Subgroups — C₂×C₃×C₄×C₈×C₉×C₁₃ #72199869

Order 22464.

1620 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×C₉×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₈×C₉×C₁₃	C₂	1	2	yes	maximal
3	C₃×C₄×C₈×C₉×C₁₃	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃²×C₄×C₈×C₁₃	C₃	1	1	yes	maximal, characteristic
5	C₂×C₄×C₈×C₉×C₁₃	C₃	1	3	yes	maximal, direct product factor
6	C₂²×C₃×C₄×C₉×C₁₃	C₄	1	2	yes	—
7	C₂²×C₃×C₄×C₉×C₁₃	C₂²	1	1	yes	characteristic
8	C₃×C₄²×C₉×C₁₃	C₄	1	2	yes	—
9	C₃×C₄²×C₉×C₁₃	C₂²	1	2	yes	—
10	C₂×C₃×C₈×C₉×C₁₃	C₄	1	8	yes	direct product factor
11	C₂×C₃×C₈×C₉×C₁₃	C₂²	1	4	yes	—
12	C₂×C₃²×C₄²×C₁₃	C₂×C₃	1	1	yes	characteristic
13	C₂²×C₃²×C₈×C₁₃	C₂×C₃	1	2	yes	—
14	C₂×C₄²×C₉×C₁₃	C₂×C₃	1	3	yes	—
15	C₂²×C₈×C₉×C₁₃	C₂×C₃	1	6	yes	—
16	C₃²×C₄×C₈×C₁₃	C₂×C₃	1	4	yes	—
17	C₄×C₈×C₉×C₁₃	C₂×C₃	1	12	yes	direct product factor
18	C₂³×C₃×C₉×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₃×C₄×C₉×C₁₃	C₈	1	8	yes	direct product factor
20	C₂×C₃×C₄×C₉×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₃×C₄×C₉×C₁₃	C₂×C₄	1	4	yes	—
22	C₂×C₃×C₄×C₉×C₁₃	C₂×C₄	1	4	yes	—
23	C₂×C₃×C₄×C₉×C₁₃	C₂³	1	1	yes	characteristic
24	C₃×C₈×C₉×C₁₃	C₂×C₄	1	8	yes	direct product factor
25	C₂×C₃×C₄×C₈×C₁₃	C₉	1	3	yes	direct product factor
26	C₂×C₃×C₄×C₈×C₁₃	C₃²	1	1	yes	characteristic
27	C₂²×C₃²×C₄×C₁₃	C₃×C₄	1	2	yes	—
28	C₂²×C₃²×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
29	C₂×C₃²×C₈×C₁₃	C₃×C₄	1	8	yes	—
30	C₂×C₃²×C₈×C₁₃	C₂²×C₃	1	4	yes	—
31	C₃²×C₄²×C₁₃	C₃×C₄	1	2	yes	—
32	C₃²×C₄²×C₁₃	C₂²×C₃	1	2	yes	—
33	C₂²×C₄×C₉×C₁₃	C₃×C₄	1	6	yes	—
34	C₂²×C₄×C₉×C₁₃	C₂²×C₃	1	3	yes	—
35	C₂×C₈×C₉×C₁₃	C₃×C₄	1	24	yes	direct product factor
36	C₂×C₈×C₉×C₁₃	C₂²×C₃	1	12	yes	—
37	C₄²×C₉×C₁₃	C₃×C₄	1	6	yes	—
38	C₄²×C₉×C₁₃	C₂²×C₃	1	6	yes	—
39	C₂×C₃×C₄×C₈×C₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
40	C₂²×C₃×C₉×C₁₃	C₄²	1	2	yes	—
41	C₂²×C₃×C₉×C₁₃	C₂×C₈	1	4	yes	—
42	C₂²×C₃×C₉×C₁₃	C₂²×C₄	1	1	yes	characteristic
43	C₃×C₄×C₉×C₁₃	C₄²	1	2	yes	—
44	C₃×C₄×C₉×C₁₃	C₂×C₈	1	8	yes	direct product factor
45	C₃×C₄×C₉×C₁₃	C₂²×C₄	1	2	yes	—
