Subgroups — #50303971

Order 38220.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#16838448	C₂	1	1	yes	maximal, characteristic
2	#27164969	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×#14274263	C₄	1	1	yes	characteristic, complemented, Hall
4	#21439681	—	5	1	no	maximal, Hall
5	C₅×C₁₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
6	#16838448	D₅	1	1	yes	characteristic
7	C₅×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	#11758267⋊C₃	—	13	1	no	maximal, Hall
9	C₅×#10587720	—	14	4	no	—
10	#14579331	—	5	1	no	Hall
11	#14274263	Dic₅	1	1	yes	characteristic, complemented, Hall
12	C₅×#64424	—	13	1	no	—
13	C₅×#63270	—	14	4	no	—
14	C₁₃×C₇⋊D₇	C₃×D₅	1	1	yes	characteristic
15	#11758267	—	13	1	no	Hall
16	C₅×C₁₃×D₇	—	14	4	no	—
17	Dic₆₅⋊C₃	—	49	1	no	maximal, Hall
18	C₅×#3861	—	13	1	no	Hall
19	C₇²×C₁₃	C₃×Dic₅	1	1	yes	characteristic, complemented, Hall
20	#5997⋊C₃	—	65	1	no	Hall
21	#10587720	—	14	4	no	—
22	C₅×C₇⋊D₇	D₁₃⋊C₃	1	1	yes	characteristic
23	C₅×C₇×C₁₃	—	2	4	no	—
24	C₂×C₅×C₁₃⋊C₃	—	49	1	no	—
25	#64424	—	13	1	no	—
26	#63270	—	14	4	no	—
27	Dic₆₅	—	49	1	no	Hall
28	C₅×C₇²	Dic₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
29	C₅×AGL(1,𝔽₇)	—	182	4	no	—
30	#5997	—	65	1	no	Hall
31	C₅×C₁₃⋊C₃	—	49	1	no	Hall
32	C₁₃×D₇	—	14	4	no	—
33	Dic₁₃⋊C₃	—	245	1	no	Hall
34	#3861	—	13	1	no	Hall
35	C₂×C₅×C₁₃	—	49	1	no	—
36	C₅×ΓL(1,𝔽₈)	—	182	4	no	—
37	C₇⋊D₇	C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic
38	C₇×C₁₃	—	2	4	no	—
39	C₂×C₁₃⋊C₃	—	49	1	no	—
40	C₅×D₇	—	14	4	no	—
41	C₅×C₁₃	#5997⋊C₃	1	1	yes	characteristic, complemented, Hall
42	C₃×Dic₅	—	637	1	no	Hall
43	Dic₁₃	—	245	1	no	Hall
44	C₇²	Dic₆₅⋊C₃	1	1	yes	characteristic, complemented, Sylow
45	AGL(1,𝔽₇)	—	182	4	no	—
46	C₁₃⋊C₃	—	49	1	no	Hall
47	C₅×C₇	—	2	4	no	—
48	C₂×C₃×C₅	—	637	1	no	—
49	C₂×C₁₃	—	49	1	no	—
50	ΓL(1,𝔽₈)	—	182	4	no	—
51	Dic₅	—	637	1	no	Hall
52	C₃×C₅	—	637	1	no	Hall
53	D₇	—	14	4	no	—
54	C₁₃	#11758267⋊C₃	1	1	yes	characteristic, complemented, Sylow
55	C₃×C₄	—	3185	1	no	Hall
56	C₂×C₅	—	49	1	no	—
57	C₇	—	2	4	no	—
58	C₂×C₃	—	637	1	no	—
59	C₅	#21439681	1	1	yes	characteristic, complemented, Sylow
60	C₄	—	3185	1	no	Sylow
61	C₃	—	637	1	no	Sylow
62	C₂	—	49	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₇²×C₁₃	C₃×C₄
prime radical	C₅×#16838448	C₂
cosocle	C₅×C₁₃×C₇⋊D₇	C₂×C₃
LCS	G ▷ C₅×C₇²×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. #27164969	C₃	semidirect
3. C₅×#14274263	C₄	semidirect
7. C₅×C₇²×C₁₃	C₃×C₄	semidirect
11. #14274263	Dic₅	semidirect
19. C₇²×C₁₃	C₃×Dic₅	semidirect
28. C₅×C₇²	Dic₁₃⋊C₃	semidirect
41. C₅×C₁₃	#5997⋊C₃	semidirect
44. C₇²	Dic₆₅⋊C₃	semidirect
54. C₁₃	#11758267⋊C₃	semidirect
59. C₅	#21439681	semidirect

Maximal subgroups

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

subgroup	index
C₅×#16838448	2
#27164969	3
#21439681	5
#11758267⋊C₃	13
Dic₆₅⋊C₃	49