Subgroups — #12069083

Order 1280.

724 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2965	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#4095	C₂	1	1	yes	maximal, characteristic
3	C₂×#64977	C₂	1	1	yes	maximal, characteristic, complemented
4	#10602432	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601748	C₂	1	2	yes	maximal, complemented
6	#10601743	C₂	1	2	yes	maximal, complemented
7	#10601654	C₂	1	2	yes	maximal, complemented
8	#10601652	C₂	1	2	yes	maximal, complemented
9	#10601549	C₂	1	1	yes	maximal, characteristic, complemented
10	#10601539	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#681	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₅×#41	C₂²	1	1	yes	characteristic
13	C₂×#4095	C₄	1	1	yes	characteristic
14	C₂²×#676	—	2	1	no	—
15	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic
16	C₅×#446	C₂²	1	1	yes	characteristic, complemented
17	C₅×#446	C₂²	1	1	yes	characteristic, complemented
18	C₅×#436	C₂²	1	1	yes	characteristic, complemented
19	C₅×#436	C₂²	1	1	yes	characteristic, complemented
20	C₅×#435	—	2	1	no	—
21	C₅×#435	—	2	1	no	—
22	C₅×#431	—	2	1	no	—
23	C₅×#431	C₂²	1	1	yes	characteristic
24	C₄×C₅×M₁₆	—	2	1	no	—
25	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	#65521	C₄	1	1	yes	characteristic
27	C₂×#3952	—	2	1	no	—
28	#65315	C₄	1	2	yes	—
29	C₄×#688	C₂²	1	2	yes	—
30	#65303	C₄	1	2	yes	—
31	C₄×#686	C₂²	1	2	yes	—
32	#65290	C₄	1	1	yes	characteristic
33	#65284	C₄	1	1	yes	characteristic
34	#65214	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
36	C₄×#681	C₂²	1	1	yes	characteristic
37	#64977	—	2	1	no	—
38	#64977	—	2	1	no	—
39	#64977	C₂²	1	2	yes	—
40	#64977	C₂²	1	2	yes	—
41	Q₈⋊#168	C₂²	1	2	yes	complemented
42	D₄⋊#168	C₂²	1	2	yes	complemented
43	#64703	C₂²	1	2	yes	—
44	#64703	C₂²	1	2	yes	—
45	#64700	C₂²	1	2	yes	complemented
46	#64699	C₂²	1	2	yes	complemented
47	#64674	C₂²	1	2	yes	complemented
48	C₈×#168	C₂²	1	2	yes	complemented
49	#17891	—	5	1	no	maximal, Sylow
50	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
51	C₂²×D₂₀	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₄×D₅	—	2	1	no	—
53	C₂×C₅×M₁₆	—	2	1	no	—
54	C₂×C₅×M₁₆	—	2	1	no	—
55	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
56	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
57	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
58	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₄×C₅×D₄	—	2	1	no	—
60	C₄×C₅×D₄	—	2	1	no	—
61	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
62	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₅×#117	—	2	1	no	—
64	C₅×#117	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₅	—	2	1	no	—
66	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
67	#4095	—	2	4	no	—
68	C₂×#688	C₂×C₄	1	2	yes	—
69	C₂×#686	C₂×C₄	1	2	yes	—
70	C₂×#685	—	2	1	no	—
71	C₂×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
72	C₂×#681	C₂×C₄	1	1	yes	characteristic
73	C₂×#681	C₂×C₄	1	1	yes	characteristic
74	C₂²×#168	—	2	1	no	—
75	C₂×#676	—	2	2	no	—
76	C₂×#676	—	2	2	no	—
77	C₂×#676	—	4	4	no	—
78	C₄×D₂₀	—	2	1	no	—
79	C₄×D₂₀	—	2	1	no	—
