Subgroups — C₁₀₁×#15521 #38797672

Order 25856.

1218 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#400×C₁₀₁	C₂	1	2	yes	maximal
2	C₂×#389×C₁₀₁	C₂	1	2	yes	maximal
3	C₁₀₁×#1445	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#1444	C₂	1	1	yes	maximal, characteristic
5	C₁₀₁×#1444	C₂	1	2	yes	maximal
6	C₁₀₁×#1442	C₂	1	2	yes	maximal
7	C₁₀₁×#1442	C₂	1	1	yes	maximal, characteristic
8	C₁₀₁×#1436	C₂	1	2	yes	maximal
9	C₁₀₁×#1434	C₂	1	2	yes	maximal
10	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
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	2	yes	—
14	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
17	#400×C₁₀₁	—	2	8	no	—
18	#389×C₁₀₁	—	2	8	no	—
19	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
20	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
21	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
22	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
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	2	yes	—
27	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
33	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
34	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
35	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
42	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
43	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
44	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
46	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
47	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
48	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
53	C₂×C₄⋊C₄×C₁₀₁	—	4	1	no	—
54	C₂×C₄⋊C₄×C₁₀₁	—	4	1	no	—
55	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
56	C₂×C₄⋊C₄×C₁₀₁	—	4	1	no	—
57	C₂×C₄⋊C₄×C₁₀₁	—	4	1	no	—
58	C₂×C₄²×C₁₀₁	—	2	4	no	—
59	C₂×C₄²×C₁₀₁	—	2	4	no	—
60	C₂×C₄²×C₁₀₁	—	4	2	no	—
61	#95×C₁₀₁	—	2	4	no	—
62	#95×C₁₀₁	—	2	4	no	—
63	#95×C₁₀₁	—	2	4	no	—
64	#95×C₁₀₁	—	2	4	no	—
65	#95×C₁₀₁	—	2	4	no	—
66	#95×C₁₀₁	—	2	4	no	—
67	#95×C₁₀₁	—	2	4	no	—
68	#95×C₁₀₁	—	2	4	no	—
69	#95×C₁₀₁	—	2	2	no	—
70	#95×C₁₀₁	—	2	4	no	—
71	#95×C₁₀₁	—	4	1	no	—
72	#95×C₁₀₁	—	4	1	no	—
73	#95×C₁₀₁	D₄	1	8	yes	—
74	#95×C₁₀₁	Q₈	1	4	yes	—
75	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
76	C₂²×C₄×C₁₀₁	—	2	2	no	—
77	C₂²×C₄×C₁₀₁	—	2	2	no	—
78	C₂²×C₄×C₁₀₁	—	2	2	no	—
79	C₂²×C₄×C₁₀₁	—	2	2	no	—
80	C₂²×C₄×C₁₀₁	—	2	2	no	—
81	C₂²×C₄×C₁₀₁	—	2	2	no	—
82	C₂²×C₄×C₁₀₁	—	2	2	no	—
83	C₂²×C₄×C₁₀₁	—	2	2	no	—
84	C₂²×C₄×C₁₀₁	—	2	2	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	2	no	—
89	C₂²×C₄×C₁₀₁	—	2	2	no	—
90	C₂²×C₄×C₁₀₁	—	2	2	no	—
91	C₂²×C₄×C₁₀₁	—	2	2	no	—
92	C₂²×C₄×C₁₀₁	—	2	2	no	—
93	C₂²×C₄×C₁₀₁	—	2	2	no	—
94	C₂²×C₄×C₁₀₁	—	2	2	no	—
95	C₂²×C₄×C₁₀₁	—	2	1	no	—
96	C₂²×C₄×C₁₀₁	—	2	1	no	—
97	C₂²×C₄×C₁₀₁	—	2	1	no	—
98	C₂²×C₄×C₁₀₁	—	2	1	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	1	no	—
105	C₂²×C₄×C₁₀₁	—	2	1	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	C₂×D₄	1	4	yes	—
125	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
128	C₂²×C₄×C₁₀₁	C₂×Q₈	1	4	yes	—
129	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
130	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
131	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
132	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
