Subgroups — C₁₀₁×#20930 #38803081

Order 25856.

1738 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#519×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#416×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×#103×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#2311	C₂	1	1	yes	maximal, characteristic
6	C₁₀₁×#1880	C₂	1	4	yes	maximal, complemented
7	C₁₀₁×#1878	C₂	1	4	yes	maximal, complemented
8	C₁₀₁×#1736	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₁×#1729	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
12	C₂×#137×C₁₀₁	—	2	4	no	—
13	C₂×#137×C₁₀₁	—	2	4	no	—
14	C₂×#137×C₁₀₁	C₄	1	8	yes	complemented
15	C₂²×Q₁₆×C₁₀₁	C₂²	1	2	yes	—
16	C₂²×SD₁₆×C₁₀₁	C₂²	1	2	yes	—
17	C₂²×M₁₆×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
19	#519×C₁₀₁	—	2	4	no	—
20	#519×C₁₀₁	—	2	4	no	—
21	C₂×C₄×Q₈×C₁₀₁	—	2	2	no	—
22	C₂×C₄×Q₈×C₁₀₁	C₂²	1	4	yes	—
23	C₂×#117×C₁₀₁	—	2	2	no	—
24	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
25	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
27	#416×C₁₀₁	—	2	4	no	—
28	C₂×#103×C₁₀₁	—	2	4	no	—
29	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
30	C₂×#103×C₁₀₁	C₂²	1	4	yes	—
31	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
32	#391×C₁₀₁	C₂²	1	2	yes	—
33	#390×C₁₀₁	C₂²	1	2	yes	—
34	#386×C₁₀₁	—	2	2	no	—
35	#380×C₁₀₁	—	2	2	no	—
36	#340×C₁₀₁	C₂²	1	4	yes	—
37	#336×C₁₀₁	C₂²	1	4	yes	—
38	C₂×#41×C₁₀₁	—	2	2	no	—
39	C₂×#41×C₁₀₁	—	2	2	no	—
40	C₂×#41×C₁₀₁	—	2	2	no	—
41	C₂×#41×C₁₀₁	—	2	2	no	—
42	C₂×#41×C₁₀₁	—	2	2	no	—
43	C₂×#41×C₁₀₁	C₂×C₄	1	4	yes	—
44	C₂²×Q₈×C₁₀₁	—	2	1	no	—
45	C₂²×Q₈×C₁₀₁	—	2	2	no	—
46	C₂²×Q₈×C₁₀₁	—	2	2	no	—
47	C₂²×Q₈×C₁₀₁	—	2	2	no	—
48	C₂²×Q₈×C₁₀₁	C₂×C₄	1	4	yes	—
49	C₂²×Q₈×C₁₀₁	D₄	1	4	yes	—
50	C₂²×Q₈×C₁₀₁	D₄	1	4	yes	—
51	C₂²×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
52	C₂²×Q₈×C₁₀₁	C₂³	1	2	yes	—
53	C₂²×D₄×C₁₀₁	—	2	1	no	—
54	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₀₁	—	2	1	no	—
56	C₂³×C₄×C₁₀₁	—	2	1	no	—
57	C₂³×C₄×C₁₀₁	—	2	1	no	—
58	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
59	#137×C₁₀₁	—	2	32	no	—
60	C₂×Q₁₆×C₁₀₁	—	2	4	no	—
61	C₂×Q₁₆×C₁₀₁	—	2	4	no	—
62	C₂×Q₁₆×C₁₀₁	C₂×C₄	1	8	yes	complemented
63	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
64	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
65	C₂×SD₁₆×C₁₀₁	C₂×C₄	1	8	yes	complemented
66	C₂×M₁₆×C₁₀₁	—	2	2	no	—
67	C₂×M₁₆×C₁₀₁	—	2	2	no	—
68	C₂×M₁₆×C₁₀₁	C₂×C₄	1	4	yes	—
69	C₂²×C₈×C₁₀₁	—	2	2	no	—
70	C₂²×C₈×C₁₀₁	—	2	2	no	—
71	C₂²×C₈×C₁₀₁	—	2	2	no	—
72	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
73	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
74	C₄×Q₈×C₁₀₁	—	2	16	no	—
75	C₄×Q₈×C₁₀₁	—	2	8	no	—
76	C₄×Q₈×C₁₀₁	—	2	8	no	—
77	#117×C₁₀₁	—	2	16	no	—
78	#117×C₁₀₁	—	2	2	no	—
