Subgroups — C₁₀₁×#23852 #38806003

Order 25856.

1900 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×SD₁₆×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#452×C₁₀₁	C₂	1	2	yes	maximal, complemented
4	C₂×#451×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#2409	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₁×#2015	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#2000	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#1892	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₁×#1877	C₂	1	2	yes	maximal, complemented
10	C₁₀₁×#1869	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₀₁×#1786	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂²×Q₁₆×C₁₀₁	C₂²	1	2	yes	complemented
16	C₂²×SD₁₆×C₁₀₁	—	2	4	no	—
17	C₂²×SD₁₆×C₁₀₁	—	2	8	no	—
18	C₂²×SD₁₆×C₁₀₁	C₂²	1	2	yes	—
19	C₂²×SD₁₆×C₁₀₁	C₂²	1	2	yes	—
20	C₂³×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
21	#546×C₁₀₁	—	2	4	no	—
22	#546×C₁₀₁	—	2	4	no	—
23	C₂×#124×C₁₀₁	C₂²	1	1	yes	characteristic
24	C₂×#123×C₁₀₁	—	2	1	no	—
25	C₂×C₂²⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₁₀₁	C₂²	1	2	yes	complemented
27	C₂×#121×C₁₀₁	—	2	1	no	—
28	C₂×#121×C₁₀₁	C₂²	1	1	yes	characteristic
29	C₂×#120×C₁₀₁	—	2	1	no	—
30	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
33	#452×C₁₀₁	—	2	8	no	—
34	#451×C₁₀₁	—	2	4	no	—
35	C₂×#103×C₁₀₁	C₂²	1	2	yes	complemented
36	C₂×#103×C₁₀₁	C₂²	1	2	yes	complemented
37	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
38	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
39	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	2	yes	complemented
41	#395×C₁₀₁	—	2	1	no	—
42	#393×C₁₀₁	—	2	1	no	—
43	#391×C₁₀₁	C₂²	1	2	yes	complemented
44	#386×C₁₀₁	—	2	1	no	—
45	#385×C₁₀₁	—	2	1	no	—
46	#380×C₁₀₁	C₂²	1	1	yes	characteristic
47	#340×C₁₀₁	C₂²	1	2	yes	complemented
48	#336×C₁₀₁	C₂²	1	2	yes	complemented
49	C₂⁵×C₁₀₁	—	2	1	no	—
50	C₂×#41×C₁₀₁	—	2	2	no	—
51	C₂×#41×C₁₀₁	—	2	2	no	—
52	C₂×#41×C₁₀₁	—	2	4	no	—
53	C₂×#41×C₁₀₁	—	4	2	no	—
54	C₂²×Q₈×C₁₀₁	—	2	1	no	—
55	C₂²×Q₈×C₁₀₁	—	2	4	no	—
56	C₂²×Q₈×C₁₀₁	—	2	2	no	—
57	C₂²×Q₈×C₁₀₁	—	2	2	no	—
58	C₂²×Q₈×C₁₀₁	—	4	2	no	—
59	C₂²×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
60	C₂²×Q₈×C₁₀₁	C₂³	1	2	yes	—
61	C₂²×D₄×C₁₀₁	—	2	4	no	—
62	C₂²×D₄×C₁₀₁	—	2	1	no	—
63	C₂²×D₄×C₁₀₁	—	2	1	no	—
64	C₂²×D₄×C₁₀₁	—	2	1	no	—
65	C₂²×D₄×C₁₀₁	—	2	2	no	—
66	C₂²×D₄×C₁₀₁	—	4	2	no	—
67	C₂²×D₄×C₁₀₁	D₄	1	1	yes	characteristic
68	C₂²×D₄×C₁₀₁	D₄	1	4	yes	—
69	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₀₁	—	2	1	no	—
72	C₂³×C₄×C₁₀₁	—	2	1	no	—
73	C₂³×C₄×C₁₀₁	—	2	1	no	—
74	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
76	C₂×Q₁₆×C₁₀₁	—	2	4	no	—
77	C₂×Q₁₆×C₁₀₁	—	2	4	no	—
78	C₂×Q₁₆×C₁₀₁	—	4	2	no	—
