Subgroups — D₃×#65309 #14430032

Order 1920.

832 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic
2	D₃×#4015	C₂	1	1	yes	maximal, characteristic
3	#11751121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65309	C₂	1	1	yes	maximal, characteristic, complemented
5	#11749358	C₂	1	2	yes	maximal, complemented
6	D₃×#3967	C₂	1	2	yes	maximal
7	D₃×#3940	C₂	1	2	yes	maximal
8	#11747417	C₂	1	2	yes	maximal, complemented
9	D₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic
10	#11746945	C₂	1	1	yes	maximal, characteristic, complemented
11	#11746927	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#65309	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
14	C₂×D₃×Dic₁₀	—	2	1	no	—
15	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
16	#91758	C₂²	1	1	yes	characteristic
17	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
18	C₅×D₃×C₄⋊C₄	—	2	1	no	—
19	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₅×#887	—	2	1	no	—
21	C₅×#887	C₂²	1	1	yes	characteristic
22	C₄²×C₅×D₃	—	2	1	no	—
23	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
24	C₄×C₅×Dic₆	—	2	1	no	—
25	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
26	C₃×#4015	C₂²	1	1	yes	characteristic
27	#91469	—	2	1	no	—
28	#91469	C₂²	1	2	yes	—
29	D₃×C₄⋊Dic₅	—	2	1	no	—
30	D₃×C₄⋊Dic₅	C₂²	1	2	yes	—
31	#91389	—	2	1	no	—
32	C₂×D₃×#168	C₂²	1	2	yes	—
33	#91119	C₂²	1	2	yes	—
34	#91092	C₂²	1	2	yes	—
35	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
36	C₃×#3967	C₂²	1	2	yes	—
37	C₃×#3940	C₂²	1	2	yes	—
38	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
39	#90986	C₂²	1	2	yes	—
40	#90985	C₂²	1	2	yes	—
41	Dic₃⋊#168	C₂²	1	2	yes	—
42	#90973	C₂²	1	2	yes	—
43	#90972	C₂²	1	2	yes	—
44	D₃×#475	—	5	1	no	maximal, Hall
45	C₂×C₄×C₅×Q₈	—	3	1	no	—
46	C₂×#4015	—	3	1	no	—
47	C₂×#3967	—	3	2	no	—
48	#65309	—	3	1	no	—
49	#65309	—	3	2	no	—
50	#65309	—	3	2	no	—
51	#65309	—	3	1	no	—
52	#65309	—	3	1	no	—
53	#65309	D₃	1	1	yes	characteristic, direct product factor
54	C₂×#3940	—	3	2	no	—
55	C₂×C₄⋊#168	—	3	1	no	—
56	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
57	C₂×Dic₃₀	—	2	1	no	—
58	C₅×D₃×Q₈	—	2	2	no	—
59	C₅×D₃×Q₈	Q₈	1	4	yes	complemented
60	C₂×C₄×C₅×D₃	—	2	1	no	—
61	C₂×C₄×C₅×D₃	—	2	1	no	—
62	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
63	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
64	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
65	C₂×C₅×Dic₆	—	2	1	no	—
