Subgroups — C₂×C₅×Q₃₂ #65670

Order 320.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₁₆	C₂	1	2	yes	maximal
2	C₅×Q₃₂	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×Q₈	—	2	2	no	—
5	C₅×Q₁₆	—	2	2	no	—
6	C₅×Q₁₆	C₂²	1	4	yes	—
7	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₅×C₁₆	C₂²	1	2	yes	—
9	C₂×Q₃₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₅×Q₈	—	2	4	no	—
11	C₅×Q₈	—	4	2	no	—
12	C₂×C₄×C₅	—	4	2	no	—
13	C₂×C₄×C₅	D₄	1	1	yes	characteristic
14	C₅×C₈	D₄	1	1	yes	characteristic
15	C₅×C₈	C₂³	1	1	yes	characteristic
16	C₂×Q₁₆	C₂×C₅	1	2	yes	—
17	Q₃₂	C₂×C₅	1	4	yes	direct product factor
18	C₂×C₁₆	C₂×C₅	1	1	yes	characteristic
19	C₂²×C₅	D₈	1	1	yes	characteristic
20	C₄×C₅	—	4	4	no	—
21	C₄×C₅	D₈	1	1	yes	characteristic
22	C₄×C₅	C₂×D₄	1	1	yes	characteristic
23	C₂×Q₈	—	2	2	no	—
24	Q₁₆	—	2	2	no	—
25	Q₁₆	C₂²×C₅	1	4	yes	—
26	C₂×C₈	C₂²×C₅	1	1	yes	characteristic
27	C₁₆	C₂²×C₅	1	2	yes	—
28	C₂×C₅	Q₃₂	1	2	yes	direct product factor
29	C₂×C₅	C₂×D₈	1	1	yes	characteristic
30	Q₈	—	2	4	no	—
31	Q₈	—	4	2	no	—
32	C₂×C₄	—	4	2	no	—
33	C₂×C₄	C₅×D₄	1	1	yes	characteristic
34	C₈	C₅×D₄	1	1	yes	characteristic
35	C₈	C₂³×C₅	1	1	yes	characteristic
36	C₅	C₂×Q₃₂	1	1	yes	characteristic, direct product factor, Sylow
37	C₂²	C₅×D₈	1	1	yes	characteristic
38	C₄	—	4	4	no	—
39	C₄	C₅×D₈	1	1	yes	characteristic
40	C₄	C₂×C₅×D₄	1	1	yes	characteristic
41	C₂	C₅×Q₃₂	1	2	yes	direct product factor
42	C₂	C₂×C₅×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₅	D₈
commutator, Frattini, cosocle	C₈	C₂³×C₅
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×Q₃₂	C₂	direct (N × H)
9. C₂×Q₃₂	C₅	direct (N × H)
17. Q₃₂	C₂×C₅	direct (N × H)
28. C₂×C₅	Q₃₂	direct (N × H)
36. C₅	C₂×Q₃₂	direct (N × H)
41. C₂	C₅×Q₃₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×Q₁₆	2
C₅×Q₃₂	2
C₂×C₅×C₁₆	2
C₂×Q₃₂	5

Subgroups — C2×C5×Q32 #65670

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×Q₃₂ #65670