46	C₂²×C₃×C₈×C₁₃	C₂×C₉	1	6	yes	—
47	C₂²×C₃×C₈×C₁₃	C₂×C₃²	1	2	yes	—
48	C₂×C₃×C₄²×C₁₃	C₂×C₉	1	3	yes	—
49	C₂×C₃×C₄²×C₁₃	C₂×C₃²	1	1	yes	characteristic
50	C₃×C₄×C₈×C₁₃	C₂×C₉	1	12	yes	direct product factor
51	C₃×C₄×C₈×C₁₃	C₂×C₃²	1	4	yes	—
52	C₂³×C₃²×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
53	C₂×C₃²×C₄×C₁₃	C₃×C₈	1	8	yes	—
54	C₂×C₃²×C₄×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
55	C₂×C₃²×C₄×C₁₃	C₂×C₃×C₄	1	4	yes	—
56	C₂×C₃²×C₄×C₁₃	C₂×C₃×C₄	1	4	yes	—
57	C₂×C₃²×C₄×C₁₃	C₂³×C₃	1	1	yes	characteristic
58	C₂³×C₉×C₁₃	C₂×C₃×C₄	1	3	yes	—
59	C₃²×C₈×C₁₃	C₂×C₃×C₄	1	8	yes	—
60	C₂×C₄×C₉×C₁₃	C₃×C₈	1	24	yes	direct product factor
61	C₂×C₄×C₉×C₁₃	C₂×C₃×C₄	1	3	yes	—
62	C₂×C₄×C₉×C₁₃	C₂×C₃×C₄	1	12	yes	—
63	C₂×C₄×C₉×C₁₃	C₂×C₃×C₄	1	12	yes	—
64	C₂×C₄×C₉×C₁₃	C₂³×C₃	1	3	yes	—
65	C₈×C₉×C₁₃	C₂×C₃×C₄	1	24	yes	direct product factor
66	C₂²×C₃×C₈×C₉	C₂×C₁₃	1	2	yes	—
67	C₂×C₃×C₄²×C₉	C₂×C₁₃	1	1	yes	characteristic
68	C₃×C₄×C₈×C₉	C₂×C₁₃	1	4	yes	direct product factor
69	C₂×C₄×C₈×C₁₃	C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
70	C₂×C₃×C₉×C₁₃	C₄×C₈	1	4	yes	direct product factor
71	C₂×C₃×C₉×C₁₃	C₂×C₄²	1	1	yes	characteristic
72	C₂×C₃×C₉×C₁₃	C₂²×C₈	1	2	yes	—
73	C₂²×C₃×C₄×C₁₃	C₄×C₉	1	6	yes	—
74	C₂²×C₃×C₄×C₁₃	C₂²×C₉	1	3	yes	—
75	C₂²×C₃×C₄×C₁₃	C₃²×C₄	1	2	yes	—
76	C₂²×C₃×C₄×C₁₃	C₂²×C₃²	1	1	yes	characteristic
77	C₂×C₃×C₈×C₁₃	C₄×C₉	1	24	yes	direct product factor
78	C₂×C₃×C₈×C₁₃	C₂²×C₉	1	12	yes	—
79	C₂×C₃×C₈×C₁₃	C₃²×C₄	1	8	yes	—
80	C₂×C₃×C₈×C₁₃	C₂²×C₃²	1	4	yes	—
81	C₃×C₄²×C₁₃	C₄×C₉	1	6	yes	—
82	C₃×C₄²×C₁₃	C₂²×C₉	1	6	yes	—
83	C₃×C₄²×C₁₃	C₃²×C₄	1	2	yes	—
84	C₃×C₄²×C₁₃	C₂²×C₃²	1	2	yes	—
85	C₂×C₃²×C₄×C₈	C₃×C₁₃	1	1	yes	characteristic
86	C₂×C₄×C₈×C₉	C₃×C₁₃	1	3	yes	direct product factor
87	C₂²×C₃²×C₁₃	C₃×C₄²	1	2	yes	—
88	C₂²×C₃²×C₁₃	C₂×C₃×C₈	1	4	yes	—
89	C₂²×C₃²×C₁₃	C₂²×C₃×C₄	1	1	yes	characteristic
90	C₃²×C₄×C₁₃	C₃×C₄²	1	2	yes	—
91	C₃²×C₄×C₁₃	C₂×C₃×C₈	1	8	yes	—
92	C₃²×C₄×C₁₃	C₂²×C₃×C₄	1	2	yes	—
93	C₂²×C₉×C₁₃	C₃×C₄²	1	6	yes	—
94	C₂²×C₉×C₁₃	C₂×C₃×C₈	1	12	yes	—
95	C₂²×C₉×C₁₃	C₂²×C₃×C₄	1	3	yes	—
96	C₄×C₉×C₁₃	C₃×C₄²	1	6	yes	—
