Subgroups — D₃×(C₇₉⋊C₃)⋊D₁₃ #49149571

Order 36972.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊((C₇₉⋊C₃)⋊D₁₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₃×C₇₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×(C₇₉⋊C₃)⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₁₀₂₇	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×(C₇₉⋊C₃)⋊D₁₃	—	3	1	no	maximal
6	C₃×C₁₃×C₇₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	(C₇₉⋊C₃)⋊D₁₃	—	2	1	no	—
8	(C₇₉⋊C₃)⋊D₁₃	—	3	1	no	—
9	(C₇₉⋊C₃)⋊D₁₃	D₃	1	1	yes	characteristic, direct product factor
10	D₃₀₈₁	C₂×C₃	1	1	yes	characteristic, complemented
11	D₃×C₁₃×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×D₁₀₂₇	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×C₁₃×C₇₉⋊C₃	—	3	1	no	—
14	C₂×D₁₀₂₇	—	3	1	no	Hall
15	C₃×C₁₃×C₇₉	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₁₃×C₇₉⋊C₃	—	2	1	no	—
17	C₁₃×C₇₉⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
18	D₃×D₇₉⋊C₃	—	13	1	no	maximal, Hall
19	C₂×C₁₃×C₇₉	—	3	1	no	—
20	D₁₀₂₇	—	3	1	no	—
21	D₁₀₂₇	C₃×D₃	1	1	yes	characteristic, complemented
22	C₃⋊(D₇₉⋊C₃)	—	13	1	no	—
23	D₃×C₇₉⋊C₃	D₁₃	1	1	yes	characteristic, complemented
24	C₃×D₇₉⋊C₃	—	13	1	no	—
25	C₁₃×C₇₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
26	D₃×D₇₉	—	13	1	no	—
27	C₂×D₇₉⋊C₃	—	39	1	no	—
28	C₃×C₇₉⋊C₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
29	D₂₃₇	—	13	1	no	—
30	C₃×D₇₉	—	13	1	no	—
31	D₃×C₇₉	C₃×D₁₃	1	1	yes	characteristic, complemented
32	C₂×C₇₉⋊C₃	—	3	1	no	—
33	D₇₉⋊C₃	—	13	1	no	—
34	D₇₉⋊C₃	—	26	1	no	—
35	D₇₉⋊C₃	—	39	1	no	—
36	C₃×D₃×D₁₃	—	79	1	no	maximal, Hall
37	C₂×D₇₉	—	39	1	no	Hall
38	C₃×C₇₉	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented
39	C₇₉⋊C₃	—	2	1	no	—
40	C₇₉⋊C₃	D₃×D₁₃	1	1	yes	characteristic, complemented
41	C₃×D₃₉	—	79	1	no	—
42	C₃×D₃×C₁₃	—	79	1	no	—
43	C₃²×D₁₃	—	79	1	no	—
44	C₂×C₇₉	—	3	1	no	—
45	D₇₉	—	13	1	no	—
46	D₇₉	—	39	1	no	—
47	C₂×C₃×D₁₃	—	237	1	no	—
48	D₃×D₁₃	—	79	1	no	—
49	C₃²×C₁₃	—	79	1	no	Hall
50	C₇₉	C₃×D₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃×C₁₃	—	237	1	no	—
52	D₃₉	—	79	1	no	—
53	C₃×D₁₃	—	79	1	no	—
54	C₃×D₁₃	—	79	1	no	—
55	C₃×D₁₃	—	158	1	no	—
56	C₃×D₁₃	—	237	1	no	—
57	D₃×C₁₃	D₇₉⋊C₃	1	1	yes	characteristic, complemented
58	C₂×D₁₃	—	237	1	no	Hall
59	C₃×C₁₃	—	79	1	no	—
60	C₃×C₁₃	—	158	1	no	—
61	C₃×C₁₃	C₂×D₇₉⋊C₃	1	1	yes	characteristic, complemented
62	C₂×C₃×D₃	—	1027	1	no	Hall
63	C₂×C₁₃	—	3	1	no	—
64	D₁₃	—	79	1	no	—
65	D₁₃	—	237	1	no	—
66	C₂×C₃²	—	1027	1	no	—
67	C₃×D₃	—	1027	1	no	—
68	C₃×D₃	—	79	1	no	—
69	C₁₃	D₃×D₇₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₃	—	3081	1	no	—
71	C₂×D₃	—	1027	1	no	—
72	C₃²	—	79	1	no	Sylow
73	C₂×C₃	—	1027	1	no	—
74	C₂×C₃	—	1027	1	no	—
75	C₂×C₃	—	2054	1	no	—
76	C₂×C₃	—	3081	1	no	—
77	C₂×C₃	—	237	1	no	—
78	D₃	—	1027	1	no	—
79	D₃	(C₇₉⋊C₃)⋊D₁₃	1	1	yes	characteristic, direct product factor
80	C₂²	—	3081	1	no	Sylow
81	C₃	—	79	1	no	—
82	C₃	—	158	1	no	—
83	C₃	C₂×(C₇₉⋊C₃)⋊D₁₃	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	1027	1	no	—
86	C₂	—	3081	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃⋊((C₇₉⋊C₃)⋊D₁₃)	C₂	semidirect
2. D₃×C₁₃×C₇₉⋊C₃	C₂	semidirect
3. C₃×(C₇₉⋊C₃)⋊D₁₃	C₂	semidirect
4. D₃×D₁₀₂₇	C₃	semidirect
6. C₃×C₁₃×C₇₉⋊C₃	C₂²	semidirect
9. (C₇₉⋊C₃)⋊D₁₃	D₃	direct (N × H)
10. D₃₀₈₁	C₂×C₃	semidirect
11. D₃×C₁₃×C₇₉	C₂×C₃	semidirect
12. C₃×D₁₀₂₇	C₂×C₃	semidirect
15. C₃×C₁₃×C₇₉	C₂²×C₃	semidirect
17. C₁₃×C₇₉⋊C₃	C₂×D₃	semidirect
21. D₁₀₂₇	C₃×D₃	semidirect
23. D₃×C₇₉⋊C₃	D₁₃	semidirect
25. C₁₃×C₇₉	C₂×C₃×D₃	semidirect
28. C₃×C₇₉⋊C₃	C₂×D₁₃	semidirect
31. D₃×C₇₉	C₃×D₁₃	semidirect
38. C₃×C₇₉	C₂×C₃×D₁₃	semidirect
40. C₇₉⋊C₃	D₃×D₁₃	semidirect
50. C₇₉	C₃×D₃×D₁₃	semidirect
57. D₃×C₁₃	D₇₉⋊C₃	semidirect
61. C₃×C₁₃	C₂×D₇₉⋊C₃	semidirect
69. C₁₃	D₃×D₇₉⋊C₃	semidirect
79. D₃	(C₇₉⋊C₃)⋊D₁₃	direct (N × H)
83. C₃	C₂×(C₇₉⋊C₃)⋊D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊((C₇₉⋊C₃)⋊D₁₃)	2
D₃×C₁₃×C₇₉⋊C₃	2
C₃×(C₇₉⋊C₃)⋊D₁₃	2
D₃×D₁₀₂₇	3
C₂×(C₇₉⋊C₃)⋊D₁₃	3
D₃×D₇₉⋊C₃	13
C₃×D₃×D₁₃	79

Subgroups — D3×(C79⋊C3)⋊D13 #49149571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×(C₇₉⋊C₃)⋊D₁₃ #49149571