Subgroups — C₁₀₁×#19674 #38801825

Order 25856.

786 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₁×#3226	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₁×#3169	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#3152	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#3141	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#487×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₁×#1723	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#1720	C₂	1	2	yes	maximal, complemented
9	C₁₀₁×#1719	C₂	1	2	yes	maximal, complemented
10	C₁₀₁×#1717	C₂	1	2	yes	maximal, complemented
11	C₁₀₁×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₁₀₁	—	2	2	no	—
13	#532×C₁₀₁	C₂²	1	1	yes	characteristic
14	#532×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
17	#500×C₁₀₁	C₂²	1	1	yes	characteristic
18	#500×C₁₀₁	C₂²	1	2	yes	—
19	#498×C₁₀₁	C₂²	1	2	yes	—
20	#497×C₁₀₁	—	2	2	no	—
21	#494×C₁₀₁	C₂²	1	2	yes	—
22	#493×C₁₀₁	C₂²	1	1	yes	characteristic
23	#492×C₁₀₁	C₂²	1	2	yes	—
24	#489×C₁₀₁	—	2	2	no	—
25	#487×C₁₀₁	—	2	2	no	—
26	#487×C₁₀₁	C₂²	1	2	yes	—
27	#487×C₁₀₁	C₂²	1	2	yes	—
28	#487×C₁₀₁	C₂²	1	2	yes	—
29	#486×C₁₀₁	C₂²	1	1	yes	characteristic
30	#486×C₁₀₁	C₂²	1	1	yes	characteristic
31	#486×C₁₀₁	C₂²	1	2	yes	—
32	#486×C₁₀₁	C₂²	1	2	yes	—
33	#486×C₁₀₁	C₂²	1	2	yes	—
34	#481×C₁₀₁	—	2	2	no	—
35	#480×C₁₀₁	—	2	2	no	—
36	#476×C₁₀₁	—	2	2	no	—
37	#474×C₁₀₁	—	2	2	no	—
38	#466×C₁₀₁	—	2	2	no	—
39	C₄×D₈×C₁₀₁	—	2	2	no	—
40	#431×C₁₀₁	C₂²	1	1	yes	characteristic
41	#417×C₁₀₁	—	2	2	no	—
42	C₂×#103×C₁₀₁	—	2	2	no	—
43	C₄×M₁₆×C₁₀₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
45	#322×C₁₀₁	C₂²	1	2	yes	—
46	#322×C₁₀₁	C₂²	1	2	yes	—
47	C₂×#41×C₁₀₁	—	2	1	no	—
48	C₂×#41×C₁₀₁	—	2	1	no	—
49	C₂²×Q₈×C₁₀₁	—	2	1	no	—
50	C₂²×Q₈×C₁₀₁	—	2	1	no	—
51	#137×C₁₀₁	—	4	8	no	—
52	C₂×Q₁₆×C₁₀₁	—	2	4	no	—
53	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
54	C₂×D₈×C₁₀₁	—	2	2	no	—
55	C₂×M₁₆×C₁₀₁	D₄	1	2	yes	—
56	C₂²×C₈×C₁₀₁	D₄	1	2	yes	—
57	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
58	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
59	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
60	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
61	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
62	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
63	C₄⋊Q₈×C₁₀₁	C₂³	1	2	yes	—
64	C₄⋊Q₈×C₁₀₁	C₂³	1	2	yes	—
65	C₄⋊Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
66	C₄⋊Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
67	#127×C₁₀₁	C₂³	1	1	yes	characteristic
68	#127×C₁₀₁	C₂³	1	1	yes	characteristic
69	#124×C₁₀₁	—	2	1	no	—
70	#124×C₁₀₁	—	2	1	no	—
71	#121×C₁₀₁	—	2	1	no	—
