Subgroups — C₉×#5654 #13153025

Order 1728.

1080 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#939	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#896	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#895	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#894	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#885	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#884	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#882	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#882	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	D₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5654	C₃	1	1	yes	maximal, characteristic
17	C₉×#546	—	3	1	no	maximal
18	C₂³×D₃×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	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₉×#67	C₂²	1	1	yes	characteristic
23	C₂×C₉×#67	C₂²	1	1	yes	characteristic
24	C₂×C₉×#67	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₉×#67	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
27	D₃×D₄×C₉	—	2	4	no	—
28	C₉×#235	—	2	4	no	—
29	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
30	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
31	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
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×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
43	C₉×#217	C₂²	1	1	yes	characteristic, complemented
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
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×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	C₉×(C₂×D₃)⋊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	C₂×C₃×D₃×D₄	C₂×C₃	1	1	yes	characteristic
56	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
57	C₃²×#123	C₂×C₃	1	1	yes	characteristic
58	C₃×#939	C₂×C₃	1	1	yes	characteristic
59	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
60	C₃×#896	C₂×C₃	1	1	yes	characteristic
61	C₃×#895	C₂×C₃	1	1	yes	characteristic
62	C₃×#894	C₂×C₃	1	1	yes	characteristic
63	C₃×#893	C₂×C₃	1	1	yes	characteristic
64	C₃×#885	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×#882	C₂×C₃	1	1	yes	characteristic
68	C₃×#67⋊C₄	C₂×C₃	1	1	yes	characteristic
69	C₃×D₃×C₂²⋊C₄	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	—	2	1	no	—
74	C₉×#123	—	3	1	no	—
75	C₉×#123	D₃	1	1	yes	characteristic, complemented
76	C₉×C₂²⋊Q₈	—	3	1	no	—
77	C₉×#121	—	3	1	no	—
78	C₉×#121	—	3	1	no	—
79	C₉×#121	—	3	1	no	—
80	C₉×#120	—	3	1	no	—
81	C₉×#120	—	3	1	no	—
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	C₂³	1	1	yes	characteristic
87	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
88	C₂²×D₃×C₉	—	2	2	no	—
89	C₂²×D₃×C₉	—	2	2	no	—
90	C₂²×D₃×C₉	—	2	2	no	—
91	C₂²×D₃×C₉	—	2	2	no	—
92	C₂²×D₃×C₉	—	4	1	no	—
93	C₂²×D₃×C₉	—	4	1	no	—
94	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
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	C₃×D₄×C₉	—	2	2	no	—
99	C₂×C₃×C₄×C₉	—	2	2	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	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
105	C₉×#67	—	2	2	no	—
106	C₉×#67	—	2	2	no	—
107	C₉×#67	—	4	1	no	—
108	C₉×#67	D₄	1	4	yes	complemented
109	C₂×C₉×Dic₃	—	4	1	no	—
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	—	2	2	no	—
115	C₉×D₁₂	—	2	2	no	—
116	C₉×D₁₂	—	2	2	no	—
117	C₉×D₁₂	—	4	1	no	—
