Subgroups — C₅×#24916 #11947636

Order 1280.

1036 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#449	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2422	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2341	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2093	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2076	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2054	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1936	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1924	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1863	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1803	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#123	—	2	1	no	—
20	C₂×C₅×#121	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
24	C₅×#449	—	2	4	no	—
25	C₅×#440	—	2	4	no	—
26	C₂×C₅×#107	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
30	C₂×C₅×#103	C₂²	1	1	yes	characteristic
31	C₂×C₅×#103	C₂²	1	1	yes	characteristic
32	C₂×C₅×#102	C₂²	1	1	yes	characteristic
33	C₂×C₅×#102	C₂²	1	1	yes	characteristic
34	C₂×C₅×#102	C₂²	1	1	yes	characteristic
35	C₂×C₅×#102	C₂²	1	1	yes	characteristic
36	C₂×C₅×#102	C₂²	1	1	yes	characteristic
37	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₅×#97	C₂²	1	1	yes	characteristic
40	C₅×#397	—	2	1	no	—
41	C₅×#394	—	2	1	no	—
42	C₅×#390	—	2	1	no	—
43	C₅×#390	—	2	1	no	—
44	C₅×#390	C₂²	1	1	yes	characteristic
45	C₅×#390	C₂²	1	1	yes	characteristic
46	C₅×#390	C₂²	1	1	yes	characteristic
47	C₅×#389	C₂²	1	1	yes	characteristic
48	C₅×#385	—	2	1	no	—
49	C₅×#384	C₂²	1	1	yes	characteristic
50	C₅×#380	—	2	1	no	—
51	C₅×#380	C₂²	1	1	yes	characteristic
52	C₅×#380	C₂²	1	1	yes	characteristic
53	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
54	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
55	C₅×#340	C₂²	1	1	yes	characteristic
56	C₅×#340	C₂²	1	1	yes	characteristic
57	C₅×#340	C₂²	1	1	yes	characteristic
58	C₅×#340	C₂²	1	1	yes	characteristic
59	C₅×#336	C₂²	1	1	yes	characteristic
60	C₅×#336	C₂²	1	1	yes	characteristic
61	#24916	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂×C₅×#41	—	2	2	no	—
63	C₂×C₅×#41	—	2	2	no	—
64	C₂×C₅×#41	—	2	2	no	—
65	C₂×C₅×#41	—	2	2	no	—
66	C₂×C₅×#41	—	4	1	no	—
67	C₂×C₅×#41	—	4	1	no	—
68	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
69	C₂²×C₅×D₄	—	2	1	no	—
70	C₂²×C₅×D₄	—	2	1	no	—
71	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
72	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₅	—	2	1	no	—
74	C₂³×C₄×C₅	—	2	1	no	—
