Subgroups — C₅×#22932 #11945652

Order 1280.

846 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#484	C₂	1	1	yes	maximal, characteristic
2	C₅×#2360	C₂	1	1	yes	maximal, characteristic
3	C₅×#2345	C₂	1	1	yes	maximal, characteristic
4	C₅×#1943	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1935	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1927	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1918	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1918	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1892	C₂	1	1	yes	maximal, characteristic
10	C₅×#1865	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1853	C₂	1	1	yes	maximal, characteristic
12	C₅×#1776	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1763	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1752	C₂	1	1	yes	maximal, characteristic
15	C₂×C₅×#340	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₅×#484	C₄	1	8	yes	complemented
22	C₂×C₅×#107	C₂²	1	1	yes	characteristic
23	C₂×C₅×#107	C₂²	1	1	yes	characteristic
24	C₂×C₅×#106	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×#103	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×#97	C₂²	1	1	yes	characteristic
32	C₂×C₅×#97	C₂²	1	1	yes	characteristic
33	C₅×#391	C₂²	1	1	yes	characteristic
34	C₅×#389	—	2	1	no	—
35	C₅×#389	C₂²	1	1	yes	characteristic
36	C₅×#389	C₂²	1	1	yes	characteristic
37	C₅×#389	C₂²	1	1	yes	characteristic
38	C₅×#387	—	2	1	no	—
39	C₅×#387	—	2	1	no	—
40	C₅×#387	—	2	1	no	—
41	C₅×#385	—	2	1	no	—
42	C₅×#380	—	2	1	no	—
43	C₅×#380	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	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
49	C₄×C₅×C₂²⋊C₄	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×#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	#22932	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₅	—	2	1	no	—
63	C₂³×C₄×C₅	—	2	1	no	—
64	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂²×C₅×C₈	—	2	2	no	—
66	C₂²×C₅×C₈	—	2	2	no	—
67	C₂²×C₅×C₈	—	4	1	no	—
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	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₅×C₂²⋊Q₈	—	2	2	no	—
73	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
74	C₄×C₅×Q₈	—	2	2	no	—
75	C₄×C₅×Q₈	—	4	1	no	—
76	C₂×C₅×C₄⋊C₄	—	2	1	no	—
77	C₂×C₅×C₄⋊C₄	—	2	1	no	—
78	C₂×C₅×C₄⋊C₄	—	2	2	no	—
79	C₂×C₅×C₄⋊C₄	—	2	2	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	—	4	1	no	—
86	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
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×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×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
97	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
104	C₅×#107	C₂×C₄	1	4	yes	complemented
105	C₅×#107	C₂×C₄	1	4	yes	complemented
106	C₅×#106	—	2	2	no	—
107	C₅×#106	—	4	1	no	—
108	C₅×#103	—	2	2	no	—
109	C₅×#103	—	4	1	no	—
110	C₅×#103	C₂×C₄	1	4	yes	complemented
111	C₅×#103	C₂×C₄	1	4	yes	complemented
112	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
113	C₅×#97	—	2	2	no	—
114	C₅×#97	—	4	1	no	—
115	C₅×#95	—	2	1	no	—
116	C₅×#95	—	2	1	no	—
117	C₅×#95	—	2	1	no	—
118	C₅×#95	—	2	1	no	—
119	C₅×#95	—	2	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	D₄	1	1	yes	characteristic
125	C₅×#95	D₄	1	1	yes	characteristic
126	C₂×#484	C₂×C₅	1	1	yes	characteristic
127	#2360	C₂×C₅	1	1	yes	characteristic
128	#2345	C₂×C₅	1	1	yes	characteristic
129	#1943	C₂×C₅	1	1	yes	characteristic, complemented
130	#1935	C₂×C₅	1	1	yes	characteristic, complemented
131	#1927	C₂×C₅	1	1	yes	characteristic, complemented
132	#1918	C₂×C₅	1	1	yes	characteristic, complemented
133	#1918	C₂×C₅	1	1	yes	characteristic, complemented
134	#1892	C₂×C₅	1	1	yes	characteristic
135	#1865	C₂×C₅	1	1	yes	characteristic, complemented
136	#1853	C₂×C₅	1	1	yes	characteristic
137	#1776	C₂×C₅	1	1	yes	characteristic, complemented
