Subgroups — C₉×#5532 #13152477

Order 1728.

784 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#930	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₉×#67	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#895	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#893	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#892	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#888	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×#875	C₂	1	2	yes	maximal, complemented
11	C₉×#872	C₂	1	2	yes	maximal, complemented
12	C₃×#5532	C₃	1	1	yes	maximal, characteristic
13	C₉×#555	—	3	1	no	maximal
14	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₉×#67	C₂²	1	1	yes	characteristic
16	C₂×C₉×#67	C₂²	1	2	yes	—
17	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
18	C₂×C₉×D₁₂	C₂²	1	2	yes	—
19	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
21	C₂×C₉×Dic₆	C₂²	1	2	yes	—
22	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₃×C₄²×C₉	C₂²	1	2	yes	—
26	C₉×#217	C₂²	1	1	yes	characteristic
27	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
28	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
29	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
30	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
31	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
32	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
33	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
34	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
35	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
36	C₄×C₉×Dic₃	C₂²	1	2	yes	—
37	C₃²×#117	C₂×C₃	1	1	yes	characteristic
38	C₃×#930	C₂×C₃	1	1	yes	characteristic
39	C₃×C₄×#67	C₂×C₃	1	1	yes	characteristic
40	C₃×#895	C₂×C₃	1	1	yes	characteristic
41	C₃×#893	C₂×C₃	1	1	yes	characteristic
42	C₃×#892	C₂×C₃	1	1	yes	characteristic
43	C₃×#888	C₂×C₃	1	1	yes	characteristic
44	C₃×#885	C₂×C₃	1	2	yes	—
45	C₃×#884	C₂×C₃	1	2	yes	—
46	C₃×#875	C₂×C₃	1	2	yes	—
47	C₃×#872	C₂×C₃	1	2	yes	—
48	C₉×C₄⋊Q₈	—	3	1	no	—
49	C₉×#124	—	3	2	no	—
50	C₉×#124	—	3	2	no	—
51	C₉×#121	—	3	1	no	—
52	C₉×#121	—	3	1	no	—
53	C₉×#121	—	3	2	no	—
54	C₄×D₄×C₉	—	3	1	no	—
55	C₄×D₄×C₉	—	3	1	no	—
56	C₉×#117	—	2	1	no	—
57	C₉×#117	—	3	1	no	—
58	C₉×#117	—	3	2	no	—
59	C₉×#117	D₃	1	1	yes	characteristic, complemented
60	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
61	C₂²×D₃×C₉	C₂³	1	2	yes	—
62	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×C₉	—	2	2	no	—
64	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
65	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
66	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₉×#67	—	2	2	no	—
69	C₉×#67	—	4	2	no	—
70	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
71	C₂×C₉×Dic₃	C₂³	1	2	yes	—
72	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
73	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
74	C₉×D₁₂	—	2	2	no	—
75	C₉×D₁₂	—	4	2	no	—
76	C₄×D₃×C₉	—	2	2	no	—
77	C₄×D₃×C₉	—	2	4	no	—
78	C₉×Dic₆	—	4	2	no	—
79	C₃×#555	—	3	1	no	—
80	#5532	C₉	1	1	yes	characteristic, direct product factor
