Subgroups — AGL(1,ℤ/9)×C₉⋊C₉ #72243183

Order 4374.

985 conjugacy classes of subgroups.

The subgroup lattice has 985 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	3₋¹⁺²×C₉⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×C₉×AGL(1,ℤ/9)	C₃	1	1	yes	maximal, characteristic
3	C₃×C₉×AGL(1,ℤ/9)	C₃	1	1	yes	maximal, characteristic
4	C₃×C₉×AGL(1,ℤ/9)	C₃	1	1	yes	maximal, characteristic
5	C₃×C₉×AGL(1,ℤ/9)	C₃	1	1	yes	maximal, characteristic
6	C₃×D₃×C₉⋊C₉	—	3	1	no	maximal
7	(D₉⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
8	(D₉⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
9	(D₉⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
10	(D₉⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
11	(D₉⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
12	(D₉⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
13	#13090635	C₃	1	1	yes	maximal, characteristic, complemented
14	#13090628	C₃	1	1	yes	maximal, characteristic, complemented
15	D₉×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
16	C₃×C₉×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic
17	C₃×C₉×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic
18	C₃×C₉×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic
19	C₃×C₉×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic
20	C₃²×C₉⋊C₉	D₃	1	1	yes	characteristic
21	#10624561	—	2	1	no	—
22	#10624561	—	2	1	no	—
23	#10624561	—	2	1	no	—
24	#10624561	—	2	1	no	—
25	#10624561	—	2	1	no	—
26	#10624561	—	2	1	no	—
27	#10624561	C₂×C₃	1	1	yes	characteristic, complemented
28	#10624561	C₂×C₃	1	1	yes	characteristic, complemented
29	#10624561	C₂×C₃	1	1	yes	characteristic, complemented
30	#10624561	C₂×C₃	1	1	yes	characteristic, complemented
31	#10624561	C₂×C₃	1	1	yes	characteristic, complemented
32	#10624561	C₂×C₃	1	1	yes	characteristic, complemented
33	#10624556	—	2	1	no	—
34	#10624556	—	2	1	no	—
35	#10624556	—	2	1	no	—
36	#10624554	—	2	1	no	—
37	#10624554	C₂×C₃	1	1	yes	characteristic, complemented
38	#10624550	—	2	1	no	—
39	#10624550	C₂×C₃	1	1	yes	characteristic, complemented
40	#10624548	—	2	1	no	—
41	C₉×C₉⋊C₉	—	2	1	no	—
42	C₉×C₉⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
43	C₃²×AGL(1,ℤ/9)	C₃²	1	1	yes	characteristic
44	C₃²×D₃×C₉	—	3	1	no	—
45	C₃²×D₃×C₉	—	3	1	no	—
46	C₃²×D₃×C₉	—	3	1	no	—
47	C₃²×D₃×C₉	—	3	1	no	—
48	C₂×C₃×C₉⋊C₉	—	9	1	no	—
49	C₉×AGL(1,ℤ/9)	—	3	1	no	—
50	C₉×AGL(1,ℤ/9)	—	3	1	no	—
51	C₉×AGL(1,ℤ/9)	—	3	1	no	—
52	C₉×AGL(1,ℤ/9)	—	3	1	no	—
53	C₉×AGL(1,ℤ/9)	—	3	1	no	—
54	C₉×AGL(1,ℤ/9)	—	3	1	no	—
55	C₉×AGL(1,ℤ/9)	—	3	1	no	—
56	C₉×AGL(1,ℤ/9)	—	3	1	no	—
57	C₉×AGL(1,ℤ/9)	—	3	1	no	—
58	C₉×AGL(1,ℤ/9)	C₉	1	1	yes	characteristic, complemented
59	C₉×AGL(1,ℤ/9)	C₉	1	1	yes	characteristic, complemented
60	C₉×AGL(1,ℤ/9)	C₉	1	1	yes	characteristic, complemented
61	C₉×AGL(1,ℤ/9)	C₉	1	1	yes	characteristic, complemented
62	C₉×AGL(1,ℤ/9)	C₉	1	1	yes	characteristic, complemented
63	C₉×AGL(1,ℤ/9)	C₉	1	1	yes	characteristic, complemented
64	C₉×AGL(1,ℤ/9)	C₉	1	1	yes	characteristic, complemented
65	C₉×AGL(1,ℤ/9)	C₉	1	1	yes	characteristic, complemented
66	C₉×AGL(1,ℤ/9)	C₉	1	1	yes	characteristic, complemented
67	D₃×C₉⋊C₉	—	3	1	no	—
68	D₃×C₉⋊C₉	—	3	1	no	—
69	D₃×C₉⋊C₉	—	3	1	no	—
70	D₃×C₉⋊C₉	—	3	1	no	—
71	D₃×C₉⋊C₉	—	3	1	no	—
72	D₃×C₉⋊C₉	—	3	1	no	—
73	D₃×C₉⋊C₉	—	3	1	no	—
74	D₃×C₉⋊C₉	—	3	1	no	—
75	D₃×C₉⋊C₉	—	3	1	no	—
76	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
77	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
78	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
79	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
80	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
81	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
82	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
83	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
84	C₃×C₉×D₉	C₃²	1	1	yes	characteristic
85	C₃×C₉×D₉	C₃²	1	1	yes	characteristic
86	C₃×C₉×D₉	C₃²	1	1	yes	characteristic
87	C₃×C₉×D₉	C₃²	1	1	yes	characteristic
