Subgroups — C₅×#107 #3982

Order 160.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₈	C₂	1	1	yes	maximal, characteristic
2	C₅×C₄⋊C₄	C₂	1	2	yes	maximal
3	C₂×C₄×C₅	—	2	2	no	—
4	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
5	C₅×C₈	C₄	1	2	yes	complemented
6	#107	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂²×C₅	D₄	1	1	yes	characteristic
8	C₄×C₅	—	4	2	no	—
9	C₄×C₅	C₂×C₄	1	1	yes	characteristic
10	C₄×C₅	Q₈	1	1	yes	characteristic
11	C₂×C₈	C₂×C₅	1	1	yes	characteristic
12	C₄⋊C₄	C₂×C₅	1	2	yes	—
13	C₂×C₅	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₅	D₈	1	1	yes	characteristic
15	C₂×C₅	Q₁₆	1	1	yes	characteristic
16	C₂×C₄	—	2	2	no	—
17	C₂×C₄	C₂²×C₅	1	1	yes	characteristic
18	C₈	C₄×C₅	1	2	yes	complemented
19	C₅	#107	1	1	yes	characteristic, direct product factor, Sylow
20	C₂²	C₅×D₄	1	1	yes	characteristic
21	C₄	—	4	2	no	—
22	C₄	C₂×C₄×C₅	1	1	yes	characteristic
23	C₄	C₅×Q₈	1	1	yes	characteristic
24	C₂	C₅×C₄⋊C₄	1	1	yes	characteristic
25	C₂	C₅×D₈	1	1	yes	characteristic
26	C₂	C₅×Q₁₆	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.