Subgroups — C₃×C₅⋊#11925890 #31827646

Order 18150.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#10597245	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊#11925890	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₁×D₅₅	—	5	1	no	maximal
4	C₃×#11925890	—	5	5	no	maximal
5	C₅×#10597245	C₂×C₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×C₁₁²	D₅	1	1	yes	characteristic, complemented
7	C₃×#10597245	D₅	1	5	yes	complemented
8	C₁₁×D₅₅	—	5	1	no	—
9	#11925890	—	5	5	no	—
10	C₃×C₅×C₁₁⋊C₅	—	22	1	no	—
11	C₃×C₁₁×D₁₁	—	25	1	no	Hall
12	C₅×C₁₁²	C₃×D₅	1	1	yes	characteristic, complemented
13	#10597245	C₃×D₅	1	5	yes	complemented
14	C₃×C₁₁²	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
15	C₃×D₅₅	—	5	1	no	—
16	C₃×D₅×C₁₁	—	55	1	no	—
17	C₅×C₁₁⋊C₅	—	22	1	no	—
18	C₁₁×D₁₁	—	25	1	no	Hall
19	C₃×C₅×C₁₁	—	2	1	no	—
20	C₃×C₅×C₁₁	—	5	1	no	—
21	C₃×C₅×C₁₁	—	5	1	no	—
22	C₃×C₁₁⋊C₅	—	22	5	no	—
23	C₃×C₅⋊D₅	—	121	1	no	maximal, Hall
24	C₁₁²	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
25	D₅₅	—	5	1	no	—
26	D₅×C₁₁	—	55	1	no	—
27	C₃×C₅²	—	121	1	no	Hall
28	C₂×C₃×C₁₁	—	275	1	no	—
29	C₃×D₁₁	—	25	1	no	—
30	C₅×C₁₁	—	2	1	no	—
31	C₅×C₁₁	—	5	1	no	—
32	C₅×C₁₁	—	5	1	no	—
33	C₁₁⋊C₅	—	22	5	no	—
34	C₅⋊D₅	—	121	1	no	Hall
35	C₃×C₁₁	—	2	1	no	—
36	C₃×C₁₁	—	5	1	no	—
37	C₃×C₁₁	—	5	1	no	—
38	C₃×D₅	—	55	1	no	—
39	C₃×D₅	—	605	5	no	—
40	C₅²	—	121	1	no	Sylow
41	C₂×C₁₁	—	275	1	no	—
42	D₁₁	—	25	1	no	—
43	C₃×C₅	—	121	5	no	—
44	C₃×C₅	#11925890	1	1	yes	characteristic, complemented
45	C₁₁	—	2	1	no	—
46	C₁₁	—	5	1	no	—
47	C₁₁	—	5	1	no	—
48	D₅	—	55	1	no	—
49	D₅	—	605	5	no	—
50	C₂×C₃	—	275	1	no	Hall
51	C₅	—	121	5	no	—
52	C₅	C₃×#11925890	1	1	yes	characteristic, complemented
53	C₃	C₅⋊#11925890	1	1	yes	characteristic, direct product factor, Sylow
54	C₂	—	275	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₅⋊#11925890
commutator, cosocle, hypocenter	C₅×#10597245	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁²	D₅
LCS	G ▷ C₅×#10597245
UCS	C₁ ◁ C₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₅×#10597245	C₂	semidirect
2. C₅⋊#11925890	C₃	direct (N × H)
5. C₅×#10597245	C₂×C₃	semidirect
6. C₃×C₅×C₁₁²	D₅	semidirect
7. C₃×#10597245	D₅	semidirect
12. C₅×C₁₁²	C₃×D₅	semidirect
13. #10597245	C₃×D₅	semidirect
14. C₃×C₁₁²	C₅⋊D₅	semidirect
24. C₁₁²	C₃×C₅⋊D₅	semidirect
44. C₃×C₅	#11925890	semidirect
52. C₅	C₃×#11925890	semidirect
53. C₃	C₅⋊#11925890	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×#10597245	2
C₅⋊#11925890	3
C₃×C₁₁×D₅₅	5
C₃×#11925890	5
C₃×C₅⋊D₅	121

Subgroups — C3×C5⋊#11925890 #31827646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅⋊#11925890 #31827646