Subgroups — C₉×#5678 #13153103

Order 1728.

826 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#947	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#946	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#939	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#937	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#886	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#884	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#884	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#883	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#882	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	D₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#879	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#876	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5678	C₃	1	1	yes	maximal, characteristic
17	C₉×#538	—	3	1	no	maximal
18	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
19	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
21	C₂×C₉×#67	C₂²	1	1	yes	characteristic
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	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
27	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic, complemented
36	C₉×#217	C₂²	1	1	yes	characteristic
37	C₉×#217	C₂²	1	1	yes	characteristic
38	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
39	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
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, complemented
45	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
47	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
48	C₉×Dic₃⋊C₄	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×#124	C₂×C₃	1	1	yes	characteristic
54	C₃×#947	C₂×C₃	1	1	yes	characteristic
55	C₃×#946	C₂×C₃	1	1	yes	characteristic
56	C₃×#939	C₂×C₃	1	1	yes	characteristic
57	C₃×#937	C₂×C₃	1	1	yes	characteristic
58	C₃×#886	C₂×C₃	1	1	yes	characteristic
59	C₃×#884	C₂×C₃	1	1	yes	characteristic
60	C₃×#884	C₂×C₃	1	1	yes	characteristic
61	C₃×#883	C₂×C₃	1	1	yes	characteristic
62	C₃×#882	C₂×C₃	1	1	yes	characteristic
63	C₃×#67⋊C₄	C₂×C₃	1	1	yes	characteristic
64	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
65	C₃×#879	C₂×C₃	1	1	yes	characteristic
66	C₃×#876	C₂×C₃	1	1	yes	characteristic
67	C₃×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
68	C₉×#126	—	3	1	no	—
69	C₉×#126	—	3	1	no	—
70	C₉×#124	—	2	1	no	—
71	C₉×#124	—	3	1	no	—
72	C₉×#124	D₃	1	1	yes	characteristic, complemented
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	—	3	1	no	—
84	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
85	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
86	C₂²×D₃×C₉	—	2	2	no	—
87	C₂²×D₃×C₉	—	4	1	no	—
88	C₂²×D₃×C₉	—	4	1	no	—
89	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
90	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
91	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
92	C₃×Q₈×C₉	—	4	1	no	—
93	C₃×D₄×C₉	—	4	1	no	—
94	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
96	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
98	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
99	C₉×#67	—	2	2	no	—
100	C₉×#67	—	4	1	no	—
101	C₉×#67	—	4	1	no	—
102	C₉×#67	—	4	1	no	—
103	C₂×C₉×Dic₃	—	4	1	no	—
104	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
105	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