75	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂×C₅×SD₁₆	—	2	2	no	—
77	C₂×C₅×SD₁₆	—	2	2	no	—
78	C₂×C₅×SD₁₆	D₄	1	4	yes	—
79	C₂×C₅×D₈	—	2	2	no	—
80	C₂×C₅×D₈	—	2	2	no	—
81	C₂×C₅×D₈	—	4	1	no	—
82	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
86	C₅×#123	—	4	4	no	—
87	C₅×#121	—	2	2	no	—
88	C₅×#121	—	4	1	no	—
89	C₄×C₅×Q₈	—	2	2	no	—
90	C₄×C₅×Q₈	—	2	2	no	—
91	C₄×C₅×Q₈	—	4	1	no	—
92	C₄×C₅×Q₈	—	4	1	no	—
93	C₄×C₅×D₄	—	2	2	no	—
94	C₄×C₅×D₄	—	4	1	no	—
95	C₂×C₅×C₄⋊C₄	—	2	1	no	—
96	C₂×C₅×C₄⋊C₄	—	2	1	no	—
97	C₂×C₅×C₄⋊C₄	—	2	1	no	—
98	C₂×C₅×C₄⋊C₄	—	2	1	no	—
99	C₂×C₅×C₄⋊C₄	—	2	1	no	—
100	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
116	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₅	—	2	1	no	—
118	C₂×C₄²×C₅	—	2	1	no	—
119	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
121	C₅×#107	—	2	2	no	—
122	C₅×#107	—	4	1	no	—
123	C₅×C₄⋊C₈	—	4	1	no	—
124	C₅×#103	—	2	2	no	—
125	C₅×#103	—	2	2	no	—
126	C₅×#103	—	2	2	no	—
127	C₅×#102	—	2	2	no	—
128	C₅×#102	—	2	2	no	—
129	C₅×#102	—	2	2	no	—
130	C₅×#102	—	4	1	no	—
131	C₅×#102	—	4	1	no	—
132	C₅×C₂²⋊C₈	—	2	2	no	—
133	C₅×C₂²⋊C₈	—	4	1	no	—
134	C₅×#97	—	2	2	no	—
135	C₅×#95	—	2	1	no	—
136	C₅×#95	—	2	1	no	—
137	C₅×#95	—	2	1	no	—
138	C₅×#95	D₄	1	1	yes	characteristic
139	C₅×#95	D₄	1	1	yes	characteristic
140	C₂×#449	C₂×C₅	1	1	yes	characteristic
141	C₂×#440	C₂×C₅	1	1	yes	characteristic, complemented
142	#2422	C₂×C₅	1	1	yes	characteristic, complemented
143	#2341	C₂×C₅	1	1	yes	characteristic, complemented
144	#2093	C₂×C₅	1	1	yes	characteristic, complemented
145	#2076	C₂×C₅	1	1	yes	characteristic, complemented
146	#2054	C₂×C₅	1	1	yes	characteristic, complemented
147	#2033	C₂×C₅	1	1	yes	characteristic, complemented
148	#1936	C₂×C₅	1	1	yes	characteristic, complemented
149	#1924	C₂×C₅	1	1	yes	characteristic, complemented
150	#1880	C₂×C₅	1	1	yes	characteristic, complemented
151	#1879	C₂×C₅	1	1	yes	characteristic, complemented
152	#1863	C₂×C₅	1	1	yes	characteristic, complemented
153	#1803	C₂×C₅	1	1	yes	characteristic, complemented
154	#1788	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂⁴×C₅	—	2	1	no	—
156	C₂⁴×C₅	—	2	1	no	—
157	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
158	C₅×#41	—	4	4	no	—
159	C₅×#41	—	4	4	no	—
160	C₅×#41	—	4	4	no	—
161	C₅×#41	—	4	4	no	—
162	C₂×C₅×Q₈	—	2	1	no	—
163	C₂×C₅×Q₈	—	2	1	no	—
164	C₂×C₅×Q₈	—	2	1	no	—
165	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
166	C₂×C₅×Q₈	#41	1	2	yes	—
167	C₂×C₅×Q₈	#41	1	2	yes	—
168	C₂×C₅×D₄	—	2	4	no	—