79	C₂×SD₁₆×C₁₀₁	—	2	32	no	—
80	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
81	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
82	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
83	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
84	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
85	C₂×SD₁₆×C₁₀₁	D₄	1	8	yes	complemented
86	C₂²×C₈×C₁₀₁	—	2	2	no	—
87	C₂²×C₈×C₁₀₁	—	2	4	no	—
88	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
89	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
90	#124×C₁₀₁	—	2	2	no	—
91	#124×C₁₀₁	—	2	2	no	—
92	#123×C₁₀₁	—	2	8	no	—
93	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
94	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
95	C₂²⋊Q₈×C₁₀₁	—	4	2	no	—
96	C₂²⋊Q₈×C₁₀₁	D₄	1	4	yes	—
97	#121×C₁₀₁	—	2	8	no	—
98	#121×C₁₀₁	—	2	2	no	—
99	#121×C₁₀₁	—	2	2	no	—
100	#120×C₁₀₁	—	2	8	no	—
101	C₄×D₄×C₁₀₁	—	2	2	no	—
102	C₄×D₄×C₁₀₁	—	2	2	no	—
103	C₄×D₄×C₁₀₁	—	2	2	no	—
104	C₄×D₄×C₁₀₁	—	2	2	no	—
105	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
106	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
107	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
111	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	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	—	2	2	no	—
117	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
121	#103×C₁₀₁	—	2	4	no	—
122	#103×C₁₀₁	—	2	4	no	—
123	#102×C₁₀₁	—	2	4	no	—
124	#102×C₁₀₁	—	4	2	no	—
125	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
126	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
127	#95×C₁₀₁	—	2	1	no	—
128	#95×C₁₀₁	—	2	2	no	—
129	#95×C₁₀₁	—	2	2	no	—
130	C₂⁴×C₁₀₁	—	2	1	no	—
131	C₂⁴×C₁₀₁	—	2	1	no	—
132	C₂⁴×C₁₀₁	—	2	4	no	—
133	C₂⁴×C₁₀₁	—	4	4	no	—
134	C₂⁴×C₁₀₁	—	4	2	no	—
135	C₂⁴×C₁₀₁	—	4	2	no	—
136	C₂⁴×C₁₀₁	—	8	2	no	—
137	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
138	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
139	#41×C₁₀₁	—	4	8	no	—
140	#41×C₁₀₁	—	4	4	no	—
141	#41×C₁₀₁	—	4	4	no	—
142	C₂×Q₈×C₁₀₁	—	2	1	no	—
143	C₂×Q₈×C₁₀₁	—	2	2	no	—
144	C₂×Q₈×C₁₀₁	—	2	8	no	—
145	C₂×Q₈×C₁₀₁	—	2	2	no	—
146	C₂×Q₈×C₁₀₁	—	2	2	no	—
147	C₂×Q₈×C₁₀₁	—	2	2	no	—
148	C₂×Q₈×C₁₀₁	—	2	2	no	—
149	C₂×Q₈×C₁₀₁	—	2	2	no	—
150	C₂×Q₈×C₁₀₁	—	2	2	no	—
151	C₂×Q₈×C₁₀₁	—	4	4	no	—
152	C₂×Q₈×C₁₀₁	—	4	8	no	—
153	C₂×Q₈×C₁₀₁	—	4	4	no	—
154	C₂×Q₈×C₁₀₁	—	4	2	no	—
155	C₂×Q₈×C₁₀₁	C₂×D₄	1	4	yes	—
156	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
157	C₂×D₄×C₁₀₁	—	2	8	no	—
158	C₂×D₄×C₁₀₁	—	2	4	no	—
159	C₂×D₄×C₁₀₁	—	2	2	no	—
160	C₂×D₄×C₁₀₁	—	2	2	no	—
161	C₂×D₄×C₁₀₁	—	2	2	no	—
162	C₂×D₄×C₁₀₁	—	2	4	no	—
163	C₂×D₄×C₁₀₁	—	2	4	no	—
164	C₂×D₄×C₁₀₁	—	2	1	no	—
165	C₂×D₄×C₁₀₁	—	2	2	no	—
166	C₂×D₄×C₁₀₁	—	2	1	no	—
167	C₂×D₄×C₁₀₁	—	2	2	no	—
