Subgroups — C₁₀₁×#10929 #38793080

Order 25856.

1010 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#104×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#416×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#408×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#341×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#339×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₁×#1729	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₁₀₁	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂×#104×C₁₀₁	—	2	2	no	—
16	C₂×#104×C₁₀₁	—	2	2	no	—
17	C₂×#104×C₁₀₁	C₄	1	4	yes	complemented
18	#416×C₁₀₁	—	2	2	no	—
19	#416×C₁₀₁	—	2	2	no	—
20	C₂×#103×C₁₀₁	C₄	1	2	yes	complemented
21	C₂×#102×C₁₀₁	C₄	1	2	yes	complemented
22	#408×C₁₀₁	—	2	2	no	—
23	#408×C₁₀₁	C₄	1	4	yes	complemented
24	C₂×C₂²⋊C₈×C₁₀₁	—	2	2	no	—
25	C₂×C₄×C₈×C₁₀₁	—	2	2	no	—
26	C₂×C₄×C₈×C₁₀₁	—	2	2	no	—
27	C₂×C₄×C₈×C₁₀₁	—	2	2	no	—
28	#341×C₁₀₁	—	2	2	no	—
29	#339×C₁₀₁	—	2	2	no	—
30	#336×C₁₀₁	—	2	2	no	—
31	C₂×#41×C₁₀₁	—	2	1	no	—
32	C₂×#41×C₁₀₁	—	2	1	no	—
33	C₂×#41×C₁₀₁	—	2	1	no	—
34	C₂×#41×C₁₀₁	—	2	1	no	—
35	C₂×#41×C₁₀₁	—	2	1	no	—
36	C₂×#41×C₁₀₁	—	2	1	no	—
37	C₂×#41×C₁₀₁	—	2	1	no	—
38	C₂×#41×C₁₀₁	—	2	1	no	—
39	C₂×#41×C₁₀₁	—	2	1	no	—
40	C₂×#41×C₁₀₁	—	2	1	no	—
41	C₂×#41×C₁₀₁	C₂×C₄	1	2	yes	—
42	C₂×#41×C₁₀₁	C₂×C₄	1	2	yes	—
43	C₂²×Q₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₀₁	—	2	1	no	—
45	C₂²×D₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₀₁	—	2	1	no	—
47	C₂³×C₄×C₁₀₁	—	2	1	no	—
48	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₁₀₁	—	2	1	no	—
50	C₂×M₁₆×C₁₀₁	—	2	1	no	—
51	C₂×M₁₆×C₁₀₁	—	2	1	no	—
52	C₂×M₁₆×C₁₀₁	—	2	1	no	—
53	C₂×M₁₆×C₁₀₁	—	2	1	no	—
54	C₂×M₁₆×C₁₀₁	—	2	1	no	—
55	C₂×M₁₆×C₁₀₁	—	2	1	no	—
56	C₂×M₁₆×C₁₀₁	—	2	1	no	—
57	C₂×M₁₆×C₁₀₁	—	2	1	no	—
58	C₂×M₁₆×C₁₀₁	—	2	1	no	—
59	C₂×M₁₆×C₁₀₁	C₂×C₄	1	2	yes	—
60	C₂×M₁₆×C₁₀₁	C₂×C₄	1	2	yes	—
61	C₂²×C₈×C₁₀₁	—	2	1	no	—
62	C₂²×C₈×C₁₀₁	—	2	1	no	—
63	C₂²×C₈×C₁₀₁	—	2	1	no	—
64	C₂²×C₈×C₁₀₁	—	2	1	no	—
65	C₂²×C₈×C₁₀₁	—	2	1	no	—
66	C₂²×C₈×C₁₀₁	—	2	1	no	—
67	C₂²×C₈×C₁₀₁	—	2	1	no	—
68	C₂²×C₈×C₁₀₁	—	2	1	no	—
69	C₂²×C₈×C₁₀₁	—	2	1	no	—
70	C₂²×C₈×C₁₀₁	—	2	1	no	—
71	C₂²×C₈×C₁₀₁	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₁₀₁	C₂×C₄	1	2	yes	—
