Subgroups — #14419194

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	#11752682	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₃₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
5	#11747702	C₂	1	2	yes	maximal, complemented
6	C₈×#1201	C₂	1	2	yes	maximal, complemented
7	#11747654	C₂	1	2	yes	maximal, complemented
8	#11747653	C₂	1	2	yes	maximal, complemented
9	#11747008	C₂	1	1	yes	maximal, characteristic, complemented
10	#11746871	C₂	1	1	yes	maximal, characteristic, complemented
11	#11746864	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611132	—	3	1	no	maximal, Hall
13	C₄×Dic₃₀	C₂²	1	1	yes	characteristic
14	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
15	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
18	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
19	#91449	C₄	1	1	yes	characteristic
20	#91447	C₄	1	2	yes	—
21	C₄×#1201	C₂²	1	2	yes	—
22	#91388	C₄	1	1	yes	characteristic
23	#91373	C₄	1	1	yes	characteristic
24	#91372	C₄	1	2	yes	—
25	#91371	C₂²	1	2	yes	—
26	#91360	C₄	1	1	yes	characteristic
27	C₂×#6650	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×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
33	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
34	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
35	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
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	#90952	C₂²	1	2	yes	—
42	#78448	—	5	1	no	maximal, Hall
43	#65891	—	3	1	no	—
44	C₅×C₈×D₄	—	3	1	no	—
45	C₈×C₂²⋊D₅	—	3	2	no	—
46	#65390	—	3	2	no	—
47	#65301	—	3	1	no	—
48	#65124	—	3	1	no	—
49	#65120	—	3	1	no	—
50	#65017	—	3	2	no	—
51	#65009	—	3	2	no	—
52	C₄×C₈×D₅	D₃	1	1	yes	characteristic, complemented
53	C₈×Dic₁₀	—	3	1	no	—
54	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
55	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
57	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
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	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
69	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
71	C₅×D₃×C₈	—	2	4	no	—
72	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
73	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
74	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
75	C₂×C₃×#168	C₂³	1	1	yes	characteristic
76	C₂×C₃×#168	C₂³	1	1	yes	characteristic
77	C₃×C₈×D₅	—	2	2	no	—
78	C₃×C₈×D₅	—	2	2	no	—
79	Dic₃⋊Dic₅	C₂×C₄	1	2	yes	—
80	Dic₃⋊Dic₅	C₂×C₄	1	2	yes	—
81	#6669	C₂×C₄	1	2	yes	—
82	(C₂×D₃)⋊Dic₅	C₂×C₄	1	2	yes	—
83	(C₂×D₃)⋊Dic₅	C₂×C₄	1	2	yes	—
84	(C₂×D₃)⋊Dic₅	C₂×C₄	1	2	yes	—
85	#6665	C₂×C₄	1	2	yes	—
86	#6650	—	2	4	no	—
