Subgroups — C₉×#5779 #13153514

Order 1728.

804 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#1010	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#1007	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#950	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×#216	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#918	C₂	1	2	yes	maximal, complemented
7	D₃×C₉×Q₁₆	C₂	1	2	yes	maximal, complemented
8	C₉×#916	C₂	1	2	yes	maximal, complemented
9	C₉×#915	C₂	1	2	yes	maximal, complemented
10	C₉×#909	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#907	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5779	C₃	1	1	yes	maximal, characteristic
13	C₉×#578	—	3	1	no	maximal
14	C₃×C₉×#41	C₂²	1	1	yes	characteristic
15	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
16	C₉×#239	—	2	1	no	—
17	C₉×#239	C₂²	1	2	yes	—
18	D₃×Q₈×C₉	—	2	1	no	—
19	D₃×Q₈×C₉	C₂²	1	2	yes	—
20	D₃×Q₈×C₉	C₂²	1	2	yes	—
21	C₉×#237	—	2	2	no	—
22	C₉×#237	C₂²	1	2	yes	—
23	C₉×#235	—	2	2	no	—
24	C₉×#235	—	2	1	no	—
25	C₉×#235	C₂²	1	1	yes	characteristic
26	C₉×#235	C₂²	1	1	yes	characteristic
27	C₂×C₉×Dic₆	—	2	1	no	—
28	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
29	C₃×C₉×Q₁₆	C₂²	1	2	yes	—
30	C₃×C₉×SD₁₆	C₂²	1	2	yes	—
31	C₃×C₉×M₁₆	C₂²	1	1	yes	characteristic
32	C₉×#216	C₂²	1	2	yes	—
33	C₉×#216	C₂²	1	2	yes	—
34	C₉×#216	C₂²	1	1	yes	characteristic
35	C₉×#215	C₂²	1	1	yes	characteristic
36	C₉×#214	C₂²	1	1	yes	characteristic
37	C₉×#213	C₂²	1	1	yes	characteristic
38	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
39	C₉×Dic₁₂	C₂²	1	2	yes	—
40	C₉×#204	C₂²	1	2	yes	—
41	C₉×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
42	D₃×C₈×C₉	C₂²	1	2	yes	—
43	C₃×#1010	C₂×C₃	1	1	yes	characteristic
44	C₃×#1007	C₂×C₃	1	1	yes	characteristic
45	C₃²×#137	C₂×C₃	1	1	yes	characteristic
46	C₃×#950	C₂×C₃	1	1	yes	characteristic
47	C₂×C₃×#216	C₂×C₃	1	1	yes	characteristic
48	C₃×#918	C₂×C₃	1	2	yes	—
49	C₃×D₃×Q₁₆	C₂×C₃	1	2	yes	—
50	C₃×#916	C₂×C₃	1	2	yes	—
51	C₃×#915	C₂×C₃	1	2	yes	—
52	C₃×#909	C₂×C₃	1	1	yes	characteristic
53	C₃×#907	C₂×C₃	1	1	yes	characteristic
54	C₉×2₋¹⁺⁴	—	3	1	no	—
55	C₉×2₋¹⁺⁴	—	3	1	no	—
56	C₉×#137	—	2	1	no	—
57	C₉×#137	—	3	2	no	—
58	C₉×#137	—	3	2	no	—
59	C₉×#137	—	3	1	no	—
60	C₉×#137	D₃	1	1	yes	characteristic, complemented
61	C₉×#135	—	3	1	no	—
62	C₉×#135	—	3	2	no	—
