Subgroups — C₁₀₁×#23541 #38805692

Order 25856.

1522 conjugacy classes of subgroups.

The subgroup lattice has 460 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
2	C₂×#424×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#419×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#418×C₁₀₁	C₂	1	1	yes	maximal, characteristic
5	C₁₀₁×#2310	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₁×#2309	C₂	1	1	yes	maximal, characteristic
7	C₁₀₁×#2055	C₂	1	8	yes	maximal, complemented
8	C₁₀₁×#1735	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂²×SD₁₆×C₁₀₁	—	2	4	no	—
12	C₂²×SD₁₆×C₁₀₁	—	2	4	no	—
13	C₂²×SD₁₆×C₁₀₁	—	2	4	no	—
14	C₂²×SD₁₆×C₁₀₁	C₂²	1	4	yes	—
15	C₂²×M₁₆×C₁₀₁	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
19	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
20	#424×C₁₀₁	—	2	4	no	—
21	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	4	yes	complemented
22	#419×C₁₀₁	—	2	4	no	—
23	#418×C₁₀₁	—	2	4	no	—
24	C₂×#103×C₁₀₁	C₂²	1	4	yes	complemented
25	C₂×#102×C₁₀₁	C₂²	1	4	yes	—
26	#391×C₁₀₁	—	2	2	no	—
27	#391×C₁₀₁	C₂²	1	4	yes	complemented
28	#390×C₁₀₁	—	2	2	no	—
29	#390×C₁₀₁	C₂²	1	4	yes	—
30	#381×C₁₀₁	—	2	2	no	—
31	#379×C₁₀₁	—	2	2	no	—
32	#340×C₁₀₁	C₂²	1	4	yes	complemented
33	C₂⁵×C₁₀₁	—	2	1	no	—
34	C₂²×Q₈×C₁₀₁	—	2	1	no	—
35	C₂²×Q₈×C₁₀₁	—	2	2	no	—
36	C₂²×Q₈×C₁₀₁	—	2	2	no	—
37	C₂²×Q₈×C₁₀₁	—	2	2	no	—
38	C₂²×Q₈×C₁₀₁	—	2	2	no	—
39	C₂²×Q₈×C₁₀₁	—	2	2	no	—
40	C₂²×Q₈×C₁₀₁	D₄	1	4	yes	—
41	C₂²×Q₈×C₁₀₁	C₂³	1	2	yes	—
42	C₂²×D₄×C₁₀₁	—	2	2	no	—
43	C₂²×D₄×C₁₀₁	—	2	2	no	—
44	C₂²×D₄×C₁₀₁	—	2	1	no	—
45	C₂²×D₄×C₁₀₁	—	2	2	no	—
46	C₂²×D₄×C₁₀₁	—	2	2	no	—
47	C₂²×D₄×C₁₀₁	—	2	2	no	—
48	C₂²×D₄×C₁₀₁	D₄	1	4	yes	—
49	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₀₁	—	2	1	no	—
51	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
52	C₂×SD₁₆×C₁₀₁	—	2	32	no	—
53	C₂×SD₁₆×C₁₀₁	—	2	8	no	—
54	C₂×SD₁₆×C₁₀₁	—	2	8	no	—
55	C₂×SD₁₆×C₁₀₁	—	2	8	no	—
56	C₂×M₁₆×C₁₀₁	—	2	2	no	—
57	C₂×M₁₆×C₁₀₁	—	2	2	no	—
58	C₂×M₁₆×C₁₀₁	—	2	2	no	—
59	C₂²×C₈×C₁₀₁	—	2	2	no	—
60	C₂²×C₈×C₁₀₁	—	2	2	no	—
61	C₂²×C₈×C₁₀₁	D₄	1	4	yes	—
62	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
63	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
64	#117×C₁₀₁	—	2	2	no	—
65	#117×C₁₀₁	—	2	2	no	—
66	#117×C₁₀₁	—	2	2	no	—
67	#117×C₁₀₁	—	2	2	no	—
68	#117×C₁₀₁	—	2	2	no	—
69	#117×C₁₀₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₀₁	D₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
73	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
76	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	2	yes	—
77	C₂×C₄²×C₁₀₁	—	2	1	no	—
78	C₂×C₄²×C₁₀₁	—	2	1	no	—
79	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
80	C₄⋊C₈×C₁₀₁	—	2	8	no	—
81	#103×C₁₀₁	—	2	8	no	—
82	#102×C₁₀₁	—	2	8	no	—
83	#95×C₁₀₁	—	2	8	no	—
