Subgroups — C₅×D₂₆₉₁ #41002086

Order 26910.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₈₉₇	—	3	1	no	maximal
3	D₂₆₉₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₃×C₂₃	D₃	1	1	yes	characteristic
5	C₅×D₂₉₉	—	9	1	no	Hall
6	C₉×C₁₃×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×D₂₀₇	—	13	1	no	maximal, Hall
8	D₈₉₇	—	3	1	no	—
9	C₅×C₁₃×C₂₃	D₉	1	1	yes	characteristic, complemented, Hall
10	C₅×D₁₁₇	—	23	1	no	maximal, Hall
11	C₅×C₉×C₂₃	D₁₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₃×C₂₃	C₅×D₃	1	1	yes	characteristic
13	C₅×D₆₉	—	39	1	no	—
14	D₂₉₉	—	9	1	no	Hall
15	C₅×C₉×C₁₃	D₂₃	1	1	yes	characteristic, complemented, Hall
16	D₂₀₇	—	13	1	no	Hall
17	C₅×D₃₉	—	69	1	no	—
18	C₃×C₅×C₂₃	D₃₉	1	1	yes	characteristic
19	C₁₃×C₂₃	C₅×D₉	1	1	yes	characteristic, complemented, Hall
20	D₁₁₇	—	23	1	no	Hall
21	C₅×D₂₃	—	117	1	no	Hall
22	C₉×C₂₃	C₅×D₁₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₁₃	D₆₉	1	1	yes	characteristic
24	D₆₉	—	39	1	no	—
25	C₅×D₁₃	—	207	1	no	Hall
26	C₉×C₁₃	C₅×D₂₃	1	1	yes	characteristic, complemented, Hall
27	C₅×C₂₃	D₁₁₇	1	1	yes	characteristic, complemented, Hall
28	C₅×D₉	—	299	1	no	Hall
29	D₃₉	—	69	1	no	—
30	C₃×C₂₃	C₅×D₃₉	1	1	yes	characteristic
31	C₅×C₁₃	D₂₀₇	1	1	yes	characteristic, complemented, Hall
32	D₂₃	—	117	1	no	Hall
33	C₅×C₉	D₂₉₉	1	1	yes	characteristic, complemented, Hall
34	C₃×C₁₃	C₅×D₆₉	1	1	yes	characteristic
35	C₅×D₃	—	897	1	no	—
36	D₁₃	—	207	1	no	Hall
37	C₂₃	C₅×D₁₁₇	1	1	yes	characteristic, complemented, Sylow
38	D₉	—	299	1	no	Hall
39	C₃×C₅	D₈₉₇	1	1	yes	characteristic
40	C₁₃	C₅×D₂₀₇	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	2691	1	no	Hall
42	C₉	C₅×D₂₉₉	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	897	1	no	—
44	C₅	D₂₆₉₁	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₅×D₈₉₇	1	1	yes	characteristic
46	C₂	—	2691	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₂₆₉₁
commutator, cosocle, hypocenter	C₉×C₁₃×C₂₃	C₂×C₅
Frattini	C₃	C₅×D₈₉₇
Fitting	C₅×C₉×C₁₃×C₂₃	C₂
socle	C₃×C₅×C₁₃×C₂₃	D₃
LCS	G ▷ C₉×C₁₃×C₂₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₁₃×C₂₃	C₂	semidirect
3. D₂₆₉₁	C₅	direct (N × H)
6. C₉×C₁₃×C₂₃	C₂×C₅	semidirect
9. C₅×C₁₃×C₂₃	D₉	semidirect
11. C₅×C₉×C₂₃	D₁₃	semidirect
15. C₅×C₉×C₁₃	D₂₃	semidirect
19. C₁₃×C₂₃	C₅×D₉	semidirect
22. C₉×C₂₃	C₅×D₁₃	semidirect
26. C₉×C₁₃	C₅×D₂₃	semidirect
27. C₅×C₂₃	D₁₁₇	semidirect
31. C₅×C₁₃	D₂₀₇	semidirect
33. C₅×C₉	D₂₉₉	semidirect
37. C₂₃	C₅×D₁₁₇	semidirect
40. C₁₃	C₅×D₂₀₇	semidirect
42. C₉	C₅×D₂₉₉	semidirect
44. C₅	D₂₆₉₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₉×C₁₃×C₂₃	2
C₅×D₈₉₇	3
D₂₆₉₁	5
C₅×D₂₀₇	13
C₅×D₁₁₇	23

Subgroups — C5×D2691 #41002086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₂₆₉₁ #41002086