Subgroups — C₅×D₇×D₂₅₃ #47978439

Order 35420.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₇₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₁×D₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×D₂₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇×C₁₁×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₇×D₂₅₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×D₂₅₃	—	7	1	no	maximal, Hall
7	D₁₇₇₁	C₂×C₅	1	1	yes	characteristic, complemented
8	C₁₁×D₇×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented
9	C₇×D₂₅₃	C₂×C₅	1	1	yes	characteristic, complemented
10	C₅×D₇×D₂₃	—	11	1	no	maximal, Hall
11	C₅×D₂₅₃	—	7	1	no	—
12	C₅×D₂₅₃	D₇	1	1	yes	characteristic, direct product factor
13	C₂×C₅×C₁₁×C₂₃	—	7	1	no	—
14	C₇×C₁₁×C₂₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
15	C₅×D₁₆₁	—	11	1	no	—
16	C₅×D₇×C₂₃	D₁₁	1	1	yes	characteristic, complemented
17	C₅×C₇×D₂₃	—	11	1	no	—
18	C₅×D₇×D₁₁	—	23	1	no	maximal, Hall
19	C₅×C₁₁×C₂₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	C₂×D₂₅₃	—	7	1	no	Hall
21	C₅×C₇×C₂₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
22	C₅×D₇₇	—	23	1	no	—
23	C₅×C₁₁×D₇	D₂₃	1	1	yes	characteristic, complemented
24	C₅×C₇×D₁₁	—	23	1	no	—
25	D₇×D₂₃	—	11	1	no	Hall
26	C₂×C₁₁×C₂₃	—	7	1	no	—
27	D₂₅₃	—	7	1	no	—
28	D₂₅₃	C₅×D₇	1	1	yes	characteristic, direct product factor
29	C₂×C₅×D₂₃	—	77	1	no	Hall
30	C₅×C₇×C₁₁	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
31	D₁₆₁	—	11	1	no	—
32	C₇×D₂₃	—	11	1	no	—
33	D₇×C₂₃	C₅×D₁₁	1	1	yes	characteristic, complemented
34	D₇×D₁₁	—	23	1	no	Hall
35	C₁₁×C₂₃	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
36	C₂×C₅×C₂₃	—	7	1	no	—
37	C₅×D₂₃	—	11	1	no	—
38	C₅×D₂₃	—	77	1	no	—
39	C₂×C₅×D₁₁	—	161	1	no	Hall
40	C₇×C₂₃	C₂×C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
41	D₇₇	—	23	1	no	—
42	C₇×D₁₁	—	23	1	no	—
43	C₁₁×D₇	C₅×D₂₃	1	1	yes	characteristic, complemented
44	C₂×C₅×D₇	—	253	1	no	Hall
45	C₅×C₂₃	D₇×D₁₁	1	1	yes	characteristic, complemented, Hall
46	C₂×C₅×C₁₁	—	7	1	no	—
47	C₅×D₁₁	—	23	1	no	—
48	C₅×D₁₁	—	161	1	no	—
49	C₂×D₂₃	—	77	1	no	Hall
50	C₇×C₁₁	C₂×C₅×D₂₃	1	1	yes	characteristic, complemented, Hall
51	C₂×C₅×C₇	—	253	1	no	—
52	C₅×D₇	—	253	1	no	—
53	C₅×D₇	D₂₅₃	1	1	yes	characteristic, direct product factor
54	C₅×C₁₁	D₇×D₂₃	1	1	yes	characteristic, complemented, Hall
55	C₂×C₂₃	—	7	1	no	—
56	D₂₃	—	11	1	no	—
57	D₂₃	—	77	1	no	—
58	C₂×D₁₁	—	161	1	no	Hall
59	C₅×C₇	C₂×D₂₅₃	1	1	yes	characteristic, complemented, Hall
60	C₂×D₇	—	253	1	no	Hall
61	C₂₃	C₅×D₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₁₁	—	7	1	no	—
63	D₁₁	—	23	1	no	—
64	D₁₁	—	161	1	no	—
65	C₂²×C₅	—	1771	1	no	Hall
66	C₂×C₇	—	253	1	no	—
67	D₇	—	253	1	no	—
68	D₇	C₅×D₂₅₃	1	1	yes	characteristic, direct product factor
69	C₁₁	C₅×D₇×D₂₃	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₅	—	7	1	no	—
71	C₂×C₅	—	1771	1	no	—
72	C₂×C₅	—	253	1	no	—
73	C₇	C₂×C₅×D₂₅₃	1	1	yes	characteristic, complemented, Sylow
74	C₅	D₇×D₂₅₃	1	1	yes	characteristic, direct product factor, Sylow
75	C₂²	—	1771	1	no	Sylow
76	C₂	—	7	1	no	—
77	C₂	—	1771	1	no	—
78	C₂	—	253	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₇×D₂₅₃
commutator, cosocle, hypocenter	C₇×C₁₁×C₂₃	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₁×C₂₃	C₂²
LCS	G ▷ C₇×C₁₁×C₂₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₇₇₁	C₂	semidirect
2. C₅×C₁₁×D₇×C₂₃	C₂	semidirect
3. C₅×C₇×D₂₅₃	C₂	semidirect
4. C₅×C₇×C₁₁×C₂₃	C₂²	semidirect
5. D₇×D₂₅₃	C₅	direct (N × H)
7. D₁₇₇₁	C₂×C₅	semidirect
8. C₁₁×D₇×C₂₃	C₂×C₅	semidirect
9. C₇×D₂₅₃	C₂×C₅	semidirect
12. C₅×D₂₅₃	D₇	direct (N × H)
14. C₇×C₁₁×C₂₃	C₂²×C₅	semidirect
16. C₅×D₇×C₂₃	D₁₁	semidirect
19. C₅×C₁₁×C₂₃	C₂×D₇	semidirect
21. C₅×C₇×C₂₃	C₂×D₁₁	semidirect
23. C₅×C₁₁×D₇	D₂₃	semidirect
28. D₂₅₃	C₅×D₇	direct (N × H)
30. C₅×C₇×C₁₁	C₂×D₂₃	semidirect
33. D₇×C₂₃	C₅×D₁₁	semidirect
35. C₁₁×C₂₃	C₂×C₅×D₇	semidirect
40. C₇×C₂₃	C₂×C₅×D₁₁	semidirect
43. C₁₁×D₇	C₅×D₂₃	semidirect
45. C₅×C₂₃	D₇×D₁₁	semidirect
50. C₇×C₁₁	C₂×C₅×D₂₃	semidirect
53. C₅×D₇	D₂₅₃	direct (N × H)
54. C₅×C₁₁	D₇×D₂₃	semidirect
59. C₅×C₇	C₂×D₂₅₃	semidirect
61. C₂₃	C₅×D₇×D₁₁	semidirect
68. D₇	C₅×D₂₅₃	direct (N × H)
69. C₁₁	C₅×D₇×D₂₃	semidirect
73. C₇	C₂×C₅×D₂₅₃	semidirect
74. C₅	D₇×D₂₅₃	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×D₁₇₇₁	2
C₅×C₁₁×D₇×C₂₃	2
C₅×C₇×D₂₅₃	2
D₇×D₂₅₃	5
C₂×C₅×D₂₅₃	7
C₅×D₇×D₂₃	11
C₅×D₇×D₁₁	23

Subgroups — C5×D7×D253 #47978439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₇×D₂₅₃ #47978439