73	C₂²×C₈×C₁₀₁	D₄	1	2	yes	—
74	C₂²×C₈×C₁₀₁	D₄	1	2	yes	—
75	C₂²×C₈×C₁₀₁	D₄	1	2	yes	—
76	C₂²×C₈×C₁₀₁	D₄	1	2	yes	—
77	#117×C₁₀₁	—	2	1	no	—
78	#117×C₁₀₁	—	2	1	no	—
79	#117×C₁₀₁	—	2	1	no	—
80	#117×C₁₀₁	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
83	C₂×C₄²×C₁₀₁	—	2	1	no	—
84	C₂×C₄²×C₁₀₁	—	2	1	no	—
85	C₂×C₄²×C₁₀₁	—	2	1	no	—
86	C₂×C₄²×C₁₀₁	—	2	1	no	—
87	C₂×C₄²×C₁₀₁	C₂×C₄	1	2	yes	—
88	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
89	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
90	#104×C₁₀₁	—	2	8	no	—
91	#103×C₁₀₁	—	2	4	no	—
92	#102×C₁₀₁	—	2	4	no	—
93	C₂²⋊C₈×C₁₀₁	—	2	8	no	—
94	C₄×C₈×C₁₀₁	—	2	8	no	—
95	C₂⁴×C₁₀₁	—	2	1	no	—
96	C₂⁴×C₁₀₁	#41	1	1	yes	characteristic
97	#41×C₁₀₁	—	2	2	no	—
98	#41×C₁₀₁	—	2	2	no	—
99	#41×C₁₀₁	—	2	2	no	—
100	#41×C₁₀₁	—	2	2	no	—
101	#41×C₁₀₁	—	2	2	no	—
102	#41×C₁₀₁	—	2	2	no	—
103	#41×C₁₀₁	—	2	2	no	—
104	#41×C₁₀₁	—	2	2	no	—
105	#41×C₁₀₁	—	4	1	no	—
106	#41×C₁₀₁	—	4	1	no	—
107	#41×C₁₀₁	—	4	1	no	—
108	#41×C₁₀₁	—	4	1	no	—
109	#41×C₁₀₁	—	4	1	no	—
110	#41×C₁₀₁	—	4	1	no	—
111	#41×C₁₀₁	—	4	1	no	—
112	#41×C₁₀₁	—	4	1	no	—
113	C₂×Q₈×C₁₀₁	—	2	1	no	—
114	C₂×Q₈×C₁₀₁	—	2	1	no	—
115	C₂×Q₈×C₁₀₁	—	2	1	no	—
116	C₂×Q₈×C₁₀₁	—	2	1	no	—
117	C₂×Q₈×C₁₀₁	—	2	1	no	—
118	C₂×Q₈×C₁₀₁	C₄²	1	2	yes	—
119	C₂×D₄×C₁₀₁	—	2	2	no	—
120	C₂×D₄×C₁₀₁	—	2	2	no	—
121	C₂×D₄×C₁₀₁	—	2	1	no	—
122	C₂×D₄×C₁₀₁	—	2	1	no	—
123	C₂×D₄×C₁₀₁	—	2	1	no	—
124	C₂×D₄×C₁₀₁	—	2	1	no	—
125	C₂×D₄×C₁₀₁	—	2	1	no	—
126	C₂×D₄×C₁₀₁	—	4	1	no	—
127	C₂×D₄×C₁₀₁	—	4	1	no	—
128	C₂×D₄×C₁₀₁	—	4	1	no	—
129	C₂×D₄×C₁₀₁	—	4	1	no	—
130	C₂×D₄×C₁₀₁	C₄²	1	2	yes	—
131	C₂²×C₄×C₁₀₁	—	2	8	no	—
132	C₂²×C₄×C₁₀₁	—	2	2	no	—
133	C₂²×C₄×C₁₀₁	—	2	2	no	—
134	C₂²×C₄×C₁₀₁	—	2	2	no	—
135	C₂²×C₄×C₁₀₁	—	2	1	no	—
136	C₂²×C₄×C₁₀₁	—	2	2	no	—
137	C₂²×C₄×C₁₀₁	—	2	2	no	—
138	C₂²×C₄×C₁₀₁	—	2	2	no	—
139	C₂²×C₄×C₁₀₁	—	4	1	no	—
140	C₂²×C₄×C₁₀₁	—	4	1	no	—
141	C₂²×C₄×C₁₀₁	—	4	1	no	—
142	C₂²×C₄×C₁₀₁	—	4	1	no	—
143	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₀₁	#41	1	1	yes	characteristic
153	C₂²×C₄×C₁₀₁	#41	1	1	yes	characteristic
154	C₂²×C₄×C₁₀₁	#41	1	1	yes	characteristic
155	C₂²×C₄×C₁₀₁	#41	1	1	yes	characteristic
156	C₂²×C₄×C₁₀₁	#41	1	1	yes	characteristic
157	M₁₆×C₁₀₁	—	2	2	no	—
158	M₁₆×C₁₀₁	—	2	2	no	—
159	M₁₆×C₁₀₁	—	2	2	no	—
