Subgroups — C₁₀₁×#7961 #38790112

Order 25856.

606 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#2920	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#2920	C₂	1	1	yes	maximal, characteristic
3	C₁₀₁×#2285	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#1286	C₂	1	4	yes	maximal, complemented
5	C₂×#117×C₁₀₁	—	2	1	no	—
6	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
7	#432×C₁₀₁	—	2	1	no	—
8	#432×C₁₀₁	—	2	1	no	—
9	#432×C₁₀₁	—	2	1	no	—
10	#432×C₁₀₁	C₄	1	2	yes	complemented
11	#431×C₁₀₁	—	2	1	no	—
12	#431×C₁₀₁	C₄	1	2	yes	complemented
13	#431×C₁₀₁	C₄	1	2	yes	complemented
14	#431×C₁₀₁	C₂²	1	2	yes	—
15	#423×C₁₀₁	—	2	1	no	—
16	#423×C₁₀₁	C₂²	1	2	yes	—
17	#407×C₁₀₁	—	2	1	no	—
18	#407×C₁₀₁	—	2	1	no	—
19	C₄×M₁₆×C₁₀₁	—	2	1	no	—
20	C₄×M₁₆×C₁₀₁	C₄	1	2	yes	complemented
21	#384×C₁₀₁	—	2	1	no	—
22	#382×C₁₀₁	C₂²	1	2	yes	—
23	#380×C₁₀₁	—	2	1	no	—
24	#380×C₁₀₁	C₄	1	2	yes	—
25	C₄×C₄⋊C₄×C₁₀₁	—	2	1	no	—
26	C₄×C₄⋊C₄×C₁₀₁	C₄	1	2	yes	—
27	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
30	C₂×M₁₆×C₁₀₁	—	2	2	no	—
31	C₂×M₁₆×C₁₀₁	—	2	2	no	—
32	#117×C₁₀₁	—	4	4	no	—
33	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
34	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
35	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
36	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
37	C₂×C₄²×C₁₀₁	—	2	2	no	—
38	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₀₁	Q₈	1	1	yes	characteristic
48	C₂×C₄²×C₁₀₁	Q₈	1	1	yes	characteristic
49	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
50	C₄⋊C₈×C₁₀₁	—	2	2	no	—
51	C₄⋊C₈×C₁₀₁	—	2	2	no	—
52	C₄⋊C₈×C₁₀₁	—	2	2	no	—
53	C₄⋊C₈×C₁₀₁	C₂×C₄	1	4	yes	—
54	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
55	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
56	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
57	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
58	#97×C₁₀₁	—	2	2	no	—
59	#97×C₁₀₁	—	2	2	no	—
60	C₄×C₈×C₁₀₁	—	2	2	no	—
61	C₄×C₈×C₁₀₁	C₂×C₄	1	4	yes	—
62	#95×C₁₀₁	—	2	2	no	—
63	#95×C₁₀₁	C₂×C₄	1	4	yes	—
64	C₂⁴×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₀₁	—	2	2	no	—
66	C₂²×C₄×C₁₀₁	—	2	2	no	—
67	C₂²×C₄×C₁₀₁	—	2	4	no	—
68	C₂²×C₄×C₁₀₁	—	4	2	no	—
69	C₂²×C₄×C₁₀₁	—	4	2	no	—
70	C₂²×C₄×C₁₀₁	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₁₀₁	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
88	M₁₆×C₁₀₁	—	4	4	no	—
89	M₁₆×C₁₀₁	—	4	2	no	—
90	M₁₆×C₁₀₁	—	4	2	no	—
91	C₂×C₈×C₁₀₁	—	2	4	no	—
92	C₂×C₈×C₁₀₁	—	2	4	no	—
93	C₄⋊C₄×C₁₀₁	—	4	4	no	—
94	C₄⋊C₄×C₁₀₁	—	4	4	no	—
95	C₄⋊C₄×C₁₀₁	—	4	4	no	—
96	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
97	C₄²×C₁₀₁	—	4	4	no	—
98	C₄²×C₁₀₁	C₄²	1	1	yes	characteristic
99	C₄²×C₁₀₁	C₄²	1	1	yes	characteristic
100	C₄²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
114	C₂³×C₁₀₁	—	2	1	no	—
115	C₂³×C₁₀₁	—	2	1	no	—
116	C₂³×C₁₀₁	—	4	1	no	—
117	C₂³×C₁₀₁	—	4	1	no	—
118	C₂³×C₁₀₁	#95	1	1	yes	characteristic
