Subgroups — #14415888

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91266	C₂	1	2	yes	maximal, complemented
2	#11752675	C₂	1	1	yes	maximal, characteristic
3	#11750789	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₈×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748140	C₂	1	2	yes	maximal, complemented
7	#11747728	C₂	1	2	yes	maximal, complemented
8	#11747705	C₂	1	2	yes	maximal, complemented
9	#11747010	C₂	1	1	yes	maximal, characteristic, complemented
10	#11746994	C₂	1	1	yes	maximal, characteristic, complemented
11	D₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
12	#10610253	—	3	1	no	maximal, Hall
13	C₂×#6771	C₂²	1	2	yes	—
14	C₂×#6705	C₂²	1	2	yes	—
15	C₄×D₆₀	C₂²	1	1	yes	characteristic
16	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
17	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
18	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
20	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
21	#91469	C₄	1	1	yes	characteristic
22	#91460	C₄	1	1	yes	characteristic
23	#91458	C₄	1	1	yes	characteristic
24	#91456	C₄	1	1	yes	characteristic
25	#91454	C₄	1	2	yes	—
26	C₄×#1202	C₂²	1	2	yes	—
27	#91353	C₄	1	2	yes	—
28	C₂×#6649	C₂²	1	2	yes	—
29	C₂×#6648	C₂²	1	2	yes	—
30	C₂×D₃×#168	C₂²	1	2	yes	—
31	#91266	—	2	8	no	—
32	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	#91104	C₂²	1	2	yes	—
34	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
35	C₅×#815	C₂²	1	1	yes	characteristic
36	C₅×#815	C₂²	1	1	yes	characteristic
37	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
38	C₃×#3952	C₂²	1	2	yes	—
39	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
40	Dic₃⋊#168	C₂²	1	2	yes	—
41	#90957	C₂²	1	2	yes	—
42	#90955	C₂²	1	2	yes	—
43	#79425	—	5	1	no	maximal, Hall
44	C₂×#4053	—	3	2	no	—
45	#65811	—	3	1	no	—
46	C₄×C₅×M₁₆	—	3	1	no	—
47	#65418	—	3	2	no	—
48	C₂×C₄⋊#168	—	3	1	no	—
49	#64995	—	3	2	no	—
50	#64995	—	3	2	no	—
51	#64977	—	3	1	no	—
52	#64977	—	3	1	no	—
53	C₈×D₂₀	—	3	1	no	—
54	C₈×D₂₀	D₃	1	1	yes	characteristic, complemented
55	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×D₁₅	C₂³	1	2	yes	—
57	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
60	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
62	C₂×#1204	C₂×C₄	1	2	yes	—
63	C₂×#1203	C₂×C₄	1	2	yes	—
64	C₂×#1202	C₂×C₄	1	2	yes	—
65	C₂×#1202	C₂×C₄	1	2	yes	—
66	C₂×#1201	C₂×C₄	1	2	yes	—
67	#6771	—	2	4	no	—
68	#6771	—	2	4	no	—
69	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
72	#6714	C₂×C₄	1	2	yes	—
73	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
74	C₂×C₃⋊#168	C₂³	1	2	yes	—
75	#6705	—	2	4	no	—
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	1	yes	characteristic
80	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
81	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
82	C₅×ΓL(1,𝔽₂₅)	D₄	1	4	yes	complemented