97	C₄×C₉×C₁₃	C₂×C₃×C₈	1	24	yes	direct product factor
98	C₄×C₉×C₁₃	C₂²×C₃×C₄	1	6	yes	—
99	C₂²×C₃×C₄×C₉	C₄×C₁₃	1	2	yes	—
100	C₂²×C₃×C₄×C₉	C₂²×C₁₃	1	1	yes	characteristic
101	C₂×C₃×C₈×C₉	C₄×C₁₃	1	8	yes	direct product factor
102	C₂×C₃×C₈×C₉	C₂²×C₁₃	1	4	yes	—
103	C₃×C₄²×C₉	C₄×C₁₃	1	2	yes	—
104	C₃×C₄²×C₉	C₂²×C₁₃	1	2	yes	—
105	C₂²×C₈×C₁₃	C₂×C₃×C₉	1	2	yes	—
106	C₂×C₄²×C₁₃	C₂×C₃×C₉	1	1	yes	characteristic
107	C₄×C₈×C₁₃	C₂×C₃×C₉	1	4	yes	direct product factor
108	C₃×C₉×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic, direct product factor, Hall
109	C₂³×C₃×C₁₃	C₂×C₄×C₉	1	3	yes	—
110	C₂³×C₃×C₁₃	C₂×C₃²×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₁₃	C₈×C₉	1	24	yes	direct product factor
112	C₂×C₃×C₄×C₁₃	C₂×C₄×C₉	1	3	yes	—
113	C₂×C₃×C₄×C₁₃	C₂×C₄×C₉	1	12	yes	—
114	C₂×C₃×C₄×C₁₃	C₂×C₄×C₉	1	12	yes	—
115	C₂×C₃×C₄×C₁₃	C₃²×C₈	1	8	yes	—
116	C₂×C₃×C₄×C₁₃	C₂³×C₉	1	3	yes	—
117	C₂×C₃×C₄×C₁₃	C₂×C₃²×C₄	1	1	yes	characteristic
118	C₂×C₃×C₄×C₁₃	C₂×C₃²×C₄	1	4	yes	—
119	C₂×C₃×C₄×C₁₃	C₂×C₃²×C₄	1	4	yes	—
120	C₂×C₃×C₄×C₁₃	C₂³×C₃²	1	1	yes	characteristic
121	C₃×C₈×C₁₃	C₂×C₄×C₉	1	24	yes	direct product factor
122	C₃×C₈×C₁₃	C₂×C₃²×C₄	1	8	yes	—
123	C₂²×C₃²×C₈	C₂×C₃×C₁₃	1	2	yes	—
124	C₂×C₃²×C₄²	C₂×C₃×C₁₃	1	1	yes	characteristic
125	C₃²×C₄×C₈	C₂×C₃×C₁₃	1	4	yes	—
126	C₂²×C₈×C₉	C₂×C₃×C₁₃	1	6	yes	—
127	C₂×C₄²×C₉	C₂×C₃×C₁₃	1	3	yes	—
128	C₄×C₈×C₉	C₂×C₃×C₁₃	1	12	yes	direct product factor
129	C₂×C₃²×C₁₃	C₃×C₄×C₈	1	4	yes	—
130	C₂×C₃²×C₁₃	C₂×C₃×C₄²	1	1	yes	characteristic
131	C₂×C₃²×C₁₃	C₂²×C₃×C₈	1	2	yes	—
132	C₂×C₉×C₁₃	C₃×C₄×C₈	1	12	yes	direct product factor
133	C₂×C₉×C₁₃	C₂×C₃×C₄²	1	3	yes	—
134	C₂×C₉×C₁₃	C₂²×C₃×C₈	1	6	yes	—
135	C₂³×C₃×C₉	C₂×C₄×C₁₃	1	1	yes	characteristic
136	C₂×C₃×C₄×C₉	C₈×C₁₃	1	8	yes	direct product factor
137	C₂×C₃×C₄×C₉	C₂×C₄×C₁₃	1	1	yes	characteristic
138	C₂×C₃×C₄×C₉	C₂×C₄×C₁₃	1	4	yes	—
139	C₂×C₃×C₄×C₉	C₂×C₄×C₁₃	1	4	yes	—
140	C₂×C₃×C₄×C₉	C₂³×C₁₃	1	1	yes	characteristic
141	C₃×C₈×C₉	C₂×C₄×C₁₃	1	8	yes	direct product factor
142	C₂²×C₄×C₁₃	C₃×C₄×C₉	1	2	yes	—
143	C₂²×C₄×C₁₃	C₂²×C₃×C₉	1	1	yes	characteristic