87	#5479	—	5	1	no	—
88	C₂×C₃×C₄×C₈	—	5	1	no	—
89	#5111	—	5	2	no	—
90	C₈×#67	—	5	2	no	—
91	#4926	—	5	1	no	—
92	#4690	—	5	2	no	—
93	#4689	—	5	2	no	—
94	#4688	—	5	1	no	—
95	C₈×D₁₂	D₅	1	1	yes	characteristic, complemented
96	#4679	—	5	1	no	—
97	C₈×Dic₆	—	5	1	no	—
98	C₂²×C₅×C₈	—	3	2	no	—
99	C₄×C₅×D₄	—	3	1	no	—
100	#4084	—	3	1	no	—
101	#4082	—	3	1	no	—
102	C₄×C₂²⋊D₅	—	3	2	no	—
103	#4072	—	3	2	no	—
104	C₂×#681	—	3	2	no	—
105	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
106	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
107	#4043	—	3	1	no	—
108	#4036	—	3	1	no	—
109	#4029	—	3	2	no	—
110	#4025	—	3	2	no	—
111	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
112	C₄×Dic₁₀	—	3	1	no	—
113	C₅×C₄⋊C₈	—	3	1	no	—
114	C₅×C₂²⋊C₈	—	3	2	no	—
115	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
116	C₂²⋊#168	—	3	2	no	—
117	#3952	—	3	2	no	—
118	#3947	—	3	2	no	—
119	#3947	—	3	2	no	—
120	#3946	—	3	2	no	—
121	#3946	—	3	2	no	—
122	C₈×Dic₅	—	3	2	no	—
123	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
124	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic
125	C₄⋊#168	—	3	1	no	—
126	C₄×#168	C₂×D₃	1	1	yes	characteristic
127	#2966	—	15	1	no	Sylow
128	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
129	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
137	C₅×D₁₂	—	2	2	no	—
138	C₄×C₅×D₃	—	2	2	no	—
139	C₄×C₅×D₃	—	2	2	no	—
140	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
143	C₃×C₄×D₅	—	2	2	no	—
144	C₃×C₄×D₅	—	2	2	no	—
145	C₃×C₄×D₅	—	2	1	no	—
146	C₃×C₄×D₅	—	2	1	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	1	no	—
152	C₃×#168	#41	1	2	yes	—
153	C₅×C₃⋊C₈	—	2	2	no	—
154	C₂²×C₃×C₈	—	5	1	no	—
155	C₂²×C₃×C₈	—	5	1	no	—
156	C₂×C₃×C₄²	—	5	1	no	—
157	#930	—	5	1	no	—
158	#929	—	5	2	no	—
159	C₄×#67	—	5	2	no	—
160	#924	—	5	1	no	—
161	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
162	C₂×D₃×C₈	C₂×D₅	1	2	yes	—
163	#876	—	5	2	no	—
164	#875	—	5	1	no	—
165	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
166	#872	—	5	2	no	—
167	#870	—	5	1	no	—
168	C₄×Dic₆	—	5	1	no	—
169	C₃×C₄×C₈	—	5	1	no	—
170	C₃×C₄×C₈	—	5	1	no	—
171	C₃×C₄×C₈	—	5	1	no	—
172	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
173	#830	—	5	2	no	—
174	(C₂×D₃)⋊C₈	—	5	2	no	—
175	(C₂×D₃)⋊C₈	C₂×D₅	1	2	yes	—
176	#815	—	5	2	no	—
177	Dic₃⋊C₈	—	5	2	no	—
178	Dic₃⋊C₈	—	5	2	no	—
179	C₈×Dic₃	—	5	2	no	—
180	C₄⋊(C₃⋊C₈)	—	5	1	no	—
181	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic
182	#803	—	5	2	no	—
183	C₂×C₅×D₄	—	3	1	no	—
184	C₂²×C₄×C₅	—	3	2	no	—
185	C₂×C₂²⋊D₅	—	3	2	no	—
186	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
187	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
