Subgroups — C₁₀₁×#14256 #38796407

Order 25856.

2554 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#123×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#386×C₁₀₁	C₂	1	2	yes	maximal
4	C₂×#381×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#1441	C₂	1	4	yes	maximal, complemented
6	C₁₀₁×#1439	C₂	1	4	yes	maximal, complemented
7	C₁₀₁×C₂²⋊#95	C₂	1	2	yes	maximal, complemented
8	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₀₁	C₂²	1	2	yes	—
11	C₂×#123×C₁₀₁	—	2	4	no	—
12	C₂×#123×C₁₀₁	—	2	4	no	—
13	C₂×#123×C₁₀₁	C₄	1	8	yes	complemented
14	C₂²×C₄⋊C₄×C₁₀₁	—	2	8	no	—
15	C₂²×C₄⋊C₄×C₁₀₁	—	2	4	no	—
16	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	4	yes	—
17	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	4	yes	—
22	#386×C₁₀₁	—	2	8	no	—
23	#381×C₁₀₁	—	2	4	no	—
24	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
25	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
26	C₂×#95×C₁₀₁	C₂²	1	8	yes	—
27	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
28	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
29	C₂²×D₄×C₁₀₁	—	2	2	no	—
30	C₂²×D₄×C₁₀₁	—	2	2	no	—
31	C₂²×D₄×C₁₀₁	—	2	4	no	—
32	C₂²×D₄×C₁₀₁	—	2	4	no	—
33	C₂²×D₄×C₁₀₁	C₂×C₄	1	4	yes	—
34	C₂³×C₄×C₁₀₁	—	2	4	no	—
35	C₂³×C₄×C₁₀₁	—	2	4	no	—
36	C₂³×C₄×C₁₀₁	—	2	4	no	—
37	C₂³×C₄×C₁₀₁	—	2	4	no	—
38	C₂³×C₄×C₁₀₁	—	4	8	no	—
39	C₂³×C₄×C₁₀₁	C₂×C₄	1	4	yes	—
40	C₂³×C₄×C₁₀₁	D₄	1	4	yes	—
41	C₂³×C₄×C₁₀₁	D₄	1	4	yes	—
42	C₂³×C₄×C₁₀₁	D₄	1	8	yes	—
43	C₂³×C₄×C₁₀₁	C₂³	1	4	yes	—
44	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₀₁	C₂³	1	4	yes	—
47	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
48	#123×C₁₀₁	—	2	32	no	—
49	C₂×C₄⋊C₄×C₁₀₁	—	2	32	no	—
50	C₂×C₄⋊C₄×C₁₀₁	—	2	16	no	—
51	C₂×C₄⋊C₄×C₁₀₁	—	2	8	no	—
52	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	8	yes	complemented
55	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
60	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
61	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
63	C₂×C₂²⋊C₄×C₁₀₁	—	4	8	no	—
64	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
65	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	8	yes	complemented
66	#95×C₁₀₁	—	2	8	no	—
67	#95×C₁₀₁	—	2	8	no	—
68	#95×C₁₀₁	—	4	8	no	—
69	C₂⁴×C₁₀₁	—	2	4	no	—
70	C₂⁴×C₁₀₁	—	2	4	no	—
71	C₂⁴×C₁₀₁	—	2	1	no	—
72	C₂⁴×C₁₀₁	—	2	1	no	—
73	C₂⁴×C₁₀₁	—	2	2	no	—
74	C₂⁴×C₁₀₁	—	2	2	no	—
75	C₂⁴×C₁₀₁	—	2	4	no	—
76	C₂⁴×C₁₀₁	—	2	4	no	—
77	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
78	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
79	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
80	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
81	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	—
82	C₂⁴×C₁₀₁	#41	1	4	yes	—
83	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
84	C₂×D₄×C₁₀₁	—	2	8	no	—
85	C₂×D₄×C₁₀₁	—	2	16	no	—
86	C₂×D₄×C₁₀₁	—	4	4	no	—
87	C₂×D₄×C₁₀₁	—	4	8	no	—
88	C₂×D₄×C₁₀₁	—	4	4	no	—
89	C₂²×C₄×C₁₀₁	—	2	16	no	—
90	C₂²×C₄×C₁₀₁	—	2	8	no	—
91	C₂²×C₄×C₁₀₁	—	2	16	no	—
