Subgroups — Dic₃×#4065 #14416298

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4065	C₂	1	1	yes	maximal, characteristic
2	Dic₃×#713	C₂	1	2	yes	maximal, complemented
3	Q₁₆×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×Dic₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#11749239	C₂	1	2	yes	maximal, complemented
6	Dic₃×#688	C₂	1	2	yes	maximal, complemented
7	#11749207	C₂	1	2	yes	maximal, complemented
8	#11747809	C₂	1	1	yes	maximal, characteristic, complemented
9	Dic₃×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
10	#11747672	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#4065	—	3	1	no	maximal, Hall
13	C₂×C₃×#713	C₂²	1	2	yes	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
15	Q₈×Dic₁₅	C₂²	1	2	yes	—
16	C₅×Q₈×Dic₃	C₂²	1	2	yes	—
17	C₂×C₃×#688	C₂²	1	2	yes	—
18	C₃×#4065	C₄	1	8	yes	complemented
19	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
21	#91434	—	2	2	no	—
22	#91434	C₂²	1	2	yes	—
23	Dic₃×D₂₀	—	2	2	no	—
24	Dic₃×D₂₀	C₂²	1	2	yes	—
25	C₄×D₅×Dic₃	—	2	2	no	—
26	C₄×D₅×Dic₃	C₂²	1	1	yes	characteristic
27	#91358	—	2	2	no	—
28	#91358	C₂²	1	2	yes	—
29	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
30	#91119	C₂²	1	2	yes	—
31	#91102	C₂²	1	1	yes	characteristic
32	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
33	C₅×#835	C₂²	1	2	yes	—
34	C₅×#818	C₂²	1	1	yes	characteristic
35	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
36	#90985	C₂²	1	2	yes	—
37	#90965	C₂²	1	2	yes	—
38	#90964	C₂²	1	2	yes	—
39	#90951	C₂²	1	1	yes	characteristic
40	Dic₃×#168	C₂²	1	1	yes	characteristic
41	Dic₃×#135	—	5	1	no	maximal, Hall
42	C₂×#4065	D₃	1	1	yes	characteristic
43	C₄×#713	—	3	2	no	—
44	C₄×C₅×Q₁₆	—	3	1	no	—
45	Q₁₆×Dic₅	—	3	1	no	—
46	C₄×#688	—	3	2	no	—
47	#65169	—	3	1	no	—
48	#65161	—	3	1	no	—
49	#65093	—	3	2	no	—
50	#65077	—	3	2	no	—
51	C₄×D₄₀	—	3	1	no	—
52	C₄×C₈×D₅	—	3	1	no	—
53	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
54	C₃×#713	—	2	4	no	—
55	C₃×#713	C₂×C₄	1	8	yes	complemented
56	C₂×C₃×D₂₀	—	2	2	no	—
57	C₂×C₃×D₂₀	C₂³	1	2	yes	—
58	C₂×C₃×C₄×D₅	—	2	2	no	—
59	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
60	C₂×D₅×Dic₃	—	2	2	no	—
61	C₂×D₅×Dic₃	—	2	2	no	—
62	C₂×D₅×Dic₃	D₄	1	1	yes	characteristic
63	C₂×D₅×Dic₃	D₄	1	1	yes	characteristic
64	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₄⋊Dic₁₅	—	2	2	no	—
67	C₄⋊Dic₁₅	C₂³	1	2	yes	—
68	C₄×Dic₁₅	—	2	2	no	—
69	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
70	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
71	C₅×C₄⋊Dic₃	—	2	2	no	—
72	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
73	C₄×C₅×Dic₃	—	2	2	no	—
