Subgroups — #4007

Order 160.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×D₅	C₂	1	1	yes	maximal, characteristic
2	C₄⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
3	D₅⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₅	—	2	1	no	—
5	C₂×AGL(1,𝔽₅)	—	2	1	no	—
6	C₅×D₄	C₄	1	1	yes	characteristic, complemented
7	C₂²⋊D₅	—	2	1	no	—
8	D₂₀	C₄	1	1	yes	characteristic, complemented
9	C₄×D₅	C₂²	1	1	yes	characteristic
10	#170	—	2	1	no	—
11	#102	—	5	1	no	maximal, Sylow
12	C₂²×C₅	—	2	1	no	—
13	C₂×D₅	—	2	1	no	—
14	C₂×D₅	—	4	1	no	—
15	C₂×D₅	—	4	1	no	—
16	C₂×D₅	D₄	1	1	yes	characteristic
17	AGL(1,𝔽₅)	—	4	1	no	—
18	C₄×C₅	C₂×C₄	1	1	yes	characteristic
19	Dic₅	D₄	1	1	yes	characteristic
20	C₂×D₄	—	5	1	no	—
21	C₂×C₈	—	5	1	no	—
22	C₄⋊C₄	—	5	1	no	—
23	C₂×C₅	—	4	1	no	—
24	C₂×C₅	C₂²⋊C₄	1	1	yes	characteristic
25	D₅	—	4	1	no	—
26	D₅	D₈	1	1	yes	characteristic
27	D₅	SD₁₆	1	1	yes	characteristic
28	C₂³	—	10	1	no	—
29	D₄	—	5	1	no	—
30	D₄	—	10	1	no	—
31	D₄	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
32	C₂×C₄	—	5	1	no	—
33	C₂×C₄	—	10	1	no	—
34	C₈	—	10	1	no	—
35	C₅	#102	1	1	yes	characteristic, complemented, Sylow
36	C₂²	—	2	1	no	—
37	C₂²	—	5	1	no	—
38	C₂²	—	10	1	no	—
39	C₂²	—	20	1	no	—
40	C₂²	—	20	1	no	—
41	C₄	—	5	1	no	—
42	C₄	—	20	1	no	—
43	C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
44	C₂	—	4	1	no	—
45	C₂	—	5	1	no	—
46	C₂	—	5	1	no	—
47	C₂	—	20	1	no	—
48	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.