Subgroups — C₉×#5694 #13153169

Order 1728.

698 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#898	C₂	1	2	yes	maximal, complemented
3	C₉×#897	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#897	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#894	C₂	1	2	yes	maximal
6	C₉×#892	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#892	C₂	1	2	yes	maximal, complemented
8	D₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#890	C₂	1	2	yes	maximal, complemented
10	C₄×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic
11	C₄×C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5694	C₃	1	1	yes	maximal, characteristic
13	C₉×#552	—	3	1	no	maximal
14	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
18	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
19	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
20	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
23	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
24	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
25	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
26	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
27	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
29	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
30	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
31	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
32	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
33	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
34	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
35	C₄×C₉×Dic₃	C₂²	1	2	yes	—
36	C₄×C₉×Dic₃	C₂²	1	2	yes	—
37	C₃²×#125	C₂×C₃	1	1	yes	characteristic
38	C₃×#898	C₂×C₃	1	2	yes	—
39	C₃×#897	C₂×C₃	1	1	yes	characteristic
40	C₃×#897	C₂×C₃	1	1	yes	characteristic
41	C₃×#894	C₂×C₃	1	2	yes	—
42	C₃×#892	C₂×C₃	1	1	yes	characteristic
43	C₃×#892	C₂×C₃	1	2	yes	—
44	C₃×D₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
45	C₃×#890	C₂×C₃	1	2	yes	—
46	C₃×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
47	C₃×C₄×Dic₆	C₂×C₃	1	1	yes	characteristic
48	C₉×#126	—	3	2	no	—
49	C₉×#125	—	2	1	no	—
50	C₉×#125	—	3	2	no	—
51	C₉×#125	D₃	1	1	yes	characteristic, complemented
52	C₉×#123	—	3	2	no	—
53	C₉×C₂²⋊Q₈	—	3	1	no	—
54	C₉×C₂²⋊Q₈	—	3	1	no	—
55	C₄×Q₈×C₉	—	3	1	no	—
56	C₄×D₄×C₉	—	3	1	no	—
57	C₉×#117	—	3	1	no	—
58	C₉×#117	—	3	2	no	—
59	C₂×C₉×C₄⋊C₄	—	3	1	no	—
60	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
61	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
63	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
66	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂×C₉×Dic₃	C₂³	1	2	yes	—
68	C₂×C₉×Dic₃	C₂³	1	2	yes	—
69	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
70	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
71	C₉×D₁₂	—	2	2	no	—
72	C₄×D₃×C₉	—	2	4	no	—
73	C₄×D₃×C₉	—	2	2	no	—
74	C₄×D₃×C₉	—	2	2	no	—
75	C₉×Dic₆	—	2	2	no	—
76	C₃×#552	—	3	1	no	—
77	#5694	C₉	1	1	yes	characteristic, direct product factor
78	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
80	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
83	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
84	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
85	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
87	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
88	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
90	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
91	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