84	C₂⁴×C₁₀₁	—	2	2	no	—
85	C₂⁴×C₁₀₁	—	2	4	no	—
86	C₂⁴×C₁₀₁	—	4	2	no	—
87	C₂⁴×C₁₀₁	—	4	2	no	—
88	C₂⁴×C₁₀₁	—	8	4	no	—
89	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
90	C₂×Q₈×C₁₀₁	—	2	4	no	—
91	C₂×Q₈×C₁₀₁	—	2	2	no	—
92	C₂×Q₈×C₁₀₁	—	2	8	no	—
93	C₂×Q₈×C₁₀₁	—	2	8	no	—
94	C₂×Q₈×C₁₀₁	—	2	2	no	—
95	C₂×Q₈×C₁₀₁	—	2	2	no	—
96	C₂×Q₈×C₁₀₁	—	2	2	no	—
97	C₂×Q₈×C₁₀₁	—	2	2	no	—
98	C₂×Q₈×C₁₀₁	—	4	2	no	—
99	C₂×Q₈×C₁₀₁	—	4	2	no	—
100	C₂×Q₈×C₁₀₁	—	4	4	no	—
101	C₂×Q₈×C₁₀₁	—	4	4	no	—
102	C₂×Q₈×C₁₀₁	C₂×D₄	1	4	yes	—
103	C₂×D₄×C₁₀₁	—	2	8	no	—
104	C₂×D₄×C₁₀₁	—	2	4	no	—
105	C₂×D₄×C₁₀₁	—	2	8	no	—
106	C₂×D₄×C₁₀₁	—	2	2	no	—
107	C₂×D₄×C₁₀₁	—	2	2	no	—
108	C₂×D₄×C₁₀₁	—	2	2	no	—
109	C₂×D₄×C₁₀₁	—	2	2	no	—
110	C₂×D₄×C₁₀₁	—	2	2	no	—
111	C₂×D₄×C₁₀₁	—	4	2	no	—
112	C₂×D₄×C₁₀₁	—	4	2	no	—
113	C₂×D₄×C₁₀₁	—	4	4	no	—
114	C₂×D₄×C₁₀₁	—	4	4	no	—
115	C₂×D₄×C₁₀₁	C₂×D₄	1	4	yes	—
116	C₂²×C₄×C₁₀₁	—	2	4	no	—
117	C₂²×C₄×C₁₀₁	—	2	2	no	—
118	C₂²×C₄×C₁₀₁	—	2	2	no	—
119	C₂²×C₄×C₁₀₁	—	2	2	no	—
120	C₂²×C₄×C₁₀₁	—	4	2	no	—
121	C₂²×C₄×C₁₀₁	—	4	2	no	—
122	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
123	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
128	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
129	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
130	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
131	SD₁₆×C₁₀₁	—	2	32	no	—
132	M₁₆×C₁₀₁	—	4	4	no	—
133	C₂×C₈×C₁₀₁	—	2	8	no	—
134	C₂×C₈×C₁₀₁	—	2	2	no	—
135	C₂×C₈×C₁₀₁	—	2	2	no	—
136	C₂×C₈×C₁₀₁	—	2	2	no	—
137	C₂×C₈×C₁₀₁	—	2	2	no	—
138	C₂×C₈×C₁₀₁	—	2	2	no	—
139	C₂×C₈×C₁₀₁	C₂×D₄	1	4	yes	—
140	C₄⋊C₄×C₁₀₁	—	2	4	no	—
141	C₄⋊C₄×C₁₀₁	—	2	2	no	—
142	C₄⋊C₄×C₁₀₁	—	2	2	no	—
143	C₄⋊C₄×C₁₀₁	—	2	2	no	—
144	C₄⋊C₄×C₁₀₁	—	2	2	no	—
145	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
146	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
147	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
148	C₂²⋊C₄×C₁₀₁	—	8	8	no	—
149	C₄²×C₁₀₁	—	2	2	no	—
150	C₄²×C₁₀₁	—	2	2	no	—
151	C₄²×C₁₀₁	—	4	2	no	—
152	C₄²×C₁₀₁	—	4	2	no	—
153	C₂³×C₁₀₁	—	2	4	no	—
154	C₂³×C₁₀₁	—	2	4	no	—
155	C₂³×C₁₀₁	—	4	2	no	—
156	C₂³×C₁₀₁	—	4	2	no	—
157	C₂³×C₁₀₁	—	4	8	no	—
158	C₂³×C₁₀₁	—	4	8	no	—
159	C₂³×C₁₀₁	—	8	8	no	—
160	C₂³×C₁₀₁	—	8	8	no	—
161	C₂³×C₁₀₁	—	8	8	no	—
162	C₂³×C₁₀₁	#121	1	2	yes	—
163	C₂³×C₁₀₁	#121	1	2	yes	—
164	C₂³×C₁₀₁	#121	1	2	yes	—
165	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₁₀₁	—	2	4	no	—
167	Q₈×C₁₀₁	—	2	4	no	—
168	Q₈×C₁₀₁	—	4	2	no	—
169	Q₈×C₁₀₁	—	4	2	no	—
170	Q₈×C₁₀₁	—	4	8	no	—
171	D₄×C₁₀₁	—	2	4	no	—
172	D₄×C₁₀₁	—	2	4	no	—
173	D₄×C₁₀₁	—	4	2	no	—
174	D₄×C₁₀₁	—	4	2	no	—
175	D₄×C₁₀₁	—	4	8	no	—
176	C₂×C₄×C₁₀₁	—	2	4	no	—
177	C₂×C₄×C₁₀₁	—	2	4	no	—
178	C₂×C₄×C₁₀₁	—	2	8	no	—
179	C₂×C₄×C₁₀₁	—	4	2	no	—
180	C₂×C₄×C₁₀₁	—	4	2	no	—
181	C₂×C₄×C₁₀₁	—	4	8	no	—
182	C₂×C₄×C₁₀₁	—	4	2	no	—
