Subgroups — C₅×#22938 #11945658

Order 1280.

958 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#480	C₂	1	1	yes	maximal, characteristic
2	C₅×#2361	C₂	1	1	yes	maximal, characteristic
3	C₅×#2344	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1943	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1936	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1926	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1921	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1921	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1893	C₂	1	1	yes	maximal, characteristic
10	C₅×#1864	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1853	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1776	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1762	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1752	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#340	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×#121	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×D₄	—	2	1	no	—
19	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₅×#117	—	2	1	no	—
21	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₅×#480	C₄	1	8	yes	complemented
24	C₂×C₅×#107	C₂²	1	1	yes	characteristic
25	C₂×C₅×#107	C₂²	1	1	yes	characteristic
26	C₂×C₅×#106	C₂²	1	1	yes	characteristic
27	C₂×C₅×#106	C₂²	1	1	yes	characteristic
28	C₂×C₅×#102	C₂²	1	1	yes	characteristic
29	C₂×C₅×#102	C₂²	1	1	yes	characteristic
30	C₂×C₅×#102	C₂²	1	1	yes	characteristic
31	C₂×C₅×#102	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×C₅×#97	C₂²	1	1	yes	characteristic
35	C₅×#390	C₂²	1	1	yes	characteristic
36	C₅×#389	C₂²	1	1	yes	characteristic
37	C₅×#389	C₂²	1	1	yes	characteristic
38	C₅×#389	C₂²	1	1	yes	characteristic
39	C₅×#388	—	2	1	no	—
40	C₅×#387	—	2	1	no	—
41	C₅×#387	—	2	1	no	—
42	C₅×#386	—	2	1	no	—
43	C₅×#385	—	2	1	no	—
44	C₅×#381	—	2	1	no	—
45	C₅×#380	C₂²	1	1	yes	characteristic
46	C₄×C₅×C₄⋊C₄	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	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	#22938	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₅×D₄	—	2	1	no	—
62	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₅	—	2	1	no	—
64	C₂³×C₄×C₅	—	2	1	no	—
65	C₂³×C₄×C₅	—	2	1	no	—
66	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₅×C₈	—	2	2	no	—
68	C₂²×C₅×C₈	—	2	2	no	—
69	C₂²×C₅×C₈	—	4	1	no	—
70	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₅×#121	—	2	2	no	—
75	C₅×#121	C₂×C₄	1	4	yes	—
76	C₄×C₅×D₄	—	2	2	no	—
77	C₄×C₅×D₄	—	4	1	no	—
78	C₄×C₅×D₄	—	4	4	no	—
79	C₅×#117	—	4	4	no	—
80	C₂×C₅×C₄⋊C₄	—	2	1	no	—
81	C₂×C₅×C₄⋊C₄	—	2	2	no	—
82	C₂×C₅×C₄⋊C₄	—	2	2	no	—
83	C₂×C₅×C₄⋊C₄	—	2	1	no	—
84	C₂×C₅×C₄⋊C₄	—	2	1	no	—
85	C₂×C₅×C₄⋊C₄	—	2	1	no	—
86	C₂×C₅×C₄⋊C₄	—	2	1	no	—
87	C₂×C₅×C₄⋊C₄	—	4	1	no	—
88	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
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×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	D₄	1	1	yes	characteristic
102	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₅	—	2	1	no	—
