Subgroups — C₂×C₃⋊D₂₅₅ #15690397

Order 3060.

120 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, complemented
2	C₃⋊D₂₅₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₂₅₅	—	3	4	no	maximal
4	C₃²×C₅×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃⋊D₅₁	—	5	1	no	maximal, Hall
6	C₂×C₃×C₅×C₁₇	D₃	1	4	yes	complemented
7	D₂₅₅	—	3	8	no	—
8	C₂×D₈₅	—	9	1	no	Hall
9	C₂×C₃²×C₁₇	D₅	1	1	yes	characteristic, complemented
10	C₃⋊D₅₁	—	5	2	no	—
11	C₃×C₅×C₁₇	C₂×D₃	1	4	yes	complemented
12	C₂×D₅₁	—	15	4	no	—
13	C₂×C₃⋊D₁₅	—	17	1	no	maximal, Hall
14	C₂×C₅×C₁₇	C₃⋊D₃	1	1	yes	characteristic, complemented
15	D₈₅	—	9	2	no	—
16	C₃²×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₇	D₁₅	1	4	yes	complemented
18	D₅₁	—	15	8	no	—
19	C₂×C₃²×C₅	D₁₇	1	1	yes	characteristic, complemented
20	C₃⋊D₁₅	—	17	2	no	—
21	C₅×C₁₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
22	C₂×D₁₇	—	45	1	no	Hall
23	C₂×D₁₅	—	51	4	no	—
24	C₃×C₁₇	C₂×D₁₅	1	4	yes	complemented
25	C₃²×C₅	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃⋊D₃	—	85	1	no	Hall
27	C₂×C₁₇	C₃⋊D₁₅	1	1	yes	characteristic, complemented
28	D₁₇	—	45	2	no	—
29	C₂×C₃×C₅	D₅₁	1	4	yes	complemented
30	D₁₅	—	51	8	no	—
31	C₂×D₅	—	153	1	no	Hall
32	C₂×C₃²	D₈₅	1	1	yes	characteristic, complemented
33	C₃⋊D₃	—	85	2	no	—
34	C₁₇	C₂×C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
35	C₃×C₅	C₂×D₅₁	1	4	yes	complemented
36	C₂×D₃	—	255	4	no	—
37	C₂×C₅	C₃⋊D₅₁	1	1	yes	characteristic, complemented
38	D₅	—	153	2	no	—
39	C₃²	C₂×D₈₅	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃	D₂₅₅	1	4	yes	complemented
41	D₃	—	255	8	no	—
42	C₅	C₂×C₃⋊D₅₁	1	1	yes	characteristic, complemented, Sylow
43	C₂²	—	765	1	no	Sylow
44	C₃	C₂×D₂₅₅	1	4	yes	complemented
45	C₂	—	765	2	no	—
46	C₂	C₃⋊D₂₅₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊D₂₅₅
commutator, cosocle, hypocenter	C₃²×C₅×C₁₇	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₁₇	C₂
LCS	G ▷ C₃²×C₅×C₁₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₅×C₁₇	C₂	semidirect
2. C₃⋊D₂₅₅	C₂	direct (N × H)
4. C₃²×C₅×C₁₇	C₂²	semidirect
6. C₂×C₃×C₅×C₁₇	D₃	semidirect
9. C₂×C₃²×C₁₇	D₅	semidirect
11. C₃×C₅×C₁₇	C₂×D₃	semidirect
14. C₂×C₅×C₁₇	C₃⋊D₃	semidirect
16. C₃²×C₁₇	C₂×D₅	semidirect
17. C₂×C₃×C₁₇	D₁₅	semidirect
19. C₂×C₃²×C₅	D₁₇	semidirect
21. C₅×C₁₇	C₂×C₃⋊D₃	semidirect
24. C₃×C₁₇	C₂×D₁₅	semidirect
25. C₃²×C₅	C₂×D₁₇	semidirect
27. C₂×C₁₇	C₃⋊D₁₅	semidirect
29. C₂×C₃×C₅	D₅₁	semidirect
32. C₂×C₃²	D₈₅	semidirect
34. C₁₇	C₂×C₃⋊D₁₅	semidirect
35. C₃×C₅	C₂×D₅₁	semidirect
37. C₂×C₅	C₃⋊D₅₁	semidirect
39. C₃²	C₂×D₈₅	semidirect
40. C₂×C₃	D₂₅₅	semidirect
42. C₅	C₂×C₃⋊D₅₁	semidirect
44. C₃	C₂×D₂₅₅	semidirect
46. C₂	C₃⋊D₂₅₅	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
C₃⋊D₂₅₅	2
C₂×D₂₅₅	3
C₂×C₃⋊D₅₁	5
C₂×C₃⋊D₁₅	17

Subgroups — C2×C3⋊D255 #15690397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊D₂₅₅ #15690397