83	C₃×#685	C₂×C₄	1	2	yes	—
84	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
85	C₂×C₃×#168	C₂³	1	2	yes	—
86	C₃×C₈×D₅	—	2	4	no	—
87	Dic₃⋊Dic₅	C₂×C₄	1	2	yes	—
88	#6667	C₂×C₄	1	2	yes	—
89	#6665	C₂×C₄	1	2	yes	—
90	#6649	—	2	4	no	—
91	#6648	—	2	4	no	—
92	D₃×#168	—	2	4	no	—
93	C₂×#901	—	5	2	no	—
94	#5548	—	5	1	no	—
95	C₃×C₈×D₄	—	5	1	no	—
96	#5111	—	5	2	no	—
97	#5012	—	5	1	no	—
98	#4834	—	5	1	no	—
99	D₃×C₄⋊C₈	—	5	1	no	—
100	#4728	—	5	2	no	—
101	#4727	—	5	2	no	—
102	#4688	—	5	1	no	—
103	C₄×ΓL(1,𝔽₂₅)	D₅	1	1	yes	characteristic, complemented
104	C₂×#709	—	3	2	no	—
105	C₂×C₅×M₁₆	—	3	1	no	—
106	C₂×C₅×M₁₆	—	3	1	no	—
107	C₂×C₄²×C₅	—	3	1	no	—
108	#4076	—	3	1	no	—
109	#4076	—	3	2	no	—
110	#4076	—	3	1	no	—
111	C₂²×#168	—	3	2	no	—
112	#4053	—	6	8	no	—
113	C₂×#676	—	3	2	no	—
114	C₂×#676	—	3	2	no	—
115	C₂×C₈×D₅	—	3	2	no	—
116	C₂×C₈×D₅	C₂×D₃	1	2	yes	—
117	#4021	—	3	2	no	—
118	#4020	—	3	1	no	—
119	C₄×D₂₀	—	3	2	no	—
120	C₄×D₂₀	—	3	1	no	—
121	C₄×D₂₀	C₂×D₃	1	1	yes	characteristic
122	#4015	—	3	1	no	—
123	C₅×#97	—	3	1	no	—
124	C₅×#97	—	3	1	no	—
125	C₄×C₅×C₈	—	3	1	no	—
126	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
127	#3952	—	3	2	no	—
128	#3952	—	3	2	no	—
129	#3952	—	3	2	no	—
130	#3952	C₂×D₃	1	2	yes	—
131	C₄⋊#168	—	3	1	no	—
132	C₄⋊#168	—	3	2	no	—
133	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
134	#2935	—	15	1	no	Sylow
135	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
136	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
141	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
142	D₆₀	—	2	2	no	—
143	C₄×D₁₅	—	2	2	no	—
144	C₄×D₁₅	—	2	2	no	—
145	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
148	C₄×C₅×D₃	—	2	2	no	—
149	C₄×C₅×D₃	—	4	1	no	—
150	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
151	C₄×C₅×D₃	#41	1	2	yes	—
152	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
153	C₃×D₂₀	—	2	2	no	—
154	C₃×C₄×D₅	—	2	2	no	—
155	C₃×C₄×D₅	—	2	2	no	—
156	#1204	—	2	4	no	—
157	#1203	—	2	4	no	—
158	#1202	—	2	4	no	—
159	#1202	—	4	2	no	—
160	#1201	—	2	4	no	—
161	C₃×C₅×C₈	—	2	1	no	—
162	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
163	C₃⋊#168	—	2	2	no	—
164	C₃×#168	—	2	2	no	—
165	C₅×C₃⋊C₈	—	2	1	no	—
166	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
167	C₂×#235	—	5	2	no	—
168	C₂²×C₃×C₈	—	5	2	no	—
169	C₃×C₄×D₄	—	5	1	no	—
170	#940	—	5	1	no	—
171	#938	—	5	1	no	—
172	C₄×#67	—	5	2	no	—
173	C₂×#208	—	5	2	no	—
174	#901	—	10	8	no	—
175	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
176	C₂×ΓL(1,𝔽₂₅)	C₂×D₅	1	1	yes	characteristic
177	C₂×ΓL(1,𝔽₂₅)	C₂×D₅	1	1	yes	characteristic
178	C₂×D₃×C₈	—	5	2	no	—
179	C₂×D₃×C₈	—	5	2	no	—
180	#895	—	5	1	no	—
181	#888	—	5	1	no	—
182	#885	—	5	2	no	—
183	#884	—	5	2	no	—
184	C₄×D₁₂	—	5	1	no	—
185	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
