Subgroups — C₅×C₃⋊(C₃⋊(C₃⋊Dic₃)) #13108509

Order 1620.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⁴×C₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃⋊(C₃⋊Dic₃)	—	3	40	no	maximal
3	C₃⁴×C₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₃⋊(C₃⋊Dic₃))	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃³×C₅	D₃	1	40	yes	—
6	C₅×C₃⋊Dic₃	—	9	130	no	—
7	C₂×C₃⁴	C₂×C₅	1	1	yes	characteristic
8	C₃³×C₅	Dic₃	1	40	yes	complemented
9	C₃⋊(C₃⋊Dic₃)	—	3	40	no	—
10	C₂×C₃²×C₅	C₃⋊D₃	1	130	yes	—
11	C₃⁴	C₄×C₅	1	1	yes	characteristic, complemented, Sylow
12	C₅×Dic₃	—	27	40	no	—
13	C₂×C₃³	C₅×D₃	1	40	yes	—
14	C₃²×C₅	C₃⋊Dic₃	1	130	yes	complemented
15	C₃⋊Dic₃	—	9	130	no	—
16	C₂×C₃×C₅	C₃⋊(C₃⋊D₃)	1	40	yes	—
17	C₃³	C₅×Dic₃	1	40	yes	complemented
18	C₄×C₅	—	81	1	no	Hall
19	C₂×C₃²	C₅×C₃⋊D₃	1	130	yes	—
20	C₃×C₅	C₃⋊(C₃⋊Dic₃)	1	40	yes	complemented
21	Dic₃	—	27	40	no	—
22	C₂×C₅	C₃⋊(C₃⋊(C₃⋊D₃))	1	1	yes	characteristic
23	C₃²	C₅×C₃⋊Dic₃	1	130	yes	complemented
24	C₂×C₃	C₅×C₃⋊(C₃⋊D₃)	1	40	yes	—
25	C₅	C₃⋊(C₃⋊(C₃⋊Dic₃))	1	1	yes	characteristic, direct product factor, Sylow
26	C₄	—	81	1	no	Sylow
27	C₃	C₅×C₃⋊(C₃⋊Dic₃)	1	40	yes	complemented
28	C₂	C₅×C₃⋊(C₃⋊(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.