Subgroups — C₁₀₁×#10731 #38792882

Order 25856.

1518 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#117×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#380×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#340×C₁₀₁	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
6	C₂³×C₈×C₁₀₁	C₂²	1	2	yes	—
7	C₂×#117×C₁₀₁	—	2	2	no	—
8	C₂×#117×C₁₀₁	—	2	8	no	—
9	C₂×#117×C₁₀₁	C₄	1	4	yes	complemented
10	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
12	C₂²×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
13	C₂²×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
14	C₂²×C₄²×C₁₀₁	—	2	1	no	—
15	C₂×C₂²⋊C₈×C₁₀₁	—	2	2	no	—
16	C₂×C₂²⋊C₈×C₁₀₁	—	2	2	no	—
17	C₂×C₂²⋊C₈×C₁₀₁	C₄	1	4	yes	complemented
18	#380×C₁₀₁	—	2	2	no	—
19	#380×C₁₀₁	C₄	1	4	yes	complemented
20	C₂×#95×C₁₀₁	—	2	1	no	—
21	#340×C₁₀₁	—	2	8	no	—
22	C₂⁵×C₁₀₁	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₀₁	—	2	4	no	—
24	C₂³×C₄×C₁₀₁	—	2	4	no	—
25	C₂³×C₄×C₁₀₁	—	2	2	no	—
26	C₂³×C₄×C₁₀₁	—	2	2	no	—
27	C₂³×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
28	C₂³×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
30	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
32	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
33	C₂³×C₄×C₁₀₁	Q₈	1	2	yes	—
34	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
35	C₂²×C₈×C₁₀₁	—	2	2	no	—
36	C₂²×C₈×C₁₀₁	—	2	2	no	—
37	C₂²×C₈×C₁₀₁	—	2	4	no	—
38	C₂²×C₈×C₁₀₁	—	2	4	no	—
39	C₂²×C₈×C₁₀₁	C₂×C₄	1	4	yes	—
40	#117×C₁₀₁	—	2	16	no	—
41	#117×C₁₀₁	—	2	16	no	—
42	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
43	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
46	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
48	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
49	C₂×C₄⋊C₄×C₁₀₁	D₄	1	8	yes	—
50	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
51	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
52	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
53	C₂×C₂²⋊C₄×C₁₀₁	—	4	4	no	—
54	C₂×C₄²×C₁₀₁	—	2	8	no	—
55	C₂×C₄²×C₁₀₁	—	2	4	no	—
56	C₂²⋊C₈×C₁₀₁	—	2	8	no	—
57	#95×C₁₀₁	—	2	4	no	—
58	C₂⁴×C₁₀₁	—	2	2	no	—
59	C₂⁴×C₁₀₁	—	2	2	no	—
60	C₂⁴×C₁₀₁	—	2	4	no	—
61	C₂⁴×C₁₀₁	—	2	2	no	—
62	C₂⁴×C₁₀₁	—	2	2	no	—
63	C₂⁴×C₁₀₁	C₂²⋊C₄	1	2	yes	—
64	C₂⁴×C₁₀₁	C₂²⋊C₄	1	2	yes	—
65	C₂⁴×C₁₀₁	C₄⋊C₄	1	2	yes	—
66	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₀₁	—	2	2	no	—
68	C₂²×C₄×C₁₀₁	—	2	2	no	—
69	C₂²×C₄×C₁₀₁	—	2	4	no	—
70	C₂²×C₄×C₁₀₁	—	2	4	no	—
71	C₂²×C₄×C₁₀₁	—	2	8	no	—
72	C₂²×C₄×C₁₀₁	—	2	8	no	—
73	C₂²×C₄×C₁₀₁	—	2	4	no	—
74	C₂²×C₄×C₁₀₁	—	2	8	no	—
75	C₂²×C₄×C₁₀₁	—	2	8	no	—
76	C₂²×C₄×C₁₀₁	—	2	4	no	—
77	C₂²×C₄×C₁₀₁	—	2	4	no	—
78	C₂²×C₄×C₁₀₁	—	2	8	no	—
79	C₂²×C₄×C₁₀₁	—	2	4	no	—
