Subgroups — C₁₀₁×#15569 #38797720

Order 25856.

1694 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#393×C₁₀₁	C₂	1	2	yes	maximal, complemented
2	C₂×#388×C₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#1446	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#1442	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#1440	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1438	C₂	1	1	yes	maximal, characteristic
7	C₁₀₁×#1438	C₂	1	2	yes	maximal
8	C₁₀₁×#1437	C₂	1	2	yes	maximal, complemented
9	C₁₀₁×#1434	C₂	1	2	yes	maximal, complemented
10	C₂³×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
14	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	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	2	yes	—
18	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
20	#393×C₁₀₁	—	2	8	no	—
21	#388×C₁₀₁	—	2	8	no	—
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	1	yes	characteristic
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	2	yes	—
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	C₂⁵×C₁₀₁	C₂³	1	2	yes	—
34	C₂²×Q₈×C₁₀₁	—	2	4	no	—
35	C₂²×Q₈×C₁₀₁	—	2	2	no	—
36	C₂²×Q₈×C₁₀₁	—	4	1	no	—
37	C₂²×Q₈×C₁₀₁	—	4	2	no	—
38	C₂²×Q₈×C₁₀₁	—	4	1	no	—
39	C₂²×D₄×C₁₀₁	—	2	4	no	—
40	C₂²×D₄×C₁₀₁	—	2	2	no	—
41	C₂²×D₄×C₁₀₁	—	4	2	no	—
42	C₂²×D₄×C₁₀₁	—	4	1	no	—
43	C₂²×D₄×C₁₀₁	—	4	1	no	—
44	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₀₁	—	4	1	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	—	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	4	no	—
63	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
67	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
68	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
69	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
70	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
71	C₂×C₂²⋊C₄×C₁₀₁	—	4	2	no	—
72	C₂×C₄²×C₁₀₁	—	2	4	no	—
73	C₂×C₄²×C₁₀₁	—	2	4	no	—
74	C₂×C₄²×C₁₀₁	—	4	2	no	—
75	#95×C₁₀₁	—	2	4	no	—
76	#95×C₁₀₁	—	2	4	no	—
77	#95×C₁₀₁	—	2	4	no	—
78	#95×C₁₀₁	—	2	4	no	—
79	#95×C₁₀₁	—	2	2	no	—
80	#95×C₁₀₁	—	4	2	no	—
81	#95×C₁₀₁	—	4	2	no	—
82	#95×C₁₀₁	—	4	1	no	—
83	#95×C₁₀₁	—	4	1	no	—
84	#95×C₁₀₁	—	4	1	no	—
85	#95×C₁₀₁	D₄	1	8	yes	complemented
86	C₂⁴×C₁₀₁	—	2	2	no	—
87	C₂⁴×C₁₀₁	—	2	2	no	—
88	C₂⁴×C₁₀₁	—	2	2	no	—
89	C₂⁴×C₁₀₁	—	2	2	no	—
90	C₂⁴×C₁₀₁	—	2	2	no	—
91	C₂⁴×C₁₀₁	—	2	2	no	—
92	C₂⁴×C₁₀₁	—	2	2	no	—
93	C₂⁴×C₁₀₁	—	2	2	no	—
94	C₂⁴×C₁₀₁	—	2	2	no	—
95	C₂⁴×C₁₀₁	—	2	2	no	—
96	C₂⁴×C₁₀₁	—	2	2	no	—
97	C₂⁴×C₁₀₁	—	2	2	no	—
98	C₂⁴×C₁₀₁	—	2	2	no	—
