Subgroups — C₄×C₅×#496 #11944419

Order 1280.

1262 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	C₂×C₅×#496	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×SD₁₆	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×C₅×D₈	C₂	1	2	yes	maximal, complemented
4	C₄×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1973	C₂	1	2	yes	maximal, complemented
7	C₅×#1972	C₂	1	2	yes	maximal, complemented
8	C₅×#1961	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1959	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1847	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×SD₁₆	C₂²	1	2	yes	—
13	C₂²×C₅×D₈	C₂²	1	2	yes	—
14	C₂×C₅×#127	C₂²	1	1	yes	characteristic
15	C₂×C₅×#124	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×D₄	—	2	2	no	—
18	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
20	C₅×#496	C₄	1	8	yes	direct product factor
21	C₄×C₅×SD₁₆	—	2	8	no	—
22	C₄×C₅×D₈	—	2	8	no	—
23	C₂×C₅×#107	C₂²	1	2	yes	—
24	C₂×C₅×#106	C₂²	1	2	yes	—
25	C₂×C₅×#103	C₂²	1	2	yes	—
26	C₂×C₅×#102	C₂²	1	2	yes	—
27	C₂×C₅×#102	C₂²	1	2	yes	—
28	C₂×C₅×#102	C₂²	1	2	yes	—
29	C₂×C₅×#97	C₂²	1	1	yes	characteristic
30	C₂×C₅×#97	C₂²	1	2	yes	—
31	C₂×C₅×#97	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
33	C₅×#391	C₂²	1	1	yes	characteristic
34	C₅×#390	—	2	2	no	—
35	C₅×#390	C₂²	1	1	yes	characteristic
36	C₅×#390	C₂²	1	2	yes	—
37	C₅×#388	—	2	2	no	—
38	C₅×#384	C₂²	1	1	yes	characteristic
39	C₅×#382	C₂²	1	1	yes	characteristic
40	C₄×C₅×C₂²⋊C₄	—	2	2	no	—
41	C₄³×C₅	C₂²	1	1	yes	characteristic
42	C₄×#496	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
44	C₂²×C₅×D₄	—	2	2	no	—
45	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
46	C₂²×C₅×D₄	C₂³	1	2	yes	—
47	C₂³×C₄×C₅	—	2	1	no	—
48	C₂³×C₄×C₅	—	2	2	no	—
49	C₂×C₅×SD₁₆	—	2	4	no	—
50	C₂×C₅×SD₁₆	—	2	4	no	—
51	C₂×C₅×SD₁₆	C₂×C₄	1	8	yes	complemented
52	C₂×C₅×D₈	—	2	4	no	—
53	C₂×C₅×D₈	—	2	4	no	—
54	C₂×C₅×D₈	C₂×C₄	1	8	yes	complemented
55	C₂²×C₅×C₈	C₂³	1	2	yes	—
56	C₂²×C₅×C₈	C₂³	1	2	yes	—
57	C₅×#127	—	2	2	no	—
58	C₅×#127	C₂×C₄	1	4	yes	complemented
59	C₅×#124	—	2	2	no	—
60	C₅×#124	C₂×C₄	1	4	yes	complemented
61	C₄×C₅×Q₈	—	2	4	no	—
62	C₄×C₅×D₄	—	2	4	no	—
63	C₄×C₅×D₄	—	2	4	no	—
64	C₄×C₅×D₄	—	2	4	no	—
65	C₄×C₅×D₄	—	4	8	no	—
66	C₂×C₅×C₄⋊C₄	—	2	2	no	—
67	C₂×C₅×C₄⋊C₄	—	2	1	no	—
68	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
76	C₂×C₄²×C₅	—	2	1	no	—
77	C₂×C₄²×C₅	D₄	1	2	yes	—
78	C₂×C₄²×C₅	D₄	1	2	yes	—
79	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₅×#107	—	2	4	no	—
83	C₅×#106	—	2	4	no	—
84	C₅×#103	—	2	4	no	—
85	C₅×#102	—	2	4	no	—
86	C₅×#102	—	2	4	no	—
87	C₅×#102	—	2	4	no	—
88	C₅×#97	—	2	4	no	—
89	C₅×#97	—	2	2	no	—
90	C₅×#97	C₂×C₄	1	4	yes	complemented
91	C₄×C₅×C₈	D₄	1	8	yes	complemented