80	C₂²×C₄×C₁₀₁	—	4	4	no	—
81	C₂²×C₄×C₁₀₁	—	4	2	no	—
82	C₂²×C₄×C₁₀₁	—	4	2	no	—
83	C₂²×C₄×C₁₀₁	—	4	2	no	—
84	C₂²×C₄×C₁₀₁	—	4	2	no	—
85	C₂²×C₄×C₁₀₁	—	4	4	no	—
86	C₂²×C₄×C₁₀₁	—	4	4	no	—
87	C₂²×C₄×C₁₀₁	C₄²	1	4	yes	—
88	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
89	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	4	yes	—
91	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	2	yes	—
92	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	4	yes	—
93	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	4	yes	—
94	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₁₀₁	#41	1	4	yes	—
102	C₂×C₈×C₁₀₁	—	2	4	no	—
103	C₂×C₈×C₁₀₁	—	2	8	no	—
104	C₂×C₈×C₁₀₁	—	4	2	no	—
105	C₂×C₈×C₁₀₁	—	4	4	no	—
106	C₂×C₈×C₁₀₁	—	4	2	no	—
107	C₄⋊C₄×C₁₀₁	—	2	4	no	—
108	C₄⋊C₄×C₁₀₁	—	2	8	no	—
109	C₄⋊C₄×C₁₀₁	—	2	8	no	—
110	C₄⋊C₄×C₁₀₁	—	4	4	no	—
111	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	8	yes	complemented
112	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
113	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
114	C₄²×C₁₀₁	—	2	16	no	—
115	C₂³×C₁₀₁	—	2	2	no	—
116	C₂³×C₁₀₁	—	2	2	no	—
117	C₂³×C₁₀₁	—	2	4	no	—
118	C₂³×C₁₀₁	—	2	4	no	—
119	C₂³×C₁₀₁	—	2	4	no	—
120	C₂³×C₁₀₁	—	2	4	no	—
121	C₂³×C₁₀₁	—	2	4	no	—
122	C₂³×C₁₀₁	—	2	2	no	—
123	C₂³×C₁₀₁	—	2	2	no	—
124	C₂³×C₁₀₁	—	2	4	no	—
125	C₂³×C₁₀₁	—	2	4	no	—
126	C₂³×C₁₀₁	—	4	4	no	—
127	C₂³×C₁₀₁	—	4	4	no	—
128	C₂³×C₁₀₁	—	4	4	no	—
129	C₂³×C₁₀₁	—	4	4	no	—
130	C₂³×C₁₀₁	#95	1	4	yes	—
131	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂³×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂³×C₁₀₁	#120	1	2	yes	—
135	C₂³×C₁₀₁	#123	1	2	yes	—
136	C₂³×C₁₀₁	#135	1	4	yes	—
137	C₂³×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
138	C₂³×C₁₀₁	#137	1	2	yes	—
139	C₂×C₄×C₁₀₁	—	2	2	no	—
140	C₂×C₄×C₁₀₁	—	2	2	no	—
141	C₂×C₄×C₁₀₁	—	2	4	no	—
142	C₂×C₄×C₁₀₁	—	2	4	no	—
143	C₂×C₄×C₁₀₁	—	2	8	no	—
144	C₂×C₄×C₁₀₁	—	2	8	no	—
145	C₂×C₄×C₁₀₁	—	2	8	no	—
146	C₂×C₄×C₁₀₁	—	2	8	no	—
147	C₂×C₄×C₁₀₁	—	2	8	no	—
148	C₂×C₄×C₁₀₁	—	4	4	no	—
149	C₂×C₄×C₁₀₁	—	4	4	no	—
150	C₂×C₄×C₁₀₁	—	4	8	no	—
151	C₂×C₄×C₁₀₁	—	4	8	no	—
152	C₂×C₄×C₁₀₁	—	4	4	no	—
153	C₂×C₄×C₁₀₁	—	4	4	no	—
154	C₂×C₄×C₁₀₁	—	4	4	no	—
155	C₂×C₄×C₁₀₁	—	8	4	no	—
156	C₂×C₄×C₁₀₁	—	8	4	no	—
157	C₂×C₄×C₁₀₁	#95	1	4	yes	—
158	C₂×C₄×C₁₀₁	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₀₁	#117	1	2	yes	—
164	C₂×C₄×C₁₀₁	C₄×D₄	1	4	yes	—
165	C₂×C₄×C₁₀₁	C₄×D₄	1	4	yes	—
166	C₂×C₄×C₁₀₁	#120	1	2	yes	—
167	C₂×C₄×C₁₀₁	#121	1	4	yes	—
168	C₂×C₄×C₁₀₁	C₂²⋊Q₈	1	4	yes	—
169	C₂×C₄×C₁₀₁	#123	1	2	yes	—
170	C₈×C₁₀₁	—	4	4	no	—
171	C₂²×C₁₀₁	—	2	4	no	—
172	C₂²×C₁₀₁	—	2	4	no	—
173	C₂²×C₁₀₁	—	2	4	no	—
174	C₂²×C₁₀₁	—	4	4	no	—
175	C₂²×C₁₀₁	—	4	8	no	—
