Subgroups — C₂×C₁₀₁×#1699 #38801290

Order 25856.

726 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#487×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#474×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#461×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#436×C₁₀₁	C₂	1	1	yes	maximal, characteristic
5	C₁₀₁×#1699	C₂	1	8	yes	maximal, direct product factor
6	C₂×#335×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#332×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#332×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×SD₁₆×C₁₀₁	—	2	1	no	—
10	C₂²×M₁₆×C₁₀₁	—	2	1	no	—
11	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
14	#487×C₁₀₁	—	2	2	no	—
15	#487×C₁₀₁	C₂²	1	4	yes	complemented
16	#474×C₁₀₁	—	2	2	no	—
17	#474×C₁₀₁	C₂²	1	4	yes	—
18	#461×C₁₀₁	—	2	2	no	—
19	#461×C₁₀₁	C₂²	1	4	yes	—
20	#436×C₁₀₁	—	2	2	no	—
21	#436×C₁₀₁	C₂²	1	4	yes	—
22	C₂×#107×C₁₀₁	—	2	1	no	—
23	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
26	C₂×#103×C₁₀₁	—	2	1	no	—
27	C₂×#103×C₁₀₁	—	2	1	no	—
28	C₂×#103×C₁₀₁	—	2	1	no	—
29	C₂×#102×C₁₀₁	—	2	1	no	—
30	C₂×C₂²⋊C₈×C₁₀₁	—	2	1	no	—
31	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
32	#335×C₁₀₁	C₂²	1	4	yes	complemented
33	#332×C₁₀₁	C₂²	1	4	yes	complemented
34	#332×C₁₀₁	C₂²	1	4	yes	complemented
35	C₂²×Q₈×C₁₀₁	—	2	1	no	—
36	C₂²×Q₈×C₁₀₁	—	2	1	no	—
37	C₂²×D₄×C₁₀₁	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₀₁	—	2	1	no	—
39	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
40	C₂×SD₁₆×C₁₀₁	—	4	4	no	—
41	C₂×M₁₆×C₁₀₁	—	2	4	no	—
42	C₂×M₁₆×C₁₀₁	—	4	4	no	—
43	C₂²×C₈×C₁₀₁	—	2	1	no	—
44	C₂²×C₈×C₁₀₁	—	2	1	no	—
45	C₂²×C₈×C₁₀₁	—	2	1	no	—
46	C₂²×C₈×C₁₀₁	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₁₀₁	D₄	1	1	yes	characteristic
48	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
49	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
50	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
51	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
52	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
53	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
54	C₄⋊Q₈×C₁₀₁	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₁₀₁	C₂³	1	2	yes	—
56	C₄×D₄×C₁₀₁	—	2	1	no	—
57	C₄×D₄×C₁₀₁	—	2	1	no	—
58	C₄×D₄×C₁₀₁	D₄	1	2	yes	—
59	C₄×D₄×C₁₀₁	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
66	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
67	#107×C₁₀₁	—	2	4	no	—
68	C₄⋊C₈×C₁₀₁	—	2	1	no	—
69	C₄⋊C₈×C₁₀₁	—	2	1	no	—
70	C₄⋊C₈×C₁₀₁	—	2	1	no	—
71	C₄⋊C₈×C₁₀₁	C₂³	1	2	yes	—
72	C₄⋊C₈×C₁₀₁	C₂³	1	2	yes	—
73	C₄⋊C₈×C₁₀₁	C₂³	1	2	yes	—
74	#103×C₁₀₁	—	2	4	no	—
75	#103×C₁₀₁	—	2	4	no	—
76	#103×C₁₀₁	—	2	4	no	—
77	#102×C₁₀₁	—	2	4	no	—
78	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
79	C₄×C₈×C₁₀₁	D₄	1	2	yes	—
80	C₄×C₈×C₁₀₁	C₂³	1	2	yes	—
81	C₂⁴×C₁₀₁	—	2	1	no	—
82	C₂×Q₈×C₁₀₁	—	2	2	no	—
83	C₂×Q₈×C₁₀₁	—	2	2	no	—
84	C₂×Q₈×C₁₀₁	—	4	1	no	—
85	C₂×Q₈×C₁₀₁	—	4	1	no	—
86	C₂×Q₈×C₁₀₁	—	4	2	no	—
87	C₂×Q₈×C₁₀₁	—	4	2	no	—
88	C₂×Q₈×C₁₀₁	—	4	2	no	—
