Subgroups — C₃×#10589870 #13153472

Order 1728.

848 conjugacy classes of subgroups.

The subgroup lattice has 500 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×#63480	C₂	1	2	yes	maximal, complemented
5	C₃×#63477	C₂	1	2	yes	maximal, complemented
6	C₃×#63476	C₂	1	2	yes	maximal, complemented
7	C₃×#63473	C₂	1	2	yes	maximal, complemented
8	C₃×#63467	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#3663	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#5768	—	3	1	no	maximal
11	#10589870	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₃×C₉×#41	C₂²	1	2	yes	complemented
13	C₃×#3701	C₂²	1	2	yes	—
14	C₃×Q₈×D₉	C₂²	1	2	yes	complemented
15	C₃×#3699	—	2	2	no	—
16	C₃×#3699	C₂²	1	2	yes	—
17	C₃×D₄×D₉	—	2	2	no	—
18	C₃×D₄×D₉	C₂²	1	2	yes	complemented
19	C₃×#3697	—	2	2	no	—
20	C₃×#3697	C₂²	1	2	yes	complemented
21	C₂×C₃×C₄×D₉	—	2	2	no	—
22	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
23	C₃×C₉×Q₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₉×SD₁₆	C₂²	1	2	yes	complemented
25	C₃×C₉×D₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic, complemented
27	C₃×#3675	C₂²	1	2	yes	complemented
28	C₃×#3674	C₂²	1	2	yes	complemented
29	C₃×#3673	C₂²	1	2	yes	complemented
30	C₃×#3672	C₂²	1	2	yes	complemented
31	C₂×C₃×C₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×D₇₂	C₂²	1	1	yes	characteristic, complemented
33	C₃×#3664	C₂²	1	2	yes	complemented
34	C₃×#3663	C₂²	1	2	yes	complemented
35	C₃×#3663	C₂²	1	2	yes	complemented
36	C₃×Dic₃₆	C₂²	1	1	yes	characteristic, complemented
37	C₃×D₃×#41	—	3	2	no	—
38	C₃²×#135	D₃	1	1	yes	characteristic
39	C₃×#950	—	3	2	no	—
40	C₃×#918	—	3	2	no	—
41	C₃×#915	—	3	2	no	—
42	C₃×#914	—	3	2	no	—
43	C₃×#911	—	3	2	no	—
44	C₃×#904	—	3	1	no	—
45	C₂×C₃×ΓL(1,𝔽₂₅)	—	3	1	no	—
46	#41×D₉	C₂×C₃	1	2	yes	complemented
47	C₉×#135	—	2	1	no	—
48	C₉×#135	C₂×C₃	1	1	yes	characteristic, complemented
49	#63513	C₂×C₃	1	2	yes	complemented
50	#63480	C₂×C₃	1	2	yes	complemented
51	#63477	C₂×C₃	1	2	yes	complemented
52	#63476	C₂×C₃	1	2	yes	complemented
53	#63473	C₂×C₃	1	2	yes	complemented
54	#63467	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×#3663	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂²×C₃×D₉	—	2	2	no	—
57	C₂²×C₃×D₉	D₄	1	1	yes	characteristic
58	C₃×Q₈×C₉	C₂³	1	2	yes	—
59	C₃×D₄×C₉	—	2	2	no	—
60	C₃×D₄×C₉	C₂³	1	2	yes	—
61	C₂×C₃×C₄×C₉	—	2	2	no	—
62	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
