Subgroups — C₃×D₇×D₁₅₅ #27189227

Order 13020.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₀₈₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₇×D₁₅₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₁₅₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₇×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₇×D₃₁	—	5	1	no	maximal, Hall
7	D₁₀₈₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×D₁₅₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₇×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₃×D₁₅₅	—	7	1	no	maximal, Hall
11	C₃×D₂₁₇	—	5	1	no	—
12	C₃×D₇×C₃₁	D₅	1	1	yes	characteristic, complemented
13	C₃×C₇×D₃₁	—	5	1	no	—
14	C₅×C₇×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅×C₃₁	—	7	1	no	—
16	C₃×D₁₅₅	—	7	1	no	—
17	C₃×D₁₅₅	D₇	1	1	yes	characteristic, direct product factor
18	D₇×D₃₁	—	5	1	no	Hall
19	C₃×C₇×C₃₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×D₁₅₅	—	7	1	no	Hall
21	C₃×C₅×C₃₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	D₂₁₇	—	5	1	no	—
23	C₇×D₃₁	—	5	1	no	—
24	D₇×C₃₁	C₃×D₅	1	1	yes	characteristic, complemented
25	C₃×D₅×D₇	—	31	1	no	maximal, Hall
26	C₂×C₃×D₃₁	—	35	1	no	Hall
27	C₂×C₅×C₃₁	—	7	1	no	—
28	D₁₅₅	—	7	1	no	—
29	D₁₅₅	C₃×D₇	1	1	yes	characteristic, direct product factor
30	C₇×C₃₁	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
31	C₃×D₃₅	—	31	1	no	—
32	C₃×C₇×D₅	—	31	1	no	—
33	C₃×C₅×D₇	D₃₁	1	1	yes	characteristic, complemented
34	C₂×C₃×C₃₁	—	7	1	no	—
35	C₃×D₃₁	—	5	1	no	—
36	C₃×D₃₁	—	35	1	no	—
37	C₅×C₃₁	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
38	D₅×D₇	—	31	1	no	Hall
39	C₂×D₃₁	—	35	1	no	Hall
40	C₃×C₅×C₇	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
41	C₃×C₃₁	D₅×D₇	1	1	yes	characteristic, complemented, Hall
42	C₂×C₃×D₇	—	155	1	no	Hall
43	D₃₅	—	31	1	no	—
44	C₅×D₇	C₃×D₃₁	1	1	yes	characteristic, complemented
45	C₇×D₅	—	31	1	no	—
46	C₂×C₃₁	—	7	1	no	—
47	D₃₁	—	5	1	no	—
48	D₃₁	—	35	1	no	—
49	C₂×C₃×D₅	—	217	1	no	Hall
50	C₂×C₃×C₇	—	155	1	no	—
51	C₃×D₇	—	155	1	no	—
52	C₃×D₇	D₁₅₅	1	1	yes	characteristic, direct product factor
53	C₅×C₇	C₂×C₃×D₃₁	1	1	yes	characteristic, complemented, Hall
54	C₃₁	C₃×D₅×D₇	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₃×C₅	—	7	1	no	—
56	C₃×D₅	—	31	1	no	—
57	C₃×D₅	—	217	1	no	—
58	C₂×D₇	—	155	1	no	Hall
59	C₃×C₇	C₂×D₁₅₅	1	1	yes	characteristic, complemented, Hall
60	C₂×D₅	—	217	1	no	Hall
61	C₃×C₅	D₇×D₃₁	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	155	1	no	—
63	D₇	—	155	1	no	—
64	D₇	C₃×D₁₅₅	1	1	yes	characteristic, direct product factor
65	C₂²×C₃	—	1085	1	no	Hall
66	C₂×C₅	—	7	1	no	—
67	D₅	—	31	1	no	—
68	D₅	—	217	1	no	—
69	C₇	C₂×C₃×D₁₅₅	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	7	1	no	—
71	C₂×C₃	—	1085	1	no	—
72	C₂×C₃	—	155	1	no	—
73	C₅	C₃×D₇×D₃₁	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	1085	1	no	Sylow
75	C₃	D₇×D₁₅₅	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	7	1	no	—
77	C₂	—	1085	1	no	—
78	C₂	—	155	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₇×D₁₅₅
commutator, cosocle, hypocenter	C₅×C₇×C₃₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₃₁	C₂²
LCS	G ▷ C₅×C₇×C₃₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₀₈₅	C₂	semidirect
2. C₃×C₇×D₁₅₅	C₂	semidirect
3. C₃×C₅×D₇×C₃₁	C₂	semidirect
4. D₇×D₁₅₅	C₃	direct (N × H)
5. C₃×C₅×C₇×C₃₁	C₂²	semidirect
7. D₁₀₈₅	C₂×C₃	semidirect
8. C₇×D₁₅₅	C₂×C₃	semidirect
9. C₅×D₇×C₃₁	C₂×C₃	semidirect
12. C₃×D₇×C₃₁	D₅	semidirect
14. C₅×C₇×C₃₁	C₂²×C₃	semidirect
17. C₃×D₁₅₅	D₇	direct (N × H)
19. C₃×C₇×C₃₁	C₂×D₅	semidirect
21. C₃×C₅×C₃₁	C₂×D₇	semidirect
24. D₇×C₃₁	C₃×D₅	semidirect
29. D₁₅₅	C₃×D₇	direct (N × H)
30. C₇×C₃₁	C₂×C₃×D₅	semidirect
33. C₃×C₅×D₇	D₃₁	semidirect
37. C₅×C₃₁	C₂×C₃×D₇	semidirect
40. C₃×C₅×C₇	C₂×D₃₁	semidirect
41. C₃×C₃₁	D₅×D₇	semidirect
44. C₅×D₇	C₃×D₃₁	semidirect
52. C₃×D₇	D₁₅₅	direct (N × H)
53. C₅×C₇	C₂×C₃×D₃₁	semidirect
54. C₃₁	C₃×D₅×D₇	semidirect
59. C₃×C₇	C₂×D₁₅₅	semidirect
61. C₃×C₅	D₇×D₃₁	semidirect
64. D₇	C₃×D₁₅₅	direct (N × H)
69. C₇	C₂×C₃×D₁₅₅	semidirect
73. C₅	C₃×D₇×D₃₁	semidirect
75. C₃	D₇×D₁₅₅	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×D₁₀₈₅	2
C₃×C₇×D₁₅₅	2
C₃×C₅×D₇×C₃₁	2
D₇×D₁₅₅	3
C₃×D₇×D₃₁	5
C₂×C₃×D₁₅₅	7
C₃×D₅×D₇	31

Subgroups — C3×D7×D155 #27189227

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₇×D₁₅₅ #27189227