Subgroups — C₃×D₅×D₅₁₉ #44528186

Order 31140.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₅×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×D₅₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₅₉₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₅₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×D₅×D₁₇₃	—	3	1	no	maximal
6	C₃²×C₅×C₁₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×D₅₁₉	—	5	1	no	maximal, Hall
8	D₂₅₉₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₅₁₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₈₆₅	—	3	1	no	—
11	C₃×D₅×C₁₇₃	—	2	1	no	—
12	C₃×D₅×C₁₇₃	D₃	1	1	yes	characteristic, complemented
13	C₃×D₅×C₁₇₃	C₂×C₃	1	1	yes	characteristic, complemented
14	C₃×C₅×D₁₇₃	—	3	1	no	—
15	D₅×D₁₇₃	—	3	1	no	Hall
16	C₃×D₅₁₉	—	5	1	no	—
17	C₃×D₅₁₉	D₅	1	1	yes	characteristic, direct product factor
18	C₂×C₃²×C₁₇₃	—	5	1	no	—
19	C₃×C₅×C₁₇₃	—	2	1	no	—
20	C₃×C₅×C₁₇₃	C₂×D₃	1	1	yes	characteristic, complemented
21	C₃×C₅×C₁₇₃	C₂²×C₃	1	1	yes	characteristic, complemented
22	C₂×C₃×D₁₇₃	—	15	1	no	—
23	C₂×D₅₁₉	—	5	1	no	—
24	D₈₆₅	—	3	1	no	—
25	C₅×D₁₇₃	—	3	1	no	—
26	D₅×C₁₇₃	C₃×D₃	1	1	yes	characteristic, complemented
27	C₃²×C₁₇₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₁₇₃	—	5	1	no	—
29	C₂×C₃×C₁₇₃	—	5	1	no	—
30	C₂×C₃×C₁₇₃	—	10	1	no	—
31	D₅₁₉	—	5	1	no	—
32	D₅₁₉	C₃×D₅	1	1	yes	characteristic, direct product factor
33	C₃×D₁₇₃	—	3	1	no	—
34	C₃×D₁₇₃	—	15	1	no	—
35	C₅×C₁₇₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
36	C₂×D₁₇₃	—	15	1	no	Hall
37	C₃×C₁₇₃	—	2	1	no	—
38	C₃×C₁₇₃	D₃×D₅	1	1	yes	characteristic, complemented
39	C₃×C₁₇₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented
40	C₂×C₁₇₃	—	5	1	no	—
41	D₁₇₃	—	3	1	no	—
42	D₁₇₃	—	15	1	no	—
43	C₃×D₃×D₅	—	173	1	no	maximal, Hall
44	C₁₇₃	C₃×D₃×D₅	1	1	yes	characteristic, complemented, Sylow
45	C₃×D₁₅	—	173	1	no	—
46	C₃×C₅×D₃	—	173	1	no	—
47	C₃²×D₅	D₁₇₃	1	1	yes	characteristic, complemented
48	C₂×C₃×D₅	—	519	1	no	—
49	D₃×D₅	—	173	1	no	—
50	C₃²×C₅	C₂×D₁₇₃	1	1	yes	characteristic, complemented, Hall
51	C₂×C₃×D₃	—	865	1	no	Hall
52	C₂×C₃×C₅	—	519	1	no	—
53	D₁₅	—	173	1	no	—
54	C₃×D₅	—	2	1	no	—
55	C₃×D₅	—	519	1	no	—
56	C₃×D₅	C₃×D₁₇₃	1	1	yes	characteristic, complemented
57	C₃×D₅	D₅₁₉	1	1	yes	characteristic, direct product factor
