Subgroups — #72243839

Order 4374.

928 conjugacy classes of subgroups.

The subgroup lattice has 883 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14552197	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×#92264	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×#92264	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×#92264	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃×D₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
6	D₃×C₉⋊H(3,𝔽₃)	—	3	1	no	maximal
7	C₃²×D₉⋊C₉	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	D₉×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
16	C₃×#6896	C₂×C₃	1	1	yes	characteristic, complemented
17	C₃×#6896	C₂×C₃	1	1	yes	characteristic, complemented
18	C₃×#6896	C₂×C₃	1	1	yes	characteristic, complemented
19	C₃×C₉⋊H(3,𝔽₃)	D₃	1	1	yes	characteristic
20	C₃×C₉⋊H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
21	C₃²×C₉⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
22	#10624566	—	2	1	no	—
23	#10624566	—	2	1	no	—
24	#10624566	—	2	1	no	—
25	#10624566	—	2	1	no	—
26	#10624566	—	2	1	no	—
27	#10624566	—	2	1	no	—
28	#10624565	—	2	1	no	—
29	#10624565	—	2	1	no	—
30	#10624565	—	2	1	no	—
31	#10624560	C₂×C₃	1	1	yes	characteristic, complemented
32	#10624560	C₂×C₃	1	1	yes	characteristic, complemented
33	#10624560	C₂×C₃	1	1	yes	characteristic, complemented
34	#10624560	C₂×C₃	1	1	yes	characteristic, complemented
35	#10624560	C₂×C₃	1	1	yes	characteristic, complemented
36	#10624560	C₂×C₃	1	1	yes	characteristic, complemented
37	#10624556	—	2	1	no	—
38	#10624556	—	2	1	no	—
39	#10624555	—	2	1	no	—
40	#10624548	—	2	1	no	—
41	#10624548	C₂×C₃	1	1	yes	characteristic, complemented
42	C₉×C₃²⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
43	C₃×D₃×3₋¹⁺²	—	3	1	no	—
44	C₃×D₃×3₋¹⁺²	—	3	1	no	—
45	C₃×D₃×3₋¹⁺²	—	3	1	no	—
46	C₃²×AGL(1,ℤ/9)	C₃²	1	1	yes	characteristic
47	C₃²×AGL(1,ℤ/9)	C₃²	1	1	yes	characteristic
48	C₃²×AGL(1,ℤ/9)	C₃²	1	1	yes	characteristic
49	C₃×D₃×H(3,𝔽₃)	—	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	#92264	—	3	1	no	—
54	#92264	—	3	1	no	—
55	#92264	—	3	1	no	—
56	#92264	—	3	1	no	—
57	#92264	—	3	1	no	—
58	#92264	—	3	1	no	—
59	#92264	—	3	1	no	—
60	#92264	—	3	1	no	—
61	#92264	—	3	1	no	—
62	D₉⋊H(3,𝔽₃)	—	3	1	no	—
63	D₉⋊H(3,𝔽₃)	—	3	2	no	—
64	C₃×D₉⋊C₉	—	3	1	no	—
65	C₃×D₉⋊C₉	—	3	1	no	—
66	C₃×D₉⋊C₉	—	3	1	no	—
67	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
68	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
69	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
70	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
71	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
72	C₃×D₉⋊C₉	C₃²	1	1	yes	characteristic
73	D₃×C₃²⋊C₉	—	3	1	no	—
74	D₃×C₃²⋊C₉	—	3	1	no	—
75	D₃×C₃²⋊C₉	—	3	1	no	—
76	D₃×C₃²⋊C₉	—	3	1	no	—
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	C₃×C₉×D₉	C₃²	1	1	yes	characteristic
82	C₃×C₉×D₉	C₃²	1	1	yes	characteristic