144	C₂×C₈×C₁₃	C₃×C₄×C₉	1	8	yes	direct product factor
145	C₂×C₈×C₁₃	C₂²×C₃×C₉	1	4	yes	—
146	C₄²×C₁₃	C₃×C₄×C₉	1	2	yes	—
147	C₄²×C₁₃	C₂²×C₃×C₉	1	2	yes	—
148	C₂×C₃×C₄×C₈	C₉×C₁₃	1	3	yes	direct product factor
149	C₂×C₃×C₄×C₈	C₃²×C₁₃	1	1	yes	characteristic
150	C₂²×C₃×C₁₃	C₄²×C₉	1	6	yes	—
151	C₂²×C₃×C₁₃	C₂×C₈×C₉	1	12	yes	—
152	C₂²×C₃×C₁₃	C₂²×C₄×C₉	1	3	yes	—
153	C₂²×C₃×C₁₃	C₃²×C₄²	1	2	yes	—
154	C₂²×C₃×C₁₃	C₂×C₃²×C₈	1	4	yes	—
155	C₂²×C₃×C₁₃	C₂²×C₃²×C₄	1	1	yes	characteristic
156	C₃×C₄×C₁₃	C₄²×C₉	1	6	yes	—
157	C₃×C₄×C₁₃	C₂×C₈×C₉	1	24	yes	direct product factor
158	C₃×C₄×C₁₃	C₂²×C₄×C₉	1	6	yes	—
159	C₃×C₄×C₁₃	C₃²×C₄²	1	2	yes	—
160	C₃×C₄×C₁₃	C₂×C₃²×C₈	1	8	yes	—
161	C₃×C₄×C₁₃	C₂²×C₃²×C₄	1	2	yes	—
162	C₂²×C₃²×C₄	C₃×C₄×C₁₃	1	2	yes	—
163	C₂²×C₃²×C₄	C₂²×C₃×C₁₃	1	1	yes	characteristic
164	C₂×C₃²×C₈	C₃×C₄×C₁₃	1	8	yes	—
165	C₂×C₃²×C₈	C₂²×C₃×C₁₃	1	4	yes	—
166	C₃²×C₄²	C₃×C₄×C₁₃	1	2	yes	—
167	C₃²×C₄²	C₂²×C₃×C₁₃	1	2	yes	—
168	C₂²×C₄×C₉	C₃×C₄×C₁₃	1	6	yes	—
169	C₂²×C₄×C₉	C₂²×C₃×C₁₃	1	3	yes	—
170	C₂×C₈×C₉	C₃×C₄×C₁₃	1	24	yes	direct product factor
171	C₂×C₈×C₉	C₂²×C₃×C₁₃	1	12	yes	—
172	C₄²×C₉	C₃×C₄×C₁₃	1	6	yes	—
173	C₄²×C₉	C₂²×C₃×C₁₃	1	6	yes	—
174	C₃²×C₁₃	C₂×C₃×C₄×C₈	1	1	yes	characteristic
175	C₉×C₁₃	C₂×C₃×C₄×C₈	1	3	yes	direct product factor
176	C₂²×C₃×C₉	C₄²×C₁₃	1	2	yes	—
177	C₂²×C₃×C₉	C₂×C₈×C₁₃	1	4	yes	—
178	C₂²×C₃×C₉	C₂²×C₄×C₁₃	1	1	yes	characteristic
179	C₃×C₄×C₉	C₄²×C₁₃	1	2	yes	—
180	C₃×C₄×C₉	C₂×C₈×C₁₃	1	8	yes	direct product factor
181	C₃×C₄×C₉	C₂²×C₄×C₁₃	1	2	yes	—
182	C₂³×C₁₃	C₂×C₃×C₄×C₉	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₃×C₈×C₉	1	8	yes	direct product factor
184	C₂×C₄×C₁₃	C₂×C₃×C₄×C₉	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×C₃×C₄×C₉	1	4	yes	—
186	C₂×C₄×C₁₃	C₂×C₃×C₄×C₉	1	4	yes	—
187	C₂×C₄×C₁₃	C₂³×C₃×C₉	1	1	yes	characteristic
188	C₈×C₁₃	C₂×C₃×C₄×C₉	1	8	yes	direct product factor
189	C₂²×C₃×C₈	C₂×C₉×C₁₃	1	6	yes	—
190	C₂²×C₃×C₈	C₂×C₃²×C₁₃	1	2	yes	—
191	C₂×C₃×C₄²	C₂×C₉×C₁₃	1	3	yes	—
192	C₂×C₃×C₄²	C₂×C₃²×C₁₃	1	1	yes	characteristic
193	C₃×C₄×C₈	C₂×C₉×C₁₃	1	12	yes	direct product factor
