Subgroups — C₅×#24332 #11947052

Order 1280.

1002 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#557	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#475	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic
4	C₅×#2582	C₂	1	1	yes	maximal, characteristic
5	C₅×#2059	C₂	1	2	yes	maximal
6	C₅×#2026	C₂	1	2	yes	maximal
7	C₅×#1990	C₂	1	1	yes	maximal, characteristic
8	C₅×#1984	C₂	1	1	yes	maximal, characteristic
9	C₅×#1878	C₂	1	2	yes	maximal
10	C₅×#1865	C₂	1	2	yes	maximal
11	C₅×#1803	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
13	C₅×#557	—	2	4	no	—
14	C₅×#557	—	2	4	no	—
15	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×#125	—	2	2	no	—
18	C₂×C₅×#125	C₂²	1	2	yes	—
19	C₂×C₄×C₅×Q₈	—	2	1	no	—
20	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
22	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
24	C₅×#475	—	2	4	no	—
25	C₄×C₅×Q₁₆	—	2	4	no	—
26	C₂×C₅×#107	C₂²	1	1	yes	characteristic
27	C₂×C₅×#106	C₂²	1	2	yes	—
28	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×#103	C₂²	1	1	yes	characteristic
30	C₂×C₅×#103	C₂²	1	2	yes	—
31	C₂×C₅×#103	C₂²	1	2	yes	—
32	C₂×C₅×#103	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
34	C₅×#398	—	2	2	no	—
35	C₅×#391	—	2	1	no	—
36	C₅×#391	C₂²	1	2	yes	—
37	C₅×#389	—	2	1	no	—
38	C₅×#389	C₂²	1	2	yes	—
39	C₅×#384	C₂²	1	1	yes	characteristic
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#340	C₂²	1	2	yes	—
42	C₅×#340	C₂²	1	2	yes	—
43	C₅×#336	C₂²	1	2	yes	—
44	C₅×#336	C₂²	1	2	yes	—
45	#24332	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂²×C₅×Q₈	—	2	1	no	—
47	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
48	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
49	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
50	C₂×C₅×Q₁₆	—	2	2	no	—
51	C₂×C₅×Q₁₆	—	2	2	no	—
52	C₂×C₅×Q₁₆	Q₈	1	4	yes	complemented
53	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₅×C₈	C₂³	1	2	yes	—
55	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₅×C₄⋊Q₈	—	2	8	no	—
57	C₅×C₄⋊Q₈	—	2	2	no	—
58	C₅×C₄⋊Q₈	D₄	1	4	yes	—
59	C₅×#125	—	2	16	no	—
60	C₅×#125	—	2	4	no	—
61	C₅×#125	—	2	4	no	—
62	C₄×C₅×Q₈	—	2	8	no	—
63	C₄×C₅×Q₈	—	2	4	no	—
64	C₄×C₅×Q₈	—	2	4	no	—
65	C₄×C₅×Q₈	—	2	2	no	—
66	C₄×C₅×Q₈	—	2	2	no	—
67	C₄×C₅×Q₈	—	2	2	no	—
68	C₄×C₅×Q₈	—	2	2	no	—
69	C₄×C₅×Q₈	—	2	2	no	—
70	C₄×C₅×Q₈	D₄	1	4	yes	—
71	C₂×C₅×C₄⋊C₄	—	2	2	no	—
72	C₂×C₅×C₄⋊C₄	—	2	1	no	—
73	C₂×C₅×C₄⋊C₄	—	2	2	no	—
74	C₂×C₅×C₄⋊C₄	—	2	1	no	—
75	C₂×C₅×C₄⋊C₄	—	2	2	no	—
76	C₂×C₅×C₄⋊C₄	—	2	1	no	—
77	C₂×C₅×C₄⋊C₄	—	2	1	no	—
78	C₂×C₅×C₄⋊C₄	—	2	1	no	—
79	C₂×C₅×C₄⋊C₄	—	2	2	no	—
80	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
81	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
82	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
85	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₅	—	2	2	no	—
87	C₂×C₄²×C₅	—	2	1	no	—
88	C₂×C₄²×C₅	—	2	1	no	—
89	C₂×C₄²×C₅	C₂³	1	2	yes	—
90	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
91	C₅×#107	—	2	2	no	—
92	C₅×#106	—	2	4	no	—
93	C₅×C₄⋊C₈	—	2	2	no	—
94	C₅×#103	—	2	2	no	—
95	C₅×#103	—	2	4	no	—
96	C₅×#103	—	2	2	no	—
97	C₅×#103	—	2	4	no	—
98	C₄×C₅×C₈	—	2	2	no	—
99	C₅×#95	—	2	2	no	—
100	C₅×#95	—	2	2	no	—
