Subgroups — C₉×#5490 #13152350

Order 1728.

1134 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×#67	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#953	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#930	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#929	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₉×#67	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#885	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#884	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#884	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#883	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#882	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	D₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#878	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5490	C₃	1	1	yes	maximal, characteristic
17	C₉×#546	—	3	1	no	maximal
18	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
19	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₉×#67	—	2	4	no	—
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
31	C₉×#235	—	2	4	no	—
32	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₉×#217	C₂²	1	1	yes	characteristic
43	C₉×#217	C₂²	1	1	yes	characteristic, complemented
44	C₉×#217	C₂²	1	1	yes	characteristic, complemented
45	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
48	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
51	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
52	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
53	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
54	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₃×#67	C₂×C₃	1	1	yes	characteristic
56	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
57	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
58	C₃×#953	C₂×C₃	1	1	yes	characteristic
59	C₃×#930	C₂×C₃	1	1	yes	characteristic
60	C₃×#929	C₂×C₃	1	1	yes	characteristic
61	C₃×C₄×#67	C₂×C₃	1	1	yes	characteristic
62	C₃×#885	C₂×C₃	1	1	yes	characteristic
63	C₃×#884	C₂×C₃	1	1	yes	characteristic
64	C₃×#884	C₂×C₃	1	1	yes	characteristic
65	C₃×#883	C₂×C₃	1	1	yes	characteristic
66	C₃×#882	C₂×C₃	1	1	yes	characteristic
67	C₃×#67⋊C₄	C₂×C₃	1	1	yes	characteristic
68	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
69	C₃×#878	C₂×C₃	1	1	yes	characteristic
70	C₂×C₉×#41	—	3	1	no	—
71	C₂²×D₄×C₉	—	3	1	no	—
72	C₉×#124	—	3	1	no	—
73	C₉×#123	—	3	1	no	—
74	C₉×#123	—	3	1	no	—
75	C₉×C₂²⋊Q₈	—	3	1	no	—
76	C₉×#121	—	3	1	no	—
77	C₉×#121	—	3	1	no	—
78	C₉×#121	—	3	1	no	—
79	C₉×#120	—	3	1	no	—
80	C₉×#120	—	3	1	no	—
81	C₄×D₄×C₉	—	3	1	no	—
82	C₄×D₄×C₉	—	3	1	no	—
83	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
85	C₂×C₉×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
86	C₂³×C₃×C₉	—	2	2	no	—
87	C₂³×C₃×C₉	—	2	2	no	—
88	C₂³×C₃×C₉	—	4	1	no	—
89	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
90	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
91	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
92	C₂²×D₃×C₉	—	2	2	no	—
93	C₂²×D₃×C₉	—	2	2	no	—
94	C₂²×D₃×C₉	—	4	1	no	—
95	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
96	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
97	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
98	C₂×C₃×C₄×C₉	—	2	2	no	—
99	C₂×C₃×C₄×C₉	—	4	1	no	—
100	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
102	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
104	C₉×#67	—	2	2	no	—
105	C₉×#67	—	2	2	no	—
106	C₉×#67	—	2	2	no	—
107	C₉×#67	—	2	2	no	—
108	C₉×#67	—	2	2	no	—
109	C₉×#67	—	4	1	no	—
110	C₉×#67	D₄	1	4	yes	complemented
111	C₂×C₉×Dic₃	—	2	2	no	—
112	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
113	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
114	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
115	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
116	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
