Subgroups — C₃⋊(C₇⋊#13049932) #41032072

Order 27300.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₃×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₇⋊#13049932	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₇×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₇⋊#63120)	—	5	2	no	maximal
5	C₇×C₁₃×C₅⋊D₅	D₃	1	1	yes	characteristic
6	C₃⋊#13049932	—	7	1	no	maximal, Hall
7	C₃×C₇×D₅×C₁₃	—	5	2	no	—
8	C₃×C₇×D₅×C₁₃	—	10	2	no	—
9	C₅²×C₇×C₁₃	Dic₃	1	1	yes	characteristic, complemented, Hall
10	C₃⋊(C₇⋊#1044)	—	13	1	no	maximal, Hall
11	C₃×C₁₃×C₅⋊D₅	D₇	1	1	yes	characteristic
12	C₇⋊#63120	—	15	2	no	—
13	C₃×C₅×C₇×C₁₃	—	2	2	no	—
14	C₃×C₅×C₇×C₁₃	AGL(1,𝔽₅)	1	2	yes	complemented
15	#13049932	—	21	1	no	Hall
16	Dic₂₇₃	—	25	1	no	Hall
17	C₃×C₇×C₅⋊D₅	D₁₃	1	1	yes	characteristic
18	C₃×C₅²×C₁₃	Dic₇	1	1	yes	characteristic, complemented, Hall
19	C₇×D₅×C₁₃	—	5	2	no	—
20	C₇×D₅×C₁₃	—	10	2	no	—
21	C₃⋊#63120	—	35	2	no	—
22	C₇⋊#1044	—	39	1	no	Hall
23	C₁₃×C₅⋊D₅	D₂₁	1	1	yes	characteristic
24	C₂×C₃×C₇×C₁₃	—	25	1	no	—
25	C₃×C₅²×C₇	Dic₁₃	1	1	yes	characteristic, complemented, Hall
26	C₅×C₇×C₁₃	—	2	2	no	—
27	C₅×C₇×C₁₃	ΓL(1,𝔽₁₆)	1	2	yes	complemented
28	C₃⋊(C₇⋊AGL(1,𝔽₅))	—	65	2	no	—
29	C₃×D₅×C₁₃	—	5	2	no	—
30	C₃×D₅×C₁₃	—	10	2	no	—
31	Dic₉₁	—	75	1	no	Hall
32	C₇×C₅⋊D₅	D₃₉	1	1	yes	characteristic
33	C₅²×C₁₃	Dic₂₁	1	1	yes	characteristic, complemented, Hall
34	C₃⋊#1044	—	91	1	no	Hall
35	C₃×C₇×C₁₃	#1044	1	1	yes	characteristic, complemented, Hall
36	#63120	—	105	2	no	—
37	C₃×C₇×D₅	—	5	2	no	—
38	C₃×C₇×D₅	—	10	2	no	—
39	C₃×C₅×C₁₃	—	2	2	no	—
40	C₃×C₅×C₁₃	C₇⋊AGL(1,𝔽₅)	1	2	yes	complemented
41	C₂×C₇×C₁₃	—	25	1	no	—
42	C₅²×C₇	Dic₃₉	1	1	yes	characteristic, complemented, Hall
43	Dic₃₉	—	175	1	no	Hall
44	C₃×C₅⋊D₅	D₉₁	1	1	yes	characteristic
45	C₇⋊AGL(1,𝔽₅)	—	195	2	no	—
46	D₅×C₁₃	—	5	2	no	—
47	D₅×C₁₃	—	10	2	no	—
48	C₃×C₅×C₇	—	2	2	no	—
49	C₃×C₅×C₇	#63120	1	2	yes	complemented
50	#1044	—	273	1	no	Hall
51	C₇×C₁₃	C₃⋊#1044	1	1	yes	characteristic, complemented, Hall
52	Dic₂₁	—	325	1	no	Hall
53	C₂×C₃×C₁₃	—	25	1	no	—
54	C₃×C₅²	Dic₉₁	1	1	yes	characteristic, complemented, Hall
55	C₇×D₅	—	5	2	no	—
56	C₇×D₅	—	10	2	no	—