104	C₂×C₄²×C₅	—	2	1	no	—
105	C₂×C₄²×C₅	—	2	1	no	—
106	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
108	C₅×#107	C₂×C₄	1	4	yes	complemented
109	C₅×#107	C₂×C₄	1	4	yes	complemented
110	C₅×#106	—	2	2	no	—
111	C₅×#106	—	4	1	no	—
112	C₅×#102	—	2	2	no	—
113	C₅×#102	—	4	1	no	—
114	C₅×#102	C₂×C₄	1	4	yes	complemented
115	C₅×#102	C₂×C₄	1	4	yes	complemented
116	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
117	C₅×#97	—	2	2	no	—
118	C₅×#97	—	4	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	—	2	1	no	—
125	C₅×#95	—	2	1	no	—
126	C₅×#95	D₄	1	1	yes	characteristic
127	C₅×#95	D₄	1	1	yes	characteristic
128	C₂×#480	C₂×C₅	1	1	yes	characteristic
129	#2361	C₂×C₅	1	1	yes	characteristic
130	#2344	C₂×C₅	1	1	yes	characteristic, complemented
131	#1943	C₂×C₅	1	1	yes	characteristic, complemented
132	#1936	C₂×C₅	1	1	yes	characteristic, complemented
133	#1926	C₂×C₅	1	1	yes	characteristic, complemented
134	#1921	C₂×C₅	1	1	yes	characteristic, complemented
135	#1921	C₂×C₅	1	1	yes	characteristic, complemented
136	#1893	C₂×C₅	1	1	yes	characteristic
137	#1864	C₂×C₅	1	1	yes	characteristic, complemented
138	#1853	C₂×C₅	1	1	yes	characteristic, complemented
139	#1776	C₂×C₅	1	1	yes	characteristic, complemented
140	#1762	C₂×C₅	1	1	yes	characteristic, complemented
141	#1752	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂×#340	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂⁴×C₅	—	2	1	no	—
144	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂×C₅×D₄	—	2	4	no	—
146	C₂×C₅×D₄	—	2	1	no	—
147	C₂×C₅×D₄	—	2	1	no	—
148	C₂×C₅×D₄	—	2	1	no	—
149	C₂×C₅×D₄	—	2	1	no	—
150	C₂×C₅×D₄	—	2	1	no	—
151	C₂×C₅×D₄	—	4	2	no	—
152	C₂×C₅×D₄	—	4	2	no	—
153	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
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	1	no	—
158	C₂²×C₄×C₅	—	2	4	no	—
159	C₂²×C₄×C₅	—	2	1	no	—
160	C₂²×C₄×C₅	—	2	1	no	—
161	C₂²×C₄×C₅	—	2	1	no	—
162	C₂²×C₄×C₅	—	2	1	no	—
163	C₂²×C₄×C₅	—	2	1	no	—
164	C₂²×C₄×C₅	—	2	1	no	—
165	C₂²×C₄×C₅	—	2	1	no	—
166	C₂²×C₄×C₅	—	4	2	no	—
167	C₂²×C₄×C₅	—	4	2	no	—
168	C₂²×C₄×C₅	—	4	2	no	—
169	C₂²×C₄×C₅	—	4	2	no	—
170	C₂²×C₄×C₅	—	4	2	no	—
171	C₂²×C₄×C₅	—	4	2	no	—
172	C₂²×C₄×C₅	—	8	1	no	—
173	C₂²×C₄×C₅	—	8	1	no	—
174	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
175	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₅	#41	1	2	yes	—
181	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	—	2	1	no	—
185	C₂×C₅×C₈	—	2	1	no	—
186	C₂×C₅×C₈	—	2	1	no	—
187	C₂×C₅×C₈	—	2	1	no	—
188	C₂×C₅×C₈	—	2	1	no	—
189	C₂×C₅×C₈	—	2	1	no	—
190	C₂×C₅×C₈	—	2	1	no	—
191	C₂×C₅×C₈	—	4	4	no	—
192	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
193	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
194	C₂×C₅×C₈	#41	1	2	yes	—
195	C₅×C₄⋊C₄	—	2	4	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	—	2	1	no	—
200	C₅×C₄⋊C₄	—	2	1	no	—
201	C₅×C₄⋊C₄	—	2	1	no	—
202	C₅×C₄⋊C₄	—	2	1	no	—
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	—	4	2	no	—
207	C₅×C₄⋊C₄	—	4	2	no	—
208	C₅×C₄⋊C₄	—	4	2	no	—
209	C₅×C₄⋊C₄	—	4	2	no	—
