Subgroups — #3957

Order 160.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#709	C₂	1	1	yes	maximal, characteristic
2	C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
5	C₂²⋊D₅	—	2	1	no	—
6	C₂×Dic₅	—	2	1	no	—
7	D₂₀	C₄	1	1	yes	characteristic, complemented
8	C₄×D₅	—	2	1	no	—
9	Dic₁₀	C₄	1	1	yes	characteristic, complemented
10	C₅×C₈	—	2	1	no	—
11	#104	—	5	1	no	maximal, Sylow
12	C₂²×C₅	D₄	1	1	yes	characteristic
13	C₂×D₅	—	2	1	no	—
14	C₄×C₅	C₂×C₄	1	1	yes	characteristic
15	C₄×C₅	D₄	1	1	yes	characteristic
16	Dic₅	—	2	2	no	—
17	Dic₅	—	2	1	no	—
18	#41	—	5	1	no	—
19	M₁₆	D₅	1	1	yes	characteristic, complemented
20	C₄²	—	5	1	no	—
21	C₂×C₅	—	2	1	no	—
22	C₂×C₅	C₂²⋊C₄	1	1	yes	characteristic
23	D₅	—	4	1	no	—
24	Q₈	—	5	1	no	—
25	D₄	—	5	1	no	—
26	D₄	—	10	1	no	—
27	C₂×C₄	—	10	1	no	—
28	C₂×C₄	—	10	1	no	—
29	C₂×C₄	C₂×D₅	1	1	yes	characteristic
30	C₈	—	2	1	no	—
31	C₅	#104	1	1	yes	characteristic, complemented, Sylow
32	C₂²	—	10	1	no	—
33	C₂²	D₂₀	1	1	yes	characteristic
34	C₄	—	10	2	no	—
35	C₄	—	10	1	no	—
36	C₄	C₄×D₅	1	1	yes	characteristic
37	C₄	C₂²⋊D₅	1	1	yes	characteristic
38	C₂	—	2	1	no	—
39	C₂	—	20	1	no	—
40	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.