Subgroups — C₂×#28413672 #44440970

Order 29412.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20301354	C₂	1	1	yes	maximal, characteristic, complemented
2	#28413672	C₂	1	2	yes	maximal, direct product factor
3	C₂×(C₁₉⋊C₃)⋊D₄₃	C₃	1	1	yes	maximal, characteristic
4	#20301354	C₂²	1	1	yes	characteristic, complemented, Hall
5	(C₁₉⋊C₃)⋊D₄₃	C₂×C₃	1	2	yes	—
6	C₂×C₄₃×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
7	C₂×D₈₁₇	C₉	1	1	yes	characteristic, complemented, Hall
8	C₄₃×C₁₉⋊C₃	C₂²×C₃	1	1	yes	characteristic
9	C₂×C₁₉×C₄₃	C₂×C₉	1	1	yes	characteristic, complemented
10	D₈₁₇	C₂×C₉	1	2	yes	complemented
11	C₂×D₄₃⋊C₉	—	19	1	no	maximal, Hall
12	C₁₉×C₄₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₄₃⋊C₉	—	19	1	no	—
14	D₄₃⋊C₉	—	19	2	no	—
15	C₂×AGL(1,𝔽₁₉)	—	43	1	no	maximal, Hall
16	C₂×C₃×D₄₃	—	19	1	no	—
17	C₄₃⋊C₉	—	19	1	no	Hall
18	C₂×#4296	—	43	1	no	—
19	AGL(1,𝔽₁₉)	—	43	2	no	—
20	C₂×C₃×C₄₃	—	19	1	no	—
21	C₃×D₄₃	—	19	2	no	—
22	C₂×D₁₉⋊C₃	—	129	1	no	—
23	C₂×D₄₃	—	171	1	no	Hall
24	#4296	—	43	1	no	Hall
25	C₃×C₄₃	—	19	1	no	—
26	C₂×C₁₉⋊C₃	D₄₃⋊C₃	1	1	yes	characteristic
27	D₁₉⋊C₃	—	129	2	no	—
28	C₂×C₄₃	AGL(1,𝔽₁₉)	1	1	yes	characteristic, complemented
29	D₄₃	—	171	2	no	—
30	C₂×D₁₉	—	129	1	no	Hall
31	C₁₉⋊C₃	C₂×D₄₃⋊C₃	1	1	yes	characteristic
32	C₄₃	C₂×AGL(1,𝔽₁₉)	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₁₉	D₄₃⋊C₉	1	1	yes	characteristic, complemented
34	D₁₉	—	129	2	no	—
35	C₂²×C₉	—	817	1	no	Hall
36	C₁₉	C₂×D₄₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₉	—	817	1	no	—
38	C₂×C₉	—	817	2	no	—
39	C₂²×C₃	—	2451	1	no	—
40	C₉	—	817	1	no	Sylow
41	C₂×C₃	—	19	1	no	—
42	C₂×C₃	—	2451	2	no	—
43	C₂²	—	7353	1	no	Sylow
44	C₃	—	19	1	no	—
45	C₂	—	7353	2	no	—
46	C₂	#28413672	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#28413672
commutator, hypocenter	C₁₉×C₄₃	C₂²×C₉
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₄₃	C₂×C₉
prime radical	C₂×(C₁₉⋊C₃)⋊D₄₃	C₃
cosocle	C₄₃×C₁₉⋊C₃	C₂²×C₃
LCS	G ▷ C₁₉×C₄₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×#20301354	C₂	semidirect
2. #28413672	C₂	direct (N × H)
4. #20301354	C₂²	semidirect
7. C₂×D₈₁₇	C₉	semidirect
9. C₂×C₁₉×C₄₃	C₂×C₉	semidirect
10. D₈₁₇	C₂×C₉	semidirect
12. C₁₉×C₄₃	C₂²×C₉	semidirect
28. C₂×C₄₃	AGL(1,𝔽₁₉)	semidirect
32. C₄₃	C₂×AGL(1,𝔽₁₉)	semidirect
33. C₂×C₁₉	D₄₃⋊C₉	semidirect
36. C₁₉	C₂×D₄₃⋊C₉	semidirect
46. C₂	#28413672	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#20301354	2
#28413672	2
C₂×(C₁₉⋊C₃)⋊D₄₃	3
C₂×D₄₃⋊C₉	19
C₂×AGL(1,𝔽₁₉)	43

Subgroups — C2×#28413672 #44440970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#28413672 #44440970