Subgroups — C₅×#23037 #11945757

Order 1280.

1082 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#469	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#428	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2363	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2361	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1972	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1941	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1926	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1925	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1875	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1874	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1864	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1862	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1776	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
17	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₅×#121	C₂²	1	1	yes	characteristic
19	C₂×C₅×#121	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×D₄	—	2	1	no	—
21	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₅×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₅×#469	C₄	1	8	yes	complemented
26	C₄×C₅×D₈	—	2	4	no	—
27	C₅×#428	—	2	4	no	—
28	C₂×C₅×#107	C₂²	1	1	yes	characteristic
29	C₂×C₅×#107	C₂²	1	1	yes	characteristic
30	C₂×C₅×#106	C₂²	1	1	yes	characteristic
31	C₂×C₅×#106	C₂²	1	1	yes	characteristic
32	C₂×C₅×#106	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×#102	C₂²	1	1	yes	characteristic
38	C₂×C₅×#102	C₂²	1	1	yes	characteristic
39	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₅×#97	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
42	C₅×#390	—	2	1	no	—
43	C₅×#390	C₂²	1	1	yes	characteristic
44	C₅×#390	C₂²	1	1	yes	characteristic
45	C₅×#389	C₂²	1	1	yes	characteristic
46	C₅×#389	C₂²	1	1	yes	characteristic
47	C₅×#388	—	2	1	no	—
48	C₅×#388	—	2	1	no	—
49	C₅×#386	—	2	1	no	—
50	C₅×#386	—	2	1	no	—
51	C₅×#385	—	2	1	no	—
52	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
54	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
55	C₄×C₅×C₂²⋊C₄	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×#340	C₂²	1	1	yes	characteristic
60	C₅×#336	C₂²	1	1	yes	characteristic
61	C₅×#336	C₂²	1	1	yes	characteristic
62	#23037	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂²×C₅×D₄	—	2	1	no	—
64	C₂²×C₅×D₄	—	2	1	no	—
65	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₅	—	2	1	no	—
68	C₂³×C₄×C₅	—	2	1	no	—
69	C₂³×C₄×C₅	—	2	1	no	—
70	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₅×D₈	—	2	2	no	—
72	C₂×C₅×D₈	—	2	2	no	—
73	C₂×C₅×D₈	C₂×C₄	1	4	yes	complemented
74	C₂×C₅×M₁₆	—	2	2	no	—
75	C₂×C₅×M₁₆	—	2	2	no	—
76	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
77	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
81	C₅×#121	—	2	2	no	—
82	C₅×#121	—	2	2	no	—
83	C₅×#121	C₂×C₄	1	4	yes	complemented
84	C₅×#121	C₂×C₄	1	4	yes	complemented
85	C₄×C₅×D₄	—	2	2	no	—
86	C₄×C₅×D₄	—	2	2	no	—
87	C₄×C₅×D₄	—	4	1	no	—
