Subgroups — C₁₀₁×#18363 #38800514

Order 25856.

1202 conjugacy classes of subgroups.

The subgroup lattice has 398 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×#3234	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#2633	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#1613	C₂	1	4	yes	maximal, complemented
5	C₁₀₁×#1607	C₂	1	4	yes	maximal, complemented
6	C₁₀₁×#1514	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1466	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×H(5,𝔽₂)×C₁₀₁	—	2	1	no	—
9	#547×C₁₀₁	—	2	2	no	—
10	#546×C₁₀₁	—	2	4	no	—
11	D₄²×C₁₀₁	—	2	2	no	—
12	#537×C₁₀₁	—	2	1	no	—
13	#534×C₁₀₁	C₂²	1	4	yes	—
14	#532×C₁₀₁	C₂²	1	2	yes	—
15	C₂×#125×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
16	C₂×#121×C₁₀₁	—	2	2	no	—
17	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
18	#501×C₁₀₁	—	2	2	no	—
19	#490×C₁₀₁	—	2	2	no	—
20	#481×C₁₀₁	C₂²	1	4	yes	complemented
21	#480×C₁₀₁	C₂²	1	4	yes	complemented
22	#478×C₁₀₁	—	2	4	no	—
23	#432×C₁₀₁	C₂²	1	2	yes	complemented
24	#399×C₁₀₁	C₂²	1	2	yes	complemented
25	#398×C₁₀₁	—	2	1	no	—
26	#397×C₁₀₁	C₂²	1	2	yes	complemented
27	#394×C₁₀₁	—	2	1	no	—
28	#385×C₁₀₁	—	2	2	no	—
29	#383×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
30	#327×C₁₀₁	C₂²	1	8	yes	complemented
31	#323×C₁₀₁	C₂²	1	4	yes	complemented
32	H(5,𝔽₂)×C₁₀₁	—	4	8	no	—
33	C₂×#41×C₁₀₁	—	2	4	no	—
34	C₂×#41×C₁₀₁	—	2	2	no	—
35	C₂²×D₄×C₁₀₁	—	2	4	no	—
36	C₂²×D₄×C₁₀₁	—	2	4	no	—
37	C₂²×D₄×C₁₀₁	—	2	2	no	—
38	C₂²×D₄×C₁₀₁	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
40	C₄⋊Q₈×C₁₀₁	D₄	1	2	yes	—
41	#127×C₁₀₁	D₄	1	2	yes	—
42	#125×C₁₀₁	—	2	2	no	—
43	#125×C₁₀₁	—	2	2	no	—
44	#124×C₁₀₁	—	2	2	no	—
45	#123×C₁₀₁	—	2	8	no	—
46	C₂²⋊Q₈×C₁₀₁	—	2	4	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	1	no	—
61	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
70	#107×C₁₀₁	—	2	4	no	—
71	#106×C₁₀₁	—	2	4	no	—
72	C₄⋊C₈×C₁₀₁	—	2	2	no	—
73	#102×C₁₀₁	—	2	4	no	—
74	#102×C₁₀₁	—	2	4	no	—
75	C₂²⋊C₈×C₁₀₁	C₂³	1	4	yes	—
76	#97×C₁₀₁	—	2	2	no	—
77	#95×C₁₀₁	—	2	2	no	—
78	#95×C₁₀₁	—	2	1	no	—
79	#95×C₁₀₁	—	2	1	no	—
80	#95×C₁₀₁	C₂³	1	2	yes	—
81	C₂⁴×C₁₀₁	—	2	4	no	—
82	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
83	#41×C₁₀₁	—	4	8	no	—
84	#41×C₁₀₁	—	4	16	no	—
85	C₂×Q₈×C₁₀₁	—	2	2	no	—
86	C₂×D₄×C₁₀₁	—	2	4	no	—
87	C₂×D₄×C₁₀₁	—	2	8	no	—
88	C₂×D₄×C₁₀₁	—	2	4	no	—
89	C₂×D₄×C₁₀₁	—	2	4	no	—
90	C₂×D₄×C₁₀₁	—	2	2	no	—
91	C₂×D₄×C₁₀₁	—	2	2	no	—
92	C₂×D₄×C₁₀₁	—	2	2	no	—
93	C₂×D₄×C₁₀₁	—	4	16	no	—
94	C₂×D₄×C₁₀₁	—	4	8	no	—
95	C₂×D₄×C₁₀₁	—	4	8	no	—
96	C₂×D₄×C₁₀₁	—	8	4	no	—
97	C₂×D₄×C₁₀₁	C₂×D₄	1	4	yes	—
98	C₂²×C₄×C₁₀₁	—	2	4	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	—	2	1	no	—
104	C₂²×C₄×C₁₀₁	—	2	1	no	—
105	C₂²×C₄×C₁₀₁	—	8	2	no	—
106	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
