Subgroups — C₃×C₃⋊(C₃⋊D₁₅) #11717703

Order 810.

380 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(C₃⋊D₁₅)	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₃⋊D₁₅	—	3	13	no	maximal
4	C₃×C₃⋊(C₃⋊D₃)	—	5	1	no	maximal, Hall
5	C₃³×C₅	—	2	13	no	—
6	C₃³×C₅	D₃	1	13	yes	complemented
7	C₃³×C₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃⋊D₁₅	—	3	13	no	—
9	C₃×D₁₅	—	9	13	no	—
10	C₃⁴	D₅	1	1	yes	characteristic, complemented, Sylow
11	C₃⋊(C₃⋊D₃)	—	5	1	no	—
12	C₃×C₃⋊D₃	—	15	13	no	—
13	C₃²×C₅	—	2	52	no	—
14	C₃²×C₅	C₃×D₃	1	13	yes	complemented
15	C₃²×C₅	C₃⋊D₃	1	13	yes	complemented
16	D₁₅	—	9	13	no	—
17	C₃×D₅	—	27	1	no	—
18	C₃³	—	2	13	no	—
19	C₃³	C₃×D₅	1	1	yes	characteristic, complemented
20	C₃³	D₁₅	1	13	yes	complemented
21	C₃⋊D₃	—	15	13	no	—
22	C₃×D₃	—	45	13	no	—
23	C₃×C₅	—	2	13	no	—
24	C₃×C₅	C₃×C₃⋊D₃	1	13	yes	complemented
25	C₃×C₅	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
26	D₅	—	27	1	no	Hall
27	C₃²	—	2	52	no	—
28	C₃²	C₃×D₁₅	1	13	yes	complemented
29	C₃²	C₃⋊D₁₅	1	13	yes	complemented
30	C₂×C₃	—	135	1	no	—
31	D₃	—	45	13	no	—
32	C₅	C₃×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented, Sylow
33	C₃	—	2	13	no	—
34	C₃	C₃×C₃⋊D₁₅	1	13	yes	complemented
35	C₃	C₃⋊(C₃⋊D₁₅)	1	1	yes	characteristic, direct product factor
36	C₂	—	135	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₃⋊(C₃⋊D₁₅)
commutator, cosocle, hypocenter	C₃³×C₅	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃⁴×C₅	C₂
LCS	G ▷ C₃³×C₅
UCS	C₁ ◁ C₃

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.