186	C₃×C₄⋊C₈	—	5	1	no	—
187	C₃×C₂²⋊C₈	—	5	2	no	—
188	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
189	#830	—	5	2	no	—
190	(C₂×D₃)⋊C₈	—	5	2	no	—
191	(C₂×D₃)⋊C₈	—	5	2	no	—
192	#815	C₂×D₅	1	1	yes	characteristic
193	#815	C₂×D₅	1	1	yes	characteristic
194	Dic₃⋊C₈	—	5	2	no	—
195	C₄⋊(C₃⋊C₈)	—	5	1	no	—
196	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
197	C₂²×C₄×C₅	—	3	1	no	—
198	C₂²×C₄×C₅	—	3	1	no	—
199	C₂²×C₄×C₅	—	3	1	no	—
200	C₂×C₂²⋊D₅	—	3	2	no	—
201	C₂×C₂²⋊D₅	—	3	2	no	—
202	#709	—	6	4	no	—
203	#709	—	6	4	no	—
204	C₂×D₂₀	—	3	2	no	—
205	C₂×D₂₀	—	3	1	no	—
206	C₂×D₂₀	—	3	2	no	—
207	C₂×D₂₀	C₄×D₃	1	1	yes	characteristic
208	C₂×C₄×D₅	—	3	2	no	—
209	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
210	C₂×Dic₁₀	—	3	2	no	—
211	C₅×M₁₆	—	3	4	no	—
212	C₅×M₁₆	—	6	2	no	—
213	C₂×C₅×C₈	—	3	1	no	—
214	C₂×C₅×C₈	—	3	1	no	—
215	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
216	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
217	C₄²×C₅	—	3	1	no	—
218	C₄²×C₅	—	3	1	no	—
219	C₄²×C₅	—	3	1	no	—
220	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
221	#685	—	3	2	no	—
222	#685	—	3	2	no	—
223	#685	—	3	2	no	—
224	#685	C₄×D₃	1	2	yes	—
225	C₄⋊Dic₅	—	3	1	no	—
226	C₄⋊Dic₅	—	3	2	no	—
227	C₄⋊Dic₅	C₄×D₃	1	1	yes	characteristic
228	C₂×#168	—	3	2	no	—
229	C₂×#168	—	6	4	no	—
230	C₂×#168	C₂²×D₃	1	2	yes	—
231	#676	—	6	4	no	—
232	#676	—	6	4	no	—
233	C₈×D₅	—	2	4	no	—
234	C₈×D₅	—	6	4	no	—
235	C₂×#131	—	15	2	no	—
236	#532	—	15	1	no	—
237	#436	—	15	1	no	—
238	#436	—	15	1	no	—
239	#435	—	15	2	no	—
240	#435	—	15	2	no	—
241	C₈×D₄	—	5	1	no	—
242	C₈×D₄	—	15	1	no	—
243	C₂×C₄⋊C₈	—	15	1	no	—
244	#408	—	15	2	no	—
245	C₄×M₁₆	—	3	1	no	—
246	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
247	C₂×D₁₅	—	2	2	no	—
248	C₂×D₁₅	—	2	2	no	—
249	C₂×D₁₅	—	2	2	no	—
250	C₂×C₅×D₃	—	2	1	no	—
251	C₂×C₅×D₃	—	2	1	no	—
252	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
253	C₂×C₃×D₅	—	2	2	no	—
254	C₂×C₃×D₅	—	2	2	no	—
255	C₂×C₃×D₅	—	2	2	no	—
256	C₃×C₄×C₅	—	2	1	no	—
257	C₃×C₄×C₅	#131	1	2	yes	complemented
258	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
259	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
260	Dic₁₅	—	2	2	no	—
261	C₃×Dic₅	—	2	2	no	—
262	C₅×Dic₃	—	2	1	no	—
263	C₅×Dic₃	—	2	1	no	—
264	C₅×Dic₃	C₄×D₄	1	2	yes	—
265	C₂×C₃×D₄	—	5	1	no	—
266	C₂²×C₃×C₄	—	5	2	no	—
267	C₂×#67	—	5	2	no	—
268	C₂×#67	—	5	2	no	—
269	C₂×#67	—	5	2	no	—
270	#235	—	10	4	no	—
271	#235	—	10	4	no	—
272	C₂×D₁₂	—	5	2	no	—
273	C₂×D₁₂	—	5	1	no	—
274	C₂×C₄×D₃	—	5	2	no	—
275	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
276	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
277	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
278	C₂×Dic₆	—	5	2	no	—
279	C₂×C₃×C₈	—	5	2	no	—
280	C₂×C₃×C₈	—	10	4	no	—
281	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
