Subgroups — C₃×D₉×#135 #13153471

Order 1728.

860 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41×D₉	C₂	1	2	yes	maximal, complemented
2	C₃×C₉×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#63513	C₂	1	2	yes	maximal, complemented
4	C₃×#63481	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×Q₁₆×D₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#63478	C₂	1	2	yes	maximal, complemented
7	C₃×SD₁₆×D₉	C₂	1	2	yes	maximal, complemented
8	C₃×#63474	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₈×D₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#63467	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×C₈×D₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×D₃×#135	—	3	1	no	maximal
13	D₉×#135	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₃×C₉×#41	C₂²	1	2	yes	complemented
15	C₃×#3701	C₂²	1	2	yes	complemented
16	C₃×Q₈×D₉	C₂²	1	2	yes	—
17	C₃×#3699	—	2	2	no	—
18	C₃×#3699	C₂²	1	2	yes	complemented
19	C₃×D₄×D₉	—	2	2	no	—
20	C₃×D₄×D₉	C₂²	1	2	yes	—
21	C₃×#3697	—	2	2	no	—
22	C₃×#3697	C₂²	1	2	yes	complemented
23	C₂×C₃×C₄×D₉	—	2	2	no	—
24	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
25	C₃×C₉×Q₁₆	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₉×SD₁₆	C₂²	1	2	yes	complemented
27	C₃×C₉×D₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic, complemented
29	C₃×#3675	C₂²	1	2	yes	complemented
30	C₃×#3674	C₂²	1	2	yes	complemented
31	C₃×#3673	C₂²	1	2	yes	complemented
32	C₃×#3672	C₂²	1	2	yes	complemented
33	C₂×C₃×C₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
34	C₃×D₇₂	C₂²	1	1	yes	characteristic, complemented
35	C₃×#3664	C₂²	1	2	yes	complemented
36	C₃×C₈×D₉	C₂²	1	1	yes	characteristic
37	C₃×C₈×D₉	C₂²	1	1	yes	characteristic
38	C₃×C₈×D₉	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₈×D₉	C₂²	1	1	yes	characteristic, complemented
40	C₃×Dic₃₆	C₂²	1	1	yes	characteristic, complemented
41	C₃×D₃×#41	—	3	2	no	—
42	C₃²×#135	D₃	1	1	yes	characteristic
43	C₃×#950	—	3	2	no	—
44	C₃×#919	—	3	1	no	—
45	C₃×D₃×Q₁₆	—	3	1	no	—
46	C₃×#916	—	3	2	no	—
47	C₃×D₃×SD₁₆	—	3	2	no	—
48	C₃×#912	—	3	1	no	—
49	C₃×D₃×D₈	—	3	1	no	—
50	C₃×#904	—	3	1	no	—
51	C₂×C₃×D₃×C₈	—	3	1	no	—
52	#41×D₉	C₂×C₃	1	2	yes	complemented
53	C₉×#135	—	2	1	no	—
54	C₉×#135	C₂×C₃	1	1	yes	characteristic, complemented
55	#63513	C₂×C₃	1	2	yes	complemented
56	#63481	C₂×C₃	1	1	yes	characteristic, complemented
57	Q₁₆×D₉	C₂×C₃	1	1	yes	characteristic, complemented
58	#63478	C₂×C₃	1	2	yes	complemented
