Subgroups — C₉×D₅×C₇₁⋊C₅ #44544031

Order 31950.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₇₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₅×C₇₁⋊C₅	C₃	1	1	yes	maximal, characteristic
3	C₉×D₅×C₇₁	C₅	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×C₇₁⋊C₅	—	5	1	no	maximal
5	C₃×C₅×C₇₁⋊C₅	C₂×C₃	1	1	yes	characteristic
6	D₅×C₇₁⋊C₅	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₉×C₇₁⋊C₅	—	2	2	no	—
8	C₉×C₇₁⋊C₅	D₅	1	1	yes	characteristic, direct product factor
9	C₅×C₉×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃×D₅×C₇₁	C₃×C₅	1	1	yes	characteristic
11	C₂×C₃×C₇₁⋊C₅	—	5	1	no	—
12	C₅×C₇₁⋊C₅	C₂×C₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₉×C₇₁	—	5	1	no	Hall
14	C₃×C₅×C₇₁	C₂×C₃×C₅	1	1	yes	characteristic
15	C₃×C₇₁⋊C₅	—	2	2	no	—
16	C₃×C₇₁⋊C₅	C₃×D₅	1	1	yes	characteristic
17	D₅×C₇₁	C₅×C₉	1	1	yes	characteristic, complemented
18	C₂×C₇₁⋊C₅	—	5	1	no	—
19	C₉×C₇₁	C₅×D₅	1	1	yes	characteristic, complemented, Hall
20	C₅×C₉×D₅	—	71	1	no	maximal, Hall
21	C₂×C₃×C₇₁	—	5	1	no	—
22	C₅×C₇₁	C₂×C₅×C₉	1	1	yes	characteristic, complemented
23	C₇₁⋊C₅	—	2	2	no	—
24	C₇₁⋊C₅	C₉×D₅	1	1	yes	characteristic, direct product factor
25	C₅²×C₉	—	71	1	no	Hall
26	C₃×C₇₁	C₃×C₅×D₅	1	1	yes	characteristic
27	C₃×C₅×D₅	—	71	1	no	—
28	C₂×C₇₁	—	5	1	no	Hall
29	C₂×C₅×C₉	—	355	1	no	—
30	C₉×D₅	C₇₁⋊C₅	1	1	yes	characteristic, direct product factor
31	C₃×C₅²	—	71	1	no	—
32	C₇₁	C₅×C₉×D₅	1	1	yes	characteristic, complemented, Sylow
33	C₅×D₅	—	71	1	no	Hall
34	C₅×C₉	—	71	1	no	—
35	C₅×C₉	—	142	2	no	—
36	C₅×C₉	C₂×C₇₁⋊C₅	1	1	yes	characteristic, complemented
37	C₂×C₃×C₅	—	355	1	no	—
38	C₃×D₅	C₃×C₇₁⋊C₅	1	1	yes	characteristic
39	C₅²	—	71	1	no	Sylow
40	C₂×C₉	—	5	1	no	Hall
41	C₃×C₅	—	71	1	no	—
42	C₃×C₅	—	142	2	no	—
43	C₃×C₅	C₂×C₃×C₇₁⋊C₅	1	1	yes	characteristic
44	C₂×C₅	—	355	1	no	—
45	D₅	C₉×C₇₁⋊C₅	1	1	yes	characteristic, direct product factor
46	C₉	D₅×C₇₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
47	C₂×C₃	—	5	1	no	—
48	C₅	—	71	1	no	—
49	C₅	—	142	2	no	—
50	C₅	C₂×C₉×C₇₁⋊C₅	1	1	yes	characteristic, complemented
51	C₃	C₃×D₅×C₇₁⋊C₅	1	1	yes	characteristic
52	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉	D₅×C₇₁⋊C₅
commutator, hypocenter	C₅×C₇₁	C₂×C₅×C₉
Frattini	C₃	C₃×D₅×C₇₁⋊C₅
Fitting	C₅×C₉×C₇₁	C₂×C₅
socle, cosocle	C₃×C₅×C₇₁	C₂×C₃×C₅
prime radical	C₃×D₅×C₇₁⋊C₅	C₃
LCS	G ▷ C₅×C₇₁
UCS	C₁ ◁ C₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₇₁⋊C₅	C₂	semidirect
3. C₉×D₅×C₇₁	C₅	semidirect
6. D₅×C₇₁⋊C₅	C₉	direct (N × H)
8. C₉×C₇₁⋊C₅	D₅	direct (N × H)
9. C₅×C₉×C₇₁	C₂×C₅	semidirect
12. C₅×C₇₁⋊C₅	C₂×C₉	semidirect
17. D₅×C₇₁	C₅×C₉	semidirect
19. C₉×C₇₁	C₅×D₅	semidirect
22. C₅×C₇₁	C₂×C₅×C₉	semidirect
24. C₇₁⋊C₅	C₉×D₅	direct (N × H)
30. C₉×D₅	C₇₁⋊C₅	direct (N × H)
32. C₇₁	C₅×C₉×D₅	semidirect
36. C₅×C₉	C₂×C₇₁⋊C₅	semidirect
45. D₅	C₉×C₇₁⋊C₅	direct (N × H)
46. C₉	D₅×C₇₁⋊C₅	direct (N × H)
50. C₅	C₂×C₉×C₇₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₉×C₇₁⋊C₅	2
C₃×D₅×C₇₁⋊C₅	3
C₉×D₅×C₇₁	5
C₂×C₉×C₇₁⋊C₅	5
C₅×C₉×D₅	71

Subgroups — C9×D5×C71⋊C5 #44544031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×D₅×C₇₁⋊C₅ #44544031