Subgroups — C₂×#19104944 #23783003

Order 10452.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19104944	C₂	1	2	yes	maximal, direct product factor
2	C₂×#14579731	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×D₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	#14579731	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₁₃×D₆₇	C₂×C₃	1	2	yes	complemented
7	C₁₃×C₆₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₆₇⋊C₃	—	13	1	no	maximal, Hall
9	C₂×C₆₇⋊C₃	—	13	1	no	—
10	D₆₇⋊C₃	—	13	2	no	—
11	C₂×D₆₇	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
12	C₆₇⋊C₃	—	13	1	no	Hall
13	C₂²×C₁₃⋊C₃	—	67	1	no	maximal, Hall
14	C₂×C₆₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
15	D₆₇	C₂×C₁₃⋊C₃	1	2	yes	complemented
16	C₂×C₁₃⋊C₃	—	67	2	no	—
17	C₂×C₁₃⋊C₃	—	67	1	no	—
18	C₆₇	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₁₃	—	67	1	no	Hall
20	C₁₃⋊C₃	—	67	1	no	Hall
21	C₂×C₁₃	—	67	2	no	—
22	C₂×C₁₃	D₆₇⋊C₃	1	1	yes	characteristic, complemented
23	C₁₃	C₂×D₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	871	1	no	Hall
25	C₂×C₃	—	871	2	no	—
26	C₂×C₃	—	871	1	no	—
27	C₂²	—	67	1	no	Sylow
28	C₃	—	871	1	no	Sylow
29	C₂	—	67	2	no	—
30	C₂	#19104944	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#19104944
commutator, cosocle, hypocenter	C₁₃×C₆₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₆₇	C₂×C₃
LCS	G ▷ C₁₃×C₆₇
UCS	C₁ ◁ C₂

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