72	#121×C₁₀₁	—	2	1	no	—
73	#121×C₁₀₁	—	2	1	no	—
74	#121×C₁₀₁	—	2	1	no	—
75	C₄×D₄×C₁₀₁	—	2	1	no	—
76	C₄×D₄×C₁₀₁	—	2	1	no	—
77	C₄×D₄×C₁₀₁	—	2	1	no	—
78	C₄×D₄×C₁₀₁	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
83	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
84	#107×C₁₀₁	—	2	2	no	—
85	#107×C₁₀₁	—	2	4	no	—
86	#106×C₁₀₁	—	2	4	no	—
87	C₄⋊C₈×C₁₀₁	D₄	1	2	yes	—
88	#103×C₁₀₁	—	2	4	no	—
89	#103×C₁₀₁	—	2	4	no	—
90	#103×C₁₀₁	—	2	4	no	—
91	#102×C₁₀₁	—	2	4	no	—
92	#102×C₁₀₁	—	2	2	no	—
93	#102×C₁₀₁	—	2	2	no	—
94	#102×C₁₀₁	—	2	4	no	—
95	#102×C₁₀₁	—	2	4	no	—
96	C₂²⋊C₈×C₁₀₁	D₄	1	2	yes	—
97	#97×C₁₀₁	D₄	1	2	yes	—
98	C₄×C₈×C₁₀₁	D₄	1	2	yes	—
99	C₄×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₁₀₁	C₂³	1	2	yes	—
102	C₄×C₈×C₁₀₁	C₂³	1	2	yes	—
103	#41×C₁₀₁	—	4	4	no	—
104	#41×C₁₀₁	—	4	4	no	—
105	C₂×Q₈×C₁₀₁	—	2	1	no	—
106	C₂×Q₈×C₁₀₁	—	2	2	no	—
107	C₂×Q₈×C₁₀₁	—	2	1	no	—
108	C₂×Q₈×C₁₀₁	—	2	2	no	—
109	C₂×Q₈×C₁₀₁	—	4	4	no	—
110	C₂×Q₈×C₁₀₁	—	4	1	no	—
111	C₂×Q₈×C₁₀₁	—	4	1	no	—
112	C₂×Q₈×C₁₀₁	—	4	4	no	—
113	C₂×D₄×C₁₀₁	—	2	1	no	—
114	C₂×D₄×C₁₀₁	—	2	1	no	—
115	C₂×D₄×C₁₀₁	—	2	1	no	—
116	C₂×D₄×C₁₀₁	—	2	1	no	—
117	C₂×D₄×C₁₀₁	—	2	1	no	—
118	C₂×D₄×C₁₀₁	—	2	1	no	—
119	C₂×D₄×C₁₀₁	—	4	1	no	—
120	C₂×D₄×C₁₀₁	—	4	1	no	—
121	C₂²×C₄×C₁₀₁	—	4	1	no	—
122	C₂²×C₄×C₁₀₁	—	4	1	no	—
123	C₂²×C₄×C₁₀₁	—	4	1	no	—
124	C₂²×C₄×C₁₀₁	—	4	1	no	—
125	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
128	Q₁₆×C₁₀₁	—	4	8	no	—
129	SD₁₆×C₁₀₁	—	4	8	no	—
130	D₈×C₁₀₁	—	4	4	no	—
131	M₁₆×C₁₀₁	—	2	4	no	—
132	C₂×C₈×C₁₀₁	—	4	2	no	—
133	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₁₀₁	C₂×D₄	1	4	yes	—
136	C₂×C₈×C₁₀₁	C₂×D₄	1	4	yes	—
137	C₄⋊C₄×C₁₀₁	—	2	2	no	—
138	C₄⋊C₄×C₁₀₁	—	2	2	no	—
139	C₄⋊C₄×C₁₀₁	—	2	2	no	—
140	C₄⋊C₄×C₁₀₁	—	2	1	no	—
141	C₄⋊C₄×C₁₀₁	—	2	1	no	—
142	C₄⋊C₄×C₁₀₁	—	2	2	no	—
143	C₄⋊C₄×C₁₀₁	—	2	1	no	—
144	C₄⋊C₄×C₁₀₁	—	2	1	no	—
145	C₄⋊C₄×C₁₀₁	—	4	1	no	—
146	C₄⋊C₄×C₁₀₁	—	4	1	no	—
147	C₄⋊C₄×C₁₀₁	—	4	1	no	—
148	C₄⋊C₄×C₁₀₁	—	4	1	no	—
149	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
150	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
151	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
152	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
153	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₀₁	C₂⁴	1	1	yes	characteristic
157	C₂³×C₁₀₁	—	4	1	no	—
158	C₂³×C₁₀₁	—	4	1	no	—
159	C₂³×C₁₀₁	#127	1	1	yes	characteristic
160	Q₈×C₁₀₁	—	4	4	no	—
161	Q₈×C₁₀₁	—	4	2	no	—
162	Q₈×C₁₀₁	—	4	2	no	—
163	Q₈×C₁₀₁	—	4	4	no	—
164	Q₈×C₁₀₁	—	8	2	no	—
165	Q₈×C₁₀₁	—	8	2	no	—
166	D₄×C₁₀₁	—	4	2	no	—
167	D₄×C₁₀₁	—	4	2	no	—
168	D₄×C₁₀₁	—	4	2	no	—
169	D₄×C₁₀₁	—	4	2	no	—
170	D₄×C₁₀₁	—	4	2	no	—