92	C₂²×C₄×C₁₀₁	—	2	8	no	—
93	C₂²×C₄×C₁₀₁	—	2	4	no	—
94	C₂²×C₄×C₁₀₁	—	2	4	no	—
95	C₂²×C₄×C₁₀₁	—	2	16	no	—
96	C₂²×C₄×C₁₀₁	—	2	2	no	—
97	C₂²×C₄×C₁₀₁	—	2	2	no	—
98	C₂²×C₄×C₁₀₁	—	2	2	no	—
99	C₂²×C₄×C₁₀₁	—	2	4	no	—
100	C₂²×C₄×C₁₀₁	—	2	4	no	—
101	C₂²×C₄×C₁₀₁	—	2	1	no	—
102	C₂²×C₄×C₁₀₁	—	2	1	no	—
103	C₂²×C₄×C₁₀₁	—	2	2	no	—
104	C₂²×C₄×C₁₀₁	—	2	4	no	—
105	C₂²×C₄×C₁₀₁	—	2	8	no	—
106	C₂²×C₄×C₁₀₁	—	2	8	no	—
107	C₂²×C₄×C₁₀₁	—	2	4	no	—
108	C₂²×C₄×C₁₀₁	—	2	4	no	—
109	C₂²×C₄×C₁₀₁	—	2	4	no	—
110	C₂²×C₄×C₁₀₁	—	2	4	no	—
111	C₂²×C₄×C₁₀₁	—	2	8	no	—
112	C₂²×C₄×C₁₀₁	—	2	8	no	—
113	C₂²×C₄×C₁₀₁	—	4	16	no	—
114	C₂²×C₄×C₁₀₁	—	4	16	no	—
115	C₂²×C₄×C₁₀₁	—	4	16	no	—
116	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	16	yes	complemented
117	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
120	C₂²×C₄×C₁₀₁	C₂×D₄	1	8	yes	—
121	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
122	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
123	C₄⋊C₄×C₁₀₁	—	2	32	no	—
124	C₄⋊C₄×C₁₀₁	—	2	16	no	—
125	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
126	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
127	C₂²⋊C₄×C₁₀₁	—	4	16	no	—
128	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
129	C₂³×C₁₀₁	—	2	8	no	—
130	C₂³×C₁₀₁	—	2	8	no	—
131	C₂³×C₁₀₁	—	2	4	no	—
132	C₂³×C₁₀₁	—	2	4	no	—
133	C₂³×C₁₀₁	—	2	8	no	—
134	C₂³×C₁₀₁	—	2	8	no	—
135	C₂³×C₁₀₁	—	2	16	no	—
136	C₂³×C₁₀₁	—	2	2	no	—
137	C₂³×C₁₀₁	—	2	4	no	—
138	C₂³×C₁₀₁	—	2	8	no	—
139	C₂³×C₁₀₁	—	4	1	no	—
140	C₂³×C₁₀₁	—	4	2	no	—
141	C₂³×C₁₀₁	—	4	1	no	—
142	C₂³×C₁₀₁	—	4	4	no	—
143	C₂³×C₁₀₁	—	4	2	no	—
144	C₂³×C₁₀₁	—	4	2	no	—
145	C₂³×C₁₀₁	—	4	4	no	—
146	C₂³×C₁₀₁	—	4	4	no	—
147	C₂³×C₁₀₁	—	4	8	no	—
148	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
149	C₂³×C₁₀₁	C₄×D₄	1	8	yes	—
150	C₂³×C₁₀₁	#120	1	4	yes	—
151	C₂³×C₁₀₁	#121	1	8	yes	—
152	C₂³×C₁₀₁	#123	1	4	yes	—
153	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
154	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
155	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
156	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
157	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
158	C₂³×C₁₀₁	H(5,𝔽₂)	1	4	yes	—
159	C₂³×C₁₀₁	2₋¹⁺⁴	1	4	yes	—
160	D₄×C₁₀₁	—	4	16	no	—
161	C₂×C₄×C₁₀₁	—	2	8	no	—
162	C₂×C₄×C₁₀₁	—	2	4	no	—
163	C₂×C₄×C₁₀₁	—	2	8	no	—
164	C₂×C₄×C₁₀₁	—	2	4	no	—
165	C₂×C₄×C₁₀₁	—	2	32	no	—
166	C₂×C₄×C₁₀₁	—	2	4	no	—
167	C₂×C₄×C₁₀₁	—	2	2	no	—
168	C₂×C₄×C₁₀₁	—	2	4	no	—
169	C₂×C₄×C₁₀₁	—	2	8	no	—
170	C₂×C₄×C₁₀₁	—	2	8	no	—
171	C₂×C₄×C₁₀₁	—	2	8	no	—
172	C₂×C₄×C₁₀₁	—	2	8	no	—
173	C₂×C₄×C₁₀₁	—	4	32	no	—
174	C₂×C₄×C₁₀₁	—	4	1	no	—
175	C₂×C₄×C₁₀₁	—	4	2	no	—
176	C₂×C₄×C₁₀₁	—	4	1	no	—
177	C₂×C₄×C₁₀₁	—	4	8	no	—
178	C₂×C₄×C₁₀₁	—	4	2	no	—
179	C₂×C₄×C₁₀₁	—	4	8	no	—
180	C₂×C₄×C₁₀₁	—	4	2	no	—
181	C₂×C₄×C₁₀₁	—	4	4	no	—
182	C₂×C₄×C₁₀₁	—	4	4	no	—
183	C₂×C₄×C₁₀₁	—	4	4	no	—
184	C₂×C₄×C₁₀₁	—	4	4	no	—
185	C₂×C₄×C₁₀₁	—	4	8	no	—
186	C₂×C₄×C₁₀₁	—	4	8	no	—
187	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	8	yes	—
