Subgroups — C₅×Dic₉₅₇ #34062320

Order 19140.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₁×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₃₁₉	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₁×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₉₅₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₁×C₂₉	D₃	1	1	yes	characteristic
6	C₂×C₃×C₁₁×C₂₉	C₂×C₅	1	1	yes	characteristic
7	C₅×Dic₈₇	—	11	1	no	maximal, Hall
8	C₅×C₁₁×C₂₉	Dic₃	1	1	yes	characteristic, complemented, Hall
9	Dic₃₁₉	—	3	1	no	Hall
10	C₃×C₁₁×C₂₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₅×C₂₉	D₁₁	1	1	yes	characteristic
12	C₅×Dic₃₃	—	29	1	no	maximal, Hall
13	C₂×C₁₁×C₂₉	C₅×D₃	1	1	yes	characteristic
14	C₅×Dic₂₉	—	33	1	no	Hall
15	C₃×C₅×C₂₉	Dic₁₁	1	1	yes	characteristic, complemented, Hall
16	Dic₈₇	—	11	1	no	Hall
17	C₂×C₃×C₅×C₁₁	D₂₉	1	1	yes	characteristic
18	C₁₁×C₂₉	C₅×Dic₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×C₂₉	D₃₃	1	1	yes	characteristic
20	C₅×Dic₁₁	—	87	1	no	Hall
21	C₂×C₃×C₂₉	C₅×D₁₁	1	1	yes	characteristic
22	C₃×C₅×C₁₁	Dic₂₉	1	1	yes	characteristic, complemented, Hall
23	C₅×C₂₉	Dic₃₃	1	1	yes	characteristic, complemented, Hall
24	Dic₃₃	—	29	1	no	Hall
25	Dic₂₉	—	33	1	no	Hall
26	C₂×C₅×C₁₁	D₈₇	1	1	yes	characteristic
27	C₃×C₂₉	C₅×Dic₁₁	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₁₁	C₅×D₂₉	1	1	yes	characteristic
29	C₅×Dic₃	—	319	1	no	Hall
30	C₂×C₂₉	C₅×D₃₃	1	1	yes	characteristic
31	C₅×C₁₁	Dic₈₇	1	1	yes	characteristic, complemented, Hall
32	Dic₁₁	—	87	1	no	Hall
33	C₃×C₁₁	C₅×Dic₂₉	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×C₅	D₃₁₉	1	1	yes	characteristic
35	C₂₉	C₅×Dic₃₃	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₁₁	C₅×D₈₇	1	1	yes	characteristic
37	C₄×C₅	—	957	1	no	Hall
38	C₃×C₅	Dic₃₁₉	1	1	yes	characteristic, complemented, Hall
39	Dic₃	—	319	1	no	Hall
40	C₁₁	C₅×Dic₈₇	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	D₉₅₇	1	1	yes	characteristic
42	C₂×C₃	C₅×D₃₁₉	1	1	yes	characteristic
43	C₅	Dic₉₅₇	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	957	1	no	Sylow
45	C₃	C₅×Dic₃₁₉	1	1	yes	characteristic, complemented, Sylow
46	C₂	C₅×D₉₅₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	D₉₅₇
commutator, hypocenter	C₃×C₁₁×C₂₉	C₄×C₅
Frattini	C₂	C₅×D₉₅₇
Fitting, socle, prime radical	C₂×C₃×C₅×C₁₁×C₂₉	C₂
cosocle	C₂×C₃×C₁₁×C₂₉	C₂×C₅
LCS	G ▷ C₃×C₁₁×C₂₉
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₁×C₂₉	C₄	semidirect
4. Dic₉₅₇	C₅	direct (N × H)
8. C₅×C₁₁×C₂₉	Dic₃	semidirect
10. C₃×C₁₁×C₂₉	C₄×C₅	semidirect
15. C₃×C₅×C₂₉	Dic₁₁	semidirect
18. C₁₁×C₂₉	C₅×Dic₃	semidirect
22. C₃×C₅×C₁₁	Dic₂₉	semidirect
23. C₅×C₂₉	Dic₃₃	semidirect
27. C₃×C₂₉	C₅×Dic₁₁	semidirect
31. C₅×C₁₁	Dic₈₇	semidirect
33. C₃×C₁₁	C₅×Dic₂₉	semidirect
35. C₂₉	C₅×Dic₃₃	semidirect
38. C₃×C₅	Dic₃₁₉	semidirect
40. C₁₁	C₅×Dic₈₇	semidirect
43. C₅	Dic₉₅₇	direct (N × H)
45. C₃	C₅×Dic₃₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₁₁×C₂₉	2
C₅×Dic₃₁₉	3
Dic₉₅₇	5
C₅×Dic₈₇	11
C₅×Dic₃₃	29

Subgroups — C5×Dic957 #34062320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Dic₉₅₇ #34062320