80	C₄×D₂₀	C₂×C₄	1	2	yes	—
81	C₄×D₂₀	C₂³	1	2	yes	—
82	C₅×C₄⋊C₈	—	2	1	no	—
83	C₅×C₄⋊C₈	—	2	1	no	—
84	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₅×C₂²⋊C₈	—	2	1	no	—
87	C₅×C₂²⋊C₈	—	2	1	no	—
88	C₅×C₂²⋊C₈	—	2	1	no	—
89	C₅×#97	—	2	1	no	—
90	C₅×#97	—	2	1	no	—
91	C₄×C₅×C₈	—	2	1	no	—
92	C₄×C₅×C₈	D₄	1	1	yes	characteristic
93	C₄×C₅×C₈	D₄	1	1	yes	characteristic
94	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
95	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
96	#3967	C₂×C₄	1	2	yes	—
97	#3964	C₂×C₄	1	2	yes	—
98	C₂²⋊#168	—	2	1	no	—
99	#3952	—	2	2	no	—
100	#3952	—	2	2	no	—
101	#3941	C₂×C₄	1	2	yes	—
102	#3941	C₂×C₄	1	2	yes	—
103	#3940	C₂×C₄	1	2	yes	—
104	#3939	C₂×C₄	1	2	yes	—
105	C₄⋊#168	—	2	1	no	—
106	C₄⋊#168	—	2	1	no	—
107	C₄⋊#168	C₂³	1	2	yes	—
108	#3935	C₂×C₄	1	2	yes	—
109	C₄×#168	C₂³	1	2	yes	—
110	C₄×#168	C₂³	1	2	yes	—
111	#2965	D₅	1	1	yes	characteristic, complemented
112	C₄×AGL(1,ℤ/8)	—	5	1	no	—
113	C₂×#436	—	5	1	no	—
114	#1594	—	5	2	no	—
115	#1592	—	5	2	no	—
116	#1590	—	5	2	no	—
117	#1589	—	5	2	no	—
118	#1565	—	5	1	no	—
119	#1478	—	5	1	no	—
120	#1477	—	5	1	no	—
121	C₈×M₁₆	—	5	1	no	—
122	C₂³×D₅	—	2	1	no	—
123	C₅×#41	—	2	2	no	—
124	C₅×#41	—	2	2	no	—
125	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₅×D₄	—	2	1	no	—
127	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	—	2	1	no	—
130	C₂²×C₄×C₅	—	2	1	no	—
131	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	#41	1	1	yes	characteristic
134	C₂²×Dic₅	—	2	1	no	—
135	C₂×D₂₀	—	2	2	no	—
136	C₂×D₂₀	—	2	2	no	—
137	C₂×D₂₀	—	2	1	no	—
138	C₂×D₂₀	C₂²×C₄	1	2	yes	—
139	C₂×C₄×D₅	—	2	2	no	—
140	C₂×C₄×D₅	—	2	2	no	—
141	C₂×C₄×D₅	—	4	2	no	—
142	C₂×C₄×D₅	—	4	2	no	—
143	C₅×M₁₆	—	4	2	no	—
144	C₅×M₁₆	—	4	2	no	—
145	C₂×C₅×C₈	—	2	2	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	2	1	no	—
148	C₂×C₅×C₈	—	4	1	no	—
149	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
150	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
151	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
152	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
153	C₅×C₄⋊C₄	—	2	1	no	—
154	C₅×C₄⋊C₄	—	2	1	no	—
155	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
156	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
157	C₅×C₂²⋊C₄	—	2	1	no	—
158	C₅×C₂²⋊C₄	—	2	1	no	—
159	C₅×C₂²⋊C₄	—	2	1	no	—
160	C₄²×C₅	—	2	1	no	—
161	C₄²×C₅	—	2	1	no	—
162	C₄²×C₅	—	2	1	no	—
163	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
164	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₅	#41	1	1	yes	characteristic
166	C₄²×C₅	C₂⁴	1	1	yes	characteristic
167	#688	—	2	4	no	—
168	#686	—	2	4	no	—
169	#685	—	2	2	no	—
170	#685	—	2	2	no	—
171	C₄⋊Dic₅	—	2	1	no	—
172	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
173	#681	—	2	2	no	—
174	#681	M₁₆	1	4	yes	complemented
175	C₂×#168	—	2	2	no	—
176	C₂×#168	—	2	2	no	—
177	C₂×#168	—	4	2	no	—
178	C₂×#168	C₂²×C₄	1	2	yes	—
179	C₂×#168	C₂²×C₄	1	2	yes	—
180	#676	—	4	4	no	—
181	#676	—	4	4	no	—
182	C₂×AGL(1,ℤ/8)	—	5	1	no	—
183	C₂²×M₁₆	—	10	1	no	—
184	C₄×#41	C₂×D₅	1	1	yes	characteristic
185	C₂×C₄×D₄	—	5	1	no	—