66	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
67	C₂×C₃×Dic₁₀	—	2	1	no	—
68	C₂×#1204	—	2	2	no	—
69	C₂×D₃×Dic₅	—	2	2	no	—
70	D₃×Dic₁₀	—	4	4	no	—
71	C₃×C₅×C₄⋊C₄	—	2	1	no	—
72	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₃×C₄²×C₅	—	2	1	no	—
74	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₄⋊Dic₁₅	—	2	1	no	—
76	C₄⋊Dic₁₅	C₂³	1	2	yes	—
77	C₂×C₃⋊#168	C₂³	1	2	yes	—
78	C₅×C₄⋊Dic₃	—	2	1	no	—
79	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
80	C₅×Dic₃⋊C₄	—	2	1	no	—
81	C₅×Dic₃⋊C₄	—	2	1	no	—
82	C₅×Dic₃⋊C₄	—	2	1	no	—
83	C₄×C₅×Dic₃	—	2	1	no	—
84	C₄×C₅×Dic₃	—	2	1	no	—
85	C₄×C₅×Dic₃	—	2	1	no	—
86	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
87	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
88	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
89	C₃×C₄⋊Dic₅	—	2	1	no	—
90	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
91	C₂×C₃×#168	C₂³	1	2	yes	—
92	Dic₃⋊Dic₅	—	2	2	no	—
93	Dic₃⋊Dic₅	—	2	2	no	—
94	D₃×#168	—	2	4	no	—
95	D₃×C₄⋊Q₈	—	5	1	no	—
96	C₄×D₃×Q₈	D₅	1	1	yes	characteristic
97	C₃×#475	—	5	1	no	—
98	#5094	—	5	1	no	—
99	#5020	—	5	1	no	—
100	D₃×#106	—	5	2	no	—
101	#4854	—	5	2	no	—
102	#4851	—	5	1	no	—
103	D₃×C₄⋊C₈	—	5	1	no	—
104	D₃×#103	—	5	2	no	—
105	#4791	—	5	2	no	—
106	C₂²×C₅×Q₈	—	3	1	no	—
107	C₂²×Dic₁₀	—	6	1	no	—
108	C₄×C₅×Q₈	—	3	1	no	—
109	C₄×C₅×Q₈	—	3	1	no	—
110	C₄×C₅×Q₈	—	3	1	no	—
111	C₄×C₅×Q₈	—	6	1	no	—
112	C₄×C₅×Q₈	—	6	1	no	—
113	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
114	C₂×C₅×C₄⋊C₄	—	3	1	no	—
115	C₂×C₅×C₄⋊C₄	—	6	1	no	—
116	C₂×C₄²×C₅	—	3	1	no	—
117	C₂×C₄²×C₅	—	6	1	no	—
118	C₂×C₄⋊Dic₅	—	3	2	no	—
119	C₂×C₄⋊Dic₅	—	6	1	no	—
120	C₂²×#168	—	3	2	no	—
121	#4015	—	3	1	no	—
122	#4015	—	3	2	no	—
123	#4015	—	6	1	no	—
124	#4015	—	6	1	no	—
125	#4015	C₂×D₃	1	1	yes	characteristic
126	#3967	—	3	2	no	—
127	#3967	—	3	2	no	—
128	#3967	—	3	2	no	—
129	#3967	C₂×D₃	1	2	yes	—
130	#3940	—	3	2	no	—
131	#3940	—	3	2	no	—
132	#3940	—	3	2	no	—
133	#3940	C₂×D₃	1	2	yes	—
134	C₄⋊#168	—	3	1	no	—
135	C₄⋊#168	—	3	2	no	—
136	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
137	C₂×#475	—	15	1	no	Sylow
138	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
139	C₃×C₅×Q₈	—	2	1	no	—
140	C₃×C₅×Q₈	C₂×Q₈	1	2	yes	complemented
141	C₂×C₃×C₄×C₅	—	2	1	no	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
146	C₂×Dic₁₅	—	2	2	no	—
147	Dic₃₀	—	4	2	no	—
148	C₂×C₅×Dic₃	—	2	1	no	—
149	C₂×C₅×Dic₃	—	2	1	no	—
150	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
