Subgroups — C₃×#10589705 #13152796

Order 1728.

742 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#121	C₂	1	1	yes	maximal, characteristic
2	C₃×#63498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#63498	C₂	1	2	yes	maximal, complemented
4	C₃×#63497	C₂	1	2	yes	maximal, complemented
5	C₃×D₄×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#63488	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#63486	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#63450	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#63449	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#63441	C₂	1	2	yes	maximal, complemented
11	C₃×#63440	C₂	1	2	yes	maximal, complemented
12	C₃×#5603	—	3	1	no	maximal
13	#10589705	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₄×C₉	C₂²	1	2	yes	—
16	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₂²×C₃×Dic₉	C₂²	1	2	yes	—
18	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×Dic₁₈	C₂²	1	2	yes	—
20	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₃×#3676	C₂²	1	2	yes	—
23	C₃×#3676	C₂²	1	1	yes	characteristic
24	C₃×#3676	C₂²	1	1	yes	characteristic
25	C₃×#3676	C₂²	1	2	yes	—
26	C₃×#3676	C₂²	1	2	yes	—
27	C₃×#3676	C₂²	1	2	yes	—
28	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
29	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
30	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
31	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
32	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
33	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
34	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
35	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
36	C₃×C₄×Dic₉	C₂²	1	2	yes	—
37	C₃²×#121	D₃	1	1	yes	characteristic
38	C₃×#936	—	3	2	no	—
39	C₃×#936	—	3	1	no	—
40	C₃×#935	—	3	2	no	—
41	C₃×D₄×Dic₃	—	3	1	no	—
42	C₃×#926	—	3	1	no	—
43	C₃×#924	—	3	1	no	—
44	C₃×#888	—	3	1	no	—
45	C₃×#887	—	3	1	no	—
46	C₃×#879	—	3	2	no	—
47	C₃×#878	—	3	2	no	—
48	C₉×#121	—	2	1	no	—
49	C₉×#121	C₂×C₃	1	1	yes	characteristic
50	#63498	C₂×C₃	1	1	yes	characteristic, complemented
51	#63498	C₂×C₃	1	2	yes	complemented
52	#63497	C₂×C₃	1	2	yes	complemented
53	D₄×Dic₉	C₂×C₃	1	1	yes	characteristic, complemented
54	#63488	C₂×C₃	1	1	yes	characteristic, complemented
55	#63486	C₂×C₃	1	1	yes	characteristic, complemented
56	#63450	C₂×C₃	1	1	yes	characteristic, complemented
57	#63449	C₂×C₃	1	1	yes	characteristic, complemented
58	#63441	C₂×C₃	1	2	yes	complemented
59	#63440	C₂×C₃	1	2	yes	complemented
60	C₂³×C₃×C₉	C₂³	1	2	yes	—
61	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
62	C₃×D₄×C₉	—	2	2	no	—
63	C₃×D₄×C₉	—	4	2	no	—
64	C₂×C₃×C₄×C₉	—	2	2	no	—
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×C₃×Dic₉	—	4	2	no	—
69	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
