Subgroups — C₅×#21124 #11943844

Order 1280.

922 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#440	C₂	1	1	yes	maximal, characteristic
2	C₅×#2293	C₂	1	1	yes	maximal, characteristic
3	C₄²×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1926	C₂	1	1	yes	maximal, characteristic
5	C₅×#1925	C₂	1	1	yes	maximal, characteristic
6	C₅×#1921	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1918	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1880	C₂	1	1	yes	maximal, characteristic
9	C₅×#1880	C₂	1	1	yes	maximal, characteristic
10	C₅×#1865	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1863	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1776	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1763	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1762	C₂	1	1	yes	maximal, characteristic
15	C₅×#1745	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₅×#117	—	2	1	no	—
22	C₅×#440	C₄	1	8	yes	complemented
23	C₂×C₅×#107	C₂²	1	1	yes	characteristic
24	C₂×C₅×#107	C₂²	1	1	yes	characteristic
25	C₂×C₅×#106	C₂²	1	1	yes	characteristic
26	C₂×C₅×#103	C₂²	1	1	yes	characteristic
27	C₂×C₅×#103	C₂²	1	1	yes	characteristic
28	C₂×C₅×#103	C₂²	1	1	yes	characteristic
29	C₂×C₅×#102	C₂²	1	1	yes	characteristic
30	C₂×C₅×#102	C₂²	1	1	yes	characteristic
31	C₂×C₅×#102	C₂²	1	1	yes	characteristic
32	C₂×C₅×#97	C₂²	1	1	yes	characteristic
33	C₂×C₅×#97	C₂²	1	1	yes	characteristic
34	C₅×#390	C₂²	1	1	yes	characteristic
35	C₅×#390	C₂²	1	1	yes	characteristic
36	C₅×#389	C₂²	1	1	yes	characteristic
37	C₅×#389	C₂²	1	1	yes	characteristic
38	C₅×#388	—	2	1	no	—
39	C₅×#388	—	2	1	no	—
40	C₄×C₅×C₄⋊C₄	—	2	1	no	—
41	C₄×C₅×C₄⋊C₄	—	2	1	no	—
42	C₄×C₅×C₄⋊C₄	—	2	1	no	—
43	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
48	C₄³×C₅	—	2	1	no	—
49	C₄³×C₅	C₂²	1	1	yes	characteristic
50	C₅×#340	C₂²	1	1	yes	characteristic
51	C₅×#340	C₂²	1	1	yes	characteristic
52	C₅×#340	C₂²	1	1	yes	characteristic
53	C₅×#340	C₂²	1	1	yes	characteristic
54	C₅×#340	C₂²	1	1	yes	characteristic
55	C₅×#340	C₂²	1	1	yes	characteristic
56	C₅×#336	C₂²	1	1	yes	characteristic
57	C₅×#336	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	C₅×#336	C₂²	1	1	yes	characteristic
60	#21124	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
62	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₅	—	2	1	no	—
64	C₂×C₅×SD₁₆	—	2	2	no	—
65	C₂×C₅×SD₁₆	—	2	2	no	—
66	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	—
67	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₄×C₅×Q₈	—	2	2	no	—
72	C₄×C₅×Q₈	—	2	2	no	—
73	C₄×C₅×Q₈	—	2	2	no	—
74	C₄×C₅×Q₈	—	2	2	no	—
75	C₄×C₅×Q₈	—	2	2	no	—
76	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
77	C₄×C₅×D₄	—	2	2	no	—
78	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
79	C₅×#117	—	4	4	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	1	no	—
84	C₂×C₅×C₄⋊C₄	—	2	1	no	—
85	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₄²×C₅	—	2	1	no	—
97	C₂×C₄²×C₅	—	2	1	no	—
98	C₂×C₄²×C₅	—	2	1	no	—
99	C₂×C₄²×C₅	—	2	1	no	—
100	C₂×C₄²×C₅	—	2	1	no	—
101	C₂×C₄²×C₅	—	2	1	no	—
102	C₂×C₄²×C₅	—	2	1	no	—
103	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
110	C₅×#107	—	2	2	no	—
111	C₅×#107	C₂×C₄	1	4	yes	—
112	C₅×#106	—	2	2	no	—
113	C₅×#103	—	2	2	no	—
114	C₅×#103	—	2	2	no	—
115	C₅×#103	C₂×C₄	1	4	yes	—
116	C₅×#102	—	2	2	no	—
117	C₅×#102	—	2	2	no	—
