Subgroups — C₂×C₉×#950 #13153690

Order 1728.

962 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#950	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₉×#216	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×#215	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₉×#214	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₉×#213	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₉×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#950	C₃	1	1	yes	maximal, characteristic
10	C₂×C₉×#135	—	3	1	no	maximal
11	C₃×C₉×#41	—	2	2	no	—
12	C₃×C₉×#41	C₂²	1	4	yes	complemented
13	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₃×D₄×C₉	—	2	1	no	—
15	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₄×C₉	—	2	1	no	—
17	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
18	C₂×C₉×#67	—	2	1	no	—
19	C₉×#235	—	2	2	no	—
20	C₉×#235	C₂²	1	4	yes	complemented
21	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₃×C₉	—	2	1	no	—
23	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
24	C₉×#216	C₂²	1	4	yes	complemented
25	C₉×#215	C₂²	1	4	yes	complemented
26	C₉×#214	C₂²	1	4	yes	complemented
27	C₉×#213	C₂²	1	4	yes	complemented
28	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₉×C₃⋊C₈	C₂²	1	4	yes	complemented
31	C₂×C₃²×#41	C₂×C₃	1	1	yes	characteristic
32	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
33	C₃×#950	C₂×C₃	1	8	yes	—
34	C₂×C₃×#216	C₂×C₃	1	1	yes	characteristic
35	C₂×C₃×#215	C₂×C₃	1	1	yes	characteristic
36	C₂×C₃×#214	C₂×C₃	1	1	yes	characteristic
37	C₂×C₃×#213	C₂×C₃	1	1	yes	characteristic
38	C₂²×C₃×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic
39	C₂×C₉×#41	—	2	1	no	—
40	C₂×C₉×#41	—	3	1	no	—
41	C₂×C₉×#41	D₃	1	1	yes	characteristic, complemented
42	C₉×#135	—	3	8	no	—
43	C₂×C₉×Q₁₆	—	3	1	no	—
44	C₂×C₉×SD₁₆	—	3	1	no	—
45	C₂×C₉×SD₁₆	—	3	1	no	—
46	C₂×C₉×D₈	—	3	1	no	—
47	C₂²×C₈×C₉	—	3	1	no	—
48	C₂³×C₃×C₉	—	2	1	no	—
49	C₂³×C₃×C₉	D₄	1	1	yes	characteristic
50	C₂²×D₃×C₉	—	2	1	no	—
51	C₃×Q₈×C₉	—	2	1	no	—
52	C₃×Q₈×C₉	C₂³	1	2	yes	—
53	C₃×D₄×C₉	—	2	4	no	—
54	C₃×D₄×C₉	—	2	1	no	—
55	C₃×D₄×C₉	C₂³	1	2	yes	—
56	C₂×C₃×C₄×C₉	—	2	1	no	—
57	C₂×C₃×C₄×C₉	—	2	4	no	—
58	C₂×C₃×C₄×C₉	D₄	1	2	yes	—
59	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
60	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
62	C₉×#67	—	2	4	no	—
63	C₂×C₉×Dic₃	—	2	1	no	—
64	C₉×D₁₂	—	2	1	no	—
65	C₉×D₁₂	C₂³	1	2	yes	—
66	C₄×D₃×C₉	—	2	4	no	—