92	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
93	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
94	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
95	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
96	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
97	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
98	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
99	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
100	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
101	C₂×Q₈×C₉	—	3	1	no	—
102	C₂×D₄×C₉	—	3	1	no	—
103	C₂²×C₄×C₉	—	3	2	no	—
104	C₂²×C₄×C₉	—	3	1	no	—
105	C₂²×C₄×C₉	—	3	1	no	—
106	C₉×C₄⋊C₄	—	2	1	no	—
107	C₉×C₄⋊C₄	—	2	1	no	—
108	C₉×C₄⋊C₄	—	2	2	no	—
109	C₉×C₄⋊C₄	—	2	2	no	—
110	C₉×C₄⋊C₄	—	3	1	no	—
111	C₉×C₄⋊C₄	—	3	2	no	—
112	C₉×C₄⋊C₄	—	3	2	no	—
113	C₉×C₄⋊C₄	—	3	1	no	—
114	C₉×C₄⋊C₄	—	3	2	no	—
115	C₉×C₄⋊C₄	—	3	2	no	—
116	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
117	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
118	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
119	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
120	C₉×C₂²⋊C₄	—	3	1	no	—
121	C₉×C₂²⋊C₄	—	3	2	no	—
122	C₉×C₂²⋊C₄	—	3	2	no	—
123	C₉×C₂²⋊C₄	—	3	1	no	—
124	C₉×C₂²⋊C₄	—	3	2	no	—
125	C₄²×C₉	—	2	1	no	—
126	C₄²×C₉	—	3	2	no	—
127	C₄²×C₉	—	3	2	no	—
128	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
129	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
130	C₂×D₃×C₉	—	2	1	no	—
131	C₂×D₃×C₉	—	2	1	no	—
132	C₂×D₃×C₉	—	2	1	no	—
133	C₂×D₃×C₉	—	2	1	no	—
134	C₂×D₃×C₉	—	2	1	no	—
135	C₂×D₃×C₉	#41	1	2	yes	—
136	C₃×C₄×C₉	—	2	2	no	—
137	C₃×C₄×C₉	—	2	1	no	—
138	C₃×C₄×C₉	—	2	1	no	—
139	C₃×C₄×C₉	—	2	2	no	—
140	C₃×C₄×C₉	#41	1	2	yes	—
141	C₉×Dic₃	—	2	2	no	—
142	C₉×Dic₃	—	2	1	no	—
143	C₉×Dic₃	—	2	1	no	—
144	C₉×Dic₃	—	2	2	no	—
145	C₃×#126	—	3	2	no	—
146	C₃×#125	—	2	1	no	—
147	C₃×#125	—	3	2	no	—
148	C₃×#125	C₂×C₉	1	1	yes	characteristic, complemented
149	C₃×#125	C₃×D₃	1	1	yes	characteristic
150	C₃×#123	—	3	2	no	—
151	C₃×C₂²⋊Q₈	—	3	1	no	—
152	C₃×C₂²⋊Q₈	—	3	1	no	—
153	C₃×C₄×Q₈	—	3	1	no	—
154	C₃×C₄×D₄	—	3	1	no	—
155	C₃×#117	—	3	1	no	—
156	C₃×#117	—	3	2	no	—
157	C₂×C₃×C₄⋊C₄	—	3	1	no	—
158	#898	C₂×C₉	1	2	yes	complemented
159	#897	C₂×C₉	1	1	yes	characteristic, complemented
160	#897	C₂×C₉	1	1	yes	characteristic, complemented
161	#894	C₂×C₉	1	2	yes	—
162	#892	C₂×C₉	1	2	yes	complemented
163	#892	C₂×C₉	1	1	yes	characteristic, complemented
164	D₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
165	#890	C₂×C₉	1	2	yes	complemented
166	C₄×D₁₂	C₂×C₉	1	1	yes	characteristic
167	C₄×Dic₆	C₂×C₉	1	1	yes	characteristic, complemented
168	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
169	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
170	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
171	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
172	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
173	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
174	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
175	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
176	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
177	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
178	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
179	C₃×D₁₂	—	2	2	no	—
180	C₃×C₄×D₃	—	2	4	no	—
181	C₃×C₄×D₃	—	2	2	no	—
182	C₃×C₄×D₃	—	2	2	no	—
183	C₃×Dic₆	—	2	2	no	—
184	C₂³×C₉	—	3	1	no	—
185	C₂³×C₉	—	3	1	no	—
186	Q₈×C₉	—	6	2	no	—
