Subgroups — C₅×#20258962 #44478298

Order 30420.

384 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₃⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₃×C₃⋊D₃₉	C₂	1	2	yes	maximal, complemented
3	C₅×D₃₉⋊D₁₃	—	3	4	no	maximal
4	C₃²×C₅×C₁₃²	C₂²	1	1	yes	characteristic, complemented, Hall
5	#20258962	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₃×D₃₉	—	3	8	no	—
7	C₃×C₅×C₁₃⋊D₁₃	D₃	1	4	yes	complemented
8	C₅×D₁₃²	—	9	1	no	Hall
9	C₁₃×C₃⋊D₃₉	C₂×C₅	1	2	yes	complemented
10	C₃²×C₁₃⋊D₁₃	C₂×C₅	1	1	yes	characteristic, complemented
11	C₃×C₅×C₁₃²	C₂×D₃	1	4	yes	complemented
12	C₅×C₃⋊D₃×D₁₃	—	13	2	no	maximal
13	D₃₉⋊D₁₃	—	3	4	no	—
14	C₅×C₁₃⋊D₁₃	C₃⋊D₃	1	1	yes	characteristic, complemented
15	C₅×C₁₃×D₁₃	—	9	2	no	—
16	C₃²×C₁₃²	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₅×C₃⋊D₃₉	D₁₃	1	2	yes	complemented
18	C₅×C₁₃×C₃⋊D₃	—	13	2	no	—
19	C₃²×C₅×D₁₃	—	13	2	no	—
20	C₃²×C₅×D₁₃	—	26	6	no	—
21	C₁₃×D₃₉	—	3	8	no	—
22	C₃×C₁₃⋊D₁₃	C₅×D₃	1	4	yes	complemented
23	C₅×C₁₃²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
24	C₅×D₃×D₁₃	—	39	8	no	—
25	D₁₃²	—	9	1	no	Hall
26	C₃²×C₅×C₁₃	—	2	6	no	—
27	C₃²×C₅×C₁₃	C₂×D₁₃	1	2	yes	complemented
28	C₃×C₁₃²	C₂×C₅×D₃	1	4	yes	complemented
29	C₃⋊D₃×D₁₃	—	13	2	no	—
30	C₅×D₃₉	—	3	8	no	—
31	C₅×D₃×C₁₃	—	39	8	no	—
32	C₃×C₅×D₁₃	—	13	8	no	—
33	C₃×C₅×D₁₃	—	26	24	no	—
34	C₁₃⋊D₁₃	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented
35	C₁₃×D₁₃	—	9	2	no	—
36	C₂×C₅×D₁₃	—	117	2	no	—
37	C₃⋊D₃₉	C₅×D₁₃	1	2	yes	complemented
38	C₁₃×C₃⋊D₃	—	13	2	no	—
39	C₃²×D₁₃	—	13	2	no	—
40	C₃²×D₁₃	—	26	6	no	—
41	C₃×C₅×C₁₃	—	2	24	no	—
42	C₃×C₅×C₁₃	D₃×D₁₃	1	8	yes	complemented
43	C₂×C₅×C₃⋊D₃	—	169	1	no	Hall
44	C₁₃²	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
45	D₃×D₁₃	—	39	8	no	—
46	C₂×C₅×C₁₃	—	117	2	no	—
47	C₅×D₁₃	—	9	2	no	—
48	C₅×D₁₃	—	13	2	no	—
49	C₅×D₁₃	—	26	6	no	—
50	C₃²×C₁₃	—	2	6	no	—
51	C₃²×C₁₃	C₂×C₅×D₁₃	1	2	yes	complemented
52	C₂×C₃²×C₅	—	169	1	no	—
53	C₅×C₃⋊D₃	—	13	2	no	—
54	D₃₉	—	3	8	no	—
55	C₃×D₁₃	—	13	8	no	—
56	C₃×D₁₃	—	26	24	no	—
57	D₃×C₁₃	—	39	8	no	—
58	C₅×C₁₃	—	2	6	no	—
59	C₅×C₁₃	C₃⋊D₃×D₁₃	1	2	yes	complemented
60	C₂×C₅×D₃	—	507	4	no	—
61	C₂×D₁₃	—	117	2	no	—
62	C₃²×C₅	D₁₃²	1	1	yes	characteristic, complemented, Hall
63	C₃×C₁₃	—	2	24	no	—
64	C₃×C₁₃	C₅×D₃×D₁₃	1	8	yes	complemented
65	C₂×C₃⋊D₃	—	169	1	no	Hall
66	C₂×C₃×C₅	—	169	4	no	—
67	C₅×D₃	—	39	8	no	—
68	C₂×C₁₃	—	117	2	no	—
69	D₁₃	—	9	2	no	—
70	D₁₃	—	13	2	no	—
71	D₁₃	—	26	6	no	—
72	C₂²×C₅	—	1521	1	no	Hall
73	C₂×C₃²	—	169	1	no	—
74	C₃⋊D₃	—	13	2	no	—
75	C₃×C₅	D₃₉⋊D₁₃	1	4	yes	complemented
76	C₁₃	—	2	6	no	—
77	C₁₃	C₅×C₃⋊D₃×D₁₃	1	2	yes	complemented
78	C₂×D₃	—	507	4	no	—
79	C₂×C₅	—	117	2	no	—
80	C₂×C₅	—	169	1	no	—
81	C₃²	C₅×D₁₃²	1	1	yes	characteristic, complemented, Sylow
82	C₂×C₃	—	169	4	no	—
83	D₃	—	39	8	no	—
84	C₅	#20258962	1	1	yes	characteristic, direct product factor, Sylow
85	C₂²	—	1521	1	no	Sylow
86	C₃	C₅×D₃₉⋊D₁₃	1	4	yes	complemented
87	C₂	—	117	2	no	—
88	C₂	—	169	1	no	—