119	C₂³×C₁₀₁	#95	1	1	yes	characteristic
120	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₁₀₁	—	2	1	no	—
122	C₂×C₄×C₁₀₁	—	2	1	no	—
123	C₂×C₄×C₁₀₁	—	2	2	no	—
124	C₂×C₄×C₁₀₁	—	2	2	no	—
125	C₂×C₄×C₁₀₁	—	2	2	no	—
126	C₂×C₄×C₁₀₁	—	2	2	no	—
127	C₂×C₄×C₁₀₁	—	2	2	no	—
128	C₂×C₄×C₁₀₁	—	2	2	no	—
129	C₂×C₄×C₁₀₁	—	2	2	no	—
130	C₂×C₄×C₁₀₁	—	2	2	no	—
131	C₂×C₄×C₁₀₁	—	2	2	no	—
132	C₂×C₄×C₁₀₁	—	2	2	no	—
133	C₂×C₄×C₁₀₁	—	4	1	no	—
134	C₂×C₄×C₁₀₁	—	4	1	no	—
135	C₂×C₄×C₁₀₁	—	4	1	no	—
136	C₂×C₄×C₁₀₁	—	4	1	no	—
137	C₂×C₄×C₁₀₁	—	4	1	no	—
138	C₂×C₄×C₁₀₁	—	4	1	no	—
139	C₂×C₄×C₁₀₁	—	4	4	no	—
140	C₂×C₄×C₁₀₁	—	4	4	no	—
141	C₂×C₄×C₁₀₁	—	4	4	no	—
142	C₂×C₄×C₁₀₁	#95	1	1	yes	characteristic
143	C₂×C₄×C₁₀₁	#95	1	1	yes	characteristic
144	C₂×C₄×C₁₀₁	#95	1	1	yes	characteristic
145	C₂×C₄×C₁₀₁	#95	1	1	yes	characteristic
146	C₂×C₄×C₁₀₁	#95	1	1	yes	characteristic
147	C₂×C₄×C₁₀₁	#95	1	1	yes	characteristic
148	C₂×C₄×C₁₀₁	C₂×C₄²	1	1	yes	characteristic
149	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
155	C₂×C₄×C₁₀₁	#137	1	2	yes	—
156	C₈×C₁₀₁	—	4	4	no	—
157	C₈×C₁₀₁	—	4	4	no	—
158	C₂²×C₁₀₁	—	2	1	no	—
159	C₂²×C₁₀₁	—	2	1	no	—
160	C₂²×C₁₀₁	—	2	1	no	—
161	C₂²×C₁₀₁	—	2	1	no	—
162	C₂²×C₁₀₁	—	2	1	no	—
163	C₂²×C₁₀₁	—	2	1	no	—
164	C₂²×C₁₀₁	—	2	1	no	—
165	C₂²×C₁₀₁	—	2	1	no	—
166	C₂²×C₁₀₁	—	4	2	no	—
167	C₂²×C₁₀₁	—	4	2	no	—
168	C₂²×C₁₀₁	C₂×#95	1	1	yes	characteristic
169	C₂²×C₁₀₁	#418	1	1	yes	characteristic
170	C₂²×C₁₀₁	#419	1	1	yes	characteristic
171	C₄×C₁₀₁	—	2	1	no	—
172	C₄×C₁₀₁	—	2	1	no	—
173	C₄×C₁₀₁	—	2	1	no	—
174	C₄×C₁₀₁	—	2	1	no	—
175	C₄×C₁₀₁	—	2	1	no	—
176	C₄×C₁₀₁	—	2	1	no	—
177	C₄×C₁₀₁	—	2	1	no	—
178	C₄×C₁₀₁	—	2	1	no	—
179	C₄×C₁₀₁	—	8	4	no	—
180	C₄×C₁₀₁	H(3,ℤ/4)	1	2	yes	—
181	C₄×C₁₀₁	#344	1	2	yes	—
182	C₄×C₁₀₁	#417	1	2	yes	—
183	C₄×C₁₀₁	#428	1	2	yes	—
184	#7961	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂×C₁₀₁	—	2	1	no	—
186	C₂×C₁₀₁	—	2	1	no	—
187	C₂×C₁₀₁	—	4	1	no	—
188	C₂×C₁₀₁	—	4	1	no	—
189	C₂×C₁₀₁	C₂×H(3,ℤ/4)	1	1	yes	characteristic
190	C₂×C₁₀₁	#1736	1	1	yes	characteristic
191	C₂×C₁₀₁	C₂×#344	1	1	yes	characteristic
192	#2920	C₂×C₁₀₁	1	1	yes	characteristic
193	#2920	C₂×C₁₀₁	1	1	yes	characteristic
194	#2285	C₂×C₁₀₁	1	1	yes	characteristic
195	#1286	C₂×C₁₀₁	1	4	yes	complemented
196	C₁₀₁	#7961	1	1	yes	characteristic, direct product factor, Sylow
197	C₂×#117	—	2	1	no	—
198	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
199	#432	—	2	1	no	—
200	#432	—	2	1	no	—
201	#432	—	2	1	no	—
202	#432	C₄×C₁₀₁	1	2	yes	complemented
203	#431	—	2	1	no	—
204	#431	C₄×C₁₀₁	1	2	yes	complemented
205	#431	C₄×C₁₀₁	1	2	yes	complemented
206	#431	C₂²×C₁₀₁	1	2	yes	—
207	#423	—	2	1	no	—
208	#423	C₂²×C₁₀₁	1	2	yes	—
209	#407	—	2	1	no	—
210	#407	—	2	1	no	—
211	C₄×M₁₆	—	2	1	no	—
212	C₄×M₁₆	C₄×C₁₀₁	1	2	yes	complemented
213	#384	—	2	1	no	—
214	#382	C₂²×C₁₀₁	1	2	yes	—
215	#380	—	2	1	no	—
216	#380	C₄×C₁₀₁	1	2	yes	—
217	C₄×C₄⋊C₄	—	2	1	no	—
