Subgroups — C₁₀₁×#17663 #38799814

Order 25856.

1230 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#2920	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#1536	C₂	1	4	yes	maximal, complemented
4	C₁₀₁×#1533	C₂	1	4	yes	maximal, complemented
5	C₁₀₁×#1525	C₂	1	4	yes	maximal, complemented
6	C₂²×#41×C₁₀₁	C₄	1	2	yes	—
7	#532×C₁₀₁	—	2	2	no	—
8	#532×C₁₀₁	—	2	2	no	—
9	#532×C₁₀₁	C₄	1	2	yes	—
10	#532×C₁₀₁	C₄	1	2	yes	—
11	#532×C₁₀₁	C₂²	1	2	yes	—
12	#532×C₁₀₁	C₂²	1	2	yes	—
13	C₂×C₄⋊Q₈×C₁₀₁	C₄	1	1	yes	characteristic
14	C₂×#127×C₁₀₁	C₄	1	1	yes	characteristic
15	C₂×#124×C₁₀₁	C₂²	1	2	yes	—
16	C₂×#121×C₁₀₁	—	2	2	no	—
17	C₂×C₄×D₄×C₁₀₁	—	2	2	no	—
18	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
19	#432×C₁₀₁	C₂²	1	4	yes	—
20	#432×C₁₀₁	C₂²	1	4	yes	complemented
21	#431×C₁₀₁	—	2	2	no	—
22	#431×C₁₀₁	—	2	2	no	—
23	#423×C₁₀₁	—	2	2	no	—
24	#407×C₁₀₁	—	2	2	no	—
25	C₄×M₁₆×C₁₀₁	C₂²	1	4	yes	complemented
26	#329×C₁₀₁	C₂²	1	16	yes	complemented
27	C₂×#41×C₁₀₁	—	2	2	no	—
28	C₂×#41×C₁₀₁	—	2	2	no	—
29	C₂×#41×C₁₀₁	—	4	8	no	—
30	C₂×#41×C₁₀₁	C₂×C₄	1	4	yes	—
31	C₂×#41×C₁₀₁	C₂×C₄	1	4	yes	—
32	C₂²×Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
33	C₂²×D₄×C₁₀₁	—	2	2	no	—
34	C₂²×D₄×C₁₀₁	—	2	2	no	—
35	C₂²×D₄×C₁₀₁	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₁₀₁	—	2	2	no	—
37	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
39	C₂×M₁₆×C₁₀₁	—	2	4	no	—
40	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
41	C₄⋊Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
42	C₄⋊Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
43	#127×C₁₀₁	—	2	2	no	—
44	#127×C₁₀₁	C₂×C₄	1	2	yes	—
45	#127×C₁₀₁	C₂×C₄	1	2	yes	—
46	#124×C₁₀₁	—	2	4	no	—
47	#124×C₁₀₁	C₂×C₄	1	4	yes	—
48	#124×C₁₀₁	C₂³	1	4	yes	—
49	#121×C₁₀₁	—	2	4	no	—
50	#121×C₁₀₁	—	2	4	no	—
51	#121×C₁₀₁	—	2	4	no	—
52	#121×C₁₀₁	—	2	4	no	—
53	C₄×D₄×C₁₀₁	—	2	4	no	—
54	C₄×D₄×C₁₀₁	—	2	4	no	—
55	C₄×D₄×C₁₀₁	—	2	4	no	—
56	C₄×D₄×C₁₀₁	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
59	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
63	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
64	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
65	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₁₀₁	—	2	4	no	—
69	C₄⋊C₈×C₁₀₁	—	2	4	no	—
70	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
71	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
72	#97×C₁₀₁	C₂³	1	8	yes	—
73	C₄×C₈×C₁₀₁	—	2	4	no	—
74	C₂⁴×C₁₀₁	—	2	2	no	—
75	C₂⁴×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
76	#41×C₁₀₁	—	4	8	no	—
77	#41×C₁₀₁	—	4	8	no	—
78	#41×C₁₀₁	—	4	8	no	—
79	#41×C₁₀₁	—	4	8	no	—
80	C₂×Q₈×C₁₀₁	—	2	2	no	—
81	C₂×Q₈×C₁₀₁	—	4	4	no	—
82	C₂×Q₈×C₁₀₁	C₂²×C₄	1	4	yes	—
83	C₂×D₄×C₁₀₁	—	2	4	no	—
84	C₂×D₄×C₁₀₁	—	2	4	no	—
85	C₂×D₄×C₁₀₁	—	2	4	no	—
86	C₂×D₄×C₁₀₁	—	2	4	no	—
87	C₂×D₄×C₁₀₁	—	2	2	no	—
88	C₂×D₄×C₁₀₁	—	4	4	no	—
89	C₂×D₄×C₁₀₁	—	4	8	no	—
90	C₂×D₄×C₁₀₁	—	4	8	no	—
91	C₂×D₄×C₁₀₁	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₁₀₁	—	2	4	no	—
