Subgroups — C₅×#16838473 #34062097

Order 19110.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#14274263	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₇²×D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#16838473	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅×#10587716	—	7	8	no	maximal
6	#14274263	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×#3861	—	13	1	no	maximal, Hall
8	C₅×#63270	—	7	8	no	—
9	C₇²×D₁₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₅×C₇×D₁₃	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	#10587716	—	7	8	no	—
14	C₂×C₅×C₇²	—	13	1	no	Hall
15	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
16	C₅×D₁₃⋊C₃	—	49	1	no	Hall
17	C₂×#3861	—	13	1	no	Hall
18	#63270	—	7	8	no	—
19	C₅×C₇²	D₁₃⋊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	C₇×D₁₃	C₅×ΓL(1,𝔽₈)	1	8	yes	complemented
23	#3861	—	13	1	no	Hall
24	C₅×D₁₃	#3861	1	1	yes	characteristic, complemented, Hall
25	C₅×ΓL(1,𝔽₈)	—	91	8	no	—
26	C₂×C₇²	—	13	1	no	Hall
27	C₇×C₁₃	C₂×C₅×ΓL(1,𝔽₈)	1	8	yes	complemented
28	D₁₃⋊C₃	—	49	1	no	Hall
29	C₂×C₅×C₇	—	13	8	no	—
30	C₅×C₁₃	C₂×#3861	1	1	yes	characteristic, complemented, Hall
31	C₇²	C₅×D₁₃⋊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	#10587716	1	8	yes	complemented
35	C₂×C₃×C₅	—	637	1	no	Hall
36	D₁₃	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	—	13	8	no	—
40	C₁₃	C₂×C₅×#3861	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	13	1	no	Hall
42	C₇	C₅×#10587716	1	8	yes	complemented
43	C₂×C₃	—	637	1	no	Hall
44	C₅	#16838473	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	—	637	1	no	Sylow
46	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	#16838473
commutator, cosocle, hypocenter	C₇²×C₁₃	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#14274263	C₂	semidirect
2. C₅×C₇²×D₁₃	C₃	semidirect
3. #16838473	C₅	direct (N × H)
4. C₅×C₇²×C₁₃	C₂×C₃	semidirect
6. #14274263	C₂×C₅	semidirect
9. C₇²×D₁₃	C₃×C₅	semidirect
10. C₅×C₇×D₁₃	ΓL(1,𝔽₈)	semidirect
12. C₇²×C₁₃	C₂×C₃×C₅	semidirect
15. C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
19. C₅×C₇²	D₁₃⋊C₃	semidirect
22. C₇×D₁₃	C₅×ΓL(1,𝔽₈)	semidirect
24. C₅×D₁₃	#3861	semidirect
27. C₇×C₁₃	C₂×C₅×ΓL(1,𝔽₈)	semidirect
30. C₅×C₁₃	C₂×#3861	semidirect
31. C₇²	C₅×D₁₃⋊C₃	semidirect
34. C₅×C₇	#10587716	semidirect
36. D₁₃	C₅×#3861	semidirect
40. C₁₃	C₂×C₅×#3861	semidirect
42. C₇	C₅×#10587716	semidirect
44. C₅	#16838473	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×#14274263	2
C₅×C₇²×D₁₃	3
#16838473	5
C₅×#10587716	7
C₂×C₅×#3861	13

Subgroups — C5×#16838473 #34062097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#16838473 #34062097