218	C₄×C₄⋊C₄	C₄×C₁₀₁	1	2	yes	—
219	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
220	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
221	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
222	C₂×M₁₆	—	2	2	no	—
223	C₂×M₁₆	—	2	2	no	—
224	#117	—	4	4	no	—
225	C₂×C₄⋊C₄	—	2	2	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₂²⋊C₄	—	2	2	no	—
229	C₂×C₄²	—	2	2	no	—
230	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
231	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
232	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
233	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
234	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
235	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
236	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
237	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
238	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
239	C₂×C₄²	Q₈×C₁₀₁	1	1	yes	characteristic
240	C₂×C₄²	Q₈×C₁₀₁	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
242	C₄⋊C₈	—	2	2	no	—
243	C₄⋊C₈	—	2	2	no	—
244	C₄⋊C₈	—	2	2	no	—
245	C₄⋊C₈	C₂×C₄×C₁₀₁	1	4	yes	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	2	2	no	—
248	C₂²⋊C₈	—	2	2	no	—
249	C₂²⋊C₈	—	2	2	no	—
250	#97	—	2	2	no	—
251	#97	—	2	2	no	—
252	C₄×C₈	—	2	2	no	—
253	C₄×C₈	C₂×C₄×C₁₀₁	1	4	yes	—
254	#95	—	2	2	no	—
255	#95	C₂×C₄×C₁₀₁	1	4	yes	—
256	C₂⁴	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	C₄²×C₁₀₁	1	1	yes	characteristic
263	C₂²×C₄	C₄²×C₁₀₁	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
265	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
266	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
267	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
268	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
269	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
270	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
271	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
272	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
273	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
274	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
275	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
276	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
277	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
279	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
280	M₁₆	—	4	4	no	—
281	M₁₆	—	4	2	no	—
282	M₁₆	—	4	2	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	4	no	—
285	C₄⋊C₄	—	4	4	no	—
286	C₄⋊C₄	—	4	4	no	—
287	C₄⋊C₄	—	4	4	no	—
288	C₂²⋊C₄	—	4	4	no	—
289	C₄²	—	4	4	no	—
290	C₄²	C₄²×C₁₀₁	1	1	yes	characteristic
291	C₄²	C₄²×C₁₀₁	1	1	yes	characteristic
292	C₄²	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
293	C₄²	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
294	C₄²	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
295	C₄²	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