168	C₂×D₄×C₁₀₁	—	2	2	no	—
169	C₂×D₄×C₁₀₁	—	4	4	no	—
170	C₂×D₄×C₁₀₁	—	4	8	no	—
171	C₂×D₄×C₁₀₁	—	4	4	no	—
172	C₂×D₄×C₁₀₁	—	4	4	no	—
173	C₂×D₄×C₁₀₁	—	8	2	no	—
174	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
175	C₂×D₄×C₁₀₁	C₂×D₄	1	4	yes	—
176	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₁₀₁	—	2	2	no	—
178	C₂²×C₄×C₁₀₁	—	2	2	no	—
179	C₂²×C₄×C₁₀₁	—	2	4	no	—
180	C₂²×C₄×C₁₀₁	—	2	2	no	—
181	C₂²×C₄×C₁₀₁	—	2	1	no	—
182	C₂²×C₄×C₁₀₁	—	2	1	no	—
183	C₂²×C₄×C₁₀₁	—	2	4	no	—
184	C₂²×C₄×C₁₀₁	—	2	2	no	—
185	C₂²×C₄×C₁₀₁	—	2	1	no	—
186	C₂²×C₄×C₁₀₁	—	2	1	no	—
187	C₂²×C₄×C₁₀₁	—	2	2	no	—
188	C₂²×C₄×C₁₀₁	—	2	2	no	—
189	C₂²×C₄×C₁₀₁	—	4	4	no	—
190	C₂²×C₄×C₁₀₁	—	4	4	no	—
191	C₂²×C₄×C₁₀₁	—	4	2	no	—
192	C₂²×C₄×C₁₀₁	—	8	2	no	—
193	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
199	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
200	Q₁₆×C₁₀₁	—	4	8	no	—
201	SD₁₆×C₁₀₁	—	2	16	no	—
202	SD₁₆×C₁₀₁	—	2	16	no	—
203	C₂×C₈×C₁₀₁	—	2	8	no	—
204	C₂×C₈×C₁₀₁	—	2	2	no	—
205	C₂×C₈×C₁₀₁	—	2	2	no	—
206	C₂×C₈×C₁₀₁	—	2	2	no	—
207	C₂×C₈×C₁₀₁	—	2	2	no	—
208	C₂×C₈×C₁₀₁	—	2	2	no	—
209	C₂×C₈×C₁₀₁	C₂×D₄	1	4	yes	—
210	C₄⋊C₄×C₁₀₁	—	2	4	no	—
211	C₄⋊C₄×C₁₀₁	—	2	2	no	—
212	C₄⋊C₄×C₁₀₁	—	2	1	no	—
213	C₄⋊C₄×C₁₀₁	—	2	2	no	—
214	C₄⋊C₄×C₁₀₁	—	2	2	no	—
215	C₄⋊C₄×C₁₀₁	—	4	4	no	—
216	C₄⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	—
217	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
218	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
219	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
220	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
221	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
222	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
223	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
224	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
225	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
226	C₄²×C₁₀₁	—	2	1	no	—
227	C₄²×C₁₀₁	—	2	1	no	—
228	C₂³×C₁₀₁	—	2	2	no	—
229	C₂³×C₁₀₁	—	2	2	no	—
230	C₂³×C₁₀₁	—	2	2	no	—
231	C₂³×C₁₀₁	—	2	4	no	—
232	C₂³×C₁₀₁	—	2	2	no	—
233	C₂³×C₁₀₁	—	2	1	no	—
234	C₂³×C₁₀₁	—	2	2	no	—
235	C₂³×C₁₀₁	—	2	1	no	—
236	C₂³×C₁₀₁	—	2	1	no	—
237	C₂³×C₁₀₁	—	2	2	no	—
238	C₂³×C₁₀₁	—	4	8	no	—
239	C₂³×C₁₀₁	—	4	1	no	—
240	C₂³×C₁₀₁	—	4	1	no	—
241	C₂³×C₁₀₁	—	4	2	no	—
242	C₂³×C₁₀₁	—	4	2	no	—
243	C₂³×C₁₀₁	—	4	1	no	—
244	C₂³×C₁₀₁	—	4	1	no	—
245	C₂³×C₁₀₁	—	4	2	no	—
246	C₂³×C₁₀₁	—	4	8	no	—
247	C₂³×C₁₀₁	—	8	4	no	—
248	C₂³×C₁₀₁	—	8	8	no	—
249	C₂³×C₁₀₁	—	8	8	no	—
250	C₂³×C₁₀₁	#120	1	2	yes	—
251	C₂³×C₁₀₁	#135	1	2	yes	—
252	C₂³×C₁₀₁	#137	1	2	yes	—
253	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
254	Q₈×C₁₀₁	—	2	4	no	—
255	Q₈×C₁₀₁	—	2	4	no	—
256	Q₈×C₁₀₁	—	2	4	no	—
257	Q₈×C₁₀₁	—	4	8	no	—
258	Q₈×C₁₀₁	—	4	1	no	—
