Subgroups — C₂×C₅⋊(C₅⋊(#4294⋊C₂)) #30685562

Order 17100.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×#4294	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅⋊(C₅⋊(#4294⋊C₂))	C₂	1	1	yes	maximal, characteristic, direct product factor
3	C₅⋊(C₅⋊(#4294⋊C₂))	C₂	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×C₅⋊D₉₅	C₃	1	1	yes	maximal, characteristic
5	C₅²×#4294	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₅⋊(#4294⋊C₂)	—	5	6	no	maximal
7	C₃×C₅⋊D₉₅	C₂×C₃	1	1	yes	characteristic
8	C₃×C₅⋊D₉₅	C₂×C₃	1	1	yes	characteristic
9	C₂×C₃×C₅²×C₁₉	C₂×C₃	1	1	yes	characteristic
10	C₂×C₅⋊D₉₅	C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×#4294	D₅	1	6	yes	complemented
12	C₅⋊(#4294⋊C₂)	—	5	6	no	—
13	C₅⋊(#4294⋊C₂)	—	5	6	no	—
14	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic
15	C₂×C₃×D₉₅	—	5	6	no	—
16	C₂×C₅²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented
17	C₅⋊D₉₅	C₂×C₉	1	1	yes	characteristic, complemented
18	C₅⋊D₉₅	C₂×C₉	1	1	yes	characteristic, complemented
19	C₂×C₉×C₅⋊D₅	—	19	1	no	maximal, Hall
20	C₅×#4294	C₂×D₅	1	6	yes	complemented
21	C₂×#4294⋊C₂	—	25	1	no	Hall
22	C₂×C₃×C₅×C₁₉	C₃×D₅	1	6	yes	—
23	C₃×D₉₅	—	5	6	no	—
24	C₃×D₉₅	—	5	6	no	—
25	C₅²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅²×C₉	—	19	1	no	—
27	C₉×C₅⋊D₅	—	19	1	no	—
28	C₉×C₅⋊D₅	—	19	1	no	—
29	C₂×D₉₅	—	5	6	no	—
30	C₂×#4294	C₅⋊D₅	1	1	yes	characteristic, complemented
31	#4294⋊C₂	—	25	1	no	—
32	#4294⋊C₂	—	25	1	no	—
33	C₂×C₃×C₅⋊D₅	—	57	1	no	—
34	C₃×C₅×C₁₉	C₂×C₃×D₅	1	6	yes	—
35	C₂×C₃×D₁₉	—	25	1	no	—
36	C₅²×C₉	—	19	1	no	Hall
37	C₂×C₅×C₁₉	C₉×D₅	1	6	yes	complemented
38	D₉₅	—	5	6	no	—
39	D₉₅	—	5	6	no	—
40	C₂×C₉×D₅	—	95	6	no	—
41	#4294	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
42	C₂×C₃×C₅²	D₁₉⋊C₃	1	1	yes	characteristic
43	C₃×C₅⋊D₅	—	19	1	no	—
44	C₃×C₅⋊D₅	—	57	1	no	—
45	C₂×C₃×C₁₉	C₃×C₅⋊D₅	1	1	yes	characteristic
46	C₃×D₁₉	—	25	1	no	—
47	C₃×D₁₉	—	25	1	no	—
48	C₂×C₅⋊D₅	—	57	1	no	Hall
49	C₅×C₁₉	C₂×C₉×D₅	1	6	yes	complemented
50	C₂×C₅×C₉	—	19	6	no	—
51	C₉×D₅	—	95	6	no	—
52	C₉×D₅	—	95	6	no	—
53	C₂×D₁₉	—	25	1	no	Hall
54	C₃×C₅²	C₂×D₁₉⋊C₃	1	1	yes	characteristic
55	C₂×C₃×D₅	—	285	6	no	—
56	C₃×C₁₉	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic
