Subgroups — C₉×D₉⋊H(3,𝔽₃) #72243807

Order 4374.

1183 conjugacy classes of subgroups.

The subgroup lattice has 1141 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₉⋊H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×D₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
3	C₃×C₉×AGL(1,ℤ/9)	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₉×AGL(1,ℤ/9)	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃×C₉×AGL(1,ℤ/9)	C₃	1	1	yes	maximal, characteristic, complemented
6	D₃×C₉×H(3,𝔽₃)	—	3	1	no	maximal
7	C₃²×C₉×D₉	C₃	1	1	yes	maximal, characteristic, complemented
8	(C₃×AGL(1,ℤ/9))⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
9	(C₃×AGL(1,ℤ/9))⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
10	(C₃×AGL(1,ℤ/9))⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
11	(C₃×AGL(1,ℤ/9))⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
12	(C₃×AGL(1,ℤ/9))⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
13	(C₃×AGL(1,ℤ/9))⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
14	#13090623	C₃	1	1	yes	maximal, characteristic, complemented
15	#13090623	C₃	1	1	yes	maximal, characteristic, complemented
16	C₃×C₉⋊H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
17	C₃×C₉×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic, complemented
18	C₃×C₉×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic, complemented
19	C₃×C₉×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic, complemented
20	C₃×C₉×H(3,𝔽₃)	D₃	1	1	yes	characteristic
21	C₃²×C₉²	C₂×C₃	1	1	yes	characteristic, complemented
22	#10624560	C₂×C₃	1	1	yes	characteristic, complemented
23	#10624560	C₂×C₃	1	1	yes	characteristic, complemented
24	#10624560	C₂×C₃	1	1	yes	characteristic, complemented
25	#10624560	C₂×C₃	1	1	yes	characteristic, complemented
26	#10624560	C₂×C₃	1	1	yes	characteristic, complemented
27	#10624560	C₂×C₃	1	1	yes	characteristic, complemented
28	#10624557	—	2	1	no	—
29	#10624557	—	2	1	no	—
30	#10624557	—	2	1	no	—
31	#10624557	—	2	1	no	—
32	#10624557	—	2	1	no	—
33	#10624557	—	2	1	no	—
34	#10624556	—	2	1	no	—
35	#10624556	—	2	1	no	—
36	#10624555	—	2	1	no	—
37	#10624548	C₂×C₃	1	1	yes	characteristic, complemented
38	#10624548	C₂×C₃	1	1	yes	characteristic, complemented
39	C₉×C₃²⋊C₉	—	2	1	no	—
40	C₉×C₃²⋊C₉	—	2	1	no	—
41	C₉×C₃²⋊C₉	—	2	1	no	—
42	C₉×C₃²⋊C₉	—	2	1	no	—
43	C₃²×AGL(1,ℤ/9)	C₃²	1	1	yes	characteristic
44	C₃²×AGL(1,ℤ/9)	C₃²	1	1	yes	characteristic
45	C₃²×AGL(1,ℤ/9)	C₃²	1	1	yes	characteristic
46	C₃×D₃×H(3,𝔽₃)	—	3	1	no	—
47	C₃²×D₃×C₉	—	3	1	no	—
48	C₃²×D₃×C₉	—	3	1	no	—
49	C₃²×D₃×C₉	—	3	1	no	—
50	C₃²×D₃×C₉	—	3	1	no	—
51	C₃³×D₉	C₃²	1	1	yes	characteristic
52	C₂×C₉×H(3,𝔽₃)	—	9	1	no	—
53	D₉⋊H(3,𝔽₃)	C₉	1	1	yes	characteristic, direct product factor
54	D₉⋊H(3,𝔽₃)	C₉	1	1	yes	characteristic, direct product factor
55	D₉⋊H(3,𝔽₃)	C₉	1	1	yes	characteristic, direct product factor
56	D₉⋊H(3,𝔽₃)	C₉	1	1	yes	characteristic, direct product factor
57	D₉⋊H(3,𝔽₃)	C₉	1	1	yes	characteristic, direct product factor
58	D₉⋊H(3,𝔽₃)	C₉	1	1	yes	characteristic, direct product factor
59	D₉⋊H(3,𝔽₃)	C₉	1	1	yes	characteristic, direct product factor
60	D₉⋊H(3,𝔽₃)	C₉	1	1	yes	characteristic, direct product factor
61	D₉⋊H(3,𝔽₃)	C₉	1	1	yes	characteristic, direct product factor
62	C₉×AGL(1,ℤ/9)	—	3	1	no	—
63	C₉×AGL(1,ℤ/9)	—	3	1	no	—
64	C₉×AGL(1,ℤ/9)	—	3	1	no	—
65	C₉×AGL(1,ℤ/9)	—	3	1	no	—
66	C₉×AGL(1,ℤ/9)	—	3	1	no	—
67	C₉×AGL(1,ℤ/9)	—	3	1	no	—
68	C₉×AGL(1,ℤ/9)	—	3	1	no	—
69	C₉×AGL(1,ℤ/9)	—	3	1	no	—
70	C₉×AGL(1,ℤ/9)	—	3	1	no	—
71	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
72	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
73	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
74	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
75	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
76	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
77	D₃×C₃²⋊C₉	—	3	1	no	—
78	D₃×C₃²⋊C₉	—	3	1	no	—
79	D₃×C₃²⋊C₉	—	3	1	no	—
80	D₃×C₃²⋊C₉	—	3	1	no	—
81	D₃×C₃²⋊C₉	—	3	1	no	—
82	D₃×C₃²⋊C₉	—	3	1	no	—
83	D₃×C₃²⋊C₉	—	3	1	no	—
84	D₃×C₃²⋊C₉	—	3	1	no	—
85	C₃×C₉×D₉	—	3	1	no	—
86	C₃×C₉×D₉	—	3	1	no	—
87	C₃×C₉×D₉	—	3	1	no	—
88	C₃×C₉×D₉	C₃²	1	1	yes	characteristic
89	C₃×C₉×D₉	C₃²	1	1	yes	characteristic
90	C₃×C₉×D₉	C₃²	1	1	yes	characteristic
91	C₃²×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
