Subgroups — C₉×#5620 #13152837

Order 1728.

850 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#940	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#939	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#939	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#938	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#937	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#937	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#930	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#929	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#898	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#894	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#886	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#884	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#882	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#879	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5620	C₃	1	1	yes	maximal, characteristic
17	C₉×#560	—	3	1	no	maximal
18	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
19	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
20	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
21	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₉×#67	C₂²	1	1	yes	characteristic
24	C₂×C₉×#67	C₂²	1	1	yes	characteristic
25	C₂×C₉×#67	C₂²	1	1	yes	characteristic
26	C₂×C₉×#67	C₂²	1	1	yes	characteristic
27	C₂×C₉×#67	C₂²	1	1	yes	characteristic
28	C₂×C₉×#67	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₉×#67	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
32	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₉×#217	C₂²	1	1	yes	characteristic
38	C₉×#217	C₂²	1	1	yes	characteristic
39	C₉×#217	C₂²	1	1	yes	characteristic, complemented
40	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
41	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
42	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
43	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
44	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
45	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
46	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
48	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
49	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
52	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
53	C₃²×#121	C₂×C₃	1	1	yes	characteristic
54	C₃×#940	C₂×C₃	1	1	yes	characteristic
55	C₃×#939	C₂×C₃	1	1	yes	characteristic
56	C₃×#939	C₂×C₃	1	1	yes	characteristic
57	C₃×#938	C₂×C₃	1	1	yes	characteristic
58	C₃×#937	C₂×C₃	1	1	yes	characteristic
59	C₃×#937	C₂×C₃	1	1	yes	characteristic
60	C₃×#930	C₂×C₃	1	1	yes	characteristic
61	C₃×#929	C₂×C₃	1	1	yes	characteristic
62	C₃×#898	C₂×C₃	1	1	yes	characteristic
63	C₃×#894	C₂×C₃	1	1	yes	characteristic
64	C₃×#886	C₂×C₃	1	1	yes	characteristic
65	C₃×#884	C₂×C₃	1	1	yes	characteristic
66	C₃×#882	C₂×C₃	1	1	yes	characteristic
67	C₃×#879	C₂×C₃	1	1	yes	characteristic
68	C₉×#127	—	3	1	no	—
69	C₉×#126	—	3	1	no	—
70	C₉×#126	—	3	1	no	—
71	C₉×#123	—	3	1	no	—
72	C₉×#123	—	3	1	no	—
73	C₉×#123	—	3	1	no	—
74	C₉×#121	—	2	1	no	—
75	C₉×#121	—	3	1	no	—
76	C₉×#121	—	3	1	no	—
77	C₉×#121	—	3	1	no	—
78	C₉×#121	—	3	1	no	—
79	C₉×#121	—	3	1	no	—
80	C₉×#121	D₃	1	1	yes	characteristic, complemented
81	C₉×#120	—	3	1	no	—
82	C₉×#120	—	3	1	no	—
83	C₉×#120	—	3	1	no	—
84	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
85	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
86	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
87	C₂²×D₃×C₉	—	4	1	no	—
88	C₂²×D₃×C₉	—	4	1	no	—
89	C₂²×D₃×C₉	—	4	1	no	—
90	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