88	C₃²×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
89	C₃³×C₉	C₃×D₃	1	1	yes	characteristic
90	C₃³×C₉	C₃×D₃	1	1	yes	characteristic
91	C₃³×C₉	C₃×D₃	1	1	yes	characteristic
92	C₃³×C₉	C₃×D₃	1	1	yes	characteristic
93	C₉×3₋¹⁺²	—	2	1	no	—
94	C₉×3₋¹⁺²	—	2	1	no	—
95	C₉×3₋¹⁺²	—	2	1	no	—
96	C₉×3₋¹⁺²	—	2	1	no	—
97	C₉×3₋¹⁺²	—	2	1	no	—
98	C₉×3₋¹⁺²	—	2	1	no	—
99	C₉×3₋¹⁺²	—	2	1	no	—
100	C₉×3₋¹⁺²	—	2	1	no	—
101	C₉×3₋¹⁺²	—	2	1	no	—
102	C₉×3₋¹⁺²	—	3	1	no	—
103	C₉×3₋¹⁺²	—	3	1	no	—
104	C₉×3₋¹⁺²	—	3	1	no	—
105	C₉×3₋¹⁺²	—	3	1	no	—
106	C₉×3₋¹⁺²	—	3	1	no	—
107	C₉×3₋¹⁺²	—	3	1	no	—
108	C₉×3₋¹⁺²	—	3	1	no	—
109	C₉×3₋¹⁺²	—	3	1	no	—
110	C₉×3₋¹⁺²	—	3	1	no	—
111	C₉×3₋¹⁺²	—	6	1	no	—
112	C₉×3₋¹⁺²	—	6	1	no	—
113	C₉×3₋¹⁺²	—	6	1	no	—
114	C₉×3₋¹⁺²	—	6	1	no	—
115	C₉×3₋¹⁺²	—	6	1	no	—
116	C₉×3₋¹⁺²	—	6	1	no	—
117	C₉×3₋¹⁺²	—	6	1	no	—
118	C₉×3₋¹⁺²	—	6	1	no	—
119	C₉×3₋¹⁺²	—	6	1	no	—
120	C₉×3₋¹⁺²	C₂×C₉	1	1	yes	characteristic, complemented
121	C₉×3₋¹⁺²	C₂×C₉	1	1	yes	characteristic, complemented
122	C₉×3₋¹⁺²	C₂×C₉	1	1	yes	characteristic, complemented
123	C₉×3₋¹⁺²	C₂×C₉	1	1	yes	characteristic, complemented
124	C₉×3₋¹⁺²	C₂×C₉	1	1	yes	characteristic, complemented
125	C₉×3₋¹⁺²	C₂×C₉	1	1	yes	characteristic, complemented
126	C₉×3₋¹⁺²	C₂×C₉	1	1	yes	characteristic, complemented
127	C₉×3₋¹⁺²	C₂×C₉	1	1	yes	characteristic, complemented
128	C₉×3₋¹⁺²	C₂×C₉	1	1	yes	characteristic, complemented
129	C₃×C₉⋊C₉	—	2	1	no	—
130	C₃×C₉⋊C₉	—	2	1	no	—
131	C₃×C₉⋊C₉	—	2	1	no	—
132	C₃×C₉⋊C₉	—	2	1	no	—
133	C₃×C₉⋊C₉	—	2	1	no	—
134	C₃×C₉⋊C₉	—	2	1	no	—
135	C₃×C₉⋊C₉	—	2	1	no	—
136	C₃×C₉⋊C₉	—	2	1	no	—
137	C₃×C₉⋊C₉	—	2	1	no	—
138	C₃×C₉⋊C₉	—	2	1	no	—
139	C₃×C₉⋊C₉	—	2	1	no	—
140	C₃×C₉⋊C₉	—	2	1	no	—
141	C₃×C₉⋊C₉	—	2	1	no	—
142	C₃×C₉⋊C₉	—	2	1	no	—
143	C₃×C₉⋊C₉	—	2	1	no	—
144	C₃×C₉⋊C₉	—	2	1	no	—
145	C₃×C₉⋊C₉	—	2	1	no	—
146	C₃×C₉⋊C₉	—	2	1	no	—
147	C₃×C₉⋊C₉	—	2	1	no	—
148	C₃×C₉⋊C₉	—	2	1	no	—
149	C₃×C₉⋊C₉	—	3	1	no	—
150	C₃×C₉⋊C₉	—	6	1	no	—
151	C₃×C₉⋊C₉	—	6	1	no	—
152	C₃×C₉⋊C₉	—	6	1	no	—
153	C₃×C₉⋊C₉	—	6	1	no	—
154	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
155	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
156	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
157	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
158	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
159	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
160	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
161	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
162	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
163	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
164	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
165	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
166	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
167	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
168	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
169	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
170	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
171	C₃×C₃²⋊C₉	—	2	1	no	—
172	C₃×C₃²⋊C₉	—	2	1	no	—
173	C₃×C₃²⋊C₉	—	2	1	no	—
174	C₃×C₃²⋊C₉	—	2	1	no	—
175	C₃×C₉²	—	2	1	no	—
176	C₃×C₉²	—	2	1	no	—
177	C₃×C₉²	—	2	1	no	—
178	C₃×C₉²	—	2	1	no	—
179	C₃×C₉²	C₂×C₃²	1	1	yes	characteristic
180	C₃×C₉²	C₂×C₃²	1	1	yes	characteristic
181	C₃×C₉²	C₂×C₃²	1	1	yes	characteristic
182	C₃×C₉²	C₂×C₃²	1	1	yes	characteristic
183	#6855	—	2	1	no	—
184	#6855	—	2	1	no	—
185	#6855	—	2	1	no	—
186	#6855	—	2	1	no	—
187	#6855	—	2	1	no	—
188	#6855	—	2	1	no	—
189	#6855	—	2	1	no	—
190	#6855	—	2	1	no	—
191	#6855	—	2	1	no	—
192	#6855	—	2	1	no	—
193	#6855	—	2	1	no	—
194	#6855	—	2	1	no	—
195	#6855	—	2	1	no	—
196	#6855	—	2	1	no	—
197	#6855	—	2	1	no	—
198	#6855	—	2	1	no	—
199	#6855	—	2	1	no	—
200	#6855	—	2	1	no	—
201	#6855	—	2	1	no	—
202	#6855	—	2	1	no	—
203	#6855	—	2	1	no	—
204	#6855	—	2	1	no	—
205	#6855	—	2	1	no	—
206	#6855	—	2	1	no	—
207	C₃³×D₃	—	3	1	no	—
208	C₂×C₃²×C₉	—	9	1	no	—
209	C₂×C₃²×C₉	—	9	1	no	—
210	C₂×C₃²×C₉	—	9	1	no	—
211	C₂×C₃²×C₉	—	9	1	no	—
212	C₃×AGL(1,ℤ/9)	C₃×C₉	1	1	yes	characteristic
