Subgroups — C₃×C₄×C₈×C₉×C₁₃ #72189713

Order 11232.

440 conjugacy classes of subgroups.

The subgroup lattice has 144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₉×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₈×C₉×C₁₃	C₂	1	2	yes	maximal
3	C₃²×C₄×C₈×C₁₃	C₃	1	1	yes	maximal, characteristic
4	C₄×C₈×C₉×C₁₃	C₃	1	3	yes	maximal, direct product factor
5	C₂×C₃×C₄×C₉×C₁₃	C₄	1	2	yes	—
6	C₂×C₃×C₄×C₉×C₁₃	C₂²	1	1	yes	characteristic
7	C₃×C₈×C₉×C₁₃	C₄	1	4	yes	direct product factor
8	C₂×C₃²×C₈×C₁₃	C₂×C₃	1	2	yes	—
9	C₃²×C₄²×C₁₃	C₂×C₃	1	1	yes	characteristic
10	C₂×C₈×C₉×C₁₃	C₂×C₃	1	6	yes	—
11	C₄²×C₉×C₁₃	C₂×C₃	1	3	yes	—
12	C₂²×C₃×C₉×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₃×C₄×C₉×C₁₃	C₈	1	4	yes	direct product factor
14	C₃×C₄×C₉×C₁₃	C₂×C₄	1	2	yes	—
15	C₃×C₄×C₈×C₁₃	C₉	1	3	yes	direct product factor
16	C₃×C₄×C₈×C₁₃	C₃²	1	1	yes	characteristic
17	C₂×C₃²×C₄×C₁₃	C₃×C₄	1	2	yes	—
18	C₂×C₃²×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
19	C₃²×C₈×C₁₃	C₃×C₄	1	4	yes	—
20	C₂×C₄×C₉×C₁₃	C₃×C₄	1	6	yes	—
21	C₂×C₄×C₉×C₁₃	C₂²×C₃	1	3	yes	—
22	C₈×C₉×C₁₃	C₃×C₄	1	12	yes	direct product factor
23	C₃×C₄×C₈×C₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₃×C₉×C₁₃	C₄²	1	1	yes	characteristic
25	C₂×C₃×C₉×C₁₃	C₂×C₈	1	2	yes	—
26	C₂×C₃×C₈×C₁₃	C₂×C₉	1	6	yes	—
27	C₂×C₃×C₈×C₁₃	C₂×C₃²	1	2	yes	—
28	C₃×C₄²×C₁₃	C₂×C₉	1	3	yes	—
29	C₃×C₄²×C₁₃	C₂×C₃²	1	1	yes	characteristic
30	C₂²×C₃²×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
31	C₃²×C₄×C₁₃	C₃×C₈	1	4	yes	—
32	C₃²×C₄×C₁₃	C₂×C₃×C₄	1	2	yes	—
33	C₂²×C₉×C₁₃	C₂×C₃×C₄	1	3	yes	—
34	C₄×C₉×C₁₃	C₃×C₈	1	12	yes	direct product factor
35	C₄×C₉×C₁₃	C₂×C₃×C₄	1	6	yes	—
36	C₂×C₃×C₈×C₉	C₂×C₁₃	1	2	yes	—
37	C₃×C₄²×C₉	C₂×C₁₃	1	1	yes	characteristic
38	C₄×C₈×C₁₃	C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
39	C₃×C₉×C₁₃	C₄×C₈	1	1	yes	characteristic, direct product factor, Hall
