Subgroups — C₁₀₁×#18395 #38800546

Order 25856.

1290 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3496	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#3227	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#2542	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#1613	C₂	1	8	yes	maximal, complemented
5	C₁₀₁×#1502	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1460	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×H(5,𝔽₂)×C₁₀₁	—	2	1	no	—
8	#547×C₁₀₁	—	2	2	no	—
9	#546×C₁₀₁	—	2	4	no	—
10	D₄²×C₁₀₁	—	2	2	no	—
11	#537×C₁₀₁	—	2	1	no	—
12	#534×C₁₀₁	C₂²	1	4	yes	—
13	#532×C₁₀₁	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
16	C₂×#121×C₁₀₁	—	2	2	no	—
17	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
18	#498×C₁₀₁	—	2	2	no	—
19	#486×C₁₀₁	—	2	2	no	—
20	#481×C₁₀₁	C₂²	1	8	yes	complemented
21	#476×C₁₀₁	—	2	4	no	—
22	#431×C₁₀₁	C₂²	1	2	yes	complemented
23	#399×C₁₀₁	C₂²	1	4	yes	complemented
24	#390×C₁₀₁	—	2	1	no	—
25	#384×C₁₀₁	—	2	1	no	—
26	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
27	#327×C₁₀₁	C₂²	1	8	yes	complemented
28	#323×C₁₀₁	C₂²	1	4	yes	complemented
29	H(5,𝔽₂)×C₁₀₁	—	4	4	no	—
30	H(5,𝔽₂)×C₁₀₁	—	4	4	no	—
31	C₂×#41×C₁₀₁	—	2	4	no	—
32	C₂×#41×C₁₀₁	—	2	2	no	—
33	C₂²×Q₈×C₁₀₁	—	2	1	no	—
34	C₂²×D₄×C₁₀₁	—	2	4	no	—
35	C₂²×D₄×C₁₀₁	—	2	4	no	—
36	C₂²×D₄×C₁₀₁	—	2	2	no	—
37	C₂²×D₄×C₁₀₁	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
39	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
40	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
41	C₄⋊Q₈×C₁₀₁	D₄	1	2	yes	—
42	#127×C₁₀₁	D₄	1	2	yes	—
43	#124×C₁₀₁	—	2	2	no	—
44	#123×C₁₀₁	—	2	8	no	—
45	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
46	C₂²⋊Q₈×C₁₀₁	—	4	8	no	—
47	#121×C₁₀₁	—	2	4	no	—
48	#121×C₁₀₁	—	2	4	no	—
49	#121×C₁₀₁	—	2	4	no	—
50	#121×C₁₀₁	—	2	2	no	—
51	#121×C₁₀₁	—	2	4	no	—
52	#121×C₁₀₁	C₂³	1	4	yes	—
53	#120×C₁₀₁	—	2	8	no	—
54	C₄×D₄×C₁₀₁	—	2	2	no	—
55	C₄×D₄×C₁₀₁	—	2	2	no	—
56	C₄×D₄×C₁₀₁	—	2	2	no	—
57	C₄×D₄×C₁₀₁	D₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
61	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
67	C₂×C₄²×C₁₀₁	—	2	1	no	—
68	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
69	#106×C₁₀₁	—	2	8	no	—
70	C₄⋊C₈×C₁₀₁	—	2	2	no	—
71	#102×C₁₀₁	—	2	8	no	—
72	C₂²⋊C₈×C₁₀₁	C₂³	1	4	yes	—
73	C₄×C₈×C₁₀₁	—	2	2	no	—
74	#95×C₁₀₁	C₂³	1	2	yes	—
75	C₂⁴×C₁₀₁	—	2	4	no	—
76	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
77	#41×C₁₀₁	—	4	16	no	—
78	#41×C₁₀₁	—	4	4	no	—
79	#41×C₁₀₁	—	4	4	no	—
80	C₂×Q₈×C₁₀₁	—	2	2	no	—
81	C₂×Q₈×C₁₀₁	—	4	4	no	—
82	C₂×Q₈×C₁₀₁	—	4	1	no	—
83	C₂×Q₈×C₁₀₁	—	4	1	no	—
84	C₂×D₄×C₁₀₁	—	2	8	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	—	2	2	no	—
89	C₂×D₄×C₁₀₁	—	2	2	no	—
90	C₂×D₄×C₁₀₁	—	2	2	no	—
91	C₂×D₄×C₁₀₁	—	4	16	no	—
92	C₂×D₄×C₁₀₁	—	4	8	no	—
93	C₂×D₄×C₁₀₁	—	4	8	no	—
94	C₂×D₄×C₁₀₁	—	8	4	no	—
95	C₂×D₄×C₁₀₁	SD₁₆	1	4	yes	—
96	C₂×D₄×C₁₀₁	C₂×D₄	1	4	yes	—
97	C₂²×C₄×C₁₀₁	—	2	4	no	—
98	C₂²×C₄×C₁₀₁	—	2	2	no	—
99	C₂²×C₄×C₁₀₁	—	2	2	no	—
100	C₂²×C₄×C₁₀₁	—	2	4	no	—
101	C₂²×C₄×C₁₀₁	—	2	2	no	—