188	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
189	C₂×Dic₁₀	—	3	1	no	—
190	C₂×C₅×C₈	—	3	2	no	—
191	C₂×C₅×C₈	—	6	4	no	—
192	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
193	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
194	C₅×C₄⋊C₄	—	3	1	no	—
195	C₅×C₂²⋊C₄	—	3	2	no	—
196	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
197	C₂²⋊Dic₅	—	3	2	no	—
198	C₂²⋊Dic₅	—	3	2	no	—
199	C₂²⋊Dic₅	—	3	2	no	—
200	#685	—	3	2	no	—
201	C₄⋊Dic₅	—	3	1	no	—
202	C₄⋊Dic₅	—	3	2	no	—
203	C₄⋊Dic₅	—	3	2	no	—
204	#683	—	3	2	no	—
205	#683	—	3	2	no	—
206	C₄×Dic₅	—	3	2	no	—
207	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
208	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
209	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
210	#681	—	6	4	no	—
211	C₂×#168	—	3	2	no	—
212	C₂×#168	C₂²×D₃	1	1	yes	characteristic
213	C₂×#168	C₂²×D₃	1	1	yes	characteristic
214	C₈×D₅	—	2	2	no	—
215	C₈×D₅	—	2	2	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	—	3	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	—	5	1	no	—
227	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₅×D₃	—	2	2	no	—
229	C₂×C₅×D₃	—	2	2	no	—
230	C₂×C₅×D₃	—	2	2	no	—
231	C₂×C₃×D₅	—	2	1	no	—
232	C₂×C₃×D₅	—	2	1	no	—
233	C₂×C₃×D₅	#131	1	2	yes	—
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	1	no	—
241	C₃×Dic₅	—	2	1	no	—
242	C₃×Dic₅	—	2	1	no	—
243	C₅×Dic₃	—	2	2	no	—
244	C₂²×C₃×C₄	—	5	1	no	—
245	C₂²×C₃×C₄	—	5	1	no	—
246	C₂²×C₃×C₄	—	5	1	no	—
247	C₂×#67	—	5	2	no	—
248	C₂×D₁₂	C₄×D₅	1	1	yes	characteristic
249	C₂×C₄×D₃	C₂²×D₅	1	2	yes	—
250	C₂×Dic₆	—	5	1	no	—
251	C₂×C₃×C₈	—	5	1	no	—
252	C₂×C₃×C₈	—	5	1	no	—
253	C₂×C₃×C₈	—	10	2	no	—
254	C₂×C₃×C₈	—	10	2	no	—
255	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
256	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
257	C₃×C₄²	—	5	1	no	—
258	C₃×C₄²	—	5	1	no	—
259	C₃×C₄²	—	5	1	no	—
260	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
261	#217	—	5	2	no	—
262	(C₂×D₃)⋊C₄	—	5	2	no	—
263	(C₂×D₃)⋊C₄	—	5	2	no	—
264	(C₂×D₃)⋊C₄	—	5	2	no	—
265	(C₂×D₃)⋊C₄	C₄×D₅	1	2	yes	—
266	C₄⋊Dic₃	—	5	1	no	—
267	C₄⋊Dic₃	C₄×D₅	1	1	yes	characteristic
268	Dic₃⋊C₄	—	5	2	no	—
269	Dic₃⋊C₄	—	5	2	no	—
270	Dic₃⋊C₄	—	5	2	no	—
271	Dic₃⋊C₄	—	5	2	no	—
272	C₄×Dic₃	—	5	2	no	—
273	C₂×C₃⋊C₈	—	5	2	no	—
274	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
275	ΓL(1,𝔽₂₅)	—	10	4	no	—
276	D₃×C₈	—	2	4	no	—
277	C₂³×C₅	—	3	2	no	—
278	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
279	C₅×D₄	—	6	2	no	—
280	C₂×C₄×C₅	—	3	2	no	—
281	C₂×C₄×C₅	—	6	2	no	—
282	C₂×C₄×C₅	—	6	2	no	—
283	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
286	C₂²⋊D₅	—	6	4	no	—
