Subgroups — C₅×#23708 #11946428

Order 1280.

1042 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#442	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2088	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2077	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2067	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2065	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2054	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2034	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2033	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1999	C₂	1	1	yes	maximal, characteristic
13	C₅×#1776	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1762	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1762	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×#121	C₂²	1	1	yes	characteristic
18	C₂×C₅×#121	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×D₄	—	2	1	no	—
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	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₅×#442	—	2	4	no	—
25	C₅×#432	—	2	4	no	—
26	C₂×C₅×#107	C₂²	1	1	yes	characteristic
27	C₂×C₅×#106	C₂²	1	1	yes	characteristic
28	C₂×C₅×#106	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×#102	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	C₂×C₅×#97	C₂²	1	1	yes	characteristic
41	C₅×#390	C₂²	1	1	yes	characteristic
42	C₅×#390	C₂²	1	1	yes	characteristic
43	C₅×#389	C₂²	1	1	yes	characteristic
44	C₅×#389	C₂²	1	1	yes	characteristic
45	C₅×#388	—	2	1	no	—
46	C₅×#388	—	2	1	no	—
47	C₅×#386	—	2	1	no	—
48	C₅×#386	—	2	1	no	—
49	C₅×#380	C₂²	1	1	yes	characteristic
50	C₅×#380	C₂²	1	1	yes	characteristic
51	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
54	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
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×#340	C₂²	1	1	yes	characteristic
60	C₅×#340	C₂²	1	1	yes	characteristic
61	#23708	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₅×D₄	—	2	1	no	—
63	C₂²×C₅×D₄	—	2	1	no	—
64	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₅	—	2	1	no	—
67	C₂³×C₄×C₅	—	2	1	no	—
68	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
69	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
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	—	2	2	no	—
74	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₅×#121	—	2	2	no	—
79	C₅×#121	—	2	2	no	—
80	C₅×#121	—	2	2	no	—
81	C₅×#121	—	2	2	no	—
82	C₄×C₅×D₄	—	2	2	no	—
83	C₄×C₅×D₄	—	2	2	no	—
84	C₄×C₅×D₄	—	2	2	no	—
85	C₄×C₅×D₄	—	2	2	no	—
86	C₄×C₅×D₄	—	4	4	no	—
87	C₄×C₅×D₄	—	4	4	no	—
88	C₂×C₅×C₄⋊C₄	—	2	1	no	—
89	C₂×C₅×C₄⋊C₄	—	2	1	no	—
90	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
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×C₄²×C₅	—	2	2	no	—
107	C₂×C₄²×C₅	—	2	2	no	—
108	C₂×C₄²×C₅	—	2	1	no	—
109	C₂×C₄²×C₅	—	2	1	no	—
110	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
114	C₅×#107	—	2	2	no	—
115	C₅×#106	—	2	2	no	—
116	C₅×#106	—	2	2	no	—
117	C₅×C₄⋊C₈	—	2	2	no	—
118	C₅×C₄⋊C₈	—	2	2	no	—
119	C₅×#102	—	2	2	no	—