118	C₄×D₃×C₉	—	2	2	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	#5654	C₉	1	1	yes	characteristic, direct product factor
125	C₂³×C₃×D₃	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	C₂²×C₃²×C₄	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	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
133	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
134	C₃×D₃×D₄	—	2	4	no	—
135	C₃×#235	—	2	4	no	—
136	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
137	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
139	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₃×C₄×D₃	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	—	3	1	no	—
146	C₂⁴×C₉	—	3	1	no	—
147	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
148	C₃²×C₄⋊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×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
154	C₃×(C₂×D₃)⋊C₄	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×(C₂×D₃)⋊C₄	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×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
164	C₉×#41	—	6	4	no	—
165	C₂×Q₈×C₉	—	3	1	no	—
166	C₂×D₄×C₉	—	2	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	—	6	4	no	—
176	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
177	C₂²×C₄×C₉	—	2	1	no	—
178	C₂²×C₄×C₉	—	3	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	C₉×C₄⋊C₄	—	2	1	no	—
185	C₉×C₄⋊C₄	—	2	1	no	—
186	C₉×C₄⋊C₄	—	3	1	no	—
187	C₉×C₄⋊C₄	—	3	1	no	—
188	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
189	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
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, complemented
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	C₂×D₄	1	2	yes	—
212	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
213	C₂×D₃×C₉	—	2	1	no	—
214	C₂×D₃×C₉	—	2	1	no	—
215	C₂×D₃×C₉	—	2	1	no	—
216	C₂×D₃×C₉	—	2	1	no	—
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	—	4	4	no	—
224	C₂×D₃×C₉	—	4	4	no	—
225	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
226	C₂×D₃×C₉	#41	1	2	yes	complemented
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	C₃×C₄×C₉	—	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	C₂×D₃×D₄	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	—	2	1	no	—
242	C₃×#123	—	3	1	no	—
243	C₃×#123	C₂×C₉	1	1	yes	characteristic, complemented
244	C₃×#123	C₃×D₃	1	1	yes	characteristic
245	C₃×C₂²⋊Q₈	—	3	1	no	—
246	C₃×#121	—	3	1	no	—
247	C₃×#121	—	3	1	no	—
248	C₃×#121	—	3	1	no	—
249	C₃×#120	—	3	1	no	—
250	C₃×#120	—	3	1	no	—
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	#939	C₂×C₉	1	1	yes	characteristic, complemented
256	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
257	#896	C₂×C₉	1	1	yes	characteristic, complemented
258	#895	C₂×C₉	1	1	yes	characteristic, complemented
259	#894	C₂×C₉	1	1	yes	characteristic, complemented
260	#893	C₂×C₉	1	1	yes	characteristic, complemented
261	#885	C₂×C₉	1	1	yes	characteristic, complemented
262	#884	C₂×C₉	1	1	yes	characteristic, complemented
263	#882	C₂×C₉	1	1	yes	characteristic, complemented
264	#882	C₂×C₉	1	1	yes	characteristic, complemented
265	#67⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
266	D₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
267	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
268	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
269	C₂²×C₃×D₃	—	2	2	no	—
270	C₂²×C₃×D₃	—	2	2	no	—