151	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
152	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
153	C₄×C₅×D₃	—	2	4	no	—
154	C₄×C₅×D₃	—	2	2	no	—
155	C₄×C₅×D₃	—	4	2	no	—
156	C₄×C₅×D₃	SD₁₆	1	4	yes	—
157	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
158	C₄×C₅×D₃	#41	1	2	yes	—
159	C₅×Dic₆	—	2	1	no	—
160	C₅×Dic₆	—	2	4	no	—
161	C₅×Dic₆	C₂×Q₈	1	2	yes	complemented
162	C₂×C₃×Dic₅	—	2	2	no	—
163	C₃×Dic₁₀	—	4	2	no	—
164	#1204	—	4	4	no	—
165	D₃×Dic₅	—	4	4	no	—
166	C₃⋊#168	—	2	2	no	—
167	C₃×#168	—	2	2	no	—
168	C₂×D₃×Q₈	—	10	1	no	—
169	C₂×D₃×Q₈	C₂×D₅	1	1	yes	characteristic
170	C₃×C₄⋊Q₈	—	5	1	no	—
171	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
172	Q₈×Dic₃	C₂×D₅	1	1	yes	characteristic
173	#944	—	10	1	no	—
174	C₂×D₃×C₈	—	5	2	no	—
175	D₃×C₄⋊C₄	—	2	1	no	—
176	D₃×C₄⋊C₄	—	5	2	no	—
177	D₃×C₄⋊C₄	—	10	1	no	—
178	D₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
179	#888	—	5	2	no	—
180	#888	—	10	1	no	—
181	#887	—	2	1	no	—
182	#887	C₂×D₅	1	1	yes	characteristic
183	C₄²×D₃	—	2	1	no	—
184	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
185	#869	—	5	1	no	—
186	C₄×Dic₆	—	2	1	no	—
187	C₄×Dic₆	C₂×D₅	1	1	yes	characteristic
188	C₃×#106	—	5	2	no	—
189	C₃×C₄⋊C₈	—	5	1	no	—
190	C₃×#103	—	5	2	no	—
191	#835	—	5	2	no	—
192	#817	—	5	2	no	—
193	#816	—	5	2	no	—
194	Dic₃⋊C₈	—	5	2	no	—
195	#810	—	5	2	no	—
196	#808	—	5	2	no	—
197	#808	—	5	2	no	—
198	C₄⋊(C₃⋊C₈)	—	5	1	no	—
199	C₂×C₅×Q₈	—	3	4	no	—
200	C₂×C₅×Q₈	—	3	1	no	—
201	C₂×C₅×Q₈	—	6	1	no	—
202	C₂×C₅×Q₈	—	6	2	no	—
203	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
204	C₂²×C₄×C₅	—	3	1	no	—
205	C₂²×C₄×C₅	—	3	1	no	—
206	C₂²×C₄×C₅	—	3	1	no	—
207	C₂²×C₄×C₅	—	6	1	no	—
208	C₂²×C₄×C₅	—	6	1	no	—
209	C₂²×Dic₅	—	6	2	no	—
210	C₂×Dic₁₀	—	2	1	no	—
211	C₂×Dic₁₀	—	6	2	no	—
212	C₂×Dic₁₀	—	6	1	no	—
213	C₂×Dic₁₀	—	12	4	no	—
214	C₅×C₄⋊C₄	—	2	1	no	—
215	C₅×C₄⋊C₄	—	3	1	no	—
216	C₅×C₄⋊C₄	—	6	1	no	—
217	C₅×C₄⋊C₄	—	6	1	no	—
218	C₅×C₄⋊C₄	—	6	1	no	—
219	C₅×C₄⋊C₄	—	6	1	no	—
220	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
221	C₄²×C₅	—	2	1	no	—
222	C₄²×C₅	—	3	1	no	—
223	C₄²×C₅	—	3	1	no	—
224	C₄²×C₅	—	3	1	no	—
225	C₄²×C₅	—	6	1	no	—
226	C₄²×C₅	—	6	1	no	—
227	C₄²×C₅	—	6	1	no	—
228	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
229	C₄⋊Dic₅	—	2	1	no	—
230	C₄⋊Dic₅	—	3	2	no	—
231	C₄⋊Dic₅	—	6	2	no	—
232	C₄⋊Dic₅	—	6	2	no	—
233	C₄⋊Dic₅	—	6	1	no	—
234	C₄⋊Dic₅	C₂²×D₃	1	2	yes	—
235	C₂×#168	—	3	2	no	—