188	C₂²×C₁₀₁	—	2	8	no	—
189	C₂²×C₁₀₁	—	2	16	no	—
190	C₂²×C₁₀₁	—	2	4	no	—
191	C₂²×C₁₀₁	—	2	4	no	—
192	C₂²×C₁₀₁	—	2	16	no	—
193	C₂²×C₁₀₁	—	2	8	no	—
194	C₂²×C₁₀₁	—	4	4	no	—
195	C₂²×C₁₀₁	—	4	8	no	—
196	C₂²×C₁₀₁	—	4	2	no	—
197	C₂²×C₁₀₁	—	8	1	no	—
198	C₂²×C₁₀₁	—	8	1	no	—
199	C₂²×C₁₀₁	—	8	4	no	—
200	C₂²×C₁₀₁	—	8	2	no	—
201	C₂²×C₁₀₁	#386	1	8	yes	—
202	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
203	C₂²×C₁₀₁	C₂×C₄×D₄	1	2	yes	—
204	C₂²×C₁₀₁	#520	1	4	yes	—
205	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
206	C₂²×C₁₀₁	C₂×#121	1	2	yes	—
207	C₂²×C₁₀₁	C₂×#123	1	1	yes	characteristic
208	C₂²×C₁₀₁	#534	1	4	yes	—
209	C₂²×C₁₀₁	#535	1	2	yes	—
210	C₂²×C₁₀₁	#536	1	2	yes	—
211	C₂²×C₁₀₁	#536	1	4	yes	—
212	C₂²×C₁₀₁	#537	1	4	yes	—
213	C₂²×C₁₀₁	#539	1	8	yes	—
214	C₄×C₁₀₁	—	2	8	no	—
215	C₄×C₁₀₁	—	4	4	no	—
216	C₄×C₁₀₁	—	4	8	no	—
217	C₄×C₁₀₁	—	4	2	no	—
218	C₄×C₁₀₁	—	8	4	no	—
219	#14256	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂×C₁₀₁	—	2	8	no	—
221	C₂×C₁₀₁	—	8	2	no	—
222	C₂×C₁₀₁	C₂×#386	1	1	yes	characteristic
223	C₂×C₁₀₁	#2311	1	2	yes	—
224	C₂×C₁₀₁	#2322	1	4	yes	—
225	C₂×C₁₀₁	#2613	1	1	yes	characteristic
226	C₂×C₁₀₁	#2614	1	1	yes	characteristic
227	C₂×C₁₀₁	#2618	1	4	yes	—
228	C₂×C₁₀₁	#2623	1	2	yes	—
229	C₂²×#123	C₂×C₁₀₁	1	1	yes	characteristic
230	C₂³×C₄⋊C₄	C₂×C₁₀₁	1	1	yes	characteristic, complemented
231	C₂×#386	C₂×C₁₀₁	1	2	yes	—
232	C₂×#381	C₂×C₁₀₁	1	1	yes	characteristic, complemented
233	#1441	C₂×C₁₀₁	1	4	yes	complemented
234	#1439	C₂×C₁₀₁	1	4	yes	complemented
235	C₂²⋊#95	C₂×C₁₀₁	1	2	yes	complemented
236	C₁₀₁	#14256	1	1	yes	characteristic, direct product factor, Sylow
237	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
238	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
239	C₂⁴×C₄	C₂²×C₁₀₁	1	2	yes	—
240	C₂×#123	—	2	4	no	—
241	C₂×#123	—	2	4	no	—
242	C₂×#123	C₄×C₁₀₁	1	8	yes	complemented
243	C₂²×C₄⋊C₄	—	2	8	no	—
244	C₂²×C₄⋊C₄	—	2	4	no	—
245	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	4	yes	—
246	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
247	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
248	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
249	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
250	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	4	yes	—
251	#386	—	2	8	no	—
252	#381	—	2	4	no	—
253	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
254	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
255	C₂×#95	C₂²×C₁₀₁	1	8	yes	—
256	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
257	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
258	C₂²×D₄	—	2	2	no	—
259	C₂²×D₄	—	2	2	no	—
260	C₂²×D₄	—	2	4	no	—
261	C₂²×D₄	—	2	4	no	—
262	C₂²×D₄	C₂×C₄×C₁₀₁	1	4	yes	—
263	C₂³×C₄	—	2	4	no	—
264	C₂³×C₄	—	2	4	no	—
265	C₂³×C₄	—	2	4	no	—
266	C₂³×C₄	—	2	4	no	—
267	C₂³×C₄	—	4	8	no	—
268	C₂³×C₄	C₂×C₄×C₁₀₁	1	4	yes	—
269	C₂³×C₄	D₄×C₁₀₁	1	4	yes	—
270	C₂³×C₄	D₄×C₁₀₁	1	4	yes	—
271	C₂³×C₄	D₄×C₁₀₁	1	8	yes	—
272	C₂³×C₄	C₂³×C₁₀₁	1	4	yes	—
