Subgroups — C₄×C₅×#466 #11944241

Order 1280.

1222 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#466	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×#121	C₂	1	2	yes	maximal, complemented
5	C₅×#1970	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1934	C₂	1	2	yes	maximal, complemented
8	C₅×#1893	C₂	1	2	yes	maximal, complemented
9	C₅×#1808	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#102	C₂	1	2	yes	maximal, complemented
12	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
13	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×#121	C₂²	1	2	yes	—
16	C₂×C₄×C₅×D₄	—	2	2	no	—
17	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
18	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₅×#466	C₄	1	8	yes	direct product factor
20	C₄×C₅×D₈	—	2	4	no	—
21	C₂×C₅×#107	C₂²	1	1	yes	characteristic
22	C₂×C₅×#107	C₂²	1	1	yes	characteristic
23	C₂×C₅×#107	C₂²	1	1	yes	characteristic
24	C₂×C₅×#102	C₂²	1	2	yes	—
25	C₂×C₅×#102	C₂²	1	2	yes	—
26	C₂×C₅×#102	C₂²	1	2	yes	—
27	C₂×C₄×C₅×C₈	—	2	4	no	—
28	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₅×#390	C₂²	1	2	yes	—
33	C₅×#389	C₂²	1	2	yes	—
34	C₅×#388	—	2	2	no	—
35	C₅×#386	—	2	2	no	—
36	C₅×#380	C₂²	1	2	yes	—
37	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
38	C₄×C₅×C₂²⋊C₄	—	2	2	no	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#340	C₂²	1	2	yes	—
42	C₄×#466	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×D₄	—	2	2	no	—
44	C₂²×C₅×D₄	C₂³	1	2	yes	—
45	C₂³×C₄×C₅	—	2	2	no	—
46	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂×C₅×D₈	—	2	2	no	—
50	C₂×C₅×D₈	—	2	2	no	—
51	C₂×C₅×D₈	C₂×C₄	1	4	yes	complemented
52	C₂²×C₅×C₈	—	2	2	no	—
53	C₂²×C₅×C₈	—	2	2	no	—
54	C₂²×C₅×C₈	—	2	2	no	—
55	C₂²×C₅×C₈	—	2	2	no	—
56	C₂²×C₅×C₈	—	2	2	no	—
57	C₂²×C₅×C₈	C₂×C₄	1	4	yes	complemented
58	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₅×#121	—	2	4	no	—
63	C₅×#121	C₂×C₄	1	8	yes	complemented
64	C₄×C₅×D₄	—	2	4	no	—
65	C₄×C₅×D₄	—	2	4	no	—
66	C₄×C₅×D₄	—	4	8	no	—
67	C₂×C₅×C₄⋊C₄	—	2	2	no	—
68	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	2	no	—
74	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₄²×C₅	—	2	2	no	—
77	C₂×C₄²×C₅	—	2	2	no	—
78	C₂×C₄²×C₅	—	2	2	no	—
79	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
83	C₅×#107	—	2	2	no	—
84	C₅×#107	—	2	2	no	—
85	C₅×#107	C₂×C₄	1	4	yes	complemented
86	C₅×#102	—	2	4	no	—
87	C₅×#102	—	2	4	no	—
88	C₅×#102	C₂×C₄	1	8	yes	complemented
89	C₄×C₅×C₈	—	2	2	no	—
90	C₄×C₅×C₈	—	2	2	no	—
91	C₄×C₅×C₈	—	2	2	no	—
92	C₄×C₅×C₈	D₄	1	4	yes	complemented
93	C₅×#95	—	2	2	no	—
94	C₅×#95	—	2	2	no	—
95	C₅×#95	—	2	2	no	—
96	C₂×#466	C₂×C₅	1	1	yes	characteristic
97	C₂×C₄×D₈	C₂×C₅	1	1	yes	characteristic, complemented
98	C₂²×C₄×C₈	C₂×C₅	1	1	yes	characteristic, complemented
99	C₄×#121	C₂×C₅	1	2	yes	complemented
100	#1970	C₂×C₅	1	1	yes	characteristic, complemented
101	#1942	C₂×C₅	1	1	yes	characteristic, complemented
102	#1934	C₂×C₅	1	2	yes	complemented
103	#1893	C₂×C₅	1	2	yes	complemented
104	#1808	C₂×C₅	1	1	yes	characteristic, complemented