194	C₃×C₄×C₈	C₂×C₃²×C₁₃	1	4	yes	—
195	C₂×C₃×C₁₃	C₄×C₈×C₉	1	12	yes	direct product factor
196	C₂×C₃×C₁₃	C₂×C₄²×C₉	1	3	yes	—
197	C₂×C₃×C₁₃	C₂²×C₈×C₉	1	6	yes	—
198	C₂×C₃×C₁₃	C₃²×C₄×C₈	1	4	yes	—
199	C₂×C₃×C₁₃	C₂×C₃²×C₄²	1	1	yes	characteristic
200	C₂×C₃×C₁₃	C₂²×C₃²×C₈	1	2	yes	—
201	C₂³×C₃²	C₂×C₃×C₄×C₁₃	1	1	yes	characteristic
202	C₂×C₃²×C₄	C₃×C₈×C₁₃	1	8	yes	—
203	C₂×C₃²×C₄	C₂×C₃×C₄×C₁₃	1	1	yes	characteristic
204	C₂×C₃²×C₄	C₂×C₃×C₄×C₁₃	1	4	yes	—
205	C₂×C₃²×C₄	C₂×C₃×C₄×C₁₃	1	4	yes	—
206	C₂×C₃²×C₄	C₂³×C₃×C₁₃	1	1	yes	characteristic
207	C₂³×C₉	C₂×C₃×C₄×C₁₃	1	3	yes	—
208	C₃²×C₈	C₂×C₃×C₄×C₁₃	1	8	yes	—
209	C₂×C₄×C₉	C₃×C₈×C₁₃	1	24	yes	direct product factor
210	C₂×C₄×C₉	C₂×C₃×C₄×C₁₃	1	3	yes	—
211	C₂×C₄×C₉	C₂×C₃×C₄×C₁₃	1	12	yes	—
212	C₂×C₄×C₉	C₂×C₃×C₄×C₁₃	1	12	yes	—
213	C₂×C₄×C₉	C₂³×C₃×C₁₃	1	3	yes	—
214	C₈×C₉	C₂×C₃×C₄×C₁₃	1	24	yes	direct product factor
215	C₂×C₄×C₈	C₃×C₉×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
216	C₂×C₃×C₉	C₄×C₈×C₁₃	1	4	yes	direct product factor
217	C₂×C₃×C₉	C₂×C₄²×C₁₃	1	1	yes	characteristic
218	C₂×C₃×C₉	C₂²×C₈×C₁₃	1	2	yes	—
219	C₂²×C₁₃	C₃×C₄²×C₉	1	2	yes	—
220	C₂²×C₁₃	C₂×C₃×C₈×C₉	1	4	yes	—
221	C₂²×C₁₃	C₂²×C₃×C₄×C₉	1	1	yes	characteristic
222	C₄×C₁₃	C₃×C₄²×C₉	1	2	yes	—
223	C₄×C₁₃	C₂×C₃×C₈×C₉	1	8	yes	direct product factor
224	C₄×C₁₃	C₂²×C₃×C₄×C₉	1	2	yes	—
225	C₂²×C₃×C₄	C₄×C₉×C₁₃	1	6	yes	—
226	C₂²×C₃×C₄	C₂²×C₉×C₁₃	1	3	yes	—
227	C₂²×C₃×C₄	C₃²×C₄×C₁₃	1	2	yes	—
228	C₂²×C₃×C₄	C₂²×C₃²×C₁₃	1	1	yes	characteristic
229	C₂×C₃×C₈	C₄×C₉×C₁₃	1	24	yes	direct product factor
230	C₂×C₃×C₈	C₂²×C₉×C₁₃	1	12	yes	—
231	C₂×C₃×C₈	C₃²×C₄×C₁₃	1	8	yes	—
232	C₂×C₃×C₈	C₂²×C₃²×C₁₃	1	4	yes	—
233	C₃×C₄²	C₄×C₉×C₁₃	1	6	yes	—
234	C₃×C₄²	C₂²×C₉×C₁₃	1	6	yes	—
235	C₃×C₄²	C₃²×C₄×C₁₃	1	2	yes	—
236	C₃×C₄²	C₂²×C₃²×C₁₃	1	2	yes	—
237	C₃×C₁₃	C₂×C₄×C₈×C₉	1	3	yes	direct product factor
238	C₃×C₁₃	C₂×C₃²×C₄×C₈	1	1	yes	characteristic
239	C₂²×C₃²	C₃×C₄²×C₁₃	1	2	yes	—
240	C₂²×C₃²	C₂×C₃×C₈×C₁₃	1	4	yes	—
241	C₂²×C₃²	C₂²×C₃×C₄×C₁₃	1	1	yes	characteristic
242	C₃²×C₄	C₃×C₄²×C₁₃	1	2	yes	—
243	C₃²×C₄	C₂×C₃×C₈×C₁₃	1	8	yes	—