70	C₂×C₃×Dic₉	C₂³	1	2	yes	—
71	C₂×C₃×Dic₉	C₂³	1	2	yes	—
72	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
73	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
74	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
75	C₃×Dic₁₈	—	2	2	no	—
76	C₃×Dic₁₈	—	4	2	no	—
77	C₃×#542	—	9	1	no	—
78	#5603	—	3	1	no	—
79	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
80	C₂×C₃²×D₄	C₂×D₃	1	2	yes	—
81	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
82	C₂²×C₃×Dic₃	—	3	2	no	—
83	C₂×C₃×Dic₆	—	3	1	no	—
84	C₂×C₃×Dic₆	—	3	2	no	—
85	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
86	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	—
87	C₃×#217	—	3	2	no	—
88	C₃×#217	—	3	2	no	—
89	C₃×#217	—	3	2	no	—
90	C₃×#217	—	3	2	no	—
91	C₃×#217	—	3	1	no	—
92	C₃×#217	—	3	1	no	—
93	C₃×C₄⋊Dic₃	—	3	1	no	—
94	C₃×C₄⋊Dic₃	—	3	1	no	—
95	C₃×C₄⋊Dic₃	—	3	1	no	—
96	C₃×Dic₃⋊C₄	—	3	2	no	—
97	C₃×Dic₃⋊C₄	—	3	2	no	—
98	C₃×Dic₃⋊C₄	—	3	2	no	—
99	C₃×C₄×Dic₃	—	3	2	no	—
100	C₃×C₄×Dic₃	—	3	1	no	—
101	C₃×C₄×Dic₃	—	3	1	no	—
102	C₂×D₄×C₉	—	2	1	no	—
103	C₂×D₄×C₉	—	2	2	no	—
104	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic
105	C₂×D₄×C₉	C₂²×C₃	1	2	yes	—
106	C₂²×C₄×C₉	—	2	1	no	—
107	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
108	C₂²×Dic₉	C₂²×C₃	1	2	yes	—
109	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
110	C₂×Dic₁₈	C₂²×C₃	1	2	yes	—
111	C₉×C₄⋊C₄	—	2	1	no	—
112	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	C₉×C₂²⋊C₄	—	2	2	no	—
114	C₉×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
115	#3676	C₂²×C₃	1	1	yes	characteristic
116	#3676	C₂²×C₃	1	1	yes	characteristic
117	#3676	C₂²×C₃	1	2	yes	—
118	#3676	C₂²×C₃	1	2	yes	—
119	#3676	C₂²×C₃	1	2	yes	—
120	#3676	C₂²×C₃	1	2	yes	—
121	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
122	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
123	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
124	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
125	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
126	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
127	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
128	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
129	C₄×Dic₉	C₂²×C₃	1	2	yes	—
130	C₂²×C₃×C₉	—	2	1	no	—
131	C₂²×C₃×C₉	—	2	2	no	—
132	C₂²×C₃×C₉	—	2	1	no	—
133	C₂²×C₃×C₉	—	2	2	no	—
134	C₂²×C₃×C₉	—	2	1	no	—
135	C₂²×C₃×C₉	—	2	2	no	—
136	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
137	C₃×C₄×C₉	—	2	1	no	—
138	C₃×C₄×C₉	—	2	2	no	—
139	C₃×C₄×C₉	#41	1	2	yes	—
140	C₃×Dic₉	—	2	2	no	—
141	C₃×Dic₉	—	2	1	no	—
142	C₃×Dic₉	—	2	2	no	—
143	C₃×Dic₉	—	2	1	no	—
144	C₃×Dic₉	—	2	1	no	—
145	C₃×Dic₉	—	2	1	no	—
146	C₃×C₄⋊Q₈	—	9	1	no	—
147	C₃×#126	—	9	2	no	—
148	C₃×#124	—	9	1	no	—
149	C₃×#124	—	9	2	no	—
