Subgroups — C₄×C₅²×C₁₁×C₁₇ #34035162

Order 18700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁×C₁₇	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₅×C₁₁×C₁₇	C₅	1	6	yes	maximal, direct product factor
4	C₂×C₅×C₁₁×C₁₇	C₂×C₅	1	6	yes	—
5	C₄×C₅²×C₁₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₄×C₅²×C₁₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₁×C₁₇	C₄×C₅	1	6	yes	direct product factor
8	C₂×C₅²×C₁₇	C₂×C₁₁	1	1	yes	characteristic
9	C₄×C₁₁×C₁₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₅²×C₁₁	C₂×C₁₇	1	1	yes	characteristic
11	C₅²×C₁₇	C₄×C₁₁	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₁₁×C₁₇	C₂×C₅²	1	1	yes	characteristic
13	C₄×C₅×C₁₇	C₅×C₁₁	1	6	yes	direct product factor
14	C₅²×C₁₁	C₄×C₁₇	1	1	yes	characteristic, direct product factor, Hall
15	C₄×C₅×C₁₁	C₅×C₁₇	1	6	yes	direct product factor
16	C₁₁×C₁₇	C₄×C₅²	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅×C₁₇	C₂×C₅×C₁₁	1	6	yes	—
18	C₂×C₅×C₁₁	C₂×C₅×C₁₇	1	6	yes	—
19	C₄×C₅²	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
20	C₅×C₁₇	C₄×C₅×C₁₁	1	6	yes	direct product factor
21	C₄×C₁₇	C₅²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
22	C₅×C₁₁	C₄×C₅×C₁₇	1	6	yes	direct product factor
23	C₂×C₅²	C₂×C₁₁×C₁₇	1	1	yes	characteristic
24	C₄×C₁₁	C₅²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₁₇	C₂×C₅²×C₁₁	1	1	yes	characteristic
26	C₅²	C₄×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₁₁	C₂×C₅²×C₁₇	1	1	yes	characteristic
28	C₄×C₅	C₅×C₁₁×C₁₇	1	6	yes	direct product factor
29	C₁₇	C₄×C₅²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₁₁	C₄×C₅²×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₅	C₂×C₅×C₁₁×C₁₇	1	6	yes	—
32	C₅	C₄×C₅×C₁₁×C₁₇	1	6	yes	direct product factor
33	C₄	C₅²×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₅²×C₁₁×C₁₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₅²×C₁₁×C₁₇
socle, prime radical	C₂×C₅²×C₁₁×C₁₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅²×C₁₁×C₁₇	C₄	direct (N × H)
3. C₄×C₅×C₁₁×C₁₇	C₅	direct (N × H)
5. C₄×C₅²×C₁₇	C₁₁	direct (N × H)
6. C₄×C₅²×C₁₁	C₁₇	direct (N × H)
7. C₅×C₁₁×C₁₇	C₄×C₅	direct (N × H)
9. C₄×C₁₁×C₁₇	C₅²	direct (N × H)
11. C₅²×C₁₇	C₄×C₁₁	direct (N × H)
13. C₄×C₅×C₁₇	C₅×C₁₁	direct (N × H)
14. C₅²×C₁₁	C₄×C₁₇	direct (N × H)
15. C₄×C₅×C₁₁	C₅×C₁₇	direct (N × H)
16. C₁₁×C₁₇	C₄×C₅²	direct (N × H)
19. C₄×C₅²	C₁₁×C₁₇	direct (N × H)
20. C₅×C₁₇	C₄×C₅×C₁₁	direct (N × H)
21. C₄×C₁₇	C₅²×C₁₁	direct (N × H)
22. C₅×C₁₁	C₄×C₅×C₁₇	direct (N × H)
24. C₄×C₁₁	C₅²×C₁₇	direct (N × H)
26. C₅²	C₄×C₁₁×C₁₇	direct (N × H)
28. C₄×C₅	C₅×C₁₁×C₁₇	direct (N × H)
29. C₁₇	C₄×C₅²×C₁₁	direct (N × H)
30. C₁₁	C₄×C₅²×C₁₇	direct (N × H)
32. C₅	C₄×C₅×C₁₁×C₁₇	direct (N × H)
33. C₄	C₅²×C₁₁×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×C₅²×C₁₁×C₁₇	2
C₄×C₅×C₁₁×C₁₇	5
C₄×C₅²×C₁₇	11
C₄×C₅²×C₁₁	17

Subgroups — C4×C52×C11×C17 #34035162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅²×C₁₁×C₁₇ #34035162