74	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
75	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
76	C₃×#688	C₂×C₄	1	8	yes	complemented
77	C₂×C₃×#168	C₂³	1	1	yes	characteristic
78	C₃×D₄₀	C₂×C₄	1	4	yes	complemented
79	C₃×C₈×D₅	C₂×C₄	1	4	yes	complemented
80	#6665	—	2	2	no	—
81	#6665	—	2	2	no	—
82	#6665	—	2	2	no	—
83	Dic₃×Dic₅	—	2	2	no	—
84	Dic₃×Dic₅	D₄	1	1	yes	characteristic
85	Dic₃×Dic₅	D₄	1	1	yes	characteristic
86	D₅×C₃⋊C₈	—	2	2	no	—
87	C₂×C₃×#135	—	5	1	no	—
88	Dic₃×#41	—	5	2	no	—
89	#5233	—	5	2	no	—
90	Dic₃×Q₁₆	—	5	1	no	—
91	Dic₃×Q₁₆	D₅	1	1	yes	characteristic, complemented
92	Dic₃×SD₁₆	—	5	2	no	—
93	Dic₃×SD₁₆	—	5	2	no	—
94	Dic₃×D₈	—	5	1	no	—
95	Dic₃×D₈	—	5	1	no	—
96	#5106	—	5	1	no	—
97	C₂×C₈×Dic₃	—	5	1	no	—
98	C₂×#713	C₂×D₃	1	2	yes	—
99	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
100	C₄×C₅×Q₈	—	3	2	no	—
101	Q₈×Dic₅	—	3	2	no	—
102	C₂×#688	C₂×D₃	1	2	yes	—
103	#4065	Dic₃	1	8	yes	direct product factor
104	C₂×D₄₀	C₂×D₃	1	1	yes	characteristic
105	C₂×C₈×D₅	—	3	1	no	—
106	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
107	#4039	—	3	2	no	—
108	#4039	—	6	2	no	—
109	#4038	—	3	2	no	—
110	#4038	—	6	2	no	—
111	C₄×D₂₀	—	3	2	no	—
112	C₄×D₂₀	—	6	2	no	—
113	C₄²×D₅	—	3	1	no	—
114	C₄²×D₅	—	6	2	no	—
115	C₅×#107	—	3	1	no	—
116	C₅×#103	—	3	2	no	—
117	C₄×C₅×C₈	—	3	1	no	—
118	#3967	—	3	2	no	—
119	#3953	—	3	2	no	—
120	#3950	—	3	1	no	—
121	C₈×Dic₅	—	3	1	no	—
122	C₈×Dic₅	—	3	1	no	—
123	#3941	—	3	2	no	—
124	#3940	—	3	2	no	—
125	C₄×#168	—	3	1	no	—
126	C₄×#135	—	15	1	no	Sylow
127	C₂²×C₃×D₅	—	2	2	no	—
128	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
133	C₂×Dic₁₅	—	2	2	no	—
134	C₂×Dic₁₅	C₂×D₄	1	1	yes	characteristic
135	C₂×Dic₁₅	C₂×D₄	1	1	yes	characteristic
136	C₂×C₅×Dic₃	—	2	2	no	—
137	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
140	C₃×D₂₀	—	2	8	no	—
141	C₃×D₂₀	—	2	2	no	—
142	C₃×D₂₀	C₂²×C₄	1	4	yes	—
143	C₃×C₄×D₅	—	2	8	no	—
144	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
145	C₃×C₄×D₅	#41	1	2	yes	—
146	D₅×Dic₃	—	2	2	no	—
147	D₅×Dic₃	—	2	2	no	—
148	D₅×Dic₃	—	4	4	no	—
149	D₅×Dic₃	—	4	4	no	—
150	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
151	C₃⋊#168	—	2	1	no	—
152	C₃×#168	C₂²×C₄	1	2	yes	—
153	C₅×C₃⋊C₈	—	2	1	no	—
154	C₂×C₃×#41	—	5	2	no	—
155	C₃×#135	—	5	8	no	—
156	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
157	C₂×C₃×SD₁₆	—	5	2	no	—
158	C₂×C₃×D₈	—	5	1	no	—
159	C₂²×C₃×C₈	—	5	1	no	—
160	Q₈×Dic₃	—	5	2	no	—
161	Q₈×Dic₃	C₂×D₅	1	2	yes	—
162	D₄×Dic₃	—	5	2	no	—
163	D₄×Dic₃	—	5	2	no	—
164	D₄×Dic₃	—	10	2	no	—
165	D₄×Dic₃	—	10	2	no	—
166	#926	—	5	2	no	—
167	#926	—	10	2	no	—
168	C₂×C₄×Dic₃	—	5	1	no	—
