Subgroups — C₂×C₅×#14274262 #34062181

Order 19110.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#14274262	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₇²×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×#14274262	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×#63271	—	7	8	no	maximal
6	#14274262	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₅×#3861	—	13	1	no	maximal, Hall
8	C₅×#63271	—	7	8	no	—
9	C₂×C₇²×C₁₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₇×C₁₃	ΓL(1,𝔽₈)	1	8	yes	complemented
11	C₅×#3861	—	13	1	no	Hall
12	C₇²×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
13	C₂×#63271	—	7	8	no	—
14	C₂×C₅×C₇²	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
16	C₂×C₅×C₁₃⋊C₃	—	49	1	no	Hall
17	C₂×#3861	—	13	1	no	Hall
18	#63271	—	7	8	no	—
19	C₅×C₇²	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×ΓL(1,𝔽₈)	—	91	8	no	—
21	C₅×C₁₃⋊C₃	—	49	1	no	Hall
22	C₂×C₇×C₁₃	C₅×ΓL(1,𝔽₈)	1	8	yes	complemented
23	#3861	—	13	1	no	Hall
24	C₂×C₅×C₁₃	#3861	1	1	yes	characteristic, complemented, Hall
25	C₅×ΓL(1,𝔽₈)	—	91	8	no	—
26	C₂×C₇²	C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
27	C₇×C₁₃	C₂×C₅×ΓL(1,𝔽₈)	1	8	yes	complemented
28	C₂×C₁₃⋊C₃	—	49	1	no	Hall
29	C₂×C₅×C₇	#63271	1	8	yes	complemented
30	C₅×C₁₃	C₂×#3861	1	1	yes	characteristic, complemented, Hall
31	C₇²	C₂×C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
32	C₂×ΓL(1,𝔽₈)	—	91	8	no	—
33	C₁₃⋊C₃	—	49	1	no	Hall
34	C₅×C₇	C₂×#63271	1	8	yes	complemented
35	C₂×C₃×C₅	—	637	1	no	Hall
36	C₂×C₁₃	C₅×#3861	1	1	yes	characteristic, complemented, Hall
37	ΓL(1,𝔽₈)	—	91	8	no	—
38	C₃×C₅	—	637	1	no	Hall
39	C₂×C₇	C₅×#63271	1	8	yes	complemented
40	C₁₃	C₂×C₅×#3861	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	#14274262	1	1	yes	characteristic, direct product factor, Hall
42	C₇	C₂×C₅×#63271	1	8	yes	complemented
43	C₂×C₃	—	637	1	no	Hall
44	C₅	C₂×#14274262	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	—	637	1	no	Sylow
46	C₂	C₅×#14274262	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₅	#14274262
commutator, cosocle, hypocenter	C₇²×C₁₃	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²×C₁₃	C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#14274262	C₂	direct (N × H)
2. C₂×C₅×C₇²×C₁₃	C₃	semidirect
3. C₂×#14274262	C₅	direct (N × H)
4. C₅×C₇²×C₁₃	C₂×C₃	semidirect
6. #14274262	C₂×C₅	direct (N × H)
9. C₂×C₇²×C₁₃	C₃×C₅	semidirect
10. C₂×C₅×C₇×C₁₃	ΓL(1,𝔽₈)	semidirect
12. C₇²×C₁₃	C₂×C₃×C₅	semidirect
14. C₂×C₅×C₇²	C₁₃⋊C₃	semidirect
15. C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
19. C₅×C₇²	C₂×C₁₃⋊C₃	semidirect
22. C₂×C₇×C₁₃	C₅×ΓL(1,𝔽₈)	semidirect
24. C₂×C₅×C₁₃	#3861	semidirect
26. C₂×C₇²	C₅×C₁₃⋊C₃	semidirect
27. C₇×C₁₃	C₂×C₅×ΓL(1,𝔽₈)	semidirect
29. C₂×C₅×C₇	#63271	semidirect
30. C₅×C₁₃	C₂×#3861	semidirect
31. C₇²	C₂×C₅×C₁₃⋊C₃	semidirect
34. C₅×C₇	C₂×#63271	semidirect
36. C₂×C₁₃	C₅×#3861	semidirect
39. C₂×C₇	C₅×#63271	semidirect
40. C₁₃	C₂×C₅×#3861	semidirect
41. C₂×C₅	#14274262	direct (N × H)
42. C₇	C₂×C₅×#63271	semidirect
44. C₅	C₂×#14274262	direct (N × H)
46. C₂	C₅×#14274262	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×#14274262	2
C₂×C₅×C₇²×C₁₃	3
C₂×#14274262	5
C₂×C₅×#63271	7
C₂×C₅×#3861	13

Subgroups — C2×C5×#14274262 #34062181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#14274262 #34062181