91	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
92	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
93	C₃×D₄×C₉	—	4	1	no	—
94	C₃×D₄×C₉	—	4	1	no	—
95	C₃×D₄×C₉	—	4	1	no	—
96	C₂×C₃×C₄×C₉	—	4	1	no	—
97	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
98	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
99	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
100	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
101	C₉×#67	—	4	1	no	—
102	C₉×#67	—	4	1	no	—
103	C₉×#67	—	4	1	no	—
104	C₉×#67	—	4	1	no	—
105	C₉×#67	—	4	1	no	—
106	C₉×#67	—	4	1	no	—
107	C₉×#67	—	4	1	no	—
108	C₂×C₉×Dic₃	—	4	1	no	—
109	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
110	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
111	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
112	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
113	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
114	C₉×D₁₂	—	4	1	no	—
115	C₉×D₁₂	—	4	1	no	—
116	C₄×D₃×C₉	—	4	1	no	—
117	C₃×#560	—	3	1	no	—
118	#5620	C₉	1	1	yes	characteristic, direct product factor
119	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
123	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
126	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
130	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
131	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
133	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
135	C₂⁴×C₉	—	3	1	no	—
136	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
137	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
138	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
139	C₃×#217	C₂²×C₃	1	1	yes	characteristic
140	C₃×#217	C₂²×C₃	1	1	yes	characteristic
141	C₃×#217	C₂²×C₃	1	1	yes	characteristic
142	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
143	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
144	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
145	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
146	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
147	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
148	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
149	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
150	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
151	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
152	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
153	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
154	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
155	C₂×D₄×C₉	—	2	1	no	—
156	C₂×D₄×C₉	—	2	1	no	—
157	C₂×D₄×C₉	—	2	1	no	—
158	C₂×D₄×C₉	—	3	1	no	—
159	C₂×D₄×C₉	—	3	1	no	—
160	C₂×D₄×C₉	—	3	1	no	—
161	C₂×D₄×C₉	—	3	1	no	—
162	C₂×D₄×C₉	—	3	1	no	—
163	C₂×D₄×C₉	—	3	1	no	—
164	C₂×D₄×C₉	—	3	1	no	—
165	C₂×D₄×C₉	—	3	1	no	—
166	C₂×D₄×C₉	—	3	1	no	—
167	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
168	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
169	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
170	C₂²×C₄×C₉	—	2	1	no	—
171	C₂²×C₄×C₉	—	3	1	no	—
172	C₂²×C₄×C₉	—	3	1	no	—
173	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
174	C₉×C₄⋊C₄	—	2	1	no	—
175	C₉×C₄⋊C₄	—	3	1	no	—
176	C₉×C₄⋊C₄	—	3	1	no	—
177	C₉×C₄⋊C₄	—	3	1	no	—
178	C₉×C₄⋊C₄	—	3	1	no	—
179	C₉×C₄⋊C₄	—	3	1	no	—
180	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
181	C₉×C₂²⋊C₄	—	2	1	no	—
182	C₉×C₂²⋊C₄	—	2	1	no	—
183	C₉×C₂²⋊C₄	—	3	1	no	—
184	C₉×C₂²⋊C₄	—	3	1	no	—
185	C₉×C₂²⋊C₄	—	3	1	no	—
186	C₉×C₂²⋊C₄	—	3	1	no	—
187	C₉×C₂²⋊C₄	—	3	1	no	—
188	C₉×C₂²⋊C₄	—	3	1	no	—
189	C₉×C₂²⋊C₄	—	3	1	no	—
190	C₉×C₂²⋊C₄	—	3	1	no	—
