Subgroups — #14419196

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11752695	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₃₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₈×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
5	#11747712	C₂	1	2	yes	maximal, complemented
6	C₈×#1201	C₂	1	2	yes	maximal, complemented
7	#11747649	C₂	1	2	yes	maximal, complemented
8	#11747645	C₂	1	2	yes	maximal, complemented
9	#11747010	C₂	1	1	yes	maximal, characteristic, complemented
10	#11746875	C₂	1	1	yes	maximal, characteristic, complemented
11	#11746865	C₂	1	1	yes	maximal, characteristic, complemented
12	#10610179	—	3	1	no	maximal, Hall
13	C₄×Dic₃₀	C₂²	1	1	yes	characteristic
14	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
16	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
18	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
19	#91456	C₄	1	1	yes	characteristic
20	#91452	C₄	1	2	yes	—
21	C₄×#1201	C₂²	1	2	yes	—
22	#91381	C₄	1	1	yes	characteristic
23	#91365	C₄	1	1	yes	characteristic
24	#91364	C₄	1	1	yes	characteristic
25	#91363	C₄	1	2	yes	—
26	#91357	C₂²	1	2	yes	—
27	C₂×#6649	C₂²	1	2	yes	—
28	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
29	#91098	C₂²	1	2	yes	—
30	C₈×Dic₁₅	C₂²	1	2	yes	—
31	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
32	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
33	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
34	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
35	C₃×#3952	C₂²	1	2	yes	—
36	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
37	#90983	C₂²	1	2	yes	—
38	(C₂×D₃)⋊#168	C₂²	1	2	yes	—
39	#90955	C₂²	1	2	yes	—
40	#90954	C₂²	1	2	yes	—
41	#90953	C₂²	1	2	yes	—
42	#79401	—	5	1	no	maximal, Hall
43	#65813	—	3	1	no	—
44	C₂×C₄×C₅×C₈	—	3	1	no	—
45	#65400	—	3	2	no	—
46	C₈×C₂²⋊D₅	—	3	2	no	—
47	#65215	—	3	1	no	—
48	#64979	—	3	2	no	—
49	#64978	—	3	2	no	—
50	#64977	—	3	1	no	—
51	C₈×D₂₀	D₃	1	1	yes	characteristic, complemented
52	#64968	—	3	1	no	—
53	C₈×Dic₁₀	—	3	1	no	—
54	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
58	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
60	C₂×#1201	C₂×C₄	1	2	yes	—
61	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
64	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
65	#6712	C₂×C₄	1	2	yes	—
66	C₄×Dic₁₅	C₂³	1	2	yes	—
67	C₂×C₃⋊#168	C₂³	1	2	yes	—
68	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
69	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
70	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
71	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
72	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
73	C₅×D₃×C₈	—	2	2	no	—
74	C₅×D₃×C₈	—	2	2	no	—
75	C₃×#685	C₂×C₄	1	2	yes	—
76	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
77	C₂×C₃×#168	C₂³	1	2	yes	—
78	C₃×C₈×D₅	—	2	4	no	—
79	#6669	C₂×C₄	1	2	yes	—
80	#6668	C₂×C₄	1	2	yes	—
81	#6668	C₂×C₄	1	2	yes	—
82	(C₂×D₃)⋊Dic₅	C₂×C₄	1	2	yes	—
83	#6665	C₂×C₄	1	2	yes	—
84	#6665	C₂×C₄	1	2	yes	—
85	#6665	C₂×C₄	1	2	yes	—
