Subgroups — C₅×#34281 #11957001

Order 1280.

2070 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#541	C₂	1	1	yes	maximal, characteristic
2	C₅×#2373	C₂	1	4	yes	maximal
3	C₅×#2373	C₂	1	4	yes	maximal
4	C₅×#2371	C₂	1	4	yes	maximal, complemented
5	C₅×#2370	C₂	1	4	yes	maximal, complemented
6	C₅×#2330	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2327	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2323	C₂	1	2	yes	maximal
9	C₅×#2314	C₂	1	1	yes	maximal, characteristic
10	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal
13	C₅×#2295	C₂	1	2	yes	maximal, complemented
14	C₅×#2276	C₂	1	2	yes	maximal, complemented
15	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic
16	C₅×#541	C₄	1	16	yes	complemented
17	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#126	C₂²	1	4	yes	—
19	C₂×C₅×#125	C₂²	1	1	yes	characteristic
20	C₂×C₅×#125	C₂²	1	4	yes	—
21	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
23	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
24	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
25	C₂×C₅×#117	C₂²	1	1	yes	characteristic
26	C₂×C₅×#117	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₅×#391	C₂²	1	2	yes	—
29	C₅×#391	C₂²	1	2	yes	—
30	C₅×#389	C₂²	1	2	yes	—
31	C₅×#389	C₂²	1	2	yes	—
32	C₅×#389	C₂²	1	4	yes	—
33	C₅×#389	C₂²	1	4	yes	—
34	C₅×#389	C₂²	1	4	yes	—
35	C₅×#388	C₂²	1	4	yes	—
36	C₅×#388	C₂²	1	4	yes	—
37	C₅×#388	C₂²	1	4	yes	—
38	C₅×#387	C₂²	1	4	yes	—
39	C₅×#387	C₂²	1	4	yes	—
40	C₅×#387	C₂²	1	4	yes	—
41	C₅×#387	C₂²	1	4	yes	—
42	C₅×#387	C₂²	1	4	yes	—
43	C₅×#387	C₂²	1	4	yes	—
44	C₅×#387	C₂²	1	4	yes	—
45	C₅×#387	C₂²	1	4	yes	—
46	C₅×#387	C₂²	1	4	yes	—
47	C₅×#385	C₂²	1	4	yes	—
48	C₅×#384	C₂²	1	1	yes	characteristic
49	C₅×#382	C₂²	1	1	yes	characteristic
50	C₅×#380	C₂²	1	2	yes	—
51	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
52	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
53	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
54	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
55	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
56	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
57	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
58	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
59	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
60	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
61	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
62	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
63	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
64	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
65	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
66	C₅×#376	C₂²	1	1	yes	characteristic
67	C₅×#376	C₂²	1	1	yes	characteristic
68	C₅×#376	C₂²	1	4	yes	—
69	C₅×#376	C₂²	1	4	yes	—
70	C₄³×C₅	C₂²	1	1	yes	characteristic
71	C₄³×C₅	C₂²	1	1	yes	characteristic
72	#34281	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂²×C₅×Q₈	C₂³	1	2	yes	—
74	C₂³×C₄×C₅	C₂³	1	2	yes	—
75	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₅×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
