Subgroups — C₁₀₁×#17953 #38800104

Order 25856.

558 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3104	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#2985	C₂	1	1	yes	maximal, characteristic
3	C₁₀₁×#2983	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#1593	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1591	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1587	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1584	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#1572	C₂	1	1	yes	maximal, characteristic
9	C₁₀₁×#1491	C₂	1	1	yes	maximal, characteristic
10	C₁₀₁×#1485	C₂	1	1	yes	maximal, characteristic
11	C₁₀₁×#1453	C₂	1	1	yes	maximal, characteristic
12	#533×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
14	#484×C₁₀₁	C₄	1	2	yes	—
15	#477×C₁₀₁	C₄	1	2	yes	—
16	#462×C₁₀₁	C₄	1	2	yes	—
17	#451×C₁₀₁	C₄	1	2	yes	—
18	#446×C₁₀₁	—	2	2	no	—
19	#446×C₁₀₁	—	2	2	no	—
20	#446×C₁₀₁	C₂²	1	2	yes	—
21	#446×C₁₀₁	C₂²	1	2	yes	—
22	#446×C₁₀₁	C₂²	1	2	yes	—
23	C₈×Q₈×C₁₀₁	C₂²	1	2	yes	—
24	C₄×Q₁₆×C₁₀₁	C₂²	1	2	yes	—
25	C₄×Q₁₆×C₁₀₁	C₂²	1	2	yes	—
26	#433×C₁₀₁	—	2	2	no	—
27	#432×C₁₀₁	—	2	2	no	—
28	#432×C₁₀₁	C₂²	1	1	yes	characteristic
29	#431×C₁₀₁	C₂²	1	1	yes	characteristic
30	#431×C₁₀₁	C₂²	1	1	yes	characteristic
31	#431×C₁₀₁	C₂²	1	1	yes	characteristic
32	C₄×M₁₆×C₁₀₁	C₂²	1	1	yes	characteristic
33	#335×C₁₀₁	C₂²	1	2	yes	—
34	#334×C₁₀₁	C₂²	1	2	yes	—
35	Q₈⋊C₈×C₁₀₁	C₂²	1	2	yes	—
36	Q₈⋊C₈×C₁₀₁	C₂²	1	2	yes	—
37	Q₈⋊C₈×C₁₀₁	C₂²	1	2	yes	—
38	Q₈⋊C₈×C₁₀₁	C₂²	1	2	yes	—
39	#322×C₁₀₁	C₂²	1	1	yes	characteristic
40	#322×C₁₀₁	C₂²	1	1	yes	characteristic
41	#322×C₁₀₁	C₂²	1	1	yes	characteristic
42	C₈²×C₁₀₁	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
44	C₂×Q₁₆×C₁₀₁	C₂×C₄	1	2	yes	—
45	C₂×Q₁₆×C₁₀₁	C₂×C₄	1	2	yes	—
46	C₂×M₁₆×C₁₀₁	—	2	1	no	—
47	C₄⋊Q₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
48	C₄⋊Q₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
49	#125×C₁₀₁	—	2	1	no	—
50	C₂²⋊Q₈×C₁₀₁	—	2	1	no	—
51	C₂²⋊Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
52	C₄×Q₈×C₁₀₁	—	2	1	no	—
53	C₄×Q₈×C₁₀₁	—	2	1	no	—
54	C₄×Q₈×C₁₀₁	—	2	1	no	—
55	C₄×Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
56	C₄×Q₈×C₁₀₁	C₂³	1	2	yes	—
57	C₄×Q₈×C₁₀₁	C₂³	1	2	yes	—
58	#117×C₁₀₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₀₁	—	2	1	no	—