67	C₉×Dic₆	—	2	1	no	—
68	C₉×Dic₆	C₂³	1	2	yes	—
69	C₉×C₃⋊C₈	C₂³	1	2	yes	—
70	C₉×C₃⋊C₈	C₂³	1	2	yes	—
71	C₂×C₃×#135	—	3	1	no	—
72	C₂×#950	C₉	1	1	yes	characteristic, direct product factor
73	C₃²×#41	—	2	2	no	—
74	C₃²×#41	C₂²×C₃	1	4	yes	—
75	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₃²×D₄	—	2	1	no	—
77	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
78	C₂²×C₃²×C₄	—	2	1	no	—
79	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₃×#67	—	2	1	no	—
81	C₃×#235	—	2	2	no	—
82	C₃×#235	C₂²×C₃	1	4	yes	—
83	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₃×C₄×D₃	—	2	1	no	—
85	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
86	C₃×#216	C₂²×C₃	1	4	yes	—
87	C₃×#215	C₂²×C₃	1	4	yes	—
88	C₃×#214	C₂²×C₃	1	4	yes	—
89	C₃×#213	C₂²×C₃	1	4	yes	—
90	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	4	yes	—
93	C₉×#41	—	2	4	no	—
94	C₉×#41	—	2	4	no	—
95	C₉×#41	—	2	2	no	—
96	C₉×#41	—	3	4	no	—
97	C₉×#41	—	6	2	no	—
98	C₉×#41	C₂×D₃	1	4	yes	complemented
99	C₂×Q₈×C₉	—	2	1	no	—
100	C₂×Q₈×C₉	—	3	1	no	—
101	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
102	C₂×D₄×C₉	—	2	2	no	—
103	C₂×D₄×C₉	—	2	1	no	—
104	C₂×D₄×C₉	—	2	1	no	—
105	C₂×D₄×C₉	—	3	1	no	—
106	C₂×D₄×C₉	—	6	1	no	—
107	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
108	C₂²×C₄×C₉	—	2	2	no	—
109	C₂²×C₄×C₉	—	2	1	no	—
110	C₂²×C₄×C₉	—	2	1	no	—
111	C₂²×C₄×C₉	—	6	1	no	—
112	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
113	C₉×Q₁₆	—	3	4	no	—
114	C₉×SD₁₆	—	3	4	no	—
115	C₉×SD₁₆	—	3	4	no	—
116	C₉×D₈	—	3	4	no	—
117	C₂×C₈×C₉	—	3	1	no	—
118	C₂×C₈×C₉	—	3	1	no	—
119	C₂×C₈×C₉	—	3	4	no	—
120	C₂²×C₃×C₉	—	2	2	no	—
121	C₂²×C₃×C₉	—	2	2	no	—
122	C₂²×C₃×C₉	—	4	2	no	—
123	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
124	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
125	C₂×D₃×C₉	—	2	2	no	—
126	C₂×D₃×C₉	—	4	2	no	—
127	C₃×C₄×C₉	—	2	2	no	—
128	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
129	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
130	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
131	C₉×Dic₃	—	2	2	no	—
132	C₂×C₃×#41	—	2	1	no	—
133	C₂×C₃×#41	—	3	1	no	—
134	C₂×C₃×#41	C₂×C₉	1	1	yes	characteristic, complemented
135	C₂×C₃×#41	C₃×D₃	1	1	yes	characteristic
136	C₂×#235	C₂×C₉	1	1	yes	characteristic, complemented
137	C₃×#135	—	3	8	no	—
138	C₂×C₃×Q₁₆	—	3	1	no	—
139	C₂×C₃×SD₁₆	—	3	1	no	—
140	C₂×C₃×SD₁₆	—	3	1	no	—
141	C₂×C₃×D₈	—	3	1	no	—
142	C₂²×C₃×C₈	—	3	1	no	—