169	C₂×C₄×Dic₃	—	10	2	no	—
170	C₂²×C₃⋊C₈	—	5	1	no	—
171	#835	—	5	2	no	—
172	#835	C₂×D₅	1	2	yes	—
173	#832	—	5	2	no	—
174	#832	—	5	2	no	—
175	#818	—	5	1	no	—
176	#818	C₂×D₅	1	1	yes	characteristic
177	#817	—	5	2	no	—
178	C₈×Dic₃	—	5	1	no	—
179	C₈×Dic₃	—	5	1	no	—
180	C₈×Dic₃	—	5	1	no	—
181	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
182	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
183	#713	—	2	4	no	—
184	#713	C₂×Dic₃	1	8	yes	complemented
185	C₂×D₂₀	—	2	2	no	—
186	C₂×D₂₀	C₂²×D₃	1	2	yes	—
187	C₂×C₄×D₅	—	2	2	no	—
188	C₂×C₄×D₅	—	3	1	no	—
189	C₂×C₄×D₅	—	3	1	no	—
190	C₂×C₄×D₅	—	6	2	no	—
191	C₂×C₄×D₅	—	6	2	no	—
192	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
193	C₅×Q₁₆	C₂×Dic₃	1	4	yes	complemented
194	C₂×C₅×C₈	—	3	1	no	—
195	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
196	C₅×C₄⋊C₄	—	3	2	no	—
197	C₅×C₄⋊C₄	—	6	2	no	—
198	C₄²×C₅	—	3	1	no	—
199	C₄²×C₅	—	6	2	no	—
200	#688	C₂×Dic₃	1	8	yes	complemented
201	#685	—	6	2	no	—
202	#685	—	6	2	no	—
203	#685	—	6	2	no	—
204	C₄⋊Dic₅	—	3	2	no	—
205	C₄⋊Dic₅	—	6	2	no	—
206	C₄×Dic₅	—	3	1	no	—
207	C₄×Dic₅	—	3	1	no	—
208	C₄×Dic₅	—	3	1	no	—
209	C₄×Dic₅	—	6	2	no	—
210	C₄×Dic₅	—	6	2	no	—
211	C₂×#168	—	3	1	no	—
212	C₂×#168	C₂²×D₃	1	1	yes	characteristic
213	D₄₀	C₂×Dic₃	1	4	yes	complemented
214	C₈×D₅	—	6	2	no	—
215	C₈×D₅	C₂×Dic₃	1	4	yes	complemented
216	C₂×#135	—	5	1	no	—
217	C₄×#41	—	15	2	no	—
218	C₄×Q₁₆	—	3	1	no	—
219	C₄×Q₁₆	—	15	1	no	—
220	C₄×SD₁₆	—	15	2	no	—
221	C₄×SD₁₆	—	15	2	no	—
222	C₄×D₈	—	15	1	no	—
223	C₄×D₈	—	15	1	no	—
224	#427	—	15	1	no	—
225	#416	—	15	2	no	—
226	C₂×C₄×C₈	—	15	1	no	—
227	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₃×D₅	—	2	1	no	—
229	C₂×C₃×D₅	—	2	1	no	—
230	C₂×C₃×D₅	—	2	4	no	—
231	C₂×C₃×D₅	—	4	2	no	—
232	C₂×C₃×D₅	—	4	2	no	—
233	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
234	C₃×C₄×C₅	—	2	4	no	—
235	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
236	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
237	Dic₁₅	—	2	1	no	—
238	Dic₁₅	—	4	2	no	—
239	Dic₁₅	#135	1	2	yes	complemented
240	C₃×Dic₅	C₄×D₄	1	2	yes	—
241	C₅×Dic₃	—	2	1	no	—
242	C₅×Dic₃	—	4	2	no	—
243	C₅×Dic₃	#135	1	2	yes	complemented
244	C₃×#41	—	5	8	no	—
245	C₃×#41	—	10	4	no	—
246	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
247	C₂×C₃×D₄	—	5	2	no	—
248	C₂×C₃×D₄	—	10	2	no	—
249	C₂²×C₃×C₄	—	5	1	no	—
250	C₂²×C₃×C₄	—	10	2	no	—
251	C₂²×Dic₃	—	5	1	no	—
252	C₂²×Dic₃	—	5	1	no	—
253	C₂²×Dic₃	—	10	2	no	—
254	C₂²×Dic₃	—	10	2	no	—
255	C₃×Q₁₆	C₄×D₅	1	4	yes	complemented
256	C₃×SD₁₆	—	5	8	no	—
257	C₃×D₈	—	5	4	no	—
258	C₂×C₃×C₈	—	5	1	no	—
259	C₂×C₃×C₈	—	5	4	no	—
