Subgroups — C₁₀₁×#15250 #38797401

Order 25856.

1778 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#390×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#389×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#388×C₁₀₁	C₂	1	4	yes	maximal, complemented
4	C₁₀₁×#1445	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1439	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1439	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1438	C₂	1	2	yes	maximal
8	C₄×#95×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	4	yes	—
15	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	4	yes	—
18	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
20	#390×C₁₀₁	—	2	4	no	—
21	#389×C₁₀₁	—	2	4	no	—
22	#388×C₁₀₁	—	2	16	no	—
23	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
24	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
25	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
26	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
27	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
28	C₂⁵×C₁₀₁	C₂³	1	2	yes	—
29	C₂²×D₄×C₁₀₁	—	2	4	no	—
30	C₂²×D₄×C₁₀₁	—	2	2	no	—
31	C₂²×D₄×C₁₀₁	—	2	4	no	—
32	C₂²×D₄×C₁₀₁	—	4	2	no	—
33	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
34	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
35	C₂³×C₄×C₁₀₁	C₂³	1	4	yes	—
36	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
42	C₂×C₄⋊C₄×C₁₀₁	—	2	8	no	—
43	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
47	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
48	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
49	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
50	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
51	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
52	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
53	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
54	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
55	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₁₀₁	—	4	4	no	—
58	C₂×C₂²⋊C₄×C₁₀₁	—	4	4	no	—
59	C₂×C₄²×C₁₀₁	—	4	2	no	—
60	C₂×C₄²×C₁₀₁	—	4	2	no	—
61	C₂×C₄²×C₁₀₁	—	4	2	no	—
62	C₂×C₄²×C₁₀₁	D₄	1	4	yes	—
63	C₂×C₄²×C₁₀₁	D₄	1	8	yes	complemented
64	#95×C₁₀₁	—	2	8	no	—
65	#95×C₁₀₁	—	2	8	no	—
66	#95×C₁₀₁	—	2	4	no	—
67	#95×C₁₀₁	—	2	4	no	—
68	#95×C₁₀₁	—	2	4	no	—
69	C₂⁴×C₁₀₁	—	2	4	no	—
70	C₂⁴×C₁₀₁	—	2	2	no	—
71	C₂⁴×C₁₀₁	—	2	4	no	—
72	C₂⁴×C₁₀₁	—	2	2	no	—
73	C₂⁴×C₁₀₁	—	2	2	no	—
74	C₂⁴×C₁₀₁	—	2	2	no	—
75	C₂⁴×C₁₀₁	—	2	4	no	—
76	C₂⁴×C₁₀₁	—	2	2	no	—
77	C₂⁴×C₁₀₁	—	2	4	no	—
78	C₂⁴×C₁₀₁	—	2	2	no	—
79	C₂⁴×C₁₀₁	#41	1	4	yes	—
80	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
81	C₂×D₄×C₁₀₁	—	2	8	no	—
82	C₂×D₄×C₁₀₁	—	4	16	no	—
83	C₂×D₄×C₁₀₁	—	4	4	no	—
84	C₂×D₄×C₁₀₁	—	4	4	no	—
85	C₂²×C₄×C₁₀₁	—	2	2	no	—
86	C₂²×C₄×C₁₀₁	—	2	2	no	—
87	C₂²×C₄×C₁₀₁	—	2	2	no	—
88	C₂²×C₄×C₁₀₁	—	2	1	no	—
89	C₂²×C₄×C₁₀₁	—	2	2	no	—
90	C₂²×C₄×C₁₀₁	—	2	2	no	—
