Subgroups — C₃×C₃⋊(C₅⋊(D₇₁⋊C₅)) #44544060

Order 31950.

96 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	1	yes	maximal, characteristic, direct product factor
3	C₃×C₅⋊(D₇₁⋊C₅)	—	3	1	no	maximal
4	C₃×D₁₀₆₅	C₅	1	1	yes	maximal, characteristic, complemented
5	C₃×C₃⋊(D₇₁⋊C₅)	—	5	1	no	maximal
6	C₃×C₅×C₇₁⋊C₅	—	2	1	no	—
7	C₃×C₅×C₇₁⋊C₅	D₃	1	1	yes	characteristic, complemented
8	C₃×C₅×C₇₁⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅⋊(D₇₁⋊C₅)	—	3	1	no	Hall
10	C₃²×C₇₁⋊C₅	—	2	2	no	—
11	C₃²×C₇₁⋊C₅	D₅	1	1	yes	characteristic, complemented
12	C₃²×C₅×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented
13	C₃⋊(D₇₁⋊C₅)	—	5	1	no	—
14	C₃×D₇₁⋊C₅	—	15	1	no	—
15	D₁₀₆₅	C₃×C₅	1	1	yes	characteristic, complemented
16	C₃×D₃₅₅	—	3	1	no	—
17	C₅×C₇₁⋊C₅	C₃×D₃	1	1	yes	characteristic, complemented, Hall
18	C₃×D₂₁₃	—	5	1	no	Hall
19	C₃×C₅×C₇₁	—	2	1	no	—
20	C₃×C₅×C₇₁	C₅×D₃	1	1	yes	characteristic, complemented
21	C₃×C₅×C₇₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
22	C₃×C₇₁⋊C₅	—	2	4	no	—
23	C₃×C₇₁⋊C₅	—	2	1	no	—
24	C₃×C₇₁⋊C₅	—	2	2	no	—
25	C₃×C₇₁⋊C₅	—	2	2	no	—
26	C₃×C₇₁⋊C₅	C₃×D₅	1	1	yes	characteristic, complemented
27	C₃×C₇₁⋊C₅	D₁₅	1	1	yes	characteristic, complemented
28	D₃₅₅	—	3	1	no	—
29	D₇₁⋊C₅	—	15	1	no	—
30	C₃²×C₇₁	C₅×D₅	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅×D₁₅	—	71	1	no	maximal, Hall
32	D₂₁₃	—	5	1	no	—
33	C₃×D₇₁	—	15	1	no	—
34	C₅×C₇₁	C₃×C₅×D₃	1	1	yes	characteristic, complemented
35	C₇₁⋊C₅	—	2	2	no	—
36	C₇₁⋊C₅	C₃×D₁₅	1	1	yes	characteristic, complemented
37	C₃²×C₅²	—	71	1	no	Hall
38	C₃×C₇₁	—	2	1	no	—
39	C₃×C₇₁	C₃×C₅×D₅	1	1	yes	characteristic, complemented
40	C₃×C₇₁	C₅×D₁₅	1	1	yes	characteristic, complemented
41	C₅×D₁₅	—	71	1	no	—
42	C₃×C₅×D₅	—	213	1	no	—
43	D₇₁	—	15	1	no	Hall
44	C₃×D₁₅	—	71	1	no	—
45	C₃×C₅×D₃	—	355	1	no	—
46	C₃×C₅²	—	71	1	no	—
47	C₃×C₅²	—	71	1	no	—
48	C₃×C₅²	—	142	1	no	—
49	C₇₁	C₃×C₅×D₁₅	1	1	yes	characteristic, complemented, Sylow
50	C₅×D₅	—	213	1	no	Hall
51	C₃²×C₅	—	71	1	no	—
52	C₃²×C₅	—	142	2	no	—
53	C₃²×C₅	D₇₁⋊C₅	1	1	yes	characteristic, complemented
54	C₂×C₃×C₅	—	1065	1	no	—
55	D₁₅	—	71	1	no	—
56	C₃×D₅	—	213	1	no	—
57	C₅×D₃	—	355	1	no	—
58	C₅²	—	71	1	no	Sylow
59	C₃×D₃	—	355	1	no	Hall
60	C₃×C₅	—	2	1	no	—
61	C₃×C₅	—	71	1	no	—
62	C₃×C₅	—	71	1	no	—
63	C₃×C₅	—	142	1	no	—
64	C₃×C₅	—	142	4	no	—
65	C₃×C₅	—	142	2	no	—
66	C₃×C₅	—	142	2	no	—
67	C₃×C₅	C₃×D₇₁⋊C₅	1	1	yes	characteristic, complemented
68	C₃×C₅	C₃⋊(D₇₁⋊C₅)	1	1	yes	characteristic, complemented
69	C₂×C₅	—	1065	1	no	—
70	D₅	—	213	1	no	—
71	C₃²	C₅⋊(D₇₁⋊C₅)	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃	—	1065	1	no	—
73	D₃	—	355	1	no	—
74	C₅	—	71	1	no	—
75	C₅	—	142	2	no	—
76	C₅	C₃×C₃⋊(D₇₁⋊C₅)	1	1	yes	characteristic, complemented
77	C₃	—	2	1	no	—
78	C₃	C₃×C₅⋊(D₇₁⋊C₅)	1	1	yes	characteristic, complemented
79	C₃	C₃⋊(C₅⋊(D₇₁⋊C₅))	1	1	yes	characteristic, direct product factor
80	C₂	—	1065	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₃⋊(C₅⋊(D₇₁⋊C₅))
commutator, cosocle, hypocenter	C₃×C₅×C₇₁	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇₁	C₂×C₅
LCS	G ▷ C₃×C₅×C₇₁
UCS	C₁ ◁ C₃

