Subgroups — C₉×#5599 #13152800

Order 1728.

1030 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#237	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#940	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	C₄×C₉×#67	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#895	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#887	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#884	C₂	1	2	yes	maximal, complemented
11	C₉×#67⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₃×#5599	C₃	1	1	yes	maximal, characteristic
13	C₉×#550	—	3	1	no	maximal
14	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₄×C₉	C₂²	1	2	yes	—
16	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₉×#67	C₂²	1	2	yes	—
18	C₂×C₉×#67	C₂²	1	2	yes	—
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	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
23	C₉×#237	—	2	4	no	—
24	C₉×#235	—	2	4	no	—
25	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
26	C₂×C₉×D₁₂	C₂²	1	2	yes	—
27	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
28	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
29	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
30	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₉×#217	C₂²	1	1	yes	characteristic
33	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
34	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
35	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
36	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
37	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
38	C₄×C₉×Dic₃	C₂²	1	2	yes	—
39	C₂×C₃×#237	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
41	C₃²×#121	C₂×C₃	1	1	yes	characteristic
42	C₃×#940	C₂×C₃	1	2	yes	—
43	C₃×#940	C₂×C₃	1	1	yes	characteristic
44	C₃×#939	C₂×C₃	1	2	yes	—
45	C₃×C₄×#67	C₂×C₃	1	1	yes	characteristic
46	C₃×#895	C₂×C₃	1	1	yes	characteristic
47	C₃×#887	C₂×C₃	1	1	yes	characteristic
48	C₃×#884	C₂×C₃	1	2	yes	—
49	C₃×#67⋊C₄	C₂×C₃	1	2	yes	—
50	C₂×C₉×#41	—	3	1	no	—
51	C₂×C₉×#41	—	3	1	no	—
52	C₉×#127	—	3	2	no	—
53	C₉×#127	—	3	1	no	—
54	C₉×#121	—	2	1	no	—
55	C₉×#121	—	3	2	no	—
56	C₉×#121	—	3	1	no	—
57	C₉×#121	—	3	2	no	—
58	C₉×#121	D₃	1	1	yes	characteristic, complemented
59	C₄×Q₈×C₉	—	3	1	no	—
60	C₄×D₄×C₉	—	3	1	no	—
61	C₄×D₄×C₉	—	3	2	no	—
62	C₂³×C₃×C₉	C₂³	1	2	yes	—
63	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
64	C₂²×D₃×C₉	C₂³	1	2	yes	—
65	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
66	C₃×D₄×C₉	—	2	2	no	—
67	C₃×D₄×C₉	—	4	2	no	—
68	C₂×C₃×C₄×C₉	—	2	2	no	—
69	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
71	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
72	C₉×#67	—	2	4	no	—
73	C₉×#67	—	2	4	no	—
74	C₉×#67	—	2	2	no	—
75	C₉×#67	—	2	4	no	—
76	C₉×#67	—	4	2	no	—
77	C₂×C₉×Dic₃	—	2	4	no	—
78	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
79	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
