Subgroups — C₉×#5592 #13152751

Order 1728.

1132 conjugacy classes of subgroups.

The subgroup lattice has 628 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	C₉×#953	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#940	C₂	1	2	yes	maximal, complemented
6	C₉×#939	C₂	1	2	yes	maximal, complemented
7	C₉×#937	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#885	C₂	1	2	yes	maximal, complemented
9	C₉×#884	C₂	1	2	yes	maximal, complemented
10	C₉×#882	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5592	C₃	1	1	yes	maximal, characteristic
13	C₉×#535	—	3	1	no	maximal
14	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
15	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
16	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₃×D₄×C₉	C₂²	1	2	yes	complemented
18	C₂×C₉×#67	—	2	4	no	—
19	C₂×C₉×#67	C₂²	1	1	yes	characteristic
20	C₂×C₉×#67	C₂²	1	2	yes	—
21	C₂×C₉×#67	C₂²	1	2	yes	—
22	C₂×C₉×#67	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₉×#67	C₂²	1	2	yes	complemented
24	C₂×C₉×#67	C₂²	1	2	yes	complemented
25	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
26	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
27	C₉×#237	—	2	4	no	—
28	C₂×C₉×D₁₂	C₂²	1	2	yes	complemented
29	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
33	C₉×#217	C₂²	1	1	yes	characteristic
34	C₉×#217	C₂²	1	2	yes	complemented
35	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
36	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
37	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
38	C₄×C₉×Dic₃	C₂²	1	2	yes	complemented
39	C₂²×C₃×#67	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×#237	C₂×C₃	1	1	yes	characteristic
41	C₃²×#120	C₂×C₃	1	1	yes	characteristic
42	C₃×#953	C₂×C₃	1	1	yes	characteristic
43	C₃×#940	C₂×C₃	1	2	yes	—
44	C₃×#939	C₂×C₃	1	2	yes	—
45	C₃×#937	C₂×C₃	1	1	yes	characteristic
46	C₃×#885	C₂×C₃	1	2	yes	—
47	C₃×#884	C₂×C₃	1	2	yes	—
48	C₃×#882	C₂×C₃	1	1	yes	characteristic
49	C₃×#877	C₂×C₃	1	1	yes	characteristic
50	C₂×C₉×#41	—	3	1	no	—
51	C₂²×D₄×C₉	—	3	1	no	—
52	C₉×#127	—	3	2	no	—
53	C₉×#124	—	3	2	no	—
54	C₉×#121	—	3	2	no	—
55	C₉×#121	—	3	2	no	—
56	C₉×#120	—	2	1	no	—
57	C₉×#120	—	3	1	no	—
58	C₉×#120	—	3	1	no	—
59	C₉×#120	—	3	1	no	—
60	C₉×#120	D₃	1	1	yes	characteristic, complemented
61	C₉×#117	—	3	1	no	—
62	C₂³×C₃×C₉	—	2	2	no	—
63	C₂³×C₃×C₉	—	4	2	no	—
64	C₂³×C₃×C₉	C₂³	1	2	yes	—
65	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
66	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
67	C₂²×D₃×C₉	—	2	2	no	—
68	C₂²×D₃×C₉	—	4	2	no	—
69	C₂²×D₃×C₉	C₂³	1	2	yes	—
70	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
71	C₃×D₄×C₉	—	2	2	no	—
72	C₃×D₄×C₉	—	4	2	no	—
