Subgroups — C₄×C₅×Dic₃ #6695

Order 240.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Dic₃	C₂	1	2	yes	maximal
3	C₄²×C₅	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₅	C₂²	1	1	yes	characteristic
5	C₃×C₄×C₅	C₄	1	2	yes	complemented
6	C₅×Dic₃	C₄	1	4	yes	direct product factor
7	C₄×Dic₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₄×C₅	—	3	2	no	—
9	C₂×C₄×C₅	D₃	1	1	yes	characteristic
10	C₂×C₃×C₅	C₂×C₄	1	2	yes	—
11	C₂×C₃×C₅	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃×C₄	C₂×C₅	1	1	yes	characteristic
13	C₂×Dic₃	C₂×C₅	1	2	yes	—
14	C₂²×C₅	C₂×D₃	1	1	yes	characteristic
15	C₄×C₅	—	3	4	no	—
16	C₄×C₅	Dic₃	1	2	yes	direct product factor
17	C₄²	—	3	1	no	Sylow
18	C₃×C₅	C₄²	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₃	C₂²×C₅	1	1	yes	characteristic
20	C₃×C₄	C₄×C₅	1	2	yes	complemented
21	Dic₃	C₄×C₅	1	4	yes	direct product factor
22	C₂×C₅	C₄×D₃	1	2	yes	—
23	C₂×C₅	C₂×Dic₃	1	1	yes	characteristic
24	C₂×C₄	—	3	2	no	—
25	C₂×C₄	C₅×D₃	1	1	yes	characteristic
26	C₂×C₃	C₂×C₄×C₅	1	2	yes	—
27	C₂×C₃	C₂×C₄×C₅	1	1	yes	characteristic
28	C₅	C₄×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²	C₂×C₅×D₃	1	1	yes	characteristic
30	C₄	—	3	4	no	—
31	C₄	C₅×Dic₃	1	2	yes	direct product factor
32	C₃	C₄²×C₅	1	1	yes	characteristic, complemented, Sylow
33	C₂	C₄×C₅×D₃	1	2	yes	—
34	C₂	C₂×C₅×Dic₃	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.