92	C₃²×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
93	C₃²×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
94	C₃²×H(3,𝔽₃)	C₃×D₃	1	1	yes	characteristic
95	C₃³×C₉	—	2	1	no	—
96	C₃³×C₉	C₃×D₃	1	1	yes	characteristic
97	C₃³×C₉	C₃×D₃	1	1	yes	characteristic
98	C₃³×C₉	C₃×D₃	1	1	yes	characteristic
99	C₃³×C₉	C₃×D₃	1	1	yes	characteristic
100	C₃³×C₉	C₂×C₃²	1	1	yes	characteristic
101	C₉⋊H(3,𝔽₃)	—	2	1	no	—
102	C₉⋊H(3,𝔽₃)	—	2	1	no	—
103	C₉⋊H(3,𝔽₃)	—	2	1	no	—
104	C₉⋊H(3,𝔽₃)	—	2	1	no	—
105	C₉⋊H(3,𝔽₃)	—	2	1	no	—
106	C₉⋊H(3,𝔽₃)	—	2	1	no	—
107	C₉⋊H(3,𝔽₃)	—	2	1	no	—
108	C₉⋊H(3,𝔽₃)	—	2	1	no	—
109	C₉⋊H(3,𝔽₃)	—	2	1	no	—
110	C₉⋊H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
111	C₉⋊H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
112	C₉⋊H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
113	C₉⋊H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
114	C₉⋊H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
115	C₉⋊H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
116	C₉⋊H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
117	C₉⋊H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
118	C₉⋊H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
119	C₉×3₋¹⁺²	—	3	1	no	—
120	C₉×3₋¹⁺²	—	3	1	no	—
121	C₉×3₋¹⁺²	—	3	1	no	—
122	C₉×3₋¹⁺²	—	3	1	no	—
123	C₉×3₋¹⁺²	—	3	1	no	—
124	C₉×3₋¹⁺²	—	3	1	no	—
125	C₉×3₋¹⁺²	—	3	1	no	—
126	C₉×3₋¹⁺²	—	3	1	no	—
127	C₉×3₋¹⁺²	—	3	1	no	—
128	C₉×3₋¹⁺²	—	6	1	no	—
129	C₉×3₋¹⁺²	—	6	1	no	—
130	C₉×3₋¹⁺²	—	6	1	no	—
131	C₉×3₋¹⁺²	—	6	1	no	—
132	C₉×3₋¹⁺²	—	6	1	no	—
133	C₉×3₋¹⁺²	—	6	1	no	—
134	C₉×3₋¹⁺²	—	6	1	no	—
135	C₉×3₋¹⁺²	—	6	1	no	—
136	C₉×3₋¹⁺²	—	6	1	no	—
137	C₉×H(3,𝔽₃)	—	6	1	no	—
138	C₉×H(3,𝔽₃)	—	6	1	no	—
139	C₉×H(3,𝔽₃)	—	6	1	no	—
140	C₉×H(3,𝔽₃)	—	6	1	no	—
141	C₉×H(3,𝔽₃)	—	6	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	C₂×C₃²	1	1	yes	characteristic
149	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
150	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
151	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
152	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
153	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
154	C₃×C₃²⋊C₉	—	2	1	no	—
155	C₃×C₃²⋊C₉	—	2	1	no	—
156	C₃×C₃²⋊C₉	—	2	1	no	—
157	C₃×C₃²⋊C₉	—	2	1	no	—
158	C₃×C₃²⋊C₉	—	2	1	no	—
159	C₃×C₃²⋊C₉	—	2	1	no	—
160	C₃×C₃²⋊C₉	—	2	1	no	—
161	C₃×C₃²⋊C₉	—	2	1	no	—
162	C₃×C₃²⋊C₉	—	2	1	no	—
163	C₃×C₃²⋊C₉	—	2	1	no	—
164	C₃×C₃²⋊C₉	—	2	1	no	—
165	C₃×C₃²⋊C₉	—	2	1	no	—
166	C₃×C₃²⋊C₉	—	2	1	no	—
167	C₃×C₃²⋊C₉	—	2	1	no	—
168	C₃×C₃²⋊C₉	—	2	1	no	—
169	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
170	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
171	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
172	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
173	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
174	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
175	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
176	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
177	C₃×C₉²	—	2	1	no	—
178	C₃×C₉²	—	2	1	no	—
179	C₃×C₉²	—	2	1	no	—
180	C₃×C₉²	—	2	1	no	—
181	C₃×C₉²	—	2	1	no	—
182	C₃×C₉²	—	2	1	no	—
183	C₃×C₉²	—	3	1	no	—
184	C₃×C₉²	—	3	1	no	—
185	C₃×C₉²	—	3	1	no	—
186	C₃×C₉²	—	6	1	no	—
187	C₃×C₉²	—	6	1	no	—
188	C₃×C₉²	—	6	1	no	—
189	C₃×C₉²	C₂×C₃²	1	1	yes	characteristic
190	C₃×C₉²	C₂×C₃²	1	1	yes	characteristic
191	C₃×C₉²	C₂×C₃²	1	1	yes	characteristic
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	#6855	—	2	1	no	—
208	#6855	—	2	1	no	—
209	#6855	—	2	1	no	—
210	#6855	—	2	1	no	—
211	#6855	—	2	1	no	—
212	#6855	—	2	1	no	—
213	#6855	—	2	1	no	—
214	#6855	—	2	1	no	—
215	#6855	—	2	1	no	—
216	C₃³×D₃	—	3	1	no	—
217	C₃³×D₃	—	3	1	no	—
218	C₃³×D₃	—	3	1	no	—
219	C₃³×D₃	—	3	1	no	—
220	C₂×C₃×H(3,𝔽₃)	—	9	1	no	—
221	C₂×C₃²×C₉	—	9	1	no	—
222	C₂×C₃²×C₉	—	9	1	no	—
223	C₂×C₃²×C₉	—	9	1	no	—
224	C₂×C₃²×C₉	—	9	1	no	—
225	C₃×AGL(1,ℤ/9)	—	3	1	no	—
226	C₃×AGL(1,ℤ/9)	—	3	1	no	—
227	C₃×AGL(1,ℤ/9)	—	3	1	no	—
228	C₃×AGL(1,ℤ/9)	—	3	1	no	—
229	C₃×AGL(1,ℤ/9)	—	3	1	no	—
230	C₃×AGL(1,ℤ/9)	—	3	1	no	—
231	C₃×AGL(1,ℤ/9)	—	3	1	no	—
232	C₃×AGL(1,ℤ/9)	—	3	1	no	—
233	C₃×AGL(1,ℤ/9)	—	3	1	no	—
234	C₃×AGL(1,ℤ/9)	C₃×C₉	1	1	yes	characteristic, complemented
235	C₃×AGL(1,ℤ/9)	C₃×C₉	1	1	yes	characteristic, complemented
236	C₃×AGL(1,ℤ/9)	C₃×C₉	1	1	yes	characteristic, complemented
