Subgroups — #14294790

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#91338	C₂	1	1	yes	maximal, characteristic
3	C₂×D₃×#681	C₂	1	1	yes	maximal, characteristic
4	#11746375	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64774	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745987	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745985	C₂	1	1	yes	maximal, characteristic, complemented
8	#10602780	—	3	1	no	maximal, Hall
9	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
12	C₂×#6710	C₂²	1	1	yes	characteristic
13	C₂×C₅×#208	C₂²	1	1	yes	characteristic
14	C₅×D₃×M₁₆	—	2	2	no	—
15	C₅×D₃×M₁₆	C₄	1	4	yes	complemented
16	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
17	C₂×C₅×D₃×C₈	—	2	1	no	—
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×#681	C₂²	1	1	yes	characteristic
20	C₂×(C₂×D₃)⋊Dic₅	C₄	1	2	yes	—
21	C₂×Dic₃×Dic₅	C₄	1	2	yes	—
22	#91338	—	2	1	no	—
23	#91338	—	2	1	no	—
24	#91338	—	2	1	no	—
25	#91338	—	2	1	no	—
26	C₂×#6650	—	2	1	no	—
27	D₃×#681	—	2	2	no	—
28	D₃×#681	C₄	1	4	yes	complemented
29	C₂×D₃×#168	—	2	1	no	—
30	#68989	—	5	1	no	maximal, Hall
31	C₂²×C₅×M₁₆	—	3	1	no	—
32	C₂×#4072	—	3	1	no	—
33	C₂²×#681	—	3	1	no	—
34	#64774	—	3	1	no	—
35	#64774	—	3	1	no	—
36	#64774	—	3	1	no	—
37	#64774	D₃	1	1	yes	characteristic, complemented
38	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×Dic₁₅	C₂×C₄	1	2	yes	—
41	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
43	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
44	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
45	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
46	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
47	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
48	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
49	C₂×C₄×C₅×D₃	Q₈	1	2	yes	—
50	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
51	C₃×C₅×M₁₆	—	2	1	no	—
52	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	—
53	C₂×C₃×C₅×C₈	—	2	1	no	—
54	C₄⋊Dic₁₅	—	2	1	no	—
55	C₄⋊Dic₁₅	—	2	1	no	—
56	#6710	—	2	1	no	—
57	#6710	C₂×C₄	1	2	yes	—
58	C₂×C₃⋊#168	—	2	1	no	—
59	C₅×#208	—	2	1	no	—
60	C₅×#208	C₂×C₄	1	2	yes	—
61	C₂×C₅×C₃⋊C₈	—	2	1	no	—
62	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
63	C₅×D₃×C₈	—	2	4	no	—
64	C₃×C₄⋊Dic₅	—	2	1	no	—
65	C₃×C₄⋊Dic₅	—	2	1	no	—
66	C₃×#681	—	2	1	no	—
67	C₃×#681	C₂×C₄	1	2	yes	—
68	C₂×C₃×#168	—	2	1	no	—
69	(C₂×D₃)⋊Dic₅	—	2	2	no	—
70	(C₂×D₃)⋊Dic₅	—	2	2	no	—
71	Dic₃×Dic₅	—	2	2	no	—
72	Dic₃×Dic₅	—	2	2	no	—
73	#6650	—	2	4	no	—
74	D₃×#168	—	2	4	no	—
75	C₂×D₃×M₁₆	—	5	1	no	—
76	C₂×D₃×M₁₆	D₅	1	1	yes	characteristic