62	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
63	#107×C₁₀₁	C₂×C₄	1	2	yes	—
64	#107×C₁₀₁	C₂×C₄	1	2	yes	—
65	C₄⋊C₈×C₁₀₁	—	2	2	no	—
66	C₄⋊C₈×C₁₀₁	—	2	2	no	—
67	C₄⋊C₈×C₁₀₁	—	2	2	no	—
68	C₄⋊C₈×C₁₀₁	—	2	2	no	—
69	C₄⋊C₈×C₁₀₁	C₂×C₄	1	2	yes	—
70	C₄⋊C₈×C₁₀₁	D₄	1	2	yes	—
71	C₄⋊C₈×C₁₀₁	C₂³	1	2	yes	—
72	C₄⋊C₈×C₁₀₁	C₂³	1	2	yes	—
73	#103×C₁₀₁	C₂×C₄	1	2	yes	—
74	#103×C₁₀₁	C₂×C₄	1	2	yes	—
75	#103×C₁₀₁	C₂×C₄	1	2	yes	—
76	#103×C₁₀₁	C₂×C₄	1	2	yes	—
77	C₂²⋊C₈×C₁₀₁	—	2	1	no	—
78	C₂²⋊C₈×C₁₀₁	—	2	1	no	—
79	C₂²⋊C₈×C₁₀₁	C₂×C₄	1	2	yes	—
80	C₂²⋊C₈×C₁₀₁	D₄	1	2	yes	—
81	#97×C₁₀₁	—	2	2	no	—
82	#97×C₁₀₁	—	2	2	no	—
83	#97×C₁₀₁	—	2	2	no	—
84	#97×C₁₀₁	—	2	1	no	—
85	#97×C₁₀₁	—	2	1	no	—
86	C₄×C₈×C₁₀₁	—	2	2	no	—
87	C₄×C₈×C₁₀₁	—	2	1	no	—
88	C₄×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₁₀₁	—	2	1	no	—
95	C₂×Q₈×C₁₀₁	—	2	1	no	—
96	C₂×Q₈×C₁₀₁	—	4	2	no	—
97	C₂×Q₈×C₁₀₁	C₂²×C₄	1	2	yes	—
98	C₂×Q₈×C₁₀₁	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₀₁	—	2	1	no	—
100	C₂²×C₄×C₁₀₁	—	2	1	no	—
101	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₀₁	#41	1	1	yes	characteristic
104	Q₁₆×C₁₀₁	—	4	2	no	—
105	Q₁₆×C₁₀₁	—	4	2	no	—
106	M₁₆×C₁₀₁	—	4	2	no	—
107	C₂×C₈×C₁₀₁	—	2	1	no	—
108	C₂×C₈×C₁₀₁	—	2	2	no	—
109	C₂×C₈×C₁₀₁	—	2	2	no	—
110	C₂×C₈×C₁₀₁	—	2	1	no	—
111	C₂×C₈×C₁₀₁	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₁₀₁	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
115	C₄⋊C₄×C₁₀₁	—	2	2	no	—
116	C₄⋊C₄×C₁₀₁	—	2	1	no	—
117	C₄⋊C₄×C₁₀₁	—	2	1	no	—
118	C₄⋊C₄×C₁₀₁	—	2	1	no	—
119	C₄⋊C₄×C₁₀₁	—	2	1	no	—
120	C₄⋊C₄×C₁₀₁	—	2	2	no	—
121	C₄⋊C₄×C₁₀₁	—	2	2	no	—
122	C₄⋊C₄×C₁₀₁	—	2	2	no	—
123	C₄⋊C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
124	C₄⋊C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
125	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
126	C₄²×C₁₀₁	—	2	2	no	—
127	C₄²×C₁₀₁	—	2	2	no	—
128	C₄²×C₁₀₁	—	2	2	no	—
129	C₄²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₀₁	#41	1	1	yes	characteristic
132	C₄²×C₁₀₁	C₂⁴	1	1	yes	characteristic
133	C₂³×C₁₀₁	C₄×D₄	1	1	yes	characteristic
134	Q₈×C₁₀₁	—	2	2	no	—
135	Q₈×C₁₀₁	—	2	2	no	—
136	Q₈×C₁₀₁	—	2	2	no	—
137	Q₈×C₁₀₁	—	2	2	no	—
138	Q₈×C₁₀₁	—	4	2	no	—
139	Q₈×C₁₀₁	—	8	1	no	—
140	C₂×C₄×C₁₀₁	—	2	2	no	—
141	C₂×C₄×C₁₀₁	—	2	2	no	—
142	C₂×C₄×C₁₀₁	—	2	2	no	—