236	C₂×#168	—	6	4	no	—
237	C₂×#168	C₂²×D₃	1	2	yes	—
238	C₂×C₄⋊Q₈	—	15	1	no	—
239	C₂×C₄×Q₈	—	3	1	no	—
240	#475	—	5	1	no	—
241	#475	—	15	2	no	—
242	#475	—	15	1	no	—
243	#475	—	15	2	no	—
244	#475	—	15	1	no	—
245	#475	—	15	1	no	—
246	C₂×#106	—	15	2	no	—
247	C₂×C₄⋊C₈	—	15	1	no	—
248	C₂×#103	—	15	2	no	—
249	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₅×D₃	C₂²⋊Q₈	1	2	yes	—
251	C₂×C₅×D₃	C₂×SD₁₆	1	2	yes	—
252	C₂×C₅×D₃	#137	1	2	yes	—
253	C₃×C₄×C₅	—	2	2	no	—
254	C₃×C₄×C₅	—	2	1	no	—
255	C₃×C₄×C₅	—	4	1	no	—
256	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	—
257	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
258	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
259	Dic₁₅	—	4	2	no	—
260	C₃×Dic₅	—	4	2	no	—
261	C₅×Dic₃	—	2	2	no	—
262	C₅×Dic₃	—	2	1	no	—
263	C₅×Dic₃	—	4	1	no	—
264	C₅×Dic₃	C₂²⋊Q₈	1	2	yes	—
265	C₅×Dic₃	C₂×SD₁₆	1	2	yes	—
266	C₂×C₃×Q₈	—	10	1	no	—
267	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
268	D₃×Q₈	—	2	2	no	—
269	D₃×Q₈	—	20	4	no	—
270	D₃×Q₈	Dic₁₀	1	4	yes	complemented
271	C₂×C₄×D₃	—	2	1	no	—
272	C₂×C₄×D₃	—	2	1	no	—
273	C₂×C₄×D₃	—	10	2	no	—
274	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
275	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
276	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
277	C₂×Dic₆	—	2	1	no	—
278	C₂×Dic₆	—	10	1	no	—
279	C₂×Dic₆	—	10	2	no	—
280	C₂×Dic₆	C₂²×D₅	1	1	yes	characteristic
281	C₂×C₃×C₈	—	5	2	no	—
282	C₃×C₄⋊C₄	—	2	1	no	—
283	C₃×C₄⋊C₄	—	5	2	no	—
284	C₃×C₄⋊C₄	—	10	1	no	—
285	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
286	C₃×C₄²	—	2	1	no	—
287	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
288	C₄⋊Dic₃	—	2	1	no	—
289	C₄⋊Dic₃	—	5	2	no	—
290	C₄⋊Dic₃	—	10	1	no	—
291	C₄⋊Dic₃	C₂²×D₅	1	1	yes	characteristic
292	Dic₃⋊C₄	—	2	1	no	—
293	Dic₃⋊C₄	—	2	1	no	—
294	Dic₃⋊C₄	—	2	1	no	—
295	Dic₃⋊C₄	—	10	2	no	—
296	Dic₃⋊C₄	—	10	2	no	—
297	C₄×Dic₃	—	2	1	no	—
298	C₄×Dic₃	—	2	1	no	—
299	C₄×Dic₃	—	2	1	no	—
300	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
301	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
302	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
303	C₂×C₃⋊C₈	—	5	2	no	—
304	D₃×C₈	—	10	4	no	—
305	C₂³×C₅	—	3	1	no	—
306	C₅×Q₈	—	2	1	no	—
307	C₅×Q₈	—	3	2	no	—
308	C₅×Q₈	—	6	4	no	—
309	C₅×Q₈	—	6	1	no	—
310	C₅×Q₈	D₃×Q₈	1	2	yes	complemented
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	3	1	no	—
314	C₂×C₄×C₅	—	3	1	no	—
315	C₂×C₄×C₅	—	3	4	no	—
316	C₂×C₄×C₅	—	3	2	no	—
