Subgroups — C₃×Dic₂₅₅ #15690339

Order 3060.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅×C₁₇	C₂	1	1	yes	maximal, characteristic
2	Dic₂₅₅	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×Dic₈₅	—	3	1	no	maximal
4	C₃²×C₅×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×Dic₅₁	—	5	1	no	maximal, Hall
6	C₂×C₃×C₅×C₁₇	—	2	1	no	—
7	C₂×C₃×C₅×C₁₇	D₃	1	1	yes	characteristic
8	C₂×C₃×C₅×C₁₇	C₂×C₃	1	1	yes	characteristic
9	Dic₈₅	—	3	1	no	Hall
10	C₂×C₃²×C₁₇	D₅	1	1	yes	characteristic
11	C₃×C₅×C₁₇	—	2	1	no	—
12	C₃×C₅×C₁₇	Dic₃	1	1	yes	characteristic, complemented
13	C₃×C₅×C₁₇	C₃×C₄	1	1	yes	characteristic, complemented
14	Dic₅₁	—	5	1	no	—
15	C₃×Dic₁₇	—	15	1	no	—
16	C₃×Dic₁₅	—	17	1	no	maximal, Hall
17	C₂×C₅×C₁₇	C₃×D₃	1	1	yes	characteristic
18	C₃²×C₁₇	Dic₅	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₁₇	—	2	1	no	—
20	C₂×C₃×C₁₇	C₃×D₅	1	1	yes	characteristic
21	C₂×C₃×C₁₇	D₁₅	1	1	yes	characteristic
22	C₂×C₃²×C₅	D₁₇	1	1	yes	characteristic
23	C₅×C₁₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
24	Dic₁₇	—	15	1	no	Hall
25	Dic₁₅	—	17	1	no	—
26	C₃×Dic₅	—	51	1	no	—
27	C₃×C₁₇	—	2	1	no	—
28	C₃×C₁₇	C₃×Dic₅	1	1	yes	characteristic, complemented
29	C₃×C₁₇	Dic₁₅	1	1	yes	characteristic, complemented
30	C₃²×C₅	Dic₁₇	1	1	yes	characteristic, complemented, Hall
31	C₃×Dic₃	—	85	1	no	Hall
32	C₂×C₁₇	C₃×D₁₅	1	1	yes	characteristic
33	C₂×C₃×C₅	—	2	1	no	—
34	C₂×C₃×C₅	C₃×D₁₇	1	1	yes	characteristic
35	C₂×C₃×C₅	D₅₁	1	1	yes	characteristic
36	Dic₅	—	51	1	no	Hall
37	C₂×C₃²	D₈₅	1	1	yes	characteristic
38	C₁₇	C₃×Dic₁₅	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	—	2	1	no	—
40	C₃×C₅	C₃×Dic₁₇	1	1	yes	characteristic, complemented
41	C₃×C₅	Dic₅₁	1	1	yes	characteristic, complemented
42	C₃×C₄	—	255	1	no	—
43	Dic₃	—	85	1	no	—
44	C₂×C₅	C₃×D₅₁	1	1	yes	characteristic
45	C₃²	Dic₈₅	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃	—	2	1	no	—
47	C₂×C₃	C₃×D₈₅	1	1	yes	characteristic
48	C₂×C₃	D₂₅₅	1	1	yes	characteristic
49	C₅	C₃×Dic₅₁	1	1	yes	characteristic, complemented, Sylow
50	C₄	—	255	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×Dic₈₅	1	1	yes	characteristic, complemented
53	C₃	Dic₂₅₅	1	1	yes	characteristic, direct product factor
54	C₂	C₃×D₂₅₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₅₅
commutator, hypocenter	C₃×C₅×C₁₇	C₃×C₄
Frattini	C₂	C₃×D₂₅₅
Fitting, socle, prime radical	C₂×C₃²×C₅×C₁₇	C₂
cosocle	C₂×C₃×C₅×C₁₇	C₂×C₃
LCS	G ▷ C₃×C₅×C₁₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. Dic₂₅₅	C₃	direct (N × H)
4. C₃²×C₅×C₁₇	C₄	semidirect
12. C₃×C₅×C₁₇	Dic₃	semidirect
13. C₃×C₅×C₁₇	C₃×C₄	semidirect
18. C₃²×C₁₇	Dic₅	semidirect
23. C₅×C₁₇	C₃×Dic₃	semidirect
28. C₃×C₁₇	C₃×Dic₅	semidirect
29. C₃×C₁₇	Dic₁₅	semidirect
30. C₃²×C₅	Dic₁₇	semidirect
38. C₁₇	C₃×Dic₁₅	semidirect
40. C₃×C₅	C₃×Dic₁₇	semidirect
41. C₃×C₅	Dic₅₁	semidirect
45. C₃²	Dic₈₅	semidirect
49. C₅	C₃×Dic₅₁	semidirect
52. C₃	C₃×Dic₈₅	semidirect
53. C₃	Dic₂₅₅	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃²×C₅×C₁₇	2
Dic₂₅₅	3
C₃×Dic₈₅	3
C₃×Dic₅₁	5
C₃×Dic₁₅	17

Subgroups — C3×Dic255 #15690339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₂₅₅ #15690339