271	C₂²×C₃×D₃	—	2	2	no	—
272	C₂²×C₃×D₃	—	2	2	no	—
273	C₂²×C₃×D₃	—	4	1	no	—
274	C₂²×C₃×D₃	—	4	1	no	—
275	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
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	C₃²×D₄	—	2	2	no	—
280	C₂×C₃²×C₄	—	2	2	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	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
286	C₃×#67	—	2	2	no	—
287	C₃×#67	—	2	2	no	—
288	C₃×#67	—	4	1	no	—
289	C₃×#67	C₃×D₄	1	4	yes	—
290	C₂×C₃×Dic₃	—	4	1	no	—
291	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
292	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
293	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
294	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
295	C₃×D₁₂	—	2	2	no	—
296	C₃×D₁₂	—	2	2	no	—
297	C₃×D₁₂	—	2	2	no	—
298	C₃×D₁₂	—	4	1	no	—
299	C₃×C₄×D₃	—	2	2	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	1	no	—
305	C₂³×C₉	—	2	1	no	—
306	C₂³×C₉	—	3	1	no	—
307	C₂³×C₉	—	3	1	no	—
308	C₂³×C₉	—	3	1	no	—
309	C₂³×C₉	—	3	1	no	—
310	C₂³×C₉	—	6	2	no	—
311	C₂³×C₉	—	6	2	no	—
312	C₂³×C₉	—	6	2	no	—
313	C₂³×C₉	—	6	2	no	—
314	C₂³×C₉	—	12	1	no	—
315	C₂³×C₉	—	12	1	no	—
316	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
317	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
318	Q₈×C₉	—	6	2	no	—
319	D₄×C₉	—	2	2	no	—
320	D₄×C₉	—	3	4	no	—
321	D₄×C₉	—	4	2	no	—
322	D₄×C₉	—	6	2	no	—
323	D₄×C₉	—	6	2	no	—
324	D₄×C₉	—	6	2	no	—
325	D₄×C₉	—	6	2	no	—
326	D₄×C₉	—	6	2	no	—
327	D₄×C₉	—	12	1	no	—
328	D₄×C₉	—	12	1	no	—
329	C₂×C₄×C₉	—	2	2	no	—
330	C₂×C₄×C₉	—	2	1	no	—
331	C₂×C₄×C₉	—	2	1	no	—
332	C₂×C₄×C₉	—	2	1	no	—
333	C₂×C₄×C₉	—	2	1	no	—
334	C₂×C₄×C₉	—	2	1	no	—
335	C₂×C₄×C₉	—	3	1	no	—
336	C₂×C₄×C₉	—	3	1	no	—
337	C₂×C₄×C₉	—	3	1	no	—
338	C₂×C₄×C₉	—	3	1	no	—
339	C₂×C₄×C₉	—	4	2	no	—
340	C₂×C₄×C₉	—	6	2	no	—
341	C₂×C₄×C₉	—	6	2	no	—
342	C₂×C₄×C₉	—	6	2	no	—
343	C₂×C₄×C₉	—	12	1	no	—
344	C₂×C₄×C₉	—	12	1	no	—
345	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
346	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
347	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
348	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
349	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
350	#546	—	3	1	no	Sylow
351	C₂×C₃×C₉	—	2	2	no	—
352	C₂×C₃×C₉	—	4	1	no	—
353	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
355	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
356	D₃×C₉	—	2	2	no	—
357	D₃×C₉	—	2	2	no	—
358	D₃×C₉	—	4	1	no	—
359	D₃×C₉	—	4	1	no	—
360	C₂⁴×C₃	—	3	1	no	—
361	C₂⁴×C₃	—	3	1	no	—
362	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
363	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
364	C₃×#41	—	6	4	no	—
365	C₂×C₃×Q₈	—	3	1	no	—
366	C₂×C₃×D₄	—	2	1	no	—
367	C₂×C₃×D₄	—	3	1	no	—
368	C₂×C₃×D₄	—	3	1	no	—
369	C₂×C₃×D₄	—	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	—	6	4	no	—
376	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
377	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
378	C₂²×C₃×C₄	—	2	1	no	—
379	C₂²×C₃×C₄	—	3	1	no	—
380	C₂²×C₃×C₄	—	3	1	no	—
381	C₂²×C₃×C₄	—	3	1	no	—
382	C₂²×C₃×C₄	—	3	1	no	—
383	C₂²×C₃×C₄	—	3	1	no	—
384	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic, complemented
385	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
386	C₂×#67	C₂²×C₉	1	1	yes	characteristic
387	C₂×#67	C₂²×C₉	1	1	yes	characteristic