83	C₃×C₉×D₉	C₃²	1	1	yes	characteristic
84	C₃²×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
85	C₃²×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
86	C₃²×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
87	C₃²×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
88	C₃²×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
89	C₃²×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
90	C₃²×H(3,𝔽₃)	C₃×D₃	1	1	yes	characteristic
91	C₃³×C₉	—	2	1	no	—
92	C₃³×C₉	C₃×D₃	1	1	yes	characteristic
93	C₃³×C₉	C₂×C₃²	1	1	yes	characteristic
94	#6896	—	3	1	no	—
95	#6896	—	3	1	no	—
96	#6896	—	3	1	no	—
97	#6896	—	3	1	no	—
98	#6896	—	3	1	no	—
99	#6896	—	3	1	no	—
100	#6896	—	3	1	no	—
101	#6896	—	3	1	no	—
102	#6896	—	3	1	no	—
103	#6896	—	6	1	no	—
104	#6896	—	6	1	no	—
105	#6896	—	6	1	no	—
106	#6896	—	6	1	no	—
107	#6896	—	6	1	no	—
108	#6896	—	6	1	no	—
109	#6896	—	6	1	no	—
110	#6896	—	6	1	no	—
111	#6896	—	6	1	no	—
112	C₉⋊H(3,𝔽₃)	—	3	1	no	—
113	C₉⋊H(3,𝔽₃)	—	3	2	no	—
114	C₉⋊H(3,𝔽₃)	—	6	1	no	—
115	C₉⋊H(3,𝔽₃)	—	6	1	no	—
116	C₉⋊H(3,𝔽₃)	—	6	1	no	—
117	C₉⋊H(3,𝔽₃)	—	6	1	no	—
118	C₉⋊H(3,𝔽₃)	—	6	1	no	—
119	C₉⋊H(3,𝔽₃)	—	6	1	no	—
120	C₉⋊H(3,𝔽₃)	—	6	2	no	—
121	C₃×C₉⋊C₉	—	2	1	no	—
122	C₃×C₉⋊C₉	—	2	1	no	—
123	C₃×C₉⋊C₉	—	2	1	no	—
124	C₃×C₉⋊C₉	—	2	1	no	—
125	C₃×C₉⋊C₉	—	2	1	no	—
126	C₃×C₉⋊C₉	—	2	1	no	—
127	C₃×C₉⋊C₉	—	2	1	no	—
128	C₃×C₉⋊C₉	—	2	1	no	—
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	—	3	1	no	—
134	C₃×C₉⋊C₉	—	3	1	no	—
135	C₃×C₉⋊C₉	—	3	1	no	—
136	C₃×C₉⋊C₉	—	6	1	no	—
137	C₃×C₉⋊C₉	—	6	1	no	—
138	C₃×C₉⋊C₉	—	6	1	no	—
139	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
140	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
141	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
142	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
143	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
144	C₃×C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
145	C₃×C₃²⋊C₉	—	2	1	no	—
146	C₃×C₃²⋊C₉	—	2	1	no	—
147	C₃×C₃²⋊C₉	—	2	1	no	—
148	C₃×C₃²⋊C₉	—	2	1	no	—
149	C₃×C₃²⋊C₉	—	2	1	no	—
150	C₃×C₃²⋊C₉	—	2	1	no	—
151	C₃×C₃²⋊C₉	—	2	1	no	—
152	C₃×C₃²⋊C₉	—	2	1	no	—
153	C₃×C₃²⋊C₉	—	2	1	no	—
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	C₃×D₃	1	1	yes	characteristic
161	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
162	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
163	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
164	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
165	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
166	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
167	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
168	C₃×C₉²	C₂×C₃²	1	1	yes	characteristic
169	C₃×C₉²	C₂×C₃²	1	1	yes	characteristic
170	C₃×C₉²	C₂×C₃²	1	1	yes	characteristic
171	#6855	—	2	1	no	—
172	#6855	—	2	1	no	—
173	#6855	—	2	1	no	—
174	#6855	—	2	1	no	—
175	#6855	—	2	1	no	—
176	#6855	—	2	1	no	—
177	#6855	—	2	1	no	—
178	#6855	—	2	1	no	—