77	C₂×#892	—	5	1	no	—
78	C₃×#343	—	5	1	no	—
79	#4554	—	5	1	no	—
80	#4554	—	5	1	no	—
81	#4530	—	5	1	no	—
82	C₂³×C₄×C₅	—	3	1	no	—
83	C₂×C₅×M₁₆	—	3	1	no	—
84	C₂×C₅×M₁₆	—	3	4	no	—
85	C₂×C₅×M₁₆	—	6	1	no	—
86	C₂×C₅×M₁₆	—	6	2	no	—
87	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
88	C₂²×C₅×C₈	—	6	1	no	—
89	C₂×C₂²⋊Dic₅	—	3	2	no	—
90	#4072	—	6	1	no	—
91	#4072	—	6	1	no	—
92	#4072	—	6	1	no	—
93	#4072	—	6	1	no	—
94	C₂×C₄⋊Dic₅	—	3	1	no	—
95	C₂×C₄⋊Dic₅	C₂×D₃	1	1	yes	characteristic
96	C₂×C₄×Dic₅	—	3	2	no	—
97	C₂×#681	—	3	1	no	—
98	C₂×#681	—	3	4	no	—
99	C₂×#681	—	6	1	no	—
100	C₂×#681	—	6	2	no	—
101	C₂×#681	C₂×D₃	1	1	yes	characteristic
102	C₂²×#168	—	6	1	no	—
103	#1742	—	15	1	no	Sylow
104	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₅×D₃	—	4	1	no	—
106	C₂²×C₅×D₃	—	4	1	no	—
107	C₂²×C₅×D₃	C₄²	1	2	yes	—
108	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₅×D₃	C₄⋊C₄	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
117	C₂×Dic₁₅	—	2	2	no	—
118	C₂×Dic₁₅	—	4	2	no	—
119	C₂×C₅×Dic₃	C₄²	1	2	yes	—
120	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₂×C₅×Dic₃	C₄⋊C₄	1	2	yes	—
123	C₄×C₅×D₃	C₂²⋊C₄	1	2	yes	—
124	C₄×C₅×D₃	C₂²⋊C₄	1	2	yes	—
125	C₄×C₅×D₃	C₂²⋊C₄	1	2	yes	—
126	C₄×C₅×D₃	C₂²⋊C₄	1	2	yes	—
127	C₄×C₅×D₃	C₄⋊C₄	1	2	yes	—
128	C₄×C₅×D₃	C₄⋊C₄	1	2	yes	—
129	C₄×C₅×D₃	C₄⋊C₄	1	2	yes	—
130	C₄×C₅×D₃	C₄⋊C₄	1	2	yes	—
131	C₂×C₃×Dic₅	—	2	2	no	—
132	C₂×C₃×Dic₅	—	4	2	no	—
133	C₃×C₅×C₈	—	2	2	no	—
134	C₃⋊#168	—	2	2	no	—
135	C₃×#168	—	2	2	no	—
136	C₅×C₃⋊C₈	—	2	2	no	—
137	C₂²×C₄×D₃	C₂×D₅	1	1	yes	characteristic
138	C₂×C₃×M₁₆	—	5	1	no	—
139	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
140	C₂×C₃×C₄⋊C₄	—	5	1	no	—
141	C₂×(C₂×D₃)⋊C₄	—	5	2	no	—
142	C₂×C₄⋊Dic₃	—	5	1	no	—
143	C₂×C₄×Dic₃	—	5	2	no	—
144	C₂×#208	—	5	1	no	—
145	C₂×#208	C₂×D₅	1	1	yes	characteristic
146	D₃×M₁₆	—	2	2	no	—
147	D₃×M₁₆	—	5	4	no	—
148	D₃×M₁₆	—	10	2	no	—
149	D₃×M₁₆	Dic₅	1	4	yes	complemented
150	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
151	C₂×ΓL(1,𝔽₂₅)	—	10	1	no	—
152	C₂×D₃×C₈	—	2	1	no	—
153	C₂×D₃×C₈	—	10	1	no	—
154	#892	—	10	1	no	—
155	#892	—	10	1	no	—
156	#892	—	10	1	no	—
157	#892	—	10	1	no	—
158	C₂⁴×C₅	—	3	1	no	—
159	C₂²×C₄×C₅	—	3	1	no	—
160	C₂²×C₄×C₅	—	3	2	no	—
161	C₂²×C₄×C₅	—	3	2	no	—
162	C₂²×C₄×C₅	—	3	1	no	—
163	C₂²×C₄×C₅	—	3	2	no	—
164	C₂²×C₄×C₅	—	3	1	no	—
165	C₂²×C₄×C₅	—	3	1	no	—
166	C₂²×C₄×C₅	—	3	1	no	—
167	C₂²×C₄×C₅	—	3	2	no	—
168	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
169	C₂²×Dic₅	—	3	2	no	—
170	C₂²×Dic₅	C₄×D₃	1	2	yes	—
171	C₅×M₁₆	—	2	1	no	—
172	C₅×M₁₆	—	3	2	no	—
173	C₅×M₁₆	—	6	4	no	—
