Subgroups — C₃×C₅×#170 #10597091

Order 600.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₅×#170	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₅²	C₄	1	1	yes	characteristic
4	C₃×#170	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₃×C₅×C₈	—	5	1	no	maximal
6	C₅×Dic₅	C₂×C₃	1	1	yes	characteristic
7	C₃×C₅²	C₈	1	1	yes	characteristic, complemented, Hall
8	C₃×C₄×C₅	—	5	1	no	—
9	C₃×Dic₅	C₂×C₅	1	1	yes	characteristic
10	C₂×C₅²	C₃×C₄	1	1	yes	characteristic
11	#170	C₃×C₅	1	1	yes	characteristic, direct product factor
12	C₅×C₈	—	5	1	no	—
13	C₂×C₃×C₅	—	4	1	no	—
14	C₂×C₃×C₅	C₄×C₅	1	1	yes	characteristic
15	C₂×C₃×C₅	AGL(1,𝔽₅)	1	1	yes	characteristic
16	C₅²	C₃×C₈	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₈	—	5	1	no	Hall
18	C₄×C₅	—	5	1	no	—
19	Dic₅	C₂×C₃×C₅	1	1	yes	characteristic
20	C₃×C₅	—	4	1	no	—
21	C₃×C₅	C₅×C₈	1	1	yes	characteristic, complemented
22	C₃×C₅	#170	1	1	yes	characteristic, direct product factor
23	C₃×C₄	—	5	1	no	—
24	C₂×C₅	—	4	1	no	—
25	C₂×C₅	C₃×C₄×C₅	1	1	yes	characteristic
26	C₂×C₅	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
27	C₈	—	5	1	no	Sylow
28	C₂×C₃	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic
29	C₅	—	4	1	no	—
30	C₅	C₃×C₅×C₈	1	1	yes	characteristic, complemented
31	C₅	C₃×#170	1	1	yes	characteristic, direct product factor
32	C₄	—	5	1	no	—
33	C₃	C₅×#170	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₃×C₅×AGL(1,𝔽₅)	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.