Subgroups — C₁₀₁×#23547 #38805698

Order 25856.

1458 conjugacy classes of subgroups.

The subgroup lattice has 554 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×#423×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#417×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#419×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#2297	C₂	1	1	yes	maximal, characteristic
6	C₂×#391×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₁×#2056	C₂	1	4	yes	maximal, complemented
8	C₁₀₁×#2055	C₂	1	4	yes	maximal, complemented
9	C₁₀₁×#1736	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	—	2	4	no	—
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	C₂²×M₁₆×C₁₀₁	C₂²	1	1	yes	characteristic
19	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
22	#423×C₁₀₁	—	2	4	no	—
23	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	4	yes	—
24	#419×C₁₀₁	—	2	4	no	—
25	#417×C₁₀₁	—	2	4	no	—
26	C₂×#103×C₁₀₁	C₂²	1	4	yes	—
27	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
28	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
29	#391×C₁₀₁	—	2	1	no	—
30	#391×C₁₀₁	—	2	1	no	—
31	#391×C₁₀₁	C₂²	1	4	yes	—
32	#391×C₁₀₁	C₂²	1	2	yes	—
33	#390×C₁₀₁	C₂²	1	2	yes	—
34	#386×C₁₀₁	—	2	2	no	—
35	C₄×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
36	C₄×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
37	C₂×#95×C₁₀₁	—	2	2	no	—
38	#340×C₁₀₁	C₂²	1	4	yes	—
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	—	2	2	no	—
44	C₂×#41×C₁₀₁	D₄	1	4	yes	—
45	C₂²×Q₈×C₁₀₁	—	2	1	no	—
46	C₂²×Q₈×C₁₀₁	—	2	2	no	—
47	C₂²×Q₈×C₁₀₁	—	2	2	no	—
48	C₂²×Q₈×C₁₀₁	—	2	2	no	—
49	C₂²×Q₈×C₁₀₁	—	2	2	no	—
50	C₂²×Q₈×C₁₀₁	—	2	2	no	—
51	C₂²×Q₈×C₁₀₁	D₄	1	4	yes	—
52	C₂²×Q₈×C₁₀₁	C₂³	1	2	yes	—
53	C₂²×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₁₀₁	—	2	1	no	—
55	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₀₁	—	2	1	no	—
57	C₂³×C₄×C₁₀₁	—	2	1	no	—
58	C₂³×C₄×C₁₀₁	—	2	1	no	—
59	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
60	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
61	#137×C₁₀₁	—	2	32	no	—
62	C₂×Q₁₆×C₁₀₁	—	2	4	no	—
63	C₂×Q₁₆×C₁₀₁	—	2	4	no	—
64	C₂×Q₁₆×C₁₀₁	—	2	4	no	—
65	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
66	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
67	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
68	C₂×M₁₆×C₁₀₁	—	2	2	no	—
69	C₂×M₁₆×C₁₀₁	—	2	2	no	—
70	C₂×M₁₆×C₁₀₁	—	2	2	no	—
71	C₂×M₁₆×C₁₀₁	—	2	2	no	—
72	C₂×M₁₆×C₁₀₁	—	2	2	no	—
73	C₂×M₁₆×C₁₀₁	D₄	1	4	yes	—
74	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
75	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
76	#117×C₁₀₁	—	2	2	no	—
