Subgroups — C₂₉×Dic₂₇₃ #44539726

Order 31668.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₃×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂₉×Dic₉₁	—	3	1	no	maximal, Hall
3	C₃×C₇×C₁₃×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₃×C₂₉	D₃	1	1	yes	characteristic
5	C₂₉×Dic₃₉	—	7	1	no	maximal, Hall
6	C₇×C₁₃×C₂₉	Dic₃	1	1	yes	characteristic, complemented, Hall
7	C₂₉×Dic₂₁	—	13	1	no	maximal, Hall
8	C₂×C₃×C₁₃×C₂₉	D₇	1	1	yes	characteristic
9	C₂₉×Dic₁₃	—	21	1	no	Hall
10	C₂×C₃×C₇×C₂₉	D₁₃	1	1	yes	characteristic
11	C₃×C₁₃×C₂₉	Dic₇	1	1	yes	characteristic, complemented, Hall
12	Dic₂₇₃	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	Dic₇×C₂₉	—	39	1	no	Hall
14	C₂×C₁₃×C₂₉	D₂₁	1	1	yes	characteristic
15	C₃×C₇×C₂₉	Dic₁₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₇×C₁₃	C₂×C₂₉	1	1	yes	characteristic
17	C₂×C₇×C₂₉	D₃₉	1	1	yes	characteristic
18	C₁₃×C₂₉	Dic₂₁	1	1	yes	characteristic, complemented, Hall
19	Dic₉₁	—	3	1	no	Hall
20	Dic₃×C₂₉	—	91	1	no	Hall
21	C₃×C₇×C₁₃	C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
22	C₇×C₂₉	Dic₃₉	1	1	yes	characteristic, complemented, Hall
23	C₂×C₇×C₁₃	D₃×C₂₉	1	1	yes	characteristic
24	C₂×C₃×C₂₉	D₉₁	1	1	yes	characteristic
25	Dic₃₉	—	7	1	no	Hall
26	C₄×C₂₉	—	273	1	no	Hall
27	C₇×C₁₃	Dic₃×C₂₉	1	1	yes	characteristic, complemented, Hall
28	C₃×C₂₉	Dic₉₁	1	1	yes	characteristic, complemented, Hall
29	Dic₂₁	—	13	1	no	Hall
30	C₂×C₃×C₁₃	D₇×C₂₉	1	1	yes	characteristic
31	C₂×C₂₉	D₂₇₃	1	1	yes	characteristic
32	Dic₁₃	—	21	1	no	Hall
33	C₂×C₃×C₇	D₁₃×C₂₉	1	1	yes	characteristic
34	C₃×C₁₃	Dic₇×C₂₉	1	1	yes	characteristic, complemented, Hall
35	C₂₉	Dic₂₇₃	1	1	yes	characteristic, direct product factor, Sylow
36	Dic₇	—	39	1	no	Hall
37	C₂×C₁₃	C₂₉×D₂₁	1	1	yes	characteristic
38	C₃×C₇	C₂₉×Dic₁₃	1	1	yes	characteristic, complemented, Hall
39	C₂×C₇	C₂₉×D₃₉	1	1	yes	characteristic
40	C₁₃	C₂₉×Dic₂₁	1	1	yes	characteristic, complemented, Sylow
41	Dic₃	—	91	1	no	Hall
42	C₇	C₂₉×Dic₃₉	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	C₂₉×D₉₁	1	1	yes	characteristic
44	C₄	—	273	1	no	Sylow
45	C₃	C₂₉×Dic₉₁	1	1	yes	characteristic, complemented, Sylow
46	C₂	C₂₉×D₂₇₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₂₉	D₂₇₃
commutator, hypocenter	C₃×C₇×C₁₃	C₄×C₂₉
Frattini	C₂	C₂₉×D₂₇₃
Fitting, socle, prime radical	C₂×C₃×C₇×C₁₃×C₂₉	C₂
cosocle	C₂×C₃×C₇×C₁₃	C₂×C₂₉
LCS	G ▷ C₃×C₇×C₁₃
UCS	C₁ ◁ C₂×C₂₉

Complements

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

N	H ≅ G/N	type
3. C₃×C₇×C₁₃×C₂₉	C₄	semidirect
6. C₇×C₁₃×C₂₉	Dic₃	semidirect
11. C₃×C₁₃×C₂₉	Dic₇	semidirect
12. Dic₂₇₃	C₂₉	direct (N × H)
15. C₃×C₇×C₂₉	Dic₁₃	semidirect
18. C₁₃×C₂₉	Dic₂₁	semidirect
21. C₃×C₇×C₁₃	C₄×C₂₉	semidirect
22. C₇×C₂₉	Dic₃₉	semidirect
27. C₇×C₁₃	Dic₃×C₂₉	semidirect
28. C₃×C₂₉	Dic₉₁	semidirect
34. C₃×C₁₃	Dic₇×C₂₉	semidirect
35. C₂₉	Dic₂₇₃	direct (N × H)
38. C₃×C₇	C₂₉×Dic₁₃	semidirect
40. C₁₃	C₂₉×Dic₂₁	semidirect
42. C₇	C₂₉×Dic₃₉	semidirect
45. C₃	C₂₉×Dic₉₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇×C₁₃×C₂₉	2
C₂₉×Dic₉₁	3
C₂₉×Dic₃₉	7
C₂₉×Dic₂₁	13
Dic₂₇₃	29

Subgroups — C29×Dic273 #44539726

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×Dic₂₇₃ #44539726