Subgroups — #14301776

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#91365	C₂	1	1	yes	maximal, characteristic
3	C₂×#91100	C₂	1	1	yes	maximal, characteristic, complemented
4	#11748786	C₂	1	1	yes	maximal, characteristic
5	C₂×#90974	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64771	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745980	C₂	1	1	yes	maximal, characteristic, complemented
8	#10602765	—	3	1	no	maximal, Hall
9	C₂²×Dic₃₀	C₂²	1	1	yes	characteristic
10	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
13	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×D₃×C₈	—	2	2	no	—
15	C₂×C₅×D₃×C₈	—	2	2	no	—
16	C₂×C₅×D₃×C₈	—	2	2	no	—
17	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
19	C₂×#6668	—	2	1	no	—
20	C₂×(C₂×D₃)⋊Dic₅	—	2	1	no	—
21	C₂×(C₂×D₃)⋊Dic₅	—	2	1	no	—
22	#91365	—	2	2	no	—
23	#91365	C₄	1	4	yes	complemented
24	#91100	—	2	2	no	—
25	#90994	—	2	1	no	—
26	#90974	—	2	2	no	—
27	#68882	—	5	1	no	maximal, Hall
28	C₂³×C₅×C₈	—	3	1	no	—
29	C₂×#4070	—	3	1	no	—
30	#65501	—	3	1	no	—
31	C₂×#3948	—	3	1	no	—
32	C₂×#3948	—	3	1	no	—
33	#64771	—	3	1	no	—
34	#64771	D₃	1	1	yes	characteristic, complemented
35	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂²×Dic₁₅	—	2	1	no	—
38	C₂²×Dic₁₅	—	2	1	no	—
39	C₂×Dic₃₀	—	2	1	no	—
40	C₂×Dic₃₀	—	2	1	no	—
41	C₂×Dic₃₀	—	2	1	no	—
42	C₂×Dic₃₀	—	2	1	no	—
43	C₂×Dic₃₀	—	2	1	no	—
44	C₂×Dic₃₀	C₂×C₄	1	2	yes	—
45	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
46	C₂×C₄×C₅×D₃	—	2	1	no	—
47	C₂×C₄×C₅×D₃	—	2	1	no	—
48	C₂×C₄×C₅×D₃	—	2	1	no	—
49	C₂×C₄×C₅×D₃	—	2	1	no	—
50	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
51	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
52	C₂²×C₃×Dic₅	—	2	1	no	—
53	C₂²×C₃×Dic₅	—	2	1	no	—
54	C₂×C₃×C₅×C₈	—	2	1	no	—
55	C₂×C₃×C₅×C₈	—	2	1	no	—
56	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
57	C₄⋊Dic₁₅	—	2	1	no	—
58	C₄⋊Dic₁₅	—	2	1	no	—
59	C₂×C₅×C₃⋊C₈	—	2	1	no	—
60	C₂×C₅×C₃⋊C₈	—	2	1	no	—
61	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
62	C₅×D₃×C₈	—	2	8	no	—
63	C₃×C₄⋊Dic₅	—	2	1	no	—
64	C₃×C₄⋊Dic₅	—	2	1	no	—
65	C₃×C₄⋊Dic₅	—	2	1	no	—
66	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
67	#6668	—	2	4	no	—
68	(C₂×D₃)⋊Dic₅	—	2	4	no	—
69	(C₂×D₃)⋊Dic₅	—	4	2	no	—
70	C₂²×D₃×C₈	D₅	1	1	yes	characteristic