77	C₅×#126	C₂×C₄	1	32	yes	—
78	C₅×#125	C₂×C₄	1	8	yes	complemented
79	C₅×#125	C₂×C₄	1	32	yes	complemented
80	C₅×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
81	C₄×C₅×Q₈	—	2	8	no	—
82	C₄×C₅×Q₈	—	2	8	no	—
83	C₄×C₅×Q₈	C₂×C₄	1	16	yes	complemented
84	C₅×#117	—	2	4	no	—
85	C₅×#117	C₂×C₄	1	8	yes	—
86	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
87	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
88	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
89	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
90	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
92	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
94	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
95	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
97	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
98	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
101	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
104	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
105	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
106	C₂×C₄²×C₅	—	2	4	no	—
107	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₅	C₂³	1	2	yes	—
109	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₅	C₂³	1	2	yes	—
111	C₂×C₄²×C₅	C₂³	1	4	yes	—
112	C₂×C₄²×C₅	C₂³	1	4	yes	—
113	C₂×C₄²×C₅	C₂³	1	2	yes	—
114	C₂×C₄²×C₅	C₂³	1	2	yes	—
115	C₂×C₄²×C₅	C₂³	1	2	yes	—
116	C₂×C₄²×C₅	C₂³	1	4	yes	—
117	C₂×C₄²×C₅	C₂³	1	4	yes	—
118	C₂×C₄²×C₅	C₂³	1	4	yes	—
119	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₅	C₂³	1	4	yes	—
122	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
124	C₅×#95	C₂³	1	2	yes	—
125	C₅×#95	C₂³	1	2	yes	—
126	C₅×#95	C₂³	1	2	yes	—
127	C₅×#95	C₂³	1	4	yes	—
128	C₅×#95	C₂³	1	2	yes	—
129	C₅×#95	C₂³	1	4	yes	—
130	C₅×#95	C₂³	1	4	yes	—
131	C₅×#95	C₂³	1	4	yes	—
132	C₅×#95	C₂³	1	4	yes	—
133	C₅×#95	C₂³	1	4	yes	—
134	C₅×#95	C₂³	1	4	yes	—
135	C₅×#95	C₂³	1	4	yes	—
136	C₅×#95	C₂³	1	4	yes	—
137	C₅×#95	C₂³	1	4	yes	—
138	C₅×#95	C₂³	1	4	yes	—
139	C₂×#541	C₂×C₅	1	1	yes	characteristic
140	#2373	C₂×C₅	1	4	yes	—
141	#2373	C₂×C₅	1	4	yes	—
142	#2371	C₂×C₅	1	4	yes	complemented
143	#2370	C₂×C₅	1	4	yes	complemented
144	#2330	C₂×C₅	1	1	yes	characteristic, complemented
145	#2327	C₂×C₅	1	1	yes	characteristic, complemented
146	#2323	C₂×C₅	1	2	yes	—
147	#2314	C₂×C₅	1	1	yes	characteristic
148	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
149	C₄×#125	C₂×C₅	1	1	yes	characteristic, complemented
150	C₄×C₂²⋊Q₈	C₂×C₅	1	2	yes	—
151	#2295	C₂×C₅	1	2	yes	complemented
152	#2276	C₂×C₅	1	2	yes	complemented
153	C₄×#117	C₂×C₅	1	1	yes	characteristic
154	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
155	C₂×C₅×Q₈	—	2	4	no	—
156	C₂×C₅×Q₈	—	2	4	no	—
157	C₂×C₅×Q₈	C₂²×C₄	1	8	yes	—
158	C₂²×C₄×C₅	—	2	2	no	—
159	C₂²×C₄×C₅	—	2	2	no	—
160	C₂²×C₄×C₅	—	2	4	no	—
161	C₂²×C₄×C₅	—	2	4	no	—
162	C₂²×C₄×C₅	—	4	2	no	—
163	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
164	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
175	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
178	C₅×C₄⋊C₄	—	2	2	no	—
179	C₅×C₄⋊C₄	—	2	2	no	—