388	C₂×#67	C₂²×C₉	1	1	yes	characteristic, complemented
389	C₂×#67	C₂²×C₉	1	1	yes	characteristic, complemented
390	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
391	D₃×D₄	—	2	4	no	—
392	#235	—	2	4	no	—
393	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
394	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
395	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic, complemented
396	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic, complemented
397	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
398	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
399	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
400	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
401	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
402	C₃×C₄⋊C₄	—	2	1	no	—
403	C₃×C₄⋊C₄	—	2	1	no	—
404	C₃×C₄⋊C₄	—	3	1	no	—
405	C₃×C₄⋊C₄	—	3	1	no	—
406	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
407	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
408	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
409	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
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	—	3	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, complemented
423	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
424	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
425	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
426	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
427	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
428	C₃×C₄²	—	3	1	no	—
429	#217	C₂²×C₉	1	1	yes	characteristic, complemented
430	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
431	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
432	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
433	(C₂×D₃)⋊C₄	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	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
439	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
440	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
441	C₂²×C₃²	—	2	1	no	—
442	C₂²×C₃²	—	2	1	no	—
443	C₂²×C₃²	—	2	1	no	—
444	C₂²×C₃²	—	2	1	no	—
445	C₂²×C₃²	—	2	1	no	—
446	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
447	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
448	C₂×C₃×D₃	—	2	1	no	—
449	C₂×C₃×D₃	—	2	1	no	—
450	C₂×C₃×D₃	—	2	1	no	—
451	C₂×C₃×D₃	—	2	1	no	—
452	C₂×C₃×D₃	—	2	1	no	—
453	C₂×C₃×D₃	—	2	1	no	—
454	C₂×C₃×D₃	—	2	1	no	—
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	—	4	4	no	—
459	C₂×C₃×D₃	—	4	4	no	—
460	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
461	C₂×C₃×D₃	C₃×#41	1	2	yes	—
462	C₃²×C₄	—	2	1	no	—
463	C₃²×C₄	—	2	1	no	—
464	C₃²×C₄	—	2	1	no	—
465	C₃²×C₄	—	2	1	no	—
466	C₃²×C₄	—	2	1	no	—
467	C₃×Dic₃	—	2	1	no	—
468	C₃×Dic₃	—	2	1	no	—
469	C₃×Dic₃	—	2	1	no	—
470	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
471	C₂²×C₉	—	2	1	no	—
472	C₂²×C₉	—	2	1	no	—
473	C₂²×C₉	—	2	1	no	—
474	C₂²×C₉	—	2	1	no	—
475	C₂²×C₉	—	2	1	no	—
476	C₂²×C₉	—	2	1	no	—
477	C₂²×C₉	—	2	2	no	—
478	C₂²×C₉	—	3	2	no	—
479	C₂²×C₉	—	3	2	no	—
480	C₂²×C₉	—	4	1	no	—
481	C₂²×C₉	—	4	1	no	—
482	C₂²×C₉	—	4	1	no	—
483	C₂²×C₉	—	4	1	no	—
484	C₂²×C₉	—	4	1	no	—
485	C₂²×C₉	—	6	1	no	—
486	C₂²×C₉	—	6	1	no	—
487	C₂²×C₉	—	6	1	no	—
488	C₂²×C₉	—	6	1	no	—
489	C₂²×C₉	—	6	1	no	—
490	C₂²×C₉	—	6	1	no	—
491	C₂²×C₉	—	6	1	no	—
492	C₂²×C₉	—	6	1	no	—
