Subgroups — C₁₀₁×#13839 #38795990

Order 25856.

2702 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×D₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₂²⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₂²⋊C₄×C₁₀₁	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1441	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1440	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1439	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#1438	C₂	1	2	yes	maximal
9	C₄×#95×C₁₀₁	C₂	1	2	yes	maximal, complemented
10	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₀₁	—	2	4	no	—
14	C₂×C₄×D₄×C₁₀₁	—	2	4	no	—
15	C₂×C₄×D₄×C₁₀₁	C₄	1	8	yes	complemented
16	C₂×#117×C₁₀₁	—	2	4	no	—
17	C₂×#117×C₁₀₁	—	2	8	no	—
18	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	4	yes	—
22	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
26	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₁₀₁	C₂²	1	2	yes	—
28	C₄×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
29	C₄×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
30	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
31	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
32	C₂×#95×C₁₀₁	C₂²	1	2	yes	—
33	C₂×#95×C₁₀₁	C₂²	1	4	yes	—
34	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
35	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
36	C₂²×D₄×C₁₀₁	—	2	2	no	—
37	C₂²×D₄×C₁₀₁	—	2	2	no	—
38	C₂²×D₄×C₁₀₁	—	2	4	no	—
39	C₂²×D₄×C₁₀₁	—	2	4	no	—
40	C₂²×D₄×C₁₀₁	C₂×C₄	1	4	yes	—
41	C₂³×C₄×C₁₀₁	—	2	4	no	—
42	C₂³×C₄×C₁₀₁	—	2	4	no	—
43	C₂³×C₄×C₁₀₁	—	2	2	no	—
44	C₂³×C₄×C₁₀₁	—	2	2	no	—
45	C₂³×C₄×C₁₀₁	—	2	4	no	—
46	C₂³×C₄×C₁₀₁	—	2	4	no	—
47	C₂³×C₄×C₁₀₁	C₂×C₄	1	4	yes	—
48	C₂³×C₄×C₁₀₁	C₂×C₄	1	4	yes	—
49	C₂³×C₄×C₁₀₁	D₄	1	4	yes	—
50	C₂³×C₄×C₁₀₁	D₄	1	4	yes	—
51	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₀₁	C₂³	1	4	yes	—
54	C₂³×C₄×C₁₀₁	C₂³	1	4	yes	—
55	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
58	C₄×D₄×C₁₀₁	—	2	32	no	—
59	#117×C₁₀₁	—	2	32	no	—
60	C₂×C₄⋊C₄×C₁₀₁	—	2	8	no	—
61	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
62	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
65	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
70	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
71	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
74	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
75	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
76	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
77	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
78	C₂×C₄²×C₁₀₁	—	2	4	no	—
79	C₂×C₄²×C₁₀₁	—	2	4	no	—
80	C₂×C₄²×C₁₀₁	—	2	2	no	—
81	C₂×C₄²×C₁₀₁	—	2	2	no	—
82	C₂×C₄²×C₁₀₁	—	2	4	no	—
83	C₂×C₄²×C₁₀₁	—	2	4	no	—
84	C₂×C₄²×C₁₀₁	—	2	4	no	—