287	C₂×Dic₅	—	3	2	no	—
288	C₂×Dic₅	—	3	2	no	—
289	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
290	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
291	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
292	C₄×D₅	—	2	2	no	—
293	C₄×D₅	—	2	2	no	—
294	C₄×D₅	—	2	1	no	—
295	C₄×D₅	—	2	1	no	—
296	Dic₁₀	—	6	2	no	—
297	C₅×C₈	—	2	1	no	—
298	C₅×C₈	—	6	2	no	—
299	C₅×C₈	#235	1	2	yes	—
300	#168	—	2	1	no	—
301	#168	—	6	2	no	—
302	#168	#235	1	2	yes	—
303	C₂×M₁₆	—	15	2	no	—
304	C₂²×C₈	—	3	2	no	—
305	C₂²×C₈	—	5	1	no	—
306	C₂²×C₈	—	5	1	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	—	3	1	no	—
315	C₄×D₄	—	15	2	no	—
316	#117	—	15	2	no	—
317	C₂×C₄²	—	5	1	no	—
318	C₄⋊C₈	—	3	1	no	—
319	C₄⋊C₈	—	15	2	no	—
320	C₄⋊C₈	—	15	2	no	—
321	C₄⋊C₈	—	15	1	no	—
322	C₂²⋊C₈	—	3	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	—	5	1	no	—
328	C₄×C₈	—	5	1	no	—
329	C₄×C₈	—	5	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	—	2	2	no	—
336	C₅×D₃	—	4	2	no	—
337	C₂³×C₃	—	5	1	no	—
338	C₂²×D₃	C₂×C₄×D₅	1	2	yes	—
339	C₂×C₃×C₄	—	5	1	no	—
340	C₂×C₃×C₄	—	5	1	no	—
341	C₂×C₃×C₄	—	5	1	no	—
342	C₂×C₃×C₄	—	10	2	no	—
343	C₂×C₃×C₄	—	10	1	no	—
344	C₂×C₃×C₄	—	10	1	no	—
345	C₂×C₃×C₄	—	10	2	no	—
346	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
347	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
348	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
349	#67	—	10	4	no	—
350	C₂×Dic₃	—	5	2	no	—
351	C₂×Dic₃	—	5	2	no	—
352	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
353	D₁₂	—	2	2	no	—
354	C₄×D₃	—	2	2	no	—
355	C₄×D₃	—	2	2	no	—
356	Dic₆	—	10	2	no	—
357	C₃×C₈	—	2	1	no	—
358	C₃×C₈	—	5	2	no	—
359	C₃×C₈	—	10	1	no	—
360	C₃×C₈	#711	1	2	yes	—
361	C₃⋊C₈	—	2	2	no	—
362	C₃⋊C₈	—	10	2	no	—
363	C₂²×C₅	—	6	2	no	—
364	C₂²×C₅	—	6	2	no	—
365	C₂²×C₅	—	6	2	no	—
366	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
367	C₂×D₅	—	2	1	no	—
368	C₂×D₅	—	2	1	no	—
369	C₂×D₅	#901	1	2	yes	—
370	C₄×C₅	—	2	1	no	—
371	C₄×C₅	—	6	2	no	—
372	C₄×C₅	#901	1	2	yes	—
373	C₄×C₅	C₂×#235	1	1	yes	characteristic
374	C₄×C₅	C₂×#235	1	1	yes	characteristic
375	Dic₅	—	2	1	no	—
376	Dic₅	—	2	1	no	—
377	Dic₅	—	2	1	no	—
378	Dic₅	—	6	2	no	—
379	Dic₅	—	6	2	no	—
380	C₂×Q₈	—	15	1	no	—
381	C₂×D₄	—	3	1	no	—
382	C₂×D₄	—	15	2	no	—
383	C₂²×C₄	—	3	2	no	—
384	C₂²×C₄	—	5	1	no	—
385	C₂²×C₄	—	5	1	no	—
386	C₂²×C₄	—	5	1	no	—
387	M₁₆	—	30	4	no	—
388	C₂×C₈	—	3	2	no	—
389	C₂×C₈	—	5	1	no	—
390	C₂×C₈	—	5	1	no	—
391	C₂×C₈	—	6	4	no	—
392	C₂×C₈	—	10	2	no	—
393	C₂×C₈	—	10	2	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	—	3	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	—	3	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	—	5	1	no	—
