Subgroups — C₁₀₁×#13823 #38795974

Order 25856.

2022 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#388×C₁₀₁	C₂	1	2	yes	maximal
2	C₂×#385×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₁₀₁	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₂²⋊C₄×C₁₀₁	C₂	1	2	yes	maximal
5	C₁₀₁×#1437	C₂	1	1	yes	maximal, characteristic
6	C₁₀₁×#1437	C₂	1	1	yes	maximal, characteristic
7	C₁₀₁×#1436	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#1436	C₂	1	2	yes	maximal, complemented
9	C₄×#95×C₁₀₁	C₂	1	2	yes	maximal, complemented
10	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
13	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
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	2	yes	—
19	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
22	#388×C₁₀₁	C₄	1	16	yes	complemented
23	#385×C₁₀₁	C₄	1	8	yes	complemented
24	C₄×C₄⋊C₄×C₁₀₁	—	2	8	no	—
25	C₄×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
26	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
27	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
28	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
29	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
30	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
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	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₁₀₁	—	2	4	no	—
37	C₂³×C₄×C₁₀₁	—	2	4	no	—
38	C₂³×C₄×C₁₀₁	—	4	1	no	—
39	C₂³×C₄×C₁₀₁	—	4	1	no	—
40	C₂³×C₄×C₁₀₁	C₂×C₄	1	4	yes	—
41	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	8	yes	—
54	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	8	yes	complemented
55	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₁₀₁	—	4	1	no	—
60	C₂×C₂²⋊C₄×C₁₀₁	—	4	1	no	—
61	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	8	yes	—
62	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	8	yes	—
63	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
64	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
65	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	8	yes	—
66	C₂×C₄²×C₁₀₁	—	2	4	no	—
67	C₂×C₄²×C₁₀₁	—	2	4	no	—
68	C₂×C₄²×C₁₀₁	—	2	4	no	—
69	C₂×C₄²×C₁₀₁	—	2	4	no	—
70	C₂×C₄²×C₁₀₁	—	2	4	no	—
71	C₂×C₄²×C₁₀₁	—	2	4	no	—
72	C₂×C₄²×C₁₀₁	—	2	4	no	—
73	C₂×C₄²×C₁₀₁	—	2	4	no	—
74	C₂×C₄²×C₁₀₁	—	4	1	no	—
75	C₂×C₄²×C₁₀₁	—	4	1	no	—
76	C₂×C₄²×C₁₀₁	—	4	2	no	—
77	C₂×C₄²×C₁₀₁	—	4	2	no	—
78	C₂×C₄²×C₁₀₁	C₂×C₄	1	8	yes	complemented
79	#95×C₁₀₁	—	2	4	no	—
80	#95×C₁₀₁	—	2	4	no	—
81	#95×C₁₀₁	—	2	4	no	—
82	#95×C₁₀₁	—	4	1	no	—
83	#95×C₁₀₁	—	4	1	no	—
84	#95×C₁₀₁	C₂×C₄	1	8	yes	—
85	#95×C₁₀₁	C₂×C₄	1	8	yes	complemented
86	#95×C₁₀₁	C₂×C₄	1	8	yes	complemented
87	#95×C₁₀₁	D₄	1	8	yes	—
88	C₂⁴×C₁₀₁	—	2	2	no	—
89	C₂⁴×C₁₀₁	—	2	2	no	—
90	C₂⁴×C₁₀₁	—	2	2	no	—
91	C₂⁴×C₁₀₁	—	2	2	no	—
92	C₂⁴×C₁₀₁	—	2	1	no	—
93	C₂⁴×C₁₀₁	—	2	1	no	—
94	C₂⁴×C₁₀₁	—	2	2	no	—
95	C₂⁴×C₁₀₁	C₂²×C₄	1	4	yes	—
96	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
97	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
98	C₂²×C₄×C₁₀₁	—	2	2	no	—