106	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
107	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
108	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
109	C₉×D₁₂	—	2	2	no	—
110	C₉×D₁₂	—	4	1	no	—
111	C₄×D₃×C₉	—	4	1	no	—
112	C₄×D₃×C₉	—	4	1	no	—
113	C₄×D₃×C₉	—	4	1	no	—
114	C₃×#538	—	3	1	no	—
115	#5678	C₉	1	1	yes	characteristic, direct product factor
116	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
123	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
126	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
129	C₂⁴×C₉	—	3	1	no	—
130	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
131	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
133	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
135	C₃×#217	C₂²×C₃	1	1	yes	characteristic
136	C₃×#217	C₂²×C₃	1	1	yes	characteristic
137	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
138	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
139	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
140	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
141	C₃×(C₂×D₃)⋊C₄	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×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
146	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
147	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
148	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
149	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
150	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
151	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
152	C₂×Q₈×C₉	—	2	1	no	—
153	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic, complemented
154	C₂×D₄×C₉	—	2	1	no	—
155	C₂×D₄×C₉	—	3	1	no	—
156	C₂×D₄×C₉	—	3	1	no	—
157	C₂×D₄×C₉	—	3	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	C₂×D₃	1	1	yes	characteristic
162	C₂²×C₄×C₉	—	3	1	no	—
163	C₂²×C₄×C₉	—	3	1	no	—
164	C₂²×C₄×C₉	—	3	1	no	—
165	C₂²×C₄×C₉	—	3	1	no	—
166	C₉×C₄⋊C₄	—	3	1	no	—
167	C₉×C₄⋊C₄	—	3	1	no	—
168	C₉×C₄⋊C₄	—	3	1	no	—
169	C₉×C₄⋊C₄	—	3	1	no	—
170	C₉×C₄⋊C₄	—	3	1	no	—
171	C₉×C₄⋊C₄	—	3	1	no	—
172	C₉×C₂²⋊C₄	—	2	1	no	—
173	C₉×C₂²⋊C₄	—	2	1	no	—
174	C₉×C₂²⋊C₄	—	2	1	no	—
175	C₉×C₂²⋊C₄	—	2	1	no	—
176	C₉×C₂²⋊C₄	—	3	1	no	—
177	C₉×C₂²⋊C₄	—	3	1	no	—
178	C₉×C₂²⋊C₄	—	3	1	no	—
179	C₉×C₂²⋊C₄	—	3	1	no	—
180	C₉×C₂²⋊C₄	—	3	1	no	—
181	C₉×C₂²⋊C₄	—	3	1	no	—
182	C₉×C₂²⋊C₄	—	3	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	C₂×D₃	1	1	yes	characteristic
187	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
188	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
189	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
190	C₄²×C₉	—	2	1	no	—
191	C₄²×C₉	—	3	1	no	—
192	C₄²×C₉	C₂×D₃	1	1	yes	characteristic, complemented
193	C₂²×C₃×C₉	—	2	1	no	—
194	C₂²×C₃×C₉	—	2	1	no	—
195	C₂²×C₃×C₉	—	2	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	C₂⁴	1	1	yes	characteristic
200	C₂×D₃×C₉	—	2	1	no	—
201	C₂×D₃×C₉	—	2	1	no	—
202	C₂×D₃×C₉	—	2	1	no	—
203	C₂×D₃×C₉	—	2	1	no	—
204	C₂×D₃×C₉	—	2	1	no	—
205	C₂×D₃×C₉	—	2	1	no	—
206	C₂×D₃×C₉	—	2	1	no	—
207	C₂×D₃×C₉	—	2	1	no	—
208	C₂×D₃×C₉	—	4	4	no	—
209	C₂×D₃×C₉	#41	1	2	yes	—
210	C₃×C₄×C₉	—	2	1	no	—
211	C₃×C₄×C₉	—	2	1	no	—
212	C₃×C₄×C₉	—	2	1	no	—
213	C₃×C₄×C₉	—	2	1	no	—
214	C₃×C₄×C₉	—	2	1	no	—
215	C₉×Dic₃	—	2	1	no	—
216	C₉×Dic₃	—	2	1	no	—
217	C₉×Dic₃	—	2	1	no	—
218	C₉×Dic₃	—	2	1	no	—