187	D₄×C₉	—	6	2	no	—
188	C₂×C₄×C₉	—	2	1	no	—
189	C₂×C₄×C₉	—	2	1	no	—
190	C₂×C₄×C₉	—	2	1	no	—
191	C₂×C₄×C₉	—	2	2	no	—
192	C₂×C₄×C₉	—	2	2	no	—
193	C₂×C₄×C₉	—	3	1	no	—
194	C₂×C₄×C₉	—	3	2	no	—
195	C₂×C₄×C₉	—	3	2	no	—
196	C₂×C₄×C₉	—	3	1	no	—
197	C₂×C₄×C₉	—	6	4	no	—
198	C₂×C₄×C₉	—	6	2	no	—
199	C₂×C₄×C₉	—	6	2	no	—
200	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
201	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
202	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
203	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
204	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
205	#552	—	3	1	no	Sylow
206	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
207	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
208	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
209	D₃×C₉	—	2	2	no	—
210	D₃×C₉	—	4	1	no	—
211	C₂×C₃×Q₈	—	3	1	no	—
212	C₂×C₃×D₄	—	3	1	no	—
213	C₂²×C₃×C₄	—	3	2	no	—
214	C₂²×C₃×C₄	—	3	1	no	—
215	C₂²×C₃×C₄	—	3	1	no	—
216	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
217	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
218	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
219	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
220	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
221	C₃×C₄⋊C₄	—	2	1	no	—
222	C₃×C₄⋊C₄	—	2	1	no	—
223	C₃×C₄⋊C₄	—	2	2	no	—
224	C₃×C₄⋊C₄	—	2	2	no	—
225	C₃×C₄⋊C₄	—	3	2	no	—
226	C₃×C₄⋊C₄	—	3	2	no	—
227	C₃×C₄⋊C₄	—	3	1	no	—
228	C₃×C₄⋊C₄	—	3	2	no	—
229	C₃×C₄⋊C₄	—	3	1	no	—
230	C₃×C₄⋊C₄	—	3	2	no	—
231	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
232	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
233	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
234	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
235	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
236	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
237	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
238	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
239	C₃×C₂²⋊C₄	—	3	1	no	—
240	C₃×C₂²⋊C₄	—	3	2	no	—
241	C₃×C₂²⋊C₄	—	3	2	no	—
242	C₃×C₂²⋊C₄	—	3	1	no	—
243	C₃×C₂²⋊C₄	—	3	2	no	—
244	C₃×C₄²	—	2	1	no	—
245	C₃×C₄²	—	3	2	no	—
246	C₃×C₄²	—	3	2	no	—
247	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
248	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
249	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
250	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
251	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
252	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
253	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
254	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
255	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
256	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
257	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
258	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
259	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
260	C₄×Dic₃	C₂²×C₉	1	2	yes	—
261	C₄×Dic₃	C₂²×C₉	1	2	yes	—
262	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
263	C₂×C₃×D₃	—	2	1	no	—
264	C₂×C₃×D₃	—	2	1	no	—
265	C₂×C₃×D₃	—	2	1	no	—
266	C₂×C₃×D₃	—	2	1	no	—
267	C₂×C₃×D₃	—	2	1	no	—
268	C₂×C₃×D₃	C₃×#41	1	2	yes	—
269	C₃²×C₄	—	2	2	no	—
270	C₃²×C₄	—	2	1	no	—
271	C₃²×C₄	—	2	1	no	—
272	C₃²×C₄	—	2	2	no	—
273	C₃²×C₄	C₃×#41	1	2	yes	—
274	C₃×Dic₃	—	2	2	no	—
275	C₃×Dic₃	—	2	1	no	—
276	C₃×Dic₃	—	2	1	no	—
277	C₃×Dic₃	—	2	2	no	—
278	C₂²×C₉	—	2	1	no	—
279	C₂²×C₉	—	3	2	no	—
