Subgroups — C₂×C₇×D₄₅₅ #27164972

Order 12740.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₄₅₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×D₉₁	—	5	1	no	maximal, Hall
5	C₂×D₄₅₅	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₇×D₆₅	—	7	1	no	maximal
7	C₂×C₇²×C₁₃	D₅	1	1	yes	characteristic, complemented
8	C₇×D₉₁	—	5	2	no	—
9	C₂×C₇×D₃₅	—	13	1	no	maximal, Hall
10	C₂×C₅×C₇×C₁₃	—	2	3	no	—
11	C₂×C₅×C₇×C₁₃	D₇	1	1	yes	characteristic, complemented
12	C₂×C₅×C₇×C₁₃	C₂×C₇	1	1	yes	characteristic, complemented
13	D₄₅₅	C₂×C₇	1	2	yes	direct product factor
14	C₇×D₆₅	—	7	2	no	—
15	C₇²×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×C₇²	D₁₃	1	1	yes	characteristic, complemented
17	C₇×D₃₅	—	13	2	no	—
18	C₅×C₇×C₁₃	—	2	3	no	—
19	C₅×C₇×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented
20	C₅×C₇×C₁₃	C₂²×C₇	1	1	yes	characteristic, complemented
21	C₂×D₉₁	—	5	1	no	—
22	C₂×C₇×D₁₃	—	35	1	no	—
23	C₂×D₆₅	—	7	1	no	Hall
24	C₅×C₇²	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₇×D₇	—	65	1	no	Hall
26	C₂×C₇×C₁₃	—	2	3	no	—
27	C₂×C₇×C₁₃	C₇×D₅	1	1	yes	characteristic, complemented
28	C₂×C₇×C₁₃	D₃₅	1	1	yes	characteristic, complemented
29	D₉₁	—	5	2	no	—
30	C₇×D₁₃	—	35	2	no	—
31	C₂×D₃₅	—	13	1	no	—
32	C₂×C₇×D₅	—	91	1	no	—
33	C₂×C₅×C₁₃	C₇×D₇	1	1	yes	characteristic, complemented
34	D₆₅	—	7	2	no	—
35	C₂×C₇²	D₆₅	1	1	yes	characteristic, complemented
36	C₇×D₇	—	65	2	no	—
37	C₇×C₁₃	—	2	3	no	—
38	C₇×C₁₃	C₂×C₇×D₅	1	1	yes	characteristic, complemented
39	C₇×C₁₃	C₂×D₃₅	1	1	yes	characteristic, complemented
40	C₂×C₅×C₇	—	2	3	no	—
41	C₂×C₅×C₇	C₇×D₁₃	1	1	yes	characteristic, complemented
42	C₂×C₅×C₇	D₉₁	1	1	yes	characteristic, complemented
43	D₃₅	—	13	2	no	—
44	C₇×D₅	—	91	2	no	—
45	C₅×C₁₃	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Hall
46	C₂×D₁₃	—	35	1	no	Hall
47	C₇²	C₂×D₆₅	1	1	yes	characteristic, complemented, Sylow
48	C₅×C₇	—	2	3	no	—
49	C₅×C₇	C₂×C₇×D₁₃	1	1	yes	characteristic, complemented
50	C₅×C₇	C₂×D₉₁	1	1	yes	characteristic, complemented
51	C₂²×C₇	—	455	1	no	—
52	C₂×D₇	—	65	1	no	—
53	C₂×C₁₃	C₇×D₃₅	1	1	yes	characteristic, complemented
54	D₁₃	—	35	2	no	—
55	C₂×D₅	—	91	1	no	Hall
56	C₂×C₇	—	2	3	no	—
57	C₂×C₇	—	455	2	no	—
58	C₂×C₇	C₇×D₆₅	1	1	yes	characteristic, complemented
59	C₂×C₇	D₄₅₅	1	1	yes	characteristic, direct product factor
60	D₇	—	65	2	no	—
61	C₁₃	C₂×C₇×D₃₅	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₅	C₇×D₉₁	1	1	yes	characteristic, complemented
63	D₅	—	91	2	no	—
64	C₇	—	2	3	no	—
65	C₇	C₂×C₇×D₆₅	1	1	yes	characteristic, complemented
66	C₇	C₂×D₄₅₅	1	1	yes	characteristic, direct product factor
67	C₅	C₂×C₇×D₉₁	1	1	yes	characteristic, complemented, Sylow
68	C₂²	—	455	1	no	Sylow
69	C₂	—	455	2	no	—
70	C₂	C₇×D₄₅₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	D₄₅₅
commutator, cosocle, hypocenter	C₅×C₇×C₁₃	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²×C₁₃	C₂
LCS	G ▷ C₅×C₇×C₁₃
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₄₅₅	C₂	direct (N × H)
2. C₂×C₅×C₇²×C₁₃	C₂	semidirect
3. C₅×C₇²×C₁₃	C₂²	semidirect
5. C₂×D₄₅₅	C₇	direct (N × H)
7. C₂×C₇²×C₁₃	D₅	semidirect
11. C₂×C₅×C₇×C₁₃	D₇	semidirect
12. C₂×C₅×C₇×C₁₃	C₂×C₇	semidirect
13. D₄₅₅	C₂×C₇	direct (N × H)
15. C₇²×C₁₃	C₂×D₅	semidirect
16. C₂×C₅×C₇²	D₁₃	semidirect
19. C₅×C₇×C₁₃	C₂×D₇	semidirect
20. C₅×C₇×C₁₃	C₂²×C₇	semidirect
24. C₅×C₇²	C₂×D₁₃	semidirect
27. C₂×C₇×C₁₃	C₇×D₅	semidirect
28. C₂×C₇×C₁₃	D₃₅	semidirect
33. C₂×C₅×C₁₃	C₇×D₇	semidirect
35. C₂×C₇²	D₆₅	semidirect
38. C₇×C₁₃	C₂×C₇×D₅	semidirect
39. C₇×C₁₃	C₂×D₃₅	semidirect
41. C₂×C₅×C₇	C₇×D₁₃	semidirect
42. C₂×C₅×C₇	D₉₁	semidirect
45. C₅×C₁₃	C₂×C₇×D₇	semidirect
47. C₇²	C₂×D₆₅	semidirect
49. C₅×C₇	C₂×C₇×D₁₃	semidirect
50. C₅×C₇	C₂×D₉₁	semidirect
53. C₂×C₁₃	C₇×D₃₅	semidirect
58. C₂×C₇	C₇×D₆₅	semidirect
59. C₂×C₇	D₄₅₅	direct (N × H)
61. C₁₃	C₂×C₇×D₃₅	semidirect
62. C₂×C₅	C₇×D₉₁	semidirect
65. C₇	C₂×C₇×D₆₅	semidirect
66. C₇	C₂×D₄₅₅	direct (N × H)
67. C₅	C₂×C₇×D₉₁	semidirect
70. C₂	C₇×D₄₅₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×D₄₅₅	2
C₂×C₅×C₇²×C₁₃	2
C₂×C₇×D₉₁	5
C₂×D₄₅₅	7
C₂×C₇×D₆₅	7
C₂×C₇×D₃₅	13

Subgroups — C2×C7×D455 #27164972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₄₅₅ #27164972