Subgroups — #12069349

Order 1280.

692 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	#10614260	C₂	1	1	yes	maximal, characteristic
3	#10610189	C₂	1	1	yes	maximal, characteristic, complemented
4	#10602434	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601730	C₂	1	2	yes	maximal, complemented
6	#10601726	C₂	1	2	yes	maximal, complemented
7	#10601634	C₂	1	2	yes	maximal, complemented
8	#10601633	C₂	1	2	yes	maximal, complemented
9	#10601554	C₂	1	1	yes	maximal, characteristic, complemented
10	#10601541	C₂	1	1	yes	maximal, characteristic, complemented
11	#10600518	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₅×#41	C₂²	1	1	yes	characteristic
13	C₂×#4047	—	2	1	no	—
14	#65811	C₂²	1	1	yes	characteristic
15	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
16	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
17	C₅×C₈×D₄	—	2	1	no	—
18	C₅×C₈×D₄	—	2	1	no	—
19	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
20	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
21	C₅×#431	—	2	1	no	—
22	C₅×#431	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×C₈	—	2	1	no	—
24	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
25	#65527	C₄	1	2	yes	—
26	#65399	—	2	1	no	—
27	#65316	C₄	1	1	yes	characteristic
28	C₄×#688	C₂²	1	2	yes	—
29	#65310	C₄	1	1	yes	characteristic
30	#65304	C₄	1	1	yes	characteristic
31	C₄×#686	C₂²	1	2	yes	—
32	#65297	C₄	1	1	yes	characteristic
33	#65292	C₄	1	2	yes	—
34	#65214	C₂²	1	1	yes	characteristic
35	#65213	C₂²	1	1	yes	characteristic
36	C₄×#681	C₂²	1	1	yes	characteristic
37	#64977	—	2	1	no	—
38	#64977	C₂²	1	2	yes	—
39	C₈×D₂₀	—	2	1	no	—
40	C₈×D₂₀	C₂²	1	2	yes	—
41	Q₈⋊#168	C₂²	1	2	yes	—
42	D₄⋊#168	C₂²	1	2	yes	—
43	#64703	C₂²	1	2	yes	—
44	#64703	C₂²	1	2	yes	—
45	#64700	C₂²	1	2	yes	—
46	#64699	C₂²	1	2	yes	—
47	#64675	C₂²	1	2	yes	—
48	#64674	C₂²	1	2	yes	—
49	#17917	—	5	1	no	maximal, Sylow
50	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
51	C₂×#709	—	2	1	no	—
52	C₂²×C₅×C₈	—	2	1	no	—
53	C₂²×C₅×C₈	—	2	1	no	—
54	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
55	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
56	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
57	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
58	C₄×C₅×D₄	—	2	1	no	—
59	C₄×C₅×D₄	—	2	1	no	—
60	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
61	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
62	C₅×#117	—	2	1	no	—
63	C₅×#117	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₅	—	2	1	no	—
65	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₂×#688	C₂×C₄	1	2	yes	—
67	C₂×#686	C₂×C₄	1	2	yes	—
68	#4076	—	2	1	no	—
69	#4076	C₂×C₄	1	2	yes	—
70	C₂×#681	—	2	1	no	—
71	C₂×#681	—	2	1	no	—
72	#4047	—	4	4	no	—
73	C₂×#676	—	2	2	no	—
74	C₂×C₈×D₅	—	2	2	no	—
75	#4021	—	2	1	no	—
76	#4020	C₂×C₄	1	1	yes	characteristic
77	C₄×D₂₀	—	2	1	no	—
78	C₄×D₂₀	C₂³	1	2	yes	—
79	#4015	C₂×C₄	1	1	yes	characteristic
80	C₅×C₄⋊C₈	—	2	1	no	—
81	C₅×C₄⋊C₈	—	2	1	no	—
82	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₅×C₂²⋊C₈	—	2	1	no	—
85	C₅×C₂²⋊C₈	—	2	1	no	—
86	C₅×C₂²⋊C₈	—	2	1	no	—
87	C₄×C₅×C₈	—	2	1	no	—
88	C₄×C₅×C₈	—	2	1	no	—
89	C₄×C₅×C₈	—	2	1	no	—
90	C₄×C₅×C₈	D₄	1	1	yes	characteristic
91	C₄×C₅×C₈	D₄	1	1	yes	characteristic
92	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
93	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
94	#3967	C₂×C₄	1	2	yes	—
95	#3964	C₂×C₄	1	2	yes	—
96	C₂²⋊#168	C₂×C₄	1	2	yes	—
97	#3952	—	2	2	no	—
