Subgroups — C₅×#22585 #11945305

Order 1280.

934 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#419	C₂	1	1	yes	maximal, characteristic
2	C₅×#2346	C₂	1	1	yes	maximal, characteristic
3	C₅×Q₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₅×#1935	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1933	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1928	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1927	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1865	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1863	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1825	C₂	1	1	yes	maximal, characteristic
11	C₅×#1809	C₂	1	1	yes	maximal, characteristic
12	C₅×#1787	C₂	1	1	yes	maximal, characteristic
13	C₅×#1763	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1753	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₂²×C₅×M₁₆	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×C₅×#117	C₂²	1	1	yes	characteristic
21	C₂×C₅×#107	C₂²	1	1	yes	characteristic
22	C₂×C₅×#106	C₂²	1	1	yes	characteristic
23	C₅×#419	C₄	1	8	yes	complemented
24	C₂×C₅×#103	C₂²	1	1	yes	characteristic
25	C₂×C₅×#103	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×#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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₅×#97	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
35	C₅×#391	—	2	1	no	—
36	C₅×#391	—	2	1	no	—
37	C₅×#391	C₂²	1	1	yes	characteristic
38	C₅×#391	C₂²	1	1	yes	characteristic
39	C₅×#389	C₂²	1	1	yes	characteristic
40	C₅×#389	C₂²	1	1	yes	characteristic
41	C₅×#388	—	2	1	no	—
42	C₅×#388	—	2	1	no	—
43	C₅×#382	—	2	1	no	—
44	C₅×#380	—	2	1	no	—
45	C₅×#380	C₂²	1	1	yes	characteristic
46	C₅×#380	C₂²	1	1	yes	characteristic
47	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
50	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
51	C₅×#376	—	2	1	no	—
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×#340	C₂²	1	1	yes	characteristic
57	C₅×#340	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	C₅×#336	C₂²	1	1	yes	characteristic
60	#22585	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₅×Q₈	—	2	1	no	—
62	C₂²×C₅×Q₈	—	2	2	no	—
63	C₂²×C₅×Q₈	—	2	2	no	—
64	C₂²×C₅×Q₈	—	2	2	no	—
65	C₂²×C₅×Q₈	—	4	1	no	—
66	C₂²×C₅×Q₈	—	4	1	no	—
67	C₂²×C₅×Q₈	C₂×C₄	1	4	yes	—
68	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
69	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₅	—	2	1	no	—
71	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₂×C₅×M₁₆	—	4	1	no	—
73	C₂×C₅×M₁₆	—	4	1	no	—
74	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
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	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₄×C₅×Q₈	—	2	2	no	—
80	C₄×C₅×Q₈	—	2	2	no	—
81	C₄×C₅×Q₈	—	4	1	no	—
82	C₄×C₅×Q₈	—	4	1	no	—
83	C₅×#117	—	2	2	no	—
84	C₅×#117	C₂×C₄	1	4	yes	—
85	C₂×C₅×C₄⋊C₄	—	2	1	no	—
86	C₂×C₅×C₄⋊C₄	—	2	1	no	—
87	C₂×C₅×C₄⋊C₄	—	2	1	no	—