91	C₂²×C₄×C₁₀₁	—	2	1	no	—
92	C₂²×C₄×C₁₀₁	—	2	4	no	—
93	C₂²×C₄×C₁₀₁	—	2	2	no	—
94	C₂²×C₄×C₁₀₁	—	2	4	no	—
95	C₂²×C₄×C₁₀₁	—	2	4	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	2	no	—
100	C₂²×C₄×C₁₀₁	—	2	4	no	—
101	C₂²×C₄×C₁₀₁	—	2	4	no	—
102	C₂²×C₄×C₁₀₁	—	2	4	no	—
103	C₂²×C₄×C₁₀₁	—	2	4	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	4	no	—
109	C₂²×C₄×C₁₀₁	—	2	2	no	—
110	C₂²×C₄×C₁₀₁	—	2	4	no	—
111	C₂²×C₄×C₁₀₁	—	2	2	no	—
112	C₂²×C₄×C₁₀₁	C₂×D₄	1	8	yes	—
113	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
117	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
118	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
119	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
120	C₄⋊C₄×C₁₀₁	—	2	8	no	—
121	C₄⋊C₄×C₁₀₁	—	4	4	no	—
122	C₄⋊C₄×C₁₀₁	—	4	4	no	—
123	C₄⋊C₄×C₁₀₁	—	4	8	no	—
124	C₂²⋊C₄×C₁₀₁	—	2	32	no	—
125	C₂²⋊C₄×C₁₀₁	—	4	16	no	—
126	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
127	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
128	C₄²×C₁₀₁	—	4	4	no	—
129	C₄²×C₁₀₁	—	4	8	no	—
130	C₂³×C₁₀₁	—	2	8	no	—
131	C₂³×C₁₀₁	—	2	4	no	—
132	C₂³×C₁₀₁	—	2	8	no	—
133	C₂³×C₁₀₁	—	2	4	no	—
134	C₂³×C₁₀₁	—	2	4	no	—
135	C₂³×C₁₀₁	—	4	2	no	—
136	C₂³×C₁₀₁	—	4	4	no	—
137	C₂³×C₁₀₁	—	4	2	no	—
138	C₂³×C₁₀₁	—	4	2	no	—
139	C₂³×C₁₀₁	—	4	2	no	—
140	C₂³×C₁₀₁	—	4	4	no	—
141	C₂³×C₁₀₁	—	4	4	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	2	no	—
148	C₂³×C₁₀₁	—	4	2	no	—
149	C₂³×C₁₀₁	—	4	4	no	—
150	C₂³×C₁₀₁	—	4	4	no	—
151	C₂³×C₁₀₁	—	4	4	no	—
152	C₂³×C₁₀₁	—	4	4	no	—
153	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
154	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
155	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
156	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
157	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
158	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
159	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
160	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂³×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
162	D₄×C₁₀₁	—	4	16	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	2	no	—
167	C₂×C₄×C₁₀₁	—	2	4	no	—
168	C₂×C₄×C₁₀₁	—	2	2	no	—
169	C₂×C₄×C₁₀₁	—	2	2	no	—
170	C₂×C₄×C₁₀₁	—	2	4	no	—
171	C₂×C₄×C₁₀₁	—	2	8	no	—
172	C₂×C₄×C₁₀₁	—	2	8	no	—
173	C₂×C₄×C₁₀₁	—	2	8	no	—
174	C₂×C₄×C₁₀₁	—	2	8	no	—
175	C₂×C₄×C₁₀₁	—	2	4	no	—
176	C₂×C₄×C₁₀₁	—	2	8	no	—
177	C₂×C₄×C₁₀₁	—	2	8	no	—
178	C₂×C₄×C₁₀₁	—	4	2	no	—
179	C₂×C₄×C₁₀₁	—	4	4	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	2	no	—
186	C₂×C₄×C₁₀₁	—	4	2	no	—
187	C₂×C₄×C₁₀₁	—	4	2	no	—
188	C₂×C₄×C₁₀₁	—	4	2	no	—
189	C₂×C₄×C₁₀₁	—	4	4	no	—
190	C₂×C₄×C₁₀₁	—	4	4	no	—
191	C₂×C₄×C₁₀₁	—	4	4	no	—
192	C₂×C₄×C₁₀₁	—	4	2	no	—
193	C₂×C₄×C₁₀₁	—	4	2	no	—
194	C₂×C₄×C₁₀₁	—	4	4	no	—
195	C₂×C₄×C₁₀₁	#124	1	4	yes	—
196	C₂×C₄×C₁₀₁	#124	1	4	yes	—
197	C₂×C₄×C₁₀₁	#127	1	4	yes	—