73	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
75	C₉×#67	—	2	2	no	—
76	C₉×#67	—	2	2	no	—
77	C₉×#67	—	2	4	no	—
78	C₉×#67	—	2	4	no	—
79	C₉×#67	—	4	2	no	—
80	C₉×#67	—	4	2	no	—
81	C₂×C₉×Dic₃	—	2	2	no	—
82	C₂×C₉×Dic₃	D₄	1	4	yes	complemented
83	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
84	C₂×C₉×Dic₃	C₂³	1	2	yes	—
85	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
86	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
87	C₉×D₁₂	—	4	2	no	—
88	C₄×D₃×C₉	—	2	2	no	—
89	C₉×Dic₆	—	2	2	no	—
90	C₃×#535	—	3	1	no	—
91	#5592	C₉	1	1	yes	characteristic, direct product factor
92	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
93	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
96	C₂×C₃×#67	—	2	4	no	—
97	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
99	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
100	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
102	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
103	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
104	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
105	C₃×#237	—	2	4	no	—
106	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
107	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
109	C₂⁴×C₉	—	2	1	no	—
110	C₂⁴×C₉	—	3	1	no	—
111	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
112	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
114	C₃×#217	C₂²×C₃	1	1	yes	characteristic
115	C₃×#217	C₂²×C₃	1	2	yes	—
116	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
117	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
118	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
119	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
120	C₉×#41	—	6	4	no	—
121	C₂×Q₈×C₉	—	3	1	no	—
122	C₂×D₄×C₉	—	2	1	no	—
123	C₂×D₄×C₉	—	2	2	no	—
124	C₂×D₄×C₉	—	3	1	no	—
125	C₂×D₄×C₉	—	3	2	no	—
126	C₂×D₄×C₉	—	3	2	no	—
127	C₂×D₄×C₉	—	3	1	no	—
128	C₂×D₄×C₉	—	3	2	no	—
129	C₂×D₄×C₉	—	3	2	no	—
130	C₂×D₄×C₉	—	3	2	no	—
131	C₂×D₄×C₉	—	6	4	no	—
132	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
133	C₂×D₄×C₉	C₂×D₃	1	2	yes	complemented
134	C₂²×C₄×C₉	—	3	1	no	—
135	C₂²×C₄×C₉	—	3	1	no	—
136	C₂²×C₄×C₉	—	3	1	no	—
137	C₉×C₄⋊C₄	—	3	2	no	—
138	C₉×C₂²⋊C₄	—	2	1	no	—
139	C₉×C₂²⋊C₄	—	2	2	no	—
140	C₉×C₂²⋊C₄	—	3	1	no	—
141	C₉×C₂²⋊C₄	—	3	2	no	—
142	C₉×C₂²⋊C₄	—	3	2	no	—
143	C₉×C₂²⋊C₄	—	3	2	no	—
144	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
145	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
146	C₄²×C₉	—	3	2	no	—
147	C₂²×C₃×C₉	—	2	2	no	—
148	C₂²×C₃×C₉	—	2	1	no	—
149	C₂²×C₃×C₉	—	2	2	no	—
150	C₂²×C₃×C₉	—	2	2	no	—
151	C₂²×C₃×C₉	—	2	2	no	—
152	C₂²×C₃×C₉	—	2	2	no	—
153	C₂²×C₃×C₉	—	4	4	no	—
