Subgroups — #14418504

Order 1920.

728 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11752500	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
4	C₃×C₈×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
5	#11747823	C₂	1	2	yes	maximal, complemented
6	C₈×#1204	C₂	1	2	yes	maximal, complemented
7	#11747655	C₂	1	2	yes	maximal
8	#11747653	C₂	1	2	yes	maximal
9	#11747011	C₂	1	1	yes	maximal, characteristic
10	#11746865	C₂	1	1	yes	maximal, characteristic, complemented
11	#11746861	C₂	1	1	yes	maximal, characteristic, complemented
12	#10610176	—	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	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
18	#91469	C₄	1	1	yes	characteristic
19	C₄×#1204	C₂²	1	2	yes	—
20	#91389	C₄	1	1	yes	characteristic
21	#91379	C₄	1	2	yes	—
22	#91371	C₂²	1	2	yes	—
23	#91369	C₄	1	1	yes	characteristic
24	#91365	C₄	1	1	yes	characteristic
25	#91352	C₄	1	2	yes	—
26	C₂×#6650	C₂²	1	2	yes	—
27	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
28	#91098	C₂²	1	2	yes	—
29	C₈×Dic₁₅	C₂²	1	2	yes	—
30	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
31	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
32	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
33	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
34	C₃×#3946	C₂²	1	2	yes	—
35	C₃×C₈×Dic₅	C₂²	1	2	yes	—
36	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
37	Dic₃⋊#168	C₂²	1	2	yes	—
38	#90983	C₂²	1	2	yes	—
39	#90982	C₂²	1	2	yes	—
40	#90954	C₂²	1	2	yes	—
41	#90952	C₂²	1	2	yes	—
42	#79917	—	5	1	no	maximal, Hall
43	#65804	—	3	1	no	—
44	C₂×C₄×C₅×C₈	—	3	1	no	—
45	#65391	—	3	2	no	—
46	#65390	—	3	2	no	—
47	#65213	—	3	1	no	—
48	#64968	—	3	1	no	—
49	#64968	—	3	2	no	—
50	#64968	—	3	1	no	—
51	C₈×Dic₁₀	—	3	1	no	—
52	C₈×Dic₁₀	—	3	2	no	—
53	C₈×Dic₁₀	D₃	1	1	yes	characteristic, complemented
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×Dic₁₀	C₂×C₄	1	1	yes	characteristic
59	C₂×#1204	C₂×C₄	1	2	yes	—
60	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
63	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
64	#6712	C₂×C₄	1	2	yes	—
65	C₄×Dic₁₅	C₂³	1	2	yes	—
66	C₂×C₃⋊#168	C₂³	1	2	yes	—
67	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
68	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
69	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
70	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
71	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
72	C₅×D₃×C₈	—	2	2	no	—
73	C₅×D₃×C₈	Q₈	1	4	yes	complemented
74	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
75	C₃×#683	C₂×C₄	1	2	yes	—
76	C₃×C₄×Dic₅	C₂³	1	2	yes	—
77	C₂×C₃×#168	C₂³	1	2	yes	—
78	Dic₃⋊Dic₅	C₂×C₄	1	2	yes	—
79	Dic₃⋊Dic₅	C₂×C₄	1	2	yes	—
80	Dic₃⋊Dic₅	C₂×C₄	1	2	yes	—
81	#6669	C₂×C₄	1	2	yes	—
82	#6668	C₂×C₄	1	2	yes	—
83	(C₂×D₃)⋊Dic₅	C₂×C₄	1	2	yes	—
84	(C₂×D₃)⋊Dic₅	C₂×C₄	1	2	yes	—
85	#6650	—	2	4	no	—
86	#5578	—	5	1	no	—
