Subgroups — C₁₀₁×#17625 #38799776

Order 25856.

1002 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3505	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#2973	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₁×#2357	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#1516	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1512	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1511	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₁×#1510	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₁×#1509	C₂	1	2	yes	maximal, complemented
9	C₁₀₁×#1508	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₀₁×#1507	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₀₁×#1501	C₂	1	2	yes	maximal, complemented
12	#553×C₁₀₁	—	2	2	no	—
13	#553×C₁₀₁	C₄	1	2	yes	complemented
14	#552×C₁₀₁	C₄	1	2	yes	complemented
15	#551×C₁₀₁	—	2	2	no	—
16	#548×C₁₀₁	C₄	1	2	yes	complemented
17	#546×C₁₀₁	C₄	1	2	yes	complemented
18	#539×C₁₀₁	—	2	1	no	—
19	#538×C₁₀₁	—	2	1	no	—
20	#534×C₁₀₁	—	2	1	no	—
21	#529×C₁₀₁	C₂²	1	2	yes	—
22	#525×C₁₀₁	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
24	C₂×#121×C₁₀₁	C₂²	1	1	yes	characteristic
25	#518×C₁₀₁	—	2	1	no	—
26	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
27	#435×C₁₀₁	—	2	2	no	—
28	#435×C₁₀₁	—	2	2	no	—
29	#432×C₁₀₁	C₂²	1	2	yes	complemented
30	#407×C₁₀₁	C₂²	1	1	yes	characteristic
31	#407×C₁₀₁	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	2	yes	complemented
33	#390×C₁₀₁	—	2	1	no	—
34	#388×C₁₀₁	—	2	1	no	—
35	#388×C₁₀₁	—	2	1	no	—
36	#382×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
37	#381×C₁₀₁	C₂²	1	1	yes	characteristic
38	#381×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₄⋊C₄×C₁₀₁	—	2	1	no	—
40	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
41	C₄×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
42	C₄×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
43	#328×C₁₀₁	C₂²	1	2	yes	complemented
44	#328×C₁₀₁	C₂²	1	2	yes	complemented
45	#328×C₁₀₁	C₂²	1	2	yes	complemented
46	#328×C₁₀₁	C₂²	1	2	yes	complemented
47	#327×C₁₀₁	C₂²	1	2	yes	—
48	#327×C₁₀₁	C₂²	1	2	yes	—
49	#327×C₁₀₁	C₂²	1	2	yes	—
50	#327×C₁₀₁	C₂²	1	2	yes	—
51	C₂×#41×C₁₀₁	C₂×C₄	1	2	yes	—
52	C₂²×Q₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
53	C₂²×D₄×C₁₀₁	—	2	1	no	—
54	C₂²×D₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
55	C₂²×D₄×C₁₀₁	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
58	C₂×M₁₆×C₁₀₁	—	2	1	no	—
59	C₂×M₁₆×C₁₀₁	—	2	1	no	—
60	C₂²×C₈×C₁₀₁	—	2	2	no	—
61	#126×C₁₀₁	—	2	2	no	—
62	#126×C₁₀₁	—	2	2	no	—
63	#126×C₁₀₁	—	2	2	no	—
64	#125×C₁₀₁	—	2	2	no	—
65	#125×C₁₀₁	C₂×C₄	1	2	yes	—
66	#124×C₁₀₁	—	2	2	no	—
