Subgroups — #13093366⋊D₁₃ #50310313

Order 38532.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34064237	C₂	1	1	yes	maximal, characteristic, complemented
2	#34064228	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#13093366	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₁₃⋊D₁₃)⋊D₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₁₃×#10625202	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₉×C₁₃⋊D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃×D₂₄₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₃×D₂₄₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₁₃²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	D₁₃×D₁₉⋊C₃	—	13	1	no	maximal
11	#13093360⋊C₂	—	13	1	no	maximal
12	D₁₃×D₁₃⋊C₃	—	19	1	no	maximal, Hall
13	#13093366	D₁₃	1	1	yes	characteristic, complemented
14	#13093364	—	13	1	no	—
15	#13093360	—	13	1	no	—
16	(C₁₉⋊C₃)⋊D₁₃	—	13	1	no	—
17	D₁₃×C₁₉⋊C₃	—	13	1	no	—
18	C₁₃×D₁₉⋊C₃	—	13	1	no	—
19	D₁₃×C₁₃⋊C₃	—	19	1	no	—
20	(C₁₃⋊C₃)⋊D₁₃	—	19	1	no	—
21	C₁₃×D₁₃⋊C₃	—	19	1	no	—
22	D₁₃×D₁₉	—	13	1	no	—
23	D₁₃×D₁₉	—	13	1	no	—
24	#10625202	C₂×D₁₃	1	1	yes	characteristic, complemented
25	C₁₃×C₁₉⋊C₃	—	13	1	no	—
26	D₁₃²	—	19	1	no	Hall
27	C₁₃×C₁₃⋊C₃	—	19	1	no	Hall
28	D₂₄₇	D₁₃⋊C₃	1	1	yes	characteristic, complemented
29	D₂₄₇	C₃×D₁₃	1	1	yes	characteristic, complemented
30	C₁₃×D₁₉	—	13	1	no	—
31	C₁₃×D₁₉	—	13	1	no	—
32	C₁₉×D₁₃	—	13	1	no	—
33	C₁₉×D₁₃	—	13	1	no	—
34	C₁₉×D₁₃	—	78	2	no	—
35	C₁₃⋊D₁₃	D₁₉⋊C₃	1	1	yes	characteristic, complemented
36	C₁₃×D₁₃	—	19	1	no	—
37	C₁₃×D₁₃	—	19	1	no	—
38	C₁₃×C₁₉	—	6	2	no	—
39	C₁₃×C₁₉	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
40	C₁₃×C₁₉	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented
41	C₂×D₁₉⋊C₃	—	169	1	no	Hall
42	C₁₃²	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃×D₁₃	—	247	1	no	—
44	C₂×D₁₃⋊C₃	—	247	1	no	—
45	C₂×C₁₉⋊C₃	—	169	1	no	—
46	D₁₉⋊C₃	—	13	1	no	—
47	D₁₉⋊C₃	—	169	1	no	—
48	C₂×C₃×C₁₃	—	247	1	no	—
49	C₃×D₁₃	—	247	1	no	—
50	C₃×D₁₃	—	247	1	no	—
51	C₂×C₁₃⋊C₃	—	247	1	no	—
52	D₁₃⋊C₃	—	19	1	no	—
53	D₁₃⋊C₃	—	247	1	no	—
54	C₂×D₁₉	—	169	1	no	Hall
55	C₁₉⋊C₃	—	13	1	no	Hall
56	C₂×D₁₃	—	247	1	no	—
57	C₂×D₁₃	—	247	1	no	—
58	C₃×C₁₃	—	247	1	no	—
59	C₁₃⋊C₃	—	19	1	no	—
60	C₂×C₁₉	—	169	1	no	—
61	D₁₉	—	13	1	no	—
62	D₁₉	—	13	1	no	—
63	C₂×C₁₃	—	247	1	no	—
64	C₂×C₁₃	—	247	1	no	—
65	D₁₃	—	13	1	no	—
66	D₁₃	—	13	1	no	—
67	D₁₃	—	19	1	no	—
68	D₁₃	—	19	1	no	—
69	D₁₃	—	78	2	no	—
70	C₁₉	D₁₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
71	C₁₃	—	6	2	no	—
72	C₁₃	#13093360⋊C₂	1	1	yes	characteristic, complemented
73	C₁₃	D₁₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented
74	C₂²×C₃	—	3211	1	no	Hall
75	C₂×C₃	—	3211	1	no	—
76	C₂×C₃	—	3211	1	no	—
77	C₂×C₃	—	247	1	no	—
78	C₂²	—	3211	1	no	Sylow
79	C₃	—	247	1	no	Sylow
80	C₂	—	169	1	no	—
81	C₂	—	247	1	no	—
82	C₂	—	247	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃²×C₁₉	C₂²×C₃
LCS	G ▷ C₁₃²×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #34064237	C₂	semidirect
2. #34064228	C₂	semidirect
3. C₁₃×#13093366	C₂	semidirect
4. (C₁₃⋊D₁₃)⋊D₁₉	C₃	semidirect
5. C₁₃×#10625202	C₂²	semidirect
6. C₁₉×C₁₃⋊D₁₃	C₂×C₃	semidirect
7. C₁₃×D₂₄₇	C₂×C₃	semidirect
8. C₁₃×D₂₄₇	C₂×C₃	semidirect
9. C₁₃²×C₁₉	C₂²×C₃	semidirect
13. #13093366	D₁₃	semidirect
24. #10625202	C₂×D₁₃	semidirect
28. D₂₄₇	D₁₃⋊C₃	semidirect
29. D₂₄₇	C₃×D₁₃	semidirect
35. C₁₃⋊D₁₃	D₁₉⋊C₃	semidirect
39. C₁₃×C₁₉	C₂×D₁₃⋊C₃	semidirect
40. C₁₃×C₁₉	C₂×C₃×D₁₃	semidirect
42. C₁₃²	C₂×D₁₉⋊C₃	semidirect
70. C₁₉	D₁₃×D₁₃⋊C₃	semidirect
72. C₁₃	#13093360⋊C₂	semidirect
73. C₁₃	D₁₃×D₁₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#34064237	2
#34064228	2
C₁₃×#13093366	2
(C₁₃⋊D₁₃)⋊D₁₉	3
D₁₃×D₁₉⋊C₃	13
#13093360⋊C₂	13
D₁₃×D₁₃⋊C₃	19

Subgroups — #13093366⋊D13 #50310313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #13093366⋊D₁₃ #50310313