160	M₁₆×C₁₀₁	—	2	2	no	—
161	M₁₆×C₁₀₁	—	4	1	no	—
162	M₁₆×C₁₀₁	—	4	1	no	—
163	M₁₆×C₁₀₁	—	4	1	no	—
164	M₁₆×C₁₀₁	—	4	1	no	—
165	C₂×C₈×C₁₀₁	—	2	2	no	—
166	C₂×C₈×C₁₀₁	—	2	2	no	—
167	C₂×C₈×C₁₀₁	—	2	2	no	—
168	C₂×C₈×C₁₀₁	—	2	2	no	—
169	C₂×C₈×C₁₀₁	—	2	2	no	—
170	C₂×C₈×C₁₀₁	—	2	2	no	—
171	C₂×C₈×C₁₀₁	—	2	2	no	—
172	C₂×C₈×C₁₀₁	—	2	2	no	—
173	C₂×C₈×C₁₀₁	—	2	2	no	—
174	C₂×C₈×C₁₀₁	—	2	2	no	—
175	C₂×C₈×C₁₀₁	—	2	2	no	—
176	C₂×C₈×C₁₀₁	—	2	2	no	—
177	C₂×C₈×C₁₀₁	—	2	2	no	—
178	C₂×C₈×C₁₀₁	—	2	2	no	—
179	C₂×C₈×C₁₀₁	—	4	1	no	—
180	C₂×C₈×C₁₀₁	—	4	1	no	—
181	C₂×C₈×C₁₀₁	—	4	1	no	—
182	C₂×C₈×C₁₀₁	—	4	1	no	—
183	C₂×C₈×C₁₀₁	C₂²⋊C₄	1	4	yes	—
184	C₂×C₈×C₁₀₁	C₂²⋊C₄	1	4	yes	—
185	C₄⋊C₄×C₁₀₁	—	2	2	no	—
186	C₄⋊C₄×C₁₀₁	—	2	2	no	—
187	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
188	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
189	C₄²×C₁₀₁	—	2	2	no	—
190	C₄²×C₁₀₁	—	2	2	no	—
191	C₄²×C₁₀₁	—	2	2	no	—
192	C₄²×C₁₀₁	—	4	1	no	—
193	C₄²×C₁₀₁	—	4	1	no	—
194	C₄²×C₁₀₁	C₂²⋊C₄	1	4	yes	—
195	C₂³×C₁₀₁	—	2	4	no	—
196	C₂³×C₁₀₁	—	2	2	no	—
197	C₂³×C₁₀₁	—	4	1	no	—
198	C₂³×C₁₀₁	—	4	1	no	—
199	C₂³×C₁₀₁	—	4	4	no	—
200	C₂³×C₁₀₁	#117	1	1	yes	characteristic
201	C₂³×C₁₀₁	C₄×D₄	1	1	yes	characteristic
202	C₂³×C₁₀₁	C₄×D₄	1	1	yes	characteristic
203	C₂³×C₁₀₁	#121	1	1	yes	characteristic
204	C₂³×C₁₀₁	#123	1	1	yes	characteristic
205	C₂³×C₁₀₁	#124	1	1	yes	characteristic
206	C₂³×C₁₀₁	#126	1	1	yes	characteristic
207	Q₈×C₁₀₁	—	2	2	no	—
208	Q₈×C₁₀₁	—	2	2	no	—
209	Q₈×C₁₀₁	—	4	1	no	—
210	Q₈×C₁₀₁	—	4	1	no	—
211	D₄×C₁₀₁	—	2	2	no	—
212	D₄×C₁₀₁	—	2	2	no	—
213	D₄×C₁₀₁	—	4	2	no	—
214	D₄×C₁₀₁	—	4	2	no	—
215	D₄×C₁₀₁	—	4	2	no	—
216	D₄×C₁₀₁	—	4	2	no	—
217	D₄×C₁₀₁	—	4	1	no	—
218	D₄×C₁₀₁	—	4	1	no	—
219	C₂×C₄×C₁₀₁	—	2	8	no	—
220	C₂×C₄×C₁₀₁	—	2	8	no	—
221	C₂×C₄×C₁₀₁	—	2	8	no	—
222	C₂×C₄×C₁₀₁	—	2	4	no	—
223	C₂×C₄×C₁₀₁	—	2	2	no	—
224	C₂×C₄×C₁₀₁	—	4	1	no	—
225	C₂×C₄×C₁₀₁	—	4	1	no	—
226	C₂×C₄×C₁₀₁	—	4	2	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	4	no	—
232	C₂×C₄×C₁₀₁	C₂×C₄²	1	1	yes	characteristic
233	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₁₀₁	#117	1	1	yes	characteristic
237	C₂×C₄×C₁₀₁	#117	1	1	yes	characteristic