282	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
283	C₃×C₄⋊C₄	—	5	1	no	—
284	C₃×C₂²⋊C₄	—	5	2	no	—
285	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
286	#217	—	5	2	no	—
287	(C₂×D₃)⋊C₄	—	5	2	no	—
288	(C₂×D₃)⋊C₄	—	5	2	no	—
289	C₄⋊Dic₃	—	5	1	no	—
290	Dic₃⋊C₄	—	5	2	no	—
291	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
292	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
293	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
294	#208	—	10	4	no	—
295	C₂×C₃⋊C₈	—	5	2	no	—
296	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
297	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
298	ΓL(1,𝔽₂₅)	—	2	2	no	—
299	ΓL(1,𝔽₂₅)	—	10	4	no	—
300	ΓL(1,𝔽₂₅)	D₂₀	1	4	yes	complemented
301	D₃×C₈	—	10	4	no	—
302	D₃×C₈	—	10	4	no	—
303	C₂³×C₅	—	3	1	no	—
304	C₂²×D₅	—	3	2	no	—
305	C₂²×D₅	C₂×C₄×D₃	1	2	yes	—
306	C₂×C₄×C₅	—	3	1	no	—
307	C₂×C₄×C₅	—	3	2	no	—
308	C₂×C₄×C₅	—	3	2	no	—
309	C₂×C₄×C₅	—	3	1	no	—
310	C₂×C₄×C₅	—	3	1	no	—
311	C₂×C₄×C₅	—	6	2	no	—
312	C₂×C₄×C₅	—	12	1	no	—
313	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
314	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
315	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
316	C₂²⋊D₅	—	6	4	no	—
317	C₂²⋊D₅	—	6	4	no	—
318	C₂×Dic₅	—	3	2	no	—
319	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
320	D₂₀	—	2	2	no	—
321	D₂₀	—	6	4	no	—
322	D₂₀	—	6	2	no	—
323	D₂₀	—	12	2	no	—
324	C₄×D₅	—	2	2	no	—
325	C₄×D₅	—	2	2	no	—
326	C₄×D₅	—	6	2	no	—
327	C₄×D₅	—	6	2	no	—
328	Dic₁₀	—	6	4	no	—
329	C₅×C₈	—	2	1	no	—
330	C₅×C₈	—	3	2	no	—
331	C₅×C₈	—	6	1	no	—
332	C₅×C₈	D₃×D₄	1	2	yes	—
333	#168	—	2	2	no	—
334	#168	—	6	2	no	—
335	C₂×#41	—	15	2	no	—
336	#131	—	30	8	no	—
337	C₂×M₁₆	—	3	1	no	—
338	C₂×M₁₆	—	3	1	no	—
339	C₂×M₁₆	—	15	2	no	—
340	C₂×M₁₆	—	15	2	no	—
341	C₂²×C₈	—	5	2	no	—
342	C₂²×C₈	—	15	2	no	—
343	C₂²×C₈	—	15	2	no	—
344	C₄⋊Q₈	—	15	1	no	—
345	#127	—	15	1	no	—
346	#124	—	15	2	no	—
347	#121	—	15	2	no	—
348	#121	—	15	1	no	—
349	#121	—	15	1	no	—
350	C₄×D₄	—	5	1	no	—
351	C₄×D₄	—	15	2	no	—
352	C₄×D₄	—	15	1	no	—
353	C₂×C₄²	—	3	1	no	—
354	C₄⋊C₈	—	5	1	no	—
355	C₄⋊C₈	—	15	2	no	—
356	C₄⋊C₈	—	15	1	no	—
357	C₂²⋊C₈	—	5	2	no	—
358	C₂²⋊C₈	—	15	2	no	—
359	C₂²⋊C₈	—	15	2	no	—
360	C₂²⋊C₈	—	15	2	no	—
361	#97	—	3	1	no	—
362	#97	—	3	1	no	—
363	C₄×C₈	—	3	1	no	—
364	C₄×C₈	D₃×D₅	1	1	yes	characteristic
365	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
366	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
367	C₂×C₃×C₅	#568	1	1	yes	characteristic
368	D₁₅	—	4	2	no	—
369	C₃×D₅	—	4	2	no	—
370	C₅×D₃	—	2	2	no	—
371	C₂³×C₃	—	5	2	no	—
372	C₂²×D₃	—	5	2	no	—
373	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
374	C₃×D₄	—	10	2	no	—
375	C₂×C₃×C₄	—	5	2	no	—
376	C₂×C₃×C₄	—	10	2	no	—
377	C₂×C₃×C₄	—	10	2	no	—
378	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
