Subgroups — C₂×C₃×C₅×#10597243 #31827697

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

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	#10597243
commutator, cosocle, hypocenter	C₁₁²	C₂×C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₁²	C₅
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₂×C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#10597243	C₂	direct (N × H)
2. C₂×C₅×#10597243	C₃	direct (N × H)
3. C₂×C₃×#10597243	C₅	direct (N × H)
4. C₂×C₃×C₅×C₁₁²	C₅	semidirect
5. C₅×#10597243	C₂×C₃	direct (N × H)
6. C₃×C₅×C₁₁²	C₂×C₅	semidirect
7. C₃×#10597243	C₂×C₅	direct (N × H)
9. C₂×C₅×C₁₁²	C₃×C₅	semidirect
10. C₂×#10597243	C₃×C₅	direct (N × H)
12. C₂×C₃×C₁₁²	C₅²	semidirect
13. C₅×C₁₁²	C₂×C₃×C₅	semidirect
14. #10597243	C₂×C₃×C₅	direct (N × H)
16. C₃×C₁₁²	C₂×C₅²	semidirect
17. C₂×C₃×C₅×C₁₁	C₁₁⋊C₅	semidirect
20. C₂×C₁₁²	C₃×C₅²	semidirect
21. C₃×C₅×C₁₁	C₂×C₁₁⋊C₅	semidirect
24. C₁₁²	C₂×C₃×C₅²	semidirect
25. C₂×C₅×C₁₁	C₃×C₁₁⋊C₅	semidirect
28. C₂×C₃×C₁₁	C₅×C₁₁⋊C₅	semidirect
29. C₅×C₁₁	C₂×C₃×C₁₁⋊C₅	semidirect
32. C₃×C₁₁	C₂×C₅×C₁₁⋊C₅	semidirect
34. C₂×C₃×C₅	#10597243	direct (N × H)
36. C₂×C₁₁	C₃×C₅×C₁₁⋊C₅	semidirect
38. C₃×C₅	C₂×#10597243	direct (N × H)
39. C₁₁	C₂×C₃×C₅×C₁₁⋊C₅	semidirect
41. C₂×C₅	C₃×#10597243	direct (N × H)
42. C₂×C₃	C₅×#10597243	direct (N × H)
44. C₅	C₂×C₃×#10597243	direct (N × H)
45. C₃	C₂×C₅×#10597243	direct (N × H)
46. C₂	C₃×C₅×#10597243	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×#10597243	2
C₂×C₅×#10597243	3
C₂×C₃×#10597243	5
C₂×C₃×C₅×C₁₁²	5
C₂×C₃×C₅×C₁₁⋊C₅	11

Subgroups — C2×C3×C5×#10597243 #31827697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#10597243 #31827697