Subgroups — C₃×C₅×Q₃₂ #91140

Order 480.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×Q₁₆	C₂	1	2	yes	maximal
2	C₃×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₅×Q₃₂	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×Q₈	—	2	2	no	—
5	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
6	C₃×Q₃₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×Q₁₆	C₂×C₃	1	2	yes	—
8	C₅×C₁₆	C₂×C₃	1	1	yes	characteristic
9	C₃×C₄×C₅	—	4	2	no	—
10	C₃×C₄×C₅	D₄	1	1	yes	characteristic
11	C₃×Q₁₆	C₂×C₅	1	2	yes	—
12	C₃×C₁₆	C₂×C₅	1	1	yes	characteristic
13	C₅×Q₈	—	2	2	no	—
14	C₅×C₈	C₂²×C₃	1	1	yes	characteristic
15	Q₃₂	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₃×C₅	D₈	1	1	yes	characteristic
17	C₃×Q₈	—	2	2	no	—
18	C₃×C₈	C₂²×C₅	1	1	yes	characteristic
19	C₄×C₅	—	4	2	no	—
20	C₄×C₅	C₃×D₄	1	1	yes	characteristic
21	Q₁₆	C₂×C₃×C₅	1	2	yes	—
22	C₁₆	C₂×C₃×C₅	1	1	yes	characteristic
23	C₃×C₅	Q₃₂	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₄	—	4	2	no	—
25	C₃×C₄	C₅×D₄	1	1	yes	characteristic
26	C₂×C₅	C₃×D₈	1	1	yes	characteristic
27	Q₈	—	2	2	no	—
28	C₈	C₂²×C₃×C₅	1	1	yes	characteristic
29	C₂×C₃	C₅×D₈	1	1	yes	characteristic
30	C₅	C₃×Q₃₂	1	1	yes	characteristic, direct product factor, Sylow
31	C₄	—	4	2	no	—
32	C₄	C₃×C₅×D₄	1	1	yes	characteristic
33	C₃	C₅×Q₃₂	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₃×C₅×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂×C₃×C₅	D₈
commutator, Frattini, cosocle	C₈	C₂²×C₃×C₅
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₃×C₄×C₅ ◁ C₃×C₅×C₈ ◁ 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.