Subgroups — #14418934

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6765	C₂	1	1	yes	maximal, characteristic
2	#11750931	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4833	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65123	C₂	1	1	yes	maximal, characteristic, complemented
5	#11747696	C₂	1	2	yes	maximal, complemented
6	#11747694	C₂	1	2	yes	maximal, complemented
7	#11747576	C₂	1	2	yes	maximal, complemented
8	C₈×D₅×Dic₃	C₂	1	2	yes	maximal, complemented
9	#11746996	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×D₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
11	#11746851	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611007	—	3	1	no	maximal, Hall
13	C₂×#6765	C₄	1	1	yes	characteristic
14	C₄×Dic₃₀	C₂²	1	1	yes	characteristic
15	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
17	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
18	#91441	C₄	1	2	yes	—
19	C₄×#1201	C₂²	1	2	yes	—
20	Dic₃×D₂₀	C₄	1	1	yes	characteristic
21	#91393	C₄	1	2	yes	—
22	C₄×D₅×Dic₃	C₂²	1	2	yes	—
23	#91340	C₄	1	1	yes	characteristic
24	#91338	C₄	1	1	yes	characteristic
25	C₂×D₃×#168	C₂²	1	1	yes	characteristic
26	C₂×D₃×#168	C₂²	1	1	yes	characteristic
27	C₂×D₅×C₃⋊C₈	C₂²	1	2	yes	—
28	C₃×C₅×C₄⋊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×C₈×Dic₃	C₂²	1	2	yes	—
34	C₅×C₄⋊(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	#90955	C₂²	1	2	yes	—
39	#90951	C₂²	1	2	yes	—
40	Dic₃×#168	C₂²	1	1	yes	characteristic
41	Dic₃×#168	C₂²	1	1	yes	characteristic
42	C₈×#237	—	5	1	no	maximal, Hall
43	C₄×#709	—	3	1	no	—
44	C₅×#431	—	3	1	no	—
45	C₂×C₄×#168	—	3	1	no	—
46	#65123	—	3	1	no	—
47	#65123	D₃	1	1	yes	characteristic, complemented
48	#65119	—	3	1	no	—
49	#65119	—	3	1	no	—
50	#65014	—	3	2	no	—
51	#65014	—	3	2	no	—
52	#64974	—	3	2	no	—
53	C₄×C₈×D₅	—	3	2	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×D₅×Dic₃	C₂×C₄	1	2	yes	—
62	C₂×D₅×Dic₃	C₂×C₄	1	2	yes	—
63	#6765	C₈	1	8	yes	complemented
64	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
65	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
67	#6712	C₂×C₄	1	2	yes	—
68	C₄×Dic₁₅	C₂³	1	2	yes	—
69	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
70	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
71	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
72	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
73	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
74	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
75	C₃×#685	C₂×C₄	1	2	yes	—
76	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
77	C₂×C₃×#168	C₂³	1	1	yes	characteristic