237	C₃×AGL(1,ℤ/9)	C₃×C₉	1	1	yes	characteristic, complemented
238	C₃×AGL(1,ℤ/9)	C₃×C₉	1	1	yes	characteristic, complemented
239	C₃×AGL(1,ℤ/9)	C₃×C₉	1	1	yes	characteristic, complemented
240	C₃×AGL(1,ℤ/9)	C₃×C₉	1	1	yes	characteristic, complemented
241	C₃×AGL(1,ℤ/9)	C₃×C₉	1	1	yes	characteristic, complemented
242	C₃×AGL(1,ℤ/9)	C₃×C₉	1	1	yes	characteristic, complemented
243	D₃×H(3,𝔽₃)	—	3	1	no	—
244	D₃×H(3,𝔽₃)	—	3	1	no	—
245	D₃×H(3,𝔽₃)	—	3	1	no	—
246	D₃×H(3,𝔽₃)	—	3	1	no	—
247	D₃×H(3,𝔽₃)	—	3	1	no	—
248	D₃×H(3,𝔽₃)	—	3	1	no	—
249	D₃×H(3,𝔽₃)	—	3	1	no	—
250	D₃×H(3,𝔽₃)	—	3	1	no	—
251	D₃×H(3,𝔽₃)	—	3	1	no	—
252	C₃×D₃×C₉	—	3	1	no	—
253	C₃×D₃×C₉	—	3	1	no	—
254	C₃×D₃×C₉	—	3	1	no	—
255	C₃×D₃×C₉	—	3	1	no	—
256	C₃×D₃×C₉	—	3	1	no	—
257	C₃×D₃×C₉	—	3	1	no	—
258	C₃×D₃×C₉	—	3	1	no	—
259	C₃×D₃×C₉	—	3	1	no	—
260	C₃×D₃×C₉	—	3	1	no	—
261	C₃×D₃×C₉	—	9	1	no	—
262	C₃×D₃×C₉	—	9	1	no	—
263	C₃×D₃×C₉	—	9	1	no	—
264	C₃×D₃×C₉	—	9	1	no	—
265	C₃×D₃×C₉	—	9	1	no	—
266	C₃×D₃×C₉	—	9	1	no	—
267	C₃×D₃×C₉	—	9	1	no	—
268	C₃×D₃×C₉	—	9	1	no	—
269	C₃×D₃×C₉	—	9	1	no	—
270	C₃×D₃×C₉	—	9	1	no	—
271	C₃×D₃×C₉	—	9	1	no	—
272	C₃×D₃×C₉	—	9	1	no	—
273	C₃²×D₉	—	3	1	no	—
274	C₃²×D₉	—	3	1	no	—
275	C₃²×D₉	—	3	1	no	—
276	C₃²×D₉	C₃×C₉	1	1	yes	characteristic, complemented
277	C₃²×D₉	C₃×C₉	1	1	yes	characteristic, complemented
278	C₃²×D₉	C₃×C₉	1	1	yes	characteristic, complemented
279	C₃²×D₉	C₃³	1	1	yes	characteristic
280	C₂×C₃²⋊C₉	—	9	1	no	—
281	C₂×C₃²⋊C₉	—	9	1	no	—
282	C₂×C₃²⋊C₉	—	9	1	no	—
283	C₂×C₃²⋊C₉	—	9	1	no	—
284	C₂×C₃²⋊C₉	—	9	1	no	—
285	C₂×C₃²⋊C₉	—	9	1	no	—
286	C₂×C₃²⋊C₉	—	9	1	no	—
287	C₂×C₃²⋊C₉	—	9	1	no	—
288	D₉⋊C₉	—	3	1	no	—
289	D₉⋊C₉	—	3	1	no	—
290	D₉⋊C₉	—	3	1	no	—
291	D₉⋊C₉	—	3	1	no	—
292	D₉⋊C₉	—	3	1	no	—
293	D₉⋊C₉	—	3	1	no	—
294	C₉×D₉	—	3	1	no	—
295	C₉×D₉	—	3	1	no	—
296	C₉×D₉	H(3,𝔽₃)	1	1	yes	characteristic, complemented
297	C₉×D₉	H(3,𝔽₃)	1	1	yes	characteristic, complemented
298	C₉×D₉	H(3,𝔽₃)	1	1	yes	characteristic, complemented
299	C₃⁴	C₃²×D₃	1	1	yes	characteristic
300	C₃⁴	C₃²×D₃	1	1	yes	characteristic
301	C₃⁴	C₃²×D₃	1	1	yes	characteristic
302	C₃⁴	C₃²×D₃	1	1	yes	characteristic
303	C₃×3₋¹⁺²	—	2	1	no	—
304	C₃×3₋¹⁺²	—	2	1	no	—
305	C₃×3₋¹⁺²	—	2	1	no	—
306	C₃×3₋¹⁺²	—	2	1	no	—
307	C₃×3₋¹⁺²	—	2	1	no	—
308	C₃×3₋¹⁺²	—	2	1	no	—
309	C₃×3₋¹⁺²	—	2	1	no	—
310	C₃×3₋¹⁺²	—	2	1	no	—
311	C₃×3₋¹⁺²	—	2	1	no	—
312	C₃×3₋¹⁺²	—	3	1	no	—
313	C₃×3₋¹⁺²	—	3	1	no	—
314	C₃×3₋¹⁺²	—	3	1	no	—
315	C₃×3₋¹⁺²	—	3	1	no	—
316	C₃×3₋¹⁺²	—	3	1	no	—
317	C₃×3₋¹⁺²	—	3	1	no	—
318	C₃×3₋¹⁺²	—	3	1	no	—
319	C₃×3₋¹⁺²	—	3	1	no	—
320	C₃×3₋¹⁺²	—	3	1	no	—
321	C₃×3₋¹⁺²	—	6	1	no	—
322	C₃×3₋¹⁺²	—	6	1	no	—
323	C₃×3₋¹⁺²	—	6	1	no	—
324	C₃×3₋¹⁺²	—	6	1	no	—
325	C₃×3₋¹⁺²	—	6	1	no	—
326	C₃×3₋¹⁺²	—	6	1	no	—
327	C₃×3₋¹⁺²	—	6	1	no	—
328	C₃×3₋¹⁺²	—	6	1	no	—
329	C₃×3₋¹⁺²	—	6	1	no	—
330	C₃×3₋¹⁺²	C₂×C₃×C₉	1	1	yes	characteristic, complemented
331	C₃×3₋¹⁺²	C₂×C₃×C₉	1	1	yes	characteristic, complemented
332	C₃×3₋¹⁺²	C₂×C₃×C₉	1	1	yes	characteristic, complemented
333	C₃×3₋¹⁺²	C₂×C₃×C₉	1	1	yes	characteristic, complemented
334	C₃×3₋¹⁺²	C₂×C₃×C₉	1	1	yes	characteristic, complemented
335	C₃×3₋¹⁺²	C₂×C₃×C₉	1	1	yes	characteristic, complemented
336	C₃×3₋¹⁺²	C₂×C₃×C₉	1	1	yes	characteristic, complemented
337	C₃×3₋¹⁺²	C₂×C₃×C₉	1	1	yes	characteristic, complemented
338	C₃×3₋¹⁺²	C₂×C₃×C₉	1	1	yes	characteristic, complemented
339	C₃×H(3,𝔽₃)	—	6	1	no	—
340	C₃×H(3,𝔽₃)	—	6	1	no	—
341	C₃×H(3,𝔽₃)	—	6	1	no	—
342	C₃×H(3,𝔽₃)	—	6	1	no	—
343	C₃×H(3,𝔽₃)	—	6	1	no	—
344	C₃×H(3,𝔽₃)	D₃×C₉	1	1	yes	characteristic
345	C₃×H(3,𝔽₃)	D₃×C₉	1	1	yes	characteristic
346	C₃×H(3,𝔽₃)	D₃×C₉	1	1	yes	characteristic
347	C₃×H(3,𝔽₃)	D₃×C₉	1	1	yes	characteristic
348	C₃×H(3,𝔽₃)	D₃×C₉	1	1	yes	characteristic
349	C₃×H(3,𝔽₃)	D₃×C₉	1	1	yes	characteristic
350	C₃×H(3,𝔽₃)	D₃×C₉	1	1	yes	characteristic
351	C₃×H(3,𝔽₃)	D₃×C₉	1	1	yes	characteristic
352	C₃×H(3,𝔽₃)	D₃×C₉	1	1	yes	characteristic
353	C₃²×C₉	—	2	1	no	—
354	C₃²×C₉	—	2	1	no	—
355	C₃²×C₉	—	2	1	no	—
356	C₃²×C₉	—	2	1	no	—
357	C₃²×C₉	—	2	1	no	—
358	C₃²×C₉	—	2	1	no	—
359	C₃²×C₉	—	2	1	no	—
360	C₃²×C₉	—	2	1	no	—
361	C₃²×C₉	—	2	1	no	—
362	C₃²×C₉	—	2	1	no	—
363	C₃²×C₉	—	2	1	no	—
364	C₃²×C₉	—	2	1	no	—
365	C₃²×C₉	—	2	1	no	—
366	C₃²×C₉	—	2	1	no	—
367	C₃²×C₉	—	2	1	no	—
368	C₃²×C₉	—	2	1	no	—
369	C₃²×C₉	—	2	1	no	—
370	C₃²×C₉	—	2	1	no	—
371	C₃²×C₉	—	2	1	no	—
372	C₃²×C₉	—	2	1	no	—
373	C₃²×C₉	—	3	1	no	—
374	C₃²×C₉	—	3	1	no	—
375	C₃²×C₉	—	3	1	no	—
