Subgroups — C₃×C₄²×C₅ #6720

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	3	yes	maximal
2	C₄²×C₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂²×C₃×C₅	C₂²	1	1	yes	characteristic
4	C₃×C₄×C₅	C₄	1	6	yes	direct product factor
5	C₃×C₄²	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₄×C₅	C₂×C₃	1	3	yes	—
7	C₂×C₃×C₅	C₂×C₄	1	3	yes	—
8	C₂×C₃×C₄	C₂×C₅	1	3	yes	—
9	C₂²×C₅	C₂²×C₃	1	1	yes	characteristic
10	C₄×C₅	C₃×C₄	1	6	yes	direct product factor
11	C₄²	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×C₅	C₄²	1	1	yes	characteristic, direct product factor, Hall
13	C₂²×C₃	C₂²×C₅	1	1	yes	characteristic
14	C₃×C₄	C₄×C₅	1	6	yes	direct product factor
15	C₂×C₅	C₂×C₃×C₄	1	3	yes	—
16	C₂×C₄	C₂×C₃×C₅	1	3	yes	—
17	C₂×C₃	C₂×C₄×C₅	1	3	yes	—
18	C₅	C₃×C₄²	1	1	yes	characteristic, direct product factor, Sylow
19	C₂²	C₂²×C₃×C₅	1	1	yes	characteristic
20	C₄	C₃×C₄×C₅	1	6	yes	direct product factor
21	C₃	C₄²×C₅	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₃×C₄×C₅	1	3	yes	—

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.