Subgroups — C₃×C₄³×C₅×C₁₇ #72194250

Order 16320.

1032 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×C₅×C₁₇	C₂	1	7	yes	maximal
2	C₄³×C₅×C₁₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂²×C₃×C₄×C₅×C₁₇	C₂²	1	7	yes	—
4	C₃×C₄²×C₅×C₁₇	C₄	1	28	yes	direct product factor
5	C₃×C₄³×C₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₄²×C₅×C₁₇	C₂×C₃	1	7	yes	—
7	C₂³×C₃×C₅×C₁₇	C₂³	1	1	yes	characteristic
8	C₂×C₃×C₄×C₅×C₁₇	C₂×C₄	1	42	yes	—
9	C₂×C₃×C₄²×C₁₇	C₂×C₅	1	7	yes	—
10	C₂²×C₄×C₅×C₁₇	C₂²×C₃	1	7	yes	—
11	C₄²×C₅×C₁₇	C₃×C₄	1	28	yes	direct product factor
12	C₄³×C₁₇	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×C₁₇	C₂²×C₄	1	7	yes	—
14	C₃×C₄×C₅×C₁₇	C₄²	1	28	yes	direct product factor
15	C₃×C₄³×C₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂²×C₃×C₄×C₁₇	C₂²×C₅	1	7	yes	—
17	C₃×C₄²×C₁₇	C₄×C₅	1	28	yes	direct product factor
18	C₂³×C₅×C₁₇	C₂³×C₃	1	1	yes	characteristic
19	C₂×C₄×C₅×C₁₇	C₂×C₃×C₄	1	42	yes	—
20	C₂×C₄²×C₁₇	C₂×C₃×C₅	1	7	yes	—
21	C₂×C₃×C₅×C₁₇	C₂×C₄²	1	7	yes	—
22	C₂×C₃×C₄²×C₅	C₂×C₁₇	1	7	yes	—
23	C₂³×C₃×C₁₇	C₂³×C₅	1	1	yes	characteristic
24	C₂×C₃×C₄×C₁₇	C₂×C₄×C₅	1	42	yes	—
25	C₂²×C₅×C₁₇	C₂²×C₃×C₄	1	7	yes	—
26	C₄×C₅×C₁₇	C₃×C₄²	1	28	yes	direct product factor
27	C₄³×C₅	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
28	C₂²×C₄×C₁₇	C₂²×C₃×C₅	1	7	yes	—
29	C₄²×C₁₇	C₃×C₄×C₅	1	28	yes	direct product factor
30	C₃×C₅×C₁₇	C₄³	1	1	yes	characteristic, direct product factor, Hall
31	C₂²×C₃×C₄×C₅	C₂²×C₁₇	1	7	yes	—
32	C₃×C₄²×C₅	C₄×C₁₇	1	28	yes	direct product factor
33	C₂²×C₃×C₁₇	C₂²×C₄×C₅	1	7	yes	—
34	C₃×C₄×C₁₇	C₄²×C₅	1	28	yes	direct product factor
35	C₃×C₄³	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
36	C₂×C₅×C₁₇	C₂×C₃×C₄²	1	7	yes	—
37	C₂×C₄²×C₅	C₂×C₃×C₁₇	1	7	yes	—
38	C₂³×C₁₇	C₂³×C₃×C₅	1	1	yes	characteristic
39	C₂×C₄×C₁₇	C₂×C₃×C₄×C₅	1	42	yes	—
40	C₂³×C₃×C₅	C₂³×C₁₇	1	1	yes	characteristic
41	C₂×C₃×C₄×C₅	C₂×C₄×C₁₇	1	42	yes	—
42	C₂×C₃×C₁₇	C₂×C₄²×C₅	1	7	yes	—
43	C₂×C₃×C₄²	C₂×C₅×C₁₇	1	7	yes	—
44	C₅×C₁₇	C₃×C₄³	1	1	yes	characteristic, direct product factor, Hall
45	C₂²×C₄×C₅	C₂²×C₃×C₁₇	1	7	yes	—
46	C₄²×C₅	C₃×C₄×C₁₇	1	28	yes	direct product factor
47	C₂²×C₁₇	C₂²×C₃×C₄×C₅	1	7	yes	—
48	C₄×C₁₇	C₃×C₄²×C₅	1	28	yes	direct product factor
49	C₄³	C₃×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
50	C₂²×C₃×C₅	C₂²×C₄×C₁₇	1	7	yes	—
51	C₃×C₄×C₅	C₄²×C₁₇	1	28	yes	direct product factor
52	C₃×C₁₇	C₄³×C₅	1	1	yes	characteristic, direct product factor, Hall
53	C₂²×C₃×C₄	C₂²×C₅×C₁₇	1	7	yes	—
54	C₃×C₄²	C₄×C₅×C₁₇	1	28	yes	direct product factor
