Subgroups — C₉×#5659 #13153029

Order 1728.

822 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#937	C₂	1	1	yes	maximal, characteristic
3	C₉×#936	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₉×#67	C₂	1	2	yes	maximal, complemented
5	C₉×#896	C₂	1	2	yes	maximal, complemented
6	C₉×#892	C₂	1	2	yes	maximal, complemented
7	C₉×#883	C₂	1	2	yes	maximal, complemented
8	D₃×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₉×#879	C₂	1	2	yes	maximal, complemented
10	C₃×#5659	C₃	1	1	yes	maximal, characteristic
11	C₉×#551	—	3	1	no	maximal
12	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₉×#67	C₂²	1	2	yes	—
16	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
17	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
18	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
20	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
22	C₉×#217	C₂²	1	2	yes	—
23	C₉×#217	C₂²	1	1	yes	characteristic
24	C₉×#217	C₂²	1	2	yes	complemented
25	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
26	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
27	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₉×C₄⋊Dic₃	C₂²	1	2	yes	complemented
29	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
30	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
31	C₄×C₉×Dic₃	C₂²	1	2	yes	complemented
32	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
33	C₃²×#123	C₂×C₃	1	1	yes	characteristic
34	C₃×#937	C₂×C₃	1	1	yes	characteristic
35	C₃×#936	C₂×C₃	1	1	yes	characteristic
36	C₃×C₄×#67	C₂×C₃	1	2	yes	—
37	C₃×#896	C₂×C₃	1	2	yes	—
38	C₃×#892	C₂×C₃	1	2	yes	—
39	C₃×#883	C₂×C₃	1	2	yes	—
40	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	2	yes	—
41	C₃×#879	C₂×C₃	1	2	yes	—
42	C₉×#126	—	3	2	no	—
43	C₉×#124	—	3	1	no	—
44	C₉×#123	—	2	1	no	—
45	C₉×#123	—	3	2	no	—
46	C₉×#123	D₃	1	1	yes	characteristic, complemented
47	C₉×C₂²⋊Q₈	—	3	2	no	—
48	C₉×#120	—	3	1	no	—
49	C₄×D₄×C₉	—	3	2	no	—
50	C₉×#117	—	3	2	no	—
51	C₂×C₉×C₂²⋊C₄	—	3	2	no	—
52	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
53	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
54	C₂²×D₃×C₉	—	2	4	no	—
55	C₂²×D₃×C₉	—	4	1	no	—
56	C₂²×D₃×C₉	C₂³	1	2	yes	—
57	C₃×D₄×C₉	—	4	1	no	—
58	C₂×C₃×C₄×C₉	—	4	1	no	—
59	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
61	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
62	C₉×#67	—	2	4	no	—
63	C₂×C₉×Dic₃	C₂³	1	2	yes	—
64	C₂×C₉×Dic₃	C₂³	1	2	yes	—
65	C₂×C₉×Dic₃	C₂³	1	2	yes	—
66	C₄×D₃×C₉	—	2	4	no	—
67	C₄×D₃×C₉	—	4	2	no	—
68	C₉×Dic₆	—	4	1	no	—
69	C₃×#551	—	3	1	no	—
70	#5659	C₉	1	1	yes	characteristic, direct product factor
71	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
75	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
76	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
77	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
