Subgroups — C₂×C₃⋊#13093361 #22580340

Order 8892.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#10625203	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊#13093361	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₃×D₅₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×#13093361	—	3	1	no	maximal
5	C₃×#10625203	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃×D₅₇	C₂×C₃	1	2	yes	complemented
8	C₂×#10625203	—	2	1	no	—
9	C₂×#10625203	D₃	1	1	yes	characteristic, complemented
10	#13093361	—	3	2	no	—
11	C₂×C₁₃×D₁₉	—	3	1	no	Hall
12	C₃×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
13	#10625203	—	2	1	no	—
14	#10625203	C₂×D₃	1	1	yes	characteristic, complemented
15	C₂×C₃⋊(D₁₉⋊C₃)	—	13	1	no	maximal, Hall
16	C₂×C₁₃×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented
17	C₁₃×D₁₉	—	3	2	no	—
18	C₂×D₃×C₁₃⋊C₃	—	19	1	no	maximal, Hall
19	C₂×C₃×C₁₉⋊C₃	—	13	1	no	—
20	C₃⋊(D₁₉⋊C₃)	—	13	2	no	—
21	C₁₃×C₁₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₁₃⋊C₃	—	19	1	no	—
23	D₃×C₁₃⋊C₃	—	19	2	no	—
24	C₂×D₅₇	C₁₃⋊C₃	1	1	yes	characteristic, complemented
25	C₂×D₁₉⋊C₃	—	39	1	no	—
26	C₃×C₁₉⋊C₃	—	13	1	no	Hall
27	C₂×D₃×C₁₃	—	19	1	no	—
28	C₂²×C₁₃⋊C₃	—	57	1	no	—
29	C₃×C₁₃⋊C₃	—	19	1	no	Hall
30	C₂×C₃×C₁₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
31	D₅₇	C₂×C₁₃⋊C₃	1	2	yes	complemented
32	C₂×C₁₉⋊C₃	—	13	1	no	—
33	C₂×C₁₉⋊C₃	—	26	1	no	—
34	D₁₉⋊C₃	—	39	2	no	—
35	C₂×C₃×C₁₃	D₁₉⋊C₃	1	1	yes	characteristic, complemented
36	D₃×C₁₃	—	19	2	no	—
37	C₂×C₁₃⋊C₃	—	19	1	no	—
38	C₂×C₁₃⋊C₃	—	38	1	no	—
39	C₂×C₁₃⋊C₃	—	57	2	no	—
40	C₂×D₁₉	—	3	1	no	Hall
41	C₃×C₁₉	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented
42	C₁₉⋊C₃	—	13	1	no	—
43	C₁₉⋊C₃	—	26	1	no	—
44	C₂²×C₁₃	—	57	1	no	Hall
45	C₃×C₁₃	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented
46	C₁₃⋊C₃	—	19	1	no	—
47	C₁₃⋊C₃	—	38	1	no	—
48	C₂×C₁₉	D₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented
49	D₁₉	—	3	2	no	—
50	C₂×C₃×D₃	—	247	1	no	Hall
51	C₂×C₁₃	—	57	2	no	—
52	C₂×C₁₃	C₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented
53	C₁₉	C₂×D₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₃²	—	247	1	no	—
55	C₃×D₃	—	247	2	no	—
56	C₁₃	C₂×C₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₃	—	741	1	no	—
58	C₂×D₃	—	19	1	no	—
59	C₃²	—	247	1	no	Sylow
60	C₂×C₃	—	741	2	no	—
61	C₂×C₃	—	494	1	no	—
62	C₂×C₃	—	247	1	no	—
63	C₂×C₃	#13093361	1	1	yes	characteristic, complemented
64	D₃	—	19	2	no	—
65	C₂²	—	57	1	no	Sylow
66	C₃	—	494	1	no	—
67	C₃	—	247	1	no	—
68	C₃	C₂×#13093361	1	1	yes	characteristic, complemented
69	C₂	—	57	2	no	—
70	C₂	C₃⋊#13093361	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊#13093361
commutator, hypocenter	C₃×C₁₃×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₁₃×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#10625203	C₂	semidirect
2. C₃⋊#13093361	C₂	direct (N × H)
3. C₂×C₁₃×D₅₇	C₃	semidirect
5. C₃×#10625203	C₂²	semidirect
6. C₂×C₃×C₁₃×C₁₉	C₂×C₃	semidirect
7. C₁₃×D₅₇	C₂×C₃	semidirect
9. C₂×#10625203	D₃	semidirect
12. C₃×C₁₃×C₁₉	C₂²×C₃	semidirect
14. #10625203	C₂×D₃	semidirect
16. C₂×C₁₃×C₁₉	C₃×D₃	semidirect
21. C₁₃×C₁₉	C₂×C₃×D₃	semidirect
24. C₂×D₅₇	C₁₃⋊C₃	semidirect
30. C₂×C₃×C₁₉	C₂×C₁₃⋊C₃	semidirect
31. D₅₇	C₂×C₁₃⋊C₃	semidirect
35. C₂×C₃×C₁₃	D₁₉⋊C₃	semidirect
41. C₃×C₁₉	C₂²×C₁₃⋊C₃	semidirect
45. C₃×C₁₃	C₂×D₁₉⋊C₃	semidirect
48. C₂×C₁₉	D₃×C₁₃⋊C₃	semidirect
52. C₂×C₁₃	C₃⋊(D₁₉⋊C₃)	semidirect
53. C₁₉	C₂×D₃×C₁₃⋊C₃	semidirect
56. C₁₃	C₂×C₃⋊(D₁₉⋊C₃)	semidirect
63. C₂×C₃	#13093361	semidirect
68. C₃	C₂×#13093361	semidirect
70. C₂	C₃⋊#13093361	direct (N × H)

Subgroups — C2×C3⋊#13093361 #22580340

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃⋊#13093361 #22580340