Subgroups — C₅×#22662 #11945382

Order 1280.

970 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#435	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#427	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2354	C₂	1	1	yes	maximal, characteristic
5	C₅×#2352	C₂	1	1	yes	maximal, characteristic
6	C₅×#1949	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1948	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1854	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1854	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1854	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1853	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1847	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1809	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1807	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1776	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₅×#117	C₂²	1	1	yes	characteristic
20	C₂×C₅×#117	C₂²	1	1	yes	characteristic
21	C₂×C₅×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₅×#435	C₄	1	8	yes	complemented
24	C₅×#428	—	2	4	no	—
25	C₅×#427	—	2	4	no	—
26	C₂×C₅×#107	C₂²	1	1	yes	characteristic
27	C₂×C₅×#107	C₂²	1	1	yes	characteristic
28	C₂×C₅×#107	C₂²	1	1	yes	characteristic
29	C₂×C₅×#107	C₂²	1	1	yes	characteristic
30	C₂×C₅×#106	C₂²	1	1	yes	characteristic
31	C₂×C₅×#106	C₂²	1	1	yes	characteristic
32	C₂×C₅×#106	C₂²	1	1	yes	characteristic
33	C₂×C₅×#106	C₂²	1	1	yes	characteristic
34	C₂×C₅×#106	C₂²	1	1	yes	characteristic
35	C₂×C₅×#106	C₂²	1	1	yes	characteristic
36	C₂×C₅×C₄⋊C₈	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	C₅×#390	—	2	1	no	—
41	C₅×#388	—	2	1	no	—
42	C₅×#388	—	2	1	no	—
43	C₅×#388	—	2	1	no	—
44	C₅×#387	—	2	1	no	—
45	C₅×#386	—	2	1	no	—
46	C₅×#384	C₂²	1	1	yes	characteristic
47	C₅×#382	C₂²	1	1	yes	characteristic
48	C₅×#380	C₂²	1	1	yes	characteristic
49	C₅×#380	C₂²	1	1	yes	characteristic
50	C₅×#380	C₂²	1	1	yes	characteristic
51	C₅×#380	C₂²	1	1	yes	characteristic
52	C₄×C₅×C₄⋊C₄	—	2	1	no	—
53	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
54	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
55	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
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	C₅×#340	C₂²	1	1	yes	characteristic
62	#22662	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₅	—	2	1	no	—
65	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂×C₅×M₁₆	—	2	2	no	—
68	C₂×C₅×M₁₆	—	2	2	no	—
69	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
70	C₂²×C₅×C₈	—	2	2	no	—
71	C₂²×C₅×C₈	—	2	2	no	—
72	C₂²×C₅×C₈	C₂×C₄	1	4	yes	complemented
73	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
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	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
78	C₄×C₅×D₄	Q₈	1	4	yes	—
79	C₅×#117	—	2	2	no	—
80	C₅×#117	—	2	2	no	—
81	C₅×#117	—	2	2	no	—
82	C₅×#117	—	4	1	no	—
83	C₅×#117	—	4	1	no	—
84	C₅×#117	—	4	1	no	—
85	C₂×C₅×C₄⋊C₄	—	2	2	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	—	4	1	no	—
90	C₂×C₅×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
107	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₅	—	2	1	no	—
109	C₂×C₄²×C₅	—	2	1	no	—
110	C₂×C₄²×C₅	—	2	1	no	—
111	C₂×C₄²×C₅	—	2	1	no	—
112	C₂×C₄²×C₅	—	2	1	no	—
113	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
114	C₅×#107	—	2	2	no	—
115	C₅×#107	—	2	2	no	—
116	C₅×#107	—	4	1	no	—
117	C₅×#107	D₄	1	4	yes	complemented
118	C₅×#106	—	2	2	no	—
119	C₅×#106	—	2	2	no	—
120	C₅×#106	—	2	2	no	—
121	C₅×#106	—	2	2	no	—
122	C₅×#106	—	2	2	no	—
123	C₅×#106	—	4	1	no	—
124	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
125	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