238	C₂×C₄×C₁₀₁	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₀₁	C₄×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₀₁	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₀₁	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₀₁	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₀₁	C₄×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₀₁	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₀₁	C₄×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₀₁	C₄×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₀₁	C₄×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
249	C₂×C₄×C₁₀₁	#121	1	1	yes	characteristic
250	C₂×C₄×C₁₀₁	#121	1	1	yes	characteristic
251	C₂×C₄×C₁₀₁	#121	1	1	yes	characteristic
252	C₂×C₄×C₁₀₁	#121	1	1	yes	characteristic
253	C₂×C₄×C₁₀₁	#121	1	1	yes	characteristic
254	C₂×C₄×C₁₀₁	#123	1	1	yes	characteristic
255	C₂×C₄×C₁₀₁	#123	1	1	yes	characteristic
256	C₂×C₄×C₁₀₁	#124	1	1	yes	characteristic
257	C₂×C₄×C₁₀₁	#124	1	1	yes	characteristic
258	C₂×C₄×C₁₀₁	#126	1	1	yes	characteristic
259	C₂×C₄×C₁₀₁	#127	1	1	yes	characteristic
260	C₈×C₁₀₁	—	2	4	no	—
261	C₈×C₁₀₁	—	2	4	no	—
262	C₈×C₁₀₁	—	4	2	no	—
263	C₈×C₁₀₁	—	4	2	no	—
264	C₂²×C₁₀₁	—	2	2	no	—
265	C₂²×C₁₀₁	—	2	2	no	—
266	C₂²×C₁₀₁	—	2	2	no	—
267	C₂²×C₁₀₁	—	2	2	no	—
268	C₂²×C₁₀₁	—	2	2	no	—
269	C₂²×C₁₀₁	—	2	2	no	—
270	C₂²×C₁₀₁	—	4	2	no	—
271	C₂²×C₁₀₁	—	4	4	no	—
272	C₂²×C₁₀₁	—	8	2	no	—
273	C₂²×C₁₀₁	—	8	2	no	—
274	C₂²×C₁₀₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
275	C₂²×C₁₀₁	#386	1	1	yes	characteristic
276	C₂²×C₁₀₁	#388	1	1	yes	characteristic
277	C₂²×C₁₀₁	#388	1	1	yes	characteristic
278	C₂²×C₁₀₁	#388	1	1	yes	characteristic
279	C₂²×C₁₀₁	#388	1	1	yes	characteristic
280	C₂²×C₁₀₁	#390	1	1	yes	characteristic
281	C₂²×C₁₀₁	#443	1	4	yes	—
282	C₄×C₁₀₁	—	2	8	no	—
283	C₄×C₁₀₁	—	4	2	no	—
284	C₄×C₁₀₁	—	8	2	no	—
285	C₄×C₁₀₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
286	C₄×C₁₀₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
287	C₄×C₁₀₁	#386	1	1	yes	characteristic
288	C₄×C₁₀₁	#386	1	1	yes	characteristic
289	C₄×C₁₀₁	#388	1	1	yes	characteristic
290	C₄×C₁₀₁	#388	1	1	yes	characteristic
291	C₄×C₁₀₁	#390	1	1	yes	characteristic
292	C₄×C₁₀₁	#390	1	1	yes	characteristic
293	#10929	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
294	C₂×C₁₀₁	—	2	1	no	—
295	C₂×C₁₀₁	—	2	1	no	—
