Subgroups — C₉×#5591 #13152763

Order 1728.

1132 conjugacy classes of subgroups.

The subgroup lattice has 872 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×#237	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×#217	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#939	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#939	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#938	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#937	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#886	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#885	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#883	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×#5591	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	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
21	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₉×#67	—	2	4	no	—
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	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
34	C₉×#237	—	2	4	no	—
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, complemented
40	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₉×#217	C₂²	1	1	yes	characteristic
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×#217	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×C₄⋊Dic₃	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×#237	C₂×C₃	1	1	yes	characteristic
57	C₃²×#120	C₂×C₃	1	1	yes	characteristic
58	C₂×C₃×#217	C₂×C₃	1	1	yes	characteristic
59	C₃×#939	C₂×C₃	1	1	yes	characteristic
60	C₃×#939	C₂×C₃	1	1	yes	characteristic
61	C₃×#938	C₂×C₃	1	1	yes	characteristic
62	C₃×#937	C₂×C₃	1	1	yes	characteristic
63	C₃×D₄×Dic₃	C₂×C₃	1	1	yes	characteristic
64	C₃×#886	C₂×C₃	1	1	yes	characteristic
65	C₃×#885	C₂×C₃	1	1	yes	characteristic
66	C₃×#883	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	—	2	1	no	—
80	C₉×#120	—	3	1	no	—
81	C₉×#120	D₃	1	1	yes	characteristic, complemented
82	C₄×D₄×C₉	—	3	1	no	—
83	C₄×D₄×C₉	—	3	1	no	—
84	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
85	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
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	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
93	C₂²×D₃×C₉	—	2	2	no	—
94	C₂²×D₃×C₉	—	2	2	no	—
95	C₂²×D₃×C₉	—	4	1	no	—
96	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
97	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
98	C₃×D₄×C₉	—	2	2	no	—
99	C₃×D₄×C₉	—	2	2	no	—
100	C₃×D₄×C₉	—	4	1	no	—
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	—	4	1	no	—
109	C₉×#67	D₄	1	4	yes	complemented
110	C₂×C₉×Dic₃	—	2	2	no	—
111	C₂×C₉×Dic₃	—	2	2	no	—
112	C₂×C₉×Dic₃	—	2	2	no	—
113	C₂×C₉×Dic₃	—	4	1	no	—
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	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
118	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
119	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
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	#5591	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	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
