Subgroups — C₅×#67 #1215

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, complemented
2	C₂×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₄	—	3	1	no	maximal, Hall
5	C₂×C₃×C₅	—	2	1	no	—
6	C₂×C₃×C₅	C₂²	1	1	yes	characteristic
7	C₅×D₃	—	2	1	no	—
8	#67	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₅	—	3	1	no	—
10	C₂²×C₅	D₃	1	1	yes	characteristic, complemented
11	C₄×C₅	—	3	1	no	—
12	C₃×C₅	D₄	1	1	yes	characteristic, complemented, Hall
13	C₂²×C₃	C₂×C₅	1	1	yes	characteristic, complemented
14	C₂×D₃	C₂×C₅	1	1	yes	characteristic, complemented
15	Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
16	C₂×C₅	—	2	1	no	—
17	C₂×C₅	—	6	1	no	—
18	C₂×C₅	C₂×D₃	1	1	yes	characteristic
19	D₄	—	3	1	no	Sylow
20	C₂×C₃	—	2	1	no	—
21	C₂×C₃	C₂²×C₅	1	1	yes	characteristic
22	D₃	—	2	1	no	—
23	C₅	#67	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²	—	3	1	no	—
25	C₂²	C₅×D₃	1	1	yes	characteristic, complemented
26	C₄	—	3	1	no	—
27	C₃	C₅×D₄	1	1	yes	characteristic, complemented, Sylow
28	C₂	—	2	1	no	—
29	C₂	—	6	1	no	—
30	C₂	C₂×C₅×D₃	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.