Subgroups — C₉×#5715 #13153266

Order 1728.

1110 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	C₂×C₉×#237	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#940	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#939	C₂	1	4	yes	maximal, complemented
6	C₉×#937	C₂	1	4	yes	maximal, complemented
7	C₉×#936	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#875	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#872	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5715	C₃	1	1	yes	maximal, characteristic
11	C₉×#535	—	3	1	no	maximal
12	C₂³×D₃×C₉	C₂²	1	2	yes	—
13	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₃×D₄×C₉	C₂²	1	4	yes	complemented
16	C₂×C₉×#67	C₂²	1	2	yes	—
17	C₂×C₉×#67	C₂²	1	2	yes	—
18	C₂×C₉×#67	C₂²	1	4	yes	complemented
19	C₂²×C₉×Dic₃	C₂²	1	2	yes	complemented
20	C₉×#237	—	2	4	no	—
21	D₃×D₄×C₉	—	2	4	no	—
22	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
24	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic, complemented
26	C₉×#217	C₂²	1	4	yes	complemented
27	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
29	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
30	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×#237	C₂×C₃	1	1	yes	characteristic
32	C₂×C₃×D₃×D₄	C₂×C₃	1	1	yes	characteristic
33	C₃²×#127	C₂×C₃	1	1	yes	characteristic
34	C₃×#940	C₂×C₃	1	1	yes	characteristic
35	C₃×#939	C₂×C₃	1	4	yes	—
36	C₃×#937	C₂×C₃	1	4	yes	—
37	C₃×#936	C₂×C₃	1	1	yes	characteristic
38	C₃×#875	C₂×C₃	1	1	yes	characteristic
39	C₃×#872	C₂×C₃	1	1	yes	characteristic
40	C₂×C₉×#41	—	3	1	no	—
41	C₂²×D₄×C₉	—	3	1	no	—
42	C₉×#127	—	2	1	no	—
43	C₉×#127	—	3	1	no	—
44	C₉×#127	D₃	1	1	yes	characteristic, complemented
45	C₉×#124	—	3	1	no	—
46	C₉×#124	—	3	1	no	—
47	C₉×#121	—	3	4	no	—
48	C₉×#120	—	3	4	no	—
49	C₉×#117	—	3	1	no	—
50	C₂³×C₃×C₉	C₂³	1	2	yes	—
51	C₂³×C₃×C₉	C₂³	1	2	yes	—
52	C₂²×D₃×C₉	—	2	4	no	—
53	C₂²×D₃×C₉	—	4	4	no	—
54	C₂²×D₃×C₉	C₂³	1	2	yes	—
55	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
56	C₃×D₄×C₉	—	2	2	no	—
57	C₃×D₄×C₉	—	2	2	no	—
58	C₃×D₄×C₉	—	4	4	no	—
59	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
60	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
61	C₉×#67	—	2	4	no	—
62	C₉×#67	—	2	4	no	—
63	C₉×#67	—	4	4	no	—
64	C₂×C₉×Dic₃	—	2	4	no	—
65	C₂×C₉×Dic₃	C₂³	1	2	yes	—
66	C₂×C₉×Dic₃	C₂³	1	2	yes	—
67	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
68	C₉×D₁₂	—	2	2	no	—
69	C₄×D₃×C₉	D₄	1	4	yes	complemented
70	C₉×Dic₆	—	2	2	no	—
71	C₃×#535	—	3	1	no	—
72	#5715	C₉	1	1	yes	characteristic, direct product factor
73	C₂³×C₃×D₃	C₂²×C₃	1	2	yes	—
74	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	—
77	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
78	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
79	C₂×C₃×#67	C₂²×C₃	1	4	yes	—