296	C₂×C₁₀₁	—	2	1	no	—
297	C₂×C₁₀₁	—	2	1	no	—
298	C₂×C₁₀₁	—	8	2	no	—
299	C₂×C₁₀₁	#1437	1	1	yes	characteristic
300	C₂×C₁₀₁	#1764	1	2	yes	—
301	C₂×C₁₀₁	#1937	1	2	yes	—
302	C₂×C₁₀₁	#1974	1	2	yes	—
303	C₂²×#104	C₂×C₁₀₁	1	1	yes	characteristic
304	C₂×#416	C₂×C₁₀₁	1	1	yes	characteristic
305	C₂×#408	C₂×C₁₀₁	1	1	yes	characteristic
306	C₂²×C₄×C₈	C₂×C₁₀₁	1	1	yes	characteristic, complemented
307	C₂×#341	C₂×C₁₀₁	1	1	yes	characteristic, complemented
308	C₂×#339	C₂×C₁₀₁	1	1	yes	characteristic, complemented
309	#1729	C₂×C₁₀₁	1	1	yes	characteristic, complemented
310	C₁₀₁	#10929	1	1	yes	characteristic, direct product factor, Sylow
311	C₂²×#41	C₂²×C₁₀₁	1	1	yes	characteristic
312	C₂²×M₁₆	C₂²×C₁₀₁	1	1	yes	characteristic
313	C₂²×M₁₆	C₂²×C₁₀₁	1	1	yes	characteristic
314	C₂³×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
315	C₂³×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
316	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
317	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
318	C₂×#104	—	2	2	no	—
319	C₂×#104	—	2	2	no	—
320	C₂×#104	C₄×C₁₀₁	1	4	yes	complemented
321	#416	—	2	2	no	—
322	#416	—	2	2	no	—
323	C₂×#103	C₄×C₁₀₁	1	2	yes	complemented
324	C₂×#102	C₄×C₁₀₁	1	2	yes	complemented
325	#408	—	2	2	no	—
326	#408	C₄×C₁₀₁	1	4	yes	complemented
327	C₂×C₂²⋊C₈	—	2	2	no	—
328	C₂×C₄×C₈	—	2	2	no	—
329	C₂×C₄×C₈	—	2	2	no	—
330	C₂×C₄×C₈	—	2	2	no	—
331	#341	—	2	2	no	—
332	#339	—	2	2	no	—
333	#336	—	2	2	no	—
334	C₂×#41	—	2	1	no	—
335	C₂×#41	—	2	1	no	—
336	C₂×#41	—	2	1	no	—
337	C₂×#41	—	2	1	no	—
338	C₂×#41	—	2	1	no	—
339	C₂×#41	—	2	1	no	—
340	C₂×#41	—	2	1	no	—
341	C₂×#41	—	2	1	no	—
342	C₂×#41	—	2	1	no	—
343	C₂×#41	—	2	1	no	—
344	C₂×#41	C₂×C₄×C₁₀₁	1	2	yes	—
345	C₂×#41	C₂×C₄×C₁₀₁	1	2	yes	—
346	C₂²×Q₈	C₂×C₄×C₁₀₁	1	1	yes	characteristic
347	C₂²×D₄	—	2	1	no	—
348	C₂²×D₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
349	C₂³×C₄	—	2	1	no	—
350	C₂³×C₄	—	2	1	no	—
351	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	C₂×C₄×C₁₀₁	1	2	yes	—
363	C₂×M₁₆	C₂×C₄×C₁₀₁	1	2	yes	—
364	C₂²×C₈	—	2	1	no	—
365	C₂²×C₈	—	2	1	no	—
366	C₂²×C₈	—	2	1	no	—
367	C₂²×C₈	—	2	1	no	—
368	C₂²×C₈	—	2	1	no	—
369	C₂²×C₈	—	2	1	no	—
370	C₂²×C₈	—	2	1	no	—