78	C₂⁴×C₉	—	3	1	no	—
79	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
80	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
81	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
82	C₃×#217	C₂²×C₃	1	1	yes	characteristic
83	C₃×#217	C₂²×C₃	1	2	yes	—
84	C₃×#217	C₂²×C₃	1	2	yes	—
85	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
86	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
87	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
88	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
89	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
90	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
91	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
92	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
93	C₂×Q₈×C₉	—	3	1	no	—
94	C₂×D₄×C₉	—	2	1	no	—
95	C₂×D₄×C₉	—	3	2	no	—
96	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
97	C₂²×C₄×C₉	—	2	1	no	—
98	C₂²×C₄×C₉	—	3	2	no	—
99	C₂²×C₄×C₉	—	3	2	no	—
100	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
101	C₉×C₄⋊C₄	—	2	2	no	—
102	C₉×C₄⋊C₄	—	3	2	no	—
103	C₉×C₄⋊C₄	—	3	2	no	—
104	C₉×C₄⋊C₄	—	3	2	no	—
105	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
106	C₉×C₂²⋊C₄	—	2	2	no	—
107	C₉×C₂²⋊C₄	—	2	1	no	—
108	C₉×C₂²⋊C₄	—	3	2	no	—
109	C₉×C₂²⋊C₄	—	3	2	no	—
110	C₉×C₂²⋊C₄	—	3	1	no	—
111	C₉×C₂²⋊C₄	—	3	2	no	—
112	C₉×C₂²⋊C₄	—	3	2	no	—
113	C₉×C₂²⋊C₄	—	3	2	no	—
114	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
115	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
116	C₄²×C₉	—	3	1	no	—
117	C₄²×C₉	—	3	2	no	—
118	C₂²×C₃×C₉	—	2	2	no	—
119	C₂²×C₃×C₉	—	2	2	no	—
120	C₂²×C₃×C₉	—	2	1	no	—
121	C₂²×C₃×C₉	—	2	1	no	—
122	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
123	C₂×D₃×C₉	—	2	2	no	—
124	C₂×D₃×C₉	—	2	2	no	—
125	C₂×D₃×C₉	—	4	4	no	—
126	C₂×D₃×C₉	#41	1	4	yes	—
127	C₃×C₄×C₉	—	2	2	no	—
128	C₃×C₄×C₉	—	2	1	no	—
129	C₃×C₄×C₉	—	2	2	no	—
130	C₉×Dic₃	—	2	2	no	—
131	C₉×Dic₃	—	2	2	no	—
132	C₉×Dic₃	—	2	2	no	—
133	C₃×#126	—	3	2	no	—
134	C₃×#124	—	3	1	no	—
135	C₃×#123	—	2	1	no	—
136	C₃×#123	—	3	2	no	—
137	C₃×#123	C₂×C₉	1	1	yes	characteristic, complemented
138	C₃×#123	C₃×D₃	1	1	yes	characteristic
139	C₃×C₂²⋊Q₈	—	3	2	no	—
140	C₃×#120	—	3	1	no	—
141	C₃×C₄×D₄	—	3	2	no	—
142	C₃×#117	—	3	2	no	—
143	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
144	#937	C₂×C₉	1	1	yes	characteristic
145	#936	C₂×C₉	1	1	yes	characteristic, complemented
146	C₄×#67	C₂×C₉	1	2	yes	complemented
147	#896	C₂×C₉	1	2	yes	complemented
148	#892	C₂×C₉	1	2	yes	complemented
149	#883	C₂×C₉	1	2	yes	complemented
150	D₃×C₂²⋊C₄	C₂×C₉	1	2	yes	complemented
151	#879	C₂×C₉	1	2	yes	complemented
152	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
153	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
154	C₂²×C₃×D₃	—	2	4	no	—
155	C₂²×C₃×D₃	—	4	1	no	—
156	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