186	#446	C₂×D₅	1	1	yes	characteristic, complemented
187	#446	C₂×D₅	1	1	yes	characteristic, complemented
188	#442	—	5	2	no	—
189	#440	—	5	2	no	—
190	C₄×SD₁₆	—	5	2	no	—
191	C₄×D₈	—	5	2	no	—
192	#436	—	5	2	no	—
193	#436	—	5	2	no	—
194	#436	—	10	1	no	—
195	#436	—	10	1	no	—
196	#436	C₂×D₅	1	1	yes	characteristic, complemented
197	#436	C₂×D₅	1	1	yes	characteristic, complemented
198	#435	—	2	1	no	—
199	#435	—	2	1	no	—
200	#431	—	2	1	no	—
201	#431	—	5	1	no	—
202	#431	C₂×D₅	1	1	yes	characteristic
203	#428	—	5	1	no	—
204	C₂×C₄⋊C₈	—	5	1	no	—
205	#418	—	5	1	no	—
206	#417	—	5	1	no	—
207	C₂×C₂²⋊C₈	—	10	1	no	—
208	C₄×M₁₆	—	2	1	no	—
209	C₄×M₁₆	—	5	1	no	—
210	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
211	#335	—	5	2	no	—
212	#334	—	5	2	no	—
213	Q₈⋊C₈	—	5	2	no	—
214	D₄⋊C₈	—	5	2	no	—
215	D₄⋊C₈	—	5	2	no	—
216	D₄⋊C₈	—	5	2	no	—
217	#322	—	5	2	no	—
218	C₈²	—	5	2	no	—
219	C₂³×C₅	—	2	1	no	—
220	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
221	C₂²×D₅	—	2	2	no	—
222	C₂²×D₅	—	4	2	no	—
223	C₂²×D₅	—	4	2	no	—
224	C₂²×D₅	—	4	2	no	—
225	C₅×Q₈	—	2	1	no	—
226	C₅×Q₈	—	2	1	no	—
227	C₅×D₄	—	2	1	no	—
228	C₅×D₄	—	2	1	no	—
229	C₅×D₄	—	4	2	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	4	1	no	—
236	C₂×C₄×C₅	—	4	2	no	—
237	C₂×C₄×C₅	—	4	1	no	—
238	C₂×C₄×C₅	—	4	1	no	—
239	C₂×C₄×C₅	—	4	2	no	—
240	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
244	C₂×C₄×C₅	#131	1	2	yes	—
245	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
248	C₂×Dic₅	—	2	2	no	—
249	C₂×Dic₅	—	4	2	no	—
250	D₂₀	—	2	2	no	—
251	D₂₀	—	2	2	no	—
252	D₂₀	—	4	2	no	—
253	C₄×D₅	—	4	4	no	—
254	C₄×D₅	—	4	2	no	—
255	C₄×D₅	—	4	2	no	—
256	C₅×C₈	—	2	1	no	—
257	C₅×C₈	—	2	1	no	—
258	C₅×C₈	—	2	1	no	—
259	C₅×C₈	—	4	1	no	—
260	C₅×C₈	—	4	1	no	—
261	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	complemented
262	#168	—	2	2	no	—
263	#168	—	4	2	no	—
264	#168	—	4	2	no	—
265	#168	C₂×M₁₆	1	4	yes	complemented
266	C₂×#41	C₄×D₅	1	1	yes	characteristic
267	C₂²×D₄	—	5	1	no	—
268	C₂³×C₄	—	10	1	no	—
269	AGL(1,ℤ/8)	—	10	4	no	—
270	C₂×SD₁₆	—	5	2	no	—
271	C₂×D₈	—	5	2	no	—
272	C₂×M₁₆	—	2	1	no	—
273	C₂×M₁₆	—	2	1	no	—
274	C₂×M₁₆	—	5	1	no	—
275	C₂×M₁₆	—	5	1	no	—
276	C₂×M₁₆	—	10	2	no	—
277	C₂×M₁₆	—	10	2	no	—
278	C₂×M₁₆	—	20	4	no	—
279	C₂²×C₈	—	10	1	no	—
280	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
281	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
282	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
283	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	—	5	2	no	—
287	C₄×D₄	—	5	2	no	—
288	C₄×D₄	—	10	1	no	—
289	C₄×D₄	—	10	1	no	—
290	C₄×D₄	C₄×D₅	1	1	yes	characteristic
291	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
292	#117	—	2	1	no	—
293	#117	C₄×D₅	1	1	yes	characteristic
294	C₂×C₄⋊C₄	—	5	1	no	—
295	C₂×C₂²⋊C₄	—	10	1	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
298	#107	—	5	2	no	—
299	#106	—	5	2	no	—
300	C₄⋊C₈	—	2	1	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	—	5	2	no	—
303	C₄⋊C₈	—	10	1	no	—
304	C₄⋊C₈	—	10	1	no	—
305	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
306	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