78	C₂×C₃×#168	C₂³	1	1	yes	characteristic
79	C₃×C₈×D₅	—	2	4	no	—
80	#6669	C₂×C₄	1	2	yes	—
81	(C₂×D₃)⋊Dic₅	C₂×C₄	1	2	yes	—
82	#6665	C₂×C₄	1	2	yes	—
83	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
84	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
85	D₃×#168	—	2	2	no	—
86	D₃×#168	—	2	2	no	—
87	D₅×C₃⋊C₈	—	2	4	no	—
88	C₄×#237	—	5	1	no	—
89	C₃×C₈×D₄	—	5	1	no	—
90	C₈×#67	—	5	2	no	—
91	C₂×C₈×Dic₃	—	5	2	no	—
92	D₄×C₃⋊C₈	—	5	1	no	—
93	#4833	D₅	1	1	yes	characteristic, complemented
94	#4830	—	5	1	no	—
95	#67⋊C₈	—	5	2	no	—
96	#4718	—	5	2	no	—
97	C₄×D₃×C₈	—	5	1	no	—
98	C₈×Dic₆	—	5	1	no	—
99	C₂×#709	—	3	1	no	—
100	C₂×C₄²×C₅	—	3	1	no	—
101	C₄×C₂²⋊D₅	—	3	2	no	—
102	C₄×C₂²⋊D₅	—	3	2	no	—
103	#4072	—	3	1	no	—
104	C₂²×#168	—	3	1	no	—
105	C₂²×#168	—	3	1	no	—
106	C₂×C₈×D₅	—	3	2	no	—
107	C₂×C₈×D₅	C₂×D₃	1	2	yes	—
108	C₄×D₂₀	—	3	1	no	—
109	C₄×D₂₀	C₂×D₃	1	1	yes	characteristic
110	#4018	—	3	2	no	—
111	C₄²×D₅	—	3	2	no	—
112	C₄×Dic₁₀	—	3	1	no	—
113	C₄×Dic₁₀	—	3	1	no	—
114	C₅×C₄⋊C₈	—	3	1	no	—
115	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
116	C₅×C₂²⋊C₈	—	3	2	no	—
117	C₄×C₅×C₈	—	3	2	no	—
118	#3952	—	3	2	no	—
119	#3952	C₂×D₃	1	2	yes	—
120	#3946	—	3	2	no	—
121	#3946	—	3	2	no	—
122	C₈×Dic₅	—	3	2	no	—
123	C₈×Dic₅	—	3	2	no	—
124	C₄×#168	—	3	1	no	—
125	C₄×#168	—	3	1	no	—
126	C₄×#168	—	3	1	no	—
127	C₄×#168	C₂×D₃	1	1	yes	characteristic
128	C₈×#41	—	15	1	no	Sylow
129	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
134	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
135	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
136	Dic₃₀	C₂×C₈	1	4	yes	complemented
137	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
140	C₄×C₅×D₃	—	2	1	no	—
141	C₄×C₅×D₃	—	2	1	no	—
142	C₄×C₅×D₃	—	2	2	no	—
143	C₄×C₅×D₃	C₂×C₈	1	4	yes	complemented
144	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
145	C₃×D₂₀	C₂×C₈	1	4	yes	complemented
146	C₃×C₄×D₅	—	2	2	no	—
147	C₃×C₄×D₅	—	2	2	no	—
148	#1201	C₂×C₈	1	8	yes	complemented
149	D₅×Dic₃	—	2	4	no	—
150	D₅×Dic₃	C₂×C₈	1	8	yes	complemented
151	C₃×C₅×C₈	—	2	2	no	—
152	C₃⋊#168	—	2	1	no	—
153	C₃⋊#168	#41	1	2	yes	complemented
154	C₃×#168	—	2	1	no	—
155	C₃×#168	#41	1	2	yes	complemented
156	C₅×C₃⋊C₈	—	2	2	no	—
157	C₂×#237	—	5	1	no	—
158	C₂²×C₃×C₈	—	5	2	no	—
159	C₃×C₄×D₄	—	5	1	no	—
160	D₄×Dic₃	—	5	1	no	—
161	C₄×#67	—	5	2	no	—
162	C₂×C₄×Dic₃	—	5	2	no	—
163	C₂²×C₃⋊C₈	—	5	2	no	—
164	C₂×D₃×C₈	—	5	1	no	—
165	C₂×D₃×C₈	—	5	1	no	—
166	#892	—	5	1	no	—
167	#887	—	5	1	no	—
168	#67⋊C₄	—	5	2	no	—
169	#877	—	5	2	no	—
170	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
171	C₄×Dic₆	—	5	1	no	—
