Subgroups — C₅×#500 #65663

Order 320.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄⋊Q₈	C₂	1	2	yes	maximal
2	C₅×#107	C₂	1	4	yes	maximal
3	C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×Q₈	—	2	2	no	—
5	C₂×C₅×C₈	C₂²	1	2	yes	—
6	C₅×C₄⋊C₄	—	2	2	no	—
7	C₅×C₄⋊C₄	C₂²	1	4	yes	—
8	C₄²×C₅	C₂²	1	1	yes	characteristic
9	#500	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₅×Q₈	—	4	4	no	—
11	C₂×C₄×C₅	—	2	4	no	—
12	C₂×C₄×C₅	D₄	1	1	yes	characteristic
13	C₂×C₄×C₅	D₄	1	1	yes	characteristic
14	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
15	C₅×C₈	Q₈	1	4	yes	complemented
16	C₄⋊Q₈	C₂×C₅	1	2	yes	—
17	#107	C₂×C₅	1	4	yes	—
18	C₄×C₈	C₂×C₅	1	1	yes	characteristic
19	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
20	C₄×C₅	—	4	4	no	—
21	C₄×C₅	D₈	1	2	yes	—
22	C₄×C₅	Q₁₆	1	2	yes	—
23	C₄×C₅	C₂×Q₈	1	2	yes	—
24	C₂×Q₈	—	2	2	no	—
25	C₂×C₈	C₂²×C₅	1	2	yes	—
26	C₄⋊C₄	—	2	2	no	—
27	C₄⋊C₄	C₂²×C₅	1	4	yes	—
28	C₄²	C₂²×C₅	1	1	yes	characteristic
29	C₂×C₅	C₄⋊Q₈	1	1	yes	characteristic
30	C₂×C₅	C₂×D₈	1	1	yes	characteristic
31	C₂×C₅	C₂×Q₁₆	1	1	yes	characteristic
32	Q₈	—	4	4	no	—
33	C₂×C₄	—	2	4	no	—
34	C₂×C₄	C₅×D₄	1	1	yes	characteristic
35	C₂×C₄	C₅×D₄	1	1	yes	characteristic
36	C₂×C₄	C₂³×C₅	1	1	yes	characteristic
37	C₈	C₅×Q₈	1	4	yes	complemented
38	C₅	#500	1	1	yes	characteristic, direct product factor, Sylow
39	C₂²	C₂×C₅×D₄	1	1	yes	characteristic
40	C₄	—	4	4	no	—
41	C₄	C₅×D₈	1	2	yes	—
42	C₄	C₅×Q₁₆	1	2	yes	—
43	C₄	C₂×C₅×Q₈	1	2	yes	—
44	C₂	C₅×C₄⋊Q₈	1	1	yes	characteristic
45	C₂	C₂×C₅×D₈	1	1	yes	characteristic
46	C₂	C₂×C₅×Q₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
9. #500	C₅	direct (N × H)
15. C₅×C₈	Q₈	semidirect
37. C₈	C₅×Q₈	semidirect
38. C₅	#500	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₄⋊Q₈	2
C₅×#107	2
C₄×C₅×C₈	2
#500	5

Subgroups — C5×#500 #65663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#500 #65663