130	C₂×C₃×#67	—	2	4	no	—
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	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
139	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
140	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
141	C₃×#237	—	2	4	no	—
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	C₃×#217	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×#217	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×C₄⋊Dic₃	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	—	2	1	no	—
168	C₂×D₄×C₉	—	2	1	no	—
169	C₂×D₄×C₉	—	2	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	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
178	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
179	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
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	—	3	1	no	—
184	C₂²×C₄×C₉	—	3	1	no	—
185	C₂²×C₄×C₉	—	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×C₄⋊C₄	—	3	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	—	3	1	no	—
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	—	2	1	no	—
214	C₂²×C₃×C₉	—	2	1	no	—
215	C₂²×C₃×C₉	—	2	1	no	—
216	C₂²×C₃×C₉	—	4	4	no	—
217	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
218	C₂²×C₃×C₉	#41	1	2	yes	complemented
219	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
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	C₉×Dic₃	—	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×#237	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	—	2	1	no	—
248	C₃×#120	—	3	1	no	—
249	C₃×#120	C₂×C₉	1	1	yes	characteristic, complemented
250	C₃×#120	C₃×D₃	1	1	yes	characteristic
251	C₃×C₄×D₄	—	3	1	no	—
252	C₃×C₄×D₄	—	3	1	no	—
253	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
254	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
255	C₂×#217	C₂×C₉	1	1	yes	characteristic, complemented
256	#939	C₂×C₉	1	1	yes	characteristic, complemented
257	#939	C₂×C₉	1	1	yes	characteristic, complemented
258	#938	C₂×C₉	1	1	yes	characteristic, complemented
259	#937	C₂×C₉	1	1	yes	characteristic, complemented
260	D₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
261	#886	C₂×C₉	1	1	yes	characteristic, complemented
262	#885	C₂×C₉	1	1	yes	characteristic, complemented
263	#883	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	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
274	C₂²×C₃×D₃	—	2	2	no	—
275	C₂²×C₃×D₃	—	2	2	no	—
276	C₂²×C₃×D₃	—	4	1	no	—
277	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
278	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
279	C₃²×D₄	—	2	2	no	—
280	C₃²×D₄	—	2	2	no	—
281	C₃²×D₄	—	4	1	no	—
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	—	4	1	no	—
290	C₃×#67	C₃×D₄	1	4	yes	—
291	C₂×C₃×Dic₃	—	2	2	no	—
292	C₂×C₃×Dic₃	—	2	2	no	—
293	C₂×C₃×Dic₃	—	2	2	no	—
294	C₂×C₃×Dic₃	—	4	1	no	—
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	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
299	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
300	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
301	C₃×C₄×D₃	—	2	2	no	—