120	C₅×#102	—	2	2	no	—
121	C₅×#102	—	2	2	no	—
122	C₅×#102	—	2	2	no	—
123	C₅×#102	—	2	2	no	—
124	C₅×#102	—	2	2	no	—
125	C₅×C₂²⋊C₈	—	2	2	no	—
126	C₅×C₂²⋊C₈	—	2	2	no	—
127	C₅×#97	—	2	2	no	—
128	C₅×#97	D₄	1	4	yes	complemented
129	C₅×#95	—	2	1	no	—
130	C₅×#95	—	2	1	no	—
131	C₅×#95	—	2	1	no	—
132	C₅×#95	—	2	1	no	—
133	C₅×#95	—	2	1	no	—
134	C₅×#95	—	2	1	no	—
135	C₂×#442	C₂×C₅	1	1	yes	characteristic, complemented
136	C₂×#432	C₂×C₅	1	1	yes	characteristic, complemented
137	C₄×#121	C₂×C₅	1	1	yes	characteristic, complemented
138	C₄×#121	C₂×C₅	1	1	yes	characteristic, complemented
139	#2088	C₂×C₅	1	1	yes	characteristic, complemented
140	#2077	C₂×C₅	1	1	yes	characteristic, complemented
141	#2067	C₂×C₅	1	1	yes	characteristic, complemented
142	#2065	C₂×C₅	1	1	yes	characteristic, complemented
143	#2054	C₂×C₅	1	1	yes	characteristic, complemented
144	#2034	C₂×C₅	1	1	yes	characteristic, complemented
145	#2033	C₂×C₅	1	1	yes	characteristic, complemented
146	#1999	C₂×C₅	1	1	yes	characteristic
147	#1776	C₂×C₅	1	1	yes	characteristic, complemented
148	#1762	C₂×C₅	1	1	yes	characteristic, complemented
149	#1762	C₂×C₅	1	1	yes	characteristic, complemented
150	C₂⁴×C₅	—	2	1	no	—
151	C₂⁴×C₅	—	2	1	no	—
152	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₅×D₄	—	2	4	no	—
154	C₂×C₅×D₄	—	2	4	no	—
155	C₂×C₅×D₄	—	2	1	no	—
156	C₂×C₅×D₄	—	2	1	no	—
157	C₂×C₅×D₄	—	2	1	no	—
158	C₂×C₅×D₄	—	2	1	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	—	4	2	no	—
166	C₂×C₅×D₄	—	4	2	no	—
167	C₂×C₅×D₄	—	4	2	no	—
168	C₂×C₅×D₄	—	4	2	no	—
169	C₂×C₅×D₄	#41	1	2	yes	—
170	C₂×C₅×D₄	#41	1	2	yes	—
171	C₂²×C₄×C₅	—	2	2	no	—
172	C₂²×C₄×C₅	—	2	1	no	—
173	C₂²×C₄×C₅	—	2	1	no	—
174	C₂²×C₄×C₅	—	2	2	no	—
175	C₂²×C₄×C₅	—	2	2	no	—
176	C₂²×C₄×C₅	—	2	2	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	—	2	1	no	—
186	C₂²×C₄×C₅	—	2	1	no	—
187	C₂²×C₄×C₅	—	4	1	no	—
188	C₂²×C₄×C₅	—	4	1	no	—
189	C₂²×C₄×C₅	—	4	2	no	—
190	C₂²×C₄×C₅	—	4	2	no	—
191	C₂²×C₄×C₅	—	4	2	no	—
192	C₂²×C₄×C₅	—	4	2	no	—
193	C₂²×C₄×C₅	—	4	2	no	—
194	C₂²×C₄×C₅	—	4	2	no	—
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	C₂⁴	1	1	yes	characteristic
201	C₅×D₈	—	2	8	no	—
202	C₂×C₅×C₈	—	2	1	no	—
203	C₂×C₅×C₈	—	2	1	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	C₂×D₄	1	2	yes	—
213	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
214	C₅×C₄⋊C₄	—	2	1	no	—
215	C₅×C₄⋊C₄	—	2	1	no	—
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	#41	1	2	yes	—
227	C₅×C₄⋊C₄	#41	1	2	yes	—
228	C₅×C₂²⋊C₄	—	2	4	no	—
229	C₅×C₂²⋊C₄	—	2	4	no	—
230	C₅×C₂²⋊C₄	—	4	2	no	—
231	C₅×C₂²⋊C₄	—	4	2	no	—
232	C₅×C₂²⋊C₄	—	4	2	no	—
233	C₅×C₂²⋊C₄	—	4	2	no	—
234	C₅×C₂²⋊C₄	—	4	2	no	—
235	C₅×C₂²⋊C₄	—	4	2	no	—
236	C₅×C₂²⋊C₄	—	4	2	no	—
237	C₅×C₂²⋊C₄	—	4	2	no	—
238	C₄²×C₅	—	2	2	no	—
239	C₄²×C₅	—	2	2	no	—
240	C₄²×C₅	—	2	1	no	—
241	C₄²×C₅	—	2	1	no	—
242	C₄²×C₅	—	4	2	no	—
243	C₄²×C₅	—	4	2	no	—
244	C₄²×C₅	C₂×D₄	1	2	yes	—
245	C₄²×C₅	#41	1	2	yes	—
246	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
247	C₂×#121	C₂²×C₅	1	1	yes	characteristic