317	C₂×C₄×C₅	—	3	2	no	—
318	C₂×C₄×C₅	—	3	1	no	—
319	C₂×C₄×C₅	—	6	2	no	—
320	C₂×C₄×C₅	—	6	4	no	—
321	C₂×C₄×C₅	—	6	1	no	—
322	C₂×C₄×C₅	—	6	1	no	—
323	C₂×C₄×C₅	—	12	2	no	—
324	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
325	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
326	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
327	C₂×Dic₅	—	2	2	no	—
328	C₂×Dic₅	—	6	2	no	—
329	C₂×Dic₅	—	12	4	no	—
330	Dic₁₀	—	4	2	no	—
331	Dic₁₀	—	12	4	no	—
332	Dic₁₀	—	12	2	no	—
333	#168	—	2	2	no	—
334	#168	—	6	2	no	—
335	C₂²×Q₈	—	3	1	no	—
336	C₂²×Q₈	—	30	1	no	—
337	C₂²×C₈	—	15	2	no	—
338	C₄⋊Q₈	—	5	1	no	—
339	C₄⋊Q₈	—	15	2	no	—
340	C₄⋊Q₈	—	15	1	no	—
341	C₄⋊Q₈	—	30	1	no	—
342	C₄⋊Q₈	—	30	1	no	—
343	C₄×Q₈	—	3	1	no	—
344	C₄×Q₈	—	3	1	no	—
345	C₄×Q₈	—	3	1	no	—
346	C₄×Q₈	—	6	1	no	—
347	C₄×Q₈	—	6	1	no	—
348	C₄×Q₈	D₃×D₅	1	1	yes	characteristic
349	C₂×C₄⋊C₄	—	3	1	no	—
350	C₂×C₄⋊C₄	—	6	1	no	—
351	C₂×C₄⋊C₄	—	15	2	no	—
352	C₂×C₄⋊C₄	—	30	1	no	—
353	C₂×C₄²	—	3	1	no	—
354	C₂×C₄²	—	6	1	no	—
355	#106	—	5	2	no	—
356	#106	—	15	2	no	—
357	#106	—	15	2	no	—
358	#106	—	15	2	no	—
359	C₄⋊C₈	—	5	1	no	—
360	C₄⋊C₈	—	15	2	no	—
361	C₄⋊C₈	—	15	1	no	—
362	#103	—	5	2	no	—
363	#103	—	15	2	no	—
364	#103	—	15	2	no	—
365	#103	—	15	2	no	—
366	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
367	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
368	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
369	C₅×D₃	#475	1	4	yes	complemented
370	C₂²×D₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
371	C₃×Q₈	—	2	1	no	—
372	C₃×Q₈	—	20	2	no	—
373	C₃×Q₈	C₂×Dic₁₀	1	2	yes	complemented
374	C₂×C₃×C₄	—	2	1	no	—
375	C₂×C₃×C₄	—	2	1	no	—
376	C₂×C₃×C₄	—	10	2	no	—
377	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
378	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
379	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
380	C₂×Dic₃	—	2	1	no	—
381	C₂×Dic₃	—	2	1	no	—
382	C₂×Dic₃	—	10	2	no	—
383	C₂×Dic₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
384	C₂×Dic₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
385	C₂×Dic₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
386	C₄×D₃	—	2	2	no	—
387	C₄×D₃	—	2	4	no	—
388	C₄×D₃	—	4	2	no	—
389	C₄×D₃	—	20	4	no	—
390	C₄×D₃	#688	1	4	yes	—
391	C₄×D₃	C₂×Dic₁₀	1	2	yes	—
392	C₄×D₃	#709	1	2	yes	—
393	Dic₆	—	2	1	no	—
394	Dic₆	—	2	4	no	—
395	Dic₆	—	20	2	no	—
396	Dic₆	—	20	4	no	—
397	Dic₆	C₂×Dic₁₀	1	2	yes	complemented
398	C₃×C₈	—	10	2	no	—
