Subgroups — C₃×C₅⋊D₅×D₃₁ #22604898

Order 9300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊D₁₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₃₁×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅²×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅⋊D₅×D₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅²×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₅×D₃₁	—	5	6	no	maximal
7	C₅⋊D₁₅₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃₁×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅²×D₃₁	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₁₅₅	—	5	6	no	—
11	C₃×D₅×C₃₁	—	5	6	no	—
12	C₃×C₅×D₃₁	D₅	1	6	yes	complemented
13	C₅²×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	D₅×D₃₁	—	5	6	no	—
15	C₃×C₅×C₃₁	C₂×D₅	1	6	yes	complemented
16	C₂×C₃×D₃₁	—	25	1	no	Hall
17	D₁₅₅	—	5	6	no	—
18	C₅×D₃₁	C₃×D₅	1	6	yes	complemented
19	D₅×C₃₁	—	5	6	no	—
20	C₂×C₃×C₅⋊D₅	—	31	1	no	maximal, Hall
21	C₂×C₃×C₃₁	—	25	1	no	—
22	C₃×D₃₁	—	25	1	no	—
23	C₃×D₃₁	C₅⋊D₅	1	1	yes	characteristic, direct product factor
24	C₅×C₃₁	C₂×C₃×D₅	1	6	yes	complemented
25	C₂×C₃×C₅²	—	31	1	no	—
26	C₃×C₅⋊D₅	—	31	1	no	—
27	C₃×C₅⋊D₅	D₃₁	1	1	yes	characteristic, direct product factor
28	C₂×D₃₁	—	25	1	no	Hall
29	C₂×C₅⋊D₅	—	31	1	no	Hall
30	C₃×C₃₁	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅²	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
32	C₂×C₃₁	—	25	1	no	—
33	D₃₁	—	25	1	no	—
34	D₃₁	C₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor
35	C₂×C₃×D₅	—	155	6	no	—
36	C₂×C₅²	—	31	1	no	—
37	C₅⋊D₅	—	31	1	no	—
38	C₅⋊D₅	C₃×D₃₁	1	1	yes	characteristic, direct product factor
39	C₃₁	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃×C₅	—	31	6	no	—
41	C₃×D₅	—	5	6	no	—
42	C₃×D₅	—	155	6	no	—
43	C₅²	C₂×C₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₅	—	155	6	no	—
45	C₃×C₅	D₅×D₃₁	1	6	yes	complemented
46	C₂²×C₃	—	775	1	no	Hall
47	C₂×C₅	—	31	6	no	—
48	D₅	—	5	6	no	—
49	D₅	—	155	6	no	—
50	C₂×C₃	—	775	1	no	—
51	C₂×C₃	—	25	1	no	—
52	C₂×C₃	—	31	1	no	—
53	C₅	C₃×D₅×D₃₁	1	6	yes	complemented
54	C₂²	—	775	1	no	Sylow
55	C₃	C₅⋊D₅×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
56	C₂	—	775	1	no	—
57	C₂	—	25	1	no	—
58	C₂	—	31	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₅⋊D₅×D₃₁
commutator, hypocenter	C₅²×C₃₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₃₁	C₂²
LCS	G ▷ C₅²×C₃₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅⋊D₁₅₅	C₂	semidirect
2. C₃×C₃₁×C₅⋊D₅	C₂	semidirect
3. C₃×C₅²×D₃₁	C₂	semidirect
4. C₅⋊D₅×D₃₁	C₃	direct (N × H)
5. C₃×C₅²×C₃₁	C₂²	semidirect
7. C₅⋊D₁₅₅	C₂×C₃	semidirect
8. C₃₁×C₅⋊D₅	C₂×C₃	semidirect
9. C₅²×D₃₁	C₂×C₃	semidirect
12. C₃×C₅×D₃₁	D₅	semidirect
13. C₅²×C₃₁	C₂²×C₃	semidirect
15. C₃×C₅×C₃₁	C₂×D₅	semidirect
18. C₅×D₃₁	C₃×D₅	semidirect
23. C₃×D₃₁	C₅⋊D₅	direct (N × H)
24. C₅×C₃₁	C₂×C₃×D₅	semidirect
27. C₃×C₅⋊D₅	D₃₁	direct (N × H)
30. C₃×C₃₁	C₂×C₅⋊D₅	semidirect
31. C₃×C₅²	C₂×D₃₁	semidirect
34. D₃₁	C₃×C₅⋊D₅	direct (N × H)
38. C₅⋊D₅	C₃×D₃₁	direct (N × H)
39. C₃₁	C₂×C₃×C₅⋊D₅	semidirect
43. C₅²	C₂×C₃×D₃₁	semidirect
45. C₃×C₅	D₅×D₃₁	semidirect
53. C₅	C₃×D₅×D₃₁	semidirect
55. C₃	C₅⋊D₅×D₃₁	direct (N × H)

Subgroups — C3×C5⋊D5×D31 #22604898

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₅⋊D₅×D₃₁ #22604898