Subgroups — #20265481

Order 6464.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₂₀₂	C₂	1	1	yes	maximal, characteristic
2	#15692188	C₂	1	1	yes	maximal, characteristic
3	#15692186	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#11717579	C₂	1	1	yes	maximal, characteristic
5	#15692178	C₂	1	1	yes	maximal, characteristic
6	#15692178	C₂	1	1	yes	maximal, characteristic
7	#125×C₁₀₁	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₂₀₂	C₂²	1	1	yes	characteristic
9	C₂×#11717579	C₂²	1	1	yes	characteristic
10	C₂×#11717579	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
12	#13108053	—	2	1	no	—
13	C₄×Dic₁₀₁	—	2	1	no	—
14	C₄⋊C₄×C₁₀₁	—	2	1	no	—
15	C₄⋊C₄×C₁₀₁	—	2	1	no	—
16	C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₁₀₁	—	2	1	no	—
20	C₂×C₄×C₁₀₁	—	2	1	no	—
21	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
22	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
23	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
24	C₂×Dic₁₀₁	—	2	1	no	—
25	C₂×Dic₁₀₁	—	2	1	no	—
26	Dic₂₀₂	—	2	1	no	—
27	Dic₂₀₂	Q₈	1	2	yes	—
28	#11717579	—	2	1	no	—
29	#11717579	—	2	1	no	—
30	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
31	C₄×C₁₀₁	—	2	1	no	—
32	C₄×C₁₀₁	—	2	1	no	—
33	C₄×C₁₀₁	—	4	1	no	—
34	C₄×C₁₀₁	—	4	1	no	—
35	C₄×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
36	C₄×C₁₀₁	#41	1	1	yes	characteristic
37	Dic₁₀₁	—	2	2	no	—
38	Dic₁₀₁	—	4	1	no	—
39	C₂×C₁₀₁	C₂²⋊Q₈	1	1	yes	characteristic
40	C₂×C₁₀₁	#135	1	1	yes	characteristic
41	C₂×C₁₀₁	#137	1	1	yes	characteristic
42	C₁₀₁	#479	1	1	yes	characteristic, complemented, Sylow
43	#479	—	101	1	no	maximal, Sylow
44	#125	D₁₀₁	1	1	yes	characteristic
45	C₄×Q₈	—	101	1	no	—
46	#107	—	101	1	no	—
47	#106	—	101	1	no	—
48	C₄⋊C₈	—	101	1	no	—
49	#103	—	101	1	no	—
50	#103	—	101	1	no	—
51	C₂×Q₈	—	101	1	no	—
52	C₂×C₈	—	101	1	no	—
53	C₂×C₈	—	101	1	no	—
54	C₄⋊C₄	—	2	1	no	—
55	C₄⋊C₄	—	2	1	no	—
56	C₄⋊C₄	—	101	1	no	—
57	C₄⋊C₄	—	202	1	no	—
58	C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
59	C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
60	C₄²	—	202	1	no	—
61	C₄²	C₂×D₁₀₁	1	1	yes	characteristic
62	Q₈	—	101	2	no	—
63	Q₈	—	202	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	202	1	no	—
67	C₂×C₄	—	202	1	no	—
68	C₂×C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
69	C₂×C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
70	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
71	C₈	—	202	1	no	—
72	C₈	—	202	1	no	—
73	C₂²	C₂×C₂²⋊D₁₀₁	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	404	1	no	—
79	C₄	—	202	2	no	—
80	C₄	Q₈×D₁₀₁	1	1	yes	characteristic
81	C₄	#13108075	1	1	yes	characteristic
82	C₂	#15692231	1	1	yes	characteristic
83	C₂	#15692275	1	1	yes	characteristic
84	C₂	#15692285	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₀₁
commutator	C₂×C₄×C₁₀₁	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	#125×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₂×D₄
hypercenter	#125	D₁₀₁
hypocenter	C₁₀₁	#479
LCS	G ▷ C₂×C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
42. C₁₀₁	#479	semidirect