79	#117×C₁₀₁	—	2	2	no	—
80	#117×C₁₀₁	—	2	2	no	—
81	#117×C₁₀₁	D₄	1	4	yes	—
82	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
83	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
85	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₀₁	D₄	1	2	yes	—
87	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
89	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
91	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	2	yes	—
92	C₂×C₄²×C₁₀₁	—	2	4	no	—
93	C₂×C₄²×C₁₀₁	—	2	1	no	—
94	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
95	#103×C₁₀₁	—	2	8	no	—
96	#103×C₁₀₁	—	2	4	no	—
97	#102×C₁₀₁	—	2	4	no	—
98	#95×C₁₀₁	—	2	4	no	—
99	C₂⁴×C₁₀₁	—	2	1	no	—
100	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
101	#41×C₁₀₁	—	2	8	no	—
102	#41×C₁₀₁	—	2	8	no	—
103	#41×C₁₀₁	—	4	4	no	—
104	#41×C₁₀₁	—	4	4	no	—
105	C₂×Q₈×C₁₀₁	—	2	4	no	—
106	C₂×Q₈×C₁₀₁	—	2	8	no	—
107	C₂×Q₈×C₁₀₁	—	2	4	no	—
108	C₂×Q₈×C₁₀₁	—	2	4	no	—
109	C₂×Q₈×C₁₀₁	—	2	8	no	—
110	C₂×Q₈×C₁₀₁	—	2	8	no	—
111	C₂×Q₈×C₁₀₁	—	2	2	no	—
112	C₂×Q₈×C₁₀₁	—	2	2	no	—
113	C₂×Q₈×C₁₀₁	—	2	2	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	—	2	1	no	—
119	C₂×Q₈×C₁₀₁	C₂²⋊C₄	1	16	yes	complemented
120	C₂×Q₈×C₁₀₁	C₂²×C₄	1	2	yes	—
121	C₂×Q₈×C₁₀₁	C₂²×C₄	1	4	yes	—
122	C₂×Q₈×C₁₀₁	C₂×D₄	1	4	yes	—
123	C₂×Q₈×C₁₀₁	C₂×D₄	1	4	yes	—
124	C₂×D₄×C₁₀₁	—	2	4	no	—
125	C₂×D₄×C₁₀₁	—	2	1	no	—
126	C₂×D₄×C₁₀₁	—	2	1	no	—
127	C₂×D₄×C₁₀₁	—	2	1	no	—
128	C₂×D₄×C₁₀₁	—	2	1	no	—
129	C₂×D₄×C₁₀₁	—	2	1	no	—
130	C₂×D₄×C₁₀₁	—	4	2	no	—
131	C₂×D₄×C₁₀₁	—	4	2	no	—
132	C₂×D₄×C₁₀₁	C₂²×C₄	1	2	yes	—
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	2	no	—
137	C₂²×C₄×C₁₀₁	—	2	1	no	—
138	C₂²×C₄×C₁₀₁	—	2	2	no	—
139	C₂²×C₄×C₁₀₁	—	2	4	no	—
140	C₂²×C₄×C₁₀₁	—	2	2	no	—
141	C₂²×C₄×C₁₀₁	—	4	2	no	—
142	C₂²×C₄×C₁₀₁	—	4	2	no	—
143	C₂²×C₄×C₁₀₁	—	4	2	no	—
144	C₂²×C₄×C₁₀₁	—	8	2	no	—
145	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
146	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
147	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
152	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
153	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
154	Q₁₆×C₁₀₁	—	2	16	no	—
155	SD₁₆×C₁₀₁	—	2	16	no	—
156	M₁₆×C₁₀₁	—	2	8	no	—
157	C₂×C₈×C₁₀₁	—	2	2	no	—
158	C₂×C₈×C₁₀₁	—	2	2	no	—
159	C₂×C₈×C₁₀₁	—	2	2	no	—
160	C₂×C₈×C₁₀₁	—	2	2	no	—
161	C₂×C₈×C₁₀₁	—	2	2	no	—
162	C₂×C₈×C₁₀₁	—	4	4	no	—
163	C₂×C₈×C₁₀₁	C₂²×C₄	1	4	yes	—
164	C₄⋊C₄×C₁₀₁	—	2	16	no	—
165	C₄⋊C₄×C₁₀₁	—	2	4	no	—
166	C₄⋊C₄×C₁₀₁	—	2	2	no	—
167	C₄⋊C₄×C₁₀₁	—	2	2	no	—
168	C₄⋊C₄×C₁₀₁	—	2	2	no	—
169	C₄⋊C₄×C₁₀₁	—	4	2	no	—
170	C₄⋊C₄×C₁₀₁	C₂×D₄	1	4	yes	—
171	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
172	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
173	C₂²⋊C₄×C₁₀₁	—	8	4	no	—
174	C₄²×C₁₀₁	—	2	16	no	—
