Subgroups — C₃×C₅×D₃×C₇₁⋊C₅ #44544059

Order 31950.

144 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	C₂×C₃×C₅×C₇₁⋊C₅	—	3	1	no	maximal
3	C₅×D₃×C₇₁⋊C₅	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×C₅×D₃×C₇₁	C₅	1	1	yes	maximal, characteristic, complemented
5	C₃×D₃×C₇₁⋊C₅	C₅	1	5	yes	maximal, direct product factor
6	C₃×C₅×C₇₁⋊C₅	—	2	1	no	—
7	C₃×C₅×C₇₁⋊C₅	D₃	1	1	yes	characteristic, direct product factor
8	C₃×C₅×C₇₁⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×C₅×C₇₁⋊C₅	—	3	1	no	Hall
10	C₃²×C₇₁⋊C₅	C₂×C₅	1	5	yes	complemented
11	C₃²×C₅×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented
12	D₃×C₇₁⋊C₅	C₃×C₅	1	5	yes	direct product factor
13	C₅×D₃×C₇₁	C₃×C₅	1	1	yes	characteristic, complemented
14	C₂×C₃×C₇₁⋊C₅	—	3	5	no	—
15	C₂×C₃×C₅×C₇₁	—	3	1	no	—
16	C₅×C₇₁⋊C₅	C₃×D₃	1	1	yes	characteristic, direct product factor, Hall
17	C₃×D₃×C₇₁	C₅²	1	1	yes	characteristic, complemented, Hall
18	C₃×C₅×C₇₁	—	2	1	no	—
19	C₃×C₅×C₇₁	C₅×D₃	1	1	yes	characteristic, complemented
20	C₃×C₅×C₇₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
21	C₃×C₇₁⋊C₅	—	2	5	no	—
22	C₃×C₇₁⋊C₅	C₅×D₃	1	5	yes	direct product factor
23	C₃×C₇₁⋊C₅	C₂×C₃×C₅	1	5	yes	complemented
24	C₂×C₅×C₇₁	—	3	1	no	—
25	C₂×C₇₁⋊C₅	—	3	5	no	—
26	C₃²×C₇₁	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
27	C₃×C₅²×D₃	—	71	1	no	maximal, Hall
28	C₂×C₃×C₇₁	—	3	1	no	—
29	D₃×C₇₁	C₃×C₅²	1	1	yes	characteristic, complemented
30	C₅×C₇₁	C₃×C₅×D₃	1	1	yes	characteristic, complemented
31	C₇₁⋊C₅	C₃×C₅×D₃	1	5	yes	direct product factor
32	C₃²×C₅²	—	71	1	no	Hall
33	C₃×C₇₁	—	2	1	no	—
34	C₃×C₇₁	C₅²×D₃	1	1	yes	characteristic, complemented
35	C₃×C₇₁	C₂×C₃×C₅²	1	1	yes	characteristic, complemented
36	C₂×C₃×C₅²	—	213	1	no	—
37	C₅²×D₃	—	71	1	no	—
38	C₂×C₇₁	—	3	1	no	Hall
39	C₃×C₅×D₃	—	71	5	no	—
40	C₃×C₅×D₃	C₇₁⋊C₅	1	1	yes	characteristic, direct product factor
41	C₃×C₅²	—	71	1	no	—
42	C₃×C₅²	—	71	1	no	—
43	C₃×C₅²	—	142	1	no	—
44	C₇₁	C₃×C₅²×D₃	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₅²	—	213	1	no	Hall
46	C₃²×C₅	—	71	5	no	—
47	C₃²×C₅	C₂×C₇₁⋊C₅	1	1	yes	characteristic, complemented
48	C₂×C₃×C₅	—	3	1	no	—
49	C₂×C₃×C₅	—	213	5	no	—
50	C₅×D₃	—	71	5	no	—
51	C₅×D₃	C₃×C₇₁⋊C₅	1	1	yes	characteristic, direct product factor
52	C₅²	—	71	1	no	Sylow