171	D₄×C₁₀₁	—	4	2	no	—
172	D₄×C₁₀₁	—	8	2	no	—
173	D₄×C₁₀₁	—	8	2	no	—
174	C₂×C₄×C₁₀₁	—	2	2	no	—
175	C₂×C₄×C₁₀₁	—	2	2	no	—
176	C₂×C₄×C₁₀₁	—	4	1	no	—
177	C₂×C₄×C₁₀₁	—	4	1	no	—
178	C₂×C₄×C₁₀₁	—	4	2	no	—
179	C₂×C₄×C₁₀₁	—	4	2	no	—
180	C₂×C₄×C₁₀₁	—	8	2	no	—
181	C₂×C₄×C₁₀₁	—	8	2	no	—
182	C₂×C₄×C₁₀₁	—	8	2	no	—
183	C₂×C₄×C₁₀₁	—	8	2	no	—
184	C₂×C₄×C₁₀₁	#127	1	1	yes	characteristic
185	C₂×C₄×C₁₀₁	#127	1	1	yes	characteristic
186	C₂×C₄×C₁₀₁	#127	1	1	yes	characteristic
187	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	4	yes	—
188	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
191	C₈×C₁₀₁	—	2	4	no	—
192	C₈×C₁₀₁	—	2	2	no	—
193	C₈×C₁₀₁	—	2	2	no	—
194	C₈×C₁₀₁	—	2	4	no	—
195	C₂²×C₁₀₁	—	2	1	no	—
196	C₂²×C₁₀₁	—	2	1	no	—
197	C₂²×C₁₀₁	—	8	1	no	—
198	C₂²×C₁₀₁	—	8	1	no	—
199	C₂²×C₁₀₁	—	8	1	no	—
200	C₂²×C₁₀₁	—	8	1	no	—
201	C₂²×C₁₀₁	—	8	1	no	—
202	C₂²×C₁₀₁	—	8	1	no	—
203	C₂²×C₁₀₁	#496	1	2	yes	—
204	C₂²×C₁₀₁	C₂×#127	1	1	yes	characteristic
205	C₄×C₁₀₁	—	2	1	no	—
206	C₄×C₁₀₁	—	2	1	no	—
207	C₄×C₁₀₁	—	8	1	no	—
208	C₄×C₁₀₁	—	8	1	no	—
209	C₄×C₁₀₁	—	8	2	no	—
210	C₄×C₁₀₁	—	8	2	no	—
211	C₄×C₁₀₁	#496	1	2	yes	—
212	C₄×C₁₀₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
213	C₄×C₁₀₁	#575	1	2	yes	—
214	C₄×C₁₀₁	#578	1	2	yes	—
215	#19674	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂×C₁₀₁	—	2	2	no	—
217	C₂×C₁₀₁	—	16	1	no	—
218	C₂×C₁₀₁	—	16	1	no	—
219	C₂×C₁₀₁	C₂×#496	1	1	yes	characteristic
220	C₂×C₁₀₁	#3153	1	1	yes	characteristic
221	C₂×C₁₀₁	#3156	1	1	yes	characteristic
222	#3227	C₂×C₁₀₁	1	1	yes	characteristic, complemented
223	#3226	C₂×C₁₀₁	1	1	yes	characteristic, complemented
224	#3169	C₂×C₁₀₁	1	1	yes	characteristic
225	#3152	C₂×C₁₀₁	1	1	yes	characteristic, complemented
226	#3141	C₂×C₁₀₁	1	1	yes	characteristic, complemented
227	C₂×#487	C₂×C₁₀₁	1	1	yes	characteristic, complemented
228	#1723	C₂×C₁₀₁	1	2	yes	complemented
229	#1720	C₂×C₁₀₁	1	2	yes	complemented
230	#1719	C₂×C₁₀₁	1	2	yes	complemented
231	#1717	C₂×C₁₀₁	1	2	yes	complemented
232	#1451	C₂×C₁₀₁	1	1	yes	characteristic, complemented
233	C₁₀₁	#19674	1	1	yes	characteristic, direct product factor, Sylow
234	C₂×#137	—	2	2	no	—
235	#532	C₂²×C₁₀₁	1	1	yes	characteristic
236	#532	C₂²×C₁₀₁	1	1	yes	characteristic
237	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
238	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
239	#500	C₂²×C₁₀₁	1	1	yes	characteristic
240	#500	C₂²×C₁₀₁	1	2	yes	—
241	#498	C₂²×C₁₀₁	1	2	yes	—
242	#497	—	2	2	no	—
243	#494	C₂²×C₁₀₁	1	2	yes	—
244	#493	C₂²×C₁₀₁	1	1	yes	characteristic
245	#492	C₂²×C₁₀₁	1	2	yes	—
246	#489	—	2	2	no	—
247	#487	—	2	2	no	—
248	#487	C₂²×C₁₀₁	1	2	yes	—
