Subgroups — D₃×D₅×C₁₁² #20300108

Order 7260.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×C₁₁²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×C₁₁²	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₅×C₁₁²	—	3	1	no	maximal, Hall
5	C₃×C₅×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₃×C₁₁²	—	5	1	no	maximal, Hall
7	C₂×C₅×C₁₁²	—	3	1	no	—
8	D₅×C₁₁²	—	3	1	no	—
9	D₅×C₁₁²	D₃	1	1	yes	characteristic, direct product factor
10	C₂×C₃×C₁₁²	—	5	1	no	—
11	D₃×C₁₁²	—	5	1	no	—
12	D₃×C₁₁²	D₅	1	1	yes	characteristic, direct product factor
13	D₃×D₅×C₁₁	C₁₁	1	12	yes	maximal, direct product factor
14	C₅×C₁₁²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₂²×C₁₁²	—	15	1	no	Hall
16	C₃×C₁₁²	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	C₁₁×D₁₅	C₂×C₁₁	1	12	yes	complemented
18	C₅×D₃×C₁₁	C₂×C₁₁	1	12	yes	complemented
19	C₃×D₅×C₁₁	C₂×C₁₁	1	12	yes	complemented
20	C₂×C₁₁²	—	3	1	no	—
21	C₂×C₁₁²	—	5	1	no	—
22	C₂×C₁₁²	—	15	1	no	—
23	C₂×D₅×C₁₁	—	3	12	no	—
24	C₃×C₅×C₁₁	C₂²×C₁₁	1	12	yes	complemented
25	C₂×D₃×C₁₁	—	5	12	no	—
26	C₁₁²	D₃×D₅	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₅×C₁₁	—	3	12	no	—
28	D₅×C₁₁	—	3	12	no	—
29	D₅×C₁₁	D₃×C₁₁	1	12	yes	direct product factor
30	C₂×C₃×C₁₁	—	5	12	no	—
31	D₃×C₁₁	—	5	12	no	—
32	D₃×C₁₁	D₅×C₁₁	1	12	yes	direct product factor
33	D₃×D₅	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
34	C₅×C₁₁	C₂×D₃×C₁₁	1	12	yes	complemented
35	C₂²×C₁₁	—	15	12	no	—
36	C₃×C₁₁	C₂×D₅×C₁₁	1	12	yes	complemented
37	D₁₅	C₂×C₁₁²	1	1	yes	characteristic, complemented
38	C₃×D₅	C₂×C₁₁²	1	1	yes	characteristic, complemented
39	C₅×D₃	C₂×C₁₁²	1	1	yes	characteristic, complemented
40	C₂×C₁₁	—	3	12	no	—
41	C₂×C₁₁	—	5	12	no	—
42	C₂×C₁₁	—	15	12	no	—
43	C₂×D₅	—	3	1	no	Hall
44	C₃×C₅	C₂²×C₁₁²	1	1	yes	characteristic, complemented, Hall
45	C₂×D₃	—	5	1	no	Hall
46	C₁₁	D₃×D₅×C₁₁	1	12	yes	direct product factor
47	C₂×C₅	—	3	1	no	—
48	D₅	—	3	1	no	—
49	D₅	D₃×C₁₁²	1	1	yes	characteristic, direct product factor
50	C₂×C₃	—	5	1	no	—
51	D₃	—	5	1	no	—
52	D₃	D₅×C₁₁²	1	1	yes	characteristic, direct product factor
53	C₅	C₂×D₃×C₁₁²	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	15	1	no	Sylow
55	C₃	C₂×D₅×C₁₁²	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	3	1	no	—
57	C₂	—	5	1	no	—
58	C₂	—	15	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁²	D₃×D₅
commutator, hypocenter	C₃×C₅	C₂²×C₁₁²
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁²	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₁₁²

Complements

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

N	H ≅ G/N	type
1. C₁₁²×D₁₅	C₂	semidirect
2. C₅×D₃×C₁₁²	C₂	semidirect
3. C₃×D₅×C₁₁²	C₂	semidirect
5. C₃×C₅×C₁₁²	C₂²	semidirect
9. D₅×C₁₁²	D₃	direct (N × H)
12. D₃×C₁₁²	D₅	direct (N × H)
13. D₃×D₅×C₁₁	C₁₁	direct (N × H)
14. C₅×C₁₁²	C₂×D₃	semidirect
16. C₃×C₁₁²	C₂×D₅	semidirect
17. C₁₁×D₁₅	C₂×C₁₁	semidirect
18. C₅×D₃×C₁₁	C₂×C₁₁	semidirect
19. C₃×D₅×C₁₁	C₂×C₁₁	semidirect
24. C₃×C₅×C₁₁	C₂²×C₁₁	semidirect
26. C₁₁²	D₃×D₅	direct (N × H)
29. D₅×C₁₁	D₃×C₁₁	direct (N × H)
32. D₃×C₁₁	D₅×C₁₁	direct (N × H)
33. D₃×D₅	C₁₁²	direct (N × H)
34. C₅×C₁₁	C₂×D₃×C₁₁	semidirect
36. C₃×C₁₁	C₂×D₅×C₁₁	semidirect
37. D₁₅	C₂×C₁₁²	semidirect
38. C₃×D₅	C₂×C₁₁²	semidirect
39. C₅×D₃	C₂×C₁₁²	semidirect
44. C₃×C₅	C₂²×C₁₁²	semidirect
46. C₁₁	D₃×D₅×C₁₁	direct (N × H)
49. D₅	D₃×C₁₁²	direct (N × H)
52. D₃	D₅×C₁₁²	direct (N × H)
53. C₅	C₂×D₃×C₁₁²	semidirect
55. C₃	C₂×D₅×C₁₁²	semidirect

Subgroups — D3×D5×C112 #20300108

Conjugacy classes of subgroups

Complements

Subgroups — D₃×D₅×C₁₁² #20300108