117	C₉×D₁₂	—	2	2	no	—
118	C₉×D₁₂	—	4	1	no	—
119	C₄×D₃×C₉	—	2	2	no	—
120	C₄×D₃×C₉	—	2	2	no	—
121	C₄×D₃×C₉	—	4	1	no	—
122	C₉×Dic₆	—	2	2	no	—
123	C₃×#546	—	3	1	no	—
124	#5490	C₉	1	1	yes	characteristic, direct product factor
125	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
126	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
127	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
128	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₃×#67	—	2	4	no	—
130	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
133	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
136	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
137	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
138	C₃×#235	—	2	4	no	—
139	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
145	C₂⁴×C₉	—	2	1	no	—
146	C₂⁴×C₉	—	3	1	no	—
147	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
148	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
149	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
150	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
151	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
152	C₃×#217	C₂²×C₃	1	1	yes	characteristic
153	C₃×#217	C₂²×C₃	1	1	yes	characteristic
154	C₃×#217	C₂²×C₃	1	1	yes	characteristic
155	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
156	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
157	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
158	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
159	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
160	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
161	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
162	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
163	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
164	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
165	C₉×#41	—	6	4	no	—
166	C₂×Q₈×C₉	—	3	1	no	—
167	C₂×D₄×C₉	—	3	1	no	—
168	C₂×D₄×C₉	—	3	1	no	—
169	C₂×D₄×C₉	—	3	1	no	—
170	C₂×D₄×C₉	—	3	1	no	—
171	C₂×D₄×C₉	—	3	1	no	—
172	C₂×D₄×C₉	—	3	1	no	—
173	C₂×D₄×C₉	—	3	1	no	—
174	C₂×D₄×C₉	—	3	1	no	—
175	C₂×D₄×C₉	—	3	1	no	—
176	C₂×D₄×C₉	—	6	4	no	—
177	C₂²×C₄×C₉	—	2	1	no	—
178	C₂²×C₄×C₉	—	2	1	no	—
179	C₂²×C₄×C₉	—	3	1	no	—
180	C₂²×C₄×C₉	—	3	1	no	—
181	C₂²×C₄×C₉	—	3	1	no	—
182	C₂²×C₄×C₉	—	3	1	no	—
183	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
184	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
185	C₉×C₄⋊C₄	—	3	1	no	—
186	C₉×C₄⋊C₄	—	3	1	no	—
187	C₉×C₄⋊C₄	—	3	1	no	—
188	C₉×C₄⋊C₄	—	3	1	no	—
189	C₉×C₂²⋊C₄	—	2	1	no	—
190	C₉×C₂²⋊C₄	—	2	1	no	—
191	C₉×C₂²⋊C₄	—	2	1	no	—
192	C₉×C₂²⋊C₄	—	2	1	no	—
193	C₉×C₂²⋊C₄	—	3	1	no	—
194	C₉×C₂²⋊C₄	—	3	1	no	—
195	C₉×C₂²⋊C₄	—	3	1	no	—
196	C₉×C₂²⋊C₄	—	3	1	no	—
197	C₉×C₂²⋊C₄	—	3	1	no	—
198	C₉×C₂²⋊C₄	—	3	1	no	—
199	C₉×C₂²⋊C₄	—	3	1	no	—
200	C₉×C₂²⋊C₄	—	3	1	no	—
201	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
202	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
203	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
204	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
205	C₄²×C₉	—	3	1	no	—
206	C₂²×C₃×C₉	—	2	1	no	—
207	C₂²×C₃×C₉	—	2	1	no	—
208	C₂²×C₃×C₉	—	2	1	no	—
209	C₂²×C₃×C₉	—	2	1	no	—
210	C₂²×C₃×C₉	—	2	1	no	—
211	C₂²×C₃×C₉	—	2	1	no	—
212	C₂²×C₃×C₉	—	2	1	no	—
213	C₂²×C₃×C₉	—	4	4	no	—
214	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
215	C₂²×C₃×C₉	#41	1	2	yes	complemented
216	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
217	C₂×D₃×C₉	—	2	1	no	—
218	C₂×D₃×C₉	—	2	1	no	—
219	C₂×D₃×C₉	—	2	1	no	—
220	C₂×D₃×C₉	—	2	1	no	—
221	C₂×D₃×C₉	—	2	1	no	—
222	C₂×D₃×C₉	—	2	1	no	—
223	C₂×D₃×C₉	—	2	1	no	—
224	C₂×D₃×C₉	—	2	1	no	—
225	C₂×D₃×C₉	—	4	4	no	—
226	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
227	C₃×C₄×C₉	—	2	1	no	—
228	C₃×C₄×C₉	—	2	1	no	—
229	C₃×C₄×C₉	—	2	1	no	—
230	C₃×C₄×C₉	—	2	1	no	—
231	C₉×Dic₃	—	2	1	no	—
232	C₉×Dic₃	—	2	1	no	—