63	C₃×#611	—	2	2	no	—
64	C₃×#611	—	2	2	no	—
65	C₃×#611	—	2	2	no	—
66	C₂×C₃×Dic₉	—	2	2	no	—
67	C₂×C₃×Dic₉	D₄	1	1	yes	characteristic
68	C₃×D₃₆	—	2	2	no	—
69	C₃×D₃₆	C₂³	1	2	yes	—
70	C₃×C₄×D₉	—	2	2	no	—
71	C₃×C₄×D₉	—	2	2	no	—
72	C₃×C₄×D₉	—	2	2	no	—
73	C₃×C₄×D₉	D₄	1	2	yes	—
74	C₃×C₄×D₉	C₂³	1	2	yes	—
75	C₃×Dic₁₈	—	2	2	no	—
76	C₃×Dic₁₈	C₂³	1	2	yes	—
77	C₃×C₈×C₉	C₂³	1	1	yes	characteristic
78	C₃×C₈×C₉	C₂³	1	1	yes	characteristic
79	C₃×C₉⋊C₈	C₂³	1	2	yes	—
80	C₃×#575	—	9	1	no	—
81	#5768	—	3	1	no	—
82	C₃²×#41	C₂×D₃	1	2	yes	—
83	C₃×#239	—	3	2	no	—
84	C₃×D₃×Q₈	—	3	2	no	—
85	C₃×#237	—	3	2	no	—
86	C₃×#237	—	6	2	no	—
87	C₃×D₃×D₄	—	3	2	no	—
88	C₃×D₃×D₄	—	6	2	no	—
89	C₃×#235	—	3	2	no	—
90	C₃×#235	—	6	2	no	—
91	C₂×C₃×C₄×D₃	—	3	1	no	—
92	C₂×C₃×C₄×D₃	—	6	2	no	—
93	C₃²×Q₁₆	C₂×D₃	1	1	yes	characteristic
94	C₃²×SD₁₆	C₂×D₃	1	2	yes	—
95	C₃²×D₈	C₂×D₃	1	1	yes	characteristic
96	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
97	C₃×#216	—	3	2	no	—
98	C₃×#215	—	3	2	no	—
99	C₃×#214	—	3	2	no	—
100	C₃×#213	—	3	2	no	—
101	C₂×C₃×C₃⋊C₈	—	3	1	no	—
102	C₃×Dic₁₂	—	3	1	no	—
103	C₃×D₂₄	—	3	1	no	—
104	C₃×#204	—	3	2	no	—
105	C₃×ΓL(1,𝔽₂₅)	—	3	2	no	—
106	C₃×ΓL(1,𝔽₂₅)	—	3	2	no	—
107	C₉×#41	—	2	2	no	—
108	C₉×#41	C₂²×C₃	1	2	yes	complemented
109	#3701	C₂²×C₃	1	2	yes	—
110	Q₈×D₉	C₂²×C₃	1	2	yes	complemented
111	#3699	—	2	2	no	—
112	#3699	C₂²×C₃	1	2	yes	—
113	D₄×D₉	—	2	2	no	—
114	D₄×D₉	C₂²×C₃	1	2	yes	complemented
115	#3697	—	2	2	no	—
116	#3697	C₂²×C₃	1	2	yes	complemented
117	C₂×C₄×D₉	—	2	2	no	—
118	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
119	C₉×Q₁₆	—	2	1	no	—
120	C₉×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
121	C₉×SD₁₆	—	2	2	no	—
122	C₉×SD₁₆	C₂²×C₃	1	2	yes	complemented
123	C₉×D₈	—	2	1	no	—
124	C₉×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₂×C₈×C₉	—	2	1	no	—
126	C₂×C₈×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
127	#3675	C₂²×C₃	1	2	yes	complemented
128	#3674	C₂²×C₃	1	2	yes	complemented
129	#3673	C₂²×C₃	1	2	yes	complemented
130	#3672	C₂²×C₃	1	2	yes	complemented
131	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
132	D₇₂	C₂²×C₃	1	1	yes	characteristic, complemented
133	#3664	C₂²×C₃	1	2	yes	complemented
134	#3663	C₂²×C₃	1	2	yes	complemented
135	#3663	C₂²×C₃	1	2	yes	complemented
136	Dic₃₆	C₂²×C₃	1	1	yes	characteristic, complemented
137	C₂²×C₃×C₉	—	2	2	no	—
138	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×D₉	—	2	2	no	—