183	C₂×C₄×C₁₀₁	—	4	2	no	—
184	C₂×C₄×C₁₀₁	—	4	4	no	—
185	C₂×C₄×C₁₀₁	—	4	4	no	—
186	C₂×C₄×C₁₀₁	#120	1	4	yes	—
187	C₂×C₄×C₁₀₁	#121	1	2	yes	—
188	C₂×C₄×C₁₀₁	#121	1	2	yes	—
189	C₂×C₄×C₁₀₁	#121	1	2	yes	—
190	C₂×C₄×C₁₀₁	#123	1	4	yes	—
191	C₂×C₄×C₁₀₁	#123	1	4	yes	—
192	C₂×C₄×C₁₀₁	#124	1	4	yes	—
193	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
199	C₈×C₁₀₁	—	2	4	no	—
200	C₈×C₁₀₁	—	4	2	no	—
201	C₂²×C₁₀₁	—	2	4	no	—
202	C₂²×C₁₀₁	—	2	4	no	—
203	C₂²×C₁₀₁	—	2	4	no	—
204	C₂²×C₁₀₁	—	4	4	no	—
205	C₂²×C₁₀₁	—	4	8	no	—
206	C₂²×C₁₀₁	—	8	16	no	—
207	C₂²×C₁₀₁	—	8	4	no	—
208	C₂²×C₁₀₁	—	8	4	no	—
209	C₂²×C₁₀₁	#394	1	4	yes	—
210	C₂²×C₁₀₁	C₂×#121	1	1	yes	characteristic
211	C₂²×C₁₀₁	C₂×#121	1	1	yes	characteristic
212	C₂²×C₁₀₁	C₂×#121	1	1	yes	characteristic
213	C₂²×C₁₀₁	#577	1	4	yes	—
214	C₄×C₁₀₁	—	4	4	no	—
215	C₄×C₁₀₁	—	4	4	no	—
216	C₄×C₁₀₁	—	8	2	no	—
217	C₄×C₁₀₁	—	8	2	no	—
218	C₄×C₁₀₁	#394	1	4	yes	—
219	C₄×C₁₀₁	C₂×#120	1	1	yes	characteristic
220	C₄×C₁₀₁	C₂×#123	1	1	yes	characteristic
221	C₄×C₁₀₁	C₂×#123	1	1	yes	characteristic
222	C₄×C₁₀₁	C₂×#124	1	1	yes	characteristic
223	#23541	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂×C₁₀₁	—	2	4	no	—
225	C₂×C₁₀₁	—	8	4	no	—
226	C₂×C₁₀₁	C₂×#394	1	1	yes	characteristic
227	C₂×C₁₀₁	#3042	1	2	yes	—
228	C₂×C₁₀₁	#3043	1	2	yes	—
229	C₂×C₁₀₁	#3057	1	2	yes	—
230	C₂³×SD₁₆	C₂×C₁₀₁	1	1	yes	characteristic
231	C₂×#424	C₂×C₁₀₁	1	1	yes	characteristic, complemented
232	C₂×#419	C₂×C₁₀₁	1	1	yes	characteristic, complemented
233	C₂×#418	C₂×C₁₀₁	1	1	yes	characteristic
234	#2310	C₂×C₁₀₁	1	1	yes	characteristic, complemented
235	#2309	C₂×C₁₀₁	1	1	yes	characteristic
236	#2055	C₂×C₁₀₁	1	8	yes	complemented
237	#1735	C₂×C₁₀₁	1	1	yes	characteristic, complemented
238	C₁₀₁	#23541	1	1	yes	characteristic, direct product factor, Sylow
239	C₂³×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
240	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
241	C₂²×SD₁₆	—	2	4	no	—
242	C₂²×SD₁₆	—	2	4	no	—
243	C₂²×SD₁₆	—	2	4	no	—
244	C₂²×SD₁₆	C₂²×C₁₀₁	1	4	yes	—
245	C₂²×M₁₆	C₂²×C₁₀₁	1	1	yes	characteristic
246	C₂³×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
247	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
248	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
249	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
250	#424	—	2	4	no	—
251	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	4	yes	complemented
252	#419	—	2	4	no	—
253	#418	—	2	4	no	—
254	C₂×#103	C₂²×C₁₀₁	1	4	yes	complemented
255	C₂×#102	C₂²×C₁₀₁	1	4	yes	—
256	#391	—	2	2	no	—
257	#391	C₂²×C₁₀₁	1	4	yes	complemented
258	#390	—	2	2	no	—
259	#390	C₂²×C₁₀₁	1	4	yes	—
260	#381	—	2	2	no	—
261	#379	—	2	2	no	—
262	#340	C₂²×C₁₀₁	1	4	yes	complemented
263	C₂⁵	—	2	1	no	—
264	C₂²×Q₈	—	2	1	no	—
265	C₂²×Q₈	—	2	2	no	—