210	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
211	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
212	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
213	C₅×C₄⋊C₄	#41	1	2	yes	—
214	C₅×C₂²⋊C₄	—	2	2	no	—
215	C₅×C₂²⋊C₄	—	2	2	no	—
216	C₅×C₂²⋊C₄	—	2	4	no	—
217	C₅×C₂²⋊C₄	—	4	2	no	—
218	C₅×C₂²⋊C₄	—	4	2	no	—
219	C₅×C₂²⋊C₄	—	4	2	no	—
220	C₅×C₂²⋊C₄	—	8	1	no	—
221	C₄²×C₅	—	2	1	no	—
222	C₄²×C₅	—	2	1	no	—
223	C₄²×C₅	—	2	1	no	—
224	C₄²×C₅	—	2	1	no	—
225	C₄²×C₅	—	4	2	no	—
226	C₄²×C₅	—	4	2	no	—
227	C₄²×C₅	—	4	2	no	—
228	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
229	C₂×#121	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₄×D₄	—	2	1	no	—
231	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
232	C₂×#117	—	2	1	no	—
233	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
234	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
235	#480	C₄×C₅	1	8	yes	complemented
236	C₂×#107	C₂²×C₅	1	1	yes	characteristic
237	C₂×#107	C₂²×C₅	1	1	yes	characteristic
238	C₂×#106	C₂²×C₅	1	1	yes	characteristic
239	C₂×#106	C₂²×C₅	1	1	yes	characteristic
240	C₂×#102	C₂²×C₅	1	1	yes	characteristic
241	C₂×#102	C₂²×C₅	1	1	yes	characteristic
242	C₂×#102	C₂²×C₅	1	1	yes	characteristic
243	C₂×#102	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
245	C₂×#97	C₂²×C₅	1	1	yes	characteristic
246	C₂×#97	C₂²×C₅	1	1	yes	characteristic
247	#390	C₂²×C₅	1	1	yes	characteristic
248	#389	C₂²×C₅	1	1	yes	characteristic
249	#389	C₂²×C₅	1	1	yes	characteristic
250	#389	C₂²×C₅	1	1	yes	characteristic
251	#388	—	2	1	no	—
252	#387	—	2	1	no	—
253	#387	—	2	1	no	—
254	#386	—	2	1	no	—
255	#385	—	2	1	no	—
256	#381	—	2	1	no	—
257	#380	C₂²×C₅	1	1	yes	characteristic
258	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
259	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
260	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
261	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
262	#340	C₂²×C₅	1	1	yes	characteristic
263	#340	C₂²×C₅	1	1	yes	characteristic
264	#340	C₂²×C₅	1	1	yes	characteristic
265	#340	C₂²×C₅	1	1	yes	characteristic
266	#340	C₂²×C₅	1	1	yes	characteristic
267	#340	C₂²×C₅	1	1	yes	characteristic
268	#340	C₂²×C₅	1	1	yes	characteristic
269	#340	C₂²×C₅	1	1	yes	characteristic
270	#336	C₂²×C₅	1	1	yes	characteristic
271	#336	C₂²×C₅	1	1	yes	characteristic
272	C₂³×C₅	—	2	1	no	—
273	C₂³×C₅	—	2	1	no	—
274	C₂³×C₅	—	2	1	no	—
275	C₂³×C₅	—	2	1	no	—
276	C₂³×C₅	—	2	2	no	—
277	C₂³×C₅	—	4	1	no	—
278	C₂³×C₅	—	4	1	no	—
279	C₂³×C₅	—	4	1	no	—
280	C₂³×C₅	—	4	1	no	—
281	C₂³×C₅	—	4	1	no	—
282	C₂³×C₅	—	4	1	no	—
283	C₂³×C₅	C₄×D₄	1	2	yes	—
284	C₂³×C₅	AGL(1,ℤ/8)	1	2	yes	—
285	C₂³×C₅	AGL(1,ℤ/8)	1	2	yes	—
286	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
287	C₅×D₄	—	2	2	no	—
288	C₅×D₄	—	2	2	no	—
289	C₅×D₄	—	4	8	no	—
290	C₅×D₄	—	4	1	no	—
291	C₅×D₄	—	4	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	2	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	—	2	2	no	—
298	C₂×C₄×C₅	—	2	2	no	—
299	C₂×C₄×C₅	—	2	2	no	—