80	C₂×C₉×Dic₃	C₂³	1	2	yes	—
81	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
82	C₉×D₁₂	—	2	2	no	—
83	C₉×D₁₂	—	4	2	no	—
84	C₄×D₃×C₉	—	2	2	no	—
85	C₄×D₃×C₉	—	2	4	no	—
86	C₉×Dic₆	D₄	1	4	yes	complemented
87	C₃×#550	—	3	1	no	—
88	#5599	C₉	1	1	yes	characteristic, direct product factor
89	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
91	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
93	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
94	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
96	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
97	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
98	C₃×#237	—	2	4	no	—
99	C₃×#235	—	2	4	no	—
100	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
102	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
103	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
105	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
106	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
107	C₃×#217	C₂²×C₃	1	1	yes	characteristic
108	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
109	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
110	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
111	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
112	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
113	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
114	C₉×#41	—	6	4	no	—
115	C₉×#41	—	6	4	no	—
116	C₂×Q₈×C₉	—	3	1	no	—
117	C₂×D₄×C₉	—	2	1	no	—
118	C₂×D₄×C₉	—	2	2	no	—
119	C₂×D₄×C₉	—	3	1	no	—
120	C₂×D₄×C₉	—	3	2	no	—
121	C₂×D₄×C₉	—	3	2	no	—
122	C₂×D₄×C₉	—	3	2	no	—
123	C₂×D₄×C₉	—	3	2	no	—
124	C₂×D₄×C₉	—	3	1	no	—
125	C₂×D₄×C₉	—	3	2	no	—
126	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
127	C₂×D₄×C₉	C₂×D₃	1	2	yes	—
128	C₂²×C₄×C₉	—	2	1	no	—
129	C₂²×C₄×C₉	—	3	2	no	—
130	C₂²×C₄×C₉	—	3	2	no	—
131	C₂²×C₄×C₉	—	3	1	no	—
132	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
133	C₉×C₄⋊C₄	—	2	1	no	—
134	C₉×C₄⋊C₄	—	3	1	no	—
135	C₉×C₄⋊C₄	—	3	2	no	—
136	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
137	C₉×C₂²⋊C₄	—	2	2	no	—
138	C₉×C₂²⋊C₄	—	3	1	no	—
139	C₉×C₂²⋊C₄	—	3	1	no	—
140	C₉×C₂²⋊C₄	—	3	2	no	—
141	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
142	C₄²×C₉	—	3	2	no	—
143	C₄²×C₉	—	3	1	no	—
144	C₂²×C₃×C₉	—	2	2	no	—
145	C₂²×C₃×C₉	—	2	1	no	—
146	C₂²×C₃×C₉	—	2	1	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	C₂⁴	1	1	yes	characteristic
151	C₂×D₃×C₉	—	2	2	no	—
152	C₂×D₃×C₉	—	2	1	no	—
153	C₂×D₃×C₉	—	2	2	no	—
154	C₂×D₃×C₉	—	2	1	no	—
155	C₂×D₃×C₉	—	2	1	no	—
156	C₂×D₃×C₉	—	2	2	no	—
157	C₃×C₄×C₉	—	2	1	no	—
158	C₃×C₄×C₉	—	2	2	no	—
159	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
160	C₉×Dic₃	—	2	1	no	—
161	C₉×Dic₃	—	2	1	no	—
162	C₉×Dic₃	C₂×D₄	1	4	yes	—
163	C₉×Dic₃	#41	1	2	yes	complemented
164	C₂×C₃×#41	—	3	1	no	—
165	C₂×C₃×#41	—	3	1	no	—