376	C₃²×C₉	—	3	1	no	—
377	C₃²×C₉	—	3	1	no	—
378	C₃²×C₉	—	3	1	no	—
379	C₃²×C₉	—	3	1	no	—
380	C₃²×C₉	—	3	1	no	—
381	C₃²×C₉	—	3	1	no	—
382	C₃²×C₉	—	3	1	no	—
383	C₃²×C₉	—	3	1	no	—
384	C₃²×C₉	—	3	1	no	—
385	C₃²×C₉	—	3	1	no	—
386	C₃²×C₉	—	3	1	no	—
387	C₃²×C₉	—	3	1	no	—
388	C₃²×C₉	—	3	1	no	—
389	C₃²×C₉	—	3	1	no	—
390	C₃²×C₉	—	3	1	no	—
391	C₃²×C₉	—	6	1	no	—
392	C₃²×C₉	—	6	1	no	—
393	C₃²×C₉	—	6	1	no	—
394	C₃²×C₉	—	6	1	no	—
395	C₃²×C₉	—	6	1	no	—
396	C₃²×C₉	—	6	1	no	—
397	C₃²×C₉	—	6	1	no	—
398	C₃²×C₉	—	6	3	no	—
399	C₃²×C₉	—	6	3	no	—
400	C₃²×C₉	—	6	1	no	—
401	C₃²×C₉	—	6	1	no	—
402	C₃²×C₉	—	6	1	no	—
403	C₃²×C₉	—	6	1	no	—
404	C₃²×C₉	—	6	1	no	—
405	C₃²×C₉	—	6	1	no	—
406	C₃²×C₉	—	6	1	no	—
407	C₃²×C₉	—	6	1	no	—
408	C₃²×C₉	—	6	1	no	—
409	C₃²×C₉	—	6	1	no	—
410	C₃²×C₉	—	6	1	no	—
411	C₃²×C₉	—	6	1	no	—
412	C₃²×C₉	—	6	1	no	—
413	C₃²×C₉	—	6	1	no	—
414	C₃²×C₉	—	6	1	no	—
415	C₃²×C₉	—	6	1	no	—
416	C₃²×C₉	—	6	1	no	—
417	C₃²×C₉	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
418	C₃²×C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
419	C₃²×C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
420	C₃²×C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
421	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
422	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
423	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
424	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
425	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
426	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
427	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
428	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
429	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
430	C₃²×C₉	C₂×C₃³	1	1	yes	characteristic
431	C₉⋊C₉	—	3	1	no	—
432	C₉⋊C₉	—	3	1	no	—
433	C₉⋊C₉	—	3	1	no	—
434	C₉⋊C₉	—	3	1	no	—
435	C₉⋊C₉	—	3	1	no	—
436	C₉⋊C₉	—	3	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	—	6	1	no	—
449	C₉⋊C₉	—	6	1	no	—
450	C₉⋊C₉	—	6	1	no	—
451	C₉⋊C₉	—	6	1	no	—
452	C₉⋊C₉	—	6	1	no	—
453	C₉⋊C₉	—	6	1	no	—
454	C₉⋊C₉	—	6	1	no	—
455	C₉⋊C₉	—	6	1	no	—
456	C₉⋊C₉	—	6	1	no	—
457	C₉⋊C₉	—	6	1	no	—
458	C₉⋊C₉	—	6	1	no	—
459	C₉⋊C₉	—	6	1	no	—
460	C₉⋊C₉	—	6	1	no	—
461	C₃²⋊C₉	—	2	1	no	—
462	C₃²⋊C₉	—	2	1	no	—
463	C₃²⋊C₉	—	2	1	no	—
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	—	2	1	no	—
474	C₃²⋊C₉	—	2	1	no	—
475	C₃²⋊C₉	—	2	1	no	—
476	C₃²⋊C₉	—	2	1	no	—
477	C₃²⋊C₉	—	2	1	no	—
478	C₃²⋊C₉	—	2	1	no	—
479	C₃²⋊C₉	—	2	1	no	—
480	C₃²⋊C₉	—	2	1	no	—
481	C₃²⋊C₉	—	2	1	no	—
482	C₃²⋊C₉	—	2	1	no	—
483	C₃²⋊C₉	—	2	1	no	—
484	C₃²⋊C₉	—	2	1	no	—
485	C₃²⋊C₉	—	2	1	no	—
486	C₃²⋊C₉	—	2	1	no	—
487	C₃²⋊C₉	—	2	1	no	—
488	C₃²⋊C₉	—	2	1	no	—
489	C₃²⋊C₉	—	2	1	no	—
490	C₃²⋊C₉	—	2	1	no	—
491	C₃²⋊C₉	—	2	1	no	—
492	C₃²⋊C₉	—	2	1	no	—
493	C₃²⋊C₉	—	2	1	no	—
494	C₃²⋊C₉	—	2	1	no	—
495	C₃²⋊C₉	—	2	1	no	—
496	C₃²⋊C₉	—	2	1	no	—
497	C₃²⋊C₉	—	3	1	no	—
498	C₃²⋊C₉	—	3	1	no	—
499	C₃²⋊C₉	—	6	1	no	—
500	C₃²⋊C₉	—	6	1	no	—
501	C₃²⋊C₉	—	6	1	no	—
502	C₃²⋊C₉	—	6	1	no	—
503	C₃²⋊C₉	—	6	1	no	—
504	C₃²⋊C₉	—	6	1	no	—
505	C₃²⋊C₉	—	6	1	no	—
506	C₃²⋊C₉	—	6	1	no	—
507	C₃²⋊C₉	—	6	1	no	—
508	C₃²⋊C₉	—	6	1	no	—
509	C₃²⋊C₉	—	6	1	no	—
510	C₃²⋊C₉	—	6	1	no	—
511	C₃²⋊C₉	—	6	1	no	—
512	C₃²⋊C₉	—	6	3	no	—
513	C₃²⋊C₉	—	6	3	no	—
514	C₃²⋊C₉	—	6	3	no	—
515	C₃²⋊C₉	—	6	3	no	—
516	C₃²⋊C₉	—	6	3	no	—
517	C₃²⋊C₉	—	6	3	no	—
518	C₃²⋊C₉	—	6	1	no	—
519	C₃²⋊C₉	—	6	1	no	—
520	C₃²⋊C₉	—	6	1	no	—
521	C₃²⋊C₉	—	6	1	no	—
522	C₃²⋊C₉	—	6	1	no	—
523	C₃²⋊C₉	—	6	1	no	—
524	C₃²⋊C₉	—	6	1	no	—
525	C₃²⋊C₉	—	6	1	no	—
526	C₃²⋊C₉	—	6	1	no	—
527	C₃²⋊C₉	—	6	1	no	—
528	C₃²⋊C₉	—	6	1	no	—
529	C₃²⋊C₉	—	6	1	no	—
530	C₃²⋊C₉	—	6	1	no	—
531	C₃²⋊C₉	—	6	1	no	—
532	C₃²⋊C₉	—	6	1	no	—
533	C₃²⋊C₉	—	6	1	no	—
534	C₉²	—	2	1	no	—
535	C₉²	—	2	1	no	—
536	C₉²	—	2	1	no	—
537	C₉²	—	3	1	no	—
538	C₉²	—	3	1	no	—
539	C₉²	—	6	1	no	—
540	C₉²	—	6	1	no	—
541	C₉²	—	6	1	no	—
542	C₉²	—	6	1	no	—
543	C₉²	—	6	1	no	—
544	C₉²	—	6	1	no	—
545	C₉²	—	6	1	no	—
546	C₉²	—	6	1	no	—
547	C₉²	—	6	1	no	—
548	C₉²	—	6	1	no	—
549	C₉²	—	6	1	no	—
550	C₉²	—	6	1	no	—
551	C₉²	—	6	1	no	—
552	C₉²	—	6	1	no	—
553	C₉²	—	6	1	no	—
554	C₉²	—	6	1	no	—
555	C₉²	—	6	1	no	—
556	C₉²	—	6	1	no	—
557	C₉²	—	6	1	no	—
558	C₉²	—	6	1	no	—
559	C₉²	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
560	C₉²	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