379	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
381	#67	—	10	4	no	—
382	#67	—	10	4	no	—
383	#67	—	20	2	no	—
384	C₂×Dic₃	—	5	2	no	—
385	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
386	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
387	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
388	D₁₂	—	10	4	no	—
389	D₁₂	—	10	2	no	—
390	C₄×D₃	—	2	2	no	—
391	C₄×D₃	—	4	1	no	—
392	C₄×D₃	—	10	2	no	—
393	C₄×D₃	—	10	2	no	—
394	C₄×D₃	C₂×D₂₀	1	2	yes	—
395	C₄×D₃	#709	1	2	yes	—
396	Dic₆	—	10	4	no	—
397	C₃×C₈	—	2	1	no	—
398	C₃×C₈	—	10	2	no	—
399	C₃×C₈	C₂×D₂₀	1	2	yes	—
400	C₃⋊C₈	—	2	1	no	—
401	C₃⋊C₈	—	10	2	no	—
402	C₃⋊C₈	C₂×D₂₀	1	2	yes	—
403	C₂²×C₅	—	3	2	no	—
404	C₂²×C₅	—	6	1	no	—
405	C₂²×C₅	—	6	1	no	—
406	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
407	C₂×D₅	—	2	2	no	—
408	C₂×D₅	—	2	2	no	—
409	C₂×D₅	—	2	2	no	—
410	C₂×D₅	—	6	2	no	—
411	C₂×D₅	—	6	2	no	—
412	C₂×D₅	—	6	2	no	—
413	C₄×C₅	—	2	1	no	—
414	C₄×C₅	—	3	2	no	—
415	C₄×C₅	—	6	1	no	—
416	C₄×C₅	—	6	1	no	—
417	C₄×C₅	#901	1	2	yes	complemented
418	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
419	C₄×C₅	D₃×#41	1	1	yes	characteristic
420	Dic₅	—	2	2	no	—
421	Dic₅	—	6	2	no	—
422	#41	—	30	4	no	—
423	#41	—	30	4	no	—
424	C₂×Q₈	—	15	2	no	—
425	C₂×D₄	—	5	1	no	—
426	C₂×D₄	—	15	2	no	—
427	C₂×D₄	—	15	2	no	—
428	C₂×D₄	—	15	2	no	—
429	C₂×D₄	—	15	2	no	—
430	C₂×D₄	—	15	1	no	—
431	C₂²×C₄	—	3	1	no	—
432	C₂²×C₄	—	3	1	no	—
433	C₂²×C₄	—	3	1	no	—
434	C₂²×C₄	—	5	2	no	—
435	C₂²×C₄	—	15	2	no	—
436	M₁₆	—	3	4	no	—
437	M₁₆	—	6	2	no	—
438	M₁₆	—	30	4	no	—
439	M₁₆	—	30	4	no	—
440	C₂×C₈	—	3	1	no	—
441	C₂×C₈	—	3	1	no	—
442	C₂×C₈	—	5	2	no	—
443	C₂×C₈	—	10	4	no	—
444	C₂×C₈	—	15	2	no	—
445	C₂×C₈	—	30	4	no	—
446	C₂×C₈	—	30	4	no	—
447	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
448	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
449	C₄⋊C₄	—	5	1	no	—
450	C₄⋊C₄	—	15	2	no	—
451	C₄⋊C₄	—	15	1	no	—
452	C₂²⋊C₄	—	5	2	no	—
453	C₂²⋊C₄	—	15	2	no	—
454	C₂²⋊C₄	—	15	2	no	—
455	C₂²⋊C₄	—	15	2	no	—
456	C₄²	—	3	1	no	—
457	C₄²	—	3	1	no	—
458	C₄²	—	3	1	no	—
459	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
460	C₃×C₅	#2935	1	1	yes	characteristic, complemented, Hall
461	C₂²×C₃	—	10	2	no	—
462	C₂²×C₃	—	10	2	no	—
463	C₂²×C₃	—	10	2	no	—
464	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
465	C₂×D₃	—	2	1	no	—
466	C₂×D₃	—	2	1	no	—
467	C₂×D₃	—	10	2	no	—
468	C₂×D₃	—	10	2	no	—
469	C₂×D₃	—	10	2	no	—
470	C₂×D₃	C₄×D₂₀	1	2	yes	—
471	C₃×C₄	—	2	1	no	—
472	C₃×C₄	—	10	2	no	—
473	C₃×C₄	#4053	1	2	yes	complemented
474	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
475	C₃×C₄	C₂×#709	1	1	yes	characteristic
476	Dic₃	—	2	1	no	—
477	Dic₃	—	2	1	no	—
478	Dic₃	—	10	2	no	—
479	Dic₃	C₄×D₂₀	1	2	yes	—
480	C₂×C₅	—	6	2	no	—
481	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