302	C₃×C₄×D₃	—	4	1	no	—
303	C₃×Dic₆	—	2	2	no	—
304	C₂³×C₉	—	2	2	no	—
305	C₂³×C₉	—	2	2	no	—
306	C₂³×C₉	—	2	1	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	—	4	2	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	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
323	Q₈×C₉	—	6	2	no	—
324	D₄×C₉	—	2	2	no	—
325	D₄×C₉	—	2	2	no	—
326	D₄×C₉	—	3	4	no	—
327	D₄×C₉	—	4	2	no	—
328	D₄×C₉	—	4	2	no	—
329	D₄×C₉	—	4	1	no	—
330	D₄×C₉	—	4	2	no	—
331	D₄×C₉	—	6	2	no	—
332	D₄×C₉	—	6	2	no	—
333	D₄×C₉	—	6	2	no	—
334	D₄×C₉	—	6	2	no	—
335	D₄×C₉	—	12	1	no	—
336	C₂×C₄×C₉	—	2	1	no	—
337	C₂×C₄×C₉	—	2	1	no	—
338	C₂×C₄×C₉	—	2	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	—	3	1	no	—
343	C₂×C₄×C₉	—	3	1	no	—
344	C₂×C₄×C₉	—	3	1	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	—	6	2	no	—
349	C₂×C₄×C₉	—	12	1	no	—
350	C₂×C₄×C₉	—	12	1	no	—
351	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
352	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
353	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
354	#546	—	3	1	no	Sylow
355	C₂×C₃×C₉	—	2	2	no	—
356	C₂×C₃×C₉	—	2	2	no	—
357	C₂×C₃×C₉	—	4	1	no	—
358	C₂×C₃×C₉	—	4	1	no	—
359	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
361	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
362	D₃×C₉	—	2	2	no	—
363	D₃×C₉	—	4	1	no	—
364	C₂⁴×C₃	—	2	1	no	—
365	C₂⁴×C₃	—	3	1	no	—
366	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
367	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
368	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
369	C₃×#41	—	6	4	no	—
370	C₂×C₃×Q₈	—	3	1	no	—
371	C₂×C₃×D₄	—	2	1	no	—
372	C₂×C₃×D₄	—	2	1	no	—
373	C₂×C₃×D₄	—	2	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	—	3	1	no	—
380	C₂×C₃×D₄	—	6	4	no	—
381	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
382	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
383	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
384	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
385	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
386	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
387	C₂²×C₃×C₄	—	3	1	no	—
388	C₂²×C₃×C₄	—	3	1	no	—
389	C₂²×C₃×C₄	—	3	1	no	—
390	C₂²×C₃×C₄	—	3	1	no	—
391	C₂²×C₃×C₄	—	3	1	no	—
392	C₂²×C₃×C₄	—	3	1	no	—
393	C₂×#67	—	2	4	no	—
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
397	C₂×#67	C₂²×C₉	1	1	yes	characteristic
398	C₂×#67	C₂²×C₉	1	1	yes	characteristic, complemented
399	C₂×#67	C₂²×C₉	1	1	yes	characteristic, complemented
400	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
401	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
402	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
403	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
404	#237	—	2	4	no	—
405	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
406	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
407	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
408	C₃×C₄⋊C₄	—	3	1	no	—
409	C₃×C₄⋊C₄	—	3	1	no	—
410	C₃×C₄⋊C₄	—	3	1	no	—
411	C₃×C₄⋊C₄	—	3	1	no	—
412	C₃×C₂²⋊C₄	—	2	1	no	—
413	C₃×C₂²⋊C₄	—	2	1	no	—