561	C₉²	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
562	C₂×C₃³	—	9	1	no	—
563	C₂×C₃³	—	9	1	no	—
564	C₂×C₃³	—	9	1	no	—
565	C₂×C₃³	—	9	1	no	—
566	C₃²×D₃	—	3	1	no	—
567	C₃²×D₃	—	3	1	no	—
568	C₃²×D₃	—	3	1	no	—
569	C₃²×D₃	—	3	1	no	—
570	C₃²×D₃	—	3	1	no	—
571	C₃²×D₃	—	3	1	no	—
572	C₃²×D₃	—	3	1	no	—
573	C₃²×D₃	—	3	1	no	—
574	C₃²×D₃	—	3	1	no	—
575	C₃²×D₃	—	3	1	no	—
576	C₃²×D₃	—	3	1	no	—
577	C₃²×D₃	—	3	1	no	—
578	C₃²×D₃	—	3	1	no	—
579	C₃²×D₃	—	9	1	no	—
580	C₃²×D₃	—	9	1	no	—
581	C₃²×D₃	—	9	1	no	—
582	C₃²×D₃	—	9	1	no	—
583	C₃²×D₃	—	9	1	no	—
584	C₃²×D₃	—	9	1	no	—
585	C₃²×D₃	—	9	1	no	—
586	C₃²×D₃	—	9	1	no	—
587	C₃²×D₃	—	9	1	no	—
588	C₃²×D₃	—	9	1	no	—
589	C₃²×D₃	—	9	1	no	—
590	C₃²×D₃	—	9	1	no	—
591	C₂×H(3,𝔽₃)	—	9	1	no	—
592	C₂×H(3,𝔽₃)	—	9	1	no	—
593	C₂×H(3,𝔽₃)	—	9	1	no	—
594	C₂×H(3,𝔽₃)	—	9	1	no	—
595	C₂×H(3,𝔽₃)	—	9	1	no	—
596	C₂×H(3,𝔽₃)	—	9	1	no	—
597	C₂×H(3,𝔽₃)	—	9	1	no	—
598	C₂×H(3,𝔽₃)	—	9	1	no	—
599	C₂×H(3,𝔽₃)	—	9	1	no	—
600	C₂×C₃×C₉	—	9	1	no	—
601	C₂×C₃×C₉	—	9	1	no	—
602	C₂×C₃×C₉	—	9	1	no	—
603	C₂×C₃×C₉	—	9	1	no	—
604	C₂×C₃×C₉	—	9	1	no	—
605	C₂×C₃×C₉	—	9	1	no	—
606	C₂×C₃×C₉	—	9	1	no	—
607	C₂×C₃×C₉	—	9	1	no	—
608	C₂×C₃×C₉	—	9	1	no	—
609	C₂×C₃×C₉	—	27	1	no	—
610	C₂×C₃×C₉	—	27	1	no	—
611	C₂×C₃×C₉	—	27	1	no	—
612	C₂×C₃×C₉	—	27	1	no	—
613	C₂×C₃×C₉	—	27	1	no	—
614	C₂×C₃×C₉	—	27	1	no	—
615	C₂×C₃×C₉	—	27	1	no	—
616	C₂×C₃×C₉	—	27	1	no	—
617	C₂×C₃×C₉	—	27	1	no	—
618	C₂×C₃×C₉	—	27	1	no	—
619	C₂×C₃×C₉	—	27	1	no	—
620	C₂×C₃×C₉	—	27	1	no	—
621	AGL(1,ℤ/9)	—	3	1	no	—
622	AGL(1,ℤ/9)	—	3	1	no	—
623	AGL(1,ℤ/9)	—	3	1	no	—
624	AGL(1,ℤ/9)	—	3	1	no	—
625	AGL(1,ℤ/9)	—	3	1	no	—
626	AGL(1,ℤ/9)	—	3	1	no	—
627	AGL(1,ℤ/9)	—	3	1	no	—
628	AGL(1,ℤ/9)	—	3	1	no	—
629	AGL(1,ℤ/9)	—	3	1	no	—
630	D₃×C₉	—	3	1	no	—
631	D₃×C₉	—	3	1	no	—
632	D₃×C₉	—	3	1	no	—
633	D₃×C₉	—	9	1	no	—
634	D₃×C₉	—	9	1	no	—
635	D₃×C₉	—	9	1	no	—
636	D₃×C₉	—	9	1	no	—
637	D₃×C₉	—	9	1	no	—
638	D₃×C₉	—	9	1	no	—
639	D₃×C₉	—	9	1	no	—
640	D₃×C₉	—	9	1	no	—
641	C₃×D₉	—	3	1	no	—
642	C₃×D₉	—	3	1	no	—
643	C₃×D₉	—	3	1	no	—
644	C₃×D₉	C₃²×C₉	1	1	yes	characteristic
645	C₃×D₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
646	C₃×D₉	#737	1	1	yes	characteristic
647	C₃×D₉	#737	1	1	yes	characteristic
648	C₃³	—	2	1	no	—
649	C₃³	—	2	1	no	—
650	C₃³	—	2	1	no	—
651	C₃³	—	2	1	no	—
652	C₃³	—	3	1	no	—
653	C₃³	—	3	1	no	—
654	C₃³	—	3	1	no	—
655	C₃³	—	3	1	no	—
656	C₃³	—	3	1	no	—
657	C₃³	—	3	1	no	—
658	C₃³	—	3	1	no	—
659	C₃³	—	3	1	no	—
660	C₃³	—	3	1	no	—
661	C₃³	—	3	1	no	—
662	C₃³	—	3	1	no	—
663	C₃³	—	3	1	no	—
664	C₃³	—	3	1	no	—
665	C₃³	—	6	1	no	—
666	C₃³	—	6	1	no	—
667	C₃³	—	6	1	no	—
668	C₃³	—	6	1	no	—
669	C₃³	—	6	1	no	—
670	C₃³	—	6	1	no	—
671	C₃³	—	6	1	no	—
672	C₃³	—	6	1	no	—
673	C₃³	—	6	1	no	—
674	C₃³	—	6	1	no	—
675	C₃³	—	6	1	no	—
676	C₃³	—	6	1	no	—
677	C₃³	—	6	1	no	—
678	C₃³	—	6	1	no	—
679	C₃³	—	6	1	no	—
680	C₃³	—	6	1	no	—
681	C₃³	—	6	1	no	—
682	C₃³	C₃×D₃×C₉	1	1	yes	characteristic
683	C₃³	C₃×D₃×C₉	1	1	yes	characteristic
684	C₃³	C₃×D₃×C₉	1	1	yes	characteristic
685	C₃³	C₃×D₃×C₉	1	1	yes	characteristic
686	C₃³	C₃×D₃×C₉	1	1	yes	characteristic
687	C₃³	C₃×D₃×C₉	1	1	yes	characteristic
688	C₃³	C₃×D₃×C₉	1	1	yes	characteristic
689	C₃³	C₃×D₃×C₉	1	1	yes	characteristic
690	C₃³	C₃×D₃×C₉	1	1	yes	characteristic
691	C₃³	C₃×D₃×C₉	1	1	yes	characteristic
692	C₃³	C₃×D₃×C₉	1	1	yes	characteristic
693	C₃³	C₃×D₃×C₉	1	1	yes	characteristic
694	C₃³	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
695	C₃³	C₃³×D₃	1	1	yes	characteristic
696	3₋¹⁺²	—	3	1	no	—
697	3₋¹⁺²	—	3	1	no	—
698	3₋¹⁺²	—	3	1	no	—
699	3₋¹⁺²	—	3	1	no	—
700	3₋¹⁺²	—	3	1	no	—
701	3₋¹⁺²	—	3	1	no	—
702	3₋¹⁺²	—	3	1	no	—
703	3₋¹⁺²	—	3	1	no	—
704	3₋¹⁺²	—	3	1	no	—
705	3₋¹⁺²	—	6	1	no	—
706	3₋¹⁺²	—	6	1	no	—
707	3₋¹⁺²	—	6	1	no	—
708	3₋¹⁺²	—	6	1	no	—
709	3₋¹⁺²	—	6	1	no	—
710	3₋¹⁺²	—	6	1	no	—
711	3₋¹⁺²	—	6	1	no	—
712	3₋¹⁺²	—	6	1	no	—
713	3₋¹⁺²	—	6	1	no	—
714	3₋¹⁺²	—	6	1	no	—
715	3₋¹⁺²	—	6	1	no	—
716	3₋¹⁺²	—	6	1	no	—
717	3₋¹⁺²	—	6	1	no	—
718	3₋¹⁺²	—	6	1	no	—
719	3₋¹⁺²	—	6	1	no	—
720	3₋¹⁺²	—	6	1	no	—
721	3₋¹⁺²	—	6	1	no	—
722	3₋¹⁺²	—	6	1	no	—
723	3₋¹⁺²	—	6	1	no	—
724	3₋¹⁺²	—	6	1	no	—
725	3₋¹⁺²	—	6	1	no	—
726	3₋¹⁺²	—	6	1	no	—
727	3₋¹⁺²	—	6	1	no	—
728	3₋¹⁺²	—	6	1	no	—
729	3₋¹⁺²	—	6	1	no	—
730	3₋¹⁺²	—	6	1	no	—
731	3₋¹⁺²	—	6	1	no	—
732	3₋¹⁺²	—	6	1	no	—
733	3₋¹⁺²	—	6	1	no	—
734	3₋¹⁺²	—	6	1	no	—
735	3₋¹⁺²	—	6	1	no	—
736	3₋¹⁺²	—	6	1	no	—
737	3₋¹⁺²	—	6	1	no	—