172	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
173	C₃×C₂²⋊C₈	—	5	2	no	—
174	C₃×C₄×C₈	—	5	1	no	—
175	#830	—	5	2	no	—
176	(C₂×D₃)⋊C₈	C₂×D₅	1	2	yes	—
177	Dic₃⋊C₈	—	5	2	no	—
178	Dic₃⋊C₈	—	5	2	no	—
179	C₈×Dic₃	—	5	2	no	—
180	C₈×Dic₃	—	5	1	no	—
181	C₈×Dic₃	—	5	1	no	—
182	C₈×Dic₃	—	5	2	no	—
183	C₈×Dic₃	C₂×D₅	1	2	yes	—
184	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic
185	C₄×C₃⋊C₈	—	5	1	no	—
186	C₂²×C₄×C₅	—	3	1	no	—
187	C₂²×C₄×C₅	—	3	1	no	—
188	C₂²×C₄×C₅	—	3	1	no	—
189	C₂×C₂²⋊D₅	—	3	2	no	—
190	#709	—	3	8	no	—
191	C₂×D₂₀	C₄×D₃	1	1	yes	characteristic
192	C₂×C₄×D₅	—	3	2	no	—
193	C₂×C₄×D₅	—	3	2	no	—
194	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
195	C₂×Dic₁₀	—	3	1	no	—
196	C₂×C₅×C₈	—	3	2	no	—
197	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
198	C₄²×C₅	—	3	1	no	—
199	C₄²×C₅	—	3	1	no	—
200	C₄²×C₅	—	3	1	no	—
201	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
202	C₂²⋊Dic₅	—	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	C₄×Dic₅	—	3	2	no	—
210	C₄×Dic₅	—	3	2	no	—
211	C₄×Dic₅	—	3	2	no	—
212	C₂×#168	—	3	1	no	—
213	C₂×#168	—	3	1	no	—
214	C₂×#168	—	6	2	no	—
215	C₂×#168	—	6	2	no	—
216	C₂×#168	C₂²×D₃	1	1	yes	characteristic
217	C₂×#168	C₂²×D₃	1	1	yes	characteristic
218	C₈×D₅	—	2	4	no	—
219	C₈×D₅	—	6	4	no	—
220	C₄×#41	—	15	1	no	—
221	C₈×Q₈	—	15	1	no	—
222	C₈×Q₈	—	15	1	no	—
223	C₈×D₄	—	5	1	no	—
224	C₈×D₄	—	15	2	no	—
225	C₈×D₄	—	15	2	no	—
226	C₈×D₄	—	15	1	no	—
227	#431	—	3	1	no	—
228	#431	—	15	2	no	—
229	C₂×C₄×C₈	—	15	2	no	—
230	C₂×C₄×C₈	—	15	1	no	—
231	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₅×D₃	—	2	1	no	—
233	C₂×C₅×D₃	—	2	1	no	—
234	C₂×C₅×D₃	C₂²×C₈	1	2	yes	—
235	C₂×C₃×D₅	—	2	2	no	—
236	C₂×C₃×D₅	—	2	2	no	—
237	C₂×C₃×D₅	C₂²×C₈	1	4	yes	—
238	C₃×C₄×C₅	—	2	1	no	—
239	C₃×C₄×C₅	C₂²×C₈	1	2	yes	—
240	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
241	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
242	Dic₁₅	—	2	2	no	—
243	Dic₁₅	C₂²×C₈	1	4	yes	—
244	C₃×Dic₅	—	2	2	no	—
245	C₅×Dic₃	—	2	1	no	—
246	C₅×Dic₃	C₂²×C₈	1	2	yes	—
247	C₅×Dic₃	#131	1	2	yes	—
248	C₂×C₃×D₄	—	5	1	no	—
249	C₂²×C₃×C₄	—	5	2	no	—
250	C₂×#67	—	5	2	no	—
251	C₂²×Dic₃	—	5	2	no	—
252	C₂²×Dic₃	—	5	2	no	—
253	#237	—	5	8	no	—
254	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
255	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
256	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
257	C₂×Dic₆	—	5	1	no	—
258	C₂×C₃×C₈	—	5	1	no	—
259	C₂×C₃×C₈	—	5	1	no	—
260	C₂×C₃×C₈	—	10	4	no	—
261	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
262	C₃×C₄⋊C₄	—	5	1	no	—
263	C₃×C₂²⋊C₄	—	5	2	no	—