219	C₉×Dic₃	—	2	1	no	—
220	C₃×#126	—	3	1	no	—
221	C₃×#126	—	3	1	no	—
222	C₃×#124	—	2	1	no	—
223	C₃×#124	—	3	1	no	—
224	C₃×#124	C₂×C₉	1	1	yes	characteristic, complemented
225	C₃×#124	C₃×D₃	1	1	yes	characteristic
226	C₃×#123	—	3	1	no	—
227	C₃×#123	—	3	1	no	—
228	C₃×C₂²⋊Q₈	—	3	1	no	—
229	C₃×#121	—	3	1	no	—
230	C₃×#121	—	3	1	no	—
231	C₃×#121	—	3	1	no	—
232	C₃×#120	—	3	1	no	—
233	C₃×#120	—	3	1	no	—
234	C₃×C₄×D₄	—	3	1	no	—
235	C₃×C₄×D₄	—	3	1	no	—
236	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
237	#947	C₂×C₉	1	1	yes	characteristic, complemented
238	#946	C₂×C₉	1	1	yes	characteristic, complemented
239	#939	C₂×C₉	1	1	yes	characteristic, complemented
240	#937	C₂×C₉	1	1	yes	characteristic, complemented
241	#886	C₂×C₉	1	1	yes	characteristic, complemented
242	#884	C₂×C₉	1	1	yes	characteristic, complemented
243	#884	C₂×C₉	1	1	yes	characteristic, complemented
244	#883	C₂×C₉	1	1	yes	characteristic, complemented
245	#882	C₂×C₉	1	1	yes	characteristic, complemented
246	#67⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
247	D₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
248	#879	C₂×C₉	1	1	yes	characteristic, complemented
249	#876	C₂×C₉	1	1	yes	characteristic, complemented
250	C₄×D₁₂	C₂×C₉	1	1	yes	characteristic, complemented
251	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
252	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
253	C₂²×C₃×D₃	—	2	2	no	—
254	C₂²×C₃×D₃	—	4	1	no	—
255	C₂²×C₃×D₃	—	4	1	no	—
256	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
257	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
258	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
259	C₃²×Q₈	—	4	1	no	—
260	C₃²×D₄	—	4	1	no	—
261	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
262	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
263	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
264	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
265	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
266	C₃×#67	—	2	2	no	—
267	C₃×#67	—	4	1	no	—
268	C₃×#67	—	4	1	no	—
269	C₃×#67	—	4	1	no	—
270	C₂×C₃×Dic₃	—	4	1	no	—
271	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
272	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
273	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
274	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
275	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
276	C₃×D₁₂	—	2	2	no	—
277	C₃×D₁₂	—	4	1	no	—
278	C₃×C₄×D₃	—	4	1	no	—
279	C₃×C₄×D₃	—	4	1	no	—
280	C₃×C₄×D₃	—	4	1	no	—
281	C₂³×C₉	—	2	1	no	—
282	C₂³×C₉	—	2	1	no	—
283	C₂³×C₉	—	3	1	no	—
284	C₂³×C₉	—	3	1	no	—
285	C₂³×C₉	—	3	1	no	—
286	C₂³×C₉	—	6	2	no	—
287	C₂³×C₉	—	12	1	no	—
288	C₂³×C₉	—	12	1	no	—
289	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
290	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
291	Q₈×C₉	—	4	1	no	—
292	Q₈×C₉	—	4	2	no	—
293	D₄×C₉	—	4	1	no	—
294	D₄×C₉	—	4	2	no	—
295	D₄×C₉	—	6	2	no	—
296	D₄×C₉	—	6	2	no	—
297	D₄×C₉	—	12	1	no	—
298	D₄×C₉	—	12	1	no	—
299	D₄×C₉	—	12	1	no	—
300	D₄×C₉	—	12	1	no	—
301	C₂×C₄×C₉	—	2	1	no	—
302	C₂×C₄×C₉	—	2	1	no	—
303	C₂×C₄×C₉	—	2	1	no	—
304	C₂×C₄×C₉	—	2	1	no	—
305	C₂×C₄×C₉	—	2	1	no	—
306	C₂×C₄×C₉	—	3	1	no	—
307	C₂×C₄×C₉	—	3	1	no	—
308	C₂×C₄×C₉	—	3	1	no	—
309	C₂×C₄×C₉	—	3	1	no	—
310	C₂×C₄×C₉	—	3	1	no	—
311	C₂×C₄×C₉	—	12	1	no	—
312	C₂×C₄×C₉	—	12	1	no	—
313	C₂×C₄×C₉	—	12	1	no	—