414	C₃×C₂²⋊C₄	—	2	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	—	3	1	no	—
423	C₃×C₂²⋊C₄	—	3	1	no	—
424	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
425	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
426	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
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
433	#217	C₂²×C₉	1	1	yes	characteristic, complemented
434	#217	C₂²×C₉	1	1	yes	characteristic, complemented
435	#217	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	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
440	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
441	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
442	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
443	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
444	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
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	—	2	1	no	—
452	C₂²×C₃²	—	2	1	no	—
453	C₂²×C₃²	—	2	1	no	—
454	C₂²×C₃²	—	2	1	no	—
455	C₂²×C₃²	—	4	4	no	—
456	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
457	C₂²×C₃²	C₃×#41	1	2	yes	—
458	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
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	—	2	1	no	—
464	C₂×C₃×D₃	—	4	4	no	—
465	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
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	—	2	1	no	—
474	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
475	C₂²×C₉	—	2	1	no	—
476	C₂²×C₉	—	2	1	no	—
477	C₂²×C₉	—	2	1	no	—
478	C₂²×C₉	—	2	1	no	—
479	C₂²×C₉	—	2	2	no	—
480	C₂²×C₉	—	2	1	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	1	no	—
486	C₂²×C₉	—	2	1	no	—
487	C₂²×C₉	—	2	2	no	—
488	C₂²×C₉	—	2	2	no	—
489	C₂²×C₉	—	3	2	no	—
490	C₂²×C₉	—	4	1	no	—
491	C₂²×C₉	—	4	1	no	—
492	C₂²×C₉	—	4	1	no	—
493	C₂²×C₉	—	4	1	no	—
494	C₂²×C₉	—	4	1	no	—
495	C₂²×C₉	—	4	1	no	—
496	C₂²×C₉	—	4	1	no	—
497	C₂²×C₉	—	4	1	no	—
498	C₂²×C₉	—	4	1	no	—
499	C₂²×C₉	—	4	4	no	—
500	C₂²×C₉	—	4	8	no	—
501	C₂²×C₉	—	6	1	no	—
502	C₂²×C₉	—	6	1	no	—
503	C₂²×C₉	—	6	1	no	—
504	C₂²×C₉	—	6	1	no	—
505	C₂²×C₉	—	6	1	no	—
506	C₂²×C₉	—	12	4	no	—
507	C₂²×C₉	D₃×D₄	1	2	yes	—
508	C₂²×C₉	#237	1	2	yes	complemented
509	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
510	C₄×C₉	—	2	1	no	—
511	C₄×C₉	—	2	1	no	—
512	C₄×C₉	—	2	1	no	—
513	C₄×C₉	—	3	2	no	—
514	C₄×C₉	—	4	1	no	—
515	C₄×C₉	—	4	1	no	—
516	C₄×C₉	—	4	1	no	—
517	C₄×C₉	—	6	1	no	—
518	C₄×C₉	—	6	1	no	—
519	C₄×C₉	—	6	1	no	—
520	C₄×C₉	—	6	1	no	—
521	C₄×C₉	—	6	1	no	—
522	C₂×#41	—	3	1	no	—
523	C₂²×D₄	—	3	1	no	—
524	#124	—	3	1	no	—
525	#123	—	3	1	no	—
526	#123	—	3	1	no	—
527	C₂²⋊Q₈	—	3	1	no	—
528	#121	—	3	1	no	—
529	#121	—	3	1	no	—
530	#121	—	3	1	no	—
531	#120	—	3	1	no	—
532	#120	D₃×C₉	1	1	yes	characteristic, complemented
533	C₄×D₄	—	3	1	no	—
534	C₄×D₄	—	3	1	no	—
535	C₂×C₂²⋊C₄	—	3	1	no	—
536	C₂×C₂²⋊C₄	—	3	1	no	—
537	C₃×C₉	#546	1	1	yes	characteristic, complemented, Sylow
538	C₂³×C₃	—	2	2	no	—
539	C₂³×C₃	—	2	2	no	—
540	C₂³×C₃	—	2	2	no	—
541	C₂³×C₃	—	2	2	no	—
542	C₂³×C₃	—	2	1	no	—
543	C₂³×C₃	—	2	1	no	—
544	C₂³×C₃	—	2	1	no	—
545	C₂³×C₃	—	2	1	no	—