67	#124×C₁₀₁	C₂×C₄	1	2	yes	—
68	#123×C₁₀₁	—	2	2	no	—
69	#123×C₁₀₁	—	2	2	no	—
70	#123×C₁₀₁	—	2	2	no	—
71	#123×C₁₀₁	—	2	2	no	—
72	#123×C₁₀₁	—	2	2	no	—
73	C₂²⋊Q₈×C₁₀₁	—	2	1	no	—
74	C₂²⋊Q₈×C₁₀₁	—	2	1	no	—
75	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
76	C₂²⋊Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
77	C₂²⋊Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
78	C₂²⋊Q₈×C₁₀₁	C₂³	1	2	yes	—
79	#121×C₁₀₁	—	2	2	no	—
80	#121×C₁₀₁	—	2	2	no	—
81	#121×C₁₀₁	—	2	1	no	—
82	#121×C₁₀₁	—	2	1	no	—
83	#121×C₁₀₁	—	2	2	no	—
84	#121×C₁₀₁	C₂×C₄	1	2	yes	—
85	#121×C₁₀₁	C₂×C₄	1	2	yes	—
86	#121×C₁₀₁	C₂³	1	2	yes	—
87	#120×C₁₀₁	—	2	2	no	—
88	#120×C₁₀₁	—	2	2	no	—
89	C₄×Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
90	C₄×D₄×C₁₀₁	—	2	2	no	—
91	C₄×D₄×C₁₀₁	—	2	2	no	—
92	C₄×D₄×C₁₀₁	—	2	2	no	—
93	C₄×D₄×C₁₀₁	—	2	2	no	—
94	C₄×D₄×C₁₀₁	—	2	2	no	—
95	C₄×D₄×C₁₀₁	C₂×C₄	1	2	yes	—
96	C₄×D₄×C₁₀₁	C₂×C₄	1	2	yes	—
97	C₄×D₄×C₁₀₁	C₂×C₄	1	2	yes	—
98	C₄×D₄×C₁₀₁	D₄	1	2	yes	—
99	C₄×D₄×C₁₀₁	D₄	1	2	yes	—
100	#117×C₁₀₁	—	2	2	no	—
101	#117×C₁₀₁	—	2	2	no	—
102	#117×C₁₀₁	C₂×C₄	1	2	yes	—
103	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
104	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
105	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
106	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
112	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₁₀₁	—	2	1	no	—
119	C₂×C₄²×C₁₀₁	—	2	1	no	—
120	C₂×C₄²×C₁₀₁	—	2	1	no	—
121	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
122	C₄⋊C₈×C₁₀₁	—	2	2	no	—
123	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
124	C₂²⋊C₈×C₁₀₁	—	2	1	no	—
125	C₂²⋊C₈×C₁₀₁	—	2	1	no	—
126	C₂²⋊C₈×C₁₀₁	C₂³	1	2	yes	—
127	C₂²⋊C₈×C₁₀₁	C₂³	1	2	yes	—
128	#97×C₁₀₁	—	2	2	no	—
129	#95×C₁₀₁	—	2	1	no	—
130	#95×C₁₀₁	—	2	1	no	—
131	#95×C₁₀₁	—	2	1	no	—
132	#95×C₁₀₁	C₂³	1	1	yes	characteristic
133	#95×C₁₀₁	C₂³	1	1	yes	characteristic
134	#95×C₁₀₁	C₂³	1	1	yes	characteristic
135	#95×C₁₀₁	C₂³	1	1	yes	characteristic
136	C₂⁴×C₁₀₁	—	2	1	no	—
137	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
138	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
139	#41×C₁₀₁	—	8	2	no	—
140	C₂×Q₈×C₁₀₁	—	2	1	no	—
141	C₂×Q₈×C₁₀₁	—	8	1	no	—
142	C₂×Q₈×C₁₀₁	C₂²×C₄	1	2	yes	—
143	C₂×D₄×C₁₀₁	—	2	2	no	—
144	C₂×D₄×C₁₀₁	—	2	2	no	—
145	C₂×D₄×C₁₀₁	—	2	2	no	—
146	C₂×D₄×C₁₀₁	—	2	2	no	—
147	C₂×D₄×C₁₀₁	—	2	1	no	—
148	C₂×D₄×C₁₀₁	—	4	1	no	—
149	C₂×D₄×C₁₀₁	—	4	1	no	—
150	C₂×D₄×C₁₀₁	—	4	2	no	—
151	C₂×D₄×C₁₀₁	—	4	2	no	—
152	C₂×D₄×C₁₀₁	—	8	1	no	—
153	C₂×D₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
154	C₂×D₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
