Subgroups — #12252416

Order 1280.

590 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#4047	C₂	1	1	yes	maximal, characteristic
2	C₅×#2163	C₂	1	1	yes	maximal, characteristic, complemented
3	#10600537	C₂	1	1	yes	maximal, characteristic, complemented
4	#10600077	C₂	1	1	yes	maximal, characteristic, complemented
5	D₅×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#10600068	C₂	1	1	yes	maximal, characteristic, complemented
7	#10600067	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599900	C₂	1	2	yes	maximal
9	#10599887	C₂	1	2	yes	maximal, complemented
10	#10599867	C₂	1	2	yes	maximal, complemented
11	#10599865	C₂	1	2	yes	maximal, complemented
12	C₂×#4047	C₄	1	1	yes	characteristic
13	C₂×#4047	C₂²	1	1	yes	characteristic
14	C₄×#709	C₄	1	1	yes	characteristic
15	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
16	#65390	C₄	1	1	yes	characteristic
17	#65390	C₂²	1	1	yes	characteristic
18	C₄×#681	C₄	1	1	yes	characteristic
19	C₂×#3930	C₂²	1	2	yes	—
20	C₂×D₅×C₁₆	C₂²	1	2	yes	—
21	#64978	C₄	1	1	yes	characteristic
22	#64978	C₄	1	1	yes	characteristic
23	#64978	C₂²	1	1	yes	characteristic
24	#64978	C₂²	1	1	yes	characteristic
25	C₄×#676	C₄	1	1	yes	characteristic
26	C₄×#676	C₄	1	1	yes	characteristic
27	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
28	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
29	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
30	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
31	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
32	C₅×#346	C₂²	1	2	yes	—
33	C₂²⋊#672	C₂²	1	2	yes	—
34	#64727	C₂²	1	2	yes	—
35	#64727	C₂²	1	2	yes	—
36	#64722	C₂²	1	2	yes	—
37	#64721	C₂²	1	2	yes	—
38	#64721	C₂²	1	2	yes	—
39	C₁₆×Dic₅	C₂²	1	2	yes	—
40	C₄⋊#672	C₂²	1	1	yes	characteristic
41	C₄⋊#672	C₂²	1	1	yes	characteristic
42	C₄×#672	C₂²	1	2	yes	—
43	#33423	—	5	1	no	maximal, Sylow
44	C₂×#709	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
47	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
48	C₄×C₂²⋊D₅	C₈	1	1	yes	characteristic
49	C₄×C₂²⋊D₅	C₈	1	1	yes	characteristic
50	C₄×C₂²⋊D₅	C₈	1	1	yes	characteristic
51	C₄×C₂²⋊D₅	C₈	1	1	yes	characteristic
52	#4072	C₂×C₄	1	1	yes	characteristic
53	C₂×#681	C₂×C₄	1	1	yes	characteristic
54	C₂×#681	C₂×C₄	1	1	yes	characteristic
55	#4047	—	2	4	no	—
56	#4047	—	2	2	no	—
57	#4047	—	2	2	no	—
58	C₂×#676	C₂×C₄	1	1	yes	characteristic
59	C₂×#676	C₂×C₄	1	1	yes	characteristic
60	C₂×#676	C₂×C₄	1	1	yes	characteristic
61	C₂×#676	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
65	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
66	C₄×D₂₀	C₈	1	1	yes	characteristic
67	C₄×D₂₀	C₈	1	1	yes	characteristic
68	#4018	C₂×C₄	1	1	yes	characteristic
69	#4018	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	C₄×Dic₁₀	C₈	1	1	yes	characteristic