63	C₂×C₉×Q₁₆	—	3	1	no	—
64	C₂×C₉×Q₁₆	—	3	2	no	—
65	C₉×#131	—	3	1	no	—
66	C₃×Q₈×C₉	—	2	1	no	—
67	C₃×Q₈×C₉	C₂³	1	1	yes	characteristic
68	C₃×Q₈×C₉	C₂³	1	2	yes	—
69	C₃×D₄×C₉	—	2	1	no	—
70	C₃×D₄×C₉	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₄×C₉	—	2	1	no	—
72	C₂×C₃×C₄×C₉	—	2	1	no	—
73	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
74	C₉×#67	—	2	1	no	—
75	C₉×#67	—	2	2	no	—
76	C₉×#67	D₄	1	2	yes	—
77	C₂×C₉×Dic₃	—	2	1	no	—
78	C₂×C₉×Dic₃	—	2	2	no	—
79	C₉×D₁₂	—	2	2	no	—
80	C₉×D₁₂	D₄	1	1	yes	characteristic
81	C₉×D₁₂	C₂³	1	1	yes	characteristic
82	C₄×D₃×C₉	—	2	2	no	—
83	C₄×D₃×C₉	—	2	2	no	—
84	C₄×D₃×C₉	—	2	1	no	—
85	C₄×D₃×C₉	—	2	2	no	—
86	C₄×D₃×C₉	C₂³	1	2	yes	—
87	C₉×Dic₆	—	2	1	no	—
88	C₉×Dic₆	—	2	2	no	—
89	C₉×Dic₆	—	2	2	no	—
90	C₉×Dic₆	D₄	1	1	yes	characteristic
91	C₉×Dic₆	C₂³	1	2	yes	—
92	C₉×Dic₆	C₂³	1	1	yes	characteristic
93	C₃×C₈×C₉	C₂³	1	2	yes	—
94	C₉×C₃⋊C₈	C₂³	1	1	yes	characteristic
95	C₉×C₃⋊C₈	C₂³	1	1	yes	characteristic
96	C₃×#578	—	3	1	no	—
97	#5779	C₉	1	1	yes	characteristic, direct product factor
98	C₃²×#41	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
100	C₃×#239	—	2	1	no	—
101	C₃×#239	C₂²×C₃	1	2	yes	—
102	C₃×D₃×Q₈	—	2	1	no	—
103	C₃×D₃×Q₈	C₂²×C₃	1	2	yes	—
104	C₃×D₃×Q₈	C₂²×C₃	1	2	yes	—
105	C₃×#237	—	2	2	no	—
106	C₃×#237	C₂²×C₃	1	2	yes	—
107	C₃×#235	—	2	2	no	—
108	C₃×#235	—	2	1	no	—
109	C₃×#235	C₂²×C₃	1	1	yes	characteristic
110	C₃×#235	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₃×Dic₆	—	2	1	no	—
112	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
113	C₃²×Q₁₆	C₂²×C₃	1	2	yes	—
114	C₃²×SD₁₆	C₂²×C₃	1	2	yes	—
115	C₃²×M₁₆	C₂²×C₃	1	1	yes	characteristic
116	C₃×#216	C₂²×C₃	1	2	yes	—
117	C₃×#216	C₂²×C₃	1	2	yes	—
118	C₃×#216	C₂²×C₃	1	1	yes	characteristic
119	C₃×#215	C₂²×C₃	1	1	yes	characteristic
120	C₃×#214	C₂²×C₃	1	1	yes	characteristic
121	C₃×#213	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
123	C₃×Dic₁₂	C₂²×C₃	1	2	yes	—
124	C₃×#204	C₂²×C₃	1	2	yes	—
125	C₃×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
126	C₃×D₃×C₈	C₂²×C₃	1	2	yes	—
127	C₉×#41	—	2	1	no	—
128	C₉×#41	—	3	1	no	—
129	C₉×#41	—	3	2	no	—
130	C₉×#41	—	3	2	no	—
131	C₉×#41	—	3	1	no	—
132	C₉×#41	—	6	2	no	—
133	C₉×#41	—	6	1	no	—
134	C₉×#41	—	6	2	no	—
135	C₉×#41	—	6	1	no	—
136	C₉×#41	C₂×D₃	1	1	yes	characteristic
137	C₂×Q₈×C₉	—	2	1	no	—
