Subgroups — C₉×#5695 #13153170

Order 1728.

770 conjugacy classes of subgroups.

The subgroup lattice has 516 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×#895	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#895	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#895	C₂	1	2	yes	maximal, complemented
6	C₉×#894	C₂	1	2	yes	maximal, complemented
7	C₉×#893	C₂	1	2	yes	maximal, complemented
8	C₉×#892	C₂	1	1	yes	maximal, characteristic, complemented
9	D₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5695	C₃	1	1	yes	maximal, characteristic
13	C₉×#553	—	3	1	no	maximal
14	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
15	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
16	C₂×C₉×D₁₂	C₂²	1	2	yes	—
17	C₂×C₉×D₁₂	C₂²	1	2	yes	—
18	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
21	C₂×C₄×D₃×C₉	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×C₄⋊C₄	C₂²	1	2	yes	—
25	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
26	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
27	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
28	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
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×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
33	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
34	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
35	C₉×Dic₃⋊C₄	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×#895	C₂×C₃	1	2	yes	—
40	C₃×#895	C₂×C₃	1	1	yes	characteristic
41	C₃×#895	C₂×C₃	1	1	yes	characteristic
42	C₃×#894	C₂×C₃	1	2	yes	—
43	C₃×#893	C₂×C₃	1	2	yes	—
44	C₃×#892	C₂×C₃	1	1	yes	characteristic
45	C₃×D₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
46	C₃×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
47	C₃×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
48	C₉×#126	—	3	2	no	—
49	C₉×#125	—	2	1	no	—
50	C₉×#125	D₃	1	1	yes	characteristic, complemented
51	C₉×#123	—	3	2	no	—
52	C₉×#121	—	3	2	no	—
53	C₉×#121	—	3	1	no	—
54	C₉×#121	—	3	1	no	—
55	C₄×D₄×C₉	—	3	2	no	—
56	C₄×D₄×C₉	—	3	1	no	—
57	C₄×D₄×C₉	—	3	1	no	—
58	C₉×#117	—	3	1	no	—
59	C₂×C₉×C₄⋊C₄	—	3	1	no	—
60	C₂²×D₃×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	C₂³	1	1	yes	characteristic
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	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	C₉×D₁₂	—	2	4	no	—
73	C₉×D₁₂	—	2	2	no	—
74	C₉×D₁₂	—	4	2	no	—
75	C₄×D₃×C₉	—	2	2	no	—
76	C₄×D₃×C₉	—	2	2	no	—
77	C₄×D₃×C₉	—	4	2	no	—
78	C₄×D₃×C₉	—	4	2	no	—
79	C₃×#553	—	3	1	no	—
80	#5695	C₉	1	1	yes	characteristic, direct product factor
81	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
82	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
85	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
88	C₂×C₃×C₄×D₃	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×C₄⋊C₄	C₂²×C₃	1	2	yes	—
92	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
93	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
94	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
95	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
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×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
100	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
101	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
102	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