154	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
155	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
156	C₂×D₃×C₉	—	2	1	no	—
157	C₂×D₃×C₉	—	2	2	no	—
158	C₂×D₃×C₉	—	2	2	no	—
159	C₂×D₃×C₉	—	2	2	no	—
160	C₂×D₃×C₉	—	2	2	no	—
161	C₂×D₃×C₉	—	4	4	no	—
162	C₃×C₄×C₉	—	2	1	no	—
163	C₃×C₄×C₉	—	2	2	no	—
164	C₉×Dic₃	—	2	1	no	—
165	C₉×Dic₃	—	2	2	no	—
166	C₉×Dic₃	C₂×D₄	1	2	yes	—
167	C₉×Dic₃	C₂×D₄	1	2	yes	—
168	C₂×C₃×#41	—	3	1	no	—
169	C₂²×C₃×D₄	—	3	1	no	—
170	C₂²×#67	C₂×C₉	1	1	yes	characteristic, complemented
171	C₂×#237	C₂×C₉	1	1	yes	characteristic, complemented
172	C₃×#127	—	3	2	no	—
173	C₃×#124	—	3	2	no	—
174	C₃×#121	—	3	2	no	—
175	C₃×#121	—	3	2	no	—
176	C₃×#120	—	2	1	no	—
177	C₃×#120	—	3	1	no	—
178	C₃×#120	—	3	1	no	—
179	C₃×#120	—	3	1	no	—
180	C₃×#120	C₂×C₉	1	1	yes	characteristic, complemented
181	C₃×#120	C₃×D₃	1	1	yes	characteristic
182	C₃×#117	—	3	1	no	—
183	#953	C₂×C₉	1	1	yes	characteristic, complemented
184	#940	C₂×C₉	1	2	yes	complemented
185	#939	C₂×C₉	1	2	yes	complemented
186	#937	C₂×C₉	1	1	yes	characteristic, complemented
187	#885	C₂×C₉	1	2	yes	complemented
188	#884	C₂×C₉	1	2	yes	complemented
189	#882	C₂×C₉	1	1	yes	characteristic, complemented
190	#877	C₂×C₉	1	1	yes	characteristic, complemented
191	C₂³×C₃²	—	2	2	no	—
192	C₂³×C₃²	—	4	2	no	—
193	C₂³×C₃²	C₂³×C₃	1	2	yes	—
194	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
195	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
196	C₂²×C₃×D₃	—	2	2	no	—
197	C₂²×C₃×D₃	—	4	2	no	—
198	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
199	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
200	C₃²×D₄	—	2	2	no	—
201	C₃²×D₄	—	4	2	no	—
202	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
203	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
204	C₃×#67	—	2	2	no	—
205	C₃×#67	—	2	2	no	—
206	C₃×#67	—	2	4	no	—
207	C₃×#67	—	2	4	no	—
208	C₃×#67	—	4	2	no	—
209	C₃×#67	—	4	2	no	—
210	C₂×C₃×Dic₃	—	2	2	no	—
211	C₂×C₃×Dic₃	C₃×D₄	1	4	yes	—
212	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
213	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
214	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
215	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
216	C₃×D₁₂	—	4	2	no	—
217	C₃×C₄×D₃	—	2	2	no	—
218	C₃×Dic₆	—	2	2	no	—
219	C₂³×C₉	—	2	2	no	—
220	C₂³×C₉	—	2	2	no	—
221	C₂³×C₉	—	2	1	no	—
222	C₂³×C₉	—	2	1	no	—
223	C₂³×C₉	—	3	2	no	—
224	C₂³×C₉	—	3	1	no	—
225	C₂³×C₉	—	4	2	no	—
226	C₂³×C₉	—	4	2	no	—
227	C₂³×C₉	—	4	4	no	—
228	C₂³×C₉	—	6	2	no	—
229	C₂³×C₉	—	12	2	no	—
230	C₂³×C₉	C₂²×D₃	1	2	yes	—
231	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
232	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
233	Q₈×C₉	—	6	2	no	—