88	C₂×C₅×C₄⋊C₄	—	2	1	no	—
89	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
99	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
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	—	2	1	no	—
104	C₂×C₄²×C₅	—	2	1	no	—
105	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
107	C₅×#107	—	4	1	no	—
108	C₅×#106	—	4	1	no	—
109	C₅×#103	—	2	2	no	—
110	C₅×#103	—	2	2	no	—
111	C₅×#103	—	4	1	no	—
112	C₅×#103	—	4	1	no	—
113	C₅×#103	C₂×C₄	1	4	yes	—
114	C₅×#103	C₂×C₄	1	4	yes	—
115	C₅×#103	C₂×C₄	1	4	yes	—
116	C₅×#103	C₂×C₄	1	4	yes	—
117	C₅×C₂²⋊C₈	—	2	2	no	—
118	C₅×#97	—	4	1	no	—
119	C₄×C₅×C₈	—	4	1	no	—
120	C₅×#95	—	2	1	no	—
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	C₅×#95	—	2	1	no	—
128	C₅×#95	—	2	1	no	—
129	C₅×#95	—	2	1	no	—
130	C₅×#95	D₄	1	1	yes	characteristic
131	C₅×#95	D₄	1	1	yes	characteristic
132	C₂×#419	C₂×C₅	1	1	yes	characteristic
133	#2346	C₂×C₅	1	1	yes	characteristic
134	Q₈×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
135	#1935	C₂×C₅	1	1	yes	characteristic, complemented
136	#1933	C₂×C₅	1	1	yes	characteristic, complemented
137	#1928	C₂×C₅	1	1	yes	characteristic, complemented
138	#1927	C₂×C₅	1	1	yes	characteristic, complemented
139	#1865	C₂×C₅	1	1	yes	characteristic, complemented
140	#1863	C₂×C₅	1	1	yes	characteristic, complemented
141	#1825	C₂×C₅	1	1	yes	characteristic
142	#1809	C₂×C₅	1	1	yes	characteristic
143	#1787	C₂×C₅	1	1	yes	characteristic
144	#1763	C₂×C₅	1	1	yes	characteristic, complemented
145	C₄×#103	C₂×C₅	1	1	yes	characteristic, complemented
146	#1753	C₂×C₅	1	1	yes	characteristic
147	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
148	C₂×C₅×Q₈	—	2	4	no	—
149	C₂×C₅×Q₈	—	2	1	no	—
150	C₂×C₅×Q₈	—	2	1	no	—
151	C₂×C₅×Q₈	—	2	1	no	—
152	C₂×C₅×Q₈	—	2	1	no	—
153	C₂×C₅×Q₈	—	2	8	no	—
154	C₂×C₅×Q₈	—	2	1	no	—
155	C₂×C₅×Q₈	—	2	1	no	—
156	C₂×C₅×Q₈	—	2	1	no	—
157	C₂×C₅×Q₈	—	2	1	no	—
158	C₂×C₅×Q₈	—	4	2	no	—
159	C₂×C₅×Q₈	—	4	2	no	—
160	C₂×C₅×Q₈	—	4	4	no	—
161	C₂×C₅×Q₈	—	4	4	no	—
162	C₂×C₅×Q₈	—	4	4	no	—
163	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
164	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
165	C₂×C₅×Q₈	#41	1	2	yes	—
166	C₂×C₅×Q₈	#41	1	2	yes	—
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	—	2	1	no	—
169	C₂²×C₄×C₅	—	2	1	no	—
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	—	2	1	no	—
172	C₂²×C₄×C₅	—	2	4	no	—
173	C₂²×C₄×C₅	—	2	1	no	—
174	C₂²×C₄×C₅	—	2	1	no	—
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	—	4	2	no	—
181	C₂²×C₄×C₅	—	4	2	no	—
182	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
183	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₅	#41	1	2	yes	—
189	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
190	C₅×M₁₆	—	4	4	no	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	2	1	no	—
193	C₂×C₅×C₈	—	2	1	no	—
194	C₂×C₅×C₈	—	2	1	no	—
195	C₂×C₅×C₈	—	2	1	no	—
196	C₂×C₅×C₈	—	2	1	no	—
197	C₂×C₅×C₈	—	2	1	no	—
198	C₂×C₅×C₈	—	2	1	no	—