77	#117×C₁₀₁	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
79	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
86	C₂×C₄²×C₁₀₁	—	2	2	no	—
87	C₂×C₄²×C₁₀₁	—	2	2	no	—
88	C₂×C₄²×C₁₀₁	—	2	1	no	—
89	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
92	C₄⋊C₈×C₁₀₁	—	2	8	no	—
93	#103×C₁₀₁	—	2	4	no	—
94	#103×C₁₀₁	—	2	8	no	—
95	#102×C₁₀₁	—	2	4	no	—
96	#95×C₁₀₁	—	2	4	no	—
97	#95×C₁₀₁	—	2	4	no	—
98	#95×C₁₀₁	—	2	2	no	—
99	#95×C₁₀₁	—	2	2	no	—
100	C₂⁴×C₁₀₁	—	2	1	no	—
101	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
102	#41×C₁₀₁	—	2	8	no	—
103	#41×C₁₀₁	—	2	8	no	—
104	#41×C₁₀₁	—	4	4	no	—
105	#41×C₁₀₁	—	4	4	no	—
106	C₂×Q₈×C₁₀₁	—	2	4	no	—
107	C₂×Q₈×C₁₀₁	—	2	2	no	—
108	C₂×Q₈×C₁₀₁	—	2	1	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	1	no	—
114	C₂×Q₈×C₁₀₁	—	2	1	no	—
115	C₂×Q₈×C₁₀₁	—	2	2	no	—
116	C₂×Q₈×C₁₀₁	—	2	2	no	—
117	C₂×Q₈×C₁₀₁	—	2	1	no	—
118	C₂×Q₈×C₁₀₁	—	2	1	no	—
119	C₂×Q₈×C₁₀₁	—	4	2	no	—
120	C₂×Q₈×C₁₀₁	—	4	2	no	—
121	C₂×Q₈×C₁₀₁	—	4	4	no	—
122	C₂×Q₈×C₁₀₁	—	4	4	no	—
123	C₂×Q₈×C₁₀₁	C₂×D₄	1	4	yes	—
124	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
125	C₂×D₄×C₁₀₁	—	2	4	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	—	2	1	no	—
131	C₂×D₄×C₁₀₁	—	4	2	no	—
132	C₂×D₄×C₁₀₁	—	4	2	no	—
133	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₀₁	—	2	4	no	—
135	C₂²×C₄×C₁₀₁	—	2	4	no	—
136	C₂²×C₄×C₁₀₁	—	2	1	no	—
137	C₂²×C₄×C₁₀₁	—	2	2	no	—
138	C₂²×C₄×C₁₀₁	—	2	4	no	—
139	C₂²×C₄×C₁₀₁	—	2	4	no	—
140	C₂²×C₄×C₁₀₁	—	2	2	no	—
141	C₂²×C₄×C₁₀₁	—	2	2	no	—
142	C₂²×C₄×C₁₀₁	—	4	2	no	—
143	C₂²×C₄×C₁₀₁	—	4	2	no	—
144	C₂²×C₄×C₁₀₁	—	4	2	no	—
145	C₂²×C₄×C₁₀₁	—	4	2	no	—
146	C₂²×C₄×C₁₀₁	—	4	2	no	—
147	C₂²×C₄×C₁₀₁	—	4	4	no	—
148	C₂²×C₄×C₁₀₁	—	4	2	no	—
149	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
156	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
157	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
158	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
159	Q₁₆×C₁₀₁	—	2	16	no	—
160	SD₁₆×C₁₀₁	—	2	16	no	—
161	M₁₆×C₁₀₁	—	2	8	no	—
162	M₁₆×C₁₀₁	—	4	4	no	—
163	C₂×C₈×C₁₀₁	—	2	2	no	—
164	C₂×C₈×C₁₀₁	—	2	2	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	C₂×D₄	1	4	yes	—
169	C₄⋊C₄×C₁₀₁	—	2	2	no	—
170	C₄⋊C₄×C₁₀₁	—	2	2	no	—
171	C₄⋊C₄×C₁₀₁	—	2	2	no	—
172	C₄⋊C₄×C₁₀₁	—	2	2	no	—
173	C₄⋊C₄×C₁₀₁	—	4	2	no	—
174	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
175	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
176	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
177	C₄²×C₁₀₁	—	2	2	no	—
178	C₄²×C₁₀₁	—	2	2	no	—
179	C₄²×C₁₀₁	—	2	2	no	—
180	C₄²×C₁₀₁	—	2	2	no	—
181	C₄²×C₁₀₁	—	4	2	no	—
182	C₂³×C₁₀₁	—	2	2	no	—
183	C₂³×C₁₀₁	—	2	2	no	—