86	#6649	—	2	4	no	—
87	#5557	—	5	1	no	—
88	C₃×C₈×D₄	—	5	1	no	—
89	C₈×#67	—	5	2	no	—
90	#5101	—	5	2	no	—
91	#5012	—	5	1	no	—
92	#4835	—	5	1	no	—
93	#4831	—	5	1	no	—
94	#4728	—	5	2	no	—
95	#4720	—	5	2	no	—
96	C₄×D₃×C₈	D₅	1	1	yes	characteristic, complemented
97	C₈×Dic₆	—	5	1	no	—
98	C₂²×C₅×C₈	—	3	1	no	—
99	C₂²×C₅×C₈	—	3	1	no	—
100	C₂×C₄²×C₅	—	3	1	no	—
101	#4076	—	3	1	no	—
102	#4075	—	3	2	no	—
103	C₄×C₂²⋊D₅	—	3	2	no	—
104	#4070	—	3	1	no	—
105	C₂×#676	—	3	2	no	—
106	C₂×C₈×D₅	C₂×D₃	1	2	yes	—
107	#4022	—	3	2	no	—
108	#4021	—	3	1	no	—
109	C₄×D₂₀	C₂×D₃	1	1	yes	characteristic
110	#4018	—	3	2	no	—
111	#4016	—	3	1	no	—
112	C₄×Dic₁₀	—	3	1	no	—
113	C₄×C₅×C₈	—	3	1	no	—
114	C₄×C₅×C₈	—	3	1	no	—
115	C₄×C₅×C₈	—	3	1	no	—
116	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
117	C₂²⋊#168	—	3	2	no	—
118	#3952	—	3	2	no	—
119	#3952	C₂×D₃	1	2	yes	—
120	#3947	—	3	2	no	—
121	#3946	—	3	2	no	—
122	#3946	—	3	2	no	—
123	C₈×Dic₅	—	3	2	no	—
124	C₄⋊#168	—	3	1	no	—
125	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
126	#3935	—	3	2	no	—
127	#2966	—	15	1	no	Sylow
128	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
133	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
134	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
135	Dic₃₀	—	2	2	no	—
136	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
139	C₄×C₅×D₃	—	2	2	no	—
140	C₄×C₅×D₃	—	2	2	no	—
141	C₄×C₅×D₃	—	2	1	no	—
142	C₄×C₅×D₃	—	2	1	no	—
143	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
144	C₃×D₂₀	—	2	2	no	—
145	C₃×C₄×D₅	—	2	2	no	—
146	C₃×C₄×D₅	—	2	2	no	—
147	#1201	—	2	4	no	—
148	C₃×C₅×C₈	—	2	1	no	—
149	C₃×C₅×C₈	#41	1	2	yes	—
150	C₃⋊#168	—	2	2	no	—
151	C₃×#168	—	2	2	no	—
152	C₅×C₃⋊C₈	—	2	1	no	—
153	C₅×C₃⋊C₈	#41	1	2	yes	—
154	C₂²×C₃×C₈	—	5	2	no	—
155	C₃×C₄×D₄	—	5	1	no	—
156	#938	—	5	1	no	—
157	#936	—	5	1	no	—
158	C₄×#67	—	5	2	no	—
159	#926	—	5	2	no	—
160	C₂×#208	—	5	2	no	—
161	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
162	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
163	#897	—	5	1	no	—
164	#890	—	5	1	no	—
165	#883	—	5	2	no	—
166	#879	—	5	2	no	—
167	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
168	C₄×Dic₆	—	5	1	no	—
169	C₃×C₄⋊C₈	—	5	1	no	—
170	C₃×C₂²⋊C₈	—	5	2	no	—
171	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
172	#830	—	5	2	no	—
173	(C₂×D₃)⋊C₈	—	5	2	no	—
174	#815	—	5	2	no	—
175	#815	—	5	2	no	—
176	Dic₃⋊C₈	—	5	2	no	—
177	Dic₃⋊C₈	—	5	2	no	—
178	C₈×Dic₃	—	5	2	no	—
179	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
180	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
181	C₄⋊(C₃⋊C₈)	—	5	1	no	—
182	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
183	C₂²×C₄×C₅	—	3	1	no	—
184	C₂²×C₄×C₅	—	3	1	no	—
185	C₂²×C₄×C₅	—	3	1	no	—
186	C₂×C₂²⋊D₅	—	3	2	no	—
187	C₂×D₂₀	C₄×D₃	1	1	yes	characteristic
188	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
189	C₂×Dic₁₀	—	3	1	no	—
190	C₂×C₅×C₈	—	3	1	no	—
191	C₂×C₅×C₈	—	3	1	no	—
192	C₂×C₅×C₈	—	6	2	no	—
193	C₂×C₅×C₈	—	6	2	no	—
194	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