99	C₂²×C₄×C₁₀₁	—	2	2	no	—
100	C₂²×C₄×C₁₀₁	—	2	2	no	—
101	C₂²×C₄×C₁₀₁	—	2	2	no	—
102	C₂²×C₄×C₁₀₁	—	2	2	no	—
103	C₂²×C₄×C₁₀₁	—	2	2	no	—
104	C₂²×C₄×C₁₀₁	—	2	2	no	—
105	C₂²×C₄×C₁₀₁	—	2	2	no	—
106	C₂²×C₄×C₁₀₁	—	2	2	no	—
107	C₂²×C₄×C₁₀₁	—	2	2	no	—
108	C₂²×C₄×C₁₀₁	—	2	2	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	2	no	—
113	C₂²×C₄×C₁₀₁	—	2	2	no	—
114	C₂²×C₄×C₁₀₁	—	2	2	no	—
115	C₂²×C₄×C₁₀₁	—	2	2	no	—
116	C₂²×C₄×C₁₀₁	—	2	2	no	—
117	C₂²×C₄×C₁₀₁	—	2	2	no	—
118	C₂²×C₄×C₁₀₁	—	2	2	no	—
119	C₂²×C₄×C₁₀₁	—	2	2	no	—
120	C₂²×C₄×C₁₀₁	—	2	2	no	—
121	C₂²×C₄×C₁₀₁	—	2	2	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	1	no	—
129	C₂²×C₄×C₁₀₁	—	2	1	no	—
130	C₂²×C₄×C₁₀₁	—	2	1	no	—
131	C₂²×C₄×C₁₀₁	—	2	1	no	—
132	C₂²×C₄×C₁₀₁	—	2	2	no	—
133	C₂²×C₄×C₁₀₁	—	2	2	no	—
134	C₂²×C₄×C₁₀₁	—	2	16	no	—
135	C₂²×C₄×C₁₀₁	—	4	4	no	—
136	C₂²×C₄×C₁₀₁	—	4	4	no	—
137	C₂²×C₄×C₁₀₁	—	4	8	no	—
138	C₂²×C₄×C₁₀₁	—	4	4	no	—
139	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
140	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
141	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
142	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
144	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
145	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
146	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
147	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
148	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
149	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
150	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
153	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
154	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
155	C₄⋊C₄×C₁₀₁	—	2	16	no	—
156	C₄⋊C₄×C₁₀₁	—	2	16	no	—
157	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
158	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
159	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
160	C₂²⋊C₄×C₁₀₁	C₄²	1	16	yes	complemented
161	C₄²×C₁₀₁	—	2	16	no	—
162	C₄²×C₁₀₁	—	4	4	no	—
163	C₄²×C₁₀₁	—	4	8	no	—
164	C₄²×C₁₀₁	—	4	8	no	—
165	C₄²×C₁₀₁	—	4	4	no	—
166	C₂³×C₁₀₁	—	2	4	no	—
167	C₂³×C₁₀₁	—	2	4	no	—
168	C₂³×C₁₀₁	—	2	4	no	—
169	C₂³×C₁₀₁	—	2	4	no	—
170	C₂³×C₁₀₁	—	2	4	no	—
171	C₂³×C₁₀₁	—	2	4	no	—
172	C₂³×C₁₀₁	—	2	2	no	—
173	C₂³×C₁₀₁	—	2	2	no	—
174	C₂³×C₁₀₁	—	2	4	no	—
175	C₂³×C₁₀₁	—	2	4	no	—
176	C₂³×C₁₀₁	—	4	1	no	—
177	C₂³×C₁₀₁	—	4	2	no	—
178	C₂³×C₁₀₁	—	4	2	no	—
179	C₂³×C₁₀₁	—	4	2	no	—
180	C₂³×C₁₀₁	—	4	1	no	—
181	C₂³×C₁₀₁	—	4	1	no	—
182	C₂³×C₁₀₁	—	4	2	no	—
183	C₂³×C₁₀₁	—	4	2	no	—
184	C₂³×C₁₀₁	—	4	2	no	—
185	C₂³×C₁₀₁	—	4	1	no	—
186	C₂³×C₁₀₁	C₂×C₄²	1	4	yes	—
187	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
188	C₂³×C₁₀₁	C₂³×C₄	1	2	yes	—
189	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
190	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
191	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
192	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
193	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂³×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