264	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
265	#217	—	5	2	no	—
266	(C₂×D₃)⋊C₄	—	5	2	no	—
267	C₄⋊Dic₃	—	5	1	no	—
268	Dic₃⋊C₄	—	5	2	no	—
269	Dic₃⋊C₄	—	5	2	no	—
270	C₄×Dic₃	—	5	2	no	—
271	C₄×Dic₃	—	5	2	no	—
272	C₄×Dic₃	—	5	2	no	—
273	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
274	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
275	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
276	C₂×C₃⋊C₈	—	5	1	no	—
277	C₂×C₃⋊C₈	—	5	1	no	—
278	C₂×C₃⋊C₈	—	10	4	no	—
279	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
280	D₃×C₈	—	10	2	no	—
281	D₃×C₈	—	10	2	no	—
282	C₂³×C₅	—	3	1	no	—
283	C₂²×D₅	C₂×C₄×D₃	1	2	yes	—
284	C₂×C₄×C₅	—	3	1	no	—
285	C₂×C₄×C₅	—	3	1	no	—
286	C₂×C₄×C₅	—	3	4	no	—
287	C₂×C₄×C₅	—	3	1	no	—
288	C₂×C₄×C₅	—	6	2	no	—
289	C₂×C₄×C₅	—	6	1	no	—
290	C₂×C₄×C₅	—	6	1	no	—
291	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
292	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
293	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
294	C₂²⋊D₅	—	3	8	no	—
295	C₂×Dic₅	—	3	2	no	—
296	C₂×Dic₅	—	3	2	no	—
297	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
298	D₂₀	D₃×C₈	1	4	yes	complemented
299	C₄×D₅	—	2	2	no	—
300	C₄×D₅	—	2	2	no	—
301	C₄×D₅	—	3	8	no	—
302	C₄×D₅	—	6	4	no	—
303	Dic₁₀	—	3	4	no	—
304	C₅×C₈	—	2	2	no	—
305	C₅×C₈	—	6	2	no	—
306	#168	—	2	1	no	—
307	#168	—	3	2	no	—
308	#168	—	6	1	no	—
309	#168	#237	1	2	yes	complemented
310	C₂×#41	—	15	1	no	—
311	C₂²×C₈	—	5	2	no	—
312	C₂²×C₈	—	15	2	no	—
313	C₂²×C₈	—	15	1	no	—
314	C₂²×C₈	—	15	1	no	—
315	C₄×Q₈	—	15	1	no	—
316	C₄×Q₈	—	15	1	no	—
317	C₄×D₄	—	5	1	no	—
318	C₄×D₄	—	15	1	no	—
319	C₄×D₄	—	15	2	no	—
320	C₄×D₄	—	15	2	no	—
321	#117	—	15	2	no	—
322	#117	—	15	1	no	—
323	C₂×C₄²	—	3	1	no	—
324	C₂×C₄²	—	15	2	no	—
325	C₄⋊C₈	—	3	1	no	—
326	C₄⋊C₈	—	15	2	no	—
327	C₄⋊C₈	—	15	2	no	—
328	C₄⋊C₈	D₃×D₅	1	1	yes	characteristic
329	C₂²⋊C₈	—	3	2	no	—
330	C₂²⋊C₈	—	5	2	no	—
331	C₂²⋊C₈	—	15	2	no	—
332	C₄×C₈	—	3	2	no	—
333	C₄×C₈	—	5	1	no	—
334	C₄×C₈	—	15	1	no	—
335	C₄×C₈	—	15	1	no	—
336	C₄×C₈	—	15	2	no	—
337	C₄×C₈	—	15	2	no	—
338	C₄×C₈	—	15	1	no	—
339	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
340	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
341	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
342	C₃×D₅	—	2	4	no	—
343	C₅×D₃	—	2	2	no	—
344	C₂³×C₃	—	5	2	no	—
345	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
346	C₃×D₄	—	5	4	no	—
347	C₂×C₃×C₄	—	5	2	no	—
348	C₂×C₃×C₄	—	10	2	no	—
349	C₂×C₃×C₄	—	10	2	no	—
350	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
353	#67	—	5	8	no	—
354	C₂×Dic₃	—	5	2	no	—