184	C₂³×C₁₀₁	—	2	2	no	—
185	C₂³×C₁₀₁	—	4	1	no	—
186	C₂³×C₁₀₁	—	4	1	no	—
187	C₂³×C₁₀₁	—	4	2	no	—
188	C₂³×C₁₀₁	—	4	2	no	—
189	C₂³×C₁₀₁	#121	1	2	yes	—
190	C₂³×C₁₀₁	#121	1	2	yes	—
191	C₂³×C₁₀₁	#121	1	2	yes	—
192	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
193	Q₈×C₁₀₁	—	2	4	no	—
194	Q₈×C₁₀₁	—	2	2	no	—
195	Q₈×C₁₀₁	—	2	4	no	—
196	Q₈×C₁₀₁	—	2	2	no	—
197	Q₈×C₁₀₁	—	4	2	no	—
198	Q₈×C₁₀₁	—	4	1	no	—
199	Q₈×C₁₀₁	—	4	2	no	—
200	Q₈×C₁₀₁	—	4	1	no	—
201	Q₈×C₁₀₁	—	4	8	no	—
202	D₄×C₁₀₁	—	2	2	no	—
203	D₄×C₁₀₁	—	2	2	no	—
204	D₄×C₁₀₁	—	4	8	no	—
205	D₄×C₁₀₁	—	4	1	no	—
206	D₄×C₁₀₁	—	4	1	no	—
207	C₂×C₄×C₁₀₁	—	2	2	no	—
208	C₂×C₄×C₁₀₁	—	2	2	no	—
209	C₂×C₄×C₁₀₁	—	2	2	no	—
210	C₂×C₄×C₁₀₁	—	2	2	no	—
211	C₂×C₄×C₁₀₁	—	2	4	no	—
212	C₂×C₄×C₁₀₁	—	2	2	no	—
213	C₂×C₄×C₁₀₁	—	2	2	no	—
214	C₂×C₄×C₁₀₁	—	4	8	no	—
215	C₂×C₄×C₁₀₁	—	4	1	no	—
216	C₂×C₄×C₁₀₁	—	4	1	no	—
217	C₂×C₄×C₁₀₁	—	4	2	no	—
218	C₂×C₄×C₁₀₁	—	4	2	no	—
219	C₂×C₄×C₁₀₁	—	4	8	no	—
220	C₂×C₄×C₁₀₁	—	4	8	no	—
221	C₂×C₄×C₁₀₁	—	4	2	no	—
222	C₂×C₄×C₁₀₁	—	4	2	no	—
223	C₂×C₄×C₁₀₁	—	4	2	no	—
224	C₂×C₄×C₁₀₁	—	4	2	no	—
225	C₂×C₄×C₁₀₁	—	4	4	no	—
226	C₂×C₄×C₁₀₁	—	8	4	no	—
227	C₂×C₄×C₁₀₁	#120	1	4	yes	—
228	C₂×C₄×C₁₀₁	#121	1	2	yes	—
229	C₂×C₄×C₁₀₁	#121	1	2	yes	—
230	C₂×C₄×C₁₀₁	#121	1	2	yes	—
231	C₂×C₄×C₁₀₁	#123	1	4	yes	—
232	C₂×C₄×C₁₀₁	#123	1	4	yes	—
233	C₂×C₄×C₁₀₁	#124	1	4	yes	—
234	C₂×C₄×C₁₀₁	#137	1	4	yes	complemented
235	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
241	C₈×C₁₀₁	—	2	4	no	—
242	C₈×C₁₀₁	—	4	2	no	—
243	C₂²×C₁₀₁	—	2	4	no	—
244	C₂²×C₁₀₁	—	2	2	no	—
245	C₂²×C₁₀₁	—	2	2	no	—
246	C₂²×C₁₀₁	—	2	4	no	—
247	C₂²×C₁₀₁	—	4	2	no	—
248	C₂²×C₁₀₁	—	4	2	no	—
249	C₂²×C₁₀₁	—	4	2	no	—
250	C₂²×C₁₀₁	—	8	2	no	—
251	C₂²×C₁₀₁	—	8	2	no	—
252	C₂²×C₁₀₁	#394	1	4	yes	—
253	C₂²×C₁₀₁	C₂×#121	1	1	yes	characteristic
254	C₂²×C₁₀₁	C₂×#121	1	1	yes	characteristic
255	C₂²×C₁₀₁	C₂×#121	1	1	yes	characteristic
256	C₂²×C₁₀₁	C₂×#137	1	2	yes	—
257	C₂²×C₁₀₁	#575	1	2	yes	—
258	C₄×C₁₀₁	—	2	4	no	—
259	C₄×C₁₀₁	—	4	2	no	—
260	C₄×C₁₀₁	—	4	4	no	—
261	C₄×C₁₀₁	—	4	2	no	—
262	C₄×C₁₀₁	—	8	2	no	—
263	C₄×C₁₀₁	—	8	2	no	—
264	C₄×C₁₀₁	#394	1	4	yes	—
265	C₄×C₁₀₁	C₂×#120	1	1	yes	characteristic
266	C₄×C₁₀₁	C₂×#123	1	1	yes	characteristic
267	C₄×C₁₀₁	C₂×#123	1	1	yes	characteristic
268	C₄×C₁₀₁	C₂×#124	1	1	yes	characteristic
269	#23547	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
270	C₂×C₁₀₁	—	2	4	no	—
271	C₂×C₁₀₁	—	8	2	no	—
272	C₂×C₁₀₁	C₂×#394	1	1	yes	characteristic
273	C₂×C₁₀₁	#3037	1	2	yes	—
274	C₂×C₁₀₁	#3039	1	1	yes	characteristic
275	C₂×C₁₀₁	#3040	1	1	yes	characteristic
276	C₂×C₁₀₁	#3056	1	2	yes	—
277	C₂²×#137	C₂×C₁₀₁	1	1	yes	characteristic