196	C₂×C₄×C₁₀₁	—	2	4	no	—
197	C₂×C₄×C₁₀₁	—	2	4	no	—
198	C₂×C₄×C₁₀₁	—	2	4	no	—
199	C₂×C₄×C₁₀₁	—	2	4	no	—
200	C₂×C₄×C₁₀₁	—	2	4	no	—
201	C₂×C₄×C₁₀₁	—	2	4	no	—
202	C₂×C₄×C₁₀₁	—	2	4	no	—
203	C₂×C₄×C₁₀₁	—	2	4	no	—
204	C₂×C₄×C₁₀₁	—	2	4	no	—
205	C₂×C₄×C₁₀₁	—	2	4	no	—
206	C₂×C₄×C₁₀₁	—	2	4	no	—
207	C₂×C₄×C₁₀₁	—	2	4	no	—
208	C₂×C₄×C₁₀₁	—	2	4	no	—
209	C₂×C₄×C₁₀₁	—	2	4	no	—
210	C₂×C₄×C₁₀₁	—	2	4	no	—
211	C₂×C₄×C₁₀₁	—	2	4	no	—
212	C₂×C₄×C₁₀₁	—	2	4	no	—
213	C₂×C₄×C₁₀₁	—	2	4	no	—
214	C₂×C₄×C₁₀₁	—	2	4	no	—
215	C₂×C₄×C₁₀₁	—	2	4	no	—
216	C₂×C₄×C₁₀₁	—	2	4	no	—
217	C₂×C₄×C₁₀₁	—	2	4	no	—
218	C₂×C₄×C₁₀₁	—	2	4	no	—
219	C₂×C₄×C₁₀₁	—	2	4	no	—
220	C₂×C₄×C₁₀₁	—	2	4	no	—
221	C₂×C₄×C₁₀₁	—	2	4	no	—
222	C₂×C₄×C₁₀₁	—	2	4	no	—
223	C₂×C₄×C₁₀₁	—	2	4	no	—
224	C₂×C₄×C₁₀₁	—	2	4	no	—
225	C₂×C₄×C₁₀₁	—	2	4	no	—
226	C₂×C₄×C₁₀₁	—	2	2	no	—
227	C₂×C₄×C₁₀₁	—	2	2	no	—
228	C₂×C₄×C₁₀₁	—	2	4	no	—
229	C₂×C₄×C₁₀₁	—	2	4	no	—
230	C₂×C₄×C₁₀₁	—	4	16	no	—
231	C₂×C₄×C₁₀₁	—	4	1	no	—
232	C₂×C₄×C₁₀₁	—	4	2	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	2	no	—
237	C₂×C₄×C₁₀₁	—	4	2	no	—
238	C₂×C₄×C₁₀₁	—	4	1	no	—
239	C₂×C₄×C₁₀₁	—	4	1	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	1	no	—
245	C₂×C₄×C₁₀₁	C₂×C₄²	1	8	yes	—
246	C₂×C₄×C₁₀₁	C₄×D₄	1	8	yes	—
247	C₂×C₄×C₁₀₁	C₄×D₄	1	8	yes	—
248	C₂×C₄×C₁₀₁	C₄×D₄	1	8	yes	—
249	C₂²×C₁₀₁	—	2	8	no	—
250	C₂²×C₁₀₁	—	2	4	no	—
251	C₂²×C₁₀₁	—	4	2	no	—
252	C₂²×C₁₀₁	—	4	4	no	—
253	C₂²×C₁₀₁	—	4	4	no	—
254	C₂²×C₁₀₁	—	4	4	no	—
255	C₂²×C₁₀₁	—	4	4	no	—
256	C₂²×C₁₀₁	—	4	4	no	—
257	C₂²×C₁₀₁	—	4	2	no	—
258	C₂²×C₁₀₁	C₂²×C₄²	1	1	yes	characteristic
259	C₂²×C₁₀₁	C₂×C₄×D₄	1	2	yes	—
260	C₂²×C₁₀₁	C₂×C₄×D₄	1	2	yes	—
261	C₂²×C₁₀₁	C₂×C₄×D₄	1	2	yes	—
262	C₂²×C₁₀₁	C₄×#41	1	2	yes	—
263	C₂²×C₁₀₁	C₄×#41	1	2	yes	—
264	C₂²×C₁₀₁	C₄×#41	1	2	yes	—
265	C₂²×C₁₀₁	#518	1	1	yes	characteristic
266	C₂²×C₁₀₁	#519	1	1	yes	characteristic
267	C₂²×C₁₀₁	#520	1	2	yes	—
268	C₂²×C₁₀₁	#520	1	2	yes	—
269	C₂²×C₁₀₁	D₄²	1	1	yes	characteristic
270	C₂²×C₁₀₁	#546	1	2	yes	—
271	C₂²×C₁₀₁	#547	1	2	yes	—
272	C₂²×C₁₀₁	#548	1	2	yes	—
273	C₂²×C₁₀₁	#551	1	1	yes	characteristic
274	C₂²×C₁₀₁	#551	1	1	yes	characteristic
275	C₂²×C₁₀₁	#552	1	2	yes	—
276	C₂²×C₁₀₁	#553	1	2	yes	—
277	C₂²×C₁₀₁	#556	1	2	yes	—
278	C₂²×C₁₀₁	#559	1	1	yes	characteristic
279	C₄×C₁₀₁	—	2	8	no	—
280	C₄×C₁₀₁	—	2	8	no	—
281	C₄×C₁₀₁	—	2	8	no	—
282	C₄×C₁₀₁	—	2	8	no	—
283	C₄×C₁₀₁	—	4	2	no	—
284	C₄×C₁₀₁	—	4	4	no	—
285	C₄×C₁₀₁	—	4	4	no	—
286	C₄×C₁₀₁	—	4	2	no	—
287	#13823	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₂×C₁₀₁	—	4	4	no	—
289	C₂×C₁₀₁	C₄²×D₄	1	2	yes	—
290	C₂×C₁₀₁	#2274	1	1	yes	characteristic
291	C₂×C₁₀₁	#2358	1	1	yes	characteristic
292	C₂×C₁₀₁	#2359	1	2	yes	—
293	C₂×C₁₀₁	#2361	1	2	yes	—
294	C₂×C₁₀₁	#2362	1	2	yes	—
295	C₂×C₁₀₁	#2367	1	2	yes	—
296	C₂×C₁₀₁	#2373	1	2	yes	—
297	C₂×C₁₀₁	#2374	1	1	yes	characteristic
298	C₂×#388	C₂×C₁₀₁	1	2	yes	—
299	C₂×#385	C₂×C₁₀₁	1	1	yes	characteristic
300	C₂×C₄×C₄⋊C₄	C₂×C₁₀₁	1	2	yes	complemented