249	#487	C₂²×C₁₀₁	1	2	yes	—
250	#487	C₂²×C₁₀₁	1	2	yes	—
251	#486	C₂²×C₁₀₁	1	2	yes	—
252	#486	C₂²×C₁₀₁	1	1	yes	characteristic
253	#486	C₂²×C₁₀₁	1	1	yes	characteristic
254	#486	C₂²×C₁₀₁	1	2	yes	—
255	#486	C₂²×C₁₀₁	1	2	yes	—
256	#481	—	2	2	no	—
257	#480	—	2	2	no	—
258	#476	—	2	2	no	—
259	#474	—	2	2	no	—
260	#466	—	2	2	no	—
261	C₄×D₈	—	2	2	no	—
262	#431	C₂²×C₁₀₁	1	1	yes	characteristic
263	#417	—	2	2	no	—
264	C₂×#103	—	2	2	no	—
265	C₄×M₁₆	C₂²×C₁₀₁	1	1	yes	characteristic
266	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
267	#322	C₂²×C₁₀₁	1	2	yes	—
268	#322	C₂²×C₁₀₁	1	2	yes	—
269	C₂×#41	—	2	1	no	—
270	C₂×#41	—	2	1	no	—
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×Q₈	—	2	1	no	—
273	#137	—	4	8	no	—
274	C₂×Q₁₆	—	2	4	no	—
275	C₂×SD₁₆	—	2	4	no	—
276	C₂×D₈	—	2	2	no	—
277	C₂×M₁₆	D₄×C₁₀₁	1	2	yes	—
278	C₂²×C₈	D₄×C₁₀₁	1	2	yes	—
279	C₄⋊Q₈	—	2	1	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	C₂³×C₁₀₁	1	2	yes	—
286	C₄⋊Q₈	C₂³×C₁₀₁	1	2	yes	—
287	C₄⋊Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
288	C₄⋊Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
289	#127	C₂³×C₁₀₁	1	1	yes	characteristic
290	#127	C₂³×C₁₀₁	1	1	yes	characteristic
291	#124	—	2	1	no	—
292	#124	—	2	1	no	—
293	#121	—	2	1	no	—
294	#121	—	2	1	no	—
295	#121	—	2	1	no	—
296	#121	—	2	1	no	—
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
306	#107	—	2	2	no	—
307	#107	—	2	4	no	—
308	#106	—	2	4	no	—
309	C₄⋊C₈	D₄×C₁₀₁	1	2	yes	—
310	#103	—	2	4	no	—
311	#103	—	2	4	no	—
312	#103	—	2	4	no	—
313	#102	—	2	4	no	—
314	#102	—	2	2	no	—
315	#102	—	2	2	no	—
316	#102	—	2	4	no	—
317	#102	—	2	4	no	—
318	C₂²⋊C₈	D₄×C₁₀₁	1	2	yes	—
319	#97	D₄×C₁₀₁	1	2	yes	—
320	C₄×C₈	D₄×C₁₀₁	1	2	yes	—
321	C₄×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
322	C₄×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
323	C₄×C₈	C₂³×C₁₀₁	1	2	yes	—
324	C₄×C₈	C₂³×C₁₀₁	1	2	yes	—
325	#41	—	4	4	no	—
326	#41	—	4	4	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	4	4	no	—
332	C₂×Q₈	—	4	1	no	—
333	C₂×Q₈	—	4	1	no	—
334	C₂×Q₈	—	4	4	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	4	1	no	—
342	C₂×D₄	—	4	1	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
350	Q₁₆	—	4	8	no	—
351	SD₁₆	—	4	8	no	—
352	D₈	—	4	4	no	—
353	M₁₆	—	2	4	no	—
354	C₂×C₈	—	4	2	no	—
355	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
356	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
357	C₂×C₈	C₂×D₄×C₁₀₁	1	4	yes	—
358	C₂×C₈	C₂×D₄×C₁₀₁	1	4	yes	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	4	1	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₂²⋊C₄	—	4	1	no	—
372	C₂²⋊C₄	—	4	1	no	—
373	C₂²⋊C₄	—	4	1	no	—
374	C₂²⋊C₄	—	4	1	no	—