143	#950	C₂×C₉	1	8	yes	direct product factor
144	C₂×#216	C₂×C₉	1	1	yes	characteristic, complemented
145	C₂×#215	C₂×C₉	1	1	yes	characteristic, complemented
146	C₂×#214	C₂×C₉	1	1	yes	characteristic, complemented
147	C₂×#213	C₂×C₉	1	1	yes	characteristic, complemented
148	C₂²×C₃⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
149	C₂³×C₃²	—	2	1	no	—
150	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
151	C₂²×C₃×D₃	—	2	1	no	—
152	C₃²×Q₈	—	2	1	no	—
153	C₃²×Q₈	C₂³×C₃	1	2	yes	—
154	C₃²×D₄	—	2	4	no	—
155	C₃²×D₄	—	2	1	no	—
156	C₃²×D₄	C₂³×C₃	1	2	yes	—
157	C₂×C₃²×C₄	—	2	1	no	—
158	C₂×C₃²×C₄	—	2	4	no	—
159	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
160	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
161	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
162	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
163	C₃×#67	—	2	4	no	—
164	C₂×C₃×Dic₃	—	2	1	no	—
165	C₃×D₁₂	—	2	1	no	—
166	C₃×D₁₂	C₂³×C₃	1	2	yes	—
167	C₃×C₄×D₃	—	2	4	no	—
168	C₃×Dic₆	—	2	1	no	—
169	C₃×Dic₆	C₂³×C₃	1	2	yes	—
170	C₂³×C₉	—	2	2	no	—
171	C₂³×C₉	—	2	1	no	—
172	C₂³×C₉	—	2	1	no	—
173	C₂³×C₉	—	6	1	no	—
174	C₂³×C₉	#67	1	1	yes	characteristic
175	C₃×C₃⋊C₈	C₂³×C₃	1	2	yes	—
176	C₃×C₃⋊C₈	C₂³×C₃	1	2	yes	—
177	Q₈×C₉	—	2	2	no	—
178	Q₈×C₉	—	2	1	no	—
179	Q₈×C₉	—	2	2	no	—
180	Q₈×C₉	—	3	2	no	—
181	Q₈×C₉	—	6	1	no	—
182	Q₈×C₉	C₂²×D₃	1	2	yes	—
183	D₄×C₉	—	2	8	no	—
184	D₄×C₉	—	2	2	no	—
185	D₄×C₉	—	2	4	no	—
186	D₄×C₉	—	2	1	no	—
187	D₄×C₉	—	2	2	no	—
188	D₄×C₉	—	3	2	no	—
189	D₄×C₉	—	6	4	no	—
190	D₄×C₉	—	6	1	no	—
191	D₄×C₉	C₂²×D₃	1	2	yes	—
192	C₂×C₄×C₉	—	2	2	no	—
193	C₂×C₄×C₉	—	2	8	no	—
194	C₂×C₄×C₉	—	2	1	no	—
195	C₂×C₄×C₉	—	2	4	no	—
196	C₂×C₄×C₉	—	2	1	no	—
197	C₂×C₄×C₉	—	2	2	no	—
198	C₂×C₄×C₉	—	2	1	no	—
199	C₂×C₄×C₉	—	2	2	no	—
200	C₂×C₄×C₉	—	6	1	no	—
201	C₂×C₄×C₉	—	6	4	no	—
202	C₂×C₄×C₉	#67	1	2	yes	—
203	C₂×C₄×C₉	#67	1	1	yes	characteristic
204	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
205	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
206	C₈×C₉	—	3	2	no	—
207	C₈×C₉	—	3	2	no	—
208	C₂×#135	—	3	1	no	Sylow
209	C₂×C₃×C₉	—	2	2	no	—
210	C₂×C₃×C₉	—	4	2	no	—
211	C₂×C₃×C₉	#135	1	2	yes	complemented
212	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
213	D₃×C₉	—	4	2	no	—
214	C₃×#41	—	2	4	no	—
215	C₃×#41	—	2	2	no	—
216	C₃×#41	—	2	2	no	—
217	C₃×#41	—	2	4	no	—
218	C₃×#41	—	3	4	no	—
219	C₃×#41	—	6	2	no	—
220	C₃×#41	C₂²×C₉	1	4	yes	complemented
