Subgroups — C₅×#24191 #11946911

Order 1280.

1050 conjugacy classes of subgroups.

The subgroup lattice has 510 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×#462	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×#2043	C₂	1	2	yes	maximal
6	C₅×#2016	C₂	1	2	yes	maximal
7	C₅×#1984	C₂	1	1	yes	maximal, characteristic
8	C₅×#1956	C₂	1	1	yes	maximal, characteristic
9	C₅×#1878	C₂	1	2	yes	maximal
10	C₅×#1863	C₂	1	2	yes	maximal
11	C₅×#1803	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₅×Q₁₆	C₂²	1	2	yes	—
14	C₅×#557	—	2	4	no	—
15	C₅×#557	—	2	4	no	—
16	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#125	—	2	1	no	—
19	C₂×C₅×#125	—	2	2	no	—
20	C₂×C₄×C₅×Q₈	—	2	1	no	—
21	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
23	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
25	C₅×#462	—	2	4	no	—
26	C₄×C₅×Q₁₆	—	2	4	no	—
27	C₂×C₅×#107	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×#103	C₂²	1	2	yes	—
30	C₂×C₅×#103	C₂²	1	1	yes	characteristic
31	C₂×C₅×#103	C₂²	1	2	yes	—
32	C₂×C₅×#103	C₂²	1	1	yes	characteristic
33	C₂×C₅×#103	C₂²	1	2	yes	—
34	C₂×C₅×#103	C₂²	1	2	yes	—
35	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
36	C₅×#398	—	2	2	no	—
37	C₅×#391	—	2	1	no	—
38	C₅×#391	C₂²	1	2	yes	—
39	C₅×#389	—	2	1	no	—
40	C₅×#389	C₂²	1	2	yes	—
41	C₅×#384	C₂²	1	1	yes	characteristic
42	C₅×#340	C₂²	1	2	yes	—
43	C₅×#336	C₂²	1	2	yes	—
44	C₅×#336	C₂²	1	2	yes	—
45	#24191	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
47	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
48	C₂²×C₅×Q₈	C₂³	1	2	yes	—
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	—	2	4	no	—
53	C₂×C₅×Q₁₆	—	2	4	no	—
54	C₂×C₅×Q₁₆	—	2	2	no	—
55	C₂×C₅×Q₁₆	—	4	2	no	—
56	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂³	1	2	yes	—
58	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₅×C₄⋊Q₈	—	2	4	no	—
60	C₅×C₄⋊Q₈	—	2	4	no	—
61	C₅×C₄⋊Q₈	—	2	2	no	—
62	C₅×C₄⋊Q₈	D₄	1	4	yes	—
63	C₅×#125	—	2	16	no	—
64	C₅×#125	—	2	8	no	—
65	C₄×C₅×Q₈	—	2	8	no	—
66	C₄×C₅×Q₈	—	2	4	no	—
67	C₄×C₅×Q₈	—	2	4	no	—
68	C₄×C₅×Q₈	—	2	2	no	—
69	C₄×C₅×Q₈	—	2	2	no	—
70	C₄×C₅×Q₈	—	2	2	no	—
71	C₄×C₅×Q₈	—	2	2	no	—
72	C₄×C₅×Q₈	—	2	2	no	—
73	C₄×C₅×Q₈	D₄	1	4	yes	—
74	C₂×C₅×C₄⋊C₄	—	2	2	no	—
75	C₂×C₅×C₄⋊C₄	—	2	1	no	—
76	C₂×C₅×C₄⋊C₄	—	2	2	no	—
77	C₂×C₅×C₄⋊C₄	—	2	1	no	—
78	C₂×C₅×C₄⋊C₄	—	2	2	no	—
79	C₂×C₅×C₄⋊C₄	—	2	1	no	—
80	C₂×C₅×C₄⋊C₄	—	2	1	no	—
81	C₂×C₅×C₄⋊C₄	—	2	1	no	—
82	C₂×C₅×C₄⋊C₄	—	2	1	no	—
83	C₂×C₅×C₄⋊C₄	—	2	2	no	—
84	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
85	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
