Subgroups — #14419047

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6771	C₂	1	1	yes	maximal, characteristic
2	#11750786	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4685	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
5	#11747820	C₂	1	2	yes	maximal, complemented
6	#11747708	C₂	1	2	yes	maximal, complemented
7	#11747706	C₂	1	2	yes	maximal, complemented
8	#11747702	C₂	1	2	yes	maximal, complemented
9	C₄×#6651	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#6650	C₂	1	1	yes	maximal, characteristic, complemented
11	#11746868	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611009	—	3	1	no	maximal, Hall
13	C₂×#6771	C₄	1	1	yes	characteristic
14	C₄²×D₁₅	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×C₄²×D₅	C₂²	1	1	yes	characteristic
18	C₄×#1204	C₄	1	1	yes	characteristic
19	C₄×#1204	C₂²	1	1	yes	characteristic
20	C₄×#1203	C₄	1	1	yes	characteristic
21	C₄×#1203	C₂²	1	1	yes	characteristic
22	C₄×#1202	C₄	1	1	yes	characteristic
23	C₄×#1202	C₂²	1	1	yes	characteristic
24	C₄×#1201	C₄	1	1	yes	characteristic
25	C₄×#1201	C₂²	1	1	yes	characteristic
26	#91386	C₄	1	1	yes	characteristic
27	#91371	C₄	1	1	yes	characteristic
28	#91357	C₄	1	1	yes	characteristic
29	C₂×#6651	C₂²	1	2	yes	—
30	C₂×#6650	C₂²	1	2	yes	—
31	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	#91104	C₂²	1	2	yes	—
33	#91098	C₂²	1	2	yes	—
34	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
35	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
36	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
37	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
38	C₃×C₈×Dic₅	C₂²	1	2	yes	—
39	C₃×C₄×#168	C₂²	1	1	yes	characteristic
40	#90982	C₂²	1	2	yes	—
41	#90955	C₂²	1	2	yes	—
42	#90954	C₂²	1	2	yes	—
43	#90953	C₂²	1	2	yes	—
44	#78447	—	5	1	no	maximal, Hall
45	C₄×#709	—	3	1	no	—
46	C₅×#431	—	3	1	no	—
47	C₄×#681	—	3	1	no	—
48	#65125	—	3	2	no	—
49	#65117	—	3	2	no	—
50	#65018	—	3	2	no	—
51	#65017	—	3	2	no	—
52	C₄×#676	—	3	1	no	—
53	#64974	—	3	1	no	—
54	#64974	—	3	1	no	—
55	C₄×C₈×D₅	D₃	1	1	yes	characteristic, complemented
56	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
59	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
64	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
65	C₂×#1204	C₂×C₄	1	1	yes	characteristic
66	C₂×#1203	C₂×C₄	1	1	yes	characteristic
67	C₂×#1202	C₂×C₄	1	1	yes	characteristic
68	C₂×#1201	C₂×C₄	1	1	yes	characteristic
69	#6771	—	2	4	no	—
70	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
71	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