199	C₂×C₅×C₈	—	2	1	no	—
200	C₂×C₅×C₈	—	2	1	no	—
201	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
202	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
203	C₅×C₄⋊C₄	—	2	1	no	—
204	C₅×C₄⋊C₄	—	2	1	no	—
205	C₅×C₄⋊C₄	—	2	1	no	—
206	C₅×C₄⋊C₄	—	2	1	no	—
207	C₅×C₄⋊C₄	—	2	1	no	—
208	C₅×C₄⋊C₄	—	2	1	no	—
209	C₅×C₄⋊C₄	—	2	1	no	—
210	C₅×C₄⋊C₄	—	2	1	no	—
211	C₅×C₄⋊C₄	—	2	1	no	—
212	C₅×C₄⋊C₄	—	2	1	no	—
213	C₅×C₄⋊C₄	—	4	2	no	—
214	C₅×C₄⋊C₄	—	4	2	no	—
215	C₅×C₄⋊C₄	—	8	1	no	—
216	C₅×C₄⋊C₄	—	8	1	no	—
217	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
218	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
219	C₅×C₂²⋊C₄	—	2	4	no	—
220	C₅×C₂²⋊C₄	—	2	2	no	—
221	C₅×C₂²⋊C₄	—	4	1	no	—
222	C₅×C₂²⋊C₄	—	4	2	no	—
223	C₅×C₂²⋊C₄	—	8	1	no	—
224	C₄²×C₅	—	2	4	no	—
225	C₄²×C₅	—	2	1	no	—
226	C₄²×C₅	—	2	1	no	—
227	C₄²×C₅	—	2	1	no	—
228	C₄²×C₅	—	2	1	no	—
229	C₄²×C₅	—	4	2	no	—
230	C₄²×C₅	—	4	2	no	—
231	C₄²×C₅	—	4	2	no	—
232	C₄²×C₅	—	4	2	no	—
233	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic
234	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
236	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
237	C₂×#117	C₂²×C₅	1	1	yes	characteristic
238	C₂×#107	C₂²×C₅	1	1	yes	characteristic
239	C₂×#106	C₂²×C₅	1	1	yes	characteristic
240	#419	C₄×C₅	1	8	yes	complemented
241	C₂×#103	C₂²×C₅	1	1	yes	characteristic
242	C₂×#103	C₂²×C₅	1	1	yes	characteristic
243	C₂×#103	C₂²×C₅	1	1	yes	characteristic
244	C₂×#103	C₂²×C₅	1	1	yes	characteristic
245	C₂×#103	C₂²×C₅	1	1	yes	characteristic
246	C₂×#103	C₂²×C₅	1	1	yes	characteristic
247	C₂×#103	C₂²×C₅	1	1	yes	characteristic
248	C₂×#103	C₂²×C₅	1	1	yes	characteristic
249	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
250	C₂×#97	C₂²×C₅	1	1	yes	characteristic
251	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
252	#391	—	2	1	no	—
253	#391	—	2	1	no	—
254	#391	C₂²×C₅	1	1	yes	characteristic
255	#391	C₂²×C₅	1	1	yes	characteristic
256	#389	C₂²×C₅	1	1	yes	characteristic
257	#389	C₂²×C₅	1	1	yes	characteristic
258	#388	—	2	1	no	—
259	#388	—	2	1	no	—
260	#382	—	2	1	no	—
261	#380	—	2	1	no	—
262	#380	C₂²×C₅	1	1	yes	characteristic
263	#380	C₂²×C₅	1	1	yes	characteristic
264	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
265	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
266	C₄×C₂²⋊C₄	—	2	1	no	—
267	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
268	#376	—	2	1	no	—
269	#340	C₂²×C₅	1	1	yes	characteristic
270	#340	C₂²×C₅	1	1	yes	characteristic
271	#340	C₂²×C₅	1	1	yes	characteristic
272	#340	C₂²×C₅	1	1	yes	characteristic
273	#340	C₂²×C₅	1	1	yes	characteristic
274	#340	C₂²×C₅	1	1	yes	characteristic
275	#336	C₂²×C₅	1	1	yes	characteristic
276	#336	C₂²×C₅	1	1	yes	characteristic
277	C₂³×C₅	—	2	1	no	—
278	C₂³×C₅	—	2	1	no	—
279	C₂³×C₅	—	2	1	no	—
280	C₂³×C₅	—	2	1	no	—
281	C₂³×C₅	—	2	1	no	—
282	C₂³×C₅	—	2	1	no	—
283	C₂³×C₅	C₄×D₄	1	2	yes	—
284	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