101	C₅×#95	—	2	2	no	—
102	C₂×#557	C₂×C₅	1	1	yes	characteristic
103	C₂×#475	C₂×C₅	1	1	yes	characteristic
104	C₂×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic
105	#2582	C₂×C₅	1	1	yes	characteristic
106	#2059	C₂×C₅	1	2	yes	—
107	#2026	C₂×C₅	1	2	yes	—
108	#1990	C₂×C₅	1	1	yes	characteristic
109	#1984	C₂×C₅	1	1	yes	characteristic
110	#1878	C₂×C₅	1	2	yes	—
111	#1865	C₂×C₅	1	2	yes	—
112	#1803	C₂×C₅	1	1	yes	characteristic
113	C₂×C₅×Q₈	—	2	2	no	—
114	C₂×C₅×Q₈	—	2	4	no	—
115	C₂×C₅×Q₈	—	2	2	no	—
116	C₂×C₅×Q₈	—	2	2	no	—
117	C₂×C₅×Q₈	—	2	1	no	—
118	C₂×C₅×Q₈	—	2	1	no	—
119	C₂×C₅×Q₈	—	2	1	no	—
120	C₂×C₅×Q₈	—	2	1	no	—
121	C₂×C₅×Q₈	—	2	1	no	—
122	C₂×C₅×Q₈	—	2	1	no	—
123	C₂×C₅×Q₈	—	2	1	no	—
124	C₂×C₅×Q₈	—	2	1	no	—
125	C₂×C₅×Q₈	—	4	2	no	—
126	C₂×C₅×Q₈	—	4	2	no	—
127	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
128	C₂×C₅×Q₈	C₂×Q₈	1	2	yes	—
129	C₂×C₅×Q₈	C₂×Q₈	1	2	yes	—
130	C₂×C₅×Q₈	#41	1	2	yes	—
131	C₂²×C₄×C₅	—	2	1	no	—
132	C₂²×C₄×C₅	—	2	1	no	—
133	C₂²×C₄×C₅	—	2	2	no	—
134	C₂²×C₄×C₅	—	2	1	no	—
135	C₂²×C₄×C₅	—	2	1	no	—
136	C₂²×C₄×C₅	—	2	2	no	—
137	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
142	C₅×Q₁₆	—	2	8	no	—
143	C₂×C₅×C₈	—	2	1	no	—
144	C₂×C₅×C₈	—	2	1	no	—
145	C₂×C₅×C₈	—	2	1	no	—
146	C₂×C₅×C₈	—	2	2	no	—
147	C₂×C₅×C₈	—	2	2	no	—
148	C₂×C₅×C₈	—	2	1	no	—
149	C₂×C₅×C₈	—	2	1	no	—
150	C₂×C₅×C₈	—	2	2	no	—
151	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
152	C₅×C₄⋊C₄	—	2	8	no	—
153	C₅×C₄⋊C₄	—	2	8	no	—
154	C₅×C₄⋊C₄	—	2	8	no	—
155	C₅×C₄⋊C₄	—	2	4	no	—
156	C₅×C₄⋊C₄	—	2	4	no	—
157	C₅×C₄⋊C₄	—	2	2	no	—
158	C₅×C₄⋊C₄	—	2	4	no	—
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₄⋊C₄	—	2	2	no	—
161	C₅×C₄⋊C₄	—	2	1	no	—
162	C₅×C₄⋊C₄	—	2	1	no	—
163	C₅×C₄⋊C₄	—	2	2	no	—
164	C₅×C₄⋊C₄	—	2	2	no	—
165	C₅×C₄⋊C₄	—	4	2	no	—
166	C₅×C₄⋊C₄	—	4	2	no	—
167	C₅×C₄⋊C₄	—	8	1	no	—
168	C₅×C₄⋊C₄	—	8	2	no	—
169	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
170	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
171	C₄²×C₅	—	2	8	no	—
172	C₄²×C₅	—	2	4	no	—
173	C₄²×C₅	—	2	2	no	—
174	C₄²×C₅	—	2	2	no	—
175	C₄²×C₅	—	4	2	no	—
176	C₄²×C₅	C₂×D₄	1	2	yes	—
177	C₄²×C₅	C₂×D₄	1	2	yes	—
178	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
179	#557	—	2	4	no	—
180	#557	—	2	4	no	—
181	C₂×C₄⋊Q₈	—	2	1	no	—
182	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
183	C₂×#125	—	2	2	no	—
184	C₂×#125	C₂²×C₅	1	2	yes	—
185	C₂×C₄×Q₈	—	2	1	no	—
186	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
187	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
188	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
189	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
190	#475	—	2	4	no	—
191	C₄×Q₁₆	—	2	4	no	—
192	C₂×#107	C₂²×C₅	1	1	yes	characteristic
193	C₂×#106	C₂²×C₅	1	2	yes	—
194	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
195	C₂×#103	C₂²×C₅	1	2	yes	—
196	C₂×#103	C₂²×C₅	1	2	yes	—
197	C₂×#103	C₂²×C₅	1	1	yes	characteristic
198	C₂×#103	C₂²×C₅	1	1	yes	characteristic
199	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
200	#398	—	2	2	no	—
201	#391	—	2	1	no	—
202	#391	C₂²×C₅	1	2	yes	—
203	#389	—	2	1	no	—
204	#389	C₂²×C₅	1	2	yes	—
205	#384	C₂²×C₅	1	1	yes	characteristic