300	C₂×C₄×C₅	—	2	2	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	1	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	—	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	—	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	8	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	—	8	4	no	—
333	C₂×C₄×C₅	—	8	4	no	—
334	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
335	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
336	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
338	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
339	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
340	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
341	C₅×C₈	—	2	2	no	—
342	C₅×C₈	—	2	2	no	—
343	C₅×C₈	—	2	2	no	—
344	C₅×C₈	—	4	1	no	—
345	C₂²×D₄	—	2	1	no	—
346	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
347	C₂³×C₄	—	2	1	no	—
348	C₂³×C₄	—	2	1	no	—
349	C₂³×C₄	—	2	1	no	—
350	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
351	C₂²×C₈	—	2	2	no	—
352	C₂²×C₈	—	2	2	no	—
353	C₂²×C₈	—	4	1	no	—
354	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
355	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
356	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
357	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
358	#121	—	2	2	no	—
359	#121	C₂×C₄×C₅	1	4	yes	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	—	4	1	no	—
362	C₄×D₄	—	4	4	no	—
363	#117	—	4	4	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	2	no	—
366	C₂×C₄⋊C₄	—	2	2	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	4	1	no	—
372	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
373	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
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	C₂³×C₅	1	1	yes	characteristic
391	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
392	#107	C₂×C₄×C₅	1	4	yes	complemented
393	#107	C₂×C₄×C₅	1	4	yes	complemented
394	#106	—	2	2	no	—
395	#106	—	4	1	no	—
396	#102	—	2	2	no	—
397	#102	—	4	1	no	—
398	#102	C₂×C₄×C₅	1	4	yes	complemented
399	#102	C₂×C₄×C₅	1	4	yes	complemented
400	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
401	#97	—	2	2	no	—
402	#97	—	4	1	no	—
403	#95	—	2	1	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	no	—
410	#95	C₅×D₄	1	1	yes	characteristic
411	#95	C₅×D₄	1	1	yes	characteristic
412	C₂²×C₅	—	2	2	no	—
413	C₂²×C₅	—	2	2	no	—
414	C₂²×C₅	—	2	2	no	—
415	C₂²×C₅	—	2	2	no	—
416	C₂²×C₅	—	2	2	no	—
417	C₂²×C₅	—	2	2	no	—
418	C₂²×C₅	—	4	2	no	—
419	C₂²×C₅	—	4	2	no	—
420	C₂²×C₅	—	4	2	no	—
421	C₂²×C₅	—	8	1	no	—
422	C₂²×C₅	—	8	1	no	—
423	C₂²×C₅	—	8	1	no	—
424	C₂²×C₅	—	8	1	no	—
425	C₂²×C₅	#442	1	4	yes	—
426	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
427	C₂²×C₅	#546	1	1	yes	characteristic
428	C₂²×C₅	#547	1	1	yes	characteristic
429	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
430	C₂²×C₅	C₂×AGL(1,ℤ/8)	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	—	4	1	no	—
435	C₄×C₅	—	4	1	no	—
436	C₄×C₅	—	4	2	no	—
437	C₄×C₅	—	4	2	no	—
438	C₄×C₅	—	4	2	no	—
439	C₄×C₅	—	4	1	no	—
440	C₄×C₅	—	4	1	no	—
441	C₄×C₅	—	4	2	no	—
442	C₄×C₅	—	8	1	no	—