260	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
261	#217	—	10	2	no	—
262	#217	—	10	2	no	—
263	#217	—	10	2	no	—
264	C₄⋊Dic₃	—	2	2	no	—
265	C₄⋊Dic₃	—	5	2	no	—
266	C₄⋊Dic₃	—	10	2	no	—
267	C₄⋊Dic₃	C₂²×D₅	1	2	yes	—
268	C₄×Dic₃	—	2	2	no	—
269	C₄×Dic₃	—	5	1	no	—
270	C₄×Dic₃	—	5	1	no	—
271	C₄×Dic₃	—	5	1	no	—
272	C₄×Dic₃	—	10	2	no	—
273	C₄×Dic₃	—	10	2	no	—
274	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
275	C₂×C₃⋊C₈	—	5	1	no	—
276	C₂×C₃⋊C₈	—	10	2	no	—
277	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
278	C₂²×D₅	—	2	2	no	—
279	C₂²×D₅	D₃×D₄	1	1	yes	characteristic
280	C₅×Q₈	—	2	2	no	—
281	C₅×Q₈	C₂²×Dic₃	1	4	yes	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	3	1	no	—
284	C₂×C₄×C₅	—	3	1	no	—
285	C₂×C₄×C₅	—	6	2	no	—
286	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
287	C₂×Dic₅	—	3	1	no	—
288	C₂×Dic₅	—	3	1	no	—
289	C₂×Dic₅	—	6	2	no	—
290	C₂×Dic₅	D₃×D₄	1	1	yes	characteristic
291	D₂₀	—	2	8	no	—
292	D₂₀	—	2	2	no	—
293	D₂₀	C₂²×Dic₃	1	4	yes	—
294	C₄×D₅	—	2	8	no	—
295	C₄×D₅	—	6	2	no	—
296	C₄×D₅	—	6	2	no	—
297	C₄×D₅	—	12	4	no	—
298	C₄×D₅	—	12	4	no	—
299	C₄×D₅	#237	1	2	yes	—
300	C₄×D₅	C₂²×Dic₃	1	2	yes	—
301	C₅×C₈	—	6	1	no	—
302	C₅×C₈	C₂²×Dic₃	1	2	yes	—
303	#168	—	6	1	no	—
304	#168	C₂²×Dic₃	1	2	yes	—
305	C₂×#41	—	5	2	no	—
306	#135	—	5	8	no	—
307	C₂×Q₁₆	D₃×D₅	1	1	yes	characteristic
308	C₂×SD₁₆	—	5	2	no	—
309	C₂×D₈	—	5	1	no	—
310	C₂²×C₈	—	5	1	no	—
311	C₂²×C₈	—	15	1	no	—
312	C₄×Q₈	—	3	2	no	—
313	C₄×Q₈	—	15	2	no	—
314	C₄×D₄	—	15	2	no	—
315	C₄×D₄	—	15	2	no	—
316	C₄×D₄	—	30	2	no	—
317	C₄×D₄	—	30	2	no	—
318	#117	—	15	2	no	—
319	#117	—	30	2	no	—
320	C₂×C₄²	—	15	1	no	—
321	C₂×C₄²	—	30	2	no	—
322	#107	—	3	1	no	—
323	#107	—	15	1	no	—
324	#106	—	15	2	no	—
325	#103	—	3	2	no	—
326	#103	—	15	2	no	—
327	#102	—	15	2	no	—
328	#102	—	15	2	no	—
329	C₄×C₈	—	3	1	no	—
330	C₄×C₈	—	15	1	no	—
331	C₄×C₈	—	15	1	no	—
332	C₄×C₈	—	15	1	no	—
333	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
334	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
335	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
336	C₃×D₅	—	2	2	no	—
337	C₃×D₅	—	4	4	no	—
338	C₂³×C₃	—	5	1	no	—
339	C₂³×C₃	—	10	2	no	—
340	C₃×Q₈	—	2	2	no	—
341	C₃×Q₈	C₂×C₄×D₅	1	4	yes	—
342	C₃×D₄	—	5	4	no	—
343	C₃×D₄	—	10	8	no	—
344	C₃×D₄	—	10	2	no	—
345	C₂×C₃×C₄	—	2	2	no	—
346	C₂×C₃×C₄	—	5	1	no	—
347	C₂×C₃×C₄	—	5	2	no	—
348	C₂×C₃×C₄	—	5	2	no	—
349	C₂×C₃×C₄	—	10	8	no	—
350	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
351	C₂×Dic₃	—	2	2	no	—
352	C₂×Dic₃	—	5	1	no	—
353	C₂×Dic₃	—	5	1	no	—
354	C₂×Dic₃	—	10	2	no	—
355	C₂×Dic₃	—	10	2	no	—
356	C₂×Dic₃	—	10	2	no	—
357	C₂×Dic₃	—	20	4	no	—