180	C₅×C₄⋊C₄	—	2	8	no	—
181	C₅×C₄⋊C₄	—	2	8	no	—
182	C₅×C₄⋊C₄	—	2	4	no	—
183	C₅×C₄⋊C₄	—	2	4	no	—
184	C₅×C₄⋊C₄	—	2	8	no	—
185	C₅×C₄⋊C₄	—	4	4	no	—
186	C₅×C₄⋊C₄	—	4	4	no	—
187	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
188	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
189	C₅×C₄⋊C₄	C₂²×C₄	1	16	yes	—
190	C₅×C₄⋊C₄	C₂²×C₄	1	16	yes	—
191	C₅×C₄⋊C₄	C₂²×C₄	1	16	yes	—
192	C₅×C₄⋊C₄	C₂²×C₄	1	16	yes	—
193	C₅×C₂²⋊C₄	—	2	2	no	—
194	C₅×C₂²⋊C₄	—	2	2	no	—
195	C₅×C₂²⋊C₄	—	4	4	no	—
196	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
197	C₅×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
198	C₄²×C₅	—	2	4	no	—
199	C₄²×C₅	—	2	2	no	—
200	C₄²×C₅	—	2	2	no	—
201	C₄²×C₅	—	2	8	no	—
202	C₄²×C₅	—	2	8	no	—
203	C₄²×C₅	—	2	4	no	—
204	C₄²×C₅	—	2	4	no	—
205	C₄²×C₅	—	4	4	no	—
206	C₄²×C₅	—	4	2	no	—
207	C₄²×C₅	—	4	2	no	—
208	C₄²×C₅	—	4	4	no	—
209	C₄²×C₅	—	4	4	no	—
210	C₄²×C₅	C₂²×C₄	1	4	yes	—
211	C₄²×C₅	C₂²×C₄	1	4	yes	—
212	C₄²×C₅	C₂²×C₄	1	16	yes	—
213	C₄²×C₅	#41	1	4	yes	—
214	C₄²×C₅	#41	1	4	yes	—
215	#541	C₄×C₅	1	16	yes	complemented
216	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
217	C₂×#126	C₂²×C₅	1	4	yes	—
218	C₂×#125	C₂²×C₅	1	1	yes	characteristic
219	C₂×#125	C₂²×C₅	1	4	yes	—
220	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
221	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
222	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
223	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
224	C₂×#117	C₂²×C₅	1	1	yes	characteristic
225	C₂×#117	C₂²×C₅	1	1	yes	characteristic
226	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
227	#391	C₂²×C₅	1	2	yes	—
228	#391	C₂²×C₅	1	2	yes	—
229	#389	C₂²×C₅	1	2	yes	—
230	#389	C₂²×C₅	1	4	yes	—
231	#389	C₂²×C₅	1	2	yes	—
232	#389	C₂²×C₅	1	4	yes	—
233	#389	C₂²×C₅	1	4	yes	—
234	#388	C₂²×C₅	1	4	yes	—
235	#388	C₂²×C₅	1	4	yes	—
236	#388	C₂²×C₅	1	4	yes	—
237	#387	C₂²×C₅	1	4	yes	—
238	#387	C₂²×C₅	1	4	yes	—
239	#387	C₂²×C₅	1	4	yes	—
240	#387	C₂²×C₅	1	4	yes	—
241	#387	C₂²×C₅	1	4	yes	—
242	#387	C₂²×C₅	1	4	yes	—
243	#387	C₂²×C₅	1	4	yes	—
244	#387	C₂²×C₅	1	4	yes	—
245	#387	C₂²×C₅	1	4	yes	—
246	#385	C₂²×C₅	1	4	yes	—
247	#384	C₂²×C₅	1	1	yes	characteristic
248	#382	C₂²×C₅	1	1	yes	characteristic
249	#380	C₂²×C₅	1	2	yes	—
250	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
251	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
252	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
253	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
254	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
255	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
256	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
257	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
258	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
259	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
260	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
261	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
262	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
263	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