195	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
196	C₄²×C₅	—	3	1	no	—
197	C₄²×C₅	—	3	1	no	—
198	C₄²×C₅	—	3	1	no	—
199	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
200	C₂²⋊Dic₅	—	3	2	no	—
201	#685	—	3	2	no	—
202	#685	—	3	2	no	—
203	#685	—	3	2	no	—
204	#685	C₄×D₃	1	2	yes	—
205	C₄⋊Dic₅	—	3	1	no	—
206	C₄⋊Dic₅	C₄×D₃	1	1	yes	characteristic
207	#683	—	3	2	no	—
208	#683	—	3	2	no	—
209	#683	—	3	2	no	—
210	#683	—	3	2	no	—
211	C₄×Dic₅	—	3	2	no	—
212	C₂×#168	—	3	2	no	—
213	C₂×#168	C₂²×D₃	1	2	yes	—
214	#676	—	6	4	no	—
215	C₈×D₅	—	2	4	no	—
216	#529	—	15	1	no	—
217	#446	—	15	1	no	—
218	C₈×Q₈	—	15	1	no	—
219	#436	—	15	1	no	—
220	#435	—	15	2	no	—
221	C₈×D₄	—	5	1	no	—
222	C₈×D₄	—	15	2	no	—
223	#433	—	15	2	no	—
224	#432	—	15	1	no	—
225	#405	—	15	2	no	—
226	C₂×C₄×C₈	—	3	1	no	—
227	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₅×D₃	—	2	1	no	—
229	C₂×C₅×D₃	—	2	1	no	—
230	C₂×C₅×D₃	#131	1	2	yes	—
231	C₂×C₃×D₅	—	2	2	no	—
232	C₂×C₃×D₅	—	2	2	no	—
233	C₂×C₃×D₅	—	2	2	no	—
234	C₃×C₄×C₅	—	2	1	no	—
235	C₃×C₄×C₅	#131	1	2	yes	—
236	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
237	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
238	Dic₁₅	—	2	2	no	—
239	Dic₁₅	—	2	2	no	—
240	C₃×Dic₅	—	2	2	no	—
241	C₅×Dic₃	—	2	1	no	—
242	C₅×Dic₃	—	2	1	no	—
243	C₅×Dic₃	—	2	1	no	—
244	C₂×C₃×D₄	—	5	1	no	—
245	C₂²×C₃×C₄	—	5	2	no	—
246	C₂×#67	—	5	2	no	—
247	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
248	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
249	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
250	C₂×Dic₆	—	5	1	no	—
251	C₂×C₃×C₈	—	5	2	no	—
252	C₂×C₃×C₈	—	10	4	no	—
253	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
254	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
255	C₃×C₄⋊C₄	—	5	1	no	—
256	C₃×C₂²⋊C₄	—	5	2	no	—
257	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
258	#217	—	5	2	no	—
259	#217	—	5	2	no	—
260	#217	—	5	2	no	—
261	(C₂×D₃)⋊C₄	—	5	2	no	—
262	C₄⋊Dic₃	—	5	1	no	—
263	C₄⋊Dic₃	—	5	2	no	—
264	C₄⋊Dic₃	—	5	2	no	—
265	Dic₃⋊C₄	—	5	2	no	—
266	Dic₃⋊C₄	—	5	2	no	—
267	C₄×Dic₃	—	5	2	no	—
268	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
269	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
270	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
271	#208	—	10	4	no	—
272	C₂×C₃⋊C₈	—	5	2	no	—
273	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
274	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
275	D₃×C₈	—	2	2	no	—
276	D₃×C₈	—	2	2	no	—
277	C₂³×C₅	—	3	1	no	—
278	C₂²×D₅	C₂×C₄×D₃	1	2	yes	—
279	C₂×C₄×C₅	—	3	1	no	—
280	C₂×C₄×C₅	—	3	1	no	—
281	C₂×C₄×C₅	—	3	1	no	—
282	C₂×C₄×C₅	—	6	2	no	—
283	C₂×C₄×C₅	—	6	2	no	—
284	C₂×C₄×C₅	—	6	1	no	—
285	C₂×C₄×C₅	—	6	1	no	—
286	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
288	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
289	C₂²⋊D₅	—	6	4	no	—
290	C₂×Dic₅	—	3	2	no	—
291	C₂×Dic₅	—	3	2	no	—
292	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
293	D₂₀	—	2	2	no	—
294	C₄×D₅	—	2	2	no	—
295	C₄×D₅	—	2	2	no	—