71	C₂×#897	—	5	1	no	—
72	C₂×#816	—	5	1	no	—
73	#4987	—	5	1	no	—
74	C₂×#810	—	5	1	no	—
75	C₃×#340	—	5	1	no	—
76	#4529	—	5	1	no	—
77	C₂³×C₄×C₅	—	3	1	no	—
78	C₂²×Dic₁₀	—	3	1	no	—
79	C₂²×C₅×C₈	—	3	1	no	—
80	C₂²×C₅×C₈	—	6	2	no	—
81	C₂²×C₅×C₈	—	6	2	no	—
82	C₂²×C₅×C₈	—	6	2	no	—
83	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
84	C₂×C₂²⋊Dic₅	—	6	1	no	—
85	C₂×C₂²⋊Dic₅	—	6	1	no	—
86	C₂×C₄⋊Dic₅	—	3	1	no	—
87	C₂×C₄⋊Dic₅	C₂×D₃	1	1	yes	characteristic
88	C₂×C₄⋊Dic₅	C₂×D₃	1	1	yes	characteristic
89	#4070	—	3	4	no	—
90	#4070	—	6	2	no	—
91	C₂×#683	—	6	1	no	—
92	#3963	—	6	1	no	—
93	#3948	—	6	2	no	—
94	#3948	—	6	2	no	—
95	#1892	—	15	1	no	Sylow
96	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₅×D₃	—	2	1	no	—
98	C₂²×C₅×D₃	—	2	1	no	—
99	C₂²×C₅×D₃	—	2	1	no	—
100	C₂²×C₅×D₃	—	2	1	no	—
101	C₂²×C₅×D₃	C₂²⋊C₄	1	2	yes	—
102	C₂²×C₅×D₃	SD₁₆	1	2	yes	—
103	C₂²×C₅×D₃	Q₁₆	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
110	C₂×Dic₁₅	—	2	2	no	—
111	C₂×Dic₁₅	—	4	1	no	—
112	C₂×Dic₁₅	—	4	1	no	—
113	C₂×Dic₁₅	—	4	1	no	—
114	C₂×Dic₁₅	—	4	1	no	—
115	C₂×Dic₁₅	—	4	1	no	—
116	Dic₃₀	—	2	2	no	—
117	Dic₃₀	—	2	2	no	—
118	Dic₃₀	—	4	1	no	—
119	Dic₃₀	—	4	1	no	—
120	C₂×C₅×Dic₃	—	2	1	no	—
121	C₂×C₅×Dic₃	—	2	1	no	—
122	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
123	C₄×C₅×D₃	—	2	2	no	—
124	C₄×C₅×D₃	—	2	2	no	—
125	C₄×C₅×D₃	—	2	2	no	—
126	C₄×C₅×D₃	—	2	2	no	—
127	C₂×C₃×Dic₅	—	2	2	no	—
128	C₂×C₃×Dic₅	—	4	1	no	—
129	C₂×C₃×Dic₅	—	4	1	no	—
130	C₂×C₃×Dic₅	—	4	1	no	—
131	C₂×C₃×Dic₅	—	4	1	no	—
132	C₂×C₃×Dic₅	—	4	1	no	—
133	C₃×C₅×C₈	—	2	2	no	—
134	C₅×C₃⋊C₈	—	2	2	no	—
135	C₂²×C₄×D₃	C₂×D₅	1	1	yes	characteristic
136	C₂²×Dic₆	—	5	1	no	—
137	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
138	C₂×C₃×C₄⋊C₄	—	5	1	no	—
139	C₂×C₃×C₄⋊C₄	—	5	1	no	—
140	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
141	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
142	C₂×C₄⋊Dic₃	—	5	1	no	—
143	C₂×C₄⋊Dic₃	—	10	1	no	—
144	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
145	C₂×D₃×C₈	—	2	2	no	—
146	C₂×D₃×C₈	—	2	2	no	—
147	C₂×D₃×C₈	—	2	2	no	—
148	#897	—	5	4	no	—
149	#897	—	10	2	no	—
150	C₃⋊#95	—	10	1	no	—
151	#816	—	10	2	no	—
152	#810	—	10	2	no	—
153	C₂⁴×C₅	—	3	1	no	—
154	C₂²×C₄×C₅	—	3	1	no	—
155	C₂²×C₄×C₅	—	3	2	no	—
156	C₂²×C₄×C₅	—	3	2	no	—
157	C₂²×C₄×C₅	—	6	1	no	—
