Subgroups — C₅×D₅₅⋊D₂₉ #44542070

Order 31900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₃₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₁×D₁₄₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₂₉×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₁₁×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅₅⋊D₂₉	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₅×D₁₁×D₂₉	—	5	1	no	maximal
7	C₂₉×D₅₅	C₂×C₅	1	1	yes	characteristic, complemented
8	C₁₁×D₁₄₅	C₂×C₅	1	1	yes	characteristic, complemented
9	C₅×D₃₁₉	—	2	2	no	—
10	C₅×D₃₁₉	D₅	1	1	yes	characteristic, complemented
11	C₅×D₃₁₉	C₂×C₅	1	1	yes	characteristic, complemented
12	C₅×D₁₁×C₂₉	—	5	1	no	—
13	C₅×C₁₁×D₂₉	—	5	1	no	—
14	C₅×D₅×D₂₉	—	11	1	no	maximal, Hall
15	C₅×C₁₁×C₂₉	—	2	2	no	—
16	C₅×C₁₁×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented
17	C₅×C₁₁×C₂₉	C₂²×C₅	1	1	yes	characteristic, complemented
18	C₅×D₁₄₅	D₁₁	1	1	yes	characteristic, complemented
19	C₅×D₅×C₂₉	—	11	1	no	—
20	C₅²×D₂₉	—	11	1	no	—
21	D₁₁×D₂₉	—	5	1	no	Hall
22	C₅×D₅×D₁₁	—	29	1	no	maximal, Hall
23	C₅²×C₂₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
24	D₃₁₉	C₅×D₅	1	1	yes	characteristic, complemented
25	C₁₁×D₂₉	—	5	1	no	—
26	D₁₁×C₂₉	—	5	1	no	—
27	C₂×C₅×D₂₉	—	55	1	no	—
28	D₅×D₂₉	—	11	1	no	—
29	C₅×D₅₅	D₂₉	1	1	yes	characteristic, complemented
30	C₅×D₅×C₁₁	—	29	1	no	—
31	C₅²×D₁₁	—	29	1	no	—
32	C₁₁×C₂₉	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
33	C₂×C₅×C₂₉	—	55	1	no	—
34	D₁₄₅	C₅×D₁₁	1	1	yes	characteristic, complemented
35	C₅×D₂₉	—	5	1	no	—
36	C₅×D₂₉	—	11	1	no	—
37	C₅×D₂₉	—	11	1	no	—
38	C₅×D₂₉	—	22	2	no	—
39	D₅×C₂₉	—	11	1	no	—
40	C₅²×C₁₁	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
41	C₂×C₅×D₁₁	—	145	1	no	—
42	D₅×D₁₁	—	29	1	no	—
43	C₅×C₂₉	—	2	2	no	—
44	C₅×C₂₉	D₅×D₁₁	1	1	yes	characteristic, complemented
45	C₅×C₂₉	C₂×C₅×D₁₁	1	1	yes	characteristic, complemented
46	C₂×D₂₉	—	55	1	no	Hall
47	C₂×C₅×C₁₁	—	145	1	no	—
48	D₅₅	C₅×D₂₉	1	1	yes	characteristic, complemented
49	C₅×D₁₁	—	5	1	no	—
50	C₅×D₁₁	—	29	1	no	—
51	C₅×D₁₁	—	29	1	no	—
52	C₅×D₁₁	—	58	2	no	—
53	D₅×C₁₁	—	29	1	no	—
54	C₂×C₅×D₅	—	319	1	no	Hall
55	C₂×C₂₉	—	55	1	no	—
56	D₂₉	—	5	1	no	—