86	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
87	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₅	—	2	2	no	—
90	C₂×C₄²×C₅	—	2	1	no	—
91	C₂×C₄²×C₅	—	2	1	no	—
92	C₂×C₄²×C₅	C₂³	1	2	yes	—
93	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
94	C₅×#107	—	2	2	no	—
95	C₅×C₄⋊C₈	—	2	2	no	—
96	C₅×#103	—	2	2	no	—
97	C₅×#103	—	2	4	no	—
98	C₅×#103	—	2	4	no	—
99	C₅×#103	—	2	2	no	—
100	C₅×#103	—	4	2	no	—
101	C₅×#103	—	4	2	no	—
102	C₄×C₅×C₈	—	2	2	no	—
103	C₅×#95	—	2	2	no	—
104	C₅×#95	—	2	2	no	—
105	C₅×#95	—	2	2	no	—
106	C₂×#557	C₂×C₅	1	1	yes	characteristic
107	C₂×#462	C₂×C₅	1	1	yes	characteristic
108	C₂×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic
109	#2582	C₂×C₅	1	1	yes	characteristic
110	#2043	C₂×C₅	1	2	yes	—
111	#2016	C₂×C₅	1	2	yes	—
112	#1984	C₂×C₅	1	1	yes	characteristic
113	#1956	C₂×C₅	1	1	yes	characteristic
114	#1878	C₂×C₅	1	2	yes	—
115	#1863	C₂×C₅	1	2	yes	—
116	#1803	C₂×C₅	1	1	yes	characteristic
117	C₂×C₅×Q₈	—	2	2	no	—
118	C₂×C₅×Q₈	—	2	2	no	—
119	C₂×C₅×Q₈	—	2	2	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	—	2	2	no	—
126	C₂×C₅×Q₈	—	2	1	no	—
127	C₂×C₅×Q₈	—	2	1	no	—
128	C₂×C₅×Q₈	—	2	2	no	—
129	C₂×C₅×Q₈	—	2	1	no	—
130	C₂×C₅×Q₈	—	2	2	no	—
131	C₂×C₅×Q₈	—	2	1	no	—
132	C₂×C₅×Q₈	—	2	1	no	—
133	C₂×C₅×Q₈	—	2	2	no	—
134	C₂×C₅×Q₈	Q₁₆	1	4	yes	complemented
135	C₂×C₅×Q₈	C₂×D₄	1	4	yes	—
136	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
137	C₂×C₅×Q₈	#41	1	2	yes	—
138	C₂²×C₄×C₅	—	2	1	no	—
139	C₂²×C₄×C₅	—	2	2	no	—
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₂²×C₄×C₅	—	2	2	no	—
144	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	C₅×Q₁₆	—	2	8	no	—
150	C₅×Q₁₆	—	4	8	no	—
151	C₂×C₅×C₈	—	2	1	no	—
152	C₂×C₅×C₈	—	2	1	no	—
153	C₂×C₅×C₈	—	2	2	no	—
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	—	2	2	no	—
156	C₂×C₅×C₈	—	2	2	no	—
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	#41	1	2	yes	—
160	C₅×C₄⋊C₄	—	2	8	no	—
161	C₅×C₄⋊C₄	—	2	8	no	—
162	C₅×C₄⋊C₄	—	2	8	no	—
163	C₅×C₄⋊C₄	—	2	4	no	—
164	C₅×C₄⋊C₄	—	2	4	no	—
165	C₅×C₄⋊C₄	—	2	4	no	—
166	C₅×C₄⋊C₄	—	2	4	no	—
167	C₅×C₄⋊C₄	—	2	2	no	—
168	C₅×C₄⋊C₄	—	2	1	no	—
169	C₅×C₄⋊C₄	—	2	1	no	—
170	C₅×C₄⋊C₄	—	2	1	no	—
171	C₅×C₄⋊C₄	—	2	2	no	—
172	C₅×C₄⋊C₄	—	2	2	no	—
173	C₅×C₄⋊C₄	—	4	2	no	—
174	C₅×C₄⋊C₄	—	4	2	no	—
175	C₅×C₄⋊C₄	—	8	1	no	—
176	C₅×C₄⋊C₄	—	8	2	no	—
177	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
178	C₄²×C₅	—	2	8	no	—
179	C₄²×C₅	—	2	4	no	—
180	C₄²×C₅	—	2	2	no	—
181	C₄²×C₅	—	2	2	no	—
182	C₄²×C₅	—	4	2	no	—
183	C₄²×C₅	C₂×D₄	1	2	yes	—
184	C₄²×C₅	C₂×D₄	1	2	yes	—
185	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