158	C₂²×C₄×C₅	—	6	1	no	—
159	C₂²×C₄×C₅	—	6	1	no	—
160	C₂²×C₄×C₅	—	6	1	no	—
161	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
162	C₂²×Dic₅	—	2	1	no	—
163	C₂²×Dic₅	—	2	1	no	—
164	C₂²×Dic₅	—	6	1	no	—
165	C₂²×Dic₅	—	6	1	no	—
166	C₂×Dic₁₀	—	3	2	no	—
167	C₂×Dic₁₀	—	6	1	no	—
168	C₂×Dic₁₀	—	6	1	no	—
169	C₂×Dic₁₀	—	6	1	no	—
170	C₂×Dic₁₀	—	6	1	no	—
171	C₂×Dic₁₀	—	6	1	no	—
172	C₂×C₅×C₈	—	2	1	no	—
173	C₂×C₅×C₈	—	2	1	no	—
174	C₂×C₅×C₈	—	3	2	no	—
175	C₂×C₅×C₈	—	6	8	no	—
176	C₂×C₅×C₈	—	6	1	no	—
177	C₂×C₅×C₈	—	6	1	no	—
178	C₂×C₅×C₈	D₁₂	1	2	yes	—
179	C₂²⋊Dic₅	—	6	4	no	—
180	C₂²⋊Dic₅	—	12	2	no	—
181	C₄⋊Dic₅	—	2	1	no	—
182	C₄⋊Dic₅	—	2	1	no	—
183	C₄⋊Dic₅	—	2	1	no	—
184	C₄⋊Dic₅	—	6	1	no	—
185	C₄⋊Dic₅	—	6	1	no	—
186	C₄⋊Dic₅	C₄×D₃	1	2	yes	—
187	#683	—	6	4	no	—
188	C₂³×C₈	—	3	1	no	—
189	C₂×C₂²⋊Q₈	—	15	1	no	—
190	C₂×#103	—	15	1	no	—
191	C₂×#103	—	15	1	no	—
192	#380	—	15	1	no	—
193	#340	—	5	1	no	—
194	#340	—	15	1	no	—
195	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂²×C₃×C₅	#121	1	1	yes	characteristic
197	C₂²×C₃×C₅	#121	1	1	yes	characteristic
198	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
199	C₂²×C₃×C₅	C₂×Q₁₆	1	1	yes	characteristic
200	C₂²×C₃×C₅	#135	1	1	yes	characteristic
201	C₂²×C₃×C₅	#135	1	1	yes	characteristic
202	C₂×C₅×D₃	—	2	2	no	—
203	C₂×C₅×D₃	—	2	2	no	—
204	C₂×C₅×D₃	—	2	2	no	—
205	C₂×C₅×D₃	—	2	2	no	—
206	C₂×C₅×D₃	—	2	2	no	—
207	C₂×C₅×D₃	—	2	2	no	—
208	C₂×C₅×D₃	#103	1	4	yes	complemented
209	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
210	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
211	C₃×C₄×C₅	#120	1	1	yes	characteristic
212	C₃×C₄×C₅	#123	1	1	yes	characteristic
213	Dic₁₅	—	4	2	no	—
214	Dic₁₅	—	8	1	no	—
215	C₃×Dic₅	—	4	2	no	—
216	C₃×Dic₅	—	8	1	no	—
217	C₅×Dic₃	—	2	2	no	—
218	C₂³×D₃	D₂₀	1	1	yes	characteristic
219	C₂²×C₃×C₄	—	10	1	no	—
220	C₂²×C₃×C₄	—	10	1	no	—
221	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
222	C₂²×Dic₃	—	10	1	no	—
223	C₂²×Dic₃	—	10	1	no	—
224	C₂²×Dic₃	D₂₀	1	1	yes	characteristic
225	C₂×C₄×D₃	—	2	1	no	—
226	C₂×C₄×D₃	—	2	1	no	—
227	C₂×C₄×D₃	—	2	1	no	—
228	C₂×C₄×D₃	—	2	1	no	—
229	C₂×C₄×D₃	C₄×D₅	1	2	yes	—
230	C₂×C₄×D₃	C₂²⋊D₅	1	2	yes	—
231	C₂×Dic₆	—	5	2	no	—
232	C₂×Dic₆	—	10	1	no	—
233	C₂×Dic₆	—	10	1	no	—
234	C₂×Dic₆	—	10	1	no	—
235	C₂×Dic₆	—	10	1	no	—
