Subgroups — C₅²×C₉×D₇₁ #44544053

Order 31950.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₉×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅²×D₇₁	C₃	1	1	yes	maximal, characteristic
3	C₅×C₉×D₇₁	C₅	1	6	yes	maximal, direct product factor
4	C₃×C₅²×C₇₁	C₂×C₃	1	1	yes	characteristic
5	C₅²×D₇₁	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₅×C₉×C₇₁	C₂×C₅	1	6	yes	complemented
7	C₃×C₅×D₇₁	C₃×C₅	1	6	yes	—
8	C₅²×C₇₁	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₉×D₇₁	C₅²	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₅×C₇₁	C₂×C₃×C₅	1	6	yes	—
11	C₅×D₇₁	C₅×C₉	1	6	yes	direct product factor
12	C₉×C₇₁	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅²×C₉	—	71	1	no	maximal, Hall
14	C₃×D₇₁	C₃×C₅²	1	1	yes	characteristic
15	C₅×C₇₁	C₂×C₅×C₉	1	6	yes	complemented
16	C₅²×C₉	D₇₁	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₇₁	C₂×C₃×C₅²	1	1	yes	characteristic
18	C₂×C₃×C₅²	—	71	1	no	—
19	D₇₁	C₅²×C₉	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₅×C₉	—	71	6	no	—
21	C₃×C₅²	C₃×D₇₁	1	1	yes	characteristic
22	C₇₁	C₂×C₅²×C₉	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₅²	—	71	1	no	Hall
24	C₅×C₉	C₅×D₇₁	1	6	yes	direct product factor
25	C₂×C₃×C₅	—	71	6	no	—
26	C₅²	C₉×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₉	—	71	1	no	Hall
28	C₃×C₅	C₃×C₅×D₇₁	1	6	yes	—
29	C₂×C₅	—	71	6	no	—
30	C₉	C₅²×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	71	1	no	—
32	C₅	C₅×C₉×D₇₁	1	6	yes	direct product factor
33	C₃	C₃×C₅²×D₇₁	1	1	yes	characteristic
34	C₂	—	71	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²×C₉	D₇₁
commutator, hypocenter	C₇₁	C₂×C₅²×C₉
Frattini	C₃	C₃×C₅²×D₇₁
Fitting	C₅²×C₉×C₇₁	C₂
socle	C₃×C₅²×C₇₁	C₂×C₃
prime radical	C₃×C₅²×D₇₁	C₃
cosocle	C₃×C₇₁	C₂×C₃×C₅²
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₅²×C₉

Complements

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

N	H ≅ G/N	type
1. C₅²×C₉×C₇₁	C₂	semidirect
3. C₅×C₉×D₇₁	C₅	direct (N × H)
5. C₅²×D₇₁	C₉	direct (N × H)
6. C₅×C₉×C₇₁	C₂×C₅	semidirect
8. C₅²×C₇₁	C₂×C₉	semidirect
9. C₉×D₇₁	C₅²	direct (N × H)
11. C₅×D₇₁	C₅×C₉	direct (N × H)
12. C₉×C₇₁	C₂×C₅²	semidirect
15. C₅×C₇₁	C₂×C₅×C₉	semidirect
16. C₅²×C₉	D₇₁	direct (N × H)
19. D₇₁	C₅²×C₉	direct (N × H)
22. C₇₁	C₂×C₅²×C₉	semidirect
24. C₅×C₉	C₅×D₇₁	direct (N × H)
26. C₅²	C₉×D₇₁	direct (N × H)
30. C₉	C₅²×D₇₁	direct (N × H)
32. C₅	C₅×C₉×D₇₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₉×C₇₁	2
C₃×C₅²×D₇₁	3
C₅×C₉×D₇₁	5
C₂×C₅²×C₉	71

Subgroups — C52×C9×D71 #44544053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×C₉×D₇₁ #44544053