Subgroups — #12065011

Order 1280.

900 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611013	C₂	1	1	yes	maximal, characteristic
2	C₄×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#676	C₂	1	1	yes	maximal, characteristic
4	C₅×#1451	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601532	C₂	1	1	yes	maximal, characteristic, complemented
6	#10600640	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×#681	C₂	1	1	yes	maximal, characteristic, complemented
8	#10598868	C₂	1	2	yes	maximal, complemented
9	#10598868	C₂	1	2	yes	maximal, complemented
10	#10598863	C₂	1	2	yes	maximal, complemented
11	#10598860	C₂	1	2	yes	maximal, complemented
12	C₂×D₅×M₁₆	C₄	1	2	yes	—
13	C₂²×#676	C₄	1	2	yes	—
14	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
15	C₅×#431	C₂²	1	1	yes	characteristic
16	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
18	M₁₆×Dic₅	C₄	1	2	yes	—
19	C₂×#3947	C₄	1	2	yes	—
20	#65214	C₂²	1	1	yes	characteristic
21	C₄×#681	C₂²	1	1	yes	characteristic
22	C₂×C₄×#168	C₂²	1	1	yes	characteristic
23	#65126	C₄	1	2	yes	—
24	#65124	C₄	1	2	yes	—
25	#65015	C₄	1	2	yes	—
26	#65008	C₄	1	2	yes	—
27	#64996	C₄	1	2	yes	—
28	D₅×#97	C₄	1	2	yes	—
29	C₄×#676	C₄	1	2	yes	—
30	C₄×#676	C₄	1	2	yes	—
31	C₄×#676	C₂²	1	1	yes	characteristic
32	C₄×#676	C₂²	1	1	yes	characteristic
33	C₄×#676	C₂²	1	1	yes	characteristic
34	C₄×#676	C₂²	1	1	yes	characteristic
35	C₄×#676	C₂²	1	2	yes	—
36	C₄×#676	C₂²	1	2	yes	—
37	#64974	C₂²	1	2	yes	—
38	C₄×C₈×D₅	C₂²	1	2	yes	—
39	C₅×#322	C₂²	1	2	yes	complemented
40	C₅×#322	C₂²	1	2	yes	complemented
41	#64674	C₂²	1	2	yes	complemented
42	#64674	C₂²	1	2	yes	complemented
43	#64674	C₂²	1	2	yes	complemented
44	#64674	C₂²	1	2	yes	complemented
45	C₈×#168	C₂²	1	2	yes	complemented
46	C₈×#168	C₂²	1	2	yes	complemented
47	M₁₆²	—	5	1	no	maximal, Sylow
48	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
51	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
52	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
54	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
57	C₂×#681	C₂×C₄	1	2	yes	—
58	C₂²×#168	C₂×C₄	1	2	yes	—
59	D₅×M₁₆	—	2	8	no	—
60	C₂×#676	—	2	8	no	—
61	C₂×#676	C₂×C₄	1	2	yes	—
62	C₂×#676	C₂×C₄	1	2	yes	—
63	C₂×#676	C₂×C₄	1	2	yes	—
64	C₂×#676	C₂×C₄	1	4	yes	—
65	C₂×#676	C₂×C₄	1	4	yes	—
66	C₂×#676	C₂×C₄	1	2	yes	—
67	C₂×C₈×D₅	C₂×C₄	1	4	yes	—
68	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
70	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
71	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
72	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
73	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
74	C₄²×D₅	C₂³	1	1	yes	characteristic
75	C₄²×D₅	C₂³	1	1	yes	characteristic
76	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
77	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
78	C₅×#97	C₂×C₄	1	2	yes	—
79	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