314	C₂×C₄×C₉	—	12	1	no	—
315	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
316	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
317	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
318	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
319	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
320	#538	—	3	1	no	Sylow
321	C₂×C₃×C₉	—	4	1	no	—
322	C₂×C₃×C₉	—	4	1	no	—
323	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
324	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
325	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
326	D₃×C₉	—	2	2	no	—
327	D₃×C₉	—	4	1	no	—
328	D₃×C₉	—	4	1	no	—
329	C₂⁴×C₃	—	3	1	no	—
330	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
331	C₂×C₃×Q₈	—	2	1	no	—
332	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
333	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
334	C₂×C₃×D₄	—	2	1	no	—
335	C₂×C₃×D₄	—	3	1	no	—
336	C₂×C₃×D₄	—	3	1	no	—
337	C₂×C₃×D₄	—	3	1	no	—
338	C₂×C₃×D₄	—	3	1	no	—
339	C₂×C₃×D₄	—	3	1	no	—
340	C₂×C₃×D₄	—	3	1	no	—
341	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
342	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
343	C₂²×C₃×C₄	—	3	1	no	—
344	C₂²×C₃×C₄	—	3	1	no	—
345	C₂²×C₃×C₄	—	3	1	no	—
346	C₂²×C₃×C₄	—	3	1	no	—
347	C₂×#67	C₂²×C₉	1	1	yes	characteristic
348	C₂×#67	C₂²×C₉	1	1	yes	characteristic
349	C₂×#67	C₂²×C₉	1	1	yes	characteristic
350	C₂×#67	C₂²×C₉	1	1	yes	characteristic, complemented
351	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
352	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
353	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
354	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
355	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
356	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
357	C₃×C₄⋊C₄	—	3	1	no	—
358	C₃×C₄⋊C₄	—	3	1	no	—
359	C₃×C₄⋊C₄	—	3	1	no	—
360	C₃×C₄⋊C₄	—	3	1	no	—
361	C₃×C₄⋊C₄	—	3	1	no	—
362	C₃×C₄⋊C₄	—	3	1	no	—
363	C₃×C₂²⋊C₄	—	2	1	no	—
364	C₃×C₂²⋊C₄	—	2	1	no	—
365	C₃×C₂²⋊C₄	—	2	1	no	—
366	C₃×C₂²⋊C₄	—	2	1	no	—
367	C₃×C₂²⋊C₄	—	3	1	no	—
368	C₃×C₂²⋊C₄	—	3	1	no	—
369	C₃×C₂²⋊C₄	—	3	1	no	—
370	C₃×C₂²⋊C₄	—	3	1	no	—
371	C₃×C₂²⋊C₄	—	3	1	no	—
372	C₃×C₂²⋊C₄	—	3	1	no	—
373	C₃×C₂²⋊C₄	—	3	1	no	—
374	C₃×C₂²⋊C₄	—	3	1	no	—
375	C₃×C₂²⋊C₄	—	3	1	no	—
376	C₃×C₂²⋊C₄	—	3	1	no	—
377	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
378	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
379	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
380	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
381	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
382	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
383	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
384	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
385	C₃×C₄²	—	2	1	no	—
386	C₃×C₄²	—	3	1	no	—
387	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic, complemented
388	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
389	#217	C₂²×C₉	1	1	yes	characteristic
390	#217	C₂²×C₉	1	1	yes	characteristic
391	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
392	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
393	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
394	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
395	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