206	#340	C₂²×C₅	1	2	yes	—
207	#340	C₂²×C₅	1	2	yes	—
208	#340	C₂²×C₅	1	2	yes	—
209	#336	C₂²×C₅	1	2	yes	—
210	#336	C₂²×C₅	1	2	yes	—
211	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
212	C₅×Q₈	—	2	2	no	—
213	C₅×Q₈	—	2	2	no	—
214	C₅×Q₈	—	2	2	no	—
215	C₅×Q₈	—	2	2	no	—
216	C₅×Q₈	—	2	2	no	—
217	C₅×Q₈	—	4	1	no	—
218	C₅×Q₈	—	4	1	no	—
219	C₅×Q₈	—	4	4	no	—
220	C₅×Q₈	—	4	8	no	—
221	C₅×Q₈	C₂²⋊Q₈	1	4	yes	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	4	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	4	1	no	—
237	C₂×C₄×C₅	—	4	1	no	—
238	C₂×C₄×C₅	—	4	2	no	—
239	C₂×C₄×C₅	—	4	2	no	—
240	C₂×C₄×C₅	—	4	1	no	—
241	C₂×C₄×C₅	—	4	1	no	—
242	C₂×C₄×C₅	—	4	1	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	1	no	—
247	C₂×C₄×C₅	—	4	1	no	—
248	C₂×C₄×C₅	#120	1	2	yes	—
249	C₂×C₄×C₅	#120	1	2	yes	—
250	C₂×C₄×C₅	#135	1	2	yes	—
251	C₂×C₄×C₅	#137	1	2	yes	—
252	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
256	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
257	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
258	C₅×C₈	—	2	2	no	—
259	C₅×C₈	—	4	1	no	—
260	C₅×C₈	—	4	2	no	—
261	C₂²×Q₈	—	2	1	no	—
262	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
263	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
264	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
265	C₂×Q₁₆	—	2	2	no	—
266	C₂×Q₁₆	—	2	2	no	—
267	C₂×Q₁₆	C₅×Q₈	1	4	yes	complemented
268	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₅	1	2	yes	—
270	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
271	C₄⋊Q₈	—	2	8	no	—
272	C₄⋊Q₈	—	2	2	no	—
273	C₄⋊Q₈	C₅×D₄	1	4	yes	—
274	#125	—	2	16	no	—
275	#125	—	2	4	no	—
276	#125	—	2	4	no	—
277	C₄×Q₈	—	2	8	no	—
278	C₄×Q₈	—	2	4	no	—
279	C₄×Q₈	—	2	4	no	—
280	C₄×Q₈	—	2	2	no	—
281	C₄×Q₈	—	2	2	no	—
282	C₄×Q₈	—	2	2	no	—
283	C₄×Q₈	—	2	2	no	—
284	C₄×Q₈	—	2	2	no	—
285	C₄×Q₈	C₅×D₄	1	4	yes	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	C₂³×C₅	1	2	yes	—
305	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
306	#107	—	2	2	no	—
307	#106	—	2	4	no	—
308	C₄⋊C₈	—	2	2	no	—
309	#103	—	2	2	no	—
310	#103	—	2	4	no	—
311	#103	—	2	2	no	—
312	#103	—	2	4	no	—
313	C₄×C₈	—	2	2	no	—
314	#95	—	2	2	no	—
315	#95	—	2	2	no	—
316	#95	—	2	2	no	—
317	C₂²×C₅	C₂×#120	1	1	yes	characteristic
318	C₂²×C₅	#548	1	1	yes	characteristic
319	C₂²×C₅	D₄×Q₈	1	1	yes	characteristic
320	C₂²×C₅	C₂×#135	1	1	yes	characteristic
321	C₂²×C₅	C₂×#137	1	1	yes	characteristic
322	C₂²×C₅	#577	1	1	yes	characteristic
323	C₂²×C₅	#578	1	1	yes	characteristic
324	C₄×C₅	—	2	4	no	—
325	C₄×C₅	—	2	2	no	—
326	C₄×C₅	—	4	2	no	—
327	C₄×C₅	—	4	2	no	—
328	C₄×C₅	—	4	4	no	—
329	C₄×C₅	—	4	2	no	—
330	C₄×C₅	—	4	2	no	—
331	C₄×C₅	—	8	2	no	—
332	C₄×C₅	—	8	1	no	—
333	C₄×C₅	#452	1	4	yes	—
334	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
335	C₄×C₅	#536	1	1	yes	characteristic
336	C₄×C₅	#548	1	1	yes	characteristic
337	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	4	2	no	—
351	C₂×Q₈	—	4	2	no	—
352	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
353	C₂×Q₈	C₂×C₅×Q₈	1	2	yes	—
354	C₂×Q₈	C₂×C₅×Q₈	1	2	yes	—
355	C₂×Q₈	C₅×#41	1	2	yes	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
363	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