118	C₅×#102	C₂×C₄	1	4	yes	—
119	C₅×#97	—	2	2	no	—
120	C₅×#97	C₂×C₄	1	4	yes	—
121	C₅×#95	—	2	1	no	—
122	C₅×#95	—	2	1	no	—
123	C₅×#95	—	2	1	no	—
124	C₅×#95	—	2	1	no	—
125	C₅×#95	—	2	1	no	—
126	C₅×#95	—	2	1	no	—
127	C₂×#440	C₂×C₅	1	1	yes	characteristic
128	#2293	C₂×C₅	1	1	yes	characteristic
129	C₄²×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
130	#1926	C₂×C₅	1	1	yes	characteristic
131	#1925	C₂×C₅	1	1	yes	characteristic
132	#1921	C₂×C₅	1	1	yes	characteristic, complemented
133	#1918	C₂×C₅	1	1	yes	characteristic, complemented
134	#1880	C₂×C₅	1	1	yes	characteristic
135	#1880	C₂×C₅	1	1	yes	characteristic
136	#1865	C₂×C₅	1	1	yes	characteristic, complemented
137	#1863	C₂×C₅	1	1	yes	characteristic, complemented
138	#1776	C₂×C₅	1	1	yes	characteristic, complemented
139	#1763	C₂×C₅	1	1	yes	characteristic, complemented
140	#1762	C₂×C₅	1	1	yes	characteristic
141	#1745	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂⁴×C₅	—	2	1	no	—
143	C₂×C₅×Q₈	—	2	1	no	—
144	C₂×C₅×Q₈	—	2	1	no	—
145	C₂×C₅×Q₈	—	2	1	no	—
146	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
147	C₂×C₅×Q₈	#41	1	2	yes	—
148	C₂×C₅×Q₈	#41	1	2	yes	—
149	C₂×C₅×D₄	—	2	1	no	—
150	C₂×C₅×D₄	—	2	1	no	—
151	C₂×C₅×D₄	—	2	1	no	—
152	C₂×C₅×D₄	—	2	1	no	—
153	C₂×C₅×D₄	—	2	1	no	—
154	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
155	C₂²×C₄×C₅	—	2	1	no	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	—	2	1	no	—
158	C₂²×C₄×C₅	—	2	1	no	—
159	C₂²×C₄×C₅	—	2	1	no	—
160	C₂²×C₄×C₅	—	2	4	no	—
161	C₂²×C₄×C₅	—	2	1	no	—
162	C₂²×C₄×C₅	—	2	1	no	—
163	C₂²×C₄×C₅	—	4	2	no	—
164	C₂²×C₄×C₅	—	4	2	no	—
165	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
172	C₅×SD₁₆	—	2	8	no	—
173	C₂×C₅×C₈	—	2	1	no	—
174	C₂×C₅×C₈	—	2	1	no	—
175	C₂×C₅×C₈	—	2	1	no	—
176	C₂×C₅×C₈	—	2	1	no	—
177	C₂×C₅×C₈	—	2	1	no	—
178	C₂×C₅×C₈	—	2	1	no	—
179	C₂×C₅×C₈	—	2	1	no	—
180	C₂×C₅×C₈	—	2	1	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
184	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
185	C₅×C₄⋊C₄	—	2	4	no	—
186	C₅×C₄⋊C₄	—	2	4	no	—
187	C₅×C₄⋊C₄	—	2	4	no	—
188	C₅×C₄⋊C₄	—	2	1	no	—
189	C₅×C₄⋊C₄	—	2	1	no	—
190	C₅×C₄⋊C₄	—	2	1	no	—
191	C₅×C₄⋊C₄	—	2	1	no	—
192	C₅×C₄⋊C₄	—	2	1	no	—
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	—	2	1	no	—
195	C₅×C₄⋊C₄	—	2	1	no	—
196	C₅×C₄⋊C₄	—	4	2	no	—
197	C₅×C₄⋊C₄	—	4	2	no	—
198	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
199	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
200	C₅×C₄⋊C₄	#41	1	2	yes	—
201	C₅×C₄⋊C₄	#41	1	2	yes	—
202	C₅×C₂²⋊C₄	—	2	4	no	—
203	C₅×C₂²⋊C₄	—	4	2	no	—
204	C₅×C₂²⋊C₄	—	4	2	no	—
205	C₅×C₂²⋊C₄	—	4	2	no	—
206	C₅×C₂²⋊C₄	—	4	2	no	—
207	C₄²×C₅	—	2	4	no	—
208	C₄²×C₅	—	2	4	no	—
209	C₄²×C₅	—	2	4	no	—
210	C₄²×C₅	—	2	2	no	—
211	C₄²×C₅	—	2	2	no	—
212	C₄²×C₅	—	2	1	no	—
213	C₄²×C₅	—	2	1	no	—
214	C₄²×C₅	—	2	1	no	—
215	C₄²×C₅	—	2	1	no	—
216	C₄²×C₅	—	4	1	no	—
217	C₄²×C₅	—	4	1	no	—
218	C₄²×C₅	—	4	2	no	—
219	C₄²×C₅	—	4	2	no	—
220	C₄²×C₅	—	4	2	no	—
221	C₄²×C₅	—	4	2	no	—
222	C₄²×C₅	C₂²×C₄	1	2	yes	—
223	C₄²×C₅	#41	1	2	yes	—
224	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
225	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
228	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
229	C₂×#117	—	2	1	no	—
230	#440	C₄×C₅	1	8	yes	complemented
231	C₂×#107	C₂²×C₅	1	1	yes	characteristic
232	C₂×#107	C₂²×C₅	1	1	yes	characteristic
