Subgroups — C₁₀₁×#23132 #38805283

Order 25856.

1066 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#466×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#2361	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#1936	C₂	1	2	yes	maximal, complemented
4	C₁₀₁×#1921	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1879	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1874	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1762	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#1752	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#340×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
12	C₂×#121×C₁₀₁	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₁₀₁	—	2	2	no	—
14	C₂×C₄×D₄×C₁₀₁	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
16	#466×C₁₀₁	C₄	1	8	yes	complemented
17	C₂×#107×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
19	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
20	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
21	C₂×C₂²⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
22	C₂×#97×C₁₀₁	C₂²	1	2	yes	—
23	#390×C₁₀₁	C₂²	1	2	yes	—
24	#389×C₁₀₁	C₂²	1	2	yes	—
25	#388×C₁₀₁	—	2	2	no	—
26	#386×C₁₀₁	—	2	2	no	—
27	#385×C₁₀₁	—	2	2	no	—
28	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
29	C₄×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
30	#340×C₁₀₁	C₂²	1	2	yes	—
31	#340×C₁₀₁	C₂²	1	2	yes	—
32	#340×C₁₀₁	C₂²	1	2	yes	—
33	#340×C₁₀₁	C₂²	1	1	yes	characteristic
34	#340×C₁₀₁	C₂²	1	1	yes	characteristic
35	#336×C₁₀₁	C₂²	1	2	yes	—
36	C₂²×D₄×C₁₀₁	—	2	2	no	—
37	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₀₁	—	2	2	no	—
39	C₂³×C₄×C₁₀₁	—	2	2	no	—
40	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
41	C₂×D₈×C₁₀₁	—	4	2	no	—
42	C₂×D₈×C₁₀₁	C₂×C₄	1	4	yes	complemented
43	C₂²×C₈×C₁₀₁	—	4	2	no	—
44	C₂²×C₈×C₁₀₁	C₂×C₄	1	4	yes	complemented
45	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
48	#121×C₁₀₁	—	2	4	no	—
49	#121×C₁₀₁	C₂×C₄	1	8	yes	complemented
50	C₄×D₄×C₁₀₁	—	2	4	no	—
51	C₄×D₄×C₁₀₁	—	4	2	no	—
52	C₄×D₄×C₁₀₁	—	4	8	no	—
53	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₀₁	—	4	2	no	—
57	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	2	yes	—
65	C₂×C₄²×C₁₀₁	—	2	2	no	—
66	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
67	#107×C₁₀₁	C₂×C₄	1	4	yes	complemented
68	#102×C₁₀₁	—	2	4	no	—
69	#102×C₁₀₁	—	4	2	no	—
70	#102×C₁₀₁	C₂×C₄	1	8	yes	complemented
71	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
72	#97×C₁₀₁	—	4	2	no	—
73	#95×C₁₀₁	—	2	2	no	—
74	#95×C₁₀₁	—	2	2	no	—
75	#95×C₁₀₁	D₄	1	1	yes	characteristic