73	C₄×Dic₁₀	C₈	1	1	yes	characteristic
74	C₂×C₅×C₁₆	C₂³	1	2	yes	—
75	C₂×C₅×C₁₆	C₂³	1	2	yes	—
76	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
78	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
80	#3947	C₂×C₄	1	1	yes	characteristic
81	#3947	C₂×C₄	1	1	yes	characteristic
82	#3947	C₂×C₄	1	1	yes	characteristic
83	#3947	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₅	C₂³	1	1	yes	characteristic
87	C₈×Dic₅	C₂³	1	1	yes	characteristic
88	C₂×#672	C₂³	1	2	yes	—
89	C₂×#672	C₂³	1	2	yes	—
90	#3935	C₂×C₄	1	1	yes	characteristic
91	#3935	C₂×C₄	1	1	yes	characteristic
92	C₄×#168	C₂×C₄	1	1	yes	characteristic
93	C₄×#168	C₂×C₄	1	1	yes	characteristic
94	#3930	—	2	4	no	—
95	D₅×C₁₆	—	2	4	no	—
96	C₄×#131	—	5	1	no	—
97	#2164	—	5	2	no	—
98	#2164	—	5	2	no	—
99	#2163	—	5	1	no	—
100	#2163	D₅	1	1	yes	characteristic, complemented
101	#2162	—	5	1	no	—
102	#2162	—	5	1	no	—
103	#2150	—	5	1	no	—
104	C₂×C₄⋊C₁₆	—	5	1	no	—
105	#2113	—	5	2	no	—
106	#2108	—	5	2	no	—
107	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
111	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
112	#709	—	2	2	no	—
113	#709	—	2	2	no	—
114	C₂×D₂₀	C₂×C₈	1	1	yes	characteristic
115	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
116	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
117	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
118	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
119	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
121	C₂×Dic₁₀	C₂×C₈	1	1	yes	characteristic
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	—	2	1	no	—
124	C₂×C₅×C₈	—	2	1	no	—
125	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
129	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
130	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
131	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
134	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
135	#685	C₂×C₈	1	1	yes	characteristic
136	#685	C₂×C₈	1	1	yes	characteristic
137	#685	C₂×C₈	1	1	yes	characteristic
138	#685	C₂×C₈	1	1	yes	characteristic
139	C₄⋊Dic₅	C₂×C₈	1	1	yes	characteristic
140	C₄⋊Dic₅	C₂×C₈	1	1	yes	characteristic
141	#683	C₂×C₈	1	1	yes	characteristic
142	#683	C₂×C₈	1	1	yes	characteristic
143	#683	C₂×C₈	1	1	yes	characteristic
144	#683	C₂×C₈	1	1	yes	characteristic
145	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
146	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
147	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
148	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
149	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
150	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
151	#681	—	2	2	no	—
152	#681	—	2	2	no	—
153	C₂×#168	C₂²×C₄	1	1	yes	characteristic
154	C₂×#168	C₂²×C₄	1	1	yes	characteristic
155	C₂×#168	C₂²×C₄	1	1	yes	characteristic