166	C₂×#237	C₂×C₉	1	1	yes	characteristic, complemented
167	C₂×#235	C₂×C₉	1	1	yes	characteristic, complemented
168	C₃×#127	—	3	2	no	—
169	C₃×#127	—	3	1	no	—
170	C₃×#121	—	2	1	no	—
171	C₃×#121	—	3	2	no	—
172	C₃×#121	—	3	1	no	—
173	C₃×#121	—	3	2	no	—
174	C₃×#121	C₂×C₉	1	1	yes	characteristic, complemented
175	C₃×#121	C₃×D₃	1	1	yes	characteristic
176	C₃×C₄×Q₈	—	3	1	no	—
177	C₃×C₄×D₄	—	3	1	no	—
178	C₃×C₄×D₄	—	3	2	no	—
179	#940	C₂×C₉	1	2	yes	complemented
180	#940	C₂×C₉	1	1	yes	characteristic, complemented
181	#939	C₂×C₉	1	2	yes	complemented
182	C₄×#67	C₂×C₉	1	1	yes	characteristic, complemented
183	#895	C₂×C₉	1	1	yes	characteristic, complemented
184	#887	C₂×C₉	1	1	yes	characteristic, complemented
185	#884	C₂×C₉	1	2	yes	complemented
186	#67⋊C₄	C₂×C₉	1	2	yes	complemented
187	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
188	C₂³×C₃²	C₂³×C₃	1	2	yes	—
189	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
190	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
191	C₃²×D₄	—	2	2	no	—
192	C₃²×D₄	—	4	2	no	—
193	C₂×C₃²×C₄	—	2	2	no	—
194	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
195	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
196	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
197	C₃×#67	—	2	4	no	—
198	C₃×#67	—	2	4	no	—
199	C₃×#67	—	2	4	no	—
200	C₃×#67	—	2	2	no	—
201	C₃×#67	—	4	2	no	—
202	C₂×C₃×Dic₃	—	2	4	no	—
203	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
204	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
205	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
206	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
207	C₃×D₁₂	—	2	2	no	—
208	C₃×D₁₂	—	4	2	no	—
209	C₃×C₄×D₃	—	2	2	no	—
210	C₃×C₄×D₃	—	2	4	no	—
211	C₃×Dic₆	C₃×D₄	1	4	yes	—
212	C₂³×C₉	—	2	1	no	—
213	C₂³×C₉	—	2	2	no	—
214	C₂³×C₉	—	3	1	no	—
215	C₂³×C₉	—	3	2	no	—
216	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
217	C₂³×C₉	C₂²×D₃	1	2	yes	—
218	Q₈×C₉	—	3	4	no	—
219	D₄×C₉	—	2	2	no	—
220	D₄×C₉	—	4	2	no	—
221	D₄×C₉	—	4	2	no	—
222	D₄×C₉	—	4	4	no	—
223	D₄×C₉	—	6	2	no	—
224	D₄×C₉	—	6	4	no	—
225	D₄×C₉	—	6	4	no	—
226	D₄×C₉	—	6	4	no	—
227	D₄×C₉	—	6	2	no	—
228	D₄×C₉	—	12	2	no	—
229	D₄×C₉	—	12	2	no	—
230	C₂×C₄×C₉	—	2	2	no	—
231	C₂×C₄×C₉	—	2	1	no	—
232	C₂×C₄×C₉	—	2	1	no	—
233	C₂×C₄×C₉	—	2	2	no	—
234	C₂×C₄×C₉	—	3	1	no	—
235	C₂×C₄×C₉	—	3	2	no	—
236	C₂×C₄×C₉	—	3	1	no	—
237	C₂×C₄×C₉	—	3	1	no	—
238	C₂×C₄×C₉	—	4	2	no	—
239	C₂×C₄×C₉	—	6	4	no	—
240	C₂×C₄×C₉	—	6	4	no	—
241	C₂×C₄×C₉	—	6	2	no	—
242	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
243	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
244	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
245	#550	—	3	1	no	Sylow
246	C₂×C₃×C₉	—	4	1	no	—
247	C₂×C₃×C₉	—	4	2	no	—
248	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
250	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
251	D₃×C₉	—	4	2	no	—
252	D₃×C₉	—	4	1	no	—
