Subgroups — #12064995

Order 1280.

734 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611014	C₂	1	1	yes	maximal, characteristic
2	#10611007	C₂	1	1	yes	maximal, characteristic
3	#10610254	C₂	1	1	yes	maximal, characteristic
4	C₅×#1453	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601537	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601535	C₂	1	1	yes	maximal, characteristic, complemented
7	M₁₆×#168	C₂	1	1	yes	maximal, characteristic, complemented
8	#10598867	C₂	1	1	yes	maximal, characteristic, complemented
9	#10598866	C₂	1	1	yes	maximal, characteristic, complemented
10	#10598864	C₂	1	1	yes	maximal, characteristic, complemented
11	#10598862	C₂	1	1	yes	maximal, characteristic, complemented
12	#10598861	C₂	1	1	yes	maximal, characteristic, complemented
13	D₅×#322	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#676	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×#676	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#709	C₂²	1	1	yes	characteristic
17	C₅×#431	C₂²	1	1	yes	characteristic
18	C₅×#431	C₂²	1	1	yes	characteristic
19	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
20	#65417	C₄	1	2	yes	—
21	#65416	C₄	1	2	yes	—
22	#65214	C₂²	1	1	yes	characteristic
23	#65214	C₂²	1	1	yes	characteristic
24	C₂×C₄×#168	C₂²	1	1	yes	characteristic
25	#65129	C₄	1	2	yes	—
26	#65128	C₄	1	2	yes	—
27	#65123	C₄	1	2	yes	—
28	#65119	C₄	1	2	yes	—
29	#65016	C₄	1	2	yes	—
30	#65014	C₄	1	2	yes	—
31	#65014	C₄	1	2	yes	—
32	#65009	C₄	1	2	yes	—
33	#64995	C₄	1	2	yes	—
34	#64990	C₄	1	2	yes	—
35	C₄×#676	C₂²	1	1	yes	characteristic
36	C₄×#676	C₂²	1	1	yes	characteristic
37	#64974	C₂²	1	1	yes	characteristic
38	#64974	C₂²	1	1	yes	characteristic
39	#64974	C₂²	1	1	yes	characteristic
40	#64974	C₂²	1	1	yes	characteristic
41	#64974	C₂²	1	1	yes	characteristic
42	#64974	C₂²	1	1	yes	characteristic
43	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
47	C₅×#322	C₂²	1	1	yes	characteristic
48	C₅×#322	C₂²	1	1	yes	characteristic
49	C₅×#322	C₂²	1	1	yes	characteristic
50	C₅×C₈²	C₂²	1	1	yes	characteristic
51	#64675	C₂²	1	1	yes	characteristic
52	#64675	C₂²	1	1	yes	characteristic
53	#64675	C₂²	1	1	yes	characteristic
54	#64675	C₂²	1	1	yes	characteristic
55	#64675	C₂²	1	1	yes	characteristic
56	#64674	C₂²	1	1	yes	characteristic
57	#64674	C₂²	1	1	yes	characteristic
58	#64674	C₂²	1	1	yes	characteristic
59	#64674	C₂²	1	1	yes	characteristic
60	C₈×#168	C₂²	1	1	yes	characteristic
61	C₈×#168	C₂²	1	1	yes	characteristic
62	C₈×#168	C₂²	1	1	yes	characteristic
63	#17331	—	5	1	no	maximal, Sylow
64	C₂×#709	C₂×C₄	1	1	yes	characteristic
65	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
68	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
69	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
70	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
71	#4072	C₂×C₄	1	1	yes	characteristic
72	C₂²×#168	C₂×C₄	1	2	yes	—
73	C₂×#676	C₂×C₄	1	2	yes	—
74	C₂×#676	C₂×C₄	1	2	yes	—
75	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
76	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
77	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
78	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
79	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