213	C₃×AGL(1,ℤ/9)	C₃×C₉	1	1	yes	characteristic
214	C₃×AGL(1,ℤ/9)	C₃×C₉	1	1	yes	characteristic
215	C₃×AGL(1,ℤ/9)	3₋¹⁺²	1	1	yes	characteristic
216	C₃×AGL(1,ℤ/9)	3₋¹⁺²	1	1	yes	characteristic
217	C₃×AGL(1,ℤ/9)	3₋¹⁺²	1	1	yes	characteristic
218	C₃×AGL(1,ℤ/9)	3₋¹⁺²	1	1	yes	characteristic
219	C₃×AGL(1,ℤ/9)	3₋¹⁺²	1	1	yes	characteristic
220	C₃×AGL(1,ℤ/9)	3₋¹⁺²	1	1	yes	characteristic
221	C₃×AGL(1,ℤ/9)	3₋¹⁺²	1	1	yes	characteristic
222	C₃×AGL(1,ℤ/9)	3₋¹⁺²	1	1	yes	characteristic
223	C₃×AGL(1,ℤ/9)	3₋¹⁺²	1	1	yes	characteristic
224	C₃×D₃×C₉	—	3	1	no	—
225	C₃×D₃×C₉	—	3	1	no	—
226	C₃×D₃×C₉	—	3	1	no	—
227	C₃×D₃×C₉	—	3	1	no	—
228	C₃×D₃×C₉	—	3	1	no	—
229	C₃×D₃×C₉	—	3	1	no	—
230	C₃×D₃×C₉	—	3	1	no	—
231	C₃×D₃×C₉	—	3	1	no	—
232	C₃×D₃×C₉	—	3	1	no	—
233	C₃×D₃×C₉	—	3	1	no	—
234	C₃×D₃×C₉	—	3	1	no	—
235	C₃×D₃×C₉	—	3	1	no	—
236	C₃×D₃×C₉	—	3	1	no	—
237	C₃×D₃×C₉	—	3	1	no	—
238	C₃×D₃×C₉	—	3	1	no	—
239	C₃×D₃×C₉	—	3	1	no	—
240	C₃×D₃×C₉	—	3	1	no	—
241	C₃×D₃×C₉	—	3	1	no	—
242	C₃×D₃×C₉	—	3	1	no	—
243	C₃×D₃×C₉	—	3	1	no	—
244	C₃×D₃×C₉	—	3	1	no	—
245	C₃×D₃×C₉	—	9	1	no	—
246	C₃×D₃×C₉	—	9	1	no	—
247	C₃×D₃×C₉	—	9	1	no	—
248	C₃×D₃×C₉	—	9	1	no	—
249	C₃×D₃×C₉	—	9	1	no	—
250	C₃×D₃×C₉	—	9	1	no	—
251	C₃×D₃×C₉	—	9	1	no	—
252	C₃×D₃×C₉	—	9	1	no	—
253	C₃×D₃×C₉	—	9	1	no	—
254	C₃²×D₉	C₃³	1	1	yes	characteristic
255	C₂×C₉⋊C₉	—	9	1	no	—
256	C₂×C₉⋊C₉	—	9	1	no	—
257	C₂×C₉⋊C₉	—	9	1	no	—
258	C₂×C₉⋊C₉	—	9	1	no	—
259	C₂×C₉⋊C₉	—	9	1	no	—
260	C₂×C₉⋊C₉	—	9	1	no	—
261	C₂×C₉⋊C₉	—	9	1	no	—
262	C₂×C₉⋊C₉	—	9	1	no	—
263	C₂×C₉⋊C₉	—	9	1	no	—
264	D₉⋊C₉	—	3	1	no	—
265	D₉⋊C₉	—	3	1	no	—
266	D₉⋊C₉	—	3	1	no	—
267	D₉⋊C₉	—	3	1	no	—
268	D₉⋊C₉	—	3	1	no	—
269	D₉⋊C₉	—	3	1	no	—
270	D₉⋊C₉	C₃×C₉	1	1	yes	characteristic, complemented
271	D₉⋊C₉	C₃×C₉	1	1	yes	characteristic, complemented
272	D₉⋊C₉	C₃×C₉	1	1	yes	characteristic, complemented
273	D₉⋊C₉	C₃×C₉	1	1	yes	characteristic, complemented
274	D₉⋊C₉	C₃×C₉	1	1	yes	characteristic, complemented
275	D₉⋊C₉	C₃×C₉	1	1	yes	characteristic, complemented
276	C₉×D₉	—	3	1	no	—
277	C₉×D₉	—	3	1	no	—
278	C₉×D₉	—	3	1	no	—
279	C₉×D₉	C₃×C₉	1	1	yes	characteristic, complemented
280	C₉×D₉	C₃×C₉	1	1	yes	characteristic, complemented
281	C₉×D₉	C₃×C₉	1	1	yes	characteristic, complemented
282	C₃⁴	C₃²×D₃	1	1	yes	characteristic
283	C₃×3₋¹⁺²	—	2	1	no	—
284	C₃×3₋¹⁺²	—	2	1	no	—
285	C₃×3₋¹⁺²	—	2	1	no	—
286	C₃×3₋¹⁺²	—	2	1	no	—
287	C₃×3₋¹⁺²	—	2	1	no	—
288	C₃×3₋¹⁺²	—	2	1	no	—
289	C₃×3₋¹⁺²	—	2	1	no	—
290	C₃×3₋¹⁺²	—	2	1	no	—
291	C₃×3₋¹⁺²	—	2	1	no	—
292	C₃×3₋¹⁺²	—	2	1	no	—
293	C₃×3₋¹⁺²	—	2	1	no	—
294	C₃×3₋¹⁺²	—	2	1	no	—
295	C₃×3₋¹⁺²	C₂×C₃×C₉	1	1	yes	characteristic
296	C₃×3₋¹⁺²	C₂×C₃×C₉	1	1	yes	characteristic
297	C₃×3₋¹⁺²	C₂×C₃×C₉	1	1	yes	characteristic
298	C₃×3₋¹⁺²	C₂×3₋¹⁺²	1	1	yes	characteristic
299	C₃×3₋¹⁺²	C₂×3₋¹⁺²	1	1	yes	characteristic
300	C₃×3₋¹⁺²	C₂×3₋¹⁺²	1	1	yes	characteristic
301	C₃×3₋¹⁺²	C₂×3₋¹⁺²	1	1	yes	characteristic
302	C₃×3₋¹⁺²	C₂×3₋¹⁺²	1	1	yes	characteristic
303	C₃×3₋¹⁺²	C₂×3₋¹⁺²	1	1	yes	characteristic
304	C₃×3₋¹⁺²	C₂×3₋¹⁺²	1	1	yes	characteristic
305	C₃×3₋¹⁺²	C₂×3₋¹⁺²	1	1	yes	characteristic
306	C₃×3₋¹⁺²	C₂×3₋¹⁺²	1	1	yes	characteristic
307	C₃²×C₉	—	2	1	no	—
308	C₃²×C₉	—	2	1	no	—
309	C₃²×C₉	—	2	1	no	—
310	C₃²×C₉	—	2	1	no	—
311	C₃²×C₉	—	2	1	no	—
312	C₃²×C₉	—	2	1	no	—
313	C₃²×C₉	—	2	1	no	—
314	C₃²×C₉	—	2	1	no	—
315	C₃²×C₉	—	2	1	no	—
316	C₃²×C₉	—	2	1	no	—
317	C₃²×C₉	—	2	1	no	—
318	C₃²×C₉	—	2	1	no	—
319	C₃²×C₉	—	2	1	no	—
320	C₃²×C₉	—	3	1	no	—
321	C₃²×C₉	—	3	1	no	—
322	C₃²×C₉	—	3	1	no	—
323	C₃²×C₉	—	3	1	no	—
324	C₃²×C₉	—	3	1	no	—
325	C₃²×C₉	—	3	1	no	—
326	C₃²×C₉	—	3	1	no	—
327	C₃²×C₉	—	3	1	no	—
328	C₃²×C₉	—	3	1	no	—
329	C₃²×C₉	—	6	1	no	—
330	C₃²×C₉	—	6	1	no	—
331	C₃²×C₉	—	6	1	no	—
332	C₃²×C₉	—	6	1	no	—
333	C₃²×C₉	—	6	1	no	—
334	C₃²×C₉	—	6	1	no	—
335	C₃²×C₉	—	6	1	no	—
336	C₃²×C₉	—	6	1	no	—
337	C₃²×C₉	—	6	1	no	—
338	C₃²×C₉	—	6	1	no	—
339	C₃²×C₉	—	6	1	no	—
340	C₃²×C₉	—	18	1	no	—
341	C₃²×C₉	—	18	1	no	—
342	C₃²×C₉	—	18	1	no	—
343	C₃²×C₉	D₃×C₉	1	1	yes	characteristic
344	C₃²×C₉	D₃×C₉	1	1	yes	characteristic
