Subgroups — D₃×#65167 #14439800

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×#4036	C₂	1	2	yes	maximal
2	#11750979	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×#107	C₂	1	1	yes	maximal, characteristic
4	C₃×#65167	C₂	1	1	yes	maximal, characteristic, complemented
5	#11747992	C₂	1	1	yes	maximal, characteristic, complemented
6	#11747986	C₂	1	1	yes	maximal, characteristic, complemented
7	D₃×#3950	C₂	1	1	yes	maximal, characteristic
8	D₃×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic
9	D₃×#3940	C₂	1	2	yes	maximal
10	#11747152	C₂	1	2	yes	maximal, complemented
11	#11747143	C₂	1	2	yes	maximal, complemented
12	C₂×#65167	—	3	1	no	maximal, Hall
13	#91779	C₂²	1	2	yes	—
14	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
15	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
16	C₃×#4036	C₂²	1	2	yes	—
17	D₃×C₄⋊Dic₅	—	2	2	no	—
18	D₃×C₄⋊Dic₅	C₂²	1	2	yes	—
19	D₃×#683	—	2	2	no	—
20	C₄×D₃×Dic₅	C₂²	1	1	yes	characteristic
21	#91388	C₂²	1	2	yes	—
22	#91384	C₂²	1	2	yes	—
23	#91346	—	2	2	no	—
24	#91343	—	2	2	no	—
25	C₂×D₃×#168	C₂²	1	1	yes	characteristic
26	C₃×C₅×#107	C₂²	1	1	yes	characteristic
27	#91102	C₂²	1	1	yes	characteristic
28	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
29	#91092	C₂²	1	2	yes	—
30	C₅×#818	C₂²	1	1	yes	characteristic
31	C₅×#807	C₂²	1	2	yes	—
32	C₃×#3950	C₂²	1	1	yes	characteristic
33	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
34	C₃×#3940	C₂²	1	2	yes	—
35	#90990	C₂²	1	2	yes	—
36	#90986	C₂²	1	2	yes	—
37	#90985	C₂²	1	2	yes	—
38	#90951	C₂²	1	1	yes	characteristic
39	Dic₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
40	D₃×#499	—	5	1	no	maximal, Hall
41	C₂×#4036	—	3	2	no	—
42	C₂×C₅×#107	—	3	1	no	—
43	C₂×#3950	—	3	1	no	—
44	C₂×C₈×Dic₅	—	3	1	no	—
45	C₂×#3940	—	3	2	no	—
46	#65167	—	3	2	no	—
47	#65167	—	3	1	no	—
48	#65167	—	3	1	no	—
49	#65167	—	3	1	no	—
50	#65167	—	3	2	no	—
51	#65167	D₃	1	1	yes	characteristic, direct product factor
52	C₂×C₄×C₅×D₃	—	2	2	no	—
53	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
54	C₂×D₃×Dic₅	—	2	2	no	—
55	C₂×D₃×Dic₅	D₄	1	1	yes	characteristic
56	C₂×D₃×Dic₅	D₄	1	1	yes	characteristic
57	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
59	C₄⋊Dic₁₅	—	2	2	no	—
60	C₄⋊Dic₁₅	C₂³	1	2	yes	—
61	#6712	—	2	2	no	—
62	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
63	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
64	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
65	C₅×Dic₃⋊C₄	—	2	2	no	—
66	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
67	C₅×D₃×C₈	Q₈	1	4	yes	—
68	C₃×C₄⋊Dic₅	—	2	2	no	—
69	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
70	C₃×#683	—	2	2	no	—
71	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
72	C₂×C₃×#168	C₂³	1	1	yes	characteristic
73	Dic₃⋊Dic₅	—	2	2	no	—