155	C₂×D₄×C₁₀₁	C₂²×C₄	1	2	yes	—
156	C₂²×C₄×C₁₀₁	—	2	1	no	—
157	C₂²×C₄×C₁₀₁	—	2	1	no	—
158	C₂²×C₄×C₁₀₁	—	2	1	no	—
159	C₂²×C₄×C₁₀₁	—	2	1	no	—
160	C₂²×C₄×C₁₀₁	—	2	2	no	—
161	C₂²×C₄×C₁₀₁	—	2	2	no	—
162	C₂²×C₄×C₁₀₁	—	2	1	no	—
163	C₂²×C₄×C₁₀₁	—	2	1	no	—
164	C₂²×C₄×C₁₀₁	—	2	1	no	—
165	C₂²×C₄×C₁₀₁	—	8	1	no	—
166	C₂²×C₄×C₁₀₁	—	8	1	no	—
167	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
170	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
178	M₁₆×C₁₀₁	—	8	1	no	—
179	M₁₆×C₁₀₁	—	8	1	no	—
180	C₂×C₈×C₁₀₁	—	2	2	no	—
181	C₂×C₈×C₁₀₁	—	2	2	no	—
182	C₂×C₈×C₁₀₁	—	8	2	no	—
183	C₄⋊C₄×C₁₀₁	—	2	2	no	—
184	C₄⋊C₄×C₁₀₁	—	2	1	no	—
185	C₄⋊C₄×C₁₀₁	—	2	1	no	—
186	C₄⋊C₄×C₁₀₁	—	2	2	no	—
187	C₄⋊C₄×C₁₀₁	—	2	2	no	—
188	C₄⋊C₄×C₁₀₁	—	2	2	no	—
189	C₄⋊C₄×C₁₀₁	—	2	2	no	—
190	C₄⋊C₄×C₁₀₁	—	2	2	no	—
191	C₄⋊C₄×C₁₀₁	—	4	2	no	—
192	C₄⋊C₄×C₁₀₁	—	4	2	no	—
193	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
194	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
195	C₄⋊C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
196	C₄⋊C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
197	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
198	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
199	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
200	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
201	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
202	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
203	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
204	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
205	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
206	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
207	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
208	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
209	C₂²⋊C₄×C₁₀₁	—	8	1	no	—
210	C₂²⋊C₄×C₁₀₁	—	8	1	no	—
211	C₂²⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
212	C₂²⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
213	C₂²⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
214	C₂²⋊C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
215	C₄²×C₁₀₁	—	2	2	no	—
216	C₄²×C₁₀₁	—	2	2	no	—
217	C₄²×C₁₀₁	—	4	2	no	—
218	C₄²×C₁₀₁	—	8	1	no	—
219	C₄²×C₁₀₁	—	8	1	no	—
220	C₄²×C₁₀₁	C₂²×C₄	1	2	yes	—
221	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
222	C₂³×C₁₀₁	—	2	1	no	—
223	C₂³×C₁₀₁	—	2	1	no	—
224	C₂³×C₁₀₁	—	2	1	no	—
225	C₂³×C₁₀₁	—	2	1	no	—
226	C₂³×C₁₀₁	—	2	2	no	—
227	C₂³×C₁₀₁	—	4	1	no	—
228	C₂³×C₁₀₁	—	4	1	no	—
229	C₂³×C₁₀₁	—	4	1	no	—
230	C₂³×C₁₀₁	—	4	1	no	—
231	C₂³×C₁₀₁	—	4	2	no	—
232	C₂³×C₁₀₁	—	8	1	no	—
233	C₂³×C₁₀₁	—	8	1	no	—
234	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