301	C₂×C₄×C₂²⋊C₄	C₂×C₁₀₁	1	2	yes	—
302	#1437	C₂×C₁₀₁	1	1	yes	characteristic
303	#1437	C₂×C₁₀₁	1	1	yes	characteristic
304	#1436	C₂×C₁₀₁	1	2	yes	complemented
305	#1436	C₂×C₁₀₁	1	2	yes	complemented
306	C₄×#95	C₂×C₁₀₁	1	2	yes	complemented
307	C₁₀₁	#13823	1	1	yes	characteristic, direct product factor, Sylow
308	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
309	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
310	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
311	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
312	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
313	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
314	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
315	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
316	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
317	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
318	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
319	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
320	#388	C₄×C₁₀₁	1	16	yes	complemented
321	#385	C₄×C₁₀₁	1	8	yes	complemented
322	C₄×C₄⋊C₄	—	2	8	no	—
323	C₄×C₂²⋊C₄	—	2	8	no	—
324	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
325	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
326	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
327	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
328	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
329	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
330	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
331	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
332	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
333	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
334	C₂³×C₄	—	2	4	no	—
335	C₂³×C₄	—	2	4	no	—
336	C₂³×C₄	—	4	1	no	—
337	C₂³×C₄	—	4	1	no	—
338	C₂³×C₄	C₂×C₄×C₁₀₁	1	4	yes	—
339	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
340	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
341	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
342	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
343	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
344	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
345	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
346	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
347	C₂×C₄⋊C₄	—	2	4	no	—
348	C₂×C₄⋊C₄	—	2	4	no	—
349	C₂×C₄⋊C₄	—	2	4	no	—
350	C₂×C₄⋊C₄	—	2	4	no	—
351	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	8	yes	—
352	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	8	yes	complemented
353	C₂×C₂²⋊C₄	—	2	4	no	—
354	C₂×C₂²⋊C₄	—	2	4	no	—
355	C₂×C₂²⋊C₄	—	2	4	no	—
356	C₂×C₂²⋊C₄	—	2	4	no	—
357	C₂×C₂²⋊C₄	—	4	1	no	—
358	C₂×C₂²⋊C₄	—	4	1	no	—
359	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	8	yes	—
360	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	8	yes	—
361	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
362	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