296	Dic₁₀	—	6	2	no	—
297	C₅×C₈	—	2	1	no	—
298	C₅×C₈	—	3	2	no	—
299	C₅×C₈	—	6	1	no	—
300	C₅×C₈	#237	1	2	yes	—
301	#168	—	2	2	no	—
302	#168	—	6	2	no	—
303	C₂×M₁₆	—	15	2	no	—
304	C₂²×C₈	—	3	1	no	—
305	C₂²×C₈	—	3	1	no	—
306	C₂²×C₈	—	5	2	no	—
307	#126	—	15	2	no	—
308	#125	—	15	1	no	—
309	#124	—	15	1	no	—
310	#123	—	15	2	no	—
311	C₂²⋊Q₈	—	15	1	no	—
312	#121	—	15	1	no	—
313	C₄×Q₈	—	15	1	no	—
314	C₄×D₄	—	5	1	no	—
315	C₄×D₄	—	15	2	no	—
316	#117	—	15	2	no	—
317	C₂×C₄²	—	3	1	no	—
318	C₄⋊C₈	—	5	1	no	—
319	C₄⋊C₈	—	15	2	no	—
320	C₄⋊C₈	—	15	2	no	—
321	C₄⋊C₈	—	15	1	no	—
322	C₂²⋊C₈	—	5	2	no	—
323	C₂²⋊C₈	—	15	2	no	—
324	C₂²⋊C₈	—	15	2	no	—
325	#97	—	15	2	no	—
326	#97	—	15	2	no	—
327	C₄×C₈	—	3	1	no	—
328	C₄×C₈	—	3	1	no	—
329	C₄×C₈	—	3	1	no	—
330	C₄×C₈	—	15	2	no	—
331	C₄×C₈	D₃×D₅	1	1	yes	characteristic
332	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
333	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
334	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
335	C₃×D₅	—	4	2	no	—
336	C₅×D₃	—	2	2	no	—
337	C₂³×C₃	—	5	2	no	—
338	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
339	C₃×D₄	—	10	2	no	—
340	C₂×C₃×C₄	—	5	2	no	—
341	C₂×C₃×C₄	—	10	2	no	—
342	C₂×C₃×C₄	—	10	2	no	—
343	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
344	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
346	#67	—	10	4	no	—
347	C₂×Dic₃	—	5	2	no	—
348	C₂×Dic₃	—	5	2	no	—
349	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
350	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
351	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
352	C₄×D₃	—	2	2	no	—
353	C₄×D₃	—	2	1	no	—
354	C₄×D₃	—	2	1	no	—
355	C₄×D₃	—	2	2	no	—
356	Dic₆	—	10	2	no	—
357	C₃×C₈	—	2	1	no	—
358	C₃×C₈	—	10	2	no	—
359	C₃×C₈	#709	1	2	yes	—
360	C₃⋊C₈	—	2	1	no	—
361	C₃⋊C₈	—	10	2	no	—
362	C₃⋊C₈	#709	1	2	yes	—
363	C₂²×C₅	—	3	2	no	—
364	C₂²×C₅	—	6	1	no	—
365	C₂²×C₅	—	6	1	no	—
366	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
367	C₂×D₅	—	2	2	no	—
368	C₂×D₅	—	2	2	no	—
369	C₂×D₅	—	2	2	no	—
370	C₄×C₅	—	2	1	no	—
371	C₄×C₅	—	6	1	no	—
372	C₄×C₅	—	6	1	no	—
373	C₄×C₅	—	6	1	no	—
374	C₄×C₅	#901	1	2	yes	—
375	C₄×C₅	C₂×#237	1	1	yes	characteristic
376	C₄×C₅	D₃×#41	1	1	yes	characteristic
377	Dic₅	—	2	2	no	—
378	Dic₅	—	6	2	no	—
379	Dic₅	—	6	2	no	—
380	C₂×Q₈	—	15	1	no	—
381	C₂×D₄	—	5	1	no	—
382	C₂×D₄	—	15	2	no	—
383	C₂²×C₄	—	3	1	no	—
384	C₂²×C₄	—	3	1	no	—
385	C₂²×C₄	—	3	1	no	—
386	C₂²×C₄	—	5	2	no	—
387	M₁₆	—	30	4	no	—
388	C₂×C₈	—	3	1	no	—
389	C₂×C₈	—	3	1	no	—
390	C₂×C₈	—	5	2	no	—
391	C₂×C₈	—	6	2	no	—
392	C₂×C₈	—	6	2	no	—
393	C₂×C₈	—	10	4	no	—
394	C₂×C₈	—	15	2	no	—
395	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
396	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
397	C₄⋊C₄	—	5	1	no	—
398	C₄⋊C₄	—	15	2	no	—
399	C₄⋊C₄	—	15	2	no	—
400	C₄⋊C₄	—	15	2	no	—
401	C₄⋊C₄	—	15	1	no	—
402	C₄⋊C₄	—	15	2	no	—
403	C₂²⋊C₄	—	5	2	no	—
404	C₂²⋊C₄	—	15	2	no	—
405	C₂²⋊C₄	—	15	2	no	—
406	C₂²⋊C₄	—	15	2	no	—
407	C₂²⋊C₄	—	15	2	no	—
408	C₄²	—	3	1	no	—
409	C₄²	—	3	1	no	—
410	C₄²	—	3	1	no	—
