Subgroups — C₂×C₅⋊#16838448 #50304311

Order 38220.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#14274263	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅⋊#16838448	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₃×C₅⋊(C₇⋊D₇)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×#14274263	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×#16838448	—	5	1	no	maximal, Hall
6	C₁₃×C₅⋊(C₇⋊D₇)	C₂×C₃	1	2	yes	complemented
7	C₂×C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₅⋊#10587720	—	7	8	no	maximal
9	C₂×#14274263	D₅	1	1	yes	characteristic, complemented
10	#16838448	—	5	2	no	—
11	C₅×C₇²×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅⋊#64424	—	13	1	no	maximal, Hall
13	C₅⋊#10587720	—	7	16	no	—
14	C₂×C₅×#63270	—	7	8	no	—
15	C₂×C₁₃×C₇⋊D₇	—	5	1	no	Hall
16	#14274263	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₃×D₃₅	—	7	8	no	—
18	C₂×C₅×#3861	—	13	1	no	—
19	C₅⋊#64424	—	13	2	no	—
20	C₅×#63270	—	7	8	no	—
21	C₂×C₇²×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented
22	C₁₃×C₇⋊D₇	—	5	2	no	—
23	C₂×#10587720	—	35	8	no	—
24	C₂×C₅⋊(C₇⋊D₇)	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₅×C₇×C₁₃	AGL(1,𝔽₇)	1	8	yes	complemented
26	C₁₃×D₃₅	—	7	16	no	—
27	C₂×D₅×C₁₃⋊C₃	—	49	1	no	Hall
28	C₅×#3861	—	13	1	no	Hall
29	C₇²×C₁₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
30	C₂×#64424	—	65	1	no	Hall
31	C₂×#63270	—	7	8	no	—
32	#10587720	—	35	16	no	—
33	C₂×C₅×C₇²	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
34	C₅⋊(C₇⋊D₇)	C₂×C₁₃⋊C₃	1	2	yes	complemented
35	C₅×C₇×C₁₃	C₂×AGL(1,𝔽₇)	1	8	yes	complemented
36	C₂×C₅⋊AGL(1,𝔽₇)	—	91	8	no	—
37	C₂×C₅×C₁₃⋊C₃	—	49	1	no	—
38	D₅×C₁₃⋊C₃	—	49	2	no	—
39	C₂×C₁₃×D₇	—	35	8	no	—
40	C₂×#3861	—	13	1	no	—
41	#64424	—	65	2	no	—
42	#63270	—	7	8	no	—
43	C₂×D₅×C₁₃	—	49	1	no	Hall
44	C₅×C₇²	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
45	C₂×C₅×ΓL(1,𝔽₈)	—	91	8	no	—
46	C₅⋊AGL(1,𝔽₇)	—	91	16	no	—
47	C₂×C₇⋊D₇	—	5	1	no	Hall
48	C₅×C₁₃⋊C₃	—	49	1	no	Hall
49	C₂×C₇×C₁₃	C₅⋊AGL(1,𝔽₇)	1	8	yes	complemented
50	C₁₃×D₇	—	35	16	no	—
51	C₂²×C₁₃⋊C₃	—	245	1	no	Hall
52	#3861	—	13	1	no	Hall
53	C₂×D₃₅	—	7	8	no	—
54	C₂×C₅×C₁₃	#64424	1	1	yes	characteristic, complemented
55	D₅×C₁₃	—	49	2	no	—
56	C₅×ΓL(1,𝔽₈)	—	91	8	no	—
57	C₂×C₇²	D₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented
58	C₇⋊D₇	—	5	2	no	—
59	C₇×C₁₃	C₂×C₅⋊AGL(1,𝔽₇)	1	8	yes	complemented
60	C₂×AGL(1,𝔽₇)	—	455	8	no	—
61	C₂×C₁₃⋊C₃	—	49	1	no	—
62	C₂×C₁₃⋊C₃	—	245	2	no	—
63	C₂×C₅×C₇	#10587720	1	8	yes	complemented
64	D₃₅	—	7	16	no	—