40	C₂×C₃×C₄×C₁₃	C₄×C₉	1	6	yes	—
41	C₂×C₃×C₄×C₁₃	C₂²×C₉	1	3	yes	—
42	C₂×C₃×C₄×C₁₃	C₃²×C₄	1	2	yes	—
43	C₂×C₃×C₄×C₁₃	C₂²×C₃²	1	1	yes	characteristic
44	C₃×C₈×C₁₃	C₄×C₉	1	12	yes	direct product factor
45	C₃×C₈×C₁₃	C₃²×C₄	1	4	yes	—
46	C₃²×C₄×C₈	C₃×C₁₃	1	1	yes	characteristic
47	C₄×C₈×C₉	C₃×C₁₃	1	3	yes	direct product factor
48	C₂×C₃²×C₁₃	C₃×C₄²	1	1	yes	characteristic
49	C₂×C₃²×C₁₃	C₂×C₃×C₈	1	2	yes	—
50	C₂×C₉×C₁₃	C₃×C₄²	1	3	yes	—
51	C₂×C₉×C₁₃	C₂×C₃×C₈	1	6	yes	—
52	C₂×C₃×C₄×C₉	C₄×C₁₃	1	2	yes	—
53	C₂×C₃×C₄×C₉	C₂²×C₁₃	1	1	yes	characteristic
54	C₃×C₈×C₉	C₄×C₁₃	1	4	yes	direct product factor
55	C₂×C₈×C₁₃	C₂×C₃×C₉	1	2	yes	—
56	C₄²×C₁₃	C₂×C₃×C₉	1	1	yes	characteristic
57	C₂²×C₃×C₁₃	C₂×C₄×C₉	1	3	yes	—
58	C₂²×C₃×C₁₃	C₂×C₃²×C₄	1	1	yes	characteristic
59	C₃×C₄×C₁₃	C₈×C₉	1	12	yes	direct product factor
60	C₃×C₄×C₁₃	C₂×C₄×C₉	1	6	yes	—
61	C₃×C₄×C₁₃	C₃²×C₈	1	4	yes	—
62	C₃×C₄×C₁₃	C₂×C₃²×C₄	1	2	yes	—
63	C₂×C₃²×C₈	C₂×C₃×C₁₃	1	2	yes	—
64	C₃²×C₄²	C₂×C₃×C₁₃	1	1	yes	characteristic
65	C₂×C₈×C₉	C₂×C₃×C₁₃	1	6	yes	—
66	C₄²×C₉	C₂×C₃×C₁₃	1	3	yes	—
67	C₃²×C₁₃	C₃×C₄×C₈	1	1	yes	characteristic
68	C₉×C₁₃	C₃×C₄×C₈	1	3	yes	direct product factor
69	C₂²×C₃×C₉	C₂×C₄×C₁₃	1	1	yes	characteristic
70	C₃×C₄×C₉	C₈×C₁₃	1	4	yes	direct product factor
71	C₃×C₄×C₉	C₂×C₄×C₁₃	1	2	yes	—
72	C₂×C₄×C₁₃	C₃×C₄×C₉	1	2	yes	—
73	C₂×C₄×C₁₃	C₂²×C₃×C₉	1	1	yes	characteristic
74	C₈×C₁₃	C₃×C₄×C₉	1	4	yes	direct product factor
75	C₃×C₄×C₈	C₉×C₁₃	1	3	yes	direct product factor
76	C₃×C₄×C₈	C₃²×C₁₃	1	1	yes	characteristic
77	C₂×C₃×C₁₃	C₄²×C₉	1	3	yes	—
78	C₂×C₃×C₁₃	C₂×C₈×C₉	1	6	yes	—
79	C₂×C₃×C₁₃	C₃²×C₄²	1	1	yes	characteristic
80	C₂×C₃×C₁₃	C₂×C₃²×C₈	1	2	yes	—
81	C₂×C₃²×C₄	C₃×C₄×C₁₃	1	2	yes	—
82	C₂×C₃²×C₄	C₂²×C₃×C₁₃	1	1	yes	characteristic
83	C₃²×C₈	C₃×C₄×C₁₃	1	4	yes	—
84	C₂×C₄×C₉	C₃×C₄×C₁₃	1	6	yes	—
85	C₂×C₄×C₉	C₂²×C₃×C₁₃	1	3	yes	—
86	C₈×C₉	C₃×C₄×C₁₃	1	12	yes	direct product factor
87	C₂×C₃×C₉	C₄²×C₁₃	1	1	yes	characteristic