93	C₂²×C₄×C₁₀₁	—	2	2	no	—
94	C₂²×C₄×C₁₀₁	—	2	4	no	—
95	C₂²×C₄×C₁₀₁	—	2	4	no	—
96	C₂²×C₄×C₁₀₁	—	4	4	no	—
97	C₂²×C₄×C₁₀₁	—	4	8	no	—
98	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
99	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
100	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
103	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
110	M₁₆×C₁₀₁	—	4	8	no	—
111	C₂×C₈×C₁₀₁	—	2	8	no	—
112	C₄⋊C₄×C₁₀₁	—	2	4	no	—
113	C₄⋊C₄×C₁₀₁	—	2	4	no	—
114	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
115	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
116	C₄²×C₁₀₁	C₂²⋊C₄	1	2	yes	—
117	C₄²×C₁₀₁	C₂²⋊C₄	1	2	yes	—
118	C₄²×C₁₀₁	C₂²⋊C₄	1	2	yes	—
119	C₄²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
123	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
124	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
125	C₄²×C₁₀₁	C₂⁴	1	1	yes	characteristic
126	C₂³×C₁₀₁	—	2	2	no	—
127	C₂³×C₁₀₁	—	2	4	no	—
128	C₂³×C₁₀₁	—	4	2	no	—
129	C₂³×C₁₀₁	—	4	8	no	—
130	C₂³×C₁₀₁	—	4	4	no	—
131	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	Q₈×C₁₀₁	—	4	4	no	—
135	Q₈×C₁₀₁	—	4	4	no	—
136	D₄×C₁₀₁	—	4	4	no	—
137	D₄×C₁₀₁	—	4	8	no	—
138	D₄×C₁₀₁	—	4	4	no	—
139	D₄×C₁₀₁	—	4	8	no	—
140	D₄×C₁₀₁	—	4	8	no	—
141	D₄×C₁₀₁	—	4	8	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	—	2	2	no	—
147	C₂×C₄×C₁₀₁	—	2	4	no	—
148	C₂×C₄×C₁₀₁	—	2	4	no	—
149	C₂×C₄×C₁₀₁	—	2	4	no	—
150	C₂×C₄×C₁₀₁	—	2	4	no	—
151	C₂×C₄×C₁₀₁	—	4	2	no	—
152	C₂×C₄×C₁₀₁	—	4	2	no	—
153	C₂×C₄×C₁₀₁	—	4	2	no	—
154	C₂×C₄×C₁₀₁	—	4	4	no	—
155	C₂×C₄×C₁₀₁	—	4	8	no	—
156	C₂×C₄×C₁₀₁	—	4	8	no	—
157	C₂×C₄×C₁₀₁	#100	1	4	yes	—
158	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
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×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
166	C₈×C₁₀₁	—	4	8	no	—
167	C₂²×C₁₀₁	—	2	2	no	—
168	C₂²×C₁₀₁	—	2	1	no	—
169	C₂²×C₁₀₁	—	2	1	no	—
170	C₂²×C₁₀₁	—	2	2	no	—
171	C₂²×C₁₀₁	—	2	2	no	—
172	C₂²×C₁₀₁	—	4	4	no	—
173	C₂²×C₁₀₁	—	4	4	no	—
174	C₂²×C₁₀₁	—	4	8	no	—
175	C₂²×C₁₀₁	—	8	8	no	—
176	C₂²×C₁₀₁	C₂×#100	1	2	yes	—
177	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
178	C₄×C₁₀₁	—	2	1	no	—
179	C₄×C₁₀₁	—	2	1	no	—
180	C₄×C₁₀₁	—	2	2	no	—
181	C₄×C₁₀₁	—	2	2	no	—
182	C₄×C₁₀₁	—	2	2	no	—
183	C₄×C₁₀₁	—	4	4	no	—
184	C₄×C₁₀₁	C₂×#100	1	2	yes	—
185	C₄×C₁₀₁	C₂×#100	1	2	yes	—
186	C₄×C₁₀₁	#421	1	4	yes	—
187	#17663	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂×C₁₀₁	—	2	2	no	—
189	C₂×C₁₀₁	—	4	1	no	—
190	C₂×C₁₀₁	—	4	1	no	—
191	C₂×C₁₀₁	—	8	4	no	—
192	C₂×C₁₀₁	C₂²×#100	1	1	yes	characteristic
193	C₂×C₁₀₁	C₂×#421	1	2	yes	—
194	C₂×#532	C₂×C₁₀₁	1	1	yes	characteristic
195	#2920	C₂×C₁₀₁	1	2	yes	complemented
196	#1536	C₂×C₁₀₁	1	4	yes	complemented
197	#1533	C₂×C₁₀₁	1	4	yes	complemented
198	#1525	C₂×C₁₀₁	1	4	yes	complemented
199	C₁₀₁	#17663	1	1	yes	characteristic, direct product factor, Sylow
200	C₂²×#41	C₄×C₁₀₁	1	2	yes	—
201	#532	—	2	2	no	—
202	#532	—	2	2	no	—
203	#532	C₄×C₁₀₁	1	2	yes	—