59	SD₁₆×D₉	C₂×C₃	1	2	yes	complemented
60	#63474	C₂×C₃	1	1	yes	characteristic, complemented
61	D₈×D₉	C₂×C₃	1	1	yes	characteristic, complemented
62	#63467	C₂×C₃	1	1	yes	characteristic, complemented
63	C₂×C₈×D₉	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂²×C₃×D₉	—	2	2	no	—
65	C₂²×C₃×D₉	D₄	1	1	yes	characteristic
66	C₃×Q₈×C₉	C₂³	1	2	yes	—
67	C₃×D₄×C₉	—	2	2	no	—
68	C₃×D₄×C₉	C₂³	1	2	yes	—
69	C₂×C₃×C₄×C₉	—	2	2	no	—
70	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
71	C₃×#611	—	2	2	no	—
72	C₃×#611	—	2	2	no	—
73	C₃×#611	—	2	2	no	—
74	C₂×C₃×Dic₉	—	2	2	no	—
75	C₂×C₃×Dic₉	D₄	1	1	yes	characteristic
76	C₃×D₃₆	—	2	2	no	—
77	C₃×D₃₆	C₂³	1	2	yes	—
78	C₃×C₄×D₉	—	2	2	no	—
79	C₃×C₄×D₉	—	2	2	no	—
80	C₃×C₄×D₉	—	2	2	no	—
81	C₃×C₄×D₉	D₄	1	1	yes	characteristic
82	C₃×C₄×D₉	D₄	1	1	yes	characteristic
83	C₃×C₄×D₉	C₂³	1	1	yes	characteristic
84	C₃×C₄×D₉	C₂³	1	1	yes	characteristic
85	C₃×Dic₁₈	—	2	2	no	—
86	C₃×Dic₁₈	C₂³	1	2	yes	—
87	C₃×C₈×C₉	C₂³	1	1	yes	characteristic
88	C₃×C₈×C₉	C₂³	1	1	yes	characteristic
89	C₃×C₉⋊C₈	C₂³	1	1	yes	characteristic
90	C₃×C₉⋊C₈	C₂³	1	1	yes	characteristic
91	C₂×C₃×#135	—	9	1	no	—
92	D₃×#135	—	3	1	no	—
93	C₃²×#41	C₂×D₃	1	2	yes	—
94	C₃×#239	—	3	2	no	—
95	C₃×D₃×Q₈	—	3	2	no	—
96	C₃×#237	—	3	2	no	—
97	C₃×#237	—	6	2	no	—
98	C₃×D₃×D₄	—	3	2	no	—
99	C₃×D₃×D₄	—	6	2	no	—
100	C₃×#235	—	3	2	no	—
101	C₃×#235	—	6	2	no	—
102	C₂×C₃×C₄×D₃	—	3	1	no	—
103	C₂×C₃×C₄×D₃	—	6	2	no	—
104	C₃²×Q₁₆	C₂×D₃	1	1	yes	characteristic
105	C₃²×SD₁₆	C₂×D₃	1	2	yes	—
106	C₃²×D₈	C₂×D₃	1	1	yes	characteristic
107	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
108	C₃×#216	—	3	2	no	—
109	C₃×#215	—	3	2	no	—
110	C₃×#214	—	3	2	no	—
111	C₃×#213	—	3	2	no	—
112	C₂×C₃×C₃⋊C₈	—	3	1	no	—
113	C₃×Dic₁₂	—	3	1	no	—
114	C₃×D₂₄	—	3	1	no	—
115	C₃×#204	—	3	2	no	—
116	C₃×D₃×C₈	—	3	1	no	—
117	C₃×D₃×C₈	—	3	1	no	—
118	C₃×D₃×C₈	—	3	1	no	—
119	C₃×D₃×C₈	—	3	1	no	—
120	C₉×#41	—	2	2	no	—
121	C₉×#41	C₂²×C₃	1	2	yes	complemented
122	#3701	C₂²×C₃	1	2	yes	complemented
123	Q₈×D₉	C₂²×C₃	1	2	yes	—
124	#3699	—	2	2	no	—
125	#3699	C₂²×C₃	1	2	yes	complemented
126	D₄×D₉	—	2	2	no	—
127	D₄×D₉	C₂²×C₃	1	2	yes	—
128	#3697	—	2	2	no	—
129	#3697	C₂²×C₃	1	2	yes	complemented
130	C₂×C₄×D₉	—	2	2	no	—
131	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
132	C₉×Q₁₆	—	2	1	no	—
133	C₉×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
134	C₉×SD₁₆	—	2	2	no	—
135	C₉×SD₁₆	C₂²×C₃	1	2	yes	complemented
136	C₉×D₈	—	2	1	no	—