58	C₅×D₃	—	173	1	no	—
59	C₂×D₅	—	519	1	no	Hall
60	C₂×C₃²	—	5	1	no	—
61	C₃×D₃	—	865	1	no	—
62	C₃×D₃	—	173	1	no	—
63	C₃×C₅	—	2	1	no	—
64	C₃×C₅	C₂×D₅₁₉	1	1	yes	characteristic, complemented
65	C₃×C₅	C₂×C₃×D₁₇₃	1	1	yes	characteristic, complemented
66	C₂²×C₃	—	2595	1	no	—
67	C₂×D₃	—	865	1	no	—
68	C₂×C₅	—	519	1	no	—
69	D₅	—	519	1	no	—
70	D₅	C₃×D₅₁₉	1	1	yes	characteristic, direct product factor
71	C₃²	D₅×D₁₇₃	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃	—	5	1	no	—
73	C₂×C₃	—	5	1	no	—
74	C₂×C₃	—	519	1	no	—
75	C₂×C₃	—	10	1	no	—
76	C₂×C₃	—	2595	1	no	—
77	D₃	—	865	1	no	—
78	D₃	—	173	1	no	—
79	C₅	C₂×C₃×D₅₁₉	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	2595	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	C₃×D₅×D₁₇₃	1	1	yes	characteristic, complemented
83	C₃	D₅×D₅₁₉	1	1	yes	characteristic, direct product factor
84	C₂	—	5	1	no	—
85	C₂	—	519	1	no	—
86	C₂	—	2595	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₅×D₅₁₉
commutator, cosocle, hypocenter	C₃×C₅×C₁₇₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₇₃	C₂²
LCS	G ▷ C₃×C₅×C₁₇₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×D₅×C₁₇₃	C₂	semidirect
2. C₃×C₅×D₅₁₉	C₂	semidirect
3. C₃×D₂₅₉₅	C₂	semidirect
4. D₅×D₅₁₉	C₃	direct (N × H)
6. C₃²×C₅×C₁₇₃	C₂²	semidirect
8. D₂₅₉₅	C₂×C₃	semidirect
9. C₅×D₅₁₉	C₂×C₃	semidirect
12. C₃×D₅×C₁₇₃	D₃	semidirect
13. C₃×D₅×C₁₇₃	C₂×C₃	semidirect
17. C₃×D₅₁₉	D₅	direct (N × H)
20. C₃×C₅×C₁₇₃	C₂×D₃	semidirect
21. C₃×C₅×C₁₇₃	C₂²×C₃	semidirect
26. D₅×C₁₇₃	C₃×D₃	semidirect
27. C₃²×C₁₇₃	C₂×D₅	semidirect
32. D₅₁₉	C₃×D₅	direct (N × H)
35. C₅×C₁₇₃	C₂×C₃×D₃	semidirect
38. C₃×C₁₇₃	D₃×D₅	semidirect
39. C₃×C₁₇₃	C₂×C₃×D₅	semidirect
44. C₁₇₃	C₃×D₃×D₅	semidirect
47. C₃²×D₅	D₁₇₃	semidirect
50. C₃²×C₅	C₂×D₁₇₃	semidirect
56. C₃×D₅	C₃×D₁₇₃	semidirect
57. C₃×D₅	D₅₁₉	direct (N × H)
64. C₃×C₅	C₂×D₅₁₉	semidirect
65. C₃×C₅	C₂×C₃×D₁₇₃	semidirect
70. D₅	C₃×D₅₁₉	direct (N × H)
71. C₃²	D₅×D₁₇₃	semidirect
79. C₅	C₂×C₃×D₅₁₉	semidirect
82. C₃	C₃×D₅×D₁₇₃	semidirect
83. C₃	D₅×D₅₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×D₅×C₁₇₃	2
C₃×C₅×D₅₁₉	2
C₃×D₂₅₉₅	2
D₅×D₅₁₉	3
C₃×D₅×D₁₇₃	3
C₂×C₃×D₅₁₉	5
C₃×D₃×D₅	173

Subgroups — C3×D5×D519 #44528186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×D₅₁₉ #44528186