Subgroups — C₃×#27164944 #50304349

Order 38220.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊(C₇⋊D₉₁)	C₂	1	1	yes	maximal, characteristic
2	#27164944	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₇²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×#14579330	—	5	1	no	maximal, Hall
5	C₅⋊(C₇⋊D₉₁)	C₂×C₃	1	1	yes	characteristic
6	C₃×C₇⋊D₉₁	—	5	1	no	—
7	C₅×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×#11758266	—	13	1	no	maximal, Hall
9	C₃×D₄₅₅	—	14	4	no	—
10	#14579330	—	5	1	no	Hall
11	C₃×C₇²×C₁₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅⋊(C₇⋊D₇)	—	13	1	no	—
13	C₃×C₅×C₇×C₁₃	—	2	4	no	—
14	C₇⋊D₉₁	—	5	1	no	—
15	#11758266	—	13	1	no	Hall
16	D₄₅₅	—	14	4	no	—
17	C₃×#63121	—	49	1	no	maximal, Hall
18	C₃×C₅×C₇²	#261	1	1	yes	characteristic, complemented, Hall
19	C₇²×C₁₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
20	C₃×#5997	—	65	1	no	Hall
21	C₃×D₉₁	—	70	4	no	—
22	C₅⋊(C₇⋊D₇)	—	13	1	no	—
23	C₅×C₇×C₁₃	—	2	4	no	—
24	C₃×D₆₅	—	49	1	no	—
25	C₃×C₇⋊D₇	—	65	1	no	—
26	C₃×C₇×C₁₃	—	2	4	no	—
27	#63121	—	49	1	no	Hall
28	C₅×C₇²	C₃×#261	1	1	yes	characteristic, complemented, Hall
29	C₃×D₃₅	—	182	4	no	—
30	#5997	—	65	1	no	Hall
31	C₃×C₅×C₁₃	#5997	1	1	yes	characteristic, complemented, Hall
32	D₉₁	—	70	4	no	—
33	C₃×#261	—	245	1	no	Hall
34	C₃×C₇²	#63121	1	1	yes	characteristic, complemented, Hall
35	D₆₅	—	49	1	no	—
36	C₃×C₅×C₇	—	2	4	no	—
37	C₇⋊D₇	—	65	1	no	—
38	C₇×C₁₃	—	2	4	no	—
39	C₃×D₁₃	—	245	1	no	—
40	D₃₅	—	182	4	no	—
41	C₅×C₁₃	C₃×#5997	1	1	yes	characteristic, complemented, Hall
42	C₃×AGL(1,𝔽₅)	—	637	1	no	Hall
43	#261	—	245	1	no	Hall
44	C₇²	C₃×#63121	1	1	yes	characteristic, complemented, Sylow
45	C₃×D₇	—	910	4	no	—
46	C₃×C₁₃	#11758266	1	1	yes	characteristic, complemented, Hall
47	C₅×C₇	—	2	4	no	—
48	C₃×D₅	—	637	1	no	—
49	D₁₃	—	245	1	no	—
50	C₃×C₇	—	2	4	no	—
51	AGL(1,𝔽₅)	—	637	1	no	Hall
52	C₃×C₅	#14579330	1	1	yes	characteristic, complemented, Hall
53	D₇	—	910	4	no	—
54	C₁₃	C₃×#11758266	1	1	yes	characteristic, complemented, Sylow
55	C₃×C₄	—	3185	1	no	Hall
56	D₅	—	637	1	no	—
57	C₇	—	2	4	no	—
58	C₂×C₃	—	3185	1	no	—
59	C₅	C₃×#14579330	1	1	yes	characteristic, complemented, Sylow
60	C₄	—	3185	1	no	Sylow
61	C₃	#27164944	1	1	yes	characteristic, direct product factor, Sylow
62	C₂	—	3185	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#27164944
commutator, hypocenter	C₅×C₇²×C₁₃	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²×C₁₃	C₄
prime radical	C₃×C₅⋊(C₇⋊D₉₁)	C₂
cosocle	C₅⋊(C₇⋊D₉₁)	C₂×C₃
LCS	G ▷ C₅×C₇²×C₁₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. #27164944	C₃	direct (N × H)
3. C₃×C₅×C₇²×C₁₃	C₄	semidirect
7. C₅×C₇²×C₁₃	C₃×C₄	semidirect
11. C₃×C₇²×C₁₃	AGL(1,𝔽₅)	semidirect
18. C₃×C₅×C₇²	#261	semidirect
19. C₇²×C₁₃	C₃×AGL(1,𝔽₅)	semidirect
28. C₅×C₇²	C₃×#261	semidirect
31. C₃×C₅×C₁₃	#5997	semidirect
34. C₃×C₇²	#63121	semidirect
41. C₅×C₁₃	C₃×#5997	semidirect
44. C₇²	C₃×#63121	semidirect
46. C₃×C₁₃	#11758266	semidirect
52. C₃×C₅	#14579330	semidirect
54. C₁₃	C₃×#11758266	semidirect
59. C₅	C₃×#14579330	semidirect
61. C₃	#27164944	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⋊(C₇⋊D₉₁)	2
#27164944	3
C₃×#14579330	5
C₃×#11758266	13
C₃×#63121	49

Subgroups — C3×#27164944 #50304349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#27164944 #50304349