150	C₃×#123	—	9	2	no	—
151	C₃×C₂²⋊Q₈	—	9	1	no	—
152	C₃×C₂²⋊Q₈	—	9	2	no	—
153	C₃×#121	—	2	1	no	—
154	C₃×#121	D₉	1	1	yes	characteristic
155	C₃×#121	C₃×D₃	1	1	yes	characteristic
156	C₃×C₄×Q₈	—	9	1	no	—
157	C₃×C₄×D₄	—	9	1	no	—
158	C₃×#117	—	9	1	no	—
159	#936	—	3	2	no	—
160	#936	—	3	1	no	—
161	#935	—	3	2	no	—
162	D₄×Dic₃	—	3	1	no	—
163	#926	—	3	1	no	—
164	#924	—	3	1	no	—
165	#888	—	3	1	no	—
166	#887	—	3	1	no	—
167	#879	—	3	2	no	—
168	#878	—	3	2	no	—
169	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
170	C₂³×C₃²	C₂²×D₃	1	2	yes	—
171	C₃²×D₄	—	2	2	no	—
172	C₃²×D₄	—	4	2	no	—
173	C₂×C₃²×C₄	—	2	2	no	—
174	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
175	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
176	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
177	C₂×C₃×Dic₃	—	3	1	no	—
178	C₂×C₃×Dic₃	—	3	1	no	—
179	C₂×C₃×Dic₃	—	3	1	no	—
180	C₂×C₃×Dic₃	—	3	2	no	—
181	C₂×C₃×Dic₃	—	3	1	no	—
182	C₂×C₃×Dic₃	—	3	2	no	—
183	C₂×C₃×Dic₃	—	12	2	no	—
184	C₃×Dic₆	—	6	2	no	—
185	C₃×Dic₆	—	12	2	no	—
186	C₂³×C₉	—	2	1	no	—
187	C₂³×C₉	—	2	2	no	—
188	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
189	C₂³×C₉	C₂³×C₃	1	2	yes	—
190	D₄×C₉	—	2	2	no	—
191	D₄×C₉	—	4	2	no	—
192	D₄×C₉	—	4	2	no	—
193	D₄×C₉	—	4	4	no	—
194	C₂×C₄×C₉	—	2	2	no	—
195	C₂×C₄×C₉	—	2	1	no	—
196	C₂×C₄×C₉	—	2	1	no	—
197	C₂×C₄×C₉	—	2	2	no	—
198	C₂×C₄×C₉	—	4	2	no	—
199	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
200	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
202	C₂×Dic₉	—	4	2	no	—
203	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
204	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
205	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
206	C₂×Dic₉	C₂³×C₃	1	2	yes	—
207	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
208	C₂×Dic₉	C₂³×C₃	1	2	yes	—
209	Dic₁₈	—	2	2	no	—
210	Dic₁₈	—	4	2	no	—
211	#542	—	9	1	no	Sylow
212	C₂×C₃×C₉	—	4	1	no	—
213	C₂×C₃×C₉	—	4	2	no	—
214	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
215	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
217	C₂×C₃×Q₈	—	9	1	no	—
218	C₂×C₃×Q₈	—	9	2	no	—
219	C₂×C₃×D₄	—	2	1	no	—
220	C₂×C₃×D₄	—	2	2	no	—
221	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic
222	C₂×C₃×D₄	C₂×D₉	1	2	yes	—
223	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
224	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
225	C₂²×C₃×C₄	—	2	1	no	—
226	C₂²×C₃×C₄	—	9	2	no	—
227	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
228	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
229	C₂²×Dic₃	—	3	2	no	—
230	C₂×Dic₆	—	3	1	no	—
231	C₂×Dic₆	—	3	2	no	—
232	C₃×C₄⋊C₄	—	2	1	no	—
233	C₃×C₄⋊C₄	—	9	2	no	—
234	C₃×C₄⋊C₄	—	9	2	no	—
235	C₃×C₄⋊C₄	—	9	2	no	—
236	C₃×C₄⋊C₄	—	9	1	no	—
237	C₃×C₄⋊C₄	—	9	1	no	—
238	C₃×C₄⋊C₄	—	9	1	no	—
