Subgroups — C₂₉×Dic₂₇₉ #44569021

Order 32364.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₂₉×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂₉×Dic₉₃	—	3	1	no	maximal
3	C₉×C₂₉×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₂₉×C₃₁	D₃	1	1	yes	characteristic
5	C₂₉×Dic₃₁	—	9	1	no	Hall
6	C₃×C₂₉×C₃₁	Dic₃	1	1	yes	characteristic
7	C₂×C₂₉×C₃₁	D₉	1	1	yes	characteristic
8	Dic₂₇₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂₉×Dic₉	—	31	1	no	maximal, Hall
10	C₂₉×C₃₁	Dic₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₉×C₃₁	C₂×C₂₉	1	1	yes	characteristic
12	C₂×C₉×C₂₉	D₃₁	1	1	yes	characteristic
13	Dic₉₃	—	3	1	no	—
14	Dic₃×C₂₉	—	93	1	no	—
15	C₉×C₃₁	C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
16	C₉×C₂₉	Dic₃₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₃₁	D₃×C₂₉	1	1	yes	characteristic
18	C₂×C₃×C₂₉	D₉₃	1	1	yes	characteristic
19	Dic₃₁	—	9	1	no	Hall
20	C₄×C₂₉	—	279	1	no	Hall
21	C₃×C₃₁	Dic₃×C₂₉	1	1	yes	characteristic
22	C₃×C₂₉	Dic₉₃	1	1	yes	characteristic
23	C₂×C₃₁	D₉×C₂₉	1	1	yes	characteristic
24	C₂×C₂₉	D₂₇₉	1	1	yes	characteristic
25	Dic₉	—	31	1	no	Hall
26	C₃₁	C₂₉×Dic₉	1	1	yes	characteristic, complemented, Sylow
27	C₂₉	Dic₂₇₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₉	C₂₉×D₃₁	1	1	yes	characteristic
29	Dic₃	—	93	1	no	—
30	C₉	C₂₉×Dic₃₁	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	C₂₉×D₉₃	1	1	yes	characteristic
32	C₄	—	279	1	no	Sylow
33	C₃	C₂₉×Dic₉₃	1	1	yes	characteristic
34	C₂	C₂₉×D₂₇₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₂₉	D₂₇₉
commutator, hypocenter	C₉×C₃₁	C₄×C₂₉
Frattini	C₂×C₃	C₂₉×D₉₃
Fitting	C₂×C₉×C₂₉×C₃₁	C₂
socle, prime radical	C₂×C₃×C₂₉×C₃₁	D₃
cosocle	C₂×C₉×C₃₁	C₂×C₂₉
LCS	G ▷ C₉×C₃₁
UCS	C₁ ◁ C₂×C₂₉

Complements

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

N	H ≅ G/N	type
3. C₉×C₂₉×C₃₁	C₄	semidirect
8. Dic₂₇₉	C₂₉	direct (N × H)
10. C₂₉×C₃₁	Dic₉	semidirect
15. C₉×C₃₁	C₄×C₂₉	semidirect
16. C₉×C₂₉	Dic₃₁	semidirect
26. C₃₁	C₂₉×Dic₉	semidirect
27. C₂₉	Dic₂₇₉	direct (N × H)
30. C₉	C₂₉×Dic₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×C₂₉×C₃₁	2
C₂₉×Dic₉₃	3
Dic₂₇₉	29
C₂₉×Dic₉	31

Subgroups — C29×Dic279 #44569021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×Dic₂₇₉ #44569021