Subgroups — C₅×#22966 #11945686

Order 1280.

846 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#478	C₂	1	1	yes	maximal, characteristic
2	C₅×#2370	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2349	C₂	1	1	yes	maximal, characteristic
4	C₅×#1991	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1949	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1941	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1921	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1920	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1864	C₂	1	1	yes	maximal, characteristic
11	C₅×#1862	C₂	1	1	yes	maximal, characteristic
12	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₅×#102	C₂	1	1	yes	maximal, characteristic
14	C₄×C₅×#102	C₂	1	1	yes	maximal, characteristic
15	C₄×C₅×#102	C₂	1	1	yes	maximal, characteristic
16	C₂×C₅×#125	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₅×#478	C₄	1	8	yes	complemented
21	C₂×C₅×#107	C₂²	1	1	yes	characteristic
22	C₂×C₅×#107	C₂²	1	1	yes	characteristic
23	C₂×C₅×#106	C₂²	1	1	yes	characteristic
24	C₂×C₅×#106	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×#102	C₂²	1	1	yes	characteristic
27	C₂×C₅×#102	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×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₅×#389	—	2	1	no	—
34	C₅×#389	C₂²	1	1	yes	characteristic
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×#385	—	2	1	no	—
41	C₅×#385	—	2	1	no	—
42	C₅×#382	C₂²	1	1	yes	characteristic
43	C₅×#380	—	2	1	no	—
44	C₄×C₅×C₄⋊C₄	—	2	1	no	—
45	C₄×C₅×C₄⋊C₄	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	C₂×C₅×#95	—	2	1	no	—
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	#22966	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₅	—	2	1	no	—
63	C₂³×C₄×C₅	—	2	1	no	—
64	C₂³×C₄×C₅	—	2	1	no	—
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₅×#125	—	2	2	no	—
70	C₅×#125	C₂×C₄	1	4	yes	complemented
71	C₄×C₅×D₄	—	2	2	no	—
72	C₄×C₅×D₄	—	2	2	no	—
73	C₄×C₅×D₄	—	2	2	no	—
74	C₄×C₅×D₄	—	4	1	no	—
75	C₄×C₅×D₄	—	4	1	no	—
76	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
77	C₂×C₅×C₄⋊C₄	—	2	1	no	—
78	C₂×C₅×C₄⋊C₄	—	2	1	no	—
79	C₂×C₅×C₄⋊C₄	—	2	1	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	D₄	1	1	yes	characteristic
84	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
85	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₄²×C₅	—	2	1	no	—
96	C₂×C₄²×C₅	—	2	1	no	—
97	C₂×C₄²×C₅	—	2	1	no	—
98	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
101	C₅×#107	—	4	1	no	—
102	C₅×#107	C₂×C₄	1	4	yes	complemented
103	C₅×#106	—	4	1	no	—
104	C₅×#106	C₂×C₄	1	4	yes	complemented
105	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
106	C₅×#102	—	2	2	no	—
107	C₅×#102	C₂×C₄	1	4	yes	—
108	C₅×#102	C₂×C₄	1	4	yes	—
109	C₅×#102	Q₈	1	4	yes	—
110	C₄×C₅×C₈	—	2	2	no	—
111	C₄×C₅×C₈	—	4	1	no	—
112	C₄×C₅×C₈	—	4	1	no	—
113	C₅×#95	—	2	1	no	—
114	C₅×#95	—	2	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	D₄	1	1	yes	characteristic
123	C₅×#95	D₄	1	1	yes	characteristic
124	C₂×#478	C₂×C₅	1	1	yes	characteristic
125	#2370	C₂×C₅	1	1	yes	characteristic, complemented
126	#2349	C₂×C₅	1	1	yes	characteristic
127	#1991	C₂×C₅	1	1	yes	characteristic, complemented
