Subgroups — C₃×C₅×#14579331 #50304338

Order 38220.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₃×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₅×#14579331	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₇²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×#14579331	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
6	C₃×C₁₃×C₇⋊D₇	C₂×C₅	1	1	yes	characteristic
7	C₅×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×C₅×#5997	—	13	1	no	maximal, Hall
9	C₃×C₅×C₁₃×D₇	—	14	4	no	—
10	#14579331	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₇²×C₁₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅×C₇⋊D₇	D₁₃	1	1	yes	characteristic
13	C₃×C₅×C₇×C₁₃	—	2	4	no	—
14	C₁₃×C₇⋊D₇	C₂×C₃×C₅	1	1	yes	characteristic
15	C₅×#5997	—	13	1	no	Hall
16	C₅×C₁₃×D₇	—	14	4	no	—
17	C₃×C₅×Dic₁₃	—	49	1	no	maximal, Hall
18	C₃×C₅×C₇²	Dic₁₃	1	1	yes	characteristic, complemented, Hall
19	C₇²×C₁₃	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
20	C₃×#5997	—	13	1	no	Hall
21	C₃×C₁₃×D₇	—	14	4	no	—
22	C₅×C₇⋊D₇	C₃×D₁₃	1	1	yes	characteristic
23	C₅×C₇×C₁₃	—	2	4	no	—
24	C₂×C₃×C₅×C₁₃	—	49	1	no	—
25	C₃×C₇⋊D₇	C₅×D₁₃	1	1	yes	characteristic
26	C₃×C₇×C₁₃	—	2	4	no	—
27	C₅×Dic₁₃	—	49	1	no	Hall
28	C₅×C₇²	C₃×Dic₁₃	1	1	yes	characteristic, complemented, Hall
29	C₃×C₅×D₇	—	14	4	no	—
30	#5997	—	13	1	no	Hall
31	C₃×C₅×C₁₃	#5997	1	1	yes	characteristic, complemented, Hall
32	C₁₃×D₇	—	14	4	no	—
33	C₃×Dic₁₃	—	49	1	no	Hall
34	C₃×C₇²	C₅×Dic₁₃	1	1	yes	characteristic, complemented, Hall
35	C₂×C₅×C₁₃	—	49	1	no	—
36	C₃×C₅×C₇	—	2	4	no	—
37	C₇⋊D₇	C₃×C₅×D₁₃	1	1	yes	characteristic
38	C₇×C₁₃	—	2	4	no	—
39	C₂×C₃×C₁₃	—	49	1	no	—
40	C₅×D₇	—	14	4	no	—
41	C₅×C₁₃	C₃×#5997	1	1	yes	characteristic, complemented, Hall
42	C₃×C₄×C₅	—	637	1	no	Hall
43	Dic₁₃	—	49	1	no	Hall
44	C₇²	C₃×C₅×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
45	C₃×D₇	—	14	4	no	—
46	C₃×C₁₃	C₅×#5997	1	1	yes	characteristic, complemented, Hall
47	C₅×C₇	—	2	4	no	—
48	C₂×C₃×C₅	—	49	1	no	—
49	C₂×C₁₃	—	49	1	no	—
50	C₃×C₇	—	2	4	no	—
51	C₄×C₅	—	637	1	no	Hall
52	C₃×C₅	#14579331	1	1	yes	characteristic, direct product factor, Hall
53	D₇	—	14	4	no	—
54	C₁₃	C₃×C₅×#5997	1	1	yes	characteristic, complemented, Sylow
55	C₃×C₄	—	637	1	no	Hall
56	C₂×C₅	—	49	1	no	—
57	C₇	—	2	4	no	—
58	C₂×C₃	—	49	1	no	—
59	C₅	C₃×#14579331	1	1	yes	characteristic, direct product factor, Sylow
60	C₄	—	637	1	no	Sylow
61	C₃	C₅×#14579331	1	1	yes	characteristic, direct product factor, Sylow
62	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₅	#14579331
commutator, hypocenter	C₇²×C₁₃	C₃×C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²×C₁₃	C₄
prime radical	C₃×C₅×C₁₃×C₇⋊D₇	C₂
cosocle	C₁₃×C₇⋊D₇	C₂×C₃×C₅
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×#14579331	C₃	direct (N × H)
3. C₃×C₅×C₇²×C₁₃	C₄	semidirect
4. C₃×#14579331	C₅	direct (N × H)
7. C₅×C₇²×C₁₃	C₃×C₄	semidirect
10. #14579331	C₃×C₅	direct (N × H)
11. C₃×C₇²×C₁₃	C₄×C₅	semidirect
18. C₃×C₅×C₇²	Dic₁₃	semidirect
19. C₇²×C₁₃	C₃×C₄×C₅	semidirect
28. C₅×C₇²	C₃×Dic₁₃	semidirect
31. C₃×C₅×C₁₃	#5997	semidirect
34. C₃×C₇²	C₅×Dic₁₃	semidirect
41. C₅×C₁₃	C₃×#5997	semidirect
44. C₇²	C₃×C₅×Dic₁₃	semidirect
46. C₃×C₁₃	C₅×#5997	semidirect
52. C₃×C₅	#14579331	direct (N × H)
54. C₁₃	C₃×C₅×#5997	semidirect
59. C₅	C₃×#14579331	direct (N × H)
61. C₃	C₅×#14579331	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₃×C₇⋊D₇	2
C₅×#14579331	3
C₃×#14579331	5
C₃×C₅×#5997	13
C₃×C₅×Dic₁₃	49

Subgroups — C3×C5×#14579331 #50304338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#14579331 #50304338