Subgroups — C₂×C₅×C₃⋊(C₁₃⋊D₁₃) #23778607

Order 10140.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊(C₁₃⋊D₁₃)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₃²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₁₃⋊D₁₃	—	3	1	no	maximal, Hall
4	C₃×C₅×C₁₃²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃⋊(C₁₃⋊D₁₃)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₁₃²	D₃	1	1	yes	characteristic, complemented
7	C₅×C₁₃⋊D₁₃	—	3	2	no	—
8	C₂×C₃×C₁₃²	C₂×C₅	1	1	yes	characteristic, complemented
9	C₃⋊(C₁₃⋊D₁₃)	C₂×C₅	1	2	yes	direct product factor
10	C₅×C₁₃²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×D₃₉	—	13	14	no	maximal
12	C₂×C₁₃⋊D₁₃	—	3	1	no	Hall
13	C₃×C₁₃²	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₅×C₁₃	D₁₃	1	14	yes	complemented
15	C₅×D₃₉	—	13	28	no	—
16	C₂×C₁₃²	C₅×D₃	1	1	yes	characteristic, complemented
17	C₁₃⋊D₁₃	—	3	2	no	—
18	C₂×C₅×D₁₃	—	39	14	no	—
19	C₃×C₅×C₁₃	C₂×D₁₃	1	14	yes	complemented
20	C₁₃²	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×D₃₉	—	13	14	no	—
22	C₂×C₅×C₁₃	D₃₉	1	14	yes	complemented
23	C₅×D₁₃	—	39	28	no	—
24	C₂×C₃×C₁₃	C₅×D₁₃	1	14	yes	complemented
25	D₃₉	—	13	28	no	—
26	C₅×C₁₃	C₂×D₃₉	1	14	yes	complemented
27	C₂×C₅×D₃	—	169	1	no	Hall
28	C₂×D₁₃	—	39	14	no	—
29	C₃×C₁₃	C₂×C₅×D₁₃	1	14	yes	complemented
30	C₂×C₃×C₅	C₁₃⋊D₁₃	1	1	yes	characteristic, complemented
31	C₅×D₃	—	169	2	no	—
32	C₂×C₁₃	C₅×D₃₉	1	14	yes	complemented
33	D₁₃	—	39	28	no	—
34	C₂²×C₅	—	507	1	no	Hall
35	C₃×C₅	C₂×C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Hall
36	C₁₃	C₂×C₅×D₃₉	1	14	yes	complemented
37	C₂×D₃	—	169	1	no	Hall
38	C₂×C₅	—	507	2	no	—
39	C₂×C₅	C₃⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic, direct product factor
40	C₂×C₃	C₅×C₁₃⋊D₁₃	1	1	yes	characteristic, complemented
41	D₃	—	169	2	no	—
42	C₅	C₂×C₃⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²	—	507	1	no	Sylow
44	C₃	C₂×C₅×C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	507	2	no	—
46	C₂	C₅×C₃⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	C₃⋊(C₁₃⋊D₁₃)
commutator, cosocle, hypocenter	C₃×C₁₃²	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₃²	C₂
LCS	G ▷ C₃×C₁₃²
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₃⋊(C₁₃⋊D₁₃)	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₃²	C₂	semidirect
4. C₃×C₅×C₁₃²	C₂²	semidirect
5. C₂×C₃⋊(C₁₃⋊D₁₃)	C₅	direct (N × H)
6. C₂×C₅×C₁₃²	D₃	semidirect
8. C₂×C₃×C₁₃²	C₂×C₅	semidirect
9. C₃⋊(C₁₃⋊D₁₃)	C₂×C₅	direct (N × H)
10. C₅×C₁₃²	C₂×D₃	semidirect
13. C₃×C₁₃²	C₂²×C₅	semidirect
14. C₂×C₃×C₅×C₁₃	D₁₃	semidirect
16. C₂×C₁₃²	C₅×D₃	semidirect
19. C₃×C₅×C₁₃	C₂×D₁₃	semidirect
20. C₁₃²	C₂×C₅×D₃	semidirect
22. C₂×C₅×C₁₃	D₃₉	semidirect
24. C₂×C₃×C₁₃	C₅×D₁₃	semidirect
26. C₅×C₁₃	C₂×D₃₉	semidirect
29. C₃×C₁₃	C₂×C₅×D₁₃	semidirect
30. C₂×C₃×C₅	C₁₃⋊D₁₃	semidirect
32. C₂×C₁₃	C₅×D₃₉	semidirect
35. C₃×C₅	C₂×C₁₃⋊D₁₃	semidirect
36. C₁₃	C₂×C₅×D₃₉	semidirect
39. C₂×C₅	C₃⋊(C₁₃⋊D₁₃)	direct (N × H)
40. C₂×C₃	C₅×C₁₃⋊D₁₃	semidirect
42. C₅	C₂×C₃⋊(C₁₃⋊D₁₃)	direct (N × H)
44. C₃	C₂×C₅×C₁₃⋊D₁₃	semidirect
46. C₂	C₅×C₃⋊(C₁₃⋊D₁₃)	direct (N × H)

Subgroups — C2×C5×C3⋊(C13⋊D13) #23778607

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×C₃⋊(C₁₃⋊D₁₃) #23778607