138	#1763	C₂×C₅	1	1	yes	characteristic, complemented
139	#1752	C₂×C₅	1	1	yes	characteristic
140	C₂×#340	C₂×C₅	1	1	yes	characteristic
141	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂×C₅×Q₈	—	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	—	2	1	no	—
147	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	—	2	1	no	—
150	C₂²×C₄×C₅	—	2	1	no	—
151	C₂²×C₄×C₅	—	2	1	no	—
152	C₂²×C₄×C₅	—	2	1	no	—
153	C₂²×C₄×C₅	—	2	1	no	—
154	C₂²×C₄×C₅	—	2	1	no	—
155	C₂²×C₄×C₅	—	2	1	no	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	—	2	4	no	—
158	C₂²×C₄×C₅	—	2	1	no	—
159	C₂²×C₄×C₅	—	2	1	no	—
160	C₂²×C₄×C₅	—	2	1	no	—
161	C₂²×C₄×C₅	—	4	2	no	—
162	C₂²×C₄×C₅	—	4	2	no	—
163	C₂²×C₄×C₅	—	8	1	no	—
164	C₂²×C₄×C₅	—	8	1	no	—
165	C₂²×C₄×C₅	—	8	1	no	—
166	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	#41	1	2	yes	—
173	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	—	4	4	no	—
184	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
185	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
186	C₂×C₅×C₈	#41	1	2	yes	—
187	C₅×C₄⋊C₄	—	2	4	no	—
188	C₅×C₄⋊C₄	—	2	4	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	—	2	1	no	—
197	C₅×C₄⋊C₄	—	2	1	no	—
198	C₅×C₄⋊C₄	—	2	1	no	—
199	C₅×C₄⋊C₄	—	4	2	no	—
200	C₅×C₄⋊C₄	—	4	2	no	—
201	C₅×C₄⋊C₄	—	8	1	no	—
202	C₅×C₄⋊C₄	—	8	1	no	—
203	C₅×C₄⋊C₄	—	8	1	no	—
204	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
205	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
206	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
207	C₅×C₄⋊C₄	#41	1	2	yes	—
208	C₅×C₂²⋊C₄	—	2	4	no	—
209	C₅×C₂²⋊C₄	—	2	2	no	—
210	C₅×C₂²⋊C₄	—	2	2	no	—
211	C₅×C₂²⋊C₄	—	4	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	2	no	—
217	C₄²×C₅	—	8	1	no	—
218	C₄²×C₅	—	8	1	no	—
219	C₄²×C₅	—	8	1	no	—
220	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
221	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
222	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
223	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
224	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
225	#484	C₄×C₅	1	8	yes	complemented
226	C₂×#107	C₂²×C₅	1	1	yes	characteristic
227	C₂×#107	C₂²×C₅	1	1	yes	characteristic
228	C₂×#106	C₂²×C₅	1	1	yes	characteristic
229	C₂×#106	C₂²×C₅	1	1	yes	characteristic
230	C₂×#103	C₂²×C₅	1	1	yes	characteristic
231	C₂×#103	C₂²×C₅	1	1	yes	characteristic
232	C₂×#103	C₂²×C₅	1	1	yes	characteristic
233	C₂×#103	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
235	C₂×#97	C₂²×C₅	1	1	yes	characteristic
236	C₂×#97	C₂²×C₅	1	1	yes	characteristic
237	#391	C₂²×C₅	1	1	yes	characteristic
238	#389	—	2	1	no	—
239	#389	C₂²×C₅	1	1	yes	characteristic
240	#389	C₂²×C₅	1	1	yes	characteristic
241	#389	C₂²×C₅	1	1	yes	characteristic
242	#387	—	2	1	no	—
243	#387	—	2	1	no	—
244	#387	—	2	1	no	—
245	#385	—	2	1	no	—
246	#380	—	2	1	no	—
247	#380	C₂²×C₅	1	1	yes	characteristic
248	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
249	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
250	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
251	C₄×C₂²⋊C₄	—	2	1	no	—
252	C₄×C₂²⋊C₄	—	2	1	no	—
253	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
254	#340	C₂²×C₅	1	1	yes	characteristic
255	#340	C₂²×C₅	1	1	yes	characteristic
256	#340	C₂²×C₅	1	1	yes	characteristic
257	#340	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	#336	C₂²×C₅	1	1	yes	characteristic
263	#336	C₂²×C₅	1	1	yes	characteristic
264	C₂³×C₅	—	2	1	no	—
265	C₂³×C₅	—	2	1	no	—
266	C₂³×C₅	—	2	1	no	—
267	C₂³×C₅	—	2	1	no	—
268	C₂³×C₅	C₄×D₄	1	2	yes	—
269	C₂³×C₅	#137	1	2	yes	—
270	C₂³×C₅	#137	1	2	yes	—
271	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
272	C₅×Q₈	—	2	2	no	—
273	C₅×Q₈	—	2	2	no	—
274	C₅×Q₈	—	4	1	no	—
275	C₅×Q₈	—	4	1	no	—
276	C₂×C₄×C₅	—	2	1	no	—
277	C₂×C₄×C₅	—	2	1	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	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	1	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	4	1	no	—