371	C₂²×C₈	—	2	1	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₂²×C₈	C₂×C₄×C₁₀₁	1	2	yes	—
375	C₂²×C₈	C₂×C₄×C₁₀₁	1	2	yes	—
376	C₂²×C₈	D₄×C₁₀₁	1	2	yes	—
377	C₂²×C₈	D₄×C₁₀₁	1	2	yes	—
378	C₂²×C₈	D₄×C₁₀₁	1	2	yes	—
379	C₂²×C₈	D₄×C₁₀₁	1	2	yes	—
380	#117	—	2	1	no	—
381	#117	—	2	1	no	—
382	#117	—	2	1	no	—
383	#117	—	2	1	no	—
384	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	—	2	1	no	—
388	C₂×C₄²	—	2	1	no	—
389	C₂×C₄²	—	2	1	no	—
390	C₂×C₄²	C₂×C₄×C₁₀₁	1	2	yes	—
391	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
392	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
393	#104	—	2	8	no	—
394	#103	—	2	4	no	—
395	#102	—	2	4	no	—
396	C₂²⋊C₈	—	2	8	no	—
397	C₄×C₈	—	2	8	no	—
398	C₂⁴	—	2	1	no	—
399	C₂⁴	#41×C₁₀₁	1	1	yes	characteristic
400	#41	—	2	2	no	—
401	#41	—	2	2	no	—
402	#41	—	2	2	no	—
403	#41	—	2	2	no	—
404	#41	—	2	2	no	—
405	#41	—	2	2	no	—
406	#41	—	2	2	no	—
407	#41	—	2	2	no	—
408	#41	—	4	1	no	—
409	#41	—	4	1	no	—
410	#41	—	4	1	no	—
411	#41	—	4	1	no	—
412	#41	—	4	1	no	—
413	#41	—	4	1	no	—
414	#41	—	4	1	no	—
415	#41	—	4	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	C₄²×C₁₀₁	1	2	yes	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	—	4	1	no	—
431	C₂×D₄	—	4	1	no	—
432	C₂×D₄	—	4	1	no	—
433	C₂×D₄	C₄²×C₁₀₁	1	2	yes	—
434	C₂²×C₄	—	2	8	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	4	1	no	—
443	C₂²×C₄	—	4	1	no	—
444	C₂²×C₄	—	4	1	no	—
445	C₂²×C₄	—	4	1	no	—
446	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
447	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
448	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
455	C₂²×C₄	#41×C₁₀₁	1	1	yes	characteristic
456	C₂²×C₄	#41×C₁₀₁	1	1	yes	characteristic
457	C₂²×C₄	#41×C₁₀₁	1	1	yes	characteristic
458	C₂²×C₄	#41×C₁₀₁	1	1	yes	characteristic
459	C₂²×C₄	#41×C₁₀₁	1	1	yes	characteristic
460	M₁₆	—	2	2	no	—
461	M₁₆	—	2	2	no	—
462	M₁₆	—	2	2	no	—
463	M₁₆	—	2	2	no	—
464	M₁₆	—	4	1	no	—
465	M₁₆	—	4	1	no	—
466	M₁₆	—	4	1	no	—
467	M₁₆	—	4	1	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	4	1	no	—
483	C₂×C₈	—	4	1	no	—
484	C₂×C₈	—	4	1	no	—
485	C₂×C₈	—	4	1	no	—
486	C₂×C₈	C₂²⋊C₄×C₁₀₁	1	4	yes	—
487	C₂×C₈	C₂²⋊C₄×C₁₀₁	1	4	yes	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₄²	—	2	2	no	—
493	C₄²	—	2	2	no	—
494	C₄²	—	2	2	no	—
