Subgroups — #50310331

Order 38532.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×#10625203	C₂	1	1	yes	maximal, characteristic
2	C₁₉⋊#10621730	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×#10625203	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃×C₁₉×D₁₃	C₂×C₃	1	1	yes	characteristic
5	C₁₃²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	(C₁₉⋊C₃)⋊#261	—	13	1	no	maximal
7	#15688286	—	13	1	no	maximal
8	#14523157	—	19	1	no	maximal, Hall
9	C₂×#10625203	—	13	1	no	—
10	D₁₃×C₁₉⋊C₃	—	13	1	no	—
11	D₁₃×C₁₃⋊C₃	—	19	1	no	—
12	C₁₉⋊#261	—	13	1	no	—
13	Dic₂₄₇	—	13	1	no	—
14	#10625203	#261	1	1	yes	characteristic, complemented
15	C₁₃×C₁₉⋊C₃	—	13	1	no	—
16	#10621730	—	19	1	no	Hall
17	C₁₃×C₁₃⋊C₃	—	19	1	no	Hall
18	C₂×C₁₃×C₁₉	—	13	1	no	—
19	C₁₉×D₁₃	D₁₃⋊C₃	1	1	yes	characteristic
20	C₁₃×D₁₃	D₁₉⋊C₃	1	1	yes	characteristic
21	C₁₃×C₁₉	—	12	1	no	—
22	C₁₃×C₁₉	Dic₁₃⋊C₃	1	1	yes	characteristic, complemented
23	C₁₃×C₁₉	C₃×#261	1	1	yes	characteristic, complemented
24	(C₁₉⋊C₃)⋊C₄	—	169	1	no	Hall
25	C₁₃²	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
26	C₃×#261	—	247	1	no	—
27	Dic₁₃⋊C₃	—	247	1	no	—
28	C₂×C₁₉⋊C₃	—	169	1	no	—
29	C₃×D₁₃	—	247	1	no	—
30	C₂×C₁₃⋊C₃	—	247	1	no	—
31	Dic₁₉	—	169	1	no	Hall
32	C₁₉⋊C₃	—	13	1	no	Hall
33	#261	—	247	1	no	—
34	Dic₁₃	—	247	1	no	—
35	C₃×C₁₃	—	247	1	no	—
36	C₁₃⋊C₃	—	19	1	no	—
37	C₂×C₁₉	—	13	1	no	—
38	C₂×C₁₃	—	13	1	no	—
39	D₁₃	#13093367	1	1	yes	characteristic
40	C₁₉	#14523157	1	1	yes	characteristic, complemented, Sylow
41	C₁₃	—	12	1	no	—
42	C₁₃	#15688286	1	1	yes	characteristic, complemented
43	C₁₃	(C₁₉⋊C₃)⋊#261	1	1	yes	characteristic, complemented
44	C₃×C₄	—	3211	1	no	Hall
45	C₂×C₃	—	3211	1	no	—
46	C₄	—	3211	1	no	Sylow
47	C₃	—	247	1	no	Sylow
48	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃²×C₁₉	C₃×C₄
prime radical	D₁₃×#10625203	C₂
cosocle	C₁₃×C₁₉×D₁₃	C₂×C₃
LCS	G ▷ C₁₃²×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₁₉⋊#10621730	C₃	semidirect
3. C₁₃×#10625203	C₄	semidirect
5. C₁₃²×C₁₉	C₃×C₄	semidirect
14. #10625203	#261	semidirect
22. C₁₃×C₁₉	Dic₁₃⋊C₃	semidirect
23. C₁₃×C₁₉	C₃×#261	semidirect
25. C₁₃²	(C₁₉⋊C₃)⋊C₄	semidirect
40. C₁₉	#14523157	semidirect
42. C₁₃	#15688286	semidirect
43. C₁₃	(C₁₉⋊C₃)⋊#261	semidirect

Maximal subgroups

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

subgroup	index
D₁₃×#10625203	2
C₁₉⋊#10621730	3
(C₁₉⋊C₃)⋊#261	13
#15688286	13
#14523157	19