137	C₉×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
138	C₂×C₈×C₉	—	2	1	no	—
139	C₂×C₈×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
140	#3675	C₂²×C₃	1	2	yes	complemented
141	#3674	C₂²×C₃	1	2	yes	complemented
142	#3673	C₂²×C₃	1	2	yes	complemented
143	#3672	C₂²×C₃	1	2	yes	complemented
144	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
145	D₇₂	C₂²×C₃	1	1	yes	characteristic, complemented
146	#3664	C₂²×C₃	1	2	yes	complemented
147	C₈×D₉	C₂²×C₃	1	1	yes	characteristic
148	C₈×D₉	C₂²×C₃	1	1	yes	characteristic
149	C₈×D₉	C₂²×C₃	1	1	yes	characteristic, complemented
150	C₈×D₉	C₂²×C₃	1	1	yes	characteristic, complemented
151	Dic₃₆	C₂²×C₃	1	1	yes	characteristic, complemented
152	C₂²×C₃×C₉	—	2	2	no	—
153	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₃×D₉	—	2	2	no	—
155	C₂×C₃×D₉	—	2	2	no	—
156	C₂×C₃×D₉	—	4	4	no	—
157	C₂×C₃×D₉	C₂×D₄	1	1	yes	characteristic
158	C₂×C₃×D₉	C₂×D₄	1	1	yes	characteristic
159	C₃×C₄×C₉	—	2	2	no	—
160	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
161	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
162	C₃×Dic₉	—	2	2	no	—
163	C₃×Dic₉	C₂×D₄	1	1	yes	characteristic
164	C₃×Dic₉	C₂×D₄	1	1	yes	characteristic
165	C₂×C₃×#41	—	9	2	no	—
166	D₃×#41	—	3	2	no	—
167	C₃×#135	—	2	1	no	—
168	C₃×#135	—	9	2	no	—
169	C₃×#135	—	9	1	no	—
170	C₃×#135	—	9	2	no	—
171	C₃×#135	—	9	1	no	—
172	C₃×#135	—	9	1	no	—
173	C₃×#135	D₉	1	1	yes	characteristic, direct product factor
174	C₃×#135	C₃×D₃	1	1	yes	characteristic
175	C₂×C₃×Q₁₆	—	9	1	no	—
176	C₂×C₃×SD₁₆	—	9	2	no	—
177	C₂×C₃×D₈	—	9	1	no	—
178	C₂²×C₃×C₈	—	9	1	no	—
179	#950	—	3	2	no	—
180	#919	—	3	1	no	—
181	D₃×Q₁₆	—	3	1	no	—
182	#916	—	3	2	no	—
183	D₃×SD₁₆	—	3	2	no	—
184	#912	—	3	1	no	—
185	D₃×D₈	—	3	1	no	—
186	#904	—	3	1	no	—
187	C₂×D₃×C₈	—	3	1	no	—
188	C₂²×C₃×D₃	—	3	1	no	—
189	C₂²×C₃×D₃	—	6	2	no	—
190	C₃²×Q₈	C₂²×D₃	1	2	yes	—
191	C₃²×D₄	—	2	2	no	—
192	C₃²×D₄	C₂²×D₃	1	2	yes	—
193	C₂×C₃²×C₄	—	2	2	no	—
194	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
195	C₃×#67	—	6	2	no	—
196	C₃×#67	—	6	2	no	—
197	C₃×#67	—	6	2	no	—
198	C₂×C₃×Dic₃	—	3	1	no	—
199	C₂×C₃×Dic₃	—	6	2	no	—
200	C₃×D₁₂	—	3	2	no	—
201	C₃×D₁₂	—	6	2	no	—
202	C₃×C₄×D₃	—	3	1	no	—
203	C₃×C₄×D₃	—	3	1	no	—
204	C₃×C₄×D₃	—	3	1	no	—
205	C₃×C₄×D₃	—	3	1	no	—
206	C₃×C₄×D₃	—	6	2	no	—
207	C₃×C₄×D₃	—	6	2	no	—
208	C₃×C₄×D₃	—	6	2	no	—
209	C₃×Dic₆	—	3	2	no	—
210	C₃×Dic₆	—	6	2	no	—
211	C₂²×D₉	—	2	2	no	—
212	C₂²×D₉	C₃×D₄	1	1	yes	characteristic
213	C₃²×C₈	C₂²×D₃	1	1	yes	characteristic