99	C₂⁴×C₁₀₁	—	2	2	no	—
100	C₂⁴×C₁₀₁	#41	1	4	yes	—
101	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
102	C₂×Q₈×C₁₀₁	—	4	4	no	—
103	C₂×Q₈×C₁₀₁	—	4	8	no	—
104	C₂×Q₈×C₁₀₁	—	4	8	no	—
105	C₂×Q₈×C₁₀₁	—	4	4	no	—
106	C₂×Q₈×C₁₀₁	—	4	4	no	—
107	C₂×D₄×C₁₀₁	—	4	8	no	—
108	C₂×D₄×C₁₀₁	—	4	4	no	—
109	C₂×D₄×C₁₀₁	—	4	4	no	—
110	C₂×D₄×C₁₀₁	—	4	8	no	—
111	C₂×D₄×C₁₀₁	—	4	4	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	—	2	2	no	—
125	C₂²×C₄×C₁₀₁	—	2	2	no	—
126	C₂²×C₄×C₁₀₁	—	2	2	no	—
127	C₂²×C₄×C₁₀₁	—	2	2	no	—
128	C₂²×C₄×C₁₀₁	—	2	2	no	—
129	C₂²×C₄×C₁₀₁	—	2	2	no	—
130	C₂²×C₄×C₁₀₁	—	2	2	no	—
131	C₂²×C₄×C₁₀₁	—	2	2	no	—
132	C₂²×C₄×C₁₀₁	—	2	1	no	—
133	C₂²×C₄×C₁₀₁	—	2	1	no	—
134	C₂²×C₄×C₁₀₁	—	2	1	no	—
135	C₂²×C₄×C₁₀₁	—	2	2	no	—
136	C₂²×C₄×C₁₀₁	—	2	1	no	—
137	C₂²×C₄×C₁₀₁	—	2	1	no	—
138	C₂²×C₄×C₁₀₁	—	2	2	no	—
139	C₂²×C₄×C₁₀₁	—	2	2	no	—
140	C₂²×C₄×C₁₀₁	—	2	2	no	—
141	C₂²×C₄×C₁₀₁	—	2	2	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	2	no	—
146	C₂²×C₄×C₁₀₁	—	2	1	no	—
147	C₂²×C₄×C₁₀₁	—	2	2	no	—
148	C₂²×C₄×C₁₀₁	—	2	2	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	2	no	—
153	C₂²×C₄×C₁₀₁	—	2	2	no	—
154	C₂²×C₄×C₁₀₁	—	2	2	no	—
155	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
156	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
157	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
159	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
160	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
161	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
162	C₄⋊C₄×C₁₀₁	—	4	4	no	—
163	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
164	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
165	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
166	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
167	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
168	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
169	C₄²×C₁₀₁	—	4	8	no	—
170	C₂³×C₁₀₁	—	2	4	no	—
171	C₂³×C₁₀₁	—	2	4	no	—
172	C₂³×C₁₀₁	—	2	4	no	—
173	C₂³×C₁₀₁	—	2	4	no	—
174	C₂³×C₁₀₁	—	2	4	no	—
175	C₂³×C₁₀₁	—	2	4	no	—
176	C₂³×C₁₀₁	—	2	4	no	—
177	C₂³×C₁₀₁	—	4	2	no	—
178	C₂³×C₁₀₁	—	4	2	no	—
179	C₂³×C₁₀₁	—	4	2	no	—
180	C₂³×C₁₀₁	—	4	2	no	—
181	C₂³×C₁₀₁	—	4	2	no	—
182	C₂³×C₁₀₁	—	4	2	no	—
183	C₂³×C₁₀₁	—	4	2	no	—
184	C₂³×C₁₀₁	—	4	2	no	—
185	C₂³×C₁₀₁	—	4	2	no	—
186	C₂³×C₁₀₁	—	4	2	no	—
187	C₂³×C₁₀₁	—	4	2	no	—
188	C₂³×C₁₀₁	—	4	2	no	—
189	C₂³×C₁₀₁	—	4	2	no	—
190	C₂³×C₁₀₁	—	4	2	no	—
191	C₂³×C₁₀₁	—	4	2	no	—
192	C₂³×C₁₀₁	—	4	2	no	—
193	C₂³×C₁₀₁	—	4	2	no	—
