Subgroups — C₁₀₁×#14606 #38796757

Order 25856.

1094 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#398×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#1445	C₂	1	1	yes	maximal, characteristic
3	C₁₀₁×#1445	C₂	1	2	yes	maximal
4	C₁₀₁×#1443	C₂	1	2	yes	maximal
5	C₁₀₁×#1436	C₂	1	1	yes	maximal, characteristic
6	C₁₀₁×#1436	C₂	1	2	yes	maximal
7	C₁₀₁×#1436	C₂	1	2	yes	maximal
8	C₁₀₁×#1434	C₂	1	2	yes	maximal
9	C₁₀₁×#1434	C₂	1	2	yes	maximal
10	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
15	#398×C₁₀₁	C₄	1	8	yes	complemented
16	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
17	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
18	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
28	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
29	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
30	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
31	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
32	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
34	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
41	C₂×C₄⋊C₄×C₁₀₁	—	4	1	no	—
42	C₂×C₄⋊C₄×C₁₀₁	—	4	1	no	—
43	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
44	C₂×C₄⋊C₄×C₁₀₁	—	4	1	no	—
45	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
46	C₂×C₄⋊C₄×C₁₀₁	—	4	1	no	—
47	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
48	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	8	yes	—
49	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
50	C₂×C₄²×C₁₀₁	—	2	4	no	—
51	C₂×C₄²×C₁₀₁	—	2	4	no	—
52	C₂×C₄²×C₁₀₁	—	4	1	no	—
53	C₂×C₄²×C₁₀₁	—	4	2	no	—
54	C₂×C₄²×C₁₀₁	—	4	2	no	—
55	#95×C₁₀₁	—	2	4	no	—
56	#95×C₁₀₁	—	2	4	no	—
57	#95×C₁₀₁	—	2	4	no	—
58	#95×C₁₀₁	—	2	4	no	—
59	#95×C₁₀₁	—	2	4	no	—
60	#95×C₁₀₁	—	2	4	no	—
61	#95×C₁₀₁	—	2	4	no	—
62	#95×C₁₀₁	—	4	2	no	—
63	#95×C₁₀₁	—	4	2	no	—
64	#95×C₁₀₁	—	4	1	no	—
65	#95×C₁₀₁	—	4	1	no	—
66	#95×C₁₀₁	—	4	2	no	—
67	#95×C₁₀₁	—	4	2	no	—
68	#95×C₁₀₁	—	4	1	no	—
69	#95×C₁₀₁	C₂×C₄	1	8	yes	—
70	#95×C₁₀₁	C₂×C₄	1	4	yes	—
71	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
72	C₂²×C₄×C₁₀₁	—	2	2	no	—
73	C₂²×C₄×C₁₀₁	—	2	2	no	—
74	C₂²×C₄×C₁₀₁	—	2	2	no	—
75	C₂²×C₄×C₁₀₁	—	2	2	no	—
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	1	no	—
94	C₂²×C₄×C₁₀₁	—	2	2	no	—
95	C₂²×C₄×C₁₀₁	—	2	2	no	—
96	C₂²×C₄×C₁₀₁	—	2	2	no	—
97	C₂²×C₄×C₁₀₁	—	2	1	no	—
98	C₂²×C₄×C₁₀₁	—	2	2	no	—
99	C₂²×C₄×C₁₀₁	—	2	1	no	—
100	C₂²×C₄×C₁₀₁	—	2	2	no	—
101	C₂²×C₄×C₁₀₁	—	2	2	no	—
102	C₂²×C₄×C₁₀₁	—	2	1	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	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
123	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
125	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
127	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
128	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
129	C₄⋊C₄×C₁₀₁	—	4	8	no	—
130	C₄⋊C₄×C₁₀₁	—	4	4	no	—
131	C₄⋊C₄×C₁₀₁	—	4	4	no	—
132	C₄²×C₁₀₁	—	4	4	no	—
133	C₄²×C₁₀₁	—	4	8	no	—
134	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
135	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
136	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
137	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
138	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
139	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
140	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
141	C₂³×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
142	C₂³×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
143	C₂×C₄×C₁₀₁	—	2	4	no	—
144	C₂×C₄×C₁₀₁	—	2	2	no	—
145	C₂×C₄×C₁₀₁	—	2	4	no	—
146	C₂×C₄×C₁₀₁	—	2	4	no	—
147	C₂×C₄×C₁₀₁	—	2	4	no	—
148	C₂×C₄×C₁₀₁	—	2	2	no	—
149	C₂×C₄×C₁₀₁	—	2	2	no	—
150	C₂×C₄×C₁₀₁	—	2	4	no	—
151	C₂×C₄×C₁₀₁	—	2	4	no	—
152	C₂×C₄×C₁₀₁	—	2	2	no	—
153	C₂×C₄×C₁₀₁	—	2	4	no	—
154	C₂×C₄×C₁₀₁	—	2	2	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	4	no	—
162	C₂×C₄×C₁₀₁	—	2	4	no	—
163	C₂×C₄×C₁₀₁	—	2	4	no	—
