Subgroups — C₅×#92789⋊A₄ #44478142

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×C₂²⋊#92788	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₃×C₂²⋊(C₁₃⋊C₃)	C₃	1	2	yes	maximal, complemented
4	C₅×C₁₃⋊C₃²	—	4	1	no	maximal, Hall
5	#92789⋊A₄	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	A₄	1	1	yes	characteristic, complemented
9	C₅×#92788	—	4	1	no	—
10	C₅×C₁₃×C₁₃⋊C₃	—	4	2	no	—
11	C₅×A₄×C₁₃⋊C₃	—	13	2	no	maximal
12	C₂²⋊#92788	C₃×C₅	1	1	yes	characteristic, complemented
13	C₁₃×C₂²⋊(C₁₃⋊C₃)	C₃×C₅	1	2	yes	complemented
14	C₂²×#92789	C₃×C₅	1	1	yes	characteristic, complemented
15	C₂×C₅×C₁₃²	—	3	1	no	—
16	C₁₃⋊C₃²	—	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	2	no	—
20	C₅×C₂²⋊(C₁₃⋊C₃)	—	39	4	no	—
21	C₅×C₂²⋊(C₁₃⋊C₃)	C₁₃⋊C₃	1	2	yes	complemented
22	C₅×A₄×C₁₃	—	13	2	no	—
23	C₂²×C₅×C₁₃⋊C₃	—	13	2	no	—
24	C₂²×C₁₃²	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
25	C₃×C₅×C₁₃⋊C₃	—	52	2	no	—
26	#92789	C₅×A₄	1	1	yes	characteristic, complemented
27	#92788	—	4	1	no	—
28	C₁₃×C₁₃⋊C₃	—	4	2	no	—
29	A₄×C₁₃⋊C₃	—	13	2	no	—
30	C₂×C₅×C₁₃⋊C₃	—	39	2	no	—
31	C₂×C₁₃²	—	3	1	no	—
32	C₂²×C₅×C₁₃	—	3	4	no	—
33	C₂²×C₅×C₁₃	C₃×C₁₃⋊C₃	1	2	yes	complemented
34	C₃×C₅×C₁₃	—	52	2	no	—
35	C₅×C₁₃⋊C₃	—	4	2	no	—
36	C₅×C₁₃⋊C₃	—	13	2	no	—
37	C₅×C₁₃⋊C₃	—	52	2	no	—
38	C₅×C₁₃⋊C₃	—	156	4	no	—
39	C₃×C₅×A₄	—	169	1	no	Hall
40	C₁₃²	C₃×C₅×A₄	1	1	yes	characteristic, complemented, Sylow
41	C₂²⋊(C₁₃⋊C₃)	—	13	2	no	—
42	C₂²⋊(C₁₃⋊C₃)	—	39	4	no	—
43	C₂²⋊(C₁₃⋊C₃)	C₅×C₁₃⋊C₃	1	2	yes	complemented
44	A₄×C₁₃	—	13	2	no	—
45	C₂²×C₁₃⋊C₃	—	13	2	no	—
46	C₂×C₅×C₁₃	—	3	2	no	—
47	C₂×C₅×C₁₃	—	9	4	no	—
48	C₃×C₁₃⋊C₃	—	52	2	no	—
49	C₂×C₁₃⋊C₃	—	39	2	no	—
50	C₅×C₁₃	—	3	4	no	—
51	C₅×C₁₃	A₄×C₁₃⋊C₃	1	2	yes	complemented
52	C₂²×C₃×C₅	—	169	1	no	—
53	C₅×A₄	—	13	2	no	—
54	C₅×A₄	—	169	1	no	—
55	C₂²×C₁₃	—	3	4	no	—
56	C₂²×C₁₃	C₃×C₅×C₁₃⋊C₃	1	2	yes	complemented
57	C₃²×C₅	—	676	1	no	Hall
58	C₃×C₁₃	—	52	2	no	—
59	C₁₃⋊C₃	—	4	2	no	—
60	C₁₃⋊C₃	—	13	2	no	—
61	C₁₃⋊C₃	—	52	2	no	—
62	C₁₃⋊C₃	—	156	4	no	—
63	C₃×A₄	—	169	1	no	Hall
64	C₂×C₃×C₅	—	507	1	no	—
65	C₂×C₁₃	—	3	2	no	—
66	C₂×C₁₃	—	9	4	no	—
67	C₂²×C₅	C₁₃⋊C₃²	1	1	yes	characteristic, complemented, Hall
68	C₃×C₅	—	52	2	no	—
69	C₃×C₅	—	676	1	no	—
70	C₃×C₅	—	169	1	no	—
71	C₁₃	—	3	4	no	—
72	C₁₃	C₅×A₄×C₁₃⋊C₃	1	2	yes	complemented
73	C₂²×C₃	—	169	1	no	—
74	A₄	—	13	2	no	—
75	A₄	—	169	1	no	—
76	C₂×C₅	—	3	1	no	—
77	C₃²	—	676	1	no	Sylow
78	C₂×C₃	—	507	1	no	—
79	C₅	#92789⋊A₄	1	1	yes	characteristic, direct product factor, Sylow
80	C₂²	C₅×C₁₃⋊C₃²	1	1	yes	characteristic, complemented, Sylow
81	C₃	—	52	2	no	—
82	C₃	—	676	1	no	—
83	C₃	—	169	1	no	—
84	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅	#92789⋊A₄
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×C₂²⋊#92788	C₃	semidirect
3. C₅×C₁₃×C₂²⋊(C₁₃⋊C₃)	C₃	semidirect
5. #92789⋊A₄	C₅	direct (N × H)
7. C₂²×C₅×C₁₃²	C₃²	semidirect
8. C₅×#92789	A₄	semidirect
12. C₂²⋊#92788	C₃×C₅	semidirect
13. C₁₃×C₂²⋊(C₁₃⋊C₃)	C₃×C₅	semidirect
14. C₂²×#92789	C₃×C₅	semidirect
18. C₅×C₁₃²	C₃×A₄	semidirect
21. C₅×C₂²⋊(C₁₃⋊C₃)	C₁₃⋊C₃	semidirect
24. C₂²×C₁₃²	C₃²×C₅	semidirect
26. #92789	C₅×A₄	semidirect
33. C₂²×C₅×C₁₃	C₃×C₁₃⋊C₃	semidirect
40. C₁₃²	C₃×C₅×A₄	semidirect
43. C₂²⋊(C₁₃⋊C₃)	C₅×C₁₃⋊C₃	semidirect
51. C₅×C₁₃	A₄×C₁₃⋊C₃	semidirect
56. C₂²×C₁₃	C₃×C₅×C₁₃⋊C₃	semidirect
67. C₂²×C₅	C₁₃⋊C₃²	semidirect
72. C₁₃	C₅×A₄×C₁₃⋊C₃	semidirect
79. C₅	#92789⋊A₄	direct (N × H)
80. C₂²	C₅×C₁₃⋊C₃²	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×C₂²⋊#92788	3
C₅×C₁₃×C₂²⋊(C₁₃⋊C₃)	3
C₅×C₁₃⋊C₃²	4
#92789⋊A₄	5
C₅×A₄×C₁₃⋊C₃	13

Subgroups — C5×#92789⋊A4 #44478142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#92789⋊A₄ #44478142