Subgroups — C₁₀₁×#18218 #38800369

Order 25856.

1222 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3497	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₁×#3100	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#2536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#1610	C₂	1	4	yes	maximal, complemented
5	C₁₀₁×#1598	C₂	1	4	yes	maximal, complemented
6	C₁₀₁×#1517	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1461	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×2₋¹⁺⁴×C₁₀₁	—	2	1	no	—
9	#550×C₁₀₁	—	2	2	no	—
10	D₄×Q₈×C₁₀₁	—	2	2	no	—
11	#548×C₁₀₁	—	2	4	no	—
12	#537×C₁₀₁	—	2	1	no	—
13	#537×C₁₀₁	C₂²	1	4	yes	—
14	#532×C₁₀₁	—	2	2	no	—
15	#532×C₁₀₁	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₁₀₁	—	2	1	no	—
17	C₂×C₄×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
19	#480×C₁₀₁	C₂²	1	4	yes	—
20	#474×C₁₀₁	—	2	2	no	—
21	#459×C₁₀₁	—	2	2	no	—
22	#447×C₁₀₁	C₂²	1	4	yes	—
23	C₄×D₈×C₁₀₁	—	2	4	no	—
24	#431×C₁₀₁	C₂²	1	2	yes	—
25	#398×C₁₀₁	C₂²	1	2	yes	—
26	#394×C₁₀₁	C₂²	1	2	yes	—
27	#388×C₁₀₁	—	2	2	no	—
28	#382×C₁₀₁	C₂²	1	1	yes	characteristic
29	#380×C₁₀₁	—	2	1	no	—
30	#327×C₁₀₁	C₂²	1	8	yes	—
31	#324×C₁₀₁	C₂²	1	4	yes	—
32	2₋¹⁺⁴×C₁₀₁	—	4	4	no	—
33	2₋¹⁺⁴×C₁₀₁	—	4	4	no	—
34	C₂×#41×C₁₀₁	—	2	4	no	—
35	C₂×#41×C₁₀₁	—	2	4	no	—
36	C₂×#41×C₁₀₁	—	2	2	no	—
37	C₂²×Q₈×C₁₀₁	—	2	4	no	—
38	C₂²×Q₈×C₁₀₁	D₄	1	1	yes	characteristic
39	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₀₁	—	2	1	no	—
41	C₂×D₈×C₁₀₁	—	2	4	no	—
42	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
43	C₄⋊Q₈×C₁₀₁	D₄	1	2	yes	—
44	#127×C₁₀₁	—	2	2	no	—
45	#127×C₁₀₁	D₄	1	2	yes	—
46	#124×C₁₀₁	—	2	4	no	—
47	#124×C₁₀₁	—	2	2	no	—
48	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
49	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
50	C₂²⋊Q₈×C₁₀₁	—	4	4	no	—
51	#121×C₁₀₁	—	2	4	no	—
52	#121×C₁₀₁	—	2	8	no	—
53	#121×C₁₀₁	—	2	2	no	—
54	#121×C₁₀₁	—	2	4	no	—
55	#121×C₁₀₁	C₂³	1	4	yes	—
56	C₄×Q₈×C₁₀₁	—	2	2	no	—
57	C₄×Q₈×C₁₀₁	—	2	2	no	—
58	C₄×D₄×C₁₀₁	—	2	4	no	—
59	C₄×D₄×C₁₀₁	—	2	4	no	—
60	C₄×D₄×C₁₀₁	—	2	2	no	—
61	C₄×D₄×C₁₀₁	—	2	2	no	—
62	C₄×D₄×C₁₀₁	—	2	2	no	—
63	C₄×D₄×C₁₀₁	D₄	1	4	yes	—
64	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
72	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
73	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
74	#107×C₁₀₁	—	2	4	no	—
75	C₄⋊C₈×C₁₀₁	—	2	2	no	—
76	#102×C₁₀₁	—	2	4	no	—