363	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	8	yes	—
364	C₂×C₄²	—	2	4	no	—
365	C₂×C₄²	—	2	4	no	—
366	C₂×C₄²	—	2	4	no	—
367	C₂×C₄²	—	2	4	no	—
368	C₂×C₄²	—	2	4	no	—
369	C₂×C₄²	—	2	4	no	—
370	C₂×C₄²	—	2	4	no	—
371	C₂×C₄²	—	2	4	no	—
372	C₂×C₄²	—	4	1	no	—
373	C₂×C₄²	—	4	1	no	—
374	C₂×C₄²	—	4	2	no	—
375	C₂×C₄²	—	4	2	no	—
376	C₂×C₄²	C₂×C₄×C₁₀₁	1	8	yes	complemented
377	#95	—	2	4	no	—
378	#95	—	2	4	no	—
379	#95	—	2	4	no	—
380	#95	—	4	1	no	—
381	#95	—	4	1	no	—
382	#95	C₂×C₄×C₁₀₁	1	8	yes	—
383	#95	C₂×C₄×C₁₀₁	1	8	yes	complemented
384	#95	C₂×C₄×C₁₀₁	1	8	yes	complemented
385	#95	D₄×C₁₀₁	1	8	yes	—
386	C₂⁴	—	2	2	no	—
387	C₂⁴	—	2	2	no	—
388	C₂⁴	—	2	2	no	—
389	C₂⁴	—	2	2	no	—
390	C₂⁴	—	2	1	no	—
391	C₂⁴	—	2	1	no	—
392	C₂⁴	—	2	2	no	—
393	C₂⁴	C₂²×C₄×C₁₀₁	1	4	yes	—
394	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
395	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	16	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	—	4	8	no	—
436	C₂²×C₄	—	4	4	no	—
437	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
438	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
439	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
440	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
441	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
442	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
443	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
444	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
445	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
446	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
447	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
448	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
449	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
450	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
451	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
452	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
453	C₄⋊C₄	—	2	16	no	—
454	C₄⋊C₄	—	2	16	no	—
455	C₂²⋊C₄	—	2	16	no	—
456	C₂²⋊C₄	—	2	16	no	—
457	C₂²⋊C₄	—	4	4	no	—
458	C₂²⋊C₄	C₄²×C₁₀₁	1	16	yes	complemented
459	C₄²	—	2	16	no	—
460	C₄²	—	4	4	no	—
461	C₄²	—	4	8	no	—
462	C₄²	—	4	8	no	—
463	C₄²	—	4	4	no	—
464	C₂³	—	2	4	no	—
465	C₂³	—	2	4	no	—
466	C₂³	—	2	4	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	2	4	no	—
469	C₂³	—	2	4	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	2	no	—
472	C₂³	—	2	4	no	—
473	C₂³	—	2	4	no	—
474	C₂³	—	4	1	no	—
475	C₂³	—	4	2	no	—
476	C₂³	—	4	2	no	—
477	C₂³	—	4	2	no	—
478	C₂³	—	4	1	no	—
479	C₂³	—	4	1	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	1	no	—
484	C₂³	C₂×C₄²×C₁₀₁	1	4	yes	—
485	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
486	C₂³	C₂³×C₄×C₁₀₁	1	2	yes	—
487	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
488	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
489	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
490	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
491	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
