Subgroups — C₇×D₇×D₁₄₅ #43249359

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	C₇²×D₁₄₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₁₀₁₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇²×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×D₇×D₂₉	—	5	1	no	maximal, Hall
6	C₂×C₇×D₁₄₅	—	7	1	no	maximal
7	D₇×D₁₄₅	C₇	1	1	yes	maximal, characteristic, direct product factor
8	C₇×D₂₀₃	—	5	1	no	—
9	C₇×D₇×C₂₉	D₅	1	1	yes	characteristic, complemented
10	C₇²×D₂₉	—	5	1	no	—
11	D₁₀₁₅	C₂×C₇	1	1	yes	characteristic, complemented
12	C₇×D₁₄₅	—	2	3	no	—
13	C₇×D₁₄₅	—	7	1	no	—
14	C₇×D₁₄₅	D₇	1	1	yes	characteristic, direct product factor
15	C₇×D₁₄₅	C₂×C₇	1	1	yes	characteristic, complemented
16	C₅×D₇×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented
17	C₂×C₅×C₇×C₂₉	—	7	1	no	—
18	C₇²×C₂₉	C₂×D₅	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	C₂²×C₇	1	1	yes	characteristic, complemented
22	C₇×D₅×D₇	—	29	1	no	maximal, Hall
23	C₂×C₇×D₂₉	—	35	1	no	—
24	D₇×D₂₉	—	5	1	no	—
25	C₂×D₁₄₅	—	7	1	no	Hall
26	C₇×D₃₅	—	29	1	no	—
27	C₇²×D₅	—	29	1	no	—
28	C₅×C₇×D₇	D₂₉	1	1	yes	characteristic, complemented
29	C₂×C₇×C₂₉	—	7	1	no	—
30	D₂₀₃	—	5	1	no	—
31	C₇×D₂₉	—	5	1	no	—
32	C₇×D₂₉	—	5	1	no	—
33	C₇×D₂₉	—	10	3	no	—
34	C₇×D₂₉	—	35	1	no	—
35	D₇×C₂₉	C₇×D₅	1	1	yes	characteristic, complemented
36	C₂×C₅×C₂₉	—	7	1	no	—
37	D₁₄₅	—	7	1	no	—
38	D₁₄₅	C₇×D₇	1	1	yes	characteristic, direct product factor
39	C₅×C₇²	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
40	C₇×C₂₉	—	2	3	no	—
41	C₇×C₂₉	D₅×D₇	1	1	yes	characteristic, complemented
42	C₇×C₂₉	C₂×C₇×D₅	1	1	yes	characteristic, complemented
43	C₂×C₇×D₇	—	145	1	no	Hall
44	C₅×C₂₉	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Hall
45	C₂×C₇×D₅	—	203	1	no	—
46	D₅×D₇	—	29	1	no	—
47	C₂×D₂₉	—	35	1	no	Hall
48	C₂×C₇²	—	145	1	no	—
49	C₇×D₇	—	145	1	no	—
50	C₇×D₇	D₁₄₅	1	1	yes	characteristic, direct product factor
51	C₂×C₅×C₇	—	7	1	no	—
52	D₃₅	—	29	1	no	—
53	C₅×D₇	C₇×D₂₉	1	1	yes	characteristic, complemented
54	C₇×D₅	—	29	1	no	—
55	C₇×D₅	—	29	1	no	—
56	C₇×D₅	—	58	3	no	—
57	C₇×D₅	—	203	1	no	—
58	C₂×C₂₉	—	7	1	no	—
59	D₂₉	—	5	1	no	—
60	D₂₉	—	35	1	no	—
61	C₇²	C₂×D₁₄₅	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×C₇×D₂₉	1	1	yes	characteristic, complemented
65	C₂₉	C₇×D₅×D₇	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₇	—	1015	1	no	—
67	C₂×D₇	—	145	1	no	—
68	C₂×D₅	—	203	1	no	Hall
69	C₂×C₇	—	7	1	no	—
70	C₂×C₇	—	290	3	no	—
71	C₂×C₇	—	145	1	no	—
72	C₂×C₇	—	145	1	no	—
73	C₂×C₇	—	1015	1	no	—
74	D₇	—	145	1	no	—
75	D₇	C₇×D₁₄₅	1	1	yes	characteristic, direct product factor
76	C₂×C₅	—	7	1	no	—
77	D₅	—	29	1	no	—
78	D₅	—	203	1	no	—
79	C₇	—	2	3	no	—
80	C₇	D₇×D₁₄₅	1	1	yes	characteristic, direct product factor
81	C₇	C₂×C₇×D₁₄₅	1	1	yes	characteristic, complemented
82	C₅	C₇×D₇×D₂₉	1	1	yes	characteristic, complemented, Sylow
83	C₂²	—	1015	1	no	Sylow
84	C₂	—	7	1	no	—
85	C₂	—	145	1	no	—
86	C₂	—	1015	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₇×D₁₄₅
commutator, cosocle, hypocenter	C₅×C₇×C₂₉	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₂₉	C₂²
LCS	G ▷ C₅×C₇×C₂₉
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×D₇×C₂₉	C₂	semidirect
2. C₇²×D₁₄₅	C₂	semidirect
3. C₇×D₁₀₁₅	C₂	semidirect
4. C₅×C₇²×C₂₉	C₂²	semidirect
7. D₇×D₁₄₅	C₇	direct (N × H)
9. C₇×D₇×C₂₉	D₅	semidirect
11. D₁₀₁₅	C₂×C₇	semidirect
14. C₇×D₁₄₅	D₇	direct (N × H)
15. C₇×D₁₄₅	C₂×C₇	semidirect
16. C₅×D₇×C₂₉	C₂×C₇	semidirect
18. C₇²×C₂₉	C₂×D₅	semidirect
20. C₅×C₇×C₂₉	C₂×D₇	semidirect
21. C₅×C₇×C₂₉	C₂²×C₇	semidirect
28. C₅×C₇×D₇	D₂₉	semidirect
35. D₇×C₂₉	C₇×D₅	semidirect
38. D₁₄₅	C₇×D₇	direct (N × H)
39. C₅×C₇²	C₂×D₂₉	semidirect
41. C₇×C₂₉	D₅×D₇	semidirect
42. C₇×C₂₉	C₂×C₇×D₅	semidirect
44. C₅×C₂₉	C₂×C₇×D₇	semidirect
50. C₇×D₇	D₁₄₅	direct (N × H)
53. C₅×D₇	C₇×D₂₉	semidirect
61. C₇²	C₂×D₁₄₅	semidirect
63. C₅×C₇	D₇×D₂₉	semidirect
64. C₅×C₇	C₂×C₇×D₂₉	semidirect
65. C₂₉	C₇×D₅×D₇	semidirect
75. D₇	C₇×D₁₄₅	direct (N × H)
80. C₇	D₇×D₁₄₅	direct (N × H)
81. C₇	C₂×C₇×D₁₄₅	semidirect
82. C₅	C₇×D₇×D₂₉	semidirect

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
C₇²×D₁₄₅	2
C₇×D₁₀₁₅	2
C₇×D₇×D₂₉	5
C₂×C₇×D₁₄₅	7
D₇×D₁₄₅	7
C₇×D₅×D₇	29

Subgroups — C7×D7×D145 #43249359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₇×D₁₄₅ #43249359