244	C₃²×C₄	C₂²×C₃×C₄×C₁₃	1	2	yes	—
245	C₂²×C₉	C₃×C₄²×C₁₃	1	6	yes	—
246	C₂²×C₉	C₂×C₃×C₈×C₁₃	1	12	yes	—
247	C₂²×C₉	C₂²×C₃×C₄×C₁₃	1	3	yes	—
248	C₄×C₉	C₃×C₄²×C₁₃	1	6	yes	—
249	C₄×C₉	C₂×C₃×C₈×C₁₃	1	24	yes	direct product factor
250	C₄×C₉	C₂²×C₃×C₄×C₁₃	1	6	yes	—
251	C₂²×C₈	C₂×C₃×C₉×C₁₃	1	2	yes	—
252	C₂×C₄²	C₂×C₃×C₉×C₁₃	1	1	yes	characteristic
253	C₄×C₈	C₂×C₃×C₉×C₁₃	1	4	yes	direct product factor
254	C₃×C₉	C₂×C₄×C₈×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
255	C₂×C₁₃	C₃×C₄×C₈×C₉	1	4	yes	direct product factor
256	C₂×C₁₃	C₂×C₃×C₄²×C₉	1	1	yes	characteristic
257	C₂×C₁₃	C₂²×C₃×C₈×C₉	1	2	yes	—
258	C₂³×C₃	C₂×C₄×C₉×C₁₃	1	3	yes	—
259	C₂³×C₃	C₂×C₃²×C₄×C₁₃	1	1	yes	characteristic
260	C₂×C₃×C₄	C₈×C₉×C₁₃	1	24	yes	direct product factor
261	C₂×C₃×C₄	C₂×C₄×C₉×C₁₃	1	3	yes	—
262	C₂×C₃×C₄	C₂×C₄×C₉×C₁₃	1	12	yes	—
263	C₂×C₃×C₄	C₂×C₄×C₉×C₁₃	1	12	yes	—
264	C₂×C₃×C₄	C₃²×C₈×C₁₃	1	8	yes	—
265	C₂×C₃×C₄	C₂³×C₉×C₁₃	1	3	yes	—
266	C₂×C₃×C₄	C₂×C₃²×C₄×C₁₃	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂×C₃²×C₄×C₁₃	1	4	yes	—
268	C₂×C₃×C₄	C₂×C₃²×C₄×C₁₃	1	4	yes	—
269	C₂×C₃×C₄	C₂³×C₃²×C₁₃	1	1	yes	characteristic
270	C₃×C₈	C₂×C₄×C₉×C₁₃	1	24	yes	direct product factor
271	C₃×C₈	C₂×C₃²×C₄×C₁₃	1	8	yes	—
272	C₂×C₃²	C₃×C₄×C₈×C₁₃	1	4	yes	—
273	C₂×C₃²	C₂×C₃×C₄²×C₁₃	1	1	yes	characteristic
274	C₂×C₃²	C₂²×C₃×C₈×C₁₃	1	2	yes	—
275	C₂×C₉	C₃×C₄×C₈×C₁₃	1	12	yes	direct product factor
276	C₂×C₉	C₂×C₃×C₄²×C₁₃	1	3	yes	—
277	C₂×C₉	C₂²×C₃×C₈×C₁₃	1	6	yes	—
278	C₂²×C₄	C₃×C₄×C₉×C₁₃	1	2	yes	—
279	C₂²×C₄	C₂²×C₃×C₉×C₁₃	1	1	yes	characteristic
280	C₂×C₈	C₃×C₄×C₉×C₁₃	1	8	yes	direct product factor
281	C₂×C₈	C₂²×C₃×C₉×C₁₃	1	4	yes	—
282	C₄²	C₃×C₄×C₉×C₁₃	1	2	yes	—
283	C₄²	C₂²×C₃×C₉×C₁₃	1	2	yes	—
284	C₁₃	C₂×C₃×C₄×C₈×C₉	1	1	yes	characteristic, direct product factor, Sylow
285	C₂²×C₃	C₄²×C₉×C₁₃	1	6	yes	—
286	C₂²×C₃	C₂×C₈×C₉×C₁₃	1	12	yes	—
287	C₂²×C₃	C₂²×C₄×C₉×C₁₃	1	3	yes	—
288	C₂²×C₃	C₃²×C₄²×C₁₃	1	2	yes	—
289	C₂²×C₃	C₂×C₃²×C₈×C₁₃	1	4	yes	—
290	C₂²×C₃	C₂²×C₃²×C₄×C₁₃	1	1	yes	characteristic
291	C₃×C₄	C₄²×C₉×C₁₃	1	6	yes	—
292	C₃×C₄	C₂×C₈×C₉×C₁₃	1	24	yes	direct product factor