73	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
74	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
75	C₂×C₃⋊#168	C₂³	1	2	yes	—
76	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
78	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
79	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
80	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
81	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
82	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
83	C₂×C₃×#168	C₂³	1	2	yes	—
84	C₃×C₈×D₅	—	2	4	no	—
85	Dic₃⋊Dic₅	C₂×C₄	1	1	yes	characteristic
86	Dic₃⋊Dic₅	C₂×C₄	1	1	yes	characteristic
87	#6669	C₂×C₄	1	1	yes	characteristic
88	#6669	C₂×C₄	1	1	yes	characteristic
89	#6668	C₂×C₄	1	1	yes	characteristic
90	#6668	C₂×C₄	1	1	yes	characteristic
91	#6667	C₂×C₄	1	1	yes	characteristic
92	#6667	C₂×C₄	1	1	yes	characteristic
93	(C₂×D₃)⋊Dic₅	C₂×C₄	1	1	yes	characteristic
94	(C₂×D₃)⋊Dic₅	C₂×C₄	1	1	yes	characteristic
95	#6665	C₂×C₄	1	1	yes	characteristic
96	#6665	C₂×C₄	1	1	yes	characteristic
97	#6651	—	2	4	no	—
98	#6650	—	2	4	no	—
99	C₄×#235	—	5	1	no	—
100	C₂×C₃×C₄×C₈	—	5	1	no	—
101	#5111	—	5	2	no	—
102	#5111	—	5	2	no	—
103	#4925	—	5	1	no	—
104	#4688	—	5	2	no	—
105	C₄×ΓL(1,𝔽₂₅)	—	5	1	no	—
106	C₄×ΓL(1,𝔽₂₅)	—	5	1	no	—
107	#4685	—	5	1	no	—
108	#4685	D₅	1	1	yes	characteristic, complemented
109	#4679	—	5	2	no	—
110	C₂×#709	—	3	1	no	—
111	C₂×C₄²×C₅	—	3	1	no	—
112	C₄×C₂²⋊D₅	—	3	1	no	—
113	C₄×C₂²⋊D₅	—	3	1	no	—
114	C₄×C₂²⋊D₅	—	3	1	no	—
115	C₄×C₂²⋊D₅	—	3	1	no	—
116	#4072	—	3	1	no	—
117	C₂×#681	—	3	2	no	—
118	C₂×#676	—	3	2	no	—
119	C₂×C₈×D₅	C₂×D₃	1	2	yes	—
120	C₄×D₂₀	—	3	1	no	—
121	C₄×D₂₀	—	3	1	no	—
122	#4018	—	3	1	no	—
123	#4018	—	3	1	no	—
124	C₄²×D₅	—	3	1	no	—
125	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
126	C₄×Dic₁₀	—	3	1	no	—
127	C₄×Dic₁₀	—	3	1	no	—
128	C₅×C₄⋊C₈	—	3	2	no	—
129	C₅×C₂²⋊C₈	—	3	2	no	—
130	C₄×C₅×C₈	—	3	1	no	—
131	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
132	#3952	—	3	2	no	—
133	#3952	—	3	2	no	—
134	#3947	—	3	2	no	—
135	#3946	—	3	2	no	—
136	#3946	—	3	2	no	—
137	C₈×Dic₅	C₂×D₃	1	2	yes	—
138	#3935	—	3	2	no	—
139	C₄×#168	—	3	1	no	—
140	C₄×#168	C₂×D₃	1	1	yes	characteristic
141	#2965	—	15	1	no	Sylow
142	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
149	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
151	C₄×D₁₅	—	2	2	no	—
152	C₄×D₁₅	—	2	2	no	—
153	C₄×D₁₅	—	2	2	no	—
154	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
157	C₄×C₅×D₃	—	2	2	no	—
158	C₄×C₅×D₃	—	2	2	no	—
159	C₄×C₅×D₃	—	2	2	no	—
160	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