175	C₄²×C₁₀₁	—	2	4	no	—
176	C₄²×C₁₀₁	—	2	2	no	—
177	C₄²×C₁₀₁	—	2	2	no	—
178	C₂³×C₁₀₁	—	2	2	no	—
179	C₂³×C₁₀₁	—	2	2	no	—
180	C₂³×C₁₀₁	—	2	2	no	—
181	C₂³×C₁₀₁	—	4	1	no	—
182	C₂³×C₁₀₁	—	4	1	no	—
183	C₂³×C₁₀₁	—	4	2	no	—
184	C₂³×C₁₀₁	—	4	2	no	—
185	C₂³×C₁₀₁	C₄×D₄	1	2	yes	—
186	C₂³×C₁₀₁	#120	1	2	yes	—
187	C₂³×C₁₀₁	#121	1	2	yes	—
188	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
189	Q₈×C₁₀₁	—	2	4	no	—
190	Q₈×C₁₀₁	—	2	4	no	—
191	Q₈×C₁₀₁	—	2	4	no	—
192	Q₈×C₁₀₁	—	2	16	no	—
193	Q₈×C₁₀₁	—	2	2	no	—
194	Q₈×C₁₀₁	—	2	2	no	—
195	Q₈×C₁₀₁	—	4	1	no	—
196	Q₈×C₁₀₁	—	4	1	no	—
197	Q₈×C₁₀₁	C₂×C₂²⋊C₄	1	8	yes	—
198	D₄×C₁₀₁	—	2	2	no	—
199	D₄×C₁₀₁	—	2	2	no	—
200	D₄×C₁₀₁	—	4	8	no	—
201	D₄×C₁₀₁	—	4	1	no	—
202	D₄×C₁₀₁	—	4	1	no	—
203	C₂×C₄×C₁₀₁	—	2	4	no	—
204	C₂×C₄×C₁₀₁	—	2	4	no	—
205	C₂×C₄×C₁₀₁	—	2	4	no	—
206	C₂×C₄×C₁₀₁	—	2	16	no	—
207	C₂×C₄×C₁₀₁	—	2	2	no	—
208	C₂×C₄×C₁₀₁	—	2	4	no	—
209	C₂×C₄×C₁₀₁	—	2	4	no	—
210	C₂×C₄×C₁₀₁	—	2	4	no	—
211	C₂×C₄×C₁₀₁	—	2	4	no	—
212	C₂×C₄×C₁₀₁	—	4	1	no	—
213	C₂×C₄×C₁₀₁	—	4	1	no	—
214	C₂×C₄×C₁₀₁	—	4	2	no	—
215	C₂×C₄×C₁₀₁	—	4	2	no	—
216	C₂×C₄×C₁₀₁	—	4	8	no	—
217	C₂×C₄×C₁₀₁	—	4	2	no	—
218	C₂×C₄×C₁₀₁	—	4	4	no	—
219	C₂×C₄×C₁₀₁	—	8	4	no	—
220	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
221	C₂×C₄×C₁₀₁	C₄×D₄	1	4	yes	—
222	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
223	C₂×C₄×C₁₀₁	#120	1	2	yes	—
224	C₂×C₄×C₁₀₁	#121	1	4	yes	—
225	C₂×C₄×C₁₀₁	#121	1	2	yes	—
226	C₂×C₄×C₁₀₁	#123	1	4	yes	—
227	C₂×C₄×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
233	C₈×C₁₀₁	—	2	4	no	—
234	C₈×C₁₀₁	—	4	2	no	—
235	C₂²×C₁₀₁	—	2	4	no	—
236	C₂²×C₁₀₁	—	2	4	no	—
237	C₂²×C₁₀₁	—	2	2	no	—
238	C₂²×C₁₀₁	—	2	2	no	—
239	C₂²×C₁₀₁	—	4	4	no	—
240	C₂²×C₁₀₁	—	4	2	no	—
241	C₂²×C₁₀₁	—	8	2	no	—
242	C₂²×C₁₀₁	—	8	1	no	—
243	C₂²×C₁₀₁	—	8	1	no	—
244	C₂²×C₁₀₁	#386	1	4	yes	—
245	C₂²×C₁₀₁	C₂×C₄×D₄	1	1	yes	characteristic
246	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
247	C₂²×C₁₀₁	C₂×#121	1	1	yes	characteristic
248	C₂²×C₁₀₁	#577	1	2	yes	—
249	C₂²×C₁₀₁	#578	1	2	yes	—
250	C₄×C₁₀₁	—	2	8	no	—
251	C₄×C₁₀₁	—	4	4	no	—
252	C₄×C₁₀₁	—	4	4	no	—
253	C₄×C₁₀₁	—	4	2	no	—
254	C₄×C₁₀₁	—	8	2	no	—
255	C₄×C₁₀₁	#386	1	4	yes	—
256	C₄×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
257	C₄×C₁₀₁	C₂×C₄×D₄	1	1	yes	characteristic
258	C₄×C₁₀₁	C₂×#121	1	1	yes	characteristic
259	C₄×C₁₀₁	C₂×#123	1	1	yes	characteristic
260	#20930	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₂×C₁₀₁	—	2	4	no	—
262	C₂×C₁₀₁	—	8	2	no	—
263	C₂×C₁₀₁	C₂×#386	1	1	yes	characteristic
264	C₂×C₁₀₁	#2947	1	2	yes	—
265	C₂×C₁₀₁	#3013	1	2	yes	—
266	C₂×C₁₀₁	#3043	1	1	yes	characteristic
267	C₂×C₁₀₁	#3044	1	1	yes	characteristic
268	C₂²×#137	C₂×C₁₀₁	1	1	yes	characteristic
269	C₂×#519	C₂×C₁₀₁	1	1	yes	characteristic, complemented