221	C₃×#41	C₂×C₃×D₃	1	4	yes	—
222	C₂×C₃×Q₈	—	2	1	no	—
223	C₂×C₃×Q₈	—	3	1	no	—
224	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
225	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
226	C₂×C₃×D₄	—	2	2	no	—
227	C₂×C₃×D₄	—	2	1	no	—
228	C₂×C₃×D₄	—	2	1	no	—
229	C₂×C₃×D₄	—	2	1	no	—
230	C₂×C₃×D₄	—	3	1	no	—
231	C₂×C₃×D₄	—	6	1	no	—
232	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
233	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
234	C₂²×C₃×C₄	—	2	2	no	—
235	C₂²×C₃×C₄	—	2	1	no	—
236	C₂²×C₃×C₄	—	2	1	no	—
237	C₂²×C₃×C₄	—	2	1	no	—
238	C₂²×C₃×C₄	—	6	1	no	—
239	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
240	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
241	C₂×#67	—	2	1	no	—
242	#235	—	2	2	no	—
243	#235	C₂²×C₉	1	4	yes	complemented
244	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
245	C₂×C₄×D₃	—	2	1	no	—
246	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
247	C₃×Q₁₆	—	3	4	no	—
248	C₃×SD₁₆	—	3	4	no	—
249	C₃×SD₁₆	—	3	4	no	—
250	C₃×D₈	—	3	4	no	—
251	C₂×C₃×C₈	—	3	1	no	—
252	C₂×C₃×C₈	—	3	1	no	—
253	C₂×C₃×C₈	—	3	4	no	—
254	#216	C₂²×C₉	1	4	yes	complemented
255	#215	C₂²×C₉	1	4	yes	complemented
256	#214	C₂²×C₉	1	4	yes	complemented
257	#213	C₂²×C₉	1	4	yes	complemented
258	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
259	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
260	C₂×C₃⋊C₈	C₂²×C₉	1	4	yes	complemented
261	C₂²×C₃²	—	2	2	no	—
262	C₂²×C₃²	—	2	2	no	—
263	C₂²×C₃²	—	4	2	no	—
264	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
265	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
266	C₂×C₃×D₃	—	2	2	no	—
267	C₂×C₃×D₃	—	4	2	no	—
268	C₃²×C₄	—	2	2	no	—
269	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
270	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
271	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
272	C₃×Dic₃	—	2	2	no	—
273	C₂²×C₉	—	2	2	no	—
274	C₂²×C₉	—	2	4	no	—
275	C₂²×C₉	—	2	2	no	—
276	C₂²×C₉	—	2	1	no	—
277	C₂²×C₉	—	2	2	no	—
278	C₂²×C₉	—	4	2	no	—
279	C₂²×C₉	—	4	4	no	—
280	C₂²×C₉	—	4	2	no	—
281	C₂²×C₉	—	6	2	no	—
282	C₂²×C₉	—	12	2	no	—
283	C₂²×C₉	C₂×#67	1	2	yes	—
284	C₂²×C₉	C₂×#67	1	1	yes	characteristic
285	C₄×C₉	—	2	4	no	—
286	C₄×C₉	—	2	2	no	—
287	C₄×C₉	—	2	1	no	—
288	C₄×C₉	—	2	2	no	—
289	C₄×C₉	—	2	1	no	—
290	C₄×C₉	—	6	2	no	—
291	C₄×C₉	C₂×#67	1	2	yes	—
292	C₄×C₉	C₂×#67	1	1	yes	characteristic
293	C₄×C₉	C₂³×D₃	1	1	yes	characteristic
294	C₂×#41	—	3	1	no	—
