Subgroups — C₅×Dic₁₂ #6692

Order 240.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Dic₆	C₂	1	2	yes	maximal
2	C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	C₅×Q₁₆	—	3	1	no	maximal, Hall
4	C₃×C₄×C₅	C₂²	1	1	yes	characteristic
5	C₅×Dic₃	—	2	2	no	—
6	Dic₁₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×Q₈	—	3	2	no	—
8	C₅×C₈	D₃	1	1	yes	characteristic
9	C₂×C₃×C₅	D₄	1	1	yes	characteristic
10	Dic₆	C₂×C₅	1	2	yes	—
11	C₃×C₈	C₂×C₅	1	1	yes	characteristic
12	C₄×C₅	—	6	2	no	—
13	C₄×C₅	C₂×D₃	1	1	yes	characteristic
14	Q₁₆	—	3	1	no	Sylow
15	C₃×C₅	Q₁₆	1	1	yes	characteristic, complemented, Hall
16	C₃×C₄	C₂²×C₅	1	1	yes	characteristic
17	Dic₃	—	2	2	no	—
18	C₂×C₅	D₁₂	1	1	yes	characteristic
19	Q₈	—	3	2	no	—
20	C₈	C₅×D₃	1	1	yes	characteristic
21	C₂×C₃	C₅×D₄	1	1	yes	characteristic
22	C₅	Dic₁₂	1	1	yes	characteristic, direct product factor, Sylow
23	C₄	—	6	2	no	—
24	C₄	C₂×C₅×D₃	1	1	yes	characteristic
25	C₃	C₅×Q₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₂	C₅×D₁₂	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.