138	C₂×Q₈×C₉	—	3	2	no	—
139	C₂×Q₈×C₉	—	3	2	no	—
140	C₂×Q₈×C₉	—	3	1	no	—
141	C₂×Q₈×C₉	—	6	1	no	—
142	C₂×Q₈×C₉	—	6	1	no	—
143	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
144	C₉×Q₁₆	—	2	2	no	—
145	C₉×Q₁₆	—	3	1	no	—
146	C₉×Q₁₆	—	3	2	no	—
147	C₉×Q₁₆	—	3	2	no	—
148	C₉×Q₁₆	—	3	2	no	—
149	C₉×Q₁₆	C₂×D₃	1	2	yes	—
150	C₉×SD₁₆	—	2	2	no	—
151	C₉×SD₁₆	—	3	1	no	—
152	C₉×SD₁₆	—	3	1	no	—
153	C₉×SD₁₆	—	3	2	no	—
154	C₉×SD₁₆	C₂×D₃	1	2	yes	—
155	C₉×D₈	—	3	1	no	—
156	C₉×M₁₆	—	2	1	no	—
157	C₉×M₁₆	—	3	2	no	—
158	C₉×M₁₆	C₂×D₃	1	1	yes	characteristic
159	C₂×C₈×C₉	—	3	1	no	—
160	C₂×C₈×C₉	—	3	2	no	—
161	C₂²×C₃×C₉	—	2	1	no	—
162	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
163	C₂×D₃×C₉	—	2	1	no	—
164	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
165	C₃×C₄×C₉	—	2	1	no	—
166	C₃×C₄×C₉	—	2	2	no	—
167	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
168	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
169	C₉×Dic₃	—	2	1	no	—
170	C₉×Dic₃	—	2	2	no	—
171	C₉×Dic₃	C₂×D₄	1	2	yes	—
172	C₃×2₋¹⁺⁴	—	3	1	no	—
173	C₃×2₋¹⁺⁴	—	3	1	no	—
174	#1010	C₂×C₉	1	1	yes	characteristic, complemented
175	#1007	C₂×C₉	1	1	yes	characteristic, complemented
176	C₃×#137	—	2	1	no	—
177	C₃×#137	—	3	2	no	—
178	C₃×#137	—	3	2	no	—
179	C₃×#137	—	3	1	no	—
180	C₃×#137	C₂×C₉	1	1	yes	characteristic, complemented
181	C₃×#137	C₃×D₃	1	1	yes	characteristic
182	C₃×#135	—	3	1	no	—
183	C₃×#135	—	3	2	no	—
184	C₂×C₃×Q₁₆	—	3	1	no	—
185	C₂×C₃×Q₁₆	—	3	2	no	—
186	C₃×#131	—	3	1	no	—
187	#950	C₂×C₉	1	1	yes	characteristic, complemented
188	C₂×#216	C₂×C₉	1	1	yes	characteristic, complemented
189	#918	C₂×C₉	1	2	yes	complemented
190	D₃×Q₁₆	C₂×C₉	1	2	yes	complemented
191	#916	C₂×C₉	1	2	yes	complemented
192	#915	C₂×C₉	1	2	yes	complemented
193	#909	C₂×C₉	1	1	yes	characteristic, complemented
194	#907	C₂×C₉	1	1	yes	characteristic, complemented
195	C₃²×Q₈	—	2	1	no	—
196	C₃²×Q₈	C₂³×C₃	1	1	yes	characteristic
197	C₃²×Q₈	C₂³×C₃	1	2	yes	—
198	C₃²×D₄	—	2	1	no	—
199	C₃²×D₄	C₂³×C₃	1	1	yes	characteristic
200	C₂×C₃²×C₄	—	2	1	no	—
201	C₂×C₃²×C₄	—	2	1	no	—
202	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
203	C₃×#67	—	2	1	no	—
204	C₃×#67	—	2	2	no	—
205	C₃×#67	C₃×D₄	1	2	yes	—
206	C₂×C₃×Dic₃	—	2	1	no	—
207	C₂×C₃×Dic₃	—	2	2	no	—
208	C₃×D₁₂	—	2	2	no	—
209	C₃×D₁₂	C₃×D₄	1	1	yes	characteristic
210	C₃×D₁₂	C₂³×C₃	1	1	yes	characteristic