163	C₃×C₄×D₅	—	2	2	no	—
164	C₃×C₄×D₅	—	2	2	no	—
165	C₃×C₄×D₅	M₁₆	1	4	yes	complemented
166	#1204	—	2	2	no	—
167	#1203	—	2	2	no	—
168	#1202	—	2	2	no	—
169	#1201	—	2	2	no	—
170	C₃×C₅×C₈	—	2	2	no	—
171	C₃⋊#168	—	2	2	no	—
172	C₃×#168	#41	1	4	yes	complemented
173	C₅×C₃⋊C₈	—	2	2	no	—
174	C₂×#235	—	5	1	no	—
175	C₂²×C₃×C₈	—	5	2	no	—
176	C₂×C₃×C₄²	—	5	1	no	—
177	C₄×#67	—	5	1	no	—
178	C₄×#67	—	5	1	no	—
179	C₄×#67	—	5	1	no	—
180	C₄×#67	—	5	1	no	—
181	#926	—	5	1	no	—
182	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
183	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
184	C₄×D₁₂	—	5	1	no	—
185	C₄×D₁₂	—	5	1	no	—
186	#872	—	5	1	no	—
187	#872	—	5	1	no	—
188	C₄²×D₃	—	5	1	no	—
189	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
190	C₄×Dic₆	—	5	1	no	—
191	C₄×Dic₆	—	5	1	no	—
192	C₃×C₄×C₈	—	5	2	no	—
193	C₃×C₄×C₈	—	5	1	no	—
194	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
195	#830	—	5	2	no	—
196	(C₂×D₃)⋊C₈	—	5	2	no	—
197	(C₂×D₃)⋊C₈	C₂×D₅	1	2	yes	—
198	#815	—	5	2	no	—
199	#815	—	5	2	no	—
200	Dic₃⋊C₈	—	5	2	no	—
201	Dic₃⋊C₈	C₂×D₅	1	2	yes	—
202	C₄⋊(C₃⋊C₈)	—	5	2	no	—
203	C₄×C₃⋊C₈	—	5	1	no	—
204	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
205	C₂²×C₄×C₅	—	3	1	no	—
206	C₂²×C₄×C₅	—	3	1	no	—
207	C₂²×C₄×C₅	—	3	1	no	—
208	C₂×C₂²⋊D₅	—	3	1	no	—
209	C₂×C₂²⋊D₅	—	3	1	no	—
210	#709	—	6	4	no	—
211	C₂×D₂₀	—	3	1	no	—
212	C₂×C₄×D₅	—	3	1	no	—
213	C₂×C₄×D₅	—	3	1	no	—
214	C₂×C₄×D₅	—	3	1	no	—
215	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
216	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
217	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
218	C₂×Dic₁₀	—	3	1	no	—
219	C₂×C₅×C₈	—	3	2	no	—
220	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
221	C₄²×C₅	—	3	1	no	—
222	C₄²×C₅	—	3	1	no	—
223	C₄²×C₅	—	3	1	no	—
224	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
225	C₂²⋊Dic₅	—	3	1	no	—
226	C₂²⋊Dic₅	—	3	1	no	—
227	#685	—	3	1	no	—
228	#685	—	3	1	no	—
229	#685	—	3	1	no	—
230	#685	—	3	1	no	—
231	C₄⋊Dic₅	—	3	1	no	—
232	C₄⋊Dic₅	—	3	1	no	—
233	#683	—	3	1	no	—
234	#683	—	3	1	no	—
235	#683	—	3	1	no	—
236	#683	—	3	1	no	—
237	C₄×Dic₅	—	3	1	no	—
238	C₄×Dic₅	—	3	1	no	—
239	C₄×Dic₅	—	3	1	no	—
240	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
241	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
242	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
243	#681	—	6	4	no	—
244	C₂×#168	—	3	2	no	—
245	C₂×#168	C₂²×D₃	1	2	yes	—
246	#676	—	6	4	no	—
247	C₈×D₅	—	2	4	no	—
248	C₄×#41	—	15	1	no	—
249	#446	—	15	2	no	—
250	#436	—	15	2	no	—