273	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
274	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
275	C₂³×C₄	C₂³×C₁₀₁	1	4	yes	—
276	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
277	#123	—	2	32	no	—
278	C₂×C₄⋊C₄	—	2	32	no	—
279	C₂×C₄⋊C₄	—	2	16	no	—
280	C₂×C₄⋊C₄	—	2	8	no	—
281	C₂×C₄⋊C₄	—	2	4	no	—
282	C₂×C₄⋊C₄	—	2	4	no	—
283	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	8	yes	complemented
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	4	no	—
287	C₂×C₂²⋊C₄	—	2	4	no	—
288	C₂×C₂²⋊C₄	—	2	4	no	—
289	C₂×C₂²⋊C₄	—	2	4	no	—
290	C₂×C₂²⋊C₄	—	2	4	no	—
291	C₂×C₂²⋊C₄	—	2	8	no	—
292	C₂×C₂²⋊C₄	—	4	8	no	—
293	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
294	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	8	yes	complemented
295	#95	—	2	8	no	—
296	#95	—	2	8	no	—
297	#95	—	4	8	no	—
298	C₂⁴	—	2	4	no	—
299	C₂⁴	—	2	4	no	—
300	C₂⁴	—	2	1	no	—
301	C₂⁴	—	2	1	no	—
302	C₂⁴	—	2	2	no	—
303	C₂⁴	—	2	2	no	—
304	C₂⁴	—	2	4	no	—
305	C₂⁴	—	2	4	no	—
306	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
307	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
308	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
309	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
310	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	—
311	C₂⁴	#41×C₁₀₁	1	4	yes	—
312	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
313	C₂×D₄	—	2	8	no	—
314	C₂×D₄	—	2	16	no	—
315	C₂×D₄	—	4	4	no	—
316	C₂×D₄	—	4	8	no	—
317	C₂×D₄	—	4	4	no	—
318	C₂²×C₄	—	2	16	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	2	16	no	—
321	C₂²×C₄	—	2	8	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	16	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	—	2	8	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	8	no	—
341	C₂²×C₄	—	2	8	no	—
342	C₂²×C₄	—	4	16	no	—
343	C₂²×C₄	—	4	16	no	—
344	C₂²×C₄	—	4	16	no	—
345	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	16	yes	complemented
346	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
347	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
348	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
349	C₂²×C₄	C₂×D₄×C₁₀₁	1	8	yes	—
350	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
351	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
352	C₄⋊C₄	—	2	32	no	—
353	C₄⋊C₄	—	2	16	no	—
354	C₂²⋊C₄	—	2	8	no	—
355	C₂²⋊C₄	—	2	16	no	—
356	C₂²⋊C₄	—	4	16	no	—
357	C₂²⋊C₄	—	4	8	no	—
358	C₂³	—	2	8	no	—
359	C₂³	—	2	8	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	8	no	—
363	C₂³	—	2	8	no	—
364	C₂³	—	2	16	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	4	no	—
367	C₂³	—	2	8	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	4	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	—	4	4	no	—
375	C₂³	—	4	4	no	—
376	C₂³	—	4	8	no	—
377	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
378	C₂³	C₄×D₄×C₁₀₁	1	8	yes	—
379	C₂³	#120×C₁₀₁	1	4	yes	—
380	C₂³	#121×C₁₀₁	1	8	yes	—
381	C₂³	#123×C₁₀₁	1	4	yes	—
382	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