128	#1949	C₂×C₅	1	1	yes	characteristic, complemented
129	#1942	C₂×C₅	1	1	yes	characteristic, complemented
130	#1941	C₂×C₅	1	1	yes	characteristic, complemented
131	#1921	C₂×C₅	1	1	yes	characteristic, complemented
132	#1920	C₂×C₅	1	1	yes	characteristic, complemented
133	#1864	C₂×C₅	1	1	yes	characteristic
134	#1862	C₂×C₅	1	1	yes	characteristic
135	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
136	C₄×#102	C₂×C₅	1	1	yes	characteristic
137	C₄×#102	C₂×C₅	1	1	yes	characteristic
138	C₄×#102	C₂×C₅	1	1	yes	characteristic
139	C₂⁴×C₅	—	2	1	no	—
140	C₂×C₅×D₄	—	2	1	no	—
141	C₂×C₅×D₄	—	2	1	no	—
142	C₂×C₅×D₄	—	2	1	no	—
143	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
144	C₂×C₅×D₄	C₂×Q₈	1	2	yes	—
145	C₂×C₅×D₄	#41	1	2	yes	—
146	C₂²×C₄×C₅	—	2	1	no	—
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	—	2	1	no	—
150	C₂²×C₄×C₅	—	2	4	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	—	4	2	no	—
155	C₂²×C₄×C₅	—	4	2	no	—
156	C₂²×C₄×C₅	—	4	2	no	—
157	C₂²×C₄×C₅	—	4	2	no	—
158	C₂²×C₄×C₅	—	8	1	no	—
159	C₂²×C₄×C₅	—	8	1	no	—
160	C₂²×C₄×C₅	—	8	1	no	—
161	C₂²×C₄×C₅	—	8	1	no	—
162	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
169	C₂×C₅×C₈	—	2	1	no	—
170	C₂×C₅×C₈	—	2	1	no	—
171	C₂×C₅×C₈	—	2	1	no	—
172	C₂×C₅×C₈	—	2	1	no	—
173	C₂×C₅×C₈	—	2	1	no	—
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	C₂²×C₄	1	2	yes	—
179	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
180	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
181	C₅×C₄⋊C₄	—	2	4	no	—
182	C₅×C₄⋊C₄	—	2	4	no	—
183	C₅×C₄⋊C₄	—	2	2	no	—
184	C₅×C₄⋊C₄	—	2	2	no	—
185	C₅×C₄⋊C₄	—	2	1	no	—
186	C₅×C₄⋊C₄	—	2	1	no	—
187	C₅×C₄⋊C₄	—	2	1	no	—
188	C₅×C₄⋊C₄	—	2	1	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	—	4	2	no	—
196	C₅×C₄⋊C₄	—	8	1	no	—
197	C₅×C₄⋊C₄	—	8	1	no	—
198	C₅×C₄⋊C₄	—	8	1	no	—
199	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
200	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
201	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
202	C₅×C₄⋊C₄	C₂×Q₈	1	2	yes	—
203	C₅×C₂²⋊C₄	—	2	4	no	—
204	C₅×C₂²⋊C₄	—	4	2	no	—
205	C₅×C₂²⋊C₄	—	4	2	no	—
206	C₄²×C₅	—	2	1	no	—
207	C₄²×C₅	—	2	1	no	—
208	C₄²×C₅	—	2	1	no	—
209	C₄²×C₅	—	2	1	no	—
210	C₄²×C₅	—	4	2	no	—
211	C₄²×C₅	—	8	1	no	—
212	C₄²×C₅	—	8	1	no	—
213	C₄²×C₅	C₂²×C₄	1	2	yes	—
214	C₄²×C₅	#41	1	2	yes	—
215	C₂×#125	C₂²×C₅	1	1	yes	characteristic
216	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
217	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
218	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
219	#478	C₄×C₅	1	8	yes	complemented
220	C₂×#107	C₂²×C₅	1	1	yes	characteristic
221	C₂×#107	C₂²×C₅	1	1	yes	characteristic
222	C₂×#106	C₂²×C₅	1	1	yes	characteristic
223	C₂×#106	C₂²×C₅	1	1	yes	characteristic
224	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
225	C₂×#102	C₂²×C₅	1	1	yes	characteristic
226	C₂×#102	C₂²×C₅	1	1	yes	characteristic
227	C₂×#102	C₂²×C₅	1	1	yes	characteristic
228	C₂×#102	C₂²×C₅	1	1	yes	characteristic
229	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
231	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
232	#389	—	2	1	no	—
233	#389	C₂²×C₅	1	1	yes	characteristic
234	#389	C₂²×C₅	1	1	yes	characteristic
235	#389	C₂²×C₅	1	1	yes	characteristic