57	D₂₉	—	11	1	no	—
58	C₅×C₁₁	—	2	2	no	—
59	C₅×C₁₁	D₅×D₂₉	1	1	yes	characteristic, complemented
60	C₅×C₁₁	C₂×C₅×D₂₉	1	1	yes	characteristic, complemented
61	C₂×C₅²	—	319	1	no	—
62	C₅×D₅	—	11	1	no	—
63	C₅×D₅	—	29	1	no	—
64	C₂×D₁₁	—	145	1	no	Hall
65	C₂₉	C₅×D₅×D₁₁	1	1	yes	characteristic, complemented, Sylow
66	C₅²	D₁₁×D₂₉	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₁₁	—	145	1	no	—
68	D₁₁	—	5	1	no	—
69	D₁₁	—	29	1	no	—
70	C₂²×C₅	—	1595	1	no	—
71	C₂×D₅	—	319	1	no	—
72	C₁₁	C₅×D₅×D₂₉	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₅	—	55	1	no	—
74	C₂×C₅	—	319	1	no	—
75	C₂×C₅	—	319	1	no	—
76	C₂×C₅	—	638	2	no	—
77	C₂×C₅	—	145	1	no	—
78	D₅	—	11	1	no	—
79	D₅	—	29	1	no	—
80	C₅	—	2	2	no	—
81	C₅	C₅×D₁₁×D₂₉	1	1	yes	characteristic, complemented
82	C₅	D₅₅⋊D₂₉	1	1	yes	characteristic, direct product factor
83	C₂²	—	1595	1	no	Sylow
84	C₂	—	55	1	no	—
85	C₂	—	319	1	no	—
86	C₂	—	145	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₅₅⋊D₂₉
commutator, cosocle, hypocenter	C₅×C₁₁×C₂₉	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₂₉	C₂²
LCS	G ▷ C₅×C₁₁×C₂₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅²×D₃₁₉	C₂	semidirect
2. C₅×C₁₁×D₁₄₅	C₂	semidirect
3. C₅×C₂₉×D₅₅	C₂	semidirect
4. C₅²×C₁₁×C₂₉	C₂²	semidirect
5. D₅₅⋊D₂₉	C₅	direct (N × H)
7. C₂₉×D₅₅	C₂×C₅	semidirect
8. C₁₁×D₁₄₅	C₂×C₅	semidirect
10. C₅×D₃₁₉	D₅	semidirect
11. C₅×D₃₁₉	C₂×C₅	semidirect
16. C₅×C₁₁×C₂₉	C₂×D₅	semidirect
17. C₅×C₁₁×C₂₉	C₂²×C₅	semidirect
18. C₅×D₁₄₅	D₁₁	semidirect
23. C₅²×C₂₉	C₂×D₁₁	semidirect
24. D₃₁₉	C₅×D₅	semidirect
29. C₅×D₅₅	D₂₉	semidirect
32. C₁₁×C₂₉	C₂×C₅×D₅	semidirect
34. D₁₄₅	C₅×D₁₁	semidirect
40. C₅²×C₁₁	C₂×D₂₉	semidirect
44. C₅×C₂₉	D₅×D₁₁	semidirect
45. C₅×C₂₉	C₂×C₅×D₁₁	semidirect
48. D₅₅	C₅×D₂₉	semidirect
59. C₅×C₁₁	D₅×D₂₉	semidirect
60. C₅×C₁₁	C₂×C₅×D₂₉	semidirect
65. C₂₉	C₅×D₅×D₁₁	semidirect
66. C₅²	D₁₁×D₂₉	semidirect
72. C₁₁	C₅×D₅×D₂₉	semidirect
81. C₅	C₅×D₁₁×D₂₉	semidirect
82. C₅	D₅₅⋊D₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×D₃₁₉	2
C₅×C₁₁×D₁₄₅	2
C₅×C₂₉×D₅₅	2
D₅₅⋊D₂₉	5
C₅×D₁₁×D₂₉	5
C₅×D₅×D₂₉	11
C₅×D₅×D₁₁	29

Subgroups — C5×D55⋊D29 #44542070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₅₅⋊D₂₉ #44542070