191	C₉×C₂²⋊C₄	—	3	1	no	—
192	C₉×C₂²⋊C₄	—	3	1	no	—
193	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
194	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
195	C₄²×C₉	—	3	1	no	—
196	C₂²×C₃×C₉	—	2	1	no	—
197	C₂²×C₃×C₉	—	2	1	no	—
198	C₂²×C₃×C₉	—	2	1	no	—
199	C₂²×C₃×C₉	—	2	1	no	—
200	C₂²×C₃×C₉	—	2	1	no	—
201	C₂²×C₃×C₉	—	2	1	no	—
202	C₂²×C₃×C₉	—	2	1	no	—
203	C₂²×C₃×C₉	—	2	1	no	—
204	C₂²×C₃×C₉	—	2	1	no	—
205	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
206	C₂×D₃×C₉	—	2	1	no	—
207	C₂×D₃×C₉	—	2	1	no	—
208	C₂×D₃×C₉	—	2	1	no	—
209	C₂×D₃×C₉	—	2	1	no	—
210	C₂×D₃×C₉	—	2	1	no	—
211	C₂×D₃×C₉	—	2	1	no	—
212	C₂×D₃×C₉	—	2	1	no	—
213	C₂×D₃×C₉	—	2	1	no	—
214	C₂×D₃×C₉	—	2	1	no	—
215	C₂×D₃×C₉	—	4	4	no	—
216	C₃×C₄×C₉	—	2	1	no	—
217	C₃×C₄×C₉	—	2	1	no	—
218	C₃×C₄×C₉	—	2	1	no	—
219	C₃×C₄×C₉	—	2	1	no	—
220	C₉×Dic₃	—	2	1	no	—
221	C₉×Dic₃	—	2	1	no	—
222	C₉×Dic₃	—	2	1	no	—
223	C₉×Dic₃	—	2	1	no	—
224	C₉×Dic₃	—	2	1	no	—
225	C₃×#127	—	3	1	no	—
226	C₃×#126	—	3	1	no	—
227	C₃×#126	—	3	1	no	—
228	C₃×#123	—	3	1	no	—
229	C₃×#123	—	3	1	no	—
230	C₃×#123	—	3	1	no	—
231	C₃×#121	—	2	1	no	—
232	C₃×#121	—	3	1	no	—
233	C₃×#121	—	3	1	no	—
234	C₃×#121	—	3	1	no	—
235	C₃×#121	—	3	1	no	—
236	C₃×#121	—	3	1	no	—
237	C₃×#121	C₂×C₉	1	1	yes	characteristic, complemented
238	C₃×#121	C₃×D₃	1	1	yes	characteristic
239	C₃×#120	—	3	1	no	—
240	C₃×#120	—	3	1	no	—
241	C₃×#120	—	3	1	no	—
242	#940	C₂×C₉	1	1	yes	characteristic, complemented
243	#939	C₂×C₉	1	1	yes	characteristic, complemented
244	#939	C₂×C₉	1	1	yes	characteristic, complemented
245	#938	C₂×C₉	1	1	yes	characteristic, complemented
246	#937	C₂×C₉	1	1	yes	characteristic, complemented
247	#937	C₂×C₉	1	1	yes	characteristic, complemented
248	#930	C₂×C₉	1	1	yes	characteristic, complemented
249	#929	C₂×C₉	1	1	yes	characteristic, complemented
250	#898	C₂×C₉	1	1	yes	characteristic, complemented
251	#894	C₂×C₉	1	1	yes	characteristic, complemented
252	#886	C₂×C₉	1	1	yes	characteristic, complemented
253	#884	C₂×C₉	1	1	yes	characteristic, complemented
254	#882	C₂×C₉	1	1	yes	characteristic, complemented
255	#879	C₂×C₉	1	1	yes	characteristic, complemented
256	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
257	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
258	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
259	C₂²×C₃×D₃	—	4	1	no	—
260	C₂²×C₃×D₃	—	4	1	no	—
261	C₂²×C₃×D₃	—	4	1	no	—
262	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
263	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
264	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
265	C₃²×D₄	—	4	1	no	—
266	C₃²×D₄	—	4	1	no	—
267	C₃²×D₄	—	4	1	no	—
268	C₂×C₃²×C₄	—	4	1	no	—
269	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
270	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
271	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
272	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
273	C₃×#67	—	4	1	no	—
274	C₃×#67	—	4	1	no	—
275	C₃×#67	—	4	1	no	—
276	C₃×#67	—	4	1	no	—
277	C₃×#67	—	4	1	no	—
278	C₃×#67	—	4	1	no	—
279	C₃×#67	—	4	1	no	—
280	C₂×C₃×Dic₃	—	4	1	no	—
281	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
282	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
283	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
284	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
285	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
286	C₃×D₁₂	—	4	1	no	—
287	C₃×D₁₂	—	4	1	no	—
288	C₃×C₄×D₃	—	4	1	no	—
289	C₂³×C₉	—	2	1	no	—
290	C₂³×C₉	—	2	1	no	—
291	C₂³×C₉	—	2	1	no	—
292	C₂³×C₉	—	3	1	no	—
293	C₂³×C₉	—	3	1	no	—
294	C₂³×C₉	—	3	1	no	—
295	C₂³×C₉	—	12	1	no	—
296	C₂³×C₉	—	12	1	no	—