133	C₄⋊C₄×C₁₀₁	—	2	16	no	—
134	C₄⋊C₄×C₁₀₁	—	4	8	no	—
135	C₄⋊C₄×C₁₀₁	—	4	4	no	—
136	C₄⋊C₄×C₁₀₁	—	4	4	no	—
137	C₄⋊C₄×C₁₀₁	—	4	8	no	—
138	C₄⋊C₄×C₁₀₁	—	4	4	no	—
139	C₄²×C₁₀₁	—	4	8	no	—
140	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
141	C₂³×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
142	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
143	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
144	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
145	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
146	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
147	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
148	C₂³×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
149	C₂³×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
150	C₂³×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
151	C₂×C₄×C₁₀₁	—	2	4	no	—
152	C₂×C₄×C₁₀₁	—	2	4	no	—
153	C₂×C₄×C₁₀₁	—	2	4	no	—
154	C₂×C₄×C₁₀₁	—	2	4	no	—
155	C₂×C₄×C₁₀₁	—	2	4	no	—
156	C₂×C₄×C₁₀₁	—	2	4	no	—
157	C₂×C₄×C₁₀₁	—	2	4	no	—
158	C₂×C₄×C₁₀₁	—	2	4	no	—
159	C₂×C₄×C₁₀₁	—	2	4	no	—
160	C₂×C₄×C₁₀₁	—	2	4	no	—
161	C₂×C₄×C₁₀₁	—	2	2	no	—
162	C₂×C₄×C₁₀₁	—	2	2	no	—
163	C₂×C₄×C₁₀₁	—	2	2	no	—
164	C₂×C₄×C₁₀₁	—	2	4	no	—
165	C₂×C₄×C₁₀₁	—	2	4	no	—
166	C₂×C₄×C₁₀₁	—	2	4	no	—
167	C₂×C₄×C₁₀₁	—	2	4	no	—
168	C₂×C₄×C₁₀₁	—	2	4	no	—
169	C₂×C₄×C₁₀₁	—	2	4	no	—
170	C₂×C₄×C₁₀₁	—	2	4	no	—
171	C₂×C₄×C₁₀₁	—	2	4	no	—
172	C₂×C₄×C₁₀₁	—	4	2	no	—
173	C₂×C₄×C₁₀₁	—	4	2	no	—
174	C₂×C₄×C₁₀₁	—	4	2	no	—
175	C₂×C₄×C₁₀₁	—	4	2	no	—
176	C₂×C₄×C₁₀₁	—	4	2	no	—
177	C₂×C₄×C₁₀₁	—	4	2	no	—
178	C₂×C₄×C₁₀₁	—	4	2	no	—
179	C₂×C₄×C₁₀₁	—	4	2	no	—
180	C₂×C₄×C₁₀₁	—	4	1	no	—
181	C₂×C₄×C₁₀₁	—	4	1	no	—
182	C₂×C₄×C₁₀₁	—	4	2	no	—
183	C₂×C₄×C₁₀₁	—	4	2	no	—
184	C₂×C₄×C₁₀₁	—	4	2	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	1	no	—
189	C₂×C₄×C₁₀₁	—	4	1	no	—
190	C₂×C₄×C₁₀₁	—	4	1	no	—
191	C₂×C₄×C₁₀₁	—	4	2	no	—
192	C₂×C₄×C₁₀₁	—	4	1	no	—
193	C₂×C₄×C₁₀₁	—	4	2	no	—
194	C₂×C₄×C₁₀₁	—	4	2	no	—
195	C₂×C₄×C₁₀₁	—	4	2	no	—
196	C₂×C₄×C₁₀₁	—	4	2	no	—
197	C₂×C₄×C₁₀₁	—	4	2	no	—
198	C₂×C₄×C₁₀₁	—	4	2	no	—
199	C₂×C₄×C₁₀₁	—	4	2	no	—
200	C₂×C₄×C₁₀₁	—	4	2	no	—
201	C₂×C₄×C₁₀₁	—	4	2	no	—
202	C₂×C₄×C₁₀₁	—	4	2	no	—
203	C₂×C₄×C₁₀₁	—	4	2	no	—
204	C₂×C₄×C₁₀₁	—	4	2	no	—
205	C₂×C₄×C₁₀₁	—	4	2	no	—
206	C₂×C₄×C₁₀₁	—	4	2	no	—
207	C₂×C₄×C₁₀₁	#125	1	8	yes	—
208	C₂²×C₁₀₁	#525	1	2	yes	—
209	C₂²×C₁₀₁	C₂×#125	1	2	yes	—
210	C₂²×C₁₀₁	#532	1	2	yes	—
211	C₂²×C₁₀₁	#536	1	2	yes	—
212	C₂²×C₁₀₁	#538	1	1	yes	characteristic
213	C₂²×C₁₀₁	#539	1	2	yes	—
214	C₂²×C₁₀₁	#539	1	1	yes	characteristic
215	C₂²×C₁₀₁	#541	1	2	yes	—
216	C₂²×C₁₀₁	#544	1	1	yes	characteristic
217	C₂²×C₁₀₁	D₄²	1	1	yes	characteristic
218	C₂²×C₁₀₁	#546	1	2	yes	—
219	C₂²×C₁₀₁	#547	1	2	yes	—
220	C₂²×C₁₀₁	D₄×Q₈	1	2	yes	—
221	C₂²×C₁₀₁	#552	1	2	yes	—
222	C₂²×C₁₀₁	#552	1	2	yes	—
223	C₂²×C₁₀₁	#554	1	1	yes	characteristic
224	C₂²×C₁₀₁	#555	1	1	yes	characteristic
225	C₂²×C₁₀₁	#556	1	2	yes	—
226	C₂²×C₁₀₁	#556	1	1	yes	characteristic
227	C₂²×C₁₀₁	#557	1	1	yes	characteristic
228	C₂²×C₁₀₁	#559	1	1	yes	characteristic
229	C₂²×C₁₀₁	#563	1	1	yes	characteristic
230	C₂²×C₁₀₁	#563	1	1	yes	characteristic
231	C₄×C₁₀₁	—	2	8	no	—
232	C₄×C₁₀₁	—	4	2	no	—
233	C₄×C₁₀₁	—	4	4	no	—
234	C₄×C₁₀₁	—	4	4	no	—
235	C₄×C₁₀₁	—	4	2	no	—
