Subgroups — C₂×D₃×#15690494 #49149607

Order 36972.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#15690494	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×#15690494	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₃×C₁₃×C₇₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×#15690494	—	3	1	no	maximal
5	C₃×#15690494	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₁₃×C₇₉	C₂×C₃	1	2	yes	complemented
7	C₂×#15690494	—	2	1	no	—
8	C₂×#15690494	—	3	2	no	—
9	C₂×#15690494	D₃	1	1	yes	characteristic, direct product factor
10	C₂×C₃×C₁₃×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂²×C₁₃×C₇₉	—	3	1	no	Hall
12	C₃×C₁₃×C₇₉	C₂²×C₃	1	1	yes	characteristic, complemented
13	#15690494	—	2	1	no	—
14	#15690494	C₂×D₃	1	1	yes	characteristic, direct product factor
15	C₂×D₃×C₇₉⋊C₃	—	13	1	no	maximal, Hall
16	C₂×C₁₃×C₇₉	—	3	2	no	—
17	C₂×C₁₃×C₇₉	C₃×D₃	1	1	yes	characteristic, complemented
18	C₂×C₃×C₇₉⋊C₃	—	13	1	no	—
19	D₃×C₇₉⋊C₃	—	13	2	no	—
20	C₁₃×C₇₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
21	C₂×D₃×C₇₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented
22	C₂²×C₇₉⋊C₃	—	39	1	no	—
23	C₃×C₇₉⋊C₃	—	13	1	no	Hall
24	C₂×C₃×C₇₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
25	D₃×C₇₉	C₂×C₁₃⋊C₃	1	2	yes	complemented
26	C₂×C₇₉⋊C₃	—	13	1	no	—
27	C₂×C₇₉⋊C₃	—	26	1	no	—
28	C₂×C₇₉⋊C₃	—	39	2	no	—
29	C₂×D₃×C₁₃⋊C₃	—	79	1	no	maximal, Hall
30	C₂²×C₇₉	—	3	1	no	Hall
31	C₃×C₇₉	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented
32	C₇₉⋊C₃	—	13	1	no	—
33	C₇₉⋊C₃	—	26	1	no	—
34	C₂×C₃×C₁₃⋊C₃	—	79	1	no	—
35	D₃×C₁₃⋊C₃	—	79	2	no	—
36	C₂×C₇₉	—	3	2	no	—
37	C₂×C₇₉	D₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented
38	C₂×D₃×C₁₃	C₇₉⋊C₃	1	1	yes	characteristic, complemented
39	C₂²×C₁₃⋊C₃	—	237	1	no	—
40	C₃×C₁₃⋊C₃	—	79	1	no	Hall
41	C₇₉	C₂×D₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃×C₁₃	C₂×C₇₉⋊C₃	1	1	yes	characteristic, complemented
43	D₃×C₁₃	C₂×C₇₉⋊C₃	1	2	yes	complemented
44	C₂×C₁₃⋊C₃	—	79	1	no	—
45	C₂×C₁₃⋊C₃	—	158	1	no	—
46	C₂×C₁₃⋊C₃	—	237	2	no	—
47	C₂²×C₁₃	—	3	1	no	Hall
48	C₃×C₁₃	C₂²×C₇₉⋊C₃	1	1	yes	characteristic, complemented
49	C₁₃⋊C₃	—	79	1	no	—
50	C₁₃⋊C₃	—	158	1	no	—
51	C₂×C₃×D₃	—	1027	1	no	Hall
52	C₂×C₁₃	—	3	2	no	—
53	C₂×C₁₃	D₃×C₇₉⋊C₃	1	1	yes	characteristic, complemented
54	C₂×C₃²	—	1027	1	no	—
55	C₃×D₃	—	1027	2	no	—
56	C₁₃	C₂×D₃×C₇₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₃	—	3081	1	no	—
58	C₂×D₃	#15690494	1	1	yes	characteristic, direct product factor
59	C₃²	—	1027	1	no	Sylow
60	C₂×C₃	—	1027	1	no	—
61	C₂×C₃	—	2054	1	no	—
62	C₂×C₃	—	3081	2	no	—
63	C₂×C₃	C₂×#15690494	1	1	yes	characteristic, complemented
64	D₃	C₂×#15690494	1	2	yes	direct product factor
65	C₂²	—	3	1	no	Sylow
66	C₃	—	1027	1	no	—
67	C₃	—	2054	1	no	—
68	C₃	C₂²×#15690494	1	1	yes	characteristic, complemented
69	C₂	—	3	2	no	—
70	C₂	D₃×#15690494	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₃×#15690494
commutator, cosocle, hypocenter	C₃×C₁₃×C₇₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₇₉	C₂×C₃
LCS	G ▷ C₃×C₁₃×C₇₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#15690494	C₂	semidirect
2. D₃×#15690494	C₂	direct (N × H)
3. C₂×D₃×C₁₃×C₇₉	C₃	semidirect
5. C₃×#15690494	C₂²	semidirect
6. D₃×C₁₃×C₇₉	C₂×C₃	semidirect
9. C₂×#15690494	D₃	direct (N × H)
10. C₂×C₃×C₁₃×C₇₉	C₂×C₃	semidirect
12. C₃×C₁₃×C₇₉	C₂²×C₃	semidirect
14. #15690494	C₂×D₃	direct (N × H)
17. C₂×C₁₃×C₇₉	C₃×D₃	semidirect
20. C₁₃×C₇₉	C₂×C₃×D₃	semidirect
21. C₂×D₃×C₇₉	C₁₃⋊C₃	semidirect
24. C₂×C₃×C₇₉	C₂×C₁₃⋊C₃	semidirect
25. D₃×C₇₉	C₂×C₁₃⋊C₃	semidirect
31. C₃×C₇₉	C₂²×C₁₃⋊C₃	semidirect
37. C₂×C₇₉	D₃×C₁₃⋊C₃	semidirect
38. C₂×D₃×C₁₃	C₇₉⋊C₃	semidirect
41. C₇₉	C₂×D₃×C₁₃⋊C₃	semidirect
42. C₂×C₃×C₁₃	C₂×C₇₉⋊C₃	semidirect
43. D₃×C₁₃	C₂×C₇₉⋊C₃	semidirect
48. C₃×C₁₃	C₂²×C₇₉⋊C₃	semidirect
53. C₂×C₁₃	D₃×C₇₉⋊C₃	semidirect
56. C₁₃	C₂×D₃×C₇₉⋊C₃	semidirect
58. C₂×D₃	#15690494	direct (N × H)
63. C₂×C₃	C₂×#15690494	semidirect
64. D₃	C₂×#15690494	direct (N × H)
68. C₃	C₂²×#15690494	semidirect
70. C₂	D₃×#15690494	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×C₃×#15690494	2
D₃×#15690494	2
C₂×D₃×C₁₃×C₇₉	3
C₂²×#15690494	3
C₂×D₃×C₇₉⋊C₃	13
C₂×D₃×C₁₃⋊C₃	79

Subgroups — C2×D3×#15690494 #49149607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×#15690494 #49149607