85	C₂×C₄²×C₁₀₁	C₂×C₄	1	4	yes	—
86	C₂×C₄²×C₁₀₁	D₄	1	8	yes	complemented
87	#95×C₁₀₁	—	2	8	no	—
88	#95×C₁₀₁	—	2	4	no	—
89	#95×C₁₀₁	—	2	8	no	—
90	#95×C₁₀₁	—	2	8	no	—
91	C₂⁴×C₁₀₁	—	2	2	no	—
92	C₂⁴×C₁₀₁	—	2	2	no	—
93	C₂⁴×C₁₀₁	—	2	1	no	—
94	C₂⁴×C₁₀₁	—	2	1	no	—
95	C₂⁴×C₁₀₁	—	2	4	no	—
96	C₂⁴×C₁₀₁	—	2	4	no	—
97	C₂⁴×C₁₀₁	—	2	2	no	—
98	C₂⁴×C₁₀₁	—	2	2	no	—
99	C₂⁴×C₁₀₁	—	2	2	no	—
100	C₂⁴×C₁₀₁	—	2	2	no	—
101	C₂⁴×C₁₀₁	—	2	2	no	—
102	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
103	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
104	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
105	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
106	C₂⁴×C₁₀₁	#41	1	4	yes	—
107	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
108	C₂×D₄×C₁₀₁	—	2	16	no	—
109	C₂×D₄×C₁₀₁	—	2	16	no	—
110	C₂×D₄×C₁₀₁	—	2	8	no	—
111	C₂×D₄×C₁₀₁	—	2	8	no	—
112	C₂×D₄×C₁₀₁	—	2	8	no	—
113	C₂²×C₄×C₁₀₁	—	2	1	no	—
114	C₂²×C₄×C₁₀₁	—	2	1	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	16	no	—
119	C₂²×C₄×C₁₀₁	—	2	8	no	—
120	C₂²×C₄×C₁₀₁	—	2	16	no	—
121	C₂²×C₄×C₁₀₁	—	2	8	no	—
122	C₂²×C₄×C₁₀₁	—	2	2	no	—
123	C₂²×C₄×C₁₀₁	—	2	4	no	—
124	C₂²×C₄×C₁₀₁	—	2	4	no	—
125	C₂²×C₄×C₁₀₁	—	2	1	no	—
126	C₂²×C₄×C₁₀₁	—	2	1	no	—
127	C₂²×C₄×C₁₀₁	—	2	4	no	—
128	C₂²×C₄×C₁₀₁	—	2	4	no	—
129	C₂²×C₄×C₁₀₁	—	2	1	no	—
130	C₂²×C₄×C₁₀₁	—	2	1	no	—
131	C₂²×C₄×C₁₀₁	—	2	4	no	—
132	C₂²×C₄×C₁₀₁	—	2	4	no	—
133	C₂²×C₄×C₁₀₁	—	2	4	no	—
134	C₂²×C₄×C₁₀₁	—	2	4	no	—
135	C₂²×C₄×C₁₀₁	—	2	4	no	—
136	C₂²×C₄×C₁₀₁	—	2	4	no	—
137	C₂²×C₄×C₁₀₁	—	2	4	no	—
138	C₂²×C₄×C₁₀₁	—	2	4	no	—
139	C₂²×C₄×C₁₀₁	—	2	4	no	—
140	C₂²×C₄×C₁₀₁	—	2	2	no	—
141	C₂²×C₄×C₁₀₁	—	2	8	no	—
142	C₂²×C₄×C₁₀₁	—	2	16	no	—
143	C₂²×C₄×C₁₀₁	—	4	4	no	—
144	C₂²×C₄×C₁₀₁	—	4	8	no	—
145	C₂²×C₄×C₁₀₁	—	4	4	no	—
146	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	16	yes	complemented
147	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
148	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
149	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
150	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
151	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
152	C₂²×C₄×C₁₀₁	C₂×D₄	1	8	yes	—
153	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₁₀₁	#41	1	8	yes	—
159	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
160	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
161	C₄⋊C₄×C₁₀₁	—	2	16	no	—
162	C₄⋊C₄×C₁₀₁	—	2	8	no	—
163	C₂²⋊C₄×C₁₀₁	—	2	32	no	—
164	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
165	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
166	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
167	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
168	C₄²×C₁₀₁	—	2	8	no	—
169	C₄²×C₁₀₁	—	2	16	no	—
170	C₄²×C₁₀₁	—	4	8	no	—
