Subgroups — C₅×C₇×Dic₂₀₇ #44394342

Order 28980.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇×C₉×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×Dic₆₉	—	3	1	no	maximal
3	C₅×C₇×C₉×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×Dic₂₀₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₅×C₇×C₂₃	D₃	1	1	yes	characteristic
6	C₅×Dic₂₀₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₇×Dic₂₃	—	9	1	no	Hall
8	C₂×C₇×C₉×C₂₃	C₂×C₅	1	1	yes	characteristic
9	C₃×C₅×C₇×C₂₃	Dic₃	1	1	yes	characteristic
10	C₂×C₅×C₉×C₂₃	C₂×C₇	1	1	yes	characteristic
11	C₇×Dic₆₉	—	3	1	no	—
12	C₂×C₅×C₇×C₂₃	D₉	1	1	yes	characteristic
13	C₇×C₉×C₂₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
14	C₅×Dic₆₉	—	3	1	no	—
15	C₅×C₇×Dic₉	—	23	1	no	maximal, Hall
16	C₅×C₉×C₂₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₇×C₂₃	C₅×D₃	1	1	yes	characteristic
18	Dic₂₀₇	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
19	C₅×C₇×C₂₃	Dic₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₅×C₂₃	D₃×C₇	1	1	yes	characteristic
21	C₇×Dic₂₃	—	9	1	no	Hall
22	C₂×C₅×C₇×C₉	D₂₃	1	1	yes	characteristic
23	C₃×C₇×C₂₃	C₅×Dic₃	1	1	yes	characteristic
24	C₅×Dic₂₃	—	9	1	no	Hall
25	C₅×C₇×Dic₃	—	69	1	no	—
26	C₂×C₉×C₂₃	C₂×C₅×C₇	1	1	yes	characteristic
27	C₃×C₅×C₂₃	C₇×Dic₃	1	1	yes	characteristic
28	C₂×C₇×C₂₃	C₅×D₉	1	1	yes	characteristic
29	C₅×C₇×C₉	Dic₂₃	1	1	yes	characteristic, complemented, Hall
30	Dic₆₉	—	3	1	no	—
31	C₇×Dic₉	—	23	1	no	Hall
32	C₂×C₅×C₂₃	C₇×D₉	1	1	yes	characteristic
33	C₂×C₃×C₅×C₇	D₆₉	1	1	yes	characteristic
34	C₉×C₂₃	C₄×C₅×C₇	1	1	yes	characteristic, complemented, Hall
35	C₅×Dic₉	—	23	1	no	Hall
36	C₇×C₂₃	C₅×Dic₉	1	1	yes	characteristic, complemented, Hall
37	C₄×C₅×C₇	—	207	1	no	Hall
38	C₂×C₃×C₂₃	C₅×D₃×C₇	1	1	yes	characteristic
39	C₂×C₇×C₉	C₅×D₂₃	1	1	yes	characteristic
40	C₅×C₂₃	C₇×Dic₉	1	1	yes	characteristic, complemented, Hall
41	C₃×C₅×C₇	Dic₆₉	1	1	yes	characteristic
42	Dic₂₃	—	9	1	no	Hall
43	C₂×C₅×C₉	C₇×D₂₃	1	1	yes	characteristic
44	C₇×Dic₃	—	69	1	no	—
45	C₂×C₅×C₇	D₂₀₇	1	1	yes	characteristic
46	C₃×C₂₃	C₅×C₇×Dic₃	1	1	yes	characteristic
47	C₇×C₉	C₅×Dic₂₃	1	1	yes	characteristic, complemented, Hall
48	C₅×Dic₃	—	69	1	no	—
49	C₂×C₂₃	C₅×C₇×D₉	1	1	yes	characteristic
50	C₅×C₉	C₇×Dic₂₃	1	1	yes	characteristic, complemented, Hall
51	C₂×C₃×C₇	C₅×D₆₉	1	1	yes	characteristic
52	Dic₉	—	23	1	no	Hall
53	C₅×C₇	Dic₂₀₇	1	1	yes	characteristic, direct product factor, Hall
54	C₂×C₃×C₅	C₇×D₆₉	1	1	yes	characteristic
55	C₄×C₇	—	207	1	no	Hall
56	C₂₃	C₅×C₇×Dic₉	1	1	yes	characteristic, complemented, Sylow
57	C₃×C₇	C₅×Dic₆₉	1	1	yes	characteristic
58	C₄×C₅	—	207	1	no	Hall
59	C₂×C₉	C₅×C₇×D₂₃	1	1	yes	characteristic
60	C₃×C₅	C₇×Dic₆₉	1	1	yes	characteristic
61	C₂×C₇	C₅×D₂₀₇	1	1	yes	characteristic
62	Dic₃	—	69	1	no	—
63	C₂×C₅	C₇×D₂₀₇	1	1	yes	characteristic
64	C₉	C₅×C₇×Dic₂₃	1	1	yes	characteristic, complemented, Sylow
65	C₇	C₅×Dic₂₀₇	1	1	yes	characteristic, direct product factor, Sylow
66	C₂×C₃	C₅×C₇×D₆₉	1	1	yes	characteristic
67	C₅	C₇×Dic₂₀₇	1	1	yes	characteristic, direct product factor, Sylow
68	C₄	—	207	1	no	Sylow
69	C₃	C₅×C₇×Dic₆₉	1	1	yes	characteristic
70	C₂	C₅×C₇×D₂₀₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇	D₂₀₇
commutator, hypocenter	C₉×C₂₃	C₄×C₅×C₇
Frattini	C₂×C₃	C₅×C₇×D₆₉
Fitting	C₂×C₅×C₇×C₉×C₂₃	C₂
socle, prime radical	C₂×C₃×C₅×C₇×C₂₃	D₃
cosocle	C₂×C₉×C₂₃	C₂×C₅×C₇
LCS	G ▷ C₉×C₂₃
UCS	C₁ ◁ C₂×C₅×C₇

Complements

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

N	H ≅ G/N	type
3. C₅×C₇×C₉×C₂₃	C₄	semidirect
4. C₇×Dic₂₀₇	C₅	direct (N × H)
6. C₅×Dic₂₀₇	C₇	direct (N × H)
13. C₇×C₉×C₂₃	C₄×C₅	semidirect
16. C₅×C₉×C₂₃	C₄×C₇	semidirect
18. Dic₂₀₇	C₅×C₇	direct (N × H)
19. C₅×C₇×C₂₃	Dic₉	semidirect
29. C₅×C₇×C₉	Dic₂₃	semidirect
34. C₉×C₂₃	C₄×C₅×C₇	semidirect
36. C₇×C₂₃	C₅×Dic₉	semidirect
40. C₅×C₂₃	C₇×Dic₉	semidirect
47. C₇×C₉	C₅×Dic₂₃	semidirect
50. C₅×C₉	C₇×Dic₂₃	semidirect
53. C₅×C₇	Dic₂₀₇	direct (N × H)
56. C₂₃	C₅×C₇×Dic₉	semidirect
64. C₉	C₅×C₇×Dic₂₃	semidirect
65. C₇	C₅×Dic₂₀₇	direct (N × H)
67. C₅	C₇×Dic₂₀₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₇×C₉×C₂₃	2
C₅×C₇×Dic₆₉	3
C₇×Dic₂₀₇	5
C₅×Dic₂₀₇	7
C₅×C₇×Dic₉	23

Subgroups — C5×C7×Dic207 #44394342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×Dic₂₀₇ #44394342