285	C₅×Q₈	—	2	2	no	—
286	C₅×Q₈	—	2	2	no	—
287	C₅×Q₈	—	2	2	no	—
288	C₅×Q₈	—	2	2	no	—
289	C₅×Q₈	—	2	2	no	—
290	C₅×Q₈	—	4	8	no	—
291	C₅×Q₈	—	4	1	no	—
292	C₅×Q₈	—	4	1	no	—
293	C₅×Q₈	#117	1	4	yes	—
294	C₂×C₄×C₅	—	2	2	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	—	2	2	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	2	2	no	—
307	C₂×C₄×C₅	—	2	2	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	4	8	no	—
318	C₂×C₄×C₅	—	4	1	no	—
319	C₂×C₄×C₅	—	4	1	no	—
320	C₂×C₄×C₅	—	4	1	no	—
321	C₂×C₄×C₅	—	4	1	no	—
322	C₂×C₄×C₅	—	4	1	no	—
323	C₂×C₄×C₅	—	4	1	no	—
324	C₂×C₄×C₅	—	4	1	no	—
325	C₂×C₄×C₅	—	4	1	no	—
326	C₂×C₄×C₅	—	4	1	no	—
327	C₂×C₄×C₅	—	4	1	no	—
328	C₂×C₄×C₅	—	4	1	no	—
329	C₂×C₄×C₅	—	4	1	no	—
330	C₂×C₄×C₅	—	4	1	no	—
331	C₂×C₄×C₅	—	4	1	no	—
332	C₂×C₄×C₅	—	4	1	no	—
333	C₂×C₄×C₅	—	4	1	no	—
334	C₂×C₄×C₅	—	4	1	no	—
335	C₂×C₄×C₅	—	4	1	no	—
336	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
337	C₂×C₄×C₅	#137	1	2	yes	—
338	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
339	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
340	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
341	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
342	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
343	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
344	C₅×C₈	—	2	2	no	—
345	C₅×C₈	—	2	2	no	—
346	C₅×C₈	—	4	1	no	—
347	C₅×C₈	—	4	1	no	—
348	C₂²×Q₈	—	2	1	no	—
349	C₂²×Q₈	—	2	2	no	—
350	C₂²×Q₈	—	2	2	no	—
351	C₂²×Q₈	—	2	2	no	—
352	C₂²×Q₈	—	4	1	no	—
353	C₂²×Q₈	—	4	1	no	—
354	C₂²×Q₈	C₂×C₄×C₅	1	4	yes	—
355	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
356	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
357	C₂³×C₄	—	2	1	no	—
358	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
359	C₂×M₁₆	—	4	1	no	—
360	C₂×M₁₆	—	4	1	no	—
361	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
362	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
363	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
365	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
366	C₄×Q₈	—	2	2	no	—
367	C₄×Q₈	—	2	2	no	—
368	C₄×Q₈	—	4	1	no	—
369	C₄×Q₈	—	4	1	no	—
370	#117	—	2	2	no	—
371	#117	C₂×C₄×C₅	1	4	yes	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
386	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
387	C₂×C₄²	—	2	1	no	—
388	C₂×C₄²	—	2	1	no	—
389	C₂×C₄²	—	2	1	no	—
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
394	#107	—	4	1	no	—
395	#106	—	4	1	no	—
396	#103	—	2	2	no	—
397	#103	—	2	2	no	—
398	#103	—	4	1	no	—
399	#103	—	4	1	no	—
400	#103	C₂×C₄×C₅	1	4	yes	—
401	#103	C₂×C₄×C₅	1	4	yes	—
402	#103	C₂×C₄×C₅	1	4	yes	—
403	#103	C₂×C₄×C₅	1	4	yes	—
404	C₂²⋊C₈	—	2	2	no	—
405	#97	—	4	1	no	—
406	C₄×C₈	—	4	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	no	—
410	#95	—	2	1	no	—
411	#95	—	2	1	no	—
412	#95	—	2	1	no	—
413	#95	—	2	1	no	—
414	#95	—	2	1	no	—
415	#95	—	2	1	no	—
416	#95	—	2	1	no	—
417	#95	C₅×D₄	1	1	yes	characteristic