204	#532	C₄×C₁₀₁	1	2	yes	—
205	#532	C₂²×C₁₀₁	1	2	yes	—
206	#532	C₂²×C₁₀₁	1	2	yes	—
207	C₂×C₄⋊Q₈	C₄×C₁₀₁	1	1	yes	characteristic
208	C₂×#127	C₄×C₁₀₁	1	1	yes	characteristic
209	C₂×#124	C₂²×C₁₀₁	1	2	yes	—
210	C₂×#121	—	2	2	no	—
211	C₂×C₄×D₄	—	2	2	no	—
212	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
213	#432	C₂²×C₁₀₁	1	4	yes	—
214	#432	C₂²×C₁₀₁	1	4	yes	complemented
215	#431	—	2	2	no	—
216	#431	—	2	2	no	—
217	#423	—	2	2	no	—
218	#407	—	2	2	no	—
219	C₄×M₁₆	C₂²×C₁₀₁	1	4	yes	complemented
220	#329	C₂²×C₁₀₁	1	16	yes	complemented
221	C₂×#41	—	2	2	no	—
222	C₂×#41	—	2	2	no	—
223	C₂×#41	—	4	8	no	—
224	C₂×#41	C₂×C₄×C₁₀₁	1	4	yes	—
225	C₂×#41	C₂×C₄×C₁₀₁	1	4	yes	—
226	C₂²×Q₈	C₂×C₄×C₁₀₁	1	2	yes	—
227	C₂²×D₄	—	2	2	no	—
228	C₂²×D₄	—	2	2	no	—
229	C₂²×D₄	C₂×C₄×C₁₀₁	1	2	yes	—
230	C₂³×C₄	—	2	2	no	—
231	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
232	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
233	C₂×M₁₆	—	2	4	no	—
234	C₄⋊Q₈	—	2	2	no	—
235	C₄⋊Q₈	C₂×C₄×C₁₀₁	1	2	yes	—
236	C₄⋊Q₈	C₂×C₄×C₁₀₁	1	2	yes	—
237	#127	—	2	2	no	—
238	#127	C₂×C₄×C₁₀₁	1	2	yes	—
239	#127	C₂×C₄×C₁₀₁	1	2	yes	—
240	#124	—	2	4	no	—
241	#124	C₂×C₄×C₁₀₁	1	4	yes	—
242	#124	C₂³×C₁₀₁	1	4	yes	—
243	#121	—	2	4	no	—
244	#121	—	2	4	no	—
245	#121	—	2	4	no	—
246	#121	—	2	4	no	—
247	C₄×D₄	—	2	4	no	—
248	C₄×D₄	—	2	4	no	—
249	C₄×D₄	—	2	4	no	—
250	C₄×D₄	—	2	4	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₂²⋊C₄	—	2	4	no	—
253	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
254	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
255	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
256	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
257	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
258	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
259	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
262	C₄⋊C₈	—	2	4	no	—
263	C₄⋊C₈	—	2	4	no	—
264	C₂²⋊C₈	—	2	4	no	—
265	C₂²⋊C₈	—	2	4	no	—
266	#97	C₂³×C₁₀₁	1	8	yes	—
267	C₄×C₈	—	2	4	no	—
268	C₂⁴	—	2	2	no	—
269	C₂⁴	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
270	#41	—	4	8	no	—
271	#41	—	4	8	no	—
272	#41	—	4	8	no	—
273	#41	—	4	8	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	4	4	no	—
276	C₂×Q₈	C₂²×C₄×C₁₀₁	1	4	yes	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	4	4	no	—
283	C₂×D₄	—	4	8	no	—
284	C₂×D₄	—	4	8	no	—
285	C₂×D₄	C₂²×C₄×C₁₀₁	1	4	yes	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	4	4	no	—
291	C₂²×C₄	—	4	8	no	—
292	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
293	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
294	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
295	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
296	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
297	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
298	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
300	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
304	M₁₆	—	4	8	no	—