179	#6855	—	2	1	no	—
180	#6855	—	2	1	no	—
181	#6855	—	2	1	no	—
182	#6855	—	2	1	no	—
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	C₃³×D₃	—	3	1	no	—
196	C₃³×D₃	—	3	1	no	—
197	C₃³×D₃	—	3	1	no	—
198	C₃³×D₃	—	3	1	no	—
199	C₂×C₃×3₋¹⁺²	—	9	1	no	—
200	C₂×C₃×3₋¹⁺²	—	9	1	no	—
201	C₂×C₃×3₋¹⁺²	—	9	1	no	—
202	C₂×C₃×H(3,𝔽₃)	—	9	1	no	—
203	C₂×C₃²×C₉	—	9	1	no	—
204	D₃×3₋¹⁺²	—	9	1	no	—
205	D₃×3₋¹⁺²	—	9	1	no	—
206	D₃×3₋¹⁺²	—	9	1	no	—
207	D₃×3₋¹⁺²	—	9	1	no	—
208	D₃×3₋¹⁺²	—	9	1	no	—
209	D₃×3₋¹⁺²	—	9	1	no	—
210	D₃×3₋¹⁺²	—	9	1	no	—
211	D₃×3₋¹⁺²	—	9	1	no	—
212	D₃×3₋¹⁺²	—	9	1	no	—
213	C₃×AGL(1,ℤ/9)	—	3	1	no	—
214	C₃×AGL(1,ℤ/9)	—	3	1	no	—
215	C₃×AGL(1,ℤ/9)	—	3	1	no	—
216	C₃×AGL(1,ℤ/9)	—	3	1	no	—
217	C₃×AGL(1,ℤ/9)	—	3	1	no	—
218	C₃×AGL(1,ℤ/9)	—	3	1	no	—
219	C₃×AGL(1,ℤ/9)	—	3	1	no	—
220	C₃×AGL(1,ℤ/9)	—	3	1	no	—
221	C₃×AGL(1,ℤ/9)	—	3	1	no	—
222	C₃×AGL(1,ℤ/9)	—	3	1	no	—
223	C₃×AGL(1,ℤ/9)	—	3	1	no	—
224	C₃×AGL(1,ℤ/9)	—	3	1	no	—
225	D₃×H(3,𝔽₃)	—	9	1	no	—
226	D₃×H(3,𝔽₃)	—	9	2	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	—	9	1	no	—
237	C₃×D₃×C₉	—	9	1	no	—
238	C₃×D₃×C₉	—	9	1	no	—
239	C₃²×D₉	—	3	1	no	—
240	C₃²×D₉	—	3	1	no	—
241	C₃²×D₉	—	3	1	no	—
242	C₃²×D₉	3₋¹⁺²	1	1	yes	characteristic, complemented
243	C₃²×D₉	3₋¹⁺²	1	2	yes	complemented
244	C₃²×D₉	C₃³	1	1	yes	characteristic
245	C₂×C₃²⋊C₉	—	9	1	no	—
246	C₂×C₃²⋊C₉	—	9	1	no	—
247	C₂×C₃²⋊C₉	—	9	1	no	—
248	C₂×C₃²⋊C₉	—	9	1	no	—
249	C₂×C₃²⋊C₉	—	9	1	no	—
250	C₂×C₃²⋊C₉	—	9	1	no	—
251	C₂×C₃²⋊C₉	—	9	1	no	—
252	C₂×C₃²⋊C₉	—	9	1	no	—
253	D₉⋊C₉	—	3	1	no	—
254	D₉⋊C₉	—	3	1	no	—
255	D₉⋊C₉	—	3	1	no	—
256	D₉⋊C₉	—	3	1	no	—
257	D₉⋊C₉	—	3	1	no	—
258	D₉⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic, complemented
259	D₉⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic, complemented
260	D₉⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic, complemented
261	C₉×D₉	—	3	1	no	—
262	C₉×D₉	—	3	1	no	—
263	C₉×D₉	—	3	1	no	—
264	C₃⁴	C₃²×D₃	1	1	yes	characteristic
265	C₃⁴	C₃²×D₃	1	1	yes	characteristic
266	C₃⁴	C₃²×D₃	1	1	yes	characteristic
267	C₃⁴	C₃²×D₃	1	1	yes	characteristic
268	C₃×3₋¹⁺²	—	3	1	no	—
269	C₃×3₋¹⁺²	—	3	1	no	—
270	C₃×3₋¹⁺²	—	3	1	no	—
271	C₃×3₋¹⁺²	—	3	1	no	—
272	C₃×3₋¹⁺²	—	3	1	no	—
273	C₃×3₋¹⁺²	—	3	1	no	—
274	C₃×3₋¹⁺²	—	3	1	no	—
275	C₃×3₋¹⁺²	—	3	1	no	—
276	C₃×3₋¹⁺²	—	3	1	no	—
277	C₃×3₋¹⁺²	—	3	1	no	—
278	C₃×3₋¹⁺²	—	3	1	no	—
279	C₃×3₋¹⁺²	—	3	1	no	—
280	C₃×3₋¹⁺²	—	3	1	no	—
281	C₃×3₋¹⁺²	—	3	1	no	—
282	C₃×3₋¹⁺²	—	3	1	no	—
283	C₃×3₋¹⁺²	—	3	1	no	—
284	C₃×3₋¹⁺²	—	3	1	no	—
285	C₃×3₋¹⁺²	—	3	1	no	—
286	C₃×3₋¹⁺²	—	3	1	no	—
287	C₃×3₋¹⁺²	—	3	1	no	—
288	C₃×3₋¹⁺²	—	3	1	no	—
289	C₃×3₋¹⁺²	—	3	1	no	—
290	C₃×3₋¹⁺²	—	3	1	no	—
291	C₃×3₋¹⁺²	—	3	1	no	—
292	C₃×3₋¹⁺²	—	6	1	no	—
293	C₃×3₋¹⁺²	—	6	1	no	—
294	C₃×3₋¹⁺²	—	6	1	no	—
295	C₃×3₋¹⁺²	—	6	1	no	—
296	C₃×3₋¹⁺²	—	6	1	no	—
297	C₃×3₋¹⁺²	—	6	1	no	—
298	C₃×3₋¹⁺²	—	6	1	no	—
299	C₃×3₋¹⁺²	—	6	1	no	—
300	C₃×3₋¹⁺²	—	6	1	no	—
301	C₃×3₋¹⁺²	—	6	1	no	—
302	C₃×3₋¹⁺²	—	6	1	no	—
303	C₃×3₋¹⁺²	—	6	1	no	—
