Subgroups — #44478209

Order 30420.

224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊(C₃⋊(C₁₃⋊D₁₃))	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
3	#20258974	—	5	1	no	maximal, Hall
4	C₅×C₃⋊(C₁₃⋊D₁₃)	—	6	2	no	—
5	#16810011	—	9	1	no	maximal, Hall
6	C₃⋊(C₃⋊(C₁₃⋊D₁₃))	D₅	1	1	yes	characteristic
7	C₃×C₅×C₁₃²	—	2	2	no	—
8	#14556846	—	13	2	no	maximal
9	C₅×C₁₃⋊D₁₃	—	9	1	no	—
10	C₃²×C₁₃²	Dic₅	1	1	yes	characteristic, complemented, Hall
11	C₅×C₃⋊D₃₉	—	13	2	no	—
12	C₅×C₃⋊D₃₉	—	26	6	no	—
13	C₃⋊(C₁₃⋊D₁₃)	—	6	2	no	—
14	C₅×C₁₃²	#157	1	1	yes	characteristic, complemented, Hall
15	#10621729	—	45	1	no	Hall
16	C₃²×C₅×C₁₃	—	2	6	no	—
17	C₃²×C₅×C₁₃	#261	1	2	yes	complemented
18	C₃×C₁₃²	—	2	2	no	—
19	#90866	—	65	2	no	—
20	C₅×D₃₉	—	78	4	no	—
21	C₅×D₃₉	—	78	24	no	—
22	C₁₃⋊D₁₃	—	9	1	no	—
23	#63118	—	117	2	no	—
24	C₃⋊D₃₉	—	13	2	no	—
25	C₃⋊D₃₉	—	26	6	no	—
26	C₃×C₅×C₁₃	—	2	24	no	—
27	C₃×C₅×C₁₃	—	2	4	no	—
28	#4379	—	169	1	no	Hall
29	C₁₃²	#4379	1	1	yes	characteristic, complemented, Sylow
30	C₅×D₁₃	—	117	2	no	—
31	C₅×D₁₃	—	234	6	no	—
32	C₃²×C₁₃	—	2	6	no	—
33	C₃²×C₁₃	#63118	1	2	yes	complemented
34	C₅×C₃⋊D₃	—	169	1	no	—
35	D₃₉	—	78	4	no	—
36	D₃₉	—	78	24	no	—
37	C₅×C₁₃	—	2	6	no	—
38	C₅×C₁₃	#90866	1	2	yes	complemented
39	#261	—	585	2	no	—
40	C₃²×C₅	#10621729	1	1	yes	characteristic, complemented, Hall
41	C₃×C₁₃	—	2	24	no	—
42	C₃×C₁₃	—	2	4	no	—
43	#157	—	845	1	no	Hall
44	C₅×D₃	—	1014	2	no	—
45	D₁₃	—	117	2	no	—
46	D₁₃	—	234	6	no	—
47	Dic₅	—	1521	1	no	Hall
48	C₃⋊D₃	—	169	1	no	—
49	C₃×C₅	—	2	2	no	—
50	C₁₃	—	2	6	no	—
51	C₁₃	#14556846	1	2	yes	complemented
52	C₂×C₅	—	1521	1	no	—
53	C₃²	#16810011	1	1	yes	characteristic, complemented, Sylow
54	D₃	—	1014	2	no	—
55	C₅	#20258974	1	1	yes	characteristic, complemented, Sylow
56	C₄	—	7605	1	no	Sylow
57	C₃	—	2	2	no	—
58	C₂	—	1521	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₁₃²	C₄
prime radical, cosocle	C₅×C₃⋊(C₃⋊(C₁₃⋊D₁₃))	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
10. C₃²×C₁₃²	Dic₅	semidirect
14. C₅×C₁₃²	#157	semidirect
17. C₃²×C₅×C₁₃	#261	semidirect
29. C₁₃²	#4379	semidirect
33. C₃²×C₁₃	#63118	semidirect
38. C₅×C₁₃	#90866	semidirect
40. C₃²×C₅	#10621729	semidirect
51. C₁₃	#14556846	semidirect
53. C₃²	#16810011	semidirect
55. C₅	#20258974	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₃⋊(C₃⋊(C₁₃⋊D₁₃))	2
#20258974	5
#16810011	9
#14556846	13