157	C₃²×D₄	—	4	1	no	—
158	C₂×C₃²×C₄	—	4	1	no	—
159	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
160	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
161	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
162	C₃×#67	—	2	4	no	—
163	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
164	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
165	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
166	C₃×C₄×D₃	—	2	4	no	—
167	C₃×C₄×D₃	—	4	2	no	—
168	C₃×Dic₆	—	4	1	no	—
169	C₂³×C₉	—	2	1	no	—
170	C₂³×C₉	—	2	1	no	—
171	C₂³×C₉	—	3	2	no	—
172	C₂³×C₉	—	6	4	no	—
173	C₂³×C₉	—	12	1	no	—
174	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
175	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
176	Q₈×C₉	—	12	1	no	—
177	D₄×C₉	—	4	1	no	—
178	D₄×C₉	—	4	2	no	—
179	D₄×C₉	—	6	4	no	—
180	C₂×C₄×C₉	—	2	2	no	—
181	C₂×C₄×C₉	—	2	2	no	—
182	C₂×C₄×C₉	—	2	1	no	—
183	C₂×C₄×C₉	—	3	2	no	—
184	C₂×C₄×C₉	—	3	2	no	—
185	C₂×C₄×C₉	—	3	2	no	—
186	C₂×C₄×C₉	—	4	1	no	—
187	C₂×C₄×C₉	—	4	2	no	—
188	C₂×C₄×C₉	—	6	4	no	—
189	C₂×C₄×C₉	—	12	2	no	—
190	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
191	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
192	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
193	#551	—	3	1	no	Sylow
194	C₂×C₃×C₉	—	4	1	no	—
195	C₂×C₃×C₉	—	4	1	no	—
196	C₂×C₃×C₉	C₂×#41	1	2	yes	—
197	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
198	D₃×C₉	—	2	4	no	—
199	C₂⁴×C₃	—	3	1	no	—
200	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
201	C₂×C₃×Q₈	—	3	1	no	—
202	C₂×C₃×D₄	—	2	1	no	—
203	C₂×C₃×D₄	—	3	2	no	—
204	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
205	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
206	C₂²×C₃×C₄	—	2	1	no	—
207	C₂²×C₃×C₄	—	3	2	no	—
208	C₂²×C₃×C₄	—	3	2	no	—
209	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic, complemented
210	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
211	C₂×#67	C₂²×C₉	1	2	yes	—
212	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
213	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
214	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
215	C₃×C₄⋊C₄	—	2	2	no	—
216	C₃×C₄⋊C₄	—	3	2	no	—
217	C₃×C₄⋊C₄	—	3	2	no	—
218	C₃×C₄⋊C₄	—	3	2	no	—
219	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
220	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
221	C₃×C₂²⋊C₄	—	2	2	no	—
222	C₃×C₂²⋊C₄	—	2	1	no	—
223	C₃×C₂²⋊C₄	—	3	2	no	—
224	C₃×C₂²⋊C₄	—	3	2	no	—
225	C₃×C₂²⋊C₄	—	3	1	no	—
226	C₃×C₂²⋊C₄	—	3	2	no	—
227	C₃×C₂²⋊C₄	—	3	2	no	—
228	C₃×C₂²⋊C₄	—	3	2	no	—
229	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
230	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
231	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
232	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
233	C₃×C₄²	—	3	1	no	—
234	C₃×C₄²	—	3	2	no	—