105	C₄×#107	C₂×C₅	1	1	yes	characteristic, complemented
106	C₄×#102	C₂×C₅	1	2	yes	complemented
107	C₂⁴×C₅	—	2	2	no	—
108	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₅×D₄	—	2	8	no	—
110	C₂×C₅×D₄	—	2	2	no	—
111	C₂×C₅×D₄	—	2	2	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	—	4	4	no	—
116	C₂×C₅×D₄	—	4	4	no	—
117	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	—	2	2	no	—
121	C₂²×C₄×C₅	—	2	2	no	—
122	C₂²×C₄×C₅	—	2	2	no	—
123	C₂²×C₄×C₅	—	2	1	no	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	2	2	no	—
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	—	4	4	no	—
131	C₂²×C₄×C₅	—	4	4	no	—
132	C₂²×C₄×C₅	—	4	4	no	—
133	C₂²×C₄×C₅	D₈	1	4	yes	complemented
134	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	#41	1	2	yes	—
141	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
142	C₅×D₈	—	2	8	no	—
143	C₂×C₅×C₈	—	2	8	no	—
144	C₂×C₅×C₈	—	2	1	no	—
145	C₂×C₅×C₈	—	2	1	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	2	1	no	—
148	C₂×C₅×C₈	—	2	1	no	—
149	C₂×C₅×C₈	—	2	1	no	—
150	C₂×C₅×C₈	—	2	8	no	—
151	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
152	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
153	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
154	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
155	C₂×C₅×C₈	#41	1	2	yes	—
156	C₂×C₅×C₈	#41	1	2	yes	—
157	C₅×C₄⋊C₄	—	2	2	no	—
158	C₅×C₄⋊C₄	—	2	2	no	—
159	C₅×C₄⋊C₄	—	2	2	no	—
160	C₅×C₄⋊C₄	—	2	2	no	—
161	C₅×C₄⋊C₄	—	2	2	no	—
162	C₅×C₄⋊C₄	—	4	4	no	—
163	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
164	C₅×C₂²⋊C₄	—	2	8	no	—
165	C₅×C₂²⋊C₄	—	4	4	no	—
166	C₅×C₂²⋊C₄	—	4	4	no	—
167	C₅×C₂²⋊C₄	—	4	4	no	—
168	C₅×C₂²⋊C₄	—	4	4	no	—
169	C₄²×C₅	—	2	2	no	—
170	C₄²×C₅	—	2	2	no	—
171	C₄²×C₅	—	2	1	no	—
172	C₄²×C₅	—	2	1	no	—
173	C₄²×C₅	—	4	4	no	—
174	C₄²×C₅	C₂×D₄	1	2	yes	—
175	C₄²×C₅	#41	1	2	yes	—
176	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
177	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
178	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
179	C₂×#121	C₂²×C₅	1	2	yes	—
180	C₂×C₄×D₄	—	2	2	no	—
181	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
182	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
183	#466	C₄×C₅	1	8	yes	direct product factor
184	C₄×D₈	—	2	4	no	—
185	C₂×#107	C₂²×C₅	1	1	yes	characteristic
186	C₂×#107	C₂²×C₅	1	1	yes	characteristic
187	C₂×#107	C₂²×C₅	1	1	yes	characteristic
188	C₂×#102	C₂²×C₅	1	2	yes	—
189	C₂×#102	C₂²×C₅	1	2	yes	—
190	C₂×#102	C₂²×C₅	1	2	yes	—
191	C₂×C₄×C₈	—	2	4	no	—
192	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
193	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
194	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
195	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
196	#390	C₂²×C₅	1	2	yes	—
197	#389	C₂²×C₅	1	2	yes	—
198	#388	—	2	2	no	—
199	#386	—	2	2	no	—
200	#380	C₂²×C₅	1	2	yes	—
201	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
202	C₄×C₂²⋊C₄	—	2	2	no	—
203	#340	C₂²×C₅	1	2	yes	—
204	#340	C₂²×C₅	1	2	yes	—
205	#340	C₂²×C₅	1	2	yes	—
206	C₂³×C₅	—	2	1	no	—
207	C₂³×C₅	—	2	1	no	—