186	C₂²×Q₁₆	C₂²×C₅	1	2	yes	—
187	#557	—	2	4	no	—
188	#557	—	2	4	no	—
189	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
190	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
191	C₂×#125	—	2	1	no	—
192	C₂×#125	—	2	2	no	—
193	C₂×C₄×Q₈	—	2	1	no	—
194	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
195	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
196	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
197	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
198	#462	—	2	4	no	—
199	C₄×Q₁₆	—	2	4	no	—
200	C₂×#107	C₂²×C₅	1	1	yes	characteristic
201	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
202	C₂×#103	C₂²×C₅	1	2	yes	—
203	C₂×#103	C₂²×C₅	1	2	yes	—
204	C₂×#103	C₂²×C₅	1	1	yes	characteristic
205	C₂×#103	C₂²×C₅	1	1	yes	characteristic
206	C₂×#103	C₂²×C₅	1	2	yes	—
207	C₂×#103	C₂²×C₅	1	2	yes	—
208	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
209	#398	—	2	2	no	—
210	#391	—	2	1	no	—
211	#391	C₂²×C₅	1	2	yes	—
212	#389	—	2	1	no	—
213	#389	C₂²×C₅	1	2	yes	—
214	#384	C₂²×C₅	1	1	yes	characteristic
215	#340	C₂²×C₅	1	2	yes	—
216	#336	C₂²×C₅	1	2	yes	—
217	#336	C₂²×C₅	1	2	yes	—
218	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
219	C₅×Q₈	—	2	8	no	—
220	C₅×Q₈	—	2	2	no	—
221	C₅×Q₈	—	2	2	no	—
222	C₅×Q₈	—	2	2	no	—
223	C₅×Q₈	—	2	2	no	—
224	C₅×Q₈	—	2	4	no	—
225	C₅×Q₈	—	2	4	no	—
226	C₅×Q₈	—	4	2	no	—
227	C₅×Q₈	—	4	2	no	—
228	C₅×Q₈	—	4	1	no	—
229	C₅×Q₈	—	4	1	no	—
230	C₅×Q₈	—	4	1	no	—
231	C₅×Q₈	—	4	1	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	4	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	4	1	no	—
244	C₂×C₄×C₅	—	4	1	no	—
245	C₂×C₄×C₅	—	4	2	no	—
246	C₂×C₄×C₅	—	4	1	no	—
247	C₂×C₄×C₅	—	4	2	no	—
248	C₂×C₄×C₅	—	4	1	no	—
249	C₂×C₄×C₅	—	4	1	no	—
250	C₂×C₄×C₅	—	4	1	no	—
251	C₂×C₄×C₅	—	4	1	no	—
252	C₂×C₄×C₅	—	4	2	no	—
253	C₂×C₄×C₅	—	4	2	no	—
254	C₂×C₄×C₅	—	4	2	no	—
255	C₂×C₄×C₅	—	4	1	no	—
256	C₂×C₄×C₅	—	4	1	no	—
257	C₂×C₄×C₅	#120	1	2	yes	—
258	C₂×C₄×C₅	#120	1	2	yes	—
259	C₂×C₄×C₅	C₂×Q₁₆	1	4	yes	—
260	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
261	C₂×C₄×C₅	#137	1	2	yes	—
262	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
266	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
267	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
268	C₅×C₈	—	2	2	no	—
269	C₅×C₈	—	4	1	no	—
270	C₅×C₈	—	4	2	no	—
271	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
272	C₂²×Q₈	C₂³×C₅	1	2	yes	—
273	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
274	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
275	C₂×Q₁₆	—	2	2	no	—
276	C₂×Q₁₆	—	2	2	no	—
277	C₂×Q₁₆	—	2	4	no	—