493	C₂²×C₉	—	6	1	no	—
494	C₂²×C₉	—	6	1	no	—
495	C₂²×C₉	—	12	4	no	—
496	C₂²×C₉	—	12	4	no	—
497	C₂²×C₉	D₃×D₄	1	2	yes	—
498	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
499	C₄×C₉	—	2	1	no	—
500	C₄×C₉	—	2	1	no	—
501	C₄×C₉	—	2	1	no	—
502	C₄×C₉	—	2	1	no	—
503	C₄×C₉	—	2	1	no	—
504	C₄×C₉	—	3	2	no	—
505	C₄×C₉	—	4	1	no	—
506	C₄×C₉	—	4	1	no	—
507	C₄×C₉	—	4	1	no	—
508	C₄×C₉	—	4	1	no	—
509	C₄×C₉	—	4	1	no	—
510	C₄×C₉	—	6	1	no	—
511	C₄×C₉	—	6	1	no	—
512	C₄×C₉	—	6	1	no	—
513	C₂×#41	—	3	1	no	—
514	C₂²×D₄	—	3	1	no	—
515	#124	—	3	1	no	—
516	#123	—	3	1	no	—
517	#123	D₃×C₉	1	1	yes	characteristic, complemented
518	C₂²⋊Q₈	—	3	1	no	—
519	#121	—	3	1	no	—
520	#121	—	3	1	no	—
521	#121	—	3	1	no	—
522	#120	—	3	1	no	—
523	#120	—	3	1	no	—
524	C₄×D₄	—	3	1	no	—
525	C₄×D₄	—	3	1	no	—
526	C₂×C₂²⋊C₄	—	3	1	no	—
527	C₂×C₂²⋊C₄	—	3	1	no	—
528	C₃×C₉	#546	1	1	yes	characteristic, complemented, Sylow
529	C₂³×C₃	—	2	1	no	—
530	C₂³×C₃	—	2	1	no	—
531	C₂³×C₃	—	3	1	no	—
532	C₂³×C₃	—	3	1	no	—
533	C₂³×C₃	—	3	1	no	—
534	C₂³×C₃	—	3	1	no	—
535	C₂³×C₃	—	6	2	no	—
536	C₂³×C₃	—	6	2	no	—
537	C₂³×C₃	—	6	2	no	—
538	C₂³×C₃	—	6	2	no	—
539	C₂³×C₃	—	12	1	no	—
540	C₂³×C₃	—	12	1	no	—
541	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
542	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
543	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
544	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
545	C₂²×D₃	—	2	2	no	—
546	C₂²×D₃	—	2	2	no	—
547	C₂²×D₃	—	2	2	no	—
548	C₂²×D₃	—	2	2	no	—
549	C₂²×D₃	—	4	1	no	—
550	C₂²×D₃	—	4	1	no	—
551	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
552	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
553	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
554	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
555	C₃×Q₈	—	6	2	no	—
556	C₃×D₄	—	2	2	no	—
557	C₃×D₄	—	2	2	no	—
558	C₃×D₄	—	3	4	no	—
559	C₃×D₄	—	4	2	no	—
560	C₃×D₄	—	6	2	no	—
561	C₃×D₄	—	6	2	no	—
562	C₃×D₄	—	6	2	no	—
563	C₃×D₄	—	6	2	no	—
564	C₃×D₄	—	6	2	no	—
565	C₃×D₄	—	12	1	no	—
566	C₃×D₄	—	12	1	no	—
567	C₂×C₃×C₄	—	2	2	no	—
568	C₂×C₃×C₄	—	2	2	no	—
569	C₂×C₃×C₄	—	2	1	no	—
570	C₂×C₃×C₄	—	2	1	no	—
571	C₂×C₃×C₄	—	2	1	no	—
572	C₂×C₃×C₄	—	2	1	no	—
573	C₂×C₃×C₄	—	2	1	no	—
574	C₂×C₃×C₄	—	3	1	no	—
575	C₂×C₃×C₄	—	3	1	no	—
576	C₂×C₃×C₄	—	3	1	no	—
577	C₂×C₃×C₄	—	3	1	no	—
578	C₂×C₃×C₄	—	4	2	no	—
579	C₂×C₃×C₄	—	6	2	no	—
580	C₂×C₃×C₄	—	6	2	no	—
581	C₂×C₃×C₄	—	6	2	no	—
582	C₂×C₃×C₄	—	12	1	no	—
583	C₂×C₃×C₄	—	12	1	no	—
584	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
585	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
586	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
587	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
588	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
589	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
590	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
591	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
592	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
593	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
594	#67	—	2	2	no	—
595	#67	—	2	2	no	—
596	#67	—	4	1	no	—
597	#67	D₄×C₉	1	4	yes	complemented
598	C₂×Dic₃	—	4	1	no	—
599	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
600	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
601	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