259	Q₈×C₁₀₁	—	4	2	no	—
260	Q₈×C₁₀₁	—	4	1	no	—
261	Q₈×C₁₀₁	—	4	2	no	—
262	D₄×C₁₀₁	—	2	2	no	—
263	D₄×C₁₀₁	—	2	2	no	—
264	D₄×C₁₀₁	—	2	2	no	—
265	D₄×C₁₀₁	—	2	4	no	—
266	D₄×C₁₀₁	—	4	8	no	—
267	D₄×C₁₀₁	—	4	8	no	—
268	D₄×C₁₀₁	—	4	4	no	—
269	D₄×C₁₀₁	—	4	2	no	—
270	D₄×C₁₀₁	—	8	4	no	—
271	D₄×C₁₀₁	#120	1	4	yes	—
272	C₂×C₄×C₁₀₁	—	2	2	no	—
273	C₂×C₄×C₁₀₁	—	2	2	no	—
274	C₂×C₄×C₁₀₁	—	2	2	no	—
275	C₂×C₄×C₁₀₁	—	2	4	no	—
276	C₂×C₄×C₁₀₁	—	2	1	no	—
277	C₂×C₄×C₁₀₁	—	2	1	no	—
278	C₂×C₄×C₁₀₁	—	2	2	no	—
279	C₂×C₄×C₁₀₁	—	2	1	no	—
280	C₂×C₄×C₁₀₁	—	2	2	no	—
281	C₂×C₄×C₁₀₁	—	2	4	no	—
282	C₂×C₄×C₁₀₁	—	2	2	no	—
283	C₂×C₄×C₁₀₁	—	2	1	no	—
284	C₂×C₄×C₁₀₁	—	2	1	no	—
285	C₂×C₄×C₁₀₁	—	2	2	no	—
286	C₂×C₄×C₁₀₁	—	4	8	no	—
287	C₂×C₄×C₁₀₁	—	4	8	no	—
288	C₂×C₄×C₁₀₁	—	4	2	no	—
289	C₂×C₄×C₁₀₁	—	4	2	no	—
290	C₂×C₄×C₁₀₁	—	4	2	no	—
291	C₂×C₄×C₁₀₁	—	4	2	no	—
292	C₂×C₄×C₁₀₁	—	4	1	no	—
293	C₂×C₄×C₁₀₁	—	4	1	no	—
294	C₂×C₄×C₁₀₁	—	4	2	no	—
295	C₂×C₄×C₁₀₁	—	4	2	no	—
296	C₂×C₄×C₁₀₁	—	4	2	no	—
297	C₂×C₄×C₁₀₁	—	4	2	no	—
298	C₂×C₄×C₁₀₁	—	8	4	no	—
299	C₂×C₄×C₁₀₁	#120	1	2	yes	—
300	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
302	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
304	C₈×C₁₀₁	—	2	4	no	—
305	C₈×C₁₀₁	—	4	2	no	—
306	C₂²×C₁₀₁	—	2	2	no	—
307	C₂²×C₁₀₁	—	2	2	no	—
308	C₂²×C₁₀₁	—	2	4	no	—
309	C₂²×C₁₀₁	—	2	4	no	—
310	C₂²×C₁₀₁	—	2	4	no	—
311	C₂²×C₁₀₁	—	4	2	no	—
312	C₂²×C₁₀₁	—	4	2	no	—
313	C₂²×C₁₀₁	—	4	4	no	—
314	C₂²×C₁₀₁	—	4	4	no	—
315	C₂²×C₁₀₁	—	4	1	no	—
316	C₂²×C₁₀₁	—	4	2	no	—
317	C₂²×C₁₀₁	—	4	1	no	—
318	C₂²×C₁₀₁	—	4	2	no	—
319	C₂²×C₁₀₁	—	4	1	no	—
320	C₂²×C₁₀₁	—	4	2	no	—
321	C₂²×C₁₀₁	—	4	2	no	—
322	C₂²×C₁₀₁	—	4	2	no	—
323	C₂²×C₁₀₁	—	8	16	no	—
324	C₂²×C₁₀₁	—	8	2	no	—
325	C₂²×C₁₀₁	—	8	2	no	—
326	C₂²×C₁₀₁	#452	1	4	yes	complemented
327	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
328	C₂²×C₁₀₁	D₄²	1	2	yes	—
329	C₂²×C₁₀₁	C₂×#135	1	1	yes	characteristic
330	C₂²×C₁₀₁	C₂×#137	1	1	yes	characteristic
331	C₂²×C₁₀₁	#577	1	2	yes	—
332	C₄×C₁₀₁	—	2	2	no	—
333	C₄×C₁₀₁	—	4	1	no	—
334	C₄×C₁₀₁	—	4	2	no	—
335	C₄×C₁₀₁	—	4	4	no	—
336	C₄×C₁₀₁	—	4	1	no	—
337	C₄×C₁₀₁	—	4	1	no	—
338	C₄×C₁₀₁	—	4	2	no	—
339	C₄×C₁₀₁	—	8	2	no	—
340	C₄×C₁₀₁	C₂×#120	1	1	yes	characteristic
341	C₄×C₁₀₁	#534	1	1	yes	characteristic
342	C₄×C₁₀₁	D₄²	1	2	yes	—
343	#23852	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
344	C₂×C₁₀₁	—	2	4	no	—
345	C₂×C₁₀₁	—	4	4	no	—
346	C₂×C₁₀₁	—	8	1	no	—
347	C₂×C₁₀₁	—	8	2	no	—
348	C₂×C₁₀₁	#2403	1	1	yes	characteristic
349	C₂×C₁₀₁	C₂×#452	1	1	yes	characteristic
350	C₂×C₁₀₁	#3009	1	1	yes	characteristic
351	C₂×C₁₀₁	#3266	1	2	yes	—
352	C₂×C₁₀₁	#3282	1	2	yes	—
353	C₂³×SD₁₆	C₂×C₁₀₁	1	1	yes	characteristic, complemented
354	C₂×#546	C₂×C₁₀₁	1	1	yes	characteristic
355	C₂×#452	C₂×C₁₀₁	1	2	yes	complemented