92	C₅×#95	—	2	2	no	—
93	C₅×#95	—	2	2	no	—
94	C₂×#496	C₂×C₅	1	1	yes	characteristic
95	C₂×C₄×SD₁₆	C₂×C₅	1	2	yes	complemented
96	C₂×C₄×D₈	C₂×C₅	1	2	yes	complemented
97	C₄×#127	C₂×C₅	1	1	yes	characteristic, complemented
98	C₄×#124	C₂×C₅	1	1	yes	characteristic, complemented
99	#1973	C₂×C₅	1	2	yes	complemented
100	#1972	C₂×C₅	1	2	yes	complemented
101	#1961	C₂×C₅	1	1	yes	characteristic, complemented
102	#1959	C₂×C₅	1	1	yes	characteristic, complemented
103	#1847	C₂×C₅	1	1	yes	characteristic, complemented
104	C₄×#97	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂⁴×C₅	—	2	1	no	—
106	C₂⁴×C₅	—	2	2	no	—
107	C₂×C₅×Q₈	—	2	1	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	—	2	2	no	—
110	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
111	C₂×C₅×D₄	—	2	8	no	—
112	C₂×C₅×D₄	—	2	2	no	—
113	C₂×C₅×D₄	—	2	2	no	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	—	2	2	no	—
116	C₂×C₅×D₄	—	2	2	no	—
117	C₂×C₅×D₄	—	2	2	no	—
118	C₂×C₅×D₄	—	2	1	no	—
119	C₂×C₅×D₄	—	2	2	no	—
120	C₂×C₅×D₄	—	4	4	no	—
121	C₂×C₅×D₄	—	4	4	no	—
122	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
123	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	—	2	2	no	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	4	2	no	—
129	C₂²×C₄×C₅	—	4	4	no	—
130	C₂²×C₄×C₅	—	4	8	no	—
131	C₂²×C₄×C₅	—	4	4	no	—
132	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
137	C₅×SD₁₆	—	2	16	no	—
138	C₅×D₈	—	2	16	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
142	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
143	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
144	C₂×C₅×C₈	#41	1	4	yes	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	2	no	—
149	C₅×C₄⋊C₄	—	4	4	no	—
150	C₅×C₄⋊C₄	—	4	2	no	—
151	C₅×C₂²⋊C₄	—	2	8	no	—
152	C₅×C₂²⋊C₄	—	4	4	no	—
153	C₅×C₂²⋊C₄	—	4	8	no	—
154	C₅×C₂²⋊C₄	—	4	2	no	—
155	C₅×C₂²⋊C₄	—	4	4	no	—
156	C₄²×C₅	—	2	4	no	—
157	C₄²×C₅	—	2	2	no	—
158	C₄²×C₅	—	4	2	no	—
159	C₄²×C₅	—	4	2	no	—
160	C₄²×C₅	C₂²×C₄	1	2	yes	—
161	C₄²×C₅	C₂×D₄	1	4	yes	—
162	C₄²×C₅	#41	1	2	yes	—
163	C₂²×SD₁₆	C₂²×C₅	1	2	yes	—
164	C₂²×D₈	C₂²×C₅	1	2	yes	—
165	C₂×#127	C₂²×C₅	1	1	yes	characteristic
166	C₂×#124	C₂²×C₅	1	1	yes	characteristic
167	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
168	C₂×C₄×D₄	—	2	2	no	—
169	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
170	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
171	#496	C₄×C₅	1	8	yes	direct product factor
172	C₄×SD₁₆	—	2	8	no	—
173	C₄×D₈	—	2	8	no	—
174	C₂×#107	C₂²×C₅	1	2	yes	—
175	C₂×#106	C₂²×C₅	1	2	yes	—
176	C₂×#103	C₂²×C₅	1	2	yes	—
177	C₂×#102	C₂²×C₅	1	2	yes	—
178	C₂×#102	C₂²×C₅	1	2	yes	—
179	C₂×#102	C₂²×C₅	1	2	yes	—
180	C₂×#97	C₂²×C₅	1	1	yes	characteristic
181	C₂×#97	C₂²×C₅	1	2	yes	—