304	C₃×3₋¹⁺²	—	6	1	no	—
305	C₃×3₋¹⁺²	—	6	1	no	—
306	C₃×3₋¹⁺²	—	6	1	no	—
307	C₃×3₋¹⁺²	—	18	1	no	—
308	C₃×3₋¹⁺²	—	18	1	no	—
309	C₃×3₋¹⁺²	—	18	1	no	—
310	C₃×H(3,𝔽₃)	—	3	1	no	—
311	C₃×H(3,𝔽₃)	—	3	1	no	—
312	C₃×H(3,𝔽₃)	—	3	2	no	—
313	C₃×H(3,𝔽₃)	—	6	1	no	—
314	C₃×H(3,𝔽₃)	—	6	1	no	—
315	C₃×H(3,𝔽₃)	—	6	2	no	—
316	C₃²×C₉	—	2	1	no	—
317	C₃²×C₉	—	2	2	no	—
318	C₃²×C₉	—	2	1	no	—
319	C₃²×C₉	—	2	1	no	—
320	C₃²×C₉	—	2	1	no	—
321	C₃²×C₉	—	2	1	no	—
322	C₃²×C₉	—	2	1	no	—
323	C₃²×C₉	—	2	1	no	—
324	C₃²×C₉	—	2	1	no	—
325	C₃²×C₉	—	2	1	no	—
326	C₃²×C₉	—	2	1	no	—
327	C₃²×C₉	—	2	1	no	—
328	C₃²×C₉	—	2	1	no	—
329	C₃²×C₉	—	2	1	no	—
330	C₃²×C₉	—	2	1	no	—
331	C₃²×C₉	—	3	1	no	—
332	C₃²×C₉	—	3	1	no	—
333	C₃²×C₉	—	3	1	no	—
334	C₃²×C₉	—	3	1	no	—
335	C₃²×C₉	—	3	1	no	—
336	C₃²×C₉	—	3	1	no	—
337	C₃²×C₉	—	3	1	no	—
338	C₃²×C₉	—	6	1	no	—
339	C₃²×C₉	—	6	1	no	—
340	C₃²×C₉	—	6	1	no	—
341	C₃²×C₉	—	6	1	no	—
342	C₃²×C₉	—	6	1	no	—
343	C₃²×C₉	—	6	1	no	—
344	C₃²×C₉	—	6	1	no	—
345	C₃²×C₉	—	6	1	no	—
346	C₃²×C₉	—	6	2	no	—
347	C₃²×C₉	—	18	1	no	—
348	C₃²×C₉	—	18	1	no	—
349	C₃²×C₉	—	18	1	no	—
350	C₃²×C₉	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented
351	C₃²×C₉	C₂×3₋¹⁺²	1	2	yes	complemented
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	C₂×C₃³	1	1	yes	characteristic
362	C₉⋊C₉	—	2	1	no	—
363	C₉⋊C₉	—	2	1	no	—
364	C₉⋊C₉	—	2	1	no	—
365	C₉⋊C₉	—	3	1	no	—
366	C₉⋊C₉	—	3	1	no	—
367	C₉⋊C₉	—	3	1	no	—
368	C₉⋊C₉	—	3	1	no	—
369	C₉⋊C₉	—	3	1	no	—
370	C₉⋊C₉	—	6	1	no	—
371	C₉⋊C₉	—	6	1	no	—
372	C₉⋊C₉	—	6	1	no	—
373	C₉⋊C₉	—	6	1	no	—
374	C₉⋊C₉	—	6	1	no	—
375	C₉⋊C₉	—	6	1	no	—
376	C₉⋊C₉	—	6	1	no	—
377	C₉⋊C₉	—	6	1	no	—
378	C₉⋊C₉	—	6	1	no	—
379	C₉⋊C₉	—	6	1	no	—
380	C₉⋊C₉	—	6	1	no	—
381	C₉⋊C₉	—	6	1	no	—
382	C₉⋊C₉	—	6	1	no	—
383	C₉⋊C₉	—	6	1	no	—
384	C₉⋊C₉	—	6	1	no	—
385	C₉⋊C₉	—	6	1	no	—
386	C₉⋊C₉	—	6	1	no	—
387	C₉⋊C₉	—	6	1	no	—
388	C₉⋊C₉	—	6	1	no	—
389	C₉⋊C₉	—	6	1	no	—
390	C₉⋊C₉	—	6	1	no	—
391	C₉⋊C₉	—	6	1	no	—
392	C₉⋊C₉	—	6	1	no	—
393	C₉⋊C₉	—	6	1	no	—
394	C₉⋊C₉	—	6	1	no	—
395	C₉⋊C₉	—	6	1	no	—
396	C₉⋊C₉	—	6	1	no	—
397	C₉⋊C₉	—	6	1	no	—
398	C₉⋊C₉	—	6	1	no	—
399	C₉⋊C₉	—	6	1	no	—
400	C₉⋊C₉	—	6	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	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
412	C₉⋊C₉	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
413	C₉⋊C₉	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
414	C₃²⋊C₉	—	2	1	no	—
415	C₃²⋊C₉	—	2	1	no	—
416	C₃²⋊C₉	—	2	1	no	—
417	C₃²⋊C₉	—	2	1	no	—
418	C₃²⋊C₉	—	3	1	no	—
419	C₃²⋊C₉	—	3	1	no	—
420	C₃²⋊C₉	—	6	1	no	—
421	C₃²⋊C₉	—	6	1	no	—
422	C₃²⋊C₉	—	6	1	no	—
423	C₃²⋊C₉	—	6	1	no	—
424	C₃²⋊C₉	—	6	2	no	—
425	C₃²⋊C₉	—	6	1	no	—
426	C₃²⋊C₉	—	6	2	no	—
427	C₃²⋊C₉	—	6	1	no	—
428	C₃²⋊C₉	—	6	2	no	—
429	C₃²⋊C₉	—	6	1	no	—
430	C₃²⋊C₉	—	6	1	no	—
431	C₃²⋊C₉	—	6	1	no	—
432	C₃²⋊C₉	—	6	1	no	—
433	C₃²⋊C₉	—	6	1	no	—
434	C₃²⋊C₉	—	6	1	no	—
435	C₃²⋊C₉	—	6	1	no	—
436	C₃²⋊C₉	—	6	1	no	—
437	C₃²⋊C₉	—	6	1	no	—
438	C₃²⋊C₉	—	6	1	no	—
439	C₃²⋊C₉	—	6	1	no	—