278	C₂×Q₁₆	—	2	4	no	—
279	C₂×Q₁₆	—	2	2	no	—
280	C₂×Q₁₆	—	4	2	no	—
281	C₂²×C₈	C₂³×C₅	1	2	yes	—
282	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
284	C₄⋊Q₈	—	2	4	no	—
285	C₄⋊Q₈	—	2	4	no	—
286	C₄⋊Q₈	—	2	2	no	—
287	C₄⋊Q₈	C₅×D₄	1	4	yes	—
288	#125	—	2	16	no	—
289	#125	—	2	8	no	—
290	C₄×Q₈	—	2	8	no	—
291	C₄×Q₈	—	2	4	no	—
292	C₄×Q₈	—	2	4	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×Q₈	—	2	2	no	—
295	C₄×Q₈	—	2	2	no	—
296	C₄×Q₈	—	2	2	no	—
297	C₄×Q₈	—	2	2	no	—
298	C₄×Q₈	C₅×D₄	1	4	yes	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
314	C₂×C₄²	—	2	2	no	—
315	C₂×C₄²	—	2	1	no	—
316	C₂×C₄²	—	2	1	no	—
317	C₂×C₄²	C₂³×C₅	1	2	yes	—
318	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
319	#107	—	2	2	no	—
320	C₄⋊C₈	—	2	2	no	—
321	#103	—	2	2	no	—
322	#103	—	2	4	no	—
323	#103	—	2	4	no	—
324	#103	—	2	2	no	—
325	#103	—	4	2	no	—
326	#103	—	4	2	no	—
327	C₄×C₈	—	2	2	no	—
328	#95	—	2	2	no	—
329	#95	—	2	2	no	—
330	#95	—	2	2	no	—
331	C₂²×C₅	C₂×#120	1	1	yes	characteristic
332	C₂²×C₅	#548	1	1	yes	characteristic
333	C₂²×C₅	#550	1	1	yes	characteristic
334	C₂²×C₅	C₂²×Q₁₆	1	1	yes	characteristic
335	C₂²×C₅	C₂×#137	1	1	yes	characteristic
336	C₂²×C₅	#577	1	1	yes	characteristic
337	C₂²×C₅	#578	1	1	yes	characteristic
338	C₄×C₅	—	2	4	no	—
339	C₄×C₅	—	2	2	no	—
340	C₄×C₅	—	4	2	no	—
341	C₄×C₅	—	4	4	no	—
342	C₄×C₅	—	4	2	no	—
343	C₄×C₅	—	4	2	no	—
344	C₄×C₅	—	4	2	no	—
345	C₄×C₅	—	8	2	no	—
346	C₄×C₅	—	8	1	no	—
347	C₄×C₅	#451	1	4	yes	—
348	C₄×C₅	#525	1	1	yes	characteristic
349	C₄×C₅	#537	1	1	yes	characteristic
350	C₄×C₅	#546	1	1	yes	characteristic
351	C₄×C₅	#547	1	1	yes	characteristic
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	C₅×Q₁₆	1	4	yes	complemented
370	C₂×Q₈	C₂×C₅×D₄	1	4	yes	—
371	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
372	C₂×Q₈	C₅×#41	1	2	yes	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
380	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
382	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
383	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
384	Q₁₆	—	2	8	no	—
385	Q₁₆	—	4	8	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	C₅×#41	1	2	yes	—
395	C₄⋊C₄	—	2	8	no	—
396	C₄⋊C₄	—	2	8	no	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	—	8	1	no	—
411	C₄⋊C₄	—	8	2	no	—
412	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
413	C₄²	—	2	8	no	—
414	C₄²	—	2	4	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	4	2	no	—
418	C₄²	C₂×C₅×D₄	1	2	yes	—
419	C₄²	C₂×C₅×D₄	1	2	yes	—
420	C₂×C₅	#2407	1	1	yes	characteristic
421	C₂×C₅	C₂×#451	1	1	yes	characteristic
