Subgroups — #3955

Order 160.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#681	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₅	C₄	1	2	yes	—
5	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
6	D₂₀	—	2	1	no	—
7	D₂₀	—	2	1	no	—
8	C₅×C₈	—	2	1	no	—
9	#168	—	2	1	no	—
10	#100	—	5	1	no	maximal, Sylow
11	C₂²×C₅	C₂×C₄	1	1	yes	characteristic
12	C₂×D₅	—	2	2	no	—
13	C₂×D₅	—	4	2	no	—
14	C₄×C₅	D₄	1	1	yes	characteristic
15	C₄×C₅	D₄	1	1	yes	characteristic
16	C₂×D₄	—	5	1	no	—
17	M₁₆	—	5	1	no	—
18	M₁₆	D₅	1	1	yes	characteristic, complemented
19	C₂×C₅	—	2	1	no	—
20	C₂×C₅	C₂²⋊C₄	1	1	yes	characteristic
21	D₅	—	4	2	no	—
22	C₂³	—	5	2	no	—
23	D₄	—	10	1	no	—
24	D₄	—	10	1	no	—
25	C₂×C₄	C₂×D₅	1	1	yes	characteristic
26	C₈	—	2	1	no	—
27	C₈	—	10	1	no	—
28	C₅	#100	1	1	yes	characteristic, complemented, Sylow
29	C₂²	—	10	2	no	—
30	C₂²	—	20	2	no	—
31	C₂²	C₄×D₅	1	1	yes	characteristic
32	C₄	D₂₀	1	1	yes	characteristic
33	C₄	C₂²⋊D₅	1	1	yes	characteristic
34	C₂	—	2	1	no	—
35	C₂	—	20	2	no	—
36	C₂	#685	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.