194	C₂³×C₁₀₁	—	4	2	no	—
195	C₂³×C₁₀₁	—	4	2	no	—
196	C₂³×C₁₀₁	—	4	2	no	—
197	C₂³×C₁₀₁	—	4	2	no	—
198	C₂³×C₁₀₁	—	4	2	no	—
199	C₂³×C₁₀₁	—	4	2	no	—
200	C₂³×C₁₀₁	—	4	2	no	—
201	C₂³×C₁₀₁	—	4	2	no	—
202	C₂³×C₁₀₁	—	4	2	no	—
203	C₂³×C₁₀₁	—	4	2	no	—
204	C₂³×C₁₀₁	—	4	2	no	—
205	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
206	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
207	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
208	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
209	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
210	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
211	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂³×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
213	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
214	C₂³×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂³×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
216	Q₈×C₁₀₁	—	4	16	no	—
217	D₄×C₁₀₁	—	4	16	no	—
218	C₂×C₄×C₁₀₁	—	2	4	no	—
219	C₂×C₄×C₁₀₁	—	2	4	no	—
220	C₂×C₄×C₁₀₁	—	2	4	no	—
221	C₂×C₄×C₁₀₁	—	2	4	no	—
222	C₂×C₄×C₁₀₁	—	2	2	no	—
223	C₂×C₄×C₁₀₁	—	2	2	no	—
224	C₂×C₄×C₁₀₁	—	2	4	no	—
225	C₂×C₄×C₁₀₁	—	2	2	no	—
226	C₂×C₄×C₁₀₁	—	2	4	no	—
227	C₂×C₄×C₁₀₁	—	2	4	no	—
228	C₂×C₄×C₁₀₁	—	2	4	no	—
229	C₂×C₄×C₁₀₁	—	2	4	no	—
230	C₂×C₄×C₁₀₁	—	2	4	no	—
231	C₂×C₄×C₁₀₁	—	2	4	no	—
232	C₂×C₄×C₁₀₁	—	2	4	no	—
233	C₂×C₄×C₁₀₁	—	2	4	no	—
234	C₂×C₄×C₁₀₁	—	2	4	no	—
235	C₂×C₄×C₁₀₁	—	2	4	no	—
236	C₂×C₄×C₁₀₁	—	4	2	no	—
237	C₂×C₄×C₁₀₁	—	4	2	no	—
238	C₂×C₄×C₁₀₁	—	4	2	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	2	no	—
244	C₂×C₄×C₁₀₁	—	4	2	no	—
245	C₂×C₄×C₁₀₁	—	4	2	no	—
246	C₂×C₄×C₁₀₁	—	4	1	no	—
247	C₂×C₄×C₁₀₁	—	4	1	no	—
248	C₂×C₄×C₁₀₁	—	4	2	no	—
249	C₂×C₄×C₁₀₁	—	4	2	no	—
250	C₂×C₄×C₁₀₁	—	4	2	no	—
251	C₂×C₄×C₁₀₁	—	4	2	no	—
252	C₂×C₄×C₁₀₁	—	4	1	no	—
253	C₂×C₄×C₁₀₁	—	4	1	no	—
254	C₂×C₄×C₁₀₁	—	4	2	no	—
255	C₂×C₄×C₁₀₁	—	4	2	no	—
256	C₂×C₄×C₁₀₁	—	4	2	no	—
257	C₂×C₄×C₁₀₁	—	4	1	no	—
258	C₂×C₄×C₁₀₁	—	4	2	no	—
259	C₂×C₄×C₁₀₁	—	4	1	no	—
260	C₂×C₄×C₁₀₁	—	4	2	no	—
261	C₂×C₄×C₁₀₁	—	4	2	no	—
262	C₂×C₄×C₁₀₁	—	4	2	no	—
263	C₂×C₄×C₁₀₁	—	4	2	no	—
264	C₂×C₄×C₁₀₁	—	4	2	no	—
265	C₂×C₄×C₁₀₁	—	4	2	no	—
266	C₂×C₄×C₁₀₁	—	4	2	no	—
267	C₂×C₄×C₁₀₁	—	4	2	no	—
268	C₂²×C₁₀₁	—	4	4	no	—
269	C₂²×C₁₀₁	—	4	4	no	—
270	C₂²×C₁₀₁	—	4	4	no	—
271	C₂²×C₁₀₁	—	4	4	no	—
272	C₂²×C₁₀₁	—	4	4	no	—
273	C₂²×C₁₀₁	—	4	4	no	—
274	C₂²×C₁₀₁	—	4	4	no	—
275	C₂²×C₁₀₁	—	8	2	no	—
276	C₂²×C₁₀₁	—	8	2	no	—
277	C₂²×C₁₀₁	—	8	2	no	—
278	C₂²×C₁₀₁	—	8	2	no	—