140	C₂×C₃×D₉	—	4	1	no	—
141	C₂×C₃×D₉	—	4	4	no	—
142	C₂×C₃×D₉	C₂×D₄	1	2	yes	—
143	C₃×C₄×C₉	—	2	2	no	—
144	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
145	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
146	C₃×Dic₉	—	2	2	no	—
147	C₃×Dic₉	C₂×D₄	1	2	yes	—
148	C₂×C₃×#41	—	9	2	no	—
149	D₃×#41	—	3	2	no	—
150	C₃×#137	—	9	2	no	—
151	C₃×#137	—	9	2	no	—
152	C₃×AGL(1,ℤ/8)	—	9	2	no	—
153	C₃×AGL(1,ℤ/8)	—	9	2	no	—
154	C₃×#135	—	2	1	no	—
155	C₃×#135	—	9	2	no	—
156	C₃×#135	—	9	1	no	—
157	C₃×#135	D₉	1	1	yes	characteristic, complemented
158	C₃×#135	C₃×D₃	1	1	yes	characteristic
159	C₂×C₃×M₁₆	—	9	1	no	—
160	#950	—	3	2	no	—
161	#918	—	3	2	no	—
162	#915	—	3	2	no	—
163	#914	—	3	2	no	—
164	#911	—	3	2	no	—
165	#904	—	3	1	no	—
166	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
167	C₂²×C₃×D₃	—	3	1	no	—
168	C₂²×C₃×D₃	—	6	2	no	—
169	C₃²×Q₈	C₂²×D₃	1	2	yes	—
170	C₃²×D₄	—	2	2	no	—
171	C₃²×D₄	C₂²×D₃	1	2	yes	—
172	C₂×C₃²×C₄	—	2	2	no	—
173	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
174	C₃×#67	—	6	2	no	—
175	C₃×#67	—	6	2	no	—
176	C₃×#67	—	6	2	no	—
177	C₂×C₃×Dic₃	—	3	1	no	—
178	C₂×C₃×Dic₃	—	6	2	no	—
179	C₃×D₁₂	—	3	2	no	—
180	C₃×D₁₂	—	6	2	no	—
181	C₃×C₄×D₃	—	3	2	no	—
182	C₃×C₄×D₃	—	3	2	no	—
183	C₃×C₄×D₃	—	6	2	no	—
184	C₃×C₄×D₃	—	6	2	no	—
185	C₃×C₄×D₃	—	6	2	no	—
186	C₃×Dic₆	—	3	2	no	—
187	C₃×Dic₆	—	6	2	no	—
188	C₂²×D₉	—	2	2	no	—
189	C₂²×D₉	C₃×D₄	1	1	yes	characteristic
190	C₃²×C₈	C₂²×D₃	1	1	yes	characteristic
191	C₃²×C₈	C₂²×D₃	1	1	yes	characteristic
192	C₃×C₃⋊C₈	—	3	2	no	—
193	Q₈×C₉	—	2	2	no	—
194	Q₈×C₉	C₂³×C₃	1	2	yes	—
195	D₄×C₉	—	2	2	no	—
196	D₄×C₉	—	2	2	no	—
197	D₄×C₉	—	4	2	no	—
198	D₄×C₉	C₂³×C₃	1	2	yes	—
199	C₂×C₄×C₉	—	2	2	no	—
200	C₂×C₄×C₉	—	2	1	no	—
201	C₂×C₄×C₉	—	4	2	no	—
202	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
203	#611	—	2	2	no	—
204	#611	—	2	2	no	—
205	#611	—	2	2	no	—
206	C₂×Dic₉	—	2	2	no	—
207	C₂×Dic₉	C₃×D₄	1	1	yes	characteristic
208	D₃₆	—	2	2	no	—
209	D₃₆	C₂³×C₃	1	2	yes	—
210	C₄×D₉	—	2	2	no	—
211	C₄×D₉	—	2	2	no	—
212	C₄×D₉	—	2	2	no	—
213	C₄×D₉	C₃×D₄	1	2	yes	—
214	C₄×D₉	C₂³×C₃	1	2	yes	—
215	Dic₁₈	—	2	2	no	—
216	Dic₁₈	C₂³×C₃	1	2	yes	—
217	C₈×C₉	—	2	1	no	—
218	C₈×C₉	—	2	1	no	—
219	C₈×C₉	C₂³×C₃	1	1	yes	characteristic
220	C₈×C₉	C₂³×C₃	1	1	yes	characteristic
221	C₉⋊C₈	C₂³×C₃	1	2	yes	—
222	#575	—	9	1	no	Sylow
223	C₂×C₃×C₉	—	2	1	no	—
224	C₂×C₃×C₉	—	4	2	no	—
225	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
