Subgroups — C₅×#622 #67125

Order 360.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×C₅	C₄	1	1	yes	characteristic
3	#622	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×Dic₃	—	6	2	no	—
5	C₃²×C₅	C₈	1	1	yes	characteristic, complemented, Hall
6	C₅×C₈	—	9	1	no	maximal, Hall
7	C₃⋊Dic₃	C₂×C₅	1	1	yes	characteristic
8	C₂×C₃×C₅	—	2	2	no	—
9	C₄×C₅	—	9	1	no	—
10	C₂×C₃²	C₄×C₅	1	1	yes	characteristic
11	C₃×C₅	—	2	2	no	—
12	Dic₃	—	6	2	no	—
13	C₂×C₅	#157	1	1	yes	characteristic
14	C₃²	C₅×C₈	1	1	yes	characteristic, complemented, Sylow
15	C₈	—	9	1	no	Sylow
16	C₂×C₃	—	2	2	no	—
17	C₅	#622	1	1	yes	characteristic, direct product factor, Sylow
18	C₄	—	9	1	no	—
19	C₃	—	2	2	no	—
20	C₂	C₅×#157	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.