300	C₂×C₄×C₅	—	4	1	no	—
301	C₂×C₄×C₅	—	4	1	no	—
302	C₂×C₄×C₅	—	4	1	no	—
303	C₂×C₄×C₅	—	4	1	no	—
304	C₂×C₄×C₅	—	4	1	no	—
305	C₂×C₄×C₅	—	4	1	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	—	8	4	no	—
319	C₂×C₄×C₅	—	8	4	no	—
320	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
321	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
322	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
323	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
324	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
325	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
326	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
327	C₅×C₈	—	2	2	no	—
328	C₅×C₈	—	2	2	no	—
329	C₅×C₈	—	2	2	no	—
330	C₅×C₈	—	4	1	no	—
331	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
332	C₂³×C₄	—	2	1	no	—
333	C₂³×C₄	—	2	1	no	—
334	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
335	C₂²×C₈	—	2	2	no	—
336	C₂²×C₈	—	2	2	no	—
337	C₂²×C₈	—	4	1	no	—
338	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
342	C₂²⋊Q₈	—	2	2	no	—
343	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
344	C₄×Q₈	—	2	2	no	—
345	C₄×Q₈	—	4	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	4	1	no	—
356	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
357	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	C₅×D₄	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
374	#107	C₂×C₄×C₅	1	4	yes	complemented
375	#107	C₂×C₄×C₅	1	4	yes	complemented
376	#106	—	2	2	no	—
377	#106	—	4	1	no	—
378	#103	—	2	2	no	—
379	#103	—	4	1	no	—
380	#103	C₂×C₄×C₅	1	4	yes	complemented
381	#103	C₂×C₄×C₅	1	4	yes	complemented
382	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	—
383	#97	—	2	2	no	—
384	#97	—	4	1	no	—
385	#95	—	2	1	no	—
386	#95	—	2	1	no	—
387	#95	—	2	1	no	—
388	#95	—	2	1	no	—
389	#95	—	2	1	no	—
390	#95	—	2	1	no	—
391	#95	—	2	1	no	—
392	#95	—	2	1	no	—
393	#95	—	2	1	no	—
394	#95	C₅×D₄	1	1	yes	characteristic
395	#95	C₅×D₄	1	1	yes	characteristic
396	C₂²×C₅	—	2	2	no	—
397	C₂²×C₅	—	2	2	no	—
398	C₂²×C₅	—	2	2	no	—
399	C₂²×C₅	—	2	2	no	—
400	C₂²×C₅	—	2	2	no	—
401	C₂²×C₅	—	2	2	no	—
402	C₂²×C₅	#441	1	4	yes	—
403	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
404	C₂²×C₅	#546	1	1	yes	characteristic
405	C₂²×C₅	#547	1	1	yes	characteristic
406	C₂²×C₅	C₂×#137	1	1	yes	characteristic
407	C₂²×C₅	C₂×#137	1	1	yes	characteristic
408	C₂²×C₅	#576	1	1	yes	characteristic
409	C₂²×C₅	#577	1	1	yes	characteristic
410	C₄×C₅	—	2	2	no	—
411	C₄×C₅	—	4	1	no	—
412	C₄×C₅	—	4	1	no	—
413	C₄×C₅	—	4	2	no	—
414	C₄×C₅	—	4	2	no	—
415	C₄×C₅	—	4	2	no	—
416	C₄×C₅	—	4	2	no	—
417	C₄×C₅	—	4	1	no	—
418	C₄×C₅	—	4	2	no	—
419	C₄×C₅	—	4	1	no	—
420	C₄×C₅	—	8	1	no	—
421	C₄×C₅	—	8	1	no	—
422	C₄×C₅	—	8	1	no	—
423	C₄×C₅	C₄×#41	1	1	yes	characteristic
424	C₄×C₅	#520	1	1	yes	characteristic
425	C₄×C₅	#551	1	1	yes	characteristic
426	C₄×C₅	#552	1	1	yes	characteristic
427	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	4	2	no	—
448	C₂²×C₄	—	4	2	no	—
449	C₂²×C₄	—	8	1	no	—
450	C₂²×C₄	—	8	1	no	—
451	C₂²×C₄	—	8	1	no	—
452	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
453	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
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	C₅×#41	1	2	yes	—
459	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	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	—	4	4	no	—
470	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
471	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
472	C₂×C₈	C₅×#41	1	2	yes	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	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	—	8	1	no	—
488	C₄⋊C₄	—	8	1	no	—
489	C₄⋊C₄	—	8	1	no	—
490	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
491	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