264	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
265	#376	C₂²×C₅	1	1	yes	characteristic
266	#376	C₂²×C₅	1	4	yes	—
267	#376	C₂²×C₅	1	4	yes	—
268	#376	C₂²×C₅	1	1	yes	characteristic
269	C₄³	C₂²×C₅	1	1	yes	characteristic
270	C₄³	C₂²×C₅	1	1	yes	characteristic
271	C₂³×C₅	—	2	1	no	—
272	C₂³×C₅	—	2	1	no	—
273	C₂³×C₅	—	2	2	no	—
274	C₂³×C₅	—	2	2	no	—
275	C₂³×C₅	C₂³×C₄	1	2	yes	—
276	C₂³×C₅	C₂⁵	1	1	yes	characteristic
277	C₅×Q₈	—	2	16	no	—
278	C₂×C₄×C₅	—	2	1	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	4	no	—
281	C₂×C₄×C₅	—	2	4	no	—
282	C₂×C₄×C₅	—	2	1	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	4	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	2	4	no	—
291	C₂×C₄×C₅	—	2	2	no	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	2	2	no	—
294	C₂×C₄×C₅	—	2	8	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	4	no	—
298	C₂×C₄×C₅	—	2	4	no	—
299	C₂×C₄×C₅	—	2	2	no	—
300	C₂×C₄×C₅	—	2	4	no	—
301	C₂×C₄×C₅	—	2	4	no	—
302	C₂×C₄×C₅	—	2	4	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	4	no	—
305	C₂×C₄×C₅	—	4	8	no	—
306	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
307	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
308	C₂×C₄×C₅	C₂³×C₄	1	8	yes	—
309	C₂×C₄×C₅	C₂³×C₄	1	8	yes	—
310	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
311	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
312	C₂×C₄×C₅	C₂×#41	1	2	yes	—
313	C₂×C₄×C₅	C₂×#41	1	4	yes	—
314	C₂×C₄×C₅	C₂×#41	1	2	yes	—
315	C₂×C₄×C₅	C₂×#41	1	2	yes	—
316	C₂×C₄×C₅	C₂×#41	1	2	yes	—
317	C₂×C₄×C₅	2₋¹⁺⁴	1	4	yes	—
318	C₂²×Q₈	C₂³×C₅	1	2	yes	—
319	C₂³×C₄	C₂³×C₅	1	2	yes	—
320	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
321	C₄⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
322	#126	C₂×C₄×C₅	1	32	yes	—
323	#125	C₂×C₄×C₅	1	8	yes	complemented
324	#125	C₂×C₄×C₅	1	32	yes	complemented
325	C₂²⋊Q₈	C₂×C₄×C₅	1	16	yes	—
326	C₄×Q₈	—	2	8	no	—
327	C₄×Q₈	—	2	8	no	—
328	C₄×Q₈	C₂×C₄×C₅	1	16	yes	complemented
329	#117	—	2	4	no	—
330	#117	C₂×C₄×C₅	1	8	yes	—
331	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
336	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
337	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
338	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
339	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
340	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
343	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
344	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
345	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
347	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
351	C₂×C₄²	—	2	4	no	—
352	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₅	1	4	yes	—
354	C₂×C₄²	C₂³×C₅	1	4	yes	—
355	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
356	C₂×C₄²	C₂³×C₅	1	2	yes	—
357	C₂×C₄²	C₂³×C₅	1	2	yes	—
358	C₂×C₄²	C₂³×C₅	1	2	yes	—
359	C₂×C₄²	C₂³×C₅	1	2	yes	—
360	C₂×C₄²	C₂³×C₅	1	2	yes	—
361	C₂×C₄²	C₂³×C₅	1	4	yes	—
362	C₂×C₄²	C₂³×C₅	1	4	yes	—
363	C₂×C₄²	C₂³×C₅	1	4	yes	—
364	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₅	1	4	yes	—
367	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
