Subgroups — C₅×#3708 #10623723

Order 720.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₄×C₅	C₄	1	1	yes	characteristic
3	#3708	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₃⋊C₈	—	6	2	no	—
5	C₂×C₃²×C₅	C₈	1	1	yes	characteristic
6	C₅×C₁₆	—	9	1	no	maximal, Hall
7	C₃⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic
8	C₃×C₄×C₅	—	2	2	no	—
9	C₃²×C₅	C₁₆	1	1	yes	characteristic, complemented, Hall
10	C₅×C₈	—	9	1	no	—
11	C₃²×C₄	C₄×C₅	1	1	yes	characteristic
12	C₂×C₃×C₅	—	2	2	no	—
13	C₃⋊C₈	—	6	2	no	—
14	C₄×C₅	#157	1	1	yes	characteristic
15	C₂×C₃²	C₅×C₈	1	1	yes	characteristic
16	C₁₆	—	9	1	no	Sylow
17	C₃×C₅	—	2	2	no	—
18	C₃×C₄	—	2	2	no	—
19	C₂×C₅	#622	1	1	yes	characteristic
20	C₃²	C₅×C₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₈	—	9	1	no	—
22	C₂×C₃	—	2	2	no	—
23	C₅	#3708	1	1	yes	characteristic, direct product factor, Sylow
24	C₄	C₅×#157	1	1	yes	characteristic
25	C₃	—	2	2	no	—
26	C₂	C₅×#622	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.