Subgroups — C₅×D₃×#10597244 #31827659

Order 18150.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#10597244	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₅×#10597244	—	3	1	no	maximal, Hall
3	C₅×D₃×C₁₁²	C₅	1	1	yes	maximal, characteristic, complemented
4	D₃×#10597244	C₅	1	5	yes	maximal, direct product factor
5	C₅×#10597244	D₃	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₅×C₁₁²	C₂×C₅	1	1	yes	characteristic, complemented
7	C₃×#10597244	C₂×C₅	1	5	yes	complemented
8	C₅×D₃×C₁₁⋊C₅	—	11	2	no	maximal
9	C₂×C₅×C₁₁²	—	3	1	no	—
10	C₂×#10597244	—	3	5	no	—
11	C₃×C₅×C₁₁⋊C₅	—	11	2	no	—
12	D₃×C₁₁²	C₅²	1	1	yes	characteristic, complemented, Hall
13	C₅×C₁₁²	C₅×D₃	1	1	yes	characteristic, complemented
14	#10597244	C₅×D₃	1	5	yes	direct product factor
15	C₂×C₅×C₁₁⋊C₅	—	33	2	no	—
16	C₃×C₁₁²	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
17	C₅×D₃×C₁₁	—	5	2	no	—
18	C₅×D₃×C₁₁	C₁₁⋊C₅	1	2	yes	complemented
19	D₃×C₁₁⋊C₅	—	11	10	no	—
20	C₅×C₁₁⋊C₅	—	11	2	no	—
21	C₂×C₁₁²	—	3	1	no	Hall
22	C₃×C₅×C₁₁	—	5	2	no	—
23	C₃×C₅×C₁₁	C₂×C₁₁⋊C₅	1	2	yes	complemented
24	C₃×C₁₁⋊C₅	—	11	10	no	—
25	C₅²×D₃	—	121	1	no	Hall
26	C₁₁²	C₅²×D₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₅×C₁₁	—	3	2	no	—
28	C₂×C₅×C₁₁	—	15	2	no	—
29	C₂×C₁₁⋊C₅	—	33	10	no	—
30	C₃×C₅²	—	121	1	no	Hall
31	D₃×C₁₁	—	5	2	no	—
32	D₃×C₁₁	C₅×C₁₁⋊C₅	1	2	yes	complemented
33	C₅×C₁₁	—	5	2	no	—
34	C₅×C₁₁	D₃×C₁₁⋊C₅	1	2	yes	complemented
35	C₁₁⋊C₅	—	11	10	no	—
36	C₂×C₅²	—	363	1	no	Hall
37	C₃×C₁₁	—	5	2	no	—
38	C₃×C₁₁	C₂×C₅×C₁₁⋊C₅	1	2	yes	complemented
39	C₅×D₃	—	121	5	no	—
40	C₅×D₃	#10597244	1	1	yes	characteristic, direct product factor
41	C₅²	—	121	1	no	Sylow
42	C₂×C₁₁	—	3	2	no	—
43	C₂×C₁₁	—	15	2	no	—
44	C₃×C₅	—	121	5	no	—
45	C₃×C₅	C₂×#10597244	1	1	yes	characteristic, complemented
46	C₁₁	—	5	2	no	—
47	C₁₁	C₅×D₃×C₁₁⋊C₅	1	2	yes	complemented
48	C₂×C₅	—	3	1	no	—
49	C₂×C₅	—	363	5	no	—
50	D₃	C₅×#10597244	1	1	yes	characteristic, direct product factor, Hall
51	C₅	—	121	5	no	—
52	C₅	D₃×#10597244	1	1	yes	characteristic, direct product factor
53	C₃	C₂×C₅×#10597244	1	1	yes	characteristic, complemented, Sylow
54	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₃×#10597244
commutator, cosocle, hypocenter	C₃×C₁₁²	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁²	C₂×C₅
LCS	G ▷ C₃×C₁₁²
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#10597244	C₂	semidirect
3. C₅×D₃×C₁₁²	C₅	semidirect
4. D₃×#10597244	C₅	direct (N × H)
5. C₅×#10597244	D₃	direct (N × H)
6. C₃×C₅×C₁₁²	C₂×C₅	semidirect
7. C₃×#10597244	C₂×C₅	semidirect
12. D₃×C₁₁²	C₅²	semidirect
13. C₅×C₁₁²	C₅×D₃	semidirect
14. #10597244	C₅×D₃	direct (N × H)
16. C₃×C₁₁²	C₂×C₅²	semidirect
18. C₅×D₃×C₁₁	C₁₁⋊C₅	semidirect
23. C₃×C₅×C₁₁	C₂×C₁₁⋊C₅	semidirect
26. C₁₁²	C₅²×D₃	semidirect
32. D₃×C₁₁	C₅×C₁₁⋊C₅	semidirect
34. C₅×C₁₁	D₃×C₁₁⋊C₅	semidirect
38. C₃×C₁₁	C₂×C₅×C₁₁⋊C₅	semidirect
40. C₅×D₃	#10597244	direct (N × H)
45. C₃×C₅	C₂×#10597244	semidirect
47. C₁₁	C₅×D₃×C₁₁⋊C₅	semidirect
50. D₃	C₅×#10597244	direct (N × H)
52. C₅	D₃×#10597244	direct (N × H)
53. C₃	C₂×C₅×#10597244	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#10597244	2
C₂×C₅×#10597244	3
C₅×D₃×C₁₁²	5
D₃×#10597244	5
C₅×D₃×C₁₁⋊C₅	11

Subgroups — C5×D3×#10597244 #31827659

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#10597244 #31827659