182	C₂×#97	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
184	#391	C₂²×C₅	1	1	yes	characteristic
185	#390	—	2	2	no	—
186	#390	C₂²×C₅	1	2	yes	—
187	#390	C₂²×C₅	1	1	yes	characteristic
188	#388	—	2	2	no	—
189	#384	C₂²×C₅	1	1	yes	characteristic
190	#382	C₂²×C₅	1	1	yes	characteristic
191	C₄×C₂²⋊C₄	—	2	2	no	—
192	C₄³	C₂²×C₅	1	1	yes	characteristic
193	C₂³×C₅	—	2	2	no	—
194	C₂³×C₅	—	2	4	no	—
195	C₂³×C₅	—	4	1	no	—
196	C₂³×C₅	—	4	2	no	—
197	C₂³×C₅	—	4	1	no	—
198	C₂³×C₅	—	4	2	no	—
199	C₂³×C₅	—	4	4	no	—
200	C₂³×C₅	—	4	2	no	—
201	C₂³×C₅	—	4	2	no	—
202	C₂³×C₅	—	4	4	no	—
203	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
204	C₅×Q₈	—	2	4	no	—
205	C₅×Q₈	—	4	2	no	—
206	C₅×D₄	—	2	4	no	—
207	C₅×D₄	—	2	4	no	—
208	C₅×D₄	—	2	4	no	—
209	C₅×D₄	—	4	16	no	—
210	C₅×D₄	—	4	2	no	—
211	C₅×D₄	—	4	2	no	—
212	C₅×D₄	—	4	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	4	1	no	—
222	C₂×C₄×C₅	—	4	1	no	—
223	C₂×C₄×C₅	—	4	1	no	—
224	C₂×C₄×C₅	—	4	2	no	—
225	C₂×C₄×C₅	—	4	4	no	—
226	C₂×C₄×C₅	—	4	2	no	—
227	C₂×C₄×C₅	—	4	2	no	—
228	C₂×C₄×C₅	—	8	8	no	—
229	C₂×C₄×C₅	—	8	4	no	—
230	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
231	C₂×C₄×C₅	#127	1	2	yes	—
232	C₂×C₄×C₅	#127	1	2	yes	—
233	C₂×C₄×C₅	AGL(1,ℤ/8)	1	4	yes	—
234	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
236	C₂×C₄×C₅	C₂×#41	1	2	yes	—
237	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
238	C₅×C₈	—	2	4	no	—
239	C₅×C₈	C₄×D₄	1	8	yes	complemented
240	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
241	C₂²×D₄	—	2	2	no	—
242	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
243	C₂²×D₄	C₂³×C₅	1	2	yes	—
244	C₂³×C₄	—	2	2	no	—
245	C₂³×C₄	—	2	1	no	—
246	C₂×SD₁₆	—	2	4	no	—
247	C₂×SD₁₆	—	2	4	no	—
248	C₂×SD₁₆	C₂×C₄×C₅	1	8	yes	complemented
249	C₂×D₈	—	2	4	no	—
250	C₂×D₈	—	2	4	no	—
251	C₂×D₈	C₂×C₄×C₅	1	8	yes	complemented
252	C₂²×C₈	C₂³×C₅	1	2	yes	—
253	C₂²×C₈	C₂³×C₅	1	2	yes	—
254	#127	—	2	2	no	—
255	#127	C₂×C₄×C₅	1	4	yes	complemented
256	#124	—	2	2	no	—
257	#124	C₂×C₄×C₅	1	4	yes	complemented
258	C₄×Q₈	—	2	4	no	—
259	C₄×D₄	—	2	4	no	—
260	C₄×D₄	—	2	4	no	—
261	C₄×D₄	—	2	4	no	—
262	C₄×D₄	—	4	8	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	4	no	—
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	C₅×D₄	1	2	yes	—
275	C₂×C₄²	C₅×D₄	1	2	yes	—
276	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
279	#107	—	2	4	no	—
280	#106	—	2	4	no	—
281	#103	—	2	4	no	—
282	#102	—	2	4	no	—
283	#102	—	2	4	no	—
284	#102	—	2	4	no	—
285	#97	—	2	4	no	—
286	#97	—	2	2	no	—
287	#97	C₂×C₄×C₅	1	4	yes	complemented
288	C₄×C₈	C₅×D₄	1	8	yes	complemented
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	C₂²×C₅	—	4	2	no	—
292	C₂²×C₅	—	4	4	no	—
293	C₂²×C₅	—	4	8	no	—
294	C₂²×C₅	—	4	4	no	—
295	C₂²×C₅	—	8	2	no	—