253	C₃×#41	—	6	4	no	—
254	C₃×#41	—	6	4	no	—
255	C₂×C₃×Q₈	—	3	1	no	—
256	C₂×C₃×D₄	—	2	1	no	—
257	C₂×C₃×D₄	—	2	2	no	—
258	C₂×C₃×D₄	—	3	1	no	—
259	C₂×C₃×D₄	—	3	2	no	—
260	C₂×C₃×D₄	—	3	2	no	—
261	C₂×C₃×D₄	—	3	2	no	—
262	C₂×C₃×D₄	—	3	2	no	—
263	C₂×C₃×D₄	—	3	1	no	—
264	C₂×C₃×D₄	—	3	2	no	—
265	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
266	C₂×C₃×D₄	C₂²×C₉	1	2	yes	—
267	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
268	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
269	C₂²×C₃×C₄	—	2	1	no	—
270	C₂²×C₃×C₄	—	3	2	no	—
271	C₂²×C₃×C₄	—	3	2	no	—
272	C₂²×C₃×C₄	—	3	1	no	—
273	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
274	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
275	C₂×#67	C₂²×C₉	1	2	yes	—
276	C₂×#67	C₂²×C₉	1	2	yes	—
277	C₂×#67	C₂²×C₉	1	1	yes	characteristic
278	C₂×#67	C₂²×C₉	1	2	yes	—
279	C₂×#67	C₂²×C₉	1	2	yes	—
280	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
281	#237	—	2	4	no	—
282	#235	—	2	4	no	—
283	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
284	C₂×D₁₂	C₂²×C₉	1	2	yes	—
285	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
286	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
287	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
288	C₃×C₄⋊C₄	—	2	1	no	—
289	C₃×C₄⋊C₄	—	3	1	no	—
290	C₃×C₄⋊C₄	—	3	2	no	—
291	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
292	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
293	C₃×C₂²⋊C₄	—	2	2	no	—
294	C₃×C₂²⋊C₄	—	3	1	no	—
295	C₃×C₂²⋊C₄	—	3	1	no	—
296	C₃×C₂²⋊C₄	—	3	2	no	—
297	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
298	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
299	C₃×C₄²	—	3	2	no	—
300	C₃×C₄²	—	3	1	no	—
301	#217	C₂²×C₉	1	1	yes	characteristic
302	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
303	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
304	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
305	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
306	C₄×Dic₃	C₂²×C₉	1	2	yes	—
307	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
308	C₂²×C₃²	—	2	1	no	—
309	C₂²×C₃²	—	2	2	no	—
310	C₂²×C₃²	—	2	1	no	—
311	C₂²×C₃²	—	2	1	no	—
312	C₂²×C₃²	—	2	2	no	—
313	C₂²×C₃²	—	2	2	no	—
314	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
315	C₂×C₃×D₃	—	2	2	no	—
316	C₂×C₃×D₃	—	2	1	no	—
317	C₂×C₃×D₃	—	2	2	no	—
318	C₂×C₃×D₃	—	2	1	no	—
319	C₂×C₃×D₃	—	2	1	no	—
320	C₂×C₃×D₃	—	2	2	no	—
321	C₃²×C₄	—	2	1	no	—
322	C₃²×C₄	—	2	2	no	—
323	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
324	C₃×Dic₃	—	2	1	no	—
325	C₃×Dic₃	—	2	1	no	—
326	C₃×Dic₃	C₂×C₃×D₄	1	4	yes	—
327	C₃×Dic₃	C₃×#41	1	2	yes	—
328	C₂²×C₉	—	2	2	no	—
329	C₂²×C₉	—	2	1	no	—
330	C₂²×C₉	—	2	2	no	—
331	C₂²×C₉	—	2	1	no	—
332	C₂²×C₉	—	2	2	no	—
333	C₂²×C₉	—	2	1	no	—
334	C₂²×C₉	—	2	2	no	—
335	C₂²×C₉	—	2	1	no	—
336	C₂²×C₉	—	4	1	no	—
337	C₂²×C₉	—	4	1	no	—
338	C₂²×C₉	—	4	2	no	—
339	C₂²×C₉	—	4	2	no	—