233	C₂×#106	C₂²×C₅	1	1	yes	characteristic
234	C₂×#103	C₂²×C₅	1	1	yes	characteristic
235	C₂×#103	C₂²×C₅	1	1	yes	characteristic
236	C₂×#103	C₂²×C₅	1	1	yes	characteristic
237	C₂×#102	C₂²×C₅	1	1	yes	characteristic
238	C₂×#102	C₂²×C₅	1	1	yes	characteristic
239	C₂×#102	C₂²×C₅	1	1	yes	characteristic
240	C₂×#97	C₂²×C₅	1	1	yes	characteristic
241	C₂×#97	C₂²×C₅	1	1	yes	characteristic
242	#390	C₂²×C₅	1	1	yes	characteristic
243	#390	C₂²×C₅	1	1	yes	characteristic
244	#389	C₂²×C₅	1	1	yes	characteristic
245	#389	C₂²×C₅	1	1	yes	characteristic
246	#388	—	2	1	no	—
247	#388	—	2	1	no	—
248	C₄×C₄⋊C₄	—	2	1	no	—
249	C₄×C₄⋊C₄	—	2	1	no	—
250	C₄×C₄⋊C₄	—	2	1	no	—
251	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
252	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
253	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
254	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
255	C₄×C₂²⋊C₄	—	2	1	no	—
256	C₄³	—	2	1	no	—
257	C₄³	C₂²×C₅	1	1	yes	characteristic
258	#340	C₂²×C₅	1	1	yes	characteristic
259	#340	C₂²×C₅	1	1	yes	characteristic
260	#340	C₂²×C₅	1	1	yes	characteristic
261	#340	C₂²×C₅	1	1	yes	characteristic
262	#340	C₂²×C₅	1	1	yes	characteristic
263	#340	C₂²×C₅	1	1	yes	characteristic
264	#336	C₂²×C₅	1	1	yes	characteristic
265	#336	C₂²×C₅	1	1	yes	characteristic
266	#336	C₂²×C₅	1	1	yes	characteristic
267	#336	C₂²×C₅	1	1	yes	characteristic
268	C₂³×C₅	—	2	2	no	—
269	C₂³×C₅	—	4	1	no	—
270	C₂³×C₅	—	4	1	no	—
271	C₂³×C₅	—	4	1	no	—
272	C₂³×C₅	—	4	1	no	—
273	C₂³×C₅	—	4	1	no	—
274	C₂³×C₅	—	4	1	no	—
275	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
276	C₅×Q₈	—	2	2	no	—
277	C₅×Q₈	—	2	2	no	—
278	C₅×Q₈	—	2	2	no	—
279	C₅×Q₈	#117	1	4	yes	complemented
280	C₅×D₄	—	2	2	no	—
281	C₅×D₄	—	2	2	no	—
282	C₅×D₄	—	4	1	no	—
283	C₅×D₄	—	4	1	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	2	no	—
300	C₂×C₄×C₅	—	2	2	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	4	8	no	—
306	C₂×C₄×C₅	—	4	1	no	—
307	C₂×C₄×C₅	—	4	1	no	—
308	C₂×C₄×C₅	—	4	1	no	—
309	C₂×C₄×C₅	—	4	1	no	—
310	C₂×C₄×C₅	—	4	1	no	—
311	C₂×C₄×C₅	—	4	1	no	—
312	C₂×C₄×C₅	—	4	1	no	—
313	C₂×C₄×C₅	—	4	1	no	—
314	C₂×C₄×C₅	—	4	1	no	—
315	C₂×C₄×C₅	—	4	1	no	—
316	C₂×C₄×C₅	—	4	1	no	—
317	C₂×C₄×C₅	—	4	1	no	—
318	C₂×C₄×C₅	—	4	1	no	—
319	C₂×C₄×C₅	—	4	1	no	—
320	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
321	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
322	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
323	C₂×C₄×C₅	#137	1	2	yes	—
324	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
325	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
326	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
327	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
328	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
329	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
330	C₅×C₈	—	2	2	no	—
331	C₅×C₈	—	2	2	no	—
332	C₅×C₈	—	4	1	no	—
333	C₅×C₈	—	4	1	no	—
334	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
335	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
336	C₂³×C₄	—	2	1	no	—
337	C₂×SD₁₆	—	2	2	no	—
338	C₂×SD₁₆	—	2	2	no	—
339	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	—
340	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
342	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
343	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