399	C₃⋊C₈	—	10	2	no	—
400	C₂²×C₅	—	3	2	no	—
401	C₂²×C₅	—	3	2	no	—
402	C₂²×C₅	—	3	2	no	—
403	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
404	C₄×C₅	—	2	1	no	—
405	C₄×C₅	—	2	2	no	—
406	C₄×C₅	—	3	2	no	—
407	C₄×C₅	—	3	2	no	—
408	C₄×C₅	—	4	1	no	—
409	C₄×C₅	—	6	1	no	—
410	C₄×C₅	—	6	2	no	—
411	C₄×C₅	—	12	1	no	—
412	C₄×C₅	D₃×SD₁₆	1	2	yes	—
413	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
414	C₄×C₅	D₃×#41	1	1	yes	characteristic
415	Dic₅	—	4	2	no	—
416	Dic₅	—	12	2	no	—
417	C₂×Q₈	—	3	4	no	—
418	C₂×Q₈	—	3	1	no	—
419	C₂×Q₈	—	6	1	no	—
420	C₂×Q₈	—	6	2	no	—
421	C₂×Q₈	—	10	1	no	—
422	C₂×Q₈	—	30	2	no	—
423	C₂×Q₈	—	30	1	no	—
424	C₂×Q₈	—	60	4	no	—
425	C₂×Q₈	C₂×D₃×D₅	1	1	yes	characteristic
426	C₂²×C₄	—	3	1	no	—
427	C₂²×C₄	—	3	1	no	—
428	C₂²×C₄	—	3	1	no	—
429	C₂²×C₄	—	6	1	no	—
430	C₂²×C₄	—	6	1	no	—
431	C₂²×C₄	—	30	2	no	—
432	C₂×C₈	—	5	2	no	—
433	C₂×C₈	—	15	2	no	—
434	C₂×C₈	—	30	4	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	3	1	no	—
437	C₄⋊C₄	—	5	2	no	—
438	C₄⋊C₄	—	6	1	no	—
439	C₄⋊C₄	—	6	1	no	—
440	C₄⋊C₄	—	6	1	no	—
441	C₄⋊C₄	—	6	1	no	—
442	C₄⋊C₄	—	10	1	no	—
443	C₄⋊C₄	—	15	2	no	—
444	C₄⋊C₄	—	30	2	no	—
445	C₄⋊C₄	—	30	2	no	—
446	C₄⋊C₄	—	30	1	no	—
447	C₄⋊C₄	C₂×D₃×D₅	1	1	yes	characteristic
448	C₄²	—	2	1	no	—
449	C₄²	—	3	1	no	—
450	C₄²	—	3	1	no	—
451	C₄²	—	3	1	no	—
452	C₄²	—	6	1	no	—
453	C₄²	—	6	1	no	—
454	C₄²	—	6	1	no	—
455	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
456	C₃×C₅	C₂×#475	1	1	yes	characteristic, complemented, Hall
457	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
458	C₂×D₃	#4070	1	2	yes	—
459	C₂×D₃	C₂×#688	1	2	yes	—
460	C₂×D₃	#4097	1	2	yes	—
461	C₃×C₄	—	2	2	no	—
462	C₃×C₄	—	2	1	no	—
463	C₃×C₄	—	4	1	no	—
464	C₃×C₄	—	20	2	no	—
465	C₃×C₄	C₂×#688	1	2	yes	—
466	C₃×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
467	C₃×C₄	C₂×#709	1	1	yes	characteristic
468	Dic₃	—	2	2	no	—
469	Dic₃	—	2	1	no	—
470	Dic₃	—	4	1	no	—
471	Dic₃	—	20	2	no	—
472	Dic₃	#4070	1	2	yes	—
473	Dic₃	C₂×#688	1	2	yes	—
474	C₂×C₅	—	3	4	no	—
475	C₂×C₅	D₃×C₂²⋊Q₈	1	1	yes	characteristic
476	C₂×C₅	C₂×D₃×SD₁₆	1	1	yes	characteristic
477	C₂×C₅	D₃×#137	1	1	yes	characteristic
478	C₂³	—	3	1	no	—
479	Q₈	—	2	1	no	—
480	Q₈	—	3	2	no	—
481	Q₈	—	6	4	no	—
482	Q₈	—	6	1	no	—
483	Q₈	—	20	2	no	—
484	Q₈	—	60	4	no	—
485	Q₈	—	60	2	no	—
486	Q₈	D₃×Dic₁₀	1	2	yes	complemented
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	3	1	no	—
490	C₂×C₄	—	3	1	no	—
491	C₂×C₄	—	3	2	no	—