198	C₂²×C₁₀₁	—	4	4	no	—
199	C₂²×C₁₀₁	—	4	4	no	—
200	C₂²×C₁₀₁	—	4	8	no	—
201	C₂²×C₁₀₁	—	4	8	no	—
202	C₂²×C₁₀₁	—	4	4	no	—
203	C₂²×C₁₀₁	—	8	2	no	—
204	C₂²×C₁₀₁	—	8	2	no	—
205	C₂²×C₁₀₁	—	8	4	no	—
206	C₂²×C₁₀₁	—	8	4	no	—
207	C₂²×C₁₀₁	—	8	2	no	—
208	C₂²×C₁₀₁	—	8	2	no	—
209	C₂²×C₁₀₁	#525	1	1	yes	characteristic
210	C₂²×C₁₀₁	#525	1	1	yes	characteristic
211	C₂²×C₁₀₁	#525	1	4	yes	—
212	C₂²×C₁₀₁	C₂×#124	1	1	yes	characteristic
213	C₂²×C₁₀₁	C₂×#124	1	1	yes	characteristic
214	C₂²×C₁₀₁	C₂×#127	1	1	yes	characteristic
215	C₂²×C₁₀₁	#532	1	4	yes	—
216	C₂²×C₁₀₁	#534	1	1	yes	characteristic
217	C₂²×C₁₀₁	#534	1	2	yes	—
218	C₂²×C₁₀₁	#537	1	1	yes	characteristic
219	C₂²×C₁₀₁	#537	1	2	yes	—
220	C₂²×C₁₀₁	#551	1	4	yes	—
221	C₂²×C₁₀₁	#552	1	2	yes	—
222	C₂²×C₁₀₁	#553	1	2	yes	—
223	C₂²×C₁₀₁	#553	1	4	yes	—
224	C₂²×C₁₀₁	#556	1	2	yes	—
225	C₂²×C₁₀₁	#559	1	2	yes	—
226	C₄×C₁₀₁	—	2	4	no	—
227	C₄×C₁₀₁	—	2	4	no	—
228	C₄×C₁₀₁	—	2	4	no	—
229	C₄×C₁₀₁	—	4	8	no	—
230	C₄×C₁₀₁	—	4	4	no	—
231	C₄×C₁₀₁	—	8	2	no	—
232	C₄×C₁₀₁	—	8	2	no	—
233	#15250	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂×C₁₀₁	—	8	4	no	—
235	C₂×C₁₀₁	#2397	1	1	yes	characteristic
236	C₂×C₁₀₁	#2561	1	1	yes	characteristic
237	C₂×C₁₀₁	#2562	1	1	yes	characteristic
238	C₂×C₁₀₁	#2591	1	1	yes	characteristic
239	C₂×C₁₀₁	#2592	1	1	yes	characteristic
240	C₂×C₁₀₁	#2601	1	4	yes	—
241	C₂×C₁₀₁	#2602	1	4	yes	—
242	C₂×C₁₀₁	#2656	1	1	yes	characteristic
243	C₂×C₁₀₁	#2858	1	1	yes	characteristic
244	C₂×#390	C₂×C₁₀₁	1	1	yes	characteristic
245	C₂×#389	C₂×C₁₀₁	1	1	yes	characteristic, complemented
246	C₂×#388	C₂×C₁₀₁	1	4	yes	complemented
247	#1445	C₂×C₁₀₁	1	2	yes	complemented
248	#1439	C₂×C₁₀₁	1	2	yes	complemented
249	#1439	C₂×C₁₀₁	1	2	yes	complemented
250	#1438	C₂×C₁₀₁	1	2	yes	—
251	C₄×#95	C₂×C₁₀₁	1	1	yes	characteristic, complemented
252	C₁₀₁	#15250	1	1	yes	characteristic, direct product factor, Sylow
253	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
254	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
255	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
256	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
257	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
258	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	4	yes	—
259	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
260	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
261	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	4	yes	—
262	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
263	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
264	#390	—	2	4	no	—
265	#389	—	2	4	no	—
266	#388	—	2	16	no	—
267	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
268	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
269	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
270	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
271	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