176	C₂²×C₁₀₁	—	4	4	no	—
177	C₂²×C₁₀₁	—	4	4	no	—
178	C₂²×C₁₀₁	—	4	4	no	—
179	C₂²×C₁₀₁	C₂×#95	1	1	yes	characteristic
180	C₂²×C₁₀₁	#379	1	1	yes	characteristic
181	C₂²×C₁₀₁	#381	1	1	yes	characteristic
182	C₂²×C₁₀₁	#385	1	2	yes	—
183	C₂²×C₁₀₁	#386	1	2	yes	—
184	C₂²×C₁₀₁	#416	1	2	yes	—
185	C₂²×C₁₀₁	#416	1	2	yes	—
186	C₂²×C₁₀₁	#417	1	2	yes	—
187	C₂²×C₁₀₁	#418	1	1	yes	characteristic
188	C₂²×C₁₀₁	#419	1	1	yes	characteristic
189	C₂²×C₁₀₁	#427	1	2	yes	—
190	C₂²×C₁₀₁	#428	1	2	yes	—
191	C₂²×C₁₀₁	#449	1	4	yes	—
192	C₂²×C₁₀₁	#452	1	4	yes	—
193	C₂²×C₁₀₁	#482	1	4	yes	—
194	C₂²×C₁₀₁	#485	1	4	yes	—
195	C₄×C₁₀₁	—	2	4	no	—
196	C₄×C₁₀₁	—	4	8	no	—
197	C₄×C₁₀₁	—	8	4	no	—
198	C₄×C₁₀₁	C₄×C₂²⋊C₄	1	2	yes	—
199	C₄×C₁₀₁	#380	1	2	yes	—
200	C₄×C₁₀₁	#385	1	2	yes	—
201	C₄×C₁₀₁	#386	1	2	yes	—
202	#10731	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂×C₁₀₁	—	4	4	no	—
204	C₂×C₁₀₁	C₂²⋊#95	1	1	yes	characteristic
205	C₂×C₁₀₁	#1735	1	1	yes	characteristic
206	C₂×C₁₀₁	#1736	1	1	yes	characteristic
207	C₂×C₁₀₁	#1788	1	2	yes	—
208	C₂×C₁₀₁	#1825	1	2	yes	—
209	C₂×C₁₀₁	#1854	1	4	yes	—
210	C₂×C₁₀₁	#1873	1	2	yes	—
211	C₂×C₁₀₁	#1875	1	2	yes	—
212	C₂²×#117	C₂×C₁₀₁	1	1	yes	characteristic
213	C₂²×C₂²⋊C₈	C₂×C₁₀₁	1	1	yes	characteristic
214	C₂×#380	C₂×C₁₀₁	1	1	yes	characteristic
215	C₂×#340	C₂×C₁₀₁	1	4	yes	complemented
216	C₁₀₁	#10731	1	1	yes	characteristic, direct product factor, Sylow
217	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
218	C₂³×C₈	C₂²×C₁₀₁	1	2	yes	—
219	C₂×#117	—	2	2	no	—
220	C₂×#117	—	2	8	no	—
221	C₂×#117	C₄×C₁₀₁	1	4	yes	complemented
222	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
223	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	2	yes	—
224	C₂²×C₂²⋊C₄	—	2	1	no	—
225	C₂²×C₂²⋊C₄	—	2	1	no	—
226	C₂²×C₄²	—	2	1	no	—
227	C₂×C₂²⋊C₈	—	2	2	no	—
228	C₂×C₂²⋊C₈	—	2	2	no	—
229	C₂×C₂²⋊C₈	C₄×C₁₀₁	1	4	yes	complemented
230	#380	—	2	2	no	—
231	#380	C₄×C₁₀₁	1	4	yes	complemented
232	C₂×#95	—	2	1	no	—
233	#340	—	2	8	no	—
234	C₂⁵	D₄×C₁₀₁	1	1	yes	characteristic
235	C₂³×C₄	—	2	4	no	—
236	C₂³×C₄	—	2	4	no	—
237	C₂³×C₄	—	2	2	no	—
238	C₂³×C₄	—	2	2	no	—
239	C₂³×C₄	C₂×C₄×C₁₀₁	1	2	yes	—
240	C₂³×C₄	C₂×C₄×C₁₀₁	1	2	yes	—
241	C₂³×C₄	C₂×C₄×C₁₀₁	1	2	yes	—
242	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
243	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
244	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
245	C₂³×C₄	Q₈×C₁₀₁	1	2	yes	—
246	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
247	C₂²×C₈	—	2	4	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	—	2	4	no	—
251	C₂²×C₈	C₂×C₄×C₁₀₁	1	4	yes	—
252	#117	—	2	16	no	—
253	#117	—	2	16	no	—
254	C₂×C₄⋊C₄	—	2	4	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	4	no	—
