Subgroups — #12064952

Order 1280.

836 conjugacy classes of subgroups.

The subgroup lattice has 452 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×#64974	C₂	1	1	yes	maximal, characteristic
4	C₅×C₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601534	C₂	1	1	yes	maximal, characteristic, complemented
6	M₁₆×#168	C₂	1	1	yes	maximal, characteristic, complemented
7	#10600518	C₂	1	1	yes	maximal, characteristic, complemented
8	#10598866	C₂	1	2	yes	maximal, complemented
9	#10598862	C₂	1	2	yes	maximal, complemented
10	#10598841	C₂	1	2	yes	maximal, complemented
11	C₈×#676	C₂	1	2	yes	maximal, complemented
12	C₂×D₅×M₁₆	C₄	1	2	yes	—
13	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
14	C₅×#431	C₂²	1	1	yes	characteristic
15	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
17	M₁₆×Dic₅	C₄	1	2	yes	—
18	C₂×#3952	C₄	1	2	yes	—
19	C₂×#3946	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	C₂²	1	2	yes	—
30	C₄×#676	C₂²	1	2	yes	—
31	#64974	C₄	1	2	yes	—
32	#64974	C₄	1	2	yes	—
33	#64974	C₂²	1	1	yes	characteristic
34	#64974	C₂²	1	1	yes	characteristic
35	#64974	C₂²	1	1	yes	characteristic
36	#64974	C₂²	1	1	yes	characteristic
37	#64974	C₂²	1	2	yes	—
38	C₄×C₈×D₅	C₂²	1	2	yes	—
39	C₅×#322	C₂²	1	2	yes	complemented
40	C₅×C₈²	C₂²	1	2	yes	complemented
41	#64675	C₂²	1	2	yes	complemented
42	#64675	C₂²	1	2	yes	complemented
43	#64675	C₂²	1	2	yes	complemented
44	#64674	C₂²	1	2	yes	complemented
45	#64674	C₂²	1	2	yes	complemented
46	C₈×#168	C₂²	1	2	yes	complemented
47	#17327	—	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	C₂×C₄	1	4	yes	—
61	C₂×#676	C₂×C₄	1	4	yes	—
62	C₂×C₈×D₅	C₂×C₄	1	4	yes	—
63	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
65	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
66	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
67	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₅	C₂³	1	1	yes	characteristic
70	C₄²×D₅	C₂³	1	1	yes	characteristic
71	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
72	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
73	C₅×#97	C₂×C₄	1	2	yes	—
74	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
75	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₄×C₅×C₈	C₂³	1	2	yes	—
77	C₄×C₅×C₈	C₂³	1	2	yes	—
78	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₂²⋊#168	C₂×C₄	1	2	yes	—
80	#3952	C₂×C₄	1	4	yes	—
81	#3952	C₂×C₄	1	2	yes	—
82	#3952	C₂×C₄	1	2	yes	—
83	#3952	C₂×C₄	1	2	yes	—
84	#3952	C₂×C₄	1	2	yes	—
85	#3947	C₂×C₄	1	4	yes	—
86	#3947	C₂×C₄	1	4	yes	—
87	#3946	C₂×C₄	1	4	yes	—
88	#3946	C₂×C₄	1	2	yes	—
89	#3946	C₂×C₄	1	2	yes	—
90	#3946	C₂×C₄	1	2	yes	—
91	#3946	C₂×C₄	1	2	yes	—
92	C₈×Dic₅	C₂×C₄	1	4	yes	—
93	C₄⋊#168	C₂×C₄	1	2	yes	—
94	#3935	C₂×C₄	1	2	yes	—
95	C₄×#168	C₂×C₄	1	2	yes	—
96	C₄×#168	C₂³	1	1	yes	characteristic
97	C₄×#168	C₂³	1	2	yes	—
98	C₄×#168	C₂³	1	1	yes	characteristic
99	C₄×#168	C₂³	1	2	yes	—
100	#2920	—	5	1	no	—
101	C₂×#431	—	5	1	no	—
102	C₂×C₄×M₁₆	—	5	1	no	—
103	#1453	—	5	2	no	—
104	#1453	—	5	2	no	—
105	#1451	—	5	1	no	—
106	#1451	—	5	1	no	—
107	#1451	—	5	2	no	—
108	C₈×M₁₆	—	5	1	no	—