55	C₂³×C₅	C₂³×C₃×C₁₇	1	1	yes	characteristic
56	C₂×C₄×C₅	C₂×C₃×C₄×C₁₇	1	42	yes	—
57	C₂×C₁₇	C₂×C₃×C₄²×C₅	1	7	yes	—
58	C₂×C₄²	C₂×C₃×C₅×C₁₇	1	7	yes	—
59	C₂×C₃×C₅	C₂×C₄²×C₁₇	1	7	yes	—
60	C₂³×C₃	C₂³×C₅×C₁₇	1	1	yes	characteristic
61	C₂×C₃×C₄	C₂×C₄×C₅×C₁₇	1	42	yes	—
62	C₂²×C₅	C₂²×C₃×C₄×C₁₇	1	7	yes	—
63	C₄×C₅	C₃×C₄²×C₁₇	1	28	yes	direct product factor
64	C₁₇	C₃×C₄³×C₅	1	1	yes	characteristic, direct product factor, Sylow
65	C₂²×C₄	C₂²×C₃×C₅×C₁₇	1	7	yes	—
66	C₄²	C₃×C₄×C₅×C₁₇	1	28	yes	direct product factor
67	C₃×C₅	C₄³×C₁₇	1	1	yes	characteristic, direct product factor, Hall
68	C₂²×C₃	C₂²×C₄×C₅×C₁₇	1	7	yes	—
69	C₃×C₄	C₄²×C₅×C₁₇	1	28	yes	direct product factor
70	C₂×C₅	C₂×C₃×C₄²×C₁₇	1	7	yes	—
71	C₂³	C₂³×C₃×C₅×C₁₇	1	1	yes	characteristic
72	C₂×C₄	C₂×C₃×C₄×C₅×C₁₇	1	42	yes	—
73	C₂×C₃	C₂×C₄²×C₅×C₁₇	1	7	yes	—
74	C₅	C₃×C₄³×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
75	C₂²	C₂²×C₃×C₄×C₅×C₁₇	1	7	yes	—
76	C₄	C₃×C₄²×C₅×C₁₇	1	28	yes	direct product factor
77	C₃	C₄³×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
78	C₂	C₂×C₃×C₄²×C₅×C₁₇	1	7	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³	C₂³×C₃×C₅×C₁₇
socle, prime radical	C₂³×C₃×C₅×C₁₇	C₂³
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄³×C₅×C₁₇	C₃	direct (N × H)
4. C₃×C₄²×C₅×C₁₇	C₄	direct (N × H)
5. C₃×C₄³×C₁₇	C₅	direct (N × H)
11. C₄²×C₅×C₁₇	C₃×C₄	direct (N × H)
12. C₄³×C₁₇	C₃×C₅	direct (N × H)
14. C₃×C₄×C₅×C₁₇	C₄²	direct (N × H)
15. C₃×C₄³×C₅	C₁₇	direct (N × H)
17. C₃×C₄²×C₁₇	C₄×C₅	direct (N × H)
26. C₄×C₅×C₁₇	C₃×C₄²	direct (N × H)
27. C₄³×C₅	C₃×C₁₇	direct (N × H)
29. C₄²×C₁₇	C₃×C₄×C₅	direct (N × H)
30. C₃×C₅×C₁₇	C₄³	direct (N × H)
32. C₃×C₄²×C₅	C₄×C₁₇	direct (N × H)
34. C₃×C₄×C₁₇	C₄²×C₅	direct (N × H)
35. C₃×C₄³	C₅×C₁₇	direct (N × H)
44. C₅×C₁₇	C₃×C₄³	direct (N × H)
46. C₄²×C₅	C₃×C₄×C₁₇	direct (N × H)
48. C₄×C₁₇	C₃×C₄²×C₅	direct (N × H)
49. C₄³	C₃×C₅×C₁₇	direct (N × H)
51. C₃×C₄×C₅	C₄²×C₁₇	direct (N × H)
52. C₃×C₁₇	C₄³×C₅	direct (N × H)
54. C₃×C₄²	C₄×C₅×C₁₇	direct (N × H)
63. C₄×C₅	C₃×C₄²×C₁₇	direct (N × H)
64. C₁₇	C₃×C₄³×C₅	direct (N × H)
66. C₄²	C₃×C₄×C₅×C₁₇	direct (N × H)
67. C₃×C₅	C₄³×C₁₇	direct (N × H)
69. C₃×C₄	C₄²×C₅×C₁₇	direct (N × H)
74. C₅	C₃×C₄³×C₁₇	direct (N × H)
76. C₄	C₃×C₄²×C₅×C₁₇	direct (N × H)
77. C₃	C₄³×C₅×C₁₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄²×C₅×C₁₇	2
C₄³×C₅×C₁₇	3
C₃×C₄³×C₁₇	5
C₃×C₄³×C₅	17

Subgroups — C3×C43×C5×C17 #72194250

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄³×C₅×C₁₇ #72194250