383	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
384	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
385	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
386	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
387	C₂³	H(5,𝔽₂)×C₁₀₁	1	4	yes	—
388	C₂³	2₋¹⁺⁴×C₁₀₁	1	4	yes	—
389	D₄	—	4	16	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	32	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	4	32	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	8	no	—
407	C₂×C₄	—	4	8	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	8	no	—
415	C₂×C₄	—	4	8	no	—
416	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	8	yes	—
417	C₂²	—	2	8	no	—
418	C₂²	—	2	16	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	2	16	no	—
422	C₂²	—	2	8	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	4	8	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	4	no	—
429	C₂²	—	8	2	no	—
430	C₂²	#386×C₁₀₁	1	8	yes	—
431	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
432	C₂²	C₂×C₄×D₄×C₁₀₁	1	2	yes	—
433	C₂²	#520×C₁₀₁	1	4	yes	—
434	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
435	C₂²	C₂×#121×C₁₀₁	1	2	yes	—
436	C₂²	C₂×#123×C₁₀₁	1	1	yes	characteristic
437	C₂²	#534×C₁₀₁	1	4	yes	—
438	C₂²	#535×C₁₀₁	1	2	yes	—
439	C₂²	#536×C₁₀₁	1	2	yes	—
440	C₂²	#536×C₁₀₁	1	4	yes	—
441	C₂²	#537×C₁₀₁	1	4	yes	—
442	C₂²	#539×C₁₀₁	1	8	yes	—
443	C₄	—	2	8	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	4	no	—
446	C₄	—	4	8	no	—
447	C₄	—	8	4	no	—
448	C₂	—	2	8	no	—
449	C₂	—	8	2	no	—
450	C₂	C₂×#386×C₁₀₁	1	1	yes	characteristic
451	C₂	C₁₀₁×#2311	1	2	yes	—
452	C₂	C₁₀₁×#2322	1	4	yes	—
453	C₂	C₁₀₁×#2613	1	1	yes	characteristic
454	C₂	C₁₀₁×#2614	1	1	yes	characteristic
455	C₂	C₁₀₁×#2618	1	4	yes	—
456	C₂	C₁₀₁×#2623	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₀₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
prime radical	C₂³×D₄×C₁₀₁	C₂²
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
2. C₂³×C₄⋊C₄×C₁₀₁	C₂	semidirect
4. C₂×#381×C₁₀₁	C₂	semidirect
5. C₁₀₁×#1441	C₂	semidirect
6. C₁₀₁×#1439	C₂	semidirect
7. C₁₀₁×C₂²⋊#95	C₂	semidirect
13. C₂×#123×C₁₀₁	C₄	semidirect
54. C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	semidirect
65. C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	semidirect
116. C₂²×C₄×C₁₀₁	C₂²⋊C₄	semidirect
219. #14256	C₁₀₁	direct (N × H)
230. C₂³×C₄⋊C₄	C₂×C₁₀₁	semidirect
232. C₂×#381	C₂×C₁₀₁	semidirect
233. #1441	C₂×C₁₀₁	semidirect
234. #1439	C₂×C₁₀₁	semidirect
235. C₂²⋊#95	C₂×C₁₀₁	semidirect
236. C₁₀₁	#14256	direct (N × H)
242. C₂×#123	C₄×C₁₀₁	semidirect
283. C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	semidirect
294. C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	semidirect
345. C₂²×C₄	C₂²⋊C₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#123×C₁₀₁	2
C₂³×C₄⋊C₄×C₁₀₁	2
C₂×#386×C₁₀₁	2
C₂×#381×C₁₀₁	2
C₁₀₁×#1441	2
C₁₀₁×#1439	2
C₁₀₁×C₂²⋊#95	2
#14256	101

Subgroups — C101×#14256 #38796407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#14256 #38796407