87	C₃×C₈×Q₈	—	5	1	no	—
88	#5024	—	5	1	no	—
89	#4839	—	5	2	no	—
90	#4837	—	5	1	no	—
91	#4831	—	5	1	no	—
92	#4828	—	5	2	no	—
93	#4689	—	5	2	no	—
94	C₄×D₃×C₈	D₅	1	1	yes	characteristic
95	C₈×Dic₆	—	5	1	no	—
96	C₈×Dic₆	—	5	2	no	—
97	C₂²×C₅×C₈	—	3	1	no	—
98	C₂²×C₅×C₈	—	3	1	no	—
99	C₂×C₄²×C₅	—	3	1	no	—
100	#4072	—	3	2	no	—
101	#4070	—	3	1	no	—
102	#4070	—	3	1	no	—
103	#4070	—	3	2	no	—
104	C₂×#681	—	3	2	no	—
105	#4016	—	3	2	no	—
106	#4015	—	3	1	no	—
107	#4015	—	3	1	no	—
108	C₄×Dic₁₀	—	3	1	no	—
109	C₄×Dic₁₀	—	3	2	no	—
110	C₄×Dic₁₀	C₂×D₃	1	1	yes	characteristic
111	C₄×C₅×C₈	—	3	1	no	—
112	C₄×C₅×C₈	—	3	1	no	—
113	C₄×C₅×C₈	—	3	1	no	—
114	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
115	#3947	—	3	2	no	—
116	#3947	—	3	2	no	—
117	#3946	—	3	2	no	—
118	#3946	—	3	2	no	—
119	#3946	—	3	2	no	—
120	#3946	C₂×D₃	1	2	yes	—
121	C₈×Dic₅	—	3	2	no	—
122	C₈×Dic₅	C₂×D₃	1	2	yes	—
123	C₄⋊#168	—	3	1	no	—
124	C₄⋊#168	—	3	2	no	—
125	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
126	#2960	—	15	1	no	Sylow
127	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
131	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
132	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
133	Dic₃₀	—	2	2	no	—
134	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
137	C₄×C₅×D₃	—	2	2	no	—
138	C₄×C₅×D₃	—	2	2	no	—
139	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
140	C₄×C₅×D₃	#41	1	2	yes	—
141	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
142	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
143	C₃×Dic₁₀	—	2	2	no	—
144	#1204	—	2	4	no	—
145	C₃×C₅×C₈	—	2	1	no	—
146	C₃×C₅×C₈	C₂×Q₈	1	2	yes	—
147	C₃⋊#168	—	2	2	no	—
148	C₃×#168	—	2	2	no	—
149	C₅×C₃⋊C₈	—	2	1	no	—
150	C₅×C₃⋊C₈	C₂×Q₈	1	2	yes	—
151	C₃×C₄×Q₈	—	5	1	no	—
152	#946	—	5	1	no	—
153	#944	—	5	1	no	—
154	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
155	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
156	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
157	#897	—	5	1	no	—
158	#896	—	5	2	no	—
159	#889	—	5	2	no	—
160	#888	—	5	1	no	—
161	#872	—	5	2	no	—
162	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
163	C₄×Dic₆	—	5	1	no	—
164	C₄×Dic₆	—	5	2	no	—
165	C₃×C₄⋊C₈	—	5	2	no	—
166	C₃×C₄⋊C₈	—	5	1	no	—
167	C₃×C₄×C₈	—	5	2	no	—
168	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
169	#815	—	5	2	no	—
170	Dic₃⋊C₈	—	5	2	no	—
171	Dic₃⋊C₈	—	5	2	no	—
172	Dic₃⋊C₈	—	5	2	no	—
173	C₈×Dic₃	—	5	2	no	—
174	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
175	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic
176	C₄⋊(C₃⋊C₈)	—	5	1	no	—
177	C₄⋊(C₃⋊C₈)	—	5	2	no	—
178	#803	—	5	2	no	—
179	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
180	C₂²×C₄×C₅	—	3	1	no	—
181	C₂²×C₄×C₅	—	3	1	no	—
182	C₂²×C₄×C₅	—	3	1	no	—
183	C₂×Dic₁₀	—	3	1	no	—
184	C₂×Dic₁₀	—	3	2	no	—
185	C₂×Dic₁₀	C₄×D₃	1	1	yes	characteristic
186	C₂×C₅×C₈	—	3	1	no	—