266	C₂²×Q₈	—	2	2	no	—
267	C₂²×Q₈	—	2	2	no	—
268	C₂²×Q₈	—	2	2	no	—
269	C₂²×Q₈	—	2	2	no	—
270	C₂²×Q₈	D₄×C₁₀₁	1	4	yes	—
271	C₂²×Q₈	C₂³×C₁₀₁	1	2	yes	—
272	C₂²×D₄	—	2	2	no	—
273	C₂²×D₄	—	2	2	no	—
274	C₂²×D₄	—	2	1	no	—
275	C₂²×D₄	—	2	2	no	—
276	C₂²×D₄	—	2	2	no	—
277	C₂²×D₄	—	2	2	no	—
278	C₂²×D₄	D₄×C₁₀₁	1	4	yes	—
279	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
280	C₂³×C₄	—	2	1	no	—
281	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
282	C₂×SD₁₆	—	2	32	no	—
283	C₂×SD₁₆	—	2	8	no	—
284	C₂×SD₁₆	—	2	8	no	—
285	C₂×SD₁₆	—	2	8	no	—
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	—	2	2	no	—
288	C₂×M₁₆	—	2	2	no	—
289	C₂²×C₈	—	2	2	no	—
290	C₂²×C₈	—	2	2	no	—
291	C₂²×C₈	D₄×C₁₀₁	1	4	yes	—
292	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
293	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
294	#117	—	2	2	no	—
295	#117	—	2	2	no	—
296	#117	—	2	2	no	—
297	#117	—	2	2	no	—
298	#117	—	2	2	no	—
299	#117	—	2	2	no	—
300	C₂×C₄⋊C₄	D₄×C₁₀₁	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	2	8	no	—
306	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	2	yes	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
310	C₄⋊C₈	—	2	8	no	—
311	#103	—	2	8	no	—
312	#102	—	2	8	no	—
313	#95	—	2	8	no	—
314	C₂⁴	—	2	2	no	—
315	C₂⁴	—	2	4	no	—
316	C₂⁴	—	4	2	no	—
317	C₂⁴	—	4	2	no	—
318	C₂⁴	—	8	4	no	—
319	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
320	C₂×Q₈	—	2	4	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	8	no	—
323	C₂×Q₈	—	2	8	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	—	4	4	no	—
331	C₂×Q₈	—	4	4	no	—
332	C₂×Q₈	C₂×D₄×C₁₀₁	1	4	yes	—
333	C₂×D₄	—	2	8	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	8	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	4	4	no	—
344	C₂×D₄	—	4	4	no	—
345	C₂×D₄	C₂×D₄×C₁₀₁	1	4	yes	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
353	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
357	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
358	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
359	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
360	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
361	SD₁₆	—	2	32	no	—
362	M₁₆	—	4	4	no	—
363	C₂×C₈	—	2	8	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	C₂×D₄×C₁₀₁	1	4	yes	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	4	2	no	—
377	C₂²⋊C₄	—	4	2	no	—
378	C₂²⋊C₄	—	8	8	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	4	2	no	—
382	C₄²	—	4	2	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	2	4	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	8	no	—
388	C₂³	—	4	8	no	—
389	C₂³	—	8	8	no	—
390	C₂³	—	8	8	no	—
391	C₂³	—	8	8	no	—
392	C₂³	#121×C₁₀₁	1	2	yes	—
393	C₂³	#121×C₁₀₁	1	2	yes	—
394	C₂³	#121×C₁₀₁	1	2	yes	—
