Subgroups — C₂×C₅×D₄₂₃ #22554875

Order 8460.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₄₂₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₉×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₁₄₁	—	3	1	no	maximal
4	C₅×C₉×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₄₂₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₃×C₅×C₄₇	D₃	1	1	yes	characteristic
7	C₅×D₁₄₁	—	3	2	no	—
8	C₂×C₅×D₄₇	—	9	1	no	Hall
9	C₂×C₉×C₄₇	C₂×C₅	1	1	yes	characteristic, complemented
10	D₄₂₃	C₂×C₅	1	2	yes	direct product factor
11	C₃×C₅×C₄₇	C₂×D₃	1	1	yes	characteristic
12	C₂×D₁₄₁	—	3	1	no	—
13	C₂×C₅×C₄₇	D₉	1	1	yes	characteristic, complemented
14	C₅×D₄₇	—	9	2	no	—
15	C₉×C₄₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₄₇	C₅×D₃	1	1	yes	characteristic
17	D₁₄₁	—	3	2	no	—
18	C₅×C₄₇	C₂×D₉	1	1	yes	characteristic, complemented, Hall
19	C₂×D₄₇	—	9	1	no	Hall
20	C₂×C₅×D₉	—	47	1	no	maximal, Hall
21	C₃×C₄₇	C₂×C₅×D₃	1	1	yes	characteristic
22	C₂×C₄₇	C₅×D₉	1	1	yes	characteristic, complemented
23	D₄₇	—	9	2	no	—
24	C₂×C₅×C₉	D₄₇	1	1	yes	characteristic, complemented
25	C₅×D₉	—	47	2	no	—
26	C₂×C₅×D₃	—	141	1	no	—
27	C₄₇	C₂×C₅×D₉	1	1	yes	characteristic, complemented, Sylow
28	C₅×C₉	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
29	C₂×D₉	—	47	1	no	Hall
30	C₂×C₃×C₅	D₁₄₁	1	1	yes	characteristic
31	C₅×D₃	—	141	2	no	—
32	C₂²×C₅	—	423	1	no	Hall
33	C₂×C₉	C₅×D₄₇	1	1	yes	characteristic, complemented
34	D₉	—	47	2	no	—
35	C₃×C₅	C₂×D₁₄₁	1	1	yes	characteristic
36	C₂×D₃	—	141	1	no	—
37	C₂×C₅	—	423	2	no	—
38	C₂×C₅	D₄₂₃	1	1	yes	characteristic, direct product factor
39	C₉	C₂×C₅×D₄₇	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃	C₅×D₁₄₁	1	1	yes	characteristic
41	D₃	—	141	2	no	—
42	C₅	C₂×D₄₂₃	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²	—	423	1	no	Sylow
44	C₃	C₂×C₅×D₁₄₁	1	1	yes	characteristic
45	C₂	—	423	2	no	—
46	C₂	C₅×D₄₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₄₂₃
commutator, hypocenter	C₉×C₄₇	C₂²×C₅
Frattini	C₃	C₂×C₅×D₁₄₁
Fitting	C₂×C₅×C₉×C₄₇	C₂
socle	C₂×C₃×C₅×C₄₇	D₃
LCS	G ▷ C₉×C₄₇
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₄₂₃	C₂	direct (N × H)
2. C₂×C₅×C₉×C₄₇	C₂	semidirect
4. C₅×C₉×C₄₇	C₂²	semidirect
5. C₂×D₄₂₃	C₅	direct (N × H)
9. C₂×C₉×C₄₇	C₂×C₅	semidirect
10. D₄₂₃	C₂×C₅	direct (N × H)
13. C₂×C₅×C₄₇	D₉	semidirect
15. C₉×C₄₇	C₂²×C₅	semidirect
18. C₅×C₄₇	C₂×D₉	semidirect
22. C₂×C₄₇	C₅×D₉	semidirect
24. C₂×C₅×C₉	D₄₇	semidirect
27. C₄₇	C₂×C₅×D₉	semidirect
28. C₅×C₉	C₂×D₄₇	semidirect
33. C₂×C₉	C₅×D₄₇	semidirect
38. C₂×C₅	D₄₂₃	direct (N × H)
39. C₉	C₂×C₅×D₄₇	semidirect
42. C₅	C₂×D₄₂₃	direct (N × H)
46. C₂	C₅×D₄₂₃	direct (N × H)

Subgroups — C2×C5×D423 #22554875

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×D₄₂₃ #22554875