236	C₂×Dic₆	—	10	1	no	—
237	C₂×C₃×C₈	—	2	1	no	—
238	C₂×C₃×C₈	—	2	1	no	—
239	C₂×C₃×C₈	C₂²⋊D₅	1	2	yes	—
240	C₃×C₄⋊C₄	—	5	2	no	—
241	C₃×C₄⋊C₄	—	10	1	no	—
242	C₃×C₄⋊C₄	—	10	1	no	—
243	C₃×C₄⋊C₄	—	10	1	no	—
244	(C₂×D₃)⋊C₄	—	10	4	no	—
245	(C₂×D₃)⋊C₄	—	20	2	no	—
246	C₄⋊Dic₃	—	10	4	no	—
247	C₄⋊Dic₃	—	10	1	no	—
248	C₄⋊Dic₃	—	10	1	no	—
249	C₂×C₃⋊C₈	—	2	1	no	—
250	C₂×C₃⋊C₈	—	2	1	no	—
251	C₂×C₃⋊C₈	C₂²⋊D₅	1	2	yes	—
252	D₃×C₈	—	2	8	no	—
253	C₂³×C₅	—	3	2	no	—
254	C₂³×C₅	—	3	2	no	—
255	C₂³×C₅	—	3	2	no	—
256	C₂³×C₅	—	6	1	no	—
257	C₂³×C₅	—	6	1	no	—
258	C₂³×C₅	—	6	1	no	—
259	C₂³×C₅	—	6	1	no	—
260	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
261	C₂×C₄×C₅	—	3	2	no	—
262	C₂×C₄×C₅	—	6	1	no	—
263	C₂×C₄×C₅	—	6	1	no	—
264	C₂×C₄×C₅	—	6	2	no	—
265	C₂×C₄×C₅	—	6	2	no	—
266	C₂×C₄×C₅	—	6	2	no	—
267	C₂×C₄×C₅	—	6	2	no	—
268	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
270	C₂×C₄×C₅	#235	1	1	yes	characteristic
271	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
272	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
273	C₂×C₄×C₅	#239	1	1	yes	characteristic
274	C₂×Dic₅	—	2	2	no	—
275	C₂×Dic₅	—	4	1	no	—
276	C₂×Dic₅	—	4	1	no	—
277	C₂×Dic₅	—	4	1	no	—
278	C₂×Dic₅	—	4	1	no	—
279	C₂×Dic₅	—	4	1	no	—
280	C₂×Dic₅	—	6	2	no	—
281	C₂×Dic₅	—	12	1	no	—
282	C₂×Dic₅	—	12	1	no	—
283	C₂×Dic₅	—	12	1	no	—
284	C₂×Dic₅	—	12	1	no	—
285	C₂×Dic₅	—	12	1	no	—
286	Dic₁₀	—	6	2	no	—
287	Dic₁₀	—	6	2	no	—
288	Dic₁₀	—	12	1	no	—
289	Dic₁₀	—	12	1	no	—
290	C₅×C₈	—	2	2	no	—
291	C₅×C₈	—	6	2	no	—
292	C₂²×Q₈	—	15	1	no	—
293	C₂³×C₄	—	3	1	no	—
294	C₂²×C₈	—	3	1	no	—
295	C₂²×C₈	—	6	2	no	—
296	C₂²×C₈	—	6	2	no	—
297	C₂²×C₈	—	6	2	no	—
298	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
299	C₂²⋊Q₈	—	15	4	no	—
300	C₂²⋊Q₈	—	30	2	no	—
301	C₂×C₄⋊C₄	—	5	1	no	—
302	C₂×C₄⋊C₄	—	5	1	no	—
303	C₂×C₄⋊C₄	—	15	1	no	—
304	C₂×C₄⋊C₄	—	30	1	no	—
305	C₂×C₂²⋊C₄	—	30	1	no	—
306	C₂×C₂²⋊C₄	—	30	1	no	—
307	#103	—	30	2	no	—
308	#103	—	30	2	no	—
309	#95	—	30	1	no	—
310	C₂×C₃×C₅	#386	1	1	yes	characteristic
311	C₂×C₃×C₅	C₂×#103	1	1	yes	characteristic
312	C₂×C₃×C₅	#416	1	1	yes	characteristic
313	C₂×C₃×C₅	#465	1	1	yes	characteristic
314	C₂×C₃×C₅	#465	1	1	yes	characteristic
315	C₂×C₃×C₅	#467	1	1	yes	characteristic
316	C₂×C₃×C₅	#467	1	1	yes	characteristic
317	C₅×D₃	—	2	4	no	—