279	C₂²×C₁₀₁	—	8	2	no	—
280	C₂²×C₁₀₁	—	8	2	no	—
281	C₂²×C₁₀₁	—	8	2	no	—
282	C₂²×C₁₀₁	—	8	2	no	—
283	C₂²×C₁₀₁	#525	1	2	yes	—
284	C₂²×C₁₀₁	#529	1	2	yes	—
285	C₂²×C₁₀₁	#532	1	2	yes	—
286	C₂²×C₁₀₁	#535	1	2	yes	—
287	C₂²×C₁₀₁	#538	1	1	yes	characteristic
288	C₂²×C₁₀₁	#538	1	2	yes	—
289	C₂²×C₁₀₁	#538	1	1	yes	characteristic
290	C₂²×C₁₀₁	#539	1	2	yes	—
291	C₂²×C₁₀₁	#539	1	1	yes	characteristic
292	C₂²×C₁₀₁	D₄²	1	1	yes	characteristic
293	C₂²×C₁₀₁	#546	1	2	yes	—
294	C₂²×C₁₀₁	#546	1	2	yes	—
295	C₂²×C₁₀₁	#548	1	2	yes	—
296	C₂²×C₁₀₁	#551	1	2	yes	—
297	C₂²×C₁₀₁	#551	1	2	yes	—
298	C₂²×C₁₀₁	#551	1	1	yes	characteristic
299	C₂²×C₁₀₁	#555	1	1	yes	characteristic
300	C₂²×C₁₀₁	#555	1	1	yes	characteristic
301	C₂²×C₁₀₁	#555	1	2	yes	—
302	C₂²×C₁₀₁	#556	1	1	yes	characteristic
303	C₂²×C₁₀₁	#559	1	1	yes	characteristic
304	C₂²×C₁₀₁	H(3,𝔽₄)	1	1	yes	characteristic
305	C₂²×C₁₀₁	#562	1	1	yes	characteristic
306	C₄×C₁₀₁	—	4	4	no	—
307	C₄×C₁₀₁	—	4	2	no	—
308	C₄×C₁₀₁	—	4	4	no	—
309	C₄×C₁₀₁	—	4	4	no	—
310	C₄×C₁₀₁	—	4	2	no	—
311	C₄×C₁₀₁	—	4	2	no	—
312	C₄×C₁₀₁	—	4	4	no	—
313	C₄×C₁₀₁	—	8	2	no	—
314	#15569	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₂×C₁₀₁	—	8	4	no	—
316	C₂×C₁₀₁	#2459	1	2	yes	—
317	C₂×C₁₀₁	#2463	1	1	yes	characteristic
318	C₂×C₁₀₁	#2555	1	1	yes	characteristic
319	C₂×C₁₀₁	#2560	1	2	yes	—
320	C₂×C₁₀₁	#2572	1	1	yes	characteristic
321	C₂×C₁₀₁	#2610	1	2	yes	—
322	C₂×C₁₀₁	#2670	1	1	yes	characteristic
323	C₂×C₁₀₁	#2696	1	2	yes	—
324	C₂×C₁₀₁	#2736	1	1	yes	characteristic
325	C₂×C₁₀₁	#2785	1	1	yes	characteristic
326	C₂×C₁₀₁	#2808	1	1	yes	characteristic
327	C₂×#393	C₂×C₁₀₁	1	2	yes	complemented
328	C₂×#388	C₂×C₁₀₁	1	2	yes	complemented
329	#1446	C₂×C₁₀₁	1	1	yes	characteristic, complemented
330	#1442	C₂×C₁₀₁	1	1	yes	characteristic, complemented
331	#1440	C₂×C₁₀₁	1	2	yes	complemented
332	#1438	C₂×C₁₀₁	1	1	yes	characteristic
333	#1438	C₂×C₁₀₁	1	2	yes	—
334	#1437	C₂×C₁₀₁	1	2	yes	complemented
335	#1434	C₂×C₁₀₁	1	2	yes	complemented
336	C₁₀₁	#15569	1	1	yes	characteristic, direct product factor, Sylow
337	C₂³×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
338	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
339	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
340	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
341	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
342	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
343	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
344	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
