Subgroups — C₂×C₅×#14274255 #34062012

Order 19110.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#14274255	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₁₃×C₄₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×#14274255	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₃×C₄₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×#63271	—	7	1	no	maximal
6	#14274255	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₅×C₄₉⋊C₃	—	13	1	no	maximal, Hall
8	C₅×#63271	—	7	1	no	—
9	C₂×C₁₃×C₄₉	C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₇×C₁₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
11	C₅×C₄₉⋊C₃	—	13	1	no	Hall
12	C₁₃×C₄₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
13	C₂×#63271	—	7	1	no	—
14	C₂×C₅×C₄₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
16	C₂×C₅×C₁₃⋊C₃	—	49	1	no	Hall
17	C₂×C₄₉⋊C₃	—	13	1	no	Hall
18	#63271	—	7	1	no	—
19	C₅×C₄₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×ΓL(1,𝔽₈)	—	91	1	no	—
21	C₅×C₁₃⋊C₃	—	49	1	no	Hall
22	C₂×C₇×C₁₃	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
23	C₄₉⋊C₃	—	13	1	no	Hall
24	C₂×C₅×C₁₃	C₄₉⋊C₃	1	1	yes	characteristic, complemented, Hall
25	C₅×ΓL(1,𝔽₈)	—	91	1	no	—
26	C₂×C₄₉	C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
27	C₇×C₁₃	C₂×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
28	C₂×C₁₃⋊C₃	—	49	1	no	Hall
29	C₂×C₅×C₇	#63271	1	1	yes	characteristic
30	C₅×C₁₃	C₂×C₄₉⋊C₃	1	1	yes	characteristic, complemented, Hall
31	C₄₉	C₂×C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
32	C₂×ΓL(1,𝔽₈)	—	91	1	no	—
33	C₁₃⋊C₃	—	49	1	no	Hall
34	C₅×C₇	C₂×#63271	1	1	yes	characteristic
35	C₂×C₃×C₅	—	637	1	no	Hall
36	C₂×C₁₃	C₅×C₄₉⋊C₃	1	1	yes	characteristic, complemented, Hall
37	ΓL(1,𝔽₈)	—	91	1	no	—
38	C₃×C₅	—	637	1	no	Hall
39	C₂×C₇	C₅×#63271	1	1	yes	characteristic
40	C₁₃	C₂×C₅×C₄₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	#14274255	1	1	yes	characteristic, direct product factor, Hall
42	C₇	C₂×C₅×#63271	1	1	yes	characteristic
43	C₂×C₃	—	637	1	no	Hall
44	C₅	C₂×#14274255	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	—	637	1	no	Sylow
46	C₂	C₅×#14274255	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₅	#14274255
commutator, cosocle, hypocenter	C₁₃×C₄₉	C₂×C₃×C₅
Frattini	C₇	C₂×C₅×#63271
Fitting	C₂×C₅×C₁₃×C₄₉	C₃
socle	C₂×C₅×C₇×C₁₃	ΓL(1,𝔽₈)
LCS	G ▷ C₁₃×C₄₉
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#14274255	C₂	direct (N × H)
2. C₂×C₅×C₁₃×C₄₉	C₃	semidirect
3. C₂×#14274255	C₅	direct (N × H)
4. C₅×C₁₃×C₄₉	C₂×C₃	semidirect
6. #14274255	C₂×C₅	direct (N × H)
9. C₂×C₁₃×C₄₉	C₃×C₅	semidirect
12. C₁₃×C₄₉	C₂×C₃×C₅	semidirect
14. C₂×C₅×C₄₉	C₁₃⋊C₃	semidirect
19. C₅×C₄₉	C₂×C₁₃⋊C₃	semidirect
24. C₂×C₅×C₁₃	C₄₉⋊C₃	semidirect
26. C₂×C₄₉	C₅×C₁₃⋊C₃	semidirect
30. C₅×C₁₃	C₂×C₄₉⋊C₃	semidirect
31. C₄₉	C₂×C₅×C₁₃⋊C₃	semidirect
36. C₂×C₁₃	C₅×C₄₉⋊C₃	semidirect
40. C₁₃	C₂×C₅×C₄₉⋊C₃	semidirect
41. C₂×C₅	#14274255	direct (N × H)
44. C₅	C₂×#14274255	direct (N × H)
46. C₂	C₅×#14274255	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×#14274255	2
C₂×C₅×C₁₃×C₄₉	3
C₂×#14274255	5
C₂×C₅×#63271	7
C₂×C₅×C₄₉⋊C₃	13

Subgroups — C2×C5×#14274255 #34062012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#14274255 #34062012