248	C₂×#121	C₂²×C₅	1	1	yes	characteristic
249	C₂×C₄×D₄	—	2	1	no	—
250	C₂×C₄×D₄	—	2	1	no	—
251	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
252	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
253	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
254	#442	—	2	4	no	—
255	#432	—	2	4	no	—
256	C₂×#107	C₂²×C₅	1	1	yes	characteristic
257	C₂×#106	C₂²×C₅	1	1	yes	characteristic
258	C₂×#106	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
260	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
261	C₂×#102	C₂²×C₅	1	1	yes	characteristic
262	C₂×#102	C₂²×C₅	1	1	yes	characteristic
263	C₂×#102	C₂²×C₅	1	1	yes	characteristic
264	C₂×#102	C₂²×C₅	1	1	yes	characteristic
265	C₂×#102	C₂²×C₅	1	1	yes	characteristic
266	C₂×#102	C₂²×C₅	1	1	yes	characteristic
267	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
268	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
269	C₂×#97	C₂²×C₅	1	1	yes	characteristic
270	C₂×#97	C₂²×C₅	1	1	yes	characteristic
271	#390	C₂²×C₅	1	1	yes	characteristic
272	#390	C₂²×C₅	1	1	yes	characteristic
273	#389	C₂²×C₅	1	1	yes	characteristic
274	#389	C₂²×C₅	1	1	yes	characteristic
275	#388	—	2	1	no	—
276	#388	—	2	1	no	—
277	#386	—	2	1	no	—
278	#386	—	2	1	no	—
279	#380	C₂²×C₅	1	1	yes	characteristic
280	#380	C₂²×C₅	1	1	yes	characteristic
281	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
282	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
283	C₄×C₂²⋊C₄	—	2	1	no	—
284	C₄×C₂²⋊C₄	—	2	1	no	—
285	#340	C₂²×C₅	1	1	yes	characteristic
286	#340	C₂²×C₅	1	1	yes	characteristic
287	#340	C₂²×C₅	1	1	yes	characteristic
288	#340	C₂²×C₅	1	1	yes	characteristic
289	#340	C₂²×C₅	1	1	yes	characteristic
290	#340	C₂²×C₅	1	1	yes	characteristic
291	C₂³×C₅	—	2	1	no	—
292	C₂³×C₅	—	2	1	no	—
293	C₂³×C₅	—	2	1	no	—
294	C₂³×C₅	—	2	1	no	—
295	C₂³×C₅	—	2	1	no	—
296	C₂³×C₅	—	2	1	no	—
297	C₂³×C₅	—	2	2	no	—
298	C₂³×C₅	—	2	2	no	—
299	C₂³×C₅	—	4	1	no	—
300	C₂³×C₅	—	4	1	no	—
301	C₂³×C₅	—	4	1	no	—
302	C₂³×C₅	—	4	1	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	AGL(1,ℤ/8)	1	2	yes	—
312	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
313	C₅×D₄	—	2	2	no	—
314	C₅×D₄	—	2	2	no	—
315	C₅×D₄	—	2	2	no	—
316	C₅×D₄	—	2	2	no	—
317	C₅×D₄	—	4	8	no	—
318	C₅×D₄	—	4	8	no	—
319	C₅×D₄	—	4	1	no	—
320	C₅×D₄	—	4	1	no	—
321	C₅×D₄	—	4	1	no	—
322	C₅×D₄	—	4	1	no	—
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	2	1	no	—
325	C₂×C₄×C₅	—	2	1	no	—
326	C₂×C₄×C₅	—	2	1	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	1	no	—
332	C₂×C₄×C₅	—	2	1	no	—
333	C₂×C₄×C₅	—	2	2	no	—
334	C₂×C₄×C₅	—	2	2	no	—
335	C₂×C₄×C₅	—	2	1	no	—
336	C₂×C₄×C₅	—	2	1	no	—
337	C₂×C₄×C₅	—	4	4	no	—
338	C₂×C₄×C₅	—	4	4	no	—
339	C₂×C₄×C₅	—	4	1	no	—
340	C₂×C₄×C₅	—	4	1	no	—
341	C₂×C₄×C₅	—	4	1	no	—
342	C₂×C₄×C₅	—	4	1	no	—
343	C₂×C₄×C₅	—	4	1	no	—
344	C₂×C₄×C₅	—	4	1	no	—
345	C₂×C₄×C₅	—	4	1	no	—
346	C₂×C₄×C₅	—	4	1	no	—
347	C₂×C₄×C₅	—	4	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	—	8	4	no	—
360	C₂×C₄×C₅	—	8	4	no	—
361	C₂×C₄×C₅	#121	1	2	yes	—
362	C₂×C₄×C₅	#121	1	2	yes	—