110	C₂×C₈×C₁₀₁	—	2	4	no	—
111	C₄⋊C₄×C₁₀₁	—	2	4	no	—
112	C₄⋊C₄×C₁₀₁	—	2	2	no	—
113	C₄⋊C₄×C₁₀₁	—	2	2	no	—
114	C₄⋊C₄×C₁₀₁	—	2	2	no	—
115	C₄⋊C₄×C₁₀₁	—	2	2	no	—
116	C₄⋊C₄×C₁₀₁	—	4	1	no	—
117	C₄⋊C₄×C₁₀₁	—	4	1	no	—
118	C₄⋊C₄×C₁₀₁	—	4	2	no	—
119	C₄⋊C₄×C₁₀₁	—	8	2	no	—
120	C₄⋊C₄×C₁₀₁	C₂×D₄	1	4	yes	—
121	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
122	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
123	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
124	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
125	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
126	C₂²⋊C₄×C₁₀₁	—	8	2	no	—
127	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
128	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
129	C₂³×C₁₀₁	—	2	2	no	—
130	C₂³×C₁₀₁	—	2	2	no	—
131	C₂³×C₁₀₁	—	2	4	no	—
132	C₂³×C₁₀₁	—	4	2	no	—
133	C₂³×C₁₀₁	—	4	2	no	—
134	C₂³×C₁₀₁	—	4	8	no	—
135	C₂³×C₁₀₁	—	8	4	no	—
136	C₂³×C₁₀₁	—	8	4	no	—
137	C₂³×C₁₀₁	AGL(1,ℤ/8)	1	4	yes	—
138	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₁₀₁	—	4	4	no	—
140	D₄×C₁₀₁	—	2	8	no	—
141	D₄×C₁₀₁	—	4	4	no	—
142	D₄×C₁₀₁	—	4	4	no	—
143	D₄×C₁₀₁	—	4	4	no	—
144	D₄×C₁₀₁	—	4	16	no	—
145	D₄×C₁₀₁	—	4	8	no	—
146	D₄×C₁₀₁	—	8	4	no	—
147	C₂×C₄×C₁₀₁	—	2	2	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	1	no	—
152	C₂×C₄×C₁₀₁	—	4	4	no	—
153	C₂×C₄×C₁₀₁	—	4	8	no	—
154	C₂×C₄×C₁₀₁	—	4	8	no	—
155	C₂×C₄×C₁₀₁	—	4	2	no	—
156	C₂×C₄×C₁₀₁	—	4	1	no	—
157	C₂×C₄×C₁₀₁	—	4	2	no	—
158	C₂×C₄×C₁₀₁	—	4	1	no	—
159	C₂×C₄×C₁₀₁	—	4	2	no	—
160	C₂×C₄×C₁₀₁	—	4	1	no	—
161	C₂×C₄×C₁₀₁	—	4	1	no	—
162	C₂×C₄×C₁₀₁	—	4	2	no	—
163	C₂×C₄×C₁₀₁	—	4	2	no	—
164	C₂×C₄×C₁₀₁	—	8	2	no	—
165	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
166	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
167	C₂×C₄×C₁₀₁	#120	1	2	yes	—
168	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
169	C₈×C₁₀₁	—	4	4	no	—
170	C₂²×C₁₀₁	—	2	1	no	—
171	C₂²×C₁₀₁	—	2	1	no	—
172	C₂²×C₁₀₁	—	2	4	no	—
173	C₂²×C₁₀₁	—	4	4	no	—
174	C₂²×C₁₀₁	—	4	2	no	—
175	C₂²×C₁₀₁	—	4	2	no	—
176	C₂²×C₁₀₁	—	4	4	no	—
177	C₂²×C₁₀₁	—	4	4	no	—
178	C₂²×C₁₀₁	—	4	4	no	—
179	C₂²×C₁₀₁	—	8	2	no	—
180	C₂²×C₁₀₁	—	16	8	no	—
181	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
182	C₂²×C₁₀₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
183	C₄×C₁₀₁	—	2	2	no	—
184	C₄×C₁₀₁	—	2	1	no	—
185	C₄×C₁₀₁	—	2	1	no	—
186	C₄×C₁₀₁	—	2	2	no	—
187	C₄×C₁₀₁	—	4	4	no	—
188	C₄×C₁₀₁	—	4	2	no	—
189	C₄×C₁₀₁	—	8	2	no	—
190	C₄×C₁₀₁	—	8	1	no	—
191	C₄×C₁₀₁	—	8	1	no	—
192	#18363	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂×C₁₀₁	—	2	2	no	—
194	C₂×C₁₀₁	—	4	4	no	—
195	C₂×C₁₀₁	—	8	4	no	—
196	C₂×C₁₀₁	#3003	1	1	yes	characteristic
197	C₂×C₁₀₁	#3019	1	1	yes	characteristic
198	C₂×C₁₀₁	#3028	1	1	yes	characteristic
199	#3496	C₂×C₁₀₁	1	1	yes	characteristic
200	#3234	C₂×C₁₀₁	1	2	yes	complemented
