Subgroups — C₂×C₅×C₁₃⋊C₃×C₇⋊D₇ #50304271

Order 38220.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₅	C₁₃⋊C₃×C₇⋊D₇
commutator, cosocle, hypocenter	C₇²×C₁₃	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₇²×C₁₃⋊C₃	C₂	semidirect
2. C₅×C₁₃⋊C₃×C₇⋊D₇	C₂	direct (N × H)
3. C₂×C₅×C₁₃×C₇⋊D₇	C₃	semidirect
4. C₅×C₇²×C₁₃⋊C₃	C₂²	semidirect
5. C₂×C₁₃⋊C₃×C₇⋊D₇	C₅	direct (N × H)
6. C₅×C₁₃×C₇⋊D₇	C₂×C₃	semidirect
7. C₂×C₅×C₇²×C₁₃	C₂×C₃	semidirect
9. C₂×C₇²×C₁₃⋊C₃	C₂×C₅	semidirect
10. C₁₃⋊C₃×C₇⋊D₇	C₂×C₅	direct (N × H)
11. C₅×C₇²×C₁₃	C₂²×C₃	semidirect
14. C₂×C₅×C₇×C₁₃⋊C₃	D₇	semidirect
15. C₂×C₁₃×C₇⋊D₇	C₃×C₅	semidirect
16. C₇²×C₁₃⋊C₃	C₂²×C₅	semidirect
20. C₅×C₇×C₁₃⋊C₃	C₂×D₇	semidirect
21. C₂×C₇²×C₁₃	C₂×C₃×C₅	semidirect
22. C₁₃×C₇⋊D₇	C₂×C₃×C₅	semidirect
24. C₂×C₅×C₇⋊D₇	C₁₃⋊C₃	direct (N × H)
25. C₂×C₅×C₇×C₁₃	C₃×D₇	semidirect
29. C₇²×C₁₃	C₂²×C₃×C₅	semidirect
31. C₂×C₇×C₁₃⋊C₃	C₅×D₇	semidirect
33. C₂×C₅×C₇²	C₂×C₁₃⋊C₃	semidirect
34. C₅×C₇⋊D₇	C₂×C₁₃⋊C₃	direct (N × H)
35. C₅×C₇×C₁₃	C₂×C₃×D₇	semidirect
38. C₂×C₅×C₁₃⋊C₃	C₇⋊D₇	direct (N × H)
42. C₇×C₁₃⋊C₃	C₂×C₅×D₇	semidirect
44. C₅×C₇²	C₂²×C₁₃⋊C₃	semidirect
47. C₂×C₇⋊D₇	C₅×C₁₃⋊C₃	direct (N × H)
48. C₅×C₁₃⋊C₃	C₂×C₇⋊D₇	direct (N × H)
49. C₂×C₇×C₁₃	C₃×C₅×D₇	semidirect
55. C₂×C₅×C₁₃	C₃×C₇⋊D₇	semidirect
57. C₂×C₇²	C₂×C₅×C₁₃⋊C₃	semidirect
58. C₇⋊D₇	C₂×C₅×C₁₃⋊C₃	direct (N × H)
59. C₇×C₁₃	C₂×C₃×C₅×D₇	semidirect
62. C₂×C₁₃⋊C₃	C₅×C₇⋊D₇	direct (N × H)
63. C₂×C₅×C₇	D₇×C₁₃⋊C₃	semidirect
65. C₅×C₁₃	C₂×C₃×C₇⋊D₇	semidirect
68. C₇²	C₂²×C₅×C₁₃⋊C₃	semidirect
71. C₁₃⋊C₃	C₂×C₅×C₇⋊D₇	direct (N × H)
72. C₅×C₇	C₂×D₇×C₁₃⋊C₃	semidirect
77. C₂×C₁₃	C₃×C₅×C₇⋊D₇	semidirect
81. C₂×C₇	C₅×D₇×C₁₃⋊C₃	semidirect
83. C₁₃	C₂×C₃×C₅×C₇⋊D₇	semidirect
86. C₂×C₅	C₁₃⋊C₃×C₇⋊D₇	direct (N × H)
87. C₇	C₂×C₅×D₇×C₁₃⋊C₃	semidirect
90. C₅	C₂×C₁₃⋊C₃×C₇⋊D₇	direct (N × H)
94. C₂	C₅×C₁₃⋊C₃×C₇⋊D₇	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×C₇²×C₁₃⋊C₃	2
C₅×C₁₃⋊C₃×C₇⋊D₇	2
C₂×C₅×C₁₃×C₇⋊D₇	3
C₂×C₁₃⋊C₃×C₇⋊D₇	5
C₂×C₅×D₇×C₁₃⋊C₃	7
C₂×C₃×C₅×C₇⋊D₇	13

Subgroups — C2×C5×C13⋊C3×C7⋊D7 #50304271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₁₃⋊C₃×C₇⋊D₇ #50304271