396	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
397	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
398	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
399	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
400	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
401	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
402	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
403	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
404	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
405	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
406	C₂²×C₃²	—	2	1	no	—
407	C₂²×C₃²	—	2	1	no	—
408	C₂²×C₃²	—	2	1	no	—
409	C₂²×C₃²	—	2	1	no	—
410	C₂²×C₃²	—	2	1	no	—
411	C₂²×C₃²	—	2	1	no	—
412	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
413	C₂×C₃×D₃	—	2	1	no	—
414	C₂×C₃×D₃	—	2	1	no	—
415	C₂×C₃×D₃	—	2	1	no	—
416	C₂×C₃×D₃	—	2	1	no	—
417	C₂×C₃×D₃	—	2	1	no	—
418	C₂×C₃×D₃	—	2	1	no	—
419	C₂×C₃×D₃	—	2	1	no	—
420	C₂×C₃×D₃	—	2	1	no	—
421	C₂×C₃×D₃	—	4	4	no	—
422	C₂×C₃×D₃	C₃×#41	1	2	yes	—
423	C₃²×C₄	—	2	1	no	—
424	C₃²×C₄	—	2	1	no	—
425	C₃²×C₄	—	2	1	no	—
426	C₃²×C₄	—	2	1	no	—
427	C₃²×C₄	—	2	1	no	—
428	C₃×Dic₃	—	2	1	no	—
429	C₃×Dic₃	—	2	1	no	—
430	C₃×Dic₃	—	2	1	no	—
431	C₃×Dic₃	—	2	1	no	—
432	C₃×Dic₃	—	2	1	no	—
433	C₂²×C₉	—	2	1	no	—
434	C₂²×C₉	—	2	1	no	—
435	C₂²×C₉	—	2	1	no	—
436	C₂²×C₉	—	2	1	no	—
437	C₂²×C₉	—	2	1	no	—
438	C₂²×C₉	—	2	1	no	—
439	C₂²×C₉	—	2	1	no	—
440	C₂²×C₉	—	3	2	no	—
441	C₂²×C₉	—	4	1	no	—
442	C₂²×C₉	—	4	1	no	—
443	C₂²×C₉	—	4	1	no	—
444	C₂²×C₉	—	4	1	no	—
445	C₂²×C₉	—	4	1	no	—
446	C₂²×C₉	—	4	1	no	—
447	C₂²×C₉	—	6	1	no	—
448	C₂²×C₉	—	6	1	no	—
449	C₂²×C₉	—	6	1	no	—
450	C₂²×C₉	—	6	1	no	—
451	C₂²×C₉	—	6	1	no	—
452	C₂²×C₉	—	6	1	no	—
453	C₂²×C₉	—	6	1	no	—
454	C₂²×C₉	—	6	1	no	—
455	C₂²×C₉	—	12	4	no	—
456	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
457	C₄×C₉	—	2	2	no	—
458	C₄×C₉	—	2	1	no	—
459	C₄×C₉	—	2	1	no	—
460	C₄×C₉	—	2	1	no	—
461	C₄×C₉	—	2	1	no	—
462	C₄×C₉	—	2	1	no	—
463	C₄×C₉	—	4	1	no	—
464	C₄×C₉	—	4	1	no	—
465	C₄×C₉	—	4	1	no	—
466	C₄×C₉	—	4	1	no	—
467	C₄×C₉	—	6	1	no	—
468	C₄×C₉	—	6	1	no	—
469	C₄×C₉	—	6	1	no	—
470	C₄×C₉	—	6	1	no	—
471	C₄×C₉	—	6	1	no	—
472	#126	—	3	1	no	—
473	#126	—	3	1	no	—
474	#124	—	3	1	no	—
475	#124	D₃×C₉	1	1	yes	characteristic, complemented
476	#123	—	3	1	no	—
477	#123	—	3	1	no	—
478	C₂²⋊Q₈	—	3	1	no	—
479	#121	—	3	1	no	—
480	#121	—	3	1	no	—
481	#121	—	3	1	no	—
482	#120	—	3	1	no	—
483	#120	—	3	1	no	—
484	C₄×D₄	—	3	1	no	—
485	C₄×D₄	—	3	1	no	—
486	C₂×C₂²⋊C₄	—	3	1	no	—
487	C₃×C₉	#538	1	1	yes	characteristic, complemented, Sylow
488	C₂³×C₃	—	2	1	no	—
489	C₂³×C₃	—	2	1	no	—
490	C₂³×C₃	—	3	1	no	—
491	C₂³×C₃	—	3	1	no	—
492	C₂³×C₃	—	3	1	no	—
493	C₂³×C₃	—	6	2	no	—
494	C₂³×C₃	—	12	1	no	—
495	C₂³×C₃	—	12	1	no	—
496	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
497	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
498	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
499	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
500	C₂²×D₃	—	2	2	no	—
501	C₂²×D₃	—	4	1	no	—
502	C₂²×D₃	—	4	1	no	—
503	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
504	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
505	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
506	C₃×Q₈	—	4	1	no	—
507	C₃×Q₈	—	4	1	no	—
508	C₃×Q₈	—	4	2	no	—
509	C₃×D₄	—	4	1	no	—
510	C₃×D₄	—	4	1	no	—
511	C₃×D₄	—	4	2	no	—