77	#102×C₁₀₁	—	2	4	no	—
78	C₂²⋊C₈×C₁₀₁	C₂³	1	4	yes	—
79	C₄×C₈×C₁₀₁	—	2	2	no	—
80	#95×C₁₀₁	—	2	2	no	—
81	#95×C₁₀₁	—	2	1	no	—
82	#95×C₁₀₁	C₂³	1	2	yes	—
83	C₂⁴×C₁₀₁	—	2	1	no	—
84	#41×C₁₀₁	—	4	8	no	—
85	#41×C₁₀₁	—	4	16	no	—
86	#41×C₁₀₁	—	4	8	no	—
87	#41×C₁₀₁	—	4	4	no	—
88	#41×C₁₀₁	—	4	4	no	—
89	C₂×Q₈×C₁₀₁	—	2	4	no	—
90	C₂×Q₈×C₁₀₁	—	2	2	no	—
91	C₂×Q₈×C₁₀₁	—	2	2	no	—
92	C₂×Q₈×C₁₀₁	—	2	2	no	—
93	C₂×Q₈×C₁₀₁	—	4	16	no	—
94	C₂×Q₈×C₁₀₁	D₈	1	4	yes	complemented
95	C₂×D₄×C₁₀₁	—	2	4	no	—
96	C₂×D₄×C₁₀₁	—	2	4	no	—
97	C₂×D₄×C₁₀₁	—	2	4	no	—
98	C₂×D₄×C₁₀₁	—	2	2	no	—
99	C₂×D₄×C₁₀₁	—	2	2	no	—
100	C₂×D₄×C₁₀₁	—	2	2	no	—
101	C₂×D₄×C₁₀₁	—	4	2	no	—
102	C₂×D₄×C₁₀₁	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₁₀₁	—	2	8	no	—
104	C₂²×C₄×C₁₀₁	—	2	4	no	—
105	C₂²×C₄×C₁₀₁	—	2	2	no	—
106	C₂²×C₄×C₁₀₁	—	2	1	no	—
107	C₂²×C₄×C₁₀₁	—	4	2	no	—
108	C₂²×C₄×C₁₀₁	—	4	2	no	—
109	C₂²×C₄×C₁₀₁	—	4	2	no	—
110	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
115	D₈×C₁₀₁	—	4	8	no	—
116	C₂×C₈×C₁₀₁	—	2	4	no	—
117	C₄⋊C₄×C₁₀₁	—	2	4	no	—
118	C₄⋊C₄×C₁₀₁	—	2	2	no	—
119	C₄⋊C₄×C₁₀₁	—	2	2	no	—
120	C₄⋊C₄×C₁₀₁	—	2	4	no	—
121	C₄⋊C₄×C₁₀₁	—	2	2	no	—
122	C₄⋊C₄×C₁₀₁	—	4	2	no	—
123	C₄⋊C₄×C₁₀₁	—	4	4	no	—
124	C₄⋊C₄×C₁₀₁	C₂×D₄	1	4	yes	—
125	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
126	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
127	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
128	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
129	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
130	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
131	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
132	C₄²×C₁₀₁	—	2	2	no	—
133	C₄²×C₁₀₁	—	2	2	no	—
134	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
135	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
136	C₂³×C₁₀₁	—	2	2	no	—
137	C₂³×C₁₀₁	—	2	4	no	—
138	C₂³×C₁₀₁	—	4	1	no	—
139	C₂³×C₁₀₁	—	4	1	no	—
140	C₂³×C₁₀₁	—	4	1	no	—
141	C₂³×C₁₀₁	—	4	1	no	—
142	C₂³×C₁₀₁	—	4	1	no	—
143	C₂³×C₁₀₁	—	4	1	no	—
144	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
145	Q₈×C₁₀₁	—	2	8	no	—
146	Q₈×C₁₀₁	—	4	8	no	—
147	Q₈×C₁₀₁	—	4	4	no	—
148	D₄×C₁₀₁	—	2	4	no	—
149	D₄×C₁₀₁	—	4	4	no	—
150	D₄×C₁₀₁	—	4	4	no	—
151	D₄×C₁₀₁	—	4	2	no	—
152	D₄×C₁₀₁	—	4	8	no	—
153	D₄×C₁₀₁	—	4	4	no	—
154	D₄×C₁₀₁	—	4	4	no	—
155	D₄×C₁₀₁	—	4	4	no	—
156	D₄×C₁₀₁	—	8	4	no	—
157	C₂×C₄×C₁₀₁	—	2	2	no	—
158	C₂×C₄×C₁₀₁	—	2	2	no	—