226	C₃×D₉	—	2	2	no	—
227	C₃×D₉	—	4	2	no	—
228	C₃×#41	—	2	2	no	—
229	C₃×#41	—	9	2	no	—
230	C₃×#41	—	9	2	no	—
231	C₃×#41	—	9	2	no	—
232	C₃×#41	—	18	2	no	—
233	C₃×#41	—	18	2	no	—
234	C₃×#41	C₂×D₉	1	2	yes	complemented
235	C₃×#41	C₂×C₃×D₃	1	2	yes	—
236	C₂×C₃×Q₈	—	9	2	no	—
237	C₂×C₃×D₄	—	9	2	no	—
238	C₂×C₃×D₄	—	18	2	no	—
239	C₂²×C₃×C₄	—	9	1	no	—
240	C₂²×C₃×C₄	—	18	2	no	—
241	#239	—	3	2	no	—
242	D₃×Q₈	—	3	2	no	—
243	#237	—	3	2	no	—
244	#237	—	6	2	no	—
245	D₃×D₄	—	3	2	no	—
246	D₃×D₄	—	6	2	no	—
247	#235	—	3	2	no	—
248	#235	—	6	2	no	—
249	C₂×C₄×D₃	—	3	1	no	—
250	C₂×C₄×D₃	—	6	2	no	—
251	C₃×Q₁₆	—	2	1	no	—
252	C₃×Q₁₆	—	9	2	no	—
253	C₃×Q₁₆	—	9	1	no	—
254	C₃×Q₁₆	C₂×D₉	1	1	yes	characteristic, complemented
255	C₃×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic
256	C₃×SD₁₆	—	2	2	no	—
257	C₃×SD₁₆	—	9	2	no	—
258	C₃×SD₁₆	—	9	2	no	—
259	C₃×SD₁₆	—	9	2	no	—
260	C₃×SD₁₆	C₂×D₉	1	2	yes	complemented
261	C₃×SD₁₆	C₂×C₃×D₃	1	2	yes	—
262	C₃×D₈	—	2	1	no	—
263	C₃×D₈	—	9	2	no	—
264	C₃×D₈	—	9	1	no	—
265	C₃×D₈	C₂×D₉	1	1	yes	characteristic, complemented
266	C₃×D₈	C₂×C₃×D₃	1	1	yes	characteristic
267	C₃×M₁₆	—	9	2	no	—
268	C₃×M₁₆	—	9	2	no	—
269	C₂×C₃×C₈	—	2	1	no	—
270	C₂×C₃×C₈	—	9	1	no	—
271	C₂×C₃×C₈	C₂×D₉	1	1	yes	characteristic, complemented
272	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
273	#216	—	3	2	no	—
274	#215	—	3	2	no	—
275	#214	—	3	2	no	—
276	#213	—	3	2	no	—
277	C₂×C₃⋊C₈	—	3	1	no	—
278	Dic₁₂	—	3	1	no	—
279	D₂₄	—	3	1	no	—
280	#204	—	3	2	no	—
281	ΓL(1,𝔽₂₅)	—	3	2	no	—
282	ΓL(1,𝔽₂₅)	—	3	2	no	—
283	C₂²×C₃²	—	2	2	no	—
284	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
285	C₂×C₃×D₃	—	3	2	no	—
286	C₂×C₃×D₃	—	6	2	no	—
287	C₂×C₃×D₃	—	12	1	no	—
288	C₂×C₃×D₃	—	12	4	no	—
289	C₃²×C₄	—	2	2	no	—
290	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
291	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
292	C₃×Dic₃	—	3	2	no	—
293	C₃×Dic₃	—	6	2	no	—
294	C₂²×C₉	—	2	2	no	—
295	C₂²×C₉	—	2	1	no	—
296	C₂²×C₉	—	4	2	no	—
297	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
298	C₂×D₉	—	2	2	no	—
299	C₂×D₉	—	4	1	no	—
300	C₂×D₉	—	4	4	no	—
301	C₂×D₉	C₂×C₃×D₄	1	2	yes	—
302	C₄×C₉	—	2	2	no	—
303	C₄×C₉	—	2	1	no	—
304	C₄×C₉	—	2	1	no	—
305	C₄×C₉	—	4	2	no	—
306	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
307	C₄×C₉	C₂⁴×C₃	1	1	yes	characteristic
308	Dic₉	—	2	2	no	—
309	Dic₉	C₂×C₃×D₄	1	2	yes	—
310	C₂×#41	—	9	2	no	—
311	#137	—	9	2	no	—
312	#137	—	9	2	no	—