80	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
81	C₃×#237	—	2	4	no	—
82	C₃×D₃×D₄	—	2	4	no	—
83	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
86	C₂⁴×C₉	—	3	2	no	—
87	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
88	C₃×#217	C₂²×C₃	1	4	yes	—
89	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
90	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
91	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
92	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
93	C₉×#41	—	6	4	no	—
94	C₂×Q₈×C₉	—	3	1	no	—
95	C₂×D₄×C₉	—	2	1	no	—
96	C₂×D₄×C₉	—	2	1	no	—
97	C₂×D₄×C₉	—	2	4	no	—
98	C₂×D₄×C₉	—	3	2	no	—
99	C₂×D₄×C₉	—	3	2	no	—
100	C₂×D₄×C₉	—	3	4	no	—
101	C₂×D₄×C₉	—	3	1	no	—
102	C₂×D₄×C₉	—	6	4	no	—
103	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
104	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
105	C₂×D₄×C₉	C₂×D₃	1	4	yes	complemented
106	C₂²×C₄×C₉	—	3	1	no	—
107	C₂²×C₄×C₉	—	3	2	no	—
108	C₉×C₄⋊C₄	—	3	2	no	—
109	C₉×C₂²⋊C₄	—	3	4	no	—
110	C₉×C₂²⋊C₄	—	3	2	no	—
111	C₉×C₂²⋊C₄	—	3	4	no	—
112	C₄²×C₉	—	2	1	no	—
113	C₄²×C₉	—	3	1	no	—
114	C₄²×C₉	C₂×D₃	1	1	yes	characteristic, complemented
115	C₂²×C₃×C₉	—	2	2	no	—
116	C₂²×C₃×C₉	—	2	2	no	—
117	C₂²×C₃×C₉	—	2	4	no	—
118	C₂²×C₃×C₉	—	2	4	no	—
119	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
120	C₂×D₃×C₉	—	2	2	no	—
121	C₂×D₃×C₉	—	2	2	no	—
122	C₂×D₃×C₉	—	2	4	no	—
123	C₂×D₃×C₉	—	4	8	no	—
124	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
125	C₃×C₄×C₉	—	2	2	no	—
126	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
127	C₉×Dic₃	—	2	2	no	—
128	C₉×Dic₃	—	2	2	no	—
129	C₉×Dic₃	C₂×D₄	1	2	yes	—
130	C₂×C₃×#41	—	3	1	no	—
131	C₂²×C₃×D₄	—	3	1	no	—
132	C₂×#237	C₂×C₉	1	1	yes	characteristic, complemented
133	C₂×D₃×D₄	C₂×C₉	1	1	yes	characteristic, complemented
134	C₃×#127	—	2	1	no	—
135	C₃×#127	—	3	1	no	—
136	C₃×#127	C₂×C₉	1	1	yes	characteristic, complemented
137	C₃×#127	C₃×D₃	1	1	yes	characteristic
138	C₃×#124	—	3	1	no	—
139	C₃×#124	—	3	1	no	—
140	C₃×#121	—	3	4	no	—
141	C₃×#120	—	3	4	no	—
142	C₃×#117	—	3	1	no	—
143	#940	C₂×C₉	1	1	yes	characteristic, complemented
144	#939	C₂×C₉	1	4	yes	complemented
145	#937	C₂×C₉	1	4	yes	complemented
146	#936	C₂×C₉	1	1	yes	characteristic, complemented
147	#875	C₂×C₉	1	1	yes	characteristic, complemented
148	#872	C₂×C₉	1	1	yes	characteristic, complemented
149	C₂³×C₃²	C₂³×C₃	1	2	yes	—
150	C₂³×C₃²	C₂³×C₃	1	2	yes	—
151	C₂²×C₃×D₃	—	2	4	no	—
152	C₂²×C₃×D₃	—	4	4	no	—
153	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
154	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
155	C₃²×D₄	—	2	2	no	—
156	C₃²×D₄	—	2	2	no	—
157	C₃²×D₄	—	4	4	no	—
158	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
159	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
160	C₃×#67	—	2	4	no	—
161	C₃×#67	—	2	4	no	—
162	C₃×#67	—	4	4	no	—
163	C₂×C₃×Dic₃	—	2	4	no	—