80	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
81	#4018	C₂×C₄	1	1	yes	characteristic
82	#4018	C₂×C₄	1	1	yes	characteristic
83	C₄²×D₅	C₂³	1	1	yes	characteristic
84	C₄²×D₅	C₂³	1	1	yes	characteristic
85	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
86	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
87	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
88	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
89	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
90	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
91	C₅×#97	C₂×C₄	1	2	yes	—
92	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
93	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
94	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
95	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
96	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
97	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
98	C₂²⋊#168	C₂×C₄	1	2	yes	—
99	C₂²⋊#168	C₂×C₄	1	2	yes	—
100	#3952	C₂×C₄	1	2	yes	—
101	#3952	C₂×C₄	1	2	yes	—
102	#3952	C₂×C₄	1	2	yes	—
103	#3952	C₂×C₄	1	2	yes	—
104	#3952	C₂×C₄	1	2	yes	—
105	#3952	C₂×C₄	1	2	yes	—
106	#3947	C₂×C₄	1	2	yes	—
107	#3947	C₂×C₄	1	2	yes	—
108	#3946	C₂×C₄	1	2	yes	—
109	#3946	C₂×C₄	1	2	yes	—
110	#3946	C₂×C₄	1	2	yes	—
111	#3946	C₂×C₄	1	2	yes	—
112	#3946	C₂×C₄	1	2	yes	—
113	#3946	C₂×C₄	1	2	yes	—
114	C₈×Dic₅	C₂×C₄	1	2	yes	—
115	C₈×Dic₅	C₂×C₄	1	2	yes	—
116	C₈×Dic₅	C₂×C₄	1	2	yes	—
117	C₈×Dic₅	C₂×C₄	1	2	yes	—
118	C₄⋊#168	C₂×C₄	1	2	yes	—
119	C₄⋊#168	C₂×C₄	1	2	yes	—
120	C₄×#168	C₂×C₄	1	2	yes	—
121	C₄×#168	C₂³	1	1	yes	characteristic
122	C₄×#168	C₂³	1	1	yes	characteristic
123	C₄×#168	C₂³	1	1	yes	characteristic
124	C₄×#168	C₂³	1	1	yes	characteristic
125	C₄×#168	C₂³	1	1	yes	characteristic
126	C₄×#168	C₂³	1	1	yes	characteristic
127	#2965	—	5	1	no	—
128	C₈×#41	—	5	1	no	—
129	#2922	—	5	1	no	—
130	#1454	—	5	1	no	—
131	#1454	—	5	1	no	—
132	#1453	—	5	1	no	—
133	#1453	D₅	1	1	yes	characteristic, complemented
134	#1452	—	5	1	no	—
135	#1452	—	5	1	no	—
136	#1451	—	5	1	no	—
137	#1450	—	5	1	no	—
138	C₈×M₁₆	—	5	1	no	—
139	C₈×M₁₆	—	5	1	no	—
140	C₈×M₁₆	—	5	1	no	—
141	C₂×#322	—	5	1	no	—
142	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₂²⋊D₅	C₄²	1	1	yes	characteristic
146	C₂×C₂²⋊D₅	C₄²	1	1	yes	characteristic
147	#709	—	2	4	no	—
148	C₂×D₂₀	C₄²	1	1	yes	characteristic
149	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
155	C₂×Dic₁₀	C₄²	1	1	yes	characteristic
156	C₅×M₁₆	—	2	4	no	—
157	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
158	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
159	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
160	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
161	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
162	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
163	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
164	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
165	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
166	C₄²×C₅	C₂⁴	1	1	yes	characteristic
167	C₂²⋊Dic₅	C₄²	1	1	yes	characteristic
168	C₂²⋊Dic₅	C₄²	1	1	yes	characteristic
169	#685	C₄²	1	1	yes	characteristic
170	#685	C₄²	1	1	yes	characteristic
171	#685	C₄²	1	1	yes	characteristic
172	#685	C₄²	1	1	yes	characteristic
