Subgroups — C₅×Dic₃₆ #10623580

Order 720.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Dic₁₈	C₂	1	2	yes	maximal
2	C₅×C₈×C₉	C₂	1	1	yes	maximal, characteristic
3	C₅×Dic₁₂	—	3	1	no	maximal
4	C₄×C₅×C₉	C₂²	1	1	yes	characteristic
5	C₅×Dic₉	—	2	2	no	—
6	Dic₃₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×Dic₆	—	3	2	no	—
8	C₃×C₅×C₈	D₃	1	1	yes	characteristic
9	C₂×C₅×C₉	D₄	1	1	yes	characteristic
10	C₅×Q₁₆	—	9	1	no	Hall
11	Dic₁₈	C₂×C₅	1	2	yes	—
12	C₈×C₉	C₂×C₅	1	1	yes	characteristic
13	C₃×C₄×C₅	C₂×D₃	1	1	yes	characteristic
14	C₅×Dic₃	—	6	2	no	—
15	Dic₁₂	—	3	1	no	—
16	C₅×C₉	Q₁₆	1	1	yes	characteristic, complemented, Hall
17	C₅×Q₈	—	9	2	no	—
18	C₅×C₈	D₉	1	1	yes	characteristic
19	C₄×C₉	C₂²×C₅	1	1	yes	characteristic
20	Dic₉	—	2	2	no	—
21	C₂×C₃×C₅	D₁₂	1	1	yes	characteristic
22	Dic₆	—	3	2	no	—
23	C₃×C₈	C₅×D₃	1	1	yes	characteristic
24	C₄×C₅	—	18	2	no	—
25	C₄×C₅	C₂×D₉	1	1	yes	characteristic
26	C₂×C₉	C₅×D₄	1	1	yes	characteristic
27	Q₁₆	—	9	1	no	Sylow
28	C₃×C₅	Dic₁₂	1	1	yes	characteristic
29	C₃×C₄	C₂×C₅×D₃	1	1	yes	characteristic
30	Dic₃	—	6	2	no	—
31	C₂×C₅	D₃₆	1	1	yes	characteristic
32	C₉	C₅×Q₁₆	1	1	yes	characteristic, complemented, Sylow
33	Q₈	—	9	2	no	—
34	C₈	C₅×D₉	1	1	yes	characteristic
35	C₂×C₃	C₅×D₁₂	1	1	yes	characteristic
36	C₅	Dic₃₆	1	1	yes	characteristic, direct product factor, Sylow
37	C₄	—	18	2	no	—
38	C₄	C₂×C₅×D₉	1	1	yes	characteristic
39	C₃	C₅×Dic₁₂	1	1	yes	characteristic
40	C₂	C₅×D₃₆	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.