103	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
104	C₂×D₄×C₉	—	3	2	no	—
105	C₂×D₄×C₉	—	3	1	no	—
106	C₂×D₄×C₉	—	3	1	no	—
107	C₂×D₄×C₉	—	3	2	no	—
108	C₂²×C₄×C₉	—	3	1	no	—
109	C₂²×C₄×C₉	—	3	1	no	—
110	C₂²×C₄×C₉	—	3	2	no	—
111	C₂²×C₄×C₉	—	3	2	no	—
112	C₉×C₄⋊C₄	—	2	1	no	—
113	C₉×C₄⋊C₄	—	2	1	no	—
114	C₉×C₄⋊C₄	—	2	2	no	—
115	C₉×C₄⋊C₄	—	2	2	no	—
116	C₉×C₄⋊C₄	—	3	1	no	—
117	C₉×C₄⋊C₄	—	3	2	no	—
118	C₉×C₄⋊C₄	—	3	1	no	—
119	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
120	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
121	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
122	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
123	C₉×C₂²⋊C₄	—	3	2	no	—
124	C₉×C₂²⋊C₄	—	3	1	no	—
125	C₉×C₂²⋊C₄	—	3	2	no	—
126	C₉×C₂²⋊C₄	—	3	2	no	—
127	C₉×C₂²⋊C₄	—	3	1	no	—
128	C₉×C₂²⋊C₄	—	3	2	no	—
129	C₄²×C₉	—	2	1	no	—
130	C₄²×C₉	—	3	2	no	—
131	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
132	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
133	C₂×D₃×C₉	—	2	1	no	—
134	C₂×D₃×C₉	—	2	1	no	—
135	C₂×D₃×C₉	—	2	1	no	—
136	C₂×D₃×C₉	—	2	2	no	—
137	C₂×D₃×C₉	—	2	1	no	—
138	C₂×D₃×C₉	—	2	2	no	—
139	C₂×D₃×C₉	—	2	2	no	—
140	C₂×D₃×C₉	—	2	1	no	—
141	C₂×D₃×C₉	#41	1	2	yes	—
142	C₃×C₄×C₉	—	2	2	no	—
143	C₃×C₄×C₉	—	2	1	no	—
144	C₃×C₄×C₉	—	2	1	no	—
145	C₃×C₄×C₉	—	2	2	no	—
146	C₃×C₄×C₉	#41	1	2	yes	—
147	C₉×Dic₃	—	2	1	no	—
148	C₉×Dic₃	—	2	1	no	—
149	C₉×Dic₃	—	2	2	no	—
150	C₃×#126	—	3	2	no	—
151	C₃×#125	—	2	1	no	—
152	C₃×#125	C₂×C₉	1	1	yes	characteristic, complemented
153	C₃×#125	C₃×D₃	1	1	yes	characteristic
154	C₃×#123	—	3	2	no	—
155	C₃×#121	—	3	2	no	—
156	C₃×#121	—	3	1	no	—
157	C₃×#121	—	3	1	no	—
158	C₃×C₄×D₄	—	3	2	no	—
159	C₃×C₄×D₄	—	3	1	no	—
160	C₃×C₄×D₄	—	3	1	no	—
161	C₃×#117	—	3	1	no	—
162	C₂×C₃×C₄⋊C₄	—	3	1	no	—
163	#898	C₂×C₉	1	2	yes	complemented
164	#895	C₂×C₉	1	2	yes	complemented
165	#895	C₂×C₉	1	1	yes	characteristic, complemented
166	#895	C₂×C₉	1	1	yes	characteristic, complemented
167	#894	C₂×C₉	1	2	yes	complemented
168	#893	C₂×C₉	1	2	yes	complemented
169	#892	C₂×C₉	1	1	yes	characteristic, complemented
170	D₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
171	C₄×D₁₂	C₂×C₉	1	1	yes	characteristic, complemented
172	C₄×D₁₂	C₂×C₉	1	1	yes	characteristic, complemented
173	C₂²×C₃×D₃	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	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
180	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
181	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
182	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
183	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
184	C₃×D₁₂	—	2	4	no	—
185	C₃×D₁₂	—	2	2	no	—
186	C₃×D₁₂	—	2	2	no	—
187	C₃×D₁₂	—	4	2	no	—
188	C₃×C₄×D₃	—	2	2	no	—
189	C₃×C₄×D₃	—	2	2	no	—
190	C₃×C₄×D₃	—	4	2	no	—
191	C₃×C₄×D₃	—	4	2	no	—
192	C₂³×C₉	—	3	1	no	—
193	C₂³×C₉	—	3	1	no	—
194	C₂³×C₉	—	3	2	no	—
195	D₄×C₉	—	6	4	no	—
196	D₄×C₉	—	6	2	no	—
197	D₄×C₉	—	6	2	no	—
198	D₄×C₉	—	12	2	no	—
199	C₂×C₄×C₉	—	2	1	no	—
200	C₂×C₄×C₉	—	2	1	no	—
201	C₂×C₄×C₉	—	2	1	no	—
202	C₂×C₄×C₉	—	2	2	no	—
203	C₂×C₄×C₉	—	2	2	no	—
204	C₂×C₄×C₉	—	3	1	no	—
205	C₂×C₄×C₉	—	3	2	no	—
206	C₂×C₄×C₉	—	3	1	no	—
207	C₂×C₄×C₉	—	6	2	no	—
208	C₂×C₄×C₉	—	6	2	no	—
209	C₂×C₄×C₉	—	12	2	no	—
210	C₂×C₄×C₉	—	12	2	no	—
211	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
212	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