418	#95	C₅×D₄	1	1	yes	characteristic
419	C₂²×C₅	—	2	2	no	—
420	C₂²×C₅	—	2	2	no	—
421	C₂²×C₅	—	2	2	no	—
422	C₂²×C₅	—	4	1	no	—
423	C₂²×C₅	—	4	1	no	—
424	C₂²×C₅	—	4	1	no	—
425	C₂²×C₅	—	4	1	no	—
426	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
427	C₂²×C₅	#546	1	1	yes	characteristic
428	C₂²×C₅	#546	1	1	yes	characteristic
429	C₂²×C₅	C₂×#137	1	1	yes	characteristic
430	C₂²×C₅	#575	1	1	yes	characteristic
431	C₂²×C₅	#577	1	1	yes	characteristic
432	C₂²×C₅	#578	1	1	yes	characteristic
433	C₄×C₅	—	2	2	no	—
434	C₄×C₅	—	2	4	no	—
435	C₄×C₅	—	2	2	no	—
436	C₄×C₅	—	4	1	no	—
437	C₄×C₅	—	4	2	no	—
438	C₄×C₅	—	4	2	no	—
439	C₄×C₅	—	4	2	no	—
440	C₄×C₅	—	4	1	no	—
441	C₄×C₅	—	4	1	no	—
442	C₄×C₅	—	8	1	no	—
443	C₄×C₅	—	8	1	no	—
444	C₄×C₅	—	8	1	no	—
445	C₄×C₅	—	8	1	no	—
446	C₄×C₅	C₂×#117	1	1	yes	characteristic
447	C₄×C₅	#518	1	1	yes	characteristic
448	C₄×C₅	#551	1	1	yes	characteristic
449	C₄×C₅	#551	1	1	yes	characteristic
450	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
451	C₂×Q₈	—	2	4	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	8	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	4	2	no	—
462	C₂×Q₈	—	4	2	no	—
463	C₂×Q₈	—	4	4	no	—
464	C₂×Q₈	—	4	4	no	—
465	C₂×Q₈	—	4	4	no	—
466	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
467	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
468	C₂×Q₈	C₅×#41	1	2	yes	—
469	C₂×Q₈	C₅×#41	1	2	yes	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	4	2	no	—
484	C₂²×C₄	—	4	2	no	—
485	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
486	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
487	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
488	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
489	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
490	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
491	C₂²×C₄	C₅×#41	1	2	yes	—
492	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
493	M₁₆	—	4	4	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
505	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	4	2	no	—
517	C₄⋊C₄	—	4	2	no	—
518	C₄⋊C₄	—	8	1	no	—
519	C₄⋊C₄	—	8	1	no	—
520	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
521	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
522	C₂²⋊C₄	—	2	4	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	4	1	no	—
525	C₂²⋊C₄	—	4	2	no	—
526	C₂²⋊C₄	—	8	1	no	—
527	C₄²	—	2	4	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	4	2	no	—
533	C₄²	—	4	2	no	—
534	C₄²	—	4	2	no	—
535	C₄²	—	4	2	no	—
536	C₂×C₅	—	4	2	no	—
537	C₂×C₅	#2342	1	1	yes	characteristic
538	C₂×C₅	C₄×#137	1	1	yes	characteristic
539	C₂×C₅	#2947	1	1	yes	characteristic
540	C₂×C₅	#3312	1	1	yes	characteristic
541	C₂×C₅	#3321	1	1	yes	characteristic
542	C₂×C₅	#3327	1	1	yes	characteristic
543	C₂×C₅	#3329	1	1	yes	characteristic
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	2	1	no	—
550	C₂³	C₄×C₅×D₄	1	2	yes	—
