Subgroups — C₃²×C₅⋊(D₇₁⋊C₅) #44544056

Order 31950.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅⋊(D₇₁⋊C₅)	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₃₅₅	C₅	1	1	yes	maximal, characteristic, complemented
4	C₃²×D₇₁⋊C₅	—	5	1	no	maximal
5	C₃×C₅×C₇₁⋊C₅	C₂×C₃	1	4	yes	complemented
6	C₅⋊(D₇₁⋊C₅)	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₇₁⋊C₅	—	2	2	no	—
8	C₃²×C₇₁⋊C₅	D₅	1	1	yes	characteristic, complemented
9	C₃²×C₅×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃×D₇₁⋊C₅	—	5	4	no	—
11	C₃×D₃₅₅	C₃×C₅	1	4	yes	complemented
12	C₅×C₇₁⋊C₅	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
13	C₃²×D₇₁	—	5	1	no	Hall
14	C₃×C₅×C₇₁	C₂×C₃×C₅	1	4	yes	complemented
15	C₃×C₇₁⋊C₅	—	2	8	no	—
16	C₃×C₇₁⋊C₅	C₃×D₅	1	4	yes	complemented
17	D₃₅₅	C₃²×C₅	1	1	yes	characteristic, complemented
18	D₇₁⋊C₅	—	5	1	no	—
19	C₃²×C₇₁	C₅×D₅	1	1	yes	characteristic, complemented, Hall
20	C₃²×C₅×D₅	—	71	1	no	maximal, Hall
21	C₃×D₇₁	—	5	4	no	—
22	C₅×C₇₁	C₂×C₃²×C₅	1	1	yes	characteristic, complemented
23	C₇₁⋊C₅	—	2	2	no	—
24	C₇₁⋊C₅	C₃²×D₅	1	1	yes	characteristic, complemented
25	C₃²×C₅²	—	71	1	no	Hall
26	C₃×C₇₁	C₃×C₅×D₅	1	4	yes	complemented
27	C₃×C₅×D₅	—	71	4	no	—
28	D₇₁	—	5	1	no	Hall
29	C₂×C₃²×C₅	—	355	1	no	—
30	C₃²×D₅	—	71	1	no	—
31	C₃×C₅²	—	71	4	no	—
32	C₇₁	C₃²×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
33	C₅×D₅	—	71	1	no	Hall
34	C₃²×C₅	—	71	1	no	—
35	C₃²×C₅	—	142	2	no	—
36	C₃²×C₅	D₇₁⋊C₅	1	1	yes	characteristic, complemented
37	C₂×C₃×C₅	—	355	4	no	—
38	C₃×D₅	—	71	4	no	—
39	C₅²	—	71	1	no	Sylow
40	C₂×C₃²	—	355	1	no	Hall
41	C₃×C₅	—	71	4	no	—
42	C₃×C₅	—	142	8	no	—
43	C₃×C₅	C₃×D₇₁⋊C₅	1	4	yes	complemented
44	C₂×C₅	—	355	1	no	—
45	D₅	—	71	1	no	—
46	C₃²	C₅⋊(D₇₁⋊C₅)	1	1	yes	characteristic, direct product factor, Sylow
47	C₂×C₃	—	355	4	no	—
48	C₅	—	71	1	no	—
49	C₅	—	142	2	no	—
50	C₅	C₃²×D₇₁⋊C₅	1	1	yes	characteristic, complemented
51	C₃	C₃×C₅⋊(D₇₁⋊C₅)	1	4	yes	direct product factor
52	C₂	—	355	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	C₅⋊(D₇₁⋊C₅)
commutator, cosocle, hypocenter	C₅×C₇₁	C₂×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇₁	C₂×C₅
LCS	G ▷ C₅×C₇₁
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇₁⋊C₅	C₂	semidirect
2. C₃×C₅⋊(D₇₁⋊C₅)	C₃	direct (N × H)
3. C₃²×D₃₅₅	C₅	semidirect
5. C₃×C₅×C₇₁⋊C₅	C₂×C₃	semidirect
6. C₅⋊(D₇₁⋊C₅)	C₃²	direct (N × H)
8. C₃²×C₇₁⋊C₅	D₅	semidirect
9. C₃²×C₅×C₇₁	C₂×C₅	semidirect
11. C₃×D₃₅₅	C₃×C₅	semidirect
12. C₅×C₇₁⋊C₅	C₂×C₃²	semidirect
14. C₃×C₅×C₇₁	C₂×C₃×C₅	semidirect
16. C₃×C₇₁⋊C₅	C₃×D₅	semidirect
17. D₃₅₅	C₃²×C₅	semidirect
19. C₃²×C₇₁	C₅×D₅	semidirect
22. C₅×C₇₁	C₂×C₃²×C₅	semidirect
24. C₇₁⋊C₅	C₃²×D₅	semidirect
26. C₃×C₇₁	C₃×C₅×D₅	semidirect
32. C₇₁	C₃²×C₅×D₅	semidirect
36. C₃²×C₅	D₇₁⋊C₅	semidirect
43. C₃×C₅	C₃×D₇₁⋊C₅	semidirect
46. C₃²	C₅⋊(D₇₁⋊C₅)	direct (N × H)
50. C₅	C₃²×D₇₁⋊C₅	semidirect
51. C₃	C₃×C₅⋊(D₇₁⋊C₅)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₇₁⋊C₅	2
C₃×C₅⋊(D₇₁⋊C₅)	3
C₃²×D₃₅₅	5
C₃²×D₇₁⋊C₅	5
C₃²×C₅×D₅	71

Subgroups — C32×C5⋊(D71⋊C5) #44544056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₅⋊(D₇₁⋊C₅) #44544056