235	#217	C₂²×C₉	1	1	yes	characteristic
236	#217	C₂²×C₉	1	2	yes	—
237	#217	C₂²×C₉	1	2	yes	complemented
238	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
239	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
240	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
241	C₄⋊Dic₃	C₂²×C₉	1	2	yes	complemented
242	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
243	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
244	C₄×Dic₃	C₂²×C₉	1	2	yes	complemented
245	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
246	C₂²×C₃²	—	2	1	no	—
247	C₂²×C₃²	—	2	2	no	—
248	C₂²×C₃²	—	2	2	no	—
249	C₂²×C₃²	—	2	1	no	—
250	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
251	C₂×C₃×D₃	—	2	2	no	—
252	C₂×C₃×D₃	—	2	2	no	—
253	C₂×C₃×D₃	—	4	4	no	—
254	C₂×C₃×D₃	C₃×#41	1	4	yes	—
255	C₃²×C₄	—	2	2	no	—
256	C₃²×C₄	—	2	1	no	—
257	C₃²×C₄	—	2	2	no	—
258	C₃×Dic₃	—	2	2	no	—
259	C₃×Dic₃	—	2	2	no	—
260	C₃×Dic₃	—	2	2	no	—
261	C₂²×C₉	—	2	2	no	—
262	C₂²×C₉	—	2	1	no	—
263	C₂²×C₉	—	2	1	no	—
264	C₂²×C₉	—	2	2	no	—
265	C₂²×C₉	—	2	2	no	—
266	C₂²×C₉	—	2	1	no	—
267	C₂²×C₉	—	3	4	no	—
268	C₂²×C₉	—	4	2	no	—
269	C₂²×C₉	—	4	1	no	—
270	C₂²×C₉	—	4	2	no	—
271	C₂²×C₉	—	6	2	no	—
272	C₂²×C₉	—	6	2	no	—
273	C₂²×C₉	—	12	4	no	—
274	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
275	C₄×C₉	—	2	2	no	—
276	C₄×C₉	—	2	1	no	—
277	C₄×C₉	—	2	2	no	—
278	C₄×C₉	—	4	2	no	—
279	C₄×C₉	—	4	2	no	—
280	C₄×C₉	—	4	1	no	—
281	C₄×C₉	—	6	2	no	—
282	C₄×C₉	—	6	2	no	—
283	C₄×C₉	—	6	2	no	—
284	#126	—	3	2	no	—
285	#124	—	3	1	no	—
286	#123	—	3	2	no	—
287	#123	D₃×C₉	1	1	yes	characteristic, complemented
288	C₂²⋊Q₈	—	3	2	no	—
289	#120	—	3	1	no	—
290	C₄×D₄	—	3	2	no	—
291	#117	—	3	2	no	—
292	C₂×C₂²⋊C₄	—	3	2	no	—
293	C₃×C₉	#551	1	1	yes	characteristic, complemented, Sylow
294	C₂³×C₃	—	2	1	no	—
295	C₂³×C₃	—	2	1	no	—
296	C₂³×C₃	—	3	2	no	—
297	C₂³×C₃	—	6	4	no	—
298	C₂³×C₃	—	12	1	no	—
299	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
300	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
301	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
302	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
303	C₂²×D₃	—	2	4	no	—
304	C₂²×D₃	—	4	1	no	—
305	C₂²×D₃	C₂³×C₉	1	2	yes	—
306	C₃×Q₈	—	12	1	no	—
307	C₃×D₄	—	4	1	no	—
308	C₃×D₄	—	4	1	no	—
309	C₃×D₄	—	4	2	no	—
310	C₃×D₄	—	6	4	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	1	no	—
314	C₂×C₃×C₄	—	3	2	no	—
315	C₂×C₃×C₄	—	3	2	no	—
316	C₂×C₃×C₄	—	3	2	no	—
317	C₂×C₃×C₄	—	4	1	no	—
318	C₂×C₃×C₄	—	4	1	no	—
319	C₂×C₃×C₄	—	4	2	no	—
320	C₂×C₃×C₄	—	6	4	no	—
321	C₂×C₃×C₄	—	12	2	no	—
322	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
323	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
325	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
327	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
328	#67	—	2	4	no	—
329	C₂×Dic₃	C₂³×C₉	1	2	yes	—