	subgroup	G/H
center, hypercenter	C₅	#20258962
commutator, cosocle, hypocenter	C₃²×C₁₃²	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃²	C₂²
LCS	G ▷ C₃²×C₁₃²
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₃⋊D₁₃	C₂	semidirect
2. C₅×C₁₃×C₃⋊D₃₉	C₂	semidirect
4. C₃²×C₅×C₁₃²	C₂²	semidirect
5. #20258962	C₅	direct (N × H)
7. C₃×C₅×C₁₃⋊D₁₃	D₃	semidirect
9. C₁₃×C₃⋊D₃₉	C₂×C₅	semidirect
10. C₃²×C₁₃⋊D₁₃	C₂×C₅	semidirect
11. C₃×C₅×C₁₃²	C₂×D₃	semidirect
14. C₅×C₁₃⋊D₁₃	C₃⋊D₃	semidirect
16. C₃²×C₁₃²	C₂²×C₅	semidirect
17. C₅×C₃⋊D₃₉	D₁₃	semidirect
22. C₃×C₁₃⋊D₁₃	C₅×D₃	semidirect
23. C₅×C₁₃²	C₂×C₃⋊D₃	semidirect
27. C₃²×C₅×C₁₃	C₂×D₁₃	semidirect
28. C₃×C₁₃²	C₂×C₅×D₃	semidirect
34. C₁₃⋊D₁₃	C₅×C₃⋊D₃	semidirect
37. C₃⋊D₃₉	C₅×D₁₃	semidirect
42. C₃×C₅×C₁₃	D₃×D₁₃	semidirect
44. C₁₃²	C₂×C₅×C₃⋊D₃	semidirect
51. C₃²×C₁₃	C₂×C₅×D₁₃	semidirect
59. C₅×C₁₃	C₃⋊D₃×D₁₃	semidirect
62. C₃²×C₅	D₁₃²	semidirect
64. C₃×C₁₃	C₅×D₃×D₁₃	semidirect
75. C₃×C₅	D₃₉⋊D₁₃	semidirect
77. C₁₃	C₅×C₃⋊D₃×D₁₃	semidirect
81. C₃²	C₅×D₁₃²	semidirect
84. C₅	#20258962	direct (N × H)
86. C₃	C₅×D₃₉⋊D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₁₃⋊D₁₃	2
C₅×C₁₃×C₃⋊D₃₉	2
C₅×D₃₉⋊D₁₃	3
#20258962	5
C₅×C₃⋊D₃×D₁₃	13

Subgroups — C5×#20258962 #44478298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20258962 #44478298