102	C₂²×C₄×C₁₀₁	—	2	2	no	—
103	C₂²×C₄×C₁₀₁	—	4	4	no	—
104	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
108	C₂×C₈×C₁₀₁	—	2	4	no	—
109	C₄⋊C₄×C₁₀₁	—	2	4	no	—
110	C₄⋊C₄×C₁₀₁	—	2	4	no	—
111	C₄⋊C₄×C₁₀₁	—	2	2	no	—
112	C₄⋊C₄×C₁₀₁	—	2	2	no	—
113	C₄⋊C₄×C₁₀₁	—	2	4	no	—
114	C₄⋊C₄×C₁₀₁	—	4	8	no	—
115	C₄⋊C₄×C₁₀₁	—	4	2	no	—
116	C₄⋊C₄×C₁₀₁	C₂×D₄	1	4	yes	—
117	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
118	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
119	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
120	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
121	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
122	C₄²×C₁₀₁	—	4	2	no	—
123	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
124	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
125	C₂³×C₁₀₁	—	2	2	no	—
126	C₂³×C₁₀₁	—	2	2	no	—
127	C₂³×C₁₀₁	—	2	4	no	—
128	C₂³×C₁₀₁	—	4	2	no	—
129	C₂³×C₁₀₁	—	4	2	no	—
130	C₂³×C₁₀₁	—	4	8	no	—
131	C₂³×C₁₀₁	—	8	4	no	—
132	C₂³×C₁₀₁	—	8	4	no	—
133	C₂³×C₁₀₁	C₂×SD₁₆	1	4	yes	—
134	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
135	Q₈×C₁₀₁	—	4	4	no	—
136	Q₈×C₁₀₁	—	8	2	no	—
137	Q₈×C₁₀₁	—	8	2	no	—
138	D₄×C₁₀₁	—	2	8	no	—
139	D₄×C₁₀₁	—	4	4	no	—
140	D₄×C₁₀₁	—	4	16	no	—
141	D₄×C₁₀₁	—	4	4	no	—
142	D₄×C₁₀₁	—	4	4	no	—
143	D₄×C₁₀₁	—	4	4	no	—
144	D₄×C₁₀₁	—	4	4	no	—
145	D₄×C₁₀₁	—	8	4	no	—
146	C₂×C₄×C₁₀₁	—	2	2	no	—
147	C₂×C₄×C₁₀₁	—	2	4	no	—
148	C₂×C₄×C₁₀₁	—	2	2	no	—
149	C₂×C₄×C₁₀₁	—	2	4	no	—
150	C₂×C₄×C₁₀₁	—	4	1	no	—
151	C₂×C₄×C₁₀₁	—	4	2	no	—
152	C₂×C₄×C₁₀₁	—	4	8	no	—
153	C₂×C₄×C₁₀₁	—	4	2	no	—
154	C₂×C₄×C₁₀₁	—	4	8	no	—
155	C₂×C₄×C₁₀₁	—	4	4	no	—
156	C₂×C₄×C₁₀₁	—	4	2	no	—
157	C₂×C₄×C₁₀₁	—	4	4	no	—
158	C₂×C₄×C₁₀₁	—	4	2	no	—
159	C₂×C₄×C₁₀₁	—	8	2	no	—
160	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
161	C₂×C₄×C₁₀₁	#120	1	2	yes	—
162	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
163	C₂×C₄×C₁₀₁	C₂×SD₁₆	1	2	yes	—
164	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
165	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
166	C₈×C₁₀₁	—	4	4	no	—
167	C₂²×C₁₀₁	—	2	1	no	—
168	C₂²×C₁₀₁	—	2	1	no	—
169	C₂²×C₁₀₁	—	2	4	no	—
170	C₂²×C₁₀₁	—	4	4	no	—
171	C₂²×C₁₀₁	—	4	2	no	—
172	C₂²×C₁₀₁	—	4	2	no	—
173	C₂²×C₁₀₁	—	4	4	no	—
174	C₂²×C₁₀₁	—	4	4	no	—
175	C₂²×C₁₀₁	—	4	4	no	—
176	C₂²×C₁₀₁	—	8	2	no	—
177	C₂²×C₁₀₁	—	16	8	no	—
178	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
179	C₂²×C₁₀₁	C₂²×SD₁₆	1	1	yes	characteristic
180	C₂²×C₁₀₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
181	C₄×C₁₀₁	—	2	1	no	—
182	C₄×C₁₀₁	—	2	2	no	—
183	C₄×C₁₀₁	—	4	4	no	—
184	C₄×C₁₀₁	—	4	4	no	—
185	C₄×C₁₀₁	—	4	2	no	—
186	C₄×C₁₀₁	—	8	2	no	—
187	C₄×C₁₀₁	#450	1	4	yes	—
188	C₄×C₁₀₁	#453	1	2	yes	—
189	#18395	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂×C₁₀₁	—	2	1	no	—
191	C₂×C₁₀₁	—	2	1	no	—
192	C₂×C₁₀₁	—	4	4	no	—
193	C₂×C₁₀₁	—	8	4	no	—
194	C₂×C₁₀₁	C₂×#450	1	1	yes	characteristic
195	C₂×C₁₀₁	C₂×#453	1	1	yes	characteristic
196	C₂×C₁₀₁	#3028	1	1	yes	characteristic
197	#3496	C₂×C₁₀₁	1	1	yes	characteristic