74	Dic₃⋊Dic₅	—	2	2	no	—
75	Dic₃⋊Dic₅	—	2	2	no	—
76	#6669	—	2	2	no	—
77	#6668	—	2	2	no	—
78	Dic₃×Dic₅	D₄	1	1	yes	characteristic
79	Dic₃×Dic₅	D₄	1	1	yes	characteristic
80	D₃×#168	Q₈	1	4	yes	—
81	D₃×#125	—	5	2	no	—
82	C₃×#499	—	5	1	no	—
83	#5065	—	5	2	no	—
84	D₃×#107	—	5	1	no	—
85	D₃×#107	D₅	1	1	yes	characteristic
86	#4878	—	5	1	no	—
87	#4878	—	5	1	no	—
88	D₃×#106	—	5	2	no	—
89	#4858	—	5	2	no	—
90	C₄×D₃×C₈	—	5	1	no	—
91	#4683	—	5	1	no	—
92	C₂²×C₅×C₈	—	3	1	no	—
93	C₂×C₅×C₄⋊C₄	—	3	2	no	—
94	C₂×C₄⋊Dic₅	—	3	2	no	—
95	C₂×C₄⋊Dic₅	—	6	2	no	—
96	C₂×#683	—	6	2	no	—
97	C₂×C₄×Dic₅	—	3	1	no	—
98	C₂²×#168	—	3	1	no	—
99	#4036	—	3	2	no	—
100	#4036	—	3	2	no	—
101	#4036	—	3	2	no	—
102	#4036	—	6	2	no	—
103	#4036	—	6	2	no	—
104	#4036	C₂×D₃	1	2	yes	—
105	C₅×#107	—	3	1	no	—
106	C₅×#107	—	3	2	no	—
107	C₅×#107	C₂×D₃	1	1	yes	characteristic
108	#3950	—	3	1	no	—
109	#3950	—	3	2	no	—
110	#3950	C₂×D₃	1	1	yes	characteristic
111	C₈×Dic₅	—	3	1	no	—
112	C₈×Dic₅	—	3	1	no	—
113	C₈×Dic₅	—	3	1	no	—
114	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
115	#3940	—	3	2	no	—
116	#3940	—	3	2	no	—
117	#3940	—	3	2	no	—
118	#3940	C₂×D₃	1	2	yes	—
119	C₂×#499	—	15	1	no	Sylow
120	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
123	C₂×Dic₁₅	—	2	2	no	—
124	C₂×Dic₁₅	C₂×D₄	1	1	yes	characteristic
125	C₂×Dic₁₅	C₂×D₄	1	1	yes	characteristic
126	C₂×C₅×Dic₃	—	2	2	no	—
127	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
128	C₄×C₅×D₃	—	4	4	no	—
129	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
130	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
131	C₂×C₃×Dic₅	—	2	2	no	—
132	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
133	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
134	D₃×Dic₅	—	2	2	no	—
135	D₃×Dic₅	—	2	2	no	—
136	D₃×Dic₅	—	4	4	no	—
137	C₃×C₅×C₈	C₂×Q₈	1	2	yes	—
138	C₃⋊#168	C₂×Q₈	1	2	yes	—
139	C₃×#168	C₂×Q₈	1	2	yes	—
140	C₅×C₃⋊C₈	C₂×Q₈	1	2	yes	—
141	C₃×#125	—	5	2	no	—
142	C₂×D₃×C₈	—	5	1	no	—
143	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
144	D₃×C₄⋊C₄	—	5	2	no	—
145	D₃×C₄⋊C₄	—	10	2	no	—
146	D₃×C₄⋊C₄	—	10	2	no	—
147	D₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
148	#890	—	5	2	no	—
149	#890	—	5	2	no	—
150	#889	—	10	2	no	—
151	#889	—	10	2	no	—
152	C₄²×D₃	—	5	1	no	—
153	#870	—	5	2	no	—
154	C₃×#107	—	5	1	no	—
155	C₃×#107	C₂×D₅	1	1	yes	characteristic
156	C₃×#106	—	5	2	no	—
157	C₃×C₄×C₈	—	5	1	no	—
158	#818	—	5	1	no	—
159	#818	C₂×D₅	1	1	yes	characteristic
160	#817	—	5	2	no	—
161	C₈×Dic₃	—	5	1	no	—
162	C₈×Dic₃	—	5	1	no	—
163	#808	—	5	2	no	—
164	#808	—	5	2	no	—
165	#807	—	5	2	no	—
166	#807	C₂×D₅	1	2	yes	—
167	C₄×C₃⋊C₈	—	5	1	no	—
168	C₂²×C₄×C₅	—	3	1	no	—
169	C₂²×C₄×C₅	—	6	2	no	—
170	C₂²×Dic₅	—	3	1	no	—
171	C₂²×Dic₅	—	3	1	no	—
172	C₂²×Dic₅	—	6	2	no	—