214	C₃²×C₈	C₂²×D₃	1	1	yes	characteristic
215	C₃×C₃⋊C₈	—	3	1	no	—
216	C₃×C₃⋊C₈	—	3	1	no	—
217	Q₈×C₉	—	2	2	no	—
218	Q₈×C₉	C₂³×C₃	1	2	yes	—
219	D₄×C₉	—	2	2	no	—
220	D₄×C₉	—	2	2	no	—
221	D₄×C₉	—	4	2	no	—
222	D₄×C₉	C₂³×C₃	1	2	yes	—
223	C₂×C₄×C₉	—	2	2	no	—
224	C₂×C₄×C₉	—	2	1	no	—
225	C₂×C₄×C₉	—	4	2	no	—
226	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
227	#611	—	2	2	no	—
228	#611	—	2	2	no	—
229	#611	—	2	2	no	—
230	C₂×Dic₉	—	2	2	no	—
231	C₂×Dic₉	C₃×D₄	1	1	yes	characteristic
232	D₃₆	—	2	2	no	—
233	D₃₆	C₂³×C₃	1	2	yes	—
234	C₄×D₉	—	2	2	no	—
235	C₄×D₉	—	2	2	no	—
236	C₄×D₉	—	2	2	no	—
237	C₄×D₉	C₃×D₄	1	1	yes	characteristic
238	C₄×D₉	C₃×D₄	1	1	yes	characteristic
239	C₄×D₉	C₂³×C₃	1	1	yes	characteristic
240	C₄×D₉	C₂³×C₃	1	1	yes	characteristic
241	Dic₁₈	—	2	2	no	—
242	Dic₁₈	C₂³×C₃	1	2	yes	—
243	C₈×C₉	—	2	1	no	—
244	C₈×C₉	—	2	1	no	—
245	C₈×C₉	C₂³×C₃	1	1	yes	characteristic
246	C₈×C₉	C₂³×C₃	1	1	yes	characteristic
247	C₉⋊C₈	C₂³×C₃	1	1	yes	characteristic
248	C₉⋊C₈	C₂³×C₃	1	1	yes	characteristic
249	C₂×#135	—	9	1	no	Sylow
250	C₂×C₃×C₉	—	2	1	no	—
251	C₂×C₃×C₉	—	4	2	no	—
252	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
253	C₃×D₉	—	2	1	no	—
254	C₃×D₉	—	4	2	no	—
255	C₃×D₉	#135	1	2	yes	direct product factor
256	C₃×#41	—	2	2	no	—
257	C₃×#41	—	9	2	no	—
258	C₃×#41	—	9	2	no	—
259	C₃×#41	—	9	2	no	—
260	C₃×#41	—	18	2	no	—
261	C₃×#41	—	18	2	no	—
262	C₃×#41	C₂×D₉	1	2	yes	complemented
263	C₃×#41	C₂×C₃×D₃	1	2	yes	—
264	C₂×C₃×Q₈	—	9	2	no	—
265	C₂×C₃×D₄	—	9	2	no	—
266	C₂×C₃×D₄	—	18	2	no	—
267	C₂²×C₃×C₄	—	9	1	no	—
268	C₂²×C₃×C₄	—	18	2	no	—
269	#239	—	3	2	no	—
270	D₃×Q₈	—	3	2	no	—
271	#237	—	3	2	no	—
272	#237	—	6	2	no	—
273	D₃×D₄	—	3	2	no	—
274	D₃×D₄	—	6	2	no	—
275	#235	—	3	2	no	—
276	#235	—	6	2	no	—
277	C₂×C₄×D₃	—	3	1	no	—
278	C₂×C₄×D₃	—	6	2	no	—
279	C₃×Q₁₆	—	2	1	no	—
280	C₃×Q₁₆	—	9	2	no	—
281	C₃×Q₁₆	—	9	1	no	—
282	C₃×Q₁₆	C₂×D₉	1	1	yes	characteristic, complemented
283	C₃×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic
284	C₃×SD₁₆	—	2	2	no	—
285	C₃×SD₁₆	—	9	2	no	—
286	C₃×SD₁₆	—	9	2	no	—
287	C₃×SD₁₆	—	9	2	no	—
288	C₃×SD₁₆	C₂×D₉	1	2	yes	complemented
289	C₃×SD₁₆	C₂×C₃×D₃	1	2	yes	—
290	C₃×D₈	—	2	1	no	—
291	C₃×D₈	—	9	2	no	—
292	C₃×D₈	—	9	1	no	—
293	C₃×D₈	C₂×D₉	1	1	yes	characteristic, complemented
294	C₃×D₈	C₂×C₃×D₃	1	1	yes	characteristic
295	C₂×C₃×C₈	—	2	1	no	—
296	C₂×C₃×C₈	—	9	1	no	—
297	C₂×C₃×C₈	—	9	1	no	—
298	C₂×C₃×C₈	—	9	1	no	—
299	C₂×C₃×C₈	—	9	1	no	—
300	C₂×C₃×C₈	—	9	1	no	—
