Subgroups — C₈×C₂₇×C₁₃₁ #72205287

Order 28296.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂₇×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₈×C₉×C₁₃₁	C₃	1	1	yes	maximal, characteristic
3	C₂×C₂₇×C₁₃₁	C₄	1	1	yes	characteristic
4	C₃×C₈×C₁₃₁	C₉	1	1	yes	characteristic
5	C₄×C₉×C₁₃₁	C₂×C₃	1	1	yes	characteristic
6	C₂₇×C₁₃₁	C₈	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₉×C₁₃₁	C₃×C₄	1	1	yes	characteristic
8	C₃×C₄×C₁₃₁	C₂×C₉	1	1	yes	characteristic
9	C₉×C₁₃₁	C₃×C₈	1	1	yes	characteristic
10	C₈×C₁₃₁	C₂₇	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₁₃₁	C₄×C₉	1	1	yes	characteristic
12	C₄×C₁₃₁	C₂×C₂₇	1	1	yes	characteristic
13	C₃×C₁₃₁	C₈×C₉	1	1	yes	characteristic
14	C₂×C₁₃₁	C₄×C₂₇	1	1	yes	characteristic
15	C₈×C₂₇	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₁₃₁	C₈×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₄×C₂₇	C₂×C₁₃₁	1	1	yes	characteristic
18	C₈×C₉	C₃×C₁₃₁	1	1	yes	characteristic
19	C₂×C₂₇	C₄×C₁₃₁	1	1	yes	characteristic
20	C₄×C₉	C₂×C₃×C₁₃₁	1	1	yes	characteristic
21	C₂₇	C₈×C₁₃₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₃×C₈	C₉×C₁₃₁	1	1	yes	characteristic
23	C₂×C₉	C₃×C₄×C₁₃₁	1	1	yes	characteristic
24	C₃×C₄	C₂×C₉×C₁₃₁	1	1	yes	characteristic
25	C₉	C₃×C₈×C₁₃₁	1	1	yes	characteristic
26	C₈	C₂₇×C₁₃₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	C₄×C₉×C₁₃₁	1	1	yes	characteristic
28	C₄	C₂×C₂₇×C₁₃₁	1	1	yes	characteristic
29	C₃	C₈×C₉×C₁₃₁	1	1	yes	characteristic
30	C₂	C₄×C₂₇×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₉	C₂×C₃×C₁₃₁
socle, prime radical	C₂×C₃×C₁₃₁	C₄×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₂₇×C₁₃₁	C₈	direct (N × H)
10. C₈×C₁₃₁	C₂₇	direct (N × H)
15. C₈×C₂₇	C₁₃₁	direct (N × H)
16. C₁₃₁	C₈×C₂₇	direct (N × H)
21. C₂₇	C₈×C₁₃₁	direct (N × H)
26. C₈	C₂₇×C₁₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₂₇×C₁₃₁	2
C₈×C₉×C₁₃₁	3
C₈×C₂₇	131

Subgroups — C8×C27×C131 #72205287

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₂₇×C₁₃₁ #72205287