297	C₂³×C₉	—	12	1	no	—
298	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
299	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
300	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
301	D₄×C₉	—	4	1	no	—
302	D₄×C₉	—	4	1	no	—
303	D₄×C₉	—	4	1	no	—
304	D₄×C₉	—	4	2	no	—
305	D₄×C₉	—	4	2	no	—
306	D₄×C₉	—	4	2	no	—
307	D₄×C₉	—	12	1	no	—
308	D₄×C₉	—	12	1	no	—
309	D₄×C₉	—	12	1	no	—
310	D₄×C₉	—	12	1	no	—
311	D₄×C₉	—	12	1	no	—
312	D₄×C₉	—	12	1	no	—
313	D₄×C₉	—	12	1	no	—
314	D₄×C₉	—	12	1	no	—
315	D₄×C₉	—	12	1	no	—
316	C₂×C₄×C₉	—	2	1	no	—
317	C₂×C₄×C₉	—	2	1	no	—
318	C₂×C₄×C₉	—	2	1	no	—
319	C₂×C₄×C₉	—	2	1	no	—
320	C₂×C₄×C₉	—	3	1	no	—
321	C₂×C₄×C₉	—	3	1	no	—
322	C₂×C₄×C₉	—	3	1	no	—
323	C₂×C₄×C₉	—	3	1	no	—
324	C₂×C₄×C₉	—	3	1	no	—
325	C₂×C₄×C₉	—	4	1	no	—
326	C₂×C₄×C₉	—	4	2	no	—
327	C₂×C₄×C₉	—	12	1	no	—
328	C₂×C₄×C₉	—	12	1	no	—
329	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
330	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
331	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
332	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
333	#560	—	3	1	no	Sylow
334	C₂×C₃×C₉	—	4	1	no	—
335	C₂×C₃×C₉	—	4	1	no	—
336	C₂×C₃×C₉	—	4	1	no	—
337	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
340	D₃×C₉	—	4	1	no	—
341	D₃×C₉	—	4	1	no	—
342	D₃×C₉	—	4	1	no	—
343	C₂⁴×C₃	—	3	1	no	—
344	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
345	C₂×C₃×D₄	—	2	1	no	—
346	C₂×C₃×D₄	—	2	1	no	—
347	C₂×C₃×D₄	—	2	1	no	—
348	C₂×C₃×D₄	—	3	1	no	—
349	C₂×C₃×D₄	—	3	1	no	—
350	C₂×C₃×D₄	—	3	1	no	—
351	C₂×C₃×D₄	—	3	1	no	—
352	C₂×C₃×D₄	—	3	1	no	—
353	C₂×C₃×D₄	—	3	1	no	—
354	C₂×C₃×D₄	—	3	1	no	—
355	C₂×C₃×D₄	—	3	1	no	—
356	C₂×C₃×D₄	—	3	1	no	—
357	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
358	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
359	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
360	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
361	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
362	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
363	C₂²×C₃×C₄	—	2	1	no	—
364	C₂²×C₃×C₄	—	3	1	no	—
365	C₂²×C₃×C₄	—	3	1	no	—
366	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic, complemented
367	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
368	C₂×#67	C₂²×C₉	1	1	yes	characteristic
369	C₂×#67	C₂²×C₉	1	1	yes	characteristic
370	C₂×#67	C₂²×C₉	1	1	yes	characteristic
371	C₂×#67	C₂²×C₉	1	1	yes	characteristic
372	C₂×#67	C₂²×C₉	1	1	yes	characteristic
373	C₂×#67	C₂²×C₉	1	1	yes	characteristic, complemented
374	C₂×#67	C₂²×C₉	1	1	yes	characteristic, complemented
375	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
376	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
377	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
378	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
379	C₃×C₄⋊C₄	—	2	1	no	—
380	C₃×C₄⋊C₄	—	3	1	no	—
381	C₃×C₄⋊C₄	—	3	1	no	—
382	C₃×C₄⋊C₄	—	3	1	no	—
383	C₃×C₄⋊C₄	—	3	1	no	—
384	C₃×C₄⋊C₄	—	3	1	no	—
385	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
386	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
387	C₃×C₂²⋊C₄	—	2	1	no	—
388	C₃×C₂²⋊C₄	—	2	1	no	—
389	C₃×C₂²⋊C₄	—	3	1	no	—
390	C₃×C₂²⋊C₄	—	3	1	no	—
391	C₃×C₂²⋊C₄	—	3	1	no	—
392	C₃×C₂²⋊C₄	—	3	1	no	—
393	C₃×C₂²⋊C₄	—	3	1	no	—
394	C₃×C₂²⋊C₄	—	3	1	no	—
395	C₃×C₂²⋊C₄	—	3	1	no	—
396	C₃×C₂²⋊C₄	—	3	1	no	—
397	C₃×C₂²⋊C₄	—	3	1	no	—
398	C₃×C₂²⋊C₄	—	3	1	no	—
399	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
400	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
401	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
402	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