307	#103	—	5	2	no	—
308	#102	—	5	2	no	—
309	#102	—	5	2	no	—
310	#102	—	5	2	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	C₂²⋊C₈	—	10	1	no	—
315	C₂²⋊C₈	—	10	2	no	—
316	C₂²⋊C₈	—	10	2	no	—
317	#97	—	2	1	no	—
318	#97	—	2	1	no	—
319	#97	—	5	2	no	—
320	C₄×C₈	—	2	1	no	—
321	C₄×C₈	—	5	2	no	—
322	C₄×C₈	—	5	2	no	—
323	C₄×C₈	C₂²⋊D₅	1	1	yes	characteristic
324	C₄×C₈	C₂²⋊D₅	1	1	yes	characteristic
325	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
327	C₂²×C₅	—	2	1	no	—
328	C₂²×C₅	—	2	1	no	—
329	C₂²×C₅	—	4	1	no	—
330	C₂²×C₅	—	4	1	no	—
331	C₂²×C₅	—	4	1	no	—
332	C₂²×C₅	#436	1	2	yes	—
333	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
334	C₂×D₅	—	4	2	no	—
335	C₂×D₅	—	4	2	no	—
336	C₂×D₅	—	4	2	no	—
337	C₂×D₅	—	8	4	no	—
338	C₄×C₅	—	2	1	no	—
339	C₄×C₅	—	2	1	no	—
340	C₄×C₅	—	2	1	no	—
341	C₄×C₅	—	4	1	no	—
342	C₄×C₅	—	4	1	no	—
343	C₄×C₅	—	4	1	no	—
344	C₄×C₅	#436	1	2	yes	—
345	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
346	C₄×C₅	C₂×#131	1	1	yes	characteristic
347	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
348	C₄×C₅	#575	1	1	yes	characteristic
349	Dic₅	—	4	2	no	—
350	C₂⁴	—	10	1	no	—
351	#41	—	2	2	no	—
352	#41	—	2	2	no	—
353	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	5	2	no	—
356	C₂×D₄	—	10	2	no	—
357	C₂×D₄	—	10	2	no	—
358	C₂×D₄	—	10	1	no	—
359	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	10	1	no	—
364	C₂²×C₄	—	10	2	no	—
365	C₂²×C₄	—	10	2	no	—
366	C₂²×C₄	—	20	2	no	—
367	C₂²×C₄	—	20	2	no	—
368	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
369	C₂²×C₄	#709	1	1	yes	characteristic
370	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
371	SD₁₆	—	10	4	no	—
372	D₈	—	10	4	no	—
373	M₁₆	—	4	2	no	—
374	M₁₆	—	4	2	no	—
375	M₁₆	—	5	4	no	—
376	M₁₆	—	10	2	no	—
377	M₁₆	—	20	4	no	—
378	M₁₆	—	20	4	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	4	1	no	—
383	C₂×C₈	—	5	2	no	—
384	C₂×C₈	—	5	2	no	—
385	C₂×C₈	—	10	2	no	—
386	C₂×C₈	—	10	2	no	—
387	C₂×C₈	—	20	2	no	—
388	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
389	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
390	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
391	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	5	2	no	—
395	C₄⋊C₄	—	10	1	no	—
396	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
397	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
398	C₂²⋊C₄	—	2	1	no	—
399	C₂²⋊C₄	—	2	1	no	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	10	2	no	—
402	C₂²⋊C₄	—	10	2	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	2	1	no	—
406	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
407	C₄²	#709	1	1	yes	characteristic
408	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
409	C₄²	C₂³×D₅	1	1	yes	characteristic
410	C₂×C₅	—	2	2	no	—
411	C₂×C₅	—	8	1	no	—
412	C₂×C₅	C₂×#436	1	1	yes	characteristic
413	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
414	C₂×C₅	#2955	1	1	yes	characteristic
415	D₅	—	8	2	no	—
416	C₂³	—	2	1	no	—
417	C₂³	—	10	2	no	—
418	C₂³	—	20	2	no	—
419	C₂³	—	20	2	no	—
420	C₂³	—	20	2	no	—
421	C₂³	C₄×C₂²⋊D₅	1	1	yes	characteristic