236	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
238	Q₈×C₁₀₁	—	4	2	no	—
239	Q₈×C₁₀₁	—	8	1	no	—
240	D₄×C₁₀₁	—	4	2	no	—
241	D₄×C₁₀₁	—	4	2	no	—
242	D₄×C₁₀₁	—	4	2	no	—
243	D₄×C₁₀₁	—	4	4	no	—
244	D₄×C₁₀₁	—	4	2	no	—
245	D₄×C₁₀₁	—	4	2	no	—
246	D₄×C₁₀₁	—	8	1	no	—
247	D₄×C₁₀₁	—	8	2	no	—
248	D₄×C₁₀₁	—	8	2	no	—
249	C₂×C₄×C₁₀₁	—	2	1	no	—
250	C₂×C₄×C₁₀₁	—	2	1	no	—
251	C₂×C₄×C₁₀₁	—	2	2	no	—
252	C₂×C₄×C₁₀₁	—	2	2	no	—
253	C₂×C₄×C₁₀₁	—	2	2	no	—
254	C₂×C₄×C₁₀₁	—	2	2	no	—
255	C₂×C₄×C₁₀₁	—	4	1	no	—
256	C₂×C₄×C₁₀₁	—	4	1	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	1	no	—
261	C₂×C₄×C₁₀₁	—	4	1	no	—
262	C₂×C₄×C₁₀₁	—	4	1	no	—
263	C₂×C₄×C₁₀₁	—	4	1	no	—
264	C₂×C₄×C₁₀₁	—	4	2	no	—
265	C₂×C₄×C₁₀₁	—	4	1	no	—
266	C₂×C₄×C₁₀₁	—	4	2	no	—
267	C₂×C₄×C₁₀₁	—	4	1	no	—
268	C₂×C₄×C₁₀₁	—	4	1	no	—
269	C₂×C₄×C₁₀₁	—	4	1	no	—
270	C₂×C₄×C₁₀₁	—	4	1	no	—
271	C₂×C₄×C₁₀₁	—	4	1	no	—
272	C₂×C₄×C₁₀₁	—	4	1	no	—
273	C₂×C₄×C₁₀₁	—	4	1	no	—
274	C₂×C₄×C₁₀₁	—	4	1	no	—
275	C₂×C₄×C₁₀₁	—	4	1	no	—
276	C₂×C₄×C₁₀₁	—	4	1	no	—
277	C₂×C₄×C₁₀₁	—	8	2	no	—
278	C₂×C₄×C₁₀₁	—	8	2	no	—
279	C₂×C₄×C₁₀₁	—	8	1	no	—
280	C₂×C₄×C₁₀₁	—	8	1	no	—
281	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
282	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
283	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
284	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
285	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
286	C₂×C₄×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
287	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
288	C₈×C₁₀₁	—	4	2	no	—
289	C₈×C₁₀₁	—	4	2	no	—
290	C₂²×C₁₀₁	—	2	1	no	—
291	C₂²×C₁₀₁	—	2	1	no	—
292	C₂²×C₁₀₁	—	2	1	no	—
293	C₂²×C₁₀₁	—	2	2	no	—
294	C₂²×C₁₀₁	—	2	1	no	—
295	C₂²×C₁₀₁	—	2	1	no	—
296	C₂²×C₁₀₁	—	2	1	no	—
297	C₂²×C₁₀₁	—	2	2	no	—
298	C₂²×C₁₀₁	—	2	1	no	—
299	C₂²×C₁₀₁	—	2	2	no	—
300	C₂²×C₁₀₁	—	2	1	no	—
301	C₂²×C₁₀₁	—	4	2	no	—
302	C₂²×C₁₀₁	—	4	2	no	—
303	C₂²×C₁₀₁	—	4	2	no	—
304	C₂²×C₁₀₁	—	8	1	no	—
305	C₂²×C₁₀₁	—	8	1	no	—
306	C₂²×C₁₀₁	—	8	1	no	—
307	C₂²×C₁₀₁	—	8	1	no	—
308	C₂²×C₁₀₁	—	16	2	no	—
309	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
310	C₂²×C₁₀₁	#575	1	1	yes	characteristic
311	C₂²×C₁₀₁	#575	1	1	yes	characteristic
312	C₄×C₁₀₁	—	2	1	no	—
313	C₄×C₁₀₁	—	2	1	no	—
314	C₄×C₁₀₁	—	2	2	no	—
315	C₄×C₁₀₁	—	2	1	no	—
316	C₄×C₁₀₁	—	2	1	no	—
317	C₄×C₁₀₁	—	2	2	no	—
318	C₄×C₁₀₁	—	2	2	no	—
319	C₄×C₁₀₁	—	4	2	no	—
320	C₄×C₁₀₁	—	4	2	no	—
321	C₄×C₁₀₁	—	4	2	no	—
322	C₄×C₁₀₁	—	4	2	no	—
323	C₄×C₁₀₁	—	8	1	no	—
324	C₄×C₁₀₁	—	8	1	no	—
325	C₄×C₁₀₁	—	8	1	no	—
326	#17625	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
327	C₂×C₁₀₁	—	2	1	no	—
328	C₂×C₁₀₁	—	2	1	no	—