512	C₃×D₄	—	6	2	no	—
513	C₃×D₄	—	6	2	no	—
514	C₃×D₄	—	12	1	no	—
515	C₃×D₄	—	12	1	no	—
516	C₃×D₄	—	12	1	no	—
517	C₃×D₄	—	12	1	no	—
518	C₂×C₃×C₄	—	2	1	no	—
519	C₂×C₃×C₄	—	2	1	no	—
520	C₂×C₃×C₄	—	2	1	no	—
521	C₂×C₃×C₄	—	2	1	no	—
522	C₂×C₃×C₄	—	2	1	no	—
523	C₂×C₃×C₄	—	3	1	no	—
524	C₂×C₃×C₄	—	3	1	no	—
525	C₂×C₃×C₄	—	3	1	no	—
526	C₂×C₃×C₄	—	3	1	no	—
527	C₂×C₃×C₄	—	3	1	no	—
528	C₂×C₃×C₄	—	12	1	no	—
529	C₂×C₃×C₄	—	12	1	no	—
530	C₂×C₃×C₄	—	12	1	no	—
531	C₂×C₃×C₄	—	12	1	no	—
532	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
533	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
534	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
535	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
536	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
537	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
538	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
539	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
540	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
541	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
542	#67	—	2	2	no	—
543	#67	—	4	1	no	—
544	#67	—	4	1	no	—
545	#67	—	4	1	no	—
546	C₂×Dic₃	—	4	1	no	—
547	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
548	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
549	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
550	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
551	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
552	D₁₂	—	2	2	no	—
553	D₁₂	—	4	1	no	—
554	C₄×D₃	—	4	1	no	—
555	C₄×D₃	—	4	1	no	—
556	C₄×D₃	—	4	1	no	—
557	C₂×C₃²	—	4	1	no	—
558	C₂×C₃²	—	4	1	no	—
559	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
560	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
561	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
562	C₃×D₃	—	2	2	no	—
563	C₃×D₃	—	4	1	no	—
564	C₃×D₃	—	4	1	no	—
565	C₂×C₉	—	2	1	no	—
566	C₂×C₉	—	2	1	no	—
567	C₂×C₉	—	2	1	no	—
568	C₂×C₉	—	4	1	no	—
569	C₂×C₉	—	4	1	no	—
570	C₂×C₉	—	6	2	no	—
571	C₂×C₉	—	8	1	no	—
572	C₂×C₉	—	8	1	no	—
573	C₂×C₉	—	12	1	no	—
574	C₂×C₉	—	12	1	no	—
575	C₂×C₉	#1004	1	1	yes	characteristic
576	C₂×C₉	D₃×#41	1	1	yes	characteristic
577	C₂×C₉	#1009	1	1	yes	characteristic
578	C₂⁴	—	3	1	no	—
579	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic, complemented
580	C₂×D₄	—	3	1	no	—
581	C₂×D₄	—	3	1	no	—
582	C₂×D₄	—	3	1	no	—
583	C₂×D₄	—	3	1	no	—
584	C₂×D₄	—	3	1	no	—
585	C₂×D₄	—	3	1	no	—
586	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
587	C₂²×C₄	—	3	1	no	—
588	C₂²×C₄	—	3	1	no	—
589	C₂²×C₄	—	3	1	no	—
590	C₂²×C₄	—	3	1	no	—
591	C₄⋊C₄	—	3	1	no	—
592	C₄⋊C₄	—	3	1	no	—
593	C₄⋊C₄	—	3	1	no	—
594	C₄⋊C₄	—	3	1	no	—
595	C₄⋊C₄	—	3	1	no	—
596	C₄⋊C₄	—	3	1	no	—
597	C₂²⋊C₄	—	3	1	no	—
598	C₂²⋊C₄	—	3	1	no	—
599	C₂²⋊C₄	—	3	1	no	—
600	C₂²⋊C₄	—	3	1	no	—
601	C₂²⋊C₄	—	3	1	no	—
602	C₂²⋊C₄	—	3	1	no	—
603	C₂²⋊C₄	—	3	1	no	—
604	C₂²⋊C₄	—	3	1	no	—
605	C₂²⋊C₄	—	3	1	no	—
606	C₂²⋊C₄	—	3	1	no	—
607	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
608	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
609	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
610	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
611	C₄²	—	3	1	no	—
612	C₄²	C₂×D₃×C₉	1	1	yes	characteristic, complemented
613	C₂²×C₃	—	2	1	no	—
614	C₂²×C₃	—	2	1	no	—
615	C₂²×C₃	—	2	1	no	—
616	C₂²×C₃	—	2	1	no	—
617	C₂²×C₃	—	2	1	no	—