295	C₂×#41	D₃×C₉	1	1	yes	characteristic, complemented
296	#135	—	3	8	no	—
297	C₂×Q₁₆	—	3	1	no	—
298	C₂×SD₁₆	—	3	1	no	—
299	C₂×SD₁₆	—	3	1	no	—
300	C₂×D₈	—	3	1	no	—
301	C₂²×C₈	—	3	1	no	—
302	C₃×C₉	C₂×#135	1	1	yes	characteristic, complemented, Sylow
303	C₂³×C₃	—	2	2	no	—
304	C₂³×C₃	—	2	1	no	—
305	C₂³×C₃	—	2	1	no	—
306	C₂³×C₃	—	2	1	no	—
307	C₂³×C₃	—	6	1	no	—
308	C₂³×C₃	D₄×C₉	1	1	yes	characteristic
309	C₂³×C₃	C₃×#67	1	1	yes	characteristic
310	C₂²×D₃	—	2	1	no	—
311	C₃×Q₈	—	2	2	no	—
312	C₃×Q₈	—	2	1	no	—
313	C₃×Q₈	—	2	1	no	—
314	C₃×Q₈	—	2	2	no	—
315	C₃×Q₈	—	3	2	no	—
316	C₃×Q₈	—	6	1	no	—
317	C₃×Q₈	C₂³×C₉	1	2	yes	—
318	C₃×Q₈	C₂²×C₃×D₃	1	2	yes	—
319	C₃×D₄	—	2	8	no	—
320	C₃×D₄	—	2	2	no	—
321	C₃×D₄	—	2	4	no	—
322	C₃×D₄	—	2	4	no	—
323	C₃×D₄	—	2	1	no	—
324	C₃×D₄	—	2	1	no	—
325	C₃×D₄	—	2	2	no	—
326	C₃×D₄	—	3	2	no	—
327	C₃×D₄	—	6	4	no	—
328	C₃×D₄	—	6	1	no	—
329	C₃×D₄	C₂³×C₉	1	2	yes	—
330	C₃×D₄	C₂²×C₃×D₃	1	2	yes	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	2	8	no	—
333	C₂×C₃×C₄	—	2	1	no	—
334	C₂×C₃×C₄	—	2	1	no	—
335	C₂×C₃×C₄	—	2	4	no	—
336	C₂×C₃×C₄	—	2	4	no	—
337	C₂×C₃×C₄	—	2	1	no	—
338	C₂×C₃×C₄	—	2	2	no	—
339	C₂×C₃×C₄	—	2	1	no	—
340	C₂×C₃×C₄	—	2	2	no	—
341	C₂×C₃×C₄	—	6	1	no	—
342	C₂×C₃×C₄	—	6	4	no	—
343	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
344	C₂×C₃×C₄	D₄×C₉	1	2	yes	—
345	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
347	C₂×C₃×C₄	C₃×#67	1	2	yes	—
348	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
349	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
350	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
351	#67	—	2	4	no	—
352	C₂×Dic₃	—	2	1	no	—
353	D₁₂	—	2	1	no	—
354	D₁₂	C₂³×C₉	1	2	yes	—
355	C₄×D₃	—	2	4	no	—
356	Dic₆	—	2	1	no	—
357	Dic₆	C₂³×C₉	1	2	yes	—
358	C₃×C₈	—	3	2	no	—
359	C₃×C₈	—	3	2	no	—
360	C₃⋊C₈	C₂³×C₉	1	2	yes	—
361	C₃⋊C₈	C₂³×C₉	1	2	yes	—
362	C₂×C₃²	—	2	2	no	—
363	C₂×C₃²	—	4	2	no	—
364	C₂×C₃²	C₃×#135	1	2	yes	—
365	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
366	C₃×D₃	—	4	2	no	—
367	C₂×C₉	—	2	2	no	—
368	C₂×C₉	—	2	2	no	—
369	C₂×C₉	—	2	1	no	—
370	C₂×C₉	—	4	2	no	—
371	C₂×C₉	—	4	4	no	—
372	C₂×C₉	—	4	2	no	—
373	C₂×C₉	—	12	2	no	—
374	C₂×C₉	#950	1	2	yes	direct product factor
375	C₂×C₉	C₂²×#67	1	1	yes	characteristic
376	#41	—	2	2	no	—
377	#41	—	3	4	no	—
378	#41	—	6	2	no	—
379	#41	C₂×D₃×C₉	1	4	yes	complemented
380	C₂×Q₈	—	3	1	no	—
381	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	3	1	no	—