356	C₂×#451	C₂×C₁₀₁	1	1	yes	characteristic, complemented
357	#2409	C₂×C₁₀₁	1	1	yes	characteristic, complemented
358	#2015	C₂×C₁₀₁	1	2	yes	complemented
359	#2000	C₂×C₁₀₁	1	2	yes	complemented
360	#1892	C₂×C₁₀₁	1	1	yes	characteristic, complemented
361	#1877	C₂×C₁₀₁	1	2	yes	complemented
362	#1869	C₂×C₁₀₁	1	1	yes	characteristic, complemented
363	#1786	C₂×C₁₀₁	1	1	yes	characteristic, complemented
364	C₁₀₁	#23852	1	1	yes	characteristic, direct product factor, Sylow
365	C₂²×#41	C₂²×C₁₀₁	1	1	yes	characteristic
366	C₂³×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
367	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
368	C₂²×Q₁₆	C₂²×C₁₀₁	1	2	yes	complemented
369	C₂²×SD₁₆	—	2	4	no	—
370	C₂²×SD₁₆	—	2	8	no	—
371	C₂²×SD₁₆	C₂²×C₁₀₁	1	2	yes	—
372	C₂²×SD₁₆	C₂²×C₁₀₁	1	2	yes	—
373	C₂³×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
374	#546	—	2	4	no	—
375	#546	—	2	4	no	—
376	C₂×#124	C₂²×C₁₀₁	1	1	yes	characteristic
377	C₂×#123	—	2	1	no	—
378	C₂×C₂²⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
379	C₂×C₂²⋊Q₈	C₂²×C₁₀₁	1	2	yes	complemented
380	C₂×#121	—	2	1	no	—
381	C₂×#121	C₂²×C₁₀₁	1	1	yes	characteristic
382	C₂×#120	—	2	1	no	—
383	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
384	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
385	C₂²×C₂²⋊C₄	—	2	1	no	—
386	#452	—	2	8	no	—
387	#451	—	2	4	no	—
388	C₂×#103	C₂²×C₁₀₁	1	2	yes	complemented
389	C₂×#103	C₂²×C₁₀₁	1	2	yes	complemented
390	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
391	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
392	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
393	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	2	yes	complemented
394	#395	—	2	1	no	—
395	#393	—	2	1	no	—
396	#391	C₂²×C₁₀₁	1	2	yes	complemented
397	#386	—	2	1	no	—
398	#385	—	2	1	no	—
399	#380	C₂²×C₁₀₁	1	1	yes	characteristic
400	#340	C₂²×C₁₀₁	1	2	yes	complemented
401	#336	C₂²×C₁₀₁	1	2	yes	complemented
402	C₂⁵	—	2	1	no	—
403	C₂×#41	—	2	2	no	—
404	C₂×#41	—	2	2	no	—
405	C₂×#41	—	2	4	no	—
406	C₂×#41	—	4	2	no	—
407	C₂²×Q₈	—	2	1	no	—
408	C₂²×Q₈	—	2	4	no	—
409	C₂²×Q₈	—	2	2	no	—
410	C₂²×Q₈	—	2	2	no	—
411	C₂²×Q₈	—	4	2	no	—
412	C₂²×Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
413	C₂²×Q₈	C₂³×C₁₀₁	1	2	yes	—
414	C₂²×D₄	—	2	4	no	—
415	C₂²×D₄	—	2	1	no	—
416	C₂²×D₄	—	2	1	no	—
417	C₂²×D₄	—	2	1	no	—
418	C₂²×D₄	—	2	2	no	—
419	C₂²×D₄	—	4	2	no	—
420	C₂²×D₄	D₄×C₁₀₁	1	1	yes	characteristic
421	C₂²×D₄	D₄×C₁₀₁	1	4	yes	—
422	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
423	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
424	C₂³×C₄	—	2	1	no	—
425	C₂³×C₄	—	2	1	no	—
426	C₂³×C₄	—	2	1	no	—
427	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