211	C₃×C₄×D₃	—	2	2	no	—
212	C₃×C₄×D₃	—	2	2	no	—
213	C₃×C₄×D₃	—	2	1	no	—
214	C₃×C₄×D₃	—	2	2	no	—
215	C₃×C₄×D₃	C₂³×C₃	1	2	yes	—
216	C₃×Dic₆	—	2	1	no	—
217	C₃×Dic₆	—	2	2	no	—
218	C₃×Dic₆	—	2	2	no	—
219	C₃×Dic₆	C₃×D₄	1	1	yes	characteristic
220	C₃×Dic₆	C₂³×C₃	1	2	yes	—
221	C₃×Dic₆	C₂³×C₃	1	1	yes	characteristic
222	C₃²×C₈	C₂³×C₃	1	2	yes	—
223	C₃×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
224	C₃×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
225	Q₈×C₉	—	2	1	no	—
226	Q₈×C₉	—	2	2	no	—
227	Q₈×C₉	—	2	1	no	—
228	Q₈×C₉	—	3	1	no	—
229	Q₈×C₉	—	3	2	no	—
230	Q₈×C₉	—	3	1	no	—
231	Q₈×C₉	—	4	1	no	—
232	Q₈×C₉	—	6	2	no	—
233	Q₈×C₉	—	6	2	no	—
234	Q₈×C₉	—	6	1	no	—
235	Q₈×C₉	C₂²×D₃	1	1	yes	characteristic
236	Q₈×C₉	C₂²×D₃	1	2	yes	—
237	D₄×C₉	—	2	1	no	—
238	D₄×C₉	—	2	1	no	—
239	D₄×C₉	—	3	2	no	—
240	D₄×C₉	—	3	1	no	—
241	D₄×C₉	—	3	1	no	—
242	D₄×C₉	—	4	1	no	—
243	D₄×C₉	—	6	2	no	—
244	D₄×C₉	—	6	2	no	—
245	D₄×C₉	—	6	1	no	—
246	D₄×C₉	C₂²×D₃	1	1	yes	characteristic
247	C₂×C₄×C₉	—	2	1	no	—
248	C₂×C₄×C₉	—	2	1	no	—
249	C₂×C₄×C₉	—	2	1	no	—
250	C₂×C₄×C₉	—	3	2	no	—
251	C₂×C₄×C₉	—	4	1	no	—
252	C₂×C₄×C₉	—	4	1	no	—
253	C₂×C₄×C₉	—	6	2	no	—
254	C₂×C₄×C₉	—	6	2	no	—
255	C₂×C₄×C₉	—	6	2	no	—
256	C₂×C₄×C₉	—	6	2	no	—
257	C₂×C₄×C₉	—	6	1	no	—
258	C₂×C₄×C₉	—	6	1	no	—
259	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
260	C₈×C₉	—	2	2	no	—
261	C₈×C₉	—	3	1	no	—
262	C₈×C₉	—	3	1	no	—
263	C₈×C₉	C₂²×D₃	1	2	yes	—
264	#578	—	3	1	no	Sylow
265	C₂×C₃×C₉	—	2	1	no	—
266	C₂×C₃×C₉	—	4	1	no	—
267	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
268	D₃×C₉	—	2	2	no	—
269	D₃×C₉	—	4	1	no	—
270	C₃×#41	—	2	1	no	—
271	C₃×#41	—	3	1	no	—
272	C₃×#41	—	3	2	no	—
273	C₃×#41	—	3	2	no	—
274	C₃×#41	—	3	1	no	—
275	C₃×#41	—	6	2	no	—
276	C₃×#41	—	6	1	no	—
277	C₃×#41	—	6	2	no	—
278	C₃×#41	—	6	1	no	—
279	C₃×#41	C₂²×C₉	1	1	yes	characteristic
280	C₃×#41	C₂×C₃×D₃	1	1	yes	characteristic
281	C₂×C₃×Q₈	—	2	1	no	—
282	C₂×C₃×Q₈	—	3	2	no	—
283	C₂×C₃×Q₈	—	3	2	no	—
284	C₂×C₃×Q₈	—	3	1	no	—
285	C₂×C₃×Q₈	—	6	1	no	—
286	C₂×C₃×Q₈	—	6	1	no	—
287	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
288	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
289	#239	—	2	1	no	—
290	#239	C₂²×C₉	1	2	yes	—
291	D₃×Q₈	—	2	1	no	—
292	D₃×Q₈	C₂²×C₉	1	2	yes	—
293	D₃×Q₈	C₂²×C₉	1	2	yes	—
294	#237	—	2	2	no	—