345	C₃²×C₉	D₃×C₉	1	1	yes	characteristic
346	C₃²×C₉	D₃×C₉	1	1	yes	characteristic
347	C₃²×C₉	D₃×C₉	1	1	yes	characteristic
348	C₃²×C₉	D₃×C₉	1	1	yes	characteristic
349	C₃²×C₉	D₃×C₉	1	1	yes	characteristic
350	C₃²×C₉	D₃×C₉	1	1	yes	characteristic
351	C₃²×C₉	D₃×C₉	1	1	yes	characteristic
352	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
353	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
354	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
355	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
356	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
357	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
358	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
359	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
360	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
361	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
362	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
363	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
364	C₃²×C₉	C₂×C₃³	1	1	yes	characteristic
365	C₉⋊C₉	—	2	1	no	—
366	C₉⋊C₉	—	2	1	no	—
367	C₉⋊C₉	—	2	1	no	—
368	C₉⋊C₉	—	2	1	no	—
369	C₉⋊C₉	—	2	1	no	—
370	C₉⋊C₉	—	2	1	no	—
371	C₉⋊C₉	—	2	1	no	—
372	C₉⋊C₉	—	2	1	no	—
373	C₉⋊C₉	—	2	1	no	—
374	C₉⋊C₉	—	2	1	no	—
375	C₉⋊C₉	—	2	1	no	—
376	C₉⋊C₉	—	2	1	no	—
377	C₉⋊C₉	—	2	1	no	—
378	C₉⋊C₉	—	2	1	no	—
379	C₉⋊C₉	—	2	1	no	—
380	C₉⋊C₉	—	2	1	no	—
381	C₉⋊C₉	—	2	1	no	—
382	C₉⋊C₉	—	2	1	no	—
383	C₉⋊C₉	—	2	1	no	—
384	C₉⋊C₉	—	2	1	no	—
385	C₉⋊C₉	—	2	1	no	—
386	C₉⋊C₉	—	2	1	no	—
387	C₉⋊C₉	—	2	1	no	—
388	C₉⋊C₉	—	2	1	no	—
389	C₉⋊C₉	—	2	1	no	—
390	C₉⋊C₉	—	2	1	no	—
391	C₉⋊C₉	—	2	1	no	—
392	C₉⋊C₉	—	2	1	no	—
393	C₉⋊C₉	—	3	1	no	—
394	C₉⋊C₉	—	3	1	no	—
395	C₉⋊C₉	—	3	1	no	—
396	C₉⋊C₉	—	3	1	no	—
397	C₉⋊C₉	—	3	1	no	—
398	C₉⋊C₉	—	3	1	no	—
399	C₉⋊C₉	—	3	1	no	—
400	C₉⋊C₉	—	3	1	no	—
401	C₉⋊C₉	—	6	1	no	—
402	C₉⋊C₉	—	6	1	no	—
403	C₉⋊C₉	—	6	1	no	—
404	C₉⋊C₉	—	6	1	no	—
405	C₉⋊C₉	—	6	1	no	—
406	C₉⋊C₉	—	6	1	no	—
407	C₉⋊C₉	—	6	1	no	—
408	C₉⋊C₉	—	6	1	no	—
409	C₉⋊C₉	—	6	1	no	—
410	C₉⋊C₉	—	6	1	no	—
411	C₉⋊C₉	—	6	1	no	—
412	C₉⋊C₉	—	6	1	no	—
413	C₉⋊C₉	—	6	1	no	—
414	C₉⋊C₉	—	6	1	no	—
415	C₉⋊C₉	—	6	1	no	—
416	C₉⋊C₉	—	6	1	no	—
417	C₉⋊C₉	—	6	1	no	—
418	C₉⋊C₉	—	6	1	no	—
419	C₉⋊C₉	—	6	1	no	—
420	C₉⋊C₉	—	6	1	no	—
421	C₉⋊C₉	—	6	1	no	—
422	C₉⋊C₉	—	6	1	no	—
423	C₉⋊C₉	—	6	1	no	—
424	C₉⋊C₉	—	6	1	no	—
425	C₉⋊C₉	—	6	1	no	—
426	C₉⋊C₉	—	6	1	no	—
427	C₉⋊C₉	—	6	1	no	—
428	C₉⋊C₉	—	6	1	no	—
429	C₉⋊C₉	—	6	1	no	—
430	C₉⋊C₉	—	6	1	no	—
431	C₉⋊C₉	—	6	1	no	—
432	C₉⋊C₉	—	6	1	no	—
433	C₉⋊C₉	—	6	1	no	—
434	C₉⋊C₉	—	6	1	no	—
435	C₉⋊C₉	—	6	1	no	—
436	C₉⋊C₉	—	6	1	no	—
437	C₉⋊C₉	—	6	1	no	—
438	C₉⋊C₉	—	6	1	no	—
439	C₉⋊C₉	—	6	1	no	—
440	C₉⋊C₉	—	6	1	no	—
441	C₉⋊C₉	—	6	1	no	—
442	C₉⋊C₉	—	6	1	no	—
443	C₉⋊C₉	—	6	1	no	—
444	C₉⋊C₉	—	6	1	no	—
445	C₉⋊C₉	—	6	1	no	—
446	C₉⋊C₉	—	6	1	no	—
447	C₉⋊C₉	—	6	1	no	—
448	C₉⋊C₉	—	18	1	no	—
449	C₉⋊C₉	—	18	1	no	—
450	C₉⋊C₉	—	18	1	no	—
451	C₉⋊C₉	—	18	1	no	—
452	C₉⋊C₉	—	18	1	no	—
453	C₉⋊C₉	—	18	1	no	—
454	C₉⋊C₉	—	18	1	no	—
455	C₉⋊C₉	—	18	1	no	—
456	C₉⋊C₉	—	18	1	no	—
457	C₉⋊C₉	AGL(1,ℤ/9)	1	1	yes	characteristic, direct product factor
458	C₉⋊C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
459	C₉⋊C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
460	C₉⋊C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
461	C₉⋊C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
462	C₉⋊C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
463	C₉⋊C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
464	C₃²⋊C₉	—	2	1	no	—
465	C₃²⋊C₉	—	2	1	no	—
466	C₃²⋊C₉	—	2	1	no	—
467	C₃²⋊C₉	—	2	1	no	—
468	C₃²⋊C₉	—	2	1	no	—
469	C₃²⋊C₉	—	2	1	no	—
470	C₃²⋊C₉	—	2	1	no	—
471	C₃²⋊C₉	—	2	1	no	—
472	C₃²⋊C₉	—	2	1	no	—
473	C₃²⋊C₉	—	6	1	no	—
474	C₃²⋊C₉	—	6	1	no	—
475	C₃²⋊C₉	—	6	1	no	—
476	C₃²⋊C₉	—	6	1	no	—
477	C₃²⋊C₉	—	6	1	no	—
478	C₃²⋊C₉	—	6	1	no	—
479	C₃²⋊C₉	—	6	1	no	—
480	C₃²⋊C₉	—	6	1	no	—
481	C₃²⋊C₉	—	6	1	no	—
482	C₉²	—	2	1	no	—
483	C₉²	—	2	1	no	—
484	C₉²	—	2	1	no	—
485	C₉²	—	2	1	no	—
486	C₉²	—	2	1	no	—
487	C₉²	—	2	1	no	—
488	C₉²	—	2	1	no	—
