Subgroups — C₅×A₄×#92789 #44478144

Order 30420.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#92789	C₃	1	1	yes	maximal, characteristic, complemented
2	C₅×A₄×C₁₃²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅×C₂²⋊#92789	C₃	1	2	yes	maximal, complemented
4	C₃×C₅×#92789	—	4	1	no	maximal, Hall
5	A₄×#92789	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×#92789	—	3	1	no	—
7	C₂²×C₅×C₁₃²	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₅×#92789	—	4	2	no	—
9	C₅×#92789	A₄	1	1	yes	characteristic, direct product factor
10	C₃×C₅×C₁₃²	—	4	1	no	—
11	C₅×A₄×C₁₃⋊C₃	—	13	2	no	maximal
12	C₂²⋊#92789	C₃×C₅	1	2	yes	complemented
13	A₄×C₁₃²	C₃×C₅	1	1	yes	characteristic, complemented
14	C₂²×#92789	C₃×C₅	1	1	yes	characteristic, complemented
15	C₂×C₅×C₁₃²	—	3	1	no	—
16	C₃×#92789	—	4	1	no	Hall
17	C₂×#92789	—	3	1	no	—
18	C₅×C₁₃²	C₃×A₄	1	1	yes	characteristic, complemented, Hall
19	C₅×C₂²⋊(C₁₃⋊C₃)	—	13	4	no	—
20	C₅×A₄×C₁₃	—	3	4	no	—
21	C₅×A₄×C₁₃	C₁₃⋊C₃	1	2	yes	complemented
22	C₂²×C₅×C₁₃⋊C₃	—	13	2	no	—
23	C₂²×C₁₃²	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×C₁₃⋊C₃	—	52	2	no	—
25	C₃×C₁₃²	—	4	1	no	—
26	#92789	—	4	2	no	—
27	#92789	C₅×A₄	1	1	yes	characteristic, direct product factor
28	A₄×C₁₃⋊C₃	—	13	2	no	—
29	C₂×C₅×C₁₃⋊C₃	—	39	2	no	—
30	C₂×C₁₃²	—	3	1	no	—
31	C₂²×C₅×C₁₃	—	3	4	no	—
32	C₂²×C₅×C₁₃	C₃×C₁₃⋊C₃	1	2	yes	complemented
33	C₃×C₅×C₁₃	—	4	2	no	—
34	C₃×C₅×C₁₃	—	12	4	no	—
35	C₅×C₁₃⋊C₃	—	13	2	no	—
36	C₅×C₁₃⋊C₃	—	52	4	no	—
37	C₃×C₅×A₄	—	169	1	no	Hall
38	C₁₃²	C₃×C₅×A₄	1	1	yes	characteristic, complemented, Sylow
39	C₂²⋊(C₁₃⋊C₃)	—	13	4	no	—
40	A₄×C₁₃	—	3	4	no	—
41	A₄×C₁₃	C₅×C₁₃⋊C₃	1	2	yes	complemented
42	C₂²×C₁₃⋊C₃	—	13	2	no	—
43	C₂×C₅×C₁₃	—	3	2	no	—
44	C₂×C₅×C₁₃	—	9	4	no	—
45	C₃×C₁₃⋊C₃	—	52	2	no	—
46	C₂×C₁₃⋊C₃	—	39	2	no	—
47	C₅×C₁₃	—	3	4	no	—
48	C₅×C₁₃	A₄×C₁₃⋊C₃	1	2	yes	complemented
49	C₂²×C₃×C₅	—	169	1	no	—
50	C₅×A₄	—	169	2	no	—
51	C₅×A₄	#92789	1	1	yes	characteristic, direct product factor
52	C₂²×C₁₃	—	3	4	no	—
53	C₂²×C₁₃	C₃×C₅×C₁₃⋊C₃	1	2	yes	complemented
54	C₃²×C₅	—	676	1	no	Hall
55	C₃×C₁₃	—	4	2	no	—
56	C₃×C₁₃	—	12	4	no	—
57	C₁₃⋊C₃	—	13	2	no	—
58	C₁₃⋊C₃	—	52	4	no	—
59	C₃×A₄	—	169	1	no	Hall
60	C₂×C₃×C₅	—	507	1	no	—
61	C₂×C₁₃	—	3	2	no	—
62	C₂×C₁₃	—	9	4	no	—
63	C₂²×C₅	C₃×#92789	1	1	yes	characteristic, complemented, Hall
64	C₃×C₅	—	4	1	no	—
65	C₃×C₅	—	676	2	no	—
66	C₃×C₅	—	169	1	no	—
67	C₁₃	—	3	4	no	—
68	C₁₃	C₅×A₄×C₁₃⋊C₃	1	2	yes	complemented
69	C₂²×C₃	—	169	1	no	—
70	A₄	—	169	2	no	—
71	A₄	C₅×#92789	1	1	yes	characteristic, direct product factor
72	C₂×C₅	—	3	1	no	—
73	C₃²	—	676	1	no	Sylow
74	C₂×C₃	—	507	1	no	—
75	C₅	A₄×#92789	1	1	yes	characteristic, direct product factor, Sylow
76	C₂²	C₃×C₅×#92789	1	1	yes	characteristic, complemented, Sylow
77	C₃	—	4	1	no	—
78	C₃	—	676	2	no	—
79	C₃	—	169	1	no	—
80	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅	A₄×#92789
commutator, cosocle, hypocenter	C₂²×C₁₃²	C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₃²	C₃²
LCS	G ▷ C₂²×C₁₃²
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#92789	C₃	semidirect
2. C₅×A₄×C₁₃²	C₃	semidirect
3. C₅×C₂²⋊#92789	C₃	semidirect
5. A₄×#92789	C₅	direct (N × H)
7. C₂²×C₅×C₁₃²	C₃²	semidirect
9. C₅×#92789	A₄	direct (N × H)
12. C₂²⋊#92789	C₃×C₅	semidirect
13. A₄×C₁₃²	C₃×C₅	semidirect
14. C₂²×#92789	C₃×C₅	semidirect
18. C₅×C₁₃²	C₃×A₄	semidirect
21. C₅×A₄×C₁₃	C₁₃⋊C₃	semidirect
23. C₂²×C₁₃²	C₃²×C₅	semidirect
27. #92789	C₅×A₄	direct (N × H)
32. C₂²×C₅×C₁₃	C₃×C₁₃⋊C₃	semidirect
38. C₁₃²	C₃×C₅×A₄	semidirect
41. A₄×C₁₃	C₅×C₁₃⋊C₃	semidirect
48. C₅×C₁₃	A₄×C₁₃⋊C₃	semidirect
51. C₅×A₄	#92789	direct (N × H)
53. C₂²×C₁₃	C₃×C₅×C₁₃⋊C₃	semidirect
63. C₂²×C₅	C₃×#92789	semidirect
68. C₁₃	C₅×A₄×C₁₃⋊C₃	semidirect
71. A₄	C₅×#92789	direct (N × H)
75. C₅	A₄×#92789	direct (N × H)
76. C₂²	C₃×C₅×#92789	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×#92789	3
C₅×A₄×C₁₃²	3
C₅×C₂²⋊#92789	3
C₃×C₅×#92789	4
A₄×#92789	5
C₅×A₄×C₁₃⋊C₃	13

Subgroups — C5×A4×#92789 #44478144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×A₄×#92789 #44478144