233	C₉×Dic₃	—	2	1	no	—
234	C₉×Dic₃	—	2	1	no	—
235	C₉×Dic₃	C₂×D₄	1	2	yes	—
236	C₂×C₃×#41	—	3	1	no	—
237	C₂²×C₃×D₄	—	3	1	no	—
238	C₂²×#67	C₂×C₉	1	1	yes	characteristic, complemented
239	C₂×#235	C₂×C₉	1	1	yes	characteristic, complemented
240	C₃×#124	—	3	1	no	—
241	C₃×#123	—	3	1	no	—
242	C₃×#123	—	3	1	no	—
243	C₃×C₂²⋊Q₈	—	3	1	no	—
244	C₃×#121	—	3	1	no	—
245	C₃×#121	—	3	1	no	—
246	C₃×#121	—	3	1	no	—
247	C₃×#120	—	3	1	no	—
248	C₃×#120	—	3	1	no	—
249	C₃×C₄×D₄	—	3	1	no	—
250	C₃×C₄×D₄	—	3	1	no	—
251	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
253	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
254	C₂×C₃×C₂²⋊C₄	C₃×D₃	1	1	yes	characteristic
255	#953	C₂×C₉	1	1	yes	characteristic, complemented
256	#930	C₂×C₉	1	1	yes	characteristic, complemented
257	#929	C₂×C₉	1	1	yes	characteristic, complemented
258	C₄×#67	C₂×C₉	1	1	yes	characteristic, complemented
259	#885	C₂×C₉	1	1	yes	characteristic, complemented
260	#884	C₂×C₉	1	1	yes	characteristic, complemented
261	#884	C₂×C₉	1	1	yes	characteristic, complemented
262	#883	C₂×C₉	1	1	yes	characteristic, complemented
263	#882	C₂×C₉	1	1	yes	characteristic, complemented
264	#67⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
265	D₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
266	#878	C₂×C₉	1	1	yes	characteristic, complemented
267	C₂³×C₃²	—	2	2	no	—
268	C₂³×C₃²	—	2	2	no	—
269	C₂³×C₃²	—	4	1	no	—
270	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
271	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
272	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
273	C₂²×C₃×D₃	—	2	2	no	—
274	C₂²×C₃×D₃	—	2	2	no	—
275	C₂²×C₃×D₃	—	4	1	no	—
276	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
277	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
278	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
279	C₂×C₃²×C₄	—	2	2	no	—
280	C₂×C₃²×C₄	—	4	1	no	—
281	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
282	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
283	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
284	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
285	C₃×#67	—	2	2	no	—
286	C₃×#67	—	2	2	no	—
287	C₃×#67	—	2	2	no	—
288	C₃×#67	—	2	2	no	—
289	C₃×#67	—	2	2	no	—
290	C₃×#67	—	4	1	no	—
291	C₃×#67	C₃×D₄	1	4	yes	—
292	C₂×C₃×Dic₃	—	2	2	no	—
293	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
294	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
295	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
296	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
297	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
298	C₃×D₁₂	—	2	2	no	—
299	C₃×D₁₂	—	4	1	no	—
300	C₃×C₄×D₃	—	2	2	no	—
301	C₃×C₄×D₃	—	2	2	no	—
302	C₃×C₄×D₃	—	4	1	no	—
303	C₃×Dic₆	—	2	2	no	—
304	C₂³×C₉	—	2	4	no	—
305	C₂³×C₉	—	2	2	no	—
306	C₂³×C₉	—	2	2	no	—
307	C₂³×C₉	—	2	1	no	—
308	C₂³×C₉	—	2	1	no	—
309	C₂³×C₉	—	2	1	no	—
310	C₂³×C₉	—	3	1	no	—
311	C₂³×C₉	—	3	1	no	—
312	C₂³×C₉	—	3	1	no	—
313	C₂³×C₉	—	4	2	no	—
314	C₂³×C₉	—	4	1	no	—
315	C₂³×C₉	—	4	2	no	—
316	C₂³×C₉	—	6	2	no	—
317	C₂³×C₉	—	6	2	no	—
318	C₂³×C₉	—	12	1	no	—
319	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
320	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
321	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
322	Q₈×C₉	—	6	2	no	—
323	D₄×C₉	—	3	4	no	—
324	D₄×C₉	—	6	2	no	—
325	D₄×C₉	—	6	2	no	—
326	D₄×C₉	—	6	2	no	—
327	D₄×C₉	—	6	2	no	—
328	D₄×C₉	—	6	2	no	—
329	D₄×C₉	—	6	2	no	—
330	D₄×C₉	—	12	1	no	—
331	D₄×C₉	—	12	1	no	—
332	C₂×C₄×C₉	—	2	2	no	—
333	C₂×C₄×C₉	—	2	1	no	—
334	C₂×C₄×C₉	—	2	1	no	—
335	C₂×C₄×C₉	—	2	1	no	—
336	C₂×C₄×C₉	—	2	1	no	—
337	C₂×C₄×C₉	—	3	1	no	—
338	C₂×C₄×C₉	—	3	1	no	—
339	C₂×C₄×C₉	—	3	1	no	—
340	C₂×C₄×C₉	—	3	1	no	—
341	C₂×C₄×C₉	—	3	1	no	—
342	C₂×C₄×C₉	—	4	2	no	—
343	C₂×C₄×C₉	—	4	1	no	—
344	C₂×C₄×C₉	—	4	2	no	—
345	C₂×C₄×C₉	—	6	2	no	—
346	C₂×C₄×C₉	—	6	2	no	—
347	C₂×C₄×C₉	—	6	2	no	—
348	C₂×C₄×C₉	—	12	1	no	—