278	C₂×#423	C₂×C₁₀₁	1	1	yes	characteristic, complemented
279	C₂×#417	C₂×C₁₀₁	1	1	yes	characteristic
280	C₂×#419	C₂×C₁₀₁	1	1	yes	characteristic, complemented
281	#2297	C₂×C₁₀₁	1	1	yes	characteristic
282	C₂×#391	C₂×C₁₀₁	1	1	yes	characteristic, complemented
283	#2056	C₂×C₁₀₁	1	4	yes	complemented
284	#2055	C₂×C₁₀₁	1	4	yes	complemented
285	#1736	C₂×C₁₀₁	1	1	yes	characteristic, complemented
286	C₁₀₁	#23547	1	1	yes	characteristic, direct product factor, Sylow
287	C₂²×#41	C₂²×C₁₀₁	1	1	yes	characteristic
288	C₂³×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
289	C₂×#137	—	2	4	no	—
290	C₂×#137	—	2	4	no	—
291	C₂×#137	—	2	4	no	—
292	C₂²×Q₁₆	C₂²×C₁₀₁	1	2	yes	—
293	C₂²×SD₁₆	C₂²×C₁₀₁	1	2	yes	—
294	C₂²×M₁₆	C₂²×C₁₀₁	1	1	yes	characteristic
295	C₂²×M₁₆	C₂²×C₁₀₁	1	1	yes	characteristic
296	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
297	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
298	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
299	#423	—	2	4	no	—
300	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	4	yes	—
301	#419	—	2	4	no	—
302	#417	—	2	4	no	—
303	C₂×#103	C₂²×C₁₀₁	1	4	yes	—
304	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
305	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
306	#391	—	2	1	no	—
307	#391	—	2	1	no	—
308	#391	C₂²×C₁₀₁	1	4	yes	—
309	#391	C₂²×C₁₀₁	1	2	yes	—
310	#390	C₂²×C₁₀₁	1	2	yes	—
311	#386	—	2	2	no	—
312	C₄×C₂²⋊C₄	—	2	1	no	—
313	C₄×C₂²⋊C₄	—	2	1	no	—
314	C₂×#95	—	2	2	no	—
315	#340	C₂²×C₁₀₁	1	4	yes	—
316	C₂×#41	—	2	2	no	—
317	C₂×#41	—	2	2	no	—
318	C₂×#41	—	2	2	no	—
319	C₂×#41	—	2	2	no	—
320	C₂×#41	—	2	2	no	—
321	C₂×#41	D₄×C₁₀₁	1	4	yes	—
322	C₂²×Q₈	—	2	1	no	—
323	C₂²×Q₈	—	2	2	no	—
324	C₂²×Q₈	—	2	2	no	—
325	C₂²×Q₈	—	2	2	no	—
326	C₂²×Q₈	—	2	2	no	—
327	C₂²×Q₈	—	2	2	no	—
328	C₂²×Q₈	D₄×C₁₀₁	1	4	yes	—
329	C₂²×Q₈	C₂³×C₁₀₁	1	2	yes	—
330	C₂²×Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
333	C₂³×C₄	—	2	1	no	—
334	C₂³×C₄	—	2	1	no	—
335	C₂³×C₄	—	2	1	no	—
336	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
337	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
338	#137	—	2	32	no	—
339	C₂×Q₁₆	—	2	4	no	—
340	C₂×Q₁₆	—	2	4	no	—
341	C₂×Q₁₆	—	2	4	no	—
342	C₂×SD₁₆	—	2	4	no	—
343	C₂×SD₁₆	—	2	4	no	—
344	C₂×SD₁₆	—	2	4	no	—
345	C₂×M₁₆	—	2	2	no	—
346	C₂×M₁₆	—	2	2	no	—
347	C₂×M₁₆	—	2	2	no	—
348	C₂×M₁₆	—	2	2	no	—
349	C₂×M₁₆	—	2	2	no	—
350	C₂×M₁₆	D₄×C₁₀₁	1	4	yes	—
351	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
352	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
353	#117	—	2	2	no	—
354	#117	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	2	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