368	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
369	#95	C₂³×C₅	1	2	yes	—
370	#95	C₂³×C₅	1	2	yes	—
371	#95	C₂³×C₅	1	2	yes	—
372	#95	C₂³×C₅	1	4	yes	—
373	#95	C₂³×C₅	1	2	yes	—
374	#95	C₂³×C₅	1	4	yes	—
375	#95	C₂³×C₅	1	4	yes	—
376	#95	C₂³×C₅	1	4	yes	—
377	#95	C₂³×C₅	1	4	yes	—
378	#95	C₂³×C₅	1	4	yes	—
379	#95	C₂³×C₅	1	4	yes	—
380	#95	C₂³×C₅	1	4	yes	—
381	#95	C₂³×C₅	1	4	yes	—
382	#95	C₂³×C₅	1	4	yes	—
383	#95	C₂³×C₅	1	4	yes	—
384	C₂²×C₅	—	2	2	no	—
385	C₂²×C₅	—	2	4	no	—
386	C₂²×C₅	—	4	2	no	—
387	C₂²×C₅	—	4	1	no	—
388	C₂²×C₅	—	4	1	no	—
389	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
390	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
391	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
392	C₂²×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
393	C₂²×C₅	#585	1	2	yes	—
394	C₄×C₅	—	2	2	no	—
395	C₄×C₅	—	2	8	no	—
396	C₄×C₅	—	2	4	no	—
397	C₄×C₅	—	2	4	no	—
398	C₄×C₅	—	2	8	no	—
399	C₄×C₅	—	2	4	no	—
400	C₄×C₅	—	2	4	no	—
401	C₄×C₅	—	2	2	no	—
402	C₄×C₅	—	2	2	no	—
403	C₄×C₅	—	4	4	no	—
404	C₄×C₅	—	4	1	no	—
405	C₄×C₅	—	4	1	no	—
406	C₄×C₅	—	4	4	no	—
407	C₄×C₅	C₄×#41	1	4	yes	—
408	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
409	C₂×Q₈	—	2	4	no	—
410	C₂×Q₈	—	2	4	no	—
411	C₂×Q₈	C₂²×C₄×C₅	1	8	yes	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	4	2	no	—
417	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
418	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
419	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
420	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
421	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
422	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
423	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
424	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
425	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
426	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
427	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
428	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
429	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
430	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
431	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	8	no	—
435	C₄⋊C₄	—	2	8	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	2	8	no	—
439	C₄⋊C₄	—	4	4	no	—
440	C₄⋊C₄	—	4	4	no	—
441	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
442	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
443	C₄⋊C₄	C₂²×C₄×C₅	1	16	yes	—
444	C₄⋊C₄	C₂²×C₄×C₅	1	16	yes	—
445	C₄⋊C₄	C₂²×C₄×C₅	1	16	yes	—
446	C₄⋊C₄	C₂²×C₄×C₅	1	16	yes	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	4	4	no	—
450	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
451	C₂²⋊C₄	C₂²×C₄×C₅	1	16	yes	—
452	C₄²	—	2	4	no	—
453	C₄²	—	2	2	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	2	8	no	—
456	C₄²	—	2	8	no	—
457	C₄²	—	2	4	no	—
458	C₄²	—	2	4	no	—
459	C₄²	—	4	4	no	—
460	C₄²	—	4	2	no	—
461	C₄²	—	4	2	no	—
462	C₄²	—	4	4	no	—
463	C₄²	—	4	4	no	—
464	C₄²	C₂²×C₄×C₅	1	4	yes	—
465	C₄²	C₂²×C₄×C₅	1	4	yes	—
466	C₄²	C₂²×C₄×C₅	1	16	yes	—