395	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
396	Q₈	—	2	4	no	—
397	Q₈	—	2	4	no	—
398	Q₈	—	4	2	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	8	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	4	no	—
403	D₄	—	4	2	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	8	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	8	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	8	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	#120×C₁₀₁	1	4	yes	—
417	C₂×C₄	#121×C₁₀₁	1	2	yes	—
418	C₂×C₄	#121×C₁₀₁	1	2	yes	—
419	C₂×C₄	#121×C₁₀₁	1	2	yes	—
420	C₂×C₄	#123×C₁₀₁	1	4	yes	—
421	C₂×C₄	#123×C₁₀₁	1	4	yes	—
422	C₂×C₄	#124×C₁₀₁	1	4	yes	—
423	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
425	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
426	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
427	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
428	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
429	C₈	—	2	4	no	—
430	C₈	—	4	2	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	4	8	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	8	16	no	—
437	C₂²	—	8	4	no	—
438	C₂²	—	8	4	no	—
439	C₂²	#394×C₁₀₁	1	4	yes	—
440	C₂²	C₂×#121×C₁₀₁	1	1	yes	characteristic
441	C₂²	C₂×#121×C₁₀₁	1	1	yes	characteristic
442	C₂²	C₂×#121×C₁₀₁	1	1	yes	characteristic
443	C₂²	#577×C₁₀₁	1	4	yes	—
444	C₄	—	4	4	no	—
445	C₄	—	4	4	no	—
446	C₄	—	8	2	no	—
447	C₄	—	8	2	no	—
448	C₄	#394×C₁₀₁	1	4	yes	—
449	C₄	C₂×#120×C₁₀₁	1	1	yes	characteristic
450	C₄	C₂×#123×C₁₀₁	1	1	yes	characteristic
451	C₄	C₂×#123×C₁₀₁	1	1	yes	characteristic
452	C₄	C₂×#124×C₁₀₁	1	1	yes	characteristic
453	C₂	—	2	4	no	—
454	C₂	—	8	4	no	—
455	C₂	C₂×#394×C₁₀₁	1	1	yes	characteristic
456	C₂	C₁₀₁×#3042	1	2	yes	—
457	C₂	C₁₀₁×#3043	1	2	yes	—
458	C₂	C₁₀₁×#3057	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂³×D₄×C₁₀₁	C₂²
LCS	G ▷ C₂²×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×#424×C₁₀₁	C₂	semidirect
3. C₂×#419×C₁₀₁	C₂	semidirect
5. C₁₀₁×#2310	C₂	semidirect
7. C₁₀₁×#2055	C₂	semidirect
8. C₁₀₁×#1735	C₂	semidirect
21. C₂×C₄⋊C₈×C₁₀₁	C₂²	semidirect
24. C₂×#103×C₁₀₁	C₂²	semidirect
27. #391×C₁₀₁	C₂²	semidirect
32. #340×C₁₀₁	C₂²	semidirect
223. #23541	C₁₀₁	direct (N × H)
231. C₂×#424	C₂×C₁₀₁	semidirect
232. C₂×#419	C₂×C₁₀₁	semidirect
234. #2310	C₂×C₁₀₁	semidirect
236. #2055	C₂×C₁₀₁	semidirect
237. #1735	C₂×C₁₀₁	semidirect
238. C₁₀₁	#23541	direct (N × H)
251. C₂×C₄⋊C₈	C₂²×C₁₀₁	semidirect
254. C₂×#103	C₂²×C₁₀₁	semidirect
257. #391	C₂²×C₁₀₁	semidirect
262. #340	C₂²×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×#424×C₁₀₁	2
C₂×#419×C₁₀₁	2
C₂×#418×C₁₀₁	2
C₁₀₁×#2310	2
C₁₀₁×#2309	2
C₁₀₁×#2055	2
C₁₀₁×#1735	2
#23541	101

Subgroups — C101×#23541 #38805692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#23541 #38805692