173	C₂×C₅×C₈	—	3	1	no	—
174	C₂×C₅×C₈	—	3	4	no	—
175	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
176	C₅×C₄⋊C₄	—	3	2	no	—
177	C₅×C₄⋊C₄	—	6	2	no	—
178	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
179	C₄⋊Dic₅	—	2	2	no	—
180	C₄⋊Dic₅	—	3	2	no	—
181	C₄⋊Dic₅	—	6	2	no	—
182	C₄⋊Dic₅	—	6	2	no	—
183	C₄⋊Dic₅	—	6	2	no	—
184	C₄⋊Dic₅	—	6	2	no	—
185	C₄⋊Dic₅	C₂²×D₃	1	2	yes	—
186	#683	—	2	2	no	—
187	#683	—	6	2	no	—
188	#683	—	6	2	no	—
189	#683	—	6	2	no	—
190	C₄×Dic₅	—	3	1	no	—
191	C₄×Dic₅	—	3	1	no	—
192	C₄×Dic₅	—	3	1	no	—
193	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
194	C₂×#168	—	3	1	no	—
195	C₂×#168	—	3	4	no	—
196	C₂×#168	C₂²×D₃	1	1	yes	characteristic
197	C₂×#125	—	15	2	no	—
198	#499	—	5	1	no	—
199	#499	—	15	1	no	—
200	#499	—	15	2	no	—
201	#499	—	15	1	no	—
202	#499	—	15	2	no	—
203	#499	—	15	1	no	—
204	C₂×#107	—	3	1	no	—
205	C₂×#107	—	15	1	no	—
206	C₂×#106	—	15	2	no	—
207	C₂×C₄×C₈	—	15	1	no	—
208	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₅×D₃	C₄⋊Q₈	1	2	yes	—
210	C₂×C₅×D₃	#135	1	2	yes	—
211	C₂×C₅×D₃	#135	1	2	yes	—
212	C₃×C₄×C₅	—	4	2	no	—
213	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
214	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
215	Dic₁₅	—	2	1	no	—
216	Dic₁₅	—	2	1	no	—
217	Dic₁₅	—	4	2	no	—
218	C₃×Dic₅	—	2	1	no	—
219	C₃×Dic₅	—	2	1	no	—
220	C₃×Dic₅	—	4	2	no	—
221	C₅×Dic₃	—	4	2	no	—
222	C₅×Dic₃	C₄⋊Q₈	1	2	yes	—
223	C₂×C₄×D₃	—	2	2	no	—
224	C₂×C₄×D₃	—	5	1	no	—
225	C₂×C₄×D₃	—	5	1	no	—
226	C₂×C₄×D₃	—	10	2	no	—
227	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
228	C₂×C₃×C₈	—	5	1	no	—
229	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
230	C₃×C₄⋊C₄	—	5	2	no	—
231	C₃×C₄⋊C₄	—	10	2	no	—
232	C₃×C₄⋊C₄	—	10	2	no	—
233	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
234	C₃×C₄²	—	5	1	no	—
235	C₄⋊Dic₃	—	5	2	no	—
236	C₄⋊Dic₃	—	10	2	no	—
237	C₄⋊Dic₃	—	10	2	no	—
238	C₄⋊Dic₃	C₂²×D₅	1	2	yes	—
239	Dic₃⋊C₄	—	2	2	no	—
240	Dic₃⋊C₄	—	10	2	no	—
241	Dic₃⋊C₄	—	10	2	no	—
242	Dic₃⋊C₄	—	10	2	no	—
243	Dic₃⋊C₄	—	10	2	no	—
244	Dic₃⋊C₄	—	10	2	no	—
245	C₄×Dic₃	—	5	1	no	—
246	C₄×Dic₃	—	5	1	no	—
247	C₄×Dic₃	—	5	1	no	—
248	C₂×C₃⋊C₈	—	5	1	no	—
249	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
250	D₃×C₈	—	5	4	no	—
251	D₃×C₈	Dic₁₀	1	4	yes	—
252	C₂³×C₅	—	3	1	no	—
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	3	1	no	—
255	C₂×C₄×C₅	—	3	2	no	—
256	C₂×C₄×C₅	—	3	2	no	—
257	C₂×C₄×C₅	—	6	2	no	—
258	C₂×C₄×C₅	—	12	4	no	—
259	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
260	C₂×Dic₅	—	2	2	no	—
261	C₂×Dic₅	—	3	1	no	—
262	C₂×Dic₅	—	3	1	no	—
263	C₂×Dic₅	—	6	2	no	—
264	C₂×Dic₅	—	6	2	no	—
265	C₂×Dic₅	—	6	2	no	—
266	C₂×Dic₅	—	12	4	no	—
267	C₂×Dic₅	D₃×D₄	1	1	yes	characteristic
268	C₂×Dic₅	D₃×D₄	1	1	yes	characteristic
269	C₅×C₈	—	3	2	no	—