143	C₂×C₄×C₁₀₁	—	2	2	no	—
144	C₂×C₄×C₁₀₁	—	2	2	no	—
145	C₂×C₄×C₁₀₁	—	2	2	no	—
146	C₂×C₄×C₁₀₁	—	4	1	no	—
147	C₂×C₄×C₁₀₁	—	4	2	no	—
148	C₂×C₄×C₁₀₁	—	8	1	no	—
149	C₂×C₄×C₁₀₁	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₀₁	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₀₁	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
155	C₈×C₁₀₁	—	2	2	no	—
156	C₈×C₁₀₁	—	2	2	no	—
157	C₈×C₁₀₁	—	2	2	no	—
158	C₈×C₁₀₁	—	2	2	no	—
159	C₈×C₁₀₁	—	2	2	no	—
160	C₈×C₁₀₁	—	4	1	no	—
161	C₈×C₁₀₁	—	4	2	no	—
162	C₈×C₁₀₁	—	4	2	no	—
163	C₂²×C₁₀₁	—	2	1	no	—
164	C₂²×C₁₀₁	—	2	1	no	—
165	C₂²×C₁₀₁	—	2	1	no	—
166	C₂²×C₁₀₁	C₂×C₄×D₄	1	1	yes	characteristic
167	C₄×C₁₀₁	—	2	1	no	—
168	C₄×C₁₀₁	—	2	1	no	—
169	C₄×C₁₀₁	—	2	1	no	—
170	C₄×C₁₀₁	—	2	1	no	—
171	C₄×C₁₀₁	—	4	2	no	—
172	C₄×C₁₀₁	—	4	2	no	—
173	C₄×C₁₀₁	—	4	2	no	—
174	C₄×C₁₀₁	—	4	2	no	—
175	C₄×C₁₀₁	#568	1	2	yes	—
176	C₄×C₁₀₁	#578	1	2	yes	—
177	#17953	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂×C₁₀₁	—	4	1	no	—
179	C₂×C₁₀₁	#2930	1	1	yes	characteristic
180	C₂×C₁₀₁	#2950	1	1	yes	characteristic
181	C₂×C₁₀₁	#2956	1	1	yes	characteristic
182	#3104	C₂×C₁₀₁	1	1	yes	characteristic
183	#2985	C₂×C₁₀₁	1	1	yes	characteristic
184	#2983	C₂×C₁₀₁	1	1	yes	characteristic
185	#1593	C₂×C₁₀₁	1	2	yes	complemented
186	#1591	C₂×C₁₀₁	1	2	yes	complemented
187	#1587	C₂×C₁₀₁	1	2	yes	complemented
188	#1584	C₂×C₁₀₁	1	2	yes	complemented
189	#1572	C₂×C₁₀₁	1	1	yes	characteristic
190	#1491	C₂×C₁₀₁	1	1	yes	characteristic
191	#1485	C₂×C₁₀₁	1	1	yes	characteristic
192	#1453	C₂×C₁₀₁	1	1	yes	characteristic
193	C₁₀₁	#17953	1	1	yes	characteristic, direct product factor, Sylow
194	#533	C₂²×C₁₀₁	1	1	yes	characteristic
195	C₂×C₄×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
196	#484	C₄×C₁₀₁	1	2	yes	—
197	#477	C₄×C₁₀₁	1	2	yes	—
198	#462	C₄×C₁₀₁	1	2	yes	—
199	#451	C₄×C₁₀₁	1	2	yes	—
200	#446	—	2	2	no	—
201	#446	—	2	2	no	—
202	#446	C₂²×C₁₀₁	1	2	yes	—
203	#446	C₂²×C₁₀₁	1	2	yes	—
204	#446	C₂²×C₁₀₁	1	2	yes	—
205	C₈×Q₈	C₂²×C₁₀₁	1	2	yes	—
206	C₄×Q₁₆	C₂²×C₁₀₁	1	2	yes	—
207	C₄×Q₁₆	C₂²×C₁₀₁	1	2	yes	—
208	#433	—	2	2	no	—
209	#432	—	2	2	no	—
210	#432	C₂²×C₁₀₁	1	1	yes	characteristic
211	#431	C₂²×C₁₀₁	1	1	yes	characteristic
212	#431	C₂²×C₁₀₁	1	1	yes	characteristic
213	#431	C₂²×C₁₀₁	1	1	yes	characteristic