329	C₂×C₁₀₁	—	4	1	no	—
330	C₂×C₁₀₁	—	4	2	no	—
331	C₂×C₁₀₁	—	4	1	no	—
332	C₂×C₁₀₁	—	8	2	no	—
333	C₂×C₁₀₁	#2883	1	1	yes	characteristic
334	C₂×C₁₀₁	#2896	1	1	yes	characteristic
335	C₂×C₁₀₁	#2901	1	1	yes	characteristic
336	#3505	C₂×C₁₀₁	1	1	yes	characteristic
337	#2973	C₂×C₁₀₁	1	1	yes	characteristic, complemented
338	#2357	C₂×C₁₀₁	1	1	yes	characteristic, complemented
339	#1516	C₂×C₁₀₁	1	2	yes	complemented
340	#1512	C₂×C₁₀₁	1	2	yes	complemented
341	#1511	C₂×C₁₀₁	1	1	yes	characteristic, complemented
342	#1510	C₂×C₁₀₁	1	1	yes	characteristic, complemented
343	#1509	C₂×C₁₀₁	1	2	yes	complemented
344	#1508	C₂×C₁₀₁	1	1	yes	characteristic, complemented
345	#1507	C₂×C₁₀₁	1	1	yes	characteristic, complemented
346	#1501	C₂×C₁₀₁	1	2	yes	complemented
347	C₁₀₁	#17625	1	1	yes	characteristic, direct product factor, Sylow
348	#553	—	2	2	no	—
349	#553	C₄×C₁₀₁	1	2	yes	complemented
350	#552	C₄×C₁₀₁	1	2	yes	complemented
351	#551	—	2	2	no	—
352	#548	C₄×C₁₀₁	1	2	yes	complemented
353	#546	C₄×C₁₀₁	1	2	yes	complemented
354	#539	—	2	1	no	—
355	#538	—	2	1	no	—
356	#534	—	2	1	no	—
357	#529	C₂²×C₁₀₁	1	2	yes	—
358	#525	C₂²×C₁₀₁	1	2	yes	—
359	C₂×C₂²⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
360	C₂×#121	C₂²×C₁₀₁	1	1	yes	characteristic
361	#518	—	2	1	no	—
362	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
363	#435	—	2	2	no	—
364	#435	—	2	2	no	—
365	#432	C₂²×C₁₀₁	1	2	yes	complemented
366	#407	C₂²×C₁₀₁	1	1	yes	characteristic
367	#407	C₂²×C₁₀₁	1	1	yes	characteristic
368	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	2	yes	complemented
369	#390	—	2	1	no	—
370	#388	—	2	1	no	—
371	#388	—	2	1	no	—
372	#382	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
373	#381	C₂²×C₁₀₁	1	1	yes	characteristic
374	#381	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
375	C₄×C₄⋊C₄	—	2	1	no	—
376	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
377	C₄×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
378	C₄×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
379	#328	C₂²×C₁₀₁	1	2	yes	complemented
380	#328	C₂²×C₁₀₁	1	2	yes	complemented
381	#328	C₂²×C₁₀₁	1	2	yes	complemented
382	#328	C₂²×C₁₀₁	1	2	yes	complemented
383	#327	C₂²×C₁₀₁	1	2	yes	—
384	#327	C₂²×C₁₀₁	1	2	yes	—
385	#327	C₂²×C₁₀₁	1	2	yes	—
386	#327	C₂²×C₁₀₁	1	2	yes	—
387	C₂×#41	C₂×C₄×C₁₀₁	1	2	yes	—
388	C₂²×Q₈	C₂×C₄×C₁₀₁	1	1	yes	characteristic
389	C₂²×D₄	—	2	1	no	—
390	C₂²×D₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
391	C₂²×D₄	D₄×C₁₀₁	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
394	C₂×M₁₆	—	2	1	no	—
395	C₂×M₁₆	—	2	1	no	—
396	C₂²×C₈	—	2	2	no	—
397	#126	—	2	2	no	—
398	#126	—	2	2	no	—
399	#126	—	2	2	no	—
