Subgroups — C₃⋊D₃×D₁₅₅ #19150155

Order 5580.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₄₆₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₃⋊D₃×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₁₅₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₁₅₅	—	3	4	no	maximal
5	C₃²×C₅×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃⋊D₃×D₃₁	—	5	1	no	maximal, Hall
7	D₄₆₅	—	3	4	no	—
8	C₅×D₃×C₃₁	—	3	4	no	—
9	C₃×D₁₅₅	D₃	1	4	yes	complemented
10	C₂×D₁₅₅	—	9	1	no	Hall
11	C₃⋊D₉₃	—	5	1	no	—
12	C₃⋊D₃×C₃₁	D₅	1	1	yes	characteristic, complemented
13	C₃²×D₃₁	—	5	1	no	—
14	C₃×C₅×C₃₁	C₂×D₃	1	4	yes	complemented
15	D₃×D₃₁	—	15	4	no	—
16	C₂×C₅×C₃₁	—	9	1	no	—
17	D₁₅₅	—	9	1	no	—
18	D₁₅₅	C₃⋊D₃	1	1	yes	characteristic, direct product factor
19	C₃²×C₃₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	D₉₃	—	15	4	no	—
21	C₃×D₃₁	—	5	4	no	—
22	D₃×C₃₁	—	3	4	no	—
23	D₅×C₃⋊D₃	—	31	1	no	maximal, Hall
24	C₅×C₃₁	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
25	C₂×D₃₁	—	45	1	no	Hall
26	C₃×C₃₁	D₃×D₅	1	4	yes	complemented
27	C₃⋊D₁₅	—	31	1	no	—
28	C₅×C₃⋊D₃	D₃₁	1	1	yes	characteristic, complemented
29	C₃²×D₅	—	31	1	no	—
30	C₂×C₃₁	—	9	1	no	—
31	D₃₁	—	5	1	no	—
32	D₃₁	—	45	1	no	—
33	D₃×D₅	—	93	4	no	—
34	C₃²×C₅	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃⋊D₃	—	155	1	no	Hall
36	C₃₁	D₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
37	D₁₅	—	93	4	no	—
38	C₃×D₅	—	31	4	no	—
39	C₅×D₃	—	3	4	no	—
40	C₂×D₅	—	279	1	no	Hall
41	C₂×C₃²	—	155	1	no	—
42	C₃⋊D₃	—	155	1	no	—
43	C₃⋊D₃	D₁₅₅	1	1	yes	characteristic, direct product factor
44	C₃×C₅	D₃×D₃₁	1	4	yes	complemented
45	C₂×D₃	—	465	4	no	—
46	C₂×C₅	—	9	1	no	—
47	D₅	—	279	1	no	—
48	D₅	—	31	1	no	—
49	C₃²	C₂×D₁₅₅	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	155	4	no	—
51	D₃	—	3	4	no	—
52	D₃	—	465	4	no	—
53	C₅	C₃⋊D₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	1395	1	no	Sylow
55	C₃	D₃×D₁₅₅	1	4	yes	complemented
56	C₂	—	9	1	no	—
57	C₂	—	1395	1	no	—
58	C₂	—	155	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₃₁	C₂²
LCS	G ▷ C₃²×C₅×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₄₆₅	C₂	semidirect
2. C₅×C₃⋊D₃×C₃₁	C₂	semidirect
3. C₃²×D₁₅₅	C₂	semidirect
5. C₃²×C₅×C₃₁	C₂²	semidirect
9. C₃×D₁₅₅	D₃	semidirect
12. C₃⋊D₃×C₃₁	D₅	semidirect
14. C₃×C₅×C₃₁	C₂×D₃	semidirect
18. D₁₅₅	C₃⋊D₃	direct (N × H)
19. C₃²×C₃₁	C₂×D₅	semidirect
24. C₅×C₃₁	C₂×C₃⋊D₃	semidirect
26. C₃×C₃₁	D₃×D₅	semidirect
28. C₅×C₃⋊D₃	D₃₁	semidirect
34. C₃²×C₅	C₂×D₃₁	semidirect
36. C₃₁	D₅×C₃⋊D₃	semidirect
43. C₃⋊D₃	D₁₅₅	direct (N × H)
44. C₃×C₅	D₃×D₃₁	semidirect
49. C₃²	C₂×D₁₅₅	semidirect
53. C₅	C₃⋊D₃×D₃₁	semidirect
55. C₃	D₃×D₁₅₅	semidirect

Subgroups — C3⋊D3×D155 #19150155

Conjugacy classes of subgroups

Complements

Subgroups — C₃⋊D₃×D₁₅₅ #19150155