257	C₂×C₄⋊C₄	—	2	4	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
260	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
261	C₂×C₄⋊C₄	D₄×C₁₀₁	1	8	yes	—
262	C₂×C₂²⋊C₄	—	2	8	no	—
263	C₂×C₂²⋊C₄	—	2	4	no	—
264	C₂×C₂²⋊C₄	—	2	4	no	—
265	C₂×C₂²⋊C₄	—	4	4	no	—
266	C₂×C₄²	—	2	8	no	—
267	C₂×C₄²	—	2	4	no	—
268	C₂²⋊C₈	—	2	8	no	—
269	#95	—	2	4	no	—
270	C₂⁴	—	2	2	no	—
271	C₂⁴	—	2	2	no	—
272	C₂⁴	—	2	4	no	—
273	C₂⁴	—	2	2	no	—
274	C₂⁴	—	2	2	no	—
275	C₂⁴	C₂²⋊C₄×C₁₀₁	1	2	yes	—
276	C₂⁴	C₂²⋊C₄×C₁₀₁	1	2	yes	—
277	C₂⁴	C₄⋊C₄×C₁₀₁	1	2	yes	—
278	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	8	no	—
284	C₂²×C₄	—	2	8	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	8	no	—
287	C₂²×C₄	—	2	8	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	4	4	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	4	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	C₄²×C₁₀₁	1	4	yes	—
300	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
301	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
302	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	4	yes	—
303	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	2	yes	—
304	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	4	yes	—
305	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	4	yes	—
306	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
308	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
312	C₂²×C₄	C₂×Q₈×C₁₀₁	1	1	yes	characteristic
313	C₂²×C₄	#41×C₁₀₁	1	4	yes	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	2	8	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	—	4	4	no	—
318	C₂×C₈	—	4	2	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	8	no	—
321	C₄⋊C₄	—	2	8	no	—
322	C₄⋊C₄	—	4	4	no	—
323	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	8	yes	complemented
324	C₂²⋊C₄	—	2	16	no	—
325	C₂²⋊C₄	—	4	8	no	—
326	C₄²	—	2	16	no	—
327	C₂³	—	2	4	no	—
328	C₂³	—	2	4	no	—
329	C₂³	—	2	4	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	4	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	4	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	4	4	no	—
339	C₂³	—	4	4	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	4	no	—
342	C₂³	#95×C₁₀₁	1	4	yes	—
343	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
344	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
345	C₂³	C₂×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
346	C₂³	#120×C₁₀₁	1	2	yes	—
347	C₂³	#123×C₁₀₁	1	2	yes	—
348	C₂³	#135×C₁₀₁	1	4	yes	—
349	C₂³	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
350	C₂³	#137×C₁₀₁	1	2	yes	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	2	8	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	8	no	—