88	C₄×C₅×D₄	—	4	1	no	—
89	C₄×C₅×D₄	—	4	4	no	—
90	C₅×#117	—	2	2	no	—
91	C₅×#117	—	4	1	no	—
92	C₂×C₅×C₄⋊C₄	—	2	2	no	—
93	C₂×C₅×C₄⋊C₄	—	2	1	no	—
94	C₂×C₅×C₄⋊C₄	—	2	1	no	—
95	C₂×C₅×C₄⋊C₄	—	2	1	no	—
96	C₂×C₅×C₄⋊C₄	—	4	1	no	—
97	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
113	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₅	—	2	1	no	—
115	C₂×C₄²×C₅	—	2	1	no	—
116	C₂×C₄²×C₅	—	2	1	no	—
117	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
119	C₅×#107	—	2	2	no	—
120	C₅×#107	D₄	1	4	yes	complemented
121	C₅×#106	—	2	2	no	—
122	C₅×#106	—	2	2	no	—
123	C₅×#106	C₂×C₄	1	4	yes	complemented
124	C₅×#102	—	2	2	no	—
125	C₅×#102	—	2	2	no	—
126	C₅×#102	—	4	1	no	—
127	C₅×#102	—	4	1	no	—
128	C₅×#102	C₂×C₄	1	4	yes	complemented
129	C₅×#102	C₂×C₄	1	4	yes	complemented
130	C₅×C₂²⋊C₈	—	2	2	no	—
131	C₅×#97	—	2	2	no	—
132	C₄×C₅×C₈	—	2	2	no	—
133	C₅×#95	—	2	1	no	—
134	C₅×#95	—	2	1	no	—
135	C₅×#95	—	2	1	no	—
136	C₅×#95	—	2	1	no	—
137	C₅×#95	D₄	1	1	yes	characteristic
138	C₅×#95	D₄	1	1	yes	characteristic
139	C₂×#469	C₂×C₅	1	1	yes	characteristic
140	C₂×C₄×D₈	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂×#428	C₂×C₅	1	1	yes	characteristic, complemented
142	#2363	C₂×C₅	1	1	yes	characteristic, complemented
143	#2361	C₂×C₅	1	1	yes	characteristic, complemented
144	#1972	C₂×C₅	1	1	yes	characteristic, complemented
145	#1941	C₂×C₅	1	1	yes	characteristic, complemented
146	#1926	C₂×C₅	1	1	yes	characteristic, complemented
147	#1925	C₂×C₅	1	1	yes	characteristic, complemented
148	#1875	C₂×C₅	1	1	yes	characteristic, complemented
149	#1874	C₂×C₅	1	1	yes	characteristic, complemented
150	#1864	C₂×C₅	1	1	yes	characteristic, complemented
151	#1862	C₂×C₅	1	1	yes	characteristic, complemented
152	#1776	C₂×C₅	1	1	yes	characteristic, complemented
153	#1753	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂⁴×C₅	—	2	1	no	—
155	C₂⁴×C₅	—	2	1	no	—
156	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂×C₅×D₄	—	2	4	no	—
158	C₂×C₅×D₄	—	2	4	no	—
159	C₂×C₅×D₄	—	2	1	no	—
160	C₂×C₅×D₄	—	2	1	no	—
161	C₂×C₅×D₄	—	2	1	no	—
162	C₂×C₅×D₄	—	2	1	no	—
163	C₂×C₅×D₄	—	2	1	no	—
164	C₂×C₅×D₄	—	2	1	no	—
165	C₂×C₅×D₄	—	2	1	no	—
166	C₂×C₅×D₄	—	2	1	no	—
167	C₂×C₅×D₄	—	2	1	no	—
168	C₂×C₅×D₄	—	2	1	no	—
169	C₂×C₅×D₄	—	4	2	no	—
170	C₂×C₅×D₄	—	4	2	no	—
171	C₂×C₅×D₄	—	8	1	no	—
172	C₂×C₅×D₄	—	8	1	no	—
173	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
174	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
175	C₂²×C₄×C₅	—	2	1	no	—
176	C₂²×C₄×C₅	—	2	1	no	—
177	C₂²×C₄×C₅	—	2	1	no	—
178	C₂²×C₄×C₅	—	2	1	no	—
179	C₂²×C₄×C₅	—	2	1	no	—
180	C₂²×C₄×C₅	—	2	1	no	—
181	C₂²×C₄×C₅	—	2	1	no	—
182	C₂²×C₄×C₅	—	2	1	no	—
183	C₂²×C₄×C₅	—	2	1	no	—
184	C₂²×C₄×C₅	—	2	1	no	—
185	C₂²×C₄×C₅	—	4	2	no	—
186	C₂²×C₄×C₅	—	4	2	no	—
187	C₂²×C₄×C₅	—	4	2	no	—
188	C₂²×C₄×C₅	—	4	2	no	—
189	C₂²×C₄×C₅	—	4	2	no	—
190	C₂²×C₄×C₅	—	4	2	no	—
191	C₂²×C₄×C₅	—	8	1	no	—
192	C₂²×C₄×C₅	—	8	1	no	—
193	C₂²×C₄×C₅	—	8	1	no	—
194	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