318	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
319	C₂²×D₃	—	2	1	no	—
320	C₂²×D₃	—	2	1	no	—
321	C₂²×D₃	—	2	1	no	—
322	C₂²×D₃	—	2	1	no	—
323	C₂²×D₃	#677	1	2	yes	—
324	C₂²×D₃	Dic₂₀	1	2	yes	—
325	C₂²×D₃	#685	1	2	yes	—
326	C₂×C₃×C₄	—	10	2	no	—
327	C₂×C₃×C₄	—	20	1	no	—
328	C₂×C₃×C₄	—	20	1	no	—
329	C₂×C₃×C₄	—	20	1	no	—
330	C₂×C₃×C₄	—	20	1	no	—
331	C₂×C₃×C₄	—	20	1	no	—
332	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
333	C₂×C₃×C₄	#709	1	1	yes	characteristic
334	C₂×C₃×C₄	#709	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
336	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
337	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
338	C₂×Dic₃	—	2	1	no	—
339	C₂×Dic₃	—	2	1	no	—
340	C₂×Dic₃	—	10	2	no	—
341	C₂×Dic₃	—	20	1	no	—
342	C₂×Dic₃	—	20	1	no	—
343	C₂×Dic₃	—	20	1	no	—
344	C₂×Dic₃	—	20	1	no	—
345	C₂×Dic₃	—	20	1	no	—
346	C₂×Dic₃	#685	1	2	yes	—
347	C₄×D₃	—	2	2	no	—
348	C₄×D₃	—	2	2	no	—
349	C₄×D₃	—	2	2	no	—
350	C₄×D₃	—	2	2	no	—
351	Dic₆	—	10	2	no	—
352	Dic₆	—	10	2	no	—
353	Dic₆	—	20	1	no	—
354	Dic₆	—	20	1	no	—
355	C₃×C₈	—	2	2	no	—
356	C₃⋊C₈	—	2	2	no	—
357	C₂²×C₅	—	3	4	no	—
358	C₂²×C₅	—	6	2	no	—
359	C₂²×C₅	—	6	2	no	—
360	C₂²×C₅	—	6	2	no	—
361	C₂²×C₅	—	6	2	no	—
362	C₂²×C₅	—	6	2	no	—
363	C₂²×C₅	—	6	2	no	—
364	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
365	C₂²×C₅	#884	1	1	yes	characteristic
366	C₂²×C₅	#895	1	1	yes	characteristic
367	C₂²×C₅	#912	1	1	yes	characteristic
368	C₂²×C₅	D₃×SD₁₆	1	1	yes	characteristic
369	C₂²×C₅	#916	1	1	yes	characteristic
370	C₂²×C₅	D₃×Q₁₆	1	1	yes	characteristic
371	C₄×C₅	—	6	2	no	—
372	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
373	C₄×C₅	#882	1	1	yes	characteristic
374	C₄×C₅	#893	1	1	yes	characteristic
375	C₄×C₅	#894	1	1	yes	characteristic
376	Dic₅	—	4	2	no	—
377	Dic₅	—	8	1	no	—
378	Dic₅	—	12	2	no	—
379	Dic₅	—	24	1	no	—
380	C₂⁴	—	3	1	no	—
381	C₂×Q₈	—	15	2	no	—
382	C₂×Q₈	—	30	1	no	—
383	C₂×Q₈	—	30	1	no	—
384	C₂×Q₈	—	30	1	no	—
385	C₂×Q₈	—	30	1	no	—
386	C₂×Q₈	—	30	1	no	—
387	C₂²×C₄	—	3	1	no	—
388	C₂²×C₄	—	3	2	no	—
389	C₂²×C₄	—	3	2	no	—
390	C₂²×C₄	—	6	1	no	—
391	C₂²×C₄	—	6	1	no	—
392	C₂²×C₄	—	6	1	no	—
393	C₂²×C₄	—	6	1	no	—
394	C₂²×C₄	—	10	1	no	—
395	C₂²×C₄	—	10	1	no	—
396	C₂²×C₄	—	30	1	no	—
397	C₂²×C₄	—	30	1	no	—
398	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	3	2	no	—
