Subgroups — #50303817

Order 38220.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊#16838454	C₂	1	1	yes	maximal, characteristic
2	#27164943	—	3	1	no	maximal, Hall
3	C₅×C₁₃×#3862	C₄	1	1	yes	characteristic, complemented, Hall
4	#21439675	—	5	1	no	maximal, Hall
5	C₅⋊(C₇⋊D₉₁)	D₃	1	1	yes	characteristic
6	#16838454	—	5	1	no	—
7	C₅×C₇²×C₁₃	Dic₃	1	1	yes	characteristic, complemented, Hall
8	#15668774	—	13	1	no	maximal, Hall
9	C₅⋊(ΓL(1,𝔽₈)⋊D₁₃)	—	14	1	no	—
10	#14579330	—	15	1	no	Hall
11	C₁₃×#3862	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₅⋊#64425	—	13	1	no	—
13	C₅×C₁₃×ΓL(1,𝔽₈)	—	14	1	no	—
14	C₇⋊D₉₁	—	5	1	no	—
15	#11758266	—	39	1	no	Hall
16	D₄₅₅	—	14	1	no	—
17	D₄₅₅	—	42	1	no	—
18	C₃⋊#63122	—	49	1	no	maximal, Hall
19	C₅×#3862	#261	1	1	yes	characteristic, complemented, Hall
20	C₇²×C₁₃	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Hall
21	#10596885	—	65	1	no	Hall
22	ΓL(1,𝔽₈)⋊D₁₃	—	70	1	no	—
23	C₅⋊(C₇⋊D₇)	—	13	1	no	—
24	C₅×C₇×C₁₃	—	2	1	no	—
25	C₅×C₇×C₁₃	—	6	1	no	—
26	C₃×D₆₅	—	49	1	no	—
27	#64425	—	65	1	no	—
28	C₁₃×ΓL(1,𝔽₈)	—	14	1	no	—
29	#63122	—	147	1	no	Hall
30	C₅×C₇²	C₃⋊#261	1	1	yes	characteristic, complemented, Hall
31	C₅⋊AGL(1,𝔽₇)	—	182	1	no	—
32	#5997	—	195	1	no	Hall
33	C₃×C₅×C₁₃	—	49	1	no	Hall
34	D₉₁	—	70	1	no	—
35	D₉₁	—	210	1	no	—
36	C₃⋊#261	—	245	1	no	Hall
37	#3862	#63122	1	1	yes	characteristic, complemented, Hall
38	D₆₅	—	49	1	no	—
39	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
40	C₇⋊D₇	—	65	1	no	—
41	C₇×C₁₃	—	2	1	no	—
42	C₇×C₁₃	—	6	1	no	—
43	C₃×D₁₃	—	245	1	no	—
44	D₃₅	—	546	1	no	—
45	D₃₅	—	182	1	no	—
46	C₅×C₁₃	#10596885	1	1	yes	characteristic, complemented, Hall
47	ΓL(1,𝔽₁₆)	—	637	1	no	Hall
48	#261	—	735	1	no	Hall
49	C₇²	C₃⋊#63122	1	1	yes	characteristic, complemented, Sylow
50	AGL(1,𝔽₇)	—	910	1	no	—
51	C₃×C₁₃	—	49	1	no	Hall
52	C₅×C₇	—	2	1	no	—
53	C₅×C₇	—	6	1	no	—
54	C₃×D₅	—	637	1	no	—
55	D₁₃	—	245	1	no	—
56	ΓL(1,𝔽₈)	—	14	1	no	—
57	AGL(1,𝔽₅)	—	1911	1	no	Hall
58	C₃×C₅	—	49	1	no	Hall
59	D₇	—	910	1	no	—
60	D₇	—	2730	1	no	—
61	C₁₃	#15668774	1	1	yes	characteristic, complemented, Sylow
62	Dic₃	—	3185	1	no	Hall
63	D₅	—	637	1	no	—
64	C₇	—	2	1	no	—
65	C₇	—	6	1	no	—
66	C₂×C₃	—	3185	1	no	—
67	C₅	#21439675	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	9555	1	no	Sylow
69	C₃	—	49	1	no	Sylow
70	C₂	—	3185	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	C₅×C₁₃×#3862	C₄
Fitting, socle	C₅×C₇²×C₁₃	Dic₃
prime radical, cosocle	C₅⋊#16838454	C₂
LCS	G ▷ C₅×C₁₃×#3862
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₅×C₁₃×#3862	C₄	semidirect
7. C₅×C₇²×C₁₃	Dic₃	semidirect
11. C₁₃×#3862	AGL(1,𝔽₅)	semidirect
19. C₅×#3862	#261	semidirect
20. C₇²×C₁₃	ΓL(1,𝔽₁₆)	semidirect
30. C₅×C₇²	C₃⋊#261	semidirect
37. #3862	#63122	semidirect
46. C₅×C₁₃	#10596885	semidirect
49. C₇²	C₃⋊#63122	semidirect
61. C₁₃	#15668774	semidirect
67. C₅	#21439675	semidirect

Maximal subgroups

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

subgroup	index
C₅⋊#16838454	2
#27164943	3
#21439675	5
#15668774	13
C₃⋊#63122	49