355	C₂×Dic₃	—	5	8	no	—
356	C₂×Dic₃	—	5	2	no	—
357	C₂×Dic₃	—	10	4	no	—
358	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
359	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
360	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
361	C₄×D₃	—	2	1	no	—
362	C₄×D₃	—	2	1	no	—
363	C₄×D₃	—	2	2	no	—
364	C₄×D₃	C₈×D₅	1	4	yes	complemented
365	Dic₆	—	5	4	no	—
366	C₃×C₈	—	2	2	no	—
367	C₃×C₈	—	5	2	no	—
368	C₃×C₈	—	10	1	no	—
369	C₃⋊C₈	—	2	2	no	—
370	C₃⋊C₈	—	5	2	no	—
371	C₃⋊C₈	—	10	1	no	—
372	C₂²×C₅	—	3	2	no	—
373	C₂²×C₅	—	6	1	no	—
374	C₂²×C₅	—	6	1	no	—
375	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
376	C₂×D₅	—	2	2	no	—
377	C₂×D₅	—	2	2	no	—
378	C₂×D₅	C₂×D₃×C₈	1	4	yes	—
379	C₄×C₅	—	2	1	no	—
380	C₄×C₅	—	3	2	no	—
381	C₄×C₅	—	3	2	no	—
382	C₄×C₅	—	6	1	no	—
383	C₄×C₅	C₂×D₃×C₈	1	2	yes	—
384	C₄×C₅	C₂×#237	1	1	yes	characteristic
385	C₄×C₅	D₃×#41	1	1	yes	characteristic
386	Dic₅	—	2	2	no	—
387	Dic₅	—	3	4	no	—
388	Dic₅	—	6	2	no	—
389	#41	—	15	8	no	—
390	C₂×Q₈	—	15	1	no	—
391	C₂×D₄	—	5	1	no	—
392	C₂×D₄	—	15	2	no	—
393	C₂²×C₄	—	3	1	no	—
394	C₂²×C₄	—	3	1	no	—
395	C₂²×C₄	—	3	1	no	—
396	C₂²×C₄	—	5	2	no	—
397	C₂²×C₄	—	15	2	no	—
398	C₂²×C₄	—	15	2	no	—
399	C₂×C₈	—	3	2	no	—
400	C₂×C₈	—	5	1	no	—
401	C₂×C₈	—	5	1	no	—
402	C₂×C₈	—	10	4	no	—
403	C₂×C₈	—	15	1	no	—
404	C₂×C₈	—	15	1	no	—
405	C₂×C₈	—	30	2	no	—
406	C₂×C₈	—	30	4	no	—
407	C₂×C₈	—	30	2	no	—
408	C₂×C₈	C₂×D₃×D₅	1	2	yes	—
409	C₄⋊C₄	—	5	1	no	—
410	C₄⋊C₄	—	15	2	no	—
411	C₄⋊C₄	—	15	2	no	—
412	C₄⋊C₄	—	15	1	no	—
413	C₂²⋊C₄	—	5	2	no	—
414	C₂²⋊C₄	—	15	2	no	—
415	C₂²⋊C₄	—	15	2	no	—
416	C₄²	—	3	1	no	—
417	C₄²	—	3	1	no	—
418	C₄²	—	3	1	no	—
419	C₄²	—	15	2	no	—
420	C₄²	—	15	2	no	—
421	C₄²	—	15	2	no	—
422	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
423	C₃×C₅	C₈×#41	1	1	yes	characteristic, complemented, Hall
424	C₂²×C₃	—	5	4	no	—
425	C₂²×C₃	—	10	2	no	—
426	C₂²×C₃	—	10	2	no	—
427	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
428	C₂×D₃	—	2	1	no	—
429	C₂×D₃	—	2	1	no	—
430	C₂×D₃	C₂×C₈×D₅	1	2	yes	—
431	C₃×C₄	—	2	1	no	—
432	C₃×C₄	—	10	2	no	—
433	C₃×C₄	C₂×C₈×D₅	1	2	yes	—
434	C₃×C₄	D₅×#41	1	1	yes	characteristic
435	C₃×C₄	D₅×#41	1	1	yes	characteristic
436	Dic₃	—	2	1	no	—
437	Dic₃	—	5	4	no	—
438	Dic₃	—	10	2	no	—
439	Dic₃	C₂×C₈×D₅	1	2	yes	—
440	Dic₃	#4053	1	2	yes	—
441	C₂×C₅	—	6	2	no	—
442	C₂×C₅	C₄×#237	1	1	yes	characteristic
443	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
444	C₂×C₅	D₃×#131	1	1	yes	characteristic
445	D₅	—	2	4	no	—
446	C₂³	—	3	1	no	—
447	C₂³	—	5	2	no	—
448	Q₈	—	15	4	no	—
449	D₄	—	5	4	no	—
450	D₄	—	15	8	no	—
451	C₂×C₄	—	3	1	no	—
452	C₂×C₄	—	3	1	no	—