313	AGL(1,ℤ/8)	—	9	2	no	—
314	AGL(1,ℤ/8)	—	9	2	no	—
315	#135	—	9	2	no	—
316	#135	—	9	1	no	—
317	#135	C₃×D₉	1	1	yes	characteristic, complemented
318	C₂×M₁₆	—	9	1	no	—
319	C₃×C₉	#575	1	1	yes	characteristic, complemented, Sylow
320	C₂³×C₃	—	9	1	no	—
321	C₂³×C₃	—	18	2	no	—
322	C₂²×D₃	—	3	1	no	—
323	C₂²×D₃	—	6	2	no	—
324	C₃×Q₈	—	2	2	no	—
325	C₃×Q₈	—	9	2	no	—
326	C₃×Q₈	—	18	2	no	—
327	C₃×Q₈	C₂²×D₉	1	2	yes	—
328	C₃×Q₈	C₂²×C₃×D₃	1	2	yes	—
329	C₃×D₄	—	2	2	no	—
330	C₃×D₄	—	2	2	no	—
331	C₃×D₄	—	2	2	no	—
332	C₃×D₄	—	4	2	no	—
333	C₃×D₄	—	9	2	no	—
334	C₃×D₄	—	18	2	no	—
335	C₃×D₄	—	18	2	no	—
336	C₃×D₄	—	18	2	no	—
337	C₃×D₄	—	18	2	no	—
338	C₃×D₄	C₂²×D₉	1	2	yes	—
339	C₃×D₄	C₂²×C₃×D₃	1	2	yes	—
340	C₂×C₃×C₄	—	2	2	no	—
341	C₂×C₃×C₄	—	2	2	no	—
342	C₂×C₃×C₄	—	2	1	no	—
343	C₂×C₃×C₄	—	4	2	no	—
344	C₂×C₃×C₄	—	9	1	no	—
345	C₂×C₃×C₄	—	9	2	no	—
346	C₂×C₃×C₄	—	9	2	no	—
347	C₂×C₃×C₄	—	18	2	no	—
348	C₂×C₃×C₄	—	18	2	no	—
349	C₂×C₃×C₄	—	18	2	no	—
350	C₂×C₃×C₄	—	18	2	no	—
351	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
353	#67	—	6	2	no	—
354	#67	—	6	2	no	—
355	#67	—	6	2	no	—
356	C₂×Dic₃	—	3	1	no	—
357	C₂×Dic₃	—	6	2	no	—
358	D₁₂	—	3	2	no	—
359	D₁₂	—	6	2	no	—
360	C₄×D₃	—	3	2	no	—
361	C₄×D₃	—	3	2	no	—
362	C₄×D₃	—	6	2	no	—
363	C₄×D₃	—	6	2	no	—
364	C₄×D₃	—	6	2	no	—
365	Dic₆	—	3	2	no	—
366	Dic₆	—	6	2	no	—
367	C₃×C₈	—	2	1	no	—
368	C₃×C₈	—	2	1	no	—
369	C₃×C₈	—	9	2	no	—
370	C₃×C₈	C₂²×D₉	1	1	yes	characteristic
371	C₃×C₈	C₂²×D₉	1	1	yes	characteristic
372	C₃×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
373	C₃×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
374	C₃⋊C₈	—	3	2	no	—
375	C₂×C₃²	—	2	1	no	—
376	C₂×C₃²	—	4	2	no	—
377	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
378	C₃×D₃	—	6	2	no	—
379	C₃×D₃	—	12	2	no	—
380	C₂×C₉	—	2	1	no	—
381	C₂×C₉	—	2	1	no	—
382	C₂×C₉	—	4	1	no	—
383	C₂×C₉	—	4	2	no	—
384	C₂×C₉	—	8	2	no	—
385	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
386	D₉	—	2	2	no	—
387	D₉	—	4	2	no	—
388	#41	—	9	2	no	—
389	#41	—	9	2	no	—
390	#41	—	9	2	no	—
391	#41	—	18	2	no	—
392	#41	—	18	2	no	—
393	#41	C₂×C₃×D₉	1	2	yes	complemented
394	C₂×Q₈	—	9	2	no	—
395	C₂×D₄	—	9	2	no	—
396	C₂×D₄	—	18	2	no	—
397	C₂²×C₄	—	9	1	no	—
398	C₂²×C₄	—	18	2	no	—
399	Q₁₆	—	9	2	no	—
400	Q₁₆	—	9	1	no	—
401	Q₁₆	C₂×C₃×D₉	1	1	yes	characteristic, complemented
402	SD₁₆	—	9	2	no	—
403	SD₁₆	—	9	2	no	—
404	SD₁₆	—	9	2	no	—
405	SD₁₆	C₂×C₃×D₉	1	2	yes	complemented