169	C₂×C₅×D₄	—	2	1	no	—
170	C₂×C₅×D₄	—	2	1	no	—
171	C₂×C₅×D₄	—	2	1	no	—
172	C₂×C₅×D₄	—	2	1	no	—
173	C₂×C₅×D₄	—	2	1	no	—
174	C₂×C₅×D₄	—	2	1	no	—
175	C₂×C₅×D₄	—	2	1	no	—
176	C₂×C₅×D₄	—	2	1	no	—
177	C₂×C₅×D₄	—	2	1	no	—
178	C₂×C₅×D₄	—	2	1	no	—
179	C₂×C₅×D₄	—	4	2	no	—
180	C₂×C₅×D₄	—	4	2	no	—
181	C₂×C₅×D₄	—	4	2	no	—
182	C₂×C₅×D₄	—	4	2	no	—
183	C₂×C₅×D₄	—	8	1	no	—
184	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
185	C₂×C₅×D₄	#41	1	2	yes	—
186	C₂²×C₄×C₅	—	2	1	no	—
187	C₂²×C₄×C₅	—	2	4	no	—
188	C₂²×C₄×C₅	—	2	1	no	—
189	C₂²×C₄×C₅	—	2	1	no	—
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	—	2	1	no	—
192	C₂²×C₄×C₅	—	2	1	no	—
193	C₂²×C₄×C₅	—	2	1	no	—
194	C₂²×C₄×C₅	—	2	1	no	—
195	C₂²×C₄×C₅	—	2	1	no	—
196	C₂²×C₄×C₅	—	2	1	no	—
197	C₂²×C₄×C₅	—	2	1	no	—
198	C₂²×C₄×C₅	—	2	1	no	—
199	C₂²×C₄×C₅	—	4	2	no	—
200	C₂²×C₄×C₅	—	4	2	no	—
201	C₂²×C₄×C₅	—	4	2	no	—
202	C₂²×C₄×C₅	—	4	2	no	—
203	C₂²×C₄×C₅	—	8	1	no	—
204	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
210	C₅×SD₁₆	—	2	8	no	—
211	C₅×D₈	—	4	4	no	—
212	C₂×C₅×C₈	—	2	1	no	—
213	C₂×C₅×C₈	—	2	1	no	—
214	C₂×C₅×C₈	—	2	1	no	—
215	C₂×C₅×C₈	—	2	1	no	—
216	C₂×C₅×C₈	—	2	1	no	—
217	C₂×C₅×C₈	—	2	1	no	—
218	C₂×C₅×C₈	—	2	1	no	—
219	C₂×C₅×C₈	—	2	1	no	—
220	C₂×C₅×C₈	—	2	1	no	—
221	C₂×C₅×C₈	—	2	1	no	—
222	C₂×C₅×C₈	—	2	1	no	—
223	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
224	C₅×C₄⋊C₄	—	2	1	no	—
225	C₅×C₄⋊C₄	—	2	1	no	—
226	C₅×C₄⋊C₄	—	2	1	no	—
227	C₅×C₄⋊C₄	—	2	1	no	—
228	C₅×C₄⋊C₄	—	2	1	no	—
229	C₅×C₄⋊C₄	—	2	1	no	—
230	C₅×C₄⋊C₄	—	2	1	no	—
231	C₅×C₄⋊C₄	—	2	1	no	—
232	C₅×C₄⋊C₄	—	2	1	no	—
233	C₅×C₄⋊C₄	—	2	1	no	—
234	C₅×C₄⋊C₄	—	4	2	no	—
235	C₅×C₄⋊C₄	—	4	2	no	—
236	C₅×C₄⋊C₄	—	4	2	no	—
237	C₅×C₄⋊C₄	—	4	2	no	—
238	C₅×C₄⋊C₄	—	8	1	no	—
239	C₅×C₂²⋊C₄	—	2	2	no	—
240	C₅×C₂²⋊C₄	—	4	1	no	—
241	C₅×C₂²⋊C₄	—	4	2	no	—
242	C₅×C₂²⋊C₄	—	4	2	no	—
243	C₅×C₂²⋊C₄	—	4	2	no	—
244	C₅×C₂²⋊C₄	—	4	2	no	—
245	C₅×C₂²⋊C₄	—	4	2	no	—
246	C₅×C₂²⋊C₄	—	4	2	no	—
247	C₅×C₂²⋊C₄	—	4	2	no	—
248	C₅×C₂²⋊C₄	—	8	1	no	—
249	C₅×C₂²⋊C₄	—	8	1	no	—
250	C₅×C₂²⋊C₄	—	8	1	no	—
251	C₄²×C₅	—	2	1	no	—
252	C₄²×C₅	—	2	1	no	—
253	C₄²×C₅	—	2	1	no	—
254	C₄²×C₅	—	2	1	no	—
255	C₄²×C₅	—	4	2	no	—
256	C₄²×C₅	—	4	2	no	—
257	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
258	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
259	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
260	C₂×#123	—	2	1	no	—
261	C₂×#121	C₂²×C₅	1	1	yes	characteristic
262	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
