Subgroups — C₁₀₁×#19697 #38801848

Order 25856.

820 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3229	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₁×#3226	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#3205	C₂	1	1	yes	maximal, characteristic
5	C₂×#492×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₁×#3131	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₁×#1719	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#1717	C₂	1	2	yes	maximal, complemented
9	C₁₀₁×#1715	C₂	1	2	yes	maximal, complemented
10	C₁₀₁×#1714	C₂	1	2	yes	maximal, complemented
11	C₁₀₁×#1452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₀₁	—	2	2	no	—
13	#533×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×#127×C₁₀₁	C₂²	1	1	yes	characteristic
17	#500×C₁₀₁	C₂²	1	2	yes	complemented
18	#498×C₁₀₁	C₂²	1	2	yes	complemented
19	#493×C₁₀₁	C₂²	1	2	yes	—
20	#492×C₁₀₁	—	2	2	no	—
21	#492×C₁₀₁	C₂²	1	2	yes	—
22	#492×C₁₀₁	C₂²	1	2	yes	—
23	#492×C₁₀₁	C₂²	1	2	yes	—
24	#488×C₁₀₁	—	2	2	no	—
25	#487×C₁₀₁	C₂²	1	2	yes	complemented
26	#487×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
27	#487×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
28	#486×C₁₀₁	C₂²	1	2	yes	—
29	#486×C₁₀₁	C₂²	1	2	yes	—
30	#486×C₁₀₁	C₂²	1	2	yes	complemented
31	#486×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
32	#486×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
33	#483×C₁₀₁	—	2	2	no	—
34	#480×C₁₀₁	—	2	2	no	—
35	#475×C₁₀₁	—	2	2	no	—
36	#474×C₁₀₁	—	2	2	no	—
37	#460×C₁₀₁	—	2	2	no	—
38	#459×C₁₀₁	—	2	2	no	—
39	#450×C₁₀₁	—	2	2	no	—
40	#447×C₁₀₁	—	2	2	no	—
41	#431×C₁₀₁	C₂²	1	1	yes	characteristic
42	#431×C₁₀₁	C₂²	1	1	yes	characteristic
43	#416×C₁₀₁	—	2	2	no	—
44	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
45	#322×C₁₀₁	C₂²	1	2	yes	complemented
46	#322×C₁₀₁	C₂²	1	2	yes	complemented
47	C₂×#41×C₁₀₁	—	2	1	no	—
48	C₂²×Q₈×C₁₀₁	—	2	1	no	—
49	C₂²×D₄×C₁₀₁	—	2	1	no	—
50	C₂²×D₄×C₁₀₁	—	2	1	no	—
51	C₂²×D₄×C₁₀₁	—	2	1	no	—
52	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
53	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
54	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
55	C₂×SD₁₆×C₁₀₁	—	4	8	no	—
56	C₂×D₈×C₁₀₁	—	2	4	no	—
57	C₂²×C₈×C₁₀₁	D₄	1	2	yes	—
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	C₂³	1	1	yes	characteristic
62	C₄⋊Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
63	C₄⋊Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₁₀₁	C₂³	1	2	yes	—
65	#127×C₁₀₁	—	2	1	no	—
66	#127×C₁₀₁	—	2	1	no	—
67	#127×C₁₀₁	—	2	1	no	—
68	#127×C₁₀₁	C₂³	1	2	yes	—
69	#127×C₁₀₁	C₂³	1	1	yes	characteristic
70	#125×C₁₀₁	—	2	1	no	—
71	#124×C₁₀₁	—	2	1	no	—
72	C₂²⋊Q₈×C₁₀₁	—	2	1	no	—
73	C₂²⋊Q₈×C₁₀₁	—	2	1	no	—
74	#121×C₁₀₁	—	2	1	no	—
75	#121×C₁₀₁	—	2	1	no	—
76	C₄×Q₈×C₁₀₁	—	2	1	no	—
77	C₄×Q₈×C₁₀₁	—	2	1	no	—
78	C₄×D₄×C₁₀₁	—	2	1	no	—
79	C₄×D₄×C₁₀₁	—	2	1	no	—