293	C₃×C₄	C₂²×C₄×C₉×C₁₃	1	6	yes	—
294	C₃×C₄	C₃²×C₄²×C₁₃	1	2	yes	—
295	C₃×C₄	C₂×C₃²×C₈×C₁₃	1	8	yes	—
296	C₃×C₄	C₂²×C₃²×C₄×C₁₃	1	2	yes	—
297	C₃²	C₂×C₃×C₄×C₈×C₁₃	1	1	yes	characteristic
298	C₉	C₂×C₃×C₄×C₈×C₁₃	1	3	yes	direct product factor
299	C₂³	C₂×C₃×C₄×C₉×C₁₃	1	1	yes	characteristic
300	C₂×C₄	C₃×C₈×C₉×C₁₃	1	8	yes	direct product factor
301	C₂×C₄	C₂×C₃×C₄×C₉×C₁₃	1	1	yes	characteristic
302	C₂×C₄	C₂×C₃×C₄×C₉×C₁₃	1	4	yes	—
303	C₂×C₄	C₂×C₃×C₄×C₉×C₁₃	1	4	yes	—
304	C₂×C₄	C₂³×C₃×C₉×C₁₃	1	1	yes	characteristic
305	C₈	C₂×C₃×C₄×C₉×C₁₃	1	8	yes	direct product factor
306	C₂×C₃	C₄×C₈×C₉×C₁₃	1	12	yes	direct product factor
307	C₂×C₃	C₃²×C₄×C₈×C₁₃	1	4	yes	—
308	C₂×C₃	C₂²×C₈×C₉×C₁₃	1	6	yes	—
309	C₂×C₃	C₂×C₄²×C₉×C₁₃	1	3	yes	—
310	C₂×C₃	C₂²×C₃²×C₈×C₁₃	1	2	yes	—
311	C₂×C₃	C₂×C₃²×C₄²×C₁₃	1	1	yes	characteristic
312	C₂²	C₂×C₃×C₈×C₉×C₁₃	1	4	yes	—
313	C₂²	C₃×C₄²×C₉×C₁₃	1	2	yes	—
314	C₂²	C₂²×C₃×C₄×C₉×C₁₃	1	1	yes	characteristic
315	C₄	C₂×C₃×C₈×C₉×C₁₃	1	8	yes	direct product factor
316	C₄	C₃×C₄²×C₉×C₁₃	1	2	yes	—
317	C₄	C₂²×C₃×C₄×C₉×C₁₃	1	2	yes	—
318	C₃	C₂×C₄×C₈×C₉×C₁₃	1	3	yes	direct product factor
319	C₃	C₂×C₃²×C₄×C₈×C₁₃	1	1	yes	characteristic
320	C₂	C₃×C₄×C₈×C₉×C₁₃	1	4	yes	direct product factor
321	C₂	C₂²×C₃×C₈×C₉×C₁₃	1	2	yes	—
322	C₂	C₂×C₃×C₄²×C₉×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃×C₄	C₂³×C₃²×C₁₃
socle, prime radical	C₂³×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
3. C₃×C₄×C₈×C₉×C₁₃	C₂	direct (N × H)
5. C₂×C₄×C₈×C₉×C₁₃	C₃	direct (N × H)
10. C₂×C₃×C₈×C₉×C₁₃	C₄	direct (N × H)
17. C₄×C₈×C₉×C₁₃	C₂×C₃	direct (N × H)
19. C₂×C₃×C₄×C₉×C₁₃	C₈	direct (N × H)
24. C₃×C₈×C₉×C₁₃	C₂×C₄	direct (N × H)
25. C₂×C₃×C₄×C₈×C₁₃	C₉	direct (N × H)
35. C₂×C₈×C₉×C₁₃	C₃×C₄	direct (N × H)
39. C₂×C₃×C₄×C₈×C₉	C₁₃	direct (N × H)
44. C₃×C₄×C₉×C₁₃	C₂×C₈	direct (N × H)
50. C₃×C₄×C₈×C₁₃	C₂×C₉	direct (N × H)
60. C₂×C₄×C₉×C₁₃	C₃×C₈	direct (N × H)
65. C₈×C₉×C₁₃	C₂×C₃×C₄	direct (N × H)
68. C₃×C₄×C₈×C₉	C₂×C₁₃	direct (N × H)
69. C₂×C₄×C₈×C₁₃	C₃×C₉	direct (N × H)
70. C₂×C₃×C₉×C₁₃	C₄×C₈	direct (N × H)
77. C₂×C₃×C₈×C₁₃	C₄×C₉	direct (N × H)