403	C₃×C₄²	—	3	1	no	—
404	#217	C₂²×C₉	1	1	yes	characteristic
405	#217	C₂²×C₉	1	1	yes	characteristic
406	#217	C₂²×C₉	1	1	yes	characteristic, complemented
407	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
408	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
409	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
410	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
411	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
412	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
413	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
414	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
415	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
416	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
417	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
418	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
419	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
420	C₂²×C₃²	—	2	1	no	—
421	C₂²×C₃²	—	2	1	no	—
422	C₂²×C₃²	—	2	1	no	—
423	C₂²×C₃²	—	2	1	no	—
424	C₂²×C₃²	—	2	1	no	—
425	C₂²×C₃²	—	2	1	no	—
426	C₂²×C₃²	—	2	1	no	—
427	C₂²×C₃²	—	2	1	no	—
428	C₂²×C₃²	—	2	1	no	—
429	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
430	C₂×C₃×D₃	—	2	1	no	—
431	C₂×C₃×D₃	—	2	1	no	—
432	C₂×C₃×D₃	—	2	1	no	—
433	C₂×C₃×D₃	—	2	1	no	—
434	C₂×C₃×D₃	—	2	1	no	—
435	C₂×C₃×D₃	—	2	1	no	—
436	C₂×C₃×D₃	—	2	1	no	—
437	C₂×C₃×D₃	—	2	1	no	—
438	C₂×C₃×D₃	—	2	1	no	—
439	C₂×C₃×D₃	—	4	4	no	—
440	C₃²×C₄	—	2	1	no	—
441	C₃²×C₄	—	2	1	no	—
442	C₃²×C₄	—	2	1	no	—
443	C₃²×C₄	—	2	1	no	—
444	C₃×Dic₃	—	2	1	no	—
445	C₃×Dic₃	—	2	1	no	—
446	C₃×Dic₃	—	2	1	no	—
447	C₃×Dic₃	—	2	1	no	—
448	C₃×Dic₃	—	2	1	no	—
449	C₂²×C₉	—	2	2	no	—
450	C₂²×C₉	—	2	1	no	—
451	C₂²×C₉	—	2	1	no	—
452	C₂²×C₉	—	2	1	no	—
453	C₂²×C₉	—	2	1	no	—
454	C₂²×C₉	—	2	1	no	—
455	C₂²×C₉	—	2	1	no	—
456	C₂²×C₉	—	2	1	no	—
457	C₂²×C₉	—	2	1	no	—
458	C₂²×C₉	—	2	1	no	—
459	C₂²×C₉	—	2	1	no	—
460	C₂²×C₉	—	4	1	no	—
461	C₂²×C₉	—	4	1	no	—
462	C₂²×C₉	—	4	1	no	—
463	C₂²×C₉	—	4	1	no	—
464	C₂²×C₉	—	4	1	no	—
465	C₂²×C₉	—	4	1	no	—
466	C₂²×C₉	—	4	1	no	—
467	C₂²×C₉	—	4	1	no	—
468	C₂²×C₉	—	6	1	no	—
469	C₂²×C₉	—	6	1	no	—
470	C₂²×C₉	—	6	1	no	—
471	C₂²×C₉	—	6	1	no	—
472	C₂²×C₉	—	6	1	no	—
473	C₂²×C₉	—	6	1	no	—
474	C₂²×C₉	—	6	1	no	—
475	C₂²×C₉	—	6	1	no	—
476	C₂²×C₉	—	6	1	no	—
477	C₂²×C₉	—	12	4	no	—
478	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
479	C₄×C₉	—	2	2	no	—
480	C₄×C₉	—	2	1	no	—
481	C₄×C₉	—	2	1	no	—
482	C₄×C₉	—	2	1	no	—
483	C₄×C₉	—	2	1	no	—
484	C₄×C₉	—	4	1	no	—
485	C₄×C₉	—	4	1	no	—
486	C₄×C₉	—	4	1	no	—
487	C₄×C₉	—	6	1	no	—
488	C₄×C₉	—	6	1	no	—
489	C₄×C₉	—	6	1	no	—
490	C₄×C₉	—	6	1	no	—
491	C₄×C₉	—	6	1	no	—
492	#127	—	3	1	no	—
493	#126	—	3	1	no	—
494	#126	—	3	1	no	—
495	#123	—	3	1	no	—
496	#123	—	3	1	no	—
497	#123	—	3	1	no	—
498	#121	—	3	1	no	—
499	#121	—	3	1	no	—
500	#121	—	3	1	no	—
501	#121	—	3	1	no	—
502	#121	—	3	1	no	—
503	#121	D₃×C₉	1	1	yes	characteristic, complemented
504	#120	—	3	1	no	—
505	#120	—	3	1	no	—
506	#120	—	3	1	no	—
507	C₃×C₉	#560	1	1	yes	characteristic, complemented, Sylow
508	C₂³×C₃	—	2	1	no	—
509	C₂³×C₃	—	2	1	no	—
510	C₂³×C₃	—	2	1	no	—
511	C₂³×C₃	—	3	1	no	—
512	C₂³×C₃	—	3	1	no	—
513	C₂³×C₃	—	3	1	no	—
514	C₂³×C₃	—	12	1	no	—
515	C₂³×C₃	—	12	1	no	—
516	C₂³×C₃	—	12	1	no	—
517	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
518	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
519	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
520	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
521	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
522	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
523	C₂²×D₃	—	4	1	no	—
