Subgroups — C₅×#16838420 #34062039

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, complemented, Hall
2	C₅×D₆₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#16838420	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₃×C₄₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅×#10587723	—	7	1	no	maximal
6	#14274255	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×D₄₉⋊C₃	—	13	1	no	maximal, Hall
8	C₅×#63271	—	7	1	no	—
9	D₆₃₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₅×D₉₁	—	7	1	no	—
11	C₅×C₄₉⋊C₃	—	13	1	no	Hall
12	C₁₃×C₄₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
13	#10587723	—	7	1	no	—
14	C₅×D₄₉	—	13	1	no	Hall
15	C₅×C₇×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic
16	C₅×D₁₃⋊C₃	—	49	1	no	Hall
17	D₄₉⋊C₃	—	13	1	no	Hall
18	#63271	—	7	1	no	—
19	C₅×C₄₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₅×AGL(1,𝔽₇)	—	91	1	no	—
21	C₅×C₁₃⋊C₃	—	49	1	no	Hall
22	D₉₁	—	7	1	no	—
23	C₄₉⋊C₃	—	13	1	no	Hall
24	C₅×D₁₃	—	49	1	no	Hall
25	C₅×ΓL(1,𝔽₈)	—	91	1	no	—
26	D₄₉	—	13	1	no	Hall
27	C₇×C₁₃	C₅×AGL(1,𝔽₇)	1	1	yes	characteristic
28	D₁₃⋊C₃	—	49	1	no	Hall
29	C₅×D₇	—	91	1	no	—
30	C₅×C₁₃	D₄₉⋊C₃	1	1	yes	characteristic, complemented, Hall
31	C₄₉	C₅×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
32	AGL(1,𝔽₇)	—	91	1	no	—
33	C₁₃⋊C₃	—	49	1	no	Hall
34	C₅×C₇	#10587723	1	1	yes	characteristic
35	C₂×C₃×C₅	—	637	1	no	Hall
36	D₁₃	—	49	1	no	Hall
37	ΓL(1,𝔽₈)	—	91	1	no	—
38	C₃×C₅	—	637	1	no	Hall
39	D₇	—	91	1	no	—
40	C₁₃	C₅×D₄₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	637	1	no	Hall
42	C₇	C₅×#10587723	1	1	yes	characteristic
43	C₂×C₃	—	637	1	no	Hall
44	C₅	#16838420	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	—	637	1	no	Sylow
46	C₂	—	637	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	#16838420
commutator, cosocle, hypocenter	C₁₃×C₄₉	C₂×C₃×C₅
Frattini	C₇	C₅×#10587723
Fitting	C₅×C₁₃×C₄₉	C₂×C₃
socle	C₅×C₇×C₁₃	AGL(1,𝔽₇)
LCS	G ▷ C₁₃×C₄₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#14274255	C₂	semidirect
2. C₅×D₆₃₇	C₃	semidirect
3. #16838420	C₅	direct (N × H)
4. C₅×C₁₃×C₄₉	C₂×C₃	semidirect
6. #14274255	C₂×C₅	semidirect
9. D₆₃₇	C₃×C₅	semidirect
12. C₁₃×C₄₉	C₂×C₃×C₅	semidirect
19. C₅×C₄₉	D₁₃⋊C₃	semidirect
30. C₅×C₁₃	D₄₉⋊C₃	semidirect
31. C₄₉	C₅×D₁₃⋊C₃	semidirect
40. C₁₃	C₅×D₄₉⋊C₃	semidirect
44. C₅	#16838420	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
C₅×D₆₃₇	3
#16838420	5
C₅×#10587723	7
C₅×D₄₉⋊C₃	13

Subgroups — C5×#16838420 #34062039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#16838420 #34062039