Subgroups — C₂×#21462843 #30626813

Order 15620.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21462843	C₂	1	1	yes	maximal, characteristic, direct product factor
2	#21462843	C₂	1	1	yes	maximal, characteristic, direct product factor
3	C₂×#16840846	C₂	1	1	yes	maximal, characteristic, complemented
4	#16840846	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₁×C₇₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂×C₁₁×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented
7	D₁₁×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented
8	D₁₁×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented
9	C₂²×C₇₁⋊C₅	—	11	1	no	maximal, Hall
10	C₁₁×C₇₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₇₁⋊C₅	—	11	1	no	—
12	C₂×C₇₁⋊C₅	—	11	1	no	—
13	C₂×C₇₁⋊C₅	—	11	1	no	—
14	C₇₁⋊C₅	—	11	1	no	Hall
15	C₂²×C₇₁	—	55	1	no	Hall
16	C₂×AGL(1,𝔽₁₁)	—	71	1	no	maximal, Hall
17	C₂×C₇₁	—	11	1	no	—
18	C₂×C₇₁	—	55	1	no	—
19	C₂×C₇₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
20	C₂×C₁₁⋊C₅	—	71	1	no	—
21	AGL(1,𝔽₁₁)	—	71	1	no	—
22	AGL(1,𝔽₁₁)	—	71	1	no	—
23	C₇₁	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
24	C₁₁⋊C₅	—	71	1	no	Hall
25	C₂×D₁₁	C₇₁⋊C₅	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₁	C₂×C₇₁⋊C₅	1	1	yes	characteristic, complemented
27	D₁₁	C₂×C₇₁⋊C₅	1	1	yes	characteristic, complemented
28	D₁₁	C₂×C₇₁⋊C₅	1	1	yes	characteristic, complemented
29	C₂²×C₅	—	781	1	no	Hall
30	C₁₁	C₂²×C₇₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	781	1	no	—
32	C₂×C₅	—	781	1	no	—
33	C₂×C₅	—	781	1	no	—
34	C₅	—	781	1	no	Sylow
35	C₂²	—	55	1	no	Sylow
36	C₂	—	55	1	no	—
37	C₂	—	55	1	no	—
38	C₂	#21462843	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#21462843
commutator, cosocle, hypocenter	C₁₁×C₇₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₇₁	C₂×C₅
LCS	G ▷ C₁₁×C₇₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. #21462843	C₂	direct (N × H)
2. #21462843	C₂	direct (N × H)
3. C₂×#16840846	C₂	semidirect
4. #16840846	C₂²	semidirect
5. C₂×D₁₁×C₇₁	C₅	semidirect
6. C₂×C₁₁×C₇₁	C₂×C₅	semidirect
7. D₁₁×C₇₁	C₂×C₅	semidirect
8. D₁₁×C₇₁	C₂×C₅	semidirect
10. C₁₁×C₇₁	C₂²×C₅	semidirect
19. C₂×C₇₁	AGL(1,𝔽₁₁)	semidirect
23. C₇₁	C₂×AGL(1,𝔽₁₁)	semidirect
25. C₂×D₁₁	C₇₁⋊C₅	semidirect
26. C₂×C₁₁	C₂×C₇₁⋊C₅	semidirect
27. D₁₁	C₂×C₇₁⋊C₅	semidirect
28. D₁₁	C₂×C₇₁⋊C₅	semidirect
30. C₁₁	C₂²×C₇₁⋊C₅	semidirect
38. C₂	#21462843	direct (N × H)

Maximal subgroups

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

subgroup	index
#21462843	2
C₂×#16840846	2
C₂×D₁₁×C₇₁	5
C₂²×C₇₁⋊C₅	11
C₂×AGL(1,𝔽₁₁)	71

Subgroups — C2×#21462843 #30626813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#21462843 #30626813