164	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
165	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
166	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
167	C₃×D₁₂	—	2	2	no	—
168	C₃×C₄×D₃	C₃×D₄	1	4	yes	—
169	C₃×Dic₆	—	2	2	no	—
170	C₂³×C₉	—	2	2	no	—
171	C₂³×C₉	—	2	2	no	—
172	C₂³×C₉	—	3	1	no	—
173	C₂³×C₉	—	3	2	no	—
174	C₂³×C₉	—	6	4	no	—
175	C₂³×C₉	—	12	4	no	—
176	C₂³×C₉	C₂²×D₃	1	2	yes	—
177	C₂³×C₉	C₂²×D₃	1	2	yes	—
178	Q₈×C₉	—	6	2	no	—
179	D₄×C₉	—	2	2	no	—
180	D₄×C₉	—	2	2	no	—
181	D₄×C₉	—	4	2	no	—
182	D₄×C₉	—	4	2	no	—
183	D₄×C₉	—	4	4	no	—
184	D₄×C₉	—	4	8	no	—
185	D₄×C₉	—	6	4	no	—
186	D₄×C₉	—	6	4	no	—
187	D₄×C₉	—	6	2	no	—
188	D₄×C₉	—	12	4	no	—
189	C₂×C₄×C₉	—	2	2	no	—
190	C₂×C₄×C₉	—	2	1	no	—
191	C₂×C₄×C₉	—	3	1	no	—
192	C₂×C₄×C₉	—	3	4	no	—
193	C₂×C₄×C₉	—	3	2	no	—
194	C₂×C₄×C₉	—	3	2	no	—
195	C₂×C₄×C₉	—	6	4	no	—
196	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
197	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
198	#535	—	3	1	no	Sylow
199	C₂×C₃×C₉	—	4	2	no	—
200	C₂×C₃×C₉	—	4	2	no	—
201	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₃×C₉	H(5,𝔽₂)	1	2	yes	—
203	D₃×C₉	—	2	2	no	—
204	D₃×C₉	—	4	2	no	—
205	C₂⁴×C₃	—	3	2	no	—
206	C₂³×D₃	C₂²×C₉	1	2	yes	—
207	C₃×#41	—	6	4	no	—
208	C₂×C₃×Q₈	—	3	1	no	—
209	C₂×C₃×D₄	—	2	1	no	—
210	C₂×C₃×D₄	—	2	1	no	—
211	C₂×C₃×D₄	—	2	4	no	—
212	C₂×C₃×D₄	—	3	2	no	—
213	C₂×C₃×D₄	—	3	2	no	—
214	C₂×C₃×D₄	—	3	4	no	—
215	C₂×C₃×D₄	—	3	1	no	—
216	C₂×C₃×D₄	—	6	4	no	—
217	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
218	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
219	C₂×C₃×D₄	C₂²×C₉	1	4	yes	complemented
220	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
221	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
222	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
223	C₂²×C₃×C₄	—	3	1	no	—
224	C₂²×C₃×C₄	—	3	2	no	—
225	C₂×#67	C₂²×C₉	1	2	yes	—
226	C₂×#67	C₂²×C₉	1	2	yes	—
227	C₂×#67	C₂²×C₉	1	4	yes	complemented
228	C₂²×Dic₃	C₂²×C₉	1	2	yes	complemented
229	#237	—	2	4	no	—
230	D₃×D₄	—	2	4	no	—
231	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
232	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
233	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
234	C₃×C₄⋊C₄	—	3	2	no	—
235	C₃×C₂²⋊C₄	—	3	4	no	—
236	C₃×C₂²⋊C₄	—	3	2	no	—
237	C₃×C₂²⋊C₄	—	3	4	no	—
238	C₃×C₄²	—	2	1	no	—
239	C₃×C₄²	—	3	1	no	—
240	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic, complemented
241	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
242	#217	C₂²×C₉	1	4	yes	complemented
243	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
244	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	complemented
245	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
246	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
247	C₂²×C₃²	—	2	2	no	—