65	C₅×C₁₃	C₂×#64424	1	1	yes	characteristic, complemented, Hall
66	C₂×C₃×D₅	—	637	1	no	Hall
67	C₂²×C₁₃	—	245	1	no	Hall
68	C₇²	C₂×D₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
69	C₂×ΓL(1,𝔽₈)	—	91	8	no	—
70	AGL(1,𝔽₇)	—	455	16	no	—
71	C₁₃⋊C₃	—	49	1	no	Hall
72	C₅×C₇	C₂×#10587720	1	8	yes	complemented
73	C₂×C₃×C₅	—	637	1	no	—
74	C₃×D₅	—	637	2	no	—
75	C₂×D₇	—	35	8	no	—
76	C₂×C₁₃	—	245	2	no	—
77	C₂×C₁₃	C₅⋊#64424	1	1	yes	characteristic, complemented
78	ΓL(1,𝔽₈)	—	91	8	no	—
79	C₂×D₅	—	49	1	no	Hall
80	C₃×C₅	—	637	1	no	Hall
81	C₂×C₇	C₅⋊#10587720	1	8	yes	complemented
82	D₇	—	35	16	no	—
83	C₁₃	C₂×C₅⋊#64424	1	1	yes	characteristic, complemented, Sylow
84	C₂²×C₃	—	3185	1	no	Hall
85	C₂×C₅	#16838448	1	1	yes	characteristic, complemented
86	D₅	—	49	2	no	—
87	C₇	C₂×C₅⋊#10587720	1	8	yes	complemented
88	C₂×C₃	—	3185	2	no	—
89	C₂×C₃	—	637	1	no	—
90	C₅	C₂×#16838448	1	1	yes	characteristic, complemented, Sylow
91	C₂²	—	245	1	no	Sylow
92	C₃	—	637	1	no	Sylow
93	C₂	—	245	2	no	—
94	C₂	C₅⋊#16838448	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊#16838448
commutator, cosocle, hypocenter	C₅×C₇²×C₁₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₅×C₇²×C₁₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#14274263	C₂	semidirect
2. C₅⋊#16838448	C₂	direct (N × H)
3. C₂×C₁₃×C₅⋊(C₇⋊D₇)	C₃	semidirect
4. C₅×#14274263	C₂²	semidirect
6. C₁₃×C₅⋊(C₇⋊D₇)	C₂×C₃	semidirect
7. C₂×C₅×C₇²×C₁₃	C₂×C₃	semidirect
9. C₂×#14274263	D₅	semidirect
11. C₅×C₇²×C₁₃	C₂²×C₃	semidirect
16. #14274263	C₂×D₅	semidirect
21. C₂×C₇²×C₁₃	C₃×D₅	semidirect
24. C₂×C₅⋊(C₇⋊D₇)	C₁₃⋊C₃	semidirect
25. C₂×C₅×C₇×C₁₃	AGL(1,𝔽₇)	semidirect
29. C₇²×C₁₃	C₂×C₃×D₅	semidirect
33. C₂×C₅×C₇²	C₂×C₁₃⋊C₃	semidirect
34. C₅⋊(C₇⋊D₇)	C₂×C₁₃⋊C₃	semidirect
35. C₅×C₇×C₁₃	C₂×AGL(1,𝔽₇)	semidirect
44. C₅×C₇²	C₂²×C₁₃⋊C₃	semidirect
49. C₂×C₇×C₁₃	C₅⋊AGL(1,𝔽₇)	semidirect
54. C₂×C₅×C₁₃	#64424	semidirect
57. C₂×C₇²	D₅×C₁₃⋊C₃	semidirect
59. C₇×C₁₃	C₂×C₅⋊AGL(1,𝔽₇)	semidirect
63. C₂×C₅×C₇	#10587720	semidirect
65. C₅×C₁₃	C₂×#64424	semidirect
68. C₇²	C₂×D₅×C₁₃⋊C₃	semidirect
72. C₅×C₇	C₂×#10587720	semidirect
77. C₂×C₁₃	C₅⋊#64424	semidirect
81. C₂×C₇	C₅⋊#10587720	semidirect
83. C₁₃	C₂×C₅⋊#64424	semidirect
85. C₂×C₅	#16838448	semidirect
87. C₇	C₂×C₅⋊#10587720	semidirect
90. C₅	C₂×#16838448	semidirect
94. C₂	C₅⋊#16838448	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#14274263	2
C₅⋊#16838448	2
C₂×C₁₃×C₅⋊(C₇⋊D₇)	3
C₂×#16838448	5
C₂×C₅⋊#10587720	7
C₂×C₅⋊#64424	13

Subgroups — C2×C5⋊#16838448 #50304311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅⋊#16838448 #50304311