Subgroups — C₃⋊((C₁₉⋊C₃)⋊D₉₁) #44528008

Order 31122.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₃×C₁₉⋊C₃	2
(C₁₉⋊C₃)⋊D₉₁	3
D₅₁₈₇	3
C₃⋊((C₁₉⋊C₃)⋊D₁₃)	7
C₃⋊((C₁₉⋊C₃)⋊D₇)	13
C₃×D₂₇₃	19

Subgroups — C3⋊((C19⋊C3)⋊D91) #44528008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊((C₁₉⋊C₃)⋊D₉₁) #44528008