Subgroups — D₃×C₅⋊D₁₅₅ #22604919

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	C₅²×D₃×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅⋊D₁₅₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅⋊D₁₅₅	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₁₅₅	—	5	6	no	maximal
7	C₂×C₅²×C₃₁	—	3	1	no	—
8	C₅⋊D₁₅₅	—	3	1	no	—
9	C₅⋊D₁₅₅	D₃	1	1	yes	characteristic, direct product factor
10	D₄₆₅	—	5	6	no	—
11	C₅×D₃×C₃₁	D₅	1	6	yes	complemented
12	C₃×D₁₅₅	—	5	6	no	—
13	C₅²×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×D₁₅₅	—	15	6	no	—
15	C₃×C₅×C₃₁	C₂×D₅	1	6	yes	complemented
16	D₃×D₃₁	—	25	1	no	Hall
17	C₂×C₅×C₃₁	—	3	6	no	—
18	D₁₅₅	—	5	6	no	—
19	D₁₅₅	—	15	6	no	—
20	D₃×C₅⋊D₅	—	31	1	no	maximal, Hall
21	D₉₃	—	25	1	no	—
22	C₃×D₃₁	—	25	1	no	—
23	D₃×C₃₁	C₅⋊D₅	1	1	yes	characteristic, complemented
24	C₅×C₃₁	D₃×D₅	1	6	yes	complemented
25	C₃⋊(C₅⋊D₅)	—	31	1	no	—
26	C₅²×D₃	D₃₁	1	1	yes	characteristic, complemented
27	C₃×C₅⋊D₅	—	31	1	no	—
28	C₂×D₃₁	—	75	1	no	Hall
29	C₂×C₅⋊D₅	—	93	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	—	3	1	no	—
33	D₃₁	—	25	1	no	—
34	D₃₁	—	75	1	no	—
35	D₃×D₅	—	155	6	no	—
36	C₂×C₅²	—	3	1	no	—
37	C₅⋊D₅	—	31	1	no	—
38	C₅⋊D₅	—	93	1	no	—
39	C₃₁	D₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
40	D₁₅	—	155	6	no	—
41	C₃×D₅	—	155	6	no	—
42	C₅×D₃	D₁₅₅	1	6	yes	complemented
43	C₅²	D₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₅	—	465	6	no	—
45	C₃×C₅	C₂×D₁₅₅	1	6	yes	complemented
46	C₂×D₃	—	775	1	no	Hall
47	C₂×C₅	—	3	6	no	—
48	D₅	—	155	6	no	—
49	D₅	—	465	6	no	—
50	C₂×C₃	—	775	1	no	—
51	D₃	—	775	1	no	—
52	D₃	C₅⋊D₁₅₅	1	1	yes	characteristic, direct product factor
53	C₅	D₃×D₁₅₅	1	6	yes	complemented
54	C₂²	—	2325	1	no	Sylow
55	C₃	C₂×C₅⋊D₁₅₅	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	3	1	no	—
57	C₂	—	775	1	no	—
58	C₂	—	2325	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₅⋊D₁₅₅)	C₂	semidirect
2. C₅²×D₃×C₃₁	C₂	semidirect
3. C₃×C₅⋊D₁₅₅	C₂	semidirect
5. C₃×C₅²×C₃₁	C₂²	semidirect
9. C₅⋊D₁₅₅	D₃	direct (N × H)
11. C₅×D₃×C₃₁	D₅	semidirect
13. C₅²×C₃₁	C₂×D₃	semidirect
15. C₃×C₅×C₃₁	C₂×D₅	semidirect
23. D₃×C₃₁	C₅⋊D₅	semidirect
24. C₅×C₃₁	D₃×D₅	semidirect
26. C₅²×D₃	D₃₁	semidirect
30. C₃×C₃₁	C₂×C₅⋊D₅	semidirect
31. C₃×C₅²	C₂×D₃₁	semidirect
39. C₃₁	D₃×C₅⋊D₅	semidirect
42. C₅×D₃	D₁₅₅	semidirect
43. C₅²	D₃×D₃₁	semidirect
45. C₃×C₅	C₂×D₁₅₅	semidirect
52. D₃	C₅⋊D₁₅₅	direct (N × H)
53. C₅	D₃×D₁₅₅	semidirect
55. C₃	C₂×C₅⋊D₁₅₅	semidirect

Subgroups — D3×C5⋊D155 #22604919

Conjugacy classes of subgroups

Complements

Subgroups — D₃×C₅⋊D₁₅₅ #22604919