453	C₂×C₄	—	3	4	no	—
454	C₂×C₄	—	3	1	no	—
455	C₂×C₄	—	5	2	no	—
456	C₂×C₄	—	6	2	no	—
457	C₂×C₄	—	6	1	no	—
458	C₂×C₄	—	6	1	no	—
459	C₂×C₄	—	10	2	no	—
460	C₂×C₄	—	10	2	no	—
461	C₂×C₄	—	15	8	no	—
462	C₂×C₄	—	15	2	no	—
463	C₂×C₄	—	15	2	no	—
464	C₂×C₄	—	30	4	no	—
465	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
466	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
467	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
468	C₈	—	2	2	no	—
469	C₈	—	5	2	no	—
470	C₈	—	6	2	no	—
471	C₈	—	10	1	no	—
472	C₈	—	15	2	no	—
473	C₈	—	30	1	no	—
474	C₂×C₃	—	10	4	no	—
475	C₂×C₃	#65856	1	1	yes	characteristic
476	C₂×C₃	C₂²×C₈×D₅	1	1	yes	characteristic
477	C₂×C₃	C₂×#4053	1	1	yes	characteristic
478	D₃	—	2	2	no	—
479	C₅	C₈×#237	1	1	yes	characteristic, complemented, Sylow
480	C₂²	—	3	2	no	—
481	C₂²	—	5	4	no	—
482	C₂²	—	6	1	no	—
483	C₂²	—	6	1	no	—
484	C₂²	—	10	2	no	—
485	C₂²	—	10	2	no	—
486	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	3	2	no	—
489	C₄	—	3	2	no	—
490	C₄	—	6	1	no	—
491	C₄	—	10	2	no	—
492	C₄	—	15	4	no	—
493	C₄	—	30	2	no	—
494	C₄	D₃×C₈×D₅	1	2	yes	—
495	C₄	D₅×#237	1	1	yes	characteristic
496	C₄	#92034	1	1	yes	characteristic
497	C₃	#10611007	1	1	yes	characteristic, complemented, Sylow
498	C₂	—	6	2	no	—
499	C₂	—	10	4	no	—
500	C₂	#11753398	1	1	yes	characteristic
501	C₂	C₂×D₃×C₈×D₅	1	1	yes	characteristic
502	C₂	D₃×#4053	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator	C₂×C₃×C₅	C₂³×C₈
Fitting	C₃×C₅×C₄⋊C₈	C₂²
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×#6765	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄⋊C₈	D₃×D₅
hypocenter	C₃×C₅	C₈×#41
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. #11750931	C₂	semidirect
3. C₅×#4833	C₂	semidirect
4. C₃×#65123	C₂	semidirect
5. #11747696	C₂	semidirect
6. #11747694	C₂	semidirect
7. #11747576	C₂	semidirect
8. C₈×D₅×Dic₃	C₂	semidirect
9. #11746996	C₂	semidirect
10. C₄×D₃×#168	C₂	semidirect
11. #11746851	C₂	semidirect
47. #65123	D₃	semidirect
63. #6765	C₈	semidirect
93. #4833	D₅	semidirect
136. Dic₃₀	C₂×C₈	semidirect
143. C₄×C₅×D₃	C₂×C₈	semidirect
145. C₃×D₂₀	C₂×C₈	semidirect
148. #1201	C₂×C₈	semidirect
150. D₅×Dic₃	C₂×C₈	semidirect
153. C₃⋊#168	#41	semidirect
155. C₃×#168	#41	semidirect
298. D₂₀	D₃×C₈	semidirect
309. #168	#237	semidirect
364. C₄×D₃	C₈×D₅	semidirect
423. C₃×C₅	C₈×#41	semidirect
479. C₅	C₈×#237	semidirect
497. C₃	#10611007	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6765	2
#11750931	2
C₅×#4833	2
C₃×#65123	2
#11747696	2
#11747694	2
#11747576	2
C₈×D₅×Dic₃	2
#11746996	2
C₄×D₃×#168	2
#11746851	2
#10611007	3
C₈×#237	5