489	C₉²	—	2	1	no	—
490	C₉²	—	2	1	no	—
491	C₉²	—	2	1	no	—
492	C₉²	—	2	1	no	—
493	C₉²	—	2	1	no	—
494	C₉²	—	3	1	no	—
495	C₉²	—	3	1	no	—
496	C₉²	—	3	1	no	—
497	C₉²	—	6	1	no	—
498	C₉²	—	6	1	no	—
499	C₉²	—	6	1	no	—
500	C₉²	—	6	1	no	—
501	C₉²	—	6	1	no	—
502	C₉²	—	6	1	no	—
503	C₉²	—	6	1	no	—
504	C₉²	—	6	1	no	—
505	C₉²	—	6	1	no	—
506	C₉²	—	6	1	no	—
507	C₉²	—	6	1	no	—
508	C₉²	—	6	1	no	—
509	C₉²	C₂×C₃×C₉	1	1	yes	characteristic, complemented
510	C₉²	C₂×C₃×C₉	1	1	yes	characteristic, complemented
511	C₉²	C₂×C₃×C₉	1	1	yes	characteristic, complemented
512	C₂×C₃³	—	9	1	no	—
513	C₃²×D₃	—	3	1	no	—
514	C₃²×D₃	—	3	1	no	—
515	C₃²×D₃	—	3	1	no	—
516	C₃²×D₃	—	3	1	no	—
517	C₃²×D₃	—	3	1	no	—
518	C₃²×D₃	—	3	1	no	—
519	C₃²×D₃	—	3	1	no	—
520	C₃²×D₃	—	3	1	no	—
521	C₃²×D₃	—	3	1	no	—
522	C₃²×D₃	—	3	1	no	—
523	C₃²×D₃	—	3	1	no	—
524	C₃²×D₃	—	3	1	no	—
525	C₃²×D₃	—	3	1	no	—
526	C₂×C₃×C₉	—	9	1	no	—
527	C₂×C₃×C₉	—	9	1	no	—
528	C₂×C₃×C₉	—	9	1	no	—
529	C₂×C₃×C₉	—	9	1	no	—
530	C₂×C₃×C₉	—	9	1	no	—
531	C₂×C₃×C₉	—	9	1	no	—
532	C₂×C₃×C₉	—	9	1	no	—
533	C₂×C₃×C₉	—	9	1	no	—
534	C₂×C₃×C₉	—	9	1	no	—
535	C₂×C₃×C₉	—	9	1	no	—
536	C₂×C₃×C₉	—	9	1	no	—
537	C₂×C₃×C₉	—	9	1	no	—
538	C₂×C₃×C₉	—	9	1	no	—
539	C₂×C₃×C₉	—	9	1	no	—
540	C₂×C₃×C₉	—	9	1	no	—
541	C₂×C₃×C₉	—	9	1	no	—
542	C₂×C₃×C₉	—	9	1	no	—
543	C₂×C₃×C₉	—	9	1	no	—
544	C₂×C₃×C₉	—	9	1	no	—
545	C₂×C₃×C₉	—	9	1	no	—
546	C₂×C₃×C₉	—	9	1	no	—
547	C₂×C₃×C₉	—	27	1	no	—
548	C₂×C₃×C₉	—	27	1	no	—
549	C₂×C₃×C₉	—	27	1	no	—
550	C₂×C₃×C₉	—	27	1	no	—
551	C₂×C₃×C₉	—	27	1	no	—
552	C₂×C₃×C₉	—	27	1	no	—
553	C₂×C₃×C₉	—	27	1	no	—
554	C₂×C₃×C₉	—	27	1	no	—
555	C₂×C₃×C₉	—	27	1	no	—
556	AGL(1,ℤ/9)	C₉⋊C₉	1	1	yes	characteristic, direct product factor
557	AGL(1,ℤ/9)	C₉⋊C₉	1	1	yes	characteristic, direct product factor
558	AGL(1,ℤ/9)	C₉⋊C₉	1	1	yes	characteristic, direct product factor
559	AGL(1,ℤ/9)	C₉⋊C₉	1	1	yes	characteristic, direct product factor
560	AGL(1,ℤ/9)	C₉⋊C₉	1	1	yes	characteristic, direct product factor
561	AGL(1,ℤ/9)	C₉⋊C₉	1	1	yes	characteristic, direct product factor
562	AGL(1,ℤ/9)	C₉⋊C₉	1	1	yes	characteristic, direct product factor
563	AGL(1,ℤ/9)	C₉⋊C₉	1	1	yes	characteristic, direct product factor
564	AGL(1,ℤ/9)	C₉⋊C₉	1	1	yes	characteristic, direct product factor
565	D₃×C₉	—	3	1	no	—
566	D₃×C₉	—	3	1	no	—
567	D₃×C₉	—	3	1	no	—
568	D₃×C₉	—	3	1	no	—
569	D₃×C₉	—	3	1	no	—
570	D₃×C₉	—	3	1	no	—
571	D₃×C₉	—	3	1	no	—
572	D₃×C₉	—	3	1	no	—
573	D₃×C₉	—	3	1	no	—
574	D₃×C₉	—	9	1	no	—
575	D₃×C₉	—	9	1	no	—
576	D₃×C₉	—	9	1	no	—
577	D₃×C₉	—	9	1	no	—
578	D₃×C₉	—	9	1	no	—
579	D₃×C₉	—	9	1	no	—
580	D₃×C₉	—	9	1	no	—
581	D₃×C₉	—	9	1	no	—
582	D₃×C₉	—	9	1	no	—
583	C₃×D₉	C₃²×C₉	1	1	yes	characteristic
584	C₃×D₉	C₃×3₋¹⁺²	1	1	yes	characteristic
585	C₃×D₉	C₃×3₋¹⁺²	1	1	yes	characteristic
586	C₃×D₉	C₃×3₋¹⁺²	1	1	yes	characteristic
587	C₃³	—	6	1	no	—
588	C₃³	—	6	1	no	—
589	C₃³	—	6	1	no	—
590	C₃³	—	6	1	no	—
591	C₃³	—	6	1	no	—
592	C₃³	C₃×D₃×C₉	1	1	yes	characteristic
593	C₃³	C₃×D₃×C₉	1	1	yes	characteristic
594	C₃³	C₃×D₃×C₉	1	1	yes	characteristic
595	C₃³	D₃×3₋¹⁺²	1	1	yes	characteristic
596	C₃³	D₃×3₋¹⁺²	1	1	yes	characteristic
597	C₃³	D₃×3₋¹⁺²	1	1	yes	characteristic
598	C₃³	D₃×3₋¹⁺²	1	1	yes	characteristic
599	C₃³	D₃×3₋¹⁺²	1	1	yes	characteristic
600	C₃³	D₃×3₋¹⁺²	1	1	yes	characteristic
601	C₃³	D₃×3₋¹⁺²	1	1	yes	characteristic
602	C₃³	D₃×3₋¹⁺²	1	1	yes	characteristic
603	C₃³	D₃×3₋¹⁺²	1	1	yes	characteristic
604	C₃³	C₃³×D₃	1	1	yes	characteristic
605	3₋¹⁺²	—	2	1	no	—
606	3₋¹⁺²	—	2	1	no	—
607	3₋¹⁺²	—	2	1	no	—
608	3₋¹⁺²	—	2	1	no	—
609	3₋¹⁺²	—	2	1	no	—
610	3₋¹⁺²	—	2	1	no	—
611	3₋¹⁺²	—	2	1	no	—
612	3₋¹⁺²	—	2	1	no	—
613	3₋¹⁺²	—	2	1	no	—
614	3₋¹⁺²	—	2	1	no	—
615	3₋¹⁺²	—	2	1	no	—
616	3₋¹⁺²	—	2	1	no	—
617	3₋¹⁺²	—	2	1	no	—
618	3₋¹⁺²	—	2	1	no	—
619	3₋¹⁺²	—	2	1	no	—
620	3₋¹⁺²	—	2	1	no	—
621	3₋¹⁺²	—	2	1	no	—
622	3₋¹⁺²	—	2	1	no	—
623	3₋¹⁺²	—	2	1	no	—
624	3₋¹⁺²	—	2	1	no	—
625	3₋¹⁺²	—	2	1	no	—
626	3₋¹⁺²	—	2	1	no	—
627	3₋¹⁺²	—	2	1	no	—
628	3₋¹⁺²	—	2	1	no	—
629	3₋¹⁺²	—	2	1	no	—
630	3₋¹⁺²	—	2	1	no	—
631	3₋¹⁺²	—	2	1	no	—
632	3₋¹⁺²	—	2	1	no	—
