Subgroups — C₃×D₁₃×D₂₁₅ #46776550

Order 33540.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₇₉₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₃×D₂₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₁₃×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₂₁₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₁₃×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₁₃×D₄₃	—	5	1	no	maximal, Hall
7	D₂₇₉₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₃×D₂₁₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₁₃×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₅₅₉	—	5	1	no	—
11	C₃×D₁₃×C₄₃	D₅	1	1	yes	characteristic, complemented
12	C₃×C₁₃×D₄₃	—	5	1	no	—
13	C₅×C₁₃×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×D₂₁₅	—	13	1	no	maximal, Hall
15	D₁₃×D₄₃	—	5	1	no	Hall
16	C₃×C₁₃×C₄₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₅×C₄₃	—	13	1	no	—
18	C₃×D₂₁₅	—	13	1	no	—
19	C₃×D₂₁₅	D₁₃	1	1	yes	characteristic, direct product factor
20	D₅₅₉	—	5	1	no	—
21	C₁₃×D₄₃	—	5	1	no	—
22	D₁₃×C₄₃	C₃×D₅	1	1	yes	characteristic, complemented
23	C₂×D₂₁₅	—	13	1	no	Hall
24	C₃×D₅×D₁₃	—	43	1	no	maximal, Hall
25	C₃×C₅×C₄₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
26	C₁₃×C₄₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×D₄₃	—	65	1	no	Hall
28	C₂×C₅×C₄₃	—	13	1	no	—
29	D₂₁₅	—	13	1	no	—
30	D₂₁₅	C₃×D₁₃	1	1	yes	characteristic, direct product factor
31	C₃×D₆₅	—	43	1	no	—
32	C₃×D₅×C₁₃	—	43	1	no	—
33	C₃×C₅×D₁₃	D₄₃	1	1	yes	characteristic, complemented
34	D₅×D₁₃	—	43	1	no	Hall
35	C₂×C₃×C₄₃	—	13	1	no	—
36	C₃×D₄₃	—	5	1	no	—
37	C₃×D₄₃	—	65	1	no	—
38	C₅×C₄₃	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
39	C₃×C₅×C₁₃	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
40	C₂×D₄₃	—	65	1	no	Hall
41	C₂×C₃×D₁₃	—	215	1	no	Hall
42	D₆₅	—	43	1	no	—
43	C₅×D₁₃	C₃×D₄₃	1	1	yes	characteristic, complemented
44	D₅×C₁₃	—	43	1	no	—
45	C₃×C₄₃	D₅×D₁₃	1	1	yes	characteristic, complemented, Hall
46	C₂×C₄₃	—	13	1	no	—
47	D₄₃	—	5	1	no	—
48	D₄₃	—	65	1	no	—
49	C₂×C₃×C₁₃	—	215	1	no	—
50	C₃×D₁₃	—	215	1	no	—
51	C₃×D₁₃	D₂₁₅	1	1	yes	characteristic, direct product factor
52	C₅×C₁₃	C₂×C₃×D₄₃	1	1	yes	characteristic, complemented, Hall
53	C₂×C₃×D₅	—	559	1	no	Hall
54	C₂×D₁₃	—	215	1	no	Hall
55	C₄₃	C₃×D₅×D₁₃	1	1	yes	characteristic, complemented, Sylow
56	C₃×C₁₃	C₂×D₂₁₅	1	1	yes	characteristic, complemented, Hall
57	C₂×C₃×C₅	—	13	1	no	—
58	C₃×D₅	—	43	1	no	—
59	C₃×D₅	—	559	1	no	—
60	C₂×C₁₃	—	215	1	no	—
61	D₁₃	—	215	1	no	—
62	D₁₃	C₃×D₂₁₅	1	1	yes	characteristic, direct product factor
63	C₂×D₅	—	559	1	no	Hall
64	C₃×C₅	D₁₃×D₄₃	1	1	yes	characteristic, complemented, Hall
65	C₁₃	C₂×C₃×D₂₁₅	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₃	—	2795	1	no	Hall
67	C₂×C₅	—	13	1	no	—
68	D₅	—	43	1	no	—
69	D₅	—	559	1	no	—
70	C₂×C₃	—	13	1	no	—
71	C₂×C₃	—	215	1	no	—
72	C₂×C₃	—	2795	1	no	—
73	C₅	C₃×D₁₃×D₄₃	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	2795	1	no	Sylow
75	C₃	D₁₃×D₂₁₅	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	13	1	no	—
77	C₂	—	215	1	no	—
78	C₂	—	2795	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₁₃×D₂₁₅
commutator, cosocle, hypocenter	C₅×C₁₃×C₄₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₄₃	C₂²
LCS	G ▷ C₅×C₁₃×C₄₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₂₇₉₅	C₂	semidirect
2. C₃×C₁₃×D₂₁₅	C₂	semidirect
3. C₃×C₅×D₁₃×C₄₃	C₂	semidirect
4. D₁₃×D₂₁₅	C₃	direct (N × H)
5. C₃×C₅×C₁₃×C₄₃	C₂²	semidirect
7. D₂₇₉₅	C₂×C₃	semidirect
8. C₁₃×D₂₁₅	C₂×C₃	semidirect
9. C₅×D₁₃×C₄₃	C₂×C₃	semidirect
11. C₃×D₁₃×C₄₃	D₅	semidirect
13. C₅×C₁₃×C₄₃	C₂²×C₃	semidirect
16. C₃×C₁₃×C₄₃	C₂×D₅	semidirect
19. C₃×D₂₁₅	D₁₃	direct (N × H)
22. D₁₃×C₄₃	C₃×D₅	semidirect
25. C₃×C₅×C₄₃	C₂×D₁₃	semidirect
26. C₁₃×C₄₃	C₂×C₃×D₅	semidirect
30. D₂₁₅	C₃×D₁₃	direct (N × H)
33. C₃×C₅×D₁₃	D₄₃	semidirect
38. C₅×C₄₃	C₂×C₃×D₁₃	semidirect
39. C₃×C₅×C₁₃	C₂×D₄₃	semidirect
43. C₅×D₁₃	C₃×D₄₃	semidirect
45. C₃×C₄₃	D₅×D₁₃	semidirect
51. C₃×D₁₃	D₂₁₅	direct (N × H)
52. C₅×C₁₃	C₂×C₃×D₄₃	semidirect
55. C₄₃	C₃×D₅×D₁₃	semidirect
56. C₃×C₁₃	C₂×D₂₁₅	semidirect
62. D₁₃	C₃×D₂₁₅	direct (N × H)
64. C₃×C₅	D₁₃×D₄₃	semidirect
65. C₁₃	C₂×C₃×D₂₁₅	semidirect
73. C₅	C₃×D₁₃×D₄₃	semidirect
75. C₃	D₁₃×D₂₁₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₂₇₉₅	2
C₃×C₁₃×D₂₁₅	2
C₃×C₅×D₁₃×C₄₃	2
D₁₃×D₂₁₅	3
C₃×D₁₃×D₄₃	5
C₂×C₃×D₂₁₅	13
C₃×D₅×D₁₃	43

Subgroups — C3×D13×D215 #46776550

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₁₃×D₂₁₅ #46776550