738	3₋¹⁺²	—	6	1	no	—
739	3₋¹⁺²	—	6	1	no	—
740	3₋¹⁺²	—	6	1	no	—
741	H(3,𝔽₃)	—	3	1	no	—
742	H(3,𝔽₃)	—	3	1	no	—
743	H(3,𝔽₃)	—	3	1	no	—
744	H(3,𝔽₃)	—	6	1	no	—
745	H(3,𝔽₃)	—	6	1	no	—
746	H(3,𝔽₃)	—	6	1	no	—
747	H(3,𝔽₃)	—	6	1	no	—
748	H(3,𝔽₃)	—	6	1	no	—
749	H(3,𝔽₃)	—	6	1	no	—
750	H(3,𝔽₃)	—	6	1	no	—
751	H(3,𝔽₃)	—	6	1	no	—
752	H(3,𝔽₃)	—	6	1	no	—
753	H(3,𝔽₃)	—	6	1	no	—
754	H(3,𝔽₃)	—	6	1	no	—
755	H(3,𝔽₃)	—	6	1	no	—
756	H(3,𝔽₃)	—	6	1	no	—
757	H(3,𝔽₃)	—	6	1	no	—
758	H(3,𝔽₃)	—	6	1	no	—
759	C₃×C₉	—	2	1	no	—
760	C₃×C₉	—	2	1	no	—
761	C₃×C₉	—	2	1	no	—
762	C₃×C₉	—	2	1	no	—
763	C₃×C₉	—	2	1	no	—
764	C₃×C₉	—	2	1	no	—
765	C₃×C₉	—	2	1	no	—
766	C₃×C₉	—	2	1	no	—
767	C₃×C₉	—	2	3	no	—
768	C₃×C₉	—	2	3	no	—
769	C₃×C₉	—	2	1	no	—
770	C₃×C₉	—	2	1	no	—
771	C₃×C₉	—	2	1	no	—
772	C₃×C₉	—	2	1	no	—
773	C₃×C₉	—	2	1	no	—
774	C₃×C₉	—	2	1	no	—
775	C₃×C₉	—	2	1	no	—
776	C₃×C₉	—	2	1	no	—
777	C₃×C₉	—	2	1	no	—
778	C₃×C₉	—	2	1	no	—
779	C₃×C₉	—	2	1	no	—
780	C₃×C₉	—	2	1	no	—
781	C₃×C₉	—	2	1	no	—
782	C₃×C₉	—	2	1	no	—
783	C₃×C₉	—	2	1	no	—
784	C₃×C₉	—	2	1	no	—
785	C₃×C₉	—	2	1	no	—
786	C₃×C₉	—	3	1	no	—
787	C₃×C₉	—	3	1	no	—
788	C₃×C₉	—	3	1	no	—
789	C₃×C₉	—	3	1	no	—
790	C₃×C₉	—	3	1	no	—
791	C₃×C₉	—	3	1	no	—
792	C₃×C₉	—	3	1	no	—
793	C₃×C₉	—	3	1	no	—
794	C₃×C₉	—	3	1	no	—
795	C₃×C₉	—	3	1	no	—
796	C₃×C₉	—	3	1	no	—
797	C₃×C₉	—	3	1	no	—
798	C₃×C₉	—	3	1	no	—
799	C₃×C₉	—	3	1	no	—
800	C₃×C₉	—	3	1	no	—
801	C₃×C₉	—	6	1	no	—
802	C₃×C₉	—	6	1	no	—
803	C₃×C₉	—	6	1	no	—
804	C₃×C₉	—	6	1	no	—
805	C₃×C₉	—	6	1	no	—
806	C₃×C₉	—	6	1	no	—
807	C₃×C₉	—	6	1	no	—
808	C₃×C₉	—	6	1	no	—
809	C₃×C₉	—	6	1	no	—
810	C₃×C₉	—	6	1	no	—
811	C₃×C₉	—	6	1	no	—
812	C₃×C₉	—	6	1	no	—
813	C₃×C₉	—	6	1	no	—
814	C₃×C₉	—	6	1	no	—
815	C₃×C₉	—	6	1	no	—
816	C₃×C₉	—	6	1	no	—
817	C₃×C₉	—	6	1	no	—
818	C₃×C₉	—	6	1	no	—
819	C₃×C₉	—	6	1	no	—
820	C₃×C₉	—	6	1	no	—
821	C₃×C₉	—	6	1	no	—
822	C₃×C₉	—	6	1	no	—
823	C₃×C₉	—	6	1	no	—
824	C₃×C₉	—	6	1	no	—
825	C₃×C₉	—	6	1	no	—
826	C₃×C₉	—	6	1	no	—
827	C₃×C₉	—	6	1	no	—
828	C₃×C₉	—	6	1	no	—
829	C₃×C₉	—	6	1	no	—
830	C₃×C₉	—	6	1	no	—
831	C₃×C₉	—	6	3	no	—
832	C₃×C₉	—	6	3	no	—
833	C₃×C₉	—	6	3	no	—
834	C₃×C₉	—	6	3	no	—
835	C₃×C₉	—	6	3	no	—
836	C₃×C₉	—	6	3	no	—
837	C₃×C₉	—	6	3	no	—
838	C₃×C₉	—	6	3	no	—
839	C₃×C₉	—	6	3	no	—
840	C₃×C₉	—	6	1	no	—
841	C₃×C₉	—	6	1	no	—
842	C₃×C₉	—	6	1	no	—
843	C₃×C₉	—	6	1	no	—
844	C₃×C₉	—	6	1	no	—
845	C₃×C₉	—	6	1	no	—
846	C₃×C₉	—	6	1	no	—
847	C₃×C₉	—	6	1	no	—
848	C₃×C₉	—	6	1	no	—
849	C₃×C₉	—	6	1	no	—
850	C₃×C₉	—	6	1	no	—
851	C₃×C₉	—	6	1	no	—
852	C₃×C₉	—	6	1	no	—
853	C₃×C₉	—	6	1	no	—
854	C₃×C₉	—	6	1	no	—
855	C₃×C₉	—	6	1	no	—
856	C₃×C₉	—	6	1	no	—
857	C₃×C₉	—	6	1	no	—
858	C₃×C₉	—	6	1	no	—
859	C₃×C₉	—	6	1	no	—
860	C₃×C₉	—	6	1	no	—
861	C₃×C₉	—	6	1	no	—
862	C₃×C₉	—	6	1	no	—
863	C₃×C₉	—	6	1	no	—
864	C₃×C₉	—	6	1	no	—
865	C₃×C₉	—	6	1	no	—
866	C₃×C₉	—	6	1	no	—
867	C₃×C₉	—	6	1	no	—
868	C₃×C₉	—	6	1	no	—
869	C₃×C₉	—	6	1	no	—
870	C₃×C₉	—	6	1	no	—
871	C₃×C₉	—	6	1	no	—
872	C₃×C₉	—	6	1	no	—
873	C₃×C₉	—	6	1	no	—
874	C₃×C₉	—	6	1	no	—
875	C₃×C₉	—	6	1	no	—
876	C₃×C₉	—	6	1	no	—
877	C₃×C₉	—	6	1	no	—
878	C₃×C₉	—	6	1	no	—
879	C₃×C₉	—	6	1	no	—
880	C₃×C₉	—	6	1	no	—
881	C₃×C₉	—	6	1	no	—
882	C₃×C₉	—	6	1	no	—
883	C₃×C₉	—	6	1	no	—
884	C₃×C₉	—	6	1	no	—
885	C₃×C₉	—	6	1	no	—
886	C₃×C₉	—	6	1	no	—
887	C₃×C₉	—	6	1	no	—
888	C₃×C₉	—	6	1	no	—
889	C₃×C₉	—	6	1	no	—
890	C₃×C₉	—	6	1	no	—
891	C₃×C₉	—	6	1	no	—
892	C₃×C₉	—	9	1	no	—
893	C₃×C₉	—	9	1	no	—
894	C₃×C₉	—	9	1	no	—
895	C₃×C₉	—	18	1	no	—
896	C₃×C₉	—	18	1	no	—
897	C₃×C₉	—	18	1	no	—
898	C₃×C₉	—	18	1	no	—
899	C₃×C₉	—	18	1	no	—
900	C₃×C₉	—	18	1	no	—
901	C₃×C₉	—	18	1	no	—
902	C₃×C₉	—	18	1	no	—
903	C₃×C₉	—	18	1	no	—
904	C₃×C₉	—	18	1	no	—
905	C₃×C₉	—	18	1	no	—
906	C₃×C₉	—	18	1	no	—
907	C₃×C₉	—	18	1	no	—
908	C₃×C₉	—	18	1	no	—
909	C₃×C₉	—	18	1	no	—
910	C₃×C₉	D₃×H(3,𝔽₃)	1	1	yes	characteristic
911	C₃×C₉	D₃×H(3,𝔽₃)	1	1	yes	characteristic
912	C₃×C₉	D₃×H(3,𝔽₃)	1	1	yes	characteristic
913	C₃×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
914	C₃×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
915	C₃×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
916	C₃×C₉	C₂×C₃²×C₉	1	1	yes	characteristic
917	C₃×C₉	C₂×C₃×H(3,𝔽₃)	1	1	yes	characteristic
918	C₃×C₉	C₂×#737	1	1	yes	characteristic
919	C₃×C₉	C₂×#737	1	1	yes	characteristic
920	C₂×C₃²	—	9	1	no	—
921	C₂×C₃²	—	9	1	no	—
922	C₂×C₃²	—	9	1	no	—
923	C₂×C₃²	—	9	1	no	—
