Subgroups — C₃×Dic₂₀ #6676

Order 240.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Dic₁₀	C₂	1	2	yes	maximal
2	C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	Dic₂₀	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₄×C₅	C₂²	1	1	yes	characteristic
5	C₃×Dic₅	—	2	2	no	—
6	C₃×Q₁₆	—	5	1	no	maximal, Hall
7	Dic₁₀	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	—	5	2	no	—
11	C₃×C₈	D₅	1	1	yes	characteristic
12	C₄×C₅	C₂²×C₃	1	1	yes	characteristic
13	Dic₅	—	2	2	no	—
14	Q₁₆	—	5	1	no	Sylow
15	C₃×C₅	Q₁₆	1	1	yes	characteristic, complemented, Hall
16	C₃×C₄	—	10	2	no	—
17	C₃×C₄	C₂×D₅	1	1	yes	characteristic
18	C₂×C₅	C₃×D₄	1	1	yes	characteristic
19	Q₈	—	5	2	no	—
20	C₈	C₃×D₅	1	1	yes	characteristic
21	C₂×C₃	D₂₀	1	1	yes	characteristic
22	C₅	C₃×Q₁₆	1	1	yes	characteristic, complemented, Sylow
23	C₄	—	10	2	no	—
24	C₄	C₂×C₃×D₅	1	1	yes	characteristic
25	C₃	Dic₂₀	1	1	yes	characteristic, direct product factor, Sylow
26	C₂	C₃×D₂₀	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.