236	#389	C₂²×C₅	1	1	yes	characteristic
237	#387	—	2	1	no	—
238	#387	—	2	1	no	—
239	#385	—	2	1	no	—
240	#385	—	2	1	no	—
241	#382	C₂²×C₅	1	1	yes	characteristic
242	#380	—	2	1	no	—
243	C₄×C₄⋊C₄	—	2	1	no	—
244	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
245	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
246	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
247	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
248	C₂×#95	—	2	1	no	—
249	#340	C₂²×C₅	1	1	yes	characteristic
250	#340	C₂²×C₅	1	1	yes	characteristic
251	#340	C₂²×C₅	1	1	yes	characteristic
252	#340	C₂²×C₅	1	1	yes	characteristic
253	#340	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	#336	C₂²×C₅	1	1	yes	characteristic
258	#336	C₂²×C₅	1	1	yes	characteristic
259	C₂³×C₅	—	2	2	no	—
260	C₂³×C₅	—	2	2	no	—
261	C₂³×C₅	—	2	2	no	—
262	C₂³×C₅	—	4	1	no	—
263	C₂³×C₅	—	4	1	no	—
264	C₂³×C₅	—	4	1	no	—
265	C₂³×C₅	—	4	1	no	—
266	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
267	C₅×D₄	—	2	2	no	—
268	C₅×D₄	—	2	2	no	—
269	C₅×D₄	—	2	2	no	—
270	C₅×D₄	C₄×Q₈	1	4	yes	—
271	C₂×C₄×C₅	—	2	1	no	—
272	C₂×C₄×C₅	—	2	1	no	—
273	C₂×C₄×C₅	—	2	1	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	1	no	—
276	C₂×C₄×C₅	—	2	1	no	—
277	C₂×C₄×C₅	—	2	1	no	—
278	C₂×C₄×C₅	—	2	1	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	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	4	1	no	—
290	C₂×C₄×C₅	—	4	1	no	—
291	C₂×C₄×C₅	—	4	1	no	—
292	C₂×C₄×C₅	—	4	1	no	—
293	C₂×C₄×C₅	—	4	1	no	—
294	C₂×C₄×C₅	—	4	1	no	—
295	C₂×C₄×C₅	—	4	1	no	—
296	C₂×C₄×C₅	—	4	1	no	—
297	C₂×C₄×C₅	—	4	1	no	—
298	C₂×C₄×C₅	—	4	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	—	8	4	no	—
307	C₂×C₄×C₅	—	8	4	no	—
308	C₂×C₄×C₅	—	8	4	no	—
309	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
310	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
311	C₂×C₄×C₅	#135	1	2	yes	—
312	C₂×C₄×C₅	#135	1	2	yes	—
313	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
314	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
315	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
316	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
317	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
318	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
319	C₅×C₈	—	2	2	no	—
320	C₅×C₈	—	2	2	no	—
321	C₅×C₈	—	2	2	no	—
322	C₅×C₈	—	4	1	no	—
323	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
324	C₂³×C₄	—	2	1	no	—
325	C₂³×C₄	—	2	1	no	—
326	C₂³×C₄	—	2	1	no	—
327	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
329	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
331	#125	—	2	2	no	—
332	#125	C₂×C₄×C₅	1	4	yes	complemented
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	—	2	2	no	—
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	—	4	1	no	—
337	C₄×D₄	—	4	1	no	—
338	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₄²	—	2	1	no	—
358	C₂×C₄²	—	2	1	no	—
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
361	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
362	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
363	#107	—	4	1	no	—
364	#107	C₂×C₄×C₅	1	4	yes	complemented
365	#106	—	4	1	no	—
366	#106	C₂×C₄×C₅	1	4	yes	complemented