440	C₃²⋊C₉	—	6	1	no	—
441	C₃²⋊C₉	—	6	1	no	—
442	C₃²⋊C₉	—	6	1	no	—
443	C₃²⋊C₉	—	6	1	no	—
444	C₃²⋊C₉	—	6	1	no	—
445	C₃²⋊C₉	—	6	2	no	—
446	C₃²⋊C₉	—	6	1	no	—
447	C₃²⋊C₉	—	6	2	no	—
448	C₃²⋊C₉	—	6	1	no	—
449	C₃²⋊C₉	—	6	1	no	—
450	C₃²⋊C₉	—	6	1	no	—
451	C₃²⋊C₉	—	6	2	no	—
452	C₃²⋊C₉	—	6	1	no	—
453	C₃²⋊C₉	—	18	1	no	—
454	C₃²⋊C₉	—	18	1	no	—
455	C₃²⋊C₉	—	18	1	no	—
456	C₃²⋊C₉	—	18	1	no	—
457	C₃²⋊C₉	—	18	1	no	—
458	C₃²⋊C₉	—	18	1	no	—
459	C₃²⋊C₉	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
460	C₉²	—	3	1	no	—
461	C₉²	—	3	1	no	—
462	C₉²	—	3	1	no	—
463	C₉²	—	6	1	no	—
464	C₉²	—	6	1	no	—
465	C₉²	—	6	1	no	—
466	C₂×C₃³	—	9	1	no	—
467	C₂×C₃³	—	9	1	no	—
468	C₂×C₃³	—	9	1	no	—
469	C₂×C₃³	—	9	1	no	—
470	C₃²×D₃	—	3	1	no	—
471	C₃²×D₃	—	3	1	no	—
472	C₃²×D₃	—	3	2	no	—
473	C₃²×D₃	—	9	1	no	—
474	C₃²×D₃	—	9	1	no	—
475	C₃²×D₃	—	9	1	no	—
476	C₃²×D₃	—	9	1	no	—
477	C₃²×D₃	—	9	1	no	—
478	C₃²×D₃	—	9	1	no	—
479	C₃²×D₃	—	9	1	no	—
480	C₃²×D₃	—	9	1	no	—
481	C₃²×D₃	—	9	1	no	—
482	C₃²×D₃	—	9	1	no	—
483	C₃²×D₃	—	9	1	no	—
484	C₃²×D₃	—	9	1	no	—
485	C₃²×D₃	—	9	1	no	—
486	C₃²×D₃	—	9	1	no	—
487	C₃²×D₃	—	9	1	no	—
488	C₂×3₋¹⁺²	—	27	1	no	—
489	C₂×3₋¹⁺²	—	27	1	no	—
490	C₂×3₋¹⁺²	—	27	1	no	—
491	C₂×3₋¹⁺²	—	27	1	no	—
492	C₂×3₋¹⁺²	—	27	1	no	—
493	C₂×3₋¹⁺²	—	27	1	no	—
494	C₂×3₋¹⁺²	—	27	1	no	—
495	C₂×3₋¹⁺²	—	27	1	no	—
496	C₂×3₋¹⁺²	—	27	1	no	—
497	C₂×H(3,𝔽₃)	—	27	1	no	—
498	C₂×H(3,𝔽₃)	—	27	2	no	—
499	C₂×C₃×C₉	—	9	1	no	—
500	C₂×C₃×C₉	—	9	1	no	—
501	C₂×C₃×C₉	—	9	1	no	—
502	C₂×C₃×C₉	—	9	1	no	—
503	C₂×C₃×C₉	—	9	1	no	—
504	C₂×C₃×C₉	—	9	1	no	—
505	C₂×C₃×C₉	—	9	1	no	—
506	C₂×C₃×C₉	—	9	1	no	—
507	C₂×C₃×C₉	—	9	1	no	—
508	C₂×C₃×C₉	—	27	1	no	—
509	C₂×C₃×C₉	—	27	1	no	—
510	C₂×C₃×C₉	—	27	1	no	—
511	AGL(1,ℤ/9)	—	9	1	no	—
512	AGL(1,ℤ/9)	—	9	1	no	—
513	AGL(1,ℤ/9)	—	9	1	no	—
514	D₃×C₉	—	3	1	no	—
515	D₃×C₉	—	3	1	no	—
516	D₃×C₉	—	3	1	no	—
517	D₃×C₉	—	9	1	no	—
518	D₃×C₉	—	9	1	no	—
519	D₃×C₉	—	9	1	no	—
520	D₃×C₉	—	9	1	no	—
521	D₃×C₉	—	9	1	no	—
522	D₃×C₉	—	9	1	no	—
523	D₃×C₉	—	9	1	no	—
524	D₃×C₉	—	9	1	no	—
525	C₃×D₉	—	3	1	no	—
526	C₃×D₉	—	3	2	no	—
527	C₃×D₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
528	C₃×D₉	C₃×3₋¹⁺²	1	1	yes	characteristic
529	C₃×D₉	#737	1	1	yes	characteristic
530	C₃×D₉	#737	1	1	yes	characteristic
531	C₃³	—	2	1	no	—
532	C₃³	—	2	2	no	—
533	C₃³	—	2	1	no	—
534	C₃³	—	3	1	no	—
535	C₃³	—	3	1	no	—
536	C₃³	—	3	1	no	—
537	C₃³	—	3	1	no	—
538	C₃³	—	3	1	no	—
539	C₃³	—	3	1	no	—
540	C₃³	—	3	1	no	—
541	C₃³	—	3	1	no	—
542	C₃³	—	3	1	no	—
543	C₃³	—	3	1	no	—
544	C₃³	—	3	1	no	—
545	C₃³	—	3	1	no	—
546	C₃³	—	3	1	no	—
547	C₃³	—	3	1	no	—
548	C₃³	—	3	1	no	—
549	C₃³	—	3	1	no	—
550	C₃³	—	6	1	no	—
551	C₃³	—	6	1	no	—
552	C₃³	—	6	1	no	—
553	C₃³	—	6	1	no	—
554	C₃³	—	6	1	no	—
555	C₃³	—	6	1	no	—
556	C₃³	—	6	1	no	—
557	C₃³	—	6	1	no	—
558	C₃³	—	6	1	no	—
559	C₃³	—	6	1	no	—
560	C₃³	—	6	1	no	—
561	C₃³	—	6	1	no	—
562	C₃³	—	6	1	no	—
563	C₃³	—	6	1	no	—
564	C₃³	—	6	1	no	—
565	C₃³	—	6	1	no	—
566	C₃³	—	6	1	no	—