76	#95×C₁₀₁	D₄	1	1	yes	characteristic
77	C₂⁴×C₁₀₁	—	2	2	no	—
78	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
79	C₂×D₄×C₁₀₁	—	2	8	no	—
80	C₂×D₄×C₁₀₁	—	2	2	no	—
81	C₂×D₄×C₁₀₁	—	2	2	no	—
82	C₂×D₄×C₁₀₁	—	2	2	no	—
83	C₂×D₄×C₁₀₁	—	2	2	no	—
84	C₂×D₄×C₁₀₁	—	2	2	no	—
85	C₂×D₄×C₁₀₁	—	4	4	no	—
86	C₂×D₄×C₁₀₁	—	4	4	no	—
87	C₂×D₄×C₁₀₁	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₁₀₁	—	2	2	no	—
89	C₂²×C₄×C₁₀₁	—	2	2	no	—
90	C₂²×C₄×C₁₀₁	—	2	2	no	—
91	C₂²×C₄×C₁₀₁	—	2	2	no	—
92	C₂²×C₄×C₁₀₁	—	2	2	no	—
93	C₂²×C₄×C₁₀₁	—	4	4	no	—
94	C₂²×C₄×C₁₀₁	—	4	4	no	—
95	C₂²×C₄×C₁₀₁	—	4	4	no	—
96	C₂²×C₄×C₁₀₁	—	4	4	no	—
97	C₂²×C₄×C₁₀₁	—	8	2	no	—
98	C₂²×C₄×C₁₀₁	—	8	2	no	—
99	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
104	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
105	D₈×C₁₀₁	—	4	4	no	—
106	C₂×C₈×C₁₀₁	—	2	2	no	—
107	C₂×C₈×C₁₀₁	—	2	2	no	—
108	C₂×C₈×C₁₀₁	—	2	2	no	—
109	C₂×C₈×C₁₀₁	—	2	2	no	—
110	C₂×C₈×C₁₀₁	—	2	2	no	—
111	C₂×C₈×C₁₀₁	—	4	4	no	—
112	C₂×C₈×C₁₀₁	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₁₀₁	C₂²×C₄	1	2	yes	—
114	C₄⋊C₄×C₁₀₁	—	2	2	no	—
115	C₄⋊C₄×C₁₀₁	—	2	2	no	—
116	C₄⋊C₄×C₁₀₁	—	2	2	no	—
117	C₄⋊C₄×C₁₀₁	—	2	2	no	—
118	C₄⋊C₄×C₁₀₁	—	4	4	no	—
119	C₄⋊C₄×C₁₀₁	—	4	4	no	—
120	C₄⋊C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
121	C₄⋊C₄×C₁₀₁	#41	1	4	yes	—
122	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
123	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
124	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
125	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
126	C₂²⋊C₄×C₁₀₁	—	8	2	no	—
127	C₄²×C₁₀₁	—	2	2	no	—
128	C₄²×C₁₀₁	—	2	2	no	—
129	C₄²×C₁₀₁	—	4	4	no	—
130	C₂³×C₁₀₁	—	2	2	no	—
131	C₂³×C₁₀₁	—	2	1	no	—
132	C₂³×C₁₀₁	—	2	1	no	—
133	C₂³×C₁₀₁	—	2	4	no	—
134	C₂³×C₁₀₁	—	4	2	no	—
135	C₂³×C₁₀₁	—	4	2	no	—
136	C₂³×C₁₀₁	—	4	2	no	—
137	C₂³×C₁₀₁	—	4	2	no	—
138	C₂³×C₁₀₁	—	4	2	no	—
139	C₂³×C₁₀₁	—	4	2	no	—
140	C₂³×C₁₀₁	C₄×D₄	1	2	yes	—
141	C₂³×C₁₀₁	AGL(1,ℤ/8)	1	4	yes	—
142	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
143	D₄×C₁₀₁	—	2	4	no	—
144	D₄×C₁₀₁	—	2	4	no	—
145	D₄×C₁₀₁	—	4	16	no	—
146	D₄×C₁₀₁	—	4	2	no	—
147	D₄×C₁₀₁	—	4	2	no	—
148	C₂×C₄×C₁₀₁	—	2	2	no	—
149	C₂×C₄×C₁₀₁	—	2	2	no	—
150	C₂×C₄×C₁₀₁	—	2	2	no	—
151	C₂×C₄×C₁₀₁	—	2	4	no	—
152	C₂×C₄×C₁₀₁	—	2	4	no	—
153	C₂×C₄×C₁₀₁	—	2	2	no	—
154	C₂×C₄×C₁₀₁	—	2	2	no	—
155	C₂×C₄×C₁₀₁	—	2	4	no	—
156	C₂×C₄×C₁₀₁	—	2	2	no	—
157	C₂×C₄×C₁₀₁	—	2	2	no	—
158	C₂×C₄×C₁₀₁	—	2	2	no	—
159	C₂×C₄×C₁₀₁	—	2	2	no	—
160	C₂×C₄×C₁₀₁	—	4	2	no	—
161	C₂×C₄×C₁₀₁	—	4	2	no	—
162	C₂×C₄×C₁₀₁	—	4	2	no	—
163	C₂×C₄×C₁₀₁	—	4	2	no	—
164	C₂×C₄×C₁₀₁	—	4	2	no	—