80	#117×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	4	no	—
85	#106×C₁₀₁	—	2	4	no	—
86	C₄⋊C₈×C₁₀₁	D₄	1	2	yes	—
87	C₄⋊C₈×C₁₀₁	D₄	1	2	yes	—
88	#103×C₁₀₁	—	2	2	no	—
89	#103×C₁₀₁	—	2	2	no	—
90	#103×C₁₀₁	—	2	4	no	—
91	#102×C₁₀₁	—	2	2	no	—
92	#102×C₁₀₁	—	2	2	no	—
93	#102×C₁₀₁	—	2	4	no	—
94	#102×C₁₀₁	—	2	4	no	—
95	#102×C₁₀₁	—	2	4	no	—
96	C₂²⋊C₈×C₁₀₁	D₄	1	2	yes	—
97	C₂²⋊C₈×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	C₂⁴×C₁₀₁	—	4	1	no	—
104	#41×C₁₀₁	—	4	4	no	—
105	C₂×Q₈×C₁₀₁	—	2	1	no	—
106	C₂×Q₈×C₁₀₁	—	2	1	no	—
107	C₂×Q₈×C₁₀₁	—	2	1	no	—
108	C₂×Q₈×C₁₀₁	—	2	2	no	—
109	C₂×Q₈×C₁₀₁	—	4	1	no	—
110	C₂×Q₈×C₁₀₁	—	4	4	no	—
111	C₂×D₄×C₁₀₁	—	2	1	no	—
112	C₂×D₄×C₁₀₁	—	2	1	no	—
113	C₂×D₄×C₁₀₁	—	2	2	no	—
114	C₂×D₄×C₁₀₁	—	2	2	no	—
115	C₂×D₄×C₁₀₁	—	2	1	no	—
116	C₂×D₄×C₁₀₁	—	2	2	no	—
117	C₂×D₄×C₁₀₁	—	4	1	no	—
118	C₂×D₄×C₁₀₁	—	4	1	no	—
119	C₂×D₄×C₁₀₁	—	4	1	no	—
120	C₂×D₄×C₁₀₁	—	4	1	no	—
121	C₂×D₄×C₁₀₁	—	4	4	no	—
122	C₂×D₄×C₁₀₁	—	8	2	no	—
123	C₂×D₄×C₁₀₁	—	8	2	no	—
124	C₂²×C₄×C₁₀₁	—	4	1	no	—
125	C₂²×C₄×C₁₀₁	—	4	1	no	—
126	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
129	SD₁₆×C₁₀₁	—	4	8	no	—
130	SD₁₆×C₁₀₁	—	4	8	no	—
131	SD₁₆×C₁₀₁	—	8	4	no	—
132	D₈×C₁₀₁	—	8	4	no	—
133	C₂×C₈×C₁₀₁	—	2	4	no	—
134	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₁₀₁	C₂×D₄	1	4	yes	—
137	C₂×C₈×C₁₀₁	C₂×D₄	1	4	yes	—
138	C₄⋊C₄×C₁₀₁	—	2	1	no	—
139	C₄⋊C₄×C₁₀₁	—	2	1	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	2	no	—
144	C₄⋊C₄×C₁₀₁	—	2	1	no	—
145	C₄⋊C₄×C₁₀₁	—	2	1	no	—
146	C₄⋊C₄×C₁₀₁	—	4	1	no	—
147	C₄⋊C₄×C₁₀₁	—	4	1	no	—
148	C₄⋊C₄×C₁₀₁	—	4	1	no	—
149	C₄⋊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	—	4	1	no	—
154	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₁₀₁	C₂⁴	1	1	yes	characteristic
158	C₂³×C₁₀₁	—	4	1	no	—
159	C₂³×C₁₀₁	—	4	2	no	—
160	C₂³×C₁₀₁	—	8	2	no	—
161	C₂³×C₁₀₁	—	8	2	no	—
162	C₂³×C₁₀₁	—	8	2	no	—
163	C₂³×C₁₀₁	#127	1	1	yes	characteristic
164	Q₈×C₁₀₁	—	4	4	no	—
165	Q₈×C₁₀₁	—	4	2	no	—
166	Q₈×C₁₀₁	—	4	2	no	—
167	Q₈×C₁₀₁	—	4	2	no	—
168	Q₈×C₁₀₁	—	8	2	no	—
169	D₄×C₁₀₁	—	4	4	no	—
170	D₄×C₁₀₁	—	4	2	no	—
171	D₄×C₁₀₁	—	4	2	no	—
172	D₄×C₁₀₁	—	4	4	no	—
173	D₄×C₁₀₁	—	4	4	no	—
174	D₄×C₁₀₁	—	4	2	no	—
175	D₄×C₁₀₁	—	8	2	no	—
176	D₄×C₁₀₁	—	8	2	no	—
177	D₄×C₁₀₁	—	8	2	no	—
178	D₄×C₁₀₁	—	8	2	no	—
179	C₂×C₄×C₁₀₁	—	2	2	no	—
180	C₂×C₄×C₁₀₁	—	2	2	no	—
181	C₂×C₄×C₁₀₁	—	4	1	no	—
182	C₂×C₄×C₁₀₁	—	4	1	no	—
183	C₂×C₄×C₁₀₁	—	4	1	no	—
184	C₂×C₄×C₁₀₁	—	4	2	no	—
185	C₂×C₄×C₁₀₁	—	8	2	no	—
186	C₂×C₄×C₁₀₁	—	8	2	no	—
187	C₂×C₄×C₁₀₁	#127	1	1	yes	characteristic
188	C₂×C₄×C₁₀₁	#127	1	1	yes	characteristic
189	C₂×C₄×C₁₀₁	#127	1	1	yes	characteristic
190	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	4	yes	—
191	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
194	C₈×C₁₀₁	—	2	2	no	—
195	C₈×C₁₀₁	—	2	2	no	—
196	C₈×C₁₀₁	—	2	4	no	—
197	C₈×C₁₀₁	—	2	4	no	—