109	C₈×M₁₆	—	5	2	no	—
110	C₈×M₁₆	D₅	1	1	yes	characteristic, complemented
111	C₂³×D₅	C₄²	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₂²×C₄	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×Dic₅	C₄²	1	1	yes	characteristic
116	C₂²×Dic₅	C₄²	1	1	yes	characteristic
117	C₂²×Dic₅	C₄²	1	1	yes	characteristic
118	C₂×C₄×D₅	—	2	4	no	—
119	C₂×C₄×D₅	—	2	4	no	—
120	C₂×C₄×D₅	—	4	2	no	—
121	C₂×C₄×D₅	C₄²	1	1	yes	characteristic
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	C₂²×C₄	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	C₅×M₁₆	M₁₆	1	8	yes	complemented
134	C₂×C₅×C₈	—	4	2	no	—
135	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
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	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
142	C₄²×C₅	C₂⁴	1	1	yes	characteristic
143	C₄×Dic₅	C₄²	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	C₂²×C₄	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	#681	—	2	4	no	—
156	C₂×#168	—	4	2	no	—
157	C₂×#168	C₂²×C₄	1	2	yes	—
158	C₂×#168	C₂²×C₄	1	2	yes	—
159	C₂×#168	C₂²×C₄	1	4	yes	—
160	C₂×#168	C₂²×C₄	1	4	yes	—
161	#676	—	2	8	no	—
162	#676	—	2	8	no	—
163	C₈×D₅	—	2	8	no	—
164	C₂²×M₁₆	—	5	2	no	—
165	C₂²×C₄²	—	5	1	no	—
166	#432	—	5	2	no	—
167	#432	—	5	2	no	—
168	#431	—	5	1	no	—
169	#431	—	5	2	no	—
170	#431	—	5	2	no	—
171	#431	—	5	1	no	—
172	#431	—	5	1	no	—
173	#431	—	5	1	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	C₂×C₄⋊C₈	—	5	2	no	—
179	#407	—	5	2	no	—
180	C₂×C₂²⋊C₈	—	5	2	no	—
181	C₄×M₁₆	—	5	2	no	—
182	C₄×M₁₆	—	5	1	no	—
183	C₄×M₁₆	—	5	2	no	—
184	C₄×M₁₆	—	5	2	no	—
185	C₄×M₁₆	—	5	2	no	—
186	C₄×M₁₆	C₂×D₅	1	1	yes	characteristic
187	C₂×#97	—	5	2	no	—
188	C₂×C₄×C₈	—	5	1	no	—
189	C₂×C₄×C₈	—	5	2	no	—
190	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
191	#322	—	5	2	no	—
192	#322	—	5	2	no	—
193	#322	—	5	2	no	—
194	#322	—	5	2	no	—
195	#322	—	5	2	no	—
196	#322	C₂×D₅	1	2	yes	complemented
197	C₈²	—	5	2	no	—
198	C₈²	C₂×D₅	1	2	yes	complemented
199	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
200	C₂²×D₅	—	2	2	no	—
201	C₂²×D₅	—	2	2	no	—
202	C₂²×D₅	—	4	1	no	—
203	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
204	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
211	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
214	C₂×Dic₅	—	2	2	no	—
215	C₂×Dic₅	—	2	2	no	—
216	C₂×Dic₅	—	4	1	no	—
217	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
218	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
219	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
220	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
221	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
222	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
223	C₄×D₅	—	2	2	no	—
224	C₄×D₅	—	2	2	no	—
225	C₄×D₅	—	2	2	no	—
226	C₄×D₅	—	2	2	no	—
227	C₄×D₅	—	2	2	no	—
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	—	4	1	no	—
233	C₄×D₅	—	4	1	no	—
234	C₄×D₅	#131	1	4	yes	—
235	C₅×C₈	—	2	4	no	—
236	C₅×C₈	—	2	2	no	—
237	C₅×C₈	—	2	2	no	—
238	C₅×C₈	C₂×M₁₆	1	8	yes	—
239	#168	—	2	4	no	—
240	#168	—	2	4	no	—
241	#168	—	2	2	no	—
242	#168	—	2	2	no	—
