Subgroups — C₁₀₁×#14879 #38797030

Order 25856.

1634 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#398×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#395×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#387×C₁₀₁	C₂	1	1	yes	maximal, characteristic
5	C₁₀₁×#1446	C₂	1	1	yes	maximal, characteristic
6	C₁₀₁×#1445	C₂	1	1	yes	maximal, characteristic
7	C₁₀₁×#1444	C₂	1	2	yes	maximal
8	C₁₀₁×#1441	C₂	1	2	yes	maximal
9	C₁₀₁×#1436	C₂	1	2	yes	maximal
10	C₁₀₁×#1436	C₂	1	2	yes	maximal
11	C₁₀₁×#1434	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₀₁	—	2	4	no	—
14	C₂×C₄×Q₈×C₁₀₁	—	2	4	no	—
15	C₂×C₄×Q₈×C₁₀₁	—	2	4	no	—
16	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
24	#398×C₁₀₁	—	2	4	no	—
25	#395×C₁₀₁	—	2	4	no	—
26	#387×C₁₀₁	—	2	4	no	—
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	1	yes	characteristic
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	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
36	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
37	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
38	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
39	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
40	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₀₁	—	2	2	no	—
42	C₂²×Q₈×C₁₀₁	—	2	2	no	—
43	C₂²×Q₈×C₁₀₁	—	2	4	no	—
44	C₂²×Q₈×C₁₀₁	—	2	4	no	—
45	C₂²×Q₈×C₁₀₁	D₄	1	4	yes	—
46	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
57	C₄×Q₈×C₁₀₁	—	2	32	no	—
58	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
59	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
60	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
61	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
68	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
69	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
72	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
73	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
74	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
75	C₂×C₄⋊C₄×C₁₀₁	D₄	1	4	yes	—
76	C₂×C₄²×C₁₀₁	—	2	4	no	—
77	C₂×C₄²×C₁₀₁	—	2	4	no	—
78	C₂×C₄²×C₁₀₁	—	2	4	no	—
79	C₂×C₄²×C₁₀₁	—	2	2	no	—
80	C₂×C₄²×C₁₀₁	—	2	2	no	—
81	C₂×C₄²×C₁₀₁	D₄	1	4	yes	—
82	#95×C₁₀₁	—	2	2	no	—
83	#95×C₁₀₁	—	2	4	no	—
84	#95×C₁₀₁	—	2	2	no	—
85	#95×C₁₀₁	—	2	4	no	—
86	#95×C₁₀₁	—	2	2	no	—
87	#95×C₁₀₁	—	2	2	no	—
88	#95×C₁₀₁	—	2	2	no	—
89	#95×C₁₀₁	—	2	2	no	—
90	#95×C₁₀₁	—	2	4	no	—
91	#95×C₁₀₁	—	2	4	no	—
92	#95×C₁₀₁	—	2	4	no	—
93	#95×C₁₀₁	—	4	2	no	—
94	#95×C₁₀₁	—	4	2	no	—
95	#95×C₁₀₁	Q₈	1	8	yes	complemented
96	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
97	C₂×Q₈×C₁₀₁	—	2	8	no	—
98	C₂×Q₈×C₁₀₁	—	2	8	no	—
99	C₂×Q₈×C₁₀₁	—	2	16	no	—
100	C₂×Q₈×C₁₀₁	—	2	8	no	—
101	C₂×Q₈×C₁₀₁	—	2	16	no	—
102	C₂²×C₄×C₁₀₁	—	2	1	no	—
103	C₂²×C₄×C₁₀₁	—	2	1	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	1	no	—
112	C₂²×C₄×C₁₀₁	—	2	1	no	—
113	C₂²×C₄×C₁₀₁	—	2	2	no	—
114	C₂²×C₄×C₁₀₁	—	2	2	no	—
115	C₂²×C₄×C₁₀₁	—	2	1	no	—
116	C₂²×C₄×C₁₀₁	—	2	2	no	—
117	C₂²×C₄×C₁₀₁	—	2	1	no	—
118	C₂²×C₄×C₁₀₁	—	2	2	no	—
119	C₂²×C₄×C₁₀₁	—	2	1	no	—
120	C₂²×C₄×C₁₀₁	—	2	1	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	1	no	—
127	C₂²×C₄×C₁₀₁	—	2	1	no	—
128	C₂²×C₄×C₁₀₁	—	2	1	no	—
129	C₂²×C₄×C₁₀₁	—	2	1	no	—