174	C₅×M₁₆	—	6	1	no	—
175	C₅×M₁₆	C₄×D₃	1	2	yes	—
176	C₂×C₅×C₈	—	2	1	no	—
177	C₂×C₅×C₈	—	6	4	no	—
178	C₂×C₅×C₈	—	6	1	no	—
179	C₂²⋊Dic₅	—	6	2	no	—
180	C₂²⋊Dic₅	—	6	2	no	—
181	C₄⋊Dic₅	—	2	1	no	—
182	C₄⋊Dic₅	—	2	1	no	—
183	C₄⋊Dic₅	—	6	1	no	—
184	C₄⋊Dic₅	—	6	1	no	—
185	C₄×Dic₅	—	6	2	no	—
186	C₄×Dic₅	—	6	2	no	—
187	#681	—	2	1	no	—
188	#681	—	3	2	no	—
189	#681	—	6	4	no	—
190	#681	—	6	1	no	—
191	#681	C₄×D₃	1	2	yes	—
192	C₂×#168	—	2	1	no	—
193	C₂×#168	—	6	4	no	—
194	C₂×#168	—	6	1	no	—
195	C₂²×M₁₆	—	3	1	no	—
196	C₂²×M₁₆	—	15	1	no	—
197	C₂×#117	—	15	1	no	—
198	#343	—	5	1	no	—
199	#343	—	15	1	no	—
200	#343	—	15	1	no	—
201	#343	—	15	1	no	—
202	C₂²×C₃×C₅	—	2	1	no	—
203	C₂²×C₃×C₅	—	2	1	no	—
204	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
205	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂×C₅×D₃	—	2	1	no	—
208	C₂×C₅×D₃	—	2	1	no	—
209	C₂×C₅×D₃	—	2	1	no	—
210	C₂×C₅×D₃	—	2	1	no	—
211	C₂×C₅×D₃	—	4	2	no	—
212	C₂×C₅×D₃	—	4	2	no	—
213	C₂×C₅×D₃	#95	1	2	yes	—
214	C₂×C₅×D₃	#95	1	2	yes	—
215	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
218	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
219	Dic₁₅	—	4	2	no	—
220	C₃×Dic₅	—	4	2	no	—
221	C₅×Dic₃	#95	1	2	yes	—
222	C₅×Dic₃	#95	1	2	yes	—
223	C₂³×D₃	C₄×D₅	1	1	yes	characteristic
224	C₂²×C₃×C₄	—	5	2	no	—
225	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
226	C₂²×Dic₃	—	5	2	no	—
227	C₂²×Dic₃	C₄×D₅	1	1	yes	characteristic
228	C₂×C₄×D₃	Dic₁₀	1	2	yes	—
229	C₂×C₄×D₃	C₄×D₅	1	2	yes	—
230	C₂×C₄×D₃	D₂₀	1	1	yes	characteristic
231	C₂×C₄×D₃	D₂₀	1	1	yes	characteristic
232	C₂×C₄×D₃	C₂×Dic₅	1	2	yes	—
233	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
234	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
235	C₂×C₄×D₃	C₂²⋊D₅	1	2	yes	—
236	C₃×M₁₆	—	2	1	no	—
237	C₃×M₁₆	—	5	2	no	—
238	C₃×M₁₆	—	10	1	no	—
239	C₃×M₁₆	C₂×Dic₅	1	2	yes	—
240	C₂×C₃×C₈	—	2	1	no	—
241	C₂×C₃×C₈	—	10	1	no	—
242	C₃×C₄⋊C₄	—	10	1	no	—
243	C₃×C₄⋊C₄	—	10	1	no	—
244	(C₂×D₃)⋊C₄	—	10	2	no	—
245	(C₂×D₃)⋊C₄	—	10	2	no	—
246	C₄⋊Dic₃	—	10	1	no	—
247	C₄⋊Dic₃	—	10	1	no	—
248	C₄×Dic₃	—	10	2	no	—
249	C₄×Dic₃	—	10	2	no	—
250	#208	—	2	1	no	—
251	#208	—	5	2	no	—
252	#208	—	10	1	no	—
253	#208	C₂×Dic₅	1	2	yes	—
254	C₂×C₃⋊C₈	—	2	1	no	—
255	C₂×C₃⋊C₈	—	10	1	no	—
256	ΓL(1,𝔽₂₅)	—	2	4	no	—
257	ΓL(1,𝔽₂₅)	—	10	4	no	—
258	D₃×C₈	—	2	4	no	—
259	D₃×C₈	—	10	4	no	—
260	C₂³×C₅	—	3	1	no	—
261	C₂³×C₅	—	3	1	no	—
262	C₂³×C₅	—	3	2	no	—
263	C₂³×C₅	—	3	2	no	—
264	C₂³×C₅	—	12	1	no	—
265	C₂³×C₅	—	12	1	no	—
266	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
267	C₂×C₄×C₅	—	3	2	no	—
268	C₂×C₄×C₅	—	3	1	no	—