263	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
264	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
265	#449	—	2	4	no	—
266	#440	—	2	4	no	—
267	C₂×#107	C₂²×C₅	1	1	yes	characteristic
268	C₂×#107	C₂²×C₅	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
270	C₂×#103	C₂²×C₅	1	1	yes	characteristic
271	C₂×#103	C₂²×C₅	1	1	yes	characteristic
272	C₂×#103	C₂²×C₅	1	1	yes	characteristic
273	C₂×#102	C₂²×C₅	1	1	yes	characteristic
274	C₂×#102	C₂²×C₅	1	1	yes	characteristic
275	C₂×#102	C₂²×C₅	1	1	yes	characteristic
276	C₂×#102	C₂²×C₅	1	1	yes	characteristic
277	C₂×#102	C₂²×C₅	1	1	yes	characteristic
278	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
279	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
280	C₂×#97	C₂²×C₅	1	1	yes	characteristic
281	#397	—	2	1	no	—
282	#394	—	2	1	no	—
283	#390	—	2	1	no	—
284	#390	—	2	1	no	—
285	#390	C₂²×C₅	1	1	yes	characteristic
286	#390	C₂²×C₅	1	1	yes	characteristic
287	#390	C₂²×C₅	1	1	yes	characteristic
288	#389	C₂²×C₅	1	1	yes	characteristic
289	#385	—	2	1	no	—
290	#384	C₂²×C₅	1	1	yes	characteristic
291	#380	—	2	1	no	—
292	#380	C₂²×C₅	1	1	yes	characteristic
293	#380	C₂²×C₅	1	1	yes	characteristic
294	C₄×C₂²⋊C₄	—	2	1	no	—
295	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
296	#340	C₂²×C₅	1	1	yes	characteristic
297	#340	C₂²×C₅	1	1	yes	characteristic
298	#340	C₂²×C₅	1	1	yes	characteristic
299	#340	C₂²×C₅	1	1	yes	characteristic
300	#336	C₂²×C₅	1	1	yes	characteristic
301	#336	C₂²×C₅	1	1	yes	characteristic
302	C₂³×C₅	—	2	1	no	—
303	C₂³×C₅	—	2	2	no	—
304	C₂³×C₅	—	2	2	no	—
305	C₂³×C₅	—	2	1	no	—
306	C₂³×C₅	—	2	1	no	—
307	C₂³×C₅	—	2	1	no	—
308	C₂³×C₅	—	2	1	no	—
309	C₂³×C₅	—	2	1	no	—
310	C₂³×C₅	—	2	1	no	—
311	C₂³×C₅	—	4	1	no	—
312	C₂³×C₅	—	4	1	no	—
313	C₂³×C₅	—	4	1	no	—
314	C₂³×C₅	—	4	1	no	—
315	C₂³×C₅	—	4	1	no	—
316	C₂³×C₅	—	4	1	no	—
317	C₂³×C₅	—	4	1	no	—
318	C₂³×C₅	—	4	1	no	—
319	C₂³×C₅	—	4	1	no	—
320	C₂³×C₅	—	4	1	no	—
321	C₂³×C₅	—	4	1	no	—
322	C₂³×C₅	—	4	1	no	—
323	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
324	C₅×Q₈	—	2	2	no	—
325	C₅×Q₈	—	2	2	no	—
326	C₅×Q₈	—	2	2	no	—
327	C₅×Q₈	#123	1	4	yes	complemented
328	C₅×D₄	—	2	2	no	—
329	C₅×D₄	—	2	2	no	—
330	C₅×D₄	—	2	2	no	—
331	C₅×D₄	—	2	2	no	—
332	C₅×D₄	—	4	8	no	—
333	C₅×D₄	—	4	1	no	—
334	C₅×D₄	—	4	1	no	—
335	C₅×D₄	—	4	1	no	—
336	C₅×D₄	—	4	1	no	—
337	C₅×D₄	—	8	4	no	—
338	C₂×C₄×C₅	—	2	2	no	—
339	C₂×C₄×C₅	—	2	2	no	—
340	C₂×C₄×C₅	—	2	1	no	—
341	C₂×C₄×C₅	—	2	2	no	—
342	C₂×C₄×C₅	—	2	1	no	—
343	C₂×C₄×C₅	—	2	1	no	—
344	C₂×C₄×C₅	—	2	1	no	—