208	C₂³×C₅	—	2	1	no	—
209	C₂³×C₅	—	2	1	no	—
210	C₂³×C₅	—	2	4	no	—
211	C₂³×C₅	—	4	2	no	—
212	C₂³×C₅	—	4	2	no	—
213	C₂³×C₅	—	4	2	no	—
214	C₂³×C₅	—	4	2	no	—
215	C₂³×C₅	—	4	2	no	—
216	C₂³×C₅	—	4	2	no	—
217	C₂³×C₅	C₄×D₄	1	2	yes	—
218	C₂³×C₅	C₂×D₈	1	2	yes	—
219	C₂³×C₅	#135	1	2	yes	—
220	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
221	C₅×D₄	—	2	4	no	—
222	C₅×D₄	—	2	4	no	—
223	C₅×D₄	—	4	16	no	—
224	C₅×D₄	—	4	2	no	—
225	C₅×D₄	—	4	2	no	—
226	C₂×C₄×C₅	—	2	8	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	1	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	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	8	no	—
240	C₂×C₄×C₅	—	2	4	no	—
241	C₂×C₄×C₅	—	4	2	no	—
242	C₂×C₄×C₅	—	4	2	no	—
243	C₂×C₄×C₅	—	4	2	no	—
244	C₂×C₄×C₅	—	4	2	no	—
245	C₂×C₄×C₅	—	4	2	no	—
246	C₂×C₄×C₅	—	4	2	no	—
247	C₂×C₄×C₅	—	4	2	no	—
248	C₂×C₄×C₅	—	4	2	no	—
249	C₂×C₄×C₅	—	8	8	no	—
250	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
251	C₂×C₄×C₅	#121	1	2	yes	—
252	C₂×C₄×C₅	#121	1	2	yes	—
253	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
254	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
255	C₂×C₄×C₅	#135	1	2	yes	—
256	C₂×C₄×C₅	#135	1	2	yes	—
257	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
263	C₅×C₈	—	2	2	no	—
264	C₅×C₈	—	2	2	no	—
265	C₅×C₈	—	2	2	no	—
266	C₅×C₈	C₄×D₄	1	4	yes	complemented
267	C₂²×D₄	—	2	2	no	—
268	C₂²×D₄	C₂³×C₅	1	2	yes	—
269	C₂³×C₄	—	2	2	no	—
270	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
271	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
272	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
273	C₂×D₈	—	2	2	no	—
274	C₂×D₈	—	2	2	no	—
275	C₂×D₈	C₂×C₄×C₅	1	4	yes	complemented
276	C₂²×C₈	—	2	2	no	—
277	C₂²×C₈	—	2	2	no	—
278	C₂²×C₈	—	2	2	no	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	C₂×C₄×C₅	1	4	yes	complemented
282	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
286	#121	—	2	4	no	—
287	#121	C₂×C₄×C₅	1	8	yes	complemented
288	C₄×D₄	—	2	4	no	—
289	C₄×D₄	—	2	4	no	—
290	C₄×D₄	—	4	8	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
304	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
306	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
307	#107	—	2	2	no	—
308	#107	—	2	2	no	—
309	#107	C₂×C₄×C₅	1	4	yes	complemented
310	#102	—	2	4	no	—
311	#102	—	2	4	no	—
312	#102	C₂×C₄×C₅	1	8	yes	complemented
313	C₄×C₈	—	2	2	no	—
314	C₄×C₈	—	2	2	no	—
315	C₄×C₈	—	2	2	no	—
316	C₄×C₈	C₅×D₄	1	4	yes	complemented
317	#95	—	2	2	no	—
318	#95	—	2	2	no	—
319	#95	—	2	2	no	—
320	C₂²×C₅	—	2	2	no	—
321	C₂²×C₅	—	2	2	no	—
322	C₂²×C₅	—	2	2	no	—
323	C₂²×C₅	—	2	2	no	—
324	C₂²×C₅	—	2	2	no	—
325	C₂²×C₅	—	2	2	no	—
326	C₂²×C₅	—	4	4	no	—
327	C₂²×C₅	—	4	4	no	—
328	C₂²×C₅	—	4	4	no	—
329	C₂²×C₅	—	8	2	no	—
330	C₂²×C₅	—	8	2	no	—
331	C₂²×C₅	—	8	2	no	—
332	C₂²×C₅	—	8	2	no	—
333	C₂²×C₅	C₄×D₈	1	4	yes	complemented
334	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
335	C₂²×C₅	C₂×#121	1	1	yes	characteristic
336	C₂²×C₅	#532	1	1	yes	characteristic
337	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
338	C₂²×C₅	C₂×#135	1	1	yes	characteristic