492	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
493	C₂³	2₋¹⁺⁴×C₁₀₁	1	2	yes	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	4	16	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	C₂×C₄²×C₁₀₁	1	8	yes	—
544	C₂×C₄	C₄×D₄×C₁₀₁	1	8	yes	—
545	C₂×C₄	C₄×D₄×C₁₀₁	1	8	yes	—
546	C₂×C₄	C₄×D₄×C₁₀₁	1	8	yes	—
547	C₂²	—	2	8	no	—
548	C₂²	—	2	4	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	4	4	no	—
553	C₂²	—	4	4	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	4	2	no	—
556	C₂²	C₂²×C₄²×C₁₀₁	1	1	yes	characteristic
557	C₂²	C₂×C₄×D₄×C₁₀₁	1	2	yes	—
558	C₂²	C₂×C₄×D₄×C₁₀₁	1	2	yes	—
559	C₂²	C₂×C₄×D₄×C₁₀₁	1	2	yes	—
560	C₂²	C₄×#41×C₁₀₁	1	2	yes	—
561	C₂²	C₄×#41×C₁₀₁	1	2	yes	—
562	C₂²	C₄×#41×C₁₀₁	1	2	yes	—
563	C₂²	#518×C₁₀₁	1	1	yes	characteristic
564	C₂²	#519×C₁₀₁	1	1	yes	characteristic
565	C₂²	#520×C₁₀₁	1	2	yes	—
566	C₂²	#520×C₁₀₁	1	2	yes	—
567	C₂²	D₄²×C₁₀₁	1	1	yes	characteristic
568	C₂²	#546×C₁₀₁	1	2	yes	—
569	C₂²	#547×C₁₀₁	1	2	yes	—
570	C₂²	#548×C₁₀₁	1	2	yes	—
571	C₂²	#551×C₁₀₁	1	1	yes	characteristic
572	C₂²	#551×C₁₀₁	1	1	yes	characteristic
573	C₂²	#552×C₁₀₁	1	2	yes	—
574	C₂²	#553×C₁₀₁	1	2	yes	—
575	C₂²	#556×C₁₀₁	1	2	yes	—
576	C₂²	#559×C₁₀₁	1	1	yes	characteristic
577	C₄	—	2	8	no	—
578	C₄	—	2	8	no	—
579	C₄	—	2	8	no	—
580	C₄	—	2	8	no	—
581	C₄	—	4	2	no	—
582	C₄	—	4	4	no	—
583	C₄	—	4	4	no	—
584	C₄	—	4	2	no	—
585	C₂	—	4	4	no	—
586	C₂	C₄²×D₄×C₁₀₁	1	2	yes	—
587	C₂	C₁₀₁×#2274	1	1	yes	characteristic
588	C₂	C₁₀₁×#2358	1	1	yes	characteristic
589	C₂	C₁₀₁×#2359	1	2	yes	—
590	C₂	C₁₀₁×#2361	1	2	yes	—
591	C₂	C₁₀₁×#2362	1	2	yes	—
592	C₂	C₁₀₁×#2367	1	2	yes	—
593	C₂	C₁₀₁×#2373	1	2	yes	—
594	C₂	C₁₀₁×#2374	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₀₁	C₂⁴
commutator	C₂²	C₂²×C₄²×C₁₀₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
prime radical	C₂⁵×C₁₀₁	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₄⋊C₄×C₁₀₁	C₂	semidirect
7. C₁₀₁×#1436	C₂	semidirect
8. C₁₀₁×#1436	C₂	semidirect
9. C₄×#95×C₁₀₁	C₂	semidirect
22. #388×C₁₀₁	C₄	semidirect
23. #385×C₁₀₁	C₄	semidirect
54. C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	semidirect
78. C₂×C₄²×C₁₀₁	C₂×C₄	semidirect
85. #95×C₁₀₁	C₂×C₄	semidirect
86. #95×C₁₀₁	C₂×C₄	semidirect
160. C₂²⋊C₄×C₁₀₁	C₄²	semidirect
287. #13823	C₁₀₁	direct (N × H)
300. C₂×C₄×C₄⋊C₄	C₂×C₁₀₁	semidirect
304. #1436	C₂×C₁₀₁	semidirect
305. #1436	C₂×C₁₀₁	semidirect
306. C₄×#95	C₂×C₁₀₁	semidirect
307. C₁₀₁	#13823	direct (N × H)
320. #388	C₄×C₁₀₁	semidirect
321. #385	C₄×C₁₀₁	semidirect
352. C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	semidirect
376. C₂×C₄²	C₂×C₄×C₁₀₁	semidirect
383. #95	C₂×C₄×C₁₀₁	semidirect
384. #95	C₂×C₄×C₁₀₁	semidirect
458. C₂²⋊C₄	C₄²×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#388×C₁₀₁	2
C₂×#385×C₁₀₁	2
C₂×C₄×C₄⋊C₄×C₁₀₁	2
C₂×C₄×C₂²⋊C₄×C₁₀₁	2
C₁₀₁×#1437	2
C₁₀₁×#1436	2
C₄×#95×C₁₀₁	2
#13823	101

Subgroups — C101×#13823 #38795974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#13823 #38795974