126	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
127	C₅×#97	C₂×C₄	1	4	yes	complemented
128	C₅×#95	—	2	1	no	—
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	C₅×#95	—	2	1	no	—
136	C₂×#435	C₂×C₅	1	1	yes	characteristic
137	C₂×#428	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂×#427	C₂×C₅	1	1	yes	characteristic, complemented
139	#2354	C₂×C₅	1	1	yes	characteristic
140	#2352	C₂×C₅	1	1	yes	characteristic
141	#1949	C₂×C₅	1	1	yes	characteristic, complemented
142	#1948	C₂×C₅	1	1	yes	characteristic, complemented
143	#1854	C₂×C₅	1	1	yes	characteristic, complemented
144	#1854	C₂×C₅	1	1	yes	characteristic, complemented
145	#1854	C₂×C₅	1	1	yes	characteristic, complemented
146	#1853	C₂×C₅	1	1	yes	characteristic, complemented
147	#1847	C₂×C₅	1	1	yes	characteristic, complemented
148	#1809	C₂×C₅	1	1	yes	characteristic, complemented
149	#1807	C₂×C₅	1	1	yes	characteristic, complemented
150	#1776	C₂×C₅	1	1	yes	characteristic, complemented
151	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₅×D₄	—	4	1	no	—
154	C₂×C₅×D₄	—	4	1	no	—
155	C₂×C₅×D₄	C₄⋊C₄	1	4	yes	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	—	2	1	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	—	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	—	2	1	no	—
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	—	4	2	no	—
173	C₂²×C₄×C₅	—	4	2	no	—
174	C₂²×C₄×C₅	—	8	1	no	—
175	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
176	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
182	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
183	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
184	C₅×M₁₆	—	2	8	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	—	2	8	no	—
192	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
193	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
194	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
195	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
196	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
197	C₂×C₅×C₈	#41	1	2	yes	—
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	—	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	—	4	2	no	—
213	C₅×C₄⋊C₄	—	4	2	no	—
214	C₅×C₄⋊C₄	—	8	1	no	—
215	C₅×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
216	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
217	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
218	C₅×C₂²⋊C₄	—	4	2	no	—
219	C₅×C₂²⋊C₄	—	4	2	no	—
220	C₅×C₂²⋊C₄	—	4	2	no	—
221	C₅×C₂²⋊C₄	—	4	2	no	—
222	C₅×C₂²⋊C₄	—	8	1	no	—
223	C₅×C₂²⋊C₄	—	8	1	no	—
224	C₅×C₂²⋊C₄	—	8	1	no	—
225	C₅×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
226	C₅×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
227	C₄²×C₅	—	4	2	no	—
228	C₄²×C₅	—	4	2	no	—
229	C₄²×C₅	—	4	2	no	—
230	C₄²×C₅	—	4	2	no	—
231	C₄²×C₅	—	8	1	no	—
232	C₄²×C₅	C₂²×C₄	1	2	yes	—
233	C₄²×C₅	C₂×Q₈	1	2	yes	—
234	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
235	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
237	C₂×#117	C₂²×C₅	1	1	yes	characteristic
238	C₂×#117	C₂²×C₅	1	1	yes	characteristic
239	C₂×#117	C₂²×C₅	1	1	yes	characteristic
240	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
241	#435	C₄×C₅	1	8	yes	complemented
242	#428	—	2	4	no	—
243	#427	—	2	4	no	—
244	C₂×#107	C₂²×C₅	1	1	yes	characteristic
245	C₂×#107	C₂²×C₅	1	1	yes	characteristic
246	C₂×#107	C₂²×C₅	1	1	yes	characteristic
247	C₂×#107	C₂²×C₅	1	1	yes	characteristic
248	C₂×#106	C₂²×C₅	1	1	yes	characteristic
249	C₂×#106	C₂²×C₅	1	1	yes	characteristic
250	C₂×#106	C₂²×C₅	1	1	yes	characteristic
251	C₂×#106	C₂²×C₅	1	1	yes	characteristic
252	C₂×#106	C₂²×C₅	1	1	yes	characteristic