88	C₂×C₃×C₉	C₂×C₈×C₁₃	1	2	yes	—
89	C₂²×C₁₃	C₂×C₃×C₄×C₉	1	1	yes	characteristic
90	C₄×C₁₃	C₃×C₈×C₉	1	4	yes	direct product factor
91	C₄×C₁₃	C₂×C₃×C₄×C₉	1	2	yes	—
92	C₂×C₃×C₈	C₂×C₉×C₁₃	1	6	yes	—
93	C₂×C₃×C₈	C₂×C₃²×C₁₃	1	2	yes	—
94	C₃×C₄²	C₂×C₉×C₁₃	1	3	yes	—
95	C₃×C₄²	C₂×C₃²×C₁₃	1	1	yes	characteristic
96	C₃×C₁₃	C₄×C₈×C₉	1	3	yes	direct product factor
97	C₃×C₁₃	C₃²×C₄×C₈	1	1	yes	characteristic
98	C₂²×C₃²	C₂×C₃×C₄×C₁₃	1	1	yes	characteristic
99	C₃²×C₄	C₃×C₈×C₁₃	1	4	yes	—
100	C₃²×C₄	C₂×C₃×C₄×C₁₃	1	2	yes	—
101	C₂²×C₉	C₂×C₃×C₄×C₁₃	1	3	yes	—
102	C₄×C₉	C₃×C₈×C₁₃	1	12	yes	direct product factor
103	C₄×C₉	C₂×C₃×C₄×C₁₃	1	6	yes	—
104	C₄×C₈	C₃×C₉×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
105	C₃×C₉	C₄×C₈×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
106	C₂×C₁₃	C₃×C₄²×C₉	1	1	yes	characteristic
107	C₂×C₁₃	C₂×C₃×C₈×C₉	1	2	yes	—
108	C₂×C₃×C₄	C₄×C₉×C₁₃	1	6	yes	—
109	C₂×C₃×C₄	C₂²×C₉×C₁₃	1	3	yes	—
110	C₂×C₃×C₄	C₃²×C₄×C₁₃	1	2	yes	—
111	C₂×C₃×C₄	C₂²×C₃²×C₁₃	1	1	yes	characteristic
112	C₃×C₈	C₄×C₉×C₁₃	1	12	yes	direct product factor
113	C₃×C₈	C₃²×C₄×C₁₃	1	4	yes	—
114	C₂×C₃²	C₃×C₄²×C₁₃	1	1	yes	characteristic
115	C₂×C₃²	C₂×C₃×C₈×C₁₃	1	2	yes	—
116	C₂×C₉	C₃×C₄²×C₁₃	1	3	yes	—
117	C₂×C₉	C₂×C₃×C₈×C₁₃	1	6	yes	—
118	C₂×C₈	C₂×C₃×C₉×C₁₃	1	2	yes	—
119	C₄²	C₂×C₃×C₉×C₁₃	1	1	yes	characteristic
120	C₁₃	C₃×C₄×C₈×C₉	1	1	yes	characteristic, direct product factor, Sylow
121	C₂²×C₃	C₂×C₄×C₉×C₁₃	1	3	yes	—
122	C₂²×C₃	C₂×C₃²×C₄×C₁₃	1	1	yes	characteristic
123	C₃×C₄	C₈×C₉×C₁₃	1	12	yes	direct product factor
124	C₃×C₄	C₂×C₄×C₉×C₁₃	1	6	yes	—
125	C₃×C₄	C₃²×C₈×C₁₃	1	4	yes	—
126	C₃×C₄	C₂×C₃²×C₄×C₁₃	1	2	yes	—
127	C₃²	C₃×C₄×C₈×C₁₃	1	1	yes	characteristic
128	C₉	C₃×C₄×C₈×C₁₃	1	3	yes	direct product factor
129	C₂×C₄	C₃×C₄×C₉×C₁₃	1	2	yes	—
130	C₂×C₄	C₂²×C₃×C₉×C₁₃	1	1	yes	characteristic
131	C₈	C₃×C₄×C₉×C₁₃	1	4	yes	direct product factor