344	C₄×Q₈	—	2	2	no	—
345	C₄×Q₈	—	2	2	no	—
346	C₄×Q₈	—	2	2	no	—
347	C₄×Q₈	—	2	2	no	—
348	C₄×Q₈	—	2	2	no	—
349	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
350	C₄×D₄	—	2	2	no	—
351	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
352	#117	—	4	4	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	—	2	1	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
377	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
378	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
379	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
383	#107	—	2	2	no	—
384	#107	C₂×C₄×C₅	1	4	yes	—
385	#106	—	2	2	no	—
386	#103	—	2	2	no	—
387	#103	—	2	2	no	—
388	#103	C₂×C₄×C₅	1	4	yes	—
389	#102	—	2	2	no	—
390	#102	—	2	2	no	—
391	#102	C₂×C₄×C₅	1	4	yes	—
392	#97	—	2	2	no	—
393	#97	C₂×C₄×C₅	1	4	yes	—
394	#95	—	2	1	no	—
395	#95	—	2	1	no	—
396	#95	—	2	1	no	—
397	#95	—	2	1	no	—
398	#95	—	2	1	no	—
399	#95	—	2	1	no	—
400	C₂²×C₅	—	4	2	no	—
401	C₂²×C₅	—	4	2	no	—
402	C₂²×C₅	—	4	2	no	—
403	C₂²×C₅	—	8	1	no	—
404	C₂²×C₅	—	8	1	no	—
405	C₂²×C₅	—	8	1	no	—
406	C₂²×C₅	—	8	1	no	—
407	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
408	C₂²×C₅	#525	1	1	yes	characteristic
409	C₂²×C₅	#525	1	1	yes	characteristic
410	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
411	C₂²×C₅	C₂×#137	1	1	yes	characteristic
412	C₂²×C₅	#575	1	1	yes	characteristic
413	C₂²×C₅	#575	1	1	yes	characteristic
414	C₄×C₅	—	2	2	no	—
415	C₄×C₅	—	2	2	no	—
416	C₄×C₅	—	2	2	no	—
417	C₄×C₅	—	2	2	no	—
418	C₄×C₅	—	2	4	no	—
419	C₄×C₅	—	4	1	no	—
420	C₄×C₅	—	4	2	no	—
421	C₄×C₅	—	4	1	no	—
422	C₄×C₅	—	4	2	no	—
423	C₄×C₅	—	4	2	no	—
424	C₄×C₅	—	4	2	no	—
425	C₄×C₅	—	8	1	no	—
426	C₄×C₅	—	8	1	no	—
427	C₄×C₅	C₂×#117	1	1	yes	characteristic
428	C₄×C₅	C₄×#41	1	1	yes	characteristic
429	C₄×C₅	#529	1	1	yes	characteristic
430	C₄×C₅	#529	1	1	yes	characteristic
431	C₂⁴	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
436	C₂×Q₈	C₅×#41	1	2	yes	—
437	C₂×Q₈	C₅×#41	1	2	yes	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	4	2	no	—
453	C₂²×C₄	—	4	2	no	—
454	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
456	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
457	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
458	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
460	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
461	SD₁₆	—	2	8	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
473	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	2	4	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	4	2	no	—
486	C₄⋊C₄	—	4	2	no	—
487	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
488	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
489	C₄⋊C₄	C₅×#41	1	2	yes	—
490	C₄⋊C₄	C₅×#41	1	2	yes	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	4	2	no	—
493	C₂²⋊C₄	—	4	2	no	—
494	C₂²⋊C₄	—	4	2	no	—
495	C₂²⋊C₄	—	4	2	no	—
496	C₄²	—	2	4	no	—
497	C₄²	—	2	4	no	—
498	C₄²	—	2	4	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	2	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	4	1	no	—
506	C₄²	—	4	1	no	—
507	C₄²	—	4	2	no	—
508	C₄²	—	4	2	no	—
509	C₄²	—	4	2	no	—
510	C₄²	—	4	2	no	—
511	C₄²	C₂²×C₄×C₅	1	2	yes	—
512	C₄²	C₅×#41	1	2	yes	—
513	C₂×C₅	—	8	2	no	—
514	C₂×C₅	#2290	1	1	yes	characteristic
515	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