159	C₂×C₄×C₁₀₁	—	2	2	no	—
160	C₂×C₄×C₁₀₁	—	2	4	no	—
161	C₂×C₄×C₁₀₁	—	4	1	no	—
162	C₂×C₄×C₁₀₁	—	4	1	no	—
163	C₂×C₄×C₁₀₁	—	4	16	no	—
164	C₂×C₄×C₁₀₁	—	4	8	no	—
165	C₂×C₄×C₁₀₁	—	4	2	no	—
166	C₂×C₄×C₁₀₁	—	4	2	no	—
167	C₂×C₄×C₁₀₁	—	4	2	no	—
168	C₂×C₄×C₁₀₁	—	4	1	no	—
169	C₂×C₄×C₁₀₁	—	4	2	no	—
170	C₂×C₄×C₁₀₁	—	4	1	no	—
171	C₂×C₄×C₁₀₁	—	4	1	no	—
172	C₂×C₄×C₁₀₁	—	8	4	no	—
173	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
174	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
175	C₂×C₄×C₁₀₁	#120	1	2	yes	—
176	C₂×C₄×C₁₀₁	C₂×D₈	1	4	yes	—
177	C₂×C₄×C₁₀₁	C₂×D₈	1	2	yes	—
178	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
179	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
180	C₈×C₁₀₁	—	4	4	no	—
181	C₂²×C₁₀₁	—	2	1	no	—
182	C₂²×C₁₀₁	—	2	1	no	—
183	C₂²×C₁₀₁	—	4	2	no	—
184	C₂²×C₁₀₁	—	4	2	no	—
185	C₂²×C₁₀₁	—	4	4	no	—
186	C₂²×C₁₀₁	—	4	4	no	—
187	C₂²×C₁₀₁	—	4	2	no	—
188	C₂²×C₁₀₁	—	4	4	no	—
189	C₂²×C₁₀₁	—	8	1	no	—
190	C₂²×C₁₀₁	—	8	1	no	—
191	C₂²×C₁₀₁	—	8	1	no	—
192	C₂²×C₁₀₁	—	8	1	no	—
193	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
194	C₂²×C₁₀₁	C₂²×D₈	1	1	yes	characteristic
195	C₂²×C₁₀₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
196	C₄×C₁₀₁	—	2	4	no	—
197	C₄×C₁₀₁	—	2	1	no	—
198	C₄×C₁₀₁	—	2	1	no	—
199	C₄×C₁₀₁	—	2	2	no	—
200	C₄×C₁₀₁	—	4	4	no	—
201	C₄×C₁₀₁	—	4	2	no	—
202	C₄×C₁₀₁	—	8	2	no	—
203	C₄×C₁₀₁	—	8	1	no	—
204	C₄×C₁₀₁	#447	1	4	yes	—
205	#18218	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂×C₁₀₁	—	2	1	no	—
207	C₂×C₁₀₁	—	2	1	no	—
208	C₂×C₁₀₁	—	8	4	no	—
209	C₂×C₁₀₁	—	8	2	no	—
210	C₂×C₁₀₁	C₂×#447	1	1	yes	characteristic
211	C₂×C₁₀₁	#3020	1	1	yes	characteristic
212	C₂×C₁₀₁	#3025	1	1	yes	characteristic
213	#3497	C₂×C₁₀₁	1	1	yes	characteristic, complemented
214	#3100	C₂×C₁₀₁	1	2	yes	complemented
215	#2536	C₂×C₁₀₁	1	1	yes	characteristic, complemented
216	#1610	C₂×C₁₀₁	1	4	yes	complemented
217	#1598	C₂×C₁₀₁	1	4	yes	complemented
218	#1517	C₂×C₁₀₁	1	2	yes	complemented
219	#1461	C₂×C₁₀₁	1	1	yes	characteristic, complemented
220	C₁₀₁	#18218	1	1	yes	characteristic, direct product factor, Sylow
221	C₂×2₋¹⁺⁴	—	2	1	no	—
222	#550	—	2	2	no	—
223	D₄×Q₈	—	2	2	no	—
224	#548	—	2	4	no	—
225	#537	—	2	1	no	—
226	#537	C₂²×C₁₀₁	1	4	yes	—
227	#532	—	2	2	no	—
228	#532	C₂²×C₁₀₁	1	2	yes	—
229	C₂×C₂²⋊Q₈	—	2	1	no	—
230	C₂×C₄×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
231	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