270	C₂×#416	C₂×C₁₀₁	1	1	yes	characteristic
271	C₂²×#103	C₂×C₁₀₁	1	1	yes	characteristic, complemented
272	#2311	C₂×C₁₀₁	1	1	yes	characteristic
273	#1880	C₂×C₁₀₁	1	4	yes	complemented
274	#1878	C₂×C₁₀₁	1	4	yes	complemented
275	#1736	C₂×C₁₀₁	1	1	yes	characteristic, complemented
276	#1729	C₂×C₁₀₁	1	1	yes	characteristic, complemented
277	C₁₀₁	#20930	1	1	yes	characteristic, direct product factor, Sylow
278	C₂²×#41	C₂²×C₁₀₁	1	1	yes	characteristic
279	C₂³×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
280	C₂×#137	—	2	4	no	—
281	C₂×#137	—	2	4	no	—
282	C₂×#137	C₄×C₁₀₁	1	8	yes	complemented
283	C₂²×Q₁₆	C₂²×C₁₀₁	1	2	yes	—
284	C₂²×SD₁₆	C₂²×C₁₀₁	1	2	yes	—
285	C₂²×M₁₆	C₂²×C₁₀₁	1	1	yes	characteristic
286	C₂³×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
287	#519	—	2	4	no	—
288	#519	—	2	4	no	—
289	C₂×C₄×Q₈	—	2	2	no	—
290	C₂×C₄×Q₈	C₂²×C₁₀₁	1	4	yes	—
291	C₂×#117	—	2	2	no	—
292	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
293	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
294	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
295	#416	—	2	4	no	—
296	C₂×#103	—	2	4	no	—
297	C₂×#103	C₂²×C₁₀₁	1	4	yes	—
298	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
299	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
300	#391	C₂²×C₁₀₁	1	2	yes	—
301	#390	C₂²×C₁₀₁	1	2	yes	—
302	#386	—	2	2	no	—
303	#380	—	2	2	no	—
304	#340	C₂²×C₁₀₁	1	4	yes	—
305	#336	C₂²×C₁₀₁	1	4	yes	—
306	C₂×#41	—	2	2	no	—
307	C₂×#41	—	2	2	no	—
308	C₂×#41	—	2	2	no	—
309	C₂×#41	—	2	2	no	—
310	C₂×#41	—	2	2	no	—
311	C₂×#41	C₂×C₄×C₁₀₁	1	4	yes	—
312	C₂²×Q₈	—	2	1	no	—
313	C₂²×Q₈	—	2	2	no	—
314	C₂²×Q₈	—	2	2	no	—
315	C₂²×Q₈	—	2	2	no	—
316	C₂²×Q₈	C₂×C₄×C₁₀₁	1	4	yes	—
317	C₂²×Q₈	D₄×C₁₀₁	1	4	yes	—
318	C₂²×Q₈	D₄×C₁₀₁	1	4	yes	—
319	C₂²×Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
320	C₂²×Q₈	C₂³×C₁₀₁	1	2	yes	—
321	C₂²×D₄	—	2	1	no	—
322	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
323	C₂³×C₄	—	2	1	no	—
324	C₂³×C₄	—	2	1	no	—
325	C₂³×C₄	—	2	1	no	—
326	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
327	#137	—	2	32	no	—
328	C₂×Q₁₆	—	2	4	no	—
329	C₂×Q₁₆	—	2	4	no	—
330	C₂×Q₁₆	C₂×C₄×C₁₀₁	1	8	yes	complemented
331	C₂×SD₁₆	—	2	4	no	—
332	C₂×SD₁₆	—	2	4	no	—
333	C₂×SD₁₆	C₂×C₄×C₁₀₁	1	8	yes	complemented
334	C₂×M₁₆	—	2	2	no	—
335	C₂×M₁₆	—	2	2	no	—
336	C₂×M₁₆	C₂×C₄×C₁₀₁	1	4	yes	—
337	C₂²×C₈	—	2	2	no	—
338	C₂²×C₈	—	2	2	no	—
339	C₂²×C₈	—	2	2	no	—
340	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
341	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
342	C₄×Q₈	—	2	16	no	—
343	C₄×Q₈	—	2	8	no	—
344	C₄×Q₈	—	2	8	no	—
345	#117	—	2	16	no	—
346	#117	—	2	2	no	—
347	#117	—	2	2	no	—
348	#117	—	2	2	no	—
349	#117	D₄×C₁₀₁	1	4	yes	—