495	C₄²	—	4	1	no	—
496	C₄²	—	4	1	no	—
497	C₄²	C₂²⋊C₄×C₁₀₁	1	4	yes	—
498	C₂³	—	2	4	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	4	4	no	—
501	C₂³	—	4	1	no	—
502	C₂³	—	4	1	no	—
503	C₂³	#117×C₁₀₁	1	1	yes	characteristic
504	C₂³	C₄×D₄×C₁₀₁	1	1	yes	characteristic
505	C₂³	C₄×D₄×C₁₀₁	1	1	yes	characteristic
506	C₂³	#121×C₁₀₁	1	1	yes	characteristic
507	C₂³	#123×C₁₀₁	1	1	yes	characteristic
508	C₂³	#124×C₁₀₁	1	1	yes	characteristic
509	C₂³	#126×C₁₀₁	1	1	yes	characteristic
510	Q₈	—	2	2	no	—
511	Q₈	—	2	2	no	—
512	Q₈	—	4	1	no	—
513	Q₈	—	4	1	no	—
514	D₄	—	2	2	no	—
515	D₄	—	2	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	1	no	—
522	C₂×C₄	—	2	8	no	—
523	C₂×C₄	—	2	8	no	—
524	C₂×C₄	—	2	8	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	2	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	4	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	C₂×C₄²×C₁₀₁	1	1	yes	characteristic
536	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
537	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
538	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
539	C₂×C₄	#117×C₁₀₁	1	1	yes	characteristic
540	C₂×C₄	#117×C₁₀₁	1	1	yes	characteristic
541	C₂×C₄	C₄×D₄×C₁₀₁	1	1	yes	characteristic
542	C₂×C₄	C₄×D₄×C₁₀₁	1	1	yes	characteristic
543	C₂×C₄	C₄×D₄×C₁₀₁	1	1	yes	characteristic
544	C₂×C₄	C₄×D₄×C₁₀₁	1	1	yes	characteristic
545	C₂×C₄	C₄×D₄×C₁₀₁	1	1	yes	characteristic
546	C₂×C₄	C₄×D₄×C₁₀₁	1	1	yes	characteristic
547	C₂×C₄	C₄×D₄×C₁₀₁	1	1	yes	characteristic
548	C₂×C₄	C₄×D₄×C₁₀₁	1	1	yes	characteristic
549	C₂×C₄	C₄×D₄×C₁₀₁	1	1	yes	characteristic
550	C₂×C₄	C₄×D₄×C₁₀₁	1	1	yes	characteristic
551	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
552	C₂×C₄	#121×C₁₀₁	1	1	yes	characteristic
553	C₂×C₄	#121×C₁₀₁	1	1	yes	characteristic
554	C₂×C₄	#121×C₁₀₁	1	1	yes	characteristic
555	C₂×C₄	#121×C₁₀₁	1	1	yes	characteristic
556	C₂×C₄	#121×C₁₀₁	1	1	yes	characteristic
557	C₂×C₄	#123×C₁₀₁	1	1	yes	characteristic
558	C₂×C₄	#123×C₁₀₁	1	1	yes	characteristic
559	C₂×C₄	#124×C₁₀₁	1	1	yes	characteristic
560	C₂×C₄	#124×C₁₀₁	1	1	yes	characteristic
561	C₂×C₄	#126×C₁₀₁	1	1	yes	characteristic
562	C₂×C₄	#127×C₁₀₁	1	1	yes	characteristic
563	C₈	—	2	4	no	—
564	C₈	—	2	4	no	—
565	C₈	—	4	2	no	—