551	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
552	Q₈	—	2	2	no	—
553	Q₈	—	2	2	no	—
554	Q₈	—	2	2	no	—
555	Q₈	—	2	2	no	—
556	Q₈	—	2	2	no	—
557	Q₈	—	4	8	no	—
558	Q₈	—	4	1	no	—
559	Q₈	—	4	1	no	—
560	Q₈	C₅×#117	1	4	yes	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	4	8	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
604	C₂×C₄	C₅×#137	1	2	yes	—
605	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
606	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
607	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
608	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
609	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
610	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
611	C₈	—	2	2	no	—
612	C₈	—	2	2	no	—
613	C₈	—	4	1	no	—
614	C₈	—	4	1	no	—
615	C₅	#22585	1	1	yes	characteristic, direct product factor, Sylow
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	1	no	—
623	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
624	C₂²	C₅×#546	1	1	yes	characteristic
625	C₂²	C₅×#546	1	1	yes	characteristic
626	C₂²	C₂×C₅×#137	1	1	yes	characteristic
627	C₂²	C₅×#575	1	1	yes	characteristic
628	C₂²	C₅×#577	1	1	yes	characteristic
629	C₂²	C₅×#578	1	1	yes	characteristic
630	C₄	—	2	2	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	4	no	—
633	C₄	—	4	1	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	1	no	—
636	C₄	—	4	2	no	—
637	C₄	—	4	2	no	—
638	C₄	—	4	2	no	—
639	C₄	—	8	1	no	—
640	C₄	—	8	1	no	—
641	C₄	—	8	1	no	—
642	C₄	—	8	1	no	—
643	C₄	C₂×C₅×#117	1	1	yes	characteristic
644	C₄	C₅×#518	1	1	yes	characteristic
645	C₄	C₅×#551	1	1	yes	characteristic
646	C₄	C₅×#551	1	1	yes	characteristic
647	C₂	—	4	2	no	—
648	C₂	C₅×#2342	1	1	yes	characteristic
649	C₂	C₄×C₅×#137	1	1	yes	characteristic
650	C₂	C₅×#2947	1	1	yes	characteristic
651	C₂	C₅×#3312	1	1	yes	characteristic
652	C₂	C₅×#3321	1	1	yes	characteristic
653	C₂	C₅×#3327	1	1	yes	characteristic
654	C₂	C₅×#3329	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	C₂⁴×C₅	C₂×D₄
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
4. C₅×#1935	C₂	semidirect
5. C₅×#1933	C₂	semidirect
6. C₅×#1928	C₂	semidirect
7. C₅×#1927	C₂	semidirect
8. C₅×#1865	C₂	semidirect
9. C₅×#1863	C₂	semidirect
13. C₅×#1763	C₂	semidirect
14. C₄×C₅×#103	C₂	semidirect
23. C₅×#419	C₄	semidirect
60. #22585	C₅	direct (N × H)
135. #1935	C₂×C₅	semidirect
136. #1933	C₂×C₅	semidirect
137. #1928	C₂×C₅	semidirect
138. #1927	C₂×C₅	semidirect
139. #1865	C₂×C₅	semidirect
140. #1863	C₂×C₅	semidirect
144. #1763	C₂×C₅	semidirect
145. C₄×#103	C₂×C₅	semidirect
240. #419	C₄×C₅	semidirect
615. C₅	#22585	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×#419	2
C₅×#2346	2
C₅×Q₈×C₂²⋊C₄	2
C₅×#1935	2
C₅×#1933	2
C₅×#1928	2
C₅×#1927	2
C₅×#1865	2
C₅×#1863	2
C₅×#1825	2
C₅×#1809	2
C₅×#1787	2
C₅×#1763	2
C₄×C₅×#103	2
C₅×#1753	2
#22585	5

Subgroups — C5×#22585 #11945305

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22585 #11945305