349	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
350	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
351	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
352	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
353	#546	—	3	1	no	Sylow
354	C₂×C₃×C₉	—	2	2	no	—
355	C₂×C₃×C₉	—	2	2	no	—
356	C₂×C₃×C₉	—	4	1	no	—
357	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
359	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
360	D₃×C₉	—	2	2	no	—
361	D₃×C₉	—	4	1	no	—
362	D₃×C₉	—	4	1	no	—
363	C₂⁴×C₃	—	2	1	no	—
364	C₂⁴×C₃	—	3	1	no	—
365	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
366	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
367	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
368	C₃×#41	—	6	4	no	—
369	C₂×C₃×Q₈	—	3	1	no	—
370	C₂×C₃×D₄	—	3	1	no	—
371	C₂×C₃×D₄	—	3	1	no	—
372	C₂×C₃×D₄	—	3	1	no	—
373	C₂×C₃×D₄	—	3	1	no	—
374	C₂×C₃×D₄	—	3	1	no	—
375	C₂×C₃×D₄	—	3	1	no	—
376	C₂×C₃×D₄	—	3	1	no	—
377	C₂×C₃×D₄	—	3	1	no	—
378	C₂×C₃×D₄	—	3	1	no	—
379	C₂×C₃×D₄	—	6	4	no	—
380	C₂²×C₃×C₄	—	2	1	no	—
381	C₂²×C₃×C₄	—	2	1	no	—
382	C₂²×C₃×C₄	—	3	1	no	—
383	C₂²×C₃×C₄	—	3	1	no	—
384	C₂²×C₃×C₄	—	3	1	no	—
385	C₂²×C₃×C₄	—	3	1	no	—
386	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic, complemented
387	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic, complemented
388	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
389	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
390	C₂×#67	—	2	4	no	—
391	C₂×#67	C₂²×C₉	1	1	yes	characteristic
392	C₂×#67	C₂²×C₉	1	1	yes	characteristic
393	C₂×#67	C₂²×C₉	1	1	yes	characteristic
394	C₂×#67	C₂²×C₉	1	1	yes	characteristic
395	C₂×#67	C₂²×C₉	1	1	yes	characteristic
396	C₂×#67	C₂²×C₉	1	1	yes	characteristic, complemented
397	C₂×#67	C₂²×C₉	1	1	yes	characteristic, complemented
398	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
399	#235	—	2	4	no	—
400	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic, complemented
401	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic, complemented
402	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
403	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
404	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
405	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
406	C₃×C₄⋊C₄	—	3	1	no	—
407	C₃×C₄⋊C₄	—	3	1	no	—
408	C₃×C₄⋊C₄	—	3	1	no	—
409	C₃×C₄⋊C₄	—	3	1	no	—
410	C₃×C₂²⋊C₄	—	2	1	no	—
411	C₃×C₂²⋊C₄	—	2	1	no	—
412	C₃×C₂²⋊C₄	—	2	1	no	—
413	C₃×C₂²⋊C₄	—	2	1	no	—
414	C₃×C₂²⋊C₄	—	3	1	no	—
415	C₃×C₂²⋊C₄	—	3	1	no	—
416	C₃×C₂²⋊C₄	—	3	1	no	—
417	C₃×C₂²⋊C₄	—	3	1	no	—
418	C₃×C₂²⋊C₄	—	3	1	no	—
419	C₃×C₂²⋊C₄	—	3	1	no	—
420	C₃×C₂²⋊C₄	—	3	1	no	—
421	C₃×C₂²⋊C₄	—	3	1	no	—
422	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
423	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
424	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
425	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
426	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
427	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
428	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
429	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
430	C₃×C₄²	—	3	1	no	—
431	#217	C₂²×C₉	1	1	yes	characteristic
432	#217	C₂²×C₉	1	1	yes	characteristic, complemented
433	#217	C₂²×C₉	1	1	yes	characteristic, complemented
434	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
435	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
436	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
437	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
438	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
439	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
440	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
441	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
442	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
