Subgroups — C₃⋊((C₁₃⋊C₃)⋊D₁₃₃) #44528001

Order 31122.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₉×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	(C₁₃⋊C₃)⋊D₁₃₃	—	3	1	no	maximal
3	D₅₁₈₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₇×C₁₉×C₁₃⋊C₃	—	2	1	no	—
5	C₇×C₁₉×C₁₃⋊C₃	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃⋊((C₁₃⋊C₃)⋊D₁₉)	—	7	1	no	maximal, Hall
8	D₁₇₂₉	—	3	1	no	Hall
9	C₃×D₃₉₉	—	13	1	no	maximal, Hall
10	C₃×C₁₉×C₁₃⋊C₃	D₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₁₃×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
12	C₃⋊((C₁₃⋊C₃)⋊D₇)	—	19	1	no	maximal, Hall
13	D₇₄₁	—	7	1	no	—
14	(C₁₃⋊C₃)⋊D₁₉	—	21	1	no	—
15	C₃²×C₇×C₁₉	—	13	1	no	Hall
16	C₃×C₇×C₁₃⋊C₃	D₁₉	1	1	yes	characteristic, complemented, Hall
17	D₃₉₉	—	13	1	no	—
18	C₃×D₁₃₃	—	39	1	no	—
19	C₃×C₁₃×C₁₉	C₃×D₇	1	1	yes	characteristic, complemented
20	C₁₉×C₁₃⋊C₃	—	2	1	no	—
21	C₁₉×C₁₃⋊C₃	D₂₁	1	1	yes	characteristic, complemented
22	D₂₇₃	—	19	1	no	—
23	(C₁₃⋊C₃)⋊D₇	—	57	1	no	—
24	D₂₄₇	—	21	1	no	Hall
25	C₃×C₇×C₁₉	—	13	1	no	—
26	C₃×C₇×C₁₉	—	26	1	no	—
27	C₃×C₇×C₁₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented
28	C₃×D₅₇	—	91	1	no	Hall
29	C₃×C₇×C₁₃	C₃×D₁₉	1	1	yes	characteristic, complemented
30	C₇×C₁₃⋊C₃	—	2	1	no	—
31	C₇×C₁₃⋊C₃	D₅₇	1	1	yes	characteristic, complemented
32	D₁₃₃	—	39	1	no	Hall
33	C₁₃×C₁₉	C₃×D₂₁	1	1	yes	characteristic, complemented, Hall
34	C₃⋊(D₁₃⋊C₃)	—	133	1	no	Hall
35	D₉₁	—	57	1	no	Hall
36	C₃²×C₁₉	—	13	1	no	Hall
37	C₇×C₁₉	C₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Hall
38	C₃×D₂₁	—	247	1	no	Hall
39	C₃×C₁₃⋊C₃	D₁₃₃	1	1	yes	characteristic, complemented, Hall
40	D₅₇	—	91	1	no	—
41	C₃×D₁₉	—	273	1	no	—
42	C₇×C₁₃	C₃×D₅₇	1	1	yes	characteristic, complemented, Hall
43	D₃₉	—	133	1	no	—
44	D₁₃⋊C₃	—	399	1	no	—
45	C₃²×C₇	—	13	1	no	Hall
46	C₃×C₁₉	—	13	1	no	—
47	C₃×C₁₉	—	26	1	no	—
48	C₃×C₁₉	(C₁₃⋊C₃)⋊D₇	1	1	yes	characteristic, complemented
49	D₂₁	—	247	1	no	—
50	C₃×D₇	—	741	1	no	—
51	C₃×C₁₃	C₃×D₁₃₃	1	1	yes	characteristic, complemented
52	C₁₃⋊C₃	—	2	1	no	—
53	C₁₃⋊C₃	D₃₉₉	1	1	yes	characteristic, complemented
54	D₁₉	—	273	1	no	Hall
55	D₁₃	—	399	1	no	Hall
56	C₃×C₇	—	13	1	no	—
57	C₃×C₇	—	26	1	no	—
58	C₃×C₇	(C₁₃⋊C₃)⋊D₁₉	1	1	yes	characteristic, complemented
59	C₁₉	C₃⋊((C₁₃⋊C₃)⋊D₇)	1	1	yes	characteristic, complemented, Sylow
60	C₃×D₃	—	1729	1	no	Hall
61	D₇	—	741	1	no	Hall
62	C₁₃	C₃×D₃₉₉	1	1	yes	characteristic, complemented, Sylow
63	C₃²	—	13	1	no	Sylow
64	C₇	C₃⋊((C₁₃⋊C₃)⋊D₁₉)	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃	—	5187	1	no	—
66	D₃	—	1729	1	no	—
67	C₃	—	13	1	no	—
68	C₃	—	26	1	no	—
69	C₃	(C₁₃⋊C₃)⋊D₁₃₃	1	1	yes	characteristic, complemented
70	C₂	—	5187	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₇×C₁₃×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₉×C₁₃⋊C₃	C₂	semidirect
3. D₅₁₈₇	C₃	semidirect
5. C₇×C₁₉×C₁₃⋊C₃	D₃	semidirect
6. C₃×C₇×C₁₃×C₁₉	C₂×C₃	semidirect
10. C₃×C₁₉×C₁₃⋊C₃	D₇	semidirect
11. C₇×C₁₃×C₁₉	C₃×D₃	semidirect
16. C₃×C₇×C₁₃⋊C₃	D₁₉	semidirect
19. C₃×C₁₃×C₁₉	C₃×D₇	semidirect
21. C₁₉×C₁₃⋊C₃	D₂₁	semidirect
27. C₃×C₇×C₁₉	D₁₃⋊C₃	semidirect
29. C₃×C₇×C₁₃	C₃×D₁₉	semidirect
31. C₇×C₁₃⋊C₃	D₅₇	semidirect
33. C₁₃×C₁₉	C₃×D₂₁	semidirect
37. C₇×C₁₉	C₃⋊(D₁₃⋊C₃)	semidirect
39. C₃×C₁₃⋊C₃	D₁₃₃	semidirect
42. C₇×C₁₃	C₃×D₅₇	semidirect
48. C₃×C₁₉	(C₁₃⋊C₃)⋊D₇	semidirect
51. C₃×C₁₃	C₃×D₁₃₃	semidirect
53. C₁₃⋊C₃	D₃₉₉	semidirect
58. C₃×C₇	(C₁₃⋊C₃)⋊D₁₉	semidirect
59. C₁₉	C₃⋊((C₁₃⋊C₃)⋊D₇)	semidirect
62. C₁₃	C₃×D₃₉₉	semidirect
64. C₇	C₃⋊((C₁₃⋊C₃)⋊D₁₉)	semidirect
69. C₃	(C₁₃⋊C₃)⋊D₁₃₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₉×C₁₃⋊C₃	2
(C₁₃⋊C₃)⋊D₁₃₃	3
D₅₁₈₇	3
C₃⋊((C₁₃⋊C₃)⋊D₁₉)	7
C₃×D₃₉₉	13
C₃⋊((C₁₃⋊C₃)⋊D₇)	19

Subgroups — C3⋊((C13⋊C3)⋊D133) #44528001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊((C₁₃⋊C₃)⋊D₁₃₃) #44528001