400	#125	—	2	2	no	—
401	#125	C₂×C₄×C₁₀₁	1	2	yes	—
402	#124	—	2	2	no	—
403	#124	C₂×C₄×C₁₀₁	1	2	yes	—
404	#123	—	2	2	no	—
405	#123	—	2	2	no	—
406	#123	—	2	2	no	—
407	#123	—	2	2	no	—
408	#123	—	2	2	no	—
409	C₂²⋊Q₈	—	2	1	no	—
410	C₂²⋊Q₈	—	2	1	no	—
411	C₂²⋊Q₈	—	2	2	no	—
412	C₂²⋊Q₈	C₂×C₄×C₁₀₁	1	2	yes	—
413	C₂²⋊Q₈	C₂×C₄×C₁₀₁	1	2	yes	—
414	C₂²⋊Q₈	C₂³×C₁₀₁	1	2	yes	—
415	#121	—	2	2	no	—
416	#121	—	2	2	no	—
417	#121	—	2	1	no	—
418	#121	—	2	1	no	—
419	#121	—	2	2	no	—
420	#121	C₂×C₄×C₁₀₁	1	2	yes	—
421	#121	C₂×C₄×C₁₀₁	1	2	yes	—
422	#121	C₂³×C₁₀₁	1	2	yes	—
423	#120	—	2	2	no	—
424	#120	—	2	2	no	—
425	C₄×Q₈	C₂×C₄×C₁₀₁	1	2	yes	—
426	C₄×D₄	—	2	2	no	—
427	C₄×D₄	—	2	2	no	—
428	C₄×D₄	—	2	2	no	—
429	C₄×D₄	—	2	2	no	—
430	C₄×D₄	—	2	2	no	—
431	C₄×D₄	C₂×C₄×C₁₀₁	1	2	yes	—
432	C₄×D₄	C₂×C₄×C₁₀₁	1	2	yes	—
433	C₄×D₄	C₂×C₄×C₁₀₁	1	2	yes	—
434	C₄×D₄	D₄×C₁₀₁	1	2	yes	—
435	C₄×D₄	D₄×C₁₀₁	1	2	yes	—
436	#117	—	2	2	no	—
437	#117	—	2	2	no	—
438	#117	C₂×C₄×C₁₀₁	1	2	yes	—
439	C₂×C₄⋊C₄	—	2	1	no	—
440	C₂×C₄⋊C₄	—	2	1	no	—
441	C₂×C₄⋊C₄	—	2	1	no	—
442	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
444	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	2	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
453	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
454	C₂×C₄²	—	2	1	no	—
455	C₂×C₄²	—	2	1	no	—
456	C₂×C₄²	—	2	1	no	—
457	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
458	C₄⋊C₈	—	2	2	no	—
459	C₂²⋊C₈	—	2	2	no	—
460	C₂²⋊C₈	—	2	1	no	—
461	C₂²⋊C₈	—	2	1	no	—
462	C₂²⋊C₈	C₂³×C₁₀₁	1	2	yes	—
463	C₂²⋊C₈	C₂³×C₁₀₁	1	2	yes	—
464	#97	—	2	2	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	—	2	1	no	—
468	#95	C₂³×C₁₀₁	1	1	yes	characteristic
469	#95	C₂³×C₁₀₁	1	1	yes	characteristic
470	#95	C₂³×C₁₀₁	1	1	yes	characteristic
471	#95	C₂³×C₁₀₁	1	1	yes	characteristic
472	C₂⁴	—	2	1	no	—
473	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
474	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
475	#41	—	8	2	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	8	1	no	—
478	C₂×Q₈	C₂²×C₄×C₁₀₁	1	2	yes	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	2	no	—
481	C₂×D₄	—	2	2	no	—
482	C₂×D₄	—	2	2	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	4	1	no	—
485	C₂×D₄	—	4	1	no	—
486	C₂×D₄	—	4	2	no	—
487	C₂×D₄	—	4	2	no	—
488	C₂×D₄	—	8	1	no	—
489	C₂×D₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
490	C₂×D₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
491	C₂×D₄	C₂²×C₄×C₁₀₁	1	2	yes	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	8	1	no	—
502	C₂²×C₄	—	8	1	no	—
503	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
504	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