301	C₂×C₃×C₈	C₂×D₉	1	1	yes	characteristic, complemented
302	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
303	#216	—	3	2	no	—
304	#215	—	3	2	no	—
305	#214	—	3	2	no	—
306	#213	—	3	2	no	—
307	C₂×C₃⋊C₈	—	3	1	no	—
308	Dic₁₂	—	3	1	no	—
309	D₂₄	—	3	1	no	—
310	#204	—	3	2	no	—
311	D₃×C₈	—	3	1	no	—
312	D₃×C₈	—	3	1	no	—
313	D₃×C₈	—	3	1	no	—
314	D₃×C₈	—	3	1	no	—
315	C₂²×C₃²	—	2	2	no	—
316	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
317	C₂×C₃×D₃	—	3	1	no	—
318	C₂×C₃×D₃	—	3	1	no	—
319	C₂×C₃×D₃	—	6	2	no	—
320	C₂×C₃×D₃	—	6	2	no	—
321	C₂×C₃×D₃	—	12	4	no	—
322	C₃²×C₄	—	2	2	no	—
323	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
324	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
325	C₃×Dic₃	—	3	1	no	—
326	C₃×Dic₃	—	3	1	no	—
327	C₃×Dic₃	—	6	2	no	—
328	C₂²×C₉	—	2	2	no	—
329	C₂²×C₉	—	2	1	no	—
330	C₂²×C₉	—	4	2	no	—
331	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
332	C₂×D₉	—	2	2	no	—
333	C₂×D₉	—	2	2	no	—
334	C₂×D₉	—	4	4	no	—
335	C₂×D₉	C₂×C₃×D₄	1	1	yes	characteristic
336	C₂×D₉	C₂×C₃×D₄	1	1	yes	characteristic
337	C₄×C₉	—	2	2	no	—
338	C₄×C₉	—	2	1	no	—
339	C₄×C₉	—	2	1	no	—
340	C₄×C₉	—	4	2	no	—
341	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
342	C₄×C₉	C₂⁴×C₃	1	1	yes	characteristic
343	Dic₉	—	2	2	no	—
344	Dic₉	C₂×C₃×D₄	1	1	yes	characteristic
345	Dic₉	C₂×C₃×D₄	1	1	yes	characteristic
346	C₂×#41	—	9	2	no	—
347	#135	—	9	2	no	—
348	#135	—	9	1	no	—
349	#135	—	9	2	no	—
350	#135	—	9	1	no	—
351	#135	—	9	1	no	—
352	#135	C₃×D₉	1	1	yes	characteristic, direct product factor
353	C₂×Q₁₆	—	9	1	no	—
354	C₂×SD₁₆	—	9	2	no	—
355	C₂×D₈	—	9	1	no	—
356	C₂²×C₈	—	9	1	no	—
357	C₃×C₉	C₂×#135	1	1	yes	characteristic, complemented, Sylow
358	C₂³×C₃	—	9	1	no	—
359	C₂³×C₃	—	18	2	no	—
360	C₂²×D₃	—	3	1	no	—
361	C₂²×D₃	—	6	2	no	—
362	C₃×Q₈	—	2	2	no	—
363	C₃×Q₈	—	9	2	no	—
364	C₃×Q₈	—	18	2	no	—
365	C₃×Q₈	C₂²×D₉	1	2	yes	—
366	C₃×Q₈	C₂²×C₃×D₃	1	2	yes	—
367	C₃×D₄	—	2	2	no	—
368	C₃×D₄	—	2	2	no	—
369	C₃×D₄	—	2	2	no	—
370	C₃×D₄	—	4	2	no	—
371	C₃×D₄	—	9	2	no	—
372	C₃×D₄	—	18	2	no	—
373	C₃×D₄	—	18	2	no	—
374	C₃×D₄	—	18	2	no	—
375	C₃×D₄	—	18	2	no	—
376	C₃×D₄	C₂²×D₉	1	2	yes	—
377	C₃×D₄	C₂²×C₃×D₃	1	2	yes	—
378	C₂×C₃×C₄	—	2	2	no	—
379	C₂×C₃×C₄	—	2	2	no	—
380	C₂×C₃×C₄	—	2	1	no	—
381	C₂×C₃×C₄	—	4	2	no	—
382	C₂×C₃×C₄	—	9	1	no	—
383	C₂×C₃×C₄	—	9	1	no	—
384	C₂×C₃×C₄	—	9	1	no	—
385	C₂×C₃×C₄	—	9	1	no	—
386	C₂×C₃×C₄	—	9	1	no	—
387	C₂×C₃×C₄	—	18	2	no	—
388	C₂×C₃×C₄	—	18	2	no	—
389	C₂×C₃×C₄	—	18	2	no	—
390	C₂×C₃×C₄	—	18	2	no	—