236	C₄×C₁₀₁	—	4	2	no	—
237	C₄×C₁₀₁	—	4	4	no	—
238	C₄×C₁₀₁	—	8	2	no	—
239	C₄×C₁₀₁	—	8	2	no	—
240	#15521	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₂×C₁₀₁	#2455	1	1	yes	characteristic
242	C₂×C₁₀₁	#2473	1	2	yes	—
243	C₂×C₁₀₁	#2506	1	2	yes	—
244	C₂×C₁₀₁	#2555	1	1	yes	characteristic
245	C₂×C₁₀₁	#2571	1	1	yes	characteristic
246	C₂×C₁₀₁	#2604	1	2	yes	—
247	C₂×C₁₀₁	#2677	1	1	yes	characteristic
248	C₂×C₁₀₁	#2689	1	2	yes	—
249	C₂×C₁₀₁	#2769	1	1	yes	characteristic
250	C₂×C₁₀₁	#2771	1	1	yes	characteristic
251	C₂×C₁₀₁	#2805	1	1	yes	characteristic
252	C₂×#400	C₂×C₁₀₁	1	2	yes	—
253	C₂×#389	C₂×C₁₀₁	1	2	yes	—
254	#1445	C₂×C₁₀₁	1	1	yes	characteristic
255	#1444	C₂×C₁₀₁	1	1	yes	characteristic
256	#1444	C₂×C₁₀₁	1	2	yes	—
257	#1442	C₂×C₁₀₁	1	2	yes	—
258	#1442	C₂×C₁₀₁	1	1	yes	characteristic
259	#1436	C₂×C₁₀₁	1	2	yes	—
260	#1434	C₂×C₁₀₁	1	2	yes	—
261	C₁₀₁	#15521	1	1	yes	characteristic, direct product factor, Sylow
262	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
263	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
265	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
266	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
267	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
268	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
269	#400	—	2	8	no	—
270	#389	—	2	8	no	—
271	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
272	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
273	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
274	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
275	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
276	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
277	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
278	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
279	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
280	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
281	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
282	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
283	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
284	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
285	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
286	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
287	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
288	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
289	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
290	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
291	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
293	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
294	C₂×C₄⋊C₄	—	2	4	no	—
295	C₂×C₄⋊C₄	—	2	4	no	—
296	C₂×C₄⋊C₄	—	2	4	no	—
297	C₂×C₄⋊C₄	—	2	4	no	—
298	C₂×C₄⋊C₄	—	2	4	no	—
299	C₂×C₄⋊C₄	—	2	4	no	—
300	C₂×C₄⋊C₄	—	2	4	no	—
301	C₂×C₄⋊C₄	—	2	4	no	—
302	C₂×C₄⋊C₄	—	2	4	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	4	2	no	—
305	C₂×C₄⋊C₄	—	4	1	no	—
306	C₂×C₄⋊C₄	—	4	1	no	—
307	C₂×C₄⋊C₄	—	4	2	no	—
308	C₂×C₄⋊C₄	—	4	1	no	—
309	C₂×C₄⋊C₄	—	4	1	no	—
310	C₂×C₄²	—	2	4	no	—
311	C₂×C₄²	—	2	4	no	—
312	C₂×C₄²	—	4	2	no	—
313	#95	—	2	4	no	—
314	#95	—	2	4	no	—
315	#95	—	2	4	no	—
316	#95	—	2	4	no	—
317	#95	—	2	4	no	—
318	#95	—	2	4	no	—
319	#95	—	2	4	no	—
320	#95	—	2	4	no	—