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)
4. C₃×D₁₀₆₅	C₅	semidirect
7. C₃×C₅×C₇₁⋊C₅	D₃	semidirect
8. C₃×C₅×C₇₁⋊C₅	C₂×C₃	semidirect
11. C₃²×C₇₁⋊C₅	D₅	semidirect
12. C₃²×C₅×C₇₁	C₂×C₅	semidirect
15. D₁₀₆₅	C₃×C₅	semidirect
17. C₅×C₇₁⋊C₅	C₃×D₃	semidirect
20. C₃×C₅×C₇₁	C₅×D₃	semidirect
21. C₃×C₅×C₇₁	C₂×C₃×C₅	semidirect
26. C₃×C₇₁⋊C₅	C₃×D₅	semidirect
27. C₃×C₇₁⋊C₅	D₁₅	semidirect
30. C₃²×C₇₁	C₅×D₅	semidirect
34. C₅×C₇₁	C₃×C₅×D₃	semidirect
36. C₇₁⋊C₅	C₃×D₁₅	semidirect
39. C₃×C₇₁	C₃×C₅×D₅	semidirect
40. C₃×C₇₁	C₅×D₁₅	semidirect
49. C₇₁	C₃×C₅×D₁₅	semidirect
53. C₃²×C₅	D₇₁⋊C₅	semidirect
67. C₃×C₅	C₃×D₇₁⋊C₅	semidirect
68. C₃×C₅	C₃⋊(D₇₁⋊C₅)	semidirect
71. C₃²	C₅⋊(D₇₁⋊C₅)	semidirect
76. C₅	C₃×C₃⋊(D₇₁⋊C₅)	semidirect
78. C₃	C₃×C₅⋊(D₇₁⋊C₅)	semidirect
79. 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
C₃×C₅⋊(D₇₁⋊C₅)	3
C₃×D₁₀₆₅	5
C₃×C₃⋊(D₇₁⋊C₅)	5
C₃×C₅×D₁₅	71

Subgroups — C3×C3⋊(C5⋊(D71⋊C5)) #44544060

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊(C₅⋊(D₇₁⋊C₅)) #44544060