Subgroups — C₁₀₁×#23568 #38805719

Order 25856.

1240 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×SD₁₆×C₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₄×#121×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#2058	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#2043	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₁×#2035	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#2023	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₁×#2013	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₁×#2000	C₂	1	2	yes	maximal
10	C₄×#103×C₁₀₁	C₂	1	2	yes	maximal, complemented
11	C₄×C₂²⋊C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₀₁	C₂²	1	2	yes	—
13	#533×C₁₀₁	—	2	8	no	—
14	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
16	C₂×#125×C₁₀₁	—	2	1	no	—
17	C₂×C₂²⋊Q₈×C₁₀₁	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₁₀₁	C₂²	1	2	yes	—
19	C₂×#121×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₀₁	—	2	1	no	—
21	C₂×C₄×Q₈×C₁₀₁	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₁₀₁	—	2	1	no	—
23	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
24	C₂×#117×C₁₀₁	—	2	1	no	—
25	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
26	C₄×SD₁₆×C₁₀₁	—	2	8	no	—
27	C₂×#106×C₁₀₁	C₂²	1	2	yes	—
28	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
29	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
30	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
31	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₁₀₁	C₂²	1	2	yes	—
34	#390×C₁₀₁	C₂²	1	1	yes	characteristic
35	#389×C₁₀₁	C₂²	1	1	yes	characteristic
36	#388×C₁₀₁	—	2	1	no	—
37	#386×C₁₀₁	—	2	1	no	—
38	#380×C₁₀₁	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
41	#340×C₁₀₁	C₂²	1	2	yes	—
42	#340×C₁₀₁	C₂²	1	2	yes	—
43	#336×C₁₀₁	C₂²	1	1	yes	characteristic
44	#336×C₁₀₁	C₂²	1	1	yes	characteristic
45	C₂²×Q₈×C₁₀₁	—	2	1	no	—
46	C₂²×Q₈×C₁₀₁	C₂³	1	2	yes	—
47	C₂²×D₄×C₁₀₁	—	2	1	no	—
48	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₀₁	—	2	1	no	—
50	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
53	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
54	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
55	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
56	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
58	C₄⋊Q₈×C₁₀₁	—	2	4	no	—
59	C₄⋊Q₈×C₁₀₁	—	2	4	no	—
60	#125×C₁₀₁	—	2	8	no	—
61	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
62	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
63	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
64	#121×C₁₀₁	—	2	2	no	—
65	#121×C₁₀₁	—	2	2	no	—
66	C₄×Q₈×C₁₀₁	—	2	8	no	—
67	C₄×Q₈×C₁₀₁	—	2	4	no	—
68	C₄×Q₈×C₁₀₁	D₄	1	8	yes	complemented
