Subgroups — #4131

Order 160.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#711	C₂	1	1	yes	maximal, characteristic
2	#704	C₂	1	2	yes	maximal, complemented
3	C₂×#170	C₂	1	2	yes	maximal, complemented
4	#700	C₂	1	1	yes	maximal, characteristic, complemented
5	D₅⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×D₄	C₄	1	1	yes	characteristic
7	C₂²⋊D₅	C₄	1	2	yes	—
8	C₂×Dic₅	C₂²	1	2	yes	—
9	C₄×D₅	C₂²	1	1	yes	characteristic
10	Dic₁₀	C₄	1	1	yes	characteristic
11	#170	C₂²	1	1	yes	characteristic
12	#170	C₂²	1	1	yes	characteristic
13	#170	C₂²	1	2	yes	—
14	#131	—	5	1	no	maximal, Sylow
15	C₂²×C₅	C₂×C₄	1	2	yes	—
16	C₂×D₅	C₂×C₄	1	1	yes	characteristic
17	C₄×C₅	C₂×C₄	1	1	yes	characteristic
18	Dic₅	C₂×C₄	1	2	yes	—
19	Dic₅	C₂³	1	1	yes	characteristic
20	#41	—	5	1	no	—
21	M₁₆	—	5	1	no	—
22	M₁₆	—	5	2	no	—
23	C₂×C₈	—	5	1	no	—
24	C₂×C₈	—	5	2	no	—
25	C₂×C₅	—	2	2	no	—
26	C₂×C₅	C₂²×C₄	1	1	yes	characteristic
27	D₅	—	2	1	no	—
28	Q₈	—	5	1	no	—
29	D₄	—	5	2	no	—
30	D₄	AGL(1,𝔽₅)	1	1	yes	characteristic
31	C₂×C₄	—	5	2	no	—
32	C₂×C₄	—	5	1	no	—
33	C₈	—	5	1	no	—
34	C₈	—	5	1	no	—
35	C₈	—	5	2	no	—
36	C₅	#131	1	1	yes	characteristic, complemented, Sylow
37	C₂²	—	5	1	no	—
38	C₂²	C₂×AGL(1,𝔽₅)	1	2	yes	—
39	C₄	—	5	1	no	—
40	C₄	—	5	2	no	—
41	C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
42	C₂	—	2	2	no	—
43	C₂	—	10	1	no	—
44	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.