280	C₂²×C₉	—	6	1	no	—
281	C₂²×C₉	—	6	1	no	—
282	C₂²×C₉	—	6	1	no	—
283	C₂²×C₉	—	6	1	no	—
284	C₂²×C₉	—	6	1	no	—
285	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
286	C₄×C₉	—	2	2	no	—
287	C₄×C₉	—	2	1	no	—
288	C₄×C₉	—	2	1	no	—
289	C₄×C₉	—	2	2	no	—
290	C₄×C₉	—	2	2	no	—
291	C₄×C₉	—	4	2	no	—
292	C₄×C₉	—	4	1	no	—
293	C₄×C₉	—	4	1	no	—
294	C₄×C₉	—	4	2	no	—
295	C₄×C₉	—	6	1	no	—
296	C₄×C₉	—	6	1	no	—
297	C₄×C₉	—	6	2	no	—
298	C₄×C₉	—	6	2	no	—
299	C₄×C₉	#239	1	2	yes	—
300	#126	—	3	2	no	—
301	#125	—	3	2	no	—
302	#125	D₃×C₉	1	1	yes	characteristic, complemented
303	#123	—	3	2	no	—
304	C₂²⋊Q₈	—	3	1	no	—
305	C₂²⋊Q₈	—	3	1	no	—
306	C₄×Q₈	—	3	1	no	—
307	C₄×D₄	—	3	1	no	—
308	#117	—	3	1	no	—
309	#117	—	3	2	no	—
310	C₂×C₄⋊C₄	—	3	1	no	—
311	C₃×C₉	#552	1	1	yes	characteristic, complemented, Sylow
312	C₂³×C₃	—	3	1	no	—
313	C₂³×C₃	—	3	1	no	—
314	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
315	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
316	C₃×Q₈	—	6	2	no	—
317	C₃×D₄	—	6	2	no	—
318	C₂×C₃×C₄	—	2	1	no	—
319	C₂×C₃×C₄	—	2	1	no	—
320	C₂×C₃×C₄	—	2	1	no	—
321	C₂×C₃×C₄	—	2	2	no	—
322	C₂×C₃×C₄	—	2	2	no	—
323	C₂×C₃×C₄	—	3	1	no	—
324	C₂×C₃×C₄	—	3	2	no	—
325	C₂×C₃×C₄	—	3	2	no	—
326	C₂×C₃×C₄	—	3	1	no	—
327	C₂×C₃×C₄	—	6	4	no	—
328	C₂×C₃×C₄	—	6	2	no	—
329	C₂×C₃×C₄	—	6	2	no	—
330	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
331	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
332	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
334	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
336	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
337	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
338	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
339	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
340	C₂×Dic₃	C₂³×C₉	1	2	yes	—
341	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
342	C₂×Dic₃	C₂³×C₉	1	2	yes	—
343	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
344	D₁₂	—	2	2	no	—
345	C₄×D₃	—	2	4	no	—
346	C₄×D₃	—	2	2	no	—
347	C₄×D₃	—	2	2	no	—
348	Dic₆	—	2	2	no	—
349	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
350	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
351	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
352	C₃×D₃	—	2	2	no	—
353	C₃×D₃	—	4	1	no	—
354	C₂×C₉	—	2	1	no	—
355	C₂×C₉	—	2	1	no	—
356	C₂×C₉	—	2	1	no	—
357	C₂×C₉	—	6	2	no	—
358	C₂×C₉	—	12	1	no	—
359	C₂×C₉	C₂×#239	1	1	yes	characteristic
360	C₂×C₉	D₃×#41	1	1	yes	characteristic
361	C₂×C₉	#1010	1	1	yes	characteristic
362	C₂×Q₈	—	3	1	no	—
363	C₂×D₄	—	3	1	no	—
364	C₂²×C₄	—	3	2	no	—
365	C₂²×C₄	—	3	1	no	—
366	C₂²×C₄	—	3	1	no	—
367	C₄⋊C₄	—	3	1	no	—
368	C₄⋊C₄	—	3	2	no	—
369	C₄⋊C₄	—	3	2	no	—
370	C₄⋊C₄	—	3	1	no	—
371	C₄⋊C₄	—	3	2	no	—
372	C₄⋊C₄	—	3	2	no	—
373	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
374	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
375	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
376	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
377	C₂²⋊C₄	—	3	1	no	—
378	C₂²⋊C₄	—	3	2	no	—
379	C₂²⋊C₄	—	3	2	no	—
380	C₂²⋊C₄	—	3	1	no	—
381	C₂²⋊C₄	—	3	2	no	—
382	C₄²	—	3	2	no	—
383	C₄²	—	3	2	no	—
384	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
385	C₂²×C₃	—	2	1	no	—
386	C₂²×C₃	—	3	2	no	—
387	C₂²×C₃	—	6	1	no	—
388	C₂²×C₃	—	6	1	no	—
389	C₂²×C₃	—	6	1	no	—
390	C₂²×C₃	—	6	1	no	—
391	C₂²×C₃	—	6	1	no	—
392	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
393	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
394	C₂×D₃	—	2	1	no	—