295	#237	C₂²×C₉	1	2	yes	—
296	#235	—	2	2	no	—
297	#235	—	2	1	no	—
298	#235	C₂²×C₉	1	1	yes	characteristic
299	#235	C₂²×C₉	1	1	yes	characteristic
300	C₂×Dic₆	—	2	1	no	—
301	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
302	C₃×Q₁₆	—	2	2	no	—
303	C₃×Q₁₆	—	3	1	no	—
304	C₃×Q₁₆	—	3	2	no	—
305	C₃×Q₁₆	—	3	2	no	—
306	C₃×Q₁₆	—	3	2	no	—
307	C₃×Q₁₆	C₂²×C₉	1	2	yes	—
308	C₃×Q₁₆	C₂×C₃×D₃	1	2	yes	—
309	C₃×SD₁₆	—	2	2	no	—
310	C₃×SD₁₆	—	3	1	no	—
311	C₃×SD₁₆	—	3	1	no	—
312	C₃×SD₁₆	—	3	2	no	—
313	C₃×SD₁₆	C₂²×C₉	1	2	yes	—
314	C₃×SD₁₆	C₂×C₃×D₃	1	2	yes	—
315	C₃×D₈	—	3	1	no	—
316	C₃×M₁₆	—	2	1	no	—
317	C₃×M₁₆	—	3	2	no	—
318	C₃×M₁₆	C₂²×C₉	1	1	yes	characteristic
319	C₃×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
320	C₂×C₃×C₈	—	3	1	no	—
321	C₂×C₃×C₈	—	3	2	no	—
322	#216	C₂²×C₉	1	2	yes	—
323	#216	C₂²×C₉	1	2	yes	—
324	#216	C₂²×C₉	1	1	yes	characteristic
325	#215	C₂²×C₉	1	1	yes	characteristic
326	#214	C₂²×C₉	1	1	yes	characteristic
327	#213	C₂²×C₉	1	1	yes	characteristic
328	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
329	Dic₁₂	C₂²×C₉	1	2	yes	—
330	#204	C₂²×C₉	1	2	yes	—
331	ΓL(1,𝔽₂₅)	C₂²×C₉	1	2	yes	—
332	D₃×C₈	C₂²×C₉	1	2	yes	—
333	C₂²×C₃²	—	2	1	no	—
334	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
335	C₂×C₃×D₃	—	2	1	no	—
336	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
337	C₃²×C₄	—	2	1	no	—
338	C₃²×C₄	—	2	2	no	—
339	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
340	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
341	C₃×Dic₃	—	2	1	no	—
342	C₃×Dic₃	—	2	2	no	—
343	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
344	C₂²×C₉	—	2	1	no	—
345	C₂²×C₉	—	2	1	no	—
346	C₂²×C₉	—	3	2	no	—
347	C₂²×C₉	—	4	1	no	—
348	C₂²×C₉	—	6	1	no	—
349	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
350	C₄×C₉	—	2	1	no	—
351	C₄×C₉	—	2	2	no	—
352	C₄×C₉	—	2	1	no	—
353	C₄×C₉	—	2	1	no	—
354	C₄×C₉	—	3	2	no	—
355	C₄×C₉	—	4	1	no	—
356	C₄×C₉	—	4	2	no	—
357	C₄×C₉	—	6	1	no	—
358	C₄×C₉	—	6	2	no	—
359	C₄×C₉	D₃×D₄	1	1	yes	characteristic
360	C₄×C₉	C₂³×D₃	1	1	yes	characteristic
361	2₋¹⁺⁴	—	3	1	no	—
362	2₋¹⁺⁴	—	3	1	no	—
363	#137	—	3	2	no	—
364	#137	—	3	2	no	—
365	#137	—	3	1	no	—
366	#137	D₃×C₉	1	1	yes	characteristic, complemented
367	#135	—	3	1	no	—
368	#135	—	3	2	no	—
369	C₂×Q₁₆	—	3	1	no	—
370	C₂×Q₁₆	—	3	2	no	—
371	#131	—	3	1	no	—