213	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
214	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
215	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
216	#553	—	3	1	no	Sylow
217	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
218	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
219	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
220	D₃×C₉	—	2	2	no	—
221	D₃×C₉	—	4	1	no	—
222	D₃×C₉	—	4	2	no	—
223	C₂×C₃×D₄	—	3	2	no	—
224	C₂×C₃×D₄	—	3	1	no	—
225	C₂×C₃×D₄	—	3	1	no	—
226	C₂×C₃×D₄	—	3	2	no	—
227	C₂²×C₃×C₄	—	3	1	no	—
228	C₂²×C₃×C₄	—	3	1	no	—
229	C₂²×C₃×C₄	—	3	2	no	—
230	C₂²×C₃×C₄	—	3	2	no	—
231	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
232	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
233	C₂×D₁₂	C₂²×C₉	1	2	yes	—
234	C₂×D₁₂	C₂²×C₉	1	2	yes	—
235	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
236	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
237	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
238	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
239	C₃×C₄⋊C₄	—	2	1	no	—
240	C₃×C₄⋊C₄	—	2	1	no	—
241	C₃×C₄⋊C₄	—	2	2	no	—
242	C₃×C₄⋊C₄	—	2	2	no	—
243	C₃×C₄⋊C₄	—	3	2	no	—
244	C₃×C₄⋊C₄	—	3	1	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	C₂²×C₉	1	2	yes	—
249	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
250	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
251	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
252	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
253	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
254	C₃×C₂²⋊C₄	—	3	2	no	—
255	C₃×C₂²⋊C₄	—	3	1	no	—
256	C₃×C₂²⋊C₄	—	3	2	no	—
257	C₃×C₂²⋊C₄	—	3	2	no	—
258	C₃×C₂²⋊C₄	—	3	1	no	—
259	C₃×C₂²⋊C₄	—	3	2	no	—
260	C₃×C₄²	—	2	1	no	—
261	C₃×C₄²	—	3	2	no	—
262	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
263	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
264	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
265	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
266	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
267	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
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	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
272	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
273	C₄×Dic₃	C₂²×C₉	1	2	yes	—
274	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
275	C₂×C₃×D₃	—	2	1	no	—
276	C₂×C₃×D₃	—	2	1	no	—
277	C₂×C₃×D₃	—	2	1	no	—
278	C₂×C₃×D₃	—	2	2	no	—
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	C₃×#41	1	2	yes	—
284	C₃²×C₄	—	2	2	no	—
285	C₃²×C₄	—	2	1	no	—
286	C₃²×C₄	—	2	1	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	C₂²×C₉	—	2	1	no	—
293	C₂²×C₉	—	3	2	no	—
294	C₂²×C₉	—	6	1	no	—
295	C₂²×C₉	—	6	1	no	—
296	C₂²×C₉	—	6	1	no	—
297	C₂²×C₉	—	6	2	no	—
298	C₂²×C₉	—	6	1	no	—
299	C₂²×C₉	—	6	2	no	—
300	C₂²×C₉	—	6	2	no	—
301	C₂²×C₉	—	6	1	no	—
302	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
303	C₄×C₉	—	2	2	no	—
304	C₄×C₉	—	2	1	no	—
305	C₄×C₉	—	2	1	no	—
306	C₄×C₉	—	2	2	no	—
307	C₄×C₉	—	2	2	no	—
308	C₄×C₉	—	4	1	no	—
309	C₄×C₉	—	4	2	no	—
310	C₄×C₉	—	4	1	no	—
311	C₄×C₉	—	4	2	no	—
312	C₄×C₉	—	6	1	no	—
313	C₄×C₉	—	6	1	no	—
314	C₄×C₉	—	6	2	no	—
315	C₄×C₉	#239	1	2	yes	—
316	#126	—	3	2	no	—
317	#125	D₃×C₉	1	1	yes	characteristic, complemented
318	#123	—	3	2	no	—
319	#121	—	3	2	no	—
320	#121	—	3	1	no	—
321	#121	—	3	1	no	—