340	C₂²×C₉	—	4	2	no	—
341	C₂²×C₉	—	6	2	no	—
342	C₂²×C₉	—	6	1	no	—
343	C₂²×C₉	—	6	1	no	—
344	C₂²×C₉	—	6	2	no	—
345	C₂²×C₉	—	6	1	no	—
346	C₂²×C₉	—	6	2	no	—
347	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
348	C₄×C₉	—	2	1	no	—
349	C₄×C₉	—	2	2	no	—
350	C₄×C₉	—	2	2	no	—
351	C₄×C₉	—	3	4	no	—
352	C₄×C₉	—	3	2	no	—
353	C₄×C₉	—	4	1	no	—
354	C₄×C₉	—	4	2	no	—
355	C₄×C₉	—	6	1	no	—
356	C₄×C₉	—	6	1	no	—
357	C₄×C₉	D₃×D₄	1	2	yes	—
358	C₂×#41	—	3	1	no	—
359	C₂×#41	—	3	1	no	—
360	#127	—	3	2	no	—
361	#127	—	3	1	no	—
362	#121	—	3	2	no	—
363	#121	—	3	1	no	—
364	#121	—	3	2	no	—
365	#121	D₃×C₉	1	1	yes	characteristic, complemented
366	C₄×Q₈	—	3	1	no	—
367	C₄×D₄	—	3	1	no	—
368	C₄×D₄	—	3	2	no	—
369	C₃×C₉	#550	1	1	yes	characteristic, complemented, Sylow
370	C₂³×C₃	—	2	1	no	—
371	C₂³×C₃	—	2	2	no	—
372	C₂³×C₃	—	3	1	no	—
373	C₂³×C₃	—	3	2	no	—
374	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
375	C₂³×C₃	C₂³×C₉	1	2	yes	—
376	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
377	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
378	C₂²×D₃	C₂³×C₉	1	2	yes	—
379	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
380	C₃×Q₈	—	3	4	no	—
381	C₃×D₄	—	2	2	no	—
382	C₃×D₄	—	2	2	no	—
383	C₃×D₄	—	4	2	no	—
384	C₃×D₄	—	4	2	no	—
385	C₃×D₄	—	4	2	no	—
386	C₃×D₄	—	4	4	no	—
387	C₃×D₄	—	6	2	no	—
388	C₃×D₄	—	6	4	no	—
389	C₃×D₄	—	6	4	no	—
390	C₃×D₄	—	6	4	no	—
391	C₃×D₄	—	6	2	no	—
392	C₃×D₄	—	12	2	no	—
393	C₃×D₄	—	12	2	no	—
394	C₂×C₃×C₄	—	2	2	no	—
395	C₂×C₃×C₄	—	2	2	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	2	no	—
399	C₂×C₃×C₄	—	3	1	no	—
400	C₂×C₃×C₄	—	3	2	no	—
401	C₂×C₃×C₄	—	3	1	no	—
402	C₂×C₃×C₄	—	3	1	no	—
403	C₂×C₃×C₄	—	4	2	no	—
404	C₂×C₃×C₄	—	6	4	no	—
405	C₂×C₃×C₄	—	6	4	no	—
406	C₂×C₃×C₄	—	6	2	no	—
407	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
408	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
409	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
410	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
411	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
412	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
413	#67	—	2	4	no	—
414	#67	—	2	4	no	—
415	#67	—	2	4	no	—
416	#67	—	2	2	no	—
417	#67	—	4	2	no	—
418	C₂×Dic₃	—	2	4	no	—
419	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
420	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
421	C₂×Dic₃	C₂³×C₉	1	2	yes	—
422	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
423	D₁₂	—	2	2	no	—
424	D₁₂	—	4	2	no	—
425	C₄×D₃	—	2	2	no	—
426	C₄×D₃	—	2	4	no	—
427	Dic₆	D₄×C₉	1	4	yes	complemented
428	C₂×C₃²	—	4	1	no	—
429	C₂×C₃²	—	4	2	no	—
430	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
431	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
432	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
433	C₃×D₃	—	4	2	no	—
434	C₃×D₃	—	4	1	no	—
435	C₂×C₉	—	2	1	no	—
436	C₂×C₉	—	2	1	no	—