363	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
364	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
366	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
367	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
368	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
369	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
370	C₅×C₈	—	2	2	no	—
371	C₅×C₈	—	2	2	no	—
372	C₅×C₈	—	4	1	no	—
373	C₅×C₈	—	4	1	no	—
374	C₂²×D₄	—	2	1	no	—
375	C₂²×D₄	—	2	1	no	—
376	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
377	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
378	C₂³×C₄	—	2	1	no	—
379	C₂³×C₄	—	2	1	no	—
380	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
381	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
382	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
383	C₂×D₈	—	2	2	no	—
384	C₂×D₈	—	2	2	no	—
385	C₂×D₈	—	2	2	no	—
386	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
387	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
388	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
389	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
390	#121	—	2	2	no	—
391	#121	—	2	2	no	—
392	#121	—	2	2	no	—
393	#121	—	2	2	no	—
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	—	2	2	no	—
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	4	4	no	—
399	C₄×D₄	—	4	4	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₄²	—	2	2	no	—
419	C₂×C₄²	—	2	2	no	—
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	—	2	1	no	—
422	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
423	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
426	#107	—	2	2	no	—
427	#106	—	2	2	no	—
428	#106	—	2	2	no	—
429	C₄⋊C₈	—	2	2	no	—
430	C₄⋊C₈	—	2	2	no	—
431	#102	—	2	2	no	—
432	#102	—	2	2	no	—
433	#102	—	2	2	no	—
434	#102	—	2	2	no	—
435	#102	—	2	2	no	—
436	#102	—	2	2	no	—
437	C₂²⋊C₈	—	2	2	no	—
438	C₂²⋊C₈	—	2	2	no	—
439	#97	—	2	2	no	—
440	#97	C₅×D₄	1	4	yes	complemented
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	C₂²×C₅	—	2	2	no	—
448	C₂²×C₅	—	2	2	no	—
449	C₂²×C₅	—	2	2	no	—
450	C₂²×C₅	—	4	1	no	—
451	C₂²×C₅	—	4	1	no	—
452	C₂²×C₅	—	4	1	no	—
453	C₂²×C₅	—	4	1	no	—
454	C₂²×C₅	—	4	2	no	—
455	C₂²×C₅	—	4	2	no	—
456	C₂²×C₅	—	4	2	no	—
457	C₂²×C₅	—	4	2	no	—
458	C₂²×C₅	—	4	2	no	—
459	C₂²×C₅	—	4	2	no	—
460	C₂²×C₅	—	8	1	no	—
461	C₂²×C₅	—	8	1	no	—
462	C₂²×C₅	—	8	1	no	—
463	C₂²×C₅	—	8	1	no	—
464	C₂²×C₅	—	8	1	no	—
465	C₂²×C₅	—	8	1	no	—
466	C₂²×C₅	—	8	1	no	—
467	C₂²×C₅	—	8	1	no	—
468	C₂²×C₅	C₂×#121	1	1	yes	characteristic
469	C₂²×C₅	#525	1	1	yes	characteristic
470	C₂²×C₅	#525	1	1	yes	characteristic
471	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
472	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
473	C₂²×C₅	#575	1	1	yes	characteristic
474	C₂²×C₅	#575	1	1	yes	characteristic
475	C₄×C₅	—	2	2	no	—
476	C₄×C₅	—	2	2	no	—
477	C₄×C₅	—	2	2	no	—
478	C₄×C₅	—	4	2	no	—
479	C₄×C₅	—	4	2	no	—
480	C₄×C₅	—	4	1	no	—
481	C₄×C₅	—	4	1	no	—
482	C₄×C₅	—	8	1	no	—
483	C₄×C₅	—	8	1	no	—
484	C₄×C₅	—	8	1	no	—
485	C₄×C₅	—	8	1	no	—