443	C₄×C₅	—	8	1	no	—
444	C₄×C₅	—	8	1	no	—
445	C₄×C₅	C₄×#41	1	1	yes	characteristic
446	C₄×C₅	#520	1	1	yes	characteristic
447	C₄×C₅	#551	1	1	yes	characteristic
448	C₄×C₅	#552	1	1	yes	characteristic
449	C₂⁴	—	2	1	no	—
450	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
451	C₂×D₄	—	2	4	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	4	2	no	—
458	C₂×D₄	—	4	2	no	—
459	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	4	2	no	—
473	C₂²×C₄	—	4	2	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	4	2	no	—
476	C₂²×C₄	—	4	2	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	8	1	no	—
479	C₂²×C₄	—	8	1	no	—
480	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
481	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
482	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
483	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
484	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
485	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
486	C₂²×C₄	C₅×#41	1	2	yes	—
487	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	4	4	no	—
498	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
499	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
500	C₂×C₈	C₅×#41	1	2	yes	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
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	—	4	2	no	—
513	C₄⋊C₄	—	4	2	no	—
514	C₄⋊C₄	—	4	2	no	—
515	C₄⋊C₄	—	4	2	no	—
516	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
517	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
518	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
519	C₄⋊C₄	C₅×#41	1	2	yes	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	4	no	—
523	C₂²⋊C₄	—	4	2	no	—
524	C₂²⋊C₄	—	4	2	no	—
525	C₂²⋊C₄	—	4	2	no	—
526	C₂²⋊C₄	—	8	1	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	4	2	no	—
532	C₄²	—	4	2	no	—
533	C₄²	—	4	2	no	—
534	C₂×C₅	—	2	4	no	—
535	C₂×C₅	—	8	2	no	—
536	C₂×C₅	#2359	1	1	yes	characteristic
537	C₂×C₅	C₂×#442	1	1	yes	characteristic
538	C₂×C₅	#2947	1	1	yes	characteristic
539	C₂×C₅	#3308	1	1	yes	characteristic
540	C₂×C₅	#3310	1	1	yes	characteristic
541	C₂×C₅	#3343	1	1	yes	characteristic
542	C₂×C₅	#3345	1	1	yes	characteristic
543	C₂³	—	2	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	1	no	—
550	C₂³	—	4	1	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	1	no	—
554	C₂³	C₄×C₅×D₄	1	2	yes	—
555	C₂³	C₅×AGL(1,ℤ/8)	1	2	yes	—
556	C₂³	C₅×AGL(1,ℤ/8)	1	2	yes	—
557	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
558	D₄	—	2	2	no	—
559	D₄	—	2	2	no	—
560	D₄	—	4	8	no	—
561	D₄	—	4	1	no	—
562	D₄	—	4	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	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	1	no	—
573	C₂×C₄	—	2	1	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	—	2	1	no	—
585	C₂×C₄	—	4	8	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	—	8	4	no	—
604	C₂×C₄	—	8	4	no	—
605	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
606	C₂×C₄	C₂³×C₄×C₅	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	C₂×C₅×#41	1	1	yes	characteristic