195	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₅	#41	1	2	yes	—
201	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
202	C₅×D₈	—	2	8	no	—
203	C₅×M₁₆	—	2	8	no	—
204	C₂×C₅×C₈	—	2	1	no	—
205	C₂×C₅×C₈	—	2	1	no	—
206	C₂×C₅×C₈	—	2	1	no	—
207	C₂×C₅×C₈	—	2	1	no	—
208	C₂×C₅×C₈	—	2	1	no	—
209	C₂×C₅×C₈	—	2	1	no	—
210	C₂×C₅×C₈	—	2	1	no	—
211	C₂×C₅×C₈	—	2	1	no	—
212	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
213	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
214	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
215	C₂×C₅×C₈	#41	1	2	yes	—
216	C₅×C₄⋊C₄	—	2	1	no	—
217	C₅×C₄⋊C₄	—	2	1	no	—
218	C₅×C₄⋊C₄	—	2	1	no	—
219	C₅×C₄⋊C₄	—	2	1	no	—
220	C₅×C₄⋊C₄	—	2	1	no	—
221	C₅×C₄⋊C₄	—	2	1	no	—
222	C₅×C₄⋊C₄	—	2	1	no	—
223	C₅×C₄⋊C₄	—	2	1	no	—
224	C₅×C₄⋊C₄	—	4	2	no	—
225	C₅×C₄⋊C₄	—	4	2	no	—
226	C₅×C₄⋊C₄	—	8	1	no	—
227	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
228	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
229	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
230	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
231	C₅×C₂²⋊C₄	—	2	4	no	—
232	C₅×C₂²⋊C₄	—	2	4	no	—
233	C₅×C₂²⋊C₄	—	2	2	no	—
234	C₅×C₂²⋊C₄	—	4	1	no	—
235	C₅×C₂²⋊C₄	—	4	2	no	—
236	C₅×C₂²⋊C₄	—	4	2	no	—
237	C₅×C₂²⋊C₄	—	4	2	no	—
238	C₅×C₂²⋊C₄	—	4	2	no	—
239	C₅×C₂²⋊C₄	—	4	2	no	—
240	C₅×C₂²⋊C₄	—	8	1	no	—
241	C₅×C₂²⋊C₄	—	8	1	no	—
242	C₄²×C₅	—	2	1	no	—
243	C₄²×C₅	—	2	1	no	—
244	C₄²×C₅	—	2	1	no	—
245	C₄²×C₅	—	2	1	no	—
246	C₄²×C₅	—	4	2	no	—
247	C₄²×C₅	—	4	2	no	—
248	C₄²×C₅	—	8	1	no	—
249	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
250	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
251	C₂×#121	C₂²×C₅	1	1	yes	characteristic
252	C₂×#121	C₂²×C₅	1	1	yes	characteristic
253	C₂×C₄×D₄	—	2	1	no	—
254	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
256	C₂×#117	C₂²×C₅	1	1	yes	characteristic
257	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
258	#469	C₄×C₅	1	8	yes	complemented
259	C₄×D₈	—	2	4	no	—
260	#428	—	2	4	no	—
261	C₂×#107	C₂²×C₅	1	1	yes	characteristic
262	C₂×#107	C₂²×C₅	1	1	yes	characteristic
263	C₂×#106	C₂²×C₅	1	1	yes	characteristic
264	C₂×#106	C₂²×C₅	1	1	yes	characteristic
265	C₂×#106	C₂²×C₅	1	1	yes	characteristic
266	C₂×#102	C₂²×C₅	1	1	yes	characteristic
267	C₂×#102	C₂²×C₅	1	1	yes	characteristic
268	C₂×#102	C₂²×C₅	1	1	yes	characteristic
269	C₂×#102	C₂²×C₅	1	1	yes	characteristic
270	C₂×#102	C₂²×C₅	1	1	yes	characteristic
271	C₂×#102	C₂²×C₅	1	1	yes	characteristic
272	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
273	C₂×#97	C₂²×C₅	1	1	yes	characteristic
274	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
275	#390	—	2	1	no	—
276	#390	C₂²×C₅	1	1	yes	characteristic
277	#390	C₂²×C₅	1	1	yes	characteristic
278	#389	C₂²×C₅	1	1	yes	characteristic
279	#389	C₂²×C₅	1	1	yes	characteristic
280	#388	—	2	1	no	—
281	#388	—	2	1	no	—
282	#386	—	2	1	no	—
283	#386	—	2	1	no	—
284	#385	—	2	1	no	—
285	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
286	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