602	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
603	D₁₂	—	2	2	no	—
604	D₁₂	—	2	2	no	—
605	D₁₂	—	2	2	no	—
606	D₁₂	—	4	1	no	—
607	C₄×D₃	—	2	2	no	—
608	C₄×D₃	—	2	2	no	—
609	C₄×D₃	—	2	2	no	—
610	C₄×D₃	—	4	1	no	—
611	Dic₆	—	2	2	no	—
612	C₂×C₃²	—	2	2	no	—
613	C₂×C₃²	—	4	1	no	—
614	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
615	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
616	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
617	C₃×D₃	—	2	2	no	—
618	C₃×D₃	—	2	2	no	—
619	C₃×D₃	—	4	1	no	—
620	C₃×D₃	—	4	1	no	—
621	C₂×C₉	—	2	2	no	—
622	C₂×C₉	—	2	1	no	—
623	C₂×C₉	—	2	1	no	—
624	C₂×C₉	—	2	1	no	—
625	C₂×C₉	—	4	2	no	—
626	C₂×C₉	—	4	1	no	—
627	C₂×C₉	—	6	2	no	—
628	C₂×C₉	—	6	2	no	—
629	C₂×C₉	—	8	1	no	—
630	C₂×C₉	—	12	1	no	—
631	C₂×C₉	—	12	1	no	—
632	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
633	C₂×C₉	D₃×#41	1	1	yes	characteristic
634	C₂×C₉	#1009	1	1	yes	characteristic
635	C₂⁴	—	3	1	no	—
636	C₂⁴	—	3	1	no	—
637	#41	—	6	4	no	—
638	C₂×Q₈	—	3	1	no	—
639	C₂×D₄	—	3	1	no	—
640	C₂×D₄	—	3	1	no	—
641	C₂×D₄	—	3	1	no	—
642	C₂×D₄	—	3	1	no	—
643	C₂×D₄	—	3	1	no	—
644	C₂×D₄	—	3	1	no	—
645	C₂×D₄	—	3	1	no	—
646	C₂×D₄	—	3	1	no	—
647	C₂×D₄	—	6	4	no	—
648	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
649	C₂²×C₄	—	3	1	no	—
650	C₂²×C₄	—	3	1	no	—
651	C₂²×C₄	—	3	1	no	—
652	C₂²×C₄	—	3	1	no	—
653	C₂²×C₄	—	3	1	no	—
654	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
655	C₄⋊C₄	—	3	1	no	—
656	C₄⋊C₄	—	3	1	no	—
657	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
658	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
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	—	3	1	no	—
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	C₂×D₃×C₉	1	1	yes	characteristic, complemented
669	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
670	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
671	C₄²	—	3	1	no	—
672	C₂²×C₃	—	2	1	no	—
673	C₂²×C₃	—	2	1	no	—
674	C₂²×C₃	—	2	1	no	—
675	C₂²×C₃	—	2	1	no	—
676	C₂²×C₃	—	2	1	no	—
677	C₂²×C₃	—	2	1	no	—
678	C₂²×C₃	—	2	1	no	—
679	C₂²×C₃	—	2	1	no	—
680	C₂²×C₃	—	2	1	no	—
681	C₂²×C₃	—	2	1	no	—
682	C₂²×C₃	—	2	1	no	—
683	C₂²×C₃	—	2	2	no	—
684	C₂²×C₃	—	3	2	no	—
685	C₂²×C₃	—	3	2	no	—
686	C₂²×C₃	—	4	1	no	—
687	C₂²×C₃	—	4	1	no	—
688	C₂²×C₃	—	4	1	no	—
689	C₂²×C₃	—	4	1	no	—
690	C₂²×C₃	—	4	1	no	—
691	C₂²×C₃	—	6	1	no	—
692	C₂²×C₃	—	6	1	no	—
693	C₂²×C₃	—	6	1	no	—
694	C₂²×C₃	—	6	1	no	—
695	C₂²×C₃	—	6	1	no	—
696	C₂²×C₃	—	6	1	no	—
697	C₂²×C₃	—	6	1	no	—
698	C₂²×C₃	—	6	1	no	—
699	C₂²×C₃	—	6	1	no	—
700	C₂²×C₃	—	6	1	no	—
701	C₂²×C₃	—	12	4	no	—
702	C₂²×C₃	—	12	4	no	—
703	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
704	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
705	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
706	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
707	C₂×D₃	—	2	1	no	—
708	C₂×D₃	—	2	1	no	—
709	C₂×D₃	—	2	1	no	—
710	C₂×D₃	—	2	1	no	—
711	C₂×D₃	—	2	1	no	—
712	C₂×D₃	—	2	1	no	—
713	C₂×D₃	—	2	1	no	—
714	C₂×D₃	—	2	1	no	—
715	C₂×D₃	—	2	1	no	—
716	C₂×D₃	—	2	1	no	—
717	C₂×D₃	—	4	4	no	—
718	C₂×D₃	—	4	4	no	—
719	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
720	C₂×D₃	C₉×#41	1	2	yes	complemented
721	C₃×C₄	—	2	1	no	—
722	C₃×C₄	—	2	1	no	—
723	C₃×C₄	—	2	1	no	—
724	C₃×C₄	—	2	1	no	—
725	C₃×C₄	—	2	1	no	—
726	C₃×C₄	—	2	1	no	—
727	C₃×C₄	—	2	1	no	—
728	C₃×C₄	—	2	1	no	—