350	C₂×C₄⋊C₄	—	2	4	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	D₄×C₁₀₁	1	2	yes	—
355	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
356	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	—	2	4	no	—
359	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	2	yes	—
360	C₂×C₄²	—	2	4	no	—
361	C₂×C₄²	—	2	1	no	—
362	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
363	#103	—	2	8	no	—
364	#103	—	2	4	no	—
365	#102	—	2	4	no	—
366	#95	—	2	4	no	—
367	C₂⁴	—	2	1	no	—
368	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
369	#41	—	2	8	no	—
370	#41	—	2	8	no	—
371	#41	—	4	4	no	—
372	#41	—	4	4	no	—
373	C₂×Q₈	—	2	4	no	—
374	C₂×Q₈	—	2	8	no	—
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	2	4	no	—
377	C₂×Q₈	—	2	8	no	—
378	C₂×Q₈	—	2	8	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	C₂²⋊C₄×C₁₀₁	1	16	yes	complemented
388	C₂×Q₈	C₂²×C₄×C₁₀₁	1	2	yes	—
389	C₂×Q₈	C₂²×C₄×C₁₀₁	1	4	yes	—
390	C₂×Q₈	C₂×D₄×C₁₀₁	1	4	yes	—
391	C₂×Q₈	C₂×D₄×C₁₀₁	1	4	yes	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	4	2	no	—
399	C₂×D₄	—	4	2	no	—
400	C₂×D₄	C₂²×C₄×C₁₀₁	1	2	yes	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	4	2	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	—	4	2	no	—
412	C₂²×C₄	—	8	2	no	—
413	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
414	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
415	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
416	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
417	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
419	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
420	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
421	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
422	Q₁₆	—	2	16	no	—
423	SD₁₆	—	2	16	no	—
424	M₁₆	—	2	8	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	4	4	no	—
431	C₂×C₈	C₂²×C₄×C₁₀₁	1	4	yes	—
432	C₄⋊C₄	—	2	16	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	4	2	no	—
438	C₄⋊C₄	C₂×D₄×C₁₀₁	1	4	yes	—
439	C₂²⋊C₄	—	2	4	no	—
440	C₂²⋊C₄	—	2	4	no	—
441	C₂²⋊C₄	—	8	4	no	—
442	C₄²	—	2	16	no	—
443	C₄²	—	2	4	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	2	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	4	1	no	—
450	C₂³	—	4	1	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	C₄×D₄×C₁₀₁	1	2	yes	—
454	C₂³	#120×C₁₀₁	1	2	yes	—
455	C₂³	#121×C₁₀₁	1	2	yes	—
456	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
457	Q₈	—	2	4	no	—
458	Q₈	—	2	4	no	—
459	Q₈	—	2	4	no	—
460	Q₈	—	2	16	no	—
461	Q₈	—	2	2	no	—
462	Q₈	—	2	2	no	—
463	Q₈	—	4	1	no	—
464	Q₈	—	4	1	no	—
465	Q₈	C₂×C₂²⋊C₄×C₁₀₁	1	8	yes	—
466	D₄	—	2	2	no	—
467	D₄	—	2	2	no	—
468	D₄	—	4	8	no	—
469	D₄	—	4	1	no	—
470	D₄	—	4	1	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	16	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	8	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	8	4	no	—