69	C₄×D₄×C₁₀₁	—	2	4	no	—
70	C₄×D₄×C₁₀₁	—	4	4	no	—
71	#117×C₁₀₁	—	2	8	no	—
72	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
77	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
88	C₂×C₄²×C₁₀₁	—	2	2	no	—
89	C₂×C₄²×C₁₀₁	—	2	4	no	—
90	C₂×C₄²×C₁₀₁	—	2	1	no	—
91	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
95	#106×C₁₀₁	—	2	4	no	—
96	#103×C₁₀₁	—	2	4	no	—
97	#103×C₁₀₁	—	2	4	no	—
98	#103×C₁₀₁	—	2	4	no	—
99	#102×C₁₀₁	—	2	4	no	—
100	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
101	C₄×C₈×C₁₀₁	—	2	4	no	—
102	#95×C₁₀₁	—	2	1	no	—
103	#95×C₁₀₁	—	2	1	no	—
104	#95×C₁₀₁	—	2	1	no	—
105	C₂⁴×C₁₀₁	—	2	1	no	—
106	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
107	C₂×Q₈×C₁₀₁	—	2	4	no	—
108	C₂×Q₈×C₁₀₁	—	2	2	no	—
109	C₂×Q₈×C₁₀₁	—	2	2	no	—
110	C₂×Q₈×C₁₀₁	—	2	2	no	—
111	C₂×Q₈×C₁₀₁	—	2	2	no	—
112	C₂×Q₈×C₁₀₁	—	2	2	no	—
113	C₂×Q₈×C₁₀₁	—	4	2	no	—
114	C₂×Q₈×C₁₀₁	—	4	2	no	—
115	C₂×Q₈×C₁₀₁	C₂×D₄	1	4	yes	—
116	C₂×D₄×C₁₀₁	—	2	4	no	—
117	C₂×D₄×C₁₀₁	—	2	2	no	—
118	C₂×D₄×C₁₀₁	—	2	2	no	—
119	C₂×D₄×C₁₀₁	—	2	1	no	—
120	C₂×D₄×C₁₀₁	—	4	2	no	—
121	C₂×D₄×C₁₀₁	—	4	2	no	—
122	C₂×D₄×C₁₀₁	#41	1	2	yes	—
123	C₂²×C₄×C₁₀₁	—	2	2	no	—
124	C₂²×C₄×C₁₀₁	—	2	2	no	—
125	C₂²×C₄×C₁₀₁	—	2	1	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	1	no	—
136	C₂²×C₄×C₁₀₁	—	4	1	no	—
137	C₂²×C₄×C₁₀₁	—	4	2	no	—
138	C₂²×C₄×C₁₀₁	—	4	2	no	—
139	C₂²×C₄×C₁₀₁	—	4	2	no	—
140	C₂²×C₄×C₁₀₁	SD₁₆	1	4	yes	complemented
141	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
147	SD₁₆×C₁₀₁	—	2	16	no	—
148	C₂×C₈×C₁₀₁	—	2	2	no	—
149	C₂×C₈×C₁₀₁	—	2	2	no	—
150	C₂×C₈×C₁₀₁	—	2	2	no	—
151	C₂×C₈×C₁₀₁	—	2	2	no	—
152	C₂×C₈×C₁₀₁	—	2	2	no	—
153	C₂×C₈×C₁₀₁	#41	1	4	yes	—
154	C₄⋊C₄×C₁₀₁	—	2	4	no	—
155	C₄⋊C₄×C₁₀₁	—	2	4	no	—
156	C₄⋊C₄×C₁₀₁	—	2	8	no	—
157	C₄⋊C₄×C₁₀₁	—	2	4	no	—
158	C₄⋊C₄×C₁₀₁	—	2	8	no	—
159	C₄⋊C₄×C₁₀₁	—	2	2	no	—
160	C₄⋊C₄×C₁₀₁	—	2	1	no	—
161	C₄⋊C₄×C₁₀₁	—	2	2	no	—
162	C₄⋊C₄×C₁₀₁	—	2	2	no	—
163	C₄⋊C₄×C₁₀₁	—	4	2	no	—
164	C₄⋊C₄×C₁₀₁	C₂×D₄	1	4	yes	—
165	C₄⋊C₄×C₁₀₁	#41	1	2	yes	—
166	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
167	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
168	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
169	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
170	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
171	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
172	C₄²×C₁₀₁	—	2	2	no	—
173	C₄²×C₁₀₁	—	2	2	no	—
174	C₄²×C₁₀₁	—	2	8	no	—
175	C₄²×C₁₀₁	—	2	2	no	—
176	C₄²×C₁₀₁	—	4	2	no	—
177	C₄²×C₁₀₁	C₂×D₄	1	4	yes	—
178	C₂³×C₁₀₁	—	2	1	no	—
179	C₂³×C₁₀₁	—	2	1	no	—
180	C₂³×C₁₀₁	—	2	1	no	—
181	C₂³×C₁₀₁	—	2	1	no	—
182	C₂³×C₁₀₁	—	2	1	no	—
183	C₂³×C₁₀₁	—	2	1	no	—
184	C₂³×C₁₀₁	—	2	2	no	—