130	C₂²×C₄×C₁₀₁	—	2	2	no	—
131	C₂²×C₄×C₁₀₁	—	2	2	no	—
132	C₂²×C₄×C₁₀₁	—	2	2	no	—
133	C₂²×C₄×C₁₀₁	—	2	2	no	—
134	C₂²×C₄×C₁₀₁	—	2	1	no	—
135	C₂²×C₄×C₁₀₁	—	2	2	no	—
136	C₂²×C₄×C₁₀₁	—	2	2	no	—
137	C₂²×C₄×C₁₀₁	—	2	2	no	—
138	C₂²×C₄×C₁₀₁	—	2	1	no	—
139	C₂²×C₄×C₁₀₁	—	2	1	no	—
140	C₂²×C₄×C₁₀₁	—	2	2	no	—
141	C₂²×C₄×C₁₀₁	—	2	1	no	—
142	C₂²×C₄×C₁₀₁	—	2	2	no	—
143	C₂²×C₄×C₁₀₁	—	2	2	no	—
144	C₂²×C₄×C₁₀₁	—	2	2	no	—
145	C₂²×C₄×C₁₀₁	—	2	1	no	—
146	C₂²×C₄×C₁₀₁	—	2	1	no	—
147	C₂²×C₄×C₁₀₁	—	2	1	no	—
148	C₂²×C₄×C₁₀₁	—	2	1	no	—
149	C₂²×C₄×C₁₀₁	—	2	2	no	—
150	C₂²×C₄×C₁₀₁	—	2	2	no	—
151	C₂²×C₄×C₁₀₁	—	2	2	no	—
152	C₂²×C₄×C₁₀₁	—	2	1	no	—
153	C₂²×C₄×C₁₀₁	—	2	2	no	—
154	C₂²×C₄×C₁₀₁	—	2	1	no	—
155	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
156	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₀₁	C₂×Q₈	1	4	yes	—
163	C₂²×C₄×C₁₀₁	C₂×Q₈	1	4	yes	—
164	C₂²×C₄×C₁₀₁	C₂×Q₈	1	4	yes	—
165	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
166	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
167	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
168	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
169	C₄⋊C₄×C₁₀₁	—	2	8	no	—
170	C₄⋊C₄×C₁₀₁	—	2	16	no	—
171	C₄⋊C₄×C₁₀₁	—	2	8	no	—
172	C₄⋊C₄×C₁₀₁	—	4	8	no	—
173	C₄⋊C₄×C₁₀₁	—	4	4	no	—
174	C₄⋊C₄×C₁₀₁	—	4	8	no	—
175	C₄²×C₁₀₁	—	2	16	no	—
176	C₄²×C₁₀₁	—	2	8	no	—
177	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
178	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
179	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
180	C₂³×C₁₀₁	C₂²×Q₈	1	2	yes	—
181	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
182	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
183	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
184	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
185	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂³×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
187	C₂³×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
188	Q₈×C₁₀₁	—	2	32	no	—
189	C₂×C₄×C₁₀₁	—	2	2	no	—
190	C₂×C₄×C₁₀₁	—	2	4	no	—
191	C₂×C₄×C₁₀₁	—	2	4	no	—
192	C₂×C₄×C₁₀₁	—	2	4	no	—
193	C₂×C₄×C₁₀₁	—	2	2	no	—
194	C₂×C₄×C₁₀₁	—	2	2	no	—
195	C₂×C₄×C₁₀₁	—	2	4	no	—
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	2	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	2	no	—
205	C₂×C₄×C₁₀₁	—	2	2	no	—
206	C₂×C₄×C₁₀₁	—	2	2	no	—
207	C₂×C₄×C₁₀₁	—	2	2	no	—
208	C₂×C₄×C₁₀₁	—	2	4	no	—
209	C₂×C₄×C₁₀₁	—	2	4	no	—
210	C₂×C₄×C₁₀₁	—	2	2	no	—
211	C₂×C₄×C₁₀₁	—	2	2	no	—
212	C₂×C₄×C₁₀₁	—	2	4	no	—
213	C₂×C₄×C₁₀₁	—	2	4	no	—
214	C₂×C₄×C₁₀₁	—	2	2	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	—	4	1	no	—
221	C₂×C₄×C₁₀₁	—	4	2	no	—
222	C₂×C₄×C₁₀₁	—	4	1	no	—
223	C₂×C₄×C₁₀₁	—	4	2	no	—
224	C₂×C₄×C₁₀₁	—	4	2	no	—
225	C₂×C₄×C₁₀₁	—	4	1	no	—
226	C₂×C₄×C₁₀₁	—	4	1	no	—
227	C₂×C₄×C₁₀₁	—	4	2	no	—
228	C₂×C₄×C₁₀₁	—	4	2	no	—
229	C₂×C₄×C₁₀₁	—	4	2	no	—
230	C₂×C₄×C₁₀₁	—	4	2	no	—
231	C₂×C₄×C₁₀₁	—	4	1	no	—
232	C₂×C₄×C₁₀₁	—	4	1	no	—
233	C₂×C₄×C₁₀₁	—	4	1	no	—
234	C₂×C₄×C₁₀₁	—	4	1	no	—
235	C₂×C₄×C₁₀₁	—	4	2	no	—
236	C₂×C₄×C₁₀₁	—	4	1	no	—
237	C₂×C₄×C₁₀₁	—	4	2	no	—
238	C₂×C₄×C₁₀₁	—	4	1	no	—
239	C₂×C₄×C₁₀₁	—	4	2	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	1	no	—