251	#435	—	15	2	no	—
252	#435	—	15	2	no	—
253	#431	—	3	1	no	—
254	#431	—	15	1	no	—
255	#431	—	15	1	no	—
256	C₄×M₁₆	—	15	1	no	—
257	C₄×M₁₆	—	15	1	no	—
258	C₂×C₄×C₈	—	5	1	no	—
259	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
260	C₂×D₁₅	—	2	1	no	—
261	C₂×D₁₅	—	2	1	no	—
262	C₂×D₁₅	—	2	1	no	—
263	C₂×C₅×D₃	—	2	1	no	—
264	C₂×C₅×D₃	—	2	1	no	—
265	C₂×C₅×D₃	—	2	1	no	—
266	C₂×C₃×D₅	—	2	1	no	—
267	C₂×C₃×D₅	—	2	1	no	—
268	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	—
269	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
270	C₃×C₄×C₅	#131	1	2	yes	—
271	C₃×C₄×C₅	C₂×#41	1	2	yes	—
272	Dic₁₅	—	2	1	no	—
273	Dic₁₅	—	2	1	no	—
274	Dic₁₅	—	2	1	no	—
275	C₃×Dic₅	—	2	1	no	—
276	C₃×Dic₅	—	2	1	no	—
277	C₃×Dic₅	C₂×M₁₆	1	2	yes	—
278	C₅×Dic₃	—	2	1	no	—
279	C₅×Dic₃	—	2	1	no	—
280	C₅×Dic₃	—	2	1	no	—
281	C₂²×C₃×C₄	—	5	1	no	—
282	C₂²×C₃×C₄	—	5	1	no	—
283	C₂²×C₃×C₄	—	5	1	no	—
284	C₂×#67	—	5	1	no	—
285	C₂×#67	—	5	1	no	—
286	#235	—	10	4	no	—
287	C₂×D₁₂	—	5	1	no	—
288	C₂×C₄×D₃	—	5	1	no	—
289	C₂×C₄×D₃	—	5	1	no	—
290	C₂×C₄×D₃	—	5	1	no	—
291	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
292	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
293	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
294	C₂×Dic₆	—	5	1	no	—
295	C₂×C₃×C₈	—	5	2	no	—
296	C₂×C₃×C₈	—	10	4	no	—
297	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
298	C₃×C₄²	—	5	1	no	—
299	C₃×C₄²	—	5	1	no	—
300	C₃×C₄²	—	5	1	no	—
301	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
302	#217	—	5	1	no	—
303	#217	—	5	1	no	—
304	(C₂×D₃)⋊C₄	—	5	1	no	—
305	(C₂×D₃)⋊C₄	—	5	1	no	—
306	(C₂×D₃)⋊C₄	—	5	1	no	—
307	(C₂×D₃)⋊C₄	—	5	1	no	—
308	C₄⋊Dic₃	—	5	1	no	—
309	C₄⋊Dic₃	—	5	1	no	—
310	Dic₃⋊C₄	—	5	1	no	—
311	Dic₃⋊C₄	—	5	1	no	—
312	Dic₃⋊C₄	—	5	1	no	—
313	Dic₃⋊C₄	—	5	1	no	—
314	C₄×Dic₃	—	5	1	no	—
315	C₄×Dic₃	—	5	1	no	—
316	C₄×Dic₃	—	5	1	no	—
317	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
318	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
319	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
320	C₂×C₃⋊C₈	—	5	2	no	—
321	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
322	ΓL(1,𝔽₂₅)	—	10	4	no	—
323	ΓL(1,𝔽₂₅)	—	10	4	no	—
324	C₂³×C₅	—	3	1	no	—
325	C₂²×D₅	—	3	1	no	—
326	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
327	C₂×C₄×C₅	—	3	1	no	—
328	C₂×C₄×C₅	—	3	1	no	—
329	C₂×C₄×C₅	—	3	1	no	—
330	C₂×C₄×C₅	—	6	2	no	—
331	C₂×C₄×C₅	—	6	2	no	—
332	C₂×C₄×C₅	—	6	2	no	—
333	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
334	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
335	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