429	C₂×Q₁₆	—	2	4	no	—
430	C₂×Q₁₆	—	2	4	no	—
431	C₂×Q₁₆	—	4	2	no	—
432	C₂×SD₁₆	—	2	32	no	—
433	C₂×SD₁₆	—	2	4	no	—
434	C₂×SD₁₆	—	2	4	no	—
435	C₂×SD₁₆	—	2	4	no	—
436	C₂×SD₁₆	—	2	4	no	—
437	C₂×SD₁₆	—	2	4	no	—
438	C₂×SD₁₆	D₄×C₁₀₁	1	8	yes	complemented
439	C₂²×C₈	—	2	2	no	—
440	C₂²×C₈	—	2	4	no	—
441	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
442	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
443	#124	—	2	2	no	—
444	#124	—	2	2	no	—
445	#123	—	2	8	no	—
446	C₂²⋊Q₈	—	2	2	no	—
447	C₂²⋊Q₈	—	2	4	no	—
448	C₂²⋊Q₈	—	4	2	no	—
449	C₂²⋊Q₈	D₄×C₁₀₁	1	4	yes	—
450	#121	—	2	8	no	—
451	#121	—	2	2	no	—
452	#121	—	2	2	no	—
453	#120	—	2	8	no	—
454	C₄×D₄	—	2	2	no	—
455	C₄×D₄	—	2	2	no	—
456	C₄×D₄	—	2	2	no	—
457	C₄×D₄	—	2	2	no	—
458	C₂×C₄⋊C₄	—	2	1	no	—
459	C₂×C₄⋊C₄	—	2	2	no	—
460	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
462	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	—	2	8	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	1	no	—
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₂²⋊C₄	—	2	1	no	—
469	C₂×C₂²⋊C₄	—	2	2	no	—
470	C₂×C₂²⋊C₄	—	2	1	no	—
471	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
472	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
473	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
474	#103	—	2	4	no	—
475	#103	—	2	4	no	—
476	#102	—	2	4	no	—
477	#102	—	4	2	no	—
478	C₂²⋊C₈	—	2	2	no	—
479	C₂²⋊C₈	—	2	4	no	—
480	#95	—	2	1	no	—
481	#95	—	2	2	no	—
482	#95	—	2	2	no	—
483	C₂⁴	—	2	1	no	—
484	C₂⁴	—	2	1	no	—
485	C₂⁴	—	2	4	no	—
486	C₂⁴	—	4	4	no	—
487	C₂⁴	—	4	2	no	—
488	C₂⁴	—	4	2	no	—
489	C₂⁴	—	8	2	no	—
490	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
491	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
492	#41	—	4	8	no	—
493	#41	—	4	4	no	—
494	#41	—	4	4	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	2	no	—
497	C₂×Q₈	—	2	8	no	—
498	C₂×Q₈	—	2	2	no	—
499	C₂×Q₈	—	2	2	no	—
500	C₂×Q₈	—	2	2	no	—
501	C₂×Q₈	—	2	2	no	—
502	C₂×Q₈	—	2	2	no	—
503	C₂×Q₈	—	2	2	no	—
504	C₂×Q₈	—	4	4	no	—
505	C₂×Q₈	—	4	8	no	—
506	C₂×Q₈	—	4	4	no	—
507	C₂×Q₈	—	4	2	no	—
508	C₂×Q₈	C₂×D₄×C₁₀₁	1	4	yes	—
509	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
510	C₂×D₄	—	2	8	no	—
511	C₂×D₄	—	2	4	no	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	2	4	no	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	2	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	2	no	—
521	C₂×D₄	—	2	2	no	—
522	C₂×D₄	—	4	4	no	—
523	C₂×D₄	—	4	8	no	—
524	C₂×D₄	—	4	4	no	—
525	C₂×D₄	—	4	4	no	—
526	C₂×D₄	—	8	2	no	—
527	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
528	C₂×D₄	C₂×D₄×C₁₀₁	1	4	yes	—
529	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	4	4	no	—
543	C₂²×C₄	—	4	4	no	—
544	C₂²×C₄	—	4	2	no	—
545	C₂²×C₄	—	8	2	no	—