185	C₂³×C₁₀₁	—	4	1	no	—
186	C₂³×C₁₀₁	—	4	1	no	—
187	C₂³×C₁₀₁	—	4	1	no	—
188	C₂³×C₁₀₁	—	4	1	no	—
189	C₂³×C₁₀₁	—	4	1	no	—
190	C₂³×C₁₀₁	—	4	1	no	—
191	C₂³×C₁₀₁	C₂×SD₁₆	1	2	yes	—
192	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
193	Q₈×C₁₀₁	—	2	4	no	—
194	Q₈×C₁₀₁	—	2	4	no	—
195	Q₈×C₁₀₁	—	4	8	no	—
196	Q₈×C₁₀₁	—	4	2	no	—
197	Q₈×C₁₀₁	—	4	2	no	—
198	D₄×C₁₀₁	—	2	4	no	—
199	D₄×C₁₀₁	—	4	8	no	—
200	D₄×C₁₀₁	—	4	2	no	—
201	C₂×C₄×C₁₀₁	—	2	1	no	—
202	C₂×C₄×C₁₀₁	—	2	1	no	—
203	C₂×C₄×C₁₀₁	—	2	1	no	—
204	C₂×C₄×C₁₀₁	—	2	1	no	—
205	C₂×C₄×C₁₀₁	—	2	1	no	—
206	C₂×C₄×C₁₀₁	—	2	1	no	—
207	C₂×C₄×C₁₀₁	—	2	8	no	—
208	C₂×C₄×C₁₀₁	—	2	1	no	—
209	C₂×C₄×C₁₀₁	—	2	4	no	—
210	C₂×C₄×C₁₀₁	—	2	4	no	—
211	C₂×C₄×C₁₀₁	—	2	1	no	—
212	C₂×C₄×C₁₀₁	—	2	2	no	—
213	C₂×C₄×C₁₀₁	—	2	1	no	—
214	C₂×C₄×C₁₀₁	—	4	4	no	—
215	C₂×C₄×C₁₀₁	—	4	2	no	—
216	C₂×C₄×C₁₀₁	—	4	2	no	—
217	C₂×C₄×C₁₀₁	—	4	1	no	—
218	C₂×C₄×C₁₀₁	—	4	2	no	—
219	C₂×C₄×C₁₀₁	—	4	1	no	—
220	C₂×C₄×C₁₀₁	—	4	2	no	—
221	C₂×C₄×C₁₀₁	—	4	2	no	—
222	C₂×C₄×C₁₀₁	—	4	2	no	—
223	C₂×C₄×C₁₀₁	—	4	1	no	—
224	C₂×C₄×C₁₀₁	—	4	1	no	—
225	C₂×C₄×C₁₀₁	—	4	1	no	—
226	C₂×C₄×C₁₀₁	—	4	1	no	—
227	C₂×C₄×C₁₀₁	—	4	1	no	—
228	C₂×C₄×C₁₀₁	—	4	1	no	—
229	C₂×C₄×C₁₀₁	—	8	4	no	—
230	C₂×C₄×C₁₀₁	#120	1	2	yes	—
231	C₂×C₄×C₁₀₁	#120	1	2	yes	—
232	C₂×C₄×C₁₀₁	C₂×SD₁₆	1	2	yes	—
233	C₂×C₄×C₁₀₁	C₂×SD₁₆	1	2	yes	—
234	C₂×C₄×C₁₀₁	#135	1	2	yes	—
235	C₂×C₄×C₁₀₁	#137	1	2	yes	—
236	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
237	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
239	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
240	C₈×C₁₀₁	—	2	4	no	—
241	C₈×C₁₀₁	—	4	2	no	—
242	C₂²×C₁₀₁	—	2	2	no	—
243	C₂²×C₁₀₁	—	2	2	no	—
244	C₂²×C₁₀₁	—	2	2	no	—
245	C₂²×C₁₀₁	—	4	1	no	—
246	C₂²×C₁₀₁	—	4	1	no	—
247	C₂²×C₁₀₁	—	4	1	no	—
248	C₂²×C₁₀₁	—	4	1	no	—
249	C₂²×C₁₀₁	—	4	2	no	—
250	C₂²×C₁₀₁	—	4	2	no	—
251	C₂²×C₁₀₁	—	4	2	no	—
252	C₂²×C₁₀₁	—	8	1	no	—
253	C₂²×C₁₀₁	—	8	1	no	—
254	C₂²×C₁₀₁	—	8	1	no	—
255	C₂²×C₁₀₁	—	8	1	no	—
256	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
257	C₂²×C₁₀₁	#525	1	1	yes	characteristic
258	C₂²×C₁₀₁	#532	1	1	yes	characteristic
259	C₂²×C₁₀₁	C₂²×SD₁₆	1	1	yes	characteristic
260	C₂²×C₁₀₁	C₂×#135	1	1	yes	characteristic
261	C₂²×C₁₀₁	C₂×#137	1	1	yes	characteristic
262	C₂²×C₁₀₁	#575	1	1	yes	characteristic
263	C₄×C₁₀₁	—	2	2	no	—
264	C₄×C₁₀₁	—	2	2	no	—
265	C₄×C₁₀₁	—	2	2	no	—
266	C₄×C₁₀₁	—	4	2	no	—
267	C₄×C₁₀₁	—	4	1	no	—
268	C₄×C₁₀₁	—	4	4	no	—
269	C₄×C₁₀₁	—	4	4	no	—
270	C₄×C₁₀₁	—	8	1	no	—
271	C₄×C₁₀₁	—	8	1	no	—
272	C₄×C₁₀₁	#448	1	4	yes	—
273	C₄×C₁₀₁	#525	1	2	yes	—
274	C₄×C₁₀₁	#532	1	2	yes	—
275	#23568	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₂×C₁₀₁	—	4	2	no	—
277	C₂×C₁₀₁	—	8	2	no	—
