Subgroups — C₁₀₁×#10046 #38792197

Order 25856.

938 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#493×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#459×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₁×#2541	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#1982	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#331×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄⋊C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₁×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₈×C₁₀₁	—	2	1	no	—
9	C₂²×D₈×C₁₀₁	—	2	2	no	—
10	C₂×#127×C₁₀₁	—	2	1	no	—
11	C₂×#127×C₁₀₁	C₂²	1	1	yes	characteristic
12	C₂×#127×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂×#121×C₁₀₁	—	2	2	no	—
14	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
15	#493×C₁₀₁	—	2	2	no	—
16	#493×C₁₀₁	—	2	2	no	—
17	#459×C₁₀₁	—	2	2	no	—
18	#459×C₁₀₁	—	2	2	no	—
19	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	1	yes	characteristic
21	C₂×#102×C₁₀₁	—	2	1	no	—
22	C₂×#102×C₁₀₁	—	2	2	no	—
23	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
24	#392×C₁₀₁	—	2	2	no	—
25	#390×C₁₀₁	—	2	1	no	—
26	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
27	#331×C₁₀₁	—	2	2	no	—
28	D₄⋊C₈×C₁₀₁	—	2	2	no	—
29	C₂²×D₄×C₁₀₁	—	2	4	no	—
30	C₂²×D₄×C₁₀₁	—	2	1	no	—
31	C₂²×D₄×C₁₀₁	—	2	1	no	—
32	C₂²×D₄×C₁₀₁	—	2	1	no	—
33	C₂²×D₄×C₁₀₁	—	2	1	no	—
34	C₂²×D₄×C₁₀₁	—	2	1	no	—
35	C₂²×D₄×C₁₀₁	D₄	1	1	yes	characteristic
36	C₂²×D₄×C₁₀₁	D₄	1	2	yes	—
37	C₂³×C₄×C₁₀₁	—	2	1	no	—
38	C₂×D₈×C₁₀₁	—	2	4	no	—
39	C₂×D₈×C₁₀₁	—	2	8	no	—
40	C₂×D₈×C₁₀₁	—	4	8	no	—
41	C₂×D₈×C₁₀₁	—	4	2	no	—
42	C₂×D₈×C₁₀₁	—	4	2	no	—
43	C₂²×C₈×C₁₀₁	—	2	1	no	—
44	C₂²×C₈×C₁₀₁	—	2	1	no	—
45	C₂²×C₈×C₁₀₁	—	2	1	no	—
46	#127×C₁₀₁	—	2	1	no	—
47	#127×C₁₀₁	—	2	1	no	—
48	#127×C₁₀₁	—	2	1	no	—
49	#127×C₁₀₁	—	2	1	no	—
50	#127×C₁₀₁	—	2	1	no	—
51	#127×C₁₀₁	—	2	1	no	—
52	#127×C₁₀₁	—	2	1	no	—
53	#127×C₁₀₁	—	4	2	no	—
54	#127×C₁₀₁	—	4	2	no	—
55	#127×C₁₀₁	D₄	1	2	yes	complemented
56	#121×C₁₀₁	—	4	4	no	—
57	#121×C₁₀₁	—	4	4	no	—
58	C₄×D₄×C₁₀₁	—	2	1	no	—
59	C₄×D₄×C₁₀₁	—	2	1	no	—
60	C₄×D₄×C₁₀₁	—	2	1	no	—
61	C₄×D₄×C₁₀₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₀₁	D₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
66	C₂×C₄²×C₁₀₁	—	2	1	no	—
67	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₁₀₁	—	2	1	no	—
69	C₄⋊C₈×C₁₀₁	—	2	1	no	—
70	C₄⋊C₈×C₁₀₁	—	2	1	no	—
71	C₄⋊C₈×C₁₀₁	D₄	1	2	yes	complemented
72	#102×C₁₀₁	—	2	4	no	—
73	#102×C₁₀₁	—	4	4	no	—
74	C₄×C₈×C₁₀₁	—	2	1	no	—
75	C₄×C₈×C₁₀₁	D₄	1	2	yes	complemented