164	C₂×C₄×C₁₀₁	—	2	4	no	—
165	C₂×C₄×C₁₀₁	—	4	2	no	—
166	C₂×C₄×C₁₀₁	—	4	2	no	—
167	C₂×C₄×C₁₀₁	—	4	2	no	—
168	C₂×C₄×C₁₀₁	—	4	2	no	—
169	C₂×C₄×C₁₀₁	—	4	2	no	—
170	C₂×C₄×C₁₀₁	—	4	2	no	—
171	C₂×C₄×C₁₀₁	—	4	2	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	2	no	—
181	C₂×C₄×C₁₀₁	—	4	1	no	—
182	C₂×C₄×C₁₀₁	—	4	1	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	2	no	—
191	C₂×C₄×C₁₀₁	—	4	2	no	—
192	C₂×C₄×C₁₀₁	—	4	2	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	C₂²×C₁₀₁	C₄×#41	1	2	yes	—
201	C₂²×C₁₀₁	C₄×#41	1	1	yes	characteristic
202	C₂²×C₁₀₁	#518	1	1	yes	characteristic
203	C₂²×C₁₀₁	#518	1	1	yes	characteristic
204	C₂²×C₁₀₁	#519	1	2	yes	—
205	C₂²×C₁₀₁	#538	1	2	yes	—
206	C₂²×C₁₀₁	#539	1	2	yes	—
207	C₂²×C₁₀₁	#539	1	2	yes	—
208	C₂²×C₁₀₁	#540	1	2	yes	—
209	C₂²×C₁₀₁	#542	1	2	yes	—
210	C₂²×C₁₀₁	#542	1	2	yes	—
211	C₂²×C₁₀₁	#551	1	1	yes	characteristic
212	C₂²×C₁₀₁	#552	1	2	yes	—
213	C₂²×C₁₀₁	#552	1	2	yes	—
214	C₂²×C₁₀₁	#552	1	2	yes	—
215	C₂²×C₁₀₁	#552	1	2	yes	—
216	C₂²×C₁₀₁	#553	1	2	yes	—
217	C₂²×C₁₀₁	#559	1	1	yes	characteristic
218	C₂²×C₁₀₁	#563	1	2	yes	—
219	C₂²×C₁₀₁	#563	1	1	yes	characteristic
220	C₂²×C₁₀₁	#563	1	1	yes	characteristic
221	C₄×C₁₀₁	—	4	4	no	—
222	C₄×C₁₀₁	—	4	2	no	—
223	C₄×C₁₀₁	—	4	4	no	—
224	C₄×C₁₀₁	—	4	2	no	—
225	C₄×C₁₀₁	—	4	2	no	—
226	C₄×C₁₀₁	—	4	4	no	—
227	C₄×C₁₀₁	—	4	4	no	—
228	C₄×C₁₀₁	—	4	4	no	—
229	C₄×C₁₀₁	—	8	2	no	—
230	#14606	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂×C₁₀₁	#2332	1	2	yes	—
232	C₂×C₁₀₁	#2333	1	1	yes	characteristic
233	C₂×C₁₀₁	#2371	1	2	yes	—
234	C₂×C₁₀₁	#2374	1	1	yes	characteristic
235	C₂×C₁₀₁	#2381	1	1	yes	characteristic
236	C₂×C₁₀₁	#2738	1	2	yes	—
237	C₂×C₁₀₁	#2765	1	2	yes	—
238	C₂×C₁₀₁	#2770	1	2	yes	—
239	C₂×C₁₀₁	#2773	1	2	yes	—
240	C₂×#398	C₂×C₁₀₁	1	1	yes	characteristic
241	#1445	C₂×C₁₀₁	1	1	yes	characteristic
242	#1445	C₂×C₁₀₁	1	2	yes	—
243	#1443	C₂×C₁₀₁	1	2	yes	—
244	#1436	C₂×C₁₀₁	1	2	yes	—
245	#1436	C₂×C₁₀₁	1	2	yes	—
246	#1436	C₂×C₁₀₁	1	1	yes	characteristic
247	#1434	C₂×C₁₀₁	1	2	yes	—
248	#1434	C₂×C₁₀₁	1	2	yes	—
249	C₁₀₁	#14606	1	1	yes	characteristic, direct product factor, Sylow
250	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
251	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
252	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
253	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
254	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
255	#398	C₄×C₁₀₁	1	8	yes	complemented
256	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
257	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
258	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
259	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
260	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
261	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
262	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
263	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
264	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
265	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
266	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
267	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
268	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
269	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
270	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
271	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
272	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
273	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
274	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
275	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
276	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
277	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
279	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
280	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
281	C₂×C₄⋊C₄	—	4	1	no	—
282	C₂×C₄⋊C₄	—	4	1	no	—