567	C₃³	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
568	C₃³	D₃×3₋¹⁺²	1	1	yes	characteristic
569	C₃³	D₃×3₋¹⁺²	1	2	yes	—
570	C₃³	C₃³×D₃	1	1	yes	characteristic
571	3₋¹⁺²	—	9	1	no	—
572	3₋¹⁺²	—	9	1	no	—
573	3₋¹⁺²	—	9	1	no	—
574	3₋¹⁺²	—	9	1	no	—
575	3₋¹⁺²	—	9	1	no	—
576	3₋¹⁺²	—	18	1	no	—
577	3₋¹⁺²	—	18	1	no	—
578	3₋¹⁺²	—	18	1	no	—
579	3₋¹⁺²	—	18	1	no	—
580	3₋¹⁺²	—	18	1	no	—
581	3₋¹⁺²	—	18	1	no	—
582	3₋¹⁺²	—	18	1	no	—
583	3₋¹⁺²	—	18	1	no	—
584	3₋¹⁺²	—	18	1	no	—
585	3₋¹⁺²	—	18	1	no	—
586	3₋¹⁺²	—	18	1	no	—
587	3₋¹⁺²	—	18	1	no	—
588	3₋¹⁺²	—	18	1	no	—
589	3₋¹⁺²	—	18	1	no	—
590	3₋¹⁺²	—	18	1	no	—
591	3₋¹⁺²	—	18	1	no	—
592	3₋¹⁺²	—	18	1	no	—
593	3₋¹⁺²	—	18	1	no	—
594	3₋¹⁺²	—	18	1	no	—
595	3₋¹⁺²	—	18	1	no	—
596	3₋¹⁺²	—	18	1	no	—
597	3₋¹⁺²	—	18	1	no	—
598	3₋¹⁺²	—	18	1	no	—
599	3₋¹⁺²	—	18	1	no	—
600	3₋¹⁺²	—	18	1	no	—
601	3₋¹⁺²	—	18	1	no	—
602	3₋¹⁺²	—	18	1	no	—
603	3₋¹⁺²	—	18	1	no	—
604	H(3,𝔽₃)	—	9	1	no	—
605	H(3,𝔽₃)	—	18	1	no	—
606	H(3,𝔽₃)	—	18	2	no	—
607	H(3,𝔽₃)	—	18	2	no	—
608	C₃×C₉	—	2	1	no	—
609	C₃×C₉	—	2	1	no	—
610	C₃×C₉	—	2	1	no	—
611	C₃×C₉	—	2	1	no	—
612	C₃×C₉	—	2	1	no	—
613	C₃×C₉	—	2	1	no	—
614	C₃×C₉	—	2	1	no	—
615	C₃×C₉	—	2	1	no	—
616	C₃×C₉	—	2	1	no	—
617	C₃×C₉	—	2	1	no	—
618	C₃×C₉	—	2	1	no	—
619	C₃×C₉	—	2	2	no	—
620	C₃×C₉	—	3	1	no	—
621	C₃×C₉	—	3	1	no	—
622	C₃×C₉	—	3	1	no	—
623	C₃×C₉	—	3	1	no	—
624	C₃×C₉	—	3	1	no	—
625	C₃×C₉	—	3	2	no	—
626	C₃×C₉	—	3	1	no	—
627	C₃×C₉	—	3	1	no	—
628	C₃×C₉	—	3	1	no	—
629	C₃×C₉	—	3	1	no	—
630	C₃×C₉	—	3	1	no	—
631	C₃×C₉	—	3	1	no	—
632	C₃×C₉	—	6	1	no	—
633	C₃×C₉	—	6	2	no	—
634	C₃×C₉	—	6	1	no	—
635	C₃×C₉	—	6	1	no	—
636	C₃×C₉	—	6	2	no	—
637	C₃×C₉	—	6	2	no	—
638	C₃×C₉	—	6	1	no	—
639	C₃×C₉	—	6	2	no	—
640	C₃×C₉	—	6	1	no	—
641	C₃×C₉	—	6	1	no	—
642	C₃×C₉	—	6	1	no	—
643	C₃×C₉	—	6	1	no	—
644	C₃×C₉	—	6	1	no	—
645	C₃×C₉	—	6	1	no	—
646	C₃×C₉	—	6	1	no	—
647	C₃×C₉	—	6	1	no	—
648	C₃×C₉	—	6	1	no	—
649	C₃×C₉	—	6	1	no	—
650	C₃×C₉	—	6	1	no	—
651	C₃×C₉	—	6	1	no	—
652	C₃×C₉	—	6	1	no	—
653	C₃×C₉	—	6	1	no	—
654	C₃×C₉	—	6	1	no	—
655	C₃×C₉	—	6	1	no	—
656	C₃×C₉	—	6	1	no	—
657	C₃×C₉	—	6	1	no	—
658	C₃×C₉	—	6	1	no	—
659	C₃×C₉	—	6	1	no	—
660	C₃×C₉	—	6	1	no	—
661	C₃×C₉	—	6	1	no	—
662	C₃×C₉	—	6	1	no	—
663	C₃×C₉	—	6	1	no	—
664	C₃×C₉	—	6	1	no	—
665	C₃×C₉	—	6	1	no	—
666	C₃×C₉	—	6	1	no	—
667	C₃×C₉	—	6	1	no	—
668	C₃×C₉	—	6	1	no	—
669	C₃×C₉	—	6	1	no	—
670	C₃×C₉	—	6	1	no	—
671	C₃×C₉	—	6	1	no	—
672	C₃×C₉	—	6	1	no	—
673	C₃×C₉	—	6	1	no	—
674	C₃×C₉	—	6	1	no	—
675	C₃×C₉	—	6	1	no	—
676	C₃×C₉	—	6	1	no	—
677	C₃×C₉	—	6	1	no	—
678	C₃×C₉	—	6	1	no	—
679	C₃×C₉	—	6	1	no	—
680	C₃×C₉	—	6	1	no	—
681	C₃×C₉	—	6	1	no	—
682	C₃×C₉	—	6	1	no	—
683	C₃×C₉	—	6	1	no	—
684	C₃×C₉	—	6	1	no	—
685	C₃×C₉	—	6	1	no	—
686	C₃×C₉	—	6	1	no	—
687	C₃×C₉	—	6	1	no	—
688	C₃×C₉	—	6	1	no	—
689	C₃×C₉	—	6	1	no	—
690	C₃×C₉	—	6	1	no	—
691	C₃×C₉	—	6	1	no	—
692	C₃×C₉	—	6	1	no	—
693	C₃×C₉	—	6	1	no	—
694	C₃×C₉	—	6	1	no	—
695	C₃×C₉	—	6	1	no	—
696	C₃×C₉	—	6	1	no	—
