Subgroups — (C₃⋊D₃)⋊D₁₅₅ #19150166

Order 5580.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊D₃×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₄₆₅	C₂	1	2	yes	maximal, complemented
3	D₃×D₁₅₅	—	3	2	no	maximal
4	C₃²×C₅×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	(C₃⋊D₃)⋊D₃₁	—	5	1	no	maximal, Hall
6	D₄₆₅	D₃	1	2	yes	complemented
7	C₅×D₃×C₃₁	—	3	2	no	—
8	C₅×D₃×C₃₁	—	6	1	no	—
9	C₃×D₁₅₅	—	3	2	no	—
10	C₂×D₁₅₅	—	9	1	no	Hall
11	C₃⋊D₃×C₃₁	D₅	1	1	yes	characteristic, complemented
12	C₃×D₉₃	—	5	2	no	—
13	C₃×C₅×C₃₁	—	2	1	no	—
14	C₃×C₅×C₃₁	C₂×D₃	1	2	yes	complemented
15	D₃×D₃₁	—	15	2	no	—
16	C₂×C₅×C₃₁	—	9	1	no	—
17	D₁₅₅	—	3	2	no	—
18	C₃²×C₃₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
19	D₉₃	—	5	2	no	—
20	C₃×D₃₁	—	15	2	no	—
21	D₃×C₃₁	—	3	2	no	—
22	D₃×C₃₁	—	6	1	no	—
23	(C₃⋊D₃)⋊D₅	—	31	1	no	maximal, Hall
24	C₅×C₃₁	D₃²	1	1	yes	characteristic, complemented, Hall
25	C₂×D₃₁	—	45	1	no	Hall
26	C₃×C₃₁	—	2	1	no	—
27	C₃×C₃₁	D₃×D₅	1	2	yes	complemented
28	C₅×C₃⋊D₃	D₃₁	1	1	yes	characteristic, complemented
29	C₃×D₁₅	—	31	2	no	—
30	C₂×C₃₁	—	9	1	no	—
31	D₃₁	—	15	2	no	—
32	D₃×D₅	—	93	2	no	—
33	C₃²×C₅	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
34	D₃²	—	155	1	no	Hall
35	C₃₁	(C₃⋊D₃)⋊D₅	1	1	yes	characteristic, complemented, Sylow
36	D₁₅	—	31	2	no	—
37	C₃×D₅	—	93	2	no	—
38	C₅×D₃	—	3	2	no	—
39	C₅×D₃	—	6	1	no	—
40	C₂×D₅	—	279	1	no	Hall
41	C₃⋊D₃	D₁₅₅	1	1	yes	characteristic, complemented
42	C₃×D₃	—	155	2	no	—
43	C₃×C₅	—	2	1	no	—
44	C₃×C₅	D₃×D₃₁	1	2	yes	complemented
45	C₂×D₃	—	465	2	no	—
46	C₂×C₅	—	9	1	no	—
47	D₅	—	93	2	no	—
48	C₃²	C₂×D₁₅₅	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₃	—	465	2	no	—
50	D₃	—	3	2	no	—
51	D₃	—	6	1	no	—
52	D₃	—	155	2	no	—
53	C₅	(C₃⋊D₃)⋊D₃₁	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	1395	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	D₃×D₁₅₅	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	465	2	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. C₅×C₃⋊D₃×C₃₁	C₂	semidirect
2. C₃×D₄₆₅	C₂	semidirect
4. C₃²×C₅×C₃₁	C₂²	semidirect
6. D₄₆₅	D₃	semidirect
11. C₃⋊D₃×C₃₁	D₅	semidirect
14. C₃×C₅×C₃₁	C₂×D₃	semidirect
18. C₃²×C₃₁	C₂×D₅	semidirect
24. C₅×C₃₁	D₃²	semidirect
27. C₃×C₃₁	D₃×D₅	semidirect
28. C₅×C₃⋊D₃	D₃₁	semidirect
33. C₃²×C₅	C₂×D₃₁	semidirect
35. C₃₁	(C₃⋊D₃)⋊D₅	semidirect
41. C₃⋊D₃	D₁₅₅	semidirect
44. C₃×C₅	D₃×D₃₁	semidirect
48. C₃²	C₂×D₁₅₅	semidirect
53. C₅	(C₃⋊D₃)⋊D₃₁	semidirect
56. C₃	D₃×D₁₅₅	semidirect

Subgroups — (C3⋊D3)⋊D155 #19150166

Conjugacy classes of subgroups

Complements

Subgroups — (C₃⋊D₃)⋊D₁₅₅ #19150166