Subgroups — C₁₃⋊C₃×(C₁₉⋊C₃)⋊D₇ #44527789

Order 31122.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃⋊C₃×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#23780594	C₃	1	1	yes	maximal, characteristic, complemented
3	#23780593	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₃⋊C₃×D₁₃₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₁₃×(C₁₉⋊C₃)⋊D₇	C₃	1	1	yes	maximal, characteristic, complemented
6	C₇×#10625203	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×#10625202	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×C₁₉×C₁₃⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₇×C₁₃×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₁₃⋊C₃×D₁₉⋊C₃	—	7	1	no	maximal, Hall
11	C₁₃×D₁₃₃	C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×(C₁₉⋊C₃)⋊D₇	—	13	1	no	maximal, Hall
13	C₁₃⋊C₃×C₁₉⋊C₃	D₇	1	1	yes	characteristic, complemented, Hall
14	C₇×C₁₃×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
15	C₃×D₇×C₁₃⋊C₃	—	19	1	no	maximal, Hall
16	#13093361	—	7	1	no	—
17	#13093360	—	7	1	no	—
18	D₁₉×C₁₃⋊C₃	—	7	1	no	—
19	C₁₃×D₁₉⋊C₃	—	7	1	no	—
20	C₃×C₇×C₁₉⋊C₃	—	13	1	no	Hall
21	C₃×C₇×C₁₃⋊C₃	—	19	1	no	Hall
22	C₃×D₁₃₃	—	13	1	no	—
23	(C₁₉⋊C₃)⋊D₇	—	13	1	no	—
24	(C₁₉⋊C₃)⋊D₇	—	13	1	no	—
25	(C₁₉⋊C₃)⋊D₇	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
26	#10625203	C₃×D₇	1	1	yes	characteristic, complemented
27	#10625202	C₃×D₇	1	1	yes	characteristic, complemented
28	C₁₃×C₁₉⋊C₃	C₃×D₇	1	1	yes	characteristic, complemented
29	C₁₉×C₁₃⋊C₃	C₃×D₇	1	1	yes	characteristic, complemented
30	C₃×C₁₃×D₇	—	19	1	no	—
31	D₇×C₁₃⋊C₃	—	19	1	no	—
32	D₇×C₁₃⋊C₃	—	19	1	no	—
33	D₇×C₁₃⋊C₃	—	19	1	no	—
34	C₁₃×D₁₉	—	7	1	no	Hall
35	C₃×C₇×C₁₉	—	13	1	no	—
36	C₇×C₁₉⋊C₃	—	13	1	no	—
37	C₇×C₁₉⋊C₃	—	13	1	no	—
38	C₇×C₁₉⋊C₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
39	C₃×D₁₉⋊C₃	—	91	1	no	Hall
40	C₃×C₇×C₁₃	—	19	1	no	—
41	C₇×C₁₃⋊C₃	—	19	1	no	—
42	C₇×C₁₃⋊C₃	—	19	1	no	—
43	C₇×C₁₃⋊C₃	D₁₉⋊C₃	1	1	yes	characteristic, complemented
44	D₁₃₃	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
45	C₁₃×C₁₉	C₃²×D₇	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃×C₁₃⋊C₃	—	133	1	no	Hall
47	C₁₃×D₇	—	19	1	no	Hall
48	C₃×C₁₉⋊C₃	—	13	1	no	Hall
49	C₇×C₁₉	C₂×C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
50	C₃²×D₇	—	247	1	no	Hall
51	C₃×C₁₃⋊C₃	—	19	1	no	Hall
52	C₃×D₁₉	—	91	1	no	—
53	D₁₉⋊C₃	—	7	1	no	—
54	D₁₉⋊C₃	—	91	1	no	—
55	D₁₉⋊C₃	—	91	1	no	—
56	C₇×C₁₃	C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
