Subgroups — C₇×D₁₈₄₅ #38788913

Order 25830.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₉×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₆₁₅	—	3	1	no	maximal
3	C₇×D₃₆₉	—	5	1	no	maximal, Hall
4	C₃×C₅×C₇×C₄₁	D₃	1	1	yes	characteristic
5	D₁₈₄₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×D₂₀₅	—	9	1	no	Hall
7	C₇×C₉×C₄₁	D₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₉×C₄₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	C₇×D₁₂₃	—	15	1	no	—
10	C₅×C₇×C₄₁	D₉	1	1	yes	characteristic, complemented, Hall
11	D₆₁₅	—	3	1	no	—
12	C₃×C₇×C₄₁	D₁₅	1	1	yes	characteristic
13	D₃₆₉	—	5	1	no	Hall
14	C₇×D₄₅	—	41	1	no	maximal, Hall
15	C₃×C₅×C₄₁	D₃×C₇	1	1	yes	characteristic
16	C₇×D₄₁	—	45	1	no	Hall
17	D₂₀₅	—	9	1	no	Hall
18	C₉×C₄₁	C₇×D₅	1	1	yes	characteristic, complemented, Hall
19	C₅×C₇×C₉	D₄₁	1	1	yes	characteristic, complemented, Hall
20	C₇×C₄₁	D₄₅	1	1	yes	characteristic, complemented, Hall
21	D₁₂₃	—	15	1	no	—
22	C₇×D₁₅	—	123	1	no	—
23	C₅×C₄₁	C₇×D₉	1	1	yes	characteristic, complemented, Hall
24	C₇×D₉	—	205	1	no	Hall
25	C₃×C₄₁	C₇×D₁₅	1	1	yes	characteristic
26	C₃×C₅×C₇	D₁₂₃	1	1	yes	characteristic
27	D₄₅	—	41	1	no	Hall
28	D₄₁	—	45	1	no	Hall
29	C₇×D₅	—	369	1	no	Hall
30	C₇×C₉	D₂₀₅	1	1	yes	characteristic, complemented, Hall
31	C₅×C₉	C₇×D₄₁	1	1	yes	characteristic, complemented, Hall
32	D₃×C₇	—	615	1	no	—
33	C₄₁	C₇×D₄₅	1	1	yes	characteristic, complemented, Sylow
34	C₅×C₇	D₃₆₉	1	1	yes	characteristic, complemented, Hall
35	D₁₅	—	123	1	no	—
36	C₃×C₇	D₆₁₅	1	1	yes	characteristic
37	D₉	—	205	1	no	Hall
38	C₃×C₅	C₇×D₁₂₃	1	1	yes	characteristic
39	C₂×C₇	—	1845	1	no	Hall
40	D₅	—	369	1	no	Hall
41	C₉	C₇×D₂₀₅	1	1	yes	characteristic, complemented, Sylow
42	C₇	D₁₈₄₅	1	1	yes	characteristic, direct product factor, Sylow
43	D₃	—	615	1	no	—
44	C₅	C₇×D₃₆₉	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₇×D₆₁₅	1	1	yes	characteristic
46	C₂	—	1845	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₁₈₄₅
commutator, cosocle, hypocenter	C₅×C₉×C₄₁	C₂×C₇
Frattini	C₃	C₇×D₆₁₅
Fitting	C₅×C₇×C₉×C₄₁	C₂
socle	C₃×C₅×C₇×C₄₁	D₃
LCS	G ▷ C₅×C₉×C₄₁
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₉×C₄₁	C₂	semidirect
5. D₁₈₄₅	C₇	direct (N × H)
7. C₇×C₉×C₄₁	D₅	semidirect
8. C₅×C₉×C₄₁	C₂×C₇	semidirect
10. C₅×C₇×C₄₁	D₉	semidirect
18. C₉×C₄₁	C₇×D₅	semidirect
19. C₅×C₇×C₉	D₄₁	semidirect
20. C₇×C₄₁	D₄₅	semidirect
23. C₅×C₄₁	C₇×D₉	semidirect
30. C₇×C₉	D₂₀₅	semidirect
31. C₅×C₉	C₇×D₄₁	semidirect
33. C₄₁	C₇×D₄₅	semidirect
34. C₅×C₇	D₃₆₉	semidirect
41. C₉	C₇×D₂₀₅	semidirect
42. C₇	D₁₈₄₅	direct (N × H)
44. C₅	C₇×D₃₆₉	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×C₉×C₄₁	2
C₇×D₆₁₅	3
C₇×D₃₆₉	5
D₁₈₄₅	7
C₇×D₄₅	41

Subgroups — C7×D1845 #38788913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₁₈₄₅ #38788913