296	C₂²×C₅	—	8	1	no	—
297	C₂²×C₅	—	8	1	no	—
298	C₂²×C₅	—	8	2	no	—
299	C₂²×C₅	—	8	4	no	—
300	C₂²×C₅	—	8	2	no	—
301	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
302	C₂²×C₅	C₂×#127	1	1	yes	characteristic
303	C₂²×C₅	#532	1	1	yes	characteristic
304	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
305	C₂²×C₅	#575	1	2	yes	—
306	C₄×C₅	—	2	2	no	—
307	C₄×C₅	—	2	4	no	—
308	C₄×C₅	—	4	2	no	—
309	C₄×C₅	—	4	2	no	—
310	C₄×C₅	—	8	2	no	—
311	C₄×C₅	—	8	1	no	—
312	C₄×C₅	—	8	1	no	—
313	C₄×C₅	#496	1	4	yes	direct product factor
314	C₄×C₅	C₂×C₄×D₄	1	2	yes	—
315	C₄×C₅	#532	1	2	yes	—
316	C₂⁴	—	2	1	no	—
317	C₂⁴	—	2	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
322	C₂×D₄	—	2	8	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	4	4	no	—
332	C₂×D₄	—	4	4	no	—
333	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
334	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	4	no	—
341	C₂²×C₄	—	4	8	no	—
342	C₂²×C₄	—	4	4	no	—
343	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
344	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
345	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
347	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
348	SD₁₆	—	2	16	no	—
349	D₈	—	2	16	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
353	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
354	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
355	C₂×C₈	C₅×#41	1	4	yes	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	4	4	no	—
361	C₄⋊C₄	—	4	2	no	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₂²⋊C₄	—	4	8	no	—
364	C₂²⋊C₄	—	4	4	no	—
365	C₂²⋊C₄	—	4	2	no	—
366	C₂²⋊C₄	—	4	4	no	—
367	C₄²	—	2	4	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	4	2	no	—
370	C₄²	—	4	2	no	—
371	C₄²	C₂²×C₄×C₅	1	2	yes	—
372	C₄²	C₂×C₅×D₄	1	4	yes	—
373	C₄²	C₅×#41	1	2	yes	—
374	C₂×C₅	—	8	4	no	—
375	C₂×C₅	—	8	2	no	—
376	C₂×C₅	C₄×#127	1	1	yes	characteristic
377	C₂×C₅	C₄×AGL(1,ℤ/8)	1	2	yes	—
378	C₂×C₅	C₂×#496	1	1	yes	characteristic
379	C₂×C₅	#3150	1	1	yes	characteristic
380	C₂×C₅	#3171	1	2	yes	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	4	no	—
383	C₂³	—	4	1	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	4	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	4	no	—
391	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
392	Q₈	—	2	4	no	—
393	Q₈	—	4	2	no	—
394	D₄	—	2	4	no	—
395	D₄	—	2	4	no	—
396	D₄	—	2	4	no	—
397	D₄	—	4	16	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	8	8	no	—
417	C₂×C₄	—	8	4	no	—
418	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
419	C₂×C₄	C₅×#127	1	2	yes	—
420	C₂×C₄	C₅×#127	1	2	yes	—
421	C₂×C₄	C₅×AGL(1,ℤ/8)	1	4	yes	—
422	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