467	C₄²	C₅×#41	1	4	yes	—
468	C₄²	C₅×#41	1	4	yes	—
469	C₂×C₅	—	4	2	no	—
470	C₂×C₅	C₂×C₄×#41	1	1	yes	characteristic
471	C₂×C₅	C₄×2₋¹⁺⁴	1	2	yes	—
472	C₂×C₅	#3495	1	2	yes	—
473	C₂×C₅	#3509	1	1	yes	characteristic
474	C₂×C₅	#3512	1	1	yes	characteristic
475	C₂³	—	2	1	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	C₂³×C₄×C₅	1	2	yes	—
480	C₂³	C₂⁵×C₅	1	1	yes	characteristic
481	Q₈	—	2	16	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	8	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	4	8	no	—
510	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
511	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
512	C₂×C₄	C₂³×C₄×C₅	1	8	yes	—
513	C₂×C₄	C₂³×C₄×C₅	1	8	yes	—
514	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
515	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
516	C₂×C₄	C₂×C₅×#41	1	2	yes	—
517	C₂×C₄	C₂×C₅×#41	1	4	yes	—
518	C₂×C₄	C₂×C₅×#41	1	2	yes	—
519	C₂×C₄	C₂×C₅×#41	1	2	yes	—
520	C₂×C₄	C₂×C₅×#41	1	2	yes	—
521	C₂×C₄	C₅×2₋¹⁺⁴	1	4	yes	—
522	C₅	#34281	1	1	yes	characteristic, direct product factor, Sylow
523	C₂²	—	2	2	no	—
524	C₂²	—	2	4	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
529	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
530	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
531	C₂²	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
532	C₂²	C₅×#585	1	2	yes	—
533	C₄	—	2	2	no	—
534	C₄	—	2	8	no	—
535	C₄	—	2	4	no	—
536	C₄	—	2	4	no	—
537	C₄	—	2	8	no	—
538	C₄	—	2	4	no	—
539	C₄	—	2	4	no	—
540	C₄	—	2	2	no	—
541	C₄	—	2	2	no	—
542	C₄	—	4	4	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	4	no	—
546	C₄	C₄×C₅×#41	1	4	yes	—
547	C₂	—	4	2	no	—
548	C₂	C₂×C₄×C₅×#41	1	1	yes	characteristic
549	C₂	C₄×C₅×2₋¹⁺⁴	1	2	yes	—
550	C₂	C₅×#3495	1	2	yes	—
551	C₂	C₅×#3509	1	1	yes	characteristic
552	C₂	C₅×#3512	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂⁴×C₅	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#2371	C₂	semidirect
5. C₅×#2370	C₂	semidirect
6. C₅×#2330	C₂	semidirect
7. C₅×#2327	C₂	semidirect
10. C₄×C₅×C₄⋊Q₈	C₂	semidirect
11. C₄×C₅×#125	C₂	semidirect
13. C₅×#2295	C₂	semidirect
14. C₅×#2276	C₂	semidirect
16. C₅×#541	C₄	semidirect
72. #34281	C₅	direct (N × H)
76. C₅×C₄⋊Q₈	C₂×C₄	semidirect
78. C₅×#125	C₂×C₄	semidirect
79. C₅×#125	C₂×C₄	semidirect
83. C₄×C₅×Q₈	C₂×C₄	semidirect
142. #2371	C₂×C₅	semidirect
143. #2370	C₂×C₅	semidirect
144. #2330	C₂×C₅	semidirect
145. #2327	C₂×C₅	semidirect
148. C₄×C₄⋊Q₈	C₂×C₅	semidirect
149. C₄×#125	C₂×C₅	semidirect
151. #2295	C₂×C₅	semidirect
152. #2276	C₂×C₅	semidirect
215. #541	C₄×C₅	semidirect
321. C₄⋊Q₈	C₂×C₄×C₅	semidirect
323. #125	C₂×C₄×C₅	semidirect
324. #125	C₂×C₄×C₅	semidirect
328. C₄×Q₈	C₂×C₄×C₅	semidirect
522. C₅	#34281	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×#541	2
C₅×#2373	2
C₅×#2371	2
C₅×#2370	2
C₅×#2330	2
C₅×#2327	2
C₅×#2323	2
C₅×#2314	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×#125	2
C₄×C₅×C₂²⋊Q₈	2
C₅×#2295	2
C₅×#2276	2
C₄×C₅×#117	2
#34281	5

Subgroups — C5×#34281 #11957001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34281 #11957001