Subgroups — C₃×C₃⋊#170 #67123

Order 360.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#170	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×#170	—	3	1	no	maximal
4	C₂×C₃²×C₅	C₄	1	1	yes	characteristic
5	C₃×C₃⋊C₈	—	5	1	no	maximal, Hall
6	C₃×Dic₅	—	2	1	no	—
7	C₃×Dic₅	D₃	1	1	yes	characteristic
8	C₃×Dic₅	C₂×C₃	1	1	yes	characteristic
9	C₃²×C₅	C₈	1	1	yes	characteristic, complemented, Hall
10	#170	—	3	1	no	Hall
11	C₃²×C₄	—	5	1	no	—
12	C₂×C₃×C₅	—	2	1	no	—
13	C₂×C₃×C₅	Dic₃	1	1	yes	characteristic
14	C₂×C₃×C₅	C₃×C₄	1	1	yes	characteristic
15	C₃×C₈	—	15	1	no	—
16	C₃⋊C₈	—	5	1	no	—
17	Dic₅	C₃×D₃	1	1	yes	characteristic
18	C₂×C₃²	AGL(1,𝔽₅)	1	1	yes	characteristic
19	C₃×C₅	—	2	1	no	—
20	C₃×C₅	C₃⋊C₈	1	1	yes	characteristic, complemented
21	C₃×C₅	C₃×C₈	1	1	yes	characteristic, complemented
22	C₃×C₄	—	5	1	no	—
23	C₃×C₄	—	5	1	no	—
24	C₃×C₄	—	10	1	no	—
25	C₂×C₅	C₃×Dic₃	1	1	yes	characteristic
26	C₃²	#170	1	1	yes	characteristic, complemented, Sylow
27	C₈	—	15	1	no	Sylow
28	C₂×C₃	—	2	1	no	—
29	C₂×C₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
30	C₂×C₃	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
31	C₅	C₃×C₃⋊C₈	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	5	1	no	—
33	C₃	—	2	1	no	—
34	C₃	C₃×#170	1	1	yes	characteristic, complemented
35	C₃	C₃⋊#170	1	1	yes	characteristic, direct product factor
36	C₂	C₃×ΓL(1,𝔽₁₆)	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.