Subgroups — C₅×C₃⋊D₃×C₇₁⋊C₅ #44544063

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, complemented, Hall
2	C₅×D₃×C₇₁⋊C₅	—	3	4	no	maximal
3	C₅×C₃⋊D₃×C₇₁	C₅	1	1	yes	maximal, characteristic, complemented
4	C₃⋊D₃×C₇₁⋊C₅	C₅	1	5	yes	maximal, direct product factor
5	C₃×C₅×C₇₁⋊C₅	D₃	1	4	yes	complemented
6	C₂×C₅×C₇₁⋊C₅	—	9	1	no	Hall
7	C₃²×C₇₁⋊C₅	C₂×C₅	1	5	yes	complemented
8	C₃²×C₅×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented
9	D₃×C₇₁⋊C₅	—	3	20	no	—
10	C₅×D₃×C₇₁	—	3	4	no	—
11	C₅×C₇₁⋊C₅	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
12	C₃⋊D₃×C₇₁	C₅²	1	1	yes	characteristic, complemented, Hall
13	C₃×C₅×C₇₁	C₅×D₃	1	4	yes	complemented
14	C₃×C₇₁⋊C₅	C₅×D₃	1	20	yes	complemented
15	C₂×C₅×C₇₁	—	9	1	no	—
16	C₂×C₇₁⋊C₅	—	9	5	no	—
17	C₃²×C₇₁	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
18	C₅²×C₃⋊D₃	—	71	1	no	maximal, Hall
19	D₃×C₇₁	—	3	4	no	—
20	C₅×C₇₁	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented
21	C₇₁⋊C₅	C₅×C₃⋊D₃	1	5	yes	direct product factor
22	C₃²×C₅²	—	71	1	no	Hall
23	C₃×C₇₁	C₅²×D₃	1	4	yes	complemented
24	C₅²×D₃	—	213	4	no	—
25	C₂×C₇₁	—	9	1	no	Hall
26	C₅×C₃⋊D₃	—	71	5	no	—
27	C₅×C₃⋊D₃	C₇₁⋊C₅	1	1	yes	characteristic, direct product factor
28	C₃×C₅²	—	71	4	no	—
29	C₇₁	C₅²×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₅²	—	639	1	no	Hall
31	C₃²×C₅	—	71	5	no	—
32	C₃²×C₅	C₂×C₇₁⋊C₅	1	1	yes	characteristic, complemented
33	C₅×D₃	—	3	4	no	—
34	C₅×D₃	—	213	20	no	—
35	C₅²	—	71	1	no	Sylow
36	C₃⋊D₃	C₅×C₇₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
37	C₃×C₅	—	71	20	no	—
38	C₃×C₅	D₃×C₇₁⋊C₅	1	4	yes	complemented
39	C₂×C₅	—	9	1	no	—
40	C₂×C₅	—	639	5	no	—
41	C₃²	C₂×C₅×C₇₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	3	4	no	—
43	C₅	—	71	5	no	—
44	C₅	C₃⋊D₃×C₇₁⋊C₅	1	1	yes	characteristic, direct product factor
45	C₃	C₅×D₃×C₇₁⋊C₅	1	4	yes	complemented
46	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₃⋊D₃×C₇₁⋊C₅
commutator, cosocle, hypocenter	C₃²×C₇₁	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇₁	C₂×C₅
LCS	G ▷ C₃²×C₇₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇₁⋊C₅	C₂	semidirect
3. C₅×C₃⋊D₃×C₇₁	C₅	semidirect
4. C₃⋊D₃×C₇₁⋊C₅	C₅	direct (N × H)
5. C₃×C₅×C₇₁⋊C₅	D₃	semidirect
7. C₃²×C₇₁⋊C₅	C₂×C₅	semidirect
8. C₃²×C₅×C₇₁	C₂×C₅	semidirect
11. C₅×C₇₁⋊C₅	C₃⋊D₃	direct (N × H)
12. C₃⋊D₃×C₇₁	C₅²	semidirect
13. C₃×C₅×C₇₁	C₅×D₃	semidirect
14. C₃×C₇₁⋊C₅	C₅×D₃	semidirect
17. C₃²×C₇₁	C₂×C₅²	semidirect
20. C₅×C₇₁	C₅×C₃⋊D₃	semidirect
21. C₇₁⋊C₅	C₅×C₃⋊D₃	direct (N × H)
23. C₃×C₇₁	C₅²×D₃	semidirect
27. C₅×C₃⋊D₃	C₇₁⋊C₅	direct (N × H)
29. C₇₁	C₅²×C₃⋊D₃	semidirect
32. C₃²×C₅	C₂×C₇₁⋊C₅	semidirect
36. C₃⋊D₃	C₅×C₇₁⋊C₅	direct (N × H)
38. C₃×C₅	D₃×C₇₁⋊C₅	semidirect
41. C₃²	C₂×C₅×C₇₁⋊C₅	semidirect
44. C₅	C₃⋊D₃×C₇₁⋊C₅	direct (N × H)
45. C₃	C₅×D₃×C₇₁⋊C₅	semidirect

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
C₅×D₃×C₇₁⋊C₅	3
C₅×C₃⋊D₃×C₇₁	5
C₃⋊D₃×C₇₁⋊C₅	5
C₅²×C₃⋊D₃	71

Subgroups — C5×C3⋊D3×C71⋊C5 #44544063

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊D₃×C₇₁⋊C₅ #44544063