80	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
81	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₄×C₅×C₈	C₂³	1	2	yes	—
83	C₄×C₅×C₈	C₂³	1	2	yes	—
84	C₂²⋊#168	C₂×C₄	1	2	yes	—
85	#3952	C₂×C₄	1	4	yes	—
86	#3947	C₂×C₄	1	4	yes	—
87	#3947	C₂×C₄	1	2	yes	—
88	#3947	C₂×C₄	1	2	yes	—
89	#3947	C₂×C₄	1	2	yes	—
90	#3947	C₂×C₄	1	2	yes	—
91	#3947	C₂×C₄	1	4	yes	—
92	#3946	C₂×C₄	1	4	yes	—
93	C₈×Dic₅	C₂×C₄	1	4	yes	—
94	C₄⋊#168	C₂×C₄	1	2	yes	—
95	#3935	C₂×C₄	1	2	yes	—
96	C₄×#168	C₂×C₄	1	2	yes	—
97	C₄×#168	C₂³	1	1	yes	characteristic
98	C₄×#168	C₂³	1	2	yes	—
99	C₄×#168	C₂³	1	2	yes	—
100	C₄×#168	C₂³	1	1	yes	characteristic
101	#2920	—	5	1	no	—
102	C₂×C₄×M₁₆	—	5	1	no	—
103	C₂×C₄×M₁₆	—	5	1	no	—
104	#1455	—	5	2	no	—
105	#1455	—	5	2	no	—
106	#1451	—	5	1	no	—
107	#1451	—	5	2	no	—
108	#1451	D₅	1	1	yes	characteristic, complemented
109	C₈×M₁₆	—	5	1	no	—
110	C₈×M₁₆	—	5	1	no	—
111	C₈×M₁₆	—	5	2	no	—
112	C₂³×D₅	C₄²	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₂²×Dic₅	C₄²	1	1	yes	characteristic
117	C₂²×Dic₅	C₄²	1	1	yes	characteristic
118	C₂²×Dic₅	C₄²	1	1	yes	characteristic
119	C₂×C₄×D₅	—	2	4	no	—
120	C₂×C₄×D₅	—	2	4	no	—
121	C₂×C₄×D₅	—	4	2	no	—
122	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
123	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
124	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
125	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
126	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
127	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
128	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
134	C₅×M₁₆	—	2	4	no	—
135	C₂×C₅×C₈	—	2	4	no	—
136	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
137	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
138	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
139	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
140	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
142	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₅	C₂⁴	1	1	yes	characteristic
144	C₄×Dic₅	C₄²	1	1	yes	characteristic
145	C₄×Dic₅	C₄²	1	1	yes	characteristic
146	C₄×Dic₅	C₄²	1	1	yes	characteristic
147	C₄×Dic₅	C₄²	1	1	yes	characteristic
148	C₄×Dic₅	C₄²	1	1	yes	characteristic
149	C₄×Dic₅	C₄²	1	1	yes	characteristic
150	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
153	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
154	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
155	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
156	#681	M₁₆	1	8	yes	complemented
157	C₂×#168	—	2	4	no	—
158	C₂×#168	C₂²×C₄	1	2	yes	—
159	C₂×#168	C₂²×C₄	1	4	yes	—
160	C₂×#168	C₂²×C₄	1	2	yes	—
161	C₂×#168	C₂²×C₄	1	4	yes	—
162	#676	—	2	4	no	—
163	#676	—	2	4	no	—
164	#676	—	2	4	no	—
165	#676	—	2	8	no	—
166	#676	—	4	4	no	—
167	#676	M₁₆	1	8	yes	complemented
168	C₈×D₅	—	2	8	no	—
169	C₂²×M₁₆	—	5	2	no	—
170	C₂²×M₁₆	—	5	2	no	—