610	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
611	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
612	C₈	—	2	2	no	—
613	C₈	—	2	2	no	—
614	C₈	—	2	2	no	—
615	C₈	—	4	1	no	—
616	C₅	#22938	1	1	yes	characteristic, direct product factor, Sylow
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	4	2	no	—
626	C₂²	—	8	1	no	—
627	C₂²	—	8	1	no	—
628	C₂²	—	8	1	no	—
629	C₂²	—	8	1	no	—
630	C₂²	C₅×#442	1	4	yes	—
631	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
632	C₂²	C₅×#546	1	1	yes	characteristic
633	C₂²	C₅×#547	1	1	yes	characteristic
634	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
635	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
636	C₂²	C₅×#577	1	1	yes	characteristic
637	C₂²	C₅×#578	1	1	yes	characteristic
638	C₄	—	2	2	no	—
639	C₄	—	4	1	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	2	no	—
642	C₄	—	4	1	no	—
643	C₄	—	4	1	no	—
644	C₄	—	4	2	no	—
645	C₄	—	4	2	no	—
646	C₄	—	4	2	no	—
647	C₄	—	8	1	no	—
648	C₄	—	8	1	no	—
649	C₄	—	8	1	no	—
650	C₄	C₄×C₅×#41	1	1	yes	characteristic
651	C₄	C₅×#520	1	1	yes	characteristic
652	C₄	C₅×#551	1	1	yes	characteristic
653	C₄	C₅×#552	1	1	yes	characteristic
654	C₂	—	2	4	no	—
655	C₂	—	8	2	no	—
656	C₂	C₅×#2359	1	1	yes	characteristic
657	C₂	C₂×C₅×#442	1	1	yes	characteristic
658	C₂	C₅×#2947	1	1	yes	characteristic
659	C₂	C₅×#3308	1	1	yes	characteristic
660	C₂	C₅×#3310	1	1	yes	characteristic
661	C₂	C₅×#3343	1	1	yes	characteristic
662	C₂	C₅×#3345	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×#121	C₂²
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
3. C₅×#2344	C₂	semidirect
4. C₅×#1943	C₂	semidirect
5. C₅×#1936	C₂	semidirect
6. C₅×#1926	C₂	semidirect
7. C₅×#1921	C₂	semidirect
8. C₅×#1921	C₂	semidirect
10. C₅×#1864	C₂	semidirect
11. C₅×#1853	C₂	semidirect
12. C₅×#1776	C₂	semidirect
13. C₅×#1762	C₂	semidirect
14. C₅×#1752	C₂	semidirect
15. C₂×C₅×#340	C₂	semidirect
23. C₅×#480	C₄	semidirect
60. #22938	C₅	direct (N × H)
88. C₂×C₅×C₄⋊C₄	C₂×C₄	semidirect
108. C₅×#107	C₂×C₄	semidirect
109. C₅×#107	C₂×C₄	semidirect
114. C₅×#102	C₂×C₄	semidirect
115. C₅×#102	C₂×C₄	semidirect
116. C₅×C₂²⋊C₈	C₂×C₄	semidirect
130. #2344	C₂×C₅	semidirect
131. #1943	C₂×C₅	semidirect
132. #1936	C₂×C₅	semidirect
133. #1926	C₂×C₅	semidirect
134. #1921	C₂×C₅	semidirect
135. #1921	C₂×C₅	semidirect
137. #1864	C₂×C₅	semidirect
138. #1853	C₂×C₅	semidirect
139. #1776	C₂×C₅	semidirect
140. #1762	C₂×C₅	semidirect
141. #1752	C₂×C₅	semidirect
142. C₂×#340	C₂×C₅	semidirect
235. #480	C₄×C₅	semidirect
372. C₂×C₄⋊C₄	C₂×C₄×C₅	semidirect
392. #107	C₂×C₄×C₅	semidirect
393. #107	C₂×C₄×C₅	semidirect
398. #102	C₂×C₄×C₅	semidirect
399. #102	C₂×C₄×C₅	semidirect
400. C₂²⋊C₈	C₂×C₄×C₅	semidirect
616. C₅	#22938	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×#480	2
C₅×#2361	2
C₅×#2344	2
C₅×#1943	2
C₅×#1936	2
C₅×#1926	2
C₅×#1921	2
C₅×#1893	2
C₅×#1864	2
C₅×#1853	2
C₅×#1776	2
C₅×#1762	2
C₅×#1752	2
C₂×C₅×#340	2
#22938	5

Subgroups — C5×#22938 #11945658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22938 #11945658