198	#3227	C₂×C₁₀₁	1	2	yes	complemented
199	#2542	C₂×C₁₀₁	1	1	yes	characteristic, complemented
200	#1613	C₂×C₁₀₁	1	8	yes	complemented
201	#1502	C₂×C₁₀₁	1	2	yes	complemented
202	#1460	C₂×C₁₀₁	1	1	yes	characteristic, complemented
203	C₁₀₁	#18395	1	1	yes	characteristic, direct product factor, Sylow
204	C₂×H(5,𝔽₂)	—	2	1	no	—
205	#547	—	2	2	no	—
206	#546	—	2	4	no	—
207	D₄²	—	2	2	no	—
208	#537	—	2	1	no	—
209	#534	C₂²×C₁₀₁	1	4	yes	—
210	#532	C₂²×C₁₀₁	1	2	yes	—
211	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
212	C₂×C₂²⋊Q₈	—	2	2	no	—
213	C₂×#121	—	2	2	no	—
214	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
215	#498	—	2	2	no	—
216	#486	—	2	2	no	—
217	#481	C₂²×C₁₀₁	1	8	yes	complemented
218	#476	—	2	4	no	—
219	#431	C₂²×C₁₀₁	1	2	yes	complemented
220	#399	C₂²×C₁₀₁	1	4	yes	complemented
221	#390	—	2	1	no	—
222	#384	—	2	1	no	—
223	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
224	#327	C₂²×C₁₀₁	1	8	yes	complemented
225	#323	C₂²×C₁₀₁	1	4	yes	complemented
226	H(5,𝔽₂)	—	4	4	no	—
227	H(5,𝔽₂)	—	4	4	no	—
228	C₂×#41	—	2	4	no	—
229	C₂×#41	—	2	2	no	—
230	C₂²×Q₈	—	2	1	no	—
231	C₂²×D₄	—	2	4	no	—
232	C₂²×D₄	—	2	4	no	—
233	C₂²×D₄	—	2	2	no	—
234	C₂²×D₄	D₄×C₁₀₁	1	1	yes	characteristic
235	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
236	C₄⋊Q₈	—	2	2	no	—
237	C₄⋊Q₈	—	2	2	no	—
238	C₄⋊Q₈	D₄×C₁₀₁	1	2	yes	—
239	#127	D₄×C₁₀₁	1	2	yes	—
240	#124	—	2	2	no	—
241	#123	—	2	8	no	—
242	C₂²⋊Q₈	—	2	4	no	—
243	C₂²⋊Q₈	—	4	8	no	—
244	#121	—	2	4	no	—
245	#121	—	2	4	no	—
246	#121	—	2	4	no	—
247	#121	—	2	2	no	—
248	#121	—	2	4	no	—
249	#121	C₂³×C₁₀₁	1	4	yes	—
250	#120	—	2	8	no	—
251	C₄×D₄	—	2	2	no	—
252	C₄×D₄	—	2	2	no	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	D₄×C₁₀₁	1	4	yes	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	4	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
261	C₂×C₂²⋊C₄	—	2	4	no	—
262	C₂×C₂²⋊C₄	—	2	4	no	—
263	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	2	yes	—
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
266	#106	—	2	8	no	—
267	C₄⋊C₈	—	2	2	no	—
268	#102	—	2	8	no	—
269	C₂²⋊C₈	C₂³×C₁₀₁	1	4	yes	—
270	C₄×C₈	—	2	2	no	—
271	#95	C₂³×C₁₀₁	1	2	yes	—
272	C₂⁴	—	2	4	no	—
273	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
274	#41	—	4	16	no	—
275	#41	—	4	4	no	—
276	#41	—	4	4	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	4	4	no	—
279	C₂×Q₈	—	4	1	no	—
280	C₂×Q₈	—	4	1	no	—
281	C₂×D₄	—	2	8	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	2	4	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	4	16	no	—
289	C₂×D₄	—	4	8	no	—
290	C₂×D₄	—	4	8	no	—
291	C₂×D₄	—	8	4	no	—
292	C₂×D₄	SD₁₆×C₁₀₁	1	4	yes	—
293	C₂×D₄	C₂×D₄×C₁₀₁	1	4	yes	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	4	4	no	—
301	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
304	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
305	C₂×C₈	—	2	4	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	4	8	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	C₂×D₄×C₁₀₁	1	4	yes	—
314	C₂²⋊C₄	—	2	8	no	—
315	C₂²⋊C₄	—	2	4	no	—