234	D₄×C₉	—	2	2	no	—
235	D₄×C₉	—	4	2	no	—
236	D₄×C₉	—	4	2	no	—
237	D₄×C₉	—	4	4	no	—
238	D₄×C₉	—	6	4	no	—
239	D₄×C₉	—	6	4	no	—
240	D₄×C₉	—	6	2	no	—
241	D₄×C₉	—	6	2	no	—
242	D₄×C₉	—	12	2	no	—
243	D₄×C₉	—	12	2	no	—
244	D₄×C₉	—	12	2	no	—
245	C₂×C₄×C₉	—	2	2	no	—
246	C₂×C₄×C₉	—	2	1	no	—
247	C₂×C₄×C₉	—	3	4	no	—
248	C₂×C₄×C₉	—	3	1	no	—
249	C₂×C₄×C₉	—	3	1	no	—
250	C₂×C₄×C₉	—	3	2	no	—
251	C₂×C₄×C₉	—	3	1	no	—
252	C₂×C₄×C₉	—	6	2	no	—
253	C₂×C₄×C₉	—	6	2	no	—
254	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
255	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
256	#535	—	3	1	no	Sylow
257	C₂×C₃×C₉	—	2	2	no	—
258	C₂×C₃×C₉	—	4	2	no	—
259	C₂×C₃×C₉	—	4	1	no	—
260	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₃×C₉	H(5,𝔽₂)	1	2	yes	—
262	D₃×C₉	—	4	1	no	—
263	D₃×C₉	—	4	2	no	—
264	C₂⁴×C₃	—	2	1	no	—
265	C₂⁴×C₃	—	3	1	no	—
266	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
267	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
268	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
269	C₃×#41	—	6	4	no	—
270	C₂×C₃×Q₈	—	3	1	no	—
271	C₂×C₃×D₄	—	2	1	no	—
272	C₂×C₃×D₄	—	2	2	no	—
273	C₂×C₃×D₄	—	3	1	no	—
274	C₂×C₃×D₄	—	3	2	no	—
275	C₂×C₃×D₄	—	3	2	no	—
276	C₂×C₃×D₄	—	3	1	no	—
277	C₂×C₃×D₄	—	3	2	no	—
278	C₂×C₃×D₄	—	3	2	no	—
279	C₂×C₃×D₄	—	3	2	no	—
280	C₂×C₃×D₄	—	6	4	no	—
281	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
282	C₂×C₃×D₄	C₂²×C₉	1	2	yes	complemented
283	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
284	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
285	C₂²×C₃×C₄	—	3	1	no	—
286	C₂²×C₃×C₄	—	3	1	no	—
287	C₂²×C₃×C₄	—	3	1	no	—
288	C₂×#67	—	2	4	no	—
289	C₂×#67	C₂²×C₉	1	1	yes	characteristic
290	C₂×#67	C₂²×C₉	1	2	yes	—
291	C₂×#67	C₂²×C₉	1	2	yes	—
292	C₂×#67	C₂²×C₉	1	1	yes	characteristic, complemented
293	C₂×#67	C₂²×C₉	1	2	yes	complemented
294	C₂×#67	C₂²×C₉	1	2	yes	complemented
295	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
296	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
297	#237	—	2	4	no	—
298	C₂×D₁₂	C₂²×C₉	1	2	yes	complemented
299	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
300	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
301	C₃×C₄⋊C₄	—	3	2	no	—
302	C₃×C₂²⋊C₄	—	2	1	no	—
303	C₃×C₂²⋊C₄	—	2	2	no	—
304	C₃×C₂²⋊C₄	—	3	1	no	—
305	C₃×C₂²⋊C₄	—	3	2	no	—
306	C₃×C₂²⋊C₄	—	3	2	no	—
307	C₃×C₂²⋊C₄	—	3	2	no	—
308	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
309	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
310	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
311	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
312	C₃×C₄²	—	3	2	no	—
313	#217	C₂²×C₉	1	1	yes	characteristic
314	#217	C₂²×C₉	1	2	yes	complemented