187	C₂×C₅×C₈	—	3	4	no	—
188	C₂×C₅×C₈	—	3	1	no	—
189	C₂×C₅×C₈	—	6	2	no	—
190	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
191	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
192	C₄²×C₅	—	3	1	no	—
193	C₄²×C₅	—	3	1	no	—
194	C₄²×C₅	—	3	1	no	—
195	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
196	C₂²⋊Dic₅	—	3	2	no	—
197	C₂²⋊Dic₅	—	3	2	no	—
198	C₄⋊Dic₅	—	3	1	no	—
199	C₄⋊Dic₅	—	3	2	no	—
200	C₄⋊Dic₅	—	3	2	no	—
201	C₄⋊Dic₅	—	3	2	no	—
202	C₄⋊Dic₅	C₄×D₃	1	1	yes	characteristic
203	#683	—	3	2	no	—
204	#683	—	3	2	no	—
205	#683	—	3	2	no	—
206	#683	C₄×D₃	1	2	yes	—
207	C₄×Dic₅	—	3	2	no	—
208	C₄×Dic₅	C₂²×D₃	1	2	yes	—
209	#681	—	6	4	no	—
210	C₂×#168	—	3	2	no	—
211	C₂×#168	C₂²×D₃	1	2	yes	—
212	#533	—	15	1	no	—
213	#446	—	15	2	no	—
214	#446	—	15	1	no	—
215	#446	—	15	1	no	—
216	C₈×Q₈	—	5	1	no	—
217	C₈×Q₈	—	15	2	no	—
218	C₈×Q₈	—	15	1	no	—
219	#424	—	15	2	no	—
220	#423	—	15	1	no	—
221	#405	—	15	2	no	—
222	C₂×C₄×C₈	—	3	1	no	—
223	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
224	C₂×C₅×D₃	—	2	1	no	—
225	C₂×C₅×D₃	—	2	1	no	—
226	C₂×C₅×D₃	C₄×Q₈	1	2	yes	—
227	C₃×C₄×C₅	—	2	1	no	—
228	C₃×C₄×C₅	#131	1	2	yes	—
229	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
230	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
231	Dic₁₅	—	2	2	no	—
232	Dic₁₅	—	2	2	no	—
233	C₃×Dic₅	—	2	2	no	—
234	C₃×Dic₅	—	2	2	no	—
235	C₅×Dic₃	—	2	1	no	—
236	C₅×Dic₃	C₄×Q₈	1	2	yes	—
237	C₅×Dic₃	#131	1	2	yes	—
238	C₂×C₃×Q₈	—	5	1	no	—
239	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
240	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
241	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
242	C₂×Dic₆	—	5	1	no	—
243	C₂×Dic₆	—	5	2	no	—
244	C₂×C₃×C₈	—	5	2	no	—
245	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
246	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
247	C₃×C₄⋊C₄	—	5	2	no	—
248	C₃×C₄⋊C₄	—	5	1	no	—
249	C₃×C₄²	—	5	2	no	—
250	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
251	(C₂×D₃)⋊C₄	—	5	2	no	—
252	(C₂×D₃)⋊C₄	—	5	2	no	—
253	C₄⋊Dic₃	—	5	1	no	—
254	C₄⋊Dic₃	—	5	2	no	—
255	Dic₃⋊C₄	—	5	2	no	—
256	Dic₃⋊C₄	—	5	2	no	—
257	Dic₃⋊C₄	—	5	2	no	—
258	Dic₃⋊C₄	—	5	2	no	—
259	Dic₃⋊C₄	—	5	2	no	—
260	C₄×Dic₃	—	5	2	no	—
261	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
262	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
263	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
264	C₂×C₃⋊C₈	—	5	2	no	—
265	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
266	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
267	ΓL(1,𝔽₂₅)	—	10	4	no	—
268	D₃×C₈	—	2	2	no	—
269	D₃×C₈	Dic₁₀	1	4	yes	complemented
270	C₂³×C₅	—	3	1	no	—
271	C₂×C₄×C₅	—	3	1	no	—
272	C₂×C₄×C₅	—	3	1	no	—
273	C₂×C₄×C₅	—	3	2	no	—
274	C₂×C₄×C₅	—	3	2	no	—
275	C₂×C₄×C₅	—	3	1	no	—
276	C₂×C₄×C₅	—	6	2	no	—
277	C₂×C₄×C₅	—	6	2	no	—
278	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
281	C₂×Dic₅	—	3	2	no	—
282	C₂×Dic₅	—	3	2	no	—