165	C₂×C₄×C₁₀₁	—	4	2	no	—
166	C₂×C₄×C₁₀₁	—	4	2	no	—
167	C₂×C₄×C₁₀₁	—	8	8	no	—
168	C₂×C₄×C₁₀₁	—	8	8	no	—
169	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
172	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
174	C₈×C₁₀₁	—	2	2	no	—
175	C₈×C₁₀₁	—	2	2	no	—
176	C₈×C₁₀₁	—	4	2	no	—
177	C₂²×C₁₀₁	—	2	2	no	—
178	C₂²×C₁₀₁	—	2	2	no	—
179	C₂²×C₁₀₁	—	2	4	no	—
180	C₂²×C₁₀₁	—	2	4	no	—
181	C₂²×C₁₀₁	—	4	4	no	—
182	C₂²×C₁₀₁	—	4	4	no	—
183	C₂²×C₁₀₁	—	4	4	no	—
184	C₂²×C₁₀₁	—	8	2	no	—
185	C₂²×C₁₀₁	—	8	2	no	—
186	C₂²×C₁₀₁	—	8	2	no	—
187	C₂²×C₁₀₁	—	8	2	no	—
188	C₂²×C₁₀₁	#442	1	4	yes	—
189	C₂²×C₁₀₁	C₂×C₄×D₄	1	1	yes	characteristic
190	C₂²×C₁₀₁	#546	1	2	yes	—
191	C₂²×C₁₀₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
192	C₂²×C₁₀₁	#576	1	1	yes	characteristic
193	C₂²×C₁₀₁	#578	1	1	yes	characteristic
194	C₄×C₁₀₁	—	2	2	no	—
195	C₄×C₁₀₁	—	4	4	no	—
196	C₄×C₁₀₁	—	4	2	no	—
197	C₄×C₁₀₁	—	4	2	no	—
198	C₄×C₁₀₁	—	4	4	no	—
199	C₄×C₁₀₁	—	8	2	no	—
200	C₄×C₁₀₁	C₄×#41	1	1	yes	characteristic
201	C₄×C₁₀₁	#518	1	1	yes	characteristic
202	C₄×C₁₀₁	#553	1	2	yes	—
203	#23132	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂×C₁₀₁	—	2	4	no	—
205	C₂×C₁₀₁	—	8	4	no	—
206	C₂×C₁₀₁	#2364	1	1	yes	characteristic
207	C₂×C₁₀₁	C₂×#442	1	1	yes	characteristic
208	C₂×C₁₀₁	#2951	1	1	yes	characteristic
209	C₂×C₁₀₁	#3308	1	2	yes	—
210	C₂×C₁₀₁	#3318	1	2	yes	—
211	C₂×#466	C₂×C₁₀₁	1	1	yes	characteristic
212	#2361	C₂×C₁₀₁	1	2	yes	complemented
213	#1936	C₂×C₁₀₁	1	2	yes	complemented
214	#1921	C₂×C₁₀₁	1	2	yes	complemented
215	#1879	C₂×C₁₀₁	1	2	yes	complemented
216	#1874	C₂×C₁₀₁	1	2	yes	complemented
217	#1762	C₂×C₁₀₁	1	2	yes	complemented
218	#1752	C₂×C₁₀₁	1	1	yes	characteristic, complemented
219	C₂×#340	C₂×C₁₀₁	1	1	yes	characteristic, complemented
220	C₁₀₁	#23132	1	1	yes	characteristic, direct product factor, Sylow
221	C₂²×D₈	C₂²×C₁₀₁	1	1	yes	characteristic
222	C₂³×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
223	C₂×#121	C₂²×C₁₀₁	1	2	yes	—
224	C₂×C₄×D₄	—	2	2	no	—
225	C₂×C₄×D₄	C₂²×C₁₀₁	1	2	yes	—
226	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
227	#466	C₄×C₁₀₁	1	8	yes	complemented
228	C₂×#107	C₂²×C₁₀₁	1	1	yes	characteristic
229	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
230	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
231	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
232	C₂×C₂²⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
233	C₂×#97	C₂²×C₁₀₁	1	2	yes	—
234	#390	C₂²×C₁₀₁	1	2	yes	—
235	#389	C₂²×C₁₀₁	1	2	yes	—
236	#388	—	2	2	no	—
237	#386	—	2	2	no	—
238	#385	—	2	2	no	—