239	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
240	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
241	C₃×C₂²⋊C₄	—	2	2	no	—
242	C₃×C₂²⋊C₄	—	9	1	no	—
243	C₃×C₂²⋊C₄	—	9	1	no	—
244	C₃×C₂²⋊C₄	—	9	2	no	—
245	C₃×C₂²⋊C₄	—	9	2	no	—
246	C₃×C₂²⋊C₄	—	9	2	no	—
247	C₃×C₂²⋊C₄	—	9	2	no	—
248	C₃×C₂²⋊C₄	C₂×D₉	1	2	yes	—
249	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
250	C₃×C₄²	—	9	1	no	—
251	C₃×C₄²	—	9	1	no	—
252	C₃×C₄²	—	9	2	no	—
253	#217	—	3	2	no	—
254	#217	—	3	2	no	—
255	#217	—	3	2	no	—
256	#217	—	3	2	no	—
257	#217	—	3	1	no	—
258	#217	—	3	1	no	—
259	C₄⋊Dic₃	—	3	1	no	—
260	C₄⋊Dic₃	—	3	1	no	—
261	C₄⋊Dic₃	—	3	1	no	—
262	Dic₃⋊C₄	—	3	2	no	—
263	Dic₃⋊C₄	—	3	2	no	—
264	Dic₃⋊C₄	—	3	2	no	—
265	C₄×Dic₃	—	3	2	no	—
266	C₄×Dic₃	—	3	1	no	—
267	C₄×Dic₃	—	3	1	no	—
268	C₂²×C₃²	—	2	1	no	—
269	C₂²×C₃²	—	2	1	no	—
270	C₂²×C₃²	—	2	2	no	—
271	C₂²×C₃²	—	2	2	no	—
272	C₂²×C₃²	—	2	1	no	—
273	C₂²×C₃²	—	2	2	no	—
274	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
275	C₃²×C₄	—	2	1	no	—
276	C₃²×C₄	—	2	2	no	—
277	C₃²×C₄	#237	1	2	yes	—
278	C₃×Dic₃	—	6	2	no	—
279	C₃×Dic₃	—	6	1	no	—
280	C₃×Dic₃	—	6	2	no	—
281	C₃×Dic₃	—	6	1	no	—
282	C₃×Dic₃	—	6	1	no	—
283	C₃×Dic₃	—	6	1	no	—
284	C₂²×C₉	—	2	2	no	—
285	C₂²×C₉	—	2	1	no	—
286	C₂²×C₉	—	2	2	no	—
287	C₂²×C₉	—	2	2	no	—
288	C₂²×C₉	—	2	1	no	—
289	C₂²×C₉	—	2	1	no	—
290	C₂²×C₉	—	2	2	no	—
291	C₂²×C₉	—	2	1	no	—
292	C₂²×C₉	—	4	1	no	—
293	C₂²×C₉	—	4	1	no	—
294	C₂²×C₉	—	4	2	no	—
295	C₂²×C₉	—	4	2	no	—
296	C₂²×C₉	—	4	2	no	—
297	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
298	C₄×C₉	—	2	1	no	—
299	C₄×C₉	—	2	2	no	—
300	C₄×C₉	—	2	2	no	—
301	C₄×C₉	—	4	1	no	—
302	C₄×C₉	—	4	2	no	—
303	C₄×C₉	C₃×#41	1	2	yes	—
304	Dic₉	—	2	2	no	—
305	Dic₉	—	2	1	no	—
306	Dic₉	—	2	2	no	—
307	Dic₉	—	2	1	no	—
308	Dic₉	—	2	1	no	—
309	Dic₉	—	2	1	no	—
310	C₄⋊Q₈	—	9	1	no	—
311	#126	—	9	2	no	—
312	#124	—	9	1	no	—
313	#124	—	9	2	no	—
314	#123	—	9	2	no	—
315	C₂²⋊Q₈	—	9	1	no	—
316	C₂²⋊Q₈	—	9	2	no	—
317	#121	C₃×D₉	1	1	yes	characteristic
318	C₄×Q₈	—	9	1	no	—
319	C₄×D₄	—	9	1	no	—
320	#117	—	9	1	no	—
321	C₃×C₉	#542	1	1	yes	characteristic, complemented, Sylow
322	C₂³×C₃	—	2	1	no	—
323	C₂³×C₃	—	2	2	no	—
324	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
325	C₂³×C₃	C₂²×D₉	1	2	yes	—
326	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
327	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
328	C₃×Q₈	—	18	2	no	—
329	C₃×Q₈	—	36	2	no	—
330	C₃×D₄	—	2	2	no	—
331	C₃×D₄	—	2	2	no	—
332	C₃×D₄	—	4	2	no	—
333	C₃×D₄	—	4	2	no	—
334	C₃×D₄	—	4	2	no	—
335	C₃×D₄	—	4	4	no	—
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	—	2	2	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	1	no	—
340	C₂×C₃×C₄	—	2	2	no	—
341	C₂×C₃×C₄	—	4	2	no	—
342	C₂×C₃×C₄	—	9	1	no	—
343	C₂×C₃×C₄	—	9	1	no	—
344	C₂×C₃×C₄	—	9	2	no	—
345	C₂×C₃×C₄	—	9	1	no	—