305	C₂×C₈	—	2	8	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₂²⋊C₄	—	2	8	no	—
309	C₂²⋊C₄	—	2	8	no	—
310	C₄²	C₂²⋊C₄×C₁₀₁	1	2	yes	—
311	C₄²	C₂²⋊C₄×C₁₀₁	1	2	yes	—
312	C₄²	C₂²⋊C₄×C₁₀₁	1	2	yes	—
313	C₄²	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
314	C₄²	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
315	C₄²	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
316	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
317	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
318	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
319	C₄²	C₂⁴×C₁₀₁	1	1	yes	characteristic
320	C₂³	—	2	2	no	—
321	C₂³	—	2	4	no	—
322	C₂³	—	4	2	no	—
323	C₂³	—	4	8	no	—
324	C₂³	—	4	4	no	—
325	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
326	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
327	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
328	Q₈	—	4	4	no	—
329	Q₈	—	4	4	no	—
330	D₄	—	4	4	no	—
331	D₄	—	4	4	no	—
332	D₄	—	4	8	no	—
333	D₄	—	4	8	no	—
334	D₄	—	4	8	no	—
335	D₄	—	4	8	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	8	no	—
350	C₂×C₄	—	4	8	no	—
351	C₂×C₄	#100×C₁₀₁	1	4	yes	—
352	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
353	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
354	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
355	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
356	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
357	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
358	C₂×C₄	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
359	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
360	C₈	—	4	8	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	8	no	—
369	C₂²	—	8	8	no	—
370	C₂²	C₂×#100×C₁₀₁	1	2	yes	—
371	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	2	2	no	—
377	C₄	—	4	4	no	—
378	C₄	C₂×#100×C₁₀₁	1	2	yes	—
379	C₄	C₂×#100×C₁₀₁	1	2	yes	—
380	C₄	#421×C₁₀₁	1	4	yes	—
381	C₂	—	2	2	no	—
382	C₂	—	4	1	no	—
383	C₂	—	4	1	no	—
384	C₂	—	8	4	no	—
385	C₂	C₂²×#100×C₁₀₁	1	1	yes	characteristic
386	C₂	C₂×#421×C₁₀₁	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₄²	C₂⁴×C₁₀₁
socle	C₂²×C₁₀₁	C₂²×C₂²⋊C₄
prime radical	C₂×#532×C₁₀₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₁ ◁ C₂²×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₁×#2920	C₂	semidirect
3. C₁₀₁×#1536	C₂	semidirect
4. C₁₀₁×#1533	C₂	semidirect
5. C₁₀₁×#1525	C₂	semidirect
20. #432×C₁₀₁	C₂²	semidirect
25. C₄×M₁₆×C₁₀₁	C₂²	semidirect
26. #329×C₁₀₁	C₂²	semidirect
187. #17663	C₁₀₁	direct (N × H)
195. #2920	C₂×C₁₀₁	semidirect
196. #1536	C₂×C₁₀₁	semidirect
197. #1533	C₂×C₁₀₁	semidirect
198. #1525	C₂×C₁₀₁	semidirect
199. C₁₀₁	#17663	direct (N × H)
214. #432	C₂²×C₁₀₁	semidirect
219. C₄×M₁₆	C₂²×C₁₀₁	semidirect
220. #329	C₂²×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#532×C₁₀₁	2
C₁₀₁×#2920	2
C₁₀₁×#1536	2
C₁₀₁×#1533	2
C₁₀₁×#1525	2
#17663	101

Subgroups — C101×#17663 #38799814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#17663 #38799814