359	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	C₂×C₄²	—	2	2	no	—
364	C₂×C₄²	—	2	2	no	—
365	C₂×C₄²	—	2	1	no	—
366	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
367	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
368	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
369	C₄⋊C₈	—	2	8	no	—
370	#103	—	2	4	no	—
371	#103	—	2	8	no	—
372	#102	—	2	4	no	—
373	#95	—	2	4	no	—
374	#95	—	2	4	no	—
375	#95	—	2	2	no	—
376	#95	—	2	2	no	—
377	C₂⁴	—	2	1	no	—
378	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
379	#41	—	2	8	no	—
380	#41	—	2	8	no	—
381	#41	—	4	4	no	—
382	#41	—	4	4	no	—
383	C₂×Q₈	—	2	4	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	8	no	—
387	C₂×Q₈	—	2	8	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	—	4	2	no	—
397	C₂×Q₈	—	4	2	no	—
398	C₂×Q₈	—	4	4	no	—
399	C₂×Q₈	—	4	4	no	—
400	C₂×Q₈	C₂×D₄×C₁₀₁	1	4	yes	—
401	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	4	2	no	—
409	C₂×D₄	—	4	2	no	—
410	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	4	2	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	—	4	2	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	—	4	4	no	—
425	C₂²×C₄	—	4	2	no	—
426	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
427	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
429	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
430	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
431	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
432	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
433	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
434	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
435	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
436	Q₁₆	—	2	16	no	—
437	SD₁₆	—	2	16	no	—
438	M₁₆	—	2	8	no	—
439	M₁₆	—	4	4	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	C₂×D₄×C₁₀₁	1	4	yes	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	4	2	no	—
451	C₂²⋊C₄	—	4	4	no	—
452	C₂²⋊C₄	—	4	2	no	—
453	C₂²⋊C₄	—	4	4	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	2	2	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	2	2	no	—
458	C₄²	—	4	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	4	1	no	—
463	C₂³	—	4	1	no	—
464	C₂³	—	4	2	no	—
465	C₂³	—	4	2	no	—
466	C₂³	#121×C₁₀₁	1	2	yes	—
467	C₂³	#121×C₁₀₁	1	2	yes	—
468	C₂³	#121×C₁₀₁	1	2	yes	—
469	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
470	Q₈	—	2	4	no	—
471	Q₈	—	2	2	no	—
472	Q₈	—	2	4	no	—
473	Q₈	—	2	2	no	—
474	Q₈	—	4	2	no	—
475	Q₈	—	4	1	no	—
476	Q₈	—	4	2	no	—
477	Q₈	—	4	1	no	—
478	Q₈	—	4	8	no	—
479	D₄	—	2	2	no	—
480	D₄	—	2	2	no	—