81	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
84	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
86	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
87	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
89	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
90	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
91	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
92	C₃²×C₄²	C₂²×C₃	1	2	yes	—
93	C₃×#217	C₂²×C₃	1	1	yes	characteristic
94	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
95	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
96	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
97	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
98	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
99	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
100	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
101	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
102	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
103	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
104	C₂×Q₈×C₉	—	3	2	no	—
105	C₂×D₄×C₉	—	3	1	no	—
106	C₂×D₄×C₉	—	3	2	no	—
107	C₂×D₄×C₉	—	3	1	no	—
108	C₂×D₄×C₉	—	3	2	no	—
109	C₂²×C₄×C₉	—	2	1	no	—
110	C₂²×C₄×C₉	—	3	2	no	—
111	C₂²×C₄×C₉	—	3	1	no	—
112	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
113	C₉×C₄⋊C₄	—	2	1	no	—
114	C₉×C₄⋊C₄	—	2	1	no	—
115	C₉×C₄⋊C₄	—	3	1	no	—
116	C₉×C₄⋊C₄	—	3	2	no	—
117	C₉×C₄⋊C₄	—	3	1	no	—
118	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
119	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
120	C₉×C₂²⋊C₄	—	2	2	no	—
121	C₉×C₂²⋊C₄	—	3	1	no	—
122	C₉×C₂²⋊C₄	—	3	2	no	—
123	C₉×C₂²⋊C₄	—	3	2	no	—
124	C₉×C₂²⋊C₄	—	3	2	no	—
125	C₉×C₂²⋊C₄	—	3	2	no	—
126	C₉×C₂²⋊C₄	—	3	1	no	—
127	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
128	C₄²×C₉	—	2	2	no	—
129	C₄²×C₉	—	3	2	no	—
130	C₄²×C₉	—	3	1	no	—
131	C₄²×C₉	C₂×D₃	1	2	yes	—
132	C₂²×C₃×C₉	—	2	1	no	—
133	C₂²×C₃×C₉	—	2	1	no	—
134	C₂²×C₃×C₉	—	2	1	no	—
135	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
136	C₂×D₃×C₉	—	2	1	no	—
137	C₂×D₃×C₉	—	2	2	no	—
138	C₂×D₃×C₉	—	2	2	no	—
139	C₂×D₃×C₉	—	2	1	no	—
140	C₂×D₃×C₉	—	2	1	no	—
141	C₂×D₃×C₉	—	2	2	no	—
142	C₃×C₄×C₉	—	2	1	no	—
143	C₃×C₄×C₉	—	2	2	no	—
144	C₃×C₄×C₉	—	2	2	no	—
145	C₃×C₄×C₉	#41	1	2	yes	—
146	C₉×Dic₃	—	2	1	no	—
147	C₉×Dic₃	—	2	1	no	—
148	C₉×Dic₃	—	2	2	no	—
149	C₉×Dic₃	#41	1	2	yes	—
150	C₃×C₄⋊Q₈	—	3	1	no	—
151	C₃×#124	—	3	2	no	—
152	C₃×#124	—	3	2	no	—
153	C₃×#121	—	3	1	no	—
154	C₃×#121	—	3	1	no	—
155	C₃×#121	—	3	2	no	—
156	C₃×C₄×D₄	—	3	1	no	—
157	C₃×C₄×D₄	—	3	1	no	—
158	C₃×#117	—	2	1	no	—
159	C₃×#117	—	3	1	no	—
160	C₃×#117	—	3	2	no	—
161	C₃×#117	C₂×C₉	1	1	yes	characteristic, complemented
162	C₃×#117	C₃×D₃	1	1	yes	characteristic
163	#930	C₂×C₉	1	1	yes	characteristic, complemented
164	C₄×#67	C₂×C₉	1	1	yes	characteristic, complemented
165	#895	C₂×C₉	1	1	yes	characteristic, complemented
166	#893	C₂×C₉	1	1	yes	characteristic, complemented
167	#892	C₂×C₉	1	1	yes	characteristic, complemented
168	#888	C₂×C₉	1	1	yes	characteristic, complemented
169	#885	C₂×C₉	1	2	yes	complemented