367	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
368	#102	—	2	2	no	—
369	#102	C₂×C₄×C₅	1	4	yes	—
370	#102	C₂×C₄×C₅	1	4	yes	—
371	#102	C₅×Q₈	1	4	yes	—
372	C₄×C₈	—	2	2	no	—
373	C₄×C₈	—	4	1	no	—
374	C₄×C₈	—	4	1	no	—
375	#95	—	2	1	no	—
376	#95	—	2	1	no	—
377	#95	—	2	1	no	—
378	#95	—	2	1	no	—
379	#95	—	2	1	no	—
380	#95	—	2	1	no	—
381	#95	—	2	1	no	—
382	#95	—	2	1	no	—
383	#95	—	2	1	no	—
384	#95	C₅×D₄	1	1	yes	characteristic
385	#95	C₅×D₄	1	1	yes	characteristic
386	C₂²×C₅	—	2	4	no	—
387	C₂²×C₅	—	4	2	no	—
388	C₂²×C₅	—	4	2	no	—
389	C₂²×C₅	—	4	2	no	—
390	C₂²×C₅	—	4	2	no	—
391	C₂²×C₅	—	4	2	no	—
392	C₂²×C₅	—	4	2	no	—
393	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
394	C₂²×C₅	#546	1	1	yes	characteristic
395	C₂²×C₅	D₄×Q₈	1	1	yes	characteristic
396	C₂²×C₅	C₂×#135	1	1	yes	characteristic
397	C₂²×C₅	C₂×#135	1	1	yes	characteristic
398	C₂²×C₅	#576	1	1	yes	characteristic
399	C₂²×C₅	#577	1	1	yes	characteristic
400	C₄×C₅	—	2	2	no	—
401	C₄×C₅	—	2	2	no	—
402	C₄×C₅	—	2	2	no	—
403	C₄×C₅	—	2	2	no	—
404	C₄×C₅	—	4	2	no	—
405	C₄×C₅	—	4	2	no	—
406	C₄×C₅	—	4	2	no	—
407	C₄×C₅	—	4	2	no	—
408	C₄×C₅	—	4	1	no	—
409	C₄×C₅	—	4	1	no	—
410	C₄×C₅	—	8	1	no	—
411	C₄×C₅	—	8	1	no	—
412	C₄×C₅	—	8	1	no	—
413	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
414	C₄×C₅	#520	1	1	yes	characteristic
415	C₄×C₅	#552	1	1	yes	characteristic
416	C₄×C₅	#554	1	1	yes	characteristic
417	C₂⁴	—	2	1	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
422	C₂×D₄	C₂×C₅×Q₈	1	2	yes	—
423	C₂×D₄	C₅×#41	1	2	yes	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	—	4	2	no	—
434	C₂²×C₄	—	4	2	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	—	8	1	no	—
437	C₂²×C₄	—	8	1	no	—
438	C₂²×C₄	—	8	1	no	—
439	C₂²×C₄	—	8	1	no	—
440	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
441	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
442	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
443	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
444	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
445	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
446	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
457	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
458	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	4	2	no	—
474	C₄⋊C₄	—	8	1	no	—
475	C₄⋊C₄	—	8	1	no	—
476	C₄⋊C₄	—	8	1	no	—
477	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
478	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
479	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
480	C₄⋊C₄	C₂×C₅×Q₈	1	2	yes	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	4	2	no	—
483	C₂²⋊C₄	—	4	2	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	4	2	no	—
489	C₄²	—	8	1	no	—
490	C₄²	—	8	1	no	—
491	C₄²	C₂²×C₄×C₅	1	2	yes	—
492	C₄²	C₅×#41	1	2	yes	—
493	C₂×C₅	—	4	4	no	—
494	C₂×C₅	#2360	1	1	yes	characteristic
495	C₂×C₅	C₄×#135	1	1	yes	characteristic
496	C₂×C₅	#2946	1	1	yes	characteristic
497	C₂×C₅	#3296	1	1	yes	characteristic
498	C₂×C₅	#3297	1	1	yes	characteristic
499	C₂×C₅	#3380	1	1	yes	characteristic
500	C₂×C₅	#3381	1	1	yes	characteristic
501	C₂³	—	2	2	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	4	1	no	—
505	C₂³	—	4	1	no	—
506	C₂³	—	4	1	no	—
507	C₂³	—	4	1	no	—