346	C₂×C₃×C₄	—	9	1	no	—
347	C₂×C₃×C₄	—	9	2	no	—
348	C₂×C₃×C₄	—	36	2	no	—
349	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
350	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
353	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
355	C₂×Dic₃	—	3	1	no	—
356	C₂×Dic₃	—	3	1	no	—
357	C₂×Dic₃	—	3	1	no	—
358	C₂×Dic₃	—	3	2	no	—
359	C₂×Dic₃	—	3	1	no	—
360	C₂×Dic₃	—	3	2	no	—
361	C₂×Dic₃	—	12	2	no	—
362	Dic₆	—	6	2	no	—
363	Dic₆	—	12	2	no	—
364	C₂×C₃²	—	4	1	no	—
365	C₂×C₃²	—	4	2	no	—
366	C₂×C₃²	C₂×#237	1	1	yes	characteristic
367	C₂×C₃²	#1004	1	1	yes	characteristic
368	C₂×C₃²	#1010	1	1	yes	characteristic
369	C₂×C₉	—	2	1	no	—
370	C₂×C₉	—	2	1	no	—
371	C₂×C₉	—	2	1	no	—
372	C₂×C₉	—	4	2	no	—
373	C₂×C₉	—	4	1	no	—
374	C₂×C₉	—	4	2	no	—
375	C₂×C₉	—	8	2	no	—
376	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
377	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
379	C₂×Q₈	—	9	1	no	—
380	C₂×Q₈	—	9	2	no	—
381	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic
382	C₂×D₄	C₂×C₃×D₉	1	2	yes	—
383	C₂²×C₄	—	9	2	no	—
384	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
385	C₄⋊C₄	—	9	1	no	—
386	C₄⋊C₄	—	9	1	no	—
387	C₄⋊C₄	—	9	1	no	—
388	C₄⋊C₄	—	9	2	no	—
389	C₄⋊C₄	—	9	2	no	—
390	C₄⋊C₄	—	9	2	no	—
391	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
392	C₂²⋊C₄	—	9	1	no	—
393	C₂²⋊C₄	—	9	1	no	—
394	C₂²⋊C₄	—	9	2	no	—
395	C₂²⋊C₄	—	9	2	no	—
396	C₂²⋊C₄	—	9	2	no	—
397	C₂²⋊C₄	—	9	2	no	—
398	C₂²⋊C₄	C₂×C₃×D₉	1	2	yes	—
399	C₄²	—	9	1	no	—
400	C₄²	—	9	1	no	—
401	C₄²	—	9	2	no	—
402	C₂²×C₃	—	2	2	no	—
403	C₂²×C₃	—	2	1	no	—
404	C₂²×C₃	—	2	2	no	—
405	C₂²×C₃	—	2	2	no	—
406	C₂²×C₃	—	2	1	no	—
407	C₂²×C₃	—	2	1	no	—
408	C₂²×C₃	—	2	2	no	—
409	C₂²×C₃	—	2	1	no	—
410	C₂²×C₃	—	2	2	no	—
411	C₂²×C₃	—	2	2	no	—
412	C₂²×C₃	—	2	1	no	—
413	C₂²×C₃	—	2	1	no	—
414	C₂²×C₃	—	2	2	no	—
415	C₂²×C₃	—	2	1	no	—
416	C₂²×C₃	—	4	1	no	—
417	C₂²×C₃	—	4	1	no	—
418	C₂²×C₃	—	4	2	no	—
419	C₂²×C₃	—	4	2	no	—
420	C₂²×C₃	—	4	2	no	—
421	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
422	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
423	C₃×C₄	—	2	1	no	—
424	C₃×C₄	—	2	2	no	—
425	C₃×C₄	—	2	1	no	—
426	C₃×C₄	—	2	2	no	—
427	C₃×C₄	—	2	2	no	—
428	C₃×C₄	—	4	1	no	—
429	C₃×C₄	—	4	2	no	—
430	C₃×C₄	—	18	2	no	—
431	C₃×C₄	—	18	1	no	—
432	C₃×C₄	—	18	2	no	—
433	C₃×C₄	—	18	1	no	—
434	C₃×C₄	—	18	1	no	—
435	C₃×C₄	—	18	1	no	—
436	C₃×C₄	#3699	1	2	yes	—
437	C₃×C₄	C₃×#237	1	2	yes	—
438	Dic₃	—	6	2	no	—
439	Dic₃	—	6	1	no	—
440	Dic₃	—	6	2	no	—
441	Dic₃	—	6	1	no	—
442	Dic₃	—	6	1	no	—
443	Dic₃	—	6	1	no	—
444	C₃²	#5603	1	1	yes	characteristic
445	C₉	—	2	1	no	—
446	C₉	C₃×#542	1	1	yes	characteristic, complemented
447	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
448	C₂³	C₂²×C₃×D₉	1	2	yes	—
449	Q₈	—	18	2	no	—
450	Q₈	—	36	2	no	—