566	C₈	—	4	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	4	no	—
575	C₂²	—	8	2	no	—
576	C₂²	—	8	2	no	—
577	C₂²	C₄×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
578	C₂²	#386×C₁₀₁	1	1	yes	characteristic
579	C₂²	#388×C₁₀₁	1	1	yes	characteristic
580	C₂²	#388×C₁₀₁	1	1	yes	characteristic
581	C₂²	#388×C₁₀₁	1	1	yes	characteristic
582	C₂²	#388×C₁₀₁	1	1	yes	characteristic
583	C₂²	#390×C₁₀₁	1	1	yes	characteristic
584	C₂²	#443×C₁₀₁	1	4	yes	—
585	C₄	—	2	8	no	—
586	C₄	—	4	2	no	—
587	C₄	—	8	2	no	—
588	C₄	C₄×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
589	C₄	C₄×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
590	C₄	#386×C₁₀₁	1	1	yes	characteristic
591	C₄	#386×C₁₀₁	1	1	yes	characteristic
592	C₄	#388×C₁₀₁	1	1	yes	characteristic
593	C₄	#388×C₁₀₁	1	1	yes	characteristic
594	C₄	#390×C₁₀₁	1	1	yes	characteristic
595	C₄	#390×C₁₀₁	1	1	yes	characteristic
596	C₂	—	2	1	no	—
597	C₂	—	2	1	no	—
598	C₂	—	2	1	no	—
599	C₂	—	2	1	no	—
600	C₂	—	8	2	no	—
601	C₂	C₁₀₁×#1437	1	1	yes	characteristic
602	C₂	C₁₀₁×#1764	1	2	yes	—
603	C₂	C₁₀₁×#1937	1	2	yes	—
604	C₂	C₁₀₁×#1974	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₀₁	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₀₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₀₁
socle	C₂³×C₁₀₁	C₄×D₄
prime radical	C₂²×#41×C₁₀₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₁ ◁ C₂³×C₈×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂²×C₄×C₈×C₁₀₁	C₂	semidirect
5. C₂×#341×C₁₀₁	C₂	semidirect
6. C₂×#339×C₁₀₁	C₂	semidirect
7. C₁₀₁×#1729	C₂	semidirect
17. C₂×#104×C₁₀₁	C₄	semidirect
20. C₂×#103×C₁₀₁	C₄	semidirect
21. C₂×#102×C₁₀₁	C₄	semidirect
23. #408×C₁₀₁	C₄	semidirect
293. #10929	C₁₀₁	direct (N × H)
306. C₂²×C₄×C₈	C₂×C₁₀₁	semidirect
307. C₂×#341	C₂×C₁₀₁	semidirect
308. C₂×#339	C₂×C₁₀₁	semidirect
309. #1729	C₂×C₁₀₁	semidirect
310. C₁₀₁	#10929	direct (N × H)
320. C₂×#104	C₄×C₁₀₁	semidirect
323. C₂×#103	C₄×C₁₀₁	semidirect
324. C₂×#102	C₄×C₁₀₁	semidirect
326. #408	C₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#104×C₁₀₁	2
C₂×#416×C₁₀₁	2
C₂×#408×C₁₀₁	2
C₂²×C₄×C₈×C₁₀₁	2
C₂×#341×C₁₀₁	2
C₂×#339×C₁₀₁	2
C₁₀₁×#1729	2
#10929	101

Subgroups — C101×#10929 #38793080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#10929 #38793080