173	C₄⋊Dic₅	C₄²	1	1	yes	characteristic
174	C₄⋊Dic₅	C₄²	1	1	yes	characteristic
175	#683	C₄²	1	1	yes	characteristic
176	#683	C₄²	1	1	yes	characteristic
177	#683	C₄²	1	1	yes	characteristic
178	#683	C₄²	1	1	yes	characteristic
179	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
180	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
181	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
182	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
183	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
184	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
185	C₂×#168	—	4	2	no	—
186	C₂×#168	C₂²×C₄	1	2	yes	—
187	C₂×#168	C₂²×C₄	1	2	yes	—
188	C₂×#168	C₂²×C₄	1	2	yes	—
189	C₂×#168	C₂²×C₄	1	2	yes	—
190	C₂×#168	C₂²×C₄	1	2	yes	—
191	C₂×#168	C₂²×C₄	1	2	yes	—
192	#676	—	2	4	no	—
193	#676	—	2	4	no	—
194	C₈×D₅	—	2	4	no	—
195	C₈×D₅	—	2	4	no	—
196	C₈×D₅	—	4	2	no	—
197	C₈×D₅	—	4	2	no	—
198	C₄×#41	—	5	1	no	—
199	#446	—	5	2	no	—
200	C₈×Q₈	—	5	2	no	—
201	#436	—	5	2	no	—
202	#435	—	5	2	no	—
203	#435	—	5	2	no	—
204	C₈×D₄	—	5	2	no	—
205	C₈×D₄	—	5	2	no	—
206	C₈×D₄	—	5	2	no	—
207	#433	—	5	2	no	—
208	#433	—	5	2	no	—
209	#431	—	5	1	no	—
210	#431	—	5	1	no	—
211	#431	—	5	1	no	—
212	#431	—	5	1	no	—
213	#431	—	5	1	no	—
214	#431	—	5	1	no	—
215	#431	—	5	1	no	—
216	#431	—	5	1	no	—
217	#431	C₂×D₅	1	1	yes	characteristic
218	#431	C₂×D₅	1	1	yes	characteristic
219	#424	—	5	2	no	—
220	#408	—	5	2	no	—
221	C₄×M₁₆	—	5	1	no	—
222	C₄×M₁₆	—	5	1	no	—
223	C₄×M₁₆	C₂×D₅	1	1	yes	characteristic
224	C₂×C₄×C₈	—	5	1	no	—
225	C₂×C₄×C₈	—	5	1	no	—
226	C₂×C₄×C₈	—	5	1	no	—
227	C₂×C₄×C₈	—	5	1	no	—
228	C₂×C₄×C₈	—	5	1	no	—
229	#322	—	5	1	no	—
230	#322	—	5	1	no	—
231	#322	—	5	1	no	—
232	#322	—	5	1	no	—
233	#322	—	5	1	no	—
234	#322	—	5	1	no	—
235	#322	—	5	1	no	—
236	#322	—	5	1	no	—
237	#322	—	5	1	no	—
238	#322	C₂×D₅	1	1	yes	characteristic
239	#322	C₂×D₅	1	1	yes	characteristic
240	#322	C₂×D₅	1	1	yes	characteristic
241	C₈²	—	5	1	no	—
242	C₈²	—	5	1	no	—
243	C₈²	—	5	1	no	—
244	C₈²	C₂×D₅	1	1	yes	characteristic
245	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
246	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
247	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
252	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
253	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
257	C₂²⋊D₅	—	2	2	no	—
258	C₂²⋊D₅	—	2	2	no	—
259	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
260	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
261	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
262	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
263	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
264	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
265	D₂₀	—	2	2	no	—
266	C₄×D₅	—	2	2	no	—
267	C₄×D₅	—	2	2	no	—
268	C₄×D₅	—	2	2	no	—
269	C₄×D₅	—	2	2	no	—
270	C₄×D₅	—	2	2	no	—
271	C₄×D₅	#131	1	4	yes	—
272	Dic₁₀	—	2	2	no	—
273	C₅×C₈	—	2	2	no	—
274	C₅×C₈	—	2	2	no	—
275	C₅×C₈	—	2	2	no	—
276	C₅×C₈	—	2	2	no	—
277	C₅×C₈	—	2	2	no	—
278	C₅×C₈	#131	1	4	yes	—
279	#168	—	2	2	no	—
280	#168	—	2	2	no	—
281	#168	—	2	2	no	—
282	#168	—	2	2	no	—
283	#168	—	2	2	no	—
284	#168	—	2	2	no	—
285	C₂×#41	—	5	1	no	—
286	C₂×M₁₆	—	5	2	no	—
287	C₂×M₁₆	—	5	2	no	—
288	C₂×M₁₆	C₄×D₅	1	2	yes	—
289	C₂²×C₈	—	5	2	no	—