296	C₄²	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
297	C₄²	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
298	C₄²	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
299	C₄²	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
300	C₄²	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
301	C₄²	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
302	C₄²	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
303	C₄²	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
304	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
305	C₄²	C₂×Q₈×C₁₀₁	1	1	yes	characteristic
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	4	1	no	—
309	C₂³	—	4	1	no	—
310	C₂³	#95×C₁₀₁	1	1	yes	characteristic
311	C₂³	#95×C₁₀₁	1	1	yes	characteristic
312	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	#95×C₁₀₁	1	1	yes	characteristic
335	C₂×C₄	#95×C₁₀₁	1	1	yes	characteristic
336	C₂×C₄	#95×C₁₀₁	1	1	yes	characteristic
337	C₂×C₄	#95×C₁₀₁	1	1	yes	characteristic
338	C₂×C₄	#95×C₁₀₁	1	1	yes	characteristic
339	C₂×C₄	#95×C₁₀₁	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄²×C₁₀₁	1	1	yes	characteristic
341	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
342	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
343	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
344	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
345	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
346	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
347	C₂×C₄	#137×C₁₀₁	1	2	yes	—
348	C₈	—	4	4	no	—
349	C₈	—	4	4	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	C₂×#95×C₁₀₁	1	1	yes	characteristic
361	C₂²	#418×C₁₀₁	1	1	yes	characteristic
362	C₂²	#419×C₁₀₁	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	8	4	no	—
372	C₄	H(3,ℤ/4)×C₁₀₁	1	2	yes	—
373	C₄	#344×C₁₀₁	1	2	yes	—
374	C₄	#417×C₁₀₁	1	2	yes	—
375	C₄	#428×C₁₀₁	1	2	yes	—
376	C₂	—	2	1	no	—
377	C₂	—	2	1	no	—
378	C₂	—	4	1	no	—
379	C₂	—	4	1	no	—
380	C₂	C₂×H(3,ℤ/4)×C₁₀₁	1	1	yes	characteristic
381	C₂	C₁₀₁×#1736	1	1	yes	characteristic
382	C₂	C₂×#344×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×#95
commutator	C₂×C₄	C₂×C₄²×C₁₀₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₀₁
prime radical	C₂⁴×C₁₀₁	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂²×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₀₁×#1286	C₂	semidirect
10. #432×C₁₀₁	C₄	semidirect
12. #431×C₁₀₁	C₄	semidirect
13. #431×C₁₀₁	C₄	semidirect
20. C₄×M₁₆×C₁₀₁	C₄	semidirect
184. #7961	C₁₀₁	direct (N × H)
195. #1286	C₂×C₁₀₁	semidirect
196. C₁₀₁	#7961	direct (N × H)
202. #432	C₄×C₁₀₁	semidirect
204. #431	C₄×C₁₀₁	semidirect
205. #431	C₄×C₁₀₁	semidirect
212. C₄×M₁₆	C₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₁×#2920	2
C₁₀₁×#2285	2
C₁₀₁×#1286	2
#7961	101

Subgroups — C101×#7961 #38790112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#7961 #38790112