270	C₅×C₈	D₃×Q₈	1	2	yes	—
271	#168	—	3	2	no	—
272	#168	D₃×Q₈	1	2	yes	—
273	C₂²×C₈	—	3	1	no	—
274	C₂²×C₈	—	15	1	no	—
275	#125	—	5	2	no	—
276	#125	—	15	2	no	—
277	#125	—	15	2	no	—
278	#125	—	15	2	no	—
279	#125	—	30	2	no	—
280	#125	—	30	2	no	—
281	C₂×C₄⋊C₄	—	3	2	no	—
282	C₂×C₄⋊C₄	—	15	2	no	—
283	C₂×C₄⋊C₄	—	30	2	no	—
284	C₂×C₄⋊C₄	—	30	2	no	—
285	C₂×C₄²	—	15	1	no	—
286	#107	—	3	1	no	—
287	#107	—	3	2	no	—
288	#107	—	5	1	no	—
289	#107	—	15	2	no	—
290	#107	—	15	1	no	—
291	#107	D₃×D₅	1	1	yes	characteristic
292	#106	—	5	2	no	—
293	#106	—	15	2	no	—
294	#106	—	15	2	no	—
295	#106	—	15	2	no	—
296	C₄×C₈	—	5	1	no	—
297	C₄×C₈	—	15	1	no	—
298	C₄×C₈	—	15	1	no	—
299	C₄×C₈	—	15	1	no	—
300	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
301	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
302	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
303	C₅×D₃	#499	1	4	yes	complemented
304	C₂²×D₃	D₄×D₅	1	1	yes	characteristic
305	C₂×C₃×C₄	—	2	2	no	—
306	C₂×C₃×C₄	—	5	1	no	—
307	C₂×C₃×C₄	—	5	1	no	—
308	C₂×C₃×C₄	—	10	2	no	—
309	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
310	C₂×Dic₃	—	2	2	no	—
311	C₂×Dic₃	—	5	1	no	—
312	C₂×Dic₃	—	5	1	no	—
313	C₂×Dic₃	—	10	2	no	—
314	C₂×Dic₃	D₄×D₅	1	1	yes	characteristic
315	C₄×D₃	—	4	4	no	—
316	C₄×D₃	—	10	2	no	—
317	C₄×D₃	—	10	2	no	—
318	C₄×D₃	—	20	4	no	—
319	C₄×D₃	C₂×Dic₁₀	1	2	yes	—
320	C₄×D₃	Q₈×D₅	1	2	yes	—
321	C₃×C₈	—	5	2	no	—
322	C₃×C₈	C₂×Dic₁₀	1	2	yes	—
323	C₃⋊C₈	—	5	2	no	—
324	C₃⋊C₈	C₂×Dic₁₀	1	2	yes	—
325	C₂²×C₅	—	3	2	no	—
326	C₂²×C₅	—	3	2	no	—
327	C₂²×C₅	—	3	2	no	—
328	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
329	C₄×C₅	—	3	2	no	—
330	C₄×C₅	—	4	2	no	—
331	C₄×C₅	—	12	2	no	—
332	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
333	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
334	Dic₅	—	2	1	no	—
335	Dic₅	—	2	1	no	—
336	Dic₅	—	4	2	no	—
337	Dic₅	—	6	1	no	—
338	Dic₅	—	6	1	no	—
339	Dic₅	—	12	2	no	—
340	C₂²×C₄	—	3	1	no	—
341	C₂²×C₄	—	6	2	no	—
342	C₂²×C₄	—	15	1	no	—
343	C₂²×C₄	—	15	1	no	—
344	C₂²×C₄	—	30	2	no	—
345	C₂×C₈	—	3	1	no	—
346	C₂×C₈	—	3	4	no	—
347	C₂×C₈	—	5	1	no	—
348	C₂×C₈	—	15	4	no	—
349	C₂×C₈	—	15	1	no	—
350	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
351	C₄⋊C₄	—	3	2	no	—
352	C₄⋊C₄	—	5	2	no	—
353	C₄⋊C₄	—	6	2	no	—
354	C₄⋊C₄	—	10	2	no	—
355	C₄⋊C₄	—	10	2	no	—
356	C₄⋊C₄	—	15	2	no	—
357	C₄⋊C₄	—	30	2	no	—
358	C₄⋊C₄	—	30	2	no	—
359	C₄⋊C₄	—	30	2	no	—
360	C₄⋊C₄	—	30	2	no	—
361	C₄⋊C₄	—	30	2	no	—
362	C₄⋊C₄	—	30	2	no	—
363	C₄⋊C₄	—	30	2	no	—
364	C₄⋊C₄	C₂×D₃×D₅	1	2	yes	—
365	C₄²	—	5	1	no	—
366	C₄²	—	15	1	no	—
367	C₄²	—	15	1	no	—
368	C₄²	—	15	1	no	—
369	C₃×C₅	C₂×#499	1	1	yes	characteristic, complemented, Hall
370	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
371	C₂×D₃	#4034	1	2	yes	—
372	C₂×D₃	#4058	1	2	yes	—