287	C₄×C₂²⋊C₄	—	2	1	no	—
288	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
289	#340	C₂²×C₅	1	1	yes	characteristic
290	#340	C₂²×C₅	1	1	yes	characteristic
291	#340	C₂²×C₅	1	1	yes	characteristic
292	#340	C₂²×C₅	1	1	yes	characteristic
293	#336	C₂²×C₅	1	1	yes	characteristic
294	#336	C₂²×C₅	1	1	yes	characteristic
295	C₂³×C₅	—	2	1	no	—
296	C₂³×C₅	—	2	1	no	—
297	C₂³×C₅	—	2	1	no	—
298	C₂³×C₅	—	2	1	no	—
299	C₂³×C₅	—	2	1	no	—
300	C₂³×C₅	—	2	1	no	—
301	C₂³×C₅	—	2	2	no	—
302	C₂³×C₅	—	2	2	no	—
303	C₂³×C₅	—	4	1	no	—
304	C₂³×C₅	—	4	1	no	—
305	C₂³×C₅	—	4	1	no	—
306	C₂³×C₅	—	4	1	no	—
307	C₂³×C₅	—	4	1	no	—
308	C₂³×C₅	—	4	1	no	—
309	C₂³×C₅	—	4	1	no	—
310	C₂³×C₅	—	4	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	C₄×D₄	1	2	yes	—
316	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
317	C₅×D₄	—	2	2	no	—
318	C₅×D₄	—	2	2	no	—
319	C₅×D₄	—	2	2	no	—
320	C₅×D₄	—	2	2	no	—
321	C₅×D₄	—	4	8	no	—
322	C₅×D₄	—	4	1	no	—
323	C₅×D₄	—	4	1	no	—
324	C₅×D₄	—	4	1	no	—
325	C₅×D₄	—	4	1	no	—
326	C₅×D₄	—	8	4	no	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	1	no	—
329	C₂×C₄×C₅	—	2	1	no	—
330	C₂×C₄×C₅	—	2	1	no	—
331	C₂×C₄×C₅	—	2	2	no	—
332	C₂×C₄×C₅	—	2	2	no	—
333	C₂×C₄×C₅	—	2	2	no	—
334	C₂×C₄×C₅	—	2	2	no	—
335	C₂×C₄×C₅	—	2	2	no	—
336	C₂×C₄×C₅	—	2	2	no	—
337	C₂×C₄×C₅	—	2	1	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	1	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	—	4	1	no	—
349	C₂×C₄×C₅	—	4	1	no	—
350	C₂×C₄×C₅	—	4	1	no	—
351	C₂×C₄×C₅	—	4	1	no	—
352	C₂×C₄×C₅	—	4	1	no	—
353	C₂×C₄×C₅	—	4	1	no	—
354	C₂×C₄×C₅	—	4	1	no	—
355	C₂×C₄×C₅	—	4	1	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	—	8	4	no	—
363	C₂×C₄×C₅	—	8	4	no	—
364	C₂×C₄×C₅	—	8	4	no	—
365	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
366	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
367	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
368	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
370	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
371	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
372	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
373	C₅×C₈	—	2	2	no	—
374	C₅×C₈	—	4	1	no	—
375	C₅×C₈	—	4	1	no	—
376	C₅×C₈	C₄×D₄	1	4	yes	complemented
377	C₂²×D₄	—	2	1	no	—
378	C₂²×D₄	—	2	1	no	—
379	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
380	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
381	C₂³×C₄	—	2	1	no	—
382	C₂³×C₄	—	2	1	no	—
383	C₂³×C₄	—	2	1	no	—
384	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
385	C₂×D₈	—	2	2	no	—
386	C₂×D₈	—	2	2	no	—
387	C₂×D₈	C₂×C₄×C₅	1	4	yes	complemented
388	C₂×M₁₆	—	2	2	no	—
389	C₂×M₁₆	—	2	2	no	—
390	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	complemented
391	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
392	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
394	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
395	#121	—	2	2	no	—
396	#121	—	2	2	no	—
397	#121	C₂×C₄×C₅	1	4	yes	complemented