272	C₂⁵	C₂³×C₁₀₁	1	2	yes	—
273	C₂²×D₄	—	2	4	no	—
274	C₂²×D₄	—	2	2	no	—
275	C₂²×D₄	—	2	4	no	—
276	C₂²×D₄	—	4	2	no	—
277	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
278	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
279	C₂³×C₄	C₂³×C₁₀₁	1	4	yes	—
280	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
281	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
282	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
283	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	4	no	—
286	C₂×C₄⋊C₄	—	2	8	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	4	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	4	no	—
291	C₂×C₄⋊C₄	—	4	2	no	—
292	C₂×C₂²⋊C₄	—	2	8	no	—
293	C₂×C₂²⋊C₄	—	2	8	no	—
294	C₂×C₂²⋊C₄	—	2	8	no	—
295	C₂×C₂²⋊C₄	—	2	8	no	—
296	C₂×C₂²⋊C₄	—	2	8	no	—
297	C₂×C₂²⋊C₄	—	2	4	no	—
298	C₂×C₂²⋊C₄	—	2	4	no	—
299	C₂×C₂²⋊C₄	—	2	4	no	—
300	C₂×C₂²⋊C₄	—	2	4	no	—
301	C₂×C₂²⋊C₄	—	4	4	no	—
302	C₂×C₂²⋊C₄	—	4	4	no	—
303	C₂×C₄²	—	4	2	no	—
304	C₂×C₄²	—	4	2	no	—
305	C₂×C₄²	—	4	2	no	—
306	C₂×C₄²	D₄×C₁₀₁	1	4	yes	—
307	C₂×C₄²	D₄×C₁₀₁	1	8	yes	complemented
308	#95	—	2	8	no	—
309	#95	—	2	8	no	—
310	#95	—	2	4	no	—
311	#95	—	2	4	no	—
312	#95	—	2	4	no	—
313	C₂⁴	—	2	4	no	—
314	C₂⁴	—	2	2	no	—
315	C₂⁴	—	2	4	no	—
316	C₂⁴	—	2	2	no	—
317	C₂⁴	—	2	2	no	—
318	C₂⁴	—	2	2	no	—
319	C₂⁴	—	2	4	no	—
320	C₂⁴	—	2	2	no	—
321	C₂⁴	—	2	4	no	—
322	C₂⁴	—	2	2	no	—
323	C₂⁴	#41×C₁₀₁	1	4	yes	—
324	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
325	C₂×D₄	—	2	8	no	—
326	C₂×D₄	—	4	16	no	—
327	C₂×D₄	—	4	4	no	—
328	C₂×D₄	—	4	4	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	C₂×D₄×C₁₀₁	1	8	yes	—
357	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
359	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
361	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
362	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
363	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
364	C₄⋊C₄	—	2	8	no	—
365	C₄⋊C₄	—	4	4	no	—
366	C₄⋊C₄	—	4	4	no	—
367	C₄⋊C₄	—	4	8	no	—
368	C₂²⋊C₄	—	2	32	no	—
369	C₂²⋊C₄	—	4	16	no	—
370	C₂²⋊C₄	—	4	8	no	—
371	C₂²⋊C₄	—	4	8	no	—
372	C₄²	—	4	4	no	—
373	C₄²	—	4	8	no	—
374	C₂³	—	2	8	no	—
375	C₂³	—	2	4	no	—
376	C₂³	—	2	8	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	2	4	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	4	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	4	4	no	—
385	C₂³	—	4	4	no	—
386	C₂³	—	4	4	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	4	no	—
390	C₂³	—	4	4	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	4	no	—
394	C₂³	—	4	4	no	—
395	C₂³	—	4	4	no	—
396	C₂³	—	4	4	no	—
397	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
398	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
399	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
400	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
