Subgroups — C₂×D₁₃×#3862 #21439733

Order 7644.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#3862	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₃×#3862	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇²×D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₃×#3862	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇²×D₁₃	C₂×C₃	1	2	yes	complemented
7	C₂×ΓL(1,𝔽₈)×D₁₃	—	7	2	no	maximal
8	C₇²×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂²×#3862	—	13	1	no	maximal, Hall
10	C₂×C₁₃×ΓL(1,𝔽₈)	—	7	2	no	—
11	ΓL(1,𝔽₈)×D₁₃	—	7	4	no	—
12	C₂×C₇×D₁₃	—	3	2	no	—
13	C₂×C₇×D₁₃	ΓL(1,𝔽₈)	1	2	yes	complemented
14	C₂×#3862	—	13	2	no	—
15	C₂×#3862	D₁₃	1	1	yes	characteristic, direct product factor
16	C₁₃×ΓL(1,𝔽₈)	—	7	2	no	—
17	C₂²×C₇²	—	13	1	no	Hall
18	C₂×C₇×C₁₃	—	3	2	no	—
19	C₂×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
20	C₇×D₁₃	—	3	4	no	—
21	C₇×D₁₃	C₂×ΓL(1,𝔽₈)	1	4	yes	complemented
22	C₂×C₃×D₁₃	—	49	1	no	Hall
23	#3862	C₂×D₁₃	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₇²	—	13	2	no	—
25	C₂×C₇²	C₃×D₁₃	1	1	yes	characteristic, complemented
26	C₇×C₁₃	—	3	2	no	—
27	C₇×C₁₃	C₂²×ΓL(1,𝔽₈)	1	2	yes	complemented
28	C₂²×ΓL(1,𝔽₈)	—	91	2	no	—
29	C₂×C₃×C₁₃	—	49	1	no	—
30	C₃×D₁₃	—	49	2	no	—
31	C₂×D₁₃	#3862	1	1	yes	characteristic, direct product factor, Hall
32	C₇²	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
33	C₂×ΓL(1,𝔽₈)	—	7	2	no	—
34	C₂×ΓL(1,𝔽₈)	—	91	4	no	—
35	C₃×C₁₃	—	49	1	no	Hall
36	C₂²×C₇	—	13	2	no	—
37	C₂²×C₇	—	39	2	no	—
38	C₂×C₁₃	C₂×#3862	1	1	yes	characteristic, complemented
39	D₁₃	C₂×#3862	1	2	yes	direct product factor
40	ΓL(1,𝔽₈)	—	7	2	no	—
41	C₂×C₇	—	3	2	no	—
42	C₂×C₇	—	13	4	no	—
43	C₂×C₇	—	39	4	no	—
44	C₂×C₇	ΓL(1,𝔽₈)×D₁₃	1	2	yes	complemented
45	C₁₃	C₂²×#3862	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₃	—	637	1	no	Hall
47	C₇	—	3	2	no	—
48	C₇	C₂×ΓL(1,𝔽₈)×D₁₃	1	2	yes	complemented
49	C₂×C₃	—	49	1	no	—
50	C₂×C₃	—	637	2	no	—
51	C₂²	—	13	1	no	Sylow
52	C₃	—	49	1	no	Sylow
53	C₂	—	13	2	no	—
54	C₂	D₁₃×#3862	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₃×#3862
commutator, hypocenter	C₇²×C₁₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#3862	C₂	semidirect
2. D₁₃×#3862	C₂	direct (N × H)
3. C₂×C₇²×D₁₃	C₃	semidirect
4. C₁₃×#3862	C₂²	semidirect
5. C₂×C₇²×C₁₃	C₂×C₃	semidirect
6. C₇²×D₁₃	C₂×C₃	semidirect
8. C₇²×C₁₃	C₂²×C₃	semidirect
13. C₂×C₇×D₁₃	ΓL(1,𝔽₈)	semidirect
15. C₂×#3862	D₁₃	direct (N × H)
19. C₂×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
21. C₇×D₁₃	C₂×ΓL(1,𝔽₈)	semidirect
23. #3862	C₂×D₁₃	direct (N × H)
25. C₂×C₇²	C₃×D₁₃	semidirect
27. C₇×C₁₃	C₂²×ΓL(1,𝔽₈)	semidirect
31. C₂×D₁₃	#3862	direct (N × H)
32. C₇²	C₂×C₃×D₁₃	semidirect
38. C₂×C₁₃	C₂×#3862	semidirect
39. D₁₃	C₂×#3862	direct (N × H)
44. C₂×C₇	ΓL(1,𝔽₈)×D₁₃	semidirect
45. C₁₃	C₂²×#3862	semidirect
48. C₇	C₂×ΓL(1,𝔽₈)×D₁₃	semidirect
54. C₂	D₁₃×#3862	direct (N × H)

Subgroups — C2×D13×#3862 #21439733

Conjugacy classes of subgroups

Complements

Subgroups — C₂×D₁₃×#3862 #21439733