198	C₂²×C₁₀₁	—	2	1	no	—
199	C₂²×C₁₀₁	—	2	1	no	—
200	C₂²×C₁₀₁	—	8	1	no	—
201	C₂²×C₁₀₁	—	8	2	no	—
202	C₂²×C₁₀₁	—	8	2	no	—
203	C₂²×C₁₀₁	—	8	2	no	—
204	C₂²×C₁₀₁	—	8	1	no	—
205	C₂²×C₁₀₁	—	8	1	no	—
206	C₂²×C₁₀₁	—	16	4	no	—
207	C₂²×C₁₀₁	#496	1	2	yes	—
208	C₂²×C₁₀₁	C₂×#127	1	1	yes	characteristic
209	C₄×C₁₀₁	—	2	1	no	—
210	C₄×C₁₀₁	—	2	1	no	—
211	C₄×C₁₀₁	—	8	1	no	—
212	C₄×C₁₀₁	—	8	2	no	—
213	C₄×C₁₀₁	—	8	1	no	—
214	C₄×C₁₀₁	—	8	1	no	—
215	C₄×C₁₀₁	#496	1	2	yes	—
216	C₄×C₁₀₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
217	C₄×C₁₀₁	#577	1	2	yes	—
218	C₄×C₁₀₁	#577	1	2	yes	—
219	#19697	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂×C₁₀₁	—	2	2	no	—
221	C₂×C₁₀₁	—	16	1	no	—
222	C₂×C₁₀₁	—	16	2	no	—
223	C₂×C₁₀₁	C₂×#496	1	1	yes	characteristic
224	C₂×C₁₀₁	#3154	1	1	yes	characteristic
225	C₂×C₁₀₁	#3154	1	1	yes	characteristic
226	#3229	C₂×C₁₀₁	1	1	yes	characteristic, complemented
227	#3226	C₂×C₁₀₁	1	1	yes	characteristic, complemented
228	#3208	C₂×C₁₀₁	1	1	yes	characteristic, complemented
229	#3205	C₂×C₁₀₁	1	1	yes	characteristic
230	C₂×#492	C₂×C₁₀₁	1	1	yes	characteristic, complemented
231	#3131	C₂×C₁₀₁	1	1	yes	characteristic, complemented
232	#1719	C₂×C₁₀₁	1	2	yes	complemented
233	#1717	C₂×C₁₀₁	1	2	yes	complemented
234	#1715	C₂×C₁₀₁	1	2	yes	complemented
235	#1714	C₂×C₁₀₁	1	2	yes	complemented
236	#1452	C₂×C₁₀₁	1	1	yes	characteristic, complemented
237	C₁₀₁	#19697	1	1	yes	characteristic, direct product factor, Sylow
238	C₂²×SD₁₆	—	2	2	no	—
239	#533	C₂²×C₁₀₁	1	1	yes	characteristic
240	#532	C₂²×C₁₀₁	1	1	yes	characteristic
241	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
242	C₂×#127	C₂²×C₁₀₁	1	1	yes	characteristic
243	#500	C₂²×C₁₀₁	1	2	yes	complemented
244	#498	C₂²×C₁₀₁	1	2	yes	complemented
245	#493	C₂²×C₁₀₁	1	2	yes	—
246	#492	—	2	2	no	—
247	#492	C₂²×C₁₀₁	1	2	yes	—
248	#492	C₂²×C₁₀₁	1	2	yes	—
249	#492	C₂²×C₁₀₁	1	2	yes	—
250	#488	—	2	2	no	—
251	#487	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
252	#487	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
253	#487	C₂²×C₁₀₁	1	2	yes	complemented
254	#486	C₂²×C₁₀₁	1	2	yes	—
255	#486	C₂²×C₁₀₁	1	2	yes	—
256	#486	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
257	#486	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
258	#486	C₂²×C₁₀₁	1	2	yes	complemented
259	#483	—	2	2	no	—
260	#480	—	2	2	no	—
261	#475	—	2	2	no	—
262	#474	—	2	2	no	—
263	#460	—	2	2	no	—
264	#459	—	2	2	no	—
265	#450	—	2	2	no	—
266	#447	—	2	2	no	—
267	#431	C₂²×C₁₀₁	1	1	yes	characteristic
268	#431	C₂²×C₁₀₁	1	1	yes	characteristic
269	#416	—	2	2	no	—
270	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
271	#322	C₂²×C₁₀₁	1	2	yes	complemented
272	#322	C₂²×C₁₀₁	1	2	yes	complemented
273	C₂×#41	—	2	1	no	—
274	C₂²×Q₈	—	2	1	no	—
275	C₂²×D₄	—	2	1	no	—
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	—	2	1	no	—