358	C₂×Dic₃	—	20	4	no	—
359	C₂×Dic₃	D₄×D₅	1	1	yes	characteristic
360	C₂×Dic₃	D₄×D₅	1	1	yes	characteristic
361	C₃×C₈	—	5	2	no	—
362	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
363	C₃⋊C₈	—	2	1	no	—
364	C₃⋊C₈	—	10	1	no	—
365	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
366	C₂×D₅	—	2	1	no	—
367	C₂×D₅	—	2	1	no	—
368	C₂×D₅	—	2	4	no	—
369	C₂×D₅	—	4	2	no	—
370	C₂×D₅	—	4	2	no	—
371	C₂×D₅	D₄×Dic₃	1	2	yes	—
372	C₄×C₅	—	2	4	no	—
373	C₄×C₅	—	3	2	no	—
374	C₄×C₅	—	6	1	no	—
375	C₄×C₅	—	12	2	no	—
376	C₄×C₅	C₂×#237	1	1	yes	characteristic
377	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
378	Dic₅	—	3	2	no	—
379	Dic₅	—	6	1	no	—
380	Dic₅	—	12	2	no	—
381	Dic₅	D₄×Dic₃	1	2	yes	—
382	#41	—	5	8	no	—
383	#41	—	10	4	no	—
384	C₂×Q₈	C₂×D₃×D₅	1	2	yes	—
385	C₂×D₄	—	5	2	no	—
386	C₂×D₄	—	10	2	no	—
387	C₂²×C₄	—	5	1	no	—
388	C₂²×C₄	—	10	2	no	—
389	C₂²×C₄	—	15	1	no	—
390	C₂²×C₄	—	15	1	no	—
391	C₂²×C₄	—	30	2	no	—
392	C₂²×C₄	—	30	2	no	—
393	Q₁₆	D₅×Dic₃	1	4	yes	complemented
394	SD₁₆	—	5	8	no	—
395	D₈	—	5	4	no	—
396	C₂×C₈	—	3	1	no	—
397	C₂×C₈	—	5	1	no	—
398	C₂×C₈	—	5	4	no	—
399	C₂×C₈	—	15	1	no	—
400	C₂×C₈	—	30	2	no	—
401	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
402	C₄⋊C₄	—	3	2	no	—
403	C₄⋊C₄	—	6	2	no	—
404	C₄⋊C₄	—	15	2	no	—
405	C₄⋊C₄	—	30	2	no	—
406	C₂²⋊C₄	—	30	2	no	—
407	C₂²⋊C₄	—	30	2	no	—
408	C₂²⋊C₄	—	30	2	no	—
409	C₄²	—	3	1	no	—
410	C₄²	—	6	2	no	—
411	C₄²	—	15	1	no	—
412	C₄²	—	15	1	no	—
413	C₄²	—	15	1	no	—
414	C₄²	—	30	2	no	—
415	C₄²	—	30	2	no	—
416	C₃×C₅	C₄×#135	1	1	yes	characteristic, complemented, Hall
417	C₂²×C₃	—	5	2	no	—
418	C₂²×C₃	—	10	1	no	—
419	C₂²×C₃	—	10	1	no	—
420	C₂²×C₃	—	10	4	no	—
421	C₂²×C₃	—	20	2	no	—
422	C₂²×C₃	—	20	2	no	—
423	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
424	C₃×C₄	—	2	4	no	—
425	C₃×C₄	—	5	2	no	—
426	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
427	C₃×C₄	D₅×#41	1	1	yes	characteristic
428	Dic₃	—	2	1	no	—
429	Dic₃	—	4	2	no	—
430	Dic₃	—	5	2	no	—
431	Dic₃	—	10	1	no	—
432	Dic₃	—	20	2	no	—
433	Dic₃	#4065	1	2	yes	direct product factor
434	C₂×C₅	D₃×#135	1	1	yes	characteristic
435	C₂×C₅	D₃×#135	1	1	yes	characteristic
436	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
437	D₅	—	2	2	no	—
438	D₅	—	4	4	no	—
439	C₂³	—	5	1	no	—
440	C₂³	—	10	2	no	—
441	Q₈	—	2	2	no	—
442	Q₈	C₂×D₅×Dic₃	1	4	yes	—
443	D₄	—	5	4	no	—
444	D₄	—	10	8	no	—
445	D₄	—	10	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	3	1	no	—
448	C₂×C₄	—	3	1	no	—
449	C₂×C₄	—	5	1	no	—
450	C₂×C₄	—	5	2	no	—
451	C₂×C₄	—	5	2	no	—
452	C₂×C₄	—	6	2	no	—
453	C₂×C₄	—	10	8	no	—
454	C₂×C₄	—	15	1	no	—
455	C₂×C₄	—	15	1	no	—
456	C₂×C₄	—	30	2	no	—