201	#2633	C₂×C₁₀₁	1	1	yes	characteristic, complemented
202	#1613	C₂×C₁₀₁	1	4	yes	complemented
203	#1607	C₂×C₁₀₁	1	4	yes	complemented
204	#1514	C₂×C₁₀₁	1	2	yes	complemented
205	#1466	C₂×C₁₀₁	1	1	yes	characteristic, complemented
206	C₁₀₁	#18363	1	1	yes	characteristic, direct product factor, Sylow
207	C₂×H(5,𝔽₂)	—	2	1	no	—
208	#547	—	2	2	no	—
209	#546	—	2	4	no	—
210	D₄²	—	2	2	no	—
211	#537	—	2	1	no	—
212	#534	C₂²×C₁₀₁	1	4	yes	—
213	#532	C₂²×C₁₀₁	1	2	yes	—
214	C₂×#125	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
215	C₂×#121	—	2	2	no	—
216	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
217	#501	—	2	2	no	—
218	#490	—	2	2	no	—
219	#481	C₂²×C₁₀₁	1	4	yes	complemented
220	#480	C₂²×C₁₀₁	1	4	yes	complemented
221	#478	—	2	4	no	—
222	#432	C₂²×C₁₀₁	1	2	yes	complemented
223	#399	C₂²×C₁₀₁	1	2	yes	complemented
224	#398	—	2	1	no	—
225	#397	C₂²×C₁₀₁	1	2	yes	complemented
226	#394	—	2	1	no	—
227	#385	—	2	2	no	—
228	#383	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
229	#327	C₂²×C₁₀₁	1	8	yes	complemented
230	#323	C₂²×C₁₀₁	1	4	yes	complemented
231	H(5,𝔽₂)	—	4	8	no	—
232	C₂×#41	—	2	4	no	—
233	C₂×#41	—	2	2	no	—
234	C₂²×D₄	—	2	4	no	—
235	C₂²×D₄	—	2	4	no	—
236	C₂²×D₄	—	2	2	no	—
237	C₂²×D₄	D₄×C₁₀₁	1	1	yes	characteristic
238	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
239	C₄⋊Q₈	D₄×C₁₀₁	1	2	yes	—
240	#127	D₄×C₁₀₁	1	2	yes	—
241	#125	—	2	2	no	—
242	#125	—	2	2	no	—
243	#124	—	2	2	no	—
244	#123	—	2	8	no	—
245	C₂²⋊Q₈	—	2	4	no	—
246	#121	—	2	4	no	—
247	#121	—	2	4	no	—
248	#121	—	2	4	no	—
249	#121	—	2	2	no	—
250	#121	—	2	4	no	—
251	#121	C₂³×C₁₀₁	1	4	yes	—
252	#120	—	2	8	no	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	—	2	2	no	—
255	C₄×D₄	—	2	2	no	—
256	C₄×D₄	D₄×C₁₀₁	1	4	yes	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	—	2	4	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	2	yes	—
268	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
269	#107	—	2	4	no	—
270	#106	—	2	4	no	—
271	C₄⋊C₈	—	2	2	no	—
272	#102	—	2	4	no	—
273	#102	—	2	4	no	—
274	C₂²⋊C₈	C₂³×C₁₀₁	1	4	yes	—
275	#97	—	2	2	no	—
276	#95	—	2	1	no	—
277	#95	—	2	1	no	—
278	#95	—	2	2	no	—
279	#95	C₂³×C₁₀₁	1	2	yes	—
280	C₂⁴	—	2	4	no	—
281	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
282	#41	—	4	8	no	—
283	#41	—	4	16	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	2	8	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	4	16	no	—
293	C₂×D₄	—	4	8	no	—
294	C₂×D₄	—	4	8	no	—
295	C₂×D₄	—	8	4	no	—
296	C₂×D₄	C₂×D₄×C₁₀₁	1	4	yes	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	8	2	no	—
305	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
308	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
309	C₂×C₈	—	2	4	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	8	2	no	—
319	C₄⋊C₄	C₂×D₄×C₁₀₁	1	4	yes	—