516	C₂×C₅	C₄×#137	1	1	yes	characteristic
517	C₂×C₅	#3111	1	1	yes	characteristic
518	C₂×C₅	#3112	1	1	yes	characteristic
519	C₂×C₅	#3115	1	1	yes	characteristic
520	C₂×C₅	#3117	1	1	yes	characteristic
521	C₂³	—	2	2	no	—
522	C₂³	—	4	1	no	—
523	C₂³	—	4	1	no	—
524	C₂³	—	4	1	no	—
525	C₂³	—	4	1	no	—
526	C₂³	—	4	1	no	—
527	C₂³	—	4	1	no	—
528	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
529	Q₈	—	2	2	no	—
530	Q₈	—	2	2	no	—
531	Q₈	—	2	2	no	—
532	Q₈	C₅×#117	1	4	yes	complemented
533	D₄	—	2	2	no	—
534	D₄	—	2	2	no	—
535	D₄	—	4	1	no	—
536	D₄	—	4	1	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	4	8	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
574	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
575	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
576	C₂×C₄	C₅×#137	1	2	yes	—
577	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
578	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
579	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
580	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
581	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
582	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
583	C₈	—	2	2	no	—
584	C₈	—	2	2	no	—
585	C₈	—	4	1	no	—
586	C₈	—	4	1	no	—
587	C₅	#21124	1	1	yes	characteristic, direct product factor, Sylow
588	C₂²	—	4	2	no	—
589	C₂²	—	4	2	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	8	1	no	—
592	C₂²	—	8	1	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
596	C₂²	C₅×#525	1	1	yes	characteristic
597	C₂²	C₅×#525	1	1	yes	characteristic
598	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
599	C₂²	C₂×C₅×#137	1	1	yes	characteristic
600	C₂²	C₅×#575	1	1	yes	characteristic
601	C₂²	C₅×#575	1	1	yes	characteristic
602	C₄	—	2	4	no	—
603	C₄	—	2	2	no	—
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	2	no	—
612	C₄	—	4	2	no	—
613	C₄	—	8	1	no	—
614	C₄	—	8	1	no	—
615	C₄	C₂×C₅×#117	1	1	yes	characteristic
616	C₄	C₄×C₅×#41	1	1	yes	characteristic
617	C₄	C₅×#529	1	1	yes	characteristic
618	C₄	C₅×#529	1	1	yes	characteristic
619	C₂	—	8	2	no	—
620	C₂	C₅×#2290	1	1	yes	characteristic
621	C₂	C₄×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
622	C₂	C₄×C₅×#137	1	1	yes	characteristic
623	C₂	C₅×#3111	1	1	yes	characteristic
624	C₂	C₅×#3112	1	1	yes	characteristic
625	C₂	C₅×#3115	1	1	yes	characteristic
626	C₂	C₅×#3117	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₄²×C₅×Q₈	C₂	semidirect
6. C₅×#1921	C₂	semidirect
7. C₅×#1918	C₂	semidirect
10. C₅×#1865	C₂	semidirect
11. C₅×#1863	C₂	semidirect
12. C₅×#1776	C₂	semidirect
13. C₅×#1763	C₂	semidirect
15. C₅×#1745	C₂	semidirect
22. C₅×#440	C₄	semidirect
60. #21124	C₅	direct (N × H)
129. C₄²×Q₈	C₂×C₅	semidirect
132. #1921	C₂×C₅	semidirect
133. #1918	C₂×C₅	semidirect
136. #1865	C₂×C₅	semidirect
137. #1863	C₂×C₅	semidirect
138. #1776	C₂×C₅	semidirect
139. #1763	C₂×C₅	semidirect
141. #1745	C₂×C₅	semidirect
230. #440	C₄×C₅	semidirect
279. C₅×Q₈	#117	semidirect
532. Q₈	C₅×#117	semidirect
587. C₅	#21124	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×#440	2
C₅×#2293	2
C₄²×C₅×Q₈	2
C₅×#1926	2
C₅×#1925	2
C₅×#1921	2
C₅×#1918	2
C₅×#1880	2
C₅×#1865	2
C₅×#1863	2
C₅×#1776	2
C₅×#1763	2
C₅×#1762	2
C₅×#1745	2
#21124	5

Subgroups — C5×#21124 #11943844

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21124 #11943844