171	C₂³×C₁₀₁	—	2	2	no	—
172	C₂³×C₁₀₁	—	2	2	no	—
173	C₂³×C₁₀₁	—	2	2	no	—
174	C₂³×C₁₀₁	—	2	2	no	—
175	C₂³×C₁₀₁	—	2	4	no	—
176	C₂³×C₁₀₁	—	2	4	no	—
177	C₂³×C₁₀₁	—	2	4	no	—
178	C₂³×C₁₀₁	—	2	4	no	—
179	C₂³×C₁₀₁	—	2	2	no	—
180	C₂³×C₁₀₁	—	2	4	no	—
181	C₂³×C₁₀₁	—	2	2	no	—
182	C₂³×C₁₀₁	—	2	4	no	—
183	C₂³×C₁₀₁	—	2	8	no	—
184	C₂³×C₁₀₁	—	2	4	no	—
185	C₂³×C₁₀₁	—	2	4	no	—
186	C₂³×C₁₀₁	—	2	4	no	—
187	C₂³×C₁₀₁	—	2	4	no	—
188	C₂³×C₁₀₁	—	2	8	no	—
189	C₂³×C₁₀₁	—	2	4	no	—
190	C₂³×C₁₀₁	—	4	1	no	—
191	C₂³×C₁₀₁	—	4	2	no	—
192	C₂³×C₁₀₁	—	4	1	no	—
193	C₂³×C₁₀₁	—	4	4	no	—
194	C₂³×C₁₀₁	—	4	2	no	—
195	C₂³×C₁₀₁	—	4	4	no	—
196	C₂³×C₁₀₁	—	4	4	no	—
197	C₂³×C₁₀₁	—	4	4	no	—
198	C₂³×C₁₀₁	—	4	4	no	—
199	C₂³×C₁₀₁	—	4	4	no	—
200	C₂³×C₁₀₁	—	4	2	no	—
201	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
202	C₂³×C₁₀₁	#117	1	4	yes	complemented
203	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
204	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
205	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
206	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
207	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
208	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
209	C₂³×C₁₀₁	C₂×#41	1	2	yes	—
210	C₂³×C₁₀₁	C₂×#41	1	4	yes	—
211	D₄×C₁₀₁	—	2	32	no	—
212	C₂×C₄×C₁₀₁	—	2	2	no	—
213	C₂×C₄×C₁₀₁	—	2	2	no	—
214	C₂×C₄×C₁₀₁	—	2	4	no	—
215	C₂×C₄×C₁₀₁	—	2	2	no	—
216	C₂×C₄×C₁₀₁	—	2	4	no	—
217	C₂×C₄×C₁₀₁	—	2	2	no	—
218	C₂×C₄×C₁₀₁	—	2	4	no	—
219	C₂×C₄×C₁₀₁	—	2	4	no	—
220	C₂×C₄×C₁₀₁	—	2	32	no	—
221	C₂×C₄×C₁₀₁	—	2	2	no	—
222	C₂×C₄×C₁₀₁	—	2	2	no	—
223	C₂×C₄×C₁₀₁	—	2	4	no	—
224	C₂×C₄×C₁₀₁	—	2	4	no	—
225	C₂×C₄×C₁₀₁	—	2	8	no	—
226	C₂×C₄×C₁₀₁	—	2	8	no	—
227	C₂×C₄×C₁₀₁	—	2	8	no	—
228	C₂×C₄×C₁₀₁	—	2	8	no	—
229	C₂×C₄×C₁₀₁	—	2	8	no	—
230	C₂×C₄×C₁₀₁	—	2	8	no	—
231	C₂×C₄×C₁₀₁	—	4	1	no	—
232	C₂×C₄×C₁₀₁	—	4	4	no	—
233	C₂×C₄×C₁₀₁	—	4	2	no	—
234	C₂×C₄×C₁₀₁	—	4	1	no	—
235	C₂×C₄×C₁₀₁	—	4	4	no	—
236	C₂×C₄×C₁₀₁	—	4	4	no	—
237	C₂×C₄×C₁₀₁	—	4	4	no	—
238	C₂×C₄×C₁₀₁	—	4	2	no	—
239	C₂×C₄×C₁₀₁	—	4	4	no	—
240	C₂×C₄×C₁₀₁	—	4	4	no	—
241	C₂×C₄×C₁₀₁	—	4	4	no	—
242	C₂×C₄×C₁₀₁	—	4	4	no	—
243	C₂×C₄×C₁₀₁	—	4	2	no	—
244	C₂×C₄×C₁₀₁	—	4	16	no	—
245	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
246	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
247	C₂×C₄×C₁₀₁	#117	1	4	yes	complemented
248	C₂×C₄×C₁₀₁	C₄×D₄	1	8	yes	—
249	C₂×C₄×C₁₀₁	#120	1	4	yes	—
250	C₂×C₄×C₁₀₁	#121	1	8	yes	—
251	C₂×C₄×C₁₀₁	#123	1	4	yes	—
252	C₂²×C₁₀₁	—	2	4	no	—
253	C₂²×C₁₀₁	—	2	4	no	—
254	C₂²×C₁₀₁	—	2	4	no	—
255	C₂²×C₁₀₁	—	2	8	no	—
256	C₂²×C₁₀₁	—	2	4	no	—
257	C₂²×C₁₀₁	—	4	4	no	—
258	C₂²×C₁₀₁	—	4	4	no	—
259	C₂²×C₁₀₁	—	4	8	no	—
260	C₂²×C₁₀₁	—	4	8	no	—
261	C₂²×C₁₀₁	—	4	4	no	—
262	C₂²×C₁₀₁	—	4	4	no	—
263	C₂²×C₁₀₁	—	4	2	no	—