53	C₃×D₃	C₅×C₇₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
54	C₃×C₅	—	2	1	no	—
55	C₃×C₅	—	71	5	no	—
56	C₃×C₅	—	71	5	no	—
57	C₃×C₅	—	142	5	no	—
58	C₃×C₅	C₂×C₃×C₇₁⋊C₅	1	1	yes	characteristic, complemented
59	C₃×C₅	D₃×C₇₁⋊C₅	1	1	yes	characteristic, direct product factor
60	C₂×C₅	—	3	1	no	—
61	C₂×C₅	—	213	5	no	—
62	C₃²	C₂×C₅×C₇₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
63	C₂×C₃	—	3	1	no	—
64	D₃	C₃×C₅×C₇₁⋊C₅	1	1	yes	characteristic, direct product factor
65	C₅	—	71	5	no	—
66	C₅	C₃×D₃×C₇₁⋊C₅	1	1	yes	characteristic, direct product factor
67	C₃	—	2	1	no	—
68	C₃	C₅×D₃×C₇₁⋊C₅	1	1	yes	characteristic, direct product factor
69	C₃	C₂×C₃×C₅×C₇₁⋊C₅	1	1	yes	characteristic, complemented
70	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅	D₃×C₇₁⋊C₅
commutator, cosocle, hypocenter	C₃×C₇₁	C₂×C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇₁	C₂×C₅
LCS	G ▷ C₃×C₇₁
UCS	C₁ ◁ C₃×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×D₃×C₇₁⋊C₅	C₃	direct (N × H)
4. C₃×C₅×D₃×C₇₁	C₅	semidirect
5. C₃×D₃×C₇₁⋊C₅	C₅	direct (N × H)
7. C₃×C₅×C₇₁⋊C₅	D₃	direct (N × H)
8. C₃×C₅×C₇₁⋊C₅	C₂×C₃	semidirect
10. C₃²×C₇₁⋊C₅	C₂×C₅	semidirect
11. C₃²×C₅×C₇₁	C₂×C₅	semidirect
12. D₃×C₇₁⋊C₅	C₃×C₅	direct (N × H)
13. C₅×D₃×C₇₁	C₃×C₅	semidirect
16. C₅×C₇₁⋊C₅	C₃×D₃	direct (N × H)
17. C₃×D₃×C₇₁	C₅²	semidirect
19. C₃×C₅×C₇₁	C₅×D₃	semidirect
20. C₃×C₅×C₇₁	C₂×C₃×C₅	semidirect
22. C₃×C₇₁⋊C₅	C₅×D₃	direct (N × H)
23. C₃×C₇₁⋊C₅	C₂×C₃×C₅	semidirect
26. C₃²×C₇₁	C₂×C₅²	semidirect
29. D₃×C₇₁	C₃×C₅²	semidirect
30. C₅×C₇₁	C₃×C₅×D₃	semidirect
31. C₇₁⋊C₅	C₃×C₅×D₃	direct (N × H)
34. C₃×C₇₁	C₅²×D₃	semidirect
35. C₃×C₇₁	C₂×C₃×C₅²	semidirect
40. C₃×C₅×D₃	C₇₁⋊C₅	direct (N × H)
44. C₇₁	C₃×C₅²×D₃	semidirect
47. C₃²×C₅	C₂×C₇₁⋊C₅	semidirect
51. C₅×D₃	C₃×C₇₁⋊C₅	direct (N × H)
53. C₃×D₃	C₅×C₇₁⋊C₅	direct (N × H)
58. C₃×C₅	C₂×C₃×C₇₁⋊C₅	semidirect
59. C₃×C₅	D₃×C₇₁⋊C₅	direct (N × H)
62. C₃²	C₂×C₅×C₇₁⋊C₅	semidirect
64. D₃	C₃×C₅×C₇₁⋊C₅	direct (N × H)
66. C₅	C₃×D₃×C₇₁⋊C₅	direct (N × H)
68. C₃	C₅×D₃×C₇₁⋊C₅	direct (N × H)
69. C₃	C₂×C₃×C₅×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
C₂×C₃×C₅×C₇₁⋊C₅	3
C₅×D₃×C₇₁⋊C₅	3
C₃×C₅×D₃×C₇₁	5
C₃×D₃×C₇₁⋊C₅	5
C₃×C₅²×D₃	71

Subgroups — C3×C5×D3×C71⋊C5 #44544059

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₃×C₇₁⋊C₅ #44544059