633	3₋¹⁺²	—	2	1	no	—
634	3₋¹⁺²	—	2	1	no	—
635	3₋¹⁺²	—	2	1	no	—
636	3₋¹⁺²	—	2	1	no	—
637	3₋¹⁺²	—	2	1	no	—
638	3₋¹⁺²	—	2	1	no	—
639	3₋¹⁺²	—	2	1	no	—
640	3₋¹⁺²	—	2	1	no	—
641	3₋¹⁺²	C₂×C₉⋊C₉	1	1	yes	characteristic, complemented
642	3₋¹⁺²	C₂×C₉⋊C₉	1	1	yes	characteristic, complemented
643	3₋¹⁺²	C₂×C₉⋊C₉	1	1	yes	characteristic, complemented
644	3₋¹⁺²	C₂×C₉⋊C₉	1	1	yes	characteristic, complemented
645	3₋¹⁺²	C₂×C₉⋊C₉	1	1	yes	characteristic, complemented
646	3₋¹⁺²	C₂×C₉⋊C₉	1	1	yes	characteristic, complemented
647	3₋¹⁺²	C₂×C₉⋊C₉	1	1	yes	characteristic, complemented
648	3₋¹⁺²	C₂×C₉⋊C₉	1	1	yes	characteristic, complemented
649	3₋¹⁺²	C₂×C₉⋊C₉	1	1	yes	characteristic, complemented
650	C₃×C₉	—	2	1	no	—
651	C₃×C₉	—	2	1	no	—
652	C₃×C₉	—	2	1	no	—
653	C₃×C₉	—	2	1	no	—
654	C₃×C₉	—	2	1	no	—
655	C₃×C₉	—	2	1	no	—
656	C₃×C₉	—	2	1	no	—
657	C₃×C₉	—	2	1	no	—
658	C₃×C₉	—	2	1	no	—
659	C₃×C₉	—	2	1	no	—
660	C₃×C₉	—	2	1	no	—
661	C₃×C₉	—	2	1	no	—
662	C₃×C₉	—	2	1	no	—
663	C₃×C₉	—	2	1	no	—
664	C₃×C₉	—	2	1	no	—
665	C₃×C₉	—	2	1	no	—
666	C₃×C₉	—	2	1	no	—
667	C₃×C₉	—	2	1	no	—
668	C₃×C₉	—	2	1	no	—
669	C₃×C₉	—	2	1	no	—
670	C₃×C₉	—	2	1	no	—
671	C₃×C₉	—	2	1	no	—
672	C₃×C₉	—	2	1	no	—
673	C₃×C₉	—	2	1	no	—
674	C₃×C₉	—	2	1	no	—
675	C₃×C₉	—	2	1	no	—
676	C₃×C₉	—	2	1	no	—
677	C₃×C₉	—	2	1	no	—
678	C₃×C₉	—	2	1	no	—
679	C₃×C₉	—	2	1	no	—
680	C₃×C₉	—	2	1	no	—
681	C₃×C₉	—	2	1	no	—
682	C₃×C₉	—	3	1	no	—
683	C₃×C₉	—	3	1	no	—
684	C₃×C₉	—	3	1	no	—
685	C₃×C₉	—	3	1	no	—
686	C₃×C₉	—	3	1	no	—
687	C₃×C₉	—	3	1	no	—
688	C₃×C₉	—	3	1	no	—
689	C₃×C₉	—	3	1	no	—
690	C₃×C₉	—	3	1	no	—
691	C₃×C₉	—	3	1	no	—
692	C₃×C₉	—	3	1	no	—
693	C₃×C₉	—	3	1	no	—
694	C₃×C₉	—	3	1	no	—
695	C₃×C₉	—	3	1	no	—
696	C₃×C₉	—	3	1	no	—
697	C₃×C₉	—	3	1	no	—
698	C₃×C₉	—	6	1	no	—
699	C₃×C₉	—	6	1	no	—
700	C₃×C₉	—	6	1	no	—
701	C₃×C₉	—	6	1	no	—
702	C₃×C₉	—	6	1	no	—
703	C₃×C₉	—	6	1	no	—
704	C₃×C₉	—	6	1	no	—
705	C₃×C₉	—	6	1	no	—
706	C₃×C₉	—	6	1	no	—
707	C₃×C₉	—	6	1	no	—
708	C₃×C₉	—	6	1	no	—
709	C₃×C₉	—	6	1	no	—
710	C₃×C₉	—	6	1	no	—
711	C₃×C₉	—	6	1	no	—
712	C₃×C₉	—	6	1	no	—
713	C₃×C₉	—	6	1	no	—
714	C₃×C₉	—	6	1	no	—
715	C₃×C₉	—	6	1	no	—
716	C₃×C₉	—	6	1	no	—
717	C₃×C₉	—	6	1	no	—
718	C₃×C₉	—	6	1	no	—
719	C₃×C₉	—	6	1	no	—
720	C₃×C₉	—	6	1	no	—
721	C₃×C₉	—	6	1	no	—
722	C₃×C₉	—	6	1	no	—
723	C₃×C₉	—	6	1	no	—
724	C₃×C₉	—	6	1	no	—
725	C₃×C₉	—	6	1	no	—
726	C₃×C₉	—	6	1	no	—
727	C₃×C₉	—	6	1	no	—
728	C₃×C₉	—	6	1	no	—
729	C₃×C₉	—	6	1	no	—
730	C₃×C₉	—	6	1	no	—
731	C₃×C₉	—	6	1	no	—
732	C₃×C₉	—	6	1	no	—
733	C₃×C₉	—	6	1	no	—
734	C₃×C₉	—	6	1	no	—
735	C₃×C₉	—	6	1	no	—
736	C₃×C₉	—	6	1	no	—
737	C₃×C₉	—	6	1	no	—
738	C₃×C₉	—	6	1	no	—
739	C₃×C₉	—	6	1	no	—
740	C₃×C₉	—	6	1	no	—
741	C₃×C₉	—	6	1	no	—
742	C₃×C₉	—	6	1	no	—
743	C₃×C₉	—	6	1	no	—
744	C₃×C₉	—	6	1	no	—
745	C₃×C₉	—	6	1	no	—
746	C₃×C₉	—	6	1	no	—
747	C₃×C₉	—	6	1	no	—
748	C₃×C₉	—	6	1	no	—
749	C₃×C₉	—	6	1	no	—
750	C₃×C₉	—	6	1	no	—
751	C₃×C₉	—	6	1	no	—
752	C₃×C₉	—	6	1	no	—
753	C₃×C₉	—	6	1	no	—
754	C₃×C₉	—	6	1	no	—
755	C₃×C₉	—	6	1	no	—
756	C₃×C₉	—	6	1	no	—
757	C₃×C₉	—	6	1	no	—
758	C₃×C₉	—	6	1	no	—
759	C₃×C₉	—	6	1	no	—
760	C₃×C₉	—	6	1	no	—
761	C₃×C₉	—	6	1	no	—
762	C₃×C₉	—	6	1	no	—
763	C₃×C₉	—	6	1	no	—
764	C₃×C₉	—	6	1	no	—
765	C₃×C₉	—	6	1	no	—
766	C₃×C₉	—	6	1	no	—
767	C₃×C₉	—	6	1	no	—
768	C₃×C₉	—	6	1	no	—
769	C₃×C₉	—	6	1	no	—
770	C₃×C₉	—	6	1	no	—
771	C₃×C₉	—	6	1	no	—
772	C₃×C₉	—	6	1	no	—
773	C₃×C₉	—	9	1	no	—
774	C₃×C₉	—	9	1	no	—
775	C₃×C₉	—	9	1	no	—
776	C₃×C₉	—	18	1	no	—
777	C₃×C₉	—	18	1	no	—
778	C₃×C₉	—	18	1	no	—
779	C₃×C₉	—	18	1	no	—
780	C₃×C₉	—	18	1	no	—
781	C₃×C₉	—	18	1	no	—
782	C₃×C₉	—	18	1	no	—
783	C₃×C₉	—	18	1	no	—
784	C₃×C₉	—	18	1	no	—
785	C₃×C₉	—	18	1	no	—
786	C₃×C₉	—	18	1	no	—
787	C₃×C₉	—	18	1	no	—
788	C₃×C₉	—	18	1	no	—
789	C₃×C₉	—	18	1	no	—
790	C₃×C₉	—	18	1	no	—
791	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
792	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
793	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
794	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
795	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
