Subgroups — C₂×C₃×C₅×#10597245 #31827700

Order 18150.

144 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, direct product factor, Hall
2	C₂×C₅×#10597245	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×#10597245	C₅	1	5	yes	maximal, direct product factor
4	C₂×C₃×C₅×C₁₁²	C₅	1	1	yes	maximal, characteristic, complemented
5	C₅×#10597245	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₅×C₁₁²	C₂×C₅	1	1	yes	characteristic, complemented
7	C₃×#10597245	C₂×C₅	1	5	yes	direct product factor
8	C₂×C₃×C₅×C₁₁⋊C₅	—	11	2	no	maximal
9	C₂×C₅×C₁₁²	C₃×C₅	1	1	yes	characteristic, complemented
10	C₂×#10597245	C₃×C₅	1	5	yes	direct product factor
11	C₃×C₅×C₁₁⋊C₅	—	11	2	no	—
12	C₂×C₃×C₁₁²	C₅²	1	1	yes	characteristic, complemented, Hall
13	C₅×C₁₁²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
14	#10597245	C₂×C₃×C₅	1	5	yes	direct product factor
15	C₂×C₅×C₁₁⋊C₅	—	11	2	no	—
16	C₃×C₁₁²	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₅×C₁₁	—	5	2	no	—
18	C₂×C₃×C₅×C₁₁	C₁₁⋊C₅	1	2	yes	complemented
19	C₂×C₃×C₁₁⋊C₅	—	11	10	no	—
20	C₅×C₁₁⋊C₅	—	11	2	no	—
21	C₂×C₁₁²	C₃×C₅²	1	1	yes	characteristic, complemented, 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	C₂×C₃×C₅²	—	121	1	no	Hall
26	C₁₁²	C₂×C₃×C₅²	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₅×C₁₁	—	5	2	no	—
28	C₂×C₅×C₁₁	C₃×C₁₁⋊C₅	1	2	yes	complemented
29	C₂×C₁₁⋊C₅	—	11	10	no	—
30	C₃×C₅²	—	121	1	no	Hall
31	C₂×C₃×C₁₁	—	5	2	no	—
32	C₂×C₃×C₁₁	C₅×C₁₁⋊C₅	1	2	yes	complemented
33	C₅×C₁₁	—	5	2	no	—
34	C₅×C₁₁	C₂×C₃×C₁₁⋊C₅	1	2	yes	complemented
35	C₁₁⋊C₅	—	11	10	no	—
36	C₂×C₅²	—	121	1	no	Hall
37	C₃×C₁₁	—	5	2	no	—
38	C₃×C₁₁	C₂×C₅×C₁₁⋊C₅	1	2	yes	complemented
39	C₂×C₃×C₅	—	121	5	no	—
40	C₂×C₃×C₅	#10597245	1	1	yes	characteristic, direct product factor
41	C₅²	—	121	1	no	Sylow
42	C₂×C₁₁	—	5	2	no	—
43	C₂×C₁₁	C₃×C₅×C₁₁⋊C₅	1	2	yes	complemented
44	C₃×C₅	—	121	5	no	—
45	C₃×C₅	C₂×#10597245	1	1	yes	characteristic, direct product factor
46	C₁₁	—	5	2	no	—
47	C₁₁	C₂×C₃×C₅×C₁₁⋊C₅	1	2	yes	complemented
48	C₂×C₅	—	121	5	no	—
49	C₂×C₅	C₃×#10597245	1	1	yes	characteristic, direct product factor
50	C₂×C₃	C₅×#10597245	1	1	yes	characteristic, direct product factor, Hall
51	C₅	—	121	5	no	—
52	C₅	C₂×C₃×#10597245	1	1	yes	characteristic, direct product factor
53	C₃	C₂×C₅×#10597245	1	1	yes	characteristic, direct product factor, Sylow
54	C₂	C₃×C₅×#10597245	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	#10597245
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×#10597245	C₂	direct (N × H)
2. C₂×C₅×#10597245	C₃	direct (N × H)
3. C₂×C₃×#10597245	C₅	direct (N × H)
4. C₂×C₃×C₅×C₁₁²	C₅	semidirect
5. C₅×#10597245	C₂×C₃	direct (N × H)
6. C₃×C₅×C₁₁²	C₂×C₅	semidirect
7. C₃×#10597245	C₂×C₅	direct (N × H)
9. C₂×C₅×C₁₁²	C₃×C₅	semidirect
10. C₂×#10597245	C₃×C₅	direct (N × H)
12. C₂×C₃×C₁₁²	C₅²	semidirect
13. C₅×C₁₁²	C₂×C₃×C₅	semidirect
14. #10597245	C₂×C₃×C₅	direct (N × H)
16. C₃×C₁₁²	C₂×C₅²	semidirect
18. C₂×C₃×C₅×C₁₁	C₁₁⋊C₅	semidirect
21. C₂×C₁₁²	C₃×C₅²	semidirect
23. C₃×C₅×C₁₁	C₂×C₁₁⋊C₅	semidirect
26. C₁₁²	C₂×C₃×C₅²	semidirect
28. C₂×C₅×C₁₁	C₃×C₁₁⋊C₅	semidirect
32. C₂×C₃×C₁₁	C₅×C₁₁⋊C₅	semidirect
34. C₅×C₁₁	C₂×C₃×C₁₁⋊C₅	semidirect
38. C₃×C₁₁	C₂×C₅×C₁₁⋊C₅	semidirect
40. C₂×C₃×C₅	#10597245	direct (N × H)
43. C₂×C₁₁	C₃×C₅×C₁₁⋊C₅	semidirect
45. C₃×C₅	C₂×#10597245	direct (N × H)
47. C₁₁	C₂×C₃×C₅×C₁₁⋊C₅	semidirect
49. C₂×C₅	C₃×#10597245	direct (N × H)
50. C₂×C₃	C₅×#10597245	direct (N × H)
52. C₅	C₂×C₃×#10597245	direct (N × H)
53. C₃	C₂×C₅×#10597245	direct (N × H)
54. C₂	C₃×C₅×#10597245	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
C₂×C₅×#10597245	3
C₂×C₃×#10597245	5
C₂×C₃×C₅×C₁₁²	5
C₂×C₃×C₅×C₁₁⋊C₅	11

Subgroups — C2×C3×C5×#10597245 #31827700

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#10597245 #31827700