Subgroups — C₂×C₂₉×D₁₁₇ #28330893

Order 13572.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×D₁₁₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₁₃×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×D₃₉	—	3	1	no	maximal
4	C₉×C₁₃×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂₉×D₃₉	—	3	2	no	—
6	C₂×C₃×C₁₃×C₂₉	D₃	1	1	yes	characteristic
7	C₂×D₁₃×C₂₉	—	9	1	no	Hall
8	C₃×C₁₃×C₂₉	C₂×D₃	1	1	yes	characteristic
9	C₂×D₉×C₂₉	—	13	1	no	maximal, Hall
10	C₂×C₁₃×C₂₉	D₉	1	1	yes	characteristic, complemented
11	D₁₃×C₂₉	—	9	2	no	—
12	C₂×C₉×C₂₉	D₁₃	1	1	yes	characteristic, complemented
13	D₉×C₂₉	—	13	2	no	—
14	C₂×D₁₁₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₁₃×C₂₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
16	C₂×D₃×C₂₉	—	39	1	no	—
17	C₉×C₂₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₉×C₁₃	C₂×C₂₉	1	1	yes	characteristic, complemented
19	D₁₁₇	C₂×C₂₉	1	2	yes	direct product factor
20	C₂×C₃×C₂₉	D₃₉	1	1	yes	characteristic
21	D₃×C₂₉	—	39	2	no	—
22	C₂×D₃₉	—	3	1	no	—
23	C₉×C₁₃	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₂₉	—	117	1	no	Hall
25	C₃×C₂₉	C₂×D₃₉	1	1	yes	characteristic
26	C₂×C₃×C₁₃	D₃×C₂₉	1	1	yes	characteristic
27	D₃₉	—	3	2	no	—
28	C₂×C₂₉	—	117	2	no	—
29	C₂×C₂₉	D₁₁₇	1	1	yes	characteristic, direct product factor
30	C₂×D₁₃	—	9	1	no	Hall
31	C₃×C₁₃	C₂×D₃×C₂₉	1	1	yes	characteristic
32	C₂×D₉	—	13	1	no	Hall
33	C₂₉	C₂×D₁₁₇	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₁₃	D₉×C₂₉	1	1	yes	characteristic, complemented
35	D₁₃	—	9	2	no	—
36	C₂×C₉	D₁₃×C₂₉	1	1	yes	characteristic, complemented
37	D₉	—	13	2	no	—
38	C₁₃	C₂×D₉×C₂₉	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₃	—	39	1	no	—
40	C₉	C₂×D₁₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	C₂₉×D₃₉	1	1	yes	characteristic
42	D₃	—	39	2	no	—
43	C₂²	—	117	1	no	Sylow
44	C₃	C₂×C₂₉×D₃₉	1	1	yes	characteristic
45	C₂	—	117	2	no	—
46	C₂	C₂₉×D₁₁₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₉	D₁₁₇
commutator, cosocle, hypocenter	C₉×C₁₃	C₂²×C₂₉
Frattini	C₃	C₂×C₂₉×D₃₉
Fitting	C₂×C₉×C₁₃×C₂₉	C₂
socle	C₂×C₃×C₁₃×C₂₉	D₃
LCS	G ▷ C₉×C₁₃
UCS	C₁ ◁ C₂×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂₉×D₁₁₇	C₂	direct (N × H)
2. C₂×C₉×C₁₃×C₂₉	C₂	semidirect
4. C₉×C₁₃×C₂₉	C₂²	semidirect
10. C₂×C₁₃×C₂₉	D₉	semidirect
12. C₂×C₉×C₂₉	D₁₃	semidirect
14. C₂×D₁₁₇	C₂₉	direct (N × H)
15. C₁₃×C₂₉	C₂×D₉	semidirect
17. C₉×C₂₉	C₂×D₁₃	semidirect
18. C₂×C₉×C₁₃	C₂×C₂₉	semidirect
19. D₁₁₇	C₂×C₂₉	direct (N × H)
23. C₉×C₁₃	C₂²×C₂₉	semidirect
29. C₂×C₂₉	D₁₁₇	direct (N × H)
33. C₂₉	C₂×D₁₁₇	direct (N × H)
34. C₂×C₁₃	D₉×C₂₉	semidirect
36. C₂×C₉	D₁₃×C₂₉	semidirect
38. C₁₃	C₂×D₉×C₂₉	semidirect
40. C₉	C₂×D₁₃×C₂₉	semidirect
46. C₂	C₂₉×D₁₁₇	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×D₁₁₇	2
C₂×C₉×C₁₃×C₂₉	2
C₂×C₂₉×D₃₉	3
C₂×D₉×C₂₉	13
C₂×D₁₁₇	29

Subgroups — C2×C29×D117 #28330893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×D₁₁₇ #28330893