Subgroups — C₂×C₃²×C₅×C₇₁⋊C₅ #44544077

Order 31950.

192 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, direct product factor, Hall
2	C₂×C₃×C₅×C₇₁⋊C₅	C₃	1	4	yes	maximal, direct product factor
3	C₂×C₃²×C₇₁⋊C₅	C₅	1	5	yes	maximal, direct product factor
4	C₂×C₃²×C₅×C₇₁	C₅	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×C₇₁⋊C₅	C₂×C₃	1	4	yes	direct product factor
6	C₂×C₅×C₇₁⋊C₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₇₁⋊C₅	C₂×C₅	1	5	yes	direct product factor
8	C₃²×C₅×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented
9	C₂×C₃×C₇₁⋊C₅	C₃×C₅	1	20	yes	direct product factor
10	C₂×C₃×C₅×C₇₁	C₃×C₅	1	4	yes	complemented
11	C₅×C₇₁⋊C₅	C₂×C₃²	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₃²×C₇₁	C₅²	1	1	yes	characteristic, complemented, Hall
13	C₃×C₅×C₇₁	C₂×C₃×C₅	1	4	yes	complemented
14	C₃×C₇₁⋊C₅	C₂×C₃×C₅	1	20	yes	direct product factor
15	C₂×C₅×C₇₁	C₃²×C₅	1	1	yes	characteristic, complemented
16	C₂×C₇₁⋊C₅	C₃²×C₅	1	5	yes	direct product factor
17	C₃²×C₇₁	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃²×C₅²	—	71	1	no	maximal, Hall
19	C₂×C₃×C₇₁	C₃×C₅²	1	4	yes	complemented
20	C₅×C₇₁	C₂×C₃²×C₅	1	1	yes	characteristic, complemented
21	C₇₁⋊C₅	C₂×C₃²×C₅	1	5	yes	direct product factor
22	C₃²×C₅²	—	71	1	no	Hall
23	C₃×C₇₁	C₂×C₃×C₅²	1	4	yes	complemented
24	C₂×C₃×C₅²	—	71	4	no	—
25	C₂×C₇₁	C₃²×C₅²	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃²×C₅	—	71	5	no	—
27	C₂×C₃²×C₅	C₇₁⋊C₅	1	1	yes	characteristic, direct product factor
28	C₃×C₅²	—	71	4	no	—
29	C₇₁	C₂×C₃²×C₅²	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₅²	—	71	1	no	Hall
31	C₃²×C₅	—	71	5	no	—
32	C₃²×C₅	C₂×C₇₁⋊C₅	1	1	yes	characteristic, direct product factor
33	C₂×C₃×C₅	—	71	20	no	—
34	C₂×C₃×C₅	C₃×C₇₁⋊C₅	1	4	yes	direct product factor
35	C₅²	—	71	1	no	Sylow
36	C₂×C₃²	C₅×C₇₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
37	C₃×C₅	—	71	20	no	—
38	C₃×C₅	C₂×C₃×C₇₁⋊C₅	1	4	yes	direct product factor
39	C₂×C₅	—	71	5	no	—
40	C₂×C₅	C₃²×C₇₁⋊C₅	1	1	yes	characteristic, direct product factor
41	C₃²	C₂×C₅×C₇₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₃	C₃×C₅×C₇₁⋊C₅	1	4	yes	direct product factor
43	C₅	—	71	5	no	—
44	C₅	C₂×C₃²×C₇₁⋊C₅	1	1	yes	characteristic, direct product factor
45	C₃	C₂×C₃×C₅×C₇₁⋊C₅	1	4	yes	direct product factor
46	C₂	C₃²×C₅×C₇₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₅	C₇₁⋊C₅
commutator, cosocle, hypocenter	C₇₁	C₂×C₃²×C₅²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₇₁	C₅
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₂×C₃²×C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇₁⋊C₅	C₂	direct (N × H)
2. C₂×C₃×C₅×C₇₁⋊C₅	C₃	direct (N × H)
3. C₂×C₃²×C₇₁⋊C₅	C₅	direct (N × H)
4. C₂×C₃²×C₅×C₇₁	C₅	semidirect
5. C₃×C₅×C₇₁⋊C₅	C₂×C₃	direct (N × H)
6. C₂×C₅×C₇₁⋊C₅	C₃²	direct (N × H)
7. C₃²×C₇₁⋊C₅	C₂×C₅	direct (N × H)
8. C₃²×C₅×C₇₁	C₂×C₅	semidirect
9. C₂×C₃×C₇₁⋊C₅	C₃×C₅	direct (N × H)
10. C₂×C₃×C₅×C₇₁	C₃×C₅	semidirect
11. C₅×C₇₁⋊C₅	C₂×C₃²	direct (N × H)
12. C₂×C₃²×C₇₁	C₅²	semidirect
13. C₃×C₅×C₇₁	C₂×C₃×C₅	semidirect
14. C₃×C₇₁⋊C₅	C₂×C₃×C₅	direct (N × H)
15. C₂×C₅×C₇₁	C₃²×C₅	semidirect
16. C₂×C₇₁⋊C₅	C₃²×C₅	direct (N × H)
17. C₃²×C₇₁	C₂×C₅²	semidirect
19. C₂×C₃×C₇₁	C₃×C₅²	semidirect
20. C₅×C₇₁	C₂×C₃²×C₅	semidirect
21. C₇₁⋊C₅	C₂×C₃²×C₅	direct (N × H)
23. C₃×C₇₁	C₂×C₃×C₅²	semidirect
25. C₂×C₇₁	C₃²×C₅²	semidirect
27. C₂×C₃²×C₅	C₇₁⋊C₅	direct (N × H)
29. C₇₁	C₂×C₃²×C₅²	semidirect
32. C₃²×C₅	C₂×C₇₁⋊C₅	direct (N × H)
34. C₂×C₃×C₅	C₃×C₇₁⋊C₅	direct (N × H)
36. C₂×C₃²	C₅×C₇₁⋊C₅	direct (N × H)
38. C₃×C₅	C₂×C₃×C₇₁⋊C₅	direct (N × H)
40. C₂×C₅	C₃²×C₇₁⋊C₅	direct (N × H)
41. C₃²	C₂×C₅×C₇₁⋊C₅	direct (N × H)
42. C₂×C₃	C₃×C₅×C₇₁⋊C₅	direct (N × H)
44. C₅	C₂×C₃²×C₇₁⋊C₅	direct (N × H)
45. C₃	C₂×C₃×C₅×C₇₁⋊C₅	direct (N × H)
46. C₂	C₃²×C₅×C₇₁⋊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
C₂×C₃×C₅×C₇₁⋊C₅	3
C₂×C₃²×C₇₁⋊C₅	5
C₂×C₃²×C₅×C₇₁	5
C₂×C₃²×C₅²	71

Subgroups — C2×C32×C5×C71⋊C5 #44544077

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₅×C₇₁⋊C₅ #44544077