Subgroups — C₅×D₁₃⋊C₃×D₄₁ #44544347

Order 31980.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×(C₁₃⋊C₃)⋊D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₄₁×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₃⋊C₃×D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₁₃×D₄₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₅×C₁₃⋊C₃×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₃⋊C₃×D₄₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×D₅₃₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×D₁₃×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₁₃×D₄₁	C₂×C₃	1	1	yes	characteristic, complemented
10	(C₁₃⋊C₃)⋊D₄₁	C₂×C₅	1	1	yes	characteristic, complemented
11	C₄₁×D₁₃⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
12	C₁₃⋊C₃×D₄₁	C₂×C₅	1	1	yes	characteristic, complemented
13	C₅×C₁₃×C₄₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₅×D₄₁	—	13	1	no	maximal, Hall
15	D₁₃×D₄₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
16	C₁₃⋊C₃×C₄₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₅×C₄₁	—	13	1	no	—
18	C₃×C₅×D₄₁	—	13	1	no	—
19	C₃×C₅×D₄₁	—	13	1	no	—
20	D₅₃₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
21	C₁₃×D₄₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
22	D₁₃×C₄₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
23	C₂×C₅×D₄₁	—	13	1	no	Hall
24	C₂×C₅×D₁₃⋊C₃	—	41	1	no	maximal, Hall
25	C₃×C₅×C₄₁	—	13	1	no	Hall
26	C₁₃×C₄₁	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×D₄₁	—	13	1	no	Hall
28	C₂×C₅×C₄₁	—	13	1	no	—
29	C₅×D₄₁	—	13	1	no	—
30	C₅×D₄₁	D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
31	C₂×C₅×C₁₃⋊C₃	—	41	1	no	—
32	C₅×D₁₃⋊C₃	—	41	1	no	—
33	C₅×D₁₃⋊C₃	D₄₁	1	1	yes	characteristic, direct product factor
34	C₂×C₅×D₁₃	—	41	1	no	Hall
35	C₂×C₃×C₄₁	—	13	1	no	—
36	C₃×D₄₁	—	13	1	no	—
37	C₃×D₄₁	—	13	1	no	—
38	C₅×C₄₁	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
39	C₅×C₁₃⋊C₃	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
40	C₂×D₄₁	—	13	1	no	Hall
41	C₂×D₁₃⋊C₃	—	41	1	no	Hall
42	C₂×C₅×C₁₃	—	41	1	no	—
43	C₅×D₁₃	—	41	1	no	—
44	C₅×D₁₃	C₃×D₄₁	1	1	yes	characteristic, complemented
45	C₃×C₄₁	—	13	1	no	Hall
46	C₂×C₄₁	—	13	1	no	—
47	D₄₁	—	13	1	no	—
48	D₄₁	C₅×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
49	C₂×C₁₃⋊C₃	—	41	1	no	—
50	D₁₃⋊C₃	—	41	1	no	—
51	D₁₃⋊C₃	C₅×D₄₁	1	1	yes	characteristic, direct product factor