411	C₄²	—	15	2	no	—
412	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
413	C₃×C₅	#2966	1	1	yes	characteristic, complemented, Hall
414	C₂²×C₃	—	10	2	no	—
415	C₂²×C₃	—	10	2	no	—
416	C₂²×C₃	—	10	2	no	—
417	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
418	C₂×D₃	—	2	1	no	—
419	C₂×D₃	—	2	1	no	—
420	C₂×D₃	#4047	1	2	yes	—
421	C₃×C₄	—	2	1	no	—
422	C₃×C₄	—	10	2	no	—
423	C₃×C₄	#4047	1	2	yes	—
424	C₃×C₄	C₂×#709	1	1	yes	characteristic
425	C₃×C₄	C₂×#709	1	1	yes	characteristic
426	Dic₃	—	2	1	no	—
427	Dic₃	—	2	1	no	—
428	Dic₃	—	2	1	no	—
429	Dic₃	—	10	2	no	—
430	Dic₃	—	10	2	no	—
431	C₂×C₅	—	6	2	no	—
432	C₂×C₅	C₄×#237	1	1	yes	characteristic
433	C₂×C₅	C₂×#901	1	1	yes	characteristic
434	C₂×C₅	D₃×#131	1	1	yes	characteristic
435	D₅	—	4	2	no	—
436	C₂³	—	3	1	no	—
437	C₂³	—	5	2	no	—
438	Q₈	—	30	2	no	—
439	D₄	—	10	2	no	—
440	D₄	—	30	4	no	—
441	C₂×C₄	—	3	1	no	—
442	C₂×C₄	—	3	1	no	—
443	C₂×C₄	—	3	1	no	—
444	C₂×C₄	—	5	2	no	—
445	C₂×C₄	—	6	2	no	—
446	C₂×C₄	—	6	1	no	—
447	C₂×C₄	—	6	1	no	—
448	C₂×C₄	—	6	2	no	—
449	C₂×C₄	—	10	2	no	—
450	C₂×C₄	—	10	2	no	—
451	C₂×C₄	—	15	2	no	—
452	C₂×C₄	—	15	2	no	—
453	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
454	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
456	C₈	—	2	1	no	—
457	C₈	—	3	2	no	—
458	C₈	—	6	1	no	—
459	C₈	—	10	2	no	—
460	C₈	—	30	2	no	—
461	C₈	#6765	1	2	yes	—
462	C₂×C₃	—	20	2	no	—
463	C₂×C₃	C₄×#709	1	1	yes	characteristic
464	C₂×C₃	C₂×#4047	1	1	yes	characteristic
465	C₂×C₃	C₂×#4047	1	1	yes	characteristic
466	D₃	—	2	2	no	—
467	C₅	#79401	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	3	2	no	—
469	C₂²	—	6	1	no	—
470	C₂²	—	6	1	no	—
471	C₂²	—	10	2	no	—
472	C₂²	—	10	2	no	—
473	C₂²	—	10	2	no	—
474	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	6	1	no	—
477	C₄	—	6	1	no	—
478	C₄	—	6	1	no	—
479	C₄	—	10	2	no	—
480	C₄	—	30	2	no	—
481	C₄	—	30	2	no	—
482	C₄	#91265	1	2	yes	—
483	C₄	C₂×#6765	1	1	yes	characteristic
484	C₄	D₃×#709	1	1	yes	characteristic
485	C₃	#10610179	1	1	yes	characteristic, complemented, Sylow
486	C₂	—	6	2	no	—
487	C₂	—	20	2	no	—
488	C₂	C₄×#6765	1	1	yes	characteristic
489	C₂	D₃×#4047	1	1	yes	characteristic
490	C₂	C₂×#91265	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₄×C₅×C₈	C₂²
prime radical	#91456	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	#2966
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₈×Dic₃₀	C₂	semidirect
3. C₄×C₅×D₃×C₈	C₂	semidirect
4. C₃×C₈×D₂₀	C₂	semidirect
5. #11747712	C₂	semidirect
6. C₈×#1201	C₂	semidirect
7. #11747649	C₂	semidirect
8. #11747645	C₂	semidirect
9. #11747010	C₂	semidirect
10. #11746875	C₂	semidirect
11. #11746865	C₂	semidirect
51. C₈×D₂₀	D₃	semidirect
96. C₄×D₃×C₈	D₅	semidirect
413. C₃×C₅	#2966	semidirect
467. C₅	#79401	semidirect
485. C₃	#10610179	semidirect

Maximal subgroups

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

subgroup	index
#11752695	2
C₈×Dic₃₀	2
C₄×C₅×D₃×C₈	2
C₃×C₈×D₂₀	2
#11747712	2
C₈×#1201	2
#11747649	2
#11747645	2
#11747010	2
#11746875	2
#11746865	2
#10610179	3
#79401	5