398	#121	C₂×C₄×C₅	1	4	yes	complemented
399	C₄×D₄	—	2	2	no	—
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	—	4	1	no	—
402	C₄×D₄	—	4	1	no	—
403	C₄×D₄	—	4	4	no	—
404	#117	—	2	2	no	—
405	#117	—	4	1	no	—
406	C₂×C₄⋊C₄	—	2	2	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	4	1	no	—
411	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
427	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
428	C₂×C₄²	—	2	1	no	—
429	C₂×C₄²	—	2	1	no	—
430	C₂×C₄²	—	2	1	no	—
431	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
433	#107	—	2	2	no	—
434	#107	C₅×D₄	1	4	yes	complemented
435	#106	—	2	2	no	—
436	#106	—	2	2	no	—
437	#106	C₂×C₄×C₅	1	4	yes	complemented
438	#102	—	2	2	no	—
439	#102	—	2	2	no	—
440	#102	—	4	1	no	—
441	#102	—	4	1	no	—
442	#102	C₂×C₄×C₅	1	4	yes	complemented
443	#102	C₂×C₄×C₅	1	4	yes	complemented
444	C₂²⋊C₈	—	2	2	no	—
445	#97	—	2	2	no	—
446	C₄×C₈	—	2	2	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	#95	—	2	1	no	—
451	#95	C₅×D₄	1	1	yes	characteristic
452	#95	C₅×D₄	1	1	yes	characteristic
453	C₂²×C₅	—	2	2	no	—
454	C₂²×C₅	—	2	2	no	—
455	C₂²×C₅	—	2	2	no	—
456	C₂²×C₅	—	4	1	no	—
457	C₂²×C₅	—	4	1	no	—
458	C₂²×C₅	—	4	1	no	—
459	C₂²×C₅	—	4	1	no	—
460	C₂²×C₅	—	4	2	no	—
461	C₂²×C₅	—	4	2	no	—
462	C₂²×C₅	—	4	2	no	—
463	C₂²×C₅	—	4	2	no	—
464	C₂²×C₅	—	4	2	no	—
465	C₂²×C₅	—	4	2	no	—
466	C₂²×C₅	—	8	1	no	—
467	C₂²×C₅	—	8	1	no	—
468	C₂²×C₅	—	8	1	no	—
469	C₂²×C₅	—	8	1	no	—
470	C₂²×C₅	—	8	1	no	—
471	C₂²×C₅	—	8	1	no	—
472	C₂²×C₅	—	8	1	no	—
473	C₂²×C₅	—	8	1	no	—
474	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
475	C₂²×C₅	D₄²	1	1	yes	characteristic
476	C₂²×C₅	#547	1	1	yes	characteristic
477	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
478	C₂²×C₅	#575	1	1	yes	characteristic
479	C₂²×C₅	#576	1	1	yes	characteristic
480	C₂²×C₅	#577	1	1	yes	characteristic
481	C₄×C₅	—	2	2	no	—
482	C₄×C₅	—	2	2	no	—
483	C₄×C₅	—	4	1	no	—
484	C₄×C₅	—	4	1	no	—
485	C₄×C₅	—	4	2	no	—
486	C₄×C₅	—	4	2	no	—
487	C₄×C₅	—	4	2	no	—
488	C₄×C₅	—	4	2	no	—
489	C₄×C₅	—	4	1	no	—
490	C₄×C₅	—	8	1	no	—
491	C₄×C₅	—	8	1	no	—
492	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
493	C₄×C₅	#520	1	1	yes	characteristic
494	C₄×C₅	#548	1	1	yes	characteristic
495	C₄×C₅	#553	1	1	yes	characteristic
496	C₂⁴	—	2	1	no	—
497	C₂⁴	—	2	1	no	—
498	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
499	C₂×D₄	—	2	4	no	—
500	C₂×D₄	—	2	4	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	4	2	no	—
512	C₂×D₄	—	4	2	no	—
513	C₂×D₄	—	8	1	no	—
514	C₂×D₄	—	8	1	no	—
515	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
516	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	4	2	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	4	2	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	4	2	no	—
532	C₂²×C₄	—	4	2	no	—
533	C₂²×C₄	—	8	1	no	—
534	C₂²×C₄	—	8	1	no	—
535	C₂²×C₄	—	8	1	no	—
536	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
537	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
538	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