482	C₂×C₅	C₂×#901	1	1	yes	characteristic
483	C₂×C₅	#5750	1	1	yes	characteristic
484	D₅	—	4	2	no	—
485	D₅	—	12	2	no	—
486	C₂³	—	3	1	no	—
487	C₂³	—	5	2	no	—
488	C₂³	—	15	2	no	—
489	Q₈	—	30	4	no	—
490	D₄	—	10	2	no	—
491	D₄	—	30	4	no	—
492	D₄	—	30	4	no	—
493	D₄	—	30	4	no	—
494	D₄	—	30	2	no	—
495	D₄	—	60	2	no	—
496	C₂×C₄	—	3	1	no	—
497	C₂×C₄	—	3	2	no	—
498	C₂×C₄	—	3	2	no	—
499	C₂×C₄	—	3	1	no	—
500	C₂×C₄	—	3	1	no	—
501	C₂×C₄	—	5	2	no	—
502	C₂×C₄	—	6	2	no	—
503	C₂×C₄	—	10	2	no	—
504	C₂×C₄	—	10	2	no	—
505	C₂×C₄	—	12	1	no	—
506	C₂×C₄	—	15	2	no	—
507	C₂×C₄	—	30	2	no	—
508	C₂×C₄	—	30	2	no	—
509	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
510	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
512	C₈	—	2	1	no	—
513	C₈	—	3	2	no	—
514	C₈	—	6	1	no	—
515	C₈	—	10	2	no	—
516	C₈	—	30	2	no	—
517	C₈	D₃×D₂₀	1	2	yes	—
518	C₂×C₃	—	20	2	no	—
519	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
520	C₂×C₃	C₂×#4053	1	1	yes	characteristic
521	C₂×C₃	#66079	1	1	yes	characteristic
522	D₃	—	2	2	no	—
523	D₃	—	20	2	no	—
524	C₅	#79425	1	1	yes	characteristic, complemented, Sylow
525	C₂²	—	3	2	no	—
526	C₂²	—	6	1	no	—
527	C₂²	—	6	1	no	—
528	C₂²	—	10	2	no	—
529	C₂²	—	10	2	no	—
530	C₂²	—	10	2	no	—
531	C₂²	—	30	2	no	—
532	C₂²	—	30	2	no	—
533	C₂²	—	30	2	no	—
534	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
535	C₄	—	2	1	no	—
536	C₄	—	3	2	no	—
537	C₄	—	6	1	no	—
538	C₄	—	6	1	no	—
539	C₄	—	10	2	no	—
540	C₄	—	30	2	no	—
541	C₄	#91266	1	2	yes	complemented
542	C₄	C₂×D₃×D₂₀	1	1	yes	characteristic
543	C₄	D₃×#709	1	1	yes	characteristic
544	C₃	#10610253	1	1	yes	characteristic, complemented, Sylow
545	C₂	—	6	2	no	—
546	C₂	—	20	2	no	—
547	C₂	—	60	2	no	—
548	C₂	C₄×D₃×D₂₀	1	1	yes	characteristic
549	C₂	#11753951	1	1	yes	characteristic
550	C₂	C₂×#91266	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₄×C₅×C₈	C₂²
prime radical	#11752675	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	#2935
LCS	G ▷ C₂²×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
1. C₂×#91266	C₂	semidirect
3. #11750789	C₂	semidirect
4. C₄×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
5. C₃×C₈×D₂₀	C₂	semidirect
6. #11748140	C₂	semidirect
7. #11747728	C₂	semidirect
8. #11747705	C₂	semidirect
9. #11747010	C₂	semidirect
10. #11746994	C₂	semidirect
11. D₃×C₄⋊#168	C₂	semidirect
54. C₈×D₂₀	D₃	semidirect
82. C₅×ΓL(1,𝔽₂₅)	D₄	semidirect
103. C₄×ΓL(1,𝔽₂₅)	D₅	semidirect
257. C₃×C₄×C₅	#131	semidirect
300. ΓL(1,𝔽₂₅)	D₂₀	semidirect
417. C₄×C₅	#901	semidirect
460. C₃×C₅	#2935	semidirect
473. C₃×C₄	#4053	semidirect
524. C₅	#79425	semidirect
541. C₄	#91266	semidirect
544. C₃	#10610253	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91266	2
#11752675	2
#11750789	2
C₄×C₅×ΓL(1,𝔽₂₅)	2
C₃×C₈×D₂₀	2
#11748140	2
#11747728	2
#11747705	2
#11747010	2
#11746994	2
D₃×C₄⋊#168	2
#10610253	3
#79425	5