Subgroups — #4036

Order 160.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₅	C₂	1	2	yes	maximal
3	C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic
4	#683	C₂	1	2	yes	maximal
5	C₄×Dic₅	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×C₅	C₂²	1	2	yes	—
7	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂×Dic₅	C₂²	1	1	yes	characteristic
9	C₂×Dic₅	C₂²	1	1	yes	characteristic
10	C₂×Dic₅	C₂²	1	2	yes	—
11	#125	—	5	1	no	maximal, Sylow
12	C₂²×C₅	C₂³	1	1	yes	characteristic
13	C₄×C₅	—	2	2	no	—
14	C₄×C₅	Q₈	1	2	yes	—
15	Dic₅	—	2	1	no	—
16	Dic₅	—	2	1	no	—
17	Dic₅	—	2	2	no	—
18	C₄⋊C₄	—	5	2	no	—
19	C₄⋊C₄	—	5	2	no	—
20	C₄⋊C₄	—	5	1	no	—
21	C₄⋊C₄	D₅	1	1	yes	characteristic
22	C₄²	—	5	1	no	—
23	C₂×C₅	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₅	#41	1	1	yes	characteristic
25	C₂×C₅	#41	1	1	yes	characteristic
26	C₂×C₄	—	5	1	no	—
27	C₂×C₄	—	5	1	no	—
28	C₂×C₄	—	5	2	no	—
29	C₂×C₄	C₂×D₅	1	2	yes	—
30	C₂×C₄	C₂×D₅	1	1	yes	characteristic
31	C₅	#125	1	1	yes	characteristic, complemented, Sylow
32	C₂²	C₂²×D₅	1	1	yes	characteristic
33	C₄	—	2	2	no	—
34	C₄	—	10	1	no	—
35	C₄	—	10	1	no	—
36	C₄	—	10	2	no	—
37	C₄	Dic₁₀	1	2	yes	—
38	C₂	C₂×Dic₁₀	1	1	yes	characteristic
39	C₂	#711	1	1	yes	characteristic
40	C₂	#713	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₅
commutator, socle, prime radical, cosocle	C₂²×C₅	C₂³
Fitting	C₅×C₄⋊C₄	C₂
hypercenter	C₄⋊C₄	D₅
hypocenter	C₅	#125
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

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

N	H ≅ G/N	type
31. C₅	#125	semidirect

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