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	2	1	no	—
347	C₂×C₄×C₅	—	2	1	no	—
348	C₂×C₄×C₅	—	2	1	no	—
349	C₂×C₄×C₅	—	2	1	no	—
350	C₂×C₄×C₅	—	2	1	no	—
351	C₂×C₄×C₅	—	2	1	no	—
352	C₂×C₄×C₅	—	2	1	no	—
353	C₂×C₄×C₅	—	2	1	no	—
354	C₂×C₄×C₅	—	2	1	no	—
355	C₂×C₄×C₅	—	4	8	no	—
356	C₂×C₄×C₅	—	4	1	no	—
357	C₂×C₄×C₅	—	4	1	no	—
358	C₂×C₄×C₅	—	4	1	no	—
359	C₂×C₄×C₅	—	4	1	no	—
360	C₂×C₄×C₅	—	4	1	no	—
361	C₂×C₄×C₅	—	4	1	no	—
362	C₂×C₄×C₅	—	4	1	no	—
363	C₂×C₄×C₅	—	4	1	no	—
364	C₂×C₄×C₅	—	4	1	no	—
365	C₂×C₄×C₅	—	4	1	no	—
366	C₂×C₄×C₅	—	4	1	no	—
367	C₂×C₄×C₅	—	4	1	no	—
368	C₂×C₄×C₅	—	4	1	no	—
369	C₂×C₄×C₅	—	4	1	no	—
370	C₂×C₄×C₅	—	4	1	no	—
371	C₂×C₄×C₅	—	4	1	no	—
372	C₂×C₄×C₅	—	4	1	no	—
373	C₂×C₄×C₅	—	4	1	no	—
374	C₂×C₄×C₅	—	4	1	no	—
375	C₂×C₄×C₅	—	8	4	no	—
376	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
377	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
379	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
380	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
381	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
382	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
383	C₅×C₈	—	2	2	no	—
384	C₅×C₈	—	4	1	no	—
385	C₅×C₈	—	4	1	no	—
386	C₅×C₈	—	4	1	no	—
387	C₂×#41	—	2	2	no	—
388	C₂×#41	—	2	2	no	—
389	C₂×#41	—	2	2	no	—
390	C₂×#41	—	2	2	no	—
391	C₂×#41	—	4	1	no	—
392	C₂×#41	—	4	1	no	—
393	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
394	C₂²×D₄	—	2	1	no	—
395	C₂²×D₄	—	2	1	no	—
396	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
397	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
398	C₂³×C₄	—	2	1	no	—
399	C₂³×C₄	—	2	1	no	—
400	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
401	C₂×SD₁₆	—	2	2	no	—
402	C₂×SD₁₆	—	2	2	no	—
403	C₂×SD₁₆	C₅×D₄	1	4	yes	—
404	C₂×D₈	—	2	2	no	—
405	C₂×D₈	—	2	2	no	—
406	C₂×D₈	—	4	1	no	—
407	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
408	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
409	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
411	#123	—	4	4	no	—
412	#121	—	2	2	no	—
413	#121	—	4	1	no	—
414	C₄×Q₈	—	2	2	no	—
415	C₄×Q₈	—	2	2	no	—
416	C₄×Q₈	—	4	1	no	—
417	C₄×Q₈	—	4	1	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	—	4	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₂²⋊C₄	—	2	1	no	—
437	C₂×C₂²⋊C₄	—	2	1	no	—
438	C₂×C₂²⋊C₄	—	2	1	no	—
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
441	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
442	C₂×C₄²	—	2	1	no	—
443	C₂×C₄²	—	2	1	no	—
444	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