345	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
346	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
347	#393	—	2	8	no	—
348	#388	—	2	8	no	—
349	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
350	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
351	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
352	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
353	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
354	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
355	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
356	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
357	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
358	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
359	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
360	C₂⁵	C₂³×C₁₀₁	1	2	yes	—
361	C₂²×Q₈	—	2	4	no	—
362	C₂²×Q₈	—	2	2	no	—
363	C₂²×Q₈	—	4	1	no	—
364	C₂²×Q₈	—	4	2	no	—
365	C₂²×Q₈	—	4	1	no	—
366	C₂²×D₄	—	2	4	no	—
367	C₂²×D₄	—	2	2	no	—
368	C₂²×D₄	—	4	2	no	—
369	C₂²×D₄	—	4	1	no	—
370	C₂²×D₄	—	4	1	no	—
371	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
372	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
373	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
374	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
375	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
376	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
377	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
378	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
379	C₂×C₄⋊C₄	—	2	4	no	—
380	C₂×C₄⋊C₄	—	4	1	no	—
381	C₂×C₂²⋊C₄	—	2	4	no	—
382	C₂×C₂²⋊C₄	—	2	4	no	—
383	C₂×C₂²⋊C₄	—	2	4	no	—
384	C₂×C₂²⋊C₄	—	2	4	no	—
385	C₂×C₂²⋊C₄	—	2	4	no	—
386	C₂×C₂²⋊C₄	—	2	4	no	—
387	C₂×C₂²⋊C₄	—	2	4	no	—
388	C₂×C₂²⋊C₄	—	2	4	no	—
389	C₂×C₂²⋊C₄	—	2	4	no	—
390	C₂×C₂²⋊C₄	—	2	4	no	—
391	C₂×C₂²⋊C₄	—	2	4	no	—
392	C₂×C₂²⋊C₄	—	2	4	no	—
393	C₂×C₂²⋊C₄	—	4	2	no	—
394	C₂×C₂²⋊C₄	—	4	2	no	—
395	C₂×C₂²⋊C₄	—	4	2	no	—
396	C₂×C₂²⋊C₄	—	4	2	no	—
397	C₂×C₂²⋊C₄	—	4	2	no	—
398	C₂×C₂²⋊C₄	—	4	2	no	—
399	C₂×C₄²	—	2	4	no	—
400	C₂×C₄²	—	2	4	no	—
401	C₂×C₄²	—	4	2	no	—
402	#95	—	2	4	no	—
403	#95	—	2	4	no	—
404	#95	—	2	4	no	—
405	#95	—	2	4	no	—
406	#95	—	2	2	no	—
407	#95	—	4	2	no	—
408	#95	—	4	2	no	—
409	#95	—	4	1	no	—
410	#95	—	4	1	no	—
411	#95	—	4	1	no	—
412	#95	D₄×C₁₀₁	1	8	yes	complemented
413	C₂⁴	—	2	2	no	—
414	C₂⁴	—	2	2	no	—
415	C₂⁴	—	2	2	no	—
416	C₂⁴	—	2	2	no	—
417	C₂⁴	—	2	2	no	—
418	C₂⁴	—	2	2	no	—
419	C₂⁴	—	2	2	no	—