492	C₂×C₄	—	3	4	no	—
493	C₂×C₄	—	3	2	no	—
494	C₂×C₄	—	3	1	no	—
495	C₂×C₄	—	6	2	no	—
496	C₂×C₄	—	6	4	no	—
497	C₂×C₄	—	6	1	no	—
498	C₂×C₄	—	6	1	no	—
499	C₂×C₄	—	10	2	no	—
500	C₂×C₄	—	12	2	no	—
501	C₂×C₄	—	30	2	no	—
502	C₂×C₄	—	60	4	no	—
503	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
504	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
505	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
506	C₈	—	10	2	no	—
507	C₈	—	30	2	no	—
508	C₂×C₃	C₂×#4070	1	1	yes	characteristic
509	C₂×C₃	C₂²×#688	1	1	yes	characteristic
510	C₂×C₃	C₂×#4097	1	1	yes	characteristic
511	D₃	#65309	1	4	yes	direct product factor
512	C₅	D₃×#475	1	1	yes	characteristic, complemented, Sylow
513	C₂²	—	3	2	no	—
514	C₂²	—	3	2	no	—
515	C₂²	—	3	2	no	—
516	C₂²	C₂×D₃×C₂²⋊D₅	1	1	yes	characteristic
517	C₄	—	2	1	no	—
518	C₄	—	2	2	no	—
519	C₄	—	3	2	no	—
520	C₄	—	3	2	no	—
521	C₄	—	4	1	no	—
522	C₄	—	6	1	no	—
523	C₄	—	6	2	no	—
524	C₄	—	12	1	no	—
525	C₄	—	20	2	no	—
526	C₄	—	60	2	no	—
527	C₄	D₃×#688	1	2	yes	—
528	C₄	C₂×D₃×Dic₁₀	1	1	yes	characteristic
529	C₄	D₃×#709	1	1	yes	characteristic
530	C₃	C₂×#65309	1	1	yes	characteristic, complemented, Sylow
531	C₂	—	3	4	no	—
532	C₂	D₃×#4070	1	1	yes	characteristic
533	C₂	C₂×D₃×#688	1	1	yes	characteristic
534	C₂	D₃×#4097	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₃×C₂²⋊D₅
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₄×C₅×Q₈	C₂²
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₅×D₃	C₂×D₄
hypercenter	C₄×Q₈	D₃×D₅
hypocenter	C₃×C₅	C₂×#475
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
3. #11751121	C₂	semidirect
4. C₃×#65309	C₂	semidirect
5. #11749358	C₂	semidirect
8. #11747417	C₂	semidirect
10. #11746945	C₂	semidirect
11. #11746927	C₂	semidirect
53. #65309	D₃	direct (N × H)
59. C₅×D₃×Q₈	Q₈	semidirect
140. C₃×C₅×Q₈	C₂×Q₈	semidirect
161. C₅×Dic₆	C₂×Q₈	semidirect
270. D₃×Q₈	Dic₁₀	semidirect
310. C₅×Q₈	D₃×Q₈	semidirect
369. C₅×D₃	#475	semidirect
373. C₃×Q₈	C₂×Dic₁₀	semidirect
397. Dic₆	C₂×Dic₁₀	semidirect
456. C₃×C₅	C₂×#475	semidirect
486. Q₈	D₃×Dic₁₀	semidirect
511. D₃	#65309	direct (N × H)
512. C₅	D₃×#475	semidirect
530. C₃	C₂×#65309	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×D₃×Q₈	2
D₃×#4015	2
#11751121	2
C₃×#65309	2
#11749358	2
D₃×#3967	2
D₃×#3940	2
#11747417	2
D₃×C₄⋊#168	2
#11746945	2
#11746927	2
C₂×#65309	3
D₃×#475	5

Subgroups — D3×#65309 #14430032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#65309 #14430032