170	#884	C₂×C₉	1	2	yes	complemented
171	#875	C₂×C₉	1	2	yes	complemented
172	#872	C₂×C₉	1	2	yes	complemented
173	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
174	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
175	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
176	C₂×C₃²×C₄	—	2	2	no	—
177	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
178	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
179	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
180	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
181	C₃×#67	—	2	2	no	—
182	C₃×#67	—	4	2	no	—
183	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
184	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
185	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
186	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
187	C₃×D₁₂	—	2	2	no	—
188	C₃×D₁₂	—	4	2	no	—
189	C₃×C₄×D₃	—	2	2	no	—
190	C₃×C₄×D₃	—	2	4	no	—
191	C₃×Dic₆	—	4	2	no	—
192	C₂³×C₉	—	2	1	no	—
193	C₂³×C₉	—	3	1	no	—
194	C₂³×C₉	—	3	2	no	—
195	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
196	Q₈×C₉	—	12	2	no	—
197	D₄×C₉	—	6	2	no	—
198	D₄×C₉	—	6	2	no	—
199	D₄×C₉	—	12	2	no	—
200	D₄×C₉	—	12	2	no	—
201	C₂×C₄×C₉	—	2	4	no	—
202	C₂×C₄×C₉	—	2	2	no	—
203	C₂×C₄×C₉	—	2	1	no	—
204	C₂×C₄×C₉	—	2	1	no	—
205	C₂×C₄×C₉	—	2	2	no	—
206	C₂×C₄×C₉	—	2	2	no	—
207	C₂×C₄×C₉	—	3	1	no	—
208	C₂×C₄×C₉	—	3	1	no	—
209	C₂×C₄×C₉	—	3	1	no	—
210	C₂×C₄×C₉	—	3	2	no	—
211	C₂×C₄×C₉	—	6	4	no	—
212	C₂×C₄×C₉	—	6	2	no	—
213	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
214	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
215	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
216	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
217	#555	—	3	1	no	Sylow
218	C₂×C₃×C₉	—	4	1	no	—
219	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
220	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
221	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
222	D₃×C₉	—	4	2	no	—
223	D₃×C₉	—	4	1	no	—
224	C₂×C₃×Q₈	—	3	2	no	—
225	C₂×C₃×D₄	—	3	1	no	—
226	C₂×C₃×D₄	—	3	2	no	—
227	C₂×C₃×D₄	—	3	1	no	—
228	C₂×C₃×D₄	—	3	2	no	—
229	C₂²×C₃×C₄	—	2	1	no	—
230	C₂²×C₃×C₄	—	3	2	no	—
231	C₂²×C₃×C₄	—	3	1	no	—
232	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
233	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
234	C₂×#67	C₂²×C₉	1	1	yes	characteristic
235	C₂×#67	C₂²×C₉	1	2	yes	—
236	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
237	C₂×D₁₂	C₂²×C₉	1	2	yes	—
238	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
239	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
240	C₂×Dic₆	C₂²×C₉	1	2	yes	—
241	C₃×C₄⋊C₄	—	2	1	no	—
242	C₃×C₄⋊C₄	—	2	1	no	—
243	C₃×C₄⋊C₄	—	3	1	no	—
244	C₃×C₄⋊C₄	—	3	2	no	—
245	C₃×C₄⋊C₄	—	3	1	no	—
246	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
247	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
248	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
249	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
250	C₃×C₂²⋊C₄	—	2	2	no	—
251	C₃×C₂²⋊C₄	—	3	1	no	—
252	C₃×C₂²⋊C₄	—	3	2	no	—
253	C₃×C₂²⋊C₄	—	3	2	no	—
254	C₃×C₂²⋊C₄	—	3	2	no	—