422	C₂×C₅	#3013	1	1	yes	characteristic
423	C₂×C₅	#3363	1	1	yes	characteristic
424	C₂×C₅	#3374	1	1	yes	characteristic
425	C₂×C₅	#3395	1	1	yes	characteristic
426	C₂×C₅	#3400	1	1	yes	characteristic
427	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
428	Q₈	—	2	8	no	—
429	Q₈	—	2	2	no	—
430	Q₈	—	2	2	no	—
431	Q₈	—	2	2	no	—
432	Q₈	—	2	2	no	—
433	Q₈	—	2	4	no	—
434	Q₈	—	2	4	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	4	2	no	—
437	Q₈	—	4	1	no	—
438	Q₈	—	4	1	no	—
439	Q₈	—	4	1	no	—
440	Q₈	—	4	1	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	C₅×#120	1	2	yes	—
467	C₂×C₄	C₅×#120	1	2	yes	—
468	C₂×C₄	C₂×C₅×Q₁₆	1	4	yes	—
469	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
470	C₂×C₄	C₅×#137	1	2	yes	—
471	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
472	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
473	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
474	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
475	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
476	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
477	C₈	—	2	2	no	—
478	C₈	—	4	1	no	—
479	C₈	—	4	2	no	—
480	C₅	#24191	1	1	yes	characteristic, direct product factor, Sylow
481	C₂²	C₂×C₅×#120	1	1	yes	characteristic
482	C₂²	C₅×#548	1	1	yes	characteristic
483	C₂²	C₅×#550	1	1	yes	characteristic
484	C₂²	C₂²×C₅×Q₁₆	1	1	yes	characteristic
485	C₂²	C₂×C₅×#137	1	1	yes	characteristic
486	C₂²	C₅×#577	1	1	yes	characteristic
487	C₂²	C₅×#578	1	1	yes	characteristic
488	C₄	—	2	4	no	—
489	C₄	—	2	2	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	2	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	4	no	—
494	C₄	—	4	2	no	—
495	C₄	—	8	1	no	—
496	C₄	—	8	2	no	—
497	C₄	C₅×#451	1	4	yes	—
498	C₄	C₅×#525	1	1	yes	characteristic
499	C₄	C₅×#537	1	1	yes	characteristic
500	C₄	C₅×#546	1	1	yes	characteristic
501	C₄	C₅×#547	1	1	yes	characteristic
502	C₂	C₅×#2407	1	1	yes	characteristic
503	C₂	C₂×C₅×#451	1	1	yes	characteristic
504	C₂	C₅×#3013	1	1	yes	characteristic
505	C₂	C₅×#3363	1	1	yes	characteristic
506	C₂	C₅×#3374	1	1	yes	characteristic
507	C₂	C₅×#3395	1	1	yes	characteristic
508	C₂	C₅×#3400	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. #24191	C₅	direct (N × H)
134. C₂×C₅×Q₈	Q₁₆	semidirect
369. C₂×Q₈	C₅×Q₁₆	semidirect
480. C₅	#24191	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×#462	2
C₂×C₄×C₅×Q₁₆	2
C₅×#2582	2
C₅×#2043	2
C₅×#2016	2
C₅×#1984	2
C₅×#1956	2
C₅×#1878	2
C₅×#1863	2
C₅×#1803	2
#24191	5

Subgroups — C5×#24191 #11946911

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#24191 #11946911