402	C₂×C₈	—	6	8	no	—
403	C₂×C₈	—	6	1	no	—
404	C₂×C₈	—	6	1	no	—
405	C₂×C₈	#1203	1	2	yes	—
406	C₄⋊C₄	—	5	2	no	—
407	C₄⋊C₄	—	10	1	no	—
408	C₄⋊C₄	—	10	1	no	—
409	C₄⋊C₄	—	10	1	no	—
410	C₄⋊C₄	—	30	4	no	—
411	C₄⋊C₄	—	30	1	no	—
412	C₄⋊C₄	—	30	1	no	—
413	C₂²⋊C₄	—	30	4	no	—
414	C₂²⋊C₄	—	60	2	no	—
415	C₃×C₅	#1892	1	1	yes	characteristic, complemented, Hall
416	C₂²×C₃	C₂×#677	1	1	yes	characteristic
417	C₂²×C₃	#4050	1	1	yes	characteristic
418	C₂²×C₃	#4050	1	1	yes	characteristic
419	C₂²×C₃	C₂×Dic₂₀	1	1	yes	characteristic
420	C₂²×C₃	C₂×#685	1	1	yes	characteristic
421	C₂²×C₃	#4076	1	1	yes	characteristic
422	C₂²×C₃	#4076	1	1	yes	characteristic
423	C₂×D₃	—	2	2	no	—
424	C₂×D₃	—	2	2	no	—
425	C₂×D₃	—	2	2	no	—
426	C₂×D₃	—	2	2	no	—
427	C₂×D₃	—	2	2	no	—
428	C₂×D₃	—	2	2	no	—
429	C₂×D₃	#3948	1	4	yes	complemented
430	C₃×C₄	—	20	2	no	—
431	C₃×C₄	—	40	1	no	—
432	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
433	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
434	C₃×C₄	#4075	1	1	yes	characteristic
435	C₃×C₄	#4099	1	1	yes	characteristic
436	Dic₃	—	2	2	no	—
437	Dic₃	—	20	2	no	—
438	Dic₃	—	40	1	no	—
439	C₂×C₅	—	6	4	no	—
440	C₂×C₅	#4665	1	1	yes	characteristic
441	C₂×C₅	#4772	1	1	yes	characteristic
442	C₂×C₅	#4778	1	1	yes	characteristic
443	C₂×C₅	D₃×#103	1	1	yes	characteristic
444	C₂×C₅	#4813	1	1	yes	characteristic
445	C₂×C₅	#4864	1	1	yes	characteristic
446	C₂×C₅	#4887	1	1	yes	characteristic
447	C₂³	—	3	2	no	—
448	C₂³	—	3	2	no	—
449	C₂³	—	3	2	no	—
450	C₂³	—	6	1	no	—
451	C₂³	—	6	1	no	—
452	C₂³	—	6	1	no	—
453	C₂³	—	6	1	no	—
454	C₂³	D₃×D₂₀	1	1	yes	characteristic
455	Q₈	—	30	2	no	—
456	Q₈	—	30	2	no	—
457	Q₈	—	60	1	no	—
458	Q₈	—	60	1	no	—
459	C₂×C₄	—	3	2	no	—
460	C₂×C₄	—	6	1	no	—
461	C₂×C₄	—	6	1	no	—
462	C₂×C₄	—	6	2	no	—
463	C₂×C₄	—	6	2	no	—
464	C₂×C₄	—	6	2	no	—
465	C₂×C₄	—	6	2	no	—
466	C₂×C₄	—	10	2	no	—
467	C₂×C₄	—	20	1	no	—
468	C₂×C₄	—	20	1	no	—
469	C₂×C₄	—	20	1	no	—
470	C₂×C₄	—	20	1	no	—
471	C₂×C₄	—	20	1	no	—
472	C₂×C₄	—	30	2	no	—
473	C₂×C₄	—	60	1	no	—
474	C₂×C₄	—	60	1	no	—
475	C₂×C₄	—	60	1	no	—
476	C₂×C₄	—	60	1	no	—
477	C₂×C₄	—	60	1	no	—
478	C₂×C₄	#6769	1	1	yes	characteristic
479	C₂×C₄	#6771	1	1	yes	characteristic
480	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
481	C₂×C₄	C₂×#1203	1	1	yes	characteristic