363	C₂×C₄	—	4	8	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	8	4	no	—
368	C₂×C₄	—	8	4	no	—
369	C₂×C₄	#95×C₁₀₁	1	4	yes	—
370	C₂×C₄	C₂×C₄²×C₁₀₁	1	1	yes	characteristic
371	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
372	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
373	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
374	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
375	C₂×C₄	#117×C₁₀₁	1	2	yes	—
376	C₂×C₄	C₄×D₄×C₁₀₁	1	4	yes	—
377	C₂×C₄	C₄×D₄×C₁₀₁	1	4	yes	—
378	C₂×C₄	#120×C₁₀₁	1	2	yes	—
379	C₂×C₄	#121×C₁₀₁	1	4	yes	—
380	C₂×C₄	C₂²⋊Q₈×C₁₀₁	1	4	yes	—
381	C₂×C₄	#123×C₁₀₁	1	2	yes	—
382	C₈	—	4	4	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	4	4	no	—
387	C₂²	—	4	4	no	—
388	C₂²	—	4	8	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	4	no	—
391	C₂²	C₂×#95×C₁₀₁	1	1	yes	characteristic
392	C₂²	#379×C₁₀₁	1	1	yes	characteristic
393	C₂²	#381×C₁₀₁	1	1	yes	characteristic
394	C₂²	#385×C₁₀₁	1	2	yes	—
395	C₂²	#386×C₁₀₁	1	2	yes	—
396	C₂²	#416×C₁₀₁	1	2	yes	—
397	C₂²	#416×C₁₀₁	1	2	yes	—
398	C₂²	#417×C₁₀₁	1	2	yes	—
399	C₂²	#418×C₁₀₁	1	1	yes	characteristic
400	C₂²	#419×C₁₀₁	1	1	yes	characteristic
401	C₂²	#427×C₁₀₁	1	2	yes	—
402	C₂²	#428×C₁₀₁	1	2	yes	—
403	C₂²	#449×C₁₀₁	1	4	yes	—
404	C₂²	#452×C₁₀₁	1	4	yes	—
405	C₂²	#482×C₁₀₁	1	4	yes	—
406	C₂²	#485×C₁₀₁	1	4	yes	—
407	C₄	—	2	4	no	—
408	C₄	—	4	8	no	—
409	C₄	—	8	4	no	—
410	C₄	C₄×C₂²⋊C₄×C₁₀₁	1	2	yes	—
411	C₄	#380×C₁₀₁	1	2	yes	—
412	C₄	#385×C₁₀₁	1	2	yes	—
413	C₄	#386×C₁₀₁	1	2	yes	—
414	C₂	—	4	4	no	—
415	C₂	C₁₀₁×C₂²⋊#95	1	1	yes	characteristic
416	C₂	C₁₀₁×#1735	1	1	yes	characteristic
417	C₂	C₁₀₁×#1736	1	1	yes	characteristic
418	C₂	C₁₀₁×#1788	1	2	yes	—
419	C₂	C₁₀₁×#1825	1	2	yes	—
420	C₂	C₁₀₁×#1854	1	4	yes	—
421	C₂	C₁₀₁×#1873	1	2	yes	—
422	C₂	C₁₀₁×#1875	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₀₁	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₀₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₀₁
prime radical	C₂⁵×C₁₀₁	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₀₁ ◁ C₂⁴×C₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×#340×C₁₀₁	C₂	semidirect
9. C₂×#117×C₁₀₁	C₄	semidirect
17. C₂×C₂²⋊C₈×C₁₀₁	C₄	semidirect
19. #380×C₁₀₁	C₄	semidirect
111. C₄⋊C₄×C₁₀₁	C₂²⋊C₄	semidirect
202. #10731	C₁₀₁	direct (N × H)
215. C₂×#340	C₂×C₁₀₁	semidirect
216. C₁₀₁	#10731	direct (N × H)
221. C₂×#117	C₄×C₁₀₁	semidirect
229. C₂×C₂²⋊C₈	C₄×C₁₀₁	semidirect
231. #380	C₄×C₁₀₁	semidirect
323. C₄⋊C₄	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×#117×C₁₀₁	2
C₂²×C₂²⋊C₈×C₁₀₁	2
C₂×#380×C₁₀₁	2
C₂×#340×C₁₀₁	2
#10731	101

Subgroups — C101×#10731 #38792882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#10731 #38792882