Subgroups — D₁₅⋊D₅₂₉ #44540682

Order 31740.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₅×C₅₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₅₈₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₆₄₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₅₂₉	—	3	1	no	maximal, Hall
5	C₃×C₅×C₅₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₅₂₉	—	5	1	no	maximal, Hall
7	D₂₆₄₅	D₃	1	1	yes	characteristic, complemented
8	C₅×D₅₂₉	—	3	1	no	—
9	D₅×C₅₂₉	—	3	1	no	—
10	D₁₅₈₇	D₅	1	1	yes	characteristic, complemented
11	C₃×D₅₂₉	—	5	1	no	—
12	D₃×C₅₂₉	—	5	1	no	—
13	C₅×C₅₂₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×D₅₂₉	—	15	1	no	Hall
15	C₃×C₅₂₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	D₁₅⋊D₂₃	—	23	1	no	maximal
17	C₂×C₅₂₉	—	15	1	no	—
18	D₅₂₉	—	3	1	no	—
19	D₅₂₉	—	5	1	no	—
20	C₂₃×D₁₅	D₂₃	1	1	yes	characteristic
21	C₅×D₆₉	—	23	1	no	—
22	C₃×D₁₁₅	—	23	1	no	—
23	C₅₂₉	D₃×D₅	1	1	yes	characteristic, complemented, Sylow
24	D₅×D₂₃	—	69	1	no	—
25	C₃×C₅×C₂₃	C₂×D₂₃	1	1	yes	characteristic
26	D₃×D₂₃	—	115	1	no	—
27	D₁₁₅	—	23	1	no	—
28	C₅×D₂₃	—	69	1	no	—
29	D₅×C₂₃	—	3	1	no	—
30	D₆₉	—	23	1	no	—
31	C₃×D₂₃	—	115	1	no	—
32	D₃×C₂₃	—	5	1	no	—
33	C₅×C₂₃	D₃×D₂₃	1	1	yes	characteristic
34	C₂×D₂₃	—	345	1	no	—
35	C₃×C₂₃	D₅×D₂₃	1	1	yes	characteristic
36	D₃×D₅	—	529	1	no	Hall
37	C₂×C₂₃	—	15	1	no	—
38	D₂₃	—	69	1	no	—
39	D₂₃	—	115	1	no	—
40	D₁₅	D₅₂₉	1	1	yes	characteristic, complemented
41	C₃×D₅	—	529	1	no	—
42	C₅×D₃	—	529	1	no	—
43	C₂₃	D₁₅⋊D₂₃	1	1	yes	characteristic
44	C₂×D₅	—	1587	1	no	Hall
45	C₃×C₅	C₂×D₅₂₉	1	1	yes	characteristic, complemented, Hall
46	C₂×D₃	—	2645	1	no	Hall
47	C₂×C₅	—	1587	1	no	—
48	D₅	—	3	1	no	—
49	D₅	—	529	1	no	—
50	C₂×C₃	—	2645	1	no	—
51	D₃	—	5	1	no	—
52	D₃	—	529	1	no	—
53	C₅	D₃×D₅₂₉	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	7935	1	no	Sylow
55	C₃	D₅×D₅₂₉	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	15	1	no	—
57	C₂	—	1587	1	no	—
58	C₂	—	2645	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₅×C₅₂₉	C₂²
Frattini	C₂₃	D₁₅⋊D₂₃
socle	C₃×C₅×C₂₃	C₂×D₂₃
LCS	G ▷ C₃×C₅×C₅₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₁₅×C₅₂₉	C₂	semidirect
2. C₅×D₁₅₈₇	C₂	semidirect
3. C₃×D₂₆₄₅	C₂	semidirect
5. C₃×C₅×C₅₂₉	C₂²	semidirect
7. D₂₆₄₅	D₃	semidirect
10. D₁₅₈₇	D₅	semidirect
13. C₅×C₅₂₉	C₂×D₃	semidirect
15. C₃×C₅₂₉	C₂×D₅	semidirect
23. C₅₂₉	D₃×D₅	semidirect
40. D₁₅	D₅₂₉	semidirect
45. C₃×C₅	C₂×D₅₂₉	semidirect
53. C₅	D₃×D₅₂₉	semidirect
55. C₃	D₅×D₅₂₉	semidirect

Maximal subgroups

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

subgroup	index
D₁₅×C₅₂₉	2
C₅×D₁₅₈₇	2
C₃×D₂₆₄₅	2
D₅×D₅₂₉	3
D₃×D₅₂₉	5
D₁₅⋊D₂₃	23

Subgroups — D15⋊D529 #44540682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₅⋊D₅₂₉ #44540682