278	C₂×C₁₀₁	#2388	1	1	yes	characteristic
279	C₂×C₁₀₁	C₂×#448	1	1	yes	characteristic
280	C₂×C₁₀₁	#3002	1	1	yes	characteristic
281	C₂×C₁₀₁	#3101	1	1	yes	characteristic
282	C₂×C₁₀₁	#3107	1	1	yes	characteristic
283	C₂×C₁₀₁	#3167	1	1	yes	characteristic
284	C₂×C₁₀₁	#3172	1	1	yes	characteristic
285	C₂×#533	C₂×C₁₀₁	1	1	yes	characteristic, complemented
286	C₂×C₄×SD₁₆	C₂×C₁₀₁	1	2	yes	complemented
287	C₄×#121	C₂×C₁₀₁	1	1	yes	characteristic
288	#2058	C₂×C₁₀₁	1	1	yes	characteristic, complemented
289	#2043	C₂×C₁₀₁	1	1	yes	characteristic, complemented
290	#2035	C₂×C₁₀₁	1	2	yes	complemented
291	#2023	C₂×C₁₀₁	1	1	yes	characteristic, complemented
292	#2013	C₂×C₁₀₁	1	1	yes	characteristic, complemented
293	#2000	C₂×C₁₀₁	1	2	yes	—
294	C₄×#103	C₂×C₁₀₁	1	2	yes	complemented
295	C₄×C₂²⋊C₈	C₂×C₁₀₁	1	1	yes	characteristic, complemented
296	C₁₀₁	#23568	1	1	yes	characteristic, direct product factor, Sylow
297	C₂²×SD₁₆	C₂²×C₁₀₁	1	2	yes	—
298	#533	—	2	8	no	—
299	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
300	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
301	C₂×#125	—	2	1	no	—
302	C₂×C₂²⋊Q₈	—	2	1	no	—
303	C₂×C₂²⋊Q₈	C₂²×C₁₀₁	1	2	yes	—
304	C₂×#121	C₂²×C₁₀₁	1	1	yes	characteristic
305	C₂×C₄×Q₈	—	2	1	no	—
306	C₂×C₄×Q₈	C₂²×C₁₀₁	1	2	yes	—
307	C₂×C₄×D₄	—	2	1	no	—
308	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
309	C₂×#117	—	2	1	no	—
310	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
311	C₄×SD₁₆	—	2	8	no	—
312	C₂×#106	C₂²×C₁₀₁	1	2	yes	—
313	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
314	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
315	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
316	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
317	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	2	yes	—
318	C₂×C₄×C₈	C₂²×C₁₀₁	1	2	yes	—
319	#390	C₂²×C₁₀₁	1	1	yes	characteristic
320	#389	C₂²×C₁₀₁	1	1	yes	characteristic
321	#388	—	2	1	no	—
322	#386	—	2	1	no	—
323	#380	C₂²×C₁₀₁	1	1	yes	characteristic
324	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
325	C₄×C₂²⋊C₄	—	2	1	no	—
326	#340	C₂²×C₁₀₁	1	2	yes	—
327	#340	C₂²×C₁₀₁	1	2	yes	—
328	#336	C₂²×C₁₀₁	1	1	yes	characteristic
329	#336	C₂²×C₁₀₁	1	1	yes	characteristic
330	C₂²×Q₈	—	2	1	no	—
331	C₂²×Q₈	C₂³×C₁₀₁	1	2	yes	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
334	C₂³×C₄	—	2	1	no	—
335	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
336	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
337	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
338	C₂×SD₁₆	—	2	4	no	—
339	C₂×SD₁₆	—	2	4	no	—
340	C₂×SD₁₆	—	2	4	no	—
341	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
342	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
