Subgroups — C₅×#64988 #13101960

Order 1600.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Dic₂₀	C₂	1	4	yes	maximal
2	C₅×#4015	C₂	1	2	yes	maximal
3	C₄×C₅²×C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×Dic₁₀	C₂²	1	4	yes	—
5	C₂×C₅²×C₈	C₂²	1	2	yes	—
6	C₄²×C₅²	C₂²	1	1	yes	characteristic
7	C₅×C₄⋊Dic₅	—	2	4	no	—
8	C₅×Dic₂₀	—	2	8	no	—
9	C₅×#494	—	5	1	no	maximal
10	#64988	C₅	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₄×C₅²	D₄	1	2	yes	—
12	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
13	C₂×C₅×Dic₅	—	2	4	no	—
14	C₅×Dic₁₀	—	2	8	no	—
15	C₅²×C₈	D₄	1	4	yes	—
16	C₂×C₅×Q₁₆	—	5	4	no	—
17	C₅×C₄⋊Q₈	—	5	2	no	—
18	C₂×Dic₂₀	C₂×C₅	1	4	yes	—
19	#4015	C₂×C₅	1	2	yes	—
20	C₄×C₅×C₈	—	2	2	no	—
21	C₄×C₅×C₈	D₅	1	1	yes	characteristic
22	C₄×C₅×C₈	C₂×C₅	1	1	yes	characteristic
23	C₂²×C₅²	C₂×D₄	1	1	yes	characteristic
24	C₄×C₅²	Q₁₆	1	4	yes	complemented
25	C₄×C₅²	C₂×D₄	1	2	yes	—
26	C₅×Dic₅	—	4	4	no	—
27	C₂×C₅×Q₈	—	5	4	no	—
28	C₂×Dic₁₀	C₂²×C₅	1	4	yes	—
29	C₅×Q₁₆	—	10	8	no	—
30	C₂×C₅×C₈	—	2	4	no	—
31	C₂×C₅×C₈	C₂×D₅	1	2	yes	—
32	C₂×C₅×C₈	C₂²×C₅	1	2	yes	—
33	C₅×C₄⋊C₄	—	10	4	no	—
34	C₄²×C₅	—	2	2	no	—
35	C₄²×C₅	C₂×D₅	1	1	yes	characteristic
36	C₄²×C₅	C₂²×C₅	1	1	yes	characteristic
37	C₄⋊Dic₅	—	2	4	no	—
38	Dic₂₀	—	2	8	no	—
39	#494	—	5	1	no	Sylow
40	C₂×C₅²	#127	1	1	yes	characteristic
41	C₂×C₅²	C₂×Q₁₆	1	2	yes	—
42	C₅×Q₈	—	10	8	no	—
43	C₂×C₄×C₅	—	2	4	no	—
44	C₂×C₄×C₅	—	2	2	no	—
45	C₂×C₄×C₅	—	10	4	no	—
46	C₂×C₄×C₅	D₂₀	1	2	yes	—
47	C₂×C₄×C₅	C₅×D₄	1	2	yes	—
48	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
49	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
50	C₂×Dic₅	—	2	4	no	—
51	Dic₁₀	—	2	8	no	—
52	C₅×C₈	—	2	8	no	—
53	C₅×C₈	D₂₀	1	4	yes	—
54	C₅×C₈	C₅×D₄	1	4	yes	—
55	C₂×Q₁₆	—	5	4	no	—
56	C₄⋊Q₈	—	5	2	no	—
57	C₄×C₈	C₅×D₅	1	1	yes	characteristic
58	C₅²	#494	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₅	—	2	2	no	—
60	C₂²×C₅	C₂×D₂₀	1	1	yes	characteristic
61	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
62	C₄×C₅	—	2	4	no	—
63	C₄×C₅	—	2	8	no	—
64	C₄×C₅	—	20	4	no	—
65	C₄×C₅	Dic₂₀	1	4	yes	complemented
66	C₄×C₅	C₅×Q₁₆	1	4	yes	complemented
67	C₄×C₅	C₂×D₂₀	1	2	yes	—
68	C₄×C₅	C₂×C₅×D₄	1	2	yes	—
69	Dic₅	—	4	4	no	—
70	C₂×Q₈	—	5	4	no	—
71	Q₁₆	—	10	8	no	—
72	C₂×C₈	C₂×C₅×D₅	1	2	yes	—
73	C₄⋊C₄	—	10	4	no	—
74	C₄²	C₂×C₅×D₅	1	1	yes	characteristic
75	C₂×C₅	—	2	4	no	—
76	C₂×C₅	—	2	2	no	—
77	C₂×C₅	#4020	1	1	yes	characteristic
78	C₂×C₅	C₂×Dic₂₀	1	2	yes	—
79	C₂×C₅	C₅×#127	1	1	yes	characteristic
80	C₂×C₅	C₂×C₅×Q₁₆	1	2	yes	—
81	Q₈	—	10	8	no	—
82	C₂×C₄	—	10	4	no	—
83	C₂×C₄	C₅×D₂₀	1	2	yes	—
84	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
85	C₈	C₅×D₂₀	1	4	yes	—
86	C₅	—	2	2	no	—
87	C₅	#64988	1	1	yes	characteristic, direct product factor
88	C₅	C₅×#494	1	1	yes	characteristic, complemented
89	C₂²	C₂×C₅×D₂₀	1	1	yes	characteristic
90	C₄	—	20	4	no	—
91	C₄	C₅×Dic₂₀	1	4	yes	complemented
92	C₄	C₂×C₅×D₂₀	1	2	yes	—
93	C₂	C₅×#4020	1	1	yes	characteristic
94	C₂	C₂×C₅×Dic₂₀	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₂₀
commutator, cosocle	C₂×C₄×C₅	C₂³×C₅
Frattini	C₂×C₄	C₂²×C₅×D₅
Fitting	C₄×C₅²×C₈	C₂
socle, prime radical	C₂²×C₅²	C₂×D₄
hypercenter	C₄×C₅×C₈	D₅
hypocenter	C₅	C₅×#494
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₄×C₅×C₈

Complements

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

N	H ≅ G/N	type
10. #64988	C₅	direct (N × H)
24. C₄×C₅²	Q₁₆	semidirect
58. C₅²	#494	semidirect
65. C₄×C₅	Dic₂₀	semidirect
66. C₄×C₅	C₅×Q₁₆	semidirect
87. C₅	#64988	direct (N × H)
88. C₅	C₅×#494	semidirect
91. C₄	C₅×Dic₂₀	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×Dic₂₀	2
C₅×#4015	2
C₄×C₅²×C₈	2
C₅×#494	5
#64988	5

Subgroups — C5×#64988 #13101960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#64988 #13101960