57	C₅×C₁₃	—	2	2	no	—
58	C₅×C₁₃	C₃⋊(C₇⋊AGL(1,𝔽₅))	1	2	yes	complemented
59	ΓL(1,𝔽₁₆)	—	455	2	no	—
60	Dic₁₃	—	525	1	no	Hall
61	C₅⋊D₅	D₂₇₃	1	1	yes	characteristic
62	C₂×C₃×C₇	—	25	1	no	—
63	C₃×C₁₃	C₇⋊#1044	1	1	yes	characteristic, complemented, Hall
64	C₅×C₇	—	2	2	no	—
65	C₅×C₇	C₃⋊#63120	1	2	yes	complemented
66	C₃×D₅	—	5	2	no	—
67	C₃×D₅	—	10	2	no	—
68	Dic₇	—	975	1	no	Hall
69	C₂×C₁₃	—	25	1	no	—
70	C₅²	Dic₂₇₃	1	1	yes	characteristic, complemented, Sylow
71	C₃×C₇	#13049932	1	1	yes	characteristic, complemented, Hall
72	AGL(1,𝔽₅)	—	1365	2	no	—
73	C₃×C₅	—	2	2	no	—
74	C₃×C₅	C₇⋊#63120	1	2	yes	complemented
75	C₂×C₇	—	25	1	no	—
76	C₁₃	C₃⋊(C₇⋊#1044)	1	1	yes	characteristic, complemented, Sylow
77	Dic₃	—	2275	1	no	Hall
78	D₅	—	5	2	no	—
79	D₅	—	10	2	no	—
80	C₇	C₃⋊#13049932	1	1	yes	characteristic, complemented, Sylow
81	C₂×C₃	—	25	1	no	—
82	C₅	—	2	2	no	—
83	C₅	C₃⋊(C₇⋊#63120)	1	2	yes	complemented
84	C₄	—	6825	1	no	Sylow
85	C₃	C₇⋊#13049932	1	1	yes	characteristic, complemented, Sylow
86	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅²×C₇×C₁₃	C₄
prime radical, cosocle	C₃×C₇×C₁₃×C₅⋊D₅	C₂
LCS	G ▷ C₃×C₅²×C₇×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₃×C₅²×C₇×C₁₃	C₄	semidirect
9. C₅²×C₇×C₁₃	Dic₃	semidirect
14. C₃×C₅×C₇×C₁₃	AGL(1,𝔽₅)	semidirect
18. C₃×C₅²×C₁₃	Dic₇	semidirect
25. C₃×C₅²×C₇	Dic₁₃	semidirect
27. C₅×C₇×C₁₃	ΓL(1,𝔽₁₆)	semidirect
33. C₅²×C₁₃	Dic₂₁	semidirect
35. C₃×C₇×C₁₃	#1044	semidirect
40. C₃×C₅×C₁₃	C₇⋊AGL(1,𝔽₅)	semidirect
42. C₅²×C₇	Dic₃₉	semidirect
49. C₃×C₅×C₇	#63120	semidirect
51. C₇×C₁₃	C₃⋊#1044	semidirect
54. C₃×C₅²	Dic₉₁	semidirect
58. C₅×C₁₃	C₃⋊(C₇⋊AGL(1,𝔽₅))	semidirect
63. C₃×C₁₃	C₇⋊#1044	semidirect
65. C₅×C₇	C₃⋊#63120	semidirect
70. C₅²	Dic₂₇₃	semidirect
71. C₃×C₇	#13049932	semidirect
74. C₃×C₅	C₇⋊#63120	semidirect
76. C₁₃	C₃⋊(C₇⋊#1044)	semidirect
80. C₇	C₃⋊#13049932	semidirect
83. C₅	C₃⋊(C₇⋊#63120)	semidirect
85. C₃	C₇⋊#13049932	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₃×C₅⋊D₅	2
C₇⋊#13049932	3
C₃⋊(C₇⋊#63120)	5
C₃⋊#13049932	7
C₃⋊(C₇⋊#1044)	13

Subgroups — C3⋊(C7⋊#13049932) #41032072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₇⋊#13049932) #41032072