697	C₃×C₉	—	6	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	—	9	1	no	—
704	C₃×C₉	—	18	1	no	—
705	C₃×C₉	—	18	1	no	—
706	C₃×C₉	—	18	1	no	—
707	C₃×C₉	—	18	1	no	—
708	C₃×C₉	—	18	1	no	—
709	C₃×C₉	—	18	1	no	—
710	C₃×C₉	—	18	1	no	—
711	C₃×C₉	—	18	1	no	—
712	C₃×C₉	—	18	2	no	—
713	C₃×C₉	—	18	2	no	—
714	C₃×C₉	—	18	2	no	—
715	C₃×C₉	D₃×H(3,𝔽₃)	1	1	yes	characteristic
716	C₃×C₉	D₃×H(3,𝔽₃)	1	1	yes	characteristic
717	C₃×C₉	D₃×H(3,𝔽₃)	1	1	yes	characteristic
718	C₃×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
719	C₃×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
720	C₃×C₉	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic
721	C₃×C₉	C₂×C₃×H(3,𝔽₃)	1	1	yes	characteristic
722	C₃×C₉	C₂×C₃×3₋¹⁺²	1	1	yes	characteristic
723	C₃×C₉	C₂×#737	1	1	yes	characteristic
724	C₃×C₉	C₂×#737	1	1	yes	characteristic
725	C₂×C₃²	—	9	1	no	—
726	C₂×C₃²	—	9	1	no	—
727	C₂×C₃²	—	9	2	no	—
728	C₂×C₃²	—	27	1	no	—
729	C₂×C₃²	—	27	1	no	—
730	C₂×C₃²	—	27	1	no	—
731	C₂×C₃²	—	27	1	no	—
732	C₂×C₃²	—	27	1	no	—
733	C₂×C₃²	—	27	1	no	—
734	C₂×C₃²	—	27	1	no	—
735	C₂×C₃²	—	27	1	no	—
736	C₂×C₃²	—	27	1	no	—
737	C₂×C₃²	—	27	1	no	—
738	C₂×C₃²	—	27	1	no	—
739	C₂×C₃²	—	27	1	no	—
740	C₂×C₃²	—	27	1	no	—
741	C₂×C₃²	—	27	1	no	—
742	C₂×C₃²	—	27	1	no	—
743	C₃×D₃	—	3	1	no	—
744	C₃×D₃	—	3	1	no	—
745	C₃×D₃	—	3	1	no	—
746	C₃×D₃	—	3	1	no	—
747	C₃×D₃	—	9	1	no	—
748	C₃×D₃	—	9	2	no	—
749	C₃×D₃	—	27	1	no	—
750	C₃×D₃	—	27	1	no	—
751	C₃×D₃	—	27	1	no	—
752	C₂×C₉	—	9	1	no	—
753	C₂×C₉	—	9	1	no	—
754	C₂×C₉	—	9	1	no	—
755	C₂×C₉	—	27	1	no	—
756	C₂×C₉	—	27	1	no	—
757	C₂×C₉	—	27	1	no	—
758	C₂×C₉	—	27	1	no	—
759	C₂×C₉	—	27	1	no	—
760	C₂×C₉	—	27	1	no	—
761	C₂×C₉	—	27	1	no	—
762	C₂×C₉	—	27	1	no	—
763	D₉	C₉⋊H(3,𝔽₃)	1	1	yes	characteristic, complemented
764	C₃²	—	2	1	no	—
765	C₃²	—	2	1	no	—
766	C₃²	—	2	1	no	—
767	C₃²	—	2	1	no	—
768	C₃²	—	2	1	no	—
769	C₃²	—	2	2	no	—
770	C₃²	—	3	1	no	—
771	C₃²	—	3	1	no	—
772	C₃²	—	3	1	no	—
773	C₃²	—	3	1	no	—
774	C₃²	—	3	2	no	—
775	C₃²	—	6	1	no	—
776	C₃²	—	6	2	no	—
777	C₃²	—	6	1	no	—
778	C₃²	—	6	2	no	—
779	C₃²	—	6	1	no	—
780	C₃²	—	6	1	no	—
781	C₃²	—	6	2	no	—
782	C₃²	—	6	2	no	—
783	C₃²	—	6	1	no	—
784	C₃²	—	6	1	no	—
785	C₃²	—	6	1	no	—
786	C₃²	—	9	1	no	—
787	C₃²	—	9	1	no	—
788	C₃²	—	9	1	no	—
789	C₃²	—	9	1	no	—
790	C₃²	—	9	1	no	—
791	C₃²	—	18	1	no	—
792	C₃²	—	18	1	no	—
793	C₃²	—	18	1	no	—
794	C₃²	—	18	1	no	—
795	C₃²	—	18	1	no	—
796	C₃²	—	18	1	no	—
797	C₃²	—	18	1	no	—
798	C₃²	—	18	1	no	—
799	C₃²	—	18	1	no	—
800	C₃²	—	18	1	no	—
801	C₃²	—	18	1	no	—
802	C₃²	—	18	1	no	—
803	C₃²	—	18	1	no	—
804	C₃²	—	18	1	no	—
805	C₃²	—	18	1	no	—
806	C₃²	—	18	1	no	—
807	C₃²	—	18	1	no	—
808	C₃²	—	18	1	no	—
809	C₃²	—	18	1	no	—
810	C₃²	—	18	1	no	—
811	C₃²	—	18	1	no	—
812	C₃²	—	18	1	no	—
813	C₃²	#92264	1	1	yes	characteristic, complemented
814	C₃²	#92264	1	2	yes	complemented
815	C₃²	C₃×D₃×H(3,𝔽₃)	1	1	yes	characteristic
816	C₃²	C₃²×AGL(1,ℤ/9)	1	1	yes	characteristic
817	C₃²	C₃×D₃×3₋¹⁺²	1	1	yes	characteristic