98	#3952	—	2	2	no	—
99	#3941	C₂×C₄	1	2	yes	—
100	#3941	C₂×C₄	1	2	yes	—
101	#3940	C₂×C₄	1	2	yes	—
102	#3939	C₂×C₄	1	2	yes	—
103	C₄⋊#168	—	2	1	no	—
104	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
105	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
106	C₄⋊#168	C₂³	1	2	yes	—
107	#3935	—	2	1	no	—
108	C₄×#168	C₂³	1	2	yes	—
109	C₄×#168	C₂³	1	2	yes	—
110	#3106	—	5	1	no	—
111	C₈×#41	D₅	1	1	yes	characteristic, complemented
112	#2931	—	5	1	no	—
113	#1583	—	5	2	no	—
114	#1581	—	5	2	no	—
115	#1580	—	5	2	no	—
116	SD₁₆⋊C₈	—	5	2	no	—
117	#1574	—	5	1	no	—
118	#1489	—	5	1	no	—
119	#1484	—	5	1	no	—
120	#1451	—	5	1	no	—
121	C₅×#41	—	2	2	no	—
122	C₅×#41	—	2	2	no	—
123	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₅×D₄	—	2	1	no	—
125	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	#41	1	1	yes	characteristic
132	C₂×C₂²⋊D₅	—	2	2	no	—
133	#709	—	4	2	no	—
134	#709	—	4	2	no	—
135	C₂×D₂₀	—	2	1	no	—
136	C₂×D₂₀	—	2	1	no	—
137	C₂×D₂₀	C₂²×C₄	1	2	yes	—
138	C₂×C₄×D₅	—	2	2	no	—
139	C₂×Dic₁₀	—	2	1	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	—	4	1	no	—
144	C₂×C₅×C₈	—	4	2	no	—
145	C₂×C₅×C₈	—	4	2	no	—
146	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
147	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
148	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
149	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
150	C₅×C₄⋊C₄	—	2	1	no	—
151	C₅×C₄⋊C₄	—	2	1	no	—
152	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
153	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
154	C₅×C₂²⋊C₄	—	2	1	no	—
155	C₅×C₂²⋊C₄	—	2	1	no	—
156	C₅×C₂²⋊C₄	—	2	1	no	—
157	C₄²×C₅	—	2	1	no	—
158	C₄²×C₅	—	2	1	no	—
159	C₄²×C₅	—	2	1	no	—
160	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₅	#41	1	1	yes	characteristic
163	C₄²×C₅	C₂⁴	1	1	yes	characteristic
164	#688	—	2	4	no	—
165	#686	—	2	4	no	—
166	#685	—	2	2	no	—
167	#685	—	2	2	no	—
168	C₄⋊Dic₅	—	2	1	no	—
169	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
170	#681	—	4	2	no	—
171	#681	—	4	2	no	—
172	C₂×#168	—	2	2	no	—
173	C₂×#168	—	2	2	no	—
174	C₂×#168	C₂²×C₄	1	2	yes	—
175	C₂×#168	C₂²×C₄	1	2	yes	—
176	#676	—	4	4	no	—
177	C₈×D₅	—	4	4	no	—
178	C₂×#131	—	10	1	no	—
179	#532	—	5	1	no	—
180	C₄×#41	C₂×D₅	1	1	yes	characteristic
181	#482	—	5	2	no	—
182	#477	—	5	1	no	—
183	#476	—	5	1	no	—
184	#460	—	5	1	no	—
185	#459	—	5	1	no	—
186	#449	—	5	2	no	—
187	C₈×Q₈	C₂×D₅	1	1	yes	characteristic
188	C₈×Q₈	C₂×D₅	1	1	yes	characteristic
189	C₄×SD₁₆	—	5	2	no	—
190	C₄×D₈	—	5	2	no	—
191	#436	—	5	2	no	—
192	#436	—	10	1	no	—
193	C₈×D₄	—	2	1	no	—
194	C₈×D₄	—	2	1	no	—
195	C₈×D₄	—	5	2	no	—
196	C₈×D₄	—	10	1	no	—
197	C₈×D₄	C₂×D₅	1	1	yes	characteristic
198	C₈×D₄	C₂×D₅	1	1	yes	characteristic
199	#431	—	2	1	no	—
200	#431	—	5	1	no	—
201	#431	C₂×D₅	1	1	yes	characteristic
202	#423	—	5	1	no	—
203	#408	—	10	1	no	—
204	C₄×M₁₆	—	5	1	no	—
205	C₂×C₄×C₈	—	2	1	no	—
206	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
207	#335	—	5	2	no	—
208	#334	—	5	2	no	—
209	Q₈⋊C₈	—	5	2	no	—
210	D₄⋊C₈	—	5	2	no	—
211	D₄⋊C₈	—	5	2	no	—
212	D₄⋊C₈	—	5	2	no	—
213	#322	—	5	2	no	—
214	#322	—	5	2	no	—
215	C₂³×C₅	—	2	1	no	—
216	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
217	C₂²×D₅	—	2	2	no	—
218	C₅×Q₈	—	2	1	no	—
219	C₅×Q₈	#131	1	2	yes	complemented
220	C₅×D₄	—	2	4	no	—
221	C₅×D₄	—	2	1	no	—
222	C₅×D₄	#131	1	2	yes	complemented
223	C₂×C₄×C₅	—	2	4	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	4	2	no	—
235	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