269	C₂×C₄×C₅	—	3	1	no	—
270	C₂×C₄×C₅	—	3	2	no	—
271	C₂×C₄×C₅	—	3	2	no	—
272	C₂×C₄×C₅	—	3	2	no	—
273	C₂×C₄×C₅	—	3	2	no	—
274	C₂×C₄×C₅	—	3	2	no	—
275	C₂×C₄×C₅	—	3	2	no	—
276	C₂×C₄×C₅	—	3	2	no	—
277	C₂×C₄×C₅	—	3	2	no	—
278	C₂×C₄×C₅	—	3	2	no	—
279	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
281	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
282	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
283	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
284	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
285	C₂×Dic₅	—	2	2	no	—
286	C₂×Dic₅	—	4	2	no	—
287	C₂×Dic₅	—	6	2	no	—
288	C₂×Dic₅	—	12	2	no	—
289	C₅×C₈	—	2	2	no	—
290	C₅×C₈	—	6	2	no	—
291	#168	—	2	2	no	—
292	#168	—	6	2	no	—
293	C₂³×C₄	—	3	1	no	—
294	C₂×M₁₆	—	3	1	no	—
295	C₂×M₁₆	—	3	4	no	—
296	C₂×M₁₆	—	5	1	no	—
297	C₂×M₁₆	—	6	1	no	—
298	C₂×M₁₆	—	6	2	no	—
299	C₂×M₁₆	—	15	4	no	—
300	C₂×M₁₆	—	15	1	no	—
301	C₂×M₁₆	—	30	1	no	—
302	C₂×M₁₆	—	30	2	no	—
303	C₂×M₁₆	D₃×D₅	1	1	yes	characteristic
304	C₂²×C₈	—	6	1	no	—
305	C₂²×C₈	—	30	1	no	—
306	#117	—	30	1	no	—
307	#117	—	30	1	no	—
308	#117	—	30	1	no	—
309	#117	—	30	1	no	—
310	C₂×C₄⋊C₄	—	5	1	no	—
311	C₂×C₄⋊C₄	—	15	1	no	—
312	C₂×C₂²⋊C₄	—	15	2	no	—
313	C₂×C₄²	—	15	2	no	—
314	C₂×C₃×C₅	—	2	1	no	—
315	C₂×C₃×C₅	—	2	1	no	—
316	C₂×C₃×C₅	C₂×#95	1	1	yes	characteristic
317	C₂×C₃×C₅	#413	1	1	yes	characteristic
318	C₂×C₃×C₅	#413	1	1	yes	characteristic
319	C₅×D₃	—	2	2	no	—
320	C₅×D₃	—	2	2	no	—
321	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
322	C₂²×D₃	—	4	1	no	—
323	C₂²×D₃	—	4	1	no	—
324	C₂²×D₃	C₄×Dic₅	1	2	yes	—
325	C₂²×D₃	#683	1	2	yes	—
326	C₂²×D₃	#685	1	1	yes	characteristic
327	C₂²×D₃	#685	1	1	yes	characteristic
328	C₂×C₃×C₄	—	10	2	no	—
329	C₂×C₃×C₄	—	20	2	no	—
330	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
331	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
334	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
336	C₂×Dic₃	—	10	2	no	—
337	C₂×Dic₃	—	20	2	no	—
338	C₂×Dic₃	C₄×Dic₅	1	2	yes	—
339	C₂×Dic₃	#683	1	2	yes	—
340	C₂×Dic₃	#685	1	1	yes	characteristic
341	C₂×Dic₃	#685	1	1	yes	characteristic
342	C₄×D₃	#683	1	2	yes	—
343	C₄×D₃	#683	1	2	yes	—
344	C₄×D₃	C₄⋊Dic₅	1	2	yes	—
345	C₄×D₃	C₄⋊Dic₅	1	2	yes	—
346	C₄×D₃	#685	1	2	yes	—
347	C₄×D₃	#685	1	2	yes	—
348	C₄×D₃	C₂²⋊Dic₅	1	2	yes	—
349	C₄×D₃	C₂²⋊Dic₅	1	2	yes	—
350	C₃×C₈	—	2	2	no	—
351	C₃×C₈	—	10	2	no	—
352	C₃⋊C₈	—	2	2	no	—
353	C₃⋊C₈	—	10	2	no	—
354	C₂²×C₅	—	2	1	no	—
355	C₂²×C₅	—	2	1	no	—
356	C₂²×C₅	—	3	2	no	—
357	C₂²×C₅	—	3	2	no	—
358	C₂²×C₅	—	6	1	no	—
359	C₂²×C₅	—	6	1	no	—
360	C₂²×C₅	—	6	1	no	—
361	C₂²×C₅	—	6	1	no	—