539	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
540	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
541	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
542	C₂²×C₄	C₅×#41	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
544	D₈	—	2	8	no	—
545	M₁₆	—	2	8	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
555	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
556	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
557	C₂×C₈	C₅×#41	1	2	yes	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	4	2	no	—
567	C₄⋊C₄	—	4	2	no	—
568	C₄⋊C₄	—	8	1	no	—
569	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
570	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
571	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
572	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	2	2	no	—
576	C₂²⋊C₄	—	4	1	no	—
577	C₂²⋊C₄	—	4	2	no	—
578	C₂²⋊C₄	—	4	2	no	—
579	C₂²⋊C₄	—	4	2	no	—
580	C₂²⋊C₄	—	4	2	no	—
581	C₂²⋊C₄	—	4	2	no	—
582	C₂²⋊C₄	—	8	1	no	—
583	C₂²⋊C₄	—	8	1	no	—
584	C₄²	—	2	1	no	—
585	C₄²	—	2	1	no	—
586	C₄²	—	2	1	no	—
587	C₄²	—	2	1	no	—
588	C₄²	—	4	2	no	—
589	C₄²	—	4	2	no	—
590	C₄²	—	8	1	no	—
591	C₂×C₅	—	4	2	no	—
592	C₂×C₅	—	8	2	no	—
593	C₂×C₅	—	8	2	no	—
594	C₂×C₅	#2361	1	1	yes	characteristic
595	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
596	C₂×C₅	#2946	1	1	yes	characteristic
597	C₂×C₅	#3264	1	1	yes	characteristic
598	C₂×C₅	#3271	1	1	yes	characteristic
599	C₂×C₅	#3354	1	1	yes	characteristic
600	C₂×C₅	#3355	1	1	yes	characteristic
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	4	1	no	—
610	C₂³	—	4	1	no	—
611	C₂³	—	4	1	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	4	1	no	—
617	C₂³	—	4	1	no	—
618	C₂³	—	4	1	no	—
619	C₂³	—	4	1	no	—
620	C₂³	—	4	1	no	—
621	C₂³	C₄×C₅×D₄	1	2	yes	—
622	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
623	D₄	—	2	2	no	—
624	D₄	—	2	2	no	—
625	D₄	—	2	2	no	—
626	D₄	—	2	2	no	—
627	D₄	—	4	8	no	—
628	D₄	—	4	1	no	—
629	D₄	—	4	1	no	—
630	D₄	—	4	1	no	—
631	D₄	—	4	1	no	—
632	D₄	—	8	4	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	8	4	no	—
669	C₂×C₄	—	8	4	no	—
670	C₂×C₄	—	8	4	no	—
671	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
672	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
673	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
674	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
675	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
676	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
677	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
678	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
679	C₈	—	2	2	no	—
680	C₈	—	4	1	no	—
681	C₈	—	4	1	no	—
682	C₈	C₄×C₅×D₄	1	4	yes	complemented
683	C₅	#23037	1	1	yes	characteristic, direct product factor, Sylow
684	C₂²	—	2	2	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	4	1	no	—
690	C₂²	—	4	1	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	8	1	no	—
698	C₂²	—	8	1	no	—
699	C₂²	—	8	1	no	—
700	C₂²	—	8	1	no	—
