Subgroups — C₁₃×C₁₇×C₁₂₈ #72205272

Order 28288.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₇×C₆₄	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₁₇×C₃₂	C₄	1	1	yes	characteristic
3	C₁₃×C₁₆×C₁₇	C₈	1	1	yes	characteristic
4	C₁₇×C₁₂₈	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₈×C₁₃×C₁₇	C₁₆	1	1	yes	characteristic
6	C₁₃×C₁₂₈	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₇×C₆₄	C₂×C₁₃	1	1	yes	characteristic
8	C₄×C₁₃×C₁₇	C₃₂	1	1	yes	characteristic
9	C₁₃×C₆₄	C₂×C₁₇	1	1	yes	characteristic
10	C₁₇×C₃₂	C₄×C₁₃	1	1	yes	characteristic
11	C₂×C₁₃×C₁₇	C₆₄	1	1	yes	characteristic
12	C₁₃×C₃₂	C₄×C₁₇	1	1	yes	characteristic
13	C₁₆×C₁₇	C₈×C₁₃	1	1	yes	characteristic
14	C₁₃×C₁₇	C₁₂₈	1	1	yes	characteristic, direct product factor, Hall
15	C₁₃×C₁₆	C₈×C₁₇	1	1	yes	characteristic
16	C₈×C₁₇	C₁₃×C₁₆	1	1	yes	characteristic
17	C₁₂₈	C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₈×C₁₃	C₁₆×C₁₇	1	1	yes	characteristic
19	C₄×C₁₇	C₁₃×C₃₂	1	1	yes	characteristic
20	C₆₄	C₂×C₁₃×C₁₇	1	1	yes	characteristic
21	C₄×C₁₃	C₁₇×C₃₂	1	1	yes	characteristic
22	C₂×C₁₇	C₁₃×C₆₄	1	1	yes	characteristic
23	C₃₂	C₄×C₁₃×C₁₇	1	1	yes	characteristic
24	C₂×C₁₃	C₁₇×C₆₄	1	1	yes	characteristic
25	C₁₇	C₁₃×C₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
26	C₁₆	C₈×C₁₃×C₁₇	1	1	yes	characteristic
27	C₁₃	C₁₇×C₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
28	C₈	C₁₃×C₁₆×C₁₇	1	1	yes	characteristic
29	C₄	C₁₃×C₁₇×C₃₂	1	1	yes	characteristic
30	C₂	C₁₃×C₁₇×C₆₄	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₆₄	C₂×C₁₃×C₁₇
socle, prime radical	C₂×C₁₃×C₁₇	C₆₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₇×C₁₂₈	C₁₃	direct (N × H)
6. C₁₃×C₁₂₈	C₁₇	direct (N × H)
14. C₁₃×C₁₇	C₁₂₈	direct (N × H)
17. C₁₂₈	C₁₃×C₁₇	direct (N × H)
25. C₁₇	C₁₃×C₁₂₈	direct (N × H)
27. C₁₃	C₁₇×C₁₂₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×C₁₇×C₆₄	2
C₁₇×C₁₂₈	13
C₁₃×C₁₂₈	17

Subgroups — C13×C17×C128 #72205272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₁₇×C₁₂₈ #72205272