232	#480	C₂²×C₁₀₁	1	4	yes	—
233	#474	—	2	2	no	—
234	#459	—	2	2	no	—
235	#447	C₂²×C₁₀₁	1	4	yes	—
236	C₄×D₈	—	2	4	no	—
237	#431	C₂²×C₁₀₁	1	2	yes	—
238	#398	C₂²×C₁₀₁	1	2	yes	—
239	#394	C₂²×C₁₀₁	1	2	yes	—
240	#388	—	2	2	no	—
241	#382	C₂²×C₁₀₁	1	1	yes	characteristic
242	#380	—	2	1	no	—
243	#327	C₂²×C₁₀₁	1	8	yes	—
244	#324	C₂²×C₁₀₁	1	4	yes	—
245	2₋¹⁺⁴	—	4	4	no	—
246	2₋¹⁺⁴	—	4	4	no	—
247	C₂×#41	—	2	4	no	—
248	C₂×#41	—	2	4	no	—
249	C₂×#41	—	2	2	no	—
250	C₂²×Q₈	—	2	4	no	—
251	C₂²×Q₈	D₄×C₁₀₁	1	1	yes	characteristic
252	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
253	C₂³×C₄	—	2	1	no	—
254	C₂×D₈	—	2	4	no	—
255	C₄⋊Q₈	—	2	2	no	—
256	C₄⋊Q₈	D₄×C₁₀₁	1	2	yes	—
257	#127	—	2	2	no	—
258	#127	D₄×C₁₀₁	1	2	yes	—
259	#124	—	2	4	no	—
260	#124	—	2	2	no	—
261	C₂²⋊Q₈	—	2	4	no	—
262	C₂²⋊Q₈	—	2	8	no	—
263	C₂²⋊Q₈	—	4	4	no	—
264	#121	—	2	4	no	—
265	#121	—	2	8	no	—
266	#121	—	2	2	no	—
267	#121	—	2	4	no	—
268	#121	C₂³×C₁₀₁	1	4	yes	—
269	C₄×Q₈	—	2	2	no	—
270	C₄×Q₈	—	2	2	no	—
271	C₄×D₄	—	2	4	no	—
272	C₄×D₄	—	2	4	no	—
273	C₄×D₄	—	2	2	no	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	D₄×C₁₀₁	1	4	yes	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
286	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
287	#107	—	2	4	no	—
288	C₄⋊C₈	—	2	2	no	—
289	#102	—	2	4	no	—
290	#102	—	2	4	no	—
291	C₂²⋊C₈	C₂³×C₁₀₁	1	4	yes	—
292	C₄×C₈	—	2	2	no	—
293	#95	—	2	2	no	—
294	#95	—	2	1	no	—
295	#95	C₂³×C₁₀₁	1	2	yes	—
296	C₂⁴	—	2	1	no	—
297	#41	—	4	8	no	—
298	#41	—	4	16	no	—
299	#41	—	4	8	no	—
300	#41	—	4	4	no	—
301	#41	—	4	4	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	4	16	no	—
307	C₂×Q₈	D₈×C₁₀₁	1	4	yes	complemented
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	C₂×D₄×C₁₀₁	1	4	yes	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
327	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
328	D₈	—	4	8	no	—
329	C₂×C₈	—	2	4	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₄⋊C₄	C₂×D₄×C₁₀₁	1	4	yes	—
338	C₂²⋊C₄	—	2	8	no	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	4	4	no	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	4	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
348	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	4	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	4	1	no	—
353	C₂³	—	4	1	no	—
354	C₂³	—	4	1	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	4	1	no	—