290	C₂²×C₈	—	5	2	no	—
291	C₂²×C₈	—	5	2	no	—
292	C₂²×C₈	—	5	2	no	—
293	C₂²×C₈	—	5	2	no	—
294	C₄×Q₈	—	5	1	no	—
295	C₄×Q₈	—	5	1	no	—
296	C₄×D₄	—	5	1	no	—
297	C₄×D₄	—	5	1	no	—
298	C₄×D₄	—	5	1	no	—
299	C₄×D₄	—	5	1	no	—
300	C₄×D₄	—	5	1	no	—
301	C₄×D₄	—	5	1	no	—
302	#117	—	5	1	no	—
303	#117	—	5	1	no	—
304	#117	—	5	1	no	—
305	C₂×C₄²	—	5	1	no	—
306	C₂×C₄²	—	5	1	no	—
307	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
308	C₄⋊C₈	—	5	2	no	—
309	C₄⋊C₈	—	5	2	no	—
310	C₄⋊C₈	—	5	2	no	—
311	C₄⋊C₈	—	5	2	no	—
312	C₄⋊C₈	—	5	2	no	—
313	C₄⋊C₈	—	5	2	no	—
314	C₄⋊C₈	—	5	2	no	—
315	C₄⋊C₈	—	5	2	no	—
316	C₄⋊C₈	C₄×D₅	1	2	yes	—
317	C₄⋊C₈	C₄×D₅	1	2	yes	—
318	C₂²⋊C₈	—	5	2	no	—
319	C₂²⋊C₈	—	5	2	no	—
320	C₂²⋊C₈	—	5	2	no	—
321	C₂²⋊C₈	—	5	2	no	—
322	C₂²⋊C₈	—	5	2	no	—
323	C₂²⋊C₈	—	5	2	no	—
324	C₂²⋊C₈	—	5	2	no	—
325	C₂²⋊C₈	—	5	2	no	—
326	C₂²⋊C₈	C₄×D₅	1	2	yes	—
327	C₂²⋊C₈	C₄×D₅	1	2	yes	—
328	#97	—	5	2	no	—
329	#97	—	5	2	no	—
330	#97	C₄×D₅	1	2	yes	—
331	C₄×C₈	—	5	2	no	—
332	C₄×C₈	—	5	2	no	—
333	C₄×C₈	—	5	2	no	—
334	C₄×C₈	—	5	2	no	—
335	C₄×C₈	—	5	2	no	—
336	C₄×C₈	—	5	1	no	—
337	C₄×C₈	—	5	1	no	—
338	C₄×C₈	—	5	1	no	—
339	C₄×C₈	—	5	1	no	—
340	C₄×C₈	—	5	1	no	—
341	C₄×C₈	—	5	1	no	—
342	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
343	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
344	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
345	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
346	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
347	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
348	C₂²×C₅	—	2	1	no	—
349	C₂²×C₅	—	2	1	no	—
350	C₂²×C₅	—	2	1	no	—
351	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
352	C₂×D₅	—	2	1	no	—
353	C₂×D₅	—	2	1	no	—
354	C₂×D₅	—	2	1	no	—
355	C₂×D₅	—	2	1	no	—
356	C₂×D₅	—	2	1	no	—
357	C₂×D₅	#405	1	2	yes	—
358	C₄×C₅	—	2	1	no	—
359	C₄×C₅	—	2	1	no	—
360	C₄×C₅	—	2	1	no	—
361	C₄×C₅	C₂×#131	1	2	yes	—
362	C₄×C₅	C₂×#131	1	2	yes	—
363	C₄×C₅	#568	1	2	yes	—
364	Dic₅	—	2	1	no	—
365	Dic₅	—	2	1	no	—
366	Dic₅	—	2	1	no	—
367	Dic₅	—	2	1	no	—
368	Dic₅	—	2	1	no	—
369	Dic₅	#405	1	2	yes	—
370	#41	—	10	4	no	—
371	C₂×Q₈	—	5	1	no	—
372	C₂×D₄	—	5	1	no	—
373	C₂×D₄	—	5	1	no	—
374	C₂×D₄	—	5	1	no	—
375	C₂²×C₄	—	5	1	no	—
376	C₂²×C₄	—	5	1	no	—
377	C₂²×C₄	—	5	1	no	—
378	C₂²×C₄	—	5	1	no	—
379	C₂²×C₄	—	5	1	no	—
380	C₂²×C₄	—	5	1	no	—
381	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
384	M₁₆	—	2	4	no	—
385	M₁₆	—	10	4	no	—
386	M₁₆	—	10	4	no	—
387	C₂×C₈	—	5	2	no	—
388	C₂×C₈	—	5	2	no	—
389	C₂×C₈	—	5	2	no	—
390	C₂×C₈	—	5	2	no	—
391	C₂×C₈	—	5	2	no	—
392	C₂×C₈	—	5	2	no	—
393	C₂×C₈	—	10	4	no	—
394	C₂×C₈	—	10	4	no	—
395	C₂×C₈	—	20	2	no	—
396	C₂×C₈	—	20	2	no	—
397	C₂×C₈	—	20	2	no	—
398	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
399	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
400	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
401	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
402	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
403	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
404	C₄⋊C₄	—	5	1	no	—
405	C₄⋊C₄	—	5	1	no	—
406	C₄⋊C₄	—	5	1	no	—
407	C₄⋊C₄	—	5	1	no	—
408	C₄⋊C₄	—	5	1	no	—
409	C₄⋊C₄	—	5	1	no	—
410	C₂²⋊C₄	—	5	1	no	—
411	C₂²⋊C₄	—	5	1	no	—
412	C₂²⋊C₄	—	5	1	no	—
413	C₂²⋊C₄	—	5	1	no	—
414	C₂²⋊C₄	—	5	1	no	—