391	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
392	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
393	#67	—	6	2	no	—
394	#67	—	6	2	no	—
395	#67	—	6	2	no	—
396	C₂×Dic₃	—	3	1	no	—
397	C₂×Dic₃	—	6	2	no	—
398	D₁₂	—	3	2	no	—
399	D₁₂	—	6	2	no	—
400	C₄×D₃	—	3	1	no	—
401	C₄×D₃	—	3	1	no	—
402	C₄×D₃	—	3	1	no	—
403	C₄×D₃	—	3	1	no	—
404	C₄×D₃	—	6	2	no	—
405	C₄×D₃	—	6	2	no	—
406	C₄×D₃	—	6	2	no	—
407	Dic₆	—	3	2	no	—
408	Dic₆	—	6	2	no	—
409	C₃×C₈	—	2	1	no	—
410	C₃×C₈	—	2	1	no	—
411	C₃×C₈	—	9	1	no	—
412	C₃×C₈	—	9	1	no	—
413	C₃×C₈	C₂²×D₉	1	1	yes	characteristic
414	C₃×C₈	C₂²×D₉	1	1	yes	characteristic
415	C₃×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
416	C₃×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
417	C₃⋊C₈	—	3	1	no	—
418	C₃⋊C₈	—	3	1	no	—
419	C₂×C₃²	—	2	1	no	—
420	C₂×C₃²	—	4	2	no	—
421	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
422	C₃×D₃	—	3	2	no	—
423	C₃×D₃	—	6	1	no	—
424	C₃×D₃	—	12	2	no	—
425	C₂×C₉	—	2	1	no	—
426	C₂×C₉	—	2	1	no	—
427	C₂×C₉	—	4	1	no	—
428	C₂×C₉	—	4	2	no	—
429	C₂×C₉	—	8	2	no	—
430	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
431	D₉	—	2	1	no	—
432	D₉	—	4	2	no	—
433	D₉	C₃×#135	1	2	yes	direct product factor
434	#41	—	9	2	no	—
435	#41	—	9	2	no	—
436	#41	—	9	2	no	—
437	#41	—	18	2	no	—
438	#41	—	18	2	no	—
439	#41	C₂×C₃×D₉	1	2	yes	complemented
440	C₂×Q₈	—	9	2	no	—
441	C₂×D₄	—	9	2	no	—
442	C₂×D₄	—	18	2	no	—
443	C₂²×C₄	—	9	1	no	—
444	C₂²×C₄	—	18	2	no	—
445	Q₁₆	—	9	2	no	—
446	Q₁₆	—	9	1	no	—
447	Q₁₆	C₂×C₃×D₉	1	1	yes	characteristic, complemented
448	SD₁₆	—	9	2	no	—
449	SD₁₆	—	9	2	no	—
450	SD₁₆	—	9	2	no	—
451	SD₁₆	C₂×C₃×D₉	1	2	yes	complemented
452	D₈	—	9	2	no	—
453	D₈	—	9	1	no	—
454	D₈	C₂×C₃×D₉	1	1	yes	characteristic, complemented
455	C₂×C₈	—	9	1	no	—
456	C₂×C₈	—	9	1	no	—
457	C₂×C₈	—	9	1	no	—
458	C₂×C₈	—	9	1	no	—
459	C₂×C₈	—	9	1	no	—
460	C₂×C₈	C₂×C₃×D₉	1	1	yes	characteristic, complemented
461	C₂²×C₃	—	2	2	no	—
462	C₂²×C₃	—	2	2	no	—
463	C₂²×C₃	—	2	1	no	—
464	C₂²×C₃	—	4	2	no	—
465	C₂²×C₃	—	9	1	no	—
466	C₂²×C₃	—	9	1	no	—
467	C₂²×C₃	—	18	2	no	—
468	C₂²×C₃	—	18	2	no	—
469	C₂²×C₃	—	36	4	no	—
470	C₂²×C₃	D₄×D₉	1	1	yes	characteristic
471	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
472	C₂×D₃	—	3	1	no	—
473	C₂×D₃	—	3	1	no	—
474	C₂×D₃	—	6	2	no	—
475	C₂×D₃	—	6	2	no	—
476	C₂×D₃	—	12	4	no	—
477	C₃×C₄	—	2	2	no	—
478	C₃×C₄	—	2	2	no	—
479	C₃×C₄	—	2	1	no	—
480	C₃×C₄	—	2	1	no	—
481	C₃×C₄	—	4	2	no	—
482	C₃×C₄	—	9	1	no	—