546	C₂³×C₃	—	3	1	no	—
547	C₂³×C₃	—	3	1	no	—
548	C₂³×C₃	—	4	2	no	—
549	C₂³×C₃	—	4	2	no	—
550	C₂³×C₃	—	4	1	no	—
551	C₂³×C₃	—	4	1	no	—
552	C₂³×C₃	—	4	2	no	—
553	C₂³×C₃	—	6	2	no	—
554	C₂³×C₃	—	6	2	no	—
555	C₂³×C₃	—	12	1	no	—
556	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
557	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
558	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
559	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
560	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
561	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
562	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
563	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
564	C₂²×D₃	—	2	2	no	—
565	C₂²×D₃	—	2	2	no	—
566	C₂²×D₃	—	4	1	no	—
567	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
568	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
569	C₃×Q₈	—	6	2	no	—
570	C₃×D₄	—	2	2	no	—
571	C₃×D₄	—	2	2	no	—
572	C₃×D₄	—	2	2	no	—
573	C₃×D₄	—	2	2	no	—
574	C₃×D₄	—	3	4	no	—
575	C₃×D₄	—	4	2	no	—
576	C₃×D₄	—	4	2	no	—
577	C₃×D₄	—	4	1	no	—
578	C₃×D₄	—	4	1	no	—
579	C₃×D₄	—	4	2	no	—
580	C₃×D₄	—	6	2	no	—
581	C₃×D₄	—	6	2	no	—
582	C₃×D₄	—	6	2	no	—
583	C₃×D₄	—	6	2	no	—
584	C₃×D₄	—	12	1	no	—
585	C₂×C₃×C₄	—	2	1	no	—
586	C₂×C₃×C₄	—	2	1	no	—
587	C₂×C₃×C₄	—	2	1	no	—
588	C₂×C₃×C₄	—	3	1	no	—
589	C₂×C₃×C₄	—	3	1	no	—
590	C₂×C₃×C₄	—	3	1	no	—
591	C₂×C₃×C₄	—	3	1	no	—
592	C₂×C₃×C₄	—	3	1	no	—
593	C₂×C₃×C₄	—	3	1	no	—
594	C₂×C₃×C₄	—	6	2	no	—
595	C₂×C₃×C₄	—	6	2	no	—
596	C₂×C₃×C₄	—	6	2	no	—
597	C₂×C₃×C₄	—	6	2	no	—
598	C₂×C₃×C₄	—	12	1	no	—
599	C₂×C₃×C₄	—	12	1	no	—
600	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
601	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
602	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
603	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
604	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
605	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
606	#67	—	2	2	no	—
607	#67	—	2	2	no	—
608	#67	—	2	2	no	—
609	#67	—	2	2	no	—
610	#67	—	4	1	no	—
611	#67	D₄×C₉	1	4	yes	complemented
612	C₂×Dic₃	—	2	2	no	—
613	C₂×Dic₃	—	2	2	no	—
614	C₂×Dic₃	—	2	2	no	—
615	C₂×Dic₃	—	4	1	no	—
616	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
617	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
618	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
619	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
620	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
621	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
622	C₄×D₃	—	2	2	no	—
623	C₄×D₃	—	4	1	no	—
624	Dic₆	—	2	2	no	—
625	C₂×C₃²	—	2	2	no	—
626	C₂×C₃²	—	2	2	no	—
627	C₂×C₃²	—	4	1	no	—
628	C₂×C₃²	—	4	1	no	—
629	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
630	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
631	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
632	C₃×D₃	—	2	2	no	—
633	C₃×D₃	—	4	1	no	—
634	C₂×C₉	—	2	2	no	—
635	C₂×C₉	—	2	2	no	—
636	C₂×C₉	—	2	1	no	—
637	C₂×C₉	—	2	1	no	—
638	C₂×C₉	—	2	1	no	—
639	C₂×C₉	—	4	2	no	—
640	C₂×C₉	—	4	2	no	—
641	C₂×C₉	—	4	2	no	—