239	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
240	C₄×C₂²⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
241	#340	C₂²×C₁₀₁	1	2	yes	—
242	#340	C₂²×C₁₀₁	1	2	yes	—
243	#340	C₂²×C₁₀₁	1	2	yes	—
244	#340	C₂²×C₁₀₁	1	1	yes	characteristic
245	#340	C₂²×C₁₀₁	1	1	yes	characteristic
246	#336	C₂²×C₁₀₁	1	2	yes	—
247	C₂²×D₄	—	2	2	no	—
248	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
249	C₂³×C₄	—	2	2	no	—
250	C₂³×C₄	—	2	2	no	—
251	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
252	C₂×D₈	—	4	2	no	—
253	C₂×D₈	C₂×C₄×C₁₀₁	1	4	yes	complemented
254	C₂²×C₈	—	4	2	no	—
255	C₂²×C₈	C₂×C₄×C₁₀₁	1	4	yes	complemented
256	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
257	C₂²×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
259	#121	—	2	4	no	—
260	#121	C₂×C₄×C₁₀₁	1	8	yes	complemented
261	C₄×D₄	—	2	4	no	—
262	C₄×D₄	—	4	2	no	—
263	C₄×D₄	—	4	8	no	—
264	C₂×C₄⋊C₄	—	2	4	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	4	2	no	—
268	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	2	yes	—
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
278	#107	C₂×C₄×C₁₀₁	1	4	yes	complemented
279	#102	—	2	4	no	—
280	#102	—	4	2	no	—
281	#102	C₂×C₄×C₁₀₁	1	8	yes	complemented
282	C₂²⋊C₈	—	2	2	no	—
283	#97	—	4	2	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	D₄×C₁₀₁	1	1	yes	characteristic
287	#95	D₄×C₁₀₁	1	1	yes	characteristic
288	C₂⁴	—	2	2	no	—
289	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
290	C₂×D₄	—	2	8	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	4	4	no	—
297	C₂×D₄	—	4	4	no	—
298	C₂×D₄	C₂²×C₄×C₁₀₁	1	4	yes	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	4	4	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	4	4	no	—
308	C₂²×C₄	—	8	2	no	—
309	C₂²×C₄	—	8	2	no	—
310	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
314	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
315	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
316	D₈	—	4	4	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	4	4	no	—
323	C₂×C₈	C₂²×C₄×C₁₀₁	1	2	yes	—
324	C₂×C₈	C₂²×C₄×C₁₀₁	1	2	yes	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₄⋊C₄	—	4	4	no	—
331	C₄⋊C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
332	C₄⋊C₄	#41×C₁₀₁	1	4	yes	—
333	C₂²⋊C₄	—	2	4	no	—
334	C₂²⋊C₄	—	2	8	no	—
335	C₂²⋊C₄	—	4	4	no	—
336	C₂²⋊C₄	—	4	4	no	—
337	C₂²⋊C₄	—	8	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	4	4	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	C₄×D₄×C₁₀₁	1	2	yes	—
352	C₂³	AGL(1,ℤ/8)×C₁₀₁	1	4	yes	—
353	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
354	D₄	—	2	4	no	—
355	D₄	—	2	4	no	—