796	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
797	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
798	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
799	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
800	C₃×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
801	C₃×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
802	C₃×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
803	C₃×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
804	C₃×C₉	C₂×C₃²×C₉	1	1	yes	characteristic
805	C₃×C₉	C₂×C₃×3₋¹⁺²	1	1	yes	characteristic
806	C₃×C₉	C₂×C₃×3₋¹⁺²	1	1	yes	characteristic
807	C₃×C₉	C₂×C₃×3₋¹⁺²	1	1	yes	characteristic
808	C₂×C₃²	—	9	1	no	—
809	C₂×C₃²	—	9	1	no	—
810	C₂×C₃²	—	9	1	no	—
811	C₂×C₃²	—	9	1	no	—
812	C₂×C₃²	—	9	1	no	—
813	C₂×C₃²	—	9	1	no	—
814	C₂×C₃²	—	9	1	no	—
815	C₂×C₃²	—	9	1	no	—
816	C₂×C₃²	—	9	1	no	—
817	C₂×C₃²	—	9	1	no	—
818	C₂×C₃²	—	9	1	no	—
819	C₂×C₃²	—	9	1	no	—
820	C₂×C₃²	—	9	1	no	—
821	C₃×D₃	—	3	1	no	—
822	C₃×D₃	—	3	1	no	—
823	C₃×D₃	—	3	1	no	—
824	C₃×D₃	—	3	1	no	—
825	C₃×D₃	—	3	1	no	—
826	C₃×D₃	—	3	1	no	—
827	C₃×D₃	—	3	1	no	—
828	C₃×D₃	—	3	1	no	—
829	C₃×D₃	—	3	1	no	—
830	C₃×D₃	—	3	1	no	—
831	C₃×D₃	—	3	1	no	—
832	C₃×D₃	—	3	1	no	—
833	C₃×D₃	—	3	1	no	—
834	C₂×C₉	—	9	1	no	—
835	C₂×C₉	—	9	1	no	—
836	C₂×C₉	—	9	1	no	—
837	C₂×C₉	—	9	1	no	—
838	C₂×C₉	—	9	1	no	—
839	C₂×C₉	—	9	1	no	—
840	C₂×C₉	—	9	1	no	—
841	C₂×C₉	—	9	1	no	—
842	C₂×C₉	—	9	1	no	—
843	C₂×C₉	—	27	1	no	—
844	C₂×C₉	—	27	1	no	—
845	C₂×C₉	—	27	1	no	—
846	C₂×C₉	—	27	1	no	—
847	C₂×C₉	—	27	1	no	—
848	C₂×C₉	—	27	1	no	—
849	C₂×C₉	—	27	1	no	—
850	C₂×C₉	—	27	1	no	—
851	C₂×C₉	—	27	1	no	—
852	D₉	C₃×C₉⋊C₉	1	1	yes	characteristic, complemented
853	C₃²	—	2	1	no	—
854	C₃²	—	2	1	no	—
855	C₃²	—	2	1	no	—
856	C₃²	—	2	1	no	—
857	C₃²	—	3	1	no	—
858	C₃²	—	3	1	no	—
859	C₃²	—	3	1	no	—
860	C₃²	—	3	1	no	—
861	C₃²	—	3	1	no	—
862	C₃²	—	6	1	no	—
863	C₃²	—	6	1	no	—
864	C₃²	—	6	1	no	—
865	C₃²	—	6	1	no	—
866	C₃²	—	6	1	no	—
867	C₃²	—	6	1	no	—
868	C₃²	—	6	1	no	—
869	C₃²	—	6	1	no	—
870	C₃²	—	6	1	no	—
871	C₃²	—	6	1	no	—
872	C₃²	—	6	1	no	—
873	C₃²	—	6	1	no	—
874	C₃²	—	6	1	no	—
875	C₃²	—	6	1	no	—
876	C₃²	—	6	1	no	—
877	C₃²	—	6	1	no	—
878	C₃²	—	6	1	no	—
879	C₃²	—	6	1	no	—
880	C₃²	—	6	1	no	—
881	C₃²	D₃×C₉⋊C₉	1	1	yes	characteristic
882	C₃²	D₃×C₉⋊C₉	1	1	yes	characteristic
883	C₃²	D₃×C₉⋊C₉	1	1	yes	characteristic
884	C₃²	D₃×C₉⋊C₉	1	1	yes	characteristic
885	C₃²	D₃×C₉⋊C₉	1	1	yes	characteristic
886	C₃²	D₃×C₉⋊C₉	1	1	yes	characteristic
887	C₃²	D₃×C₉⋊C₉	1	1	yes	characteristic
888	C₃²	D₃×C₉⋊C₉	1	1	yes	characteristic
889	C₃²	D₃×C₉⋊C₉	1	1	yes	characteristic
890	C₃²	C₃²×D₃×C₉	1	1	yes	characteristic
891	C₃²	C₃²×AGL(1,ℤ/9)	1	1	yes	characteristic
892	C₃²	C₃×D₃×3₋¹⁺²	1	1	yes	characteristic
893	C₃²	C₃×D₃×3₋¹⁺²	1	1	yes	characteristic
894	C₃²	C₃×D₃×3₋¹⁺²	1	1	yes	characteristic
895	C₉	—	2	1	no	—
896	C₉	—	2	1	no	—
897	C₉	—	2	1	no	—
898	C₉	—	2	1	no	—
899	C₉	—	2	1	no	—
900	C₉	—	2	1	no	—
901	C₉	—	2	1	no	—
902	C₉	—	2	1	no	—
903	C₉	—	2	1	no	—
904	C₉	—	2	1	no	—
905	C₉	—	2	1	no	—
906	C₉	—	2	1	no	—
907	C₉	—	2	1	no	—
908	C₉	—	2	1	no	—
909	C₉	—	2	1	no	—
910	C₉	—	2	1	no	—
911	C₉	—	3	1	no	—
912	C₉	—	3	1	no	—
913	C₉	—	3	1	no	—
914	C₉	—	6	1	no	—
915	C₉	—	6	1	no	—
916	C₉	—	6	1	no	—
917	C₉	—	6	1	no	—
918	C₉	—	6	1	no	—
919	C₉	—	6	1	no	—
920	C₉	—	6	1	no	—
921	C₉	—	6	1	no	—
922	C₉	—	6	1	no	—
923	C₉	—	6	1	no	—
924	C₉	—	6	1	no	—
925	C₉	—	6	1	no	—
926	C₉	—	6	1	no	—
927	C₉	—	6	1	no	—
928	C₉	—	6	1	no	—
929	C₉	—	6	1	no	—
930	C₉	—	6	1	no	—
931	C₉	—	6	1	no	—
932	C₉	—	9	1	no	—
933	C₉	—	9	1	no	—
934	C₉	—	9	1	no	—
935	C₉	—	18	1	no	—
936	C₉	—	18	1	no	—
937	C₉	—	18	1	no	—
938	C₉	—	18	1	no	—
939	C₉	—	18	1	no	—
940	C₉	—	18	1	no	—
941	C₉	—	18	1	no	—
942	C₉	—	18	1	no	—
943	C₉	—	18	1	no	—
944	C₉	—	18	1	no	—
945	C₉	—	18	1	no	—
946	C₉	—	18	1	no	—
947	C₉	C₉×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
948	C₉	C₉×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
949	C₉	C₉×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