89	C₂×Q₈×C₁₀₁	—	4	2	no	—
90	C₂×D₄×C₁₀₁	—	2	1	no	—
91	C₂×D₄×C₁₀₁	—	2	2	no	—
92	C₂×D₄×C₁₀₁	—	2	2	no	—
93	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₀₁	—	2	1	no	—
95	C₂²×C₄×C₁₀₁	—	2	2	no	—
96	C₂²×C₄×C₁₀₁	—	2	2	no	—
97	C₂²×C₄×C₁₀₁	—	4	2	no	—
98	C₂²×C₄×C₁₀₁	—	4	2	no	—
99	C₂²×C₄×C₁₀₁	—	4	1	no	—
100	C₂²×C₄×C₁₀₁	—	4	1	no	—
101	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₀₁	#41	1	1	yes	characteristic
104	SD₁₆×C₁₀₁	—	4	8	no	—
105	M₁₆×C₁₀₁	—	4	8	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	2	no	—
112	C₂×C₈×C₁₀₁	—	4	2	no	—
113	C₂×C₈×C₁₀₁	—	4	2	no	—
114	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
116	C₄⋊C₄×C₁₀₁	—	2	1	no	—
117	C₄⋊C₄×C₁₀₁	—	2	2	no	—
118	C₄⋊C₄×C₁₀₁	—	2	2	no	—
119	C₄⋊C₄×C₁₀₁	—	2	2	no	—
120	C₄⋊C₄×C₁₀₁	—	2	2	no	—
121	C₄⋊C₄×C₁₀₁	—	4	1	no	—
122	C₄⋊C₄×C₁₀₁	—	4	1	no	—
123	C₄⋊C₄×C₁₀₁	—	4	1	no	—
124	C₄⋊C₄×C₁₀₁	—	4	1	no	—
125	C₄⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	—
126	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
127	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
128	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₀₁	#41	1	1	yes	characteristic
131	C₄²×C₁₀₁	C₂⁴	1	1	yes	characteristic
132	C₂³×C₁₀₁	—	2	2	no	—
133	C₂³×C₁₀₁	—	4	2	no	—
134	C₂³×C₁₀₁	—	4	2	no	—
135	C₂³×C₁₀₁	—	4	2	no	—
136	C₂³×C₁₀₁	#121	1	1	yes	characteristic
137	Q₈×C₁₀₁	—	4	2	no	—
138	Q₈×C₁₀₁	—	4	2	no	—
139	Q₈×C₁₀₁	—	4	2	no	—
140	Q₈×C₁₀₁	—	4	2	no	—
141	Q₈×C₁₀₁	—	8	2	no	—
142	Q₈×C₁₀₁	—	8	2	no	—
143	D₄×C₁₀₁	—	2	2	no	—
144	D₄×C₁₀₁	—	2	2	no	—
145	D₄×C₁₀₁	—	4	2	no	—
146	C₂×C₄×C₁₀₁	—	2	2	no	—
147	C₂×C₄×C₁₀₁	—	2	2	no	—
148	C₂×C₄×C₁₀₁	—	4	2	no	—
149	C₂×C₄×C₁₀₁	—	4	2	no	—
150	C₂×C₄×C₁₀₁	—	4	2	no	—
151	C₂×C₄×C₁₀₁	—	4	4	no	—
152	C₂×C₄×C₁₀₁	—	4	2	no	—
153	C₂×C₄×C₁₀₁	—	4	2	no	—
154	C₂×C₄×C₁₀₁	—	8	2	no	—
155	C₂×C₄×C₁₀₁	—	8	2	no	—
156	C₂×C₄×C₁₀₁	#121	1	1	yes	characteristic
157	C₂×C₄×C₁₀₁	#121	1	1	yes	characteristic
158	C₂×C₄×C₁₀₁	#121	1	1	yes	characteristic
159	C₂×C₄×C₁₀₁	#135	1	2	yes	—
160	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
161	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
162	C₂×C₄×C₁₀₁	#137	1	2	yes	—
163	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₀₁	C₂×#41	1	1	yes	characteristic
166	C₈×C₁₀₁	—	2	2	no	—
167	C₈×C₁₀₁	—	2	2	no	—
168	C₈×C₁₀₁	—	4	2	no	—
169	C₈×C₁₀₁	—	4	2	no	—
170	C₈×C₁₀₁	—	4	2	no	—
171	C₂²×C₁₀₁	—	4	2	no	—
172	C₂²×C₁₀₁	—	4	2	no	—
173	C₂²×C₁₀₁	—	4	2	no	—
174	C₂²×C₁₀₁	—	8	4	no	—
175	C₂²×C₁₀₁	#463	1	2	yes	—
176	C₂²×C₁₀₁	#468	1	2	yes	—
177	C₂²×C₁₀₁	#473	1	2	yes	—
178	C₂²×C₁₀₁	C₂×#121	1	1	yes	characteristic
179	C₄×C₁₀₁	—	2	1	no	—
180	C₄×C₁₀₁	—	2	1	no	—
181	C₄×C₁₀₁	—	4	2	no	—
182	C₄×C₁₀₁	—	8	2	no	—
183	C₄×C₁₀₁	—	8	2	no	—
184	C₄×C₁₀₁	#463	1	2	yes	—
185	C₄×C₁₀₁	#468	1	2	yes	—
186	C₄×C₁₀₁	C₂×#135	1	1	yes	characteristic
187	C₄×C₁₀₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₄×C₁₀₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₄×C₁₀₁	C₂×#137	1	1	yes	characteristic
190	C₂×#1699	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂×C₁₀₁	—	8	2	no	—