321	#95	—	2	2	no	—
322	#95	—	2	4	no	—
323	#95	—	4	1	no	—
324	#95	—	4	1	no	—
325	#95	D₄×C₁₀₁	1	8	yes	—
326	#95	Q₈×C₁₀₁	1	4	yes	—
327	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
377	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
378	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
379	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
380	C₂²×C₄	C₂×Q₈×C₁₀₁	1	4	yes	—
381	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
382	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
383	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
384	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
385	C₄⋊C₄	—	2	16	no	—
386	C₄⋊C₄	—	4	8	no	—
387	C₄⋊C₄	—	4	4	no	—
388	C₄⋊C₄	—	4	4	no	—
389	C₄⋊C₄	—	4	8	no	—
390	C₄⋊C₄	—	4	4	no	—
391	C₄²	—	4	8	no	—
392	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
393	C₂³	C₂²×Q₈×C₁₀₁	1	1	yes	characteristic
394	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
395	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
396	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
397	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
398	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
399	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
400	C₂³	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
401	C₂³	2₋¹⁺⁴×C₁₀₁	1	2	yes	—
402	C₂³	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	#125×C₁₀₁	1	8	yes	—
460	C₂²	#525×C₁₀₁	1	2	yes	—
461	C₂²	C₂×#125×C₁₀₁	1	2	yes	—
462	C₂²	#532×C₁₀₁	1	2	yes	—
463	C₂²	#536×C₁₀₁	1	2	yes	—
464	C₂²	#538×C₁₀₁	1	1	yes	characteristic
465	C₂²	#539×C₁₀₁	1	2	yes	—
466	C₂²	#539×C₁₀₁	1	1	yes	characteristic
467	C₂²	#541×C₁₀₁	1	2	yes	—
468	C₂²	#544×C₁₀₁	1	1	yes	characteristic
469	C₂²	D₄²×C₁₀₁	1	1	yes	characteristic
470	C₂²	#546×C₁₀₁	1	2	yes	—
471	C₂²	#547×C₁₀₁	1	2	yes	—
472	C₂²	D₄×Q₈×C₁₀₁	1	2	yes	—
473	C₂²	#552×C₁₀₁	1	2	yes	—
474	C₂²	#552×C₁₀₁	1	2	yes	—
475	C₂²	#554×C₁₀₁	1	1	yes	characteristic
476	C₂²	#555×C₁₀₁	1	1	yes	characteristic
477	C₂²	#556×C₁₀₁	1	2	yes	—
478	C₂²	#556×C₁₀₁	1	1	yes	characteristic
479	C₂²	#557×C₁₀₁	1	1	yes	characteristic
480	C₂²	#559×C₁₀₁	1	1	yes	characteristic
481	C₂²	#563×C₁₀₁	1	1	yes	characteristic
482	C₂²	#563×C₁₀₁	1	1	yes	characteristic
483	C₄	—	2	8	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	4	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	4	no	—
490	C₄	—	8	2	no	—
491	C₄	—	8	2	no	—
492	C₂	C₁₀₁×#2455	1	1	yes	characteristic
493	C₂	C₁₀₁×#2473	1	2	yes	—
494	C₂	C₁₀₁×#2506	1	2	yes	—
495	C₂	C₁₀₁×#2555	1	1	yes	characteristic
496	C₂	C₁₀₁×#2571	1	1	yes	characteristic
497	C₂	C₁₀₁×#2604	1	2	yes	—
498	C₂	C₁₀₁×#2677	1	1	yes	characteristic
499	C₂	C₁₀₁×#2689	1	2	yes	—
500	C₂	C₁₀₁×#2769	1	1	yes	characteristic
501	C₂	C₁₀₁×#2771	1	1	yes	characteristic
502	C₂	C₁₀₁×#2805	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₀₁	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
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
240. #15521	C₁₀₁	direct (N × H)
261. C₁₀₁	#15521	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×#400×C₁₀₁	2
C₂×#389×C₁₀₁	2
C₁₀₁×#1445	2
C₁₀₁×#1444	2
C₁₀₁×#1442	2
C₁₀₁×#1436	2
C₁₀₁×#1434	2
#15521	101

Subgroups — C101×#15521 #38797672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#15521 #38797672