76	#95×C₁₀₁	—	2	1	no	—
77	C₂⁴×C₁₀₁	—	2	1	no	—
78	C₂⁴×C₁₀₁	—	2	2	no	—
79	C₂⁴×C₁₀₁	—	4	1	no	—
80	C₂×D₄×C₁₀₁	—	2	1	no	—
81	C₂×D₄×C₁₀₁	—	2	2	no	—
82	C₂×D₄×C₁₀₁	—	2	2	no	—
83	C₂×D₄×C₁₀₁	—	2	2	no	—
84	C₂×D₄×C₁₀₁	—	2	1	no	—
85	C₂×D₄×C₁₀₁	—	2	2	no	—
86	C₂×D₄×C₁₀₁	—	2	2	no	—
87	C₂×D₄×C₁₀₁	—	2	1	no	—
88	C₂×D₄×C₁₀₁	—	2	1	no	—
89	C₂×D₄×C₁₀₁	—	2	1	no	—
90	C₂×D₄×C₁₀₁	—	4	4	no	—
91	C₂×D₄×C₁₀₁	—	4	4	no	—
92	C₂×D₄×C₁₀₁	—	4	8	no	—
93	C₂×D₄×C₁₀₁	—	4	8	no	—
94	C₂×D₄×C₁₀₁	—	4	1	no	—
95	C₂×D₄×C₁₀₁	—	4	1	no	—
96	C₂×D₄×C₁₀₁	—	4	1	no	—
97	C₂×D₄×C₁₀₁	—	4	1	no	—
98	C₂×D₄×C₁₀₁	—	4	1	no	—
99	C₂×D₄×C₁₀₁	—	4	1	no	—
100	C₂×D₄×C₁₀₁	—	4	1	no	—
101	C₂×D₄×C₁₀₁	—	4	2	no	—
102	C₂×D₄×C₁₀₁	—	4	1	no	—
103	C₂×D₄×C₁₀₁	—	4	2	no	—
104	C₂×D₄×C₁₀₁	—	4	1	no	—
105	C₂×D₄×C₁₀₁	—	4	1	no	—
106	C₂×D₄×C₁₀₁	—	4	1	no	—
107	C₂×D₄×C₁₀₁	—	4	1	no	—
108	C₂×D₄×C₁₀₁	—	4	1	no	—
109	C₂×D₄×C₁₀₁	—	4	2	no	—
110	C₂×D₄×C₁₀₁	—	4	2	no	—
111	C₂×D₄×C₁₀₁	—	4	1	no	—
112	C₂×D₄×C₁₀₁	—	4	1	no	—
113	C₂×D₄×C₁₀₁	—	8	4	no	—
114	C₂×D₄×C₁₀₁	D₈	1	2	yes	complemented
115	C₂²×C₄×C₁₀₁	—	2	2	no	—
116	C₂²×C₄×C₁₀₁	—	2	1	no	—
117	C₂²×C₄×C₁₀₁	—	4	1	no	—
118	C₂²×C₄×C₁₀₁	—	4	1	no	—
119	C₂²×C₄×C₁₀₁	—	4	2	no	—
120	C₂²×C₄×C₁₀₁	—	4	2	no	—
121	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
124	D₈×C₁₀₁	—	4	16	no	—
125	D₈×C₁₀₁	—	4	8	no	—
126	C₂×C₈×C₁₀₁	—	2	4	no	—
127	C₂×C₈×C₁₀₁	—	2	2	no	—
128	C₂×C₈×C₁₀₁	—	2	2	no	—
129	C₂×C₈×C₁₀₁	—	4	1	no	—
130	C₂×C₈×C₁₀₁	—	4	1	no	—
131	C₂×C₈×C₁₀₁	—	4	1	no	—
132	C₂×C₈×C₁₀₁	—	4	2	no	—
133	C₄⋊C₄×C₁₀₁	—	2	2	no	—
134	C₄⋊C₄×C₁₀₁	—	2	1	no	—
135	C₄⋊C₄×C₁₀₁	—	2	1	no	—
136	C₄⋊C₄×C₁₀₁	D₈	1	4	yes	complemented
137	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
138	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
139	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
140	C₄²×C₁₀₁	—	4	1	no	—
141	C₄²×C₁₀₁	—	4	1	no	—
142	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₁₀₁	#41	1	1	yes	characteristic
146	C₂³×C₁₀₁	—	2	2	no	—
147	C₂³×C₁₀₁	—	4	1	no	—
148	C₂³×C₁₀₁	—	4	2	no	—
149	C₂³×C₁₀₁	—	4	1	no	—
150	C₂³×C₁₀₁	—	4	2	no	—
151	C₂³×C₁₀₁	—	4	2	no	—
152	C₂³×C₁₀₁	—	4	2	no	—
153	C₂³×C₁₀₁	—	4	4	no	—
154	C₂³×C₁₀₁	—	4	2	no	—
155	C₂³×C₁₀₁	—	4	2	no	—
156	C₂³×C₁₀₁	—	4	4	no	—
157	C₂³×C₁₀₁	—	8	1	no	—
158	C₂³×C₁₀₁	—	8	2	no	—
159	C₂³×C₁₀₁	—	8	1	no	—
160	C₂³×C₁₀₁	—	8	2	no	—
161	C₂³×C₁₀₁	#120	1	1	yes	characteristic
162	D₄×C₁₀₁	—	2	2	no	—
163	D₄×C₁₀₁	—	2	2	no	—
164	D₄×C₁₀₁	—	4	4	no	—
165	D₄×C₁₀₁	—	4	4	no	—
166	D₄×C₁₀₁	—	4	2	no	—
167	D₄×C₁₀₁	—	4	1	no	—
168	D₄×C₁₀₁	—	4	2	no	—
169	D₄×C₁₀₁	—	4	4	no	—