322	C₄×D₄	—	3	2	no	—
323	C₄×D₄	—	3	1	no	—
324	C₄×D₄	—	3	1	no	—
325	#117	—	3	1	no	—
326	C₂×C₄⋊C₄	—	3	1	no	—
327	C₃×C₉	#553	1	1	yes	characteristic, complemented, Sylow
328	C₂³×C₃	—	3	1	no	—
329	C₂³×C₃	—	3	1	no	—
330	C₂³×C₃	—	3	2	no	—
331	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
332	C₂²×D₃	C₂³×C₉	1	2	yes	—
333	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
334	C₃×D₄	—	6	4	no	—
335	C₃×D₄	—	6	2	no	—
336	C₃×D₄	—	6	2	no	—
337	C₃×D₄	—	12	2	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	1	no	—
340	C₂×C₃×C₄	—	2	1	no	—
341	C₂×C₃×C₄	—	2	2	no	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	—	3	1	no	—
344	C₂×C₃×C₄	—	3	2	no	—
345	C₂×C₃×C₄	—	3	1	no	—
346	C₂×C₃×C₄	—	6	2	no	—
347	C₂×C₃×C₄	—	6	2	no	—
348	C₂×C₃×C₄	—	12	2	no	—
349	C₂×C₃×C₄	—	12	2	no	—
350	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
351	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
352	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
355	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
356	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
357	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
358	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
359	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
360	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
361	C₂×Dic₃	C₂³×C₉	1	2	yes	—
362	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
363	D₁₂	—	2	2	no	—
364	D₁₂	—	2	4	no	—
365	D₁₂	—	2	2	no	—
366	D₁₂	—	4	2	no	—
367	C₄×D₃	—	2	2	no	—
368	C₄×D₃	—	2	2	no	—
369	C₄×D₃	—	4	2	no	—
370	C₄×D₃	—	4	2	no	—
371	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
372	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
373	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
374	C₃×D₃	—	2	2	no	—
375	C₃×D₃	—	4	1	no	—
376	C₃×D₃	—	4	2	no	—
377	C₂×C₉	—	2	1	no	—
378	C₂×C₉	—	2	1	no	—
379	C₂×C₉	—	2	1	no	—
380	C₂×C₉	—	6	2	no	—
381	C₂×C₉	—	12	1	no	—
382	C₂×C₉	—	12	2	no	—
383	C₂×C₉	C₂×#239	1	1	yes	characteristic
384	C₂×C₉	D₃×#41	1	1	yes	characteristic
385	C₂×C₉	#1009	1	1	yes	characteristic
386	C₂×D₄	—	3	2	no	—
387	C₂×D₄	—	3	1	no	—
388	C₂×D₄	—	3	1	no	—
389	C₂×D₄	—	3	2	no	—
390	C₂²×C₄	—	3	1	no	—
391	C₂²×C₄	—	3	1	no	—
392	C₂²×C₄	—	3	2	no	—
393	C₂²×C₄	—	3	2	no	—
394	C₄⋊C₄	—	3	1	no	—
395	C₄⋊C₄	—	3	2	no	—
396	C₄⋊C₄	—	3	1	no	—
397	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
398	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
399	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
400	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
401	C₂²⋊C₄	—	3	2	no	—
402	C₂²⋊C₄	—	3	1	no	—
403	C₂²⋊C₄	—	3	2	no	—
404	C₂²⋊C₄	—	3	2	no	—
405	C₂²⋊C₄	—	3	1	no	—
406	C₂²⋊C₄	—	3	2	no	—
407	C₄²	—	3	2	no	—
408	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
409	C₂²×C₃	—	2	1	no	—
410	C₂²×C₃	—	3	2	no	—
411	C₂²×C₃	—	6	1	no	—
412	C₂²×C₃	—	6	1	no	—
413	C₂²×C₃	—	6	1	no	—
414	C₂²×C₃	—	6	2	no	—
415	C₂²×C₃	—	6	1	no	—
416	C₂²×C₃	—	6	2	no	—
417	C₂²×C₃	—	6	2	no	—
418	C₂²×C₃	—	6	1	no	—
419	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
420	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
421	C₂×D₃	—	2	1	no	—
422	C₂×D₃	—	2	1	no	—
423	C₂×D₃	—	2	1	no	—
424	C₂×D₃	—	2	2	no	—
425	C₂×D₃	—	2	1	no	—
426	C₂×D₃	—	2	2	no	—
427	C₂×D₃	—	2	2	no	—
428	C₂×D₃	—	2	1	no	—
429	C₂×D₃	C₉×#41	1	2	yes	—
430	C₃×C₄	—	2	2	no	—
431	C₃×C₄	—	2	1	no	—
432	C₃×C₄	—	2	1	no	—