483	C₃×C₄	—	9	1	no	—
484	C₃×C₄	—	18	2	no	—
485	C₃×C₄	D₄×D₉	1	1	yes	characteristic
486	C₃×C₄	C₂³×D₉	1	1	yes	characteristic
487	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
488	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
489	Dic₃	—	3	1	no	—
490	Dic₃	—	3	1	no	—
491	Dic₃	—	6	2	no	—
492	C₃²	D₃×#135	1	1	yes	characteristic
493	C₉	—	2	1	no	—
494	C₉	C₂×C₃×#135	1	1	yes	characteristic, complemented
495	C₂³	—	9	1	no	—
496	C₂³	—	18	2	no	—
497	Q₈	—	9	2	no	—
498	Q₈	—	18	2	no	—
499	Q₈	C₂²×C₃×D₉	1	2	yes	—
500	D₄	—	2	2	no	—
501	D₄	—	9	2	no	—
502	D₄	—	18	2	no	—
503	D₄	—	18	2	no	—
504	D₄	—	18	2	no	—
505	D₄	—	18	2	no	—
506	D₄	C₂²×C₃×D₉	1	2	yes	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	9	1	no	—
509	C₂×C₄	—	9	1	no	—
510	C₂×C₄	—	9	1	no	—
511	C₂×C₄	—	9	1	no	—
512	C₂×C₄	—	9	1	no	—
513	C₂×C₄	—	18	2	no	—
514	C₂×C₄	—	18	2	no	—
515	C₂×C₄	—	18	2	no	—
516	C₂×C₄	—	18	2	no	—
517	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
518	C₈	—	9	1	no	—
519	C₈	—	9	1	no	—
520	C₈	C₂²×C₃×D₉	1	1	yes	characteristic
521	C₈	C₂²×C₃×D₉	1	1	yes	characteristic
522	C₂×C₃	—	2	1	no	—
523	C₂×C₃	—	2	1	no	—
524	C₂×C₃	—	2	1	no	—
525	C₂×C₃	—	4	1	no	—
526	C₂×C₃	—	4	2	no	—
527	C₂×C₃	—	4	2	no	—
528	C₂×C₃	—	8	2	no	—
529	C₂×C₃	—	9	2	no	—
530	C₂×C₃	—	18	1	no	—
531	C₂×C₃	—	36	2	no	—
532	C₂×C₃	C₂×D₄×D₉	1	1	yes	characteristic
533	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
534	D₃	—	3	2	no	—
535	D₃	—	6	1	no	—
536	D₃	—	12	2	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	9	1	no	—
539	C₂²	—	9	1	no	—
540	C₂²	—	18	2	no	—
541	C₂²	—	18	2	no	—
542	C₂²	—	36	4	no	—
543	C₂²	C₃×D₄×D₉	1	1	yes	characteristic
544	C₄	—	2	2	no	—
545	C₄	—	9	1	no	—
546	C₄	—	9	1	no	—
547	C₄	—	18	2	no	—
548	C₄	C₃×D₄×D₉	1	1	yes	characteristic
549	C₄	C₂³×C₃×D₉	1	1	yes	characteristic
550	C₃	—	2	1	no	—
551	C₃	D₉×#135	1	1	yes	characteristic, direct product factor
552	C₃	C₃×D₃×#135	1	1	yes	characteristic
553	C₂	—	2	1	no	—
554	C₂	—	4	2	no	—
555	C₂	—	9	2	no	—
556	C₂	—	18	1	no	—
557	C₂	—	36	2	no	—
558	C₂	C₂×C₃×D₄×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	D₄×D₉
commutator, cosocle	C₄×C₉	C₂⁴×C₃
Frattini	C₃×C₄	C₂³×C₃×D₃
Fitting	C₃×C₉×#135	C₂
socle	C₂×C₃²	C₂×D₃×D₄
hypercenter	C₃×#135	D₉
hypocenter	C₉	C₂×C₃×#135
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ C₃×#135

Complements

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

N	H ≅ G/N	type
1. C₃×#41×D₉	C₂	semidirect
2. C₃×C₉×#135	C₂	semidirect
3. C₃×#63513	C₂	semidirect