170	D₄×C₁₀₁	—	4	1	no	—
171	D₄×C₁₀₁	—	8	2	no	—
172	D₄×C₁₀₁	—	8	2	no	—
173	D₄×C₁₀₁	—	8	16	no	—
174	D₄×C₁₀₁	—	8	1	no	—
175	D₄×C₁₀₁	—	8	1	no	—
176	D₄×C₁₀₁	—	8	2	no	—
177	D₄×C₁₀₁	—	8	1	no	—
178	D₄×C₁₀₁	—	8	1	no	—
179	D₄×C₁₀₁	—	8	1	no	—
180	D₄×C₁₀₁	—	8	1	no	—
181	D₄×C₁₀₁	—	8	1	no	—
182	D₄×C₁₀₁	—	8	1	no	—
183	D₄×C₁₀₁	—	8	1	no	—
184	D₄×C₁₀₁	—	8	1	no	—
185	C₂×C₄×C₁₀₁	—	2	2	no	—
186	C₂×C₄×C₁₀₁	—	2	4	no	—
187	C₂×C₄×C₁₀₁	—	4	2	no	—
188	C₂×C₄×C₁₀₁	—	4	2	no	—
189	C₂×C₄×C₁₀₁	—	4	1	no	—
190	C₂×C₄×C₁₀₁	—	4	2	no	—
191	C₂×C₄×C₁₀₁	—	8	2	no	—
192	C₂×C₄×C₁₀₁	—	8	1	no	—
193	C₂×C₄×C₁₀₁	—	8	1	no	—
194	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
195	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
196	C₂×C₄×C₁₀₁	#121	1	1	yes	characteristic
197	C₂×C₄×C₁₀₁	#121	1	1	yes	characteristic
198	C₂×C₄×C₁₀₁	#121	1	1	yes	characteristic
199	C₂×C₄×C₁₀₁	#127	1	1	yes	characteristic
200	C₂×C₄×C₁₀₁	C₂×D₈	1	1	yes	characteristic
201	C₂×C₄×C₁₀₁	C₂×D₈	1	2	yes	—
202	C₂×C₄×C₁₀₁	#135	1	1	yes	characteristic
203	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	1	yes	characteristic
204	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	1	yes	characteristic
205	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
206	C₈×C₁₀₁	—	2	4	no	—
207	C₈×C₁₀₁	—	4	2	no	—
208	C₈×C₁₀₁	—	8	1	no	—
209	C₂²×C₁₀₁	—	4	4	no	—
210	C₂²×C₁₀₁	—	4	2	no	—
211	C₂²×C₁₀₁	—	8	2	no	—
212	C₂²×C₁₀₁	—	8	1	no	—
213	C₂²×C₁₀₁	—	8	1	no	—
214	C₂²×C₁₀₁	—	8	4	no	—
215	C₂²×C₁₀₁	—	8	4	no	—
216	C₂²×C₁₀₁	—	8	2	no	—
217	C₂²×C₁₀₁	—	8	2	no	—
218	C₂²×C₁₀₁	—	8	2	no	—
219	C₂²×C₁₀₁	—	8	2	no	—
220	C₂²×C₁₀₁	—	8	2	no	—
221	C₂²×C₁₀₁	—	8	2	no	—
222	C₂²×C₁₀₁	—	16	2	no	—
223	C₂²×C₁₀₁	—	16	2	no	—
224	C₂²×C₁₀₁	#392	1	1	yes	characteristic
225	C₂²×C₁₀₁	#447	1	1	yes	characteristic
226	C₂²×C₁₀₁	#447	1	2	yes	—
227	C₂²×C₁₀₁	#449	1	1	yes	characteristic
228	C₂²×C₁₀₁	#453	1	2	yes	—
229	C₄×C₁₀₁	—	2	1	no	—
230	C₄×C₁₀₁	—	2	1	no	—
231	C₄×C₁₀₁	—	4	4	no	—
232	C₄×C₁₀₁	—	8	1	no	—
233	C₄×C₁₀₁	#447	1	1	yes	characteristic
234	C₄×C₁₀₁	#449	1	1	yes	characteristic
235	C₄×C₁₀₁	#459	1	2	yes	—
236	C₄×C₁₀₁	#466	1	1	yes	characteristic
237	C₄×C₁₀₁	#469	1	1	yes	characteristic
238	C₄×C₁₀₁	#493	1	1	yes	characteristic
239	C₄×C₁₀₁	#496	1	1	yes	characteristic
240	#10046	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₂×C₁₀₁	—	8	2	no	—
242	C₂×C₁₀₁	—	16	2	no	—
243	C₂×C₁₀₁	—	16	2	no	—
244	C₂×C₁₀₁	#1619	1	2	yes	—
245	C₂×C₁₀₁	#1621	1	2	yes	—
246	C₂×C₁₀₁	#1999	1	1	yes	characteristic
247	C₂×C₁₀₁	#2002	1	1	yes	characteristic