546	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
547	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
549	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
550	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
551	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
553	Q₁₆	—	4	8	no	—
554	SD₁₆	—	2	16	no	—
555	SD₁₆	—	2	16	no	—
556	C₂×C₈	—	2	8	no	—
557	C₂×C₈	—	2	2	no	—
558	C₂×C₈	—	2	2	no	—
559	C₂×C₈	—	2	2	no	—
560	C₂×C₈	—	2	2	no	—
561	C₂×C₈	—	2	2	no	—
562	C₂×C₈	C₂×D₄×C₁₀₁	1	4	yes	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	4	4	no	—
569	C₄⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	—
570	C₂²⋊C₄	—	2	4	no	—
571	C₂²⋊C₄	—	2	4	no	—
572	C₂²⋊C₄	—	2	4	no	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	2	no	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	2	no	—
577	C₂²⋊C₄	—	4	4	no	—
578	C₂²⋊C₄	—	4	2	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	1	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	4	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	1	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	4	8	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	2	no	—
595	C₂³	—	4	8	no	—
596	C₂³	—	4	2	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	2	no	—
600	C₂³	—	8	4	no	—
601	C₂³	—	8	8	no	—
602	C₂³	—	8	8	no	—
603	C₂³	#120×C₁₀₁	1	2	yes	—
604	C₂³	#135×C₁₀₁	1	2	yes	—
605	C₂³	#137×C₁₀₁	1	2	yes	—
606	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
607	Q₈	—	2	4	no	—
608	Q₈	—	2	4	no	—
609	Q₈	—	2	4	no	—
610	Q₈	—	4	8	no	—
611	Q₈	—	4	1	no	—
612	Q₈	—	4	2	no	—
613	Q₈	—	4	1	no	—
614	Q₈	—	4	2	no	—
615	D₄	—	2	2	no	—
616	D₄	—	2	2	no	—
617	D₄	—	2	2	no	—
618	D₄	—	2	4	no	—
619	D₄	—	4	8	no	—
620	D₄	—	4	8	no	—
621	D₄	—	4	4	no	—
622	D₄	—	4	2	no	—
623	D₄	—	8	4	no	—
624	D₄	#120×C₁₀₁	1	4	yes	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	4	8	no	—
640	C₂×C₄	—	4	8	no	—
641	C₂×C₄	—	4	2	no	—
642	C₂×C₄	—	4	2	no	—
643	C₂×C₄	—	4	2	no	—
644	C₂×C₄	—	4	2	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	2	no	—
648	C₂×C₄	—	4	2	no	—
649	C₂×C₄	—	4	2	no	—
650	C₂×C₄	—	4	2	no	—
651	C₂×C₄	—	8	4	no	—
652	C₂×C₄	#120×C₁₀₁	1	2	yes	—
653	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
654	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
655	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
656	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
657	C₈	—	2	4	no	—
658	C₈	—	4	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	4	no	—
662	C₂²	—	2	4	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	4	4	no	—
667	C₂²	—	4	4	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	2	no	—
670	C₂²	—	4	1	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	4	1	no	—