336	C₂²⋊D₅	—	6	2	no	—
337	C₂²⋊D₅	—	6	2	no	—
338	C₂×Dic₅	—	3	1	no	—
339	C₂×Dic₅	—	3	1	no	—
340	C₂×Dic₅	—	3	1	no	—
341	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
342	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
343	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
344	D₂₀	—	6	2	no	—
345	C₄×D₅	—	2	2	no	—
346	C₄×D₅	—	2	2	no	—
347	C₄×D₅	—	6	2	no	—
348	C₄×D₅	—	6	2	no	—
349	C₄×D₅	—	6	2	no	—
350	C₄×D₅	ΓL(1,𝔽₂₅)	1	4	yes	complemented
351	Dic₁₀	—	6	2	no	—
352	C₅×C₈	—	2	2	no	—
353	C₅×C₈	—	6	2	no	—
354	#168	—	6	2	no	—
355	#168	#235	1	4	yes	complemented
356	C₂×#41	—	15	1	no	—
357	C₂×M₁₆	—	15	2	no	—
358	C₂×M₁₆	—	15	2	no	—
359	C₂²×C₈	—	5	2	no	—
360	C₄×Q₈	—	15	1	no	—
361	C₄×Q₈	—	15	1	no	—
362	C₄×D₄	—	15	1	no	—
363	C₄×D₄	—	15	1	no	—
364	C₄×D₄	—	15	1	no	—
365	C₄×D₄	—	15	1	no	—
366	C₄×D₄	—	15	1	no	—
367	C₄×D₄	—	15	1	no	—
368	#117	—	15	1	no	—
369	#117	—	15	1	no	—
370	#117	—	15	1	no	—
371	C₂×C₄²	—	3	1	no	—
372	C₂×C₄²	—	5	1	no	—
373	C₂×C₄²	—	15	1	no	—
374	C₄⋊C₈	—	3	2	no	—
375	C₄⋊C₈	—	15	2	no	—
376	C₄⋊C₈	—	15	2	no	—
377	C₂²⋊C₈	—	3	2	no	—
378	C₂²⋊C₈	—	15	2	no	—
379	C₂²⋊C₈	—	15	2	no	—
380	#97	—	15	2	no	—
381	#97	—	15	2	no	—
382	C₄×C₈	—	3	1	no	—
383	C₄×C₈	—	5	2	no	—
384	C₄×C₈	—	5	1	no	—
385	C₄×C₈	—	15	1	no	—
386	C₄×C₈	D₃×D₅	1	1	yes	characteristic
387	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
388	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
389	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
390	D₁₅	—	4	1	no	—
391	C₃×D₅	—	2	2	no	—
392	C₅×D₃	—	4	1	no	—
393	C₂³×C₃	—	5	1	no	—
394	C₂²×D₃	—	5	1	no	—
395	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
396	C₂×C₃×C₄	—	5	1	no	—
397	C₂×C₃×C₄	—	5	4	no	—
398	C₂×C₃×C₄	—	5	1	no	—
399	C₂×C₃×C₄	—	5	1	no	—
400	C₂×C₃×C₄	—	10	2	no	—
401	C₂×C₃×C₄	—	10	2	no	—
402	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
403	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
404	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
405	#67	—	10	2	no	—
406	#67	—	10	2	no	—
407	C₂×Dic₃	—	5	1	no	—
408	C₂×Dic₃	—	5	1	no	—
409	C₂×Dic₃	—	5	1	no	—
410	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
411	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
412	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
413	D₁₂	—	10	2	no	—
414	C₄×D₃	—	2	2	no	—
415	C₄×D₃	—	2	2	no	—
416	C₄×D₃	—	2	2	no	—
417	C₄×D₃	—	10	2	no	—
418	C₄×D₃	—	10	2	no	—
419	C₄×D₃	—	10	2	no	—
420	Dic₆	—	10	2	no	—
421	C₃×C₈	—	2	2	no	—
422	C₃×C₈	—	5	4	no	—
423	C₃⋊C₈	—	2	2	no	—
424	C₃⋊C₈	—	10	2	no	—
425	C₂²×C₅	—	6	1	no	—