524	C₂²×D₃	—	4	1	no	—
525	C₂²×D₃	—	4	1	no	—
526	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
527	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
528	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
529	C₃×D₄	—	4	1	no	—
530	C₃×D₄	—	4	1	no	—
531	C₃×D₄	—	4	1	no	—
532	C₃×D₄	—	4	1	no	—
533	C₃×D₄	—	4	1	no	—
534	C₃×D₄	—	4	1	no	—
535	C₃×D₄	—	4	2	no	—
536	C₃×D₄	—	4	2	no	—
537	C₃×D₄	—	4	2	no	—
538	C₃×D₄	—	12	1	no	—
539	C₃×D₄	—	12	1	no	—
540	C₃×D₄	—	12	1	no	—
541	C₃×D₄	—	12	1	no	—
542	C₃×D₄	—	12	1	no	—
543	C₃×D₄	—	12	1	no	—
544	C₃×D₄	—	12	1	no	—
545	C₃×D₄	—	12	1	no	—
546	C₃×D₄	—	12	1	no	—
547	C₂×C₃×C₄	—	2	1	no	—
548	C₂×C₃×C₄	—	2	1	no	—
549	C₂×C₃×C₄	—	2	1	no	—
550	C₂×C₃×C₄	—	2	1	no	—
551	C₂×C₃×C₄	—	3	1	no	—
552	C₂×C₃×C₄	—	3	1	no	—
553	C₂×C₃×C₄	—	3	1	no	—
554	C₂×C₃×C₄	—	3	1	no	—
555	C₂×C₃×C₄	—	3	1	no	—
556	C₂×C₃×C₄	—	4	1	no	—
557	C₂×C₃×C₄	—	4	1	no	—
558	C₂×C₃×C₄	—	4	2	no	—
559	C₂×C₃×C₄	—	12	1	no	—
560	C₂×C₃×C₄	—	12	1	no	—
561	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
562	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
563	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
564	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
565	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
566	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
567	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
568	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
569	#67	—	4	1	no	—
570	#67	—	4	1	no	—
571	#67	—	4	1	no	—
572	#67	—	4	1	no	—
573	#67	—	4	1	no	—
574	#67	—	4	1	no	—
575	#67	—	4	1	no	—
576	C₂×Dic₃	—	4	1	no	—
577	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
578	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
579	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
580	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
581	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
582	D₁₂	—	4	1	no	—
583	D₁₂	—	4	1	no	—
584	C₄×D₃	—	4	1	no	—
585	C₂×C₃²	—	4	1	no	—
586	C₂×C₃²	—	4	1	no	—
587	C₂×C₃²	—	4	1	no	—
588	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
589	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
590	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
591	C₃×D₃	—	4	1	no	—
592	C₃×D₃	—	4	1	no	—
593	C₃×D₃	—	4	1	no	—
594	C₂×C₉	—	2	1	no	—
595	C₂×C₉	—	2	1	no	—
596	C₂×C₉	—	2	1	no	—
597	C₂×C₉	—	4	2	no	—
598	C₂×C₉	—	4	1	no	—
599	C₂×C₉	—	4	1	no	—
600	C₂×C₉	—	4	1	no	—
601	C₂×C₉	—	8	1	no	—
602	C₂×C₉	—	8	1	no	—
603	C₂×C₉	—	12	1	no	—
604	C₂×C₉	—	12	1	no	—
605	C₂×C₉	—	12	1	no	—
606	C₂×C₉	#1004	1	1	yes	characteristic
607	C₂×C₉	#1004	1	1	yes	characteristic
608	C₂×C₉	#1009	1	1	yes	characteristic
609	C₂⁴	—	3	1	no	—
610	C₂×D₄	—	3	1	no	—
611	C₂×D₄	—	3	1	no	—
612	C₂×D₄	—	3	1	no	—
613	C₂×D₄	—	3	1	no	—
614	C₂×D₄	—	3	1	no	—
615	C₂×D₄	—	3	1	no	—
616	C₂×D₄	—	3	1	no	—
617	C₂×D₄	—	3	1	no	—
618	C₂×D₄	—	3	1	no	—
619	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
620	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
621	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
622	C₂²×C₄	—	3	1	no	—
623	C₂²×C₄	—	3	1	no	—
624	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
625	C₄⋊C₄	—	3	1	no	—
626	C₄⋊C₄	—	3	1	no	—
627	C₄⋊C₄	—	3	1	no	—
628	C₄⋊C₄	—	3	1	no	—
629	C₄⋊C₄	—	3	1	no	—
630	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
631	C₂²⋊C₄	—	3	1	no	—
632	C₂²⋊C₄	—	3	1	no	—
633	C₂²⋊C₄	—	3	1	no	—
634	C₂²⋊C₄	—	3	1	no	—
635	C₂²⋊C₄	—	3	1	no	—
636	C₂²⋊C₄	—	3	1	no	—
637	C₂²⋊C₄	—	3	1	no	—
638	C₂²⋊C₄	—	3	1	no	—
639	C₂²⋊C₄	—	3	1	no	—
640	C₂²⋊C₄	—	3	1	no	—
641	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