409	C₄²	—	5	1	no	—
410	C₄²	—	5	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	—	5	2	no	—
415	C₂²×C₃	—	10	1	no	—
416	C₂²×C₃	—	10	1	no	—
417	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
418	C₂×D₃	—	2	2	no	—
419	C₂×D₃	—	2	2	no	—
420	C₂×D₃	—	2	2	no	—
421	C₃×C₄	—	2	1	no	—
422	C₃×C₄	—	10	1	no	—
423	C₃×C₄	—	10	1	no	—
424	C₃×C₄	—	10	1	no	—
425	C₃×C₄	#4047	1	2	yes	—
426	C₃×C₄	C₂×#711	1	1	yes	characteristic
427	C₃×C₄	D₅×#41	1	1	yes	characteristic
428	Dic₃	—	2	2	no	—
429	Dic₃	—	10	2	no	—
430	Dic₃	—	10	2	no	—
431	C₂×C₅	—	12	2	no	—
432	C₂×C₅	C₄×#235	1	1	yes	characteristic
433	C₂×C₅	C₂×#901	1	1	yes	characteristic
434	C₂×C₅	C₂×#901	1	1	yes	characteristic
435	D₅	—	2	2	no	—
436	C₂³	—	3	2	no	—
437	C₂³	—	5	1	no	—
438	Q₈	—	30	2	no	—
439	D₄	—	6	2	no	—
440	D₄	—	30	4	no	—
441	C₂×C₄	—	3	2	no	—
442	C₂×C₄	—	5	1	no	—
443	C₂×C₄	—	5	1	no	—
444	C₂×C₄	—	5	1	no	—
445	C₂×C₄	—	6	2	no	—
446	C₂×C₄	—	6	2	no	—
447	C₂×C₄	—	10	2	no	—
448	C₂×C₄	—	10	1	no	—
449	C₂×C₄	—	10	1	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	—	5	2	no	—
458	C₈	—	6	2	no	—
459	C₈	—	10	1	no	—
460	C₈	—	30	2	no	—
461	C₈	#6772	1	2	yes	—
462	C₂×C₃	—	10	2	no	—
463	C₂×C₃	C₄×#711	1	1	yes	characteristic
464	C₂×C₃	C₂×#4047	1	1	yes	characteristic
465	C₂×C₃	D₅×#131	1	1	yes	characteristic
466	D₃	—	4	2	no	—
467	C₅	#78448	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	5	2	no	—
469	C₂²	—	6	2	no	—
470	C₂²	—	6	2	no	—
471	C₂²	—	6	2	no	—
472	C₂²	—	10	1	no	—
473	C₂²	—	10	1	no	—
474	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	6	2	no	—
477	C₄	—	10	1	no	—
478	C₄	—	10	1	no	—
479	C₄	—	10	1	no	—
480	C₄	—	30	2	no	—
481	C₄	—	30	2	no	—
482	C₄	#91265	1	2	yes	—
483	C₄	C₂×#6772	1	1	yes	characteristic
484	C₄	D₅×#235	1	1	yes	characteristic
485	C₃	#10611132	1	1	yes	characteristic, complemented, Sylow
486	C₂	—	10	2	no	—
487	C₂	—	12	2	no	—
488	C₂	C₄×#6772	1	1	yes	characteristic
489	C₂	D₅×#901	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	#91449	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. C₅×C₈×D₁₂	C₂	semidirect
4. C₃×C₄×C₈×D₅	C₂	semidirect
5. #11747702	C₂	semidirect
6. C₈×#1201	C₂	semidirect
7. #11747654	C₂	semidirect
8. #11747653	C₂	semidirect
9. #11747008	C₂	semidirect
10. #11746871	C₂	semidirect
11. #11746864	C₂	semidirect
52. C₄×C₈×D₅	D₃	semidirect
95. C₈×D₁₂	D₅	semidirect
413. C₃×C₅	#2966	semidirect
467. C₅	#78448	semidirect
485. C₃	#10611132	semidirect

Maximal subgroups

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

subgroup	index
#11752682	2
C₈×Dic₃₀	2
C₅×C₈×D₁₂	2
C₃×C₄×C₈×D₅	2
#11747702	2
C₈×#1201	2
#11747654	2
#11747653	2
#11747008	2
#11746871	2
#11746864	2
#10611132	3
#78448	5