Subgroups — D₃×(C₃₁⋊C₃)⋊D₁₉ #35234470

Order 21204.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊((C₃₁⋊C₃)⋊D₁₉)	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₉×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×(C₃₁⋊C₃)⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₅₈₉	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×(C₃₁⋊C₃)⋊D₁₉	—	3	1	no	maximal
6	C₃×C₁₉×C₃₁⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	(C₃₁⋊C₃)⋊D₁₉	—	2	1	no	—
8	(C₃₁⋊C₃)⋊D₁₉	—	3	1	no	—
9	(C₃₁⋊C₃)⋊D₁₉	D₃	1	1	yes	characteristic, direct product factor
10	D₁₇₆₇	C₂×C₃	1	1	yes	characteristic, complemented
11	D₃×C₁₉×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×D₅₈₉	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×C₁₉×C₃₁⋊C₃	—	3	1	no	—
14	C₂×D₅₈₉	—	3	1	no	Hall
15	C₃×C₁₉×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₁₉×C₃₁⋊C₃	—	2	1	no	—
17	C₁₉×C₃₁⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
18	C₂×C₁₉×C₃₁	—	3	1	no	—
19	D₅₈₉	—	3	1	no	—
20	D₅₈₉	C₃×D₃	1	1	yes	characteristic, complemented
21	D₃×D₃₁⋊C₃	—	19	1	no	maximal, Hall
22	C₃×D₃×D₁₉	—	31	1	no	maximal, Hall
23	C₁₉×C₃₁	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
24	C₃⋊(D₃₁⋊C₃)	—	19	1	no	—
25	D₃×C₃₁⋊C₃	D₁₉	1	1	yes	characteristic, complemented
26	C₃×D₃₁⋊C₃	—	19	1	no	—
27	D₃×D₃₁	—	19	1	no	—
28	C₂×D₃₁⋊C₃	—	57	1	no	—
29	C₃×D₅₇	—	31	1	no	—
30	C₃×D₃×C₁₉	—	62	1	no	—
31	C₃²×D₁₉	—	31	1	no	—
32	C₃×C₃₁⋊C₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×D₁₉	—	93	1	no	—
34	D₃×D₁₉	—	31	1	no	—
35	D₉₃	—	19	1	no	—
36	C₃×D₃₁	—	19	1	no	—
37	D₃×C₃₁	C₃×D₁₉	1	1	yes	characteristic, complemented
38	C₂×C₃₁⋊C₃	—	3	1	no	—
39	D₃₁⋊C₃	—	19	1	no	—
40	D₃₁⋊C₃	—	38	1	no	—
41	D₃₁⋊C₃	—	57	1	no	—
42	C₃²×C₁₉	—	62	1	no	Hall
43	C₂×D₃₁	—	57	1	no	Hall
44	C₂×C₃×C₁₉	—	186	1	no	—
45	D₅₇	—	31	1	no	—
46	C₃×D₁₉	—	31	1	no	—
47	C₃×D₁₉	—	31	1	no	—
48	C₃×D₁₉	—	62	1	no	—
49	C₃×D₁₉	—	93	1	no	—
50	D₃×C₁₉	D₃₁⋊C₃	1	1	yes	characteristic, complemented
51	C₃×C₃₁	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented
52	C₃₁⋊C₃	—	2	1	no	—
53	C₃₁⋊C₃	D₃×D₁₉	1	1	yes	characteristic, complemented
54	C₂×D₁₉	—	93	1	no	Hall
55	C₂×C₃₁	—	3	1	no	—
56	D₃₁	—	19	1	no	—
57	D₃₁	—	57	1	no	—
58	C₃×C₁₉	—	62	1	no	—
59	C₃×C₁₉	—	124	1	no	—
60	C₃×C₁₉	C₂×D₃₁⋊C₃	1	1	yes	characteristic, complemented
61	C₂×C₁₉	—	3	1	no	—
62	D₁₉	—	31	1	no	—
63	D₁₉	—	93	1	no	—
64	C₂×C₃×D₃	—	589	1	no	Hall
65	C₃₁	C₃×D₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
66	C₁₉	D₃×D₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₃²	—	589	1	no	—
68	C₃×D₃	—	62	1	no	—
69	C₃×D₃	—	589	1	no	—
70	C₂²×C₃	—	1767	1	no	—
71	C₂×D₃	—	589	1	no	—
72	C₃²	—	62	1	no	Sylow
73	C₂×C₃	—	589	1	no	—
74	C₂×C₃	—	589	1	no	—
75	C₂×C₃	—	93	1	no	—
76	C₂×C₃	—	1178	1	no	—
77	C₂×C₃	—	1767	1	no	—
78	D₃	—	589	1	no	—
79	D₃	(C₃₁⋊C₃)⋊D₁₉	1	1	yes	characteristic, direct product factor
80	C₂²	—	1767	1	no	Sylow
81	C₃	—	31	1	no	—
82	C₃	—	124	1	no	—
83	C₃	C₂×(C₃₁⋊C₃)⋊D₁₉	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	589	1	no	—
86	C₂	—	1767	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₉×C₃₁	C₂²×C₃
LCS	G ▷ C₃×C₁₉×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊((C₃₁⋊C₃)⋊D₁₉)	C₂	semidirect
2. D₃×C₁₉×C₃₁⋊C₃	C₂	semidirect
3. C₃×(C₃₁⋊C₃)⋊D₁₉	C₂	semidirect
4. D₃×D₅₈₉	C₃	semidirect
6. C₃×C₁₉×C₃₁⋊C₃	C₂²	semidirect
9. (C₃₁⋊C₃)⋊D₁₉	D₃	direct (N × H)
10. D₁₇₆₇	C₂×C₃	semidirect
11. D₃×C₁₉×C₃₁	C₂×C₃	semidirect
12. C₃×D₅₈₉	C₂×C₃	semidirect
15. C₃×C₁₉×C₃₁	C₂²×C₃	semidirect
17. C₁₉×C₃₁⋊C₃	C₂×D₃	semidirect
20. D₅₈₉	C₃×D₃	semidirect
23. C₁₉×C₃₁	C₂×C₃×D₃	semidirect
25. D₃×C₃₁⋊C₃	D₁₉	semidirect
32. C₃×C₃₁⋊C₃	C₂×D₁₉	semidirect
37. D₃×C₃₁	C₃×D₁₉	semidirect
50. D₃×C₁₉	D₃₁⋊C₃	semidirect
51. C₃×C₃₁	C₂×C₃×D₁₉	semidirect
53. C₃₁⋊C₃	D₃×D₁₉	semidirect
60. C₃×C₁₉	C₂×D₃₁⋊C₃	semidirect
65. C₃₁	C₃×D₃×D₁₉	semidirect
66. C₁₉	D₃×D₃₁⋊C₃	semidirect
79. D₃	(C₃₁⋊C₃)⋊D₁₉	direct (N × H)
83. C₃	C₂×(C₃₁⋊C₃)⋊D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊((C₃₁⋊C₃)⋊D₁₉)	2
D₃×C₁₉×C₃₁⋊C₃	2
C₃×(C₃₁⋊C₃)⋊D₁₉	2
D₃×D₅₈₉	3
C₂×(C₃₁⋊C₃)⋊D₁₉	3
D₃×D₃₁⋊C₃	19
C₃×D₃×D₁₉	31

Subgroups — D3×(C31⋊C3)⋊D19 #35234470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×(C₃₁⋊C₃)⋊D₁₉ #35234470