395	C₂×D₃	—	2	1	no	—
396	C₂×D₃	—	2	1	no	—
397	C₂×D₃	—	2	1	no	—
398	C₂×D₃	—	2	1	no	—
399	C₂×D₃	C₉×#41	1	2	yes	—
400	C₃×C₄	—	2	2	no	—
401	C₃×C₄	—	2	1	no	—
402	C₃×C₄	—	2	1	no	—
403	C₃×C₄	—	2	2	no	—
404	C₃×C₄	—	2	2	no	—
405	C₃×C₄	—	2	1	no	—
406	C₃×C₄	—	2	1	no	—
407	C₃×C₄	—	2	2	no	—
408	C₃×C₄	—	2	2	no	—
409	C₃×C₄	—	4	2	no	—
410	C₃×C₄	—	4	1	no	—
411	C₃×C₄	—	4	1	no	—
412	C₃×C₄	—	4	2	no	—
413	C₃×C₄	—	6	1	no	—
414	C₃×C₄	—	6	1	no	—
415	C₃×C₄	—	6	2	no	—
416	C₃×C₄	—	6	2	no	—
417	C₃×C₄	C₉×#41	1	2	yes	—
418	C₃×C₄	C₃×#239	1	2	yes	—
419	Dic₃	—	2	2	no	—
420	Dic₃	—	2	1	no	—
421	Dic₃	—	2	1	no	—
422	Dic₃	—	2	2	no	—
423	C₃²	C₃×#552	1	1	yes	characteristic
424	C₉	—	2	1	no	—
425	C₉	#5694	1	1	yes	characteristic, direct product factor
426	C₂³	—	3	1	no	—
427	C₂³	—	3	1	no	—
428	Q₈	—	6	2	no	—
429	D₄	—	6	2	no	—
430	C₂×C₄	—	3	1	no	—
431	C₂×C₄	—	3	2	no	—
432	C₂×C₄	—	3	2	no	—
433	C₂×C₄	—	3	1	no	—
434	C₂×C₄	—	6	4	no	—
435	C₂×C₄	—	6	2	no	—
436	C₂×C₄	—	6	2	no	—
437	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
438	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
439	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
440	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
441	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
442	C₂×C₃	—	2	1	no	—
443	C₂×C₃	—	2	1	no	—
444	C₂×C₃	—	2	1	no	—
445	C₂×C₃	—	6	2	no	—
446	C₂×C₃	—	12	1	no	—
447	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
448	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
449	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
450	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
451	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
452	C₂×C₃	C₃×#1010	1	1	yes	characteristic
453	D₃	—	2	2	no	—
454	D₃	—	4	1	no	—
455	C₂²	—	3	2	no	—
456	C₂²	—	6	1	no	—
457	C₂²	—	6	1	no	—
458	C₂²	—	6	1	no	—
459	C₂²	—	6	1	no	—
460	C₂²	—	6	1	no	—
461	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	2	no	—
466	C₄	—	6	1	no	—
467	C₄	—	6	1	no	—
468	C₄	—	6	2	no	—
469	C₄	—	6	2	no	—
470	C₄	C₉×#239	1	2	yes	—
471	C₃	—	2	1	no	—
472	C₃	C₉×#552	1	1	yes	characteristic, complemented
473	C₃	C₃×#5694	1	1	yes	characteristic
474	C₂	—	6	2	no	—
475	C₂	—	12	1	no	—
476	C₂	C₂×C₉×#239	1	1	yes	characteristic
477	C₂	D₃×C₉×#41	1	1	yes	characteristic
478	C₂	C₉×#1010	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×#125	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂×C₃×D₁₂	C₂²×C₃
hypercenter	C₉×#125	D₃
hypocenter	C₃	C₉×#552
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#125

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#125	C₂	semidirect
2. C₉×#898	C₂	semidirect
3. C₉×#897	C₂	semidirect
4. C₉×#897	C₂	semidirect
6. C₉×#892	C₂	semidirect
7. C₉×#892	C₂	semidirect
8. D₃×C₉×C₄⋊C₄	C₂	semidirect
9. C₉×#890	C₂	semidirect
11. C₄×C₉×Dic₆	C₂	semidirect
51. C₉×#125	D₃	semidirect
77. #5694	C₉	direct (N × H)
148. C₃×#125	C₂×C₉	semidirect
158. #898	C₂×C₉	semidirect
159. #897	C₂×C₉	semidirect
160. #897	C₂×C₉	semidirect
162. #892	C₂×C₉	semidirect
163. #892	C₂×C₉	semidirect
164. D₃×C₄⋊C₄	C₂×C₉	semidirect
165. #890	C₂×C₉	semidirect
167. C₄×Dic₆	C₂×C₉	semidirect
302. #125	D₃×C₉	semidirect
311. C₃×C₉	#552	semidirect
425. C₉	#5694	direct (N × H)
472. C₃	C₉×#552	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×#125	2
C₉×#898	2
C₉×#897	2
C₉×#894	2
C₉×#892	2
D₃×C₉×C₄⋊C₄	2
C₉×#890	2
C₄×C₉×D₁₂	2
C₄×C₉×Dic₆	2
C₃×#5694	3
C₉×#552	3

Subgroups — C9×#5694 #13153169

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5694 #13153169