406	D₈	—	9	2	no	—
407	D₈	—	9	1	no	—
408	D₈	C₂×C₃×D₉	1	1	yes	characteristic, complemented
409	M₁₆	—	9	2	no	—
410	M₁₆	—	9	2	no	—
411	C₂×C₈	—	9	1	no	—
412	C₂×C₈	C₂×C₃×D₉	1	1	yes	characteristic, complemented
413	C₂²×C₃	—	2	2	no	—
414	C₂²×C₃	—	2	2	no	—
415	C₂²×C₃	—	2	1	no	—
416	C₂²×C₃	—	4	2	no	—
417	C₂²×C₃	—	9	2	no	—
418	C₂²×C₃	—	18	2	no	—
419	C₂²×C₃	—	36	1	no	—
420	C₂²×C₃	—	36	4	no	—
421	C₂²×C₃	D₄×D₉	1	1	yes	characteristic
422	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
423	C₂×D₃	—	3	2	no	—
424	C₂×D₃	—	6	2	no	—
425	C₂×D₃	—	12	1	no	—
426	C₂×D₃	—	12	4	no	—
427	C₃×C₄	—	2	2	no	—
428	C₃×C₄	—	2	2	no	—
429	C₃×C₄	—	2	1	no	—
430	C₃×C₄	—	2	1	no	—
431	C₃×C₄	—	4	2	no	—
432	C₃×C₄	—	9	2	no	—
433	C₃×C₄	—	18	2	no	—
434	C₃×C₄	D₄×D₉	1	1	yes	characteristic
435	C₃×C₄	C₂³×D₉	1	1	yes	characteristic
436	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
437	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
438	Dic₃	—	3	2	no	—
439	Dic₃	—	6	2	no	—
440	C₃²	#5768	1	1	yes	characteristic
441	C₉	—	2	1	no	—
442	C₉	C₃×#575	1	1	yes	characteristic, complemented
443	C₂³	—	9	1	no	—
444	C₂³	—	18	2	no	—
445	Q₈	—	9	2	no	—
446	Q₈	—	18	2	no	—
447	Q₈	C₂²×C₃×D₉	1	2	yes	—
448	D₄	—	2	2	no	—
449	D₄	—	9	2	no	—
450	D₄	—	18	2	no	—
451	D₄	—	18	2	no	—
452	D₄	—	18	2	no	—
453	D₄	—	18	2	no	—
454	D₄	C₂²×C₃×D₉	1	2	yes	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	9	1	no	—
457	C₂×C₄	—	9	2	no	—
458	C₂×C₄	—	9	2	no	—
459	C₂×C₄	—	18	2	no	—
460	C₂×C₄	—	18	2	no	—
461	C₂×C₄	—	18	2	no	—
462	C₂×C₄	—	18	2	no	—
463	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
464	C₈	—	9	2	no	—
465	C₈	C₂²×C₃×D₉	1	1	yes	characteristic
466	C₈	C₂²×C₃×D₉	1	1	yes	characteristic
467	C₂×C₃	—	2	1	no	—
468	C₂×C₃	—	2	1	no	—
469	C₂×C₃	—	2	1	no	—
470	C₂×C₃	—	4	1	no	—
471	C₂×C₃	—	4	2	no	—
472	C₂×C₃	—	4	2	no	—
473	C₂×C₃	—	8	2	no	—
474	C₂×C₃	—	18	2	no	—
475	C₂×C₃	—	36	2	no	—
476	C₂×C₃	C₂×D₄×D₉	1	1	yes	characteristic
477	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
478	D₃	—	6	2	no	—
479	D₃	—	12	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	9	2	no	—
482	C₂²	—	18	2	no	—
483	C₂²	—	36	1	no	—
484	C₂²	—	36	4	no	—
485	C₂²	C₃×D₄×D₉	1	1	yes	characteristic
486	C₄	—	2	2	no	—
487	C₄	—	9	2	no	—
488	C₄	—	18	2	no	—
489	C₄	C₃×D₄×D₉	1	1	yes	characteristic
490	C₄	C₂³×C₃×D₉	1	1	yes	characteristic
491	C₃	—	2	1	no	—
492	C₃	#10589870	1	1	yes	characteristic, direct product factor
493	C₃	C₃×#5768	1	1	yes	characteristic