729	C₃×C₄	—	2	1	no	—
730	C₃×C₄	—	2	1	no	—
731	C₃×C₄	—	3	2	no	—
732	C₃×C₄	—	4	1	no	—
733	C₃×C₄	—	4	1	no	—
734	C₃×C₄	—	4	1	no	—
735	C₃×C₄	—	4	1	no	—
736	C₃×C₄	—	4	1	no	—
737	C₃×C₄	—	6	1	no	—
738	C₃×C₄	—	6	1	no	—
739	C₃×C₄	—	6	1	no	—
740	Dic₃	—	2	1	no	—
741	Dic₃	—	2	1	no	—
742	Dic₃	—	2	1	no	—
743	Dic₃	C₂×D₄×C₉	1	2	yes	—
744	C₃²	C₃×#546	1	1	yes	characteristic
745	C₉	—	2	1	no	—
746	C₉	#5654	1	1	yes	characteristic, direct product factor
747	C₂³	—	3	1	no	—
748	C₂³	—	3	1	no	—
749	C₂³	—	3	1	no	—
750	C₂³	—	3	1	no	—
751	C₂³	—	6	2	no	—
752	C₂³	—	6	2	no	—
753	C₂³	—	6	2	no	—
754	C₂³	—	6	2	no	—
755	C₂³	—	12	1	no	—
756	C₂³	—	12	1	no	—
757	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
758	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
759	Q₈	—	6	2	no	—
760	D₄	—	2	2	no	—
761	D₄	—	3	4	no	—
762	D₄	—	6	2	no	—
763	D₄	—	6	2	no	—
764	D₄	—	6	2	no	—
765	D₄	—	6	2	no	—
766	D₄	—	6	2	no	—
767	D₄	—	12	1	no	—
768	D₄	—	12	1	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	3	1	no	—
771	C₂×C₄	—	3	1	no	—
772	C₂×C₄	—	3	1	no	—
773	C₂×C₄	—	3	1	no	—
774	C₂×C₄	—	6	2	no	—
775	C₂×C₄	—	6	2	no	—
776	C₂×C₄	—	6	2	no	—
777	C₂×C₄	—	12	1	no	—
778	C₂×C₄	—	12	1	no	—
779	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
780	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
781	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
782	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
784	C₂×C₃	—	2	2	no	—
785	C₂×C₃	—	2	2	no	—
786	C₂×C₃	—	2	1	no	—
787	C₂×C₃	—	2	1	no	—
788	C₂×C₃	—	2	1	no	—
789	C₂×C₃	—	4	2	no	—
790	C₂×C₃	—	4	1	no	—
791	C₂×C₃	—	4	1	no	—
792	C₂×C₃	—	6	2	no	—
793	C₂×C₃	—	6	2	no	—
794	C₂×C₃	—	8	1	no	—
795	C₂×C₃	—	12	1	no	—
796	C₂×C₃	—	12	1	no	—
797	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
798	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
799	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
800	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
801	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
802	C₂×C₃	C₃×#1009	1	1	yes	characteristic
803	D₃	—	2	2	no	—
804	D₃	—	2	2	no	—
805	D₃	—	4	1	no	—
806	D₃	—	4	1	no	—
807	C₂²	—	2	1	no	—
808	C₂²	—	2	1	no	—
809	C₂²	—	2	1	no	—
810	C₂²	—	2	1	no	—
811	C₂²	—	2	1	no	—
812	C₂²	—	3	2	no	—
813	C₂²	—	3	2	no	—
814	C₂²	—	6	1	no	—
815	C₂²	—	6	1	no	—
816	C₂²	—	6	1	no	—
817	C₂²	—	6	1	no	—
818	C₂²	—	6	1	no	—
819	C₂²	—	6	1	no	—
820	C₂²	—	6	1	no	—
821	C₂²	—	6	1	no	—
822	C₂²	—	6	1	no	—
823	C₂²	—	6	1	no	—
824	C₂²	—	12	4	no	—
825	C₂²	—	12	4	no	—
826	C₂²	D₃×D₄×C₉	1	2	yes	—
827	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
828	C₄	—	2	1	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	3	2	no	—
834	C₄	—	6	1	no	—
835	C₄	—	6	1	no	—
836	C₄	—	6	1	no	—
837	C₃	—	2	1	no	—
838	C₃	C₉×#546	1	1	yes	characteristic, complemented
839	C₃	C₃×#5654	1	1	yes	characteristic
840	C₂	—	2	2	no	—
841	C₂	—	4	1	no	—
842	C₂	—	6	2	no	—
843	C₂	—	6	2	no	—
844	C₂	—	12	1	no	—
845	C₂	—	12	1	no	—
846	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
847	C₂	D₃×C₉×#41	1	1	yes	characteristic
848	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×#123	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5654	C₃
hypercenter	C₉×#123	D₃
hypocenter	C₃	C₉×#546
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#123

Complements

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

N	H ≅ G/N	type
1. C₂×D₃×D₄×C₉	C₂	semidirect