401	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
402	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
403	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
404	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
405	C₂³	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
406	D₄	—	4	16	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	—	2	8	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	8	no	—
421	C₂×C₄	—	2	8	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	4	4	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	#124×C₁₀₁	1	4	yes	—
440	C₂×C₄	#124×C₁₀₁	1	4	yes	—
441	C₂×C₄	#127×C₁₀₁	1	4	yes	—
442	C₂²	—	4	4	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	4	8	no	—
446	C₂²	—	4	8	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	2	no	—
449	C₂²	—	8	2	no	—
450	C₂²	—	8	4	no	—
451	C₂²	—	8	4	no	—
452	C₂²	—	8	2	no	—
453	C₂²	#525×C₁₀₁	1	1	yes	characteristic
454	C₂²	#525×C₁₀₁	1	1	yes	characteristic
455	C₂²	#525×C₁₀₁	1	4	yes	—
456	C₂²	C₂×#124×C₁₀₁	1	1	yes	characteristic
457	C₂²	C₂×#124×C₁₀₁	1	1	yes	characteristic
458	C₂²	C₂×#127×C₁₀₁	1	1	yes	characteristic
459	C₂²	#532×C₁₀₁	1	4	yes	—
460	C₂²	#534×C₁₀₁	1	1	yes	characteristic
461	C₂²	#534×C₁₀₁	1	2	yes	—
462	C₂²	#537×C₁₀₁	1	1	yes	characteristic
463	C₂²	#537×C₁₀₁	1	2	yes	—
464	C₂²	#551×C₁₀₁	1	4	yes	—
465	C₂²	#552×C₁₀₁	1	2	yes	—
466	C₂²	#553×C₁₀₁	1	2	yes	—
467	C₂²	#553×C₁₀₁	1	4	yes	—
468	C₂²	#556×C₁₀₁	1	2	yes	—
469	C₂²	#559×C₁₀₁	1	2	yes	—
470	C₄	—	2	4	no	—
471	C₄	—	2	4	no	—
472	C₄	—	2	4	no	—
473	C₄	—	4	4	no	—
474	C₄	—	4	8	no	—
475	C₄	—	8	2	no	—
476	C₄	—	8	2	no	—
477	C₂	—	8	4	no	—
478	C₂	C₁₀₁×#2397	1	1	yes	characteristic
479	C₂	C₁₀₁×#2561	1	1	yes	characteristic
480	C₂	C₁₀₁×#2562	1	1	yes	characteristic
481	C₂	C₁₀₁×#2591	1	1	yes	characteristic
482	C₂	C₁₀₁×#2592	1	1	yes	characteristic
483	C₂	C₁₀₁×#2601	1	4	yes	—
484	C₂	C₁₀₁×#2602	1	4	yes	—
485	C₂	C₁₀₁×#2656	1	1	yes	characteristic
486	C₂	C₁₀₁×#2858	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₀₁	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
prime radical	C₂³×D₄×C₁₀₁	C₂²
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#389×C₁₀₁	C₂	semidirect
3. C₂×#388×C₁₀₁	C₂	semidirect
4. C₁₀₁×#1445	C₂	semidirect
5. C₁₀₁×#1439	C₂	semidirect
6. C₁₀₁×#1439	C₂	semidirect
8. C₄×#95×C₁₀₁	C₂	semidirect
63. C₂×C₄²×C₁₀₁	D₄	semidirect
233. #15250	C₁₀₁	direct (N × H)
245. C₂×#389	C₂×C₁₀₁	semidirect
246. C₂×#388	C₂×C₁₀₁	semidirect
247. #1445	C₂×C₁₀₁	semidirect
248. #1439	C₂×C₁₀₁	semidirect
249. #1439	C₂×C₁₀₁	semidirect
251. C₄×#95	C₂×C₁₀₁	semidirect
252. C₁₀₁	#15250	direct (N × H)
307. C₂×C₄²	D₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#390×C₁₀₁	2
C₂×#389×C₁₀₁	2
C₂×#388×C₁₀₁	2
C₁₀₁×#1445	2
C₁₀₁×#1439	2
C₁₀₁×#1438	2
C₄×#95×C₁₀₁	2
#15250	101

Subgroups — C101×#15250 #38797401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#15250 #38797401