315	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
316	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
317	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
318	C₄×Dic₃	C₂²×C₉	1	2	yes	complemented
319	C₂²×C₃²	—	2	2	no	—
320	C₂²×C₃²	—	2	2	no	—
321	C₂²×C₃²	—	2	1	no	—
322	C₂²×C₃²	—	2	2	no	—
323	C₂²×C₃²	—	2	2	no	—
324	C₂²×C₃²	—	2	2	no	—
325	C₂²×C₃²	—	4	4	no	—
326	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
327	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
328	C₂×C₃×D₃	—	2	1	no	—
329	C₂×C₃×D₃	—	2	2	no	—
330	C₂×C₃×D₃	—	2	2	no	—
331	C₂×C₃×D₃	—	2	2	no	—
332	C₂×C₃×D₃	—	2	2	no	—
333	C₂×C₃×D₃	—	4	4	no	—
334	C₃²×C₄	—	2	1	no	—
335	C₃²×C₄	—	2	2	no	—
336	C₃×Dic₃	—	2	1	no	—
337	C₃×Dic₃	—	2	2	no	—
338	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
339	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
340	C₂²×C₉	—	2	2	no	—
341	C₂²×C₉	—	2	4	no	—
342	C₂²×C₉	—	2	1	no	—
343	C₂²×C₉	—	2	2	no	—
344	C₂²×C₉	—	2	2	no	—
345	C₂²×C₉	—	2	2	no	—
346	C₂²×C₉	—	2	2	no	—
347	C₂²×C₉	—	2	1	no	—
348	C₂²×C₉	—	2	2	no	—
349	C₂²×C₉	—	4	2	no	—
350	C₂²×C₉	—	4	2	no	—
351	C₂²×C₉	—	4	2	no	—
352	C₂²×C₉	—	4	1	no	—
353	C₂²×C₉	—	4	2	no	—
354	C₂²×C₉	—	4	4	no	—
355	C₂²×C₉	—	4	8	no	—
356	C₂²×C₉	—	6	1	no	—
357	C₂²×C₉	—	6	2	no	—
358	C₂²×C₉	—	6	2	no	—
359	C₂²×C₉	—	6	2	no	—
360	C₂²×C₉	—	6	2	no	—
361	C₂²×C₉	—	12	4	no	—
362	C₂²×C₉	D₃×D₄	1	2	yes	—
363	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
364	C₄×C₉	—	2	1	no	—
365	C₄×C₉	—	2	2	no	—
366	C₄×C₉	—	3	2	no	—
367	C₄×C₉	—	3	2	no	—
368	C₄×C₉	—	4	1	no	—
369	C₄×C₉	—	4	2	no	—
370	C₄×C₉	—	6	1	no	—
371	C₄×C₉	—	6	2	no	—
372	C₂×#41	—	3	1	no	—
373	C₂²×D₄	—	3	1	no	—
374	#127	—	3	2	no	—
375	#124	—	3	2	no	—
376	#121	—	3	2	no	—
377	#121	—	3	2	no	—
378	#120	—	3	1	no	—
379	#120	—	3	1	no	—
380	#120	—	3	1	no	—
381	#120	D₃×C₉	1	1	yes	characteristic, complemented
382	#117	—	3	1	no	—
383	C₃×C₉	#535	1	1	yes	characteristic, complemented, Sylow
384	C₂³×C₃	—	2	2	no	—
385	C₂³×C₃	—	2	2	no	—
386	C₂³×C₃	—	2	2	no	—
387	C₂³×C₃	—	2	1	no	—
388	C₂³×C₃	—	2	1	no	—
389	C₂³×C₃	—	3	2	no	—
390	C₂³×C₃	—	3	1	no	—
391	C₂³×C₃	—	4	2	no	—
392	C₂³×C₃	—	4	2	no	—
393	C₂³×C₃	—	4	2	no	—
394	C₂³×C₃	—	4	4	no	—
395	C₂³×C₃	—	6	2	no	—
396	C₂³×C₃	—	12	2	no	—
397	C₂³×C₃	C₂³×C₉	1	2	yes	—
398	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
399	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
400	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
401	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
402	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
403	C₂²×D₃	—	2	2	no	—
404	C₂²×D₃	—	4	2	no	—
405	C₂²×D₃	C₂³×C₉	1	2	yes	—
406	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
407	C₃×Q₈	—	6	2	no	—