244	C₂×C₄×C₁₀₁	—	4	2	no	—
245	C₂×C₄×C₁₀₁	—	4	1	no	—
246	C₂×C₄×C₁₀₁	—	4	1	no	—
247	C₂×C₄×C₁₀₁	—	4	2	no	—
248	C₂×C₄×C₁₀₁	—	4	1	no	—
249	C₂×C₄×C₁₀₁	—	4	1	no	—
250	C₂×C₄×C₁₀₁	—	4	1	no	—
251	C₂×C₄×C₁₀₁	—	4	2	no	—
252	C₂×C₄×C₁₀₁	—	4	2	no	—
253	C₂×C₄×C₁₀₁	#120	1	4	yes	—
254	C₂×C₄×C₁₀₁	#123	1	8	yes	—
255	C₂×C₄×C₁₀₁	C₄⋊Q₈	1	4	yes	—
256	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
257	C₂²×C₁₀₁	C₂×#123	1	2	yes	—
258	C₂²×C₁₀₁	#525	1	1	yes	characteristic
259	C₂²×C₁₀₁	#525	1	1	yes	characteristic
260	C₂²×C₁₀₁	#525	1	2	yes	—
261	C₂²×C₁₀₁	#525	1	1	yes	characteristic
262	C₂²×C₁₀₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
263	C₂²×C₁₀₁	#533	1	2	yes	—
264	C₂²×C₁₀₁	#533	1	2	yes	—
265	C₂²×C₁₀₁	#536	1	1	yes	characteristic
266	C₂²×C₁₀₁	#537	1	1	yes	characteristic
267	C₂²×C₁₀₁	#541	1	2	yes	—
268	C₂²×C₁₀₁	#542	1	2	yes	—
269	C₂²×C₁₀₁	#546	1	1	yes	characteristic
270	C₂²×C₁₀₁	#547	1	1	yes	characteristic
271	C₂²×C₁₀₁	#548	1	1	yes	characteristic
272	C₂²×C₁₀₁	D₄×Q₈	1	2	yes	—
273	C₂²×C₁₀₁	D₄×Q₈	1	2	yes	—
274	C₂²×C₁₀₁	#550	1	1	yes	characteristic
275	C₂²×C₁₀₁	#552	1	2	yes	—
276	C₂²×C₁₀₁	#554	1	2	yes	—
277	C₂²×C₁₀₁	#556	1	2	yes	—
278	C₂²×C₁₀₁	#557	1	2	yes	—
279	C₄×C₁₀₁	—	2	4	no	—
280	C₄×C₁₀₁	—	2	8	no	—
281	C₄×C₁₀₁	—	2	4	no	—
282	C₄×C₁₀₁	—	4	2	no	—
283	C₄×C₁₀₁	—	4	2	no	—
284	C₄×C₁₀₁	—	4	4	no	—
285	C₄×C₁₀₁	—	4	2	no	—
286	C₄×C₁₀₁	—	4	4	no	—
287	C₄×C₁₀₁	—	4	4	no	—
288	C₄×C₁₀₁	—	8	1	no	—
289	C₄×C₁₀₁	—	8	1	no	—
290	#14879	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
291	C₂×C₁₀₁	#2399	1	1	yes	characteristic
292	C₂×C₁₀₁	#2407	1	1	yes	characteristic
293	C₂×C₁₀₁	#2423	1	2	yes	—
294	C₂×C₁₀₁	#2434	1	1	yes	characteristic
295	C₂×C₁₀₁	#2446	1	2	yes	—
296	C₂×C₁₀₁	#2462	1	2	yes	—
297	C₂×C₁₀₁	#2465	1	2	yes	—
298	C₂×C₁₀₁	#2584	1	1	yes	characteristic
299	C₂×C₁₀₁	#2599	1	1	yes	characteristic
300	C₂×C₁₀₁	#2637	1	1	yes	characteristic
301	C₂×C₁₀₁	#2849	1	1	yes	characteristic
302	C₂²×C₄×Q₈	C₂×C₁₀₁	1	1	yes	characteristic
303	C₂×#398	C₂×C₁₀₁	1	1	yes	characteristic
304	C₂×#395	C₂×C₁₀₁	1	1	yes	characteristic
305	C₂×#387	C₂×C₁₀₁	1	1	yes	characteristic
306	#1446	C₂×C₁₀₁	1	1	yes	characteristic
307	#1445	C₂×C₁₀₁	1	1	yes	characteristic
308	#1444	C₂×C₁₀₁	1	2	yes	—
309	#1441	C₂×C₁₀₁	1	2	yes	—
310	#1436	C₂×C₁₀₁	1	2	yes	—
311	#1436	C₂×C₁₀₁	1	2	yes	—
312	#1434	C₂×C₁₀₁	1	1	yes	characteristic
313	C₁₀₁	#14879	1	1	yes	characteristic, direct product factor, Sylow
314	C₂³×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
315	C₂×C₄×Q₈	—	2	4	no	—
316	C₂×C₄×Q₈	—	2	4	no	—
317	C₂×C₄×Q₈	—	2	4	no	—
318	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
319	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
320	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
321	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
322	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
323	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
324	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
325	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
326	#398	—	2	4	no	—
327	#395	—	2	4	no	—
328	#387	—	2	4	no	—
329	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
330	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