283	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
284	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
285	Dic₁₀	—	2	2	no	—
286	Dic₁₀	—	6	4	no	—
287	Dic₁₀	—	6	2	no	—
288	C₅×C₈	—	2	1	no	—
289	C₅×C₈	—	3	2	no	—
290	C₅×C₈	—	6	1	no	—
291	C₅×C₈	D₃×Q₈	1	2	yes	—
292	#168	—	2	2	no	—
293	#168	—	6	2	no	—
294	C₂×M₁₆	—	15	2	no	—
295	C₂²×C₈	—	3	1	no	—
296	C₂²×C₈	—	3	1	no	—
297	C₄⋊Q₈	—	15	1	no	—
298	C₄⋊Q₈	—	15	1	no	—
299	#125	—	15	2	no	—
300	C₂²⋊Q₈	—	15	2	no	—
301	C₂²⋊Q₈	—	15	1	no	—
302	C₂²⋊Q₈	—	15	1	no	—
303	C₄×Q₈	—	5	1	no	—
304	C₄×Q₈	—	15	2	no	—
305	C₄×Q₈	—	15	1	no	—
306	#117	—	15	2	no	—
307	C₂×C₄²	—	3	1	no	—
308	C₄⋊C₈	—	5	2	no	—
309	C₄⋊C₈	—	5	1	no	—
310	C₄⋊C₈	—	15	2	no	—
311	C₄⋊C₈	—	15	2	no	—
312	C₄⋊C₈	—	15	2	no	—
313	C₄⋊C₈	—	15	2	no	—
314	C₄⋊C₈	—	15	1	no	—
315	#97	—	15	2	no	—
316	#97	—	15	2	no	—
317	C₄×C₈	—	3	1	no	—
318	C₄×C₈	—	3	1	no	—
319	C₄×C₈	—	3	1	no	—
320	C₄×C₈	—	5	2	no	—
321	C₄×C₈	—	15	2	no	—
322	C₄×C₈	D₃×D₅	1	1	yes	characteristic
323	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
324	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
325	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
326	C₅×D₃	—	2	2	no	—
327	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
328	C₃×Q₈	—	10	2	no	—
329	C₂×C₃×C₄	—	5	2	no	—
330	C₂×C₃×C₄	—	5	2	no	—
331	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
334	C₂×Dic₃	—	5	2	no	—
335	C₂×Dic₃	—	5	2	no	—
336	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
337	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
338	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
339	C₄×D₃	—	2	2	no	—
340	C₄×D₃	—	2	2	no	—
341	C₄×D₃	C₂×Dic₁₀	1	2	yes	—
342	C₄×D₃	#709	1	2	yes	—
343	Dic₆	—	10	2	no	—
344	Dic₆	—	10	4	no	—
345	C₃×C₈	—	2	1	no	—
346	C₃×C₈	—	10	2	no	—
347	C₃×C₈	C₂×Dic₁₀	1	2	yes	—
348	C₃⋊C₈	—	2	1	no	—
349	C₃⋊C₈	—	10	2	no	—
350	C₃⋊C₈	C₂×Dic₁₀	1	2	yes	—
351	C₂²×C₅	—	3	2	no	—
352	C₂²×C₅	—	6	1	no	—
353	C₂²×C₅	—	6	1	no	—
354	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
355	C₄×C₅	—	2	1	no	—
356	C₄×C₅	—	3	2	no	—
357	C₄×C₅	—	3	2	no	—
358	C₄×C₅	—	6	1	no	—
359	C₄×C₅	#901	1	2	yes	—
360	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
361	C₄×C₅	D₃×#41	1	1	yes	characteristic
362	Dic₅	—	2	2	no	—
363	Dic₅	—	2	2	no	—
364	Dic₅	—	6	2	no	—
365	Dic₅	—	6	2	no	—
366	C₂×Q₈	—	5	1	no	—
367	C₂×Q₈	—	15	2	no	—
368	C₂×Q₈	—	15	1	no	—
369	C₂²×C₄	—	3	1	no	—
370	C₂²×C₄	—	3	1	no	—
371	C₂²×C₄	—	3	1	no	—
372	M₁₆	—	30	4	no	—
373	C₂×C₈	—	3	1	no	—
374	C₂×C₈	—	3	4	no	—
375	C₂×C₈	—	3	1	no	—
376	C₂×C₈	—	5	2	no	—
377	C₂×C₈	—	6	2	no	—
378	C₂×C₈	—	15	2	no	—
379	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
380	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
381	C₄⋊C₄	—	5	2	no	—
382	C₄⋊C₄	—	5	1	no	—
383	C₄⋊C₄	—	15	2	no	—
384	C₄⋊C₄	—	15	2	no	—
385	C₄⋊C₄	—	15	2	no	—
386	C₄⋊C₄	—	15	2	no	—
387	C₄⋊C₄	—	15	2	no	—
388	C₄⋊C₄	—	15	2	no	—
389	C₄⋊C₄	—	15	1	no	—