264	C₂²×C₁₀₁	—	4	4	no	—
265	C₂²×C₁₀₁	—	4	4	no	—
266	C₂²×C₁₀₁	—	4	4	no	—
267	C₂²×C₁₀₁	—	4	2	no	—
268	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
269	C₂²×C₁₀₁	C₂×#117	1	1	yes	characteristic
270	C₂²×C₁₀₁	C₂×#117	1	1	yes	characteristic
271	C₂²×C₁₀₁	C₂×C₄×D₄	1	2	yes	—
272	C₂²×C₁₀₁	C₄×#41	1	2	yes	—
273	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
274	C₂²×C₁₀₁	C₂×#121	1	2	yes	—
275	C₂²×C₁₀₁	C₂×#123	1	1	yes	characteristic
276	C₂²×C₁₀₁	#525	1	4	yes	—
277	C₂²×C₁₀₁	#525	1	2	yes	—
278	C₂²×C₁₀₁	#525	1	2	yes	—
279	C₂²×C₁₀₁	#525	1	2	yes	—
280	C₂²×C₁₀₁	#529	1	4	yes	—
281	C₂²×C₁₀₁	#529	1	4	yes	—
282	C₂²×C₁₀₁	#532	1	4	yes	—
283	C₂²×C₁₀₁	#532	1	2	yes	—
284	C₄×C₁₀₁	—	2	4	no	—
285	C₄×C₁₀₁	—	2	4	no	—
286	C₄×C₁₀₁	—	4	8	no	—
287	C₄×C₁₀₁	—	4	8	no	—
288	C₄×C₁₀₁	—	4	2	no	—
289	C₄×C₁₀₁	—	4	2	no	—
290	C₄×C₁₀₁	#386	1	8	yes	—
291	#13839	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
292	C₂×C₁₀₁	—	4	4	no	—
293	C₂×C₁₀₁	—	4	4	no	—
294	C₂×C₁₀₁	#2280	1	1	yes	characteristic
295	C₂×C₁₀₁	C₂×#386	1	1	yes	characteristic
296	C₂×C₁₀₁	#2290	1	2	yes	—
297	C₂×C₁₀₁	#2293	1	2	yes	—
298	C₂×C₁₀₁	#2297	1	1	yes	characteristic
299	C₂×C₁₀₁	#2388	1	2	yes	—
300	C₂×C₁₀₁	#2392	1	4	yes	—
301	C₂×C₁₀₁	#2395	1	2	yes	—
302	C₂²×C₄×D₄	C₂×C₁₀₁	1	1	yes	characteristic
303	C₂²×#117	C₂×C₁₀₁	1	1	yes	characteristic, complemented
304	C₂×C₄×C₂²⋊C₄	C₂×C₁₀₁	1	2	yes	complemented
305	C₂×C₄×C₂²⋊C₄	C₂×C₁₀₁	1	1	yes	characteristic, complemented
306	#1441	C₂×C₁₀₁	1	2	yes	complemented
307	#1440	C₂×C₁₀₁	1	2	yes	complemented
308	#1439	C₂×C₁₀₁	1	2	yes	complemented
309	#1438	C₂×C₁₀₁	1	2	yes	—
310	C₄×#95	C₂×C₁₀₁	1	2	yes	complemented
311	C₁₀₁	#13839	1	1	yes	characteristic, direct product factor, Sylow
312	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
313	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
314	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
315	C₂×C₄×D₄	—	2	4	no	—
316	C₂×C₄×D₄	—	2	4	no	—
317	C₂×C₄×D₄	C₄×C₁₀₁	1	8	yes	complemented
318	C₂×#117	—	2	4	no	—
319	C₂×#117	—	2	8	no	—
320	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
321	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
322	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
323	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	4	yes	—
324	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	2	yes	—
325	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
326	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
327	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
328	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
329	C₂²×C₄²	C₂²×C₁₀₁	1	2	yes	—
330	C₄×C₂²⋊C₄	—	2	4	no	—
331	C₄×C₂²⋊C₄	—	2	8	no	—
332	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
333	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