415	C₂²⋊C₄	—	5	1	no	—
416	C₄²	—	5	1	no	—
417	C₄²	—	5	1	no	—
418	C₄²	—	5	1	no	—
419	C₄²	—	5	1	no	—
420	C₄²	—	5	1	no	—
421	C₄²	—	5	1	no	—
422	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
423	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
424	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
425	C₄²	C₂³×D₅	1	1	yes	characteristic
426	C₂×C₅	—	4	1	no	—
427	C₂×C₅	C₂×#405	1	1	yes	characteristic
428	C₂×C₅	C₄×#131	1	1	yes	characteristic
429	C₂×C₅	#2875	1	1	yes	characteristic
430	D₅	—	2	2	no	—
431	D₅	—	4	1	no	—
432	C₂³	—	5	1	no	—
433	C₂³	—	5	1	no	—
434	C₂³	C₄²×D₅	1	1	yes	characteristic
435	Q₈	—	10	2	no	—
436	D₄	—	10	2	no	—
437	D₄	—	10	2	no	—
438	D₄	—	10	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	5	1	no	—
443	C₂×C₄	—	5	4	no	—
444	C₂×C₄	—	5	1	no	—
445	C₂×C₄	—	5	1	no	—
446	C₂×C₄	—	5	1	no	—
447	C₂×C₄	—	5	1	no	—
448	C₂×C₄	—	5	1	no	—
449	C₂×C₄	—	10	2	no	—
450	C₂×C₄	—	10	2	no	—
451	C₂×C₄	—	10	2	no	—
452	C₂×C₄	—	10	2	no	—
453	C₂×C₄	—	10	2	no	—
454	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
455	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
456	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
457	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
458	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
459	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
460	C₈	—	2	2	no	—
461	C₈	—	2	2	no	—
462	C₈	—	2	2	no	—
463	C₈	—	2	2	no	—
464	C₈	—	2	2	no	—
465	C₈	—	10	2	no	—
466	C₈	—	10	2	no	—
467	C₈	—	10	2	no	—
468	C₈	—	10	2	no	—
469	C₈	—	10	2	no	—
470	C₈	—	10	2	no	—
471	C₈	#4053	1	4	yes	—
472	C₅	#17331	1	1	yes	characteristic, complemented, Sylow
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	5	2	no	—
477	C₂²	—	10	1	no	—
478	C₂²	—	10	1	no	—
479	C₂²	—	10	1	no	—
480	C₂²	—	10	1	no	—
481	C₂²	—	10	1	no	—
482	C₂²	C₂×C₄²×D₅	1	1	yes	characteristic
483	C₄	—	2	1	no	—
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	5	2	no	—
487	C₄	—	10	1	no	—
488	C₄	—	10	1	no	—
489	C₄	—	10	1	no	—
490	C₄	—	10	1	no	—
491	C₄	—	10	1	no	—
492	C₄	C₂×#4053	1	2	yes	—
493	C₄	D₅×#131	1	2	yes	—
494	C₄	#66084	1	2	yes	—
495	C₂	—	4	1	no	—
496	C₂	—	10	2	no	—
497	C₂	—	20	1	no	—
498	C₂	C₄×#4053	1	1	yes	characteristic
499	C₂	D₅×#405	1	1	yes	characteristic
500	C₂	#10610281	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₅
commutator, socle	C₂²×C₅	C₂²×C₄²
Fitting	C₅×#1453	C₂
prime radical	C₂×#709	C₂×C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1453	D₅
hypocenter	C₅	#17331
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₄² ◁ #1453

Complements

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

N	H ≅ G/N	type
4. C₅×#1453	C₂	semidirect
5. #10601537	C₂	semidirect
6. #10601535	C₂	semidirect
7. M₁₆×#168	C₂	semidirect
8. #10598867	C₂	semidirect
9. #10598866	C₂	semidirect
10. #10598864	C₂	semidirect
11. #10598862	C₂	semidirect
12. #10598861	C₂	semidirect
13. D₅×#322	C₂	semidirect
14. C₈×#676	C₂	semidirect
15. C₈×#676	C₂	semidirect
133. #1453	D₅	semidirect
472. C₅	#17331	semidirect

Maximal subgroups

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

subgroup	index
#10611014	2
#10611007	2
#10610254	2
C₅×#1453	2
#10601537	2
#10601535	2
M₁₆×#168	2
#10598867	2
#10598866	2
#10598864	2
#10598862	2
#10598861	2
D₅×#322	2
C₈×#676	2
#17331	5