437	C₂×C₉	—	2	1	no	—
438	C₂×C₉	—	4	2	no	—
439	C₂×C₉	—	4	1	no	—
440	C₂×C₉	—	4	2	no	—
441	C₂×C₉	—	8	2	no	—
442	C₂×C₉	—	12	2	no	—
443	C₂×C₉	—	12	1	no	—
444	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
445	C₂×C₉	#1004	1	1	yes	characteristic
446	C₂×C₉	D₃×#41	1	1	yes	characteristic
447	#41	—	6	4	no	—
448	#41	—	6	4	no	—
449	C₂×Q₈	—	3	1	no	—
450	C₂×D₄	—	3	1	no	—
451	C₂×D₄	—	3	2	no	—
452	C₂×D₄	—	3	2	no	—
453	C₂×D₄	—	3	2	no	—
454	C₂×D₄	—	3	2	no	—
455	C₂×D₄	—	3	1	no	—
456	C₂×D₄	—	3	2	no	—
457	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
458	C₂×D₄	C₂×D₃×C₉	1	2	yes	—
459	C₂²×C₄	—	3	2	no	—
460	C₂²×C₄	—	3	2	no	—
461	C₂²×C₄	—	3	1	no	—
462	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
463	C₄⋊C₄	—	3	1	no	—
464	C₄⋊C₄	—	3	2	no	—
465	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
466	C₂²⋊C₄	—	3	1	no	—
467	C₂²⋊C₄	—	3	1	no	—
468	C₂²⋊C₄	—	3	2	no	—
469	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
470	C₄²	—	3	2	no	—
471	C₄²	—	3	1	no	—
472	C₂²×C₃	—	2	2	no	—
473	C₂²×C₃	—	2	1	no	—
474	C₂²×C₃	—	2	2	no	—
475	C₂²×C₃	—	2	1	no	—
476	C₂²×C₃	—	2	2	no	—
477	C₂²×C₃	—	2	1	no	—
478	C₂²×C₃	—	2	2	no	—
479	C₂²×C₃	—	2	2	no	—
480	C₂²×C₃	—	2	1	no	—
481	C₂²×C₃	—	2	1	no	—
482	C₂²×C₃	—	2	2	no	—
483	C₂²×C₃	—	2	2	no	—
484	C₂²×C₃	—	2	1	no	—
485	C₂²×C₃	—	2	1	no	—
486	C₂²×C₃	—	4	1	no	—
487	C₂²×C₃	—	4	1	no	—
488	C₂²×C₃	—	4	2	no	—
489	C₂²×C₃	—	4	2	no	—
490	C₂²×C₃	—	4	2	no	—
491	C₂²×C₃	—	6	2	no	—
492	C₂²×C₃	—	6	1	no	—
493	C₂²×C₃	—	6	1	no	—
494	C₂²×C₃	—	6	2	no	—
495	C₂²×C₃	—	6	1	no	—
496	C₂²×C₃	—	6	2	no	—
497	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
498	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
499	C₂×D₃	—	2	2	no	—
500	C₂×D₃	—	2	1	no	—
501	C₂×D₃	—	2	2	no	—
502	C₂×D₃	—	2	1	no	—
503	C₂×D₃	—	2	1	no	—
504	C₂×D₃	—	2	2	no	—
505	C₃×C₄	—	2	1	no	—
506	C₃×C₄	—	2	2	no	—
507	C₃×C₄	—	2	1	no	—
508	C₃×C₄	—	2	2	no	—
509	C₃×C₄	—	2	2	no	—
510	C₃×C₄	—	3	4	no	—
511	C₃×C₄	—	3	2	no	—
512	C₃×C₄	—	4	1	no	—
513	C₃×C₄	—	4	2	no	—
514	C₃×C₄	—	6	1	no	—
515	C₃×C₄	—	6	1	no	—
516	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
517	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
518	Dic₃	—	2	1	no	—
519	Dic₃	—	2	1	no	—
520	Dic₃	C₂×D₄×C₉	1	4	yes	—
521	Dic₃	C₉×#41	1	2	yes	complemented
522	C₃²	C₃×#550	1	1	yes	characteristic
523	C₉	—	2	1	no	—
524	C₉	#5599	1	1	yes	characteristic, direct product factor
525	C₂³	—	3	1	no	—
526	C₂³	—	3	2	no	—
527	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
528	C₂³	C₂²×D₃×C₉	1	2	yes	—
529	Q₈	—	3	4	no	—
530	D₄	—	2	2	no	—
531	D₄	—	4	2	no	—
532	D₄	—	6	4	no	—
533	D₄	—	6	4	no	—
534	D₄	—	6	2	no	—
535	D₄	—	6	4	no	—
536	D₄	—	6	2	no	—
537	D₄	—	12	2	no	—
538	D₄	—	12	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	3	1	no	—
541	C₂×C₄	—	3	2	no	—
542	C₂×C₄	—	3	1	no	—
543	C₂×C₄	—	3	1	no	—
544	C₂×C₄	—	6	4	no	—
545	C₂×C₄	—	6	4	no	—
546	C₂×C₄	—	6	2	no	—
