Subgroups — #1039×#3861 #28413158

Order 14700.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×#3861	C₂	1	1	yes	maximal, characteristic
2	C₇²×#1039	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×#3861	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₅×#3861	—	5	6	no	maximal
5	C₂×C₅²×C₇²	C₂×C₃	1	1	yes	characteristic
6	ΓL(1,𝔽₈)×#1039	—	7	8	no	maximal
7	C₂×C₅×#3861	D₅	1	6	yes	—
8	C₅²×C₇²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅²×ΓL(1,𝔽₈)	—	7	8	no	—
10	C₇²×Dic₅	—	5	6	no	—
11	C₅×#3861	Dic₅	1	6	yes	complemented
12	C₇×#1039	ΓL(1,𝔽₈)	1	8	yes	complemented
13	C₄×#3861	—	25	1	no	Hall
14	C₅²×ΓL(1,𝔽₈)	—	7	8	no	—
15	C₂×C₅×C₇²	C₃×D₅	1	6	yes	—
16	Dic₅×ΓL(1,𝔽₈)	—	35	48	no	—
17	C₂×C₅²×C₇	C₂×ΓL(1,𝔽₈)	1	8	yes	—
18	C₃×#1039	—	49	1	no	Hall
19	C₂×#3861	C₅⋊D₅	1	1	yes	characteristic
20	C₅×C₇²	C₃×Dic₅	1	6	yes	complemented
21	C₂×C₅×ΓL(1,𝔽₈)	—	7	48	no	—
22	C₄×C₇²	—	25	1	no	Hall
23	C₅²×C₇	C₄×ΓL(1,𝔽₈)	1	8	yes	complemented
24	C₂×C₃×C₅²	—	49	1	no	—
25	#3861	#1039	1	1	yes	characteristic, direct product factor, Hall
26	C₇×Dic₅	—	5	48	no	—
27	C₅×ΓL(1,𝔽₈)	—	7	48	no	—
28	#1039	#3861	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₇²	C₃×C₅⋊D₅	1	1	yes	characteristic
30	C₄×ΓL(1,𝔽₈)	—	175	8	no	—
31	C₃×C₅²	—	49	1	no	Hall
32	C₂×C₅×C₇	D₅×ΓL(1,𝔽₈)	1	48	yes	—
33	C₃×Dic₅	—	245	6	no	—
34	C₂×C₅²	C₂×#3861	1	1	yes	characteristic
35	C₇²	C₃×#1039	1	1	yes	characteristic, complemented, Sylow
36	C₂×ΓL(1,𝔽₈)	—	7	8	no	—
37	C₅×C₇	Dic₅×ΓL(1,𝔽₈)	1	48	yes	complemented
38	C₂×C₃×C₅	—	49	6	no	—
39	C₄×C₇	—	25	8	no	—
40	C₅²	C₄×#3861	1	1	yes	characteristic, complemented, Sylow
41	ΓL(1,𝔽₈)	—	7	8	no	—
42	Dic₅	—	5	6	no	—
43	C₃×C₅	—	49	6	no	—
44	C₂×C₇	ΓL(1,𝔽₈)×C₅⋊D₅	1	8	yes	—
45	C₃×C₄	—	1225	1	no	Hall
46	C₂×C₅	D₅×#3861	1	6	yes	—
47	C₇	ΓL(1,𝔽₈)×#1039	1	8	yes	complemented
48	C₂×C₃	—	49	1	no	—
49	C₅	Dic₅×#3861	1	6	yes	complemented
50	C₄	—	25	1	no	Sylow
51	C₃	—	49	1	no	Sylow
52	C₂	C₅⋊D₅×#3861	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅⋊D₅×#3861
commutator, hypocenter	C₅²×C₇²	C₃×C₄
Fitting, socle, cosocle	C₂×C₅²×C₇²	C₂×C₃
prime radical	C₂×C₅²×#3861	C₂
LCS	G ▷ C₅²×C₇²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₇²×#1039	C₃	semidirect
3. C₅²×#3861	C₄	semidirect
8. C₅²×C₇²	C₃×C₄	semidirect
11. C₅×#3861	Dic₅	semidirect
12. C₇×#1039	ΓL(1,𝔽₈)	semidirect
20. C₅×C₇²	C₃×Dic₅	semidirect
23. C₅²×C₇	C₄×ΓL(1,𝔽₈)	semidirect
25. #3861	#1039	direct (N × H)
28. #1039	#3861	direct (N × H)
35. C₇²	C₃×#1039	semidirect
37. C₅×C₇	Dic₅×ΓL(1,𝔽₈)	semidirect
40. C₅²	C₄×#3861	semidirect
47. C₇	ΓL(1,𝔽₈)×#1039	semidirect
49. C₅	Dic₅×#3861	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅²×#3861	2
C₇²×#1039	3
Dic₅×#3861	5
ΓL(1,𝔽₈)×#1039	7