Subgroups — C₂×C₅×(C₁₃⋊C₃)⋊(C₇⋊D₇) #50304270

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×C₇⋊D₉₁	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×C₇⋊D₉₁	C₂×C₃	1	2	yes	complemented
7	C₂×C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₅×(C₁₃⋊C₃)⋊D₇	—	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×(C₁₃⋊C₃)⋊D₇	—	7	16	no	—
14	C₂×C₅×C₇×C₁₃⋊C₃	D₇	1	8	yes	complemented
15	C₂×C₇⋊D₉₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
16	C₇²×C₁₃⋊C₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×D₉₁	—	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	C₇⋊D₉₁	C₂×C₃×C₅	1	2	yes	complemented
23	C₂×(C₁₃⋊C₃)⋊D₇	—	7	8	no	—
24	C₂×C₅×C₇⋊D₇	—	13	1	no	Hall
25	C₂×C₅×C₇×C₁₃	C₃×D₇	1	8	yes	complemented
26	C₅×D₉₁	—	7	16	no	—
27	C₂×C₅×D₁₃⋊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	(C₁₃⋊C₃)⋊D₇	—	7	16	no	—
33	C₂×C₅×C₇²	D₁₃⋊C₃	1	1	yes	characteristic, complemented
34	C₅×C₇⋊D₇	—	13	2	no	—
35	C₅×C₇×C₁₃	C₂×C₃×D₇	1	8	yes	complemented
36	C₂×C₃×C₅×D₇	—	91	8	no	—
37	C₂×C₅×C₁₃⋊C₃	C₇⋊D₇	1	1	yes	characteristic, complemented
38	C₅×D₁₃⋊C₃	—	49	2	no	—
39	C₂×D₉₁	—	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	C₂×C₅×D₁₃	—	49	1	no	Hall
44	C₅×C₇²	C₂×D₁₃⋊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	—	13	1	no	Hall
48	C₅×C₁₃⋊C₃	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
49	C₂×C₇×C₁₃	C₃×C₅×D₇	1	8	yes	complemented
50	D₉₁	—	7	16	no	—
51	C₂×D₁₃⋊C₃	—	49	1	no	Hall
52	C₃×C₇²	—	13	1	no	Hall
53	C₂×C₅×D₇	—	91	8	no	—
54	C₂×C₅×C₁₃	C₃×C₇⋊D₇	1	1	yes	characteristic, complemented
55	C₅×D₁₃	—	49	2	no	—
56	C₃×C₅×C₇	—	13	8	no	—
57	C₂×C₇²	C₅×D₁₃⋊C₃	1	1	yes	characteristic, complemented
58	C₇⋊D₇	—	13	2	no	—
59	C₇×C₁₃	C₂×C₃×C₅×D₇	1	8	yes	complemented
60	C₂×C₃×D₇	—	91	8	no	—
61	C₂×C₁₃⋊C₃	C₅×C₇⋊D₇	1	1	yes	characteristic, complemented
62	D₁₃⋊C₃	—	49	2	no	—
63	C₂×C₅×C₇	(C₁₃⋊C₃)⋊D₇	1	8	yes	complemented
64	C₅×D₇	—	91	16	no	—
65	C₅×C₁₃	C₂×C₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
66	C₂²×C₃×C₅	—	637	1	no	Hall
67	C₂×D₁₃	—	49	1	no	Hall
68	C₇²	C₂×C₅×D₁₃⋊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, complemented, Hall
72	C₅×C₇	C₂×(C₁₃⋊C₃)⋊D₇	1	8	yes	complemented
73	C₂×C₃×C₅	—	13	1	no	—
74	C₂×C₃×C₅	—	637	2	no	—
75	C₂×D₇	—	91	8	no	—
76	C₂×C₁₃	C₃×C₅×C₇⋊D₇	1	1	yes	characteristic, complemented
77	D₁₃	—	49	2	no	—
78	C₃×C₇	—	13	8	no	—
79	C₂²×C₅	—	637	1	no	Hall
80	C₃×C₅	—	13	1	no	Hall
81	C₂×C₇	C₅×(C₁₃⋊C₃)⋊D₇	1	8	yes	complemented
82	D₇	—	91	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	—	637	2	no	—
86	C₂×C₅	(C₁₃⋊C₃)⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor
87	C₇	C₂×C₅×(C₁₃⋊C₃)⋊D₇	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	—	637	1	no	Sylow
92	C₃	—	13	1	no	Sylow
93	C₂	—	637	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×C₇⋊D₉₁	C₃	semidirect
4. C₅×C₇²×C₁₃⋊C₃	C₂²	semidirect
5. C₂×(C₁₃⋊C₃)⋊(C₇⋊D₇)	C₅	direct (N × H)
6. C₅×C₇⋊D₉₁	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×C₇⋊D₉₁	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. C₇⋊D₉₁	C₂×C₃×C₅	semidirect
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	D₁₃⋊C₃	semidirect
35. C₅×C₇×C₁₃	C₂×C₃×D₇	semidirect
37. C₂×C₅×C₁₃⋊C₃	C₇⋊D₇	semidirect
42. C₇×C₁₃⋊C₃	C₂×C₅×D₇	semidirect
44. C₅×C₇²	C₂×D₁₃⋊C₃	semidirect
48. C₅×C₁₃⋊C₃	C₂×C₇⋊D₇	semidirect
49. C₂×C₇×C₁₃	C₃×C₅×D₇	semidirect
54. C₂×C₅×C₁₃	C₃×C₇⋊D₇	semidirect
57. C₂×C₇²	C₅×D₁₃⋊C₃	semidirect
59. C₇×C₁₃	C₂×C₃×C₅×D₇	semidirect
61. C₂×C₁₃⋊C₃	C₅×C₇⋊D₇	semidirect
63. C₂×C₅×C₇	(C₁₃⋊C₃)⋊D₇	semidirect
65. C₅×C₁₃	C₂×C₃×C₇⋊D₇	semidirect
68. C₇²	C₂×C₅×D₁₃⋊C₃	semidirect
71. C₁₃⋊C₃	C₂×C₅×C₇⋊D₇	semidirect
72. C₅×C₇	C₂×(C₁₃⋊C₃)⋊D₇	semidirect
76. C₂×C₁₃	C₃×C₅×C₇⋊D₇	semidirect
81. C₂×C₇	C₅×(C₁₃⋊C₃)⋊D₇	semidirect
83. C₁₃	C₂×C₃×C₅×C₇⋊D₇	semidirect
86. C₂×C₅	(C₁₃⋊C₃)⋊(C₇⋊D₇)	direct (N × H)
87. C₇	C₂×C₅×(C₁₃⋊C₃)⋊D₇	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×C₇⋊D₉₁	3
C₂×(C₁₃⋊C₃)⋊(C₇⋊D₇)	5
C₂×C₅×(C₁₃⋊C₃)⋊D₇	7
C₂×C₃×C₅×C₇⋊D₇	13

Subgroups — C2×C5×(C13⋊C3)⋊(C7⋊D7) #50304270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×(C₁₃⋊C₃)⋊(C₇⋊D₇) #50304270