171	C₂²×C₄²	—	5	1	no	—
172	#432	—	5	2	no	—
173	#432	—	5	2	no	—
174	#431	—	5	1	no	—
175	#431	—	5	2	no	—
176	#431	C₂×D₅	1	1	yes	characteristic
177	#423	—	5	2	no	—
178	#407	—	5	2	no	—
179	C₄×M₁₆	—	5	2	no	—
180	C₄×M₁₆	—	5	1	no	—
181	C₄×M₁₆	—	5	2	no	—
182	C₄×M₁₆	—	5	2	no	—
183	C₄×M₁₆	—	5	2	no	—
184	C₄×M₁₆	—	5	1	no	—
185	C₄×M₁₆	—	5	1	no	—
186	C₄×M₁₆	—	5	2	no	—
187	C₄×M₁₆	—	5	1	no	—
188	C₄×M₁₆	—	5	1	no	—
189	C₄×M₁₆	—	5	2	no	—
190	C₄×M₁₆	C₂×D₅	1	1	yes	characteristic
191	C₂×#97	—	5	2	no	—
192	C₂×#97	—	5	2	no	—
193	C₂×C₄×C₈	—	5	1	no	—
194	C₂×C₄×C₈	—	5	2	no	—
195	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
196	#322	—	5	2	no	—
197	#322	—	5	2	no	—
198	#322	—	5	2	no	—
199	#322	—	5	2	no	—
200	#322	C₂×D₅	1	2	yes	complemented
201	#322	C₂×D₅	1	2	yes	complemented
202	C₈²	—	5	2	no	—
203	C₈²	—	5	2	no	—
204	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
205	C₂²×D₅	—	2	2	no	—
206	C₂²×D₅	—	2	2	no	—
207	C₂²×D₅	—	4	1	no	—
208	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
209	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
216	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
219	C₂×Dic₅	—	2	2	no	—
220	C₂×Dic₅	—	2	2	no	—
221	C₂×Dic₅	—	4	1	no	—
222	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
223	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
224	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
225	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
226	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
227	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
228	C₄×D₅	—	2	2	no	—
229	C₄×D₅	—	2	2	no	—
230	C₄×D₅	—	2	2	no	—
231	C₄×D₅	—	2	2	no	—
232	C₄×D₅	—	2	2	no	—
233	C₄×D₅	—	2	2	no	—
234	C₄×D₅	—	2	2	no	—
235	C₄×D₅	—	2	2	no	—
236	C₄×D₅	—	2	2	no	—
237	C₄×D₅	—	4	1	no	—
238	C₄×D₅	—	4	1	no	—
239	C₄×D₅	C₂×M₁₆	1	4	yes	—
240	C₅×C₈	—	2	4	no	—
241	C₅×C₈	—	2	2	no	—
242	C₅×C₈	—	2	4	no	—
243	C₅×C₈	C₂×M₁₆	1	4	yes	complemented
244	#168	—	2	2	no	—
245	#168	—	2	4	no	—
246	#168	C₂×M₁₆	1	8	yes	complemented
247	#168	C₂×M₁₆	1	4	yes	complemented
248	C₂³×C₄	—	5	1	no	—
249	C₂³×C₄	—	5	1	no	—
250	C₂³×C₄	—	5	1	no	—
251	C₂×M₁₆	—	5	2	no	—
252	C₂×M₁₆	—	5	2	no	—
253	C₂×M₁₆	—	5	4	no	—
254	C₂×M₁₆	—	5	2	no	—
255	C₂×M₁₆	—	5	2	no	—
256	C₂×M₁₆	—	5	2	no	—
257	C₂×M₁₆	—	5	4	no	—
258	C₂×M₁₆	—	10	8	no	—
259	C₂×M₁₆	—	10	8	no	—
260	C₂×M₁₆	C₄×D₅	1	2	yes	—
261	C₂²×C₈	—	5	2	no	—
262	C₂²×C₈	—	5	4	no	—
263	C₂²×C₈	C₄×D₅	1	2	yes	—
264	C₂×C₄²	—	5	1	no	—
265	C₂×C₄²	—	5	1	no	—
266	C₂×C₄²	—	5	1	no	—
267	C₂×C₄²	—	5	1	no	—
268	C₂×C₄²	—	5	1	no	—
269	C₂×C₄²	—	5	1	no	—
270	C₂×C₄²	—	5	1	no	—
271	C₂×C₄²	—	5	1	no	—
272	C₂×C₄²	—	5	1	no	—
273	C₂×C₄²	—	5	1	no	—
274	C₂×C₄²	—	5	1	no	—
275	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
276	C₄⋊C₈	—	5	4	no	—
277	C₄⋊C₈	—	5	2	no	—
278	C₄⋊C₈	C₄×D₅	1	2	yes	—
279	C₂²⋊C₈	—	5	2	no	—
280	C₂²⋊C₈	—	5	4	no	—
281	C₂²⋊C₈	C₄×D₅	1	2	yes	—
282	#97	—	5	4	no	—
