Subgroups — #44478199

Order 30420.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊D₁₉₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
3	#20258975	—	5	1	no	maximal, Hall
4	C₁₃×D₁₉₅	—	6	2	no	—
5	#16810006	—	9	1	no	maximal, Hall
6	C₁₃×C₃⋊D₃₉	—	5	1	no	—
7	C₃×C₅×C₁₃²	—	2	2	no	—
8	#14556844	—	13	1	no	maximal
9	#14556843	—	13	1	no	maximal
10	C₁₃×D₆₅	—	9	1	no	—
11	C₃²×C₁₃²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₃⋊D₁₉₅	D₁₃	1	1	yes	characteristic
13	C₁₃×C₃⋊D₁₅	—	13	1	no	—
14	C₁₃×D₃₉	—	30	2	no	—
15	C₅×C₁₃²	#157	1	1	yes	characteristic, complemented, Hall
16	#10621730	—	45	1	no	Hall
17	C₃²×C₅×C₁₃	—	4	3	no	—
18	C₃²×C₅×C₁₃	Dic₁₃	1	1	yes	characteristic, complemented
19	C₃²×C₅×C₁₃	#261	1	1	yes	characteristic, complemented
20	C₃×C₁₃²	—	2	2	no	—
21	#90866	—	65	1	no	—
22	#90865	—	65	1	no	—
23	D₁₉₅	—	6	2	no	—
24	C₁₃×D₁₅	—	78	2	no	—
25	C₁₃×D₁₃	—	45	1	no	—
26	#63121	—	117	1	no	—
27	#63120	—	117	1	no	—
28	C₃⋊D₃₉	—	5	1	no	—
29	C₁₃×C₃⋊D₃	—	65	1	no	—
30	C₃×C₅×C₁₃	—	2	2	no	—
31	C₃×C₅×C₁₃	—	2	2	no	—
32	C₃×C₅×C₁₃	—	4	12	no	—
33	#4380	—	169	1	no	Hall
34	C₁₃²	#4380	1	1	yes	characteristic, complemented, Sylow
35	D₆₅	—	9	1	no	—
36	D₅×C₁₃	—	117	1	no	—
37	C₃²×C₁₃	—	4	3	no	—
38	C₃²×C₁₃	#63120	1	1	yes	characteristic, complemented
39	C₃²×C₁₃	#63121	1	1	yes	characteristic, complemented
40	C₃⋊D₁₅	—	13	1	no	—
41	D₃₉	—	30	2	no	—
42	D₃×C₁₃	—	390	2	no	—
43	C₅×C₁₃	—	4	3	no	—
44	C₅×C₁₃	#90865	1	1	yes	characteristic, complemented
45	C₅×C₁₃	#90866	1	1	yes	characteristic, complemented
46	#261	—	585	1	no	—
47	Dic₁₃	—	585	1	no	—
48	C₃²×C₅	#10621730	1	1	yes	characteristic, complemented, Hall
49	C₃×C₁₃	—	2	2	no	—
50	C₃×C₁₃	—	2	2	no	—
51	C₃×C₁₃	—	4	12	no	—
52	#157	—	845	1	no	Hall
53	D₁₅	—	78	2	no	—
54	C₂×C₁₃	—	585	1	no	—
55	D₁₃	—	45	1	no	—
56	AGL(1,𝔽₅)	—	1521	1	no	Hall
57	C₃⋊D₃	—	65	1	no	—
58	C₃×C₅	—	2	2	no	—
59	C₁₃	—	4	3	no	—
60	C₁₃	#14556843	1	1	yes	characteristic, complemented
61	C₁₃	#14556844	1	1	yes	characteristic, complemented
62	D₅	—	117	1	no	—
63	C₃²	#16810006	1	1	yes	characteristic, complemented, Sylow
64	D₃	—	390	2	no	—
65	C₅	#20258975	1	1	yes	characteristic, complemented, Sylow
66	C₄	—	7605	1	no	Sylow
67	C₃	—	2	2	no	—
68	C₂	—	585	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₁₃²	C₄
prime radical, cosocle	C₁₃×C₃⋊D₁₉₅	C₂
LCS	G ▷ C₃²×C₅×C₁₃²
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₁₃²	C₄	semidirect
11. C₃²×C₁₃²	AGL(1,𝔽₅)	semidirect
15. C₅×C₁₃²	#157	semidirect
18. C₃²×C₅×C₁₃	Dic₁₃	semidirect
19. C₃²×C₅×C₁₃	#261	semidirect
34. C₁₃²	#4380	semidirect
38. C₃²×C₁₃	#63120	semidirect
39. C₃²×C₁₃	#63121	semidirect
44. C₅×C₁₃	#90865	semidirect
45. C₅×C₁₃	#90866	semidirect
48. C₃²×C₅	#10621730	semidirect
60. C₁₃	#14556843	semidirect
61. C₁₃	#14556844	semidirect
63. C₃²	#16810006	semidirect
65. C₅	#20258975	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₃⋊D₁₉₅	2
#20258975	5
#16810006	9
#14556844	13
#14556843	13