156	C₂×#168	C₂²×C₄	1	1	yes	characteristic
157	#676	—	2	2	no	—
158	#676	—	2	2	no	—
159	#676	—	2	2	no	—
160	#676	M₁₆	1	4	yes	—
161	C₈×D₅	—	2	2	no	—
162	C₈×D₅	—	2	1	no	—
163	C₈×D₅	—	2	1	no	—
164	C₈×D₅	—	2	2	no	—
165	C₈×D₅	#41	1	2	yes	—
166	C₈×D₅	#41	1	2	yes	—
167	C₅×C₁₆	—	2	2	no	—
168	C₅×C₁₆	—	2	2	no	—
169	#672	—	2	2	no	—
170	#672	—	2	2	no	—
171	C₂×#131	—	5	1	no	—
172	C₂×#131	—	5	1	no	—
173	C₄×#41	—	5	1	no	—
174	C₂×M₃₂	—	5	2	no	—
175	C₂²×C₁₆	—	5	2	no	—
176	#405	—	5	1	no	—
177	#405	—	5	1	no	—
178	#405	—	5	1	no	—
179	#405	—	5	1	no	—
180	#405	—	5	1	no	—
181	#405	—	5	1	no	—
182	C₄×M₁₆	—	5	1	no	—
183	C₄×M₁₆	—	5	1	no	—
184	C₄×M₁₆	—	5	1	no	—
185	C₂×C₄×C₈	—	5	1	no	—
186	C₂×C₄×C₈	—	5	1	no	—
187	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
188	C₄⋊C₁₆	—	5	2	no	—
189	C₄⋊C₁₆	—	5	2	no	—
190	C₄⋊C₁₆	—	5	1	no	—
191	C₄⋊C₁₆	—	5	1	no	—
192	C₄⋊C₁₆	C₂×D₅	1	1	yes	characteristic
193	C₄⋊C₁₆	C₂×D₅	1	1	yes	characteristic
194	C₂²⋊C₁₆	—	5	2	no	—
195	C₂²⋊C₁₆	—	5	2	no	—
196	C₂²⋊C₁₆	—	5	2	no	—
197	C₂²⋊C₁₆	C₂×D₅	1	2	yes	—
198	#346	—	5	2	no	—
199	#346	C₂×D₅	1	2	yes	—
200	C₄×C₁₆	—	5	2	no	—
201	C₄×C₁₆	—	5	2	no	—
202	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
203	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
204	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	4	1	no	—
209	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
215	C₂²⋊D₅	—	2	2	no	—
216	C₂²⋊D₅	—	2	2	no	—
217	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
218	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
219	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
220	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
221	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
222	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
223	D₂₀	—	2	2	no	—
224	C₄×D₅	—	2	1	no	—
225	C₄×D₅	—	2	1	no	—
226	C₄×D₅	—	2	2	no	—
227	C₄×D₅	—	2	2	no	—
228	C₄×D₅	—	4	1	no	—
229	C₄×D₅	—	4	1	no	—
230	C₄×D₅	#117	1	2	yes	—
231	C₄×D₅	C₂×M₁₆	1	2	yes	—
232	Dic₁₀	—	2	2	no	—
233	C₅×C₈	—	2	1	no	—
234	C₅×C₈	—	2	1	no	—
235	C₅×C₈	C₂×M₁₆	1	2	yes	—
236	C₅×C₈	C₂×#41	1	1	yes	characteristic
237	C₅×C₈	C₂×#41	1	1	yes	characteristic
238	#168	—	2	1	no	—
239	#168	—	2	1	no	—
240	#168	#117	1	2	yes	—
241	#168	C₂×M₁₆	1	2	yes	—
242	C₂×#41	—	5	1	no	—
243	#131	—	10	2	no	—
244	#131	—	10	2	no	—
245	#131	—	10	4	no	—
246	C₂×M₁₆	—	5	1	no	—
247	C₂×M₁₆	—	5	1	no	—
248	C₂×M₁₆	—	5	1	no	—
249	C₂×M₁₆	—	5	1	no	—
250	C₂×M₁₆	—	5	1	no	—
251	C₂×M₁₆	—	5	1	no	—
252	C₂²×C₈	—	5	1	no	—
253	C₂²×C₈	—	5	1	no	—
254	C₂²×C₈	—	5	1	no	—
255	C₂²×C₈	—	5	1	no	—
256	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
257	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
258	C₄×Q₈	—	5	1	no	—
259	C₄×Q₈	—	5	1	no	—
260	C₄×D₄	—	5	1	no	—
261	C₄×D₄	—	5	1	no	—
262	C₄×D₄	—	5	1	no	—