445	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
446	#107	—	2	2	no	—
447	#107	—	4	1	no	—
448	C₄⋊C₈	—	4	1	no	—
449	#103	—	2	2	no	—
450	#103	—	2	2	no	—
451	#103	—	2	2	no	—
452	#102	—	2	2	no	—
453	#102	—	2	2	no	—
454	#102	—	2	2	no	—
455	#102	—	4	1	no	—
456	#102	—	4	1	no	—
457	C₂²⋊C₈	—	2	2	no	—
458	C₂²⋊C₈	—	4	1	no	—
459	#97	—	2	2	no	—
460	#95	—	2	1	no	—
461	#95	—	2	1	no	—
462	#95	—	2	1	no	—
463	#95	C₅×D₄	1	1	yes	characteristic
464	#95	C₅×D₄	1	1	yes	characteristic
465	C₂²×C₅	—	4	1	no	—
466	C₂²×C₅	—	4	2	no	—
467	C₂²×C₅	—	4	1	no	—
468	C₂²×C₅	—	4	2	no	—
469	C₂²×C₅	—	4	2	no	—
470	C₂²×C₅	—	4	1	no	—
471	C₂²×C₅	—	4	2	no	—
472	C₂²×C₅	—	4	1	no	—
473	C₂²×C₅	—	4	2	no	—
474	C₂²×C₅	—	4	2	no	—
475	C₂²×C₅	—	4	1	no	—
476	C₂²×C₅	—	4	1	no	—
477	C₂²×C₅	—	4	1	no	—
478	C₂²×C₅	—	8	1	no	—
479	C₂²×C₅	—	8	1	no	—
480	C₂²×C₅	—	8	1	no	—
481	C₂²×C₅	—	8	1	no	—
482	C₂²×C₅	—	8	1	no	—
483	C₂²×C₅	—	8	1	no	—
484	C₂²×C₅	—	8	1	no	—
485	C₂²×C₅	—	8	1	no	—
486	C₂²×C₅	#525	1	1	yes	characteristic
487	C₂²×C₅	D₄²	1	1	yes	characteristic
488	C₂²×C₅	#546	1	1	yes	characteristic
489	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
490	C₂²×C₅	#575	1	1	yes	characteristic
491	C₂²×C₅	#576	1	1	yes	characteristic
492	C₂²×C₅	#578	1	1	yes	characteristic
493	C₄×C₅	—	2	4	no	—
494	C₄×C₅	—	2	2	no	—
495	C₄×C₅	—	4	1	no	—
496	C₄×C₅	—	4	1	no	—
497	C₄×C₅	—	4	1	no	—
498	C₄×C₅	—	4	1	no	—
499	C₄×C₅	—	8	1	no	—
500	C₄×C₅	—	8	1	no	—
501	C₄×C₅	—	8	1	no	—
502	C₄×C₅	—	8	1	no	—
503	C₄×C₅	—	8	1	no	—
504	C₄×C₅	C₂×#123	1	1	yes	characteristic
505	C₄×C₅	#538	1	1	yes	characteristic
506	C₄×C₅	#546	1	1	yes	characteristic
507	C₄×C₅	#551	1	1	yes	characteristic
508	C₂⁴	—	2	1	no	—
509	C₂⁴	—	2	1	no	—
510	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
511	#41	—	4	4	no	—
512	#41	—	4	4	no	—
513	#41	—	4	4	no	—
514	#41	—	4	4	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
519	C₂×Q₈	C₅×#41	1	2	yes	—
520	C₂×Q₈	C₅×#41	1	2	yes	—
521	C₂×D₄	—	2	4	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	2	1	no	—
527	C₂×D₄	—	2	1	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	2	1	no	—
532	C₂×D₄	—	4	2	no	—
533	C₂×D₄	—	4	2	no	—
534	C₂×D₄	—	4	2	no	—
535	C₂×D₄	—	4	2	no	—
536	C₂×D₄	—	8	1	no	—
537	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
538	C₂×D₄	C₅×#41	1	2	yes	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	4	2	no	—
553	C₂²×C₄	—	4	2	no	—
554	C₂²×C₄	—	4	2	no	—
555	C₂²×C₄	—	4	2	no	—
556	C₂²×C₄	—	8	1	no	—
557	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