248	C₂×C₁₀₁	#2011	1	1	yes	characteristic
249	C₂×#493	C₂×C₁₀₁	1	1	yes	characteristic, complemented
250	C₂×#459	C₂×C₁₀₁	1	1	yes	characteristic, complemented
251	#2541	C₂×C₁₀₁	1	1	yes	characteristic, complemented
252	#1982	C₂×C₁₀₁	1	1	yes	characteristic, complemented
253	C₂×#331	C₂×C₁₀₁	1	1	yes	characteristic, complemented
254	C₂×D₄⋊C₈	C₂×C₁₀₁	1	1	yes	characteristic, complemented
255	#1279	C₂×C₁₀₁	1	1	yes	characteristic, complemented
256	C₁₀₁	#10046	1	1	yes	characteristic, direct product factor, Sylow
257	C₂²×D₈	—	2	2	no	—
258	C₂²×D₈	—	2	1	no	—
259	C₂×#127	—	2	1	no	—
260	C₂×#127	C₂²×C₁₀₁	1	1	yes	characteristic
261	C₂×#127	C₂²×C₁₀₁	1	1	yes	characteristic
262	C₂×#121	—	2	2	no	—
263	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
264	#493	—	2	2	no	—
265	#493	—	2	2	no	—
266	#459	—	2	2	no	—
267	#459	—	2	2	no	—
268	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	1	yes	characteristic
270	C₂×#102	—	2	1	no	—
271	C₂×#102	—	2	2	no	—
272	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
273	#392	—	2	2	no	—
274	#390	—	2	1	no	—
275	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
276	#331	—	2	2	no	—
277	D₄⋊C₈	—	2	2	no	—
278	C₂²×D₄	—	2	4	no	—
279	C₂²×D₄	—	2	1	no	—
280	C₂²×D₄	—	2	1	no	—
281	C₂²×D₄	—	2	1	no	—
282	C₂²×D₄	—	2	1	no	—
283	C₂²×D₄	—	2	1	no	—
284	C₂²×D₄	D₄×C₁₀₁	1	1	yes	characteristic
285	C₂²×D₄	D₄×C₁₀₁	1	2	yes	—
286	C₂³×C₄	—	2	1	no	—
287	C₂×D₈	—	2	4	no	—
288	C₂×D₈	—	2	8	no	—
289	C₂×D₈	—	4	8	no	—
290	C₂×D₈	—	4	2	no	—
291	C₂×D₈	—	4	2	no	—
292	C₂²×C₈	—	2	1	no	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	2	1	no	—
295	#127	—	2	1	no	—
296	#127	—	2	1	no	—
297	#127	—	2	1	no	—
298	#127	—	2	1	no	—
299	#127	—	2	1	no	—
300	#127	—	2	1	no	—
301	#127	—	2	1	no	—
302	#127	—	4	2	no	—
303	#127	—	4	2	no	—
304	#127	D₄×C₁₀₁	1	2	yes	complemented
305	#121	—	4	4	no	—
306	#121	—	4	4	no	—
307	C₄×D₄	—	2	1	no	—
308	C₄×D₄	—	2	1	no	—
309	C₄×D₄	—	2	1	no	—
310	C₄×D₄	—	2	1	no	—
311	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
312	C₂×C₄⋊C₄	D₄×C₁₀₁	1	2	yes	—
313	C₂×C₂²⋊C₄	—	2	4	no	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₄²	—	2	1	no	—
316	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
317	C₄⋊C₈	—	2	1	no	—
318	C₄⋊C₈	—	2	1	no	—
319	C₄⋊C₈	—	2	1	no	—
320	C₄⋊C₈	D₄×C₁₀₁	1	2	yes	complemented
321	#102	—	2	4	no	—
322	#102	—	4	4	no	—
323	C₄×C₈	—	2	1	no	—
324	C₄×C₈	D₄×C₁₀₁	1	2	yes	complemented
325	#95	—	2	1	no	—
326	C₂⁴	—	2	1	no	—
327	C₂⁴	—	2	2	no	—
328	C₂⁴	—	4	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	4	4	no	—