362	C₂²×C₅	—	12	2	no	—
363	C₂²×C₅	—	12	2	no	—
364	C₂²×C₅	C₄²×D₃	1	1	yes	characteristic
365	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
366	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
367	C₄×C₅	—	3	2	no	—
368	C₄×C₅	—	3	2	no	—
369	C₄×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
370	C₄×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
371	C₄×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
372	C₄×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
373	Dic₅	—	4	2	no	—
374	Dic₅	—	12	2	no	—
375	C₂⁴	—	3	1	no	—
376	C₂²×C₄	—	3	1	no	—
377	C₂²×C₄	—	3	2	no	—
378	C₂²×C₄	—	3	2	no	—
379	C₂²×C₄	—	3	1	no	—
380	C₂²×C₄	—	3	1	no	—
381	C₂²×C₄	—	3	2	no	—
382	C₂²×C₄	—	3	1	no	—
383	C₂²×C₄	—	3	1	no	—
384	C₂²×C₄	—	3	2	no	—
385	C₂²×C₄	—	5	2	no	—
386	C₂²×C₄	—	15	2	no	—
387	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
388	M₁₆	—	2	1	no	—
389	M₁₆	—	3	2	no	—
390	M₁₆	—	5	2	no	—
391	M₁₆	—	6	4	no	—
392	M₁₆	—	6	1	no	—
393	M₁₆	—	10	1	no	—
394	M₁₆	—	15	2	no	—
395	M₁₆	—	30	4	no	—
396	M₁₆	—	30	1	no	—
397	M₁₆	D₃×Dic₅	1	2	yes	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	6	4	no	—
400	C₂×C₈	—	6	1	no	—
401	C₂×C₈	—	10	1	no	—
402	C₂×C₈	—	30	4	no	—
403	C₂×C₈	—	30	1	no	—
404	C₄⋊C₄	—	10	1	no	—
405	C₄⋊C₄	—	10	1	no	—
406	C₄⋊C₄	—	30	1	no	—
407	C₄⋊C₄	—	30	1	no	—
408	C₂²⋊C₄	—	30	2	no	—
409	C₂²⋊C₄	—	30	2	no	—
410	C₄²	—	30	2	no	—
411	C₄²	—	30	2	no	—
412	C₃×C₅	#1742	1	1	yes	characteristic, complemented, Hall
413	C₂²×C₃	—	2	1	no	—
414	C₂²×C₃	—	2	1	no	—
415	C₂²×C₃	C₂×C₄×Dic₅	1	1	yes	characteristic
416	C₂²×C₃	C₂×#683	1	1	yes	characteristic
417	C₂²×C₃	C₂×#685	1	1	yes	characteristic
418	C₂×D₃	—	2	1	no	—
419	C₂×D₃	—	2	1	no	—
420	C₂×D₃	—	2	1	no	—
421	C₂×D₃	—	2	1	no	—
422	C₂×D₃	—	4	2	no	—
423	C₂×D₃	—	4	2	no	—
424	C₂×D₃	#3963	1	2	yes	—
425	C₂×D₃	#3963	1	2	yes	—
426	C₃×C₄	—	20	2	no	—
427	C₃×C₄	C₂×#683	1	1	yes	characteristic
428	C₃×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
429	C₃×C₄	C₂×#685	1	1	yes	characteristic
430	C₃×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
431	Dic₃	—	20	2	no	—
432	Dic₃	#3963	1	2	yes	—
433	Dic₃	#3963	1	2	yes	—
434	C₂×C₅	—	2	1	no	—
435	C₂×C₅	—	2	1	no	—
436	C₂×C₅	—	6	2	no	—
437	C₂×C₅	—	6	2	no	—
438	C₂×C₅	D₃×#95	1	1	yes	characteristic
439	C₂×C₅	#4745	1	1	yes	characteristic
440	C₂×C₅	#4751	1	1	yes	characteristic
441	C₂³	—	3	1	no	—
442	C₂³	—	3	1	no	—
443	C₂³	—	3	2	no	—
444	C₂³	—	3	2	no	—
445	C₂³	—	12	1	no	—
446	C₂³	—	12	1	no	—
447	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
448	C₂×C₄	—	3	2	no	—
449	C₂×C₄	—	3	2	no	—
450	C₂×C₄	—	3	1	no	—