57	C₂×C₃×C₁₃	—	133	1	no	—
58	C₂×C₁₃⋊C₃	—	133	1	no	—
59	C₂×C₁₃⋊C₃	—	133	1	no	—
60	C₂×C₁₃⋊C₃	—	133	1	no	—
61	C₃²×C₇	—	247	1	no	Hall
62	C₃×C₁₉	—	13	1	no	—
63	C₁₉⋊C₃	—	13	1	no	—
64	C₁₉⋊C₃	—	13	1	no	—
65	C₁₉⋊C₃	D₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
66	C₃×D₇	—	19	1	no	—
67	C₃×D₇	—	247	1	no	—
68	C₃×D₇	—	247	1	no	—
69	C₃×D₇	—	247	1	no	—
70	C₃×C₁₃	—	19	1	no	—
71	C₁₃⋊C₃	—	19	1	no	—
72	C₁₃⋊C₃	—	19	1	no	—
73	C₁₃⋊C₃	(C₁₉⋊C₃)⋊D₇	1	1	yes	characteristic, direct product factor
74	D₁₉	—	7	1	no	Hall
75	C₂×C₁₃	—	133	1	no	Hall
76	C₃×C₇	—	13	1	no	—
77	C₃×C₇	—	19	1	no	—
78	C₃×C₇	—	247	1	no	—
79	C₃×C₇	—	247	1	no	—
80	C₁₉	C₃×D₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
81	C₂×C₃²	—	1729	1	no	Hall
82	D₇	—	19	1	no	Hall
83	C₁₃	C₃×(C₁₉⋊C₃)⋊D₇	1	1	yes	characteristic, complemented, Sylow
84	C₃²	—	247	1	no	Sylow
85	C₇	C₁₃⋊C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
86	C₂×C₃	—	133	1	no	—
87	C₂×C₃	—	1729	1	no	—
88	C₂×C₃	—	1729	1	no	—
89	C₂×C₃	—	1729	1	no	—
90	C₃	—	13	1	no	—
91	C₃	—	19	1	no	—
92	C₃	—	247	1	no	—
93	C₃	—	247	1	no	—
94	C₂	—	133	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₃×C₁₉	C₂×C₃²
LCS	G ▷ C₇×C₁₃×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₃⋊C₃×C₁₉⋊C₃	C₂	semidirect
2. #23780594	C₃	semidirect
3. #23780593	C₃	semidirect
4. C₁₃⋊C₃×D₁₃₃	C₃	semidirect
5. C₁₃×(C₁₉⋊C₃)⋊D₇	C₃	semidirect
6. C₇×#10625203	C₂×C₃	semidirect
7. C₇×#10625202	C₂×C₃	semidirect
8. C₇×C₁₉×C₁₃⋊C₃	C₂×C₃	semidirect
9. C₇×C₁₃×C₁₉⋊C₃	C₂×C₃	semidirect
11. C₁₃×D₁₃₃	C₃²	semidirect
13. C₁₃⋊C₃×C₁₉⋊C₃	D₇	semidirect
14. C₇×C₁₃×C₁₉	C₂×C₃²	semidirect
25. (C₁₉⋊C₃)⋊D₇	C₁₃⋊C₃	direct (N × H)
26. #10625203	C₃×D₇	semidirect
27. #10625202	C₃×D₇	semidirect
28. C₁₃×C₁₉⋊C₃	C₃×D₇	semidirect
29. C₁₉×C₁₃⋊C₃	C₃×D₇	semidirect
38. C₇×C₁₉⋊C₃	C₂×C₁₃⋊C₃	semidirect
43. C₇×C₁₃⋊C₃	D₁₉⋊C₃	semidirect
44. D₁₃₃	C₃×C₁₃⋊C₃	semidirect
45. C₁₃×C₁₉	C₃²×D₇	semidirect
49. C₇×C₁₉	C₂×C₃×C₁₃⋊C₃	semidirect
56. C₇×C₁₃	C₃×D₁₉⋊C₃	semidirect
65. C₁₉⋊C₃	D₇×C₁₃⋊C₃	semidirect
73. C₁₃⋊C₃	(C₁₉⋊C₃)⋊D₇	direct (N × H)
80. C₁₉	C₃×D₇×C₁₃⋊C₃	semidirect
83. C₁₃	C₃×(C₁₉⋊C₃)⋊D₇	semidirect
85. C₇	C₁₃⋊C₃×D₁₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₃⋊C₃×C₁₉⋊C₃	2
#23780594	3
#23780593	3
C₁₃⋊C₃×D₁₃₃	3
C₁₃×(C₁₉⋊C₃)⋊D₇	3
C₁₃⋊C₃×D₁₉⋊C₃	7
C₃×(C₁₉⋊C₃)⋊D₇	13
C₃×D₇×C₁₃⋊C₃	19

Subgroups — C13⋊C3×(C19⋊C3)⋊D7 #44527789

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃⋊C₃×(C₁₉⋊C₃)⋊D₇ #44527789