253	C₂×#106	C₂²×C₅	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
256	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
257	C₂×#97	C₂²×C₅	1	1	yes	characteristic
258	#390	—	2	1	no	—
259	#388	—	2	1	no	—
260	#388	—	2	1	no	—
261	#388	—	2	1	no	—
262	#387	—	2	1	no	—
263	#386	—	2	1	no	—
264	#384	C₂²×C₅	1	1	yes	characteristic
265	#382	C₂²×C₅	1	1	yes	characteristic
266	#380	C₂²×C₅	1	1	yes	characteristic
267	#380	C₂²×C₅	1	1	yes	characteristic
268	#380	C₂²×C₅	1	1	yes	characteristic
269	#380	C₂²×C₅	1	1	yes	characteristic
270	C₄×C₄⋊C₄	—	2	1	no	—
271	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
272	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
273	C₄×C₂²⋊C₄	—	2	1	no	—
274	#340	C₂²×C₅	1	1	yes	characteristic
275	#340	C₂²×C₅	1	1	yes	characteristic
276	#340	C₂²×C₅	1	1	yes	characteristic
277	#340	C₂²×C₅	1	1	yes	characteristic
278	#340	C₂²×C₅	1	1	yes	characteristic
279	#340	C₂²×C₅	1	1	yes	characteristic
280	C₂³×C₅	—	2	1	no	—
281	C₂³×C₅	—	2	1	no	—
282	C₂³×C₅	—	2	1	no	—
283	C₂³×C₅	—	2	1	no	—
284	C₂³×C₅	—	2	1	no	—
285	C₂³×C₅	—	2	1	no	—
286	C₂³×C₅	—	2	1	no	—
287	C₂³×C₅	—	2	1	no	—
288	C₂³×C₅	—	2	1	no	—
289	C₂³×C₅	—	2	1	no	—
290	C₂³×C₅	—	2	1	no	—
291	C₂³×C₅	—	2	1	no	—
292	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
293	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
294	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
295	C₅×D₄	—	4	4	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	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	1	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	2	no	—
309	C₂×C₄×C₅	—	2	2	no	—
310	C₂×C₄×C₅	—	2	2	no	—
311	C₂×C₄×C₅	—	2	2	no	—
312	C₂×C₄×C₅	—	2	2	no	—
313	C₂×C₄×C₅	—	2	2	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	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	—	8	4	no	—
337	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
338	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
339	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
340	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
341	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
342	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
344	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
345	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
346	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
347	C₅×C₈	—	2	2	no	—
348	C₅×C₈	—	2	2	no	—
349	C₅×C₈	—	2	2	no	—
350	C₅×C₈	C₄×D₄	1	4	yes	—
351	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
352	C₂³×C₄	—	2	1	no	—
353	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
354	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
355	C₂×M₁₆	—	2	2	no	—
356	C₂×M₁₆	—	2	2	no	—
357	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
358	C₂²×C₈	—	2	2	no	—
359	C₂²×C₈	—	2	2	no	—
360	C₂²×C₈	C₂×C₄×C₅	1	4	yes	complemented
361	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
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	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
366	C₄×D₄	C₅×Q₈	1	4	yes	—
367	#117	—	2	2	no	—
368	#117	—	2	2	no	—
369	#117	—	2	2	no	—
370	#117	—	4	1	no	—
371	#117	—	4	1	no	—
372	#117	—	4	1	no	—
373	C₂×C₄⋊C₄	—	2	2	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	4	1	no	—
378	C₂×C₄⋊C₄	C₅×D₄	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×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₂²⋊C₄	—	2	1	no	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
395	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	—	2	1	no	—
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	—	2	1	no	—
401	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
402	#107	—	2	2	no	—