52	C₅×C₁₃	C₂×C₃×D₄₁	1	1	yes	characteristic, complemented, Hall
53	C₂²×C₃×C₅	—	533	1	no	Hall
54	C₂×D₁₃	—	41	1	no	Hall
55	C₄₁	C₂×C₅×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
56	C₁₃⋊C₃	C₂×C₅×D₄₁	1	1	yes	characteristic, complemented, Hall
57	C₂×C₃×C₅	—	13	1	no	—
58	C₂×C₃×C₅	—	533	1	no	—
59	C₂×C₃×C₅	—	533	1	no	—
60	C₂×C₁₃	—	41	1	no	—
61	D₁₃	—	41	1	no	—
62	D₁₃	C₃×C₅×D₄₁	1	1	yes	characteristic, complemented
63	C₂²×C₅	—	533	1	no	Hall
64	C₃×C₅	—	13	1	no	Hall
65	C₁₃	C₂×C₃×C₅×D₄₁	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₃	—	533	1	no	Hall
67	C₂×C₅	—	13	1	no	—
68	C₂×C₅	—	533	1	no	—
69	C₂×C₅	—	41	1	no	—
70	C₂×C₃	—	13	1	no	—
71	C₂×C₃	—	533	1	no	—
72	C₂×C₃	—	533	1	no	—
73	C₅	D₁₃⋊C₃×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²	—	533	1	no	Sylow
75	C₃	—	13	1	no	Sylow
76	C₂	—	13	1	no	—
77	C₂	—	533	1	no	—
78	C₂	—	41	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₁₃⋊C₃×D₄₁
commutator, cosocle, hypocenter	C₁₃×C₄₁	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₄₁	C₂²×C₃
LCS	G ▷ C₁₃×C₄₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×(C₁₃⋊C₃)⋊D₄₁	C₂	semidirect
2. C₅×C₄₁×D₁₃⋊C₃	C₂	semidirect
3. C₅×C₁₃⋊C₃×D₄₁	C₂	semidirect
4. C₅×D₁₃×D₄₁	C₃	semidirect
5. C₅×C₁₃⋊C₃×C₄₁	C₂²	semidirect
6. D₁₃⋊C₃×D₄₁	C₅	direct (N × H)
7. C₅×D₅₃₃	C₂×C₃	semidirect
8. C₅×D₁₃×C₄₁	C₂×C₃	semidirect
9. C₅×C₁₃×D₄₁	C₂×C₃	semidirect
10. (C₁₃⋊C₃)⋊D₄₁	C₂×C₅	semidirect
11. C₄₁×D₁₃⋊C₃	C₂×C₅	semidirect
12. C₁₃⋊C₃×D₄₁	C₂×C₅	semidirect
13. C₅×C₁₃×C₄₁	C₂²×C₃	semidirect
15. D₁₃×D₄₁	C₃×C₅	semidirect
16. C₁₃⋊C₃×C₄₁	C₂²×C₅	semidirect
20. D₅₃₃	C₂×C₃×C₅	semidirect
21. C₁₃×D₄₁	C₂×C₃×C₅	semidirect
22. D₁₃×C₄₁	C₂×C₃×C₅	semidirect
26. C₁₃×C₄₁	C₂²×C₃×C₅	semidirect
30. C₅×D₄₁	D₁₃⋊C₃	direct (N × H)
33. C₅×D₁₃⋊C₃	D₄₁	direct (N × H)
38. C₅×C₄₁	C₂×D₁₃⋊C₃	semidirect
39. C₅×C₁₃⋊C₃	C₂×D₄₁	semidirect
44. C₅×D₁₃	C₃×D₄₁	semidirect
48. D₄₁	C₅×D₁₃⋊C₃	direct (N × H)
51. D₁₃⋊C₃	C₅×D₄₁	direct (N × H)
52. C₅×C₁₃	C₂×C₃×D₄₁	semidirect
55. C₄₁	C₂×C₅×D₁₃⋊C₃	semidirect
56. C₁₃⋊C₃	C₂×C₅×D₄₁	semidirect
62. D₁₃	C₃×C₅×D₄₁	semidirect
65. C₁₃	C₂×C₃×C₅×D₄₁	semidirect
73. C₅	D₁₃⋊C₃×D₄₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×(C₁₃⋊C₃)⋊D₄₁	2
C₅×C₄₁×D₁₃⋊C₃	2
C₅×C₁₃⋊C₃×D₄₁	2
C₅×D₁₃×D₄₁	3
D₁₃⋊C₃×D₄₁	5
C₂×C₃×C₅×D₄₁	13
C₂×C₅×D₁₃⋊C₃	41

Subgroups — C5×D13⋊C3×D41 #44544347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₁₃⋊C₃×D₄₁ #44544347