408	C₃×D₄	—	2	2	no	—
409	C₃×D₄	—	2	2	no	—
410	C₃×D₄	—	4	2	no	—
411	C₃×D₄	—	4	2	no	—
412	C₃×D₄	—	4	2	no	—
413	C₃×D₄	—	4	4	no	—
414	C₃×D₄	—	6	4	no	—
415	C₃×D₄	—	6	4	no	—
416	C₃×D₄	—	6	2	no	—
417	C₃×D₄	—	6	2	no	—
418	C₃×D₄	—	12	2	no	—
419	C₃×D₄	—	12	2	no	—
420	C₃×D₄	—	12	2	no	—
421	C₂×C₃×C₄	—	2	2	no	—
422	C₂×C₃×C₄	—	2	1	no	—
423	C₂×C₃×C₄	—	3	1	no	—
424	C₂×C₃×C₄	—	3	1	no	—
425	C₂×C₃×C₄	—	3	4	no	—
426	C₂×C₃×C₄	—	3	2	no	—
427	C₂×C₃×C₄	—	3	1	no	—
428	C₂×C₃×C₄	—	6	2	no	—
429	C₂×C₃×C₄	—	6	2	no	—
430	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
431	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
432	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
433	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
434	#67	—	2	2	no	—
435	#67	—	2	2	no	—
436	#67	—	2	4	no	—
437	#67	—	2	4	no	—
438	#67	—	4	2	no	—
439	#67	—	4	2	no	—
440	C₂×Dic₃	—	2	2	no	—
441	C₂×Dic₃	D₄×C₉	1	4	yes	complemented
442	C₂×Dic₃	C₂³×C₉	1	2	yes	—
443	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
444	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
445	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
446	D₁₂	—	4	2	no	—
447	C₄×D₃	—	2	2	no	—
448	Dic₆	—	2	2	no	—
449	C₂×C₃²	—	2	2	no	—
450	C₂×C₃²	—	4	2	no	—
451	C₂×C₃²	—	4	1	no	—
452	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
453	C₂×C₃²	C₃×H(5,𝔽₂)	1	2	yes	—
454	C₃×D₃	—	4	1	no	—
455	C₃×D₃	—	4	2	no	—
456	C₂×C₉	—	2	2	no	—
457	C₂×C₉	—	2	1	no	—
458	C₂×C₉	—	2	2	no	—
459	C₂×C₉	—	4	2	no	—
460	C₂×C₉	—	4	4	no	—
461	C₂×C₉	—	4	1	no	—
462	C₂×C₉	—	4	2	no	—
463	C₂×C₉	—	8	1	no	—
464	C₂×C₉	—	12	1	no	—
465	C₂×C₉	—	12	2	no	—
466	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
467	C₂×C₉	#1004	1	2	yes	—
468	C₂⁴	—	3	1	no	—
469	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
470	#41	—	6	4	no	—
471	C₂×Q₈	—	3	1	no	—
472	C₂×D₄	—	3	1	no	—
473	C₂×D₄	—	3	2	no	—
474	C₂×D₄	—	3	2	no	—
475	C₂×D₄	—	3	1	no	—
476	C₂×D₄	—	3	2	no	—
477	C₂×D₄	—	3	2	no	—
478	C₂×D₄	—	3	2	no	—
479	C₂×D₄	—	6	4	no	—
480	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
481	C₂×D₄	C₂×D₃×C₉	1	2	yes	complemented
482	C₂²×C₄	—	3	1	no	—
483	C₂²×C₄	—	3	1	no	—
484	C₂²×C₄	—	3	1	no	—
485	C₄⋊C₄	—	3	2	no	—
486	C₂²⋊C₄	—	3	1	no	—
487	C₂²⋊C₄	—	3	2	no	—
488	C₂²⋊C₄	—	3	2	no	—
489	C₂²⋊C₄	—	3	2	no	—
490	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
491	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
492	C₄²	—	3	2	no	—
493	C₂²×C₃	—	2	2	no	—
494	C₂²×C₃	—	2	2	no	—
495	C₂²×C₃	—	2	4	no	—
496	C₂²×C₃	—	2	1	no	—
497	C₂²×C₃	—	2	2	no	—
498	C₂²×C₃	—	2	2	no	—
499	C₂²×C₃	—	2	2	no	—
500	C₂²×C₃	—	2	2	no	—
501	C₂²×C₃	—	2	1	no	—
502	C₂²×C₃	—	2	2	no	—
503	C₂²×C₃	—	2	2	no	—
504	C₂²×C₃	—	2	2	no	—
505	C₂²×C₃	—	2	2	no	—