950	C₉	C₂×C₃×C₉⋊C₉	1	1	yes	characteristic, complemented
951	C₂×C₃	—	9	1	no	—
952	C₂×C₃	—	9	1	no	—
953	C₂×C₃	—	9	1	no	—
954	C₂×C₃	—	9	1	no	—
955	C₂×C₃	—	9	1	no	—
956	C₂×C₃	—	9	1	no	—
957	C₂×C₃	—	9	1	no	—
958	C₂×C₃	—	9	1	no	—
959	C₂×C₃	—	9	1	no	—
960	C₂×C₃	—	9	1	no	—
961	C₂×C₃	—	9	1	no	—
962	C₂×C₃	—	9	1	no	—
963	C₂×C₃	—	9	1	no	—
964	D₃	—	3	1	no	—
965	C₃	—	2	1	no	—
966	C₃	—	2	1	no	—
967	C₃	—	2	1	no	—
968	C₃	—	2	1	no	—
969	C₃	—	3	1	no	—
970	C₃	—	3	1	no	—
971	C₃	—	3	1	no	—
972	C₃	—	3	1	no	—
973	C₃	—	6	1	no	—
974	C₃	—	6	1	no	—
975	C₃	—	6	1	no	—
976	C₃	—	6	1	no	—
977	C₃	—	6	1	no	—
978	C₃	C₃×D₃×C₉⋊C₉	1	1	yes	characteristic
979	C₃	C₃×C₉×AGL(1,ℤ/9)	1	1	yes	characteristic
980	C₃	3₋¹⁺²×AGL(1,ℤ/9)	1	1	yes	characteristic
981	C₃	3₋¹⁺²×AGL(1,ℤ/9)	1	1	yes	characteristic
982	C₃	3₋¹⁺²×AGL(1,ℤ/9)	1	1	yes	characteristic
983	C₂	—	9	1	no	Sylow

	subgroup	G/H
center	C₃²	C₃²×AGL(1,ℤ/9)
commutator	C₃×C₉	C₂×C₃²×C₉
Frattini, socle	C₃³	C₃³×D₃
Fitting	3₋¹⁺²×C₉⋊C₉	C₂
prime radical	C₃²×AGL(1,ℤ/9)	C₃²
cosocle	C₃²×C₉	C₂×C₃³
hypercenter	C₉⋊C₉	AGL(1,ℤ/9)
hypocenter	C₉	C₂×C₃×C₉⋊C₉
LCS	G ▷ C₃×C₉ ▷ C₉
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

Complements

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

N	H ≅ G/N	type
1. 3₋¹⁺²×C₉⋊C₉	C₂	semidirect
7. (D₉⋊C₉)⋊C₉	C₃	semidirect
8. (D₉⋊C₉)⋊C₉	C₃	semidirect
9. (D₉⋊C₉)⋊C₉	C₃	semidirect
10. (D₉⋊C₉)⋊C₉	C₃	semidirect
11. (D₉⋊C₉)⋊C₉	C₃	semidirect
12. (D₉⋊C₉)⋊C₉	C₃	semidirect
13. #13090635	C₃	semidirect
14. #13090628	C₃	semidirect
15. D₉×C₉⋊C₉	C₃	semidirect
27. #10624561	C₂×C₃	semidirect
28. #10624561	C₂×C₃	semidirect
29. #10624561	C₂×C₃	semidirect
30. #10624561	C₂×C₃	semidirect
31. #10624561	C₂×C₃	semidirect
32. #10624561	C₂×C₃	semidirect
37. #10624554	C₂×C₃	semidirect
39. #10624550	C₂×C₃	semidirect
42. C₉×C₉⋊C₉	C₂×C₃	semidirect
58. C₉×AGL(1,ℤ/9)	C₉	semidirect
59. C₉×AGL(1,ℤ/9)	C₉	semidirect
60. C₉×AGL(1,ℤ/9)	C₉	semidirect
61. C₉×AGL(1,ℤ/9)	C₉	semidirect
62. C₉×AGL(1,ℤ/9)	C₉	semidirect
63. C₉×AGL(1,ℤ/9)	C₉	semidirect
64. C₉×AGL(1,ℤ/9)	C₉	semidirect
65. C₉×AGL(1,ℤ/9)	C₉	semidirect
66. C₉×AGL(1,ℤ/9)	C₉	semidirect
120. C₉×3₋¹⁺²	C₂×C₉	semidirect
121. C₉×3₋¹⁺²	C₂×C₉	semidirect
122. C₉×3₋¹⁺²	C₂×C₉	semidirect
123. C₉×3₋¹⁺²	C₂×C₉	semidirect
124. C₉×3₋¹⁺²	C₂×C₉	semidirect
125. C₉×3₋¹⁺²	C₂×C₉	semidirect
126. C₉×3₋¹⁺²	C₂×C₉	semidirect
127. C₉×3₋¹⁺²	C₂×C₉	semidirect
128. C₉×3₋¹⁺²	C₂×C₉	semidirect
270. D₉⋊C₉	C₃×C₉	semidirect
271. D₉⋊C₉	C₃×C₉	semidirect
272. D₉⋊C₉	C₃×C₉	semidirect
273. D₉⋊C₉	C₃×C₉	semidirect
274. D₉⋊C₉	C₃×C₉	semidirect
275. D₉⋊C₉	C₃×C₉	semidirect
279. C₉×D₉	C₃×C₉	semidirect
280. C₉×D₉	C₃×C₉	semidirect
281. C₉×D₉	C₃×C₉	semidirect
457. C₉⋊C₉	AGL(1,ℤ/9)	direct (N × H)
458. C₉⋊C₉	C₂×C₃×C₉	semidirect
459. C₉⋊C₉	C₂×C₃×C₉	semidirect
460. C₉⋊C₉	C₂×C₃×C₉	semidirect
461. C₉⋊C₉	C₂×C₃×C₉	semidirect
462. C₉⋊C₉	C₂×C₃×C₉	semidirect
463. C₉⋊C₉	C₂×C₃×C₉	semidirect
509. C₉²	C₂×C₃×C₉	semidirect
510. C₉²	C₂×C₃×C₉	semidirect
511. C₉²	C₂×C₃×C₉	semidirect
556. AGL(1,ℤ/9)	C₉⋊C₉	direct (N × H)
557. AGL(1,ℤ/9)	C₉⋊C₉	direct (N × H)
558. AGL(1,ℤ/9)	C₉⋊C₉	direct (N × H)
559. AGL(1,ℤ/9)	C₉⋊C₉	direct (N × H)
560. AGL(1,ℤ/9)	C₉⋊C₉	direct (N × H)
561. AGL(1,ℤ/9)	C₉⋊C₉	direct (N × H)
562. AGL(1,ℤ/9)	C₉⋊C₉	direct (N × H)
563. AGL(1,ℤ/9)	C₉⋊C₉	direct (N × H)
564. AGL(1,ℤ/9)	C₉⋊C₉	direct (N × H)
641. 3₋¹⁺²	C₂×C₉⋊C₉	semidirect
642. 3₋¹⁺²	C₂×C₉⋊C₉	semidirect
643. 3₋¹⁺²	C₂×C₉⋊C₉	semidirect
644. 3₋¹⁺²	C₂×C₉⋊C₉	semidirect
645. 3₋¹⁺²	C₂×C₉⋊C₉	semidirect
646. 3₋¹⁺²	C₂×C₉⋊C₉	semidirect
647. 3₋¹⁺²	C₂×C₉⋊C₉	semidirect
648. 3₋¹⁺²	C₂×C₉⋊C₉	semidirect
649. 3₋¹⁺²	C₂×C₉⋊C₉	semidirect
852. D₉	C₃×C₉⋊C₉	semidirect
947. C₉	C₉×AGL(1,ℤ/9)	semidirect
948. C₉	C₉×AGL(1,ℤ/9)	semidirect
949. C₉	C₉×AGL(1,ℤ/9)	semidirect
950. C₉	C₂×C₃×C₉⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
3₋¹⁺²×C₉⋊C₉	2
C₃×C₉×AGL(1,ℤ/9)	3
C₃×D₃×C₉⋊C₉	3
(D₉⋊C₉)⋊C₉	3
#13090635	3
#13090628	3
D₉×C₉⋊C₉	3

Subgroups — AGL(1,ℤ/9)×C9⋊C9 #72243183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — AGL(1,ℤ/9)×C₉⋊C₉ #72243183