Subgroups — C₅×D₇×D₂₀₃ #43249331

Order 28420.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₇×D₂₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇⋊D₂₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇²×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₇×D₂₀₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×D₂₀₃	—	7	1	no	maximal
7	C₅×D₇×D₂₉	—	7	1	no	maximal
8	C₇⋊D₂₀₃	C₂×C₅	1	1	yes	characteristic, complemented
9	C₇×D₂₀₃	C₂×C₅	1	1	yes	characteristic, complemented
10	C₇×D₇×C₂₉	C₂×C₅	1	1	yes	characteristic, complemented
11	C₅×D₂₀₃	—	7	1	no	—
12	C₅×D₂₀₃	—	7	1	no	—
13	C₅×D₂₀₃	—	14	3	no	—
14	C₅×D₂₀₃	D₇	1	1	yes	characteristic, direct product factor
15	C₅×D₇×C₂₉	D₇	1	1	yes	characteristic, complemented
16	C₅×C₇×D₂₉	—	7	1	no	—
17	C₂×C₅×C₇×C₂₉	—	7	1	no	—
18	C₇²×C₂₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
19	C₅×C₇×C₂₉	—	2	3	no	—
20	C₅×C₇×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented
21	C₅×C₇×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented
22	C₅×D₇²	—	29	1	no	maximal, Hall
23	C₂×D₂₀₃	—	7	1	no	—
24	D₇×D₂₉	—	7	1	no	—
25	C₂×C₅×D₂₉	—	49	1	no	Hall
26	C₅×C₇⋊D₇	—	29	1	no	—
27	C₅×C₇×D₇	—	29	1	no	—
28	C₅×C₇×D₇	D₂₉	1	1	yes	characteristic, complemented
29	C₂×C₇×C₂₉	—	7	1	no	—
30	D₂₀₃	—	7	1	no	—
31	D₂₀₃	—	7	1	no	—
32	D₂₀₃	—	14	3	no	—
33	D₂₀₃	C₅×D₇	1	1	yes	characteristic, direct product factor
34	C₇×D₂₉	—	7	1	no	—
35	D₇×C₂₉	C₅×D₇	1	1	yes	characteristic, complemented
36	C₂×C₅×C₂₉	—	7	1	no	—
37	C₅×D₂₉	—	7	1	no	—
38	C₅×D₂₉	—	49	1	no	—
39	C₅×C₇²	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
40	C₇×C₂₉	—	2	3	no	—
41	C₇×C₂₉	C₂×C₅×D₇	1	1	yes	characteristic, complemented
42	C₇×C₂₉	C₂×C₅×D₇	1	1	yes	characteristic, complemented
43	D₇²	—	29	1	no	Hall
44	C₅×C₂₉	D₇²	1	1	yes	characteristic, complemented, Hall
45	C₂×C₅×D₇	—	203	1	no	—
46	C₂×C₅×D₇	—	203	1	no	—
47	C₂×D₂₉	—	49	1	no	Hall
48	C₇⋊D₇	—	29	1	no	—
49	C₇×D₇	—	29	1	no	—
50	C₇×D₇	C₅×D₂₉	1	1	yes	characteristic, complemented
51	C₂×C₅×C₇	—	7	1	no	—
52	C₂×C₅×C₇	—	203	1	no	—
53	C₅×D₇	—	29	1	no	—
54	C₅×D₇	—	406	3	no	—
55	C₅×D₇	—	203	1	no	—
56	C₅×D₇	—	203	1	no	—
57	C₅×D₇	D₂₀₃	1	1	yes	characteristic, direct product factor
58	C₂×C₂₉	—	7	1	no	—
59	D₂₉	—	7	1	no	—
