Subgroups — C₄×C₅×C₈×C₁₇ #72182575

Order 2720.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₈×C₁₇	C₂	1	2	yes	maximal
2	C₄²×C₅×C₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×C₁₇	C₄	1	2	yes	—
4	C₂×C₄×C₅×C₁₇	C₂²	1	1	yes	characteristic
5	C₅×C₈×C₁₇	C₄	1	4	yes	direct product factor
6	C₄×C₈×C₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₅×C₁₇	C₂×C₄	1	1	yes	characteristic
8	C₄×C₅×C₁₇	C₈	1	4	yes	direct product factor
9	C₄×C₅×C₁₇	C₂×C₄	1	2	yes	—
10	C₂×C₈×C₁₇	C₂×C₅	1	2	yes	—
11	C₄²×C₁₇	C₂×C₅	1	1	yes	characteristic
12	C₂×C₅×C₁₇	C₄²	1	1	yes	characteristic
13	C₂×C₅×C₁₇	C₂×C₈	1	2	yes	—
14	C₄×C₅×C₈	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₄×C₁₇	C₄×C₅	1	2	yes	—
16	C₂×C₄×C₁₇	C₂²×C₅	1	1	yes	characteristic
17	C₈×C₁₇	C₄×C₅	1	4	yes	direct product factor
18	C₅×C₁₇	C₄×C₈	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₅×C₈	C₂×C₁₇	1	2	yes	—
20	C₄²×C₅	C₂×C₁₇	1	1	yes	characteristic
21	C₂²×C₁₇	C₂×C₄×C₅	1	1	yes	characteristic
22	C₄×C₁₇	C₅×C₈	1	4	yes	direct product factor
23	C₄×C₁₇	C₂×C₄×C₅	1	2	yes	—
24	C₂×C₄×C₅	C₄×C₁₇	1	2	yes	—
25	C₂×C₄×C₅	C₂²×C₁₇	1	1	yes	characteristic
26	C₅×C₈	C₄×C₁₇	1	4	yes	direct product factor
27	C₂×C₁₇	C₄²×C₅	1	1	yes	characteristic
28	C₂×C₁₇	C₂×C₅×C₈	1	2	yes	—
29	C₄×C₈	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂²×C₅	C₂×C₄×C₁₇	1	1	yes	characteristic
31	C₄×C₅	C₈×C₁₇	1	4	yes	direct product factor
32	C₄×C₅	C₂×C₄×C₁₇	1	2	yes	—
33	C₁₇	C₄×C₅×C₈	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₈	C₂×C₅×C₁₇	1	2	yes	—
35	C₄²	C₂×C₅×C₁₇	1	1	yes	characteristic
36	C₂×C₅	C₄²×C₁₇	1	1	yes	characteristic
37	C₂×C₅	C₂×C₈×C₁₇	1	2	yes	—
38	C₂×C₄	C₄×C₅×C₁₇	1	2	yes	—
39	C₂×C₄	C₂²×C₅×C₁₇	1	1	yes	characteristic
40	C₈	C₄×C₅×C₁₇	1	4	yes	direct product factor
41	C₅	C₄×C₈×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
42	C₂²	C₂×C₄×C₅×C₁₇	1	1	yes	characteristic
43	C₄	C₅×C₈×C₁₇	1	4	yes	direct product factor
44	C₄	C₂×C₄×C₅×C₁₇	1	2	yes	—
45	C₂	C₄²×C₅×C₁₇	1	1	yes	characteristic
46	C₂	C₂×C₅×C₈×C₁₇	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂²×C₅×C₁₇
socle, prime radical	C₂²×C₅×C₁₇	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₅×C₈×C₁₇	C₄	direct (N × H)
6. C₄×C₈×C₁₇	C₅	direct (N × H)
8. C₄×C₅×C₁₇	C₈	direct (N × H)
14. C₄×C₅×C₈	C₁₇	direct (N × H)
17. C₈×C₁₇	C₄×C₅	direct (N × H)
18. C₅×C₁₇	C₄×C₈	direct (N × H)
22. C₄×C₁₇	C₅×C₈	direct (N × H)
26. C₅×C₈	C₄×C₁₇	direct (N × H)
29. C₄×C₈	C₅×C₁₇	direct (N × H)
31. C₄×C₅	C₈×C₁₇	direct (N × H)
33. C₁₇	C₄×C₅×C₈	direct (N × H)
40. C₈	C₄×C₅×C₁₇	direct (N × H)
41. C₅	C₄×C₈×C₁₇	direct (N × H)
43. C₄	C₅×C₈×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×C₅×C₈×C₁₇	2
C₄²×C₅×C₁₇	2
C₄×C₈×C₁₇	5
C₄×C₅×C₈	17

Subgroups — C4×C5×C8×C17 #72182575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×C₈×C₁₇ #72182575