255	C₃×C₂²⋊C₄	—	3	2	no	—
256	C₃×C₂²⋊C₄	—	3	1	no	—
257	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
258	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
259	C₃×C₄²	—	2	2	no	—
260	C₃×C₄²	—	3	2	no	—
261	C₃×C₄²	—	3	1	no	—
262	C₃×C₄²	C₂²×C₉	1	2	yes	—
263	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
264	#217	C₂²×C₉	1	1	yes	characteristic
265	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
266	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
267	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
268	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
269	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
270	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
271	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
272	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
273	C₄×Dic₃	C₂²×C₉	1	2	yes	—
274	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
275	C₂²×C₃²	—	2	1	no	—
276	C₂²×C₃²	—	2	1	no	—
277	C₂²×C₃²	—	2	1	no	—
278	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
279	C₂×C₃×D₃	—	2	1	no	—
280	C₂×C₃×D₃	—	2	2	no	—
281	C₂×C₃×D₃	—	2	2	no	—
282	C₂×C₃×D₃	—	2	1	no	—
283	C₂×C₃×D₃	—	2	1	no	—
284	C₂×C₃×D₃	—	2	2	no	—
285	C₃²×C₄	—	2	1	no	—
286	C₃²×C₄	—	2	2	no	—
287	C₃²×C₄	—	2	2	no	—
288	C₃²×C₄	C₃×#41	1	2	yes	—
289	C₃×Dic₃	—	2	1	no	—
290	C₃×Dic₃	—	2	1	no	—
291	C₃×Dic₃	—	2	2	no	—
292	C₃×Dic₃	C₃×#41	1	2	yes	—
293	C₂²×C₉	—	2	2	no	—
294	C₂²×C₉	—	2	1	no	—
295	C₂²×C₉	—	2	1	no	—
296	C₂²×C₉	—	2	1	no	—
297	C₂²×C₉	—	2	1	no	—
298	C₂²×C₉	—	4	1	no	—
299	C₂²×C₉	—	4	1	no	—
300	C₂²×C₉	—	6	1	no	—
301	C₂²×C₉	—	6	2	no	—
302	C₂²×C₉	—	6	2	no	—
303	C₂²×C₉	—	6	1	no	—
304	C₂²×C₉	—	6	1	no	—
305	C₂²×C₉	—	6	2	no	—
306	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
307	C₄×C₉	—	2	2	no	—
308	C₄×C₉	—	2	1	no	—
309	C₄×C₉	—	2	2	no	—
310	C₄×C₉	—	2	2	no	—
311	C₄×C₉	—	2	2	no	—
312	C₄×C₉	—	3	2	no	—
313	C₄×C₉	—	4	2	no	—
314	C₄×C₉	—	4	2	no	—
315	C₄×C₉	—	6	1	no	—
316	C₄×C₉	—	6	2	no	—
317	C₄×C₉	—	6	1	no	—
318	C₄×C₉	#235	1	2	yes	—
319	C₄⋊Q₈	—	3	1	no	—
320	#124	—	3	2	no	—
321	#124	—	3	2	no	—
322	#121	—	3	1	no	—
323	#121	—	3	1	no	—
324	#121	—	3	2	no	—
325	C₄×D₄	—	3	1	no	—
326	C₄×D₄	—	3	1	no	—
327	#117	—	3	1	no	—
328	#117	—	3	2	no	—
329	#117	D₃×C₉	1	1	yes	characteristic, complemented
330	C₃×C₉	#555	1	1	yes	characteristic, complemented, Sylow
331	C₂³×C₃	—	2	1	no	—
332	C₂³×C₃	—	3	1	no	—
333	C₂³×C₃	—	3	2	no	—
334	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
335	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
336	C₂²×D₃	C₂³×C₉	1	2	yes	—
337	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
338	C₃×Q₈	—	12	2	no	—
339	C₃×D₄	—	6	2	no	—
340	C₃×D₄	—	6	2	no	—
341	C₃×D₄	—	12	2	no	—
342	C₃×D₄	—	12	2	no	—
343	C₂×C₃×C₄	—	2	4	no	—
344	C₂×C₃×C₄	—	2	2	no	—
345	C₂×C₃×C₄	—	2	2	no	—
346	C₂×C₃×C₄	—	2	1	no	—
347	C₂×C₃×C₄	—	2	1	no	—
348	C₂×C₃×C₄	—	2	2	no	—
349	C₂×C₃×C₄	—	2	2	no	—
350	C₂×C₃×C₄	—	3	1	no	—
351	C₂×C₃×C₄	—	3	1	no	—
352	C₂×C₃×C₄	—	3	1	no	—
353	C₂×C₃×C₄	—	3	2	no	—
354	C₂×C₃×C₄	—	6	4	no	—
355	C₂×C₃×C₄	—	6	2	no	—
356	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