372	C₃×C₉	#578	1	1	yes	characteristic, complemented, Sylow
373	C₃×Q₈	—	2	1	no	—
374	C₃×Q₈	—	2	1	no	—
375	C₃×Q₈	—	2	2	no	—
376	C₃×Q₈	—	2	1	no	—
377	C₃×Q₈	—	3	1	no	—
378	C₃×Q₈	—	3	2	no	—
379	C₃×Q₈	—	3	1	no	—
380	C₃×Q₈	—	4	1	no	—
381	C₃×Q₈	—	6	2	no	—
382	C₃×Q₈	—	6	2	no	—
383	C₃×Q₈	—	6	1	no	—
384	C₃×Q₈	C₂³×C₉	1	1	yes	characteristic
385	C₃×Q₈	C₂³×C₉	1	2	yes	—
386	C₃×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
387	C₃×Q₈	C₂²×C₃×D₃	1	2	yes	—
388	C₃×D₄	—	2	1	no	—
389	C₃×D₄	—	2	1	no	—
390	C₃×D₄	—	2	1	no	—
391	C₃×D₄	—	3	2	no	—
392	C₃×D₄	—	3	1	no	—
393	C₃×D₄	—	3	1	no	—
394	C₃×D₄	—	4	1	no	—
395	C₃×D₄	—	6	2	no	—
396	C₃×D₄	—	6	2	no	—
397	C₃×D₄	—	6	1	no	—
398	C₃×D₄	C₂³×C₉	1	1	yes	characteristic
399	C₃×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
400	C₂×C₃×C₄	—	2	1	no	—
401	C₂×C₃×C₄	—	2	1	no	—
402	C₂×C₃×C₄	—	2	1	no	—
403	C₂×C₃×C₄	—	2	1	no	—
404	C₂×C₃×C₄	—	2	1	no	—
405	C₂×C₃×C₄	—	3	2	no	—
406	C₂×C₃×C₄	—	4	1	no	—
407	C₂×C₃×C₄	—	4	1	no	—
408	C₂×C₃×C₄	—	6	2	no	—
409	C₂×C₃×C₄	—	6	2	no	—
410	C₂×C₃×C₄	—	6	2	no	—
411	C₂×C₃×C₄	—	6	2	no	—
412	C₂×C₃×C₄	—	6	1	no	—
413	C₂×C₃×C₄	—	6	1	no	—
414	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
415	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
416	#67	—	2	1	no	—
417	#67	—	2	2	no	—
418	#67	D₄×C₉	1	2	yes	—
419	C₂×Dic₃	—	2	1	no	—
420	C₂×Dic₃	—	2	2	no	—
421	D₁₂	—	2	2	no	—
422	D₁₂	D₄×C₉	1	1	yes	characteristic
423	D₁₂	C₂³×C₉	1	1	yes	characteristic
424	C₄×D₃	—	2	2	no	—
425	C₄×D₃	—	2	2	no	—
426	C₄×D₃	—	2	1	no	—
427	C₄×D₃	—	2	2	no	—
428	C₄×D₃	C₂³×C₉	1	2	yes	—
429	Dic₆	—	2	1	no	—
430	Dic₆	—	2	2	no	—
431	Dic₆	—	2	2	no	—
432	Dic₆	D₄×C₉	1	1	yes	characteristic
433	Dic₆	C₂³×C₉	1	2	yes	—
434	Dic₆	C₂³×C₉	1	1	yes	characteristic
435	C₃×C₈	—	2	2	no	—
436	C₃×C₈	—	3	1	no	—
437	C₃×C₈	—	3	1	no	—
438	C₃×C₈	C₂³×C₉	1	2	yes	—
439	C₃×C₈	C₂²×C₃×D₃	1	2	yes	—
440	C₃⋊C₈	C₂³×C₉	1	1	yes	characteristic
441	C₃⋊C₈	C₂³×C₉	1	1	yes	characteristic
442	C₂×C₃²	—	2	1	no	—
443	C₂×C₃²	—	4	1	no	—
444	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
445	C₃×D₃	—	2	2	no	—
446	C₃×D₃	—	4	1	no	—
447	C₂×C₉	—	2	1	no	—
448	C₂×C₉	—	2	1	no	—
449	C₂×C₉	—	4	1	no	—
450	C₂×C₉	—	4	1	no	—
451	C₂×C₉	—	6	2	no	—
452	C₂×C₉	—	8	1	no	—
453	C₂×C₉	—	12	1	no	—
454	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
455	#41	—	3	1	no	—
456	#41	—	3	2	no	—
457	#41	—	3	2	no	—
458	#41	—	3	1	no	—