642	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
643	C₄²	—	3	1	no	—
644	C₂²×C₃	—	2	2	no	—
645	C₂²×C₃	—	2	1	no	—
646	C₂²×C₃	—	2	1	no	—
647	C₂²×C₃	—	2	1	no	—
648	C₂²×C₃	—	2	1	no	—
649	C₂²×C₃	—	2	1	no	—
650	C₂²×C₃	—	2	1	no	—
651	C₂²×C₃	—	2	1	no	—
652	C₂²×C₃	—	2	1	no	—
653	C₂²×C₃	—	2	1	no	—
654	C₂²×C₃	—	2	1	no	—
655	C₂²×C₃	—	2	1	no	—
656	C₂²×C₃	—	2	1	no	—
657	C₂²×C₃	—	2	1	no	—
658	C₂²×C₃	—	2	1	no	—
659	C₂²×C₃	—	2	1	no	—
660	C₂²×C₃	—	2	1	no	—
661	C₂²×C₃	—	2	1	no	—
662	C₂²×C₃	—	2	1	no	—
663	C₂²×C₃	—	2	1	no	—
664	C₂²×C₃	—	4	1	no	—
665	C₂²×C₃	—	4	1	no	—
666	C₂²×C₃	—	4	1	no	—
667	C₂²×C₃	—	4	1	no	—
668	C₂²×C₃	—	4	1	no	—
669	C₂²×C₃	—	4	1	no	—
670	C₂²×C₃	—	4	1	no	—
671	C₂²×C₃	—	4	1	no	—
672	C₂²×C₃	—	6	1	no	—
673	C₂²×C₃	—	6	1	no	—
674	C₂²×C₃	—	6	1	no	—
675	C₂²×C₃	—	6	1	no	—
676	C₂²×C₃	—	6	1	no	—
677	C₂²×C₃	—	6	1	no	—
678	C₂²×C₃	—	6	1	no	—
679	C₂²×C₃	—	6	1	no	—
680	C₂²×C₃	—	6	1	no	—
681	C₂²×C₃	—	12	4	no	—
682	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
683	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
684	C₂×D₃	—	2	1	no	—
685	C₂×D₃	—	2	1	no	—
686	C₂×D₃	—	2	1	no	—
687	C₂×D₃	—	2	1	no	—
688	C₂×D₃	—	2	1	no	—
689	C₂×D₃	—	2	1	no	—
690	C₂×D₃	—	2	1	no	—
691	C₂×D₃	—	2	1	no	—
692	C₂×D₃	—	2	1	no	—
693	C₂×D₃	—	4	4	no	—
694	C₃×C₄	—	2	2	no	—
695	C₃×C₄	—	2	1	no	—
696	C₃×C₄	—	2	1	no	—
697	C₃×C₄	—	2	1	no	—
698	C₃×C₄	—	2	1	no	—
699	C₃×C₄	—	2	1	no	—
700	C₃×C₄	—	2	1	no	—
701	C₃×C₄	—	2	1	no	—
702	C₃×C₄	—	2	1	no	—
703	C₃×C₄	—	4	1	no	—
704	C₃×C₄	—	4	1	no	—
705	C₃×C₄	—	4	1	no	—
706	C₃×C₄	—	6	1	no	—
707	C₃×C₄	—	6	1	no	—
708	C₃×C₄	—	6	1	no	—
709	C₃×C₄	—	6	1	no	—
710	C₃×C₄	—	6	1	no	—
711	Dic₃	—	2	1	no	—
712	Dic₃	—	2	1	no	—
713	Dic₃	—	2	1	no	—
714	Dic₃	—	2	1	no	—
715	Dic₃	—	2	1	no	—
716	C₃²	C₃×#560	1	1	yes	characteristic
717	C₉	—	2	1	no	—
718	C₉	#5620	1	1	yes	characteristic, direct product factor
719	C₂³	—	3	1	no	—
720	C₂³	—	3	1	no	—
721	C₂³	—	3	1	no	—
722	C₂³	—	12	1	no	—
723	C₂³	—	12	1	no	—
724	C₂³	—	12	1	no	—
725	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
726	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
727	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
728	D₄	—	4	1	no	—
729	D₄	—	4	1	no	—
730	D₄	—	4	1	no	—
731	D₄	—	12	1	no	—
732	D₄	—	12	1	no	—
733	D₄	—	12	1	no	—
734	D₄	—	12	1	no	—
735	D₄	—	12	1	no	—
736	D₄	—	12	1	no	—
737	D₄	—	12	1	no	—
738	D₄	—	12	1	no	—
739	D₄	—	12	1	no	—
740	C₂×C₄	—	3	1	no	—
741	C₂×C₄	—	3	1	no	—
742	C₂×C₄	—	3	1	no	—
743	C₂×C₄	—	3	1	no	—
744	C₂×C₄	—	3	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	12	1	no	—
747	C₂×C₄	—	12	1	no	—
748	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
750	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
751	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
752	C₂×C₃	—	2	1	no	—
753	C₂×C₃	—	2	1	no	—
754	C₂×C₃	—	2	1	no	—
755	C₂×C₃	—	4	2	no	—
756	C₂×C₃	—	4	1	no	—
757	C₂×C₃	—	4	1	no	—
758	C₂×C₃	—	4	1	no	—
759	C₂×C₃	—	4	1	no	—
760	C₂×C₃	—	4	1	no	—
761	C₂×C₃	—	4	1	no	—
762	C₂×C₃	—	8	1	no	—
763	C₂×C₃	—	8	1	no	—
764	C₂×C₃	—	12	1	no	—
765	C₂×C₃	—	12	1	no	—
766	C₂×C₃	—	12	1	no	—
767	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
768	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
769	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
770	C₂×C₃	C₃×#1004	1	1	yes	characteristic
771	C₂×C₃	C₃×#1004	1	1	yes	characteristic
772	C₂×C₃	C₃×#1009	1	1	yes	characteristic
773	D₃	—	4	1	no	—
774	D₃	—	4	1	no	—
775	D₃	—	4	1	no	—
776	C₂²	—	2	1	no	—
777	C₂²	—	2	1	no	—
778	C₂²	—	2	1	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	2	1	no	—
781	C₂²	—	2	1	no	—
782	C₂²	—	2	1	no	—
783	C₂²	—	2	1	no	—
784	C₂²	—	2	1	no	—
785	C₂²	—	6	1	no	—
