Subgroups — #4094

Order 160.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#41	C₂	1	1	yes	maximal, characteristic
2	#681	C₂	1	3	yes	maximal, complemented
3	C₂×#168	C₂	1	3	yes	maximal, complemented
4	C₅×Q₈	C₄	1	1	yes	characteristic
5	C₅×D₄	C₄	1	3	yes	—
6	C₂×C₄×C₅	C₂²	1	3	yes	—
7	#168	C₂²	1	1	yes	characteristic
8	#168	C₂²	1	3	yes	—
9	#131	—	5	1	no	maximal, Sylow
10	C₂²×C₅	C₂×C₄	1	3	yes	—
11	C₄×C₅	C₂×C₄	1	3	yes	—
12	C₄×C₅	C₂³	1	1	yes	characteristic
13	#41	D₅	1	1	yes	characteristic
14	M₁₆	—	5	3	no	—
15	C₂×C₈	—	5	3	no	—
16	C₂×C₅	—	2	3	no	—
17	C₂×C₅	C₂²×C₄	1	1	yes	characteristic
18	Q₈	Dic₅	1	1	yes	characteristic
19	D₄	Dic₅	1	3	yes	—
20	C₂×C₄	C₂×D₅	1	3	yes	—
21	C₈	—	5	1	no	—
22	C₈	—	5	3	no	—
23	C₅	#131	1	1	yes	characteristic, complemented, Sylow
24	C₂²	C₂×Dic₅	1	3	yes	—
25	C₄	C₂×Dic₅	1	3	yes	—
26	C₄	C₂²×D₅	1	1	yes	characteristic
27	C₂	—	2	3	no	—
28	C₂	C₂²×Dic₅	1	1	yes	characteristic

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.