459	#41	—	6	2	no	—
460	#41	—	6	1	no	—
461	#41	—	6	2	no	—
462	#41	—	6	1	no	—
463	#41	C₂×D₃×C₉	1	1	yes	characteristic
464	C₂×Q₈	—	3	2	no	—
465	C₂×Q₈	—	3	2	no	—
466	C₂×Q₈	—	3	1	no	—
467	C₂×Q₈	—	6	1	no	—
468	C₂×Q₈	—	6	1	no	—
469	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
470	Q₁₆	—	3	1	no	—
471	Q₁₆	—	3	2	no	—
472	Q₁₆	—	3	2	no	—
473	Q₁₆	—	3	2	no	—
474	Q₁₆	C₂×D₃×C₉	1	2	yes	—
475	SD₁₆	—	3	1	no	—
476	SD₁₆	—	3	1	no	—
477	SD₁₆	—	3	2	no	—
478	SD₁₆	C₂×D₃×C₉	1	2	yes	—
479	D₈	—	3	1	no	—
480	M₁₆	—	3	2	no	—
481	M₁₆	C₂×D₃×C₉	1	1	yes	characteristic
482	C₂×C₈	—	3	1	no	—
483	C₂×C₈	—	3	2	no	—
484	C₂²×C₃	—	2	1	no	—
485	C₂²×C₃	—	2	1	no	—
486	C₂²×C₃	—	2	1	no	—
487	C₂²×C₃	—	3	2	no	—
488	C₂²×C₃	—	4	1	no	—
489	C₂²×C₃	—	6	1	no	—
490	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
491	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
492	C₂×D₃	—	2	1	no	—
493	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
494	C₃×C₄	—	2	1	no	—
495	C₃×C₄	—	2	2	no	—
496	C₃×C₄	—	2	1	no	—
497	C₃×C₄	—	2	2	no	—
498	C₃×C₄	—	2	1	no	—
499	C₃×C₄	—	2	1	no	—
500	C₃×C₄	—	3	2	no	—
501	C₃×C₄	—	4	1	no	—
502	C₃×C₄	—	4	2	no	—
503	C₃×C₄	—	6	1	no	—
504	C₃×C₄	—	6	2	no	—
505	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
506	C₃×C₄	C₂⁴×C₉	1	1	yes	characteristic
507	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
508	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
509	Dic₃	—	2	1	no	—
510	Dic₃	—	2	2	no	—
511	Dic₃	C₂×D₄×C₉	1	2	yes	—
512	C₃²	C₃×#578	1	1	yes	characteristic
513	C₉	—	2	1	no	—
514	C₉	#5779	1	1	yes	characteristic, direct product factor
515	Q₈	—	2	1	no	—
516	Q₈	—	3	1	no	—
517	Q₈	—	3	1	no	—
518	Q₈	—	3	2	no	—
519	Q₈	—	6	2	no	—
520	Q₈	—	6	2	no	—
521	Q₈	—	6	1	no	—
522	Q₈	C₂²×D₃×C₉	1	1	yes	characteristic
523	Q₈	C₂²×D₃×C₉	1	2	yes	—
524	D₄	—	2	1	no	—
525	D₄	—	3	2	no	—
526	D₄	—	3	1	no	—
527	D₄	—	3	1	no	—
528	D₄	—	6	2	no	—
529	D₄	—	6	2	no	—
530	D₄	—	6	1	no	—
531	D₄	C₂²×D₃×C₉	1	1	yes	characteristic
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	3	2	no	—
535	C₂×C₄	—	6	2	no	—
536	C₂×C₄	—	6	2	no	—
537	C₂×C₄	—	6	2	no	—
538	C₂×C₄	—	6	2	no	—
539	C₂×C₄	—	6	1	no	—
540	C₂×C₄	—	6	1	no	—
541	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
542	C₈	—	3	1	no	—
543	C₈	—	3	1	no	—
544	C₈	C₂²×D₃×C₉	1	2	yes	—
545	C₂×C₃	—	2	1	no	—
546	C₂×C₃	—	2	1	no	—
547	C₂×C₃	—	2	1	no	—