4. C₃×#63481	C₂	semidirect
5. C₃×Q₁₆×D₉	C₂	semidirect
6. C₃×#63478	C₂	semidirect
7. C₃×SD₁₆×D₉	C₂	semidirect
8. C₃×#63474	C₂	semidirect
9. C₃×D₈×D₉	C₂	semidirect
10. C₃×#63467	C₂	semidirect
11. C₂×C₃×C₈×D₉	C₂	semidirect
13. D₉×#135	C₃	direct (N × H)
14. C₃×C₉×#41	C₂²	semidirect
15. C₃×#3701	C₂²	semidirect
18. C₃×#3699	C₂²	semidirect
22. C₃×#3697	C₂²	semidirect
25. C₃×C₉×Q₁₆	C₂²	semidirect
26. C₃×C₉×SD₁₆	C₂²	semidirect
27. C₃×C₉×D₈	C₂²	semidirect
28. C₂×C₃×C₈×C₉	C₂²	semidirect
29. C₃×#3675	C₂²	semidirect
30. C₃×#3674	C₂²	semidirect
31. C₃×#3673	C₂²	semidirect
32. C₃×#3672	C₂²	semidirect
33. C₂×C₃×C₉⋊C₈	C₂²	semidirect
34. C₃×D₇₂	C₂²	semidirect
35. C₃×#3664	C₂²	semidirect
38. C₃×C₈×D₉	C₂²	semidirect
39. C₃×C₈×D₉	C₂²	semidirect
40. C₃×Dic₃₆	C₂²	semidirect
52. #41×D₉	C₂×C₃	semidirect
54. C₉×#135	C₂×C₃	semidirect
55. #63513	C₂×C₃	semidirect
56. #63481	C₂×C₃	semidirect
57. Q₁₆×D₉	C₂×C₃	semidirect
58. #63478	C₂×C₃	semidirect
59. SD₁₆×D₉	C₂×C₃	semidirect
60. #63474	C₂×C₃	semidirect
61. D₈×D₉	C₂×C₃	semidirect
62. #63467	C₂×C₃	semidirect
63. C₂×C₈×D₉	C₂×C₃	semidirect
121. C₉×#41	C₂²×C₃	semidirect
122. #3701	C₂²×C₃	semidirect
125. #3699	C₂²×C₃	semidirect
129. #3697	C₂²×C₃	semidirect
133. C₉×Q₁₆	C₂²×C₃	semidirect
135. C₉×SD₁₆	C₂²×C₃	semidirect
137. C₉×D₈	C₂²×C₃	semidirect
139. C₂×C₈×C₉	C₂²×C₃	semidirect
140. #3675	C₂²×C₃	semidirect
141. #3674	C₂²×C₃	semidirect
142. #3673	C₂²×C₃	semidirect
143. #3672	C₂²×C₃	semidirect
144. C₂×C₉⋊C₈	C₂²×C₃	semidirect
145. D₇₂	C₂²×C₃	semidirect
146. #3664	C₂²×C₃	semidirect
149. C₈×D₉	C₂²×C₃	semidirect
150. C₈×D₉	C₂²×C₃	semidirect
151. Dic₃₆	C₂²×C₃	semidirect
173. C₃×#135	D₉	direct (N × H)
255. C₃×D₉	#135	direct (N × H)
262. C₃×#41	C₂×D₉	semidirect
282. C₃×Q₁₆	C₂×D₉	semidirect
288. C₃×SD₁₆	C₂×D₉	semidirect
293. C₃×D₈	C₂×D₉	semidirect
301. C₂×C₃×C₈	C₂×D₉	semidirect
352. #135	C₃×D₉	direct (N × H)
357. C₃×C₉	C₂×#135	semidirect
433. D₉	C₃×#135	direct (N × H)
439. #41	C₂×C₃×D₉	semidirect
447. Q₁₆	C₂×C₃×D₉	semidirect
451. SD₁₆	C₂×C₃×D₉	semidirect
454. D₈	C₂×C₃×D₉	semidirect
460. C₂×C₈	C₂×C₃×D₉	semidirect
494. C₉	C₂×C₃×#135	semidirect
551. C₃	D₉×#135	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×#41×D₉	2
C₃×C₉×#135	2
C₃×#63513	2
C₃×#63481	2
C₃×Q₁₆×D₉	2
C₃×#63478	2
C₃×SD₁₆×D₉	2
C₃×#63474	2
C₃×D₈×D₉	2
C₃×#63467	2
C₂×C₃×C₈×D₉	2
C₃×D₃×#135	3
D₉×#135	3

Subgroups — C3×D9×#135 #13153471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₉×#135 #13153471