558	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
559	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
560	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
561	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
563	SD₁₆	—	2	8	no	—
564	D₈	—	4	4	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	4	2	no	—
588	C₄⋊C₄	—	4	2	no	—
589	C₄⋊C₄	—	4	2	no	—
590	C₄⋊C₄	—	4	2	no	—
591	C₄⋊C₄	—	8	1	no	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	—	4	1	no	—
594	C₂²⋊C₄	—	4	2	no	—
595	C₂²⋊C₄	—	4	2	no	—
596	C₂²⋊C₄	—	4	2	no	—
597	C₂²⋊C₄	—	4	2	no	—
598	C₂²⋊C₄	—	4	2	no	—
599	C₂²⋊C₄	—	4	2	no	—
600	C₂²⋊C₄	—	4	2	no	—
601	C₂²⋊C₄	—	8	1	no	—
602	C₂²⋊C₄	—	8	1	no	—
603	C₂²⋊C₄	—	8	1	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	2	1	no	—
606	C₄²	—	2	1	no	—
607	C₄²	—	2	1	no	—
608	C₄²	—	4	2	no	—
609	C₄²	—	4	2	no	—
610	C₂×C₅	—	8	1	no	—
611	C₂×C₅	—	8	2	no	—
612	C₂×C₅	—	8	2	no	—
613	C₂×C₅	#2418	1	1	yes	characteristic
614	C₂×C₅	#3115	1	1	yes	characteristic
615	C₂×C₅	#3124	1	1	yes	characteristic
616	C₂×C₅	#3269	1	1	yes	characteristic
617	C₂×C₅	#3274	1	1	yes	characteristic
618	C₂×C₅	#3308	1	1	yes	characteristic
619	C₂×C₅	#3309	1	1	yes	characteristic
620	C₂³	—	2	1	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	4	1	no	—
630	C₂³	—	4	1	no	—
631	C₂³	—	4	1	no	—
632	C₂³	—	4	1	no	—
633	C₂³	—	4	1	no	—
634	C₂³	—	4	1	no	—
635	C₂³	—	4	1	no	—
636	C₂³	—	4	1	no	—
637	C₂³	—	4	1	no	—
638	C₂³	—	4	1	no	—
639	C₂³	—	4	1	no	—
640	C₂³	—	4	1	no	—
641	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
642	Q₈	—	2	2	no	—
643	Q₈	—	2	2	no	—
644	Q₈	—	2	2	no	—
645	Q₈	C₅×#123	1	4	yes	complemented
646	D₄	—	2	2	no	—
647	D₄	—	2	2	no	—
648	D₄	—	2	2	no	—
649	D₄	—	2	2	no	—
650	D₄	—	4	8	no	—
651	D₄	—	4	1	no	—
652	D₄	—	4	1	no	—
653	D₄	—	4	1	no	—
654	D₄	—	4	1	no	—
655	D₄	—	8	4	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	4	8	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	8	4	no	—
694	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
695	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
696	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
697	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
698	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
699	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
700	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
701	C₈	—	2	2	no	—
702	C₈	—	4	1	no	—
703	C₈	—	4	1	no	—
704	C₈	—	4	1	no	—
705	C₅	#24916	1	1	yes	characteristic, direct product factor, Sylow
