Subgroups — C₅×#585 #66296

Order 320.

810 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×2₋¹⁺⁴	C₂	1	6	yes	maximal, complemented
2	C₅×H(5,𝔽₂)	C₂	1	10	yes	maximal, complemented
3	C₂×C₅×#41	C₂	1	15	yes	maximal, complemented
4	C₅×#41	C₂²	1	20	yes	complemented
5	C₅×#41	C₂²	1	60	yes	complemented
6	C₂×C₅×Q₈	C₂²	1	15	yes	complemented
7	C₂×C₅×D₄	C₂²	1	45	yes	complemented
8	C₂²×C₄×C₅	C₂²	1	15	yes	complemented
9	#585	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂³×C₅	C₂³	1	15	yes	—
11	C₅×Q₈	C₂³	1	20	yes	—
12	C₅×D₄	C₂³	1	60	yes	—
13	C₂×C₄×C₅	C₂³	1	45	yes	—
14	C₂×C₄×C₅	C₂³	1	15	yes	—
15	2₋¹⁺⁴	C₂×C₅	1	6	yes	complemented
16	H(5,𝔽₂)	C₂×C₅	1	10	yes	complemented
17	C₂×#41	C₂×C₅	1	15	yes	complemented
18	C₂²×C₅	—	4	15	no	—
19	C₂²×C₅	C₂⁴	1	15	yes	—
20	C₄×C₅	C₂⁴	1	15	yes	—
21	C₄×C₅	C₂⁴	1	1	yes	characteristic
22	#41	C₂²×C₅	1	20	yes	complemented
23	#41	C₂²×C₅	1	60	yes	complemented
24	C₂×Q₈	C₂²×C₅	1	15	yes	complemented
25	C₂×D₄	C₂²×C₅	1	45	yes	complemented
26	C₂²×C₄	C₂²×C₅	1	15	yes	complemented
27	C₂×C₅	—	2	15	no	—
28	C₂×C₅	C₂⁵	1	1	yes	characteristic
29	C₂³	C₂³×C₅	1	15	yes	—
30	Q₈	C₂³×C₅	1	20	yes	—
31	D₄	C₂³×C₅	1	60	yes	—
32	C₂×C₄	C₂³×C₅	1	15	yes	—
33	C₂×C₄	C₂³×C₅	1	45	yes	—
34	C₅	#585	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²	—	4	15	no	—
36	C₂²	C₂⁴×C₅	1	15	yes	—
37	C₄	C₂⁴×C₅	1	1	yes	characteristic
38	C₄	C₂⁴×C₅	1	15	yes	—
39	C₂	—	2	15	no	—
40	C₂	C₂⁵×C₅	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	C₂⁴
commutator, Frattini, cosocle	C₂	C₂⁵×C₅
socle	C₂×C₅	C₂⁵
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅ ◁ G

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

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