618	C₂²×C₃	—	2	1	no	—
619	C₂²×C₃	—	2	1	no	—
620	C₂²×C₃	—	2	1	no	—
621	C₂²×C₃	—	2	1	no	—
622	C₂²×C₃	—	2	1	no	—
623	C₂²×C₃	—	2	1	no	—
624	C₂²×C₃	—	2	1	no	—
625	C₂²×C₃	—	2	1	no	—
626	C₂²×C₃	—	3	2	no	—
627	C₂²×C₃	—	4	1	no	—
628	C₂²×C₃	—	4	1	no	—
629	C₂²×C₃	—	4	1	no	—
630	C₂²×C₃	—	4	1	no	—
631	C₂²×C₃	—	4	1	no	—
632	C₂²×C₃	—	4	1	no	—
633	C₂²×C₃	—	6	1	no	—
634	C₂²×C₃	—	6	1	no	—
635	C₂²×C₃	—	6	1	no	—
636	C₂²×C₃	—	6	1	no	—
637	C₂²×C₃	—	6	1	no	—
638	C₂²×C₃	—	6	1	no	—
639	C₂²×C₃	—	6	1	no	—
640	C₂²×C₃	—	6	1	no	—
641	C₂²×C₃	—	12	4	no	—
642	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
643	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
644	C₂×D₃	—	2	1	no	—
645	C₂×D₃	—	2	1	no	—
646	C₂×D₃	—	2	1	no	—
647	C₂×D₃	—	2	1	no	—
648	C₂×D₃	—	2	1	no	—
649	C₂×D₃	—	2	1	no	—
650	C₂×D₃	—	2	1	no	—
651	C₂×D₃	—	2	1	no	—
652	C₂×D₃	—	4	4	no	—
653	C₂×D₃	C₉×#41	1	2	yes	—
654	C₃×C₄	—	2	2	no	—
655	C₃×C₄	—	2	1	no	—
656	C₃×C₄	—	2	1	no	—
657	C₃×C₄	—	2	1	no	—
658	C₃×C₄	—	2	1	no	—
659	C₃×C₄	—	2	1	no	—
660	C₃×C₄	—	2	1	no	—
661	C₃×C₄	—	2	1	no	—
662	C₃×C₄	—	2	1	no	—
663	C₃×C₄	—	2	1	no	—
664	C₃×C₄	—	2	1	no	—
665	C₃×C₄	—	4	1	no	—
666	C₃×C₄	—	4	1	no	—
667	C₃×C₄	—	4	1	no	—
668	C₃×C₄	—	4	1	no	—
669	C₃×C₄	—	6	1	no	—
670	C₃×C₄	—	6	1	no	—
671	C₃×C₄	—	6	1	no	—
672	C₃×C₄	—	6	1	no	—
673	C₃×C₄	—	6	1	no	—
674	Dic₃	—	2	1	no	—
675	Dic₃	—	2	1	no	—
676	Dic₃	—	2	1	no	—
677	Dic₃	—	2	1	no	—
678	Dic₃	—	2	1	no	—
679	C₃²	C₃×#538	1	1	yes	characteristic
680	C₉	—	2	1	no	—
681	C₉	#5678	1	1	yes	characteristic, direct product factor
682	C₂³	—	3	1	no	—
683	C₂³	—	3	1	no	—
684	C₂³	—	3	1	no	—
685	C₂³	—	6	2	no	—
686	C₂³	—	12	1	no	—
687	C₂³	—	12	1	no	—
688	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
689	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
690	Q₈	—	4	1	no	—
691	D₄	—	4	1	no	—
692	D₄	—	6	2	no	—
693	D₄	—	6	2	no	—
694	D₄	—	12	1	no	—
695	D₄	—	12	1	no	—
696	D₄	—	12	1	no	—
697	D₄	—	12	1	no	—
698	C₂×C₄	—	3	1	no	—
699	C₂×C₄	—	3	1	no	—
700	C₂×C₄	—	3	1	no	—
701	C₂×C₄	—	3	1	no	—
702	C₂×C₄	—	3	1	no	—
703	C₂×C₄	—	12	1	no	—
704	C₂×C₄	—	12	1	no	—
705	C₂×C₄	—	12	1	no	—
706	C₂×C₄	—	12	1	no	—
707	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
711	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
712	C₂×C₃	—	2	1	no	—
713	C₂×C₃	—	2	1	no	—
714	C₂×C₃	—	2	1	no	—
715	C₂×C₃	—	4	1	no	—
716	C₂×C₃	—	4	1	no	—
717	C₂×C₃	—	4	1	no	—
718	C₂×C₃	—	4	1	no	—
719	C₂×C₃	—	6	2	no	—
720	C₂×C₃	—	8	1	no	—
721	C₂×C₃	—	8	1	no	—
722	C₂×C₃	—	12	1	no	—
723	C₂×C₃	—	12	1	no	—
724	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
725	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
726	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
727	C₂×C₃	C₃×#1004	1	1	yes	characteristic
728	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
729	C₂×C₃	C₃×#1009	1	1	yes	characteristic
730	D₃	—	2	2	no	—
731	D₃	—	4	1	no	—
732	D₃	—	4	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	2	1	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	3	2	no	—
740	C₂²	—	6	1	no	—
741	C₂²	—	6	1	no	—
742	C₂²	—	6	1	no	—
743	C₂²	—	6	1	no	—
744	C₂²	—	6	1	no	—
745	C₂²	—	6	1	no	—
746	C₂²	—	6	1	no	—
747	C₂²	—	6	1	no	—
748	C₂²	—	12	4	no	—
749	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
750	C₄	—	2	1	no	—
751	C₄	—	2	1	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	1	no	—
754	C₄	—	2	1	no	—
