Subgroups — C₅×(C₃⋊D₃)⋊D₁₃ #14556830

Order 2340.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×D₃₉	C₂	1	2	yes	maximal, complemented
3	C₅×D₃×D₁₃	—	3	2	no	maximal
4	C₃²×C₅×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	(C₃⋊D₃)⋊D₁₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₃₉	D₃	1	2	yes	complemented
7	C₅×D₃×C₁₃	—	3	2	no	—
8	C₅×D₃×C₁₃	—	6	1	no	—
9	C₃×C₅×D₁₃	—	3	2	no	—
10	C₂×C₅×D₁₃	—	9	1	no	Hall
11	C₁₃×C₃⋊D₃	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃×D₃₉	C₂×C₅	1	2	yes	complemented
13	C₃×C₅×C₁₃	—	2	1	no	—
14	C₃×C₅×C₁₃	C₂×D₃	1	2	yes	complemented
15	C₅×D₃²	—	13	1	no	maximal, Hall
16	D₃×D₁₃	—	3	2	no	—
17	C₂×C₅×C₁₃	—	9	1	no	—
18	C₅×D₁₃	—	3	2	no	—
19	C₃²×C₁₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₅×C₃⋊D₃	D₁₃	1	1	yes	characteristic, complemented
21	C₃×C₅×D₃	—	13	2	no	—
22	D₃₉	C₅×D₃	1	2	yes	complemented
23	C₃×D₁₃	—	3	2	no	—
24	D₃×C₁₃	—	3	2	no	—
25	D₃×C₁₃	—	6	1	no	—
26	C₅×C₁₃	D₃²	1	1	yes	characteristic, complemented, Hall
27	C₂×C₅×D₃	—	39	2	no	—
28	C₂×D₁₃	—	9	1	no	Hall
29	C₃²×C₅	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
30	C₃×C₁₃	—	2	1	no	—
31	C₃×C₁₃	C₂×C₅×D₃	1	2	yes	complemented
32	D₃²	—	13	1	no	Hall
33	C₂×C₃×C₅	—	39	2	no	—
34	C₅×D₃	—	3	2	no	—
35	C₅×D₃	—	6	1	no	—
36	C₅×D₃	—	13	2	no	—
37	C₂×C₁₃	—	9	1	no	—
38	D₁₃	—	3	2	no	—
39	C₂²×C₅	—	117	1	no	Hall
40	C₃⋊D₃	C₅×D₁₃	1	1	yes	characteristic, complemented
41	C₃×D₃	—	13	2	no	—
42	C₃×C₅	—	2	1	no	—
43	C₃×C₅	D₃×D₁₃	1	2	yes	complemented
44	C₁₃	C₅×D₃²	1	1	yes	characteristic, complemented, Sylow
45	C₂×D₃	—	39	2	no	—
46	C₂×C₅	—	9	1	no	—
47	C₂×C₅	—	39	2	no	—
48	C₃²	C₂×C₅×D₁₃	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₃	—	39	2	no	—
50	D₃	—	3	2	no	—
51	D₃	—	6	1	no	—
52	D₃	—	13	2	no	—
53	C₅	(C₃⋊D₃)⋊D₁₃	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²	—	117	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	C₅×D₃×D₁₃	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	39	2	no	—

	subgroup	G/H
center, hypercenter	C₅	(C₃⋊D₃)⋊D₁₃
commutator, cosocle, hypocenter	C₃²×C₁₃	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃	C₂²
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃×C₃⋊D₃	C₂	semidirect
2. C₃×C₅×D₃₉	C₂	semidirect
4. C₃²×C₅×C₁₃	C₂²	semidirect
5. (C₃⋊D₃)⋊D₁₃	C₅	direct (N × H)
6. C₅×D₃₉	D₃	semidirect
11. C₁₃×C₃⋊D₃	C₂×C₅	semidirect
12. C₃×D₃₉	C₂×C₅	semidirect
14. C₃×C₅×C₁₃	C₂×D₃	semidirect
19. C₃²×C₁₃	C₂²×C₅	semidirect
20. C₅×C₃⋊D₃	D₁₃	semidirect
22. D₃₉	C₅×D₃	semidirect
26. C₅×C₁₃	D₃²	semidirect
29. C₃²×C₅	C₂×D₁₃	semidirect
31. C₃×C₁₃	C₂×C₅×D₃	semidirect
40. C₃⋊D₃	C₅×D₁₃	semidirect
43. C₃×C₅	D₃×D₁₃	semidirect
44. C₁₃	C₅×D₃²	semidirect
48. C₃²	C₂×C₅×D₁₃	semidirect
53. C₅	(C₃⋊D₃)⋊D₁₃	direct (N × H)
56. C₃	C₅×D₃×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₃×C₃⋊D₃	2
C₃×C₅×D₃₉	2
C₅×D₃×D₁₃	3
(C₃⋊D₃)⋊D₁₃	5
C₅×D₃²	13

Subgroups — C5×(C3⋊D3)⋊D13 #14556830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×(C₃⋊D₃)⋊D₁₃ #14556830