642	C₂×C₉	—	4	1	no	—
643	C₂×C₉	—	4	1	no	—
644	C₂×C₉	—	6	2	no	—
645	C₂×C₉	—	8	1	no	—
646	C₂×C₉	—	12	1	no	—
647	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
648	C₂×C₉	C₂×#237	1	1	yes	characteristic
649	C₂×C₉	#1004	1	1	yes	characteristic
650	C₂⁴	—	3	1	no	—
651	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
652	#41	—	6	4	no	—
653	C₂×Q₈	—	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	—	3	1	no	—
659	C₂×D₄	—	3	1	no	—
660	C₂×D₄	—	6	4	no	—
661	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
662	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
663	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
664	C₂²×C₄	—	3	1	no	—
665	C₂²×C₄	—	3	1	no	—
666	C₂²×C₄	—	3	1	no	—
667	C₂²×C₄	—	3	1	no	—
668	C₂²×C₄	—	3	1	no	—
669	C₂²×C₄	—	3	1	no	—
670	C₄⋊C₄	—	3	1	no	—
671	C₄⋊C₄	—	3	1	no	—
672	C₄⋊C₄	—	3	1	no	—
673	C₄⋊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	—	3	1	no	—
678	C₂²⋊C₄	—	3	1	no	—
679	C₂²⋊C₄	—	3	1	no	—
680	C₂²⋊C₄	—	3	1	no	—
681	C₂²⋊C₄	—	3	1	no	—
682	C₂²⋊C₄	—	3	1	no	—
683	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
684	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
685	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
686	C₄²	—	3	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	1	no	—
693	C₂²×C₃	—	2	1	no	—
694	C₂²×C₃	—	2	1	no	—
695	C₂²×C₃	—	2	2	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	1	no	—
701	C₂²×C₃	—	2	1	no	—
702	C₂²×C₃	—	2	1	no	—
703	C₂²×C₃	—	2	1	no	—
704	C₂²×C₃	—	2	1	no	—
705	C₂²×C₃	—	2	1	no	—
706	C₂²×C₃	—	2	1	no	—
707	C₂²×C₃	—	2	1	no	—
708	C₂²×C₃	—	2	1	no	—
709	C₂²×C₃	—	2	2	no	—
710	C₂²×C₃	—	2	2	no	—
711	C₂²×C₃	—	3	2	no	—
712	C₂²×C₃	—	4	1	no	—
713	C₂²×C₃	—	4	1	no	—
714	C₂²×C₃	—	4	1	no	—
715	C₂²×C₃	—	4	1	no	—
716	C₂²×C₃	—	4	1	no	—
717	C₂²×C₃	—	4	1	no	—
718	C₂²×C₃	—	4	1	no	—
719	C₂²×C₃	—	4	1	no	—
720	C₂²×C₃	—	4	1	no	—
721	C₂²×C₃	—	4	4	no	—
722	C₂²×C₃	—	4	4	no	—
723	C₂²×C₃	—	4	8	no	—
724	C₂²×C₃	—	6	1	no	—
725	C₂²×C₃	—	6	1	no	—
726	C₂²×C₃	—	6	1	no	—
727	C₂²×C₃	—	6	1	no	—
728	C₂²×C₃	—	6	1	no	—
729	C₂²×C₃	—	12	4	no	—
730	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
731	C₂²×C₃	C₉×#41	1	2	yes	complemented
732	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
733	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
734	C₂²×C₃	C₃×#237	1	2	yes	—
735	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
736	C₂×D₃	—	2	1	no	—
737	C₂×D₃	—	2	1	no	—
738	C₂×D₃	—	2	1	no	—
739	C₂×D₃	—	2	1	no	—
740	C₂×D₃	—	2	1	no	—
741	C₂×D₃	—	4	4	no	—
742	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
743	C₃×C₄	—	2	1	no	—
744	C₃×C₄	—	2	1	no	—
745	C₃×C₄	—	2	1	no	—
746	C₃×C₄	—	2	1	no	—
747	C₃×C₄	—	2	1	no	—
748	C₃×C₄	—	2	1	no	—
749	C₃×C₄	—	3	2	no	—
750	C₃×C₄	—	4	1	no	—
751	C₃×C₄	—	4	1	no	—
752	C₃×C₄	—	4	1	no	—
753	C₃×C₄	—	6	1	no	—
754	C₃×C₄	—	6	1	no	—
755	C₃×C₄	—	6	1	no	—
756	C₃×C₄	—	6	1	no	—
757	C₃×C₄	—	6	1	no	—
758	Dic₃	—	2	1	no	—
759	Dic₃	—	2	1	no	—
760	Dic₃	—	2	1	no	—
761	Dic₃	—	2	1	no	—
762	Dic₃	—	2	1	no	—
763	Dic₃	C₂×D₄×C₉	1	2	yes	—
764	C₃²	C₃×#546	1	1	yes	characteristic
765	C₉	—	2	1	no	—