443	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
444	C₂²×C₃²	—	2	1	no	—
445	C₂²×C₃²	—	2	1	no	—
446	C₂²×C₃²	—	2	1	no	—
447	C₂²×C₃²	—	2	1	no	—
448	C₂²×C₃²	—	2	1	no	—
449	C₂²×C₃²	—	2	1	no	—
450	C₂²×C₃²	—	2	1	no	—
451	C₂²×C₃²	—	4	4	no	—
452	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
453	C₂²×C₃²	C₃×#41	1	2	yes	—
454	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
455	C₂×C₃×D₃	—	2	1	no	—
456	C₂×C₃×D₃	—	2	1	no	—
457	C₂×C₃×D₃	—	2	1	no	—
458	C₂×C₃×D₃	—	2	1	no	—
459	C₂×C₃×D₃	—	2	1	no	—
460	C₂×C₃×D₃	—	2	1	no	—
461	C₂×C₃×D₃	—	2	1	no	—
462	C₂×C₃×D₃	—	2	1	no	—
463	C₂×C₃×D₃	—	4	4	no	—
464	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
465	C₃²×C₄	—	2	1	no	—
466	C₃²×C₄	—	2	1	no	—
467	C₃²×C₄	—	2	1	no	—
468	C₃²×C₄	—	2	1	no	—
469	C₃×Dic₃	—	2	1	no	—
470	C₃×Dic₃	—	2	1	no	—
471	C₃×Dic₃	—	2	1	no	—
472	C₃×Dic₃	—	2	1	no	—
473	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
474	C₂²×C₉	—	2	2	no	—
475	C₂²×C₉	—	2	2	no	—
476	C₂²×C₉	—	2	1	no	—
477	C₂²×C₉	—	2	1	no	—
478	C₂²×C₉	—	2	1	no	—
479	C₂²×C₉	—	2	1	no	—
480	C₂²×C₉	—	2	2	no	—
481	C₂²×C₉	—	2	1	no	—
482	C₂²×C₉	—	2	1	no	—
483	C₂²×C₉	—	2	1	no	—
484	C₂²×C₉	—	2	1	no	—
485	C₂²×C₉	—	2	2	no	—
486	C₂²×C₉	—	2	2	no	—
487	C₂²×C₉	—	3	2	no	—
488	C₂²×C₉	—	4	1	no	—
489	C₂²×C₉	—	4	1	no	—
490	C₂²×C₉	—	4	1	no	—
491	C₂²×C₉	—	4	1	no	—
492	C₂²×C₉	—	4	4	no	—
493	C₂²×C₉	—	4	8	no	—
494	C₂²×C₉	—	6	1	no	—
495	C₂²×C₉	—	6	1	no	—
496	C₂²×C₉	—	6	1	no	—
497	C₂²×C₉	—	6	1	no	—
498	C₂²×C₉	—	6	1	no	—
499	C₂²×C₉	—	6	1	no	—
500	C₂²×C₉	—	6	1	no	—
501	C₂²×C₉	—	6	1	no	—
502	C₂²×C₉	—	12	4	no	—
503	C₂²×C₉	#235	1	2	yes	complemented
504	C₂²×C₉	D₃×D₄	1	2	yes	—
505	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
506	C₄×C₉	—	2	1	no	—
507	C₄×C₉	—	2	1	no	—
508	C₄×C₉	—	2	1	no	—
509	C₄×C₉	—	2	1	no	—
510	C₄×C₉	—	3	2	no	—
511	C₄×C₉	—	4	1	no	—
512	C₄×C₉	—	4	1	no	—
513	C₄×C₉	—	4	1	no	—
514	C₄×C₉	—	4	1	no	—
515	C₄×C₉	—	6	1	no	—
516	C₄×C₉	—	6	1	no	—
517	C₄×C₉	—	6	1	no	—
518	C₄×C₉	—	6	1	no	—
519	C₂×#41	—	3	1	no	—
520	C₂²×D₄	—	3	1	no	—
521	#124	—	3	1	no	—
522	#123	—	3	1	no	—
523	#123	—	3	1	no	—
524	C₂²⋊Q₈	—	3	1	no	—
525	#121	—	3	1	no	—
526	#121	—	3	1	no	—
527	#121	—	3	1	no	—
528	#120	—	3	1	no	—
529	#120	—	3	1	no	—
530	C₄×D₄	—	3	1	no	—
531	C₄×D₄	—	3	1	no	—
532	C₂×C₂²⋊C₄	—	3	1	no	—
533	C₂×C₂²⋊C₄	D₃×C₉	1	1	yes	characteristic, complemented
534	C₃×C₉	#546	1	1	yes	characteristic, complemented, Sylow
535	C₂³×C₃	—	2	4	no	—
536	C₂³×C₃	—	2	2	no	—
537	C₂³×C₃	—	2	2	no	—
538	C₂³×C₃	—	2	2	no	—
539	C₂³×C₃	—	2	2	no	—
540	C₂³×C₃	—	2	1	no	—
541	C₂³×C₃	—	2	1	no	—
542	C₂³×C₃	—	2	1	no	—
543	C₂³×C₃	—	3	1	no	—
544	C₂³×C₃	—	3	1	no	—
545	C₂³×C₃	—	3	1	no	—
546	C₂³×C₃	—	4	2	no	—
547	C₂³×C₃	—	4	1	no	—
548	C₂³×C₃	—	4	1	no	—
549	C₂³×C₃	—	4	2	no	—
550	C₂³×C₃	—	6	2	no	—
551	C₂³×C₃	—	6	2	no	—
552	C₂³×C₃	—	12	1	no	—
553	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
554	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
555	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
556	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
557	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
558	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
559	C₂²×D₃	—	2	2	no	—
560	C₂²×D₃	—	2	2	no	—
561	C₂²×D₃	—	4	1	no	—
562	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
563	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
564	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
565	C₃×Q₈	—	6	2	no	—
566	C₃×D₄	—	3	4	no	—
567	C₃×D₄	—	6	2	no	—
568	C₃×D₄	—	6	2	no	—
569	C₃×D₄	—	6	2	no	—
570	C₃×D₄	—	6	2	no	—
571	C₃×D₄	—	6	2	no	—
572	C₃×D₄	—	6	2	no	—
573	C₃×D₄	—	12	1	no	—
574	C₃×D₄	—	12	1	no	—
575	C₂×C₃×C₄	—	2	2	no	—
576	C₂×C₃×C₄	—	2	2	no	—
577	C₂×C₃×C₄	—	2	1	no	—
578	C₂×C₃×C₄	—	2	1	no	—
579	C₂×C₃×C₄	—	2	1	no	—
580	C₂×C₃×C₄	—	2	1	no	—
581	C₂×C₃×C₄	—	3	1	no	—
582	C₂×C₃×C₄	—	3	1	no	—
583	C₂×C₃×C₄	—	3	1	no	—
584	C₂×C₃×C₄	—	3	1	no	—
585	C₂×C₃×C₄	—	3	1	no	—
586	C₂×C₃×C₄	—	4	2	no	—