505	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
506	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
509	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
512	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
513	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
514	M₁₆	—	8	1	no	—
515	M₁₆	—	8	1	no	—
516	C₂×C₈	—	2	2	no	—
517	C₂×C₈	—	2	2	no	—
518	C₂×C₈	—	8	2	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	4	2	no	—
528	C₄⋊C₄	—	4	2	no	—
529	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
530	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
531	C₄⋊C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
532	C₄⋊C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	2	no	—
535	C₂²⋊C₄	—	2	2	no	—
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	2	2	no	—
542	C₂²⋊C₄	—	2	2	no	—
543	C₂²⋊C₄	—	4	2	no	—
544	C₂²⋊C₄	—	4	2	no	—
545	C₂²⋊C₄	—	8	1	no	—
546	C₂²⋊C₄	—	8	1	no	—
547	C₂²⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
548	C₂²⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
549	C₂²⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
550	C₂²⋊C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
551	C₄²	—	2	2	no	—
552	C₄²	—	2	2	no	—
553	C₄²	—	4	2	no	—
554	C₄²	—	8	1	no	—
555	C₄²	—	8	1	no	—
556	C₄²	C₂²×C₄×C₁₀₁	1	2	yes	—
557	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	2	no	—
563	C₂³	—	4	1	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	4	2	no	—
568	C₂³	—	8	1	no	—
569	C₂³	—	8	1	no	—
570	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
571	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
572	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
573	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
574	Q₈	—	4	2	no	—
575	Q₈	—	8	1	no	—
576	D₄	—	4	2	no	—
577	D₄	—	4	2	no	—
578	D₄	—	4	2	no	—
579	D₄	—	4	4	no	—
580	D₄	—	4	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	8	1	no	—
583	D₄	—	8	2	no	—
584	D₄	—	8	2	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	8	2	no	—
614	C₂×C₄	—	8	2	no	—
615	C₂×C₄	—	8	1	no	—
616	C₂×C₄	—	8	1	no	—
617	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
618	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
619	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
620	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
621	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
622	C₂×C₄	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
623	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
624	C₈	—	4	2	no	—
625	C₈	—	4	2	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	1	no	—
637	C₂²	—	4	2	no	—