426	C₂²×C₅	—	6	1	no	—
427	C₂²×C₅	—	6	1	no	—
428	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
429	C₂×D₅	—	2	1	no	—
430	C₂×D₅	—	2	1	no	—
431	C₂×D₅	—	6	1	no	—
432	C₂×D₅	—	6	1	no	—
433	C₂×D₅	—	6	1	no	—
434	C₂×D₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
435	C₄×C₅	—	6	1	no	—
436	C₄×C₅	—	6	1	no	—
437	C₄×C₅	—	6	1	no	—
438	C₄×C₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
439	C₄×C₅	#901	1	2	yes	—
440	C₄×C₅	C₂×#235	1	2	yes	—
441	Dic₅	—	2	1	no	—
442	Dic₅	—	2	1	no	—
443	Dic₅	—	6	1	no	—
444	Dic₅	—	6	1	no	—
445	Dic₅	—	6	1	no	—
446	Dic₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
447	#41	—	30	4	no	—
448	C₂×Q₈	—	15	1	no	—
449	C₂×D₄	—	15	1	no	—
450	C₂×D₄	—	15	1	no	—
451	C₂×D₄	—	15	1	no	—
452	C₂²×C₄	—	3	1	no	—
453	C₂²×C₄	—	3	1	no	—
454	C₂²×C₄	—	3	1	no	—
455	C₂²×C₄	—	5	1	no	—
456	C₂²×C₄	—	5	1	no	—
457	C₂²×C₄	—	5	1	no	—
458	C₂²×C₄	—	15	1	no	—
459	C₂²×C₄	—	15	1	no	—
460	C₂²×C₄	—	15	1	no	—
461	M₁₆	—	30	4	no	—
462	M₁₆	—	30	4	no	—
463	C₂×C₈	—	3	2	no	—
464	C₂×C₈	—	5	2	no	—
465	C₂×C₈	—	10	4	no	—
466	C₂×C₈	—	15	2	no	—
467	C₂×C₈	C₂×D₃×D₅	1	2	yes	—
468	C₄⋊C₄	—	15	1	no	—
469	C₄⋊C₄	—	15	1	no	—
470	C₄⋊C₄	—	15	1	no	—
471	C₄⋊C₄	—	15	1	no	—
472	C₄⋊C₄	—	15	1	no	—
473	C₄⋊C₄	—	15	1	no	—
474	C₂²⋊C₄	—	15	1	no	—
475	C₂²⋊C₄	—	15	1	no	—
476	C₂²⋊C₄	—	15	1	no	—
477	C₂²⋊C₄	—	15	1	no	—
478	C₂²⋊C₄	—	15	1	no	—
479	C₂²⋊C₄	—	15	1	no	—
480	C₄²	—	3	1	no	—
481	C₄²	—	3	1	no	—
482	C₄²	—	3	1	no	—
483	C₄²	—	5	1	no	—
484	C₄²	—	5	1	no	—
485	C₄²	—	5	1	no	—
486	C₄²	—	15	1	no	—
487	C₄²	—	15	1	no	—
488	C₄²	—	15	1	no	—
489	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
490	C₃×C₅	#2965	1	1	yes	characteristic, complemented, Hall
491	C₂²×C₃	—	5	2	no	—
492	C₂²×C₃	—	10	1	no	—
493	C₂²×C₃	—	10	1	no	—
494	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
495	C₂×D₃	—	2	1	no	—
496	C₂×D₃	—	2	1	no	—
497	C₂×D₃	—	2	1	no	—
498	C₂×D₃	—	10	1	no	—
499	C₂×D₃	—	10	1	no	—
500	C₂×D₃	—	10	1	no	—
501	C₃×C₄	—	5	2	no	—
502	C₃×C₄	—	10	1	no	—
503	C₃×C₄	—	10	1	no	—
504	C₃×C₄	#4047	1	2	yes	—
505	C₃×C₄	D₅×M₁₆	1	2	yes	—
506	C₃×C₄	D₅×#41	1	2	yes	—
507	Dic₃	—	2	1	no	—
508	Dic₃	—	2	1	no	—
509	Dic₃	—	2	1	no	—
510	Dic₃	—	10	1	no	—
511	Dic₃	—	10	1	no	—
512	Dic₃	—	10	1	no	—
513	C₂×C₅	—	12	1	no	—
514	C₂×C₅	C₄×#235	1	1	yes	characteristic
515	C₂×C₅	C₂²×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
516	C₂×C₅	C₂×#901	1	1	yes	characteristic
517	D₅	—	2	2	no	—
518	D₅	—	12	1	no	—
519	C₂³	—	3	1	no	—
520	C₂³	—	5	1	no	—
521	C₂³	—	15	1	no	—
522	Q₈	—	30	2	no	—
523	D₄	—	30	2	no	—
524	D₄	—	30	2	no	—
525	D₄	—	30	2	no	—
