Subgroups — C₅×#3746 #10623886

Order 720.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#634	C₂	1	2	yes	maximal
2	C₃²×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	C₅×Dic₁₂	—	3	4	no	maximal
4	C₃²×C₄×C₅	C₂²	1	1	yes	characteristic
5	C₅×C₃⋊Dic₃	—	2	2	no	—
6	#3746	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×Dic₆	—	3	8	no	—
8	C₃×C₅×C₈	D₃	1	4	yes	—
9	C₂×C₃²×C₅	D₄	1	1	yes	characteristic
10	C₅×Q₁₆	—	9	1	no	Hall
11	#634	C₂×C₅	1	2	yes	—
12	C₃²×C₈	C₂×C₅	1	1	yes	characteristic
13	C₃×C₄×C₅	C₂×D₃	1	4	yes	—
14	C₅×Dic₃	—	6	8	no	—
15	Dic₁₂	—	3	4	no	—
16	C₃²×C₅	Q₁₆	1	1	yes	characteristic, complemented, Hall
17	C₅×Q₈	—	9	2	no	—
18	C₅×C₈	C₃⋊D₃	1	1	yes	characteristic
19	C₃²×C₄	C₂²×C₅	1	1	yes	characteristic
20	C₃⋊Dic₃	—	2	2	no	—
21	C₂×C₃×C₅	D₁₂	1	4	yes	—
22	Dic₆	—	3	8	no	—
23	C₃×C₈	C₅×D₃	1	4	yes	—
24	C₄×C₅	—	18	2	no	—
25	C₄×C₅	C₂×C₃⋊D₃	1	1	yes	characteristic
26	C₂×C₃²	C₅×D₄	1	1	yes	characteristic
27	Q₁₆	—	9	1	no	Sylow
28	C₃×C₅	Dic₁₂	1	4	yes	complemented
29	C₃×C₄	C₂×C₅×D₃	1	4	yes	—
30	Dic₃	—	6	8	no	—
31	C₂×C₅	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
32	C₃²	C₅×Q₁₆	1	1	yes	characteristic, complemented, Sylow
33	Q₈	—	9	2	no	—
34	C₈	C₅×C₃⋊D₃	1	1	yes	characteristic
35	C₂×C₃	C₅×D₁₂	1	4	yes	—
36	C₅	#3746	1	1	yes	characteristic, direct product factor, Sylow
37	C₄	—	18	2	no	—
38	C₄	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic
39	C₃	C₅×Dic₁₂	1	4	yes	complemented
40	C₂	C₅×C₄⋊(C₃⋊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.