339	C₂²×C₅	C₂×#135	1	1	yes	characteristic
340	C₂²×C₅	C₂×#135	1	1	yes	characteristic
341	C₄×C₅	—	2	2	no	—
342	C₄×C₅	—	2	2	no	—
343	C₄×C₅	—	2	2	no	—
344	C₄×C₅	—	2	2	no	—
345	C₄×C₅	—	4	4	no	—
346	C₄×C₅	—	8	2	no	—
347	C₄×C₅	—	8	2	no	—
348	C₄×C₅	#466	1	4	yes	direct product factor
349	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
350	C₄×C₅	C₄×#41	1	1	yes	characteristic
351	C₄×C₅	#525	1	1	yes	characteristic
352	C₄×C₅	#529	1	1	yes	characteristic
353	C₂⁴	—	2	2	no	—
354	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
355	C₂×D₄	—	2	8	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	4	4	no	—
362	C₂×D₄	—	4	4	no	—
363	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	4	4	no	—
377	C₂²×C₄	—	4	4	no	—
378	C₂²×C₄	—	4	4	no	—
379	C₂²×C₄	C₅×D₈	1	4	yes	complemented
380	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
381	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
386	C₂²×C₄	C₅×#41	1	2	yes	—
387	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
388	D₈	—	2	8	no	—
389	C₂×C₈	—	2	8	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	8	no	—
397	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
398	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
399	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
400	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
401	C₂×C₈	C₅×#41	1	2	yes	—
402	C₂×C₈	C₅×#41	1	2	yes	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	4	4	no	—
409	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
410	C₂²⋊C₄	—	2	8	no	—
411	C₂²⋊C₄	—	4	4	no	—
412	C₂²⋊C₄	—	4	4	no	—
413	C₂²⋊C₄	—	4	4	no	—
414	C₂²⋊C₄	—	4	4	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	4	4	no	—
420	C₄²	C₂×C₅×D₄	1	2	yes	—
421	C₄²	C₅×#41	1	2	yes	—
422	C₂×C₅	—	2	4	no	—
423	C₂×C₅	—	8	4	no	—
424	C₂×C₅	C₄×#121	1	1	yes	characteristic
425	C₂×C₅	C₂×C₄×D₈	1	1	yes	characteristic
426	C₂×C₅	C₄×#135	1	1	yes	characteristic
427	C₂×C₅	C₂×#466	1	1	yes	characteristic
428	C₂×C₅	#3050	1	1	yes	characteristic
429	C₂×C₅	#3168	1	1	yes	characteristic
430	C₂×C₅	#3169	1	1	yes	characteristic
431	C₂³	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	C₄×C₅×D₄	1	2	yes	—
443	C₂³	C₂×C₅×D₈	1	2	yes	—
444	C₂³	C₅×#135	1	2	yes	—
445	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
446	D₄	—	2	4	no	—
447	D₄	—	2	4	no	—
448	D₄	—	4	16	no	—
449	D₄	—	4	2	no	—
450	D₄	—	4	2	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	8	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	8	8	no	—
475	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
476	C₂×C₄	C₅×#121	1	2	yes	—
477	C₂×C₄	C₅×#121	1	2	yes	—
478	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
479	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
480	C₂×C₄	C₅×#135	1	2	yes	—
481	C₂×C₄	C₅×#135	1	2	yes	—
482	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
483	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
484	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
485	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
486	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