488	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
489	C₂×C₄	C₄×D₄×C₁₀₁	1	4	yes	—
490	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
491	C₂×C₄	#120×C₁₀₁	1	2	yes	—
492	C₂×C₄	#121×C₁₀₁	1	4	yes	—
493	C₂×C₄	#121×C₁₀₁	1	2	yes	—
494	C₂×C₄	#123×C₁₀₁	1	4	yes	—
495	C₂×C₄	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
496	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
498	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
499	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
500	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
501	C₈	—	2	4	no	—
502	C₈	—	4	2	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	2	4	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	1	no	—
511	C₂²	—	8	1	no	—
512	C₂²	#386×C₁₀₁	1	4	yes	—
513	C₂²	C₂×C₄×D₄×C₁₀₁	1	1	yes	characteristic
514	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
515	C₂²	C₂×#121×C₁₀₁	1	1	yes	characteristic
516	C₂²	#577×C₁₀₁	1	2	yes	—
517	C₂²	#578×C₁₀₁	1	2	yes	—
518	C₄	—	2	8	no	—
519	C₄	—	4	4	no	—
520	C₄	—	4	4	no	—
521	C₄	—	4	2	no	—
522	C₄	—	8	2	no	—
523	C₄	#386×C₁₀₁	1	4	yes	—
524	C₄	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
525	C₄	C₂×C₄×D₄×C₁₀₁	1	1	yes	characteristic
526	C₄	C₂×#121×C₁₀₁	1	1	yes	characteristic
527	C₄	C₂×#123×C₁₀₁	1	1	yes	characteristic
528	C₂	—	2	4	no	—
529	C₂	—	8	2	no	—
530	C₂	C₂×#386×C₁₀₁	1	1	yes	characteristic
531	C₂	C₁₀₁×#2947	1	2	yes	—
532	C₂	C₁₀₁×#3013	1	2	yes	—
533	C₂	C₁₀₁×#3043	1	1	yes	characteristic
534	C₂	C₁₀₁×#3044	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂²×#41×C₁₀₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂×#117×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#519×C₁₀₁	C₂	semidirect
4. C₂²×#103×C₁₀₁	C₂	semidirect
6. C₁₀₁×#1880	C₂	semidirect
7. C₁₀₁×#1878	C₂	semidirect
8. C₁₀₁×#1736	C₂	semidirect
9. C₁₀₁×#1729	C₂	semidirect
14. C₂×#137×C₁₀₁	C₄	semidirect
62. C₂×Q₁₆×C₁₀₁	C₂×C₄	semidirect
65. C₂×SD₁₆×C₁₀₁	C₂×C₄	semidirect
119. C₂×Q₈×C₁₀₁	C₂²⋊C₄	semidirect
260. #20930	C₁₀₁	direct (N × H)
269. C₂×#519	C₂×C₁₀₁	semidirect
271. C₂²×#103	C₂×C₁₀₁	semidirect
273. #1880	C₂×C₁₀₁	semidirect
274. #1878	C₂×C₁₀₁	semidirect
275. #1736	C₂×C₁₀₁	semidirect
276. #1729	C₂×C₁₀₁	semidirect
277. C₁₀₁	#20930	direct (N × H)
282. C₂×#137	C₄×C₁₀₁	semidirect
330. C₂×Q₁₆	C₂×C₄×C₁₀₁	semidirect
333. C₂×SD₁₆	C₂×C₄×C₁₀₁	semidirect
387. C₂×Q₈	C₂²⋊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×#137×C₁₀₁	2
C₂×#519×C₁₀₁	2
C₂×#416×C₁₀₁	2
C₂²×#103×C₁₀₁	2
C₁₀₁×#2311	2
C₁₀₁×#1880	2
C₁₀₁×#1878	2
C₁₀₁×#1736	2
C₁₀₁×#1729	2
#20930	101

Subgroups — C101×#20930 #38803081

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#20930 #38803081