481	D₄	—	4	8	no	—
482	D₄	—	4	1	no	—
483	D₄	—	4	1	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	4	8	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	8	no	—
497	C₂×C₄	—	4	8	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	4	no	—
503	C₂×C₄	—	8	4	no	—
504	C₂×C₄	#120×C₁₀₁	1	4	yes	—
505	C₂×C₄	#121×C₁₀₁	1	2	yes	—
506	C₂×C₄	#121×C₁₀₁	1	2	yes	—
507	C₂×C₄	#121×C₁₀₁	1	2	yes	—
508	C₂×C₄	#123×C₁₀₁	1	4	yes	—
509	C₂×C₄	#123×C₁₀₁	1	4	yes	—
510	C₂×C₄	#124×C₁₀₁	1	4	yes	—
511	C₂×C₄	#137×C₁₀₁	1	4	yes	complemented
512	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
515	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
516	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
517	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
518	C₈	—	2	4	no	—
519	C₈	—	4	2	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	4	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	8	2	no	—
528	C₂²	—	8	2	no	—
529	C₂²	#394×C₁₀₁	1	4	yes	—
530	C₂²	C₂×#121×C₁₀₁	1	1	yes	characteristic
531	C₂²	C₂×#121×C₁₀₁	1	1	yes	characteristic
532	C₂²	C₂×#121×C₁₀₁	1	1	yes	characteristic
533	C₂²	C₂×#137×C₁₀₁	1	2	yes	—
534	C₂²	#575×C₁₀₁	1	2	yes	—
535	C₄	—	2	4	no	—
536	C₄	—	4	2	no	—
537	C₄	—	4	2	no	—
538	C₄	—	4	4	no	—
539	C₄	—	8	2	no	—
540	C₄	—	8	2	no	—
541	C₄	#394×C₁₀₁	1	4	yes	—
542	C₄	C₂×#120×C₁₀₁	1	1	yes	characteristic
543	C₄	C₂×#123×C₁₀₁	1	1	yes	characteristic
544	C₄	C₂×#123×C₁₀₁	1	1	yes	characteristic
545	C₄	C₂×#124×C₁₀₁	1	1	yes	characteristic
546	C₂	—	2	4	no	—
547	C₂	—	8	2	no	—
548	C₂	C₂×#394×C₁₀₁	1	1	yes	characteristic
549	C₂	C₁₀₁×#3037	1	2	yes	—
550	C₂	C₁₀₁×#3039	1	1	yes	characteristic
551	C₂	C₁₀₁×#3040	1	1	yes	characteristic
552	C₂	C₁₀₁×#3056	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂²×#41×C₁₀₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂²×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#423×C₁₀₁	C₂	semidirect
4. C₂×#419×C₁₀₁	C₂	semidirect
6. C₂×#391×C₁₀₁	C₂	semidirect
7. C₁₀₁×#2056	C₂	semidirect
8. C₁₀₁×#2055	C₂	semidirect
9. C₁₀₁×#1736	C₂	semidirect
234. C₂×C₄×C₁₀₁	#137	semidirect
269. #23547	C₁₀₁	direct (N × H)
278. C₂×#423	C₂×C₁₀₁	semidirect
280. C₂×#419	C₂×C₁₀₁	semidirect
282. C₂×#391	C₂×C₁₀₁	semidirect
283. #2056	C₂×C₁₀₁	semidirect
284. #2055	C₂×C₁₀₁	semidirect
285. #1736	C₂×C₁₀₁	semidirect
286. C₁₀₁	#23547	direct (N × H)
511. C₂×C₄	#137×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×#423×C₁₀₁	2
C₂×#417×C₁₀₁	2
C₂×#419×C₁₀₁	2
C₁₀₁×#2297	2
C₂×#391×C₁₀₁	2
C₁₀₁×#2056	2
C₁₀₁×#2055	2
C₁₀₁×#1736	2
#23547	101

Subgroups — C101×#23547 #38805698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#23547 #38805698