334	C₂×#95	C₂²×C₁₀₁	1	2	yes	—
335	C₂×#95	C₂²×C₁₀₁	1	4	yes	—
336	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
337	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
338	C₂²×D₄	—	2	2	no	—
339	C₂²×D₄	—	2	2	no	—
340	C₂²×D₄	—	2	4	no	—
341	C₂²×D₄	—	2	4	no	—
342	C₂²×D₄	C₂×C₄×C₁₀₁	1	4	yes	—
343	C₂³×C₄	—	2	4	no	—
344	C₂³×C₄	—	2	4	no	—
345	C₂³×C₄	—	2	2	no	—
346	C₂³×C₄	—	2	2	no	—
347	C₂³×C₄	—	2	4	no	—
348	C₂³×C₄	—	2	4	no	—
349	C₂³×C₄	C₂×C₄×C₁₀₁	1	4	yes	—
350	C₂³×C₄	C₂×C₄×C₁₀₁	1	4	yes	—
351	C₂³×C₄	D₄×C₁₀₁	1	4	yes	—
352	C₂³×C₄	D₄×C₁₀₁	1	4	yes	—
353	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
354	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
355	C₂³×C₄	C₂³×C₁₀₁	1	4	yes	—
356	C₂³×C₄	C₂³×C₁₀₁	1	4	yes	—
357	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
359	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
360	C₄×D₄	—	2	32	no	—
361	#117	—	2	32	no	—
362	C₂×C₄⋊C₄	—	2	8	no	—
363	C₂×C₄⋊C₄	—	2	4	no	—
364	C₂×C₄⋊C₄	—	2	2	no	—
365	C₂×C₄⋊C₄	—	2	2	no	—
366	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
367	C₂×C₂²⋊C₄	—	2	4	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₂²⋊C₄	—	2	4	no	—
371	C₂×C₂²⋊C₄	—	2	8	no	—
372	C₂×C₂²⋊C₄	—	2	8	no	—
373	C₂×C₂²⋊C₄	—	2	2	no	—
374	C₂×C₂²⋊C₄	—	2	2	no	—
375	C₂×C₂²⋊C₄	—	2	8	no	—
376	C₂×C₂²⋊C₄	—	2	8	no	—
377	C₂×C₂²⋊C₄	—	2	8	no	—
378	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
379	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
380	C₂×C₄²	—	2	4	no	—
381	C₂×C₄²	—	2	4	no	—
382	C₂×C₄²	—	2	2	no	—
383	C₂×C₄²	—	2	2	no	—
384	C₂×C₄²	—	2	4	no	—
385	C₂×C₄²	—	2	4	no	—
386	C₂×C₄²	—	2	4	no	—
387	C₂×C₄²	C₂×C₄×C₁₀₁	1	4	yes	—
388	C₂×C₄²	D₄×C₁₀₁	1	8	yes	complemented
389	#95	—	2	8	no	—
390	#95	—	2	4	no	—
391	#95	—	2	8	no	—
392	#95	—	2	8	no	—
393	C₂⁴	—	2	2	no	—
394	C₂⁴	—	2	2	no	—
395	C₂⁴	—	2	1	no	—
396	C₂⁴	—	2	1	no	—
397	C₂⁴	—	2	4	no	—
398	C₂⁴	—	2	4	no	—
399	C₂⁴	—	2	2	no	—
400	C₂⁴	—	2	2	no	—
401	C₂⁴	—	2	2	no	—
402	C₂⁴	—	2	2	no	—
403	C₂⁴	—	2	2	no	—
404	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
405	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
406	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
407	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
408	C₂⁴	#41×C₁₀₁	1	4	yes	—
409	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
410	C₂×D₄	—	2	16	no	—
411	C₂×D₄	—	2	16	no	—
412	C₂×D₄	—	2	8	no	—
413	C₂×D₄	—	2	8	no	—
414	C₂×D₄	—	2	8	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	16	no	—
421	C₂²×C₄	—	2	8	no	—
422	C₂²×C₄	—	2	16	no	—
423	C₂²×C₄	—	2	8	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	8	no	—
444	C₂²×C₄	—	2	16	no	—
445	C₂²×C₄	—	4	4	no	—
446	C₂²×C₄	—	4	8	no	—
447	C₂²×C₄	—	4	4	no	—