384	C₂×D₄	—	6	1	no	—
385	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	6	1	no	—
388	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
389	Q₁₆	—	3	4	no	—
390	SD₁₆	—	3	4	no	—
391	SD₁₆	—	3	4	no	—
392	D₈	—	3	4	no	—
393	C₂×C₈	—	3	1	no	—
394	C₂×C₈	—	3	1	no	—
395	C₂×C₈	—	3	4	no	—
396	C₂²×C₃	—	2	2	no	—
397	C₂²×C₃	—	2	2	no	—
398	C₂²×C₃	—	2	4	no	—
399	C₂²×C₃	—	2	2	no	—
400	C₂²×C₃	—	2	2	no	—
401	C₂²×C₃	—	2	1	no	—
402	C₂²×C₃	—	2	2	no	—
403	C₂²×C₃	—	4	2	no	—
404	C₂²×C₃	—	4	4	no	—
405	C₂²×C₃	—	4	2	no	—
406	C₂²×C₃	—	4	2	no	—
407	C₂²×C₃	—	6	2	no	—
408	C₂²×C₃	—	12	2	no	—
409	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
410	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
411	C₂²×C₃	C₂×C₃×#67	1	2	yes	—
412	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
413	C₂×D₃	—	2	2	no	—
414	C₂×D₃	—	4	2	no	—
415	C₃×C₄	—	2	4	no	—
416	C₃×C₄	—	2	2	no	—
417	C₃×C₄	—	2	2	no	—
418	C₃×C₄	—	2	1	no	—
419	C₃×C₄	—	2	2	no	—
420	C₃×C₄	—	2	1	no	—
421	C₃×C₄	—	6	2	no	—
422	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
423	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
424	C₃×C₄	C₂⁴×C₉	1	1	yes	characteristic
425	C₃×C₄	C₂×C₃×#67	1	2	yes	—
426	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
427	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
428	Dic₃	—	2	2	no	—
429	C₃²	C₂×C₃×#135	1	1	yes	characteristic
430	C₉	—	2	1	no	—
431	C₉	C₂×#950	1	1	yes	characteristic, direct product factor
432	C₂³	—	2	1	no	—
433	C₂³	—	6	1	no	—
434	C₂³	C₉×#67	1	1	yes	characteristic
435	Q₈	—	2	1	no	—
436	Q₈	—	3	2	no	—
437	Q₈	—	6	1	no	—
438	Q₈	C₂²×D₃×C₉	1	2	yes	—
439	D₄	—	2	4	no	—
440	D₄	—	2	1	no	—
441	D₄	—	3	2	no	—
442	D₄	—	6	4	no	—
443	D₄	—	6	1	no	—
444	D₄	C₂²×D₃×C₉	1	2	yes	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	6	1	no	—
448	C₂×C₄	—	6	4	no	—
449	C₂×C₄	C₉×#67	1	1	yes	characteristic
450	C₂×C₄	C₉×#67	1	2	yes	—
451	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
453	C₈	—	3	2	no	—
454	C₈	—	3	2	no	—
455	C₂×C₃	—	2	2	no	—
456	C₂×C₃	—	2	2	no	—
457	C₂×C₃	—	2	1	no	—
458	C₂×C₃	—	2	2	no	—
459	C₂×C₃	—	4	2	no	—
460	C₂×C₃	—	4	4	no	—
461	C₂×C₃	—	4	2	no	—
462	C₂×C₃	—	4	2	no	—
463	C₂×C₃	—	12	2	no	—
464	C₂×C₃	C₉×#135	1	2	yes	complemented
465	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
466	C₂×C₃	C₃×#950	1	2	yes	—
467	C₂×C₃	C₂²×C₃×#67	1	1	yes	characteristic
468	D₃	—	4	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	6	2	no	—