673	C₂²	—	4	2	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	4	2	no	—
676	C₂²	—	8	16	no	—
677	C₂²	—	8	2	no	—
678	C₂²	—	8	2	no	—
679	C₂²	#452×C₁₀₁	1	4	yes	complemented
680	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
681	C₂²	D₄²×C₁₀₁	1	2	yes	—
682	C₂²	C₂×#135×C₁₀₁	1	1	yes	characteristic
683	C₂²	C₂×#137×C₁₀₁	1	1	yes	characteristic
684	C₂²	#577×C₁₀₁	1	2	yes	—
685	C₄	—	2	2	no	—
686	C₄	—	4	1	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	4	no	—
689	C₄	—	4	1	no	—
690	C₄	—	4	1	no	—
691	C₄	—	4	2	no	—
692	C₄	—	8	2	no	—
693	C₄	C₂×#120×C₁₀₁	1	1	yes	characteristic
694	C₄	#534×C₁₀₁	1	1	yes	characteristic
695	C₄	D₄²×C₁₀₁	1	2	yes	—
696	C₂	—	2	4	no	—
697	C₂	—	4	4	no	—
698	C₂	—	8	1	no	—
699	C₂	—	8	2	no	—
700	C₂	C₁₀₁×#2403	1	1	yes	characteristic
701	C₂	C₂×#452×C₁₀₁	1	1	yes	characteristic
702	C₂	C₁₀₁×#3009	1	1	yes	characteristic
703	C₂	C₁₀₁×#3266	1	2	yes	—
704	C₂	C₁₀₁×#3282	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂×#546×C₁₀₁	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂×C₄×D₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×SD₁₆×C₁₀₁	C₂	semidirect
3. C₂×#452×C₁₀₁	C₂	semidirect
4. C₂×#451×C₁₀₁	C₂	semidirect
5. C₁₀₁×#2409	C₂	semidirect
6. C₁₀₁×#2015	C₂	semidirect
7. C₁₀₁×#2000	C₂	semidirect
8. C₁₀₁×#1892	C₂	semidirect
9. C₁₀₁×#1877	C₂	semidirect
10. C₁₀₁×#1869	C₂	semidirect
11. C₁₀₁×#1786	C₂	semidirect
15. C₂²×Q₁₆×C₁₀₁	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₁₀₁	C₂²	semidirect
35. C₂×#103×C₁₀₁	C₂²	semidirect
36. C₂×#103×C₁₀₁	C₂²	semidirect
40. C₂×C₂²⋊C₈×C₁₀₁	C₂²	semidirect
43. #391×C₁₀₁	C₂²	semidirect
47. #340×C₁₀₁	C₂²	semidirect
48. #336×C₁₀₁	C₂²	semidirect
85. C₂×SD₁₆×C₁₀₁	D₄	semidirect
326. C₂²×C₁₀₁	#452	semidirect
343. #23852	C₁₀₁	direct (N × H)
353. C₂³×SD₁₆	C₂×C₁₀₁	semidirect
355. C₂×#452	C₂×C₁₀₁	semidirect
356. C₂×#451	C₂×C₁₀₁	semidirect
357. #2409	C₂×C₁₀₁	semidirect
358. #2015	C₂×C₁₀₁	semidirect
359. #2000	C₂×C₁₀₁	semidirect
360. #1892	C₂×C₁₀₁	semidirect
361. #1877	C₂×C₁₀₁	semidirect
362. #1869	C₂×C₁₀₁	semidirect
363. #1786	C₂×C₁₀₁	semidirect
364. C₁₀₁	#23852	direct (N × H)
368. C₂²×Q₁₆	C₂²×C₁₀₁	semidirect
379. C₂×C₂²⋊Q₈	C₂²×C₁₀₁	semidirect
388. C₂×#103	C₂²×C₁₀₁	semidirect
389. C₂×#103	C₂²×C₁₀₁	semidirect
393. C₂×C₂²⋊C₈	C₂²×C₁₀₁	semidirect
396. #391	C₂²×C₁₀₁	semidirect
400. #340	C₂²×C₁₀₁	semidirect
401. #336	C₂²×C₁₀₁	semidirect
438. C₂×SD₁₆	D₄×C₁₀₁	semidirect
679. C₂²	#452×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂³×SD₁₆×C₁₀₁	2
C₂×#546×C₁₀₁	2
C₂×#452×C₁₀₁	2
C₂×#451×C₁₀₁	2
C₁₀₁×#2409	2
C₁₀₁×#2015	2
C₁₀₁×#2000	2
C₁₀₁×#1892	2
C₁₀₁×#1877	2
C₁₀₁×#1869	2
C₁₀₁×#1786	2
#23852	101

Subgroups — C101×#23852 #38806003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#23852 #38806003