214	C₄×M₁₆	C₂²×C₁₀₁	1	1	yes	characteristic
215	#335	C₂²×C₁₀₁	1	2	yes	—
216	#334	C₂²×C₁₀₁	1	2	yes	—
217	Q₈⋊C₈	C₂²×C₁₀₁	1	2	yes	—
218	Q₈⋊C₈	C₂²×C₁₀₁	1	2	yes	—
219	Q₈⋊C₈	C₂²×C₁₀₁	1	2	yes	—
220	Q₈⋊C₈	C₂²×C₁₀₁	1	2	yes	—
221	#322	C₂²×C₁₀₁	1	1	yes	characteristic
222	#322	C₂²×C₁₀₁	1	1	yes	characteristic
223	#322	C₂²×C₁₀₁	1	1	yes	characteristic
224	C₈²	C₂²×C₁₀₁	1	1	yes	characteristic
225	C₂²×Q₈	C₂×C₄×C₁₀₁	1	1	yes	characteristic
226	C₂×Q₁₆	C₂×C₄×C₁₀₁	1	2	yes	—
227	C₂×Q₁₆	C₂×C₄×C₁₀₁	1	2	yes	—
228	C₂×M₁₆	—	2	1	no	—
229	C₄⋊Q₈	C₂×C₄×C₁₀₁	1	1	yes	characteristic
230	C₄⋊Q₈	C₂×C₄×C₁₀₁	1	1	yes	characteristic
231	#125	—	2	1	no	—
232	C₂²⋊Q₈	—	2	1	no	—
233	C₂²⋊Q₈	C₂×C₄×C₁₀₁	1	2	yes	—
234	C₄×Q₈	—	2	1	no	—
235	C₄×Q₈	—	2	1	no	—
236	C₄×Q₈	—	2	1	no	—
237	C₄×Q₈	C₂×C₄×C₁₀₁	1	2	yes	—
238	C₄×Q₈	C₂³×C₁₀₁	1	2	yes	—
239	C₄×Q₈	C₂³×C₁₀₁	1	2	yes	—
240	#117	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
243	C₂×C₄²	—	2	1	no	—
244	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
245	#107	C₂×C₄×C₁₀₁	1	2	yes	—
246	#107	C₂×C₄×C₁₀₁	1	2	yes	—
247	C₄⋊C₈	—	2	2	no	—
248	C₄⋊C₈	—	2	2	no	—
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	—	2	2	no	—
251	C₄⋊C₈	C₂×C₄×C₁₀₁	1	2	yes	—
252	C₄⋊C₈	D₄×C₁₀₁	1	2	yes	—
253	C₄⋊C₈	C₂³×C₁₀₁	1	2	yes	—
254	C₄⋊C₈	C₂³×C₁₀₁	1	2	yes	—
255	#103	C₂×C₄×C₁₀₁	1	2	yes	—
256	#103	C₂×C₄×C₁₀₁	1	2	yes	—
257	#103	C₂×C₄×C₁₀₁	1	2	yes	—
258	#103	C₂×C₄×C₁₀₁	1	2	yes	—
259	C₂²⋊C₈	—	2	1	no	—
260	C₂²⋊C₈	—	2	1	no	—
261	C₂²⋊C₈	C₂×C₄×C₁₀₁	1	2	yes	—
262	C₂²⋊C₈	D₄×C₁₀₁	1	2	yes	—
263	#97	—	2	2	no	—
264	#97	—	2	2	no	—
265	#97	—	2	2	no	—
266	#97	—	2	1	no	—
267	#97	—	2	1	no	—
268	C₄×C₈	—	2	2	no	—
269	C₄×C₈	—	2	1	no	—
270	C₄×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
271	C₄×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
272	C₄×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
274	C₄×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
275	C₄×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
276	C₂×Q₈	—	2	1	no	—
277	C₂×Q₈	—	2	1	no	—
278	C₂×Q₈	—	4	2	no	—
279	C₂×Q₈	C₂²×C₄×C₁₀₁	1	2	yes	—
280	C₂×Q₈	C₂²×C₄×C₁₀₁	1	2	yes	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
285	C₂²×C₄	#41×C₁₀₁	1	1	yes	characteristic
286	Q₁₆	—	4	2	no	—
287	Q₁₆	—	4	2	no	—
288	M₁₆	—	4	2	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	C₂²×C₄×C₁₀₁	1	2	yes	—