57	C₂×C₅²	#4294⋊C₂	1	1	yes	characteristic, complemented
58	C₅⋊D₅	—	19	1	no	—
59	C₅⋊D₅	—	57	1	no	—
60	C₅×C₉	—	19	6	no	—
61	C₂×C₁₉	C₉×C₅⋊D₅	1	1	yes	characteristic, complemented
62	D₁₉	—	25	1	no	—
63	D₁₉	—	25	1	no	—
64	C₂²×C₉	—	475	1	no	Hall
65	C₂×C₃×C₅	C₅⋊(D₁₉⋊C₃)	1	6	yes	—
66	C₃×D₅	—	285	6	no	—
67	C₃×D₅	—	285	6	no	—
68	C₅²	C₂×#4294⋊C₂	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₅	—	285	6	no	—
70	C₁₉	C₂×C₉×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₉	—	19	1	no	—
72	C₂×C₉	—	475	1	no	—
73	C₂×C₉	—	475	1	no	—
74	C₃×C₅	C₂×C₅⋊(D₁₉⋊C₃)	1	6	yes	—
75	C₂²×C₃	—	475	1	no	—
76	C₂×C₅	C₅⋊(#4294⋊C₂)	1	6	yes	complemented
77	D₅	—	285	6	no	—
78	D₅	—	285	6	no	—
79	C₉	—	19	1	no	Sylow
80	C₂×C₃	—	1425	1	no	—
81	C₂×C₃	—	1425	1	no	—
82	C₂×C₃	C₅⋊(C₅⋊(D₁₉⋊C₃))	1	1	yes	characteristic
83	C₅	C₂×C₅⋊(#4294⋊C₂)	1	6	yes	complemented
84	C₂²	—	475	1	no	Sylow
85	C₃	C₂×C₅⋊(C₅⋊(D₁₉⋊C₃))	1	1	yes	characteristic
86	C₂	—	1425	1	no	—
87	C₂	—	1425	1	no	—
88	C₂	C₅⋊(C₅⋊(#4294⋊C₂))	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₅⋊(C₅⋊(D₁₉⋊C₃))
commutator, hypocenter	C₅²×C₁₉	C₂²×C₉
Frattini	C₃	C₂×C₅⋊(C₅⋊(D₁₉⋊C₃))
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₅⋊D₉₅	C₃
cosocle	C₃×C₅²×C₁₉	C₂²×C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₅²×#4294	C₂	semidirect
2. C₅⋊(C₅⋊(#4294⋊C₂))	C₂	direct (N × H)
3. C₅⋊(C₅⋊(#4294⋊C₂))	C₂	direct (N × H)
5. C₅²×#4294	C₂²	semidirect
10. C₂×C₅⋊D₉₅	C₉	semidirect
11. C₂×C₅×#4294	D₅	semidirect
16. C₂×C₅²×C₁₉	C₂×C₉	semidirect
17. C₅⋊D₉₅	C₂×C₉	semidirect
18. C₅⋊D₉₅	C₂×C₉	semidirect
20. C₅×#4294	C₂×D₅	semidirect
25. C₅²×C₁₉	C₂²×C₉	semidirect
30. C₂×#4294	C₅⋊D₅	semidirect
37. C₂×C₅×C₁₉	C₉×D₅	semidirect
41. #4294	C₂×C₅⋊D₅	semidirect
49. C₅×C₁₉	C₂×C₉×D₅	semidirect
57. C₂×C₅²	#4294⋊C₂	semidirect
61. C₂×C₁₉	C₉×C₅⋊D₅	semidirect
68. C₅²	C₂×#4294⋊C₂	semidirect
70. C₁₉	C₂×C₉×C₅⋊D₅	semidirect
76. C₂×C₅	C₅⋊(#4294⋊C₂)	semidirect
83. C₅	C₂×C₅⋊(#4294⋊C₂)	semidirect
88. C₂	C₅⋊(C₅⋊(#4294⋊C₂))	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×C₅²×#4294	2
C₅⋊(C₅⋊(#4294⋊C₂))	2
C₂×C₃×C₅⋊D₉₅	3
C₂×C₅⋊(#4294⋊C₂)	5
C₂×C₉×C₅⋊D₅	19

Subgroups — C2×C5⋊(C5⋊(#4294⋊C2)) #30685562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅⋊(C₅⋊(#4294⋊C₂)) #30685562