433	C₃×C₄	—	2	2	no	—
434	C₃×C₄	—	2	2	no	—
435	C₃×C₄	—	2	1	no	—
436	C₃×C₄	—	2	1	no	—
437	C₃×C₄	—	2	2	no	—
438	C₃×C₄	—	2	2	no	—
439	C₃×C₄	—	4	1	no	—
440	C₃×C₄	—	4	2	no	—
441	C₃×C₄	—	4	1	no	—
442	C₃×C₄	—	4	2	no	—
443	C₃×C₄	—	6	1	no	—
444	C₃×C₄	—	6	1	no	—
445	C₃×C₄	—	6	2	no	—
446	C₃×C₄	C₉×#41	1	2	yes	—
447	C₃×C₄	C₃×#239	1	2	yes	—
448	Dic₃	—	2	1	no	—
449	Dic₃	—	2	1	no	—
450	Dic₃	—	2	2	no	—
451	C₃²	C₃×#553	1	1	yes	characteristic
452	C₉	—	2	1	no	—
453	C₉	#5695	1	1	yes	characteristic, direct product factor
454	C₂³	—	3	1	no	—
455	C₂³	—	3	1	no	—
456	C₂³	—	3	2	no	—
457	D₄	—	6	4	no	—
458	D₄	—	6	2	no	—
459	D₄	—	6	2	no	—
460	D₄	—	12	2	no	—
461	C₂×C₄	—	3	1	no	—
462	C₂×C₄	—	3	2	no	—
463	C₂×C₄	—	3	1	no	—
464	C₂×C₄	—	6	2	no	—
465	C₂×C₄	—	6	2	no	—
466	C₂×C₄	—	12	2	no	—
467	C₂×C₄	—	12	2	no	—
468	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
469	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
471	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
472	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
473	C₂×C₃	—	2	1	no	—
474	C₂×C₃	—	2	1	no	—
475	C₂×C₃	—	2	1	no	—
476	C₂×C₃	—	6	2	no	—
477	C₂×C₃	—	12	1	no	—
478	C₂×C₃	—	12	2	no	—
479	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
480	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
481	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
482	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
483	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
484	C₂×C₃	C₃×#1009	1	1	yes	characteristic
485	D₃	—	2	2	no	—
486	D₃	—	4	1	no	—
487	D₃	—	4	2	no	—
488	C₂²	—	3	2	no	—
489	C₂²	—	6	1	no	—
490	C₂²	—	6	1	no	—
491	C₂²	—	6	1	no	—
492	C₂²	—	6	2	no	—
493	C₂²	—	6	1	no	—
494	C₂²	—	6	2	no	—
495	C₂²	—	6	2	no	—
496	C₂²	—	6	1	no	—
497	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
498	C₄	—	2	2	no	—
499	C₄	—	2	1	no	—
500	C₄	—	2	1	no	—
501	C₄	—	2	2	no	—
502	C₄	—	6	1	no	—
503	C₄	—	6	1	no	—
504	C₄	—	6	2	no	—
505	C₄	C₉×#239	1	2	yes	—
506	C₃	—	2	1	no	—
507	C₃	C₉×#553	1	1	yes	characteristic, complemented
508	C₃	C₃×#5695	1	1	yes	characteristic
509	C₂	—	6	2	no	—
510	C₂	—	12	1	no	—
511	C₂	—	12	2	no	—
512	C₂	C₂×C₉×#239	1	1	yes	characteristic
513	C₂	D₃×C₉×#41	1	1	yes	characteristic
514	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×#125	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5695	C₃
hypercenter	C₉×#125	D₃
hypocenter	C₃	C₉×#553
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×#895	C₂	semidirect
4. C₉×#895	C₂	semidirect
5. C₉×#895	C₂	semidirect
6. C₉×#894	C₂	semidirect
7. C₉×#893	C₂	semidirect
8. C₉×#892	C₂	semidirect
9. D₃×C₉×C₄⋊C₄	C₂	semidirect
10. C₄×C₉×D₁₂	C₂	semidirect
11. C₄×C₉×D₁₂	C₂	semidirect
50. C₉×#125	D₃	semidirect
80. #5695	C₉	direct (N × H)
152. C₃×#125	C₂×C₉	semidirect
163. #898	C₂×C₉	semidirect
164. #895	C₂×C₉	semidirect
165. #895	C₂×C₉	semidirect
166. #895	C₂×C₉	semidirect
167. #894	C₂×C₉	semidirect
168. #893	C₂×C₉	semidirect
169. #892	C₂×C₉	semidirect
170. D₃×C₄⋊C₄	C₂×C₉	semidirect
171. C₄×D₁₂	C₂×C₉	semidirect
172. C₄×D₁₂	C₂×C₉	semidirect
317. #125	D₃×C₉	semidirect
327. C₃×C₉	#553	semidirect
453. C₉	#5695	direct (N × H)
507. C₃	C₉×#553	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×#895	2
C₉×#894	2
C₉×#893	2
C₉×#892	2
D₃×C₉×C₄⋊C₄	2
C₄×C₉×D₁₂	2
C₃×#5695	3
C₉×#553	3

Subgroups — C9×#5695 #13153170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5695 #13153170