241	C₂²⋊D₅	—	4	4	no	—
242	C₂×Dic₅	—	2	2	no	—
243	D₂₀	—	2	2	no	—
244	D₂₀	—	2	2	no	—
245	D₂₀	—	4	2	no	—
246	D₂₀	—	4	2	no	—
247	C₄×D₅	—	4	2	no	—
248	C₄×D₅	—	4	2	no	—
249	Dic₁₀	—	4	2	no	—
250	C₅×C₈	—	2	1	no	—
251	C₅×C₈	—	2	1	no	—
252	C₅×C₈	—	2	1	no	—
253	C₅×C₈	—	4	1	no	—
254	C₅×C₈	—	4	1	no	—
255	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
256	#168	—	2	2	no	—
257	#168	—	2	2	no	—
258	#168	—	4	2	no	—
259	#168	—	4	2	no	—
260	C₂×#41	—	10	1	no	—
261	C₂×#41	C₄×D₅	1	1	yes	characteristic
262	C₂×SD₁₆	—	5	2	no	—
263	C₂×D₈	—	5	2	no	—
264	#131	—	20	4	no	—
265	C₂×M₁₆	—	10	1	no	—
266	C₂×M₁₆	—	10	1	no	—
267	C₂×M₁₆	—	10	2	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	10	2	no	—
271	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
272	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
273	C₄⋊Q₈	—	5	1	no	—
274	#127	—	5	1	no	—
275	#124	—	10	1	no	—
276	#121	—	5	2	no	—
277	#121	—	10	1	no	—
278	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
279	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
280	C₄×D₄	—	2	1	no	—
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	—	5	2	no	—
283	C₄×D₄	—	10	1	no	—
284	C₄×D₄	C₄×D₅	1	1	yes	characteristic
285	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
286	#117	—	2	1	no	—
287	#117	C₄×D₅	1	1	yes	characteristic
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
290	#107	—	5	2	no	—
291	#106	—	5	2	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	5	1	no	—
295	C₄⋊C₈	—	5	1	no	—
296	C₄⋊C₈	—	5	2	no	—
297	C₄⋊C₈	—	10	1	no	—
298	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
299	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
300	#103	—	5	2	no	—
301	#102	—	5	2	no	—
302	#102	—	5	2	no	—
303	#102	—	5	2	no	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	—	2	1	no	—
306	C₂²⋊C₈	—	2	1	no	—
307	C₂²⋊C₈	—	5	2	no	—
308	C₂²⋊C₈	—	10	2	no	—
309	C₂²⋊C₈	—	10	2	no	—
310	#97	—	10	1	no	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	—	2	1	no	—
314	C₄×C₈	—	5	2	no	—
315	C₄×C₈	—	5	2	no	—
316	C₄×C₈	C₂²⋊D₅	1	1	yes	characteristic
317	C₄×C₈	C₂²⋊D₅	1	1	yes	characteristic
318	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
319	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
320	C₂²×C₅	—	2	1	no	—
321	C₂²×C₅	—	2	2	no	—
322	C₂²×C₅	—	2	1	no	—
323	C₂²×C₅	—	2	1	no	—
324	C₂²×C₅	—	4	1	no	—
325	C₂²×C₅	—	4	1	no	—
326	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
327	C₂×D₅	—	4	2	no	—
328	C₂×D₅	—	4	2	no	—
329	C₂×D₅	—	4	2	no	—
330	C₄×C₅	—	2	1	no	—
331	C₄×C₅	—	2	2	no	—
332	C₄×C₅	—	2	1	no	—
333	C₄×C₅	—	2	1	no	—
334	C₄×C₅	—	4	1	no	—
335	C₄×C₅	—	4	1	no	—
336	C₄×C₅	#444	1	2	yes	—
337	C₄×C₅	C₂×#131	1	1	yes	characteristic
338	C₄×C₅	C₂×#131	1	1	yes	characteristic
339	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
340	C₄×C₅	#575	1	1	yes	characteristic
341	Dic₅	—	4	2	no	—
342	#41	—	2	2	no	—
343	#41	—	2	2	no	—
344	#41	—	20	2	no	—
345	#41	—	20	2	no	—
346	C₂×Q₈	—	10	1	no	—
347	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	5	2	no	—
350	C₂×D₄	—	10	2	no	—
351	C₂×D₄	—	10	1	no	—
352	C₂×D₄	—	10	1	no	—
353	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	10	2	no	—
358	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
359	C₂²×C₄	#709	1	1	yes	characteristic
360	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
361	SD₁₆	—	10	4	no	—
362	D₈	—	10	4	no	—
363	M₁₆	—	20	2	no	—
364	M₁₆	—	20	2	no	—
365	M₁₆	—	20	4	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	—	4	2	no	—
