Subgroups — C₅×D₃×D₅₂₉ #44540677

Order 31740.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₅₈₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×C₅₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₅₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₅₂₉	—	3	1	no	maximal, Hall
5	C₃×C₅×C₅₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₅₂₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×D₅₂₉	—	3	1	no	—
8	C₅×D₅₂₉	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₅×C₅₂₉	—	3	1	no	—
10	D₁₅₈₇	C₂×C₅	1	1	yes	characteristic, complemented
11	C₃×D₅₂₉	C₂×C₅	1	1	yes	characteristic, complemented
12	D₃×C₅₂₉	C₂×C₅	1	1	yes	characteristic, complemented
13	C₅×C₅₂₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×D₅₂₉	—	3	1	no	Hall
15	C₃×C₅₂₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₅×D₃×D₂₃	—	23	1	no	maximal
17	C₂×C₅₂₉	—	3	1	no	—
18	D₅₂₉	—	3	1	no	—
19	D₅₂₉	C₅×D₃	1	1	yes	characteristic, direct product factor
20	C₅×D₆₉	—	23	1	no	—
21	C₅×D₃×C₂₃	D₂₃	1	1	yes	characteristic
22	C₃×C₅×D₂₃	—	23	1	no	—
23	C₅₂₉	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₅×D₂₃	—	69	1	no	—
25	C₃×C₅×C₂₃	C₂×D₂₃	1	1	yes	characteristic
26	D₃×D₂₃	—	23	1	no	—
27	C₂×C₅×C₂₃	—	3	1	no	—
28	C₅×D₂₃	—	23	1	no	—
29	C₅×D₂₃	—	69	1	no	—
30	D₆₉	—	23	1	no	—
31	C₃×D₂₃	—	23	1	no	—
32	D₃×C₂₃	C₅×D₂₃	1	1	yes	characteristic
33	C₅×C₂₃	D₃×D₂₃	1	1	yes	characteristic
34	C₂×D₂₃	—	69	1	no	—
35	C₃×C₂₃	C₂×C₅×D₂₃	1	1	yes	characteristic
36	C₂×C₅×D₃	—	529	1	no	Hall
37	C₂×C₂₃	—	3	1	no	—
38	D₂₃	—	23	1	no	—
39	D₂₃	—	69	1	no	—
40	C₂×C₃×C₅	—	529	1	no	—
41	C₅×D₃	—	529	1	no	—
42	C₅×D₃	D₅₂₉	1	1	yes	characteristic, direct product factor
43	C₂₃	C₅×D₃×D₂₃	1	1	yes	characteristic
44	C₂²×C₅	—	1587	1	no	Hall
45	C₃×C₅	C₂×D₅₂₉	1	1	yes	characteristic, complemented, Hall
46	C₂×D₃	—	529	1	no	Hall
47	C₂×C₅	—	3	1	no	—
48	C₂×C₅	—	529	1	no	—
49	C₂×C₅	—	1587	1	no	—
50	C₂×C₃	—	529	1	no	—
51	D₃	—	529	1	no	—
52	D₃	C₅×D₅₂₉	1	1	yes	characteristic, direct product factor
53	C₅	D₃×D₅₂₉	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²	—	1587	1	no	Sylow
55	C₃	C₂×C₅×D₅₂₉	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	3	1	no	—
57	C₂	—	529	1	no	—
58	C₂	—	1587	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₃×D₅₂₉
commutator, cosocle, hypocenter	C₃×C₅₂₉	C₂²×C₅
Frattini	C₂₃	C₅×D₃×D₂₃
Fitting	C₃×C₅×C₅₂₉	C₂²
socle	C₃×C₅×C₂₃	C₂×D₂₃
LCS	G ▷ C₃×C₅₂₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₅₈₇	C₂	semidirect
2. C₅×D₃×C₅₂₉	C₂	semidirect
3. C₃×C₅×D₅₂₉	C₂	semidirect
5. C₃×C₅×C₅₂₉	C₂²	semidirect
6. D₃×D₅₂₉	C₅	direct (N × H)
8. C₅×D₅₂₉	D₃	direct (N × H)
10. D₁₅₈₇	C₂×C₅	semidirect
11. C₃×D₅₂₉	C₂×C₅	semidirect
12. D₃×C₅₂₉	C₂×C₅	semidirect
13. C₅×C₅₂₉	C₂×D₃	semidirect
15. C₃×C₅₂₉	C₂²×C₅	semidirect
19. D₅₂₉	C₅×D₃	direct (N × H)
23. C₅₂₉	C₂×C₅×D₃	semidirect
42. C₅×D₃	D₅₂₉	direct (N × H)
45. C₃×C₅	C₂×D₅₂₉	semidirect
52. D₃	C₅×D₅₂₉	direct (N × H)
53. C₅	D₃×D₅₂₉	direct (N × H)
55. C₃	C₂×C₅×D₅₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₁₅₈₇	2
C₅×D₃×C₅₂₉	2
C₃×C₅×D₅₂₉	2
C₂×C₅×D₅₂₉	3
D₃×D₅₂₉	5
C₅×D₃×D₂₃	23

Subgroups — C5×D3×D529 #44540677

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×D₅₂₉ #44540677