Subgroups — C₅×D₂₄ #6691

Order 240.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₂	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₈	—	3	1	no	maximal, Hall
4	C₂×C₅×D₃	—	2	2	no	—
5	C₃×C₄×C₅	C₂²	1	1	yes	characteristic
6	D₂₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×D₄	—	3	2	no	—
8	C₅×C₈	D₃	1	1	yes	characteristic, complemented
9	C₂×C₃×C₅	D₄	1	1	yes	characteristic
10	C₅×D₃	—	4	2	no	—
11	D₁₂	C₂×C₅	1	2	yes	complemented
12	C₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
13	C₂²×C₅	—	6	2	no	—
14	C₄×C₅	C₂×D₃	1	1	yes	characteristic
15	D₈	—	3	1	no	Sylow
16	C₃×C₅	D₈	1	1	yes	characteristic, complemented, Hall
17	C₂×D₃	—	2	2	no	—
18	C₃×C₄	C₂²×C₅	1	1	yes	characteristic
19	C₂×C₅	—	12	2	no	—
20	C₂×C₅	D₁₂	1	1	yes	characteristic
21	D₄	—	3	2	no	—
22	C₈	C₅×D₃	1	1	yes	characteristic, complemented
23	C₂×C₃	C₅×D₄	1	1	yes	characteristic
24	D₃	—	4	2	no	—
25	C₅	D₂₄	1	1	yes	characteristic, direct product factor, Sylow
26	C₂²	—	6	2	no	—
27	C₄	C₂×C₅×D₃	1	1	yes	characteristic
28	C₃	C₅×D₈	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	12	2	no	—
30	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.