486	C₄×C₅	#525	1	1	yes	characteristic
487	C₄×C₅	#529	1	1	yes	characteristic
488	C₄×C₅	#529	1	1	yes	characteristic
489	C₄×C₅	#532	1	1	yes	characteristic
490	C₂⁴	—	2	1	no	—
491	C₂⁴	—	2	1	no	—
492	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
493	C₂×D₄	—	2	4	no	—
494	C₂×D₄	—	2	4	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	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	—	4	2	no	—
506	C₂×D₄	—	4	2	no	—
507	C₂×D₄	—	4	2	no	—
508	C₂×D₄	—	4	2	no	—
509	C₂×D₄	C₅×#41	1	2	yes	—
510	C₂×D₄	C₅×#41	1	2	yes	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	2	no	—
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	1	no	—
528	C₂²×C₄	—	4	1	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	—	4	2	no	—
534	C₂²×C₄	—	4	2	no	—
535	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
536	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
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	C₂⁴×C₅	1	1	yes	characteristic
541	D₈	—	2	8	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	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	C₂×C₅×D₄	1	2	yes	—
553	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
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	—	4	2	no	—
565	C₄⋊C₄	—	4	2	no	—
566	C₄⋊C₄	C₅×#41	1	2	yes	—
567	C₄⋊C₄	C₅×#41	1	2	yes	—
568	C₂²⋊C₄	—	2	4	no	—
569	C₂²⋊C₄	—	2	4	no	—
570	C₂²⋊C₄	—	4	2	no	—
571	C₂²⋊C₄	—	4	2	no	—
572	C₂²⋊C₄	—	4	2	no	—
573	C₂²⋊C₄	—	4	2	no	—
574	C₂²⋊C₄	—	4	2	no	—
575	C₂²⋊C₄	—	4	2	no	—
576	C₂²⋊C₄	—	4	2	no	—
577	C₂²⋊C₄	—	4	2	no	—
578	C₄²	—	2	2	no	—
579	C₄²	—	2	2	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	2	1	no	—
582	C₄²	—	4	2	no	—
583	C₄²	—	4	2	no	—
584	C₄²	C₂×C₅×D₄	1	2	yes	—
585	C₄²	C₅×#41	1	2	yes	—
586	C₂×C₅	—	4	2	no	—
587	C₂×C₅	—	8	2	no	—
588	C₂×C₅	—	8	2	no	—
589	C₂×C₅	#2392	1	1	yes	characteristic
590	C₂×C₅	#3055	1	1	yes	characteristic
591	C₂×C₅	#3055	1	1	yes	characteristic
592	C₂×C₅	#3109	1	1	yes	characteristic
593	C₂×C₅	#3111	1	1	yes	characteristic
594	C₂×C₅	#3114	1	1	yes	characteristic
595	C₂×C₅	#3115	1	1	yes	characteristic
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	1	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	C₅×AGL(1,ℤ/8)	1	2	yes	—
617	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
618	D₄	—	2	2	no	—
619	D₄	—	2	2	no	—
620	D₄	—	2	2	no	—
621	D₄	—	2	2	no	—
622	D₄	—	4	8	no	—
623	D₄	—	4	8	no	—
624	D₄	—	4	1	no	—
625	D₄	—	4	1	no	—
626	D₄	—	4	1	no	—
627	D₄	—	4	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	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	1	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	4	4	no	—
643	C₂×C₄	—	4	4	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	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	—	8	4	no	—
665	C₂×C₄	—	8	4	no	—
666	C₂×C₄	C₅×#121	1	2	yes	—
667	C₂×C₄	C₅×#121	1	2	yes	—
668	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
669	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
670	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