294	C₂×C₈	C₂²×C₄×C₁₀₁	1	2	yes	—
295	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
296	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
306	C₄⋊C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
312	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
313	C₄²	#41×C₁₀₁	1	1	yes	characteristic
314	C₄²	C₂⁴×C₁₀₁	1	1	yes	characteristic
315	C₂³	C₄×D₄×C₁₀₁	1	1	yes	characteristic
316	Q₈	—	2	2	no	—
317	Q₈	—	2	2	no	—
318	Q₈	—	2	2	no	—
319	Q₈	—	2	2	no	—
320	Q₈	—	4	2	no	—
321	Q₈	—	8	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	8	1	no	—
331	C₂×C₄	C₄×D₄×C₁₀₁	1	1	yes	characteristic
332	C₂×C₄	C₄×D₄×C₁₀₁	1	1	yes	characteristic
333	C₂×C₄	C₄×D₄×C₁₀₁	1	1	yes	characteristic
334	C₂×C₄	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
335	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
336	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
337	C₈	—	2	2	no	—
338	C₈	—	2	2	no	—
339	C₈	—	2	2	no	—
340	C₈	—	2	2	no	—
341	C₈	—	2	2	no	—
342	C₈	—	4	1	no	—
343	C₈	—	4	2	no	—
344	C₈	—	4	2	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	C₂×C₄×D₄×C₁₀₁	1	1	yes	characteristic
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	2	no	—
355	C₄	—	4	2	no	—
356	C₄	—	4	2	no	—
357	C₄	#568×C₁₀₁	1	2	yes	—
358	C₄	#578×C₁₀₁	1	2	yes	—
359	C₂	—	4	1	no	—
360	C₂	C₁₀₁×#2930	1	1	yes	characteristic
361	C₂	C₁₀₁×#2950	1	1	yes	characteristic
362	C₂	C₁₀₁×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₀₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₄²	C₂⁴×C₁₀₁
socle	C₂²×C₁₀₁	C₂×C₄×D₄
prime radical	C₂³×C₁₀₁	C₄×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₁ ◁ #431×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₀₁×#1593	C₂	semidirect
5. C₁₀₁×#1591	C₂	semidirect
6. C₁₀₁×#1587	C₂	semidirect
7. C₁₀₁×#1584	C₂	semidirect
177. #17953	C₁₀₁	direct (N × H)
185. #1593	C₂×C₁₀₁	semidirect
186. #1591	C₂×C₁₀₁	semidirect
187. #1587	C₂×C₁₀₁	semidirect
188. #1584	C₂×C₁₀₁	semidirect
193. C₁₀₁	#17953	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₀₁×#3104	2
C₁₀₁×#2985	2
C₁₀₁×#2983	2
C₁₀₁×#1593	2
C₁₀₁×#1591	2
C₁₀₁×#1587	2
C₁₀₁×#1584	2
C₁₀₁×#1572	2
C₁₀₁×#1491	2
C₁₀₁×#1485	2
C₁₀₁×#1453	2
#17953	101

Subgroups — C101×#17953 #38800104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#17953 #38800104