506	C₂²×C₃	—	2	1	no	—
507	C₂²×C₃	—	2	2	no	—
508	C₂²×C₃	—	4	2	no	—
509	C₂²×C₃	—	4	2	no	—
510	C₂²×C₃	—	4	2	no	—
511	C₂²×C₃	—	4	1	no	—
512	C₂²×C₃	—	4	2	no	—
513	C₂²×C₃	—	4	4	no	—
514	C₂²×C₃	—	4	4	no	—
515	C₂²×C₃	—	4	8	no	—
516	C₂²×C₃	—	6	1	no	—
517	C₂²×C₃	—	6	2	no	—
518	C₂²×C₃	—	6	2	no	—
519	C₂²×C₃	—	6	2	no	—
520	C₂²×C₃	—	6	2	no	—
521	C₂²×C₃	—	12	4	no	—
522	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
523	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
524	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
525	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
526	C₂×D₃	—	2	1	no	—
527	C₂×D₃	—	2	2	no	—
528	C₂×D₃	—	2	2	no	—
529	C₂×D₃	—	2	2	no	—
530	C₂×D₃	—	2	2	no	—
531	C₂×D₃	—	4	4	no	—
532	C₃×C₄	—	2	1	no	—
533	C₃×C₄	—	2	2	no	—
534	C₃×C₄	—	2	1	no	—
535	C₃×C₄	—	2	2	no	—
536	C₃×C₄	—	3	2	no	—
537	C₃×C₄	—	3	2	no	—
538	C₃×C₄	—	4	1	no	—
539	C₃×C₄	—	4	2	no	—
540	C₃×C₄	—	6	1	no	—
541	C₃×C₄	—	6	2	no	—
542	Dic₃	—	2	1	no	—
543	Dic₃	—	2	2	no	—
544	Dic₃	C₂×D₄×C₉	1	2	yes	—
545	Dic₃	C₂×D₄×C₉	1	2	yes	—
546	C₃²	C₃×#535	1	1	yes	characteristic
547	C₉	—	2	1	no	—
548	C₉	#5592	1	1	yes	characteristic, direct product factor
549	C₂³	—	2	2	no	—
550	C₂³	—	3	2	no	—
551	C₂³	—	3	1	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	6	2	no	—
554	C₂³	—	12	2	no	—
555	C₂³	C₂²×D₃×C₉	1	2	yes	—
556	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
557	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
558	Q₈	—	6	2	no	—
559	D₄	—	2	2	no	—
560	D₄	—	4	2	no	—
561	D₄	—	6	4	no	—
562	D₄	—	6	4	no	—
563	D₄	—	6	2	no	—
564	D₄	—	6	2	no	—
565	D₄	—	12	2	no	—
566	D₄	—	12	2	no	—
567	D₄	—	12	2	no	—
568	C₂×C₄	—	3	1	no	—
569	C₂×C₄	—	3	1	no	—
570	C₂×C₄	—	3	4	no	—
571	C₂×C₄	—	3	2	no	—
572	C₂×C₄	—	3	1	no	—
573	C₂×C₄	—	6	2	no	—
574	C₂×C₄	—	6	2	no	—
575	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
576	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
577	C₂×C₃	—	2	2	no	—
578	C₂×C₃	—	2	2	no	—
579	C₂×C₃	—	2	1	no	—
580	C₂×C₃	—	2	2	no	—
581	C₂×C₃	—	4	2	no	—
582	C₂×C₃	—	4	4	no	—
583	C₂×C₃	—	4	2	no	—
584	C₂×C₃	—	4	1	no	—
585	C₂×C₃	—	4	2	no	—
586	C₂×C₃	—	4	1	no	—
587	C₂×C₃	—	8	1	no	—
588	C₂×C₃	—	12	2	no	—
589	C₂×C₃	—	12	1	no	—
590	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
591	C₂×C₃	C₉×H(5,𝔽₂)	1	2	yes	—
592	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
593	C₂×C₃	C₃×#1004	1	2	yes	—
594	D₃	—	4	2	no	—
595	D₃	—	4	1	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	1	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	4	4	no	—
603	C₂²	—	6	1	no	—
604	C₂²	—	6	2	no	—
605	C₂²	—	6	2	no	—
606	C₂²	—	6	2	no	—
607	C₂²	—	6	2	no	—
608	C₂²	—	12	4	no	—
609	C₂²	D₃×D₄×C₉	1	2	yes	—
610	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
