Subgroups — C₂×C₂₉×D₂₇₉ #44569050

Order 32364.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×D₂₇₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₂₉×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×D₉₃	—	3	1	no	maximal
4	C₉×C₂₉×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂₉×D₉₃	—	3	2	no	—
6	C₂×C₃×C₂₉×C₃₁	D₃	1	1	yes	characteristic
7	C₂×C₂₉×D₃₁	—	9	1	no	Hall
8	C₃×C₂₉×C₃₁	C₂×D₃	1	1	yes	characteristic
9	C₂×C₂₉×C₃₁	D₉	1	1	yes	characteristic, complemented
10	C₂₉×D₃₁	—	9	2	no	—
11	C₂×D₂₇₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×D₉×C₂₉	—	31	1	no	maximal, Hall
13	C₂₉×C₃₁	C₂×D₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₉×C₃₁	C₂×C₂₉	1	1	yes	characteristic, complemented
15	D₂₇₉	C₂×C₂₉	1	2	yes	direct product factor
16	C₂×C₉×C₂₉	D₃₁	1	1	yes	characteristic, complemented
17	D₉×C₂₉	—	31	2	no	—
18	C₂×D₉₃	—	3	1	no	—
19	C₂×D₃×C₂₉	—	93	1	no	—
20	C₉×C₃₁	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
21	C₉×C₂₉	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₃₁	D₃×C₂₉	1	1	yes	characteristic
23	D₉₃	—	3	2	no	—
24	C₂×C₃×C₂₉	D₉₃	1	1	yes	characteristic
25	D₃×C₂₉	—	93	2	no	—
26	C₂×D₃₁	—	9	1	no	Hall
27	C₂²×C₂₉	—	279	1	no	Hall
28	C₃×C₃₁	C₂×D₃×C₂₉	1	1	yes	characteristic
29	C₃×C₂₉	C₂×D₉₃	1	1	yes	characteristic
30	C₂×C₃₁	D₉×C₂₉	1	1	yes	characteristic, complemented
31	D₃₁	—	9	2	no	—
32	C₂×C₂₉	—	279	2	no	—
33	C₂×C₂₉	D₂₇₉	1	1	yes	characteristic, direct product factor
34	C₂×D₉	—	31	1	no	Hall
35	C₃₁	C₂×D₉×C₂₉	1	1	yes	characteristic, complemented, Sylow
36	C₂₉	C₂×D₂₇₉	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₉	C₂₉×D₃₁	1	1	yes	characteristic, complemented
38	D₉	—	31	2	no	—
39	C₂×D₃	—	93	1	no	—
40	C₉	C₂×C₂₉×D₃₁	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	C₂₉×D₉₃	1	1	yes	characteristic
42	D₃	—	93	2	no	—
43	C₂²	—	279	1	no	Sylow
44	C₃	C₂×C₂₉×D₉₃	1	1	yes	characteristic
45	C₂	—	279	2	no	—
46	C₂	C₂₉×D₂₇₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₉	D₂₇₉
commutator, cosocle, hypocenter	C₉×C₃₁	C₂²×C₂₉
Frattini	C₃	C₂×C₂₉×D₉₃
Fitting	C₂×C₉×C₂₉×C₃₁	C₂
socle	C₂×C₃×C₂₉×C₃₁	D₃
LCS	G ▷ C₉×C₃₁
UCS	C₁ ◁ C₂×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂₉×D₂₇₉	C₂	direct (N × H)
2. C₂×C₉×C₂₉×C₃₁	C₂	semidirect
4. C₉×C₂₉×C₃₁	C₂²	semidirect
9. C₂×C₂₉×C₃₁	D₉	semidirect
11. C₂×D₂₇₉	C₂₉	direct (N × H)
13. C₂₉×C₃₁	C₂×D₉	semidirect
14. C₂×C₉×C₃₁	C₂×C₂₉	semidirect
15. D₂₇₉	C₂×C₂₉	direct (N × H)
16. C₂×C₉×C₂₉	D₃₁	semidirect
20. C₉×C₃₁	C₂²×C₂₉	semidirect
21. C₉×C₂₉	C₂×D₃₁	semidirect
30. C₂×C₃₁	D₉×C₂₉	semidirect
33. C₂×C₂₉	D₂₇₉	direct (N × H)
35. C₃₁	C₂×D₉×C₂₉	semidirect
36. C₂₉	C₂×D₂₇₉	direct (N × H)
37. C₂×C₉	C₂₉×D₃₁	semidirect
40. C₉	C₂×C₂₉×D₃₁	semidirect
46. C₂	C₂₉×D₂₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×D₂₇₉	2
C₂×C₉×C₂₉×C₃₁	2
C₂×C₂₉×D₉₃	3
C₂×D₂₇₉	29
C₂×D₉×C₂₉	31

Subgroups — C2×C29×D279 #44569050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×D₂₇₉ #44569050