375	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
376	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
377	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
378	C₄²	C₂⁴×C₁₀₁	1	1	yes	characteristic
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	#127×C₁₀₁	1	1	yes	characteristic
382	Q₈	—	4	4	no	—
383	Q₈	—	4	2	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	4	4	no	—
386	Q₈	—	8	2	no	—
387	Q₈	—	8	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	8	2	no	—
395	D₄	—	8	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	8	2	no	—
403	C₂×C₄	—	8	2	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	#127×C₁₀₁	1	1	yes	characteristic
407	C₂×C₄	#127×C₁₀₁	1	1	yes	characteristic
408	C₂×C₄	#127×C₁₀₁	1	1	yes	characteristic
409	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	4	yes	—
410	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
413	C₈	—	2	4	no	—
414	C₈	—	2	2	no	—
415	C₈	—	2	2	no	—
416	C₈	—	2	4	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	#496×C₁₀₁	1	2	yes	—
426	C₂²	C₂×#127×C₁₀₁	1	1	yes	characteristic
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	8	1	no	—
430	C₄	—	8	1	no	—
431	C₄	—	8	2	no	—
432	C₄	—	8	2	no	—
433	C₄	#496×C₁₀₁	1	2	yes	—
434	C₄	C₂×AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
435	C₄	#575×C₁₀₁	1	2	yes	—
436	C₄	#578×C₁₀₁	1	2	yes	—
437	C₂	—	2	2	no	—
438	C₂	—	16	1	no	—
439	C₂	—	16	1	no	—
440	C₂	C₂×#496×C₁₀₁	1	1	yes	characteristic
441	C₂	C₁₀₁×#3153	1	1	yes	characteristic
442	C₂	C₁₀₁×#3156	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₁
prime radical	C₁₀₁×#3169	C₂
LCS	G ▷ C₄² ▷ 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
1. C₁₀₁×#3227	C₂	semidirect
2. C₁₀₁×#3226	C₂	semidirect
4. C₁₀₁×#3152	C₂	semidirect
5. C₁₀₁×#3141	C₂	semidirect
6. C₂×#487×C₁₀₁	C₂	semidirect
7. C₁₀₁×#1723	C₂	semidirect
8. C₁₀₁×#1720	C₂	semidirect
9. C₁₀₁×#1719	C₂	semidirect
10. C₁₀₁×#1717	C₂	semidirect
11. C₁₀₁×#1451	C₂	semidirect
215. #19674	C₁₀₁	direct (N × H)
222. #3227	C₂×C₁₀₁	semidirect
223. #3226	C₂×C₁₀₁	semidirect
225. #3152	C₂×C₁₀₁	semidirect
226. #3141	C₂×C₁₀₁	semidirect
227. C₂×#487	C₂×C₁₀₁	semidirect
228. #1723	C₂×C₁₀₁	semidirect
229. #1720	C₂×C₁₀₁	semidirect
230. #1719	C₂×C₁₀₁	semidirect
231. #1717	C₂×C₁₀₁	semidirect
232. #1451	C₂×C₁₀₁	semidirect
233. C₁₀₁	#19674	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×#3227	2
C₁₀₁×#3226	2
C₁₀₁×#3169	2
C₁₀₁×#3152	2
C₁₀₁×#3141	2
C₂×#487×C₁₀₁	2
C₁₀₁×#1723	2
C₁₀₁×#1720	2
C₁₀₁×#1719	2
C₁₀₁×#1717	2
C₁₀₁×#1451	2
#19674	101

Subgroups — C101×#19674 #38801825

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#19674 #38801825