192	C₂×C₁₀₁	#1699	1	4	yes	direct product factor
193	C₂×C₁₀₁	C₂×#463	1	1	yes	characteristic
194	C₂×C₁₀₁	C₂×#468	1	1	yes	characteristic
195	C₂×C₁₀₁	C₂×#473	1	1	yes	characteristic
196	C₂×#487	C₂×C₁₀₁	1	1	yes	characteristic, complemented
197	C₂×#474	C₂×C₁₀₁	1	1	yes	characteristic
198	C₂×#461	C₂×C₁₀₁	1	1	yes	characteristic
199	C₂×#436	C₂×C₁₀₁	1	1	yes	characteristic
200	#1699	C₂×C₁₀₁	1	8	yes	direct product factor
201	C₂×#335	C₂×C₁₀₁	1	1	yes	characteristic, complemented
202	C₂×#332	C₂×C₁₀₁	1	1	yes	characteristic, complemented
203	C₂×#332	C₂×C₁₀₁	1	1	yes	characteristic, complemented
204	C₁₀₁	C₂×#1699	1	1	yes	characteristic, direct product factor, Sylow
205	C₂²×SD₁₆	—	2	1	no	—
206	C₂²×M₁₆	—	2	1	no	—
207	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
208	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
209	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
210	#487	—	2	2	no	—
211	#487	C₂²×C₁₀₁	1	4	yes	complemented
212	#474	—	2	2	no	—
213	#474	C₂²×C₁₀₁	1	4	yes	—
214	#461	—	2	2	no	—
215	#461	C₂²×C₁₀₁	1	4	yes	—
216	#436	—	2	2	no	—
217	#436	C₂²×C₁₀₁	1	4	yes	—
218	C₂×#107	—	2	1	no	—
219	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
221	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
222	C₂×#103	—	2	1	no	—
223	C₂×#103	—	2	1	no	—
224	C₂×#103	—	2	1	no	—
225	C₂×#102	—	2	1	no	—
226	C₂×C₂²⋊C₈	—	2	1	no	—
227	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
228	#335	C₂²×C₁₀₁	1	4	yes	complemented
229	#332	C₂²×C₁₀₁	1	4	yes	complemented
230	#332	C₂²×C₁₀₁	1	4	yes	complemented
231	C₂²×Q₈	—	2	1	no	—
232	C₂²×Q₈	—	2	1	no	—
233	C₂²×D₄	D₄×C₁₀₁	1	1	yes	characteristic
234	C₂³×C₄	—	2	1	no	—
235	C₂×SD₁₆	—	2	4	no	—
236	C₂×SD₁₆	—	4	4	no	—
237	C₂×M₁₆	—	2	4	no	—
238	C₂×M₁₆	—	4	4	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	D₄×C₁₀₁	1	1	yes	characteristic
243	C₂²×C₈	D₄×C₁₀₁	1	1	yes	characteristic
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	1	no	—
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	C₂³×C₁₀₁	1	2	yes	—
251	C₄⋊Q₈	C₂³×C₁₀₁	1	2	yes	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	D₄×C₁₀₁	1	2	yes	—
255	C₄×D₄	C₂³×C₁₀₁	1	2	yes	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
261	C₂×C₂²⋊C₄	—	2	1	no	—
262	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
263	#107	—	2	4	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	C₂³×C₁₀₁	1	2	yes	—
268	C₄⋊C₈	C₂³×C₁₀₁	1	2	yes	—
269	C₄⋊C₈	C₂³×C₁₀₁	1	2	yes	—
270	#103	—	2	4	no	—
271	#103	—	2	4	no	—
272	#103	—	2	4	no	—
273	#102	—	2	4	no	—
274	C₂²⋊C₈	—	2	4	no	—
275	C₄×C₈	D₄×C₁₀₁	1	2	yes	—
276	C₄×C₈	C₂³×C₁₀₁	1	2	yes	—
277	C₂⁴	—	2	1	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	4	1	no	—
281	C₂×Q₈	—	4	1	no	—
282	C₂×Q₈	—	4	2	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×Q₈	—	4	2	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
299	C₂²×C₄	#41×C₁₀₁	1	1	yes	characteristic
300	SD₁₆	—	4	8	no	—
301	M₁₆	—	4	8	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	4	2	no	—