320	C₂²⋊C₄	—	2	8	no	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	2	4	no	—
323	C₂²⋊C₄	—	2	4	no	—
324	C₂²⋊C₄	—	4	4	no	—
325	C₂²⋊C₄	—	8	2	no	—
326	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
327	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	4	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	8	no	—
334	C₂³	—	8	4	no	—
335	C₂³	—	8	4	no	—
336	C₂³	AGL(1,ℤ/8)×C₁₀₁	1	4	yes	—
337	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
338	Q₈	—	4	4	no	—
339	D₄	—	2	8	no	—
340	D₄	—	4	4	no	—
341	D₄	—	4	4	no	—
342	D₄	—	4	4	no	—
343	D₄	—	4	16	no	—
344	D₄	—	4	8	no	—
345	D₄	—	8	4	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	8	no	—
353	C₂×C₄	—	4	8	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	8	2	no	—
364	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
365	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
366	C₂×C₄	#120×C₁₀₁	1	2	yes	—
367	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
368	C₈	—	4	4	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	4	no	—
376	C₂²	—	4	4	no	—
377	C₂²	—	4	4	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	16	8	no	—
380	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
381	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
382	C₄	—	2	2	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	4	no	—
387	C₄	—	4	2	no	—
388	C₄	—	8	2	no	—
389	C₄	—	8	1	no	—
390	C₄	—	8	1	no	—
391	C₂	—	2	2	no	—
392	C₂	—	4	4	no	—
393	C₂	—	8	4	no	—
394	C₂	C₁₀₁×#3003	1	1	yes	characteristic
395	C₂	C₁₀₁×#3019	1	1	yes	characteristic
396	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×#3234	C₂	semidirect
3. C₁₀₁×#2633	C₂	semidirect
4. C₁₀₁×#1613	C₂	semidirect
5. C₁₀₁×#1607	C₂	semidirect
6. C₁₀₁×#1514	C₂	semidirect
7. C₁₀₁×#1466	C₂	semidirect
15. C₂×#125×C₁₀₁	C₂²	semidirect
20. #481×C₁₀₁	C₂²	semidirect
21. #480×C₁₀₁	C₂²	semidirect
23. #432×C₁₀₁	C₂²	semidirect
24. #399×C₁₀₁	C₂²	semidirect
26. #397×C₁₀₁	C₂²	semidirect
29. #383×C₁₀₁	C₂²	semidirect
30. #327×C₁₀₁	C₂²	semidirect
31. #323×C₁₀₁	C₂²	semidirect
192. #18363	C₁₀₁	direct (N × H)
200. #3234	C₂×C₁₀₁	semidirect
201. #2633	C₂×C₁₀₁	semidirect
202. #1613	C₂×C₁₀₁	semidirect
203. #1607	C₂×C₁₀₁	semidirect
204. #1514	C₂×C₁₀₁	semidirect
205. #1466	C₂×C₁₀₁	semidirect
206. C₁₀₁	#18363	direct (N × H)
214. C₂×#125	C₂²×C₁₀₁	semidirect
219. #481	C₂²×C₁₀₁	semidirect
220. #480	C₂²×C₁₀₁	semidirect
222. #432	C₂²×C₁₀₁	semidirect
223. #399	C₂²×C₁₀₁	semidirect
225. #397	C₂²×C₁₀₁	semidirect
228. #383	C₂²×C₁₀₁	semidirect
229. #327	C₂²×C₁₀₁	semidirect
230. #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×#3234	2
C₁₀₁×#2633	2
C₁₀₁×#1613	2
C₁₀₁×#1607	2
C₁₀₁×#1514	2
C₁₀₁×#1466	2
#18363	101

Subgroups — C101×#18363 #38800514

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#18363 #38800514