263	C₄×D₄	—	5	1	no	—
264	C₄×D₄	—	5	1	no	—
265	C₄×D₄	—	5	1	no	—
266	#117	—	5	1	no	—
267	#117	—	5	1	no	—
268	#117	—	5	1	no	—
269	C₂×C₄²	—	5	1	no	—
270	C₂×C₄²	—	5	1	no	—
271	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
272	M₃₂	—	10	4	no	—
273	C₂×C₁₆	—	5	2	no	—
274	C₂×C₁₆	—	5	2	no	—
275	C₂×C₁₆	—	10	4	no	—
276	C₂×C₁₆	C₂²×D₅	1	2	yes	—
277	C₂×C₁₆	C₂²×D₅	1	2	yes	—
278	#97	—	5	1	no	—
279	#97	—	5	1	no	—
280	#97	—	5	1	no	—
281	#97	—	5	1	no	—
282	#97	—	5	1	no	—
283	#97	—	5	1	no	—
284	C₄×C₈	—	5	1	no	—
285	C₄×C₈	—	5	1	no	—
286	C₄×C₈	—	5	1	no	—
287	C₄×C₈	—	5	1	no	—
288	C₄×C₈	—	5	1	no	—
289	C₄×C₈	—	5	1	no	—
290	C₄×C₈	C₄×D₅	1	1	yes	characteristic
291	C₄×C₈	C₄×D₅	1	1	yes	characteristic
292	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
293	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
294	C₂²×C₅	—	2	1	no	—
295	C₂²×C₅	—	2	1	no	—
296	C₂²×C₅	—	2	1	no	—
297	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
298	C₂×D₅	—	2	1	no	—
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	#431	1	2	yes	—
304	C₄×C₅	—	2	1	no	—
305	C₄×C₅	—	2	1	no	—
306	C₄×C₅	—	2	1	no	—
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	#504	1	2	yes	—
309	C₄×C₅	C₂×#117	1	1	yes	characteristic
310	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
311	Dic₅	—	2	1	no	—
312	Dic₅	—	2	1	no	—
313	Dic₅	—	2	1	no	—
314	Dic₅	—	2	1	no	—
315	Dic₅	—	2	1	no	—
316	Dic₅	#431	1	2	yes	—
317	#41	—	10	2	no	—
318	#41	—	10	2	no	—
319	C₂×Q₈	—	5	1	no	—
320	C₂×D₄	—	5	1	no	—
321	C₂×D₄	—	5	1	no	—
322	C₂×D₄	—	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	C₈×D₅	1	1	yes	characteristic
330	C₂²×C₄	C₈×D₅	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
332	M₁₆	—	5	4	no	—
333	M₁₆	—	10	2	no	—
334	M₁₆	—	10	2	no	—
335	M₁₆	—	10	2	no	—
336	M₁₆	—	10	2	no	—
337	M₁₆	—	10	2	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	5	1	no	—
342	C₂×C₈	—	5	1	no	—
343	C₂×C₈	—	5	2	no	—
344	C₂×C₈	—	5	2	no	—
345	C₂×C₈	—	5	1	no	—
346	C₂×C₈	—	5	1	no	—
347	C₂×C₈	—	10	2	no	—
348	C₂×C₈	—	10	2	no	—
349	C₂×C₈	—	10	1	no	—
350	C₂×C₈	—	10	1	no	—
351	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
352	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
353	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
354	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
355	C₄⋊C₄	—	5	1	no	—
356	C₄⋊C₄	—	5	1	no	—
357	C₄⋊C₄	—	5	1	no	—
358	C₄⋊C₄	—	5	1	no	—
359	C₄⋊C₄	—	5	1	no	—
360	C₄⋊C₄	—	5	1	no	—
361	C₂²⋊C₄	—	5	1	no	—
362	C₂²⋊C₄	—	5	1	no	—
363	C₂²⋊C₄	—	5	1	no	—
364	C₂²⋊C₄	—	5	1	no	—
365	C₂²⋊C₄	—	5	1	no	—
366	C₂²⋊C₄	—	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	C₈×D₅	1	1	yes	characteristic
374	C₄²	C₈×D₅	1	1	yes	characteristic
375	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
376	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
377	C₁₆	—	2	2	no	—