278	C₂×SD₁₆	—	2	4	no	—
279	C₂×SD₁₆	—	2	4	no	—
280	C₂×SD₁₆	—	2	4	no	—
281	C₂×SD₁₆	—	4	8	no	—
282	C₂×D₈	—	2	4	no	—
283	C₂²×C₈	D₄×C₁₀₁	1	2	yes	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	C₂³×C₁₀₁	1	2	yes	—
288	C₄⋊Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
289	C₄⋊Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
290	C₄⋊Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
291	#127	—	2	1	no	—
292	#127	—	2	1	no	—
293	#127	—	2	1	no	—
294	#127	C₂³×C₁₀₁	1	2	yes	—
295	#127	C₂³×C₁₀₁	1	1	yes	characteristic
296	#125	—	2	1	no	—
297	#124	—	2	1	no	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₂²⋊Q₈	—	2	1	no	—
300	#121	—	2	1	no	—
301	#121	—	2	1	no	—
302	C₄×Q₈	—	2	1	no	—
303	C₄×Q₈	—	2	1	no	—
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	—	2	1	no	—
306	#117	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
310	#107	—	2	4	no	—
311	#106	—	2	4	no	—
312	C₄⋊C₈	D₄×C₁₀₁	1	2	yes	—
313	C₄⋊C₈	D₄×C₁₀₁	1	2	yes	—
314	#103	—	2	2	no	—
315	#103	—	2	2	no	—
316	#103	—	2	4	no	—
317	#102	—	2	2	no	—
318	#102	—	2	2	no	—
319	#102	—	2	4	no	—
320	#102	—	2	4	no	—
321	#102	—	2	4	no	—
322	C₂²⋊C₈	D₄×C₁₀₁	1	2	yes	—
323	C₂²⋊C₈	D₄×C₁₀₁	1	2	yes	—
324	C₄×C₈	D₄×C₁₀₁	1	2	yes	—
325	C₄×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
326	C₄×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
327	C₄×C₈	C₂³×C₁₀₁	1	2	yes	—
328	C₄×C₈	C₂³×C₁₀₁	1	2	yes	—
329	C₂⁴	—	4	1	no	—
330	#41	—	4	4	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	4	1	no	—
336	C₂×Q₈	—	4	4	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	—	4	1	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂×D₄	—	4	1	no	—
347	C₂×D₄	—	4	4	no	—
348	C₂×D₄	—	8	2	no	—
349	C₂×D₄	—	8	2	no	—
350	C₂²×C₄	—	4	1	no	—
351	C₂²×C₄	—	4	1	no	—
352	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
355	SD₁₆	—	4	8	no	—
356	SD₁₆	—	4	8	no	—
357	SD₁₆	—	8	4	no	—
358	D₈	—	8	4	no	—
359	C₂×C₈	—	2	4	no	—
360	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
361	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
362	C₂×C₈	C₂×D₄×C₁₀₁	1	4	yes	—
363	C₂×C₈	C₂×D₄×C₁₀₁	1	4	yes	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	4	1	no	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₂²⋊C₄	—	4	1	no	—
378	C₂²⋊C₄	—	4	1	no	—
379	C₄²	—	4	1	no	—
380	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
381	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
382	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
383	C₄²	C₂⁴×C₁₀₁	1	1	yes	characteristic
384	C₂³	—	4	1	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	8	2	no	—
387	C₂³	—	8	2	no	—
388	C₂³	—	8	2	no	—
389	C₂³	#127×C₁₀₁	1	1	yes	characteristic
390	Q₈	—	4	4	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	—	8	2	no	—
395	D₄	—	4	4	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	4	no	—
399	D₄	—	4	4	no	—
400	D₄	—	4	2	no	—
