Subgroups — C₂×#20269529 #27211863

Order 13420.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20269529	C₂	1	2	yes	maximal, direct product factor
2	C₂×#16809821	C₂	1	1	yes	maximal, characteristic, complemented
3	#16809821	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₆₇₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₁₁×C₆₁	C₂×C₅	1	1	yes	characteristic, complemented
6	D₆₇₁	C₂×C₅	1	2	yes	complemented
7	C₂×D₆₁⋊C₅	—	11	1	no	maximal, Hall
8	C₁₁×C₆₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₆₁⋊C₅	—	11	1	no	—
10	D₆₁⋊C₅	—	11	2	no	—
11	C₆₁⋊C₅	—	11	1	no	Hall
12	C₂×D₆₁	—	11	1	no	Hall
13	C₂×AGL(1,𝔽₁₁)	—	61	1	no	maximal, Hall
14	C₂×C₆₁	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
15	D₆₁	—	11	2	no	—
16	C₂×C₁₁⋊C₅	—	61	1	no	—
17	AGL(1,𝔽₁₁)	—	61	2	no	—
18	C₆₁	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
19	C₁₁⋊C₅	—	61	1	no	Hall
20	C₂×D₁₁	—	61	1	no	Hall
21	C₂×C₁₁	D₆₁⋊C₅	1	1	yes	characteristic, complemented
22	D₁₁	—	61	2	no	—
23	C₂²×C₅	—	671	1	no	Hall
24	C₁₁	C₂×D₆₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₅	—	671	2	no	—
26	C₂×C₅	—	671	1	no	—
27	C₅	—	671	1	no	Sylow
28	C₂²	—	671	1	no	Sylow
29	C₂	—	671	2	no	—
30	C₂	#20269529	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#20269529
commutator, cosocle, hypocenter	C₁₁×C₆₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₆₁	C₂×C₅
LCS	G ▷ C₁₁×C₆₁
UCS	C₁ ◁ C₂

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

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