Subgroups — C₃×C₅×Q₁₆ #6727

Order 240.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, socle, prime radical	C₂×C₃×C₅	D₄
commutator, Frattini, cosocle	C₄	C₂²×C₃×C₅
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₃×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.