Subgroups — #4013

Order 160.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic
2	#704	C₂	1	2	yes	maximal, complemented
3	C₂³×C₅	C₄	1	1	yes	characteristic
4	C₂²×D₅	C₄	1	1	yes	characteristic
5	C₂²⋊D₅	—	2	2	no	—
6	C₂×Dic₅	C₂²	1	1	yes	characteristic
7	#170	—	2	2	no	—
8	#100	—	5	1	no	maximal, Sylow
9	C₂²×C₅	—	2	1	no	—
10	C₂²×C₅	—	4	1	no	—
11	C₂²×C₅	C₂×C₄	1	1	yes	characteristic
12	C₂×D₅	—	2	1	no	—
13	C₂×D₅	—	4	1	no	—
14	Dic₅	D₄	1	2	yes	—
15	C₂×D₄	—	5	1	no	—
16	M₁₆	—	5	2	no	—
17	C₂×C₅	—	2	1	no	—
18	C₂×C₅	—	4	1	no	—
19	C₂×C₅	C₂²⋊C₄	1	1	yes	characteristic
20	D₅	—	4	1	no	—
21	C₂³	—	5	1	no	—
22	C₂³	AGL(1,𝔽₅)	1	1	yes	characteristic
23	D₄	—	10	2	no	—
24	C₂×C₄	—	5	1	no	—
25	C₈	—	10	2	no	—
26	C₅	#100	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	2	1	no	—
28	C₂²	—	4	1	no	—
29	C₂²	—	10	1	no	—
30	C₂²	—	20	1	no	—
31	C₂²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
32	C₄	—	5	2	no	—
33	C₂	—	2	1	no	—
34	C₂	—	4	1	no	—
35	C₂	—	20	1	no	—
36	C₂	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #704	C₂	semidirect
26. C₅	#100	semidirect

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