448	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	16	yes	complemented
449	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
450	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
451	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
452	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
453	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
454	C₂²×C₄	C₂×D₄×C₁₀₁	1	8	yes	—
455	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
456	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
457	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
458	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
459	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
460	C₂²×C₄	#41×C₁₀₁	1	8	yes	—
461	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
462	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
463	C₄⋊C₄	—	2	16	no	—
464	C₄⋊C₄	—	2	8	no	—
465	C₂²⋊C₄	—	2	32	no	—
466	C₂²⋊C₄	—	2	16	no	—
467	C₂²⋊C₄	—	2	16	no	—
468	C₂²⋊C₄	—	2	8	no	—
469	C₂²⋊C₄	—	2	8	no	—
470	C₄²	—	2	8	no	—
471	C₄²	—	2	16	no	—
472	C₄²	—	4	8	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	4	no	—
478	C₂³	—	2	4	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	4	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	2	8	no	—
486	C₂³	—	2	4	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	8	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	2	no	—
496	C₂³	—	4	4	no	—
497	C₂³	—	4	4	no	—
498	C₂³	—	4	4	no	—
499	C₂³	—	4	4	no	—
500	C₂³	—	4	4	no	—
501	C₂³	—	4	4	no	—
502	C₂³	—	4	2	no	—
503	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
504	C₂³	#117×C₁₀₁	1	4	yes	complemented
505	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
506	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
507	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
508	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
509	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
510	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
511	C₂³	C₂×#41×C₁₀₁	1	2	yes	—
512	C₂³	C₂×#41×C₁₀₁	1	4	yes	—
513	D₄	—	2	32	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	32	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	8	no	—
528	C₂×C₄	—	2	8	no	—
529	C₂×C₄	—	2	8	no	—
530	C₂×C₄	—	2	8	no	—
531	C₂×C₄	—	2	8	no	—
532	C₂×C₄	—	2	8	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	4	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	4	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	4	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	—	4	4	no	—
542	C₂×C₄	—	4	4	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	4	no	—
545	C₂×C₄	—	4	4	no	—
546	C₂×C₄	—	4	16	no	—
547	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
548	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