401	D₄	—	8	2	no	—
402	D₄	—	8	2	no	—
403	D₄	—	8	2	no	—
404	D₄	—	8	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	8	2	no	—
412	C₂×C₄	—	8	2	no	—
413	C₂×C₄	#127×C₁₀₁	1	1	yes	characteristic
414	C₂×C₄	#127×C₁₀₁	1	1	yes	characteristic
415	C₂×C₄	#127×C₁₀₁	1	1	yes	characteristic
416	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	4	yes	—
417	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
418	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
419	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
420	C₈	—	2	2	no	—
421	C₈	—	2	2	no	—
422	C₈	—	2	4	no	—
423	C₈	—	2	4	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	16	4	no	—
433	C₂²	#496×C₁₀₁	1	2	yes	—
434	C₂²	C₂×#127×C₁₀₁	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	8	1	no	—
438	C₄	—	8	2	no	—
439	C₄	—	8	1	no	—
440	C₄	—	8	1	no	—
441	C₄	#496×C₁₀₁	1	2	yes	—
442	C₄	C₂×AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
443	C₄	#577×C₁₀₁	1	2	yes	—
444	C₄	#577×C₁₀₁	1	2	yes	—
445	C₂	—	2	2	no	—
446	C₂	—	16	2	no	—
447	C₂	—	16	1	no	—
448	C₂	C₂×#496×C₁₀₁	1	1	yes	characteristic
449	C₂	C₁₀₁×#3154	1	1	yes	characteristic
450	C₂	C₁₀₁×#3154	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₁
prime radical	C₁₀₁×#3205	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×#3229	C₂	semidirect
2. C₁₀₁×#3226	C₂	semidirect
3. C₁₀₁×#3208	C₂	semidirect
5. C₂×#492×C₁₀₁	C₂	semidirect
6. C₁₀₁×#3131	C₂	semidirect
7. C₁₀₁×#1719	C₂	semidirect
8. C₁₀₁×#1717	C₂	semidirect
9. C₁₀₁×#1715	C₂	semidirect
10. C₁₀₁×#1714	C₂	semidirect
11. C₁₀₁×#1452	C₂	semidirect
17. #500×C₁₀₁	C₂²	semidirect
18. #498×C₁₀₁	C₂²	semidirect
25. #487×C₁₀₁	C₂²	semidirect
26. #487×C₁₀₁	C₂²	semidirect
27. #487×C₁₀₁	C₂²	semidirect
30. #486×C₁₀₁	C₂²	semidirect
31. #486×C₁₀₁	C₂²	semidirect
32. #486×C₁₀₁	C₂²	semidirect
45. #322×C₁₀₁	C₂²	semidirect
46. #322×C₁₀₁	C₂²	semidirect
219. #19697	C₁₀₁	direct (N × H)
226. #3229	C₂×C₁₀₁	semidirect
227. #3226	C₂×C₁₀₁	semidirect
228. #3208	C₂×C₁₀₁	semidirect
230. C₂×#492	C₂×C₁₀₁	semidirect
231. #3131	C₂×C₁₀₁	semidirect
232. #1719	C₂×C₁₀₁	semidirect
233. #1717	C₂×C₁₀₁	semidirect
234. #1715	C₂×C₁₀₁	semidirect
235. #1714	C₂×C₁₀₁	semidirect
236. #1452	C₂×C₁₀₁	semidirect
237. C₁₀₁	#19697	direct (N × H)
243. #500	C₂²×C₁₀₁	semidirect
244. #498	C₂²×C₁₀₁	semidirect
251. #487	C₂²×C₁₀₁	semidirect
252. #487	C₂²×C₁₀₁	semidirect
253. #487	C₂²×C₁₀₁	semidirect
256. #486	C₂²×C₁₀₁	semidirect
257. #486	C₂²×C₁₀₁	semidirect
258. #486	C₂²×C₁₀₁	semidirect
271. #322	C₂²×C₁₀₁	semidirect
272. #322	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×#3229	2
C₁₀₁×#3226	2
C₁₀₁×#3208	2
C₁₀₁×#3205	2
C₂×#492×C₁₀₁	2
C₁₀₁×#3131	2
C₁₀₁×#1719	2
C₁₀₁×#1717	2
C₁₀₁×#1715	2
C₁₀₁×#1714	2
C₁₀₁×#1452	2
#19697	101

Subgroups — C101×#19697 #38801848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#19697 #38801848