357	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
358	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
359	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
360	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
361	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
362	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
363	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
364	#67	—	2	2	no	—
365	#67	—	4	2	no	—
366	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
367	C₂×Dic₃	C₂³×C₉	1	2	yes	—
368	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
369	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
370	D₁₂	—	2	2	no	—
371	D₁₂	—	4	2	no	—
372	C₄×D₃	—	2	2	no	—
373	C₄×D₃	—	2	4	no	—
374	Dic₆	—	4	2	no	—
375	C₂×C₃²	—	4	1	no	—
376	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
377	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
378	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
379	C₃×D₃	—	4	2	no	—
380	C₃×D₃	—	4	1	no	—
381	C₂×C₉	—	2	1	no	—
382	C₂×C₉	—	2	1	no	—
383	C₂×C₉	—	2	1	no	—
384	C₂×C₉	—	4	2	no	—
385	C₂×C₉	—	4	1	no	—
386	C₂×C₉	—	12	1	no	—
387	C₂×C₉	—	12	2	no	—
388	C₂×C₉	C₂×#235	1	1	yes	characteristic
389	C₂×C₉	D₃×#41	1	1	yes	characteristic
390	C₂×C₉	#1009	1	1	yes	characteristic
391	C₂×Q₈	—	3	2	no	—
392	C₂×D₄	—	3	1	no	—
393	C₂×D₄	—	3	2	no	—
394	C₂×D₄	—	3	1	no	—
395	C₂×D₄	—	3	2	no	—
396	C₂²×C₄	—	3	2	no	—
397	C₂²×C₄	—	3	1	no	—
398	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
399	C₄⋊C₄	—	3	1	no	—
400	C₄⋊C₄	—	3	2	no	—
401	C₄⋊C₄	—	3	1	no	—
402	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
403	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
404	C₂²⋊C₄	—	3	1	no	—
405	C₂²⋊C₄	—	3	2	no	—
406	C₂²⋊C₄	—	3	2	no	—
407	C₂²⋊C₄	—	3	2	no	—
408	C₂²⋊C₄	—	3	2	no	—
409	C₂²⋊C₄	—	3	1	no	—
410	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
411	C₄²	—	3	2	no	—
412	C₄²	—	3	1	no	—
413	C₄²	C₂×D₃×C₉	1	2	yes	—
414	C₂²×C₃	—	2	2	no	—
415	C₂²×C₃	—	2	1	no	—
416	C₂²×C₃	—	2	1	no	—
417	C₂²×C₃	—	2	1	no	—
418	C₂²×C₃	—	2	1	no	—
419	C₂²×C₃	—	2	1	no	—
420	C₂²×C₃	—	2	1	no	—
421	C₂²×C₃	—	2	1	no	—
422	C₂²×C₃	—	4	1	no	—
423	C₂²×C₃	—	4	1	no	—
424	C₂²×C₃	—	6	1	no	—
425	C₂²×C₃	—	6	2	no	—
426	C₂²×C₃	—	6	2	no	—
427	C₂²×C₃	—	6	1	no	—
428	C₂²×C₃	—	6	1	no	—
429	C₂²×C₃	—	6	2	no	—
430	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
431	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
432	C₂×D₃	—	2	1	no	—
433	C₂×D₃	—	2	2	no	—
434	C₂×D₃	—	2	2	no	—
435	C₂×D₃	—	2	1	no	—
436	C₂×D₃	—	2	1	no	—
437	C₂×D₃	—	2	2	no	—
438	C₃×C₄	—	2	2	no	—
439	C₃×C₄	—	2	1	no	—
440	C₃×C₄	—	2	2	no	—
441	C₃×C₄	—	2	2	no	—
442	C₃×C₄	—	2	2	no	—
443	C₃×C₄	—	2	1	no	—
444	C₃×C₄	—	2	2	no	—
445	C₃×C₄	—	2	2	no	—
446	C₃×C₄	—	3	2	no	—
447	C₃×C₄	—	4	2	no	—
448	C₃×C₄	—	4	2	no	—
449	C₃×C₄	—	6	1	no	—
450	C₃×C₄	—	6	2	no	—
451	C₃×C₄	—	6	1	no	—
452	C₃×C₄	C₉×#41	1	2	yes	—
453	C₃×C₄	C₃×#235	1	2	yes	—
454	Dic₃	—	2	1	no	—
455	Dic₃	—	2	1	no	—
456	Dic₃	—	2	2	no	—
457	Dic₃	C₉×#41	1	2	yes	—
458	C₃²	C₃×#555	1	1	yes	characteristic
459	C₉	—	2	1	no	—