132	C₂×C₃	C₄²×C₉×C₁₃	1	3	yes	—
133	C₂×C₃	C₂×C₈×C₉×C₁₃	1	6	yes	—
134	C₂×C₃	C₃²×C₄²×C₁₃	1	1	yes	characteristic
135	C₂×C₃	C₂×C₃²×C₈×C₁₃	1	2	yes	—
136	C₂²	C₂×C₃×C₄×C₉×C₁₃	1	1	yes	characteristic
137	C₄	C₃×C₈×C₉×C₁₃	1	4	yes	direct product factor
138	C₄	C₂×C₃×C₄×C₉×C₁₃	1	2	yes	—
139	C₃	C₄×C₈×C₉×C₁₃	1	3	yes	direct product factor
140	C₃	C₃²×C₄×C₈×C₁₃	1	1	yes	characteristic
141	C₂	C₂×C₃×C₈×C₉×C₁₃	1	2	yes	—
142	C₂	C₃×C₄²×C₉×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃×C₄	C₂²×C₃²×C₁₃
socle, prime radical	C₂²×C₃²×C₁₃	C₂×C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄×C₈×C₉×C₁₃	C₃	direct (N × H)
7. C₃×C₈×C₉×C₁₃	C₄	direct (N × H)
13. C₃×C₄×C₉×C₁₃	C₈	direct (N × H)
15. C₃×C₄×C₈×C₁₃	C₉	direct (N × H)
22. C₈×C₉×C₁₃	C₃×C₄	direct (N × H)
23. C₃×C₄×C₈×C₉	C₁₃	direct (N × H)
34. C₄×C₉×C₁₃	C₃×C₈	direct (N × H)
38. C₄×C₈×C₁₃	C₃×C₉	direct (N × H)
39. C₃×C₉×C₁₃	C₄×C₈	direct (N × H)
44. C₃×C₈×C₁₃	C₄×C₉	direct (N × H)
47. C₄×C₈×C₉	C₃×C₁₃	direct (N × H)
54. C₃×C₈×C₉	C₄×C₁₃	direct (N × H)
59. C₃×C₄×C₁₃	C₈×C₉	direct (N × H)
68. C₉×C₁₃	C₃×C₄×C₈	direct (N × H)
70. C₃×C₄×C₉	C₈×C₁₃	direct (N × H)
74. C₈×C₁₃	C₃×C₄×C₉	direct (N × H)
75. C₃×C₄×C₈	C₉×C₁₃	direct (N × H)
86. C₈×C₉	C₃×C₄×C₁₃	direct (N × H)
90. C₄×C₁₃	C₃×C₈×C₉	direct (N × H)
96. C₃×C₁₃	C₄×C₈×C₉	direct (N × H)
102. C₄×C₉	C₃×C₈×C₁₃	direct (N × H)
104. C₄×C₈	C₃×C₉×C₁₃	direct (N × H)
105. C₃×C₉	C₄×C₈×C₁₃	direct (N × H)
112. C₃×C₈	C₄×C₉×C₁₃	direct (N × H)
120. C₁₃	C₃×C₄×C₈×C₉	direct (N × H)
123. C₃×C₄	C₈×C₉×C₁₃	direct (N × H)
128. C₉	C₃×C₄×C₈×C₁₃	direct (N × H)
131. C₈	C₃×C₄×C₉×C₁₃	direct (N × H)
137. C₄	C₃×C₈×C₉×C₁₃	direct (N × H)
139. C₃	C₄×C₈×C₉×C₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄²×C₉×C₁₃	2
C₂×C₃×C₈×C₉×C₁₃	2
C₃²×C₄×C₈×C₁₃	3
C₄×C₈×C₉×C₁₃	3
C₃×C₄×C₈×C₉	13

Subgroups — C3×C4×C8×C9×C13 #72189713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₈×C₉×C₁₃ #72189713