451	C₂×C₄	—	3	1	no	—
452	C₂×C₄	—	3	2	no	—
453	C₂×C₄	—	3	2	no	—
454	C₂×C₄	—	3	2	no	—
455	C₂×C₄	—	3	2	no	—
456	C₂×C₄	—	3	2	no	—
457	C₂×C₄	—	3	2	no	—
458	C₂×C₄	—	3	2	no	—
459	C₂×C₄	—	3	2	no	—
460	C₂×C₄	—	10	2	no	—
461	C₂×C₄	—	20	2	no	—
462	C₂×C₄	—	30	2	no	—
463	C₂×C₄	—	60	2	no	—
464	C₂×C₄	D₃×Dic₁₀	1	1	yes	characteristic
465	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
466	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
467	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
468	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
469	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
470	C₈	—	2	2	no	—
471	C₈	—	6	2	no	—
472	C₈	—	10	2	no	—
473	C₈	—	30	2	no	—
474	C₂×C₃	—	2	1	no	—
475	C₂×C₃	—	2	1	no	—
476	C₂×C₃	#65421	1	1	yes	characteristic
477	C₂×C₃	#65421	1	1	yes	characteristic
478	C₂×C₃	C₂×#3963	1	1	yes	characteristic
479	D₃	—	2	2	no	—
480	D₃	—	2	2	no	—
481	C₅	#68989	1	1	yes	characteristic, complemented, Sylow
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	3	2	no	—
485	C₂²	—	3	2	no	—
486	C₂²	—	6	1	no	—
487	C₂²	—	6	1	no	—
488	C₂²	—	6	1	no	—
489	C₂²	—	6	1	no	—
490	C₂²	—	12	2	no	—
491	C₂²	—	12	2	no	—
492	C₂²	C₄×D₃×Dic₅	1	1	yes	characteristic
493	C₂²	D₃×#683	1	1	yes	characteristic
494	C₂²	D₃×#685	1	1	yes	characteristic
495	C₄	—	3	2	no	—
496	C₄	—	3	2	no	—
497	C₄	—	20	2	no	—
498	C₄	—	60	2	no	—
499	C₄	D₃×#683	1	1	yes	characteristic
500	C₄	D₃×C₄⋊Dic₅	1	1	yes	characteristic
501	C₄	D₃×#685	1	1	yes	characteristic
502	C₄	D₃×C₂²⋊Dic₅	1	1	yes	characteristic
503	C₃	#10602780	1	1	yes	characteristic, complemented, Sylow
504	C₂	—	2	1	no	—
505	C₂	—	2	1	no	—
506	C₂	—	6	2	no	—
507	C₂	—	6	2	no	—
508	C₂	#11748234	1	1	yes	characteristic
509	C₂	#11748235	1	1	yes	characteristic
510	C₂	D₃×#3963	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×#685
commutator	C₂²×C₃×C₅	C₂×C₄²
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₅×M₁₆	C₂²
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂³×C₅×D₃	C₂×C₄
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×M₁₆	D₃×D₅
hypocenter	C₃×C₅	#1742
LCS	G ▷ C₂²×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
4. #11746375	C₂	semidirect
5. C₃×#64774	C₂	semidirect
6. #11745987	C₂	semidirect
7. #11745985	C₂	semidirect
15. C₅×D₃×M₁₆	C₄	semidirect
28. D₃×#681	C₄	semidirect
37. #64774	D₃	semidirect
149. D₃×M₁₆	Dic₅	semidirect
412. C₃×C₅	#1742	semidirect
481. C₅	#68989	semidirect
503. C₃	#10602780	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×M₁₆	2
C₂×#91338	2
C₂×D₃×#681	2
#11746375	2
C₃×#64774	2
#11745987	2
#11745985	2
#10602780	3
#68989	5