473	C₂²	—	12	2	no	—
474	C₂²	C₂×C₉×#67	1	2	yes	—
475	C₂²	C₂×C₉×#67	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	6	2	no	—
478	C₄	C₂×C₉×#67	1	2	yes	—
479	C₄	C₂×C₉×#67	1	1	yes	characteristic
480	C₄	C₂³×D₃×C₉	1	1	yes	characteristic
481	C₃	—	2	1	no	—
482	C₃	C₂×C₉×#135	1	1	yes	characteristic, complemented
483	C₃	C₂×C₃×#950	1	1	yes	characteristic
484	C₂	—	2	2	no	—
485	C₂	—	4	2	no	—
486	C₂	—	12	2	no	—
487	C₂	C₉×#950	1	2	yes	direct product factor
488	C₂	C₂²×C₉×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	#67
commutator	C₃×C₄	C₂⁴×C₉
Frattini	C₃×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×#41	C₂
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₂×C₃×#950	C₃
cosocle	C₃²×C₄	C₂⁴×C₃
hypercenter	C₂×C₉×#41	D₃
hypocenter	C₃	C₂×C₉×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₂²×C₄×C₉ ◁ C₂×C₉×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₉×#41	C₂	semidirect
2. C₂×C₉×#235	C₂	semidirect
3. C₉×#950	C₂	direct (N × H)
4. C₂×C₉×#216	C₂	semidirect
5. C₂×C₉×#215	C₂	semidirect
6. C₂×C₉×#214	C₂	semidirect
7. C₂×C₉×#213	C₂	semidirect
8. C₂²×C₉×C₃⋊C₈	C₂	semidirect
12. C₃×C₉×#41	C₂²	semidirect
20. C₉×#235	C₂²	semidirect
24. C₉×#216	C₂²	semidirect
25. C₉×#215	C₂²	semidirect
26. C₉×#214	C₂²	semidirect
27. C₉×#213	C₂²	semidirect
30. C₂×C₉×C₃⋊C₈	C₂²	semidirect
41. C₂×C₉×#41	D₃	semidirect
72. C₂×#950	C₉	direct (N × H)
98. C₉×#41	C₂×D₃	semidirect
134. C₂×C₃×#41	C₂×C₉	semidirect
136. C₂×#235	C₂×C₉	semidirect
143. #950	C₂×C₉	direct (N × H)
144. C₂×#216	C₂×C₉	semidirect
145. C₂×#215	C₂×C₉	semidirect
146. C₂×#214	C₂×C₉	semidirect
147. C₂×#213	C₂×C₉	semidirect
148. C₂²×C₃⋊C₈	C₂×C₉	semidirect
211. C₂×C₃×C₉	#135	semidirect
220. C₃×#41	C₂²×C₉	semidirect
243. #235	C₂²×C₉	semidirect
254. #216	C₂²×C₉	semidirect
255. #215	C₂²×C₉	semidirect
256. #214	C₂²×C₉	semidirect
257. #213	C₂²×C₉	semidirect
260. C₂×C₃⋊C₈	C₂²×C₉	semidirect
295. C₂×#41	D₃×C₉	semidirect
302. C₃×C₉	C₂×#135	semidirect
374. C₂×C₉	#950	direct (N × H)
379. #41	C₂×D₃×C₉	semidirect
431. C₉	C₂×#950	direct (N × H)
464. C₂×C₃	C₉×#135	semidirect
482. C₃	C₂×C₉×#135	semidirect
487. C₂	C₉×#950	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₉×#41	2
C₂×C₉×#235	2
C₉×#950	2
C₂×C₉×#216	2
C₂×C₉×#215	2
C₂×C₉×#214	2
C₂×C₉×#213	2
C₂²×C₉×C₃⋊C₈	2
C₂×C₃×#950	3
C₂×C₉×#135	3

Subgroups — C2×C9×#950 #13153690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#950 #13153690