547	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
548	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
549	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
550	C₂×C₃	—	2	1	no	—
551	C₂×C₃	—	2	1	no	—
552	C₂×C₃	—	2	1	no	—
553	C₂×C₃	—	4	2	no	—
554	C₂×C₃	—	4	1	no	—
555	C₂×C₃	—	4	2	no	—
556	C₂×C₃	—	4	1	no	—
557	C₂×C₃	—	4	2	no	—
558	C₂×C₃	—	8	2	no	—
559	C₂×C₃	—	12	2	no	—
560	C₂×C₃	—	12	1	no	—
561	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
562	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
563	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
564	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
565	C₂×C₃	C₃×#1004	1	1	yes	characteristic
566	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
567	D₃	—	4	2	no	—
568	D₃	—	4	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	6	2	no	—
576	C₂²	—	6	1	no	—
577	C₂²	—	6	1	no	—
578	C₂²	—	6	2	no	—
579	C₂²	—	6	1	no	—
580	C₂²	—	6	2	no	—
581	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
582	C₄	—	2	1	no	—
583	C₄	—	2	2	no	—
584	C₄	—	3	4	no	—
585	C₄	—	3	2	no	—
586	C₄	—	6	1	no	—
587	C₄	—	6	1	no	—
588	C₄	D₃×D₄×C₉	1	2	yes	—
589	C₃	—	2	1	no	—
590	C₃	C₉×#550	1	1	yes	characteristic, complemented
591	C₃	C₃×#5599	1	1	yes	characteristic
592	C₂	—	4	1	no	—
593	C₂	—	4	2	no	—
594	C₂	—	12	2	no	—
595	C₂	—	12	1	no	—
596	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
597	C₂	C₉×#1004	1	1	yes	characteristic
598	C₂	D₃×C₉×#41	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×#121	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5599	C₃
hypercenter	C₉×#121	D₃
hypocenter	C₃	C₉×#550
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#121

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#237	C₂	semidirect
2. C₂×C₉×#235	C₂	semidirect
3. C₃×C₉×#121	C₂	semidirect
4. C₉×#940	C₂	semidirect
5. C₉×#940	C₂	semidirect
6. C₉×#939	C₂	semidirect
7. C₄×C₉×#67	C₂	semidirect
8. C₉×#895	C₂	semidirect
9. C₉×#887	C₂	semidirect
10. C₉×#884	C₂	semidirect
11. C₉×#67⋊C₄	C₂	semidirect
58. C₉×#121	D₃	semidirect
86. C₉×Dic₆	D₄	semidirect
88. #5599	C₉	direct (N × H)
163. C₉×Dic₃	#41	semidirect
166. C₂×#237	C₂×C₉	semidirect
167. C₂×#235	C₂×C₉	semidirect
174. C₃×#121	C₂×C₉	semidirect
179. #940	C₂×C₉	semidirect
180. #940	C₂×C₉	semidirect
181. #939	C₂×C₉	semidirect
182. C₄×#67	C₂×C₉	semidirect
183. #895	C₂×C₉	semidirect
184. #887	C₂×C₉	semidirect
185. #884	C₂×C₉	semidirect
186. #67⋊C₄	C₂×C₉	semidirect
365. #121	D₃×C₉	semidirect
369. C₃×C₉	#550	semidirect
427. Dic₆	D₄×C₉	semidirect
521. Dic₃	C₉×#41	semidirect
524. C₉	#5599	direct (N × H)
590. C₃	C₉×#550	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#237	2
C₂×C₉×#235	2
C₃×C₉×#121	2
C₉×#940	2
C₉×#939	2
C₄×C₉×#67	2
C₉×#895	2
C₉×#887	2
C₉×#884	2
C₉×#67⋊C₄	2
C₃×#5599	3
C₉×#550	3

Subgroups — C9×#5599 #13152800

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5599 #13152800