Subgroups — C₂×C₃×C₄×C₅ #1221

Order 120.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₄×C₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₅	C₄	1	2	yes	direct product factor
5	C₂×C₃×C₅	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₅	C₂×C₃	1	1	yes	characteristic
8	C₄×C₅	C₂×C₃	1	2	yes	direct product factor
9	C₃×C₅	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
10	C₂²×C₃	C₂×C₅	1	1	yes	characteristic
11	C₃×C₄	C₂×C₅	1	2	yes	direct product factor
12	C₂×C₅	C₃×C₄	1	2	yes	direct product factor
13	C₂×C₅	C₂²×C₃	1	1	yes	characteristic
14	C₂×C₄	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
15	C₂×C₃	C₄×C₅	1	2	yes	direct product factor
16	C₂×C₃	C₂²×C₅	1	1	yes	characteristic
17	C₅	C₂×C₃×C₄	1	1	yes	characteristic, direct product factor, Sylow
18	C₂²	C₂×C₃×C₅	1	1	yes	characteristic
19	C₄	C₂×C₃×C₅	1	2	yes	direct product factor
20	C₃	C₂×C₄×C₅	1	1	yes	characteristic, direct product factor, Sylow
21	C₂	C₃×C₄×C₅	1	2	yes	direct product factor
22	C₂	C₂²×C₃×C₅	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.