638	C₂²	—	4	2	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	8	1	no	—
641	C₂²	—	8	1	no	—
642	C₂²	—	8	1	no	—
643	C₂²	—	8	1	no	—
644	C₂²	—	16	2	no	—
645	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
646	C₂²	#575×C₁₀₁	1	1	yes	characteristic
647	C₂²	#575×C₁₀₁	1	1	yes	characteristic
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	4	2	no	—
656	C₄	—	4	2	no	—
657	C₄	—	4	2	no	—
658	C₄	—	4	2	no	—
659	C₄	—	8	1	no	—
660	C₄	—	8	1	no	—
661	C₄	—	8	1	no	—
662	C₂	—	2	1	no	—
663	C₂	—	2	1	no	—
664	C₂	—	4	1	no	—
665	C₂	—	4	1	no	—
666	C₂	—	4	2	no	—
667	C₂	—	8	2	no	—
668	C₂	C₁₀₁×#2883	1	1	yes	characteristic
669	C₂	C₁₀₁×#2896	1	1	yes	characteristic
670	C₂	C₁₀₁×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₁₀₁×#3505	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂×C₄×D₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₁×#2973	C₂	semidirect
3. C₁₀₁×#2357	C₂	semidirect
4. C₁₀₁×#1516	C₂	semidirect
5. C₁₀₁×#1512	C₂	semidirect
6. C₁₀₁×#1511	C₂	semidirect
7. C₁₀₁×#1510	C₂	semidirect
8. C₁₀₁×#1509	C₂	semidirect
9. C₁₀₁×#1508	C₂	semidirect
10. C₁₀₁×#1507	C₂	semidirect
11. C₁₀₁×#1501	C₂	semidirect
13. #553×C₁₀₁	C₄	semidirect
14. #552×C₁₀₁	C₄	semidirect
16. #548×C₁₀₁	C₄	semidirect
17. #546×C₁₀₁	C₄	semidirect
29. #432×C₁₀₁	C₂²	semidirect
32. C₂×C₂²⋊C₈×C₁₀₁	C₂²	semidirect
36. #382×C₁₀₁	C₂²	semidirect
38. #381×C₁₀₁	C₂²	semidirect
40. C₄×C₄⋊C₄×C₁₀₁	C₂²	semidirect
42. C₄×C₂²⋊C₄×C₁₀₁	C₂²	semidirect
43. #328×C₁₀₁	C₂²	semidirect
44. #328×C₁₀₁	C₂²	semidirect
45. #328×C₁₀₁	C₂²	semidirect
46. #328×C₁₀₁	C₂²	semidirect
326. #17625	C₁₀₁	direct (N × H)
337. #2973	C₂×C₁₀₁	semidirect
338. #2357	C₂×C₁₀₁	semidirect
339. #1516	C₂×C₁₀₁	semidirect
340. #1512	C₂×C₁₀₁	semidirect
341. #1511	C₂×C₁₀₁	semidirect
342. #1510	C₂×C₁₀₁	semidirect
343. #1509	C₂×C₁₀₁	semidirect
344. #1508	C₂×C₁₀₁	semidirect
345. #1507	C₂×C₁₀₁	semidirect
346. #1501	C₂×C₁₀₁	semidirect
347. C₁₀₁	#17625	direct (N × H)
349. #553	C₄×C₁₀₁	semidirect
350. #552	C₄×C₁₀₁	semidirect
352. #548	C₄×C₁₀₁	semidirect
353. #546	C₄×C₁₀₁	semidirect
365. #432	C₂²×C₁₀₁	semidirect
368. C₂×C₂²⋊C₈	C₂²×C₁₀₁	semidirect
372. #382	C₂²×C₁₀₁	semidirect
374. #381	C₂²×C₁₀₁	semidirect
376. C₄×C₄⋊C₄	C₂²×C₁₀₁	semidirect
378. C₄×C₂²⋊C₄	C₂²×C₁₀₁	semidirect
379. #328	C₂²×C₁₀₁	semidirect
380. #328	C₂²×C₁₀₁	semidirect
381. #328	C₂²×C₁₀₁	semidirect
382. #328	C₂²×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₁×#3505	2
C₁₀₁×#2973	2
C₁₀₁×#2357	2
C₁₀₁×#1516	2
C₁₀₁×#1512	2
C₁₀₁×#1511	2
C₁₀₁×#1510	2
C₁₀₁×#1509	2
C₁₀₁×#1508	2
C₁₀₁×#1507	2
C₁₀₁×#1501	2
#17625	101

Subgroups — C101×#17625 #38799776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#17625 #38799776