364	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
365	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
367	Q₁₆	—	2	8	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
377	C₄⋊C₄	—	2	8	no	—
378	C₄⋊C₄	—	2	8	no	—
379	C₄⋊C₄	—	2	8	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₄⋊C₄	—	8	1	no	—
393	C₄⋊C₄	—	8	2	no	—
394	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
395	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
396	C₄²	—	2	8	no	—
397	C₄²	—	2	4	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	4	2	no	—
401	C₄²	C₂×C₅×D₄	1	2	yes	—
402	C₄²	C₂×C₅×D₄	1	2	yes	—
403	C₂×C₅	#2409	1	1	yes	characteristic
404	C₂×C₅	C₂×#452	1	1	yes	characteristic
405	C₂×C₅	#3013	1	1	yes	characteristic
406	C₂×C₅	#3365	1	1	yes	characteristic
407	C₂×C₅	#3374	1	1	yes	characteristic
408	C₂×C₅	#3383	1	1	yes	characteristic
409	C₂×C₅	#3387	1	1	yes	characteristic
410	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
411	Q₈	—	2	2	no	—
412	Q₈	—	2	2	no	—
413	Q₈	—	2	2	no	—
414	Q₈	—	2	2	no	—
415	Q₈	—	2	2	no	—
416	Q₈	—	4	4	no	—
417	Q₈	—	4	8	no	—
418	Q₈	—	4	1	no	—
419	Q₈	—	4	1	no	—
420	Q₈	C₅×C₂²⋊Q₈	1	4	yes	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	C₅×#120	1	2	yes	—
448	C₂×C₄	C₅×#120	1	2	yes	—
449	C₂×C₄	C₅×#135	1	2	yes	—
450	C₂×C₄	C₅×#137	1	2	yes	—
451	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
452	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
453	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
454	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
455	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
456	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
457	C₈	—	2	2	no	—
458	C₈	—	4	1	no	—
459	C₈	—	4	2	no	—
460	C₅	#24332	1	1	yes	characteristic, direct product factor, Sylow
461	C₂²	C₂×C₅×#120	1	1	yes	characteristic
462	C₂²	C₅×#548	1	1	yes	characteristic
463	C₂²	C₅×D₄×Q₈	1	1	yes	characteristic
464	C₂²	C₂×C₅×#135	1	1	yes	characteristic
465	C₂²	C₂×C₅×#137	1	1	yes	characteristic
466	C₂²	C₅×#577	1	1	yes	characteristic
467	C₂²	C₅×#578	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	4	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	4	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	8	1	no	—
476	C₄	—	8	2	no	—
477	C₄	C₅×#452	1	4	yes	—
478	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
479	C₄	C₅×#536	1	1	yes	characteristic
480	C₄	C₅×#548	1	1	yes	characteristic
481	C₄	C₅×D₄×Q₈	1	1	yes	characteristic
482	C₂	C₅×#2409	1	1	yes	characteristic
483	C₂	C₂×C₅×#452	1	1	yes	characteristic
484	C₂	C₅×#3013	1	1	yes	characteristic
485	C₂	C₅×#3365	1	1	yes	characteristic
486	C₂	C₅×#3374	1	1	yes	characteristic
487	C₂	C₅×#3383	1	1	yes	characteristic
488	C₂	C₅×#3387	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
45. #24332	C₅	direct (N × H)
52. C₂×C₅×Q₁₆	Q₈	semidirect
267. C₂×Q₁₆	C₅×Q₈	semidirect
460. C₅	#24332	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×#557	2
C₂×C₅×#475	2
C₂×C₄×C₅×Q₁₆	2
C₅×#2582	2
C₅×#2059	2
C₅×#2026	2
C₅×#1990	2
C₅×#1984	2
C₅×#1878	2
C₅×#1865	2
C₅×#1803	2
#24332	5

Subgroups — C5×#24332 #11947052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#24332 #11947052