283	#97	—	5	2	no	—
284	#97	—	5	2	no	—
285	#97	—	5	2	no	—
286	#97	—	5	2	no	—
287	#97	—	5	4	no	—
288	#97	—	5	2	no	—
289	#97	C₄×D₅	1	2	yes	—
290	C₄×C₈	—	5	4	no	—
291	C₄×C₈	—	5	2	no	—
292	C₄×C₈	—	5	1	no	—
293	C₄×C₈	—	5	2	no	—
294	C₄×C₈	—	5	2	no	—
295	C₄×C₈	—	5	1	no	—
296	C₄×C₈	C₄×D₅	1	2	yes	—
297	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₅	1	2	yes	—
299	C₄×C₈	C₂²×D₅	1	2	yes	—
300	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	2	1	no	—
303	C₂²×C₅	C₄×M₁₆	1	2	yes	—
304	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
305	C₂×D₅	—	2	1	no	—
306	C₂×D₅	—	2	1	no	—
307	C₂×D₅	—	2	1	no	—
308	C₂×D₅	—	2	1	no	—
309	C₂×D₅	—	2	1	no	—
310	C₂×D₅	—	4	4	no	—
311	C₂×D₅	C₄×M₁₆	1	2	yes	—
312	C₄×C₅	—	2	1	no	—
313	C₄×C₅	—	2	1	no	—
314	C₄×C₅	C₄×M₁₆	1	2	yes	—
315	C₄×C₅	C₂²×M₁₆	1	2	yes	—
316	C₄×C₅	C₂²×M₁₆	1	2	yes	—
317	C₄×C₅	#568	1	2	yes	—
318	Dic₅	—	2	1	no	—
319	Dic₅	—	2	1	no	—
320	Dic₅	—	2	1	no	—
321	Dic₅	—	2	1	no	—
322	Dic₅	—	2	1	no	—
323	Dic₅	C₄×M₁₆	1	2	yes	—
324	C₂⁴	—	5	1	no	—
325	C₂²×C₄	—	5	1	no	—
326	C₂²×C₄	—	5	1	no	—
327	C₂²×C₄	—	5	1	no	—
328	C₂²×C₄	—	5	1	no	—
329	C₂²×C₄	—	5	1	no	—
330	C₂²×C₄	—	5	1	no	—
331	C₂²×C₄	—	5	1	no	—
332	C₂²×C₄	—	5	1	no	—
333	C₂²×C₄	—	5	1	no	—
334	C₂²×C₄	—	5	1	no	—
335	C₂²×C₄	—	5	1	no	—
336	C₂²×C₄	—	5	1	no	—
337	C₂²×C₄	—	5	1	no	—
338	C₂²×C₄	—	5	1	no	—
339	C₂²×C₄	—	5	1	no	—
340	C₂²×C₄	—	10	4	no	—
341	C₂²×C₄	—	10	4	no	—
342	C₂²×C₄	—	20	2	no	—
343	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
346	M₁₆	—	2	4	no	—
347	M₁₆	—	5	8	no	—
348	M₁₆	—	5	8	no	—
349	M₁₆	—	10	4	no	—
350	M₁₆	—	10	8	no	—
351	M₁₆	—	10	4	no	—
352	M₁₆	—	10	4	no	—
353	M₁₆	—	20	4	no	—
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	5	4	no	—
356	C₂×C₈	—	5	2	no	—
357	C₂×C₈	—	5	2	no	—
358	C₂×C₈	—	5	4	no	—
359	C₂×C₈	—	10	8	no	—
360	C₂×C₈	—	10	4	no	—
361	C₂×C₈	C₂×C₄×D₅	1	4	yes	—
362	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
363	C₂×C₈	C₂×C₄×D₅	1	4	yes	—
364	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
365	C₄²	—	5	1	no	—
366	C₄²	—	5	1	no	—
367	C₄²	—	5	1	no	—
368	C₄²	—	5	1	no	—
369	C₄²	—	5	1	no	—
370	C₄²	—	5	1	no	—
371	C₄²	—	5	1	no	—
372	C₄²	—	5	1	no	—
373	C₄²	—	5	1	no	—
374	C₄²	—	5	1	no	—
375	C₄²	—	5	1	no	—
376	C₄²	—	5	1	no	—
377	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
378	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
379	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
380	C₄²	C₂³×D₅	1	1	yes	characteristic
381	C₂×C₅	—	2	2	no	—
382	C₂×C₅	C₂×C₄×M₁₆	1	1	yes	characteristic
383	C₂×C₅	C₂×C₄×M₁₆	1	1	yes	characteristic
384	C₂×C₅	#2873	1	1	yes	characteristic
385	D₅	—	2	2	no	—
386	D₅	—	4	1	no	—
387	C₂³	—	5	1	no	—
388	C₂³	—	5	1	no	—
389	C₂³	—	10	2	no	—
390	C₂³	—	10	2	no	—
391	C₂³	—	20	1	no	—
392	C₂³	C₄²×D₅	1	1	yes	characteristic
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	5	1	no	—
396	C₂×C₄	—	5	4	no	—
397	C₂×C₄	—	5	1	no	—
398	C₂×C₄	—	5	1	no	—
