Subgroups — C₅×D₃×#10597243 #31827657

Order 18150.

448 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#10597243	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₅×#10597243	—	3	1	no	maximal, Hall
3	C₅×D₃×C₁₁²	C₅	1	1	yes	maximal, characteristic, complemented
4	D₃×#10597243	C₅	1	5	yes	maximal, direct product factor
5	C₅×#10597243	D₃	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₅×C₁₁²	C₂×C₅	1	1	yes	characteristic, complemented
7	C₃×#10597243	C₂×C₅	1	5	yes	complemented
8	C₅×D₃×C₁₁⋊C₅	—	11	12	no	maximal
9	C₂×C₅×C₁₁²	—	3	1	no	—
10	C₂×#10597243	—	3	5	no	—
11	C₃×C₅×C₁₁⋊C₅	—	11	12	no	—
12	D₃×C₁₁²	C₅²	1	1	yes	characteristic, complemented, Hall
13	C₅×C₁₁²	C₅×D₃	1	1	yes	characteristic, complemented
14	#10597243	C₅×D₃	1	5	yes	direct product factor
15	C₂×C₅×C₁₁⋊C₅	—	33	12	no	—
16	C₃×C₁₁²	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
17	C₅×D₃×C₁₁	C₁₁⋊C₅	1	12	yes	complemented
18	D₃×C₁₁⋊C₅	—	11	60	no	—
19	C₅×C₁₁⋊C₅	—	11	12	no	—
20	C₂×C₁₁²	—	3	1	no	Hall
21	C₃×C₅×C₁₁	C₂×C₁₁⋊C₅	1	12	yes	complemented
22	C₃×C₁₁⋊C₅	—	11	60	no	—
23	C₅²×D₃	—	121	1	no	Hall
24	C₁₁²	C₅²×D₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₅×C₁₁	—	3	12	no	—
26	C₂×C₁₁⋊C₅	—	33	60	no	—
27	C₃×C₅²	—	121	1	no	Hall
28	D₃×C₁₁	C₅×C₁₁⋊C₅	1	12	yes	complemented
29	C₅×C₁₁	D₃×C₁₁⋊C₅	1	12	yes	complemented
30	C₁₁⋊C₅	—	11	60	no	—
31	C₂×C₅²	—	363	1	no	Hall
32	C₃×C₁₁	C₂×C₅×C₁₁⋊C₅	1	12	yes	complemented
33	C₅×D₃	—	121	5	no	—
34	C₅×D₃	#10597243	1	1	yes	characteristic, direct product factor
35	C₅²	—	121	1	no	Sylow
36	C₂×C₁₁	—	3	12	no	—
37	C₃×C₅	—	121	5	no	—
38	C₃×C₅	C₂×#10597243	1	1	yes	characteristic, complemented
39	C₁₁	C₅×D₃×C₁₁⋊C₅	1	12	yes	complemented
40	C₂×C₅	—	3	1	no	—
41	C₂×C₅	—	363	5	no	—
42	D₃	C₅×#10597243	1	1	yes	characteristic, direct product factor, Hall
43	C₅	—	121	5	no	—
44	C₅	D₃×#10597243	1	1	yes	characteristic, direct product factor
45	C₃	C₂×C₅×#10597243	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₃×#10597243
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×#10597243	C₂	semidirect
3. C₅×D₃×C₁₁²	C₅	semidirect
4. D₃×#10597243	C₅	direct (N × H)
5. C₅×#10597243	D₃	direct (N × H)
6. C₃×C₅×C₁₁²	C₂×C₅	semidirect
7. C₃×#10597243	C₂×C₅	semidirect
12. D₃×C₁₁²	C₅²	semidirect
13. C₅×C₁₁²	C₅×D₃	semidirect
14. #10597243	C₅×D₃	direct (N × H)
16. C₃×C₁₁²	C₂×C₅²	semidirect
17. C₅×D₃×C₁₁	C₁₁⋊C₅	semidirect
21. C₃×C₅×C₁₁	C₂×C₁₁⋊C₅	semidirect
24. C₁₁²	C₅²×D₃	semidirect
28. D₃×C₁₁	C₅×C₁₁⋊C₅	semidirect
29. C₅×C₁₁	D₃×C₁₁⋊C₅	semidirect
32. C₃×C₁₁	C₂×C₅×C₁₁⋊C₅	semidirect
34. C₅×D₃	#10597243	direct (N × H)
38. C₃×C₅	C₂×#10597243	semidirect
39. C₁₁	C₅×D₃×C₁₁⋊C₅	semidirect
42. D₃	C₅×#10597243	direct (N × H)
44. C₅	D₃×#10597243	direct (N × H)
45. C₃	C₂×C₅×#10597243	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#10597243	2
C₂×C₅×#10597243	3
C₅×D₃×C₁₁²	5
D₃×#10597243	5
C₅×D₃×C₁₁⋊C₅	11

Subgroups — C5×D3×#10597243 #31827657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#10597243 #31827657