611	C₄	—	2	1	no	—
612	C₄	—	2	2	no	—
613	C₄	—	3	2	no	—
614	C₄	—	3	2	no	—
615	C₄	—	6	1	no	—
616	C₄	—	6	2	no	—
617	C₃	—	2	1	no	—
618	C₃	C₉×#535	1	1	yes	characteristic, complemented
619	C₃	C₃×#5592	1	1	yes	characteristic
620	C₂	—	2	2	no	—
621	C₂	—	4	2	no	—
622	C₂	—	4	1	no	—
623	C₂	—	12	2	no	—
624	C₂	—	12	1	no	—
625	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
626	C₂	C₉×#1004	1	2	yes	—

	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×#5592	C₃
hypercenter	C₉×#120	D₃
hypocenter	C₃	C₉×#535
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. C₉×#953	C₂	semidirect
5. C₉×#940	C₂	semidirect
6. C₉×#939	C₂	semidirect
7. C₉×#937	C₂	semidirect
8. C₉×#885	C₂	semidirect
9. C₉×#884	C₂	semidirect
10. C₉×#882	C₂	semidirect
11. C₉×#877	C₂	semidirect
17. C₂×C₃×D₄×C₉	C₂²	semidirect
22. C₂×C₉×#67	C₂²	semidirect
23. C₂×C₉×#67	C₂²	semidirect
24. C₂×C₉×#67	C₂²	semidirect
26. C₂²×C₉×Dic₃	C₂²	semidirect
28. C₂×C₉×D₁₂	C₂²	semidirect
29. C₂×C₄×D₃×C₉	C₂²	semidirect
30. C₂×C₉×Dic₆	C₂²	semidirect
32. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
34. C₉×#217	C₂²	semidirect
35. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
37. C₉×Dic₃⋊C₄	C₂²	semidirect
38. C₄×C₉×Dic₃	C₂²	semidirect
60. C₉×#120	D₃	semidirect
82. C₂×C₉×Dic₃	D₄	semidirect
91. #5592	C₉	direct (N × H)
133. C₂×D₄×C₉	C₂×D₃	semidirect
145. C₉×C₂²⋊C₄	C₂×D₃	semidirect
170. C₂²×#67	C₂×C₉	semidirect
171. C₂×#237	C₂×C₉	semidirect
180. C₃×#120	C₂×C₉	semidirect
183. #953	C₂×C₉	semidirect
184. #940	C₂×C₉	semidirect
185. #939	C₂×C₉	semidirect
186. #937	C₂×C₉	semidirect
187. #885	C₂×C₉	semidirect
188. #884	C₂×C₉	semidirect
189. #882	C₂×C₉	semidirect
190. #877	C₂×C₉	semidirect
282. C₂×C₃×D₄	C₂²×C₉	semidirect
292. C₂×#67	C₂²×C₉	semidirect
293. C₂×#67	C₂²×C₉	semidirect
294. C₂×#67	C₂²×C₉	semidirect
296. C₂²×Dic₃	C₂²×C₉	semidirect
298. C₂×D₁₂	C₂²×C₉	semidirect
299. C₂×C₄×D₃	C₂²×C₉	semidirect
300. C₂×Dic₆	C₂²×C₉	semidirect
309. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
314. #217	C₂²×C₉	semidirect
315. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
316. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
317. Dic₃⋊C₄	C₂²×C₉	semidirect
318. C₄×Dic₃	C₂²×C₉	semidirect
381. #120	D₃×C₉	semidirect
383. C₃×C₉	#535	semidirect
441. C₂×Dic₃	D₄×C₉	semidirect
481. C₂×D₄	C₂×D₃×C₉	semidirect
491. C₂²⋊C₄	C₂×D₃×C₉	semidirect
548. C₉	#5592	direct (N × H)
618. C₃	C₉×#535	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
C₉×#953	2
C₉×#940	2
C₉×#939	2
C₉×#937	2
C₉×#885	2
C₉×#884	2
C₉×#882	2
C₉×#877	2
C₃×#5592	3
C₉×#535	3

Subgroups — C9×#5592 #13152751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5592 #13152751