924	C₂×C₃²	—	9	1	no	—
925	C₂×C₃²	—	9	1	no	—
926	C₂×C₃²	—	9	1	no	—
927	C₂×C₃²	—	9	1	no	—
928	C₂×C₃²	—	9	1	no	—
929	C₂×C₃²	—	9	1	no	—
930	C₂×C₃²	—	9	1	no	—
931	C₂×C₃²	—	9	1	no	—
932	C₂×C₃²	—	9	1	no	—
933	C₂×C₃²	—	27	1	no	—
934	C₂×C₃²	—	27	1	no	—
935	C₂×C₃²	—	27	1	no	—
936	C₂×C₃²	—	27	1	no	—
937	C₂×C₃²	—	27	1	no	—
938	C₂×C₃²	—	27	1	no	—
939	C₂×C₃²	—	27	1	no	—
940	C₂×C₃²	—	27	1	no	—
941	C₂×C₃²	—	27	1	no	—
942	C₂×C₃²	—	27	1	no	—
943	C₂×C₃²	—	27	1	no	—
944	C₂×C₃²	—	27	1	no	—
945	C₃×D₃	—	3	1	no	—
946	C₃×D₃	—	3	1	no	—
947	C₃×D₃	—	3	1	no	—
948	C₃×D₃	—	3	1	no	—
949	C₃×D₃	—	9	1	no	—
950	C₃×D₃	—	9	1	no	—
951	C₃×D₃	—	9	1	no	—
952	C₃×D₃	—	9	1	no	—
953	C₃×D₃	—	9	1	no	—
954	C₃×D₃	—	9	1	no	—
955	C₃×D₃	—	9	1	no	—
956	C₃×D₃	—	9	1	no	—
957	C₃×D₃	—	9	1	no	—
958	C₃×D₃	—	9	1	no	—
959	C₃×D₃	—	9	1	no	—
960	C₃×D₃	—	9	1	no	—
961	C₂×C₉	—	9	1	no	—
962	C₂×C₉	—	9	1	no	—
963	C₂×C₉	—	9	1	no	—
964	C₂×C₉	—	27	1	no	—
965	C₂×C₉	—	27	1	no	—
966	C₂×C₉	—	27	1	no	—
967	C₂×C₉	—	27	1	no	—
968	C₂×C₉	—	27	1	no	—
969	C₂×C₉	—	27	1	no	—
970	C₂×C₉	—	27	1	no	—
971	C₂×C₉	—	27	1	no	—
972	D₉	C₉×H(3,𝔽₃)	1	1	yes	characteristic, complemented
973	C₃²	—	2	1	no	—
974	C₃²	—	2	1	no	—
975	C₃²	—	2	1	no	—
976	C₃²	—	2	1	no	—
977	C₃²	—	2	1	no	—
978	C₃²	—	2	1	no	—
979	C₃²	—	2	1	no	—
980	C₃²	—	3	1	no	—
981	C₃²	—	3	1	no	—
982	C₃²	—	3	1	no	—
983	C₃²	—	3	1	no	—
984	C₃²	—	3	1	no	—
985	C₃²	—	3	1	no	—
986	C₃²	—	3	1	no	—
987	C₃²	—	3	1	no	—
988	C₃²	—	3	1	no	—
989	C₃²	—	3	1	no	—
990	C₃²	—	3	1	no	—
991	C₃²	—	3	1	no	—
992	C₃²	—	3	1	no	—
993	C₃²	—	3	1	no	—
994	C₃²	—	3	1	no	—
995	C₃²	—	3	1	no	—
996	C₃²	—	3	1	no	—
997	C₃²	—	3	1	no	—
998	C₃²	—	6	1	no	—
999	C₃²	—	6	1	no	—
1000	C₃²	—	6	1	no	—
1001	C₃²	—	6	1	no	—
1002	C₃²	—	6	1	no	—
1003	C₃²	—	6	1	no	—
1004	C₃²	—	6	1	no	—
1005	C₃²	—	6	1	no	—
1006	C₃²	—	6	1	no	—
1007	C₃²	—	6	1	no	—
1008	C₃²	—	6	1	no	—
1009	C₃²	—	6	1	no	—
1010	C₃²	—	6	1	no	—
1011	C₃²	—	6	1	no	—
1012	C₃²	—	6	1	no	—
1013	C₃²	—	6	1	no	—
1014	C₃²	—	6	1	no	—
1015	C₃²	—	6	1	no	—
1016	C₃²	—	6	1	no	—
1017	C₃²	—	6	1	no	—
1018	C₃²	—	6	1	no	—
1019	C₃²	—	6	1	no	—
1020	C₃²	—	6	1	no	—
1021	C₃²	—	6	1	no	—
1022	C₃²	—	6	1	no	—
1023	C₃²	—	6	1	no	—
1024	C₃²	—	6	1	no	—
1025	C₃²	—	6	1	no	—
1026	C₃²	—	6	1	no	—
1027	C₃²	—	6	1	no	—
1028	C₃²	—	9	1	no	—
1029	C₃²	—	9	1	no	—
1030	C₃²	—	18	1	no	—
1031	C₃²	—	18	1	no	—
1032	C₃²	—	18	1	no	—
1033	C₃²	—	18	1	no	—
1034	C₃²	—	18	1	no	—
1035	C₃²	—	18	1	no	—
1036	C₃²	—	18	1	no	—
1037	C₃²	—	18	1	no	—
1038	C₃²	—	18	1	no	—
1039	C₃²	—	18	1	no	—
1040	C₃²	—	18	1	no	—
1041	C₃²	—	18	1	no	—
1042	C₃²	—	18	1	no	—
1043	C₃²	—	18	1	no	—
1044	C₃²	—	18	1	no	—
1045	C₃²	—	18	1	no	—
1046	C₃²	C₉×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
1047	C₃²	C₉×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
1048	C₃²	C₉×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
1049	C₃²	C₃²×D₃×C₉	1	1	yes	characteristic
1050	C₃²	C₃×D₃×H(3,𝔽₃)	1	1	yes	characteristic
1051	C₃²	C₃²×AGL(1,ℤ/9)	1	1	yes	characteristic
1052	C₃²	D₃×#737	1	1	yes	characteristic
1053	C₃²	D₃×#737	1	1	yes	characteristic
1054	C₉	—	2	1	no	—
1055	C₉	—	2	1	no	—
1056	C₉	—	2	1	no	—
1057	C₉	—	2	1	no	—
1058	C₉	—	2	1	no	—
1059	C₉	—	2	1	no	—
1060	C₉	—	2	1	no	—
1061	C₉	—	3	1	no	—
1062	C₉	—	3	1	no	—
1063	C₉	—	6	3	no	—
1064	C₉	—	6	3	no	—
1065	C₉	—	6	1	no	—
1066	C₉	—	6	1	no	—
1067	C₉	—	6	1	no	—
1068	C₉	—	6	1	no	—
1069	C₉	—	6	1	no	—
1070	C₉	—	6	1	no	—
1071	C₉	—	6	1	no	—
1072	C₉	—	6	1	no	—
1073	C₉	—	6	1	no	—
1074	C₉	—	6	1	no	—
1075	C₉	—	6	1	no	—
1076	C₉	—	6	1	no	—
1077	C₉	—	6	1	no	—
1078	C₉	—	6	1	no	—
1079	C₉	—	6	1	no	—
1080	C₉	—	6	1	no	—
1081	C₉	—	6	1	no	—
1082	C₉	—	9	1	no	—
1083	C₉	—	18	1	no	—
1084	C₉	—	18	1	no	—
1085	C₉	—	18	1	no	—
1086	C₉	—	18	1	no	—
1087	C₉	—	18	1	no	—
1088	C₉	—	18	1	no	—
1089	C₉	—	18	1	no	—
1090	C₉	—	18	1	no	—
1091	C₉	—	18	1	no	—
1092	C₉	—	18	1	no	—
1093	C₉	—	18	1	no	—
1094	C₉	D₉⋊H(3,𝔽₃)	1	1	yes	characteristic, direct product factor
1095	C₉	D₉⋊H(3,𝔽₃)	1	1	yes	characteristic, direct product factor
1096	C₉	D₉⋊H(3,𝔽₃)	1	1	yes	characteristic, direct product factor
1097	C₉	C₂×C₉×H(3,𝔽₃)	1	1	yes	characteristic, complemented
1098	C₂×C₃	—	9	1	no	—
1099	C₂×C₃	—	9	1	no	—
1100	C₂×C₃	—	9	1	no	—
1101	C₂×C₃	—	9	1	no	—
1102	C₂×C₃	—	27	1	no	—
1103	C₂×C₃	—	27	1	no	—
1104	C₂×C₃	—	27	1	no	—
1105	C₂×C₃	—	27	1	no	—
1106	C₂×C₃	—	27	1	no	—
1107	C₂×C₃	—	27	1	no	—
1108	C₂×C₃	—	27	1	no	—