420	C₂⁴	—	2	2	no	—
421	C₂⁴	—	2	2	no	—
422	C₂⁴	—	2	2	no	—
423	C₂⁴	—	2	2	no	—
424	C₂⁴	—	2	2	no	—
425	C₂⁴	—	2	2	no	—
426	C₂⁴	—	2	2	no	—
427	C₂⁴	#41×C₁₀₁	1	4	yes	—
428	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
429	C₂×Q₈	—	4	4	no	—
430	C₂×Q₈	—	4	8	no	—
431	C₂×Q₈	—	4	8	no	—
432	C₂×Q₈	—	4	4	no	—
433	C₂×Q₈	—	4	4	no	—
434	C₂×D₄	—	4	8	no	—
435	C₂×D₄	—	4	4	no	—
436	C₂×D₄	—	4	4	no	—
437	C₂×D₄	—	4	8	no	—
438	C₂×D₄	—	4	4	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
483	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
484	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
485	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
486	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
487	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
488	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
489	C₄⋊C₄	—	4	4	no	—
490	C₂²⋊C₄	—	2	16	no	—
491	C₂²⋊C₄	—	4	8	no	—
492	C₂²⋊C₄	—	4	8	no	—
493	C₂²⋊C₄	—	4	8	no	—
494	C₂²⋊C₄	—	4	8	no	—
495	C₂²⋊C₄	—	4	8	no	—
496	C₄²	—	4	8	no	—
497	C₂³	—	2	4	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	2	4	no	—
502	C₂³	—	2	4	no	—
503	C₂³	—	2	4	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	2	no	—
507	C₂³	—	4	2	no	—
508	C₂³	—	4	2	no	—
509	C₂³	—	4	2	no	—
510	C₂³	—	4	2	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	4	2	no	—
515	C₂³	—	4	2	no	—
516	C₂³	—	4	2	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	4	2	no	—
519	C₂³	—	4	2	no	—
520	C₂³	—	4	2	no	—
521	C₂³	—	4	2	no	—
522	C₂³	—	4	2	no	—
523	C₂³	—	4	2	no	—
524	C₂³	—	4	2	no	—
525	C₂³	—	4	2	no	—
526	C₂³	—	4	2	no	—
527	C₂³	—	4	2	no	—
528	C₂³	—	4	2	no	—
529	C₂³	—	4	2	no	—
530	C₂³	—	4	2	no	—
531	C₂³	—	4	2	no	—
532	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
533	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
534	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
535	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
536	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
537	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
538	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
539	C₂³	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
540	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
541	C₂³	H(5,𝔽₂)×C₁₀₁	1	1	yes	characteristic
542	C₂³	2₋¹⁺⁴×C₁₀₁	1	1	yes	characteristic
543	Q₈	—	4	16	no	—
544	D₄	—	4	16	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	2	no	—
578	C₂×C₄	—	4	2	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂²	—	4	4	no	—
596	C₂²	—	4	4	no	—