457	C₂×C₄	—	30	2	no	—
458	C₂×C₄	—	30	2	no	—
459	C₂×C₄	—	60	4	no	—
460	C₂×C₄	—	60	4	no	—
461	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
462	C₈	—	5	2	no	—
463	C₈	—	6	1	no	—
464	C₈	—	30	1	no	—
465	C₈	C₂×D₅×Dic₃	1	2	yes	—
466	C₂×C₃	—	10	2	no	—
467	C₂×C₃	—	20	4	no	—
468	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
469	C₂×C₃	C₂×#4065	1	1	yes	characteristic
470	C₂×C₃	D₅×#135	1	1	yes	characteristic
471	C₅	Dic₃×#135	1	1	yes	characteristic, complemented, Sylow
472	C₂²	—	5	2	no	—
473	C₂²	—	10	1	no	—
474	C₂²	—	10	1	no	—
475	C₂²	—	10	4	no	—
476	C₂²	—	20	2	no	—
477	C₂²	—	20	2	no	—
478	C₂²	D₃×D₄×D₅	1	1	yes	characteristic
479	C₄	—	2	4	no	—
480	C₄	—	3	2	no	—
481	C₄	—	5	2	no	—
482	C₄	—	6	1	no	—
483	C₄	—	12	2	no	—
484	C₄	—	15	2	no	—
485	C₄	—	30	1	no	—
486	C₄	—	60	2	no	—
487	C₄	D₅×#237	1	1	yes	characteristic
488	C₄	C₂²×D₅×Dic₃	1	1	yes	characteristic
489	C₃	C₄×#4065	1	1	yes	characteristic, complemented, Sylow
490	C₂	—	10	2	no	—
491	C₂	—	20	4	no	—
492	C₂	D₃×#4065	1	1	yes	characteristic
493	C₂	#11754105	1	1	yes	characteristic
494	C₂	D₄×D₅×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×D₄×D₅
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂×C₃×C₅×Q₁₆	C₂²
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4065	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×Q₁₆	D₃×D₅
hypocenter	C₃×C₅	C₄×#135
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
2. Dic₃×#713	C₂	semidirect
3. Q₁₆×Dic₁₅	C₂	semidirect
4. C₅×Dic₃×Q₁₆	C₂	semidirect
5. #11749239	C₂	semidirect
6. Dic₃×#688	C₂	semidirect
7. #11749207	C₂	semidirect
8. #11747809	C₂	semidirect
9. Dic₃×D₄₀	C₂	semidirect
10. #11747672	C₂	semidirect
11. C₈×D₅×Dic₃	C₂	semidirect
18. C₃×#4065	C₄	semidirect
55. C₃×#713	C₂×C₄	semidirect
64. C₃×C₅×Q₁₆	C₂×C₄	semidirect
76. C₃×#688	C₂×C₄	semidirect
78. C₃×D₄₀	C₂×C₄	semidirect
79. C₃×C₈×D₅	C₂×C₄	semidirect
91. Dic₃×Q₁₆	D₅	semidirect
103. #4065	Dic₃	direct (N × H)
184. #713	C₂×Dic₃	semidirect
193. C₅×Q₁₆	C₂×Dic₃	semidirect
200. #688	C₂×Dic₃	semidirect
213. D₄₀	C₂×Dic₃	semidirect
215. C₈×D₅	C₂×Dic₃	semidirect
239. Dic₁₅	#135	semidirect
243. C₅×Dic₃	#135	semidirect
255. C₃×Q₁₆	C₄×D₅	semidirect
393. Q₁₆	D₅×Dic₃	semidirect
416. C₃×C₅	C₄×#135	semidirect
433. Dic₃	#4065	direct (N × H)
471. C₅	Dic₃×#135	semidirect
489. C₃	C₄×#4065	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#4065	2
Dic₃×#713	2
Q₁₆×Dic₁₅	2
C₅×Dic₃×Q₁₆	2
#11749239	2
Dic₃×#688	2
#11749207	2
#11747809	2
Dic₃×D₄₀	2
#11747672	2
C₈×D₅×Dic₃	2
C₄×#4065	3
Dic₃×#135	5

Subgroups — Dic3×#4065 #14416298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃×#4065 #14416298