755	C₄	—	6	1	no	—
756	C₄	—	6	1	no	—
757	C₄	—	6	1	no	—
758	C₄	—	6	1	no	—
759	C₄	—	6	1	no	—
760	C₃	—	2	1	no	—
761	C₃	C₉×#538	1	1	yes	characteristic, complemented
762	C₃	C₃×#5678	1	1	yes	characteristic
763	C₂	—	4	1	no	—
764	C₂	—	4	1	no	—
765	C₂	—	6	2	no	—
766	C₂	—	12	1	no	—
767	C₂	—	12	1	no	—
768	C₂	C₉×#1004	1	1	yes	characteristic
769	C₂	D₃×C₉×#41	1	1	yes	characteristic
770	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×#124	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5678	C₃
hypercenter	C₉×#124	D₃
hypocenter	C₃	C₉×#538
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#124

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#124	C₂	semidirect
2. C₉×#947	C₂	semidirect
3. C₉×#946	C₂	semidirect
4. C₉×#939	C₂	semidirect
5. C₉×#937	C₂	semidirect
6. C₉×#886	C₂	semidirect
7. C₉×#884	C₂	semidirect
8. C₉×#884	C₂	semidirect
9. C₉×#883	C₂	semidirect
10. C₉×#882	C₂	semidirect
11. C₉×#67⋊C₄	C₂	semidirect
12. D₃×C₉×C₂²⋊C₄	C₂	semidirect
13. C₉×#879	C₂	semidirect
14. C₉×#876	C₂	semidirect
15. C₄×C₉×D₁₂	C₂	semidirect
19. C₂×C₃×Q₈×C₉	C₂²	semidirect
24. C₂×C₉×#67	C₂²	semidirect
25. C₂²×C₉×Dic₃	C₂²	semidirect
30. C₂×C₄×D₃×C₉	C₂²	semidirect
33. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
34. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
35. C₃×C₄²×C₉	C₂²	semidirect
44. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
45. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
46. C₉×C₄⋊Dic₃	C₂²	semidirect
47. C₉×C₄⋊Dic₃	C₂²	semidirect
48. C₉×Dic₃⋊C₄	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
72. C₉×#124	D₃	semidirect
115. #5678	C₉	direct (N × H)
153. C₂×Q₈×C₉	C₂×D₃	semidirect
188. C₉×C₂²⋊C₄	C₂×D₃	semidirect
189. C₉×C₂²⋊C₄	C₂×D₃	semidirect
192. C₄²×C₉	C₂×D₃	semidirect
224. C₃×#124	C₂×C₉	semidirect
237. #947	C₂×C₉	semidirect
238. #946	C₂×C₉	semidirect
239. #939	C₂×C₉	semidirect
240. #937	C₂×C₉	semidirect
241. #886	C₂×C₉	semidirect
242. #884	C₂×C₉	semidirect
243. #884	C₂×C₉	semidirect
244. #883	C₂×C₉	semidirect
245. #882	C₂×C₉	semidirect
246. #67⋊C₄	C₂×C₉	semidirect
247. D₃×C₂²⋊C₄	C₂×C₉	semidirect
248. #879	C₂×C₉	semidirect
249. #876	C₂×C₉	semidirect
250. C₄×D₁₂	C₂×C₉	semidirect
332. C₂×C₃×Q₈	C₂²×C₉	semidirect
350. C₂×#67	C₂²×C₉	semidirect
351. C₂²×Dic₃	C₂²×C₉	semidirect
356. C₂×C₄×D₃	C₂²×C₉	semidirect
379. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
380. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
387. C₃×C₄²	C₂²×C₉	semidirect
397. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
398. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
399. C₄⋊Dic₃	C₂²×C₉	semidirect
400. C₄⋊Dic₃	C₂²×C₉	semidirect
401. Dic₃⋊C₄	C₂²×C₉	semidirect
402. Dic₃⋊C₄	C₂²×C₉	semidirect
403. Dic₃⋊C₄	C₂²×C₉	semidirect
404. Dic₃⋊C₄	C₂²×C₉	semidirect
405. C₄×Dic₃	C₂²×C₉	semidirect
475. #124	D₃×C₉	semidirect
487. C₃×C₉	#538	semidirect
579. C₂×Q₈	C₂×D₃×C₉	semidirect
609. C₂²⋊C₄	C₂×D₃×C₉	semidirect
610. C₂²⋊C₄	C₂×D₃×C₉	semidirect
612. C₄²	C₂×D₃×C₉	semidirect
681. C₉	#5678	direct (N × H)
761. C₃	C₉×#538	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×#124	2
C₉×#947	2
C₉×#946	2
C₉×#939	2
C₉×#937	2
C₉×#886	2
C₉×#884	2
C₉×#883	2
C₉×#882	2
C₉×#67⋊C₄	2
D₃×C₉×C₂²⋊C₄	2
C₉×#879	2
C₉×#876	2
C₄×C₉×D₁₂	2
C₃×#5678	3
C₉×#538	3

Subgroups — C9×#5678 #13153103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5678 #13153103