331	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
332	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
333	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
334	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
335	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
336	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
337	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
338	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
339	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
340	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
341	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
342	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
343	C₂²×Q₈	—	2	2	no	—
344	C₂²×Q₈	—	2	2	no	—
345	C₂²×Q₈	—	2	4	no	—
346	C₂²×Q₈	—	2	4	no	—
347	C₂²×Q₈	D₄×C₁₀₁	1	4	yes	—
348	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
349	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
350	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
351	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
352	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
353	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
354	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
355	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
356	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
357	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
359	C₄×Q₈	—	2	32	no	—
360	C₂×C₄⋊C₄	—	2	4	no	—
361	C₂×C₄⋊C₄	—	2	4	no	—
362	C₂×C₄⋊C₄	—	2	4	no	—
363	C₂×C₄⋊C₄	—	2	2	no	—
364	C₂×C₄⋊C₄	—	2	2	no	—
365	C₂×C₄⋊C₄	—	2	2	no	—
366	C₂×C₄⋊C₄	—	2	2	no	—
367	C₂×C₄⋊C₄	—	2	2	no	—
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	—	2	2	no	—
370	C₂×C₄⋊C₄	—	2	4	no	—
371	C₂×C₄⋊C₄	—	2	4	no	—
372	C₂×C₄⋊C₄	—	2	2	no	—
373	C₂×C₄⋊C₄	—	2	4	no	—
374	C₂×C₄⋊C₄	—	2	4	no	—
375	C₂×C₄⋊C₄	—	2	4	no	—
376	C₂×C₄⋊C₄	—	4	2	no	—
377	C₂×C₄⋊C₄	D₄×C₁₀₁	1	4	yes	—
378	C₂×C₄²	—	2	4	no	—
379	C₂×C₄²	—	2	4	no	—
380	C₂×C₄²	—	2	4	no	—
381	C₂×C₄²	—	2	2	no	—
382	C₂×C₄²	—	2	2	no	—
383	C₂×C₄²	D₄×C₁₀₁	1	4	yes	—
384	#95	—	2	2	no	—
385	#95	—	2	2	no	—
386	#95	—	2	2	no	—
387	#95	—	2	2	no	—
388	#95	—	2	2	no	—
389	#95	—	2	4	no	—
390	#95	—	2	2	no	—
391	#95	—	2	4	no	—
392	#95	—	2	4	no	—
393	#95	—	2	4	no	—
394	#95	—	2	4	no	—
395	#95	—	4	2	no	—
396	#95	—	4	2	no	—
397	#95	Q₈×C₁₀₁	1	8	yes	complemented
398	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
399	C₂×Q₈	—	2	8	no	—
400	C₂×Q₈	—	2	16	no	—
401	C₂×Q₈	—	2	8	no	—
402	C₂×Q₈	—	2	8	no	—
403	C₂×Q₈	—	2	16	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	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	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
458	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
459	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
460	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
461	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
462	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
463	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
464	C₂²×C₄	C₂×Q₈×C₁₀₁	1	4	yes	—
465	C₂²×C₄	C₂×Q₈×C₁₀₁	1	4	yes	—
466	C₂²×C₄	C₂×Q₈×C₁₀₁	1	4	yes	—
467	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