460	C₉	#5532	1	1	yes	characteristic, direct product factor
461	C₂³	—	3	1	no	—
462	C₂³	—	3	2	no	—
463	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
464	Q₈	—	12	2	no	—
465	D₄	—	6	2	no	—
466	D₄	—	6	2	no	—
467	D₄	—	12	2	no	—
468	D₄	—	12	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	3	1	no	—
471	C₂×C₄	—	3	1	no	—
472	C₂×C₄	—	3	1	no	—
473	C₂×C₄	—	3	2	no	—
474	C₂×C₄	—	6	4	no	—
475	C₂×C₄	—	6	2	no	—
476	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
477	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
478	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
479	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
480	C₂×C₃	—	2	1	no	—
481	C₂×C₃	—	2	1	no	—
482	C₂×C₃	—	2	1	no	—
483	C₂×C₃	—	4	2	no	—
484	C₂×C₃	—	4	1	no	—
485	C₂×C₃	—	4	1	no	—
486	C₂×C₃	—	12	1	no	—
487	C₂×C₃	—	12	2	no	—
488	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
489	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
490	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
491	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
492	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
493	C₂×C₃	C₃×#1009	1	1	yes	characteristic
494	D₃	—	4	2	no	—
495	D₃	—	4	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	6	1	no	—
500	C₂²	—	6	2	no	—
501	C₂²	—	6	2	no	—
502	C₂²	—	6	1	no	—
503	C₂²	—	6	1	no	—
504	C₂²	—	6	2	no	—
505	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	3	2	no	—
510	C₄	—	6	1	no	—
511	C₄	—	6	2	no	—
512	C₄	—	6	1	no	—
513	C₄	C₉×#235	1	2	yes	—
514	C₃	—	2	1	no	—
515	C₃	C₉×#555	1	1	yes	characteristic, complemented
516	C₃	C₃×#5532	1	1	yes	characteristic
517	C₂	—	4	1	no	—
518	C₂	—	12	1	no	—
519	C₂	—	12	2	no	—
520	C₂	C₂×C₉×#235	1	1	yes	characteristic
521	C₂	D₃×C₉×#41	1	1	yes	characteristic
522	C₂	C₉×#1009	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×#117	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5532	C₃
hypercenter	C₉×#117	D₃
hypocenter	C₃	C₉×#555
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#117

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#117	C₂	semidirect
2. C₉×#930	C₂	semidirect
3. C₄×C₉×#67	C₂	semidirect
4. C₉×#895	C₂	semidirect
5. C₉×#893	C₂	semidirect
6. C₉×#892	C₂	semidirect
7. C₉×#888	C₂	semidirect
8. C₉×#885	C₂	semidirect
9. C₉×#884	C₂	semidirect
10. C₉×#875	C₂	semidirect
11. C₉×#872	C₂	semidirect
59. C₉×#117	D₃	semidirect
80. #5532	C₉	direct (N × H)
161. C₃×#117	C₂×C₉	semidirect
163. #930	C₂×C₉	semidirect
164. C₄×#67	C₂×C₉	semidirect
165. #895	C₂×C₉	semidirect
166. #893	C₂×C₉	semidirect
167. #892	C₂×C₉	semidirect
168. #888	C₂×C₉	semidirect
169. #885	C₂×C₉	semidirect
170. #884	C₂×C₉	semidirect
171. #875	C₂×C₉	semidirect
172. #872	C₂×C₉	semidirect
329. #117	D₃×C₉	semidirect
330. C₃×C₉	#555	semidirect
460. C₉	#5532	direct (N × H)
515. C₃	C₉×#555	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×#117	2
C₉×#930	2
C₄×C₉×#67	2
C₉×#895	2
C₉×#893	2
C₉×#892	2
C₉×#888	2
C₉×#885	2
C₉×#884	2
C₉×#875	2
C₉×#872	2
C₃×#5532	3
C₉×#555	3

Subgroups — C9×#5532 #13152477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5532 #13152477