Subgroups — C₂×C₅×Q₁₆ #4120

Order 160.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₈	C₂	1	2	yes	maximal
2	C₅×Q₁₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₅×C₈	C₂	1	1	yes	maximal, characteristic
4	C₅×Q₈	—	2	2	no	—
5	C₅×Q₈	C₂²	1	4	yes	—
6	C₂×C₄×C₅	—	2	2	no	—
7	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₅×C₈	C₂²	1	2	yes	—
9	C₂×Q₁₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂²×C₅	D₄	1	1	yes	characteristic
11	C₄×C₅	—	2	4	no	—
12	C₄×C₅	D₄	1	1	yes	characteristic
13	C₄×C₅	C₂³	1	1	yes	characteristic
14	C₂×Q₈	C₂×C₅	1	2	yes	—
15	Q₁₆	C₂×C₅	1	4	yes	direct product factor
16	C₂×C₈	C₂×C₅	1	1	yes	characteristic
17	C₂×C₅	Q₁₆	1	2	yes	direct product factor
18	C₂×C₅	C₂×D₄	1	1	yes	characteristic
19	Q₈	—	2	2	no	—
20	Q₈	C₂²×C₅	1	4	yes	—
21	C₂×C₄	—	2	2	no	—
22	C₂×C₄	C₂²×C₅	1	1	yes	characteristic
23	C₈	C₂²×C₅	1	2	yes	—
24	C₅	C₂×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²	C₅×D₄	1	1	yes	characteristic
26	C₄	—	2	4	no	—
27	C₄	C₅×D₄	1	1	yes	characteristic
28	C₄	C₂³×C₅	1	1	yes	characteristic
29	C₂	C₅×Q₁₆	1	2	yes	direct product factor
30	C₂	C₂×C₅×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₅	D₄
commutator, Frattini, cosocle	C₄	C₂³×C₅
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ G

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.