343	C₄⋊Q₈	—	2	4	no	—
344	C₄⋊Q₈	—	2	4	no	—
345	#125	—	2	8	no	—
346	C₂²⋊Q₈	—	2	8	no	—
347	C₂²⋊Q₈	—	2	4	no	—
348	C₂²⋊Q₈	—	2	4	no	—
349	#121	—	2	2	no	—
350	#121	—	2	2	no	—
351	C₄×Q₈	—	2	8	no	—
352	C₄×Q₈	—	2	4	no	—
353	C₄×Q₈	D₄×C₁₀₁	1	8	yes	complemented
354	C₄×D₄	—	2	4	no	—
355	C₄×D₄	—	4	4	no	—
356	#117	—	2	8	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	—	2	2	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₄²	—	2	2	no	—
374	C₂×C₄²	—	2	4	no	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
377	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
378	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
380	#106	—	2	4	no	—
381	#103	—	2	4	no	—
382	#103	—	2	4	no	—
383	#103	—	2	4	no	—
384	#102	—	2	4	no	—
385	C₂²⋊C₈	—	2	4	no	—
386	C₄×C₈	—	2	4	no	—
387	#95	—	2	1	no	—
388	#95	—	2	1	no	—
389	#95	—	2	1	no	—
390	C₂⁴	—	2	1	no	—
391	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	4	2	no	—
399	C₂×Q₈	—	4	2	no	—
400	C₂×Q₈	C₂×D₄×C₁₀₁	1	4	yes	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	4	2	no	—
406	C₂×D₄	—	4	2	no	—
407	C₂×D₄	#41×C₁₀₁	1	2	yes	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	4	1	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	—	4	2	no	—
425	C₂²×C₄	SD₁₆×C₁₀₁	1	4	yes	complemented
426	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
431	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
432	SD₁₆	—	2	16	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	#41×C₁₀₁	1	4	yes	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	8	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	8	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	4	2	no	—
449	C₄⋊C₄	C₂×D₄×C₁₀₁	1	4	yes	—
450	C₄⋊C₄	#41×C₁₀₁	1	2	yes	—
451	C₂²⋊C₄	—	2	8	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	4	2	no	—
454	C₂²⋊C₄	—	4	2	no	—
455	C₂²⋊C₄	—	4	2	no	—
456	C₂²⋊C₄	—	4	2	no	—
457	C₄²	—	2	2	no	—
458	C₄²	—	2	2	no	—
459	C₄²	—	2	8	no	—
460	C₄²	—	2	2	no	—
461	C₄²	—	4	2	no	—
462	C₄²	C₂×D₄×C₁₀₁	1	4	yes	—
463	C₂³	—	2	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	1	no	—
466	C₂³	—	2	1	no	—
467	C₂³	—	2	1	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	1	no	—
473	C₂³	—	4	1	no	—
474	C₂³	—	4	1	no	—
475	C₂³	—	4	1	no	—
476	C₂³	C₂×SD₁₆×C₁₀₁	1	2	yes	—
477	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
478	Q₈	—	2	4	no	—
479	Q₈	—	2	4	no	—
480	Q₈	—	4	8	no	—
481	Q₈	—	4	2	no	—
482	Q₈	—	4	2	no	—
483	D₄	—	2	4	no	—
484	D₄	—	4	8	no	—
485	D₄	—	4	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	8	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	8	4	no	—
515	C₂×C₄	#120×C₁₀₁	1	2	yes	—
516	C₂×C₄	#120×C₁₀₁	1	2	yes	—
517	C₂×C₄	C₂×SD₁₆×C₁₀₁	1	2	yes	—
518	C₂×C₄	C₂×SD₁₆×C₁₀₁	1	2	yes	—