587	C₂×C₃×C₄	—	4	1	no	—
588	C₂×C₃×C₄	—	4	1	no	—
589	C₂×C₃×C₄	—	4	2	no	—
590	C₂×C₃×C₄	—	6	2	no	—
591	C₂×C₃×C₄	—	6	2	no	—
592	C₂×C₃×C₄	—	6	2	no	—
593	C₂×C₃×C₄	—	12	1	no	—
594	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
595	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
596	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
597	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
598	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
599	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
600	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
601	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
602	#67	—	2	2	no	—
603	#67	—	2	2	no	—
604	#67	—	2	2	no	—
605	#67	—	2	2	no	—
606	#67	—	2	2	no	—
607	#67	—	4	1	no	—
608	#67	D₄×C₉	1	4	yes	complemented
609	C₂×Dic₃	—	2	2	no	—
610	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
611	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
612	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
613	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
614	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
615	D₁₂	—	2	2	no	—
616	D₁₂	—	4	1	no	—
617	C₄×D₃	—	2	2	no	—
618	C₄×D₃	—	2	2	no	—
619	C₄×D₃	—	4	1	no	—
620	Dic₆	—	2	2	no	—
621	C₂×C₃²	—	2	2	no	—
622	C₂×C₃²	—	2	2	no	—
623	C₂×C₃²	—	4	1	no	—
624	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
625	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
626	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
627	C₃×D₃	—	2	2	no	—
628	C₃×D₃	—	4	1	no	—
629	C₃×D₃	—	4	1	no	—
630	C₂×C₉	—	2	4	no	—
631	C₂×C₉	—	2	2	no	—
632	C₂×C₉	—	2	2	no	—
633	C₂×C₉	—	2	1	no	—
634	C₂×C₉	—	2	1	no	—
635	C₂×C₉	—	2	1	no	—
636	C₂×C₉	—	4	2	no	—
637	C₂×C₉	—	4	2	no	—
638	C₂×C₉	—	4	1	no	—
639	C₂×C₉	—	6	2	no	—
640	C₂×C₉	—	12	1	no	—
641	C₂×C₉	—	12	1	no	—
642	C₂×C₉	C₂×#235	1	1	yes	characteristic
643	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
644	C₂×C₉	#1004	1	1	yes	characteristic
645	C₂⁴	—	3	1	no	—
646	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
647	#41	—	6	4	no	—
648	C₂×Q₈	—	3	1	no	—
649	C₂×D₄	—	3	1	no	—
650	C₂×D₄	—	3	1	no	—
651	C₂×D₄	—	3	1	no	—
652	C₂×D₄	—	3	1	no	—
653	C₂×D₄	—	3	1	no	—
654	C₂×D₄	—	3	1	no	—
655	C₂×D₄	—	3	1	no	—
656	C₂×D₄	—	3	1	no	—
657	C₂×D₄	—	3	1	no	—
658	C₂×D₄	—	6	4	no	—
659	C₂²×C₄	—	3	1	no	—
660	C₂²×C₄	—	3	1	no	—
661	C₂²×C₄	—	3	1	no	—
662	C₂²×C₄	—	3	1	no	—
663	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
664	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
665	C₄⋊C₄	—	3	1	no	—
666	C₄⋊C₄	—	3	1	no	—
667	C₄⋊C₄	—	3	1	no	—
668	C₄⋊C₄	—	3	1	no	—
669	C₂²⋊C₄	—	3	1	no	—
670	C₂²⋊C₄	—	3	1	no	—
671	C₂²⋊C₄	—	3	1	no	—
672	C₂²⋊C₄	—	3	1	no	—
673	C₂²⋊C₄	—	3	1	no	—
674	C₂²⋊C₄	—	3	1	no	—
675	C₂²⋊C₄	—	3	1	no	—
676	C₂²⋊C₄	—	3	1	no	—
677	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
678	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
679	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
680	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
681	C₄²	—	3	1	no	—
682	C₂²×C₃	—	2	2	no	—
683	C₂²×C₃	—	2	2	no	—
684	C₂²×C₃	—	2	1	no	—
685	C₂²×C₃	—	2	1	no	—
686	C₂²×C₃	—	2	1	no	—
687	C₂²×C₃	—	2	1	no	—
688	C₂²×C₃	—	2	1	no	—
689	C₂²×C₃	—	2	1	no	—
690	C₂²×C₃	—	2	1	no	—
691	C₂²×C₃	—	2	1	no	—
692	C₂²×C₃	—	2	2	no	—
693	C₂²×C₃	—	2	1	no	—
694	C₂²×C₃	—	2	1	no	—
695	C₂²×C₃	—	2	1	no	—
696	C₂²×C₃	—	2	1	no	—
697	C₂²×C₃	—	2	1	no	—
698	C₂²×C₃	—	2	1	no	—
699	C₂²×C₃	—	2	1	no	—
700	C₂²×C₃	—	2	2	no	—
701	C₂²×C₃	—	2	2	no	—
702	C₂²×C₃	—	3	2	no	—
703	C₂²×C₃	—	4	1	no	—
704	C₂²×C₃	—	4	1	no	—
705	C₂²×C₃	—	4	1	no	—
706	C₂²×C₃	—	4	1	no	—
707	C₂²×C₃	—	4	4	no	—
708	C₂²×C₃	—	4	4	no	—
709	C₂²×C₃	—	4	8	no	—
710	C₂²×C₃	—	6	1	no	—
711	C₂²×C₃	—	6	1	no	—
712	C₂²×C₃	—	6	1	no	—
713	C₂²×C₃	—	6	1	no	—
714	C₂²×C₃	—	6	1	no	—
715	C₂²×C₃	—	6	1	no	—
716	C₂²×C₃	—	6	1	no	—
717	C₂²×C₃	—	6	1	no	—
718	C₂²×C₃	—	12	4	no	—
719	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