818	C₃²	D₃×#737	1	1	yes	characteristic
819	C₃²	D₃×#737	1	1	yes	characteristic
820	C₉	—	2	1	no	—
821	C₉	—	2	1	no	—
822	C₉	—	2	1	no	—
823	C₉	—	2	1	no	—
824	C₉	—	3	1	no	—
825	C₉	—	3	1	no	—
826	C₉	—	3	1	no	—
827	C₉	—	3	1	no	—
828	C₉	—	6	1	no	—
829	C₉	—	6	1	no	—
830	C₉	—	6	1	no	—
831	C₉	—	6	1	no	—
832	C₉	—	6	2	no	—
833	C₉	—	6	1	no	—
834	C₉	—	6	1	no	—
835	C₉	—	6	1	no	—
836	C₉	—	6	1	no	—
837	C₉	—	6	1	no	—
838	C₉	—	9	1	no	—
839	C₉	—	18	1	no	—
840	C₉	—	18	1	no	—
841	C₉	—	18	1	no	—
842	C₉	—	18	1	no	—
843	C₉	—	18	1	no	—
844	C₉	—	18	1	no	—
845	C₉	—	18	1	no	—
846	C₉	—	18	1	no	—
847	C₉	—	18	1	no	—
848	C₉	—	18	1	no	—
849	C₉	—	18	1	no	—
850	C₉	—	18	1	no	—
851	C₉	—	18	1	no	—
852	C₉	—	18	1	no	—
853	C₉	—	18	1	no	—
854	C₉	C₂×C₉⋊H(3,𝔽₃)	1	1	yes	characteristic, complemented
855	C₂×C₃	—	9	1	no	—
856	C₂×C₃	—	9	1	no	—
857	C₂×C₃	—	9	1	no	—
858	C₂×C₃	—	9	1	no	—
859	C₂×C₃	—	27	1	no	—
860	C₂×C₃	—	27	2	no	—
861	C₂×C₃	—	81	1	no	—
862	C₂×C₃	—	81	1	no	—
863	C₂×C₃	—	81	1	no	—
864	D₃	—	3	1	no	—
865	C₃	—	2	1	no	—
866	C₃	—	2	1	no	—
867	C₃	—	2	1	no	—
868	C₃	—	2	1	no	—
869	C₃	—	3	1	no	—
870	C₃	—	3	2	no	—
871	C₃	—	6	1	no	—
872	C₃	—	6	2	no	—
873	C₃	—	27	1	no	—
874	C₃	—	27	1	no	—
875	C₃	—	54	1	no	—
876	C₃	D₃×C₉⋊H(3,𝔽₃)	1	1	yes	characteristic
877	C₃	C₃×#92264	1	1	yes	characteristic
878	C₃	H(3,𝔽₃)×AGL(1,ℤ/9)	1	1	yes	characteristic
879	C₃	#10624901⋊C₂	1	1	yes	characteristic
880	C₃	#10624901⋊C₂	1	1	yes	characteristic
881	C₂	—	9	1	no	Sylow

	subgroup	G/H
center	C₃²	C₃²×AGL(1,ℤ/9)
commutator, cosocle	C₃²×C₉	C₂×C₃³
Frattini, socle	C₃³	C₃³×D₃
Fitting	#14552197	C₂
prime radical	C₃×D₉⋊H(3,𝔽₃)	C₃
hypercenter	C₃²⋊C₉	AGL(1,ℤ/9)
hypocenter	C₉	C₂×C₉⋊H(3,𝔽₃)
LCS	G ▷ C₃²×C₉ ▷ C₉
UCS	C₁ ◁ C₃² ◁ C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
1. #14552197	C₂	semidirect
2. C₃×#92264	C₃	semidirect
3. C₃×#92264	C₃	semidirect
4. C₃×#92264	C₃	semidirect
7. C₃²×D₉⋊C₉	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. D₉×C₃²⋊C₉	C₃	semidirect
16. C₃×#6896	C₂×C₃	semidirect
17. C₃×#6896	C₂×C₃	semidirect
18. C₃×#6896	C₂×C₃	semidirect
21. C₃²×C₉⋊C₉	C₂×C₃	semidirect
31. #10624560	C₂×C₃	semidirect
32. #10624560	C₂×C₃	semidirect
33. #10624560	C₂×C₃	semidirect
34. #10624560	C₂×C₃	semidirect
35. #10624560	C₂×C₃	semidirect
36. #10624560	C₂×C₃	semidirect
41. #10624548	C₂×C₃	semidirect
42. C₉×C₃²⋊C₉	C₂×C₃	semidirect
242. C₃²×D₉	3₋¹⁺²	semidirect
243. C₃²×D₉	3₋¹⁺²	semidirect
258. D₉⋊C₉	H(3,𝔽₃)	semidirect
259. D₉⋊C₉	H(3,𝔽₃)	semidirect
260. D₉⋊C₉	H(3,𝔽₃)	semidirect
350. C₃²×C₉	C₂×3₋¹⁺²	semidirect
351. C₃²×C₉	C₂×3₋¹⁺²	semidirect
411. C₉⋊C₉	C₂×H(3,𝔽₃)	semidirect
412. C₉⋊C₉	C₂×H(3,𝔽₃)	semidirect
413. C₉⋊C₉	C₂×H(3,𝔽₃)	semidirect
459. C₃²⋊C₉	AGL(1,ℤ/9)	semidirect
763. D₉	C₉⋊H(3,𝔽₃)	semidirect
813. C₃²	#92264	semidirect
814. C₃²	#92264	semidirect
854. 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
#14552197	2
C₃×#92264	3
C₃×D₉⋊H(3,𝔽₃)	3
D₃×C₉⋊H(3,𝔽₃)	3
C₃²×D₉⋊C₉	3
(C₃×AGL(1,ℤ/9))⋊C₉	3
#13090623	3
D₉×C₃²⋊C₉	3