494	C₂	—	2	1	no	—
495	C₂	—	4	2	no	—
496	C₂	—	18	2	no	—
497	C₂	—	36	2	no	—
498	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	C₃×#575
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×#63480	C₂	semidirect
5. C₃×#63477	C₂	semidirect
6. C₃×#63476	C₂	semidirect
7. C₃×#63473	C₂	semidirect
8. C₃×#63467	C₂	semidirect
9. C₂×C₃×#3663	C₂	semidirect
11. #10589870	C₃	direct (N × H)
12. C₃×C₉×#41	C₂²	semidirect
14. C₃×Q₈×D₉	C₂²	semidirect
18. C₃×D₄×D₉	C₂²	semidirect
20. C₃×#3697	C₂²	semidirect
23. C₃×C₉×Q₁₆	C₂²	semidirect
24. C₃×C₉×SD₁₆	C₂²	semidirect
25. C₃×C₉×D₈	C₂²	semidirect
26. C₂×C₃×C₈×C₉	C₂²	semidirect
27. C₃×#3675	C₂²	semidirect
28. C₃×#3674	C₂²	semidirect
29. C₃×#3673	C₂²	semidirect
30. C₃×#3672	C₂²	semidirect
31. C₂×C₃×C₉⋊C₈	C₂²	semidirect
32. C₃×D₇₂	C₂²	semidirect
33. C₃×#3664	C₂²	semidirect
34. C₃×#3663	C₂²	semidirect
35. C₃×#3663	C₂²	semidirect
36. C₃×Dic₃₆	C₂²	semidirect
46. #41×D₉	C₂×C₃	semidirect
48. C₉×#135	C₂×C₃	semidirect
49. #63513	C₂×C₃	semidirect
50. #63480	C₂×C₃	semidirect
51. #63477	C₂×C₃	semidirect
52. #63476	C₂×C₃	semidirect
53. #63473	C₂×C₃	semidirect
54. #63467	C₂×C₃	semidirect
55. C₂×#3663	C₂×C₃	semidirect
108. C₉×#41	C₂²×C₃	semidirect
110. Q₈×D₉	C₂²×C₃	semidirect
114. D₄×D₉	C₂²×C₃	semidirect
116. #3697	C₂²×C₃	semidirect
120. C₉×Q₁₆	C₂²×C₃	semidirect
122. C₉×SD₁₆	C₂²×C₃	semidirect
124. C₉×D₈	C₂²×C₃	semidirect
126. C₂×C₈×C₉	C₂²×C₃	semidirect
127. #3675	C₂²×C₃	semidirect
128. #3674	C₂²×C₃	semidirect
129. #3673	C₂²×C₃	semidirect
130. #3672	C₂²×C₃	semidirect
131. C₂×C₉⋊C₈	C₂²×C₃	semidirect
132. D₇₂	C₂²×C₃	semidirect
133. #3664	C₂²×C₃	semidirect
134. #3663	C₂²×C₃	semidirect
135. #3663	C₂²×C₃	semidirect
136. Dic₃₆	C₂²×C₃	semidirect
157. C₃×#135	D₉	semidirect
234. C₃×#41	C₂×D₉	semidirect
254. C₃×Q₁₆	C₂×D₉	semidirect
260. C₃×SD₁₆	C₂×D₉	semidirect
265. C₃×D₈	C₂×D₉	semidirect
271. C₂×C₃×C₈	C₂×D₉	semidirect
317. #135	C₃×D₉	semidirect
319. C₃×C₉	#575	semidirect
393. #41	C₂×C₃×D₉	semidirect
401. Q₁₆	C₂×C₃×D₉	semidirect
405. SD₁₆	C₂×C₃×D₉	semidirect
408. D₈	C₂×C₃×D₉	semidirect
412. C₂×C₈	C₂×C₃×D₉	semidirect
442. C₉	C₃×#575	semidirect
492. C₃	#10589870	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×#63480	2
C₃×#63477	2
C₃×#63476	2
C₃×#63473	2
C₃×#63467	2
C₂×C₃×#3663	2
C₃×#5768	3
#10589870	3

Subgroups — C3×#10589870 #13153472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589870 #13153472