399	C₂×C₄	—	5	1	no	—
400	C₂×C₄	—	5	1	no	—
401	C₂×C₄	—	5	1	no	—
402	C₂×C₄	—	10	2	no	—
403	C₂×C₄	—	10	2	no	—
404	C₂×C₄	—	10	2	no	—
405	C₂×C₄	—	10	2	no	—
406	C₂×C₄	—	10	2	no	—
407	C₂×C₄	—	10	2	no	—
408	C₂×C₄	—	10	2	no	—
409	C₂×C₄	—	10	2	no	—
410	C₂×C₄	—	10	2	no	—
411	C₂×C₄	—	10	2	no	—
412	C₂×C₄	—	10	2	no	—
413	C₂×C₄	—	20	1	no	—
414	C₂×C₄	—	20	1	no	—
415	C₂×C₄	—	20	1	no	—
416	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
417	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
418	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
419	C₂×C₄	D₅×M₁₆	1	4	yes	—
420	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
421	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
423	C₈	—	2	2	no	—
424	C₈	—	2	4	no	—
425	C₈	—	2	4	no	—
426	C₈	—	5	8	no	—
427	C₈	—	5	4	no	—
428	C₈	—	10	2	no	—
429	C₈	—	10	4	no	—
430	C₈	D₅×M₁₆	1	4	yes	complemented
431	C₅	M₁₆²	1	1	yes	characteristic, complemented, Sylow
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	5	2	no	—
435	C₂²	—	10	1	no	—
436	C₂²	—	10	1	no	—
437	C₂²	—	10	1	no	—
438	C₂²	—	10	1	no	—
439	C₂²	—	10	1	no	—
440	C₂²	—	20	4	no	—
441	C₂²	#64996	1	2	yes	—
442	C₂²	C₂×C₄²×D₅	1	1	yes	characteristic
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	5	2	no	—
446	C₄	—	10	1	no	—
447	C₄	—	10	1	no	—
448	C₄	—	10	1	no	—
449	C₄	—	10	1	no	—
450	C₄	—	10	1	no	—
451	C₄	#64996	1	2	yes	—
452	C₄	C₂×D₅×M₁₆	1	2	yes	—
453	C₄	C₂×D₅×M₁₆	1	2	yes	—
454	C₄	#66084	1	2	yes	—
455	C₂	—	2	2	no	—
456	C₂	—	10	2	no	—
457	C₂	—	20	1	no	—
458	C₂	C₂×#64996	1	1	yes	characteristic
459	C₂	C₄×D₅×M₁₆	1	1	yes	characteristic
460	C₂	#10610279	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₅
commutator, socle	C₂²×C₅	C₂²×C₄²
Fitting	C₅×#1451	C₂
prime radical	C₂³×D₅	C₄²
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1451	D₅
hypocenter	C₅	M₁₆²
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₄² ◁ #1451

Complements

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

N	H ≅ G/N	type
4. C₅×#1451	C₂	semidirect
5. #10601532	C₂	semidirect
6. #10600640	C₂	semidirect
7. C₈×#681	C₂	semidirect
8. #10598868	C₂	semidirect
9. #10598868	C₂	semidirect
10. #10598863	C₂	semidirect
11. #10598860	C₂	semidirect
39. C₅×#322	C₂²	semidirect
40. C₅×#322	C₂²	semidirect
41. #64674	C₂²	semidirect
42. #64674	C₂²	semidirect
43. #64674	C₂²	semidirect
44. #64674	C₂²	semidirect
45. C₈×#168	C₂²	semidirect
46. C₈×#168	C₂²	semidirect
108. #1451	D₅	semidirect
156. #681	M₁₆	semidirect
167. #676	M₁₆	semidirect
200. #322	C₂×D₅	semidirect
201. #322	C₂×D₅	semidirect
243. C₅×C₈	C₂×M₁₆	semidirect
246. #168	C₂×M₁₆	semidirect
247. #168	C₂×M₁₆	semidirect
430. C₈	D₅×M₁₆	semidirect
431. C₅	M₁₆²	semidirect

Maximal subgroups

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

subgroup	index
#10611013	2
C₄×D₅×M₁₆	2
C₂×C₄×#676	2
C₅×#1451	2
#10601532	2
#10600640	2
C₈×#681	2
#10598868	2
#10598863	2
#10598860	2
M₁₆²	5