597	C₂²	—	4	4	no	—
598	C₂²	—	4	4	no	—
599	C₂²	—	4	4	no	—
600	C₂²	—	4	4	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	8	2	no	—
603	C₂²	—	8	2	no	—
604	C₂²	—	8	2	no	—
605	C₂²	—	8	2	no	—
606	C₂²	—	8	2	no	—
607	C₂²	—	8	2	no	—
608	C₂²	—	8	2	no	—
609	C₂²	—	8	2	no	—
610	C₂²	#525×C₁₀₁	1	2	yes	—
611	C₂²	#529×C₁₀₁	1	2	yes	—
612	C₂²	#532×C₁₀₁	1	2	yes	—
613	C₂²	#535×C₁₀₁	1	2	yes	—
614	C₂²	#538×C₁₀₁	1	1	yes	characteristic
615	C₂²	#538×C₁₀₁	1	2	yes	—
616	C₂²	#538×C₁₀₁	1	1	yes	characteristic
617	C₂²	#539×C₁₀₁	1	2	yes	—
618	C₂²	#539×C₁₀₁	1	1	yes	characteristic
619	C₂²	D₄²×C₁₀₁	1	1	yes	characteristic
620	C₂²	#546×C₁₀₁	1	2	yes	—
621	C₂²	#546×C₁₀₁	1	2	yes	—
622	C₂²	#548×C₁₀₁	1	2	yes	—
623	C₂²	#551×C₁₀₁	1	2	yes	—
624	C₂²	#551×C₁₀₁	1	1	yes	characteristic
625	C₂²	#551×C₁₀₁	1	2	yes	—
626	C₂²	#555×C₁₀₁	1	2	yes	—
627	C₂²	#555×C₁₀₁	1	1	yes	characteristic
628	C₂²	#555×C₁₀₁	1	1	yes	characteristic
629	C₂²	#556×C₁₀₁	1	1	yes	characteristic
630	C₂²	#559×C₁₀₁	1	1	yes	characteristic
631	C₂²	H(3,𝔽₄)×C₁₀₁	1	1	yes	characteristic
632	C₂²	#562×C₁₀₁	1	1	yes	characteristic
633	C₄	—	4	4	no	—
634	C₄	—	4	2	no	—
635	C₄	—	4	4	no	—
636	C₄	—	4	4	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	2	no	—
639	C₄	—	4	4	no	—
640	C₄	—	8	2	no	—
641	C₂	—	8	4	no	—
642	C₂	C₁₀₁×#2459	1	2	yes	—
643	C₂	C₁₀₁×#2463	1	1	yes	characteristic
644	C₂	C₁₀₁×#2555	1	1	yes	characteristic
645	C₂	C₁₀₁×#2560	1	2	yes	—
646	C₂	C₁₀₁×#2572	1	1	yes	characteristic
647	C₂	C₁₀₁×#2610	1	2	yes	—
648	C₂	C₁₀₁×#2670	1	1	yes	characteristic
649	C₂	C₁₀₁×#2696	1	2	yes	—
650	C₂	C₁₀₁×#2736	1	1	yes	characteristic
651	C₂	C₁₀₁×#2785	1	1	yes	characteristic
652	C₂	C₁₀₁×#2808	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
1. C₂×#393×C₁₀₁	C₂	semidirect
2. C₂×#388×C₁₀₁	C₂	semidirect
3. C₁₀₁×#1446	C₂	semidirect
4. C₁₀₁×#1442	C₂	semidirect
5. C₁₀₁×#1440	C₂	semidirect
8. C₁₀₁×#1437	C₂	semidirect
9. C₁₀₁×#1434	C₂	semidirect
85. #95×C₁₀₁	D₄	semidirect
314. #15569	C₁₀₁	direct (N × H)
327. C₂×#393	C₂×C₁₀₁	semidirect
328. C₂×#388	C₂×C₁₀₁	semidirect
329. #1446	C₂×C₁₀₁	semidirect
330. #1442	C₂×C₁₀₁	semidirect
331. #1440	C₂×C₁₀₁	semidirect
334. #1437	C₂×C₁₀₁	semidirect
335. #1434	C₂×C₁₀₁	semidirect
336. C₁₀₁	#15569	direct (N × H)
412. #95	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×#393×C₁₀₁	2
C₂×#388×C₁₀₁	2
C₁₀₁×#1446	2
C₁₀₁×#1442	2
C₁₀₁×#1440	2
C₁₀₁×#1438	2
C₁₀₁×#1437	2
C₁₀₁×#1434	2
#15569	101

Subgroups — C101×#15569 #38797720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#15569 #38797720