60	D₂₉	—	49	1	no	—
61	C₇²	C₂×C₅×D₂₉	1	1	yes	characteristic, complemented, Sylow
62	C₅×C₇	—	2	3	no	—
63	C₅×C₇	D₇×D₂₉	1	1	yes	characteristic, complemented
64	C₅×C₇	C₂×D₂₀₃	1	1	yes	characteristic, complemented
65	C₂₉	C₅×D₇²	1	1	yes	characteristic, complemented, Sylow
66	C₂×D₇	—	203	1	no	—
67	C₂×D₇	—	203	1	no	—
68	C₂²×C₅	—	1421	1	no	Hall
69	C₂×C₇	—	7	1	no	—
70	C₂×C₇	—	203	1	no	—
71	D₇	—	29	1	no	—
72	D₇	—	406	3	no	—
73	D₇	—	203	1	no	—
74	D₇	—	203	1	no	—
75	D₇	C₅×D₂₀₃	1	1	yes	characteristic, direct product factor
76	C₂×C₅	—	7	1	no	—
77	C₂×C₅	—	1421	1	no	—
78	C₂×C₅	—	203	1	no	—
79	C₇	—	2	3	no	—
80	C₇	C₅×D₇×D₂₉	1	1	yes	characteristic, complemented
81	C₇	C₂×C₅×D₂₀₃	1	1	yes	characteristic, complemented
82	C₅	D₇×D₂₀₃	1	1	yes	characteristic, direct product factor, Sylow
83	C₂²	—	1421	1	no	Sylow
84	C₂	—	7	1	no	—
85	C₂	—	1421	1	no	—
86	C₂	—	203	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₇×D₂₀₃
commutator, cosocle, hypocenter	C₇²×C₂₉	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₂₉	C₂²
LCS	G ▷ C₇²×C₂₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×D₇×C₂₉	C₂	semidirect
2. C₅×C₇×D₂₀₃	C₂	semidirect
3. C₅×C₇⋊D₂₀₃	C₂	semidirect
4. C₅×C₇²×C₂₉	C₂²	semidirect
5. D₇×D₂₀₃	C₅	direct (N × H)
8. C₇⋊D₂₀₃	C₂×C₅	semidirect
9. C₇×D₂₀₃	C₂×C₅	semidirect
10. C₇×D₇×C₂₉	C₂×C₅	semidirect
14. C₅×D₂₀₃	D₇	direct (N × H)
15. C₅×D₇×C₂₉	D₇	semidirect
18. C₇²×C₂₉	C₂²×C₅	semidirect
20. C₅×C₇×C₂₉	C₂×D₇	semidirect
21. C₅×C₇×C₂₉	C₂×D₇	semidirect
28. C₅×C₇×D₇	D₂₉	semidirect
33. D₂₀₃	C₅×D₇	direct (N × H)
35. D₇×C₂₉	C₅×D₇	semidirect
39. C₅×C₇²	C₂×D₂₉	semidirect
41. C₇×C₂₉	C₂×C₅×D₇	semidirect
42. C₇×C₂₉	C₂×C₅×D₇	semidirect
44. C₅×C₂₉	D₇²	semidirect
50. C₇×D₇	C₅×D₂₉	semidirect
57. C₅×D₇	D₂₀₃	direct (N × H)
61. C₇²	C₂×C₅×D₂₉	semidirect
63. C₅×C₇	D₇×D₂₉	semidirect
64. C₅×C₇	C₂×D₂₀₃	semidirect
65. C₂₉	C₅×D₇²	semidirect
75. D₇	C₅×D₂₀₃	direct (N × H)
80. C₇	C₅×D₇×D₂₉	semidirect
81. C₇	C₂×C₅×D₂₀₃	semidirect
82. C₅	D₇×D₂₀₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₇×D₇×C₂₉	2
C₅×C₇×D₂₀₃	2
C₅×C₇⋊D₂₀₃	2
D₇×D₂₀₃	5
C₂×C₅×D₂₀₃	7
C₅×D₇×D₂₉	7
C₅×D₇²	29

Subgroups — C5×D7×D203 #43249331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₇×D₂₀₃ #43249331