766	C₉	#5591	1	1	yes	characteristic, direct product factor
767	C₂³	—	2	2	no	—
768	C₂³	—	2	2	no	—
769	C₂³	—	3	1	no	—
770	C₂³	—	3	1	no	—
771	C₂³	—	4	1	no	—
772	C₂³	—	6	2	no	—
773	C₂³	—	6	2	no	—
774	C₂³	—	12	1	no	—
775	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
776	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
777	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
778	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
779	Q₈	—	6	2	no	—
780	D₄	—	2	2	no	—
781	D₄	—	2	2	no	—
782	D₄	—	3	4	no	—
783	D₄	—	4	1	no	—
784	D₄	—	6	2	no	—
785	D₄	—	6	2	no	—
786	D₄	—	6	2	no	—
787	D₄	—	6	2	no	—
788	D₄	—	12	1	no	—
789	C₂×C₄	—	3	1	no	—
790	C₂×C₄	—	3	1	no	—
791	C₂×C₄	—	3	1	no	—
792	C₂×C₄	—	3	1	no	—
793	C₂×C₄	—	3	1	no	—
794	C₂×C₄	—	3	1	no	—
795	C₂×C₄	—	6	2	no	—
796	C₂×C₄	—	6	2	no	—
797	C₂×C₄	—	6	2	no	—
798	C₂×C₄	—	6	2	no	—
799	C₂×C₄	—	12	1	no	—
800	C₂×C₄	—	12	1	no	—
801	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
803	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
804	C₂×C₃	—	2	2	no	—
805	C₂×C₃	—	2	2	no	—
806	C₂×C₃	—	2	2	no	—
807	C₂×C₃	—	2	2	no	—
808	C₂×C₃	—	2	1	no	—
809	C₂×C₃	—	2	1	no	—
810	C₂×C₃	—	2	1	no	—
811	C₂×C₃	—	4	2	no	—
812	C₂×C₃	—	4	2	no	—
813	C₂×C₃	—	4	2	no	—
814	C₂×C₃	—	4	1	no	—
815	C₂×C₃	—	4	1	no	—
816	C₂×C₃	—	4	1	no	—
817	C₂×C₃	—	4	1	no	—
818	C₂×C₃	—	6	2	no	—
819	C₂×C₃	—	8	1	no	—
820	C₂×C₃	—	12	1	no	—
821	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
822	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
823	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
824	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
825	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
826	C₂×C₃	C₃×#1004	1	1	yes	characteristic
827	D₃	—	2	2	no	—
828	D₃	—	4	1	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	2	1	no	—
831	C₂²	—	2	1	no	—
832	C₂²	—	2	1	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	1	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	3	2	no	—
840	C₂²	—	4	4	no	—
841	C₂²	—	6	1	no	—
842	C₂²	—	6	1	no	—
843	C₂²	—	6	1	no	—
844	C₂²	—	6	1	no	—
845	C₂²	—	6	1	no	—
846	C₂²	—	12	4	no	—
847	C₂²	D₃×D₄×C₉	1	2	yes	—
848	C₂²	C₉×#237	1	2	yes	complemented
849	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
850	C₄	—	2	1	no	—
851	C₄	—	2	1	no	—
852	C₄	—	2	1	no	—
853	C₄	—	3	2	no	—
854	C₄	—	6	1	no	—
855	C₄	—	6	1	no	—
856	C₄	—	6	1	no	—
857	C₄	—	6	1	no	—
858	C₄	—	6	1	no	—
859	C₃	—	2	1	no	—
860	C₃	C₉×#546	1	1	yes	characteristic, complemented
861	C₃	C₃×#5591	1	1	yes	characteristic
862	C₂	—	2	2	no	—
863	C₂	—	2	2	no	—
864	C₂	—	4	1	no	—
865	C₂	—	4	1	no	—
866	C₂	—	6	2	no	—
867	C₂	—	12	1	no	—
868	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
869	C₂	C₂×C₉×#237	1	1	yes	characteristic
870	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	C₃×C₉×#120	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5591	C₃
hypercenter	C₉×#120	D₃
hypocenter	C₃	C₉×#546
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#120

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×#237	C₂	semidirect
3. C₃×C₉×#120	C₂	semidirect
4. C₂×C₉×#217	C₂	semidirect