330	C₂×Dic₃	C₂³×C₉	1	2	yes	—
331	C₂×Dic₃	C₂³×C₉	1	2	yes	—
332	C₄×D₃	—	2	4	no	—
333	C₄×D₃	—	4	2	no	—
334	Dic₆	—	4	1	no	—
335	C₂×C₃²	—	4	1	no	—
336	C₂×C₃²	—	4	1	no	—
337	C₂×C₃²	C₂×C₃×#41	1	2	yes	—
338	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
339	C₃×D₃	—	2	4	no	—
340	C₂×C₉	—	2	1	no	—
341	C₂×C₉	—	2	2	no	—
342	C₂×C₉	—	4	2	no	—
343	C₂×C₉	—	4	1	no	—
344	C₂×C₉	—	4	1	no	—
345	C₂×C₉	—	6	4	no	—
346	C₂×C₉	—	8	1	no	—
347	C₂×C₉	#1004	1	1	yes	characteristic
348	C₂×C₉	D₃×#41	1	2	yes	—
349	C₂⁴	—	3	1	no	—
350	C₂×Q₈	—	3	1	no	—
351	C₂×D₄	—	3	2	no	—
352	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
353	C₂²×C₄	—	3	2	no	—
354	C₂²×C₄	—	3	2	no	—
355	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
356	C₄⋊C₄	—	3	2	no	—
357	C₄⋊C₄	—	3	2	no	—
358	C₄⋊C₄	—	3	2	no	—
359	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
360	C₂²⋊C₄	—	3	2	no	—
361	C₂²⋊C₄	—	3	2	no	—
362	C₂²⋊C₄	—	3	1	no	—
363	C₂²⋊C₄	—	3	2	no	—
364	C₂²⋊C₄	—	3	2	no	—
365	C₂²⋊C₄	—	3	2	no	—
366	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
367	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
368	C₄²	—	3	1	no	—
369	C₄²	—	3	2	no	—
370	C₂²×C₃	—	2	2	no	—
371	C₂²×C₃	—	2	1	no	—
372	C₂²×C₃	—	2	1	no	—
373	C₂²×C₃	—	2	2	no	—
374	C₂²×C₃	—	2	2	no	—
375	C₂²×C₃	—	2	2	no	—
376	C₂²×C₃	—	2	2	no	—
377	C₂²×C₃	—	2	1	no	—
378	C₂²×C₃	—	2	1	no	—
379	C₂²×C₃	—	2	1	no	—
380	C₂²×C₃	—	3	4	no	—
381	C₂²×C₃	—	4	2	no	—
382	C₂²×C₃	—	4	1	no	—
383	C₂²×C₃	—	4	2	no	—
384	C₂²×C₃	—	6	2	no	—
385	C₂²×C₃	—	6	2	no	—
386	C₂²×C₃	—	12	4	no	—
387	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
388	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
389	C₂×D₃	—	2	2	no	—
390	C₂×D₃	—	2	2	no	—
391	C₂×D₃	—	4	4	no	—
392	C₂×D₃	C₉×#41	1	4	yes	—
393	C₃×C₄	—	2	2	no	—
394	C₃×C₄	—	2	1	no	—
395	C₃×C₄	—	2	2	no	—
396	C₃×C₄	—	2	2	no	—
397	C₃×C₄	—	2	1	no	—
398	C₃×C₄	—	2	2	no	—
399	C₃×C₄	—	4	2	no	—
400	C₃×C₄	—	4	1	no	—
401	C₃×C₄	—	4	2	no	—
402	C₃×C₄	—	6	2	no	—
403	C₃×C₄	—	6	2	no	—
404	C₃×C₄	—	6	2	no	—
405	Dic₃	—	2	2	no	—
406	Dic₃	—	2	2	no	—
407	Dic₃	—	2	2	no	—
408	C₃²	C₃×#551	1	1	yes	characteristic
409	C₉	—	2	1	no	—
410	C₉	#5659	1	1	yes	characteristic, direct product factor
411	C₂³	—	3	2	no	—
412	C₂³	—	6	4	no	—
413	C₂³	—	12	1	no	—
414	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
415	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
416	Q₈	—	12	1	no	—
417	D₄	—	4	1	no	—
418	D₄	—	6	4	no	—
419	C₂×C₄	—	3	2	no	—
420	C₂×C₄	—	3	2	no	—
421	C₂×C₄	—	3	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	6	4	no	—
424	C₂×C₄	—	12	2	no	—
425	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
426	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
427	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
428	C₂×C₃	—	2	1	no	—
429	C₂×C₃	—	2	2	no	—
430	C₂×C₃	—	4	2	no	—
431	C₂×C₃	—	4	1	no	—
432	C₂×C₃	—	4	1	no	—