357	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
358	Q₈	—	2	8	no	—
359	Q₈	—	4	8	no	—
360	Q₈	—	4	4	no	—
361	D₄	—	2	4	no	—
362	D₄	—	4	4	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	8	no	—
365	D₄	—	4	4	no	—
366	D₄	—	4	4	no	—
367	D₄	—	4	4	no	—
368	D₄	—	4	4	no	—
369	D₄	—	8	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	16	no	—
377	C₂×C₄	—	4	8	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	8	4	no	—
386	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
387	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
388	C₂×C₄	#120×C₁₀₁	1	2	yes	—
389	C₂×C₄	C₂×D₈×C₁₀₁	1	4	yes	—
390	C₂×C₄	C₂×D₈×C₁₀₁	1	2	yes	—
391	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
392	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
393	C₈	—	4	4	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	4	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	8	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	8	1	no	—
406	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
407	C₂²	C₂²×D₈×C₁₀₁	1	1	yes	characteristic
408	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
409	C₄	—	2	4	no	—
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	2	no	—
413	C₄	—	4	4	no	—
414	C₄	—	4	2	no	—
415	C₄	—	8	2	no	—
416	C₄	—	8	1	no	—
417	C₄	#447×C₁₀₁	1	4	yes	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	8	2	no	—
421	C₂	—	8	4	no	—
422	C₂	C₂×#447×C₁₀₁	1	1	yes	characteristic
423	C₂	C₁₀₁×#3020	1	1	yes	characteristic
424	C₂	C₁₀₁×#3025	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
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
1. C₁₀₁×#3497	C₂	semidirect
2. C₁₀₁×#3100	C₂	semidirect
3. C₁₀₁×#2536	C₂	semidirect
4. C₁₀₁×#1610	C₂	semidirect
5. C₁₀₁×#1598	C₂	semidirect
6. C₁₀₁×#1517	C₂	semidirect
7. C₁₀₁×#1461	C₂	semidirect
94. C₂×Q₈×C₁₀₁	D₈	semidirect
205. #18218	C₁₀₁	direct (N × H)
213. #3497	C₂×C₁₀₁	semidirect
214. #3100	C₂×C₁₀₁	semidirect
215. #2536	C₂×C₁₀₁	semidirect
216. #1610	C₂×C₁₀₁	semidirect
217. #1598	C₂×C₁₀₁	semidirect
218. #1517	C₂×C₁₀₁	semidirect
219. #1461	C₂×C₁₀₁	semidirect
220. C₁₀₁	#18218	direct (N × H)
307. C₂×Q₈	D₈×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₁×#3497	2
C₁₀₁×#3100	2
C₁₀₁×#2536	2
C₁₀₁×#1610	2
C₁₀₁×#1598	2
C₁₀₁×#1517	2
C₁₀₁×#1461	2
#18218	101

Subgroups — C101×#18218 #38800369

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#18218 #38800369