Subgroups — D₅×D₁₅₅₇ #44528136

Order 31140.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₇₈₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₅₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×D₅×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₅₁₉	—	3	1	no	maximal
5	C₅×C₉×C₁₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₁₅₅₇	—	5	1	no	maximal, Hall
7	D₂₅₉₅	—	3	1	no	—
8	C₅×D₅₁₉	—	3	1	no	—
9	C₃×D₅×C₁₇₃	D₃	1	1	yes	characteristic
10	D₅×D₁₇₃	—	9	1	no	Hall
11	D₁₅₅₇	—	5	1	no	—
12	D₁₅₅₇	D₅	1	1	yes	characteristic, direct product factor
13	C₂×C₉×C₁₇₃	—	5	1	no	—
14	C₃×C₅×C₁₇₃	C₂×D₃	1	1	yes	characteristic
15	C₂×D₅₁₉	—	15	1	no	—
16	D₈₆₅	—	9	1	no	—
17	C₅×D₁₇₃	—	9	1	no	—
18	D₅×C₁₇₃	D₉	1	1	yes	characteristic, complemented
19	C₉×C₁₇₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₁₇₃	—	5	1	no	—
21	D₅₁₉	—	3	1	no	—
22	D₅₁₉	—	15	1	no	—
23	C₅×C₁₇₃	C₂×D₉	1	1	yes	characteristic, complemented, Hall
24	C₂×D₁₇₃	—	45	1	no	Hall
25	C₃×C₁₇₃	D₃×D₅	1	1	yes	characteristic
26	C₂×C₁₇₃	—	5	1	no	—
27	D₁₇₃	—	9	1	no	—
28	D₁₇₃	—	45	1	no	—
29	D₅×D₉	—	173	1	no	maximal, Hall
30	C₁₇₃	D₅×D₉	1	1	yes	characteristic, complemented, Sylow
31	D₄₅	—	173	1	no	—
32	C₉×D₅	D₁₇₃	1	1	yes	characteristic, complemented
33	C₅×D₉	—	173	1	no	—
34	D₃×D₅	—	519	1	no	—
35	C₅×C₉	C₂×D₁₇₃	1	1	yes	characteristic, complemented, Hall
36	C₂×D₉	—	865	1	no	Hall
37	D₁₅	—	519	1	no	—
38	C₃×D₅	D₅₁₉	1	1	yes	characteristic
39	C₅×D₃	—	519	1	no	—
40	C₂×D₅	—	1557	1	no	Hall
41	C₂×C₉	—	5	1	no	—
42	D₉	—	865	1	no	—
43	D₉	—	173	1	no	—
44	C₃×C₅	C₂×D₅₁₉	1	1	yes	characteristic
45	C₂×D₃	—	2595	1	no	—
46	C₂×C₅	—	1557	1	no	—
47	D₅	—	1557	1	no	—
48	D₅	D₁₅₅₇	1	1	yes	characteristic, direct product factor
49	C₉	D₅×D₁₇₃	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	5	1	no	—
51	D₃	—	519	1	no	—
52	D₃	—	2595	1	no	—
53	C₅	C₂×D₁₅₅₇	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	7785	1	no	Sylow
55	C₃	D₅×D₅₁₉	1	1	yes	characteristic
56	C₂	—	5	1	no	—
57	C₂	—	1557	1	no	—
58	C₂	—	7785	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₉×C₁₇₃	C₂²
Frattini	C₃	D₅×D₅₁₉
socle	C₃×C₅×C₁₇₃	C₂×D₃
LCS	G ▷ C₅×C₉×C₁₇₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₇₇₈₅	C₂	semidirect
2. C₅×D₁₅₅₇	C₂	semidirect
3. C₉×D₅×C₁₇₃	C₂	semidirect
5. C₅×C₉×C₁₇₃	C₂²	semidirect
12. D₁₅₅₇	D₅	direct (N × H)
18. D₅×C₁₇₃	D₉	semidirect
19. C₉×C₁₇₃	C₂×D₅	semidirect
23. C₅×C₁₇₃	C₂×D₉	semidirect
30. C₁₇₃	D₅×D₉	semidirect
32. C₉×D₅	D₁₇₃	semidirect
35. C₅×C₉	C₂×D₁₇₃	semidirect
48. D₅	D₁₅₅₇	direct (N × H)
49. C₉	D₅×D₁₇₃	semidirect
53. C₅	C₂×D₁₅₅₇	semidirect

Maximal subgroups

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

subgroup	index
D₇₇₈₅	2
C₅×D₁₅₅₇	2
C₉×D₅×C₁₇₃	2
D₅×D₅₁₉	3
C₂×D₁₅₅₇	5
D₅×D₉	173

Subgroups — D5×D1557 #44528136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×D₁₅₅₇ #44528136