422	Q₈	—	2	1	no	—
423	Q₈	—	2	1	no	—
424	D₄	—	2	1	no	—
425	D₄	—	2	1	no	—
426	D₄	—	4	2	no	—
427	D₄	—	10	2	no	—
428	D₄	—	10	2	no	—
429	D₄	—	20	2	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	10	2	no	—
441	C₂×C₄	—	20	4	no	—
442	C₂×C₄	—	20	2	no	—
443	C₂×C₄	—	20	2	no	—
444	C₂×C₄	—	20	2	no	—
445	C₂×C₄	D₅×M₁₆	1	2	yes	—
446	C₂×C₄	#4053	1	2	yes	—
447	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
448	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
449	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
450	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
451	C₂×C₄	C₂×#709	1	1	yes	characteristic
452	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
453	C₈	—	2	1	no	—
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	4	1	no	—
457	C₈	—	4	1	no	—
458	C₈	—	5	4	no	—
459	C₈	—	10	2	no	—
460	C₈	—	20	2	no	—
461	C₈	—	20	2	no	—
462	C₈	#4095	1	2	yes	complemented
463	C₅	#17891	1	1	yes	characteristic, complemented, Sylow
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	4	1	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	20	2	no	—
470	C₂²	—	20	2	no	—
471	C₂²	—	20	2	no	—
472	C₂²	—	40	4	no	—
473	C₂²	#65417	1	2	yes	—
474	C₂²	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	4	1	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	1	no	—
481	C₄	—	20	2	no	—
482	C₄	#65417	1	2	yes	—
483	C₄	C₂×D₅×M₁₆	1	1	yes	characteristic
484	C₄	C₂×#4053	1	1	yes	characteristic
485	C₄	C₂×#4095	1	1	yes	characteristic
486	C₄	#66156	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	8	1	no	—
489	C₂	—	40	2	no	—
490	C₂	C₄×#4095	1	1	yes	characteristic
491	C₂	C₂×#65417	1	1	yes	characteristic
492	C₂	#10615523	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×#2965	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×#4095	C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#2965	D₅
hypocenter	C₅	#17891
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2965

Complements

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

N	H ≅ G/N	type
1. C₅×#2965	C₂	semidirect
3. C₂×#64977	C₂	semidirect
4. #10602432	C₂	semidirect
5. #10601748	C₂	semidirect
6. #10601743	C₂	semidirect
7. #10601654	C₂	semidirect
8. #10601652	C₂	semidirect
9. #10601549	C₂	semidirect
10. #10601539	C₂	semidirect
11. C₈×#681	C₂	semidirect
16. C₅×#446	C₂²	semidirect
17. C₅×#446	C₂²	semidirect
18. C₅×#436	C₂²	semidirect
19. C₅×#436	C₂²	semidirect
41. Q₈⋊#168	C₂²	semidirect
42. D₄⋊#168	C₂²	semidirect
45. #64700	C₂²	semidirect
46. #64699	C₂²	semidirect
47. #64674	C₂²	semidirect
48. C₈×#168	C₂²	semidirect
111. #2965	D₅	semidirect
174. #681	M₁₆	semidirect
186. #446	C₂×D₅	semidirect
187. #446	C₂×D₅	semidirect
196. #436	C₂×D₅	semidirect
197. #436	C₂×D₅	semidirect
261. C₅×C₈	AGL(1,ℤ/8)	semidirect
265. #168	C₂×M₁₆	semidirect
462. C₈	#4095	semidirect
463. C₅	#17891	semidirect

Maximal subgroups

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

subgroup	index
C₅×#2965	2
C₄×#4095	2
C₂×#64977	2
#10602432	2
#10601748	2
#10601743	2
#10601654	2
#10601652	2
#10601549	2
#10601539	2
C₈×#681	2
#17891	5