Subgroups — C₅×C₃⋊#168 #10597070

Order 600.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅²	C₂	1	1	yes	maximal, characteristic
2	C₅×#168	—	3	1	no	maximal, Hall
3	C₂×C₃×C₅²	C₄	1	1	yes	characteristic
4	C₃⋊#168	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×C₃⋊C₈	—	5	1	no	maximal
6	C₄×C₅²	D₃	1	1	yes	characteristic
7	C₃×C₅²	C₈	1	1	yes	characteristic, complemented, Hall
8	C₃×C₄×C₅	—	2	2	no	—
9	C₃×C₄×C₅	D₅	1	1	yes	characteristic
10	C₃×C₄×C₅	C₂×C₅	1	1	yes	characteristic
11	C₂×C₅²	Dic₃	1	1	yes	characteristic
12	C₅×C₈	—	15	1	no	—
13	#168	—	3	1	no	—
14	C₂×C₃×C₅	—	2	2	no	—
15	C₂×C₃×C₅	Dic₅	1	1	yes	characteristic
16	C₂×C₃×C₅	C₄×C₅	1	1	yes	characteristic
17	C₅²	C₃⋊C₈	1	1	yes	characteristic, complemented, Sylow
18	C₃⋊C₈	—	5	1	no	Hall
19	C₄×C₅	—	2	2	no	—
20	C₄×C₅	C₅×D₃	1	1	yes	characteristic
21	C₄×C₅	D₁₅	1	1	yes	characteristic
22	C₃×C₅	—	2	2	no	—
23	C₃×C₅	#168	1	1	yes	characteristic, complemented
24	C₃×C₅	C₅×C₈	1	1	yes	characteristic, complemented
25	C₃×C₄	C₅×D₅	1	1	yes	characteristic
26	C₂×C₅	—	2	2	no	—
27	C₂×C₅	C₅×Dic₃	1	1	yes	characteristic
28	C₂×C₅	Dic₁₅	1	1	yes	characteristic
29	C₈	—	15	1	no	Sylow
30	C₂×C₃	C₅×Dic₅	1	1	yes	characteristic
31	C₅	—	2	2	no	—
32	C₅	C₅×C₃⋊C₈	1	1	yes	characteristic, complemented
33	C₅	C₃⋊#168	1	1	yes	characteristic, direct product factor
34	C₄	C₅×D₁₅	1	1	yes	characteristic
35	C₃	C₅×#168	1	1	yes	characteristic, complemented, Sylow
36	C₂	C₅×Dic₁₅	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.