371	C₂×C₈	—	4	2	no	—
372	C₂×C₈	—	5	2	no	—
373	C₂×C₈	—	5	2	no	—
374	C₂×C₈	—	10	2	no	—
375	C₂×C₈	—	10	2	no	—
376	C₂×C₈	—	20	4	no	—
377	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
378	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
379	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
380	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	5	2	no	—
384	C₄⋊C₄	—	10	1	no	—
385	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
386	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
387	C₂²⋊C₄	—	2	1	no	—
388	C₂²⋊C₄	—	2	1	no	—
389	C₂²⋊C₄	—	2	1	no	—
390	C₂²⋊C₄	—	10	2	no	—
391	C₂²⋊C₄	—	10	2	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
396	C₄²	#709	1	1	yes	characteristic
397	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
398	C₄²	C₂³×D₅	1	1	yes	characteristic
399	C₂×C₅	—	4	1	no	—
400	C₂×C₅	—	4	2	no	—
401	C₂×C₅	#2929	1	1	yes	characteristic
402	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
403	C₂×C₅	C₂×#444	1	1	yes	characteristic
404	D₅	—	8	2	no	—
405	C₂³	—	2	1	no	—
406	C₂³	—	10	2	no	—
407	C₂³	C₄×C₂²⋊D₅	1	1	yes	characteristic
408	Q₈	—	2	1	no	—
409	Q₈	—	20	2	no	—
410	Q₈	#4047	1	2	yes	complemented
411	D₄	—	2	4	no	—
412	D₄	—	2	1	no	—
413	D₄	—	10	2	no	—
414	D₄	—	10	2	no	—
415	D₄	—	20	2	no	—
416	D₄	—	20	4	no	—
417	D₄	—	20	2	no	—
418	D₄	#4047	1	2	yes	complemented
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	10	2	no	—
432	C₂×C₄	—	20	2	no	—
433	C₂×C₄	—	20	2	no	—
434	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
435	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
436	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
437	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
438	C₂×C₄	C₂×#709	1	1	yes	characteristic
439	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
440	C₈	—	2	1	no	—
441	C₈	—	2	1	no	—
442	C₈	—	2	1	no	—
443	C₈	—	4	1	no	—
444	C₈	—	4	1	no	—
445	C₈	—	10	2	no	—
446	C₈	—	10	2	no	—
447	C₈	—	20	2	no	—
448	C₈	—	20	2	no	—
449	C₈	#4095	1	2	yes	—
450	C₅	#17917	1	1	yes	characteristic, complemented, Sylow
451	C₂²	—	2	1	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	20	2	no	—
458	C₂²	—	20	2	no	—
459	C₂²	—	20	2	no	—
460	C₂²	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	1	no	—
467	C₄	—	20	2	no	—
468	C₄	#65434	1	2	yes	—
469	C₄	C₂×#4047	1	1	yes	characteristic
470	C₄	C₂×#4047	1	1	yes	characteristic
471	C₄	C₂×#4095	1	1	yes	characteristic
472	C₄	#66156	1	1	yes	characteristic
473	C₂	—	4	1	no	—
474	C₂	—	4	2	no	—
475	C₂	—	40	2	no	—
476	C₂	C₄×#4095	1	1	yes	characteristic
477	C₂	#10615465	1	1	yes	characteristic
478	C₂	C₂×#65434	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×C₈×#41	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	#10614260	C₂
cosocle	C₄²×C₅	C₂⁴
hypercenter	C₈×#41	D₅
hypocenter	C₅	#17917
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. C₅×C₈×#41	C₂	semidirect
3. #10610189	C₂	semidirect
4. #10602434	C₂	semidirect
5. #10601730	C₂	semidirect
6. #10601726	C₂	semidirect
7. #10601634	C₂	semidirect
8. #10601633	C₂	semidirect
9. #10601554	C₂	semidirect
10. #10601541	C₂	semidirect
11. #10600518	C₂	semidirect
111. C₈×#41	D₅	semidirect
219. C₅×Q₈	#131	semidirect
222. C₅×D₄	#131	semidirect
410. Q₈	#4047	semidirect
418. D₄	#4047	semidirect
450. C₅	#17917	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₈×#41	2
#10614260	2
#10610189	2
#10602434	2
#10601730	2
#10601726	2
#10601634	2
#10601633	2
#10601554	2
#10601541	2
#10600518	2
#17917	5