248	C₂²×C₃²	—	2	2	no	—
249	C₂²×C₃²	—	2	4	no	—
250	C₂²×C₃²	—	2	4	no	—
251	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
252	C₂×C₃×D₃	—	2	2	no	—
253	C₂×C₃×D₃	—	2	2	no	—
254	C₂×C₃×D₃	—	2	4	no	—
255	C₂×C₃×D₃	—	4	8	no	—
256	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
257	C₃²×C₄	—	2	2	no	—
258	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
259	C₃×Dic₃	—	2	2	no	—
260	C₃×Dic₃	—	2	2	no	—
261	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
262	C₂²×C₉	—	2	2	no	—
263	C₂²×C₉	—	2	2	no	—
264	C₂²×C₉	—	2	4	no	—
265	C₂²×C₉	—	2	4	no	—
266	C₂²×C₉	—	2	1	no	—
267	C₂²×C₉	—	3	2	no	—
268	C₂²×C₉	—	4	2	no	—
269	C₂²×C₉	—	4	2	no	—
270	C₂²×C₉	—	4	4	no	—
271	C₂²×C₉	—	4	4	no	—
272	C₂²×C₉	—	6	2	no	—
273	C₂²×C₉	—	6	2	no	—
274	C₂²×C₉	—	6	4	no	—
275	C₂²×C₉	—	12	8	no	—
276	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
277	C₄×C₉	—	2	4	no	—
278	C₄×C₉	—	2	2	no	—
279	C₄×C₉	—	2	2	no	—
280	C₄×C₉	—	3	2	no	—
281	C₄×C₉	—	6	2	no	—
282	C₄×C₉	—	6	2	no	—
283	C₄×C₉	D₃×D₄	1	2	yes	—
284	C₂×#41	—	3	1	no	—
285	C₂²×D₄	—	3	1	no	—
286	#127	—	3	1	no	—
287	#127	D₃×C₉	1	1	yes	characteristic, complemented
288	#124	—	3	1	no	—
289	#124	—	3	1	no	—
290	#121	—	3	4	no	—
291	#120	—	3	4	no	—
292	#117	—	3	1	no	—
293	C₃×C₉	#535	1	1	yes	characteristic, complemented, Sylow
294	C₂³×C₃	—	2	2	no	—
295	C₂³×C₃	—	2	2	no	—
296	C₂³×C₃	—	3	1	no	—
297	C₂³×C₃	—	3	2	no	—
298	C₂³×C₃	—	6	4	no	—
299	C₂³×C₃	—	12	4	no	—
300	C₂³×C₃	C₂³×C₉	1	2	yes	—
301	C₂³×C₃	C₂³×C₉	1	2	yes	—
302	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
303	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
304	C₂²×D₃	—	2	4	no	—
305	C₂²×D₃	—	4	4	no	—
306	C₂²×D₃	C₂³×C₉	1	2	yes	—
307	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
308	C₃×Q₈	—	6	2	no	—
309	C₃×D₄	—	2	2	no	—
310	C₃×D₄	—	2	2	no	—
311	C₃×D₄	—	2	2	no	—
312	C₃×D₄	—	2	2	no	—
313	C₃×D₄	—	4	2	no	—
314	C₃×D₄	—	4	2	no	—
315	C₃×D₄	—	4	4	no	—
316	C₃×D₄	—	4	4	no	—
317	C₃×D₄	—	4	8	no	—
318	C₃×D₄	—	6	4	no	—
319	C₃×D₄	—	6	4	no	—
320	C₃×D₄	—	6	2	no	—
321	C₃×D₄	—	12	4	no	—
322	C₂×C₃×C₄	—	2	2	no	—
323	C₂×C₃×C₄	—	2	1	no	—
324	C₂×C₃×C₄	—	3	1	no	—
325	C₂×C₃×C₄	—	3	4	no	—
326	C₂×C₃×C₄	—	3	2	no	—
327	C₂×C₃×C₄	—	3	2	no	—
328	C₂×C₃×C₄	—	6	4	no	—
329	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
330	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
331	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
332	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
333	#67	—	2	4	no	—
334	#67	—	2	4	no	—
335	#67	—	4	4	no	—
336	C₂×Dic₃	—	2	4	no	—
337	C₂×Dic₃	C₂³×C₉	1	2	yes	—
338	C₂×Dic₃	C₂³×C₉	1	2	yes	—
339	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
340	D₁₂	—	2	2	no	—
341	C₄×D₃	D₄×C₉	1	4	yes	complemented
342	Dic₆	—	2	2	no	—
343	C₂×C₃²	—	4	2	no	—
344	C₂×C₃²	—	4	2	no	—
345	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