403	#107	—	2	2	no	—
404	#107	—	4	1	no	—
405	#107	C₅×D₄	1	4	yes	complemented
406	#106	—	2	2	no	—
407	#106	—	2	2	no	—
408	#106	—	2	2	no	—
409	#106	—	2	2	no	—
410	#106	—	2	2	no	—
411	#106	—	4	1	no	—
412	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
413	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	—
414	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
415	#97	C₂×C₄×C₅	1	4	yes	complemented
416	#95	—	2	1	no	—
417	#95	—	2	1	no	—
418	#95	—	2	1	no	—
419	#95	—	2	1	no	—
420	#95	—	2	1	no	—
421	#95	—	2	1	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	C₂²×C₅	—	2	2	no	—
425	C₂²×C₅	—	2	2	no	—
426	C₂²×C₅	—	2	2	no	—
427	C₂²×C₅	—	2	2	no	—
428	C₂²×C₅	—	2	2	no	—
429	C₂²×C₅	—	2	2	no	—
430	C₂²×C₅	—	4	1	no	—
431	C₂²×C₅	—	4	1	no	—
432	C₂²×C₅	—	4	1	no	—
433	C₂²×C₅	—	4	1	no	—
434	C₂²×C₅	—	4	1	no	—
435	C₂²×C₅	—	4	1	no	—
436	C₂²×C₅	—	4	1	no	—
437	C₂²×C₅	—	4	1	no	—
438	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
439	C₂²×C₅	D₄²	1	1	yes	characteristic
440	C₂²×C₅	#547	1	1	yes	characteristic
441	C₂²×C₅	#575	1	1	yes	characteristic
442	C₂²×C₅	#575	1	1	yes	characteristic
443	C₂²×C₅	#577	1	1	yes	characteristic
444	C₂²×C₅	#577	1	1	yes	characteristic
445	C₄×C₅	—	2	2	no	—
446	C₄×C₅	—	2	2	no	—
447	C₄×C₅	—	2	2	no	—
448	C₄×C₅	—	2	2	no	—
449	C₄×C₅	—	4	2	no	—
450	C₄×C₅	—	4	2	no	—
451	C₄×C₅	—	8	1	no	—
452	C₄×C₅	—	8	1	no	—
453	C₄×C₅	—	8	1	no	—
454	C₄×C₅	—	8	1	no	—
455	C₄×C₅	—	8	1	no	—
456	C₄×C₅	—	8	1	no	—
457	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
458	C₄×C₅	#520	1	1	yes	characteristic
459	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
460	C₄×C₅	#554	1	1	yes	characteristic
461	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
462	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
463	C₂×D₄	—	4	1	no	—
464	C₂×D₄	—	4	1	no	—
465	C₂×D₄	C₅×C₄⋊C₄	1	4	yes	—
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	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	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	—	4	2	no	—
483	C₂²×C₄	—	4	2	no	—
484	C₂²×C₄	—	8	1	no	—
485	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
486	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
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	C₂×C₅×Q₈	1	2	yes	—
492	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
493	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
494	M₁₆	—	2	8	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	8	no	—
502	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
503	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
504	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
505	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
506	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
507	C₂×C₈	C₅×#41	1	2	yes	—
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	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	4	2	no	—
523	C₄⋊C₄	—	4	2	no	—
524	C₄⋊C₄	—	8	1	no	—
525	C₄⋊C₄	C₅×C₄⋊C₄	1	4	yes	—
526	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
527	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
528	C₂²⋊C₄	—	4	2	no	—
529	C₂²⋊C₄	—	4	2	no	—
530	C₂²⋊C₄	—	4	2	no	—
531	C₂²⋊C₄	—	4	2	no	—
532	C₂²⋊C₄	—	8	1	no	—
533	C₂²⋊C₄	—	8	1	no	—
534	C₂²⋊C₄	—	8	1	no	—
535	C₂²⋊C₄	C₅×C₄⋊C₄	1	4	yes	—
536	C₂²⋊C₄	C₅×C₄⋊C₄	1	4	yes	—
537	C₄²	—	4	2	no	—
538	C₄²	—	4	2	no	—
539	C₄²	—	4	2	no	—
540	C₄²	—	4	2	no	—
541	C₄²	—	8	1	no	—
542	C₄²	C₂²×C₄×C₅	1	2	yes	—
543	C₄²	C₂×C₅×Q₈	1	2	yes	—
544	C₂×C₅	—	4	2	no	—
545	C₂×C₅	—	4	2	no	—
546	C₂×C₅	D₄×C₄⋊C₄	1	1	yes	characteristic
547	C₂×C₅	#2911	1	1	yes	characteristic
548	C₂×C₅	#2912	1	1	yes	characteristic
549	C₂×C₅	#3267	1	1	yes	characteristic