373	C₂×D₃	#4065	1	2	yes	—
374	C₃×C₄	—	4	2	no	—
375	C₃×C₄	—	10	1	no	—
376	C₃×C₄	—	10	1	no	—
377	C₃×C₄	—	20	2	no	—
378	C₃×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
379	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
380	Dic₃	—	4	2	no	—
381	Dic₃	—	10	1	no	—
382	Dic₃	—	10	1	no	—
383	Dic₃	—	20	2	no	—
384	Dic₃	#4034	1	2	yes	—
385	C₂×C₅	—	3	4	no	—
386	C₂×C₅	D₃×C₄⋊Q₈	1	1	yes	characteristic
387	C₂×C₅	D₃×#135	1	1	yes	characteristic
388	C₂×C₅	D₃×#135	1	1	yes	characteristic
389	C₂³	—	3	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	3	1	no	—
392	C₂×C₄	—	3	2	no	—
393	C₂×C₄	—	3	2	no	—
394	C₂×C₄	—	5	1	no	—
395	C₂×C₄	—	5	1	no	—
396	C₂×C₄	—	6	2	no	—
397	C₂×C₄	—	10	2	no	—
398	C₂×C₄	—	12	4	no	—
399	C₂×C₄	—	15	1	no	—
400	C₂×C₄	—	15	1	no	—
401	C₂×C₄	—	30	2	no	—
402	C₂×C₄	—	30	2	no	—
403	C₂×C₄	—	30	2	no	—
404	C₂×C₄	—	60	4	no	—
405	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
406	C₈	—	3	2	no	—
407	C₈	—	5	2	no	—
408	C₈	—	15	2	no	—
409	C₈	D₃×Dic₁₀	1	2	yes	—
410	C₂×C₃	C₂×#4034	1	1	yes	characteristic
411	C₂×C₃	C₂×#4058	1	1	yes	characteristic
412	C₂×C₃	C₂×#4065	1	1	yes	characteristic
413	D₃	#65167	1	4	yes	direct product factor
414	C₅	D₃×#499	1	1	yes	characteristic, complemented, Sylow
415	C₂²	—	3	2	no	—
416	C₂²	—	3	2	no	—
417	C₂²	—	3	2	no	—
418	C₂²	D₃×D₄×D₅	1	1	yes	characteristic
419	C₄	—	3	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	10	1	no	—
422	C₄	—	10	1	no	—
423	C₄	—	12	2	no	—
424	C₄	—	20	2	no	—
425	C₄	—	30	1	no	—
426	C₄	—	30	1	no	—
427	C₄	—	60	2	no	—
428	C₄	C₂×D₃×Dic₁₀	1	1	yes	characteristic
429	C₄	D₃×Q₈×D₅	1	1	yes	characteristic
430	C₃	C₂×#65167	1	1	yes	characteristic, complemented, Sylow
431	C₂	—	3	4	no	—
432	C₂	D₃×#4034	1	1	yes	characteristic
433	C₂	D₃×#4058	1	1	yes	characteristic
434	C₂	D₃×#4065	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×D₄×D₅
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₅×#107	C₂²
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₅×D₃	C₂×D₄
hypercenter	#107	D₃×D₅
hypocenter	C₃×C₅	C₂×#499
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
2. #11750979	C₂	semidirect
4. C₃×#65167	C₂	semidirect
5. #11747992	C₂	semidirect
6. #11747986	C₂	semidirect
10. #11747152	C₂	semidirect
11. #11747143	C₂	semidirect
51. #65167	D₃	direct (N × H)
303. C₅×D₃	#499	semidirect
369. C₃×C₅	C₂×#499	semidirect
413. D₃	#65167	direct (N × H)
414. C₅	D₃×#499	semidirect
430. C₃	C₂×#65167	semidirect

Maximal subgroups

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

subgroup	index
D₃×#4036	2
#11750979	2
C₅×D₃×#107	2
C₃×#65167	2
#11747992	2
#11747986	2
D₃×#3950	2
D₃×C₈×Dic₅	2
D₃×#3940	2
#11747152	2
#11747143	2
C₂×#65167	3
D₃×#499	5

Subgroups — D3×#65167 #14439800

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#65167 #14439800