Subgroups — C₃×Dic₂₆₈₅ #44567347

Order 32220.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅×C₁₇₉	C₂	1	1	yes	maximal, characteristic
2	Dic₂₆₈₅	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×Dic₈₉₅	—	3	1	no	maximal
4	C₃²×C₅×C₁₇₉	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×Dic₅₃₇	—	5	1	no	maximal, Hall
6	C₂×C₃×C₅×C₁₇₉	—	2	1	no	—
7	C₂×C₃×C₅×C₁₇₉	D₃	1	1	yes	characteristic
8	C₂×C₃×C₅×C₁₇₉	C₂×C₃	1	1	yes	characteristic
9	Dic₈₉₅	—	3	1	no	Hall
10	C₂×C₃²×C₁₇₉	D₅	1	1	yes	characteristic
11	C₃×C₅×C₁₇₉	—	2	1	no	—
12	C₃×C₅×C₁₇₉	Dic₃	1	1	yes	characteristic, complemented
13	C₃×C₅×C₁₇₉	C₃×C₄	1	1	yes	characteristic, complemented
14	Dic₅₃₇	—	5	1	no	—
15	C₃×Dic₁₇₉	—	15	1	no	—
16	C₂×C₅×C₁₇₉	C₃×D₃	1	1	yes	characteristic
17	C₃²×C₁₇₉	Dic₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₁₇₉	—	2	1	no	—
19	C₂×C₃×C₁₇₉	C₃×D₅	1	1	yes	characteristic
20	C₂×C₃×C₁₇₉	D₁₅	1	1	yes	characteristic
21	C₅×C₁₇₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
22	Dic₁₇₉	—	15	1	no	Hall
23	C₃×C₁₇₉	—	2	1	no	—
24	C₃×C₁₇₉	C₃×Dic₅	1	1	yes	characteristic, complemented
25	C₃×C₁₇₉	Dic₁₅	1	1	yes	characteristic, complemented
26	C₂×C₁₇₉	C₃×D₁₅	1	1	yes	characteristic
27	C₃×Dic₁₅	—	179	1	no	maximal, Hall
28	C₁₇₉	C₃×Dic₁₅	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃²×C₅	D₁₇₉	1	1	yes	characteristic
30	Dic₁₅	—	179	1	no	—
31	C₃×Dic₅	—	537	1	no	—
32	C₃²×C₅	Dic₁₇₉	1	1	yes	characteristic, complemented, Hall
33	C₃×Dic₃	—	895	1	no	Hall
34	C₂×C₃×C₅	—	2	1	no	—
35	C₂×C₃×C₅	C₃×D₁₇₉	1	1	yes	characteristic
36	C₂×C₃×C₅	D₅₃₇	1	1	yes	characteristic
37	Dic₅	—	537	1	no	Hall
38	C₂×C₃²	D₈₉₅	1	1	yes	characteristic
39	C₃×C₅	—	2	1	no	—
40	C₃×C₅	C₃×Dic₁₇₉	1	1	yes	characteristic, complemented
41	C₃×C₅	Dic₅₃₇	1	1	yes	characteristic, complemented
42	C₃×C₄	—	2685	1	no	—
43	Dic₃	—	895	1	no	—
44	C₂×C₅	C₃×D₅₃₇	1	1	yes	characteristic
45	C₃²	Dic₈₉₅	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃	—	2	1	no	—
47	C₂×C₃	C₃×D₈₉₅	1	1	yes	characteristic
48	C₂×C₃	D₂₆₈₅	1	1	yes	characteristic
49	C₅	C₃×Dic₅₃₇	1	1	yes	characteristic, complemented, Sylow
50	C₄	—	2685	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×Dic₈₉₅	1	1	yes	characteristic, complemented
53	C₃	Dic₂₆₈₅	1	1	yes	characteristic, direct product factor
54	C₂	C₃×D₂₆₈₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₆₈₅
commutator, hypocenter	C₃×C₅×C₁₇₉	C₃×C₄
Frattini	C₂	C₃×D₂₆₈₅
Fitting, socle, prime radical	C₂×C₃²×C₅×C₁₇₉	C₂
cosocle	C₂×C₃×C₅×C₁₇₉	C₂×C₃
LCS	G ▷ C₃×C₅×C₁₇₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. Dic₂₆₈₅	C₃	direct (N × H)
4. C₃²×C₅×C₁₇₉	C₄	semidirect
12. C₃×C₅×C₁₇₉	Dic₃	semidirect
13. C₃×C₅×C₁₇₉	C₃×C₄	semidirect
17. C₃²×C₁₇₉	Dic₅	semidirect
21. C₅×C₁₇₉	C₃×Dic₃	semidirect
24. C₃×C₁₇₉	C₃×Dic₅	semidirect
25. C₃×C₁₇₉	Dic₁₅	semidirect
28. C₁₇₉	C₃×Dic₁₅	semidirect
32. C₃²×C₅	Dic₁₇₉	semidirect
40. C₃×C₅	C₃×Dic₁₇₉	semidirect
41. C₃×C₅	Dic₅₃₇	semidirect
45. C₃²	Dic₈₉₅	semidirect
49. C₅	C₃×Dic₅₃₇	semidirect
52. C₃	C₃×Dic₈₉₅	semidirect
53. C₃	Dic₂₆₈₅	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×C₁₇₉	2
Dic₂₆₈₅	3
C₃×Dic₈₉₅	3
C₃×Dic₅₃₇	5
C₃×Dic₁₅	179

Subgroups — C3×Dic2685 #44567347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₂₆₈₅ #44567347