468	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
469	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
470	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
471	C₄⋊C₄	—	2	8	no	—
472	C₄⋊C₄	—	2	16	no	—
473	C₄⋊C₄	—	2	8	no	—
474	C₄⋊C₄	—	4	8	no	—
475	C₄⋊C₄	—	4	4	no	—
476	C₄⋊C₄	—	4	8	no	—
477	C₄²	—	2	16	no	—
478	C₄²	—	2	8	no	—
479	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
480	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
481	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
482	C₂³	C₂²×Q₈×C₁₀₁	1	2	yes	—
483	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
484	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
485	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
486	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
487	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
488	C₂³	2₋¹⁺⁴×C₁₀₁	1	2	yes	—
489	C₂³	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
490	Q₈	—	2	32	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	2	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	2	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	2	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	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	#120×C₁₀₁	1	4	yes	—
556	C₂×C₄	#123×C₁₀₁	1	8	yes	—
557	C₂×C₄	C₄⋊Q₈×C₁₀₁	1	4	yes	—
558	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
559	C₂²	C₂×#123×C₁₀₁	1	2	yes	—
560	C₂²	#525×C₁₀₁	1	1	yes	characteristic
561	C₂²	#525×C₁₀₁	1	1	yes	characteristic
562	C₂²	#525×C₁₀₁	1	2	yes	—
563	C₂²	#525×C₁₀₁	1	1	yes	characteristic
564	C₂²	C₂×C₄⋊Q₈×C₁₀₁	1	1	yes	characteristic
565	C₂²	#533×C₁₀₁	1	2	yes	—
566	C₂²	#533×C₁₀₁	1	2	yes	—
567	C₂²	#536×C₁₀₁	1	1	yes	characteristic
568	C₂²	#537×C₁₀₁	1	1	yes	characteristic
569	C₂²	#541×C₁₀₁	1	2	yes	—
570	C₂²	#542×C₁₀₁	1	2	yes	—
571	C₂²	#546×C₁₀₁	1	1	yes	characteristic
572	C₂²	#547×C₁₀₁	1	1	yes	characteristic
573	C₂²	#548×C₁₀₁	1	1	yes	characteristic
574	C₂²	D₄×Q₈×C₁₀₁	1	2	yes	—
575	C₂²	D₄×Q₈×C₁₀₁	1	2	yes	—
576	C₂²	#550×C₁₀₁	1	1	yes	characteristic
577	C₂²	#552×C₁₀₁	1	2	yes	—
578	C₂²	#554×C₁₀₁	1	2	yes	—
579	C₂²	#556×C₁₀₁	1	2	yes	—
580	C₂²	#557×C₁₀₁	1	2	yes	—
581	C₄	—	2	4	no	—
582	C₄	—	2	4	no	—
583	C₄	—	2	8	no	—
584	C₄	—	4	2	no	—
585	C₄	—	4	4	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	4	no	—
588	C₄	—	4	4	no	—
589	C₄	—	4	2	no	—
590	C₄	—	8	1	no	—
591	C₄	—	8	1	no	—
592	C₂	C₁₀₁×#2399	1	1	yes	characteristic
593	C₂	C₁₀₁×#2407	1	1	yes	characteristic
594	C₂	C₁₀₁×#2423	1	2	yes	—
595	C₂	C₁₀₁×#2434	1	1	yes	characteristic
596	C₂	C₁₀₁×#2446	1	2	yes	—
597	C₂	C₁₀₁×#2462	1	2	yes	—
598	C₂	C₁₀₁×#2465	1	2	yes	—
599	C₂	C₁₀₁×#2584	1	1	yes	characteristic
600	C₂	C₁₀₁×#2599	1	1	yes	characteristic
601	C₂	C₁₀₁×#2637	1	1	yes	characteristic
602	C₂	C₁₀₁×#2849	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
95. #95×C₁₀₁	Q₈	semidirect
290. #14879	C₁₀₁	direct (N × H)
313. C₁₀₁	#14879	direct (N × H)
397. #95	Q₈×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×Q₈×C₁₀₁	2
C₂×#398×C₁₀₁	2
C₂×#395×C₁₀₁	2
C₂×#387×C₁₀₁	2
C₁₀₁×#1446	2
C₁₀₁×#1445	2
C₁₀₁×#1444	2
C₁₀₁×#1441	2
C₁₀₁×#1436	2
C₁₀₁×#1434	2
#14879	101

Subgroups — C101×#14879 #38797030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#14879 #38797030