701	C₂²	—	8	1	no	—
702	C₂²	—	8	1	no	—
703	C₂²	—	8	1	no	—
704	C₂²	—	8	1	no	—
705	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
706	C₂²	C₅×D₄²	1	1	yes	characteristic
707	C₂²	C₅×#547	1	1	yes	characteristic
708	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
709	C₂²	C₅×#575	1	1	yes	characteristic
710	C₂²	C₅×#576	1	1	yes	characteristic
711	C₂²	C₅×#577	1	1	yes	characteristic
712	C₄	—	2	2	no	—
713	C₄	—	2	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	1	no	—
717	C₄	—	4	1	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	8	1	no	—
722	C₄	—	8	1	no	—
723	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
724	C₄	C₅×#520	1	1	yes	characteristic
725	C₄	C₅×#548	1	1	yes	characteristic
726	C₄	C₅×#553	1	1	yes	characteristic
727	C₂	—	4	2	no	—
728	C₂	—	8	2	no	—
729	C₂	—	8	2	no	—
730	C₂	C₅×#2361	1	1	yes	characteristic
731	C₂	C₄×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
732	C₂	C₅×#2946	1	1	yes	characteristic
733	C₂	C₅×#3264	1	1	yes	characteristic
734	C₂	C₅×#3271	1	1	yes	characteristic
735	C₂	C₅×#3354	1	1	yes	characteristic
736	C₂	C₅×#3355	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	C₂×C₅×#469	C₂
LCS	G ▷ C₂×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×C₄×C₅×D₈	C₂	semidirect
3. C₂×C₅×#428	C₂	semidirect
4. C₅×#2363	C₂	semidirect
5. C₅×#2361	C₂	semidirect
6. C₅×#1972	C₂	semidirect
7. C₅×#1941	C₂	semidirect
8. C₅×#1926	C₂	semidirect
9. C₅×#1925	C₂	semidirect
10. C₅×#1875	C₂	semidirect
11. C₅×#1874	C₂	semidirect
12. C₅×#1864	C₂	semidirect
13. C₅×#1862	C₂	semidirect
14. C₅×#1776	C₂	semidirect
15. C₅×#1753	C₂	semidirect
25. C₅×#469	C₄	semidirect
62. #23037	C₅	direct (N × H)
73. C₂×C₅×D₈	C₂×C₄	semidirect
76. C₂×C₅×M₁₆	C₂×C₄	semidirect
83. C₅×#121	C₂×C₄	semidirect
84. C₅×#121	C₂×C₄	semidirect
120. C₅×#107	D₄	semidirect
123. C₅×#106	C₂×C₄	semidirect
128. C₅×#102	C₂×C₄	semidirect
129. C₅×#102	C₂×C₄	semidirect
140. C₂×C₄×D₈	C₂×C₅	semidirect
141. C₂×#428	C₂×C₅	semidirect
142. #2363	C₂×C₅	semidirect
143. #2361	C₂×C₅	semidirect
144. #1972	C₂×C₅	semidirect
145. #1941	C₂×C₅	semidirect
146. #1926	C₂×C₅	semidirect
147. #1925	C₂×C₅	semidirect
148. #1875	C₂×C₅	semidirect
149. #1874	C₂×C₅	semidirect
150. #1864	C₂×C₅	semidirect
151. #1862	C₂×C₅	semidirect
152. #1776	C₂×C₅	semidirect
153. #1753	C₂×C₅	semidirect
258. #469	C₄×C₅	semidirect
376. C₅×C₈	C₄×D₄	semidirect
387. C₂×D₈	C₂×C₄×C₅	semidirect
390. C₂×M₁₆	C₂×C₄×C₅	semidirect
397. #121	C₂×C₄×C₅	semidirect
398. #121	C₂×C₄×C₅	semidirect
434. #107	C₅×D₄	semidirect
437. #106	C₂×C₄×C₅	semidirect
442. #102	C₂×C₄×C₅	semidirect
443. #102	C₂×C₄×C₅	semidirect
682. C₈	C₄×C₅×D₄	semidirect
683. C₅	#23037	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×#469	2
C₂×C₄×C₅×D₈	2
C₂×C₅×#428	2
C₅×#2363	2
C₅×#2361	2
C₅×#1972	2
C₅×#1941	2
C₅×#1926	2
C₅×#1925	2
C₅×#1875	2
C₅×#1874	2
C₅×#1864	2
C₅×#1862	2
C₅×#1776	2
C₅×#1753	2
#23037	5

Subgroups — C5×#23037 #11945757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23037 #11945757