550	C₂×C₅	#3271	1	1	yes	characteristic
551	C₂×C₅	#3348	1	1	yes	characteristic
552	C₂×C₅	#3350	1	1	yes	characteristic
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
566	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
567	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
568	D₄	—	4	4	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	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	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	8	4	no	—
610	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
611	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
612	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
613	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
614	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
615	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
616	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
617	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
618	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
619	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
620	C₈	—	2	2	no	—
621	C₈	—	2	2	no	—
622	C₈	—	2	2	no	—
623	C₈	C₄×C₅×D₄	1	4	yes	—
624	C₅	#22662	1	1	yes	characteristic, direct product factor, Sylow
625	C₂²	—	2	2	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
640	C₂²	C₅×D₄²	1	1	yes	characteristic
641	C₂²	C₅×#547	1	1	yes	characteristic
642	C₂²	C₅×#575	1	1	yes	characteristic
643	C₂²	C₅×#575	1	1	yes	characteristic
644	C₂²	C₅×#577	1	1	yes	characteristic
645	C₂²	C₅×#577	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	4	2	no	—
651	C₄	—	4	2	no	—
652	C₄	—	8	1	no	—
653	C₄	—	8	1	no	—
654	C₄	—	8	1	no	—
655	C₄	—	8	1	no	—
656	C₄	—	8	1	no	—
657	C₄	—	8	1	no	—
658	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
659	C₄	C₅×#520	1	1	yes	characteristic
660	C₄	C₅×D₄×Q₈	1	1	yes	characteristic
661	C₄	C₅×#554	1	1	yes	characteristic
662	C₂	—	4	2	no	—
663	C₂	—	4	2	no	—
664	C₂	C₅×D₄×C₄⋊C₄	1	1	yes	characteristic
665	C₂	C₅×#2911	1	1	yes	characteristic
666	C₂	C₅×#2912	1	1	yes	characteristic
667	C₂	C₅×#3267	1	1	yes	characteristic
668	C₂	C₅×#3271	1	1	yes	characteristic
669	C₂	C₅×#3348	1	1	yes	characteristic
670	C₂	C₅×#3350	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	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#428	C₂	semidirect
3. C₂×C₅×#427	C₂	semidirect
6. C₅×#1949	C₂	semidirect
7. C₅×#1948	C₂	semidirect
8. C₅×#1854	C₂	semidirect
9. C₅×#1854	C₂	semidirect
10. C₅×#1854	C₂	semidirect
11. C₅×#1853	C₂	semidirect
12. C₅×#1847	C₂	semidirect
13. C₅×#1809	C₂	semidirect
14. C₅×#1807	C₂	semidirect
15. C₅×#1776	C₂	semidirect
23. C₅×#435	C₄	semidirect
62. #22662	C₅	direct (N × H)
72. C₂²×C₅×C₈	C₂×C₄	semidirect
117. C₅×#107	D₄	semidirect
124. C₅×C₄⋊C₈	C₂×C₄	semidirect
126. C₅×C₂²⋊C₈	C₂×C₄	semidirect
127. C₅×#97	C₂×C₄	semidirect
137. C₂×#428	C₂×C₅	semidirect
138. C₂×#427	C₂×C₅	semidirect
141. #1949	C₂×C₅	semidirect
142. #1948	C₂×C₅	semidirect
143. #1854	C₂×C₅	semidirect
144. #1854	C₂×C₅	semidirect
145. #1854	C₂×C₅	semidirect
146. #1853	C₂×C₅	semidirect
147. #1847	C₂×C₅	semidirect
148. #1809	C₂×C₅	semidirect
149. #1807	C₂×C₅	semidirect
150. #1776	C₂×C₅	semidirect
241. #435	C₄×C₅	semidirect
360. C₂²×C₈	C₂×C₄×C₅	semidirect
405. #107	C₅×D₄	semidirect
412. C₄⋊C₈	C₂×C₄×C₅	semidirect
414. C₂²⋊C₈	C₂×C₄×C₅	semidirect
415. #97	C₂×C₄×C₅	semidirect
624. C₅	#22662	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×#435	2
C₂×C₅×#428	2
C₂×C₅×#427	2
C₅×#2354	2
C₅×#2352	2
C₅×#1949	2
C₅×#1948	2
C₅×#1854	2
C₅×#1853	2
C₅×#1847	2
C₅×#1809	2
C₅×#1807	2
C₅×#1776	2
#22662	5

Subgroups — C5×#22662 #11945382

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22662 #11945382