340	C₂×D₄	—	4	4	no	—
341	C₂×D₄	—	4	8	no	—
342	C₂×D₄	—	4	8	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	1	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂×D₄	—	4	1	no	—
350	C₂×D₄	—	4	2	no	—
351	C₂×D₄	—	4	1	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	1	no	—
354	C₂×D₄	—	4	1	no	—
355	C₂×D₄	—	4	1	no	—
356	C₂×D₄	—	4	1	no	—
357	C₂×D₄	—	4	1	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	1	no	—
361	C₂×D₄	—	4	1	no	—
362	C₂×D₄	—	8	4	no	—
363	C₂×D₄	D₈×C₁₀₁	1	2	yes	complemented
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	4	1	no	—
367	C₂²×C₄	—	4	1	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
373	D₈	—	4	16	no	—
374	D₈	—	4	8	no	—
375	C₂×C₈	—	2	4	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	4	1	no	—
379	C₂×C₈	—	4	1	no	—
380	C₂×C₈	—	4	1	no	—
381	C₂×C₈	—	4	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	D₈×C₁₀₁	1	4	yes	complemented
386	C₂²⋊C₄	—	4	8	no	—
387	C₂²⋊C₄	—	4	1	no	—
388	C₂²⋊C₄	—	4	1	no	—
389	C₄²	—	4	1	no	—
390	C₄²	—	4	1	no	—
391	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
392	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
393	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
394	C₄²	#41×C₁₀₁	1	1	yes	characteristic
395	C₂³	—	2	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	4	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	4	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	8	1	no	—
407	C₂³	—	8	2	no	—
408	C₂³	—	8	1	no	—
409	C₂³	—	8	2	no	—
410	C₂³	#120×C₁₀₁	1	1	yes	characteristic
411	D₄	—	2	2	no	—
412	D₄	—	2	2	no	—
413	D₄	—	4	4	no	—
414	D₄	—	4	4	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	1	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	4	no	—
419	D₄	—	4	1	no	—
420	D₄	—	8	2	no	—
421	D₄	—	8	2	no	—
422	D₄	—	8	16	no	—
423	D₄	—	8	1	no	—
424	D₄	—	8	1	no	—
425	D₄	—	8	2	no	—
426	D₄	—	8	1	no	—
427	D₄	—	8	1	no	—
428	D₄	—	8	1	no	—
429	D₄	—	8	1	no	—
430	D₄	—	8	1	no	—
431	D₄	—	8	1	no	—
432	D₄	—	8	1	no	—
433	D₄	—	8	1	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	8	2	no	—
441	C₂×C₄	—	8	1	no	—
442	C₂×C₄	—	8	1	no	—
443	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
444	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
445	C₂×C₄	#121×C₁₀₁	1	1	yes	characteristic
446	C₂×C₄	#121×C₁₀₁	1	1	yes	characteristic
447	C₂×C₄	#121×C₁₀₁	1	1	yes	characteristic
448	C₂×C₄	#127×C₁₀₁	1	1	yes	characteristic
449	C₂×C₄	C₂×D₈×C₁₀₁	1	1	yes	characteristic
450	C₂×C₄	C₂×D₈×C₁₀₁	1	2	yes	—
451	C₂×C₄	#135×C₁₀₁	1	1	yes	characteristic