492	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
493	C₄⋊C₄	C₅×#41	1	2	yes	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	4	2	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	4	2	no	—
503	C₄²	—	8	1	no	—
504	C₄²	—	8	1	no	—
505	C₄²	—	8	1	no	—
506	C₂×C₅	—	2	4	no	—
507	C₂×C₅	#2359	1	1	yes	characteristic
508	C₂×C₅	C₂×#441	1	1	yes	characteristic
509	C₂×C₅	#2946	1	1	yes	characteristic
510	C₂×C₅	#3314	1	1	yes	characteristic
511	C₂×C₅	#3320	1	1	yes	characteristic
512	C₂×C₅	#3344	1	1	yes	characteristic
513	C₂×C₅	#3346	1	1	yes	characteristic
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	C₄×C₅×D₄	1	2	yes	—
519	C₂³	C₅×#137	1	2	yes	—
520	C₂³	C₅×#137	1	2	yes	—
521	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
522	Q₈	—	2	2	no	—
523	Q₈	—	2	2	no	—
524	Q₈	—	4	1	no	—
525	Q₈	—	4	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	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	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	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	—	8	4	no	—
569	C₂×C₄	—	8	4	no	—
570	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
571	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
572	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
573	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
574	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
575	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
576	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
577	C₈	—	2	2	no	—
578	C₈	—	2	2	no	—
579	C₈	—	2	2	no	—
580	C₈	—	4	1	no	—
581	C₅	#22932	1	1	yes	characteristic, direct product factor, Sylow
582	C₂²	—	2	2	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	2	no	—
588	C₂²	C₅×#441	1	4	yes	—
589	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
590	C₂²	C₅×#546	1	1	yes	characteristic
591	C₂²	C₅×#547	1	1	yes	characteristic
592	C₂²	C₂×C₅×#137	1	1	yes	characteristic
593	C₂²	C₂×C₅×#137	1	1	yes	characteristic
594	C₂²	C₅×#576	1	1	yes	characteristic
595	C₂²	C₅×#577	1	1	yes	characteristic
596	C₄	—	2	2	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	2	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	2	no	—
603	C₄	—	4	2	no	—
604	C₄	—	4	2	no	—
605	C₄	—	4	2	no	—
606	C₄	—	8	1	no	—
607	C₄	—	8	1	no	—
608	C₄	—	8	1	no	—
609	C₄	C₄×C₅×#41	1	1	yes	characteristic
610	C₄	C₅×#520	1	1	yes	characteristic
611	C₄	C₅×#551	1	1	yes	characteristic
612	C₄	C₅×#552	1	1	yes	characteristic
613	C₂	—	2	4	no	—
614	C₂	C₅×#2359	1	1	yes	characteristic
615	C₂	C₂×C₅×#441	1	1	yes	characteristic
616	C₂	C₅×#2946	1	1	yes	characteristic
617	C₂	C₅×#3314	1	1	yes	characteristic
618	C₂	C₅×#3320	1	1	yes	characteristic
619	C₂	C₅×#3344	1	1	yes	characteristic
620	C₂	C₅×#3346	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×#1943	C₂	semidirect
5. C₅×#1935	C₂	semidirect
6. C₅×#1927	C₂	semidirect
7. C₅×#1918	C₂	semidirect
8. C₅×#1918	C₂	semidirect
10. C₅×#1865	C₂	semidirect
12. C₅×#1776	C₂	semidirect
13. C₅×#1763	C₂	semidirect
21. C₅×#484	C₄	semidirect
60. #22932	C₅	direct (N × H)
104. C₅×#107	C₂×C₄	semidirect
105. C₅×#107	C₂×C₄	semidirect
110. C₅×#103	C₂×C₄	semidirect
111. C₅×#103	C₂×C₄	semidirect
129. #1943	C₂×C₅	semidirect
130. #1935	C₂×C₅	semidirect
131. #1927	C₂×C₅	semidirect
132. #1918	C₂×C₅	semidirect
133. #1918	C₂×C₅	semidirect
135. #1865	C₂×C₅	semidirect
137. #1776	C₂×C₅	semidirect
138. #1763	C₂×C₅	semidirect
225. #484	C₄×C₅	semidirect
374. #107	C₂×C₄×C₅	semidirect
375. #107	C₂×C₄×C₅	semidirect
380. #103	C₂×C₄×C₅	semidirect
381. #103	C₂×C₄×C₅	semidirect
581. C₅	#22932	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×#484	2
C₅×#2360	2
C₅×#2345	2
C₅×#1943	2
C₅×#1935	2
C₅×#1927	2
C₅×#1918	2
C₅×#1892	2
C₅×#1865	2
C₅×#1853	2
C₅×#1776	2
C₅×#1763	2
C₅×#1752	2
C₂×C₅×#340	2
#22932	5

Subgroups — C5×#22932 #11945652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22932 #11945652