519	C₂×C₄	#135×C₁₀₁	1	2	yes	—
520	C₂×C₄	#137×C₁₀₁	1	2	yes	—
521	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
522	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
523	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
524	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
525	C₈	—	2	4	no	—
526	C₈	—	4	2	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	8	1	no	—
538	C₂²	—	8	1	no	—
539	C₂²	—	8	1	no	—
540	C₂²	—	8	1	no	—
541	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
542	C₂²	#525×C₁₀₁	1	1	yes	characteristic
543	C₂²	#532×C₁₀₁	1	1	yes	characteristic
544	C₂²	C₂²×SD₁₆×C₁₀₁	1	1	yes	characteristic
545	C₂²	C₂×#135×C₁₀₁	1	1	yes	characteristic
546	C₂²	C₂×#137×C₁₀₁	1	1	yes	characteristic
547	C₂²	#575×C₁₀₁	1	1	yes	characteristic
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	2	no	—
551	C₄	—	4	4	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	4	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₄	#448×C₁₀₁	1	4	yes	—
558	C₄	#525×C₁₀₁	1	2	yes	—
559	C₄	#532×C₁₀₁	1	2	yes	—
560	C₂	—	4	2	no	—
561	C₂	—	8	2	no	—
562	C₂	C₁₀₁×#2388	1	1	yes	characteristic
563	C₂	C₂×#448×C₁₀₁	1	1	yes	characteristic
564	C₂	C₁₀₁×#3002	1	1	yes	characteristic
565	C₂	C₁₀₁×#3101	1	1	yes	characteristic
566	C₂	C₁₀₁×#3107	1	1	yes	characteristic
567	C₂	C₁₀₁×#3167	1	1	yes	characteristic
568	C₂	C₁₀₁×#3172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₀₁	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
socle	C₂³×C₁₀₁	C₂²×D₄
prime radical	C₂×#121×C₁₀₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₁ ◁ C₂²×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₁₀₁	C₂	semidirect
2. C₂×C₄×SD₁₆×C₁₀₁	C₂	semidirect
4. C₁₀₁×#2058	C₂	semidirect
5. C₁₀₁×#2043	C₂	semidirect
6. C₁₀₁×#2035	C₂	semidirect
7. C₁₀₁×#2023	C₂	semidirect
8. C₁₀₁×#2013	C₂	semidirect
10. C₄×#103×C₁₀₁	C₂	semidirect
11. C₄×C₂²⋊C₈×C₁₀₁	C₂	semidirect
68. C₄×Q₈×C₁₀₁	D₄	semidirect
140. C₂²×C₄×C₁₀₁	SD₁₆	semidirect
275. #23568	C₁₀₁	direct (N × H)
285. C₂×#533	C₂×C₁₀₁	semidirect
286. C₂×C₄×SD₁₆	C₂×C₁₀₁	semidirect
288. #2058	C₂×C₁₀₁	semidirect
289. #2043	C₂×C₁₀₁	semidirect
290. #2035	C₂×C₁₀₁	semidirect
291. #2023	C₂×C₁₀₁	semidirect
292. #2013	C₂×C₁₀₁	semidirect
294. C₄×#103	C₂×C₁₀₁	semidirect
295. C₄×C₂²⋊C₈	C₂×C₁₀₁	semidirect
296. C₁₀₁	#23568	direct (N × H)
353. C₄×Q₈	D₄×C₁₀₁	semidirect
425. C₂²×C₄	SD₁₆×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₁₀₁	2
C₂×C₄×SD₁₆×C₁₀₁	2
C₄×#121×C₁₀₁	2
C₁₀₁×#2058	2
C₁₀₁×#2043	2
C₁₀₁×#2035	2
C₁₀₁×#2023	2
C₁₀₁×#2013	2
C₁₀₁×#2000	2
C₄×#103×C₁₀₁	2
C₄×C₂²⋊C₈×C₁₀₁	2
#23568	101

Subgroups — C101×#23568 #38805719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#23568 #38805719