549	C₂×C₄	#117×C₁₀₁	1	4	yes	complemented
550	C₂×C₄	C₄×D₄×C₁₀₁	1	8	yes	—
551	C₂×C₄	#120×C₁₀₁	1	4	yes	—
552	C₂×C₄	#121×C₁₀₁	1	8	yes	—
553	C₂×C₄	#123×C₁₀₁	1	4	yes	—
554	C₂²	—	2	4	no	—
555	C₂²	—	2	4	no	—
556	C₂²	—	2	4	no	—
557	C₂²	—	2	8	no	—
558	C₂²	—	2	4	no	—
559	C₂²	—	4	8	no	—
560	C₂²	—	4	8	no	—
561	C₂²	—	4	4	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	4	no	—
569	C₂²	—	4	4	no	—
570	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
571	C₂²	C₂×#117×C₁₀₁	1	1	yes	characteristic
572	C₂²	C₂×#117×C₁₀₁	1	1	yes	characteristic
573	C₂²	C₂×C₄×D₄×C₁₀₁	1	2	yes	—
574	C₂²	C₄×#41×C₁₀₁	1	2	yes	—
575	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
576	C₂²	C₂×#121×C₁₀₁	1	2	yes	—
577	C₂²	C₂×#123×C₁₀₁	1	1	yes	characteristic
578	C₂²	#525×C₁₀₁	1	2	yes	—
579	C₂²	#525×C₁₀₁	1	2	yes	—
580	C₂²	#525×C₁₀₁	1	4	yes	—
581	C₂²	#525×C₁₀₁	1	2	yes	—
582	C₂²	#529×C₁₀₁	1	4	yes	—
583	C₂²	#529×C₁₀₁	1	4	yes	—
584	C₂²	#532×C₁₀₁	1	4	yes	—
585	C₂²	#532×C₁₀₁	1	2	yes	—
586	C₄	—	2	4	no	—
587	C₄	—	2	4	no	—
588	C₄	—	4	8	no	—
589	C₄	—	4	2	no	—
590	C₄	—	4	2	no	—
591	C₄	—	4	8	no	—
592	C₄	#386×C₁₀₁	1	8	yes	—
593	C₂	—	4	4	no	—
594	C₂	—	4	4	no	—
595	C₂	C₁₀₁×#2280	1	1	yes	characteristic
596	C₂	C₂×#386×C₁₀₁	1	1	yes	characteristic
597	C₂	C₁₀₁×#2290	1	2	yes	—
598	C₂	C₁₀₁×#2293	1	2	yes	—
599	C₂	C₁₀₁×#2297	1	1	yes	characteristic
600	C₂	C₁₀₁×#2388	1	2	yes	—
601	C₂	C₁₀₁×#2392	1	4	yes	—
602	C₂	C₁₀₁×#2395	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₀₁	C₂³
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
socle	C₂⁴×C₁₀₁	C₂⁴
prime radical	C₂³×D₄×C₁₀₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#117×C₁₀₁	C₂	semidirect
3. C₂×C₄×C₂²⋊C₄×C₁₀₁	C₂	semidirect
4. C₂×C₄×C₂²⋊C₄×C₁₀₁	C₂	semidirect
5. C₁₀₁×#1441	C₂	semidirect
6. C₁₀₁×#1440	C₂	semidirect
7. C₁₀₁×#1439	C₂	semidirect
9. C₄×#95×C₁₀₁	C₂	semidirect
15. C₂×C₄×D₄×C₁₀₁	C₄	semidirect
86. C₂×C₄²×C₁₀₁	D₄	semidirect
146. C₂²×C₄×C₁₀₁	C₂²⋊C₄	semidirect
202. C₂³×C₁₀₁	#117	semidirect
247. C₂×C₄×C₁₀₁	#117	semidirect
291. #13839	C₁₀₁	direct (N × H)
303. C₂²×#117	C₂×C₁₀₁	semidirect
304. C₂×C₄×C₂²⋊C₄	C₂×C₁₀₁	semidirect
305. C₂×C₄×C₂²⋊C₄	C₂×C₁₀₁	semidirect
306. #1441	C₂×C₁₀₁	semidirect
307. #1440	C₂×C₁₀₁	semidirect
308. #1439	C₂×C₁₀₁	semidirect
310. C₄×#95	C₂×C₁₀₁	semidirect
311. C₁₀₁	#13839	direct (N × H)
317. C₂×C₄×D₄	C₄×C₁₀₁	semidirect
388. C₂×C₄²	D₄×C₁₀₁	semidirect
448. C₂²×C₄	C₂²⋊C₄×C₁₀₁	semidirect
504. C₂³	#117×C₁₀₁	semidirect
549. C₂×C₄	#117×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×D₄×C₁₀₁	2
C₂²×#117×C₁₀₁	2
C₂×C₄×C₂²⋊C₄×C₁₀₁	2
C₁₀₁×#1441	2
C₁₀₁×#1440	2
C₁₀₁×#1439	2
C₁₀₁×#1438	2
C₄×#95×C₁₀₁	2
#13839	101

Subgroups — C101×#13839 #38795990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#13839 #38795990