5. C₉×#939	C₂	semidirect
6. C₉×#939	C₂	semidirect
7. C₉×#938	C₂	semidirect
8. C₉×#937	C₂	semidirect
9. D₄×C₉×Dic₃	C₂	semidirect
10. C₉×#886	C₂	semidirect
11. C₉×#885	C₂	semidirect
12. C₉×#883	C₂	semidirect
13. C₉×#67⋊C₄	C₂	semidirect
14. D₃×C₉×C₂²⋊C₄	C₂	semidirect
15. C₉×#878	C₂	semidirect
21. C₂×C₃×D₄×C₉	C₂²	semidirect
22. C₂×C₃×D₄×C₉	C₂²	semidirect
28. C₂×C₉×#67	C₂²	semidirect
29. C₂×C₉×#67	C₂²	semidirect
31. C₂²×C₉×Dic₃	C₂²	semidirect
32. C₂²×C₉×Dic₃	C₂²	semidirect
33. C₂²×C₉×Dic₃	C₂²	semidirect
35. C₂×C₄×D₃×C₉	C₂²	semidirect
36. C₂×C₄×D₃×C₉	C₂²	semidirect
37. C₂×C₉×Dic₆	C₂²	semidirect
39. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
40. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
43. C₉×#217	C₂²	semidirect
44. C₉×#217	C₂²	semidirect
45. C₉×#217	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×C₄⋊Dic₃	C₂²	semidirect
52. C₉×Dic₃⋊C₄	C₂²	semidirect
53. C₉×Dic₃⋊C₄	C₂²	semidirect
54. C₄×C₉×Dic₃	C₂²	semidirect
81. C₉×#120	D₃	semidirect
109. C₉×#67	D₄	semidirect
124. #5591	C₉	direct (N × H)
178. C₂×D₄×C₉	C₂×D₃	semidirect
179. C₂×D₄×C₉	C₂×D₃	semidirect
203. C₉×C₂²⋊C₄	C₂×D₃	semidirect
204. C₉×C₂²⋊C₄	C₂×D₃	semidirect
218. C₂²×C₃×C₉	#41	semidirect
238. C₂²×#67	C₂×C₉	semidirect
239. C₂×#237	C₂×C₉	semidirect
249. C₃×#120	C₂×C₉	semidirect
255. C₂×#217	C₂×C₉	semidirect
256. #939	C₂×C₉	semidirect
257. #939	C₂×C₉	semidirect
258. #938	C₂×C₉	semidirect
259. #937	C₂×C₉	semidirect
260. D₄×Dic₃	C₂×C₉	semidirect
261. #886	C₂×C₉	semidirect
262. #885	C₂×C₉	semidirect
263. #883	C₂×C₉	semidirect
264. #67⋊C₄	C₂×C₉	semidirect
265. D₃×C₂²⋊C₄	C₂×C₉	semidirect
266. #878	C₂×C₉	semidirect
382. C₂×C₃×D₄	C₂²×C₉	semidirect
383. C₂×C₃×D₄	C₂²×C₉	semidirect
398. C₂×#67	C₂²×C₉	semidirect
399. C₂×#67	C₂²×C₉	semidirect
401. C₂²×Dic₃	C₂²×C₉	semidirect
402. C₂²×Dic₃	C₂²×C₉	semidirect
403. C₂²×Dic₃	C₂²×C₉	semidirect
405. C₂×C₄×D₃	C₂²×C₉	semidirect
406. C₂×C₄×D₃	C₂²×C₉	semidirect
407. C₂×Dic₆	C₂²×C₉	semidirect
425. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
426. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
433. #217	C₂²×C₉	semidirect
434. #217	C₂²×C₉	semidirect
435. #217	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. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
440. C₄⋊Dic₃	C₂²×C₉	semidirect
441. C₄⋊Dic₃	C₂²×C₉	semidirect
442. Dic₃⋊C₄	C₂²×C₉	semidirect
443. Dic₃⋊C₄	C₂²×C₉	semidirect
444. C₄×Dic₃	C₂²×C₉	semidirect
508. C₂²×C₉	#237	semidirect
532. #120	D₃×C₉	semidirect
537. C₃×C₉	#546	semidirect
611. #67	D₄×C₉	semidirect
662. C₂×D₄	C₂×D₃×C₉	semidirect
663. C₂×D₄	C₂×D₃×C₉	semidirect
684. C₂²⋊C₄	C₂×D₃×C₉	semidirect
685. C₂²⋊C₄	C₂×D₃×C₉	semidirect
731. C₂²×C₃	C₉×#41	semidirect
766. C₉	#5591	direct (N × H)
848. C₂²	C₉×#237	semidirect
860. 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×#237	2
C₃×C₉×#120	2
C₂×C₉×#217	2
C₉×#939	2
C₉×#938	2
C₉×#937	2
D₄×C₉×Dic₃	2
C₉×#886	2
C₉×#885	2
C₉×#883	2
C₉×#67⋊C₄	2
D₃×C₉×C₂²⋊C₄	2
C₉×#878	2
C₃×#5591	3
C₉×#546	3

Subgroups — C9×#5591 #13152763

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5591 #13152763