482	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
483	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
484	C₈	—	2	2	no	—
485	C₈	—	6	2	no	—
486	C₂×C₃	C₂×#3948	1	1	yes	characteristic
487	C₂×C₃	#65402	1	1	yes	characteristic
488	C₂×C₃	#65403	1	1	yes	characteristic
489	C₂×C₃	#65403	1	1	yes	characteristic
490	C₂×C₃	#65405	1	1	yes	characteristic
491	C₂×C₃	#65405	1	1	yes	characteristic
492	C₂×C₃	#65502	1	1	yes	characteristic
493	D₃	—	2	4	no	—
494	C₅	#68882	1	1	yes	characteristic, complemented, Sylow
495	C₂²	—	3	4	no	—
496	C₂²	—	6	2	no	—
497	C₂²	—	6	2	no	—
498	C₂²	—	6	2	no	—
499	C₂²	—	6	2	no	—
500	C₂²	—	6	2	no	—
501	C₂²	—	6	2	no	—
502	C₂²	D₃×#677	1	1	yes	characteristic
503	C₂²	D₃×Dic₂₀	1	1	yes	characteristic
504	C₂²	#91272	1	1	yes	characteristic
505	C₂²	#91273	1	1	yes	characteristic
506	C₂²	#91454	1	1	yes	characteristic
507	C₂²	#91460	1	1	yes	characteristic
508	C₂²	D₃×#685	1	1	yes	characteristic
509	C₄	—	6	2	no	—
510	C₄	—	20	2	no	—
511	C₄	—	40	1	no	—
512	C₄	—	60	2	no	—
513	C₄	—	120	1	no	—
514	C₄	#91351	1	1	yes	characteristic
515	C₄	C₄×#1203	1	1	yes	characteristic
516	C₄	#91446	1	1	yes	characteristic
517	C₄	#91570	1	1	yes	characteristic
518	C₃	#10602765	1	1	yes	characteristic, complemented, Sylow
519	C₂	—	6	4	no	—
520	C₂	D₃×#3948	1	1	yes	characteristic
521	C₂	#11747908	1	1	yes	characteristic
522	C₂	#11747914	1	1	yes	characteristic
523	C₂	#11747947	1	1	yes	characteristic
524	C₂	#11747950	1	1	yes	characteristic
525	C₂	#11748137	1	1	yes	characteristic
526	C₂	#11748914	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₃×D₂₀
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂²×C₃×C₅×C₈	C₂²
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂³×C₅×D₃	D₄
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	#1892
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×#91100	C₂	semidirect
5. C₂×#90974	C₂	semidirect
6. C₃×#64771	C₂	semidirect
7. #11745980	C₂	semidirect
23. #91365	C₄	semidirect
34. #64771	D₃	semidirect
208. C₂×C₅×D₃	#103	semidirect
415. C₃×C₅	#1892	semidirect
429. C₂×D₃	#3948	semidirect
494. C₅	#68882	semidirect
518. C₃	#10602765	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×D₃×C₈	2
C₂×#91365	2
C₂×#91100	2
#11748786	2
C₂×#90974	2
C₃×#64771	2
#11745980	2
#10602765	3
#68882	5