671	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
672	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
673	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
674	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
675	C₈	—	2	2	no	—
676	C₈	—	2	2	no	—
677	C₈	—	4	1	no	—
678	C₈	—	4	1	no	—
679	C₅	#23708	1	1	yes	characteristic, direct product factor, Sylow
680	C₂²	—	2	2	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	1	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	2	no	—
688	C₂²	—	4	2	no	—
689	C₂²	—	4	2	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	8	1	no	—
694	C₂²	—	8	1	no	—
695	C₂²	—	8	1	no	—
696	C₂²	—	8	1	no	—
697	C₂²	—	8	1	no	—
698	C₂²	—	8	1	no	—
699	C₂²	—	8	1	no	—
700	C₂²	—	8	1	no	—
701	C₂²	C₂×C₅×#121	1	1	yes	characteristic
702	C₂²	C₅×#525	1	1	yes	characteristic
703	C₂²	C₅×#525	1	1	yes	characteristic
704	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
705	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
706	C₂²	C₅×#575	1	1	yes	characteristic
707	C₂²	C₅×#575	1	1	yes	characteristic
708	C₄	—	2	2	no	—
709	C₄	—	2	2	no	—
710	C₄	—	2	2	no	—
711	C₄	—	4	1	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	1	no	—
715	C₄	—	8	1	no	—
716	C₄	—	8	1	no	—
717	C₄	—	8	1	no	—
718	C₄	—	8	1	no	—
719	C₄	C₅×#525	1	1	yes	characteristic
720	C₄	C₅×#529	1	1	yes	characteristic
721	C₄	C₅×#529	1	1	yes	characteristic
722	C₄	C₅×#532	1	1	yes	characteristic
723	C₂	—	4	2	no	—
724	C₂	—	8	2	no	—
725	C₂	—	8	2	no	—
726	C₂	C₅×#2392	1	1	yes	characteristic
727	C₂	C₅×#3055	1	1	yes	characteristic
728	C₂	C₅×#3055	1	1	yes	characteristic
729	C₂	C₅×#3109	1	1	yes	characteristic
730	C₂	C₅×#3111	1	1	yes	characteristic
731	C₂	C₅×#3114	1	1	yes	characteristic
732	C₂	C₅×#3115	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₅×#1999	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#442	C₂	semidirect
2. C₂×C₅×#432	C₂	semidirect
3. C₄×C₅×#121	C₂	semidirect
4. C₄×C₅×#121	C₂	semidirect
5. C₅×#2088	C₂	semidirect
6. C₅×#2077	C₂	semidirect
7. C₅×#2067	C₂	semidirect
8. C₅×#2065	C₂	semidirect
9. C₅×#2054	C₂	semidirect
10. C₅×#2034	C₂	semidirect
11. C₅×#2033	C₂	semidirect
13. C₅×#1776	C₂	semidirect
14. C₅×#1762	C₂	semidirect
15. C₅×#1762	C₂	semidirect
61. #23708	C₅	direct (N × H)
128. C₅×#97	D₄	semidirect
135. C₂×#442	C₂×C₅	semidirect
136. C₂×#432	C₂×C₅	semidirect
137. C₄×#121	C₂×C₅	semidirect
138. C₄×#121	C₂×C₅	semidirect
139. #2088	C₂×C₅	semidirect
140. #2077	C₂×C₅	semidirect
141. #2067	C₂×C₅	semidirect
142. #2065	C₂×C₅	semidirect
143. #2054	C₂×C₅	semidirect
144. #2034	C₂×C₅	semidirect
145. #2033	C₂×C₅	semidirect
147. #1776	C₂×C₅	semidirect
148. #1762	C₂×C₅	semidirect
149. #1762	C₂×C₅	semidirect
440. #97	C₅×D₄	semidirect
679. C₅	#23708	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×#442	2
C₂×C₅×#432	2
C₄×C₅×#121	2
C₅×#2088	2
C₅×#2077	2
C₅×#2067	2
C₅×#2065	2
C₅×#2054	2
C₅×#2034	2
C₅×#2033	2
C₅×#1999	2
C₅×#1776	2
C₅×#1762	2
#23708	5

Subgroups — C5×#23708 #11946428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23708 #11946428