2. C₂×C₉×#235	C₂	semidirect
3. C₃×C₉×#123	C₂	semidirect
4. C₉×#939	C₂	semidirect
5. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₉×#896	C₂	semidirect
7. C₉×#895	C₂	semidirect
8. C₉×#894	C₂	semidirect
9. C₉×#893	C₂	semidirect
10. C₉×#885	C₂	semidirect
11. C₉×#884	C₂	semidirect
12. C₉×#882	C₂	semidirect
13. C₉×#882	C₂	semidirect
14. C₉×#67⋊C₄	C₂	semidirect
15. D₃×C₉×C₂²⋊C₄	C₂	semidirect
21. C₂²×C₃×C₄×C₉	C₂²	semidirect
24. C₂×C₉×#67	C₂²	semidirect
25. C₂×C₉×#67	C₂²	semidirect
26. C₂²×C₉×Dic₃	C₂²	semidirect
31. C₂×C₉×D₁₂	C₂²	semidirect
32. 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
38. C₃×C₉×C₄⋊C₄	C₂²	semidirect
39. C₃×C₉×C₄⋊C₄	C₂²	semidirect
40. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
41. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
42. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
43. C₉×#217	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×(C₂×D₃)⋊C₄	C₂²	semidirect
51. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
52. C₉×Dic₃⋊C₄	C₂²	semidirect
53. C₉×Dic₃⋊C₄	C₂²	semidirect
54. C₄×C₉×Dic₃	C₂²	semidirect
75. C₉×#123	D₃	semidirect
108. C₉×#67	D₄	semidirect
124. #5654	C₉	direct (N × H)
183. C₂²×C₄×C₉	C₂×D₃	semidirect
188. C₉×C₄⋊C₄	C₂×D₃	semidirect
189. C₉×C₄⋊C₄	C₂×D₃	semidirect
202. C₉×C₂²⋊C₄	C₂×D₃	semidirect
203. C₉×C₂²⋊C₄	C₂×D₃	semidirect
204. C₉×C₂²⋊C₄	C₂×D₃	semidirect
226. C₂×D₃×C₉	#41	semidirect
238. C₂×D₃×D₄	C₂×C₉	semidirect
239. C₂×#235	C₂×C₉	semidirect
243. C₃×#123	C₂×C₉	semidirect
255. #939	C₂×C₉	semidirect
256. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
257. #896	C₂×C₉	semidirect
258. #895	C₂×C₉	semidirect
259. #894	C₂×C₉	semidirect
260. #893	C₂×C₉	semidirect
261. #885	C₂×C₉	semidirect
262. #884	C₂×C₉	semidirect
263. #882	C₂×C₉	semidirect
264. #882	C₂×C₉	semidirect
265. #67⋊C₄	C₂×C₉	semidirect
266. D₃×C₂²⋊C₄	C₂×C₉	semidirect
384. C₂²×C₃×C₄	C₂²×C₉	semidirect
388. C₂×#67	C₂²×C₉	semidirect
389. C₂×#67	C₂²×C₉	semidirect
390. C₂²×Dic₃	C₂²×C₉	semidirect
395. C₂×D₁₂	C₂²×C₉	semidirect
396. C₂×D₁₂	C₂²×C₉	semidirect
398. C₂×C₄×D₃	C₂²×C₉	semidirect
399. C₂×C₄×D₃	C₂²×C₉	semidirect
400. C₂×C₄×D₃	C₂²×C₉	semidirect
401. C₂×Dic₆	C₂²×C₉	semidirect
406. C₃×C₄⋊C₄	C₂²×C₉	semidirect
407. C₃×C₄⋊C₄	C₂²×C₉	semidirect
422. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
423. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
424. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
429. #217	C₂²×C₉	semidirect
433. (C₂×D₃)⋊C₄	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. Dic₃⋊C₄	C₂²×C₉	semidirect
439. Dic₃⋊C₄	C₂²×C₉	semidirect
440. C₄×Dic₃	C₂²×C₉	semidirect
517. #123	D₃×C₉	semidirect
528. C₃×C₉	#546	semidirect
597. #67	D₄×C₉	semidirect
654. C₂²×C₄	C₂×D₃×C₉	semidirect
657. C₄⋊C₄	C₂×D₃×C₉	semidirect
658. C₄⋊C₄	C₂×D₃×C₉	semidirect
668. C₂²⋊C₄	C₂×D₃×C₉	semidirect
669. C₂²⋊C₄	C₂×D₃×C₉	semidirect
670. C₂²⋊C₄	C₂×D₃×C₉	semidirect
720. C₂×D₃	C₉×#41	semidirect
746. C₉	#5654	direct (N × H)
838. 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
C₂×D₃×D₄×C₉	2
C₂×C₉×#235	2
C₃×C₉×#123	2
C₉×#939	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₉×#896	2
C₉×#895	2
C₉×#894	2
C₉×#893	2
C₉×#885	2
C₉×#884	2
C₉×#882	2
C₉×#67⋊C₄	2
D₃×C₉×C₂²⋊C₄	2
C₃×#5654	3
C₉×#546	3

Subgroups — C9×#5654 #13153025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5654 #13153025