508	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
509	D₄	—	2	2	no	—
510	D₄	—	2	2	no	—
511	D₄	—	2	2	no	—
512	D₄	C₄×C₅×Q₈	1	4	yes	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	8	4	no	—
549	C₂×C₄	—	8	4	no	—
550	C₂×C₄	—	8	4	no	—
551	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
552	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
553	C₂×C₄	C₅×#135	1	2	yes	—
554	C₂×C₄	C₅×#135	1	2	yes	—
555	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
556	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
557	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
558	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
559	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
560	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
561	C₈	—	2	2	no	—
562	C₈	—	2	2	no	—
563	C₈	—	2	2	no	—
564	C₈	—	4	1	no	—
565	C₅	#22966	1	1	yes	characteristic, direct product factor, Sylow
566	C₂²	—	2	4	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	2	no	—
573	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
574	C₂²	C₅×#546	1	1	yes	characteristic
575	C₂²	C₅×D₄×Q₈	1	1	yes	characteristic
576	C₂²	C₂×C₅×#135	1	1	yes	characteristic
577	C₂²	C₂×C₅×#135	1	1	yes	characteristic
578	C₂²	C₅×#576	1	1	yes	characteristic
579	C₂²	C₅×#577	1	1	yes	characteristic
580	C₄	—	2	2	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	2	no	—
583	C₄	—	2	2	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	2	no	—
588	C₄	—	4	2	no	—
589	C₄	—	4	2	no	—
590	C₄	—	8	1	no	—
591	C₄	—	8	1	no	—
592	C₄	—	8	1	no	—
593	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
594	C₄	C₅×#520	1	1	yes	characteristic
595	C₄	C₅×#552	1	1	yes	characteristic
596	C₄	C₅×#554	1	1	yes	characteristic
597	C₂	—	4	4	no	—
598	C₂	C₅×#2360	1	1	yes	characteristic
599	C₂	C₄×C₅×#135	1	1	yes	characteristic
600	C₂	C₅×#2946	1	1	yes	characteristic
601	C₂	C₅×#3296	1	1	yes	characteristic
602	C₂	C₅×#3297	1	1	yes	characteristic
603	C₂	C₅×#3380	1	1	yes	characteristic
604	C₂	C₅×#3381	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	C₂²×C₅×D₄	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2370	C₂	semidirect
4. C₅×#1991	C₂	semidirect
5. C₅×#1949	C₂	semidirect
6. C₅×#1942	C₂	semidirect
7. C₅×#1941	C₂	semidirect
8. C₅×#1921	C₂	semidirect
9. C₅×#1920	C₂	semidirect
12. C₅×C₈×C₄⋊C₄	C₂	semidirect
20. C₅×#478	C₄	semidirect
60. #22966	C₅	direct (N × H)
70. C₅×#125	C₂×C₄	semidirect
102. C₅×#107	C₂×C₄	semidirect
104. C₅×#106	C₂×C₄	semidirect
105. C₅×C₄⋊C₈	C₂×C₄	semidirect
125. #2370	C₂×C₅	semidirect
127. #1991	C₂×C₅	semidirect
128. #1949	C₂×C₅	semidirect
129. #1942	C₂×C₅	semidirect
130. #1941	C₂×C₅	semidirect
131. #1921	C₂×C₅	semidirect
132. #1920	C₂×C₅	semidirect
135. C₈×C₄⋊C₄	C₂×C₅	semidirect
219. #478	C₄×C₅	semidirect
332. #125	C₂×C₄×C₅	semidirect
364. #107	C₂×C₄×C₅	semidirect
366. #106	C₂×C₄×C₅	semidirect
367. C₄⋊C₈	C₂×C₄×C₅	semidirect
565. C₅	#22966	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×#478	2
C₅×#2370	2
C₅×#2349	2
C₅×#1991	2
C₅×#1949	2
C₅×#1942	2
C₅×#1941	2
C₅×#1921	2
C₅×#1920	2
C₅×#1864	2
C₅×#1862	2
C₅×C₈×C₄⋊C₄	2
C₄×C₅×#102	2
#22966	5

Subgroups — C5×#22966 #11945686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22966 #11945686