Subgroups — #4003

Order 160.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×#170	C₂	1	2	yes	maximal, complemented
3	C₂²×D₅	C₄	1	1	yes	characteristic
4	C₂×C₄×C₅	C₄	1	1	yes	characteristic
5	C₂×Dic₅	C₂²	1	1	yes	characteristic
6	C₄×D₅	—	2	2	no	—
7	#170	—	2	2	no	—
8	C₂²⋊C₈	—	5	1	no	maximal, Sylow
9	C₂²×C₅	C₂×C₄	1	1	yes	characteristic
10	C₂×D₅	—	2	1	no	—
11	C₂×D₅	—	2	1	no	—
12	C₂×D₅	C₈	1	2	yes	complemented
13	C₄×C₅	—	2	1	no	—
14	Dic₅	D₄	1	2	yes	—
15	C₂²×C₄	—	5	1	no	—
16	C₂×C₈	—	5	2	no	—
17	C₂×C₅	C₂²⋊C₄	1	1	yes	characteristic
18	C₂×C₅	C₂×C₈	1	1	yes	characteristic
19	C₂×C₅	M₁₆	1	1	yes	characteristic
20	D₅	—	2	2	no	—
21	C₂³	—	5	1	no	—
22	C₂×C₄	—	5	1	no	—
23	C₂×C₄	—	10	2	no	—
24	C₂×C₄	AGL(1,𝔽₅)	1	1	yes	characteristic
25	C₈	—	10	2	no	—
26	C₅	C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	5	2	no	—
28	C₂²	—	10	1	no	—
29	C₂²	—	10	1	no	—
30	C₂²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
31	C₄	—	2	1	no	—
32	C₄	—	5	2	no	—
33	C₂	—	10	2	no	—
34	C₂	D₅⋊C₈	1	1	yes	characteristic
35	C₂	#700	1	1	yes	characteristic
36	C₂	C₂²⋊AGL(1,𝔽₅)	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.