1109	C₂×C₃	—	27	1	no	—
1110	C₂×C₃	—	27	1	no	—
1111	C₂×C₃	—	27	1	no	—
1112	C₂×C₃	—	27	1	no	—
1113	C₂×C₃	—	27	1	no	—
1114	D₃	—	3	1	no	—
1115	C₃	—	2	1	no	—
1116	C₃	—	2	1	no	—
1117	C₃	—	2	1	no	—
1118	C₃	—	2	1	no	—
1119	C₃	—	3	1	no	—
1120	C₃	—	3	1	no	—
1121	C₃	—	3	1	no	—
1122	C₃	—	6	1	no	—
1123	C₃	—	6	1	no	—
1124	C₃	—	6	1	no	—
1125	C₃	—	9	1	no	—
1126	C₃	—	9	1	no	—
1127	C₃	—	9	1	no	—
1128	C₃	—	9	1	no	—
1129	C₃	—	18	1	no	—
1130	C₃	—	18	1	no	—
1131	C₃	—	18	1	no	—
1132	C₃	—	18	1	no	—
1133	C₃	—	18	1	no	—
1134	C₃	D₃×C₉×H(3,𝔽₃)	1	1	yes	characteristic
1135	C₃	C₃×C₉×AGL(1,ℤ/9)	1	1	yes	characteristic
1136	C₃	C₃×D₉⋊H(3,𝔽₃)	1	1	yes	characteristic
1137	C₃	#13091462	1	1	yes	characteristic
1138	C₃	#13091462	1	1	yes	characteristic
1139	C₂	—	9	1	no	Sylow

	subgroup	G/H
center	C₃×C₉	C₃×AGL(1,ℤ/9)
commutator	C₃×C₉	C₂×C₃²×C₉
Frattini, socle	C₃³	C₃³×D₃
Fitting	C₉×C₉⋊H(3,𝔽₃)	C₂
prime radical	C₃×D₉⋊H(3,𝔽₃)	C₃
cosocle	C₃²×C₉	C₂×C₃³
hypercenter	C₃²×C₉	AGL(1,ℤ/9)
hypocenter	C₉	C₂×C₉×H(3,𝔽₃)
LCS	G ▷ C₃×C₉ ▷ C₉
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. C₉×C₉⋊H(3,𝔽₃)	C₂	semidirect
3. C₃×C₉×AGL(1,ℤ/9)	C₃	semidirect
4. C₃×C₉×AGL(1,ℤ/9)	C₃	semidirect
5. C₃×C₉×AGL(1,ℤ/9)	C₃	semidirect
7. C₃²×C₉×D₉	C₃	semidirect
8. (C₃×AGL(1,ℤ/9))⋊C₉	C₃	semidirect
9. (C₃×AGL(1,ℤ/9))⋊C₉	C₃	semidirect
10. (C₃×AGL(1,ℤ/9))⋊C₉	C₃	semidirect
11. (C₃×AGL(1,ℤ/9))⋊C₉	C₃	semidirect
12. (C₃×AGL(1,ℤ/9))⋊C₉	C₃	semidirect
13. (C₃×AGL(1,ℤ/9))⋊C₉	C₃	semidirect
14. #13090623	C₃	semidirect
15. #13090623	C₃	semidirect
17. C₃×C₉×3₋¹⁺²	C₂×C₃	semidirect
18. C₃×C₉×3₋¹⁺²	C₂×C₃	semidirect
19. C₃×C₉×3₋¹⁺²	C₂×C₃	semidirect
21. C₃²×C₉²	C₂×C₃	semidirect
22. #10624560	C₂×C₃	semidirect
23. #10624560	C₂×C₃	semidirect
24. #10624560	C₂×C₃	semidirect
25. #10624560	C₂×C₃	semidirect
26. #10624560	C₂×C₃	semidirect
27. #10624560	C₂×C₃	semidirect
37. #10624548	C₂×C₃	semidirect
38. #10624548	C₂×C₃	semidirect
53. D₉⋊H(3,𝔽₃)	C₉	direct (N × H)
54. D₉⋊H(3,𝔽₃)	C₉	direct (N × H)
55. D₉⋊H(3,𝔽₃)	C₉	direct (N × H)
56. D₉⋊H(3,𝔽₃)	C₉	direct (N × H)
57. D₉⋊H(3,𝔽₃)	C₉	direct (N × H)
58. D₉⋊H(3,𝔽₃)	C₉	direct (N × H)
59. D₉⋊H(3,𝔽₃)	C₉	direct (N × H)
60. D₉⋊H(3,𝔽₃)	C₉	direct (N × H)
61. D₉⋊H(3,𝔽₃)	C₉	direct (N × H)
110. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
111. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
112. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
113. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
114. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
115. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
116. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
117. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
118. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
234. C₃×AGL(1,ℤ/9)	C₃×C₉	semidirect
235. C₃×AGL(1,ℤ/9)	C₃×C₉	semidirect
236. C₃×AGL(1,ℤ/9)	C₃×C₉	semidirect
237. C₃×AGL(1,ℤ/9)	C₃×C₉	semidirect
238. C₃×AGL(1,ℤ/9)	C₃×C₉	semidirect
239. C₃×AGL(1,ℤ/9)	C₃×C₉	semidirect
240. C₃×AGL(1,ℤ/9)	C₃×C₉	semidirect
241. C₃×AGL(1,ℤ/9)	C₃×C₉	semidirect
242. C₃×AGL(1,ℤ/9)	C₃×C₉	semidirect
276. C₃²×D₉	C₃×C₉	semidirect
277. C₃²×D₉	C₃×C₉	semidirect
278. C₃²×D₉	C₃×C₉	semidirect
296. C₉×D₉	H(3,𝔽₃)	semidirect
297. C₉×D₉	H(3,𝔽₃)	semidirect
298. C₉×D₉	H(3,𝔽₃)	semidirect
330. C₃×3₋¹⁺²	C₂×C₃×C₉	semidirect
331. C₃×3₋¹⁺²	C₂×C₃×C₉	semidirect
332. C₃×3₋¹⁺²	C₂×C₃×C₉	semidirect
333. C₃×3₋¹⁺²	C₂×C₃×C₉	semidirect
334. C₃×3₋¹⁺²	C₂×C₃×C₉	semidirect
335. C₃×3₋¹⁺²	C₂×C₃×C₉	semidirect
336. C₃×3₋¹⁺²	C₂×C₃×C₉	semidirect
337. C₃×3₋¹⁺²	C₂×C₃×C₉	semidirect
338. C₃×3₋¹⁺²	C₂×C₃×C₉	semidirect
417. C₃²×C₉	AGL(1,ℤ/9)	semidirect
418. C₃²×C₉	C₂×C₃×C₉	semidirect
419. C₃²×C₉	C₂×C₃×C₉	semidirect
420. C₃²×C₉	C₂×C₃×C₉	semidirect
559. C₉²	C₂×H(3,𝔽₃)	semidirect
560. C₉²	C₂×H(3,𝔽₃)	semidirect
561. C₉²	C₂×H(3,𝔽₃)	semidirect
972. D₉	C₉×H(3,𝔽₃)	semidirect
1046. C₃²	C₉×AGL(1,ℤ/9)	semidirect
1047. C₃²	C₉×AGL(1,ℤ/9)	semidirect
1048. C₃²	C₉×AGL(1,ℤ/9)	semidirect
1094. C₉	D₉⋊H(3,𝔽₃)	direct (N × H)
1095. C₉	D₉⋊H(3,𝔽₃)	direct (N × H)
1096. C₉	D₉⋊H(3,𝔽₃)	direct (N × H)
1097. C₉	C₂×C₉×H(3,𝔽₃)	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₉⋊H(3,𝔽₃)	2
C₃×D₉⋊H(3,𝔽₃)	3
C₃×C₉×AGL(1,ℤ/9)	3
D₃×C₉×H(3,𝔽₃)	3
C₃²×C₉×D₉	3
(C₃×AGL(1,ℤ/9))⋊C₉	3
#13090623	3

Subgroups — C9×D9⋊H(3,𝔽3) #72243807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×D₉⋊H(3,𝔽₃) #72243807