390	C₂²⋊C₄	—	15	2	no	—
391	C₂²⋊C₄	—	15	2	no	—
392	C₄²	—	3	1	no	—
393	C₄²	—	3	1	no	—
394	C₄²	—	3	1	no	—
395	C₄²	—	5	2	no	—
396	C₄²	—	15	2	no	—
397	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
398	C₃×C₅	#2960	1	1	yes	characteristic, complemented, Hall
399	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
400	C₂×D₃	—	2	1	no	—
401	C₂×D₃	—	2	1	no	—
402	C₂×D₃	C₄×Dic₁₀	1	2	yes	—
403	C₃×C₄	—	2	1	no	—
404	C₃×C₄	—	10	2	no	—
405	C₃×C₄	—	10	2	no	—
406	C₃×C₄	#4047	1	2	yes	—
407	C₃×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
408	C₃×C₄	C₂×#709	1	1	yes	characteristic
409	Dic₃	—	2	1	no	—
410	Dic₃	—	10	2	no	—
411	Dic₃	—	10	2	no	—
412	Dic₃	C₄×Dic₁₀	1	2	yes	—
413	Dic₃	#4047	1	2	yes	—
414	C₂×C₅	—	6	2	no	—
415	C₂×C₅	C₄×D₃×Q₈	1	1	yes	characteristic
416	C₂×C₅	C₂×#901	1	1	yes	characteristic
417	C₂×C₅	D₃×#131	1	1	yes	characteristic
418	C₂³	—	3	1	no	—
419	Q₈	—	10	2	no	—
420	Q₈	—	30	4	no	—
421	Q₈	—	30	2	no	—
422	C₂×C₄	—	3	1	no	—
423	C₂×C₄	—	3	1	no	—
424	C₂×C₄	—	3	2	no	—
425	C₂×C₄	—	3	2	no	—
426	C₂×C₄	—	3	1	no	—
427	C₂×C₄	—	5	2	no	—
428	C₂×C₄	—	5	2	no	—
429	C₂×C₄	—	6	2	no	—
430	C₂×C₄	—	6	2	no	—
431	C₂×C₄	—	15	2	no	—
432	C₂×C₄	—	15	2	no	—
433	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
434	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
436	C₈	—	2	1	no	—
437	C₈	—	3	2	no	—
438	C₈	—	6	1	no	—
439	C₈	—	10	2	no	—
440	C₈	—	30	2	no	—
441	C₈	D₃×Dic₁₀	1	2	yes	—
442	C₂×C₃	C₂×C₄×Dic₁₀	1	1	yes	characteristic
443	C₂×C₃	C₂×#4047	1	1	yes	characteristic
444	C₂×C₃	C₂×#4047	1	1	yes	characteristic
445	D₃	—	2	2	no	—
446	C₅	#79917	1	1	yes	characteristic, complemented, Sylow
447	C₂²	—	3	2	no	—
448	C₂²	—	6	1	no	—
449	C₂²	—	6	1	no	—
450	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	3	2	no	—
453	C₄	—	3	2	no	—
454	C₄	—	6	1	no	—
455	C₄	—	10	2	no	—
456	C₄	—	10	2	no	—
457	C₄	—	30	2	no	—
458	C₄	—	30	2	no	—
459	C₄	#91265	1	2	yes	—
460	C₄	C₂×D₃×Dic₁₀	1	1	yes	characteristic
461	C₄	D₃×#709	1	1	yes	characteristic
462	C₃	#10610176	1	1	yes	characteristic, complemented, Sylow
463	C₂	—	6	2	no	—
464	C₂	C₄×D₃×Dic₁₀	1	1	yes	characteristic
465	C₂	D₃×#4047	1	1	yes	characteristic
466	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	C₂²×C₅×D₃	C₂²×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	#2960
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
4. C₃×C₈×Dic₁₀	C₂	semidirect
5. #11747823	C₂	semidirect
6. C₈×#1204	C₂	semidirect
10. #11746865	C₂	semidirect
11. #11746861	C₂	semidirect
53. C₈×Dic₁₀	D₃	semidirect
73. C₅×D₃×C₈	Q₈	semidirect
269. D₃×C₈	Dic₁₀	semidirect
398. C₃×C₅	#2960	semidirect
446. C₅	#79917	semidirect
462. C₃	#10610176	semidirect

Maximal subgroups

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

subgroup	index
#11752500	2
C₈×Dic₃₀	2
C₄×C₅×D₃×C₈	2
C₃×C₈×Dic₁₀	2
#11747823	2
C₈×#1204	2
#11747655	2
#11747653	2
#11747011	2
#11746865	2
#11746861	2
#10610176	3
#79917	5