Subgroups — #4005

Order 160.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₀	C₂	1	1	yes	maximal, characteristic
2	#704	C₂	1	2	yes	maximal
3	C₂×C₄×C₅	C₄	1	1	yes	characteristic
4	C₂×Dic₅	C₄	1	1	yes	characteristic
5	C₂×Dic₅	C₂²	1	1	yes	characteristic
6	Dic₁₀	—	2	2	no	—
7	#170	—	2	2	no	—
8	#101	—	5	1	no	maximal, Sylow
9	C₂²×C₅	C₂×C₄	1	1	yes	characteristic
10	C₄×C₅	—	2	1	no	—
11	Dic₅	—	2	1	no	—
12	Dic₅	D₄	1	2	yes	—
13	C₂×Q₈	—	5	1	no	—
14	M₁₆	—	5	2	no	—
15	C₂×C₅	—	2	1	no	—
16	C₂×C₅	C₂²⋊C₄	1	1	yes	characteristic
17	Q₈	—	10	2	no	—
18	C₂×C₄	—	5	1	no	—
19	C₂×C₄	—	5	1	no	—
20	C₂×C₄	AGL(1,𝔽₅)	1	1	yes	characteristic
21	C₈	—	10	2	no	—
22	C₅	#101	1	1	yes	characteristic, complemented, Sylow
23	C₂²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
24	C₄	—	2	1	no	—
25	C₄	—	5	2	no	—
26	C₄	—	10	1	no	—
27	C₂	—	2	1	no	—
28	C₂	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic

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

N	H ≅ G/N	type
22. C₅	#101	semidirect

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