786	C₂²	—	6	1	no	—
787	C₂²	—	6	1	no	—
788	C₂²	—	6	1	no	—
789	C₂²	—	6	1	no	—
790	C₂²	—	6	1	no	—
791	C₂²	—	6	1	no	—
792	C₂²	—	6	1	no	—
793	C₂²	—	6	1	no	—
794	C₂²	—	12	4	no	—
795	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
796	C₄	—	2	1	no	—
797	C₄	—	2	1	no	—
798	C₄	—	2	1	no	—
799	C₄	—	2	1	no	—
800	C₄	—	6	1	no	—
801	C₄	—	6	1	no	—
802	C₄	—	6	1	no	—
803	C₄	—	6	1	no	—
804	C₄	—	6	1	no	—
805	C₃	—	2	1	no	—
806	C₃	C₉×#560	1	1	yes	characteristic, complemented
807	C₃	C₃×#5620	1	1	yes	characteristic
808	C₂	—	4	1	no	—
809	C₂	—	4	1	no	—
810	C₂	—	4	1	no	—
811	C₂	—	12	1	no	—
812	C₂	—	12	1	no	—
813	C₂	—	12	1	no	—
814	C₂	C₉×#1004	1	1	yes	characteristic
815	C₂	C₉×#1004	1	1	yes	characteristic
816	C₂	C₉×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#121	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5620	C₃
hypercenter	C₉×#121	D₃
hypocenter	C₃	C₉×#560
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#121

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#121	C₂	semidirect
2. C₉×#940	C₂	semidirect
3. C₉×#939	C₂	semidirect
4. C₉×#939	C₂	semidirect
5. C₉×#938	C₂	semidirect
6. C₉×#937	C₂	semidirect
7. C₉×#937	C₂	semidirect
8. C₉×#930	C₂	semidirect
9. C₉×#929	C₂	semidirect
10. C₉×#898	C₂	semidirect
11. C₉×#894	C₂	semidirect
12. C₉×#886	C₂	semidirect
13. C₉×#884	C₂	semidirect
14. C₉×#882	C₂	semidirect
15. C₉×#879	C₂	semidirect
21. C₂×C₃×D₄×C₉	C₂²	semidirect
22. C₂²×C₃×C₄×C₉	C₂²	semidirect
28. C₂×C₉×#67	C₂²	semidirect
29. C₂×C₉×#67	C₂²	semidirect
30. C₂²×C₉×Dic₃	C₂²	semidirect
33. C₂×C₄×D₃×C₉	C₂²	semidirect
34. C₃×C₉×C₄⋊C₄	C₂²	semidirect
36. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
39. C₉×#217	C₂²	semidirect
46. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
47. C₉×C₄⋊Dic₃	C₂²	semidirect
48. C₉×C₄⋊Dic₃	C₂²	semidirect
49. C₉×Dic₃⋊C₄	C₂²	semidirect
50. C₉×Dic₃⋊C₄	C₂²	semidirect
51. C₉×Dic₃⋊C₄	C₂²	semidirect
52. C₄×C₉×Dic₃	C₂²	semidirect
80. C₉×#121	D₃	semidirect
118. #5620	C₉	direct (N × H)
169. C₂×D₄×C₉	C₂×D₃	semidirect
173. C₂²×C₄×C₉	C₂×D₃	semidirect
180. C₉×C₄⋊C₄	C₂×D₃	semidirect
194. C₉×C₂²⋊C₄	C₂×D₃	semidirect
237. C₃×#121	C₂×C₉	semidirect
242. #940	C₂×C₉	semidirect
243. #939	C₂×C₉	semidirect
244. #939	C₂×C₉	semidirect
245. #938	C₂×C₉	semidirect
246. #937	C₂×C₉	semidirect
247. #937	C₂×C₉	semidirect
248. #930	C₂×C₉	semidirect
249. #929	C₂×C₉	semidirect
250. #898	C₂×C₉	semidirect
251. #894	C₂×C₉	semidirect
252. #886	C₂×C₉	semidirect
253. #884	C₂×C₉	semidirect
254. #882	C₂×C₉	semidirect
255. #879	C₂×C₉	semidirect
359. C₂×C₃×D₄	C₂²×C₉	semidirect
366. C₂²×C₃×C₄	C₂²×C₉	semidirect
373. C₂×#67	C₂²×C₉	semidirect
374. C₂×#67	C₂²×C₉	semidirect
375. C₂²×Dic₃	C₂²×C₉	semidirect
378. C₂×C₄×D₃	C₂²×C₉	semidirect
385. C₃×C₄⋊C₄	C₂²×C₉	semidirect
400. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
406. #217	C₂²×C₉	semidirect
413. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
414. C₄⋊Dic₃	C₂²×C₉	semidirect
415. C₄⋊Dic₃	C₂²×C₉	semidirect
416. Dic₃⋊C₄	C₂²×C₉	semidirect
417. Dic₃⋊C₄	C₂²×C₉	semidirect
418. Dic₃⋊C₄	C₂²×C₉	semidirect
419. C₄×Dic₃	C₂²×C₉	semidirect
503. #121	D₃×C₉	semidirect
507. C₃×C₉	#560	semidirect
621. C₂×D₄	C₂×D₃×C₉	semidirect
624. C₂²×C₄	C₂×D₃×C₉	semidirect
630. C₄⋊C₄	C₂×D₃×C₉	semidirect
642. C₂²⋊C₄	C₂×D₃×C₉	semidirect
718. C₉	#5620	direct (N × H)
806. C₃	C₉×#560	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×#121	2
C₉×#940	2
C₉×#939	2
C₉×#938	2
C₉×#937	2
C₉×#930	2
C₉×#929	2
C₉×#898	2
C₉×#894	2
C₉×#886	2
C₉×#884	2
C₉×#882	2
C₉×#879	2
C₃×#5620	3
C₉×#560	3

Subgroups — C9×#5620 #13152837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5620 #13152837