433	C₂×C₃	—	4	1	no	—
434	C₂×C₃	—	4	1	no	—
435	C₂×C₃	—	6	4	no	—
436	C₂×C₃	—	8	1	no	—
437	C₂×C₃	C₂×C₉×#41	1	2	yes	—
438	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
439	C₂×C₃	C₃×#1004	1	1	yes	characteristic
440	C₂×C₃	C₃×D₃×#41	1	2	yes	—
441	D₃	—	2	4	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	3	4	no	—
447	C₂²	—	6	2	no	—
448	C₂²	—	6	2	no	—
449	C₂²	—	12	4	no	—
450	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
451	C₄	—	2	2	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	2	no	—
454	C₄	—	6	2	no	—
455	C₄	—	6	2	no	—
456	C₄	—	6	2	no	—
457	C₃	—	2	1	no	—
458	C₃	C₉×#551	1	1	yes	characteristic, complemented
459	C₃	C₃×#5659	1	1	yes	characteristic
460	C₂	—	4	1	no	—
461	C₂	—	4	1	no	—
462	C₂	—	6	4	no	—
463	C₂	C₉×#1004	1	1	yes	characteristic
464	C₂	D₃×C₉×#41	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×#123	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#937	C₂×C₃
hypercenter	C₉×#123	D₃
hypocenter	C₃	C₉×#551
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#123

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#123	C₂	semidirect
3. C₉×#936	C₂	semidirect
4. C₄×C₉×#67	C₂	semidirect
5. C₉×#896	C₂	semidirect
6. C₉×#892	C₂	semidirect
7. C₉×#883	C₂	semidirect
8. D₃×C₉×C₂²⋊C₄	C₂	semidirect
9. C₉×#879	C₂	semidirect
14. C₂²×C₃×C₄×C₉	C₂²	semidirect
18. C₂×C₉×Dic₆	C₂²	semidirect
19. C₃×C₉×C₄⋊C₄	C₂²	semidirect
21. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
24. C₉×#217	C₂²	semidirect
28. C₉×C₄⋊Dic₃	C₂²	semidirect
29. C₉×Dic₃⋊C₄	C₂²	semidirect
30. C₉×Dic₃⋊C₄	C₂²	semidirect
31. C₄×C₉×Dic₃	C₂²	semidirect
32. C₄×C₉×Dic₃	C₂²	semidirect
46. C₉×#123	D₃	semidirect
70. #5659	C₉	direct (N × H)
100. C₂²×C₄×C₉	C₂×D₃	semidirect
105. C₉×C₄⋊C₄	C₂×D₃	semidirect
115. C₉×C₂²⋊C₄	C₂×D₃	semidirect
137. C₃×#123	C₂×C₉	semidirect
145. #936	C₂×C₉	semidirect
146. C₄×#67	C₂×C₉	semidirect
147. #896	C₂×C₉	semidirect
148. #892	C₂×C₉	semidirect
149. #883	C₂×C₉	semidirect
150. D₃×C₂²⋊C₄	C₂×C₉	semidirect
151. #879	C₂×C₉	semidirect
209. C₂²×C₃×C₄	C₂²×C₉	semidirect
214. C₂×Dic₆	C₂²×C₉	semidirect
219. C₃×C₄⋊C₄	C₂²×C₉	semidirect
230. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
237. #217	C₂²×C₉	semidirect
241. C₄⋊Dic₃	C₂²×C₉	semidirect
242. Dic₃⋊C₄	C₂²×C₉	semidirect
243. Dic₃⋊C₄	C₂²×C₉	semidirect
244. C₄×Dic₃	C₂²×C₉	semidirect
245. C₄×Dic₃	C₂²×C₉	semidirect
287. #123	D₃×C₉	semidirect
293. C₃×C₉	#551	semidirect
355. C₂²×C₄	C₂×D₃×C₉	semidirect
359. C₄⋊C₄	C₂×D₃×C₉	semidirect
367. C₂²⋊C₄	C₂×D₃×C₉	semidirect
410. C₉	#5659	direct (N × H)
458. C₃	C₉×#551	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×#123	2
C₉×#937	2
C₉×#936	2
C₄×C₉×#67	2
C₉×#896	2
C₉×#892	2
C₉×#883	2
D₃×C₉×C₂²⋊C₄	2
C₉×#879	2
C₃×#5659	3
C₉×#551	3

Subgroups — C9×#5659 #13153029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5659 #13153029