243	C₂³×C₄	—	5	1	no	—
244	C₂³×C₄	—	5	1	no	—
245	C₂³×C₄	—	5	1	no	—
246	C₂×M₁₆	—	5	2	no	—
247	C₂×M₁₆	—	5	4	no	—
248	C₂×M₁₆	—	5	4	no	—
249	C₂×M₁₆	—	10	8	no	—
250	C₂×M₁₆	C₄×D₅	1	2	yes	—
251	C₂²×C₈	—	5	2	no	—
252	C₂²×C₈	—	5	4	no	—
253	C₂²×C₈	C₄×D₅	1	2	yes	—
254	C₂×C₄²	—	5	1	no	—
255	C₂×C₄²	—	5	1	no	—
256	C₂×C₄²	—	5	1	no	—
257	C₂×C₄²	—	5	1	no	—
258	C₂×C₄²	—	5	1	no	—
259	C₂×C₄²	—	5	1	no	—
260	C₂×C₄²	—	5	1	no	—
261	C₂×C₄²	—	5	1	no	—
262	C₂×C₄²	—	5	1	no	—
263	C₂×C₄²	—	5	1	no	—
264	C₂×C₄²	—	5	1	no	—
265	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
266	C₄⋊C₈	—	5	2	no	—
267	C₄⋊C₈	—	5	2	no	—
268	C₄⋊C₈	—	5	2	no	—
269	C₄⋊C₈	—	5	2	no	—
270	C₄⋊C₈	—	5	4	no	—
271	C₄⋊C₈	—	5	2	no	—
272	C₄⋊C₈	C₄×D₅	1	2	yes	—
273	C₂²⋊C₈	—	5	2	no	—
274	C₂²⋊C₈	—	5	2	no	—
275	C₂²⋊C₈	—	5	2	no	—
276	C₂²⋊C₈	—	5	2	no	—
277	C₂²⋊C₈	—	5	2	no	—
278	C₂²⋊C₈	—	5	4	no	—
279	C₂²⋊C₈	C₄×D₅	1	2	yes	—
280	#97	—	5	4	no	—
281	#97	—	5	4	no	—
282	#97	—	5	2	no	—
283	#97	C₄×D₅	1	2	yes	—
284	C₄×C₈	—	5	4	no	—
285	C₄×C₈	—	5	2	no	—
286	C₄×C₈	—	5	1	no	—
287	C₄×C₈	—	5	2	no	—
288	C₄×C₈	—	5	2	no	—
289	C₄×C₈	—	5	1	no	—
290	C₄×C₈	C₄×D₅	1	2	yes	—
291	C₄×C₈	C₂²×D₅	1	2	yes	—
292	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
293	C₄×C₈	C₂²×D₅	1	2	yes	—
294	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
295	C₂²×C₅	—	2	1	no	—
296	C₂²×C₅	—	2	1	no	—
297	C₂²×C₅	C₄×M₁₆	1	2	yes	—
298	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
299	C₂×D₅	—	2	1	no	—
300	C₂×D₅	—	2	1	no	—
301	C₂×D₅	—	2	1	no	—
302	C₂×D₅	—	2	1	no	—
303	C₂×D₅	—	2	1	no	—
304	C₂×D₅	—	4	4	no	—
305	C₂×D₅	#405	1	2	yes	—
306	C₄×C₅	—	2	1	no	—
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	C₄×M₁₆	1	2	yes	—
309	C₄×C₅	C₂²×M₁₆	1	2	yes	—
310	C₄×C₅	C₂×#131	1	2	yes	—
311	C₄×C₅	#568	1	2	yes	—
312	Dic₅	—	2	1	no	—
313	Dic₅	—	2	1	no	—
314	Dic₅	—	2	1	no	—
315	Dic₅	—	2	1	no	—
316	Dic₅	—	2	1	no	—
317	Dic₅	#405	1	2	yes	—
318	C₂⁴	—	5	1	no	—
319	C₂²×C₄	—	5	1	no	—
320	C₂²×C₄	—	5	1	no	—
321	C₂²×C₄	—	5	1	no	—
322	C₂²×C₄	—	5	1	no	—
323	C₂²×C₄	—	5	1	no	—
324	C₂²×C₄	—	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	—	10	4	no	—
335	C₂²×C₄	—	10	4	no	—
336	C₂²×C₄	—	20	2	no	—
337	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
340	M₁₆	—	10	8	no	—
341	M₁₆	—	10	4	no	—
342	M₁₆	—	10	8	no	—
343	M₁₆	#676	1	8	yes	complemented
344	C₂×C₈	—	4	2	no	—
345	C₂×C₈	—	5	4	no	—
346	C₂×C₈	—	5	2	no	—
347	C₂×C₈	—	5	2	no	—
348	C₂×C₈	—	5	4	no	—
349	C₂×C₈	—	10	8	no	—
350	C₂×C₈	—	20	2	no	—
351	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
352	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
353	C₂×C₈	C₂×C₄×D₅	1	4	yes	—
354	C₂×C₈	C₂×C₄×D₅	1	4	yes	—
355	C₄²	—	5	1	no	—
356	C₄²	—	5	1	no	—
357	C₄²	—	5	1	no	—
358	C₄²	—	5	1	no	—
359	C₄²	—	5	1	no	—
360	C₄²	—	5	1	no	—
361	C₄²	—	5	1	no	—
362	C₄²	—	5	1	no	—
363	C₄²	—	5	1	no	—
364	C₄²	—	5	1	no	—
365	C₄²	—	5	1	no	—
366	C₄²	—	5	1	no	—
367	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
368	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
369	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
370	C₄²	C₂³×D₅	1	1	yes	characteristic