706	C₂²	—	4	1	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	8	1	no	—
720	C₂²	—	8	1	no	—
721	C₂²	—	8	1	no	—
722	C₂²	—	8	1	no	—
723	C₂²	—	8	1	no	—
724	C₂²	—	8	1	no	—
725	C₂²	—	8	1	no	—
726	C₂²	—	8	1	no	—
727	C₂²	C₅×#525	1	1	yes	characteristic
728	C₂²	C₅×D₄²	1	1	yes	characteristic
729	C₂²	C₅×#546	1	1	yes	characteristic
730	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
731	C₂²	C₅×#575	1	1	yes	characteristic
732	C₂²	C₅×#576	1	1	yes	characteristic
733	C₂²	C₅×#578	1	1	yes	characteristic
734	C₄	—	2	2	no	—
735	C₄	—	2	4	no	—
736	C₄	—	4	1	no	—
737	C₄	—	4	1	no	—
738	C₄	—	4	1	no	—
739	C₄	—	4	1	no	—
740	C₄	—	8	1	no	—
741	C₄	—	8	1	no	—
742	C₄	—	8	1	no	—
743	C₄	—	8	1	no	—
744	C₄	—	8	1	no	—
745	C₄	C₂×C₅×#123	1	1	yes	characteristic
746	C₄	C₅×#538	1	1	yes	characteristic
747	C₄	C₅×#546	1	1	yes	characteristic
748	C₄	C₅×#551	1	1	yes	characteristic
749	C₂	—	8	1	no	—
750	C₂	—	8	2	no	—
751	C₂	—	8	2	no	—
752	C₂	C₅×#2418	1	1	yes	characteristic
753	C₂	C₅×#3115	1	1	yes	characteristic
754	C₂	C₅×#3124	1	1	yes	characteristic
755	C₂	C₅×#3269	1	1	yes	characteristic
756	C₂	C₅×#3274	1	1	yes	characteristic
757	C₂	C₅×#3308	1	1	yes	characteristic
758	C₂	C₅×#3309	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#449	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#440	C₂	semidirect
3. C₅×#2422	C₂	semidirect
4. C₅×#2341	C₂	semidirect
5. C₅×#2093	C₂	semidirect
6. C₅×#2076	C₂	semidirect
7. C₅×#2054	C₂	semidirect
8. C₅×#2033	C₂	semidirect
9. C₅×#1936	C₂	semidirect
10. C₅×#1924	C₂	semidirect
11. C₅×#1880	C₂	semidirect
12. C₅×#1879	C₂	semidirect
13. C₅×#1863	C₂	semidirect
14. C₅×#1803	C₂	semidirect
15. C₅×#1788	C₂	semidirect
61. #24916	C₅	direct (N × H)
141. C₂×#440	C₂×C₅	semidirect
142. #2422	C₂×C₅	semidirect
143. #2341	C₂×C₅	semidirect
144. #2093	C₂×C₅	semidirect
145. #2076	C₂×C₅	semidirect
146. #2054	C₂×C₅	semidirect
147. #2033	C₂×C₅	semidirect
148. #1936	C₂×C₅	semidirect
149. #1924	C₂×C₅	semidirect
150. #1880	C₂×C₅	semidirect
151. #1879	C₂×C₅	semidirect
152. #1863	C₂×C₅	semidirect
153. #1803	C₂×C₅	semidirect
154. #1788	C₂×C₅	semidirect
327. C₅×Q₈	#123	semidirect
645. Q₈	C₅×#123	semidirect
705. C₅	#24916	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×#449	2
C₂×C₅×#440	2
C₅×#2422	2
C₅×#2341	2
C₅×#2093	2
C₅×#2076	2
C₅×#2054	2
C₅×#2033	2
C₅×#1936	2
C₅×#1924	2
C₅×#1880	2
C₅×#1879	2
C₅×#1863	2
C₅×#1803	2
C₅×#1788	2
#24916	5

Subgroups — C5×#24916 #11947636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#24916 #11947636