526	C₂×C₄	—	3	1	no	—
527	C₂×C₄	—	3	1	no	—
528	C₂×C₄	—	3	1	no	—
529	C₂×C₄	—	5	1	no	—
530	C₂×C₄	—	5	4	no	—
531	C₂×C₄	—	5	1	no	—
532	C₂×C₄	—	5	1	no	—
533	C₂×C₄	—	6	2	no	—
534	C₂×C₄	—	6	2	no	—
535	C₂×C₄	—	6	2	no	—
536	C₂×C₄	—	10	2	no	—
537	C₂×C₄	—	10	2	no	—
538	C₂×C₄	—	15	1	no	—
539	C₂×C₄	—	15	1	no	—
540	C₂×C₄	—	15	1	no	—
541	C₂×C₄	—	30	2	no	—
542	C₂×C₄	—	30	2	no	—
543	C₂×C₄	—	30	2	no	—
544	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
545	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
546	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
547	C₈	—	2	2	no	—
548	C₈	—	5	4	no	—
549	C₈	—	6	2	no	—
550	C₈	—	30	2	no	—
551	C₂×C₃	—	10	2	no	—
552	C₂×C₃	#65856	1	1	yes	characteristic
553	C₂×C₃	C₂×#4047	1	1	yes	characteristic
554	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
555	D₃	—	4	1	no	—
556	D₃	—	20	1	no	—
557	C₅	#78447	1	1	yes	characteristic, complemented, Sylow
558	C₂²	—	5	2	no	—
559	C₂²	—	6	1	no	—
560	C₂²	—	6	1	no	—
561	C₂²	—	6	1	no	—
562	C₂²	—	10	1	no	—
563	C₂²	—	10	1	no	—
564	C₂²	—	30	1	no	—
565	C₂²	—	30	1	no	—
566	C₂²	—	30	1	no	—
567	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
568	C₄	—	5	2	no	—
569	C₄	—	6	1	no	—
570	C₄	—	6	1	no	—
571	C₄	—	6	1	no	—
572	C₄	—	10	1	no	—
573	C₄	—	10	1	no	—
574	C₄	—	30	1	no	—
575	C₄	—	30	1	no	—
576	C₄	—	30	1	no	—
577	C₄	D₅×ΓL(1,𝔽₂₅)	1	2	yes	—
578	C₄	#91265	1	2	yes	—
579	C₄	D₅×#235	1	2	yes	—
580	C₃	#10611009	1	1	yes	characteristic, complemented, Sylow
581	C₂	—	10	2	no	—
582	C₂	—	12	1	no	—
583	C₂	—	60	1	no	—
584	C₂	#11752665	1	1	yes	characteristic
585	C₂	C₂×D₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
586	C₂	C₂×#91265	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₄×C₅×C₈	C₂²
prime radical	C₂×#6771	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	#2965
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #11750786	C₂	semidirect
3. C₅×#4685	C₂	semidirect
4. C₃×C₄×C₈×D₅	C₂	semidirect
5. #11747820	C₂	semidirect
6. #11747708	C₂	semidirect
7. #11747706	C₂	semidirect
8. #11747702	C₂	semidirect
9. C₄×#6651	C₂	semidirect
10. C₄×#6650	C₂	semidirect
11. #11746868	C₂	semidirect
55. C₄×C₈×D₅	D₃	semidirect
108. #4685	D₅	semidirect
165. C₃×C₄×D₅	M₁₆	semidirect
172. C₃×#168	#41	semidirect
350. C₄×D₅	ΓL(1,𝔽₂₅)	semidirect
355. #168	#235	semidirect
490. C₃×C₅	#2965	semidirect
557. C₅	#78447	semidirect
580. C₃	#10611009	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6771	2
#11750786	2
C₅×#4685	2
C₃×C₄×C₈×D₅	2
#11747820	2
#11747708	2
#11747706	2
#11747702	2
C₄×#6651	2
C₄×#6650	2
#11746868	2
#10611009	3
#78447	5