371	C₂×C₅	—	2	2	no	—
372	C₂×C₅	C₂×C₄×M₁₆	1	1	yes	characteristic
373	C₂×C₅	C₂×#405	1	1	yes	characteristic
374	C₂×C₅	#2873	1	1	yes	characteristic
375	D₅	—	2	2	no	—
376	D₅	—	4	1	no	—
377	C₂³	—	5	1	no	—
378	C₂³	—	5	1	no	—
379	C₂³	—	10	2	no	—
380	C₂³	—	10	2	no	—
381	C₂³	—	20	1	no	—
382	C₂³	C₄²×D₅	1	1	yes	characteristic
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	5	1	no	—
386	C₂×C₄	—	5	4	no	—
387	C₂×C₄	—	5	1	no	—
388	C₂×C₄	—	5	1	no	—
389	C₂×C₄	—	5	1	no	—
390	C₂×C₄	—	5	1	no	—
391	C₂×C₄	—	5	1	no	—
392	C₂×C₄	—	10	2	no	—
393	C₂×C₄	—	10	2	no	—
394	C₂×C₄	—	10	2	no	—
395	C₂×C₄	—	10	2	no	—
396	C₂×C₄	—	10	2	no	—
397	C₂×C₄	—	10	2	no	—
398	C₂×C₄	—	10	2	no	—
399	C₂×C₄	—	10	2	no	—
400	C₂×C₄	—	10	2	no	—
401	C₂×C₄	—	10	2	no	—
402	C₂×C₄	—	10	2	no	—
403	C₂×C₄	—	20	1	no	—
404	C₂×C₄	—	20	1	no	—
405	C₂×C₄	—	20	1	no	—
406	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
407	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
408	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
409	C₂×C₄	C₂×#676	1	4	yes	—
410	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
411	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
413	C₈	—	2	2	no	—
414	C₈	—	2	2	no	—
415	C₈	—	2	4	no	—
416	C₈	—	10	4	no	—
417	C₈	—	10	2	no	—
418	C₈	—	10	2	no	—
419	C₈	—	10	4	no	—
420	C₈	C₂×#676	1	8	yes	—
421	C₅	#17327	1	1	yes	characteristic, complemented, Sylow
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	5	2	no	—
425	C₂²	—	10	1	no	—
426	C₂²	—	10	1	no	—
427	C₂²	—	10	1	no	—
428	C₂²	—	10	1	no	—
429	C₂²	—	10	1	no	—
430	C₂²	—	20	4	no	—
431	C₂²	C₄×#676	1	2	yes	—
432	C₂²	C₂×C₄²×D₅	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	5	2	no	—
436	C₄	—	10	1	no	—
437	C₄	—	10	1	no	—
438	C₄	—	10	1	no	—
439	C₄	—	10	1	no	—
440	C₄	—	10	1	no	—
441	C₄	C₄×#676	1	2	yes	—
442	C₄	C₂²×#676	1	2	yes	—
443	C₄	#66079	1	2	yes	—
444	C₄	D₅×#131	1	2	yes	—
445	C₂	—	2	2	no	—
446	C₂	—	10	2	no	—
447	C₂	—	20	1	no	—
448	C₂	C₂×C₄×#676	1	1	yes	characteristic
449	C₂	#10610245	1	1	yes	characteristic
450	C₂	D₅×#405	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₅
commutator, socle	C₂²×C₅	C₂²×C₄²
Fitting	C₅×C₈×M₁₆	C₂
prime radical	C₂³×D₅	C₄²
cosocle	C₄²×C₅	C₂⁴
hypercenter	C₈×M₁₆	D₅
hypocenter	C₅	#17327
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₄² ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
4. C₅×C₈×M₁₆	C₂	semidirect
5. #10601534	C₂	semidirect
6. M₁₆×#168	C₂	semidirect
7. #10600518	C₂	semidirect
8. #10598866	C₂	semidirect
9. #10598862	C₂	semidirect
10. #10598841	C₂	semidirect
11. C₈×#676	C₂	semidirect
39. C₅×#322	C₂²	semidirect
40. C₅×C₈²	C₂²	semidirect
41. #64675	C₂²	semidirect
42. #64675	C₂²	semidirect
43. #64675	C₂²	semidirect
44. #64674	C₂²	semidirect
45. #64674	C₂²	semidirect
46. C₈×#168	C₂²	semidirect
110. C₈×M₁₆	D₅	semidirect
133. C₅×M₁₆	M₁₆	semidirect
196. #322	C₂×D₅	semidirect
198. C₈²	C₂×D₅	semidirect
343. M₁₆	#676	semidirect
421. C₅	#17327	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×#64974	2
C₅×C₈×M₁₆	2
#10601534	2
M₁₆×#168	2
#10600518	2
#10598866	2
#10598862	2
#10598841	2
C₈×#676	2
#17327	5