346	C₂×C₃²	C₃×H(5,𝔽₂)	1	2	yes	—
347	C₃×D₃	—	2	2	no	—
348	C₃×D₃	—	4	2	no	—
349	C₂×C₉	—	2	1	no	—
350	C₂×C₉	—	2	2	no	—
351	C₂×C₉	—	4	2	no	—
352	C₂×C₉	—	4	2	no	—
353	C₂×C₉	—	6	2	no	—
354	C₂×C₉	—	8	2	no	—
355	C₂×C₉	—	8	2	no	—
356	C₂×C₉	—	12	2	no	—
357	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
358	C₂×C₉	#1004	1	2	yes	—
359	C₂⁴	—	3	2	no	—
360	#41	—	6	4	no	—
361	C₂×Q₈	—	3	1	no	—
362	C₂×D₄	—	3	2	no	—
363	C₂×D₄	—	3	2	no	—
364	C₂×D₄	—	3	4	no	—
365	C₂×D₄	—	3	1	no	—
366	C₂×D₄	—	6	4	no	—
367	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
368	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
369	C₂×D₄	C₂×D₃×C₉	1	4	yes	complemented
370	C₂²×C₄	—	3	1	no	—
371	C₂²×C₄	—	3	2	no	—
372	C₄⋊C₄	—	3	2	no	—
373	C₂²⋊C₄	—	3	4	no	—
374	C₂²⋊C₄	—	3	2	no	—
375	C₂²⋊C₄	—	3	4	no	—
376	C₄²	—	3	1	no	—
377	C₄²	C₂×D₃×C₉	1	1	yes	characteristic, complemented
378	C₂²×C₃	—	2	2	no	—
379	C₂²×C₃	—	2	2	no	—
380	C₂²×C₃	—	2	4	no	—
381	C₂²×C₃	—	2	4	no	—
382	C₂²×C₃	—	2	2	no	—
383	C₂²×C₃	—	2	2	no	—
384	C₂²×C₃	—	2	4	no	—
385	C₂²×C₃	—	2	4	no	—
386	C₂²×C₃	—	2	1	no	—
387	C₂²×C₃	—	3	2	no	—
388	C₂²×C₃	—	4	2	no	—
389	C₂²×C₃	—	4	2	no	—
390	C₂²×C₃	—	4	4	no	—
391	C₂²×C₃	—	4	4	no	—
392	C₂²×C₃	—	6	2	no	—
393	C₂²×C₃	—	6	2	no	—
394	C₂²×C₃	—	6	4	no	—
395	C₂²×C₃	—	12	8	no	—
396	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
397	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
398	C₂×D₃	—	2	2	no	—
399	C₂×D₃	—	2	2	no	—
400	C₂×D₃	—	2	4	no	—
401	C₂×D₃	—	4	8	no	—
402	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
403	C₃×C₄	—	2	4	no	—
404	C₃×C₄	—	2	2	no	—
405	C₃×C₄	—	2	2	no	—
406	C₃×C₄	—	2	2	no	—
407	C₃×C₄	—	3	2	no	—
408	C₃×C₄	—	6	2	no	—
409	C₃×C₄	—	6	2	no	—
410	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
411	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
412	Dic₃	—	2	2	no	—
413	Dic₃	—	2	2	no	—
414	Dic₃	C₂×D₄×C₉	1	2	yes	—
415	C₃²	C₃×#535	1	1	yes	characteristic
416	C₉	—	2	1	no	—
417	C₉	#5715	1	1	yes	characteristic, direct product factor
418	C₂³	—	3	1	no	—
419	C₂³	—	3	2	no	—
420	C₂³	—	6	4	no	—
421	C₂³	—	12	4	no	—
422	C₂³	C₂²×D₃×C₉	1	2	yes	—
423	C₂³	C₂²×D₃×C₉	1	2	yes	—
424	Q₈	—	6	2	no	—
425	D₄	—	2	2	no	—
426	D₄	—	2	2	no	—
427	D₄	—	4	4	no	—
428	D₄	—	6	4	no	—
429	D₄	—	6	4	no	—
430	D₄	—	6	2	no	—
431	D₄	—	12	4	no	—
432	C₂×C₄	—	3	1	no	—
433	C₂×C₄	—	3	4	no	—
434	C₂×C₄	—	3	2	no	—
435	C₂×C₄	—	3	2	no	—
436	C₂×C₄	—	6	4	no	—
437	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
438	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
439	C₂×C₃	—	2	1	no	—
440	C₂×C₃	—	2	2	no	—
441	C₂×C₃	—	4	2	no	—
442	C₂×C₃	—	4	2	no	—
443	C₂×C₃	—	4	2	no	—
444	C₂×C₃	—	4	2	no	—
445	C₂×C₃	—	6	2	no	—
446	C₂×C₃	—	8	2	no	—
447	C₂×C₃	—	8	2	no	—
448	C₂×C₃	—	12	2	no	—
449	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
450	C₂×C₃	C₉×H(5,𝔽₂)	1	2	yes	—