424	C₂×C₄	C₂×C₅×#41	1	2	yes	—
425	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
426	C₈	—	2	4	no	—
427	C₈	C₄×C₅×D₄	1	8	yes	complemented
428	C₅	C₄×#496	1	1	yes	characteristic, direct product factor, Sylow
429	C₂²	—	4	2	no	—
430	C₂²	—	4	4	no	—
431	C₂²	—	4	8	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	8	1	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	8	4	no	—
438	C₂²	—	8	2	no	—
439	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
440	C₂²	C₂×C₅×#127	1	1	yes	characteristic
441	C₂²	C₅×#532	1	1	yes	characteristic
442	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
443	C₂²	C₅×#575	1	2	yes	—
444	C₄	—	2	2	no	—
445	C₄	—	2	4	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	8	2	no	—
449	C₄	—	8	1	no	—
450	C₄	—	8	1	no	—
451	C₄	C₅×#496	1	4	yes	direct product factor
452	C₄	C₂×C₄×C₅×D₄	1	2	yes	—
453	C₄	C₅×#532	1	2	yes	—
454	C₂	—	8	4	no	—
455	C₂	—	8	2	no	—
456	C₂	C₄×C₅×#127	1	1	yes	characteristic
457	C₂	C₄×C₅×AGL(1,ℤ/8)	1	2	yes	—
458	C₂	C₂×C₅×#496	1	1	yes	characteristic
459	C₂	C₅×#3150	1	1	yes	characteristic
460	C₂	C₅×#3171	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂²×D₄
prime radical	C₂×C₅×#496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₄³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₅×SD₁₆	C₂	semidirect
3. C₂×C₄×C₅×D₈	C₂	semidirect
4. C₄×C₅×#127	C₂	semidirect
5. C₄×C₅×#124	C₂	semidirect
6. C₅×#1973	C₂	semidirect
7. C₅×#1972	C₂	semidirect
8. C₅×#1961	C₂	semidirect
9. C₅×#1959	C₂	semidirect
10. C₅×#1847	C₂	semidirect
11. C₄×C₅×#97	C₂	semidirect
20. C₅×#496	C₄	direct (N × H)
42. C₄×#496	C₅	direct (N × H)
51. C₂×C₅×SD₁₆	C₂×C₄	semidirect
54. C₂×C₅×D₈	C₂×C₄	semidirect
58. C₅×#127	C₂×C₄	semidirect
60. C₅×#124	C₂×C₄	semidirect
90. C₅×#97	C₂×C₄	semidirect
91. C₄×C₅×C₈	D₄	semidirect
95. C₂×C₄×SD₁₆	C₂×C₅	semidirect
96. C₂×C₄×D₈	C₂×C₅	semidirect
97. C₄×#127	C₂×C₅	semidirect
98. C₄×#124	C₂×C₅	semidirect
99. #1973	C₂×C₅	semidirect
100. #1972	C₂×C₅	semidirect
101. #1961	C₂×C₅	semidirect
102. #1959	C₂×C₅	semidirect
103. #1847	C₂×C₅	semidirect
104. C₄×#97	C₂×C₅	semidirect
171. #496	C₄×C₅	direct (N × H)
239. C₅×C₈	C₄×D₄	semidirect
248. C₂×SD₁₆	C₂×C₄×C₅	semidirect
251. C₂×D₈	C₂×C₄×C₅	semidirect
255. #127	C₂×C₄×C₅	semidirect
257. #124	C₂×C₄×C₅	semidirect
287. #97	C₂×C₄×C₅	semidirect
288. C₄×C₈	C₅×D₄	semidirect
313. C₄×C₅	#496	direct (N × H)
427. C₈	C₄×C₅×D₄	semidirect
428. C₅	C₄×#496	direct (N × H)
451. C₄	C₅×#496	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#496	2
C₂×C₄×C₅×SD₁₆	2
C₂×C₄×C₅×D₈	2
C₄×C₅×#127	2
C₄×C₅×#124	2
C₅×#1973	2
C₅×#1972	2
C₅×#1961	2
C₅×#1959	2
C₅×#1847	2
C₄×C₅×#97	2
C₄×#496	5

Subgroups — C4×C5×#496 #11944419

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#496 #11944419