283	C₂×C₄⋊C₄	—	4	2	no	—
284	C₂×C₄⋊C₄	—	4	1	no	—
285	C₂×C₄⋊C₄	—	4	2	no	—
286	C₂×C₄⋊C₄	—	4	1	no	—
287	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
288	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	8	yes	—
289	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
290	C₂×C₄²	—	2	4	no	—
291	C₂×C₄²	—	2	4	no	—
292	C₂×C₄²	—	4	1	no	—
293	C₂×C₄²	—	4	2	no	—
294	C₂×C₄²	—	4	2	no	—
295	#95	—	2	4	no	—
296	#95	—	2	4	no	—
297	#95	—	2	4	no	—
298	#95	—	2	4	no	—
299	#95	—	2	4	no	—
300	#95	—	2	4	no	—
301	#95	—	2	4	no	—
302	#95	—	4	2	no	—
303	#95	—	4	2	no	—
304	#95	—	4	1	no	—
305	#95	—	4	1	no	—
306	#95	—	4	2	no	—
307	#95	—	4	2	no	—
308	#95	—	4	1	no	—
309	#95	C₂×C₄×C₁₀₁	1	8	yes	—
310	#95	C₂×C₄×C₁₀₁	1	4	yes	—
311	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
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	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	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	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
362	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
363	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
364	C₂²×C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
365	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
366	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
367	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
368	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
369	C₄⋊C₄	—	4	8	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	—	4	4	no	—
372	C₄²	—	4	4	no	—
373	C₄²	—	4	8	no	—
374	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
375	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
376	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
377	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
378	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
379	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
380	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
381	C₂³	2₋¹⁺⁴×C₁₀₁	1	2	yes	—
382	C₂³	2₋¹⁺⁴×C₁₀₁	1	2	yes	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	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	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	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	C₂²	C₄×#41×C₁₀₁	1	2	yes	—
441	C₂²	C₄×#41×C₁₀₁	1	1	yes	characteristic
442	C₂²	#518×C₁₀₁	1	1	yes	characteristic
443	C₂²	#518×C₁₀₁	1	1	yes	characteristic
444	C₂²	#519×C₁₀₁	1	2	yes	—
445	C₂²	#538×C₁₀₁	1	2	yes	—
446	C₂²	#539×C₁₀₁	1	2	yes	—
447	C₂²	#539×C₁₀₁	1	2	yes	—
448	C₂²	#540×C₁₀₁	1	2	yes	—
449	C₂²	#542×C₁₀₁	1	2	yes	—
450	C₂²	#542×C₁₀₁	1	2	yes	—
451	C₂²	#551×C₁₀₁	1	1	yes	characteristic
452	C₂²	#552×C₁₀₁	1	2	yes	—
453	C₂²	#552×C₁₀₁	1	2	yes	—
454	C₂²	#552×C₁₀₁	1	2	yes	—
455	C₂²	#552×C₁₀₁	1	2	yes	—
456	C₂²	#553×C₁₀₁	1	2	yes	—
457	C₂²	#559×C₁₀₁	1	1	yes	characteristic
458	C₂²	#563×C₁₀₁	1	2	yes	—
459	C₂²	#563×C₁₀₁	1	1	yes	characteristic
460	C₂²	#563×C₁₀₁	1	1	yes	characteristic
461	C₄	—	4	4	no	—
462	C₄	—	4	4	no	—
463	C₄	—	4	4	no	—
464	C₄	—	4	4	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	4	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	8	2	no	—
470	C₂	C₁₀₁×#2332	1	2	yes	—
471	C₂	C₁₀₁×#2333	1	1	yes	characteristic
472	C₂	C₁₀₁×#2371	1	2	yes	—
473	C₂	C₁₀₁×#2374	1	1	yes	characteristic
474	C₂	C₁₀₁×#2381	1	1	yes	characteristic
475	C₂	C₁₀₁×#2738	1	2	yes	—
476	C₂	C₁₀₁×#2765	1	2	yes	—
477	C₂	C₁₀₁×#2770	1	2	yes	—
478	C₂	C₁₀₁×#2773	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₀₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
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
15. #398×C₁₀₁	C₄	semidirect
230. #14606	C₁₀₁	direct (N × H)
249. C₁₀₁	#14606	direct (N × H)
255. #398	C₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#398×C₁₀₁	2
C₁₀₁×#1445	2
C₁₀₁×#1443	2
C₁₀₁×#1436	2
C₁₀₁×#1434	2
#14606	101

Subgroups — C101×#14606 #38796757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#14606 #38796757