451	D₄	—	2	2	no	—
452	D₄	—	4	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	9	1	no	—
455	C₂×C₄	—	9	1	no	—
456	C₂×C₄	—	9	2	no	—
457	C₂×C₄	—	9	1	no	—
458	C₂×C₄	—	9	1	no	—
459	C₂×C₄	—	9	2	no	—
460	C₂×C₄	—	36	2	no	—
461	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
462	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
463	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
464	C₂×C₃	—	2	1	no	—
465	C₂×C₃	—	2	1	no	—
466	C₂×C₃	—	2	1	no	—
467	C₂×C₃	—	4	2	no	—
468	C₂×C₃	—	4	1	no	—
469	C₂×C₃	—	4	2	no	—
470	C₂×C₃	—	4	1	no	—
471	C₂×C₃	—	4	2	no	—
472	C₂×C₃	—	8	2	no	—
473	C₂×C₃	C₂×#3699	1	1	yes	characteristic
474	C₂×C₃	#63710	1	1	yes	characteristic
475	C₂×C₃	#63716	1	1	yes	characteristic
476	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
477	C₂×C₃	C₃×#1004	1	1	yes	characteristic
478	C₂×C₃	C₃×#1010	1	1	yes	characteristic
479	C₂²	—	2	1	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	2	no	—
485	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
486	C₄	—	2	1	no	—
487	C₄	—	2	2	no	—
488	C₄	—	18	2	no	—
489	C₄	—	18	1	no	—
490	C₄	—	18	2	no	—
491	C₄	—	18	1	no	—
492	C₄	—	18	1	no	—
493	C₄	—	18	1	no	—
494	C₄	C₃×#3699	1	2	yes	—
495	C₃	—	2	1	no	—
496	C₃	#10589705	1	1	yes	characteristic, direct product factor
497	C₃	C₃×#5603	1	1	yes	characteristic
498	C₂	—	4	1	no	—
499	C₂	—	4	2	no	—
500	C₂	C₂×C₃×#3699	1	1	yes	characteristic
501	C₂	C₃×#63710	1	1	yes	characteristic
502	C₂	C₃×#63716	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₉
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#121	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₃²×#121	D₃
hypercenter	C₃×#121	D₉
hypocenter	C₉	C₃×#542
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#121

Complements

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

N	H ≅ G/N	type
2. C₃×#63498	C₂	semidirect
3. C₃×#63498	C₂	semidirect
4. C₃×#63497	C₂	semidirect
5. C₃×D₄×Dic₉	C₂	semidirect
6. C₃×#63488	C₂	semidirect
7. C₃×#63486	C₂	semidirect
8. C₃×#63450	C₂	semidirect
9. C₃×#63449	C₂	semidirect
10. C₃×#63441	C₂	semidirect
11. C₃×#63440	C₂	semidirect
13. #10589705	C₃	direct (N × H)
50. #63498	C₂×C₃	semidirect
51. #63498	C₂×C₃	semidirect
52. #63497	C₂×C₃	semidirect
53. D₄×Dic₉	C₂×C₃	semidirect
54. #63488	C₂×C₃	semidirect
55. #63486	C₂×C₃	semidirect
56. #63450	C₂×C₃	semidirect
57. #63449	C₂×C₃	semidirect
58. #63441	C₂×C₃	semidirect
59. #63440	C₂×C₃	semidirect
321. C₃×C₉	#542	semidirect
446. C₉	C₃×#542	semidirect
496. C₃	#10589705	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₉×#121	2
C₃×#63498	2
C₃×#63497	2
C₃×D₄×Dic₉	2
C₃×#63488	2
C₃×#63486	2
C₃×#63450	2
C₃×#63449	2
C₃×#63441	2
C₃×#63440	2
C₃×#5603	3
#10589705	3

Subgroups — C3×#10589705 #13152796

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589705 #13152796