720	C₂²×C₃	C₉×#41	1	2	yes	complemented
721	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
722	C₂²×C₃	C₃×#235	1	2	yes	—
723	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
724	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
725	C₂×D₃	—	2	1	no	—
726	C₂×D₃	—	2	1	no	—
727	C₂×D₃	—	2	1	no	—
728	C₂×D₃	—	2	1	no	—
729	C₂×D₃	—	2	1	no	—
730	C₂×D₃	—	2	1	no	—
731	C₂×D₃	—	2	1	no	—
732	C₂×D₃	—	2	1	no	—
733	C₂×D₃	—	4	4	no	—
734	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
735	C₃×C₄	—	2	1	no	—
736	C₃×C₄	—	2	1	no	—
737	C₃×C₄	—	2	1	no	—
738	C₃×C₄	—	2	1	no	—
739	C₃×C₄	—	2	1	no	—
740	C₃×C₄	—	2	1	no	—
741	C₃×C₄	—	2	1	no	—
742	C₃×C₄	—	2	1	no	—
743	C₃×C₄	—	3	2	no	—
744	C₃×C₄	—	4	1	no	—
745	C₃×C₄	—	4	1	no	—
746	C₃×C₄	—	4	1	no	—
747	C₃×C₄	—	4	1	no	—
748	C₃×C₄	—	6	1	no	—
749	C₃×C₄	—	6	1	no	—
750	C₃×C₄	—	6	1	no	—
751	C₃×C₄	—	6	1	no	—
752	Dic₃	—	2	1	no	—
753	Dic₃	—	2	1	no	—
754	Dic₃	—	2	1	no	—
755	Dic₃	—	2	1	no	—
756	Dic₃	C₂×D₄×C₉	1	2	yes	—
757	C₃²	C₃×#546	1	1	yes	characteristic
758	C₉	—	2	1	no	—
759	C₉	#5490	1	1	yes	characteristic, direct product factor
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	3	1	no	—
763	C₂³	—	3	1	no	—
764	C₂³	—	3	1	no	—
765	C₂³	—	4	1	no	—
766	C₂³	—	6	2	no	—
767	C₂³	—	6	2	no	—
768	C₂³	—	12	1	no	—
769	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
770	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
771	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
772	Q₈	—	6	2	no	—
773	D₄	—	3	4	no	—
774	D₄	—	6	2	no	—
775	D₄	—	6	2	no	—
776	D₄	—	6	2	no	—
777	D₄	—	6	2	no	—
778	D₄	—	6	2	no	—
779	D₄	—	6	2	no	—
780	D₄	—	12	1	no	—
781	D₄	—	12	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	3	1	no	—
784	C₂×C₄	—	3	1	no	—
785	C₂×C₄	—	3	1	no	—
786	C₂×C₄	—	3	1	no	—
787	C₂×C₄	—	3	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	6	2	no	—
790	C₂×C₄	—	6	2	no	—
791	C₂×C₄	—	6	2	no	—
792	C₂×C₄	—	12	1	no	—
793	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
794	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
795	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
796	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
797	C₂×C₃	—	2	4	no	—
798	C₂×C₃	—	2	2	no	—
799	C₂×C₃	—	2	2	no	—
800	C₂×C₃	—	2	2	no	—
801	C₂×C₃	—	2	2	no	—
802	C₂×C₃	—	2	1	no	—
803	C₂×C₃	—	2	1	no	—
804	C₂×C₃	—	2	1	no	—
805	C₂×C₃	—	4	2	no	—
806	C₂×C₃	—	4	2	no	—
807	C₂×C₃	—	4	1	no	—
808	C₂×C₃	—	4	1	no	—
809	C₂×C₃	—	6	2	no	—
810	C₂×C₃	—	12	1	no	—
811	C₂×C₃	—	12	1	no	—
812	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
813	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
814	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
815	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
816	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
817	C₂×C₃	C₃×#1004	1	1	yes	characteristic
818	D₃	—	2	2	no	—
819	D₃	—	4	1	no	—
820	D₃	—	4	1	no	—
821	C₂²	—	2	1	no	—
822	C₂²	—	2	1	no	—
823	C₂²	—	2	1	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	3	2	no	—
829	C₂²	—	4	4	no	—
830	C₂²	—	6	1	no	—
831	C₂²	—	6	1	no	—
832	C₂²	—	6	1	no	—
833	C₂²	—	6	1	no	—
834	C₂²	—	6	1	no	—
835	C₂²	—	6	1	no	—
836	C₂²	—	6	1	no	—
837	C₂²	—	6	1	no	—
838	C₂²	—	12	4	no	—
839	C₂²	C₉×#235	1	2	yes	complemented
840	C₂²	D₃×D₄×C₉	1	2	yes	—
841	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
842	C₄	—	2	1	no	—
843	C₄	—	2	1	no	—
844	C₄	—	2	1	no	—
845	C₄	—	2	1	no	—
846	C₄	—	3	2	no	—
847	C₄	—	6	1	no	—
848	C₄	—	6	1	no	—
849	C₄	—	6	1	no	—
850	C₄	—	6	1	no	—
851	C₃	—	2	1	no	—
852	C₃	C₉×#546	1	1	yes	characteristic, complemented
853	C₃	C₃×#5490	1	1	yes	characteristic
854	C₂	—	2	2	no	—
855	C₂	—	2	2	no	—
856	C₂	—	4	1	no	—
857	C₂	—	6	2	no	—
858	C₂	—	12	1	no	—
859	C₂	—	12	1	no	—
860	C₂	C₂×C₉×#235	1	1	yes	characteristic
861	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
862	C₂	C₉×#1004	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×C₂²⋊C₄	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5490	C₃
