1	1	yes	characteristic
641	C₄	—	2	4	no	—
642	C₄	—	4	4	no	—
643	C₄	—	4	4	no	—
644	C₄	—	4	2	no	—
645	C₄	—	4	2	no	—
646	C₄	—	4	2	no	—
647	C₄	—	4	2	no	—
648	C₄	—	4	2	no	—
649	C₄	—	8	2	no	—
650	C₄	—	8	2	no	—
651	C₂	—	2	8	no	—
652	C₂	C₂×#383×C₁₀₁	1	1	yes	characteristic
653	C₂	C₁₀₁×#2290	1	1	yes	characteristic
654	C₂	C₁₀₁×#2318	1	1	yes	characteristic
655	C₂	C₁₀₁×#2342	1	1	yes	characteristic
656	C₂	C₁₀₁×#2343	1	1	yes	characteristic
657	C₂	C₁₀₁×#2352	1	1	yes	characteristic
658	C₂	C₁₀₁×#2353	1	1	yes	characteristic
659	C₂	C₁₀₁×#2480	1	2	yes	—
660	C₂	C₁₀₁×#2481	1	2	yes	—
661	C₂	C₁₀₁×#2493	1	2	yes	—
662	C₂	C₁₀₁×#2510	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₀₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
prime radical	C₂⁵×C₁₀₁	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#383×C₁₀₁	C₂	semidirect
4. C₁₀₁×#1443	C₂	semidirect
5. C₁₀₁×#1443	C₂	semidirect
6. C₁₀₁×#1434	C₂	semidirect
7. C₁₀₁×#1434	C₂	semidirect
8. C₁₀₁×#1434	C₂	semidirect
20. C₄×C₂²⋊C₄×C₁₀₁	C₄	semidirect
72. C₂×C₄²×C₁₀₁	C₂×C₄	semidirect
73. C₂×C₄²×C₁₀₁	C₂×C₄	semidirect
87. #95×C₁₀₁	C₂×C₄	semidirect
88. #95×C₁₀₁	C₂×C₄	semidirect
285. C₂²×C₁₀₁	#383	semidirect
319. #13901	C₁₀₁	direct (N × H)
332. C₂×#383	C₂×C₁₀₁	semidirect
335. #1443	C₂×C₁₀₁	semidirect
336. #1443	C₂×C₁₀₁	semidirect
337. #1434	C₂×C₁₀₁	semidirect
338. #1434	C₂×C₁₀₁	semidirect
339. #1434	C₂×C₁₀₁	semidirect
343. C₁₀₁	#13901	direct (N × H)
352. C₄×C₂²⋊C₄	C₄×C₁₀₁	semidirect
404. C₂×C₄²	C₂×C₄×C₁₀₁	semidirect
405. C₂×C₄²	C₂×C₄×C₁₀₁	semidirect
419. #95	C₂×C₄×C₁₀₁	semidirect
420. #95	C₂×C₄×C₁₀₁	semidirect
617. C₂²	#383×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#383×C₁₀₁	2
C₂×C₄×C₂²⋊C₄×C₁₀₁	2
C₂²×#95×C₁₀₁	2
C₁₀₁×#1443	2
C₁₀₁×#1434	2
C₁₀₁×C₂²⋊#95	2
#13901	101

Subgroups — C101×#13901 #38796052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#13901 #38796052