487	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
488	C₈	—	2	2	no	—
489	C₈	—	2	2	no	—
490	C₈	—	2	2	no	—
491	C₈	C₄×C₅×D₄	1	4	yes	complemented
492	C₅	C₄×#466	1	1	yes	characteristic, direct product factor, Sylow
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	8	2	no	—
503	C₂²	—	8	2	no	—
504	C₂²	—	8	2	no	—
505	C₂²	—	8	2	no	—
506	C₂²	C₄×C₅×D₈	1	4	yes	complemented
507	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
508	C₂²	C₂×C₅×#121	1	1	yes	characteristic
509	C₂²	C₅×#532	1	1	yes	characteristic
510	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
511	C₂²	C₂×C₅×#135	1	1	yes	characteristic
512	C₂²	C₂×C₅×#135	1	1	yes	characteristic
513	C₂²	C₂×C₅×#135	1	1	yes	characteristic
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	4	4	no	—
519	C₄	—	8	2	no	—
520	C₄	—	8	2	no	—
521	C₄	C₅×#466	1	4	yes	direct product factor
522	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
523	C₄	C₄×C₅×#41	1	1	yes	characteristic
524	C₄	C₅×#525	1	1	yes	characteristic
525	C₄	C₅×#529	1	1	yes	characteristic
526	C₂	—	2	4	no	—
527	C₂	—	8	4	no	—
528	C₂	C₄×C₅×#121	1	1	yes	characteristic
529	C₂	C₂×C₄×C₅×D₈	1	1	yes	characteristic
530	C₂	C₄×C₅×#135	1	1	yes	characteristic
531	C₂	C₂×C₅×#466	1	1	yes	characteristic
532	C₂	C₅×#3050	1	1	yes	characteristic
533	C₂	C₅×#3168	1	1	yes	characteristic
534	C₂	C₅×#3169	1	1	yes	characteristic

	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×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₅×D₈	C₂	semidirect
3. C₂²×C₄×C₅×C₈	C₂	semidirect
4. C₄×C₅×#121	C₂	semidirect
5. C₅×#1970	C₂	semidirect
6. C₅×#1942	C₂	semidirect
7. C₅×#1934	C₂	semidirect
8. C₅×#1893	C₂	semidirect
9. C₅×#1808	C₂	semidirect
10. C₄×C₅×#107	C₂	semidirect
11. C₄×C₅×#102	C₂	semidirect
19. C₅×#466	C₄	direct (N × H)
42. C₄×#466	C₅	direct (N × H)
51. C₂×C₅×D₈	C₂×C₄	semidirect
57. C₂²×C₅×C₈	C₂×C₄	semidirect
63. C₅×#121	C₂×C₄	semidirect
85. C₅×#107	C₂×C₄	semidirect
88. C₅×#102	C₂×C₄	semidirect
92. C₄×C₅×C₈	D₄	semidirect
97. C₂×C₄×D₈	C₂×C₅	semidirect
98. C₂²×C₄×C₈	C₂×C₅	semidirect
99. C₄×#121	C₂×C₅	semidirect
100. #1970	C₂×C₅	semidirect
101. #1942	C₂×C₅	semidirect
102. #1934	C₂×C₅	semidirect
103. #1893	C₂×C₅	semidirect
104. #1808	C₂×C₅	semidirect
105. C₄×#107	C₂×C₅	semidirect
106. C₄×#102	C₂×C₅	semidirect
133. C₂²×C₄×C₅	D₈	semidirect
183. #466	C₄×C₅	direct (N × H)
266. C₅×C₈	C₄×D₄	semidirect
275. C₂×D₈	C₂×C₄×C₅	semidirect
281. C₂²×C₈	C₂×C₄×C₅	semidirect
287. #121	C₂×C₄×C₅	semidirect
309. #107	C₂×C₄×C₅	semidirect
312. #102	C₂×C₄×C₅	semidirect
316. C₄×C₈	C₅×D₄	semidirect
333. C₂²×C₅	C₄×D₈	semidirect
348. C₄×C₅	#466	direct (N × H)
379. C₂²×C₄	C₅×D₈	semidirect
491. C₈	C₄×C₅×D₄	semidirect
492. C₅	C₄×#466	direct (N × H)
506. C₂²	C₄×C₅×D₈	semidirect
521. C₄	C₅×#466	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×#466	2
C₂×C₄×C₅×D₈	2
C₂²×C₄×C₅×C₈	2
C₄×C₅×#121	2
C₅×#1970	2
C₅×#1942	2
C₅×#1934	2
C₅×#1893	2
C₅×#1808	2
C₄×C₅×#107	2
C₄×C₅×#102	2
C₄×#466	5

Subgroups — C4×C5×#466 #11944241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#466 #11944241