hypercenter	C₂×C₉×C₂²⋊C₄	D₃
hypocenter	C₃	C₉×#546
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₉×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₉×#67	C₂	semidirect
2. C₂×C₉×#235	C₂	semidirect
3. C₂×C₃×C₉×C₂²⋊C₄	C₂	semidirect
4. C₉×#953	C₂	semidirect
5. C₉×#930	C₂	semidirect
6. C₉×#929	C₂	semidirect
7. C₄×C₉×#67	C₂	semidirect
8. C₉×#885	C₂	semidirect
9. C₉×#884	C₂	semidirect
10. C₉×#884	C₂	semidirect
11. C₉×#883	C₂	semidirect
12. C₉×#882	C₂	semidirect
13. C₉×#67⋊C₄	C₂	semidirect
14. D₃×C₉×C₂²⋊C₄	C₂	semidirect
15. C₉×#878	C₂	semidirect
20. C₂²×C₃×C₄×C₉	C₂²	semidirect
21. C₂²×C₃×C₄×C₉	C₂²	semidirect
28. C₂×C₉×#67	C₂²	semidirect
29. C₂×C₉×#67	C₂²	semidirect
32. C₂×C₉×D₁₂	C₂²	semidirect
33. C₂×C₉×D₁₂	C₂²	semidirect
34. C₂×C₄×D₃×C₉	C₂²	semidirect
35. C₂×C₄×D₃×C₉	C₂²	semidirect
36. C₂×C₄×D₃×C₉	C₂²	semidirect
37. C₂×C₉×Dic₆	C₂²	semidirect
40. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
41. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
43. C₉×#217	C₂²	semidirect
44. C₉×#217	C₂²	semidirect
45. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
46. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
47. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
48. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
49. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
50. C₉×C₄⋊Dic₃	C₂²	semidirect
51. C₉×Dic₃⋊C₄	C₂²	semidirect
52. C₉×Dic₃⋊C₄	C₂²	semidirect
53. C₉×Dic₃⋊C₄	C₂²	semidirect
54. C₄×C₉×Dic₃	C₂²	semidirect
85. C₂×C₉×C₂²⋊C₄	D₃	semidirect
110. C₉×#67	D₄	semidirect
124. #5490	C₉	direct (N × H)
183. C₂²×C₄×C₉	C₂×D₃	semidirect
184. C₂²×C₄×C₉	C₂×D₃	semidirect
203. C₉×C₂²⋊C₄	C₂×D₃	semidirect
204. C₉×C₂²⋊C₄	C₂×D₃	semidirect
215. C₂²×C₃×C₉	#41	semidirect
238. C₂²×#67	C₂×C₉	semidirect
239. C₂×#235	C₂×C₉	semidirect
253. C₂×C₃×C₂²⋊C₄	C₂×C₉	semidirect
255. #953	C₂×C₉	semidirect
256. #930	C₂×C₉	semidirect
257. #929	C₂×C₉	semidirect
258. C₄×#67	C₂×C₉	semidirect
259. #885	C₂×C₉	semidirect
260. #884	C₂×C₉	semidirect
261. #884	C₂×C₉	semidirect
262. #883	C₂×C₉	semidirect
263. #882	C₂×C₉	semidirect
264. #67⋊C₄	C₂×C₉	semidirect
265. D₃×C₂²⋊C₄	C₂×C₉	semidirect
266. #878	C₂×C₉	semidirect
386. C₂²×C₃×C₄	C₂²×C₉	semidirect
387. C₂²×C₃×C₄	C₂²×C₉	semidirect
396. C₂×#67	C₂²×C₉	semidirect
397. C₂×#67	C₂²×C₉	semidirect
400. C₂×D₁₂	C₂²×C₉	semidirect
401. C₂×D₁₂	C₂²×C₉	semidirect
402. C₂×C₄×D₃	C₂²×C₉	semidirect
403. C₂×C₄×D₃	C₂²×C₉	semidirect
404. C₂×C₄×D₃	C₂²×C₉	semidirect
405. C₂×Dic₆	C₂²×C₉	semidirect
424. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
425. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
432. #217	C₂²×C₉	semidirect
433. #217	C₂²×C₉	semidirect
434. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
435. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
436. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
437. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
438. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
439. C₄⋊Dic₃	C₂²×C₉	semidirect
440. Dic₃⋊C₄	C₂²×C₉	semidirect
441. Dic₃⋊C₄	C₂²×C₉	semidirect
442. Dic₃⋊C₄	C₂²×C₉	semidirect
443. C₄×Dic₃	C₂²×C₉	semidirect
503. C₂²×C₉	#235	semidirect
533. C₂×C₂²⋊C₄	D₃×C₉	semidirect
534. C₃×C₉	#546	semidirect
608. #67	D₄×C₉	semidirect
663. C₂²×C₄	C₂×D₃×C₉	semidirect
664. C₂²×C₄	C₂×D₃×C₉	semidirect
679. C₂²⋊C₄	C₂×D₃×C₉	semidirect
680. C₂²⋊C₄	C₂×D₃×C₉	semidirect
720. C₂²×C₃	C₉×#41	semidirect
759. C₉	#5490	direct (N × H)
839. C₂²	C₉×#235	semidirect
852. C₃	C₉×#546	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₉×#67	2
C₂×C₉×#235	2
C₂×C₃×C₉×C₂²⋊C₄	2
C₉×#953	2
C₉×#930	2
C₉×#929	2
C₄×C₉×#67	2
C₉×#885	2
C₉×#884	2
C₉×#883	2
C₉×#882	2
C₉×#67⋊C₄	2
D₃×C₉×C₂²⋊C₄	2
C₉×#878	2
C₃×#5490	3
C₉×#546	3

Subgroups — C9×#5490 #13152350

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5490 #13152350