308	C₂×C₈	—	4	2	no	—
309	C₂×C₈	—	4	2	no	—
310	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
311	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
325	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
326	C₄²	#41×C₁₀₁	1	1	yes	characteristic
327	C₄²	C₂⁴×C₁₀₁	1	1	yes	characteristic
328	C₂³	—	2	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	#121×C₁₀₁	1	1	yes	characteristic
333	Q₈	—	4	2	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	4	2	no	—
336	Q₈	—	4	2	no	—
337	Q₈	—	8	2	no	—
338	Q₈	—	8	2	no	—
339	D₄	—	2	2	no	—
340	D₄	—	2	2	no	—
341	D₄	—	4	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	—	8	2	no	—
352	C₂×C₄	#121×C₁₀₁	1	1	yes	characteristic
353	C₂×C₄	#121×C₁₀₁	1	1	yes	characteristic
354	C₂×C₄	#121×C₁₀₁	1	1	yes	characteristic
355	C₂×C₄	#135×C₁₀₁	1	2	yes	—
356	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
357	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
358	C₂×C₄	#137×C₁₀₁	1	2	yes	—
359	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
361	C₂×C₄	C₂×#41×C₁₀₁	1	1	yes	characteristic
362	C₈	—	2	2	no	—
363	C₈	—	2	2	no	—
364	C₈	—	4	2	no	—
365	C₈	—	4	2	no	—
366	C₈	—	4	2	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	8	4	no	—
371	C₂²	#463×C₁₀₁	1	2	yes	—
372	C₂²	#468×C₁₀₁	1	2	yes	—
373	C₂²	#473×C₁₀₁	1	2	yes	—
374	C₂²	C₂×#121×C₁₀₁	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	8	2	no	—
379	C₄	—	8	2	no	—
380	C₄	#463×C₁₀₁	1	2	yes	—
381	C₄	#468×C₁₀₁	1	2	yes	—
382	C₄	C₂×#135×C₁₀₁	1	1	yes	characteristic
383	C₄	C₂×AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
384	C₄	C₂×AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
385	C₄	C₂×#137×C₁₀₁	1	1	yes	characteristic
386	C₂	—	8	2	no	—
387	C₂	C₁₀₁×#1699	1	4	yes	direct product factor
388	C₂	C₂×#463×C₁₀₁	1	1	yes	characteristic
389	C₂	C₂×#468×C₁₀₁	1	1	yes	characteristic
390	C₂	C₂×#473×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₁	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₁
prime radical	C₂²×D₄×C₁₀₁	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#487×C₁₀₁	C₂	semidirect
5. C₁₀₁×#1699	C₂	direct (N × H)
6. C₂×#335×C₁₀₁	C₂	semidirect
7. C₂×#332×C₁₀₁	C₂	semidirect
8. C₂×#332×C₁₀₁	C₂	semidirect
15. #487×C₁₀₁	C₂²	semidirect
32. #335×C₁₀₁	C₂²	semidirect
33. #332×C₁₀₁	C₂²	semidirect
34. #332×C₁₀₁	C₂²	semidirect
190. C₂×#1699	C₁₀₁	direct (N × H)
192. C₂×C₁₀₁	#1699	direct (N × H)
196. C₂×#487	C₂×C₁₀₁	semidirect
200. #1699	C₂×C₁₀₁	direct (N × H)
201. C₂×#335	C₂×C₁₀₁	semidirect
202. C₂×#332	C₂×C₁₀₁	semidirect
203. C₂×#332	C₂×C₁₀₁	semidirect
204. C₁₀₁	C₂×#1699	direct (N × H)
211. #487	C₂²×C₁₀₁	semidirect
228. #335	C₂²×C₁₀₁	semidirect
229. #332	C₂²×C₁₀₁	semidirect
230. #332	C₂²×C₁₀₁	semidirect
387. C₂	C₁₀₁×#1699	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#487×C₁₀₁	2
C₂×#474×C₁₀₁	2
C₂×#461×C₁₀₁	2
C₂×#436×C₁₀₁	2
C₁₀₁×#1699	2
C₂×#335×C₁₀₁	2
C₂×#332×C₁₀₁	2
C₂×#1699	101

Subgroups — C2×C101×#1699 #38801290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₁×#1699 #38801290