356	D₄	—	4	16	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	8	8	no	—
379	C₂×C₄	—	8	8	no	—
380	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
381	C₂×C₄	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
382	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
383	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
384	C₂×C₄	H(5,𝔽₂)×C₁₀₁	1	2	yes	—
385	C₈	—	2	2	no	—
386	C₈	—	2	2	no	—
387	C₈	—	4	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	4	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	#442×C₁₀₁	1	4	yes	—
400	C₂²	C₂×C₄×D₄×C₁₀₁	1	1	yes	characteristic
401	C₂²	#546×C₁₀₁	1	2	yes	—
402	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
403	C₂²	#576×C₁₀₁	1	1	yes	characteristic
404	C₂²	#578×C₁₀₁	1	1	yes	characteristic
405	C₄	—	2	2	no	—
406	C₄	—	4	4	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	4	no	—
410	C₄	—	8	2	no	—
411	C₄	C₄×#41×C₁₀₁	1	1	yes	characteristic
412	C₄	#518×C₁₀₁	1	1	yes	characteristic
413	C₄	#553×C₁₀₁	1	2	yes	—
414	C₂	—	2	4	no	—
415	C₂	—	8	4	no	—
416	C₂	C₁₀₁×#2364	1	1	yes	characteristic
417	C₂	C₂×#442×C₁₀₁	1	1	yes	characteristic
418	C₂	C₁₀₁×#2951	1	1	yes	characteristic
419	C₂	C₁₀₁×#3308	1	2	yes	—
420	C₂	C₁₀₁×#3318	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂×#466×C₁₀₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₄×C₂²⋊C₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₁×#2361	C₂	semidirect
3. C₁₀₁×#1936	C₂	semidirect
4. C₁₀₁×#1921	C₂	semidirect
5. C₁₀₁×#1879	C₂	semidirect
6. C₁₀₁×#1874	C₂	semidirect
7. C₁₀₁×#1762	C₂	semidirect
8. C₁₀₁×#1752	C₂	semidirect
9. C₂×#340×C₁₀₁	C₂	semidirect
16. #466×C₁₀₁	C₄	semidirect
42. C₂×D₈×C₁₀₁	C₂×C₄	semidirect
44. C₂²×C₈×C₁₀₁	C₂×C₄	semidirect
49. #121×C₁₀₁	C₂×C₄	semidirect
67. #107×C₁₀₁	C₂×C₄	semidirect
70. #102×C₁₀₁	C₂×C₄	semidirect
203. #23132	C₁₀₁	direct (N × H)
212. #2361	C₂×C₁₀₁	semidirect
213. #1936	C₂×C₁₀₁	semidirect
214. #1921	C₂×C₁₀₁	semidirect
215. #1879	C₂×C₁₀₁	semidirect
216. #1874	C₂×C₁₀₁	semidirect
217. #1762	C₂×C₁₀₁	semidirect
218. #1752	C₂×C₁₀₁	semidirect
219. C₂×#340	C₂×C₁₀₁	semidirect
220. C₁₀₁	#23132	direct (N × H)
227. #466	C₄×C₁₀₁	semidirect
253. C₂×D₈	C₂×C₄×C₁₀₁	semidirect
255. C₂²×C₈	C₂×C₄×C₁₀₁	semidirect
260. #121	C₂×C₄×C₁₀₁	semidirect
278. #107	C₂×C₄×C₁₀₁	semidirect
281. #102	C₂×C₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#466×C₁₀₁	2
C₁₀₁×#2361	2
C₁₀₁×#1936	2
C₁₀₁×#1921	2
C₁₀₁×#1879	2
C₁₀₁×#1874	2
C₁₀₁×#1762	2
C₁₀₁×#1752	2
C₂×#340×C₁₀₁	2
#23132	101

Subgroups — C101×#23132 #38805283

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#23132 #38805283