548	C₂×C₃	—	4	1	no	—
549	C₂×C₃	—	4	1	no	—
550	C₂×C₃	—	4	1	no	—
551	C₂×C₃	—	6	2	no	—
552	C₂×C₃	—	8	1	no	—
553	C₂×C₃	—	12	1	no	—
554	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
555	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
556	D₃	—	2	2	no	—
557	D₃	—	4	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	3	2	no	—
560	C₂²	—	6	1	no	—
561	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
562	C₄	—	2	1	no	—
563	C₄	—	2	2	no	—
564	C₄	—	3	2	no	—
565	C₄	—	6	1	no	—
566	C₄	—	6	2	no	—
567	C₄	D₃×D₄×C₉	1	1	yes	characteristic
568	C₄	C₂³×D₃×C₉	1	1	yes	characteristic
569	C₃	—	2	1	no	—
570	C₃	C₉×#578	1	1	yes	characteristic, complemented
571	C₃	C₃×#5779	1	1	yes	characteristic
572	C₂	—	2	1	no	—
573	C₂	—	4	1	no	—
574	C₂	—	6	2	no	—
575	C₂	—	12	1	no	—
576	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉	C₂×D₃×D₄
commutator	C₃×C₄	C₂⁴×C₉
Frattini	C₃×C₄	C₂³×C₃×D₃
Fitting	C₃×C₉×#137	C₂
socle	C₂×C₃²	C₂²×C₃×D₄
prime radical	C₃×#5779	C₃
cosocle	C₃²×C₄	C₂⁴×C₃
hypercenter	C₉×#137	D₃
hypocenter	C₃	C₉×#578
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₉ ◁ C₂×C₄×C₉ ◁ C₉×#137

Complements

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

N	H ≅ G/N	type
1. C₉×#1010	C₂	semidirect
2. C₉×#1007	C₂	semidirect
3. C₃×C₉×#137	C₂	semidirect
4. C₉×#950	C₂	semidirect
5. C₂×C₉×#216	C₂	semidirect
6. C₉×#918	C₂	semidirect
7. D₃×C₉×Q₁₆	C₂	semidirect
8. C₉×#916	C₂	semidirect
9. C₉×#915	C₂	semidirect
10. C₉×#909	C₂	semidirect
11. C₉×#907	C₂	semidirect
60. C₉×#137	D₃	semidirect
97. #5779	C₉	direct (N × H)
174. #1010	C₂×C₉	semidirect
175. #1007	C₂×C₉	semidirect
180. C₃×#137	C₂×C₉	semidirect
187. #950	C₂×C₉	semidirect
188. C₂×#216	C₂×C₉	semidirect
189. #918	C₂×C₉	semidirect
190. D₃×Q₁₆	C₂×C₉	semidirect
191. #916	C₂×C₉	semidirect
192. #915	C₂×C₉	semidirect
193. #909	C₂×C₉	semidirect
194. #907	C₂×C₉	semidirect
366. #137	D₃×C₉	semidirect
372. C₃×C₉	#578	semidirect
514. C₉	#5779	direct (N × H)
570. C₃	C₉×#578	semidirect

Maximal subgroups

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

subgroup	index
C₉×#1010	2
C₉×#1007	2
C₃×C₉×#137	2
C₉×#950	2
C₂×C₉×#216	2
C₉×#918	2
D₃×C₉×Q₁₆	2
C₉×#916	2
C₉×#915	2
C₉×#909	2
C₉×#907	2
C₃×#5779	3
C₉×#578	3

Subgroups — C9×#5779 #13153514

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5779 #13153514