316	C₂²⋊C₄	—	2	4	no	—
317	C₂²⋊C₄	—	2	4	no	—
318	C₂²⋊C₄	—	4	8	no	—
319	C₄²	—	4	2	no	—
320	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
321	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
322	C₂³	—	2	2	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	2	4	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	8	no	—
328	C₂³	—	8	4	no	—
329	C₂³	—	8	4	no	—
330	C₂³	C₂×SD₁₆×C₁₀₁	1	4	yes	—
331	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
332	Q₈	—	4	4	no	—
333	Q₈	—	8	2	no	—
334	Q₈	—	8	2	no	—
335	D₄	—	2	8	no	—
336	D₄	—	4	4	no	—
337	D₄	—	4	16	no	—
338	D₄	—	4	4	no	—
339	D₄	—	4	4	no	—
340	D₄	—	4	4	no	—
341	D₄	—	4	4	no	—
342	D₄	—	8	4	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	8	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	8	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	8	2	no	—
357	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
358	C₂×C₄	#120×C₁₀₁	1	2	yes	—
359	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
360	C₂×C₄	C₂×SD₁₆×C₁₀₁	1	2	yes	—
361	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
362	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
363	C₈	—	4	4	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	4	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	4	no	—
371	C₂²	—	4	4	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	16	8	no	—
375	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
376	C₂²	C₂²×SD₁₆×C₁₀₁	1	1	yes	characteristic
377	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
378	C₄	—	2	1	no	—
379	C₄	—	2	2	no	—
380	C₄	—	4	4	no	—
381	C₄	—	4	4	no	—
382	C₄	—	4	2	no	—
383	C₄	—	8	2	no	—
384	C₄	#450×C₁₀₁	1	4	yes	—
385	C₄	#453×C₁₀₁	1	2	yes	—
386	C₂	—	2	1	no	—
387	C₂	—	2	1	no	—
388	C₂	—	4	4	no	—
389	C₂	—	8	4	no	—
390	C₂	C₂×#450×C₁₀₁	1	1	yes	characteristic
391	C₂	C₂×#453×C₁₀₁	1	1	yes	characteristic
392	C₂	C₁₀₁×#3028	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₁₀₁×#3496	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₁×#3227	C₂	semidirect
3. C₁₀₁×#2542	C₂	semidirect
4. C₁₀₁×#1613	C₂	semidirect
5. C₁₀₁×#1502	C₂	semidirect
6. C₁₀₁×#1460	C₂	semidirect
14. C₂×C₄⋊Q₈×C₁₀₁	C₂²	semidirect
20. #481×C₁₀₁	C₂²	semidirect
22. #431×C₁₀₁	C₂²	semidirect
23. #399×C₁₀₁	C₂²	semidirect
26. C₄×C₄⋊C₄×C₁₀₁	C₂²	semidirect
27. #327×C₁₀₁	C₂²	semidirect
28. #323×C₁₀₁	C₂²	semidirect
189. #18395	C₁₀₁	direct (N × H)
198. #3227	C₂×C₁₀₁	semidirect
199. #2542	C₂×C₁₀₁	semidirect
200. #1613	C₂×C₁₀₁	semidirect
201. #1502	C₂×C₁₀₁	semidirect
202. #1460	C₂×C₁₀₁	semidirect
203. C₁₀₁	#18395	direct (N × H)
211. C₂×C₄⋊Q₈	C₂²×C₁₀₁	semidirect
217. #481	C₂²×C₁₀₁	semidirect
219. #431	C₂²×C₁₀₁	semidirect
220. #399	C₂²×C₁₀₁	semidirect
223. C₄×C₄⋊C₄	C₂²×C₁₀₁	semidirect
224. #327	C₂²×C₁₀₁	semidirect
225. #323	C₂²×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₁×#3496	2
C₁₀₁×#3227	2
C₁₀₁×#2542	2
C₁₀₁×#1613	2
C₁₀₁×#1502	2
C₁₀₁×#1460	2
#18395	101

Subgroups — C101×#18395 #38800546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#18395 #38800546