378	C₁₆	—	2	2	no	—
379	C₁₆	—	10	2	no	—
380	C₁₆	—	10	2	no	—
381	C₂×C₅	—	4	1	no	—
382	C₂×C₅	C₂×#431	1	1	yes	characteristic
383	C₂×C₅	C₂×#504	1	1	yes	characteristic
384	C₂×C₅	#3407	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	C₂×C₈×D₅	1	1	yes	characteristic
390	Q₈	—	10	2	no	—
391	D₄	—	10	2	no	—
392	D₄	—	10	2	no	—
393	D₄	—	10	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	5	1	no	—
399	C₂×C₄	—	5	2	no	—
400	C₂×C₄	—	5	2	no	—
401	C₂×C₄	—	5	1	no	—
402	C₂×C₄	—	5	1	no	—
403	C₂×C₄	—	5	1	no	—
404	C₂×C₄	—	5	1	no	—
405	C₂×C₄	—	5	1	no	—
406	C₂×C₄	—	10	1	no	—
407	C₂×C₄	—	10	1	no	—
408	C₂×C₄	—	10	2	no	—
409	C₂×C₄	—	10	2	no	—
410	C₂×C₄	—	20	1	no	—
411	C₂×C₄	—	20	1	no	—
412	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
413	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
414	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
415	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
416	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
417	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
418	C₈	—	2	1	no	—
419	C₈	—	2	1	no	—
420	C₈	—	5	2	no	—
421	C₈	—	5	2	no	—
422	C₈	—	10	1	no	—
423	C₈	—	10	1	no	—
424	C₈	D₅×M₁₆	1	2	yes	—
425	C₈	D₅×#41	1	1	yes	characteristic
426	C₈	D₅×#41	1	1	yes	characteristic
427	C₅	#33423	1	1	yes	characteristic, complemented, Sylow
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	5	2	no	—
432	C₂²	—	10	1	no	—
433	C₂²	—	10	1	no	—
434	C₂²	—	10	1	no	—
435	C₂²	—	10	1	no	—
436	C₂²	—	10	1	no	—
437	C₂²	C₂²×C₈×D₅	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	5	2	no	—
443	C₄	—	10	1	no	—
444	C₄	—	10	1	no	—
445	C₄	—	10	1	no	—
446	C₄	—	10	1	no	—
447	C₄	—	10	1	no	—
448	C₄	#65196	1	2	yes	—
449	C₄	D₅×#117	1	1	yes	characteristic
450	C₄	C₂×D₅×M₁₆	1	1	yes	characteristic
451	C₂	—	4	1	no	—
452	C₂	—	10	2	no	—
453	C₂	—	20	1	no	—
454	C₂	D₅×#431	1	1	yes	characteristic
455	C₂	C₂×#65196	1	1	yes	characteristic
456	C₂	#10613738	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₅
commutator, socle	C₂²×C₅	C₂³×C₈
Fitting	C₅×#2163	C₂
prime radical	C₂×#709	C₂×C₄
cosocle	C₂×C₅×C₈	C₂⁴
hypercenter	#2163	D₅
hypocenter	C₅	#33423
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ #2163

Complements

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

N	H ≅ G/N	type
2. C₅×#2163	C₂	semidirect
3. #10600537	C₂	semidirect
4. #10600077	C₂	semidirect
5. D₅×C₄⋊C₁₆	C₂	semidirect
6. #10600068	C₂	semidirect
7. #10600067	C₂	semidirect
9. #10599887	C₂	semidirect
10. #10599867	C₂	semidirect
11. #10599865	C₂	semidirect
100. #2163	D₅	semidirect
427. C₅	#33423	semidirect

Maximal subgroups

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

subgroup	index
C₄×#4047	2
C₅×#2163	2
#10600537	2
#10600077	2
D₅×C₄⋊C₁₆	2
#10600068	2
#10600067	2
#10599900	2
#10599887	2
#10599867	2
#10599865	2
#33423	5