Subgroups — C₃⋊D₃×D₅₃₉ #34084591

Order 19404.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₁₆₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₃⋊D₃×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₅₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₅₃₉	—	3	4	no	maximal
5	C₃²×C₁₁×C₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₆₁₇	—	3	4	no	—
7	D₃×C₁₁×C₄₉	—	3	4	no	—
8	C₃×D₅₃₉	D₃	1	4	yes	complemented
9	C₃⋊D₃×D₇₇	—	7	1	no	maximal
10	C₂×D₅₃₉	—	9	1	no	Hall
11	C₃⋊D₃×D₄₉	—	11	1	no	maximal, Hall
12	C₃×C₁₁×C₄₉	C₂×D₃	1	4	yes	complemented
13	C₃⋊D₂₃₁	—	7	1	no	—
14	C₇×C₁₁×C₃⋊D₃	D₇	1	1	yes	characteristic
15	C₃²×D₇₇	—	7	1	no	—
16	C₂×C₁₁×C₄₉	—	9	1	no	—
17	D₅₃₉	—	9	1	no	—
18	D₅₃₉	C₃⋊D₃	1	1	yes	characteristic, direct product factor
19	D₃×D₇₇	—	21	4	no	—
20	C₃⋊D₁₄₇	—	11	1	no	—
21	C₃⋊D₃×C₄₉	D₁₁	1	1	yes	characteristic, complemented
22	C₃²×D₄₉	—	11	1	no	—
23	C₃²×C₇×C₁₁	C₂×D₇	1	1	yes	characteristic
24	D₃×D₄₉	—	33	4	no	—
25	C₁₁×C₄₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
26	D₂₃₁	—	21	4	no	—
27	D₃×C₇×C₁₁	—	3	4	no	—
28	C₃×D₇₇	—	7	4	no	—
29	C₃²×C₄₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
30	C₃⋊D₃×D₁₁	—	49	1	no	Hall
31	C₂×D₇₇	—	63	1	no	—
32	D₁₄₇	—	33	4	no	—
33	C₃×D₄₉	—	11	4	no	—
34	D₃×C₄₉	—	3	4	no	—
35	D₇×C₃⋊D₃	—	77	1	no	—
36	C₃×C₇×C₁₁	D₃×D₇	1	4	yes	—
37	C₃⋊D₃₃	—	49	1	no	—
38	C₁₁×C₃⋊D₃	D₄₉	1	1	yes	characteristic, complemented
39	C₃²×D₁₁	—	49	1	no	—
40	C₂×D₄₉	—	99	1	no	Hall
41	C₂×C₇×C₁₁	—	9	1	no	—
42	D₇₇	—	7	1	no	—
43	D₇₇	—	63	1	no	—
44	C₃×C₄₉	D₃×D₁₁	1	4	yes	complemented
45	D₃×D₁₁	—	147	4	no	—
46	C₃⋊D₂₁	—	77	1	no	—
47	C₇×C₃⋊D₃	D₇₇	1	1	yes	characteristic
48	C₃²×D₇	—	77	1	no	—
49	C₃²×C₁₁	C₂×D₄₉	1	1	yes	characteristic, complemented, Hall
50	C₂×C₄₉	—	9	1	no	—
51	D₄₉	—	11	1	no	—
52	D₄₉	—	99	1	no	—
53	D₃×D₇	—	231	4	no	—
54	C₇×C₁₁	D₇×C₃⋊D₃	1	1	yes	characteristic
55	D₃₃	—	147	4	no	—
56	C₃×D₁₁	—	49	4	no	—
57	D₃×C₁₁	—	3	4	no	—
58	C₃²×C₇	C₂×D₇₇	1	1	yes	characteristic
59	C₄₉	C₃⋊D₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
60	C₂×D₁₁	—	441	1	no	Hall
61	D₂₁	—	231	4	no	—
62	C₃×D₇	—	77	4	no	—
63	D₃×C₇	—	3	4	no	—
64	C₂×C₃⋊D₃	—	539	1	no	Hall
65	C₃×C₁₁	D₃×D₄₉	1	4	yes	complemented
66	C₂×D₇	—	693	1	no	—
67	C₂×C₁₁	—	9	1	no	—
68	D₁₁	—	49	1	no	—
69	D₁₁	—	441	1	no	—
70	C₃×C₇	D₃×D₇₇	1	4	yes	—
71	C₂×C₃²	—	539	1	no	—
72	C₃⋊D₃	—	539	1	no	—
73	C₃⋊D₃	D₅₃₉	1	1	yes	characteristic, direct product factor
74	C₂×C₇	—	9	1	no	—
75	D₇	—	77	1	no	—
76	D₇	—	693	1	no	—
77	C₂×D₃	—	1617	4	no	—
78	C₁₁	C₃⋊D₃×D₄₉	1	1	yes	characteristic, complemented, Sylow
79	C₃²	C₂×D₅₃₉	1	1	yes	characteristic, complemented, Sylow
80	C₇	C₃⋊D₃×D₇₇	1	1	yes	characteristic
81	C₂×C₃	—	539	4	no	—
82	D₃	—	3	4	no	—
83	D₃	—	1617	4	no	—
84	C₂²	—	4851	1	no	Sylow
85	C₃	D₃×D₅₃₉	1	4	yes	complemented
86	C₂	—	9	1	no	—
87	C₂	—	539	1	no	—
88	C₂	—	4851	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃²×C₁₁×C₄₉	C₂²
Frattini	C₇	C₃⋊D₃×D₇₇
socle	C₃²×C₇×C₁₁	C₂×D₇
LCS	G ▷ C₃²×C₁₁×C₄₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₁₆₁₇	C₂	semidirect
2. C₁₁×C₃⋊D₃×C₄₉	C₂	semidirect
3. C₃²×D₅₃₉	C₂	semidirect
5. C₃²×C₁₁×C₄₉	C₂²	semidirect
8. C₃×D₅₃₉	D₃	semidirect
12. C₃×C₁₁×C₄₉	C₂×D₃	semidirect
18. D₅₃₉	C₃⋊D₃	direct (N × H)
21. C₃⋊D₃×C₄₉	D₁₁	semidirect
25. C₁₁×C₄₉	C₂×C₃⋊D₃	semidirect
29. C₃²×C₄₉	C₂×D₁₁	semidirect
38. C₁₁×C₃⋊D₃	D₄₉	semidirect
44. C₃×C₄₉	D₃×D₁₁	semidirect
49. C₃²×C₁₁	C₂×D₄₉	semidirect
59. C₄₉	C₃⋊D₃×D₁₁	semidirect
65. C₃×C₁₁	D₃×D₄₉	semidirect
73. C₃⋊D₃	D₅₃₉	direct (N × H)
78. C₁₁	C₃⋊D₃×D₄₉	semidirect
79. C₃²	C₂×D₅₃₉	semidirect
85. C₃	D₃×D₅₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₁₆₁₇	2
C₁₁×C₃⋊D₃×C₄₉	2
C₃²×D₅₃₉	2
D₃×D₅₃₉	3
C₃⋊D₃×D₇₇	7
C₃⋊D₃×D₄₉	11

Subgroups — C3⋊D3×D539 #34084591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×D₅₃₉ #34084591