86. C₂×C₄×C₈×C₉	C₃×C₁₃	direct (N × H)
97. C₄×C₉×C₁₃	C₂×C₃×C₈	direct (N × H)
101. C₂×C₃×C₈×C₉	C₄×C₁₃	direct (N × H)
107. C₄×C₈×C₁₃	C₂×C₃×C₉	direct (N × H)
108. C₃×C₉×C₁₃	C₂×C₄×C₈	direct (N × H)
111. C₂×C₃×C₄×C₁₃	C₈×C₉	direct (N × H)
121. C₃×C₈×C₁₃	C₂×C₄×C₉	direct (N × H)
128. C₄×C₈×C₉	C₂×C₃×C₁₃	direct (N × H)
132. C₂×C₉×C₁₃	C₃×C₄×C₈	direct (N × H)
136. C₂×C₃×C₄×C₉	C₈×C₁₃	direct (N × H)
141. C₃×C₈×C₉	C₂×C₄×C₁₃	direct (N × H)
144. C₂×C₈×C₁₃	C₃×C₄×C₉	direct (N × H)
148. C₂×C₃×C₄×C₈	C₉×C₁₃	direct (N × H)
157. C₃×C₄×C₁₃	C₂×C₈×C₉	direct (N × H)
170. C₂×C₈×C₉	C₃×C₄×C₁₃	direct (N × H)
175. C₉×C₁₃	C₂×C₃×C₄×C₈	direct (N × H)
180. C₃×C₄×C₉	C₂×C₈×C₁₃	direct (N × H)
183. C₂×C₄×C₁₃	C₃×C₈×C₉	direct (N × H)
188. C₈×C₁₃	C₂×C₃×C₄×C₉	direct (N × H)
193. C₃×C₄×C₈	C₂×C₉×C₁₃	direct (N × H)
195. C₂×C₃×C₁₃	C₄×C₈×C₉	direct (N × H)
209. C₂×C₄×C₉	C₃×C₈×C₁₃	direct (N × H)
214. C₈×C₉	C₂×C₃×C₄×C₁₃	direct (N × H)
215. C₂×C₄×C₈	C₃×C₉×C₁₃	direct (N × H)
216. C₂×C₃×C₉	C₄×C₈×C₁₃	direct (N × H)
223. C₄×C₁₃	C₂×C₃×C₈×C₉	direct (N × H)
229. C₂×C₃×C₈	C₄×C₉×C₁₃	direct (N × H)
237. C₃×C₁₃	C₂×C₄×C₈×C₉	direct (N × H)
249. C₄×C₉	C₂×C₃×C₈×C₁₃	direct (N × H)
253. C₄×C₈	C₂×C₃×C₉×C₁₃	direct (N × H)
254. C₃×C₉	C₂×C₄×C₈×C₁₃	direct (N × H)
255. C₂×C₁₃	C₃×C₄×C₈×C₉	direct (N × H)
260. C₂×C₃×C₄	C₈×C₉×C₁₃	direct (N × H)
270. C₃×C₈	C₂×C₄×C₉×C₁₃	direct (N × H)
275. C₂×C₉	C₃×C₄×C₈×C₁₃	direct (N × H)
280. C₂×C₈	C₃×C₄×C₉×C₁₃	direct (N × H)
284. C₁₃	C₂×C₃×C₄×C₈×C₉	direct (N × H)
292. C₃×C₄	C₂×C₈×C₉×C₁₃	direct (N × H)
298. C₉	C₂×C₃×C₄×C₈×C₁₃	direct (N × H)
300. C₂×C₄	C₃×C₈×C₉×C₁₃	direct (N × H)
305. C₈	C₂×C₃×C₄×C₉×C₁₃	direct (N × H)
306. C₂×C₃	C₄×C₈×C₉×C₁₃	direct (N × H)
315. C₄	C₂×C₃×C₈×C₉×C₁₃	direct (N × H)
318. C₃	C₂×C₄×C₈×C₉×C₁₃	direct (N × H)
320. C₂	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
C₂×C₃×C₄²×C₉×C₁₃	2
C₂²×C₃×C₈×C₉×C₁₃	2
C₃×C₄×C₈×C₉×C₁₃	2
C₂×C₃²×C₄×C₈×C₁₃	3
C₂×C₄×C₈×C₉×C₁₃	3
C₂×C₃×C₄×C₈×C₉	13

Subgroups — C2×C3×C4×C8×C9×C13 #72199869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄×C₈×C₉×C₁₃ #72199869