452	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
453	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
454	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
455	C₈	—	2	4	no	—
456	C₈	—	4	2	no	—
457	C₈	—	8	1	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	8	1	no	—
461	C₂²	—	8	1	no	—
462	C₂²	—	8	2	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	2	no	—
466	C₂²	—	8	2	no	—
467	C₂²	—	8	2	no	—
468	C₂²	—	8	2	no	—
469	C₂²	—	8	4	no	—
470	C₂²	—	8	4	no	—
471	C₂²	—	16	2	no	—
472	C₂²	—	16	2	no	—
473	C₂²	#392×C₁₀₁	1	1	yes	characteristic
474	C₂²	#447×C₁₀₁	1	1	yes	characteristic
475	C₂²	#447×C₁₀₁	1	2	yes	—
476	C₂²	#449×C₁₀₁	1	1	yes	characteristic
477	C₂²	#453×C₁₀₁	1	2	yes	—
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	4	4	no	—
481	C₄	—	8	1	no	—
482	C₄	#447×C₁₀₁	1	1	yes	characteristic
483	C₄	#449×C₁₀₁	1	1	yes	characteristic
484	C₄	#459×C₁₀₁	1	2	yes	—
485	C₄	#466×C₁₀₁	1	1	yes	characteristic
486	C₄	#469×C₁₀₁	1	1	yes	characteristic
487	C₄	#493×C₁₀₁	1	1	yes	characteristic
488	C₄	#496×C₁₀₁	1	1	yes	characteristic
489	C₂	—	8	2	no	—
490	C₂	—	16	2	no	—
491	C₂	—	16	2	no	—
492	C₂	C₁₀₁×#1619	1	2	yes	—
493	C₂	C₁₀₁×#1621	1	2	yes	—
494	C₂	C₁₀₁×#1999	1	1	yes	characteristic
495	C₂	C₁₀₁×#2002	1	1	yes	characteristic
496	C₂	C₁₀₁×#2011	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₁	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₀₁
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#493×C₁₀₁	C₂	semidirect
2. C₂×#459×C₁₀₁	C₂	semidirect
3. C₁₀₁×#2541	C₂	semidirect
4. C₁₀₁×#1982	C₂	semidirect
5. C₂×#331×C₁₀₁	C₂	semidirect
6. C₂×D₄⋊C₈×C₁₀₁	C₂	semidirect
7. C₁₀₁×#1279	C₂	semidirect
55. #127×C₁₀₁	D₄	semidirect
71. C₄⋊C₈×C₁₀₁	D₄	semidirect
75. C₄×C₈×C₁₀₁	D₄	semidirect
114. C₂×D₄×C₁₀₁	D₈	semidirect
136. C₄⋊C₄×C₁₀₁	D₈	semidirect
240. #10046	C₁₀₁	direct (N × H)
249. C₂×#493	C₂×C₁₀₁	semidirect
250. C₂×#459	C₂×C₁₀₁	semidirect
251. #2541	C₂×C₁₀₁	semidirect
252. #1982	C₂×C₁₀₁	semidirect
253. C₂×#331	C₂×C₁₀₁	semidirect
254. C₂×D₄⋊C₈	C₂×C₁₀₁	semidirect
255. #1279	C₂×C₁₀₁	semidirect
256. C₁₀₁	#10046	direct (N × H)
304. #127	D₄×C₁₀₁	semidirect
320. C₄⋊C₈	D₄×C₁₀₁	semidirect
324. C₄×C₈	D₄×C₁₀₁	semidirect
363. C₂×D₄	D₈×C₁₀₁	semidirect
385. C₄⋊C₄	D₈×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#493×C₁₀₁	2
C₂×#459×C₁₀₁	2
C₁₀₁×#2541	2
C₁₀₁×#1982	2
C₂×#331×C₁₀₁	2
C₂×D₄⋊C₈×C₁₀₁	2
C₁₀₁×#1279	2
#10046	101

Subgroups — C101×#10046 #38792197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#10046 #38792197