451	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
452	C₂×C₃	C₃×#1004	1	2	yes	—
453	D₃	—	2	2	no	—
454	D₃	—	4	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	4	no	—
458	C₂²	—	2	4	no	—
459	C₂²	—	3	2	no	—
460	C₂²	—	6	2	no	—
461	C₂²	—	6	2	no	—
462	C₂²	—	6	4	no	—
463	C₂²	—	12	8	no	—
464	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
465	C₄	—	2	2	no	—
466	C₄	—	3	2	no	—
467	C₄	—	6	2	no	—
468	C₄	—	6	2	no	—
469	C₄	D₃×D₄×C₉	1	2	yes	—
470	C₃	—	2	1	no	—
471	C₃	C₉×#535	1	1	yes	characteristic, complemented
472	C₃	C₃×#5715	1	1	yes	characteristic
473	C₂	—	4	2	no	—
474	C₂	—	4	2	no	—
475	C₂	—	6	2	no	—
476	C₂	—	12	2	no	—
477	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
478	C₂	C₉×#1004	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×#127	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5715	C₃
hypercenter	C₉×#127	D₃
hypocenter	C₃	C₉×#535
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#127

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#237	C₂	semidirect
2. C₂×D₃×D₄×C₉	C₂	semidirect
3. C₃×C₉×#127	C₂	semidirect
4. C₉×#940	C₂	semidirect
5. C₉×#939	C₂	semidirect
6. C₉×#937	C₂	semidirect
7. C₉×#936	C₂	semidirect
8. C₉×#875	C₂	semidirect
9. C₉×#872	C₂	semidirect
14. C₂×C₃×D₄×C₉	C₂²	semidirect
15. C₂×C₃×D₄×C₉	C₂²	semidirect
18. C₂×C₉×#67	C₂²	semidirect
19. C₂²×C₉×Dic₃	C₂²	semidirect
24. C₂×C₉×Dic₆	C₂²	semidirect
25. C₃×C₄²×C₉	C₂²	semidirect
26. C₉×#217	C₂²	semidirect
28. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
29. C₉×Dic₃⋊C₄	C₂²	semidirect
30. C₄×C₉×Dic₃	C₂²	semidirect
44. C₉×#127	D₃	semidirect
69. C₄×D₃×C₉	D₄	semidirect
72. #5715	C₉	direct (N × H)
104. C₂×D₄×C₉	C₂×D₃	semidirect
105. C₂×D₄×C₉	C₂×D₃	semidirect
114. C₄²×C₉	C₂×D₃	semidirect
132. C₂×#237	C₂×C₉	semidirect
133. C₂×D₃×D₄	C₂×C₉	semidirect
136. C₃×#127	C₂×C₉	semidirect
143. #940	C₂×C₉	semidirect
144. #939	C₂×C₉	semidirect
145. #937	C₂×C₉	semidirect
146. #936	C₂×C₉	semidirect
147. #875	C₂×C₉	semidirect
148. #872	C₂×C₉	semidirect
218. C₂×C₃×D₄	C₂²×C₉	semidirect
219. C₂×C₃×D₄	C₂²×C₉	semidirect
227. C₂×#67	C₂²×C₉	semidirect
228. C₂²×Dic₃	C₂²×C₉	semidirect
233. C₂×Dic₆	C₂²×C₉	semidirect
240. C₃×C₄²	C₂²×C₉	semidirect
242. #217	C₂²×C₉	semidirect
244. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
245. Dic₃⋊C₄	C₂²×C₉	semidirect
246. C₄×Dic₃	C₂²×C₉	semidirect
287. #127	D₃×C₉	semidirect
293. C₃×C₉	#535	semidirect
341. C₄×D₃	D₄×C₉	semidirect
368. C₂×D₄	C₂×D₃×C₉	semidirect
369. C₂×D₄	C₂×D₃×C₉	semidirect
377. C₄²	C₂×D₃×C₉	semidirect
417. C₉	#5715	direct (N × H)
471. C₃	C₉×#535	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×D₃×D₄×C₉	2
C₃×C₉×#127	2
C₉×#940	2
C₉×#939	2
C₉×#937	2
C₉×#936	2
C₉×#875	2
C₉×#872	2
C₃×#5715	3
C₉×#535	3

Subgroups — C9×#5715 #13153266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5715 #13153266