Subgroups — C₅×#64740 #13099432

Order 1600.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₁₆	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₄₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3926	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×D₈	—	2	1	no	—
5	C₅×Dic₂₀	—	2	1	no	—
6	C₅²×C₁₆	C₂²	1	1	yes	characteristic
7	C₅×SD₆₄	—	5	1	no	maximal
8	#64740	C₅	1	1	yes	maximal, characteristic, direct product factor
9	C₅²×D₄	—	4	1	no	—
10	C₅×Dic₁₀	—	4	1	no	—
11	C₅²×C₈	D₄	1	1	yes	characteristic
12	C₅×Q₃₂	—	5	1	no	—
13	C₅×D₁₆	—	2	2	no	—
14	C₅×D₁₆	D₅	1	1	yes	characteristic
15	C₅×D₁₆	C₂×C₅	1	1	yes	characteristic
16	Dic₄₀	C₂×C₅	1	1	yes	characteristic, complemented
17	C₅×C₃₂	—	5	1	no	—
18	#3926	C₂×C₅	1	1	yes	characteristic, complemented
19	C₂²×C₅²	—	8	1	no	—
20	C₄×C₅²	D₈	1	1	yes	characteristic
21	C₅×Dic₅	—	8	1	no	—
22	C₅×Q₁₆	—	10	1	no	—
23	C₅×D₈	—	2	4	no	—
24	C₅×D₈	—	2	1	no	—
25	C₅×D₈	—	2	1	no	—
26	Dic₂₀	—	2	1	no	—
27	C₅×C₁₆	—	2	2	no	—
28	C₅×C₁₆	C₂×D₅	1	1	yes	characteristic
29	C₅×C₁₆	C₂²×C₅	1	1	yes	characteristic
30	SD₆₄	—	5	1	no	Sylow
31	C₂×C₅²	—	16	1	no	—
32	C₂×C₅²	D₁₆	1	1	yes	characteristic
33	C₅×Q₈	—	20	1	no	—
34	C₅×D₄	—	4	4	no	—
35	C₅×D₄	—	4	1	no	—
36	C₅×D₄	—	4	1	no	—
37	Dic₁₀	—	4	1	no	—
38	C₅×C₈	—	2	2	no	—
39	C₅×C₈	C₂²⋊D₅	1	1	yes	characteristic
40	C₅×C₈	C₅×D₄	1	1	yes	characteristic
41	Q₃₂	—	5	1	no	—
42	D₁₆	C₅×D₅	1	1	yes	characteristic
43	C₃₂	—	5	1	no	—
44	C₅²	SD₆₄	1	1	yes	characteristic, complemented, Sylow
45	C₂²×C₅	—	8	4	no	—
46	C₂²×C₅	—	8	1	no	—
47	C₂²×C₅	—	8	1	no	—
48	C₄×C₅	—	2	2	no	—
49	C₄×C₅	—	40	1	no	—
50	C₄×C₅	#686	1	1	yes	characteristic
51	C₄×C₅	C₅×D₈	1	1	yes	characteristic
52	Dic₅	—	8	1	no	—
53	Q₁₆	—	10	1	no	—
54	D₈	—	2	1	no	—
55	C₁₆	C₂×C₅×D₅	1	1	yes	characteristic
56	C₂×C₅	—	2	2	no	—
57	C₂×C₅	—	16	4	no	—
58	C₂×C₅	—	16	1	no	—
59	C₂×C₅	—	16	1	no	—
60	C₂×C₅	#3958	1	1	yes	characteristic
61	C₂×C₅	C₅×D₁₆	1	1	yes	characteristic
62	Q₈	—	20	1	no	—
63	D₄	—	4	1	no	—
64	C₈	C₅×C₂²⋊D₅	1	1	yes	characteristic
65	C₅	—	2	2	no	—
66	C₅	#64740	1	1	yes	characteristic, direct product factor
67	C₅	C₅×SD₆₄	1	1	yes	characteristic, complemented
68	C₂²	—	8	1	no	—
69	C₄	—	40	1	no	—
70	C₄	C₅×#686	1	1	yes	characteristic
71	C₂	—	16	1	no	—
72	C₂	C₅×#3958	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	#3958
commutator, cosocle	C₅×C₁₆	C₂²×C₅
Frattini	C₁₆	C₂×C₅×D₅
Fitting, prime radical	C₅²×D₁₆	C₂
socle	C₂×C₅²	D₁₆
hypercenter	C₅×D₁₆	D₅
hypocenter	C₅	C₅×SD₆₄
LCS	G ▷ C₅×C₁₆ ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈ ◁ C₅×C₁₆ ◁ C₅×D₁₆

Complements

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

N	H ≅ G/N	type
2. C₅×Dic₄₀	C₂	semidirect
3. C₅×#3926	C₂	semidirect
8. #64740	C₅	direct (N × H)
16. Dic₄₀	C₂×C₅	semidirect
18. #3926	C₂×C₅	semidirect
44. C₅²	SD₆₄	semidirect
66. C₅	#64740	direct (N × H)
67. C₅	C₅×SD₆₄	semidirect

Maximal subgroups

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

subgroup	index
C₅²×D₁₆	2
C₅×Dic₄₀	2
C₅×#3926	2
C₅×SD₆₄	5
#64740	5

Subgroups — C5×#64740 #13099432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#64740 #13099432