Subgroups — C₅×#21039 #11943759

Order 1280.

898 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#427	C₂	1	1	yes	maximal, characteristic
2	C₅×#2317	C₂	1	1	yes	maximal, characteristic
3	C₅×#2274	C₂	1	1	yes	maximal, characteristic
4	C₅×#1921	C₂	1	2	yes	maximal, complemented
5	C₅×#1920	C₂	1	2	yes	maximal, complemented
6	C₅×#1919	C₂	1	2	yes	maximal, complemented
7	C₅×#1918	C₂	1	2	yes	maximal, complemented
8	C₅×#1736	C₂	1	1	yes	maximal, characteristic
9	C₅×#1736	C₂	1	1	yes	maximal, characteristic
10	C₂×C₅×#340	C₂	1	1	yes	maximal, characteristic
11	C₅×#1729	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×#117	C₂²	1	1	yes	characteristic
15	C₂×C₅×#117	C₂²	1	1	yes	characteristic
16	C₂×C₅×#117	C₂²	1	1	yes	characteristic
17	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₅×#427	C₄	1	8	yes	complemented
20	C₂×C₅×#107	C₂²	1	1	yes	characteristic
21	C₂×C₅×#107	C₂²	1	1	yes	characteristic
22	C₂×C₅×#106	C₂²	1	1	yes	characteristic
23	C₂×C₅×#106	C₂²	1	1	yes	characteristic
24	C₅×#389	C₂²	1	2	yes	—
25	C₅×#389	C₂²	1	2	yes	—
26	C₅×#385	—	2	2	no	—
27	C₅×#384	—	2	1	no	—
28	C₅×#382	—	2	1	no	—
29	C₄×C₅×C₄⋊C₄	—	2	1	no	—
30	C₄×C₅×C₄⋊C₄	—	2	1	no	—
31	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
32	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
33	C₄×C₅×C₂²⋊C₄	—	2	2	no	—
34	C₅×#340	C₂²	1	2	yes	—
35	C₅×#340	C₂²	1	2	yes	—
36	C₅×#340	C₂²	1	2	yes	—
37	C₅×#340	C₂²	1	2	yes	—
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	2	yes	—
42	#21039	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂³×C₄×C₅	—	2	1	no	—
44	C₂³×C₄×C₅	—	2	1	no	—
45	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂×C₅×M₁₆	—	2	2	no	—
47	C₂×C₅×M₁₆	—	2	2	no	—
48	C₂×C₅×M₁₆	—	2	2	no	—
49	C₂²×C₅×C₈	—	2	2	no	—
50	C₂²×C₅×C₈	—	2	2	no	—
51	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
52	C₂²×C₅×C₈	C₂³	1	2	yes	—
53	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₅×#117	—	2	2	no	—
56	C₅×#117	—	2	2	no	—
57	C₅×#117	—	2	2	no	—
58	C₅×#117	—	2	2	no	—
59	C₅×#117	C₂×C₄	1	4	yes	—
60	C₅×#117	C₂×C₄	1	4	yes	—
61	C₂×C₅×C₄⋊C₄	—	2	1	no	—
62	C₂×C₅×C₄⋊C₄	—	2	2	no	—
63	C₂×C₅×C₄⋊C₄	—	2	2	no	—
64	C₂×C₅×C₄⋊C₄	—	2	2	no	—
65	C₂×C₅×C₄⋊C₄	—	2	1	no	—
66	C₂×C₅×C₄⋊C₄	—	2	2	no	—
67	C₂×C₅×C₄⋊C₄	—	2	2	no	—
68	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₅×C₄⋊C₄	Q₈	1	4	yes	—
71	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
80	C₂×C₄²×C₅	—	2	1	no	—
81	C₂×C₄²×C₅	—	2	1	no	—
82	C₂×C₄²×C₅	—	2	2	no	—
83	C₂×C₄²×C₅	—	2	2	no	—
84	C₂×C₄²×C₅	C₂³	1	2	yes	—
85	C₅×#107	C₂×C₄	1	4	yes	complemented
86	C₅×#107	C₂×C₄	1	4	yes	complemented
87	C₅×#106	C₂×C₄	1	4	yes	complemented
88	C₅×#106	C₂×C₄	1	4	yes	complemented
89	C₅×#95	—	2	2	no	—
90	C₅×#95	—	2	2	no	—
91	C₅×#95	—	2	2	no	—
92	C₅×#95	—	2	2	no	—
93	C₂×#427	C₂×C₅	1	1	yes	characteristic
94	#2317	C₂×C₅	1	1	yes	characteristic
95	#2274	C₂×C₅	1	1	yes	characteristic
96	#1921	C₂×C₅	1	2	yes	complemented
97	#1920	C₂×C₅	1	2	yes	complemented
98	#1919	C₂×C₅	1	2	yes	complemented
99	#1918	C₂×C₅	1	2	yes	complemented
100	#1736	C₂×C₅	1	1	yes	characteristic
101	#1736	C₂×C₅	1	1	yes	characteristic
102	C₂×#340	C₂×C₅	1	1	yes	characteristic
103	#1729	C₂×C₅	1	1	yes	characteristic
104	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₅	—	2	1	no	—
106	C₂²×C₄×C₅	—	2	1	no	—
107	C₂²×C₄×C₅	—	2	2	no	—
108	C₂²×C₄×C₅	—	2	1	no	—
109	C₂²×C₄×C₅	—	2	1	no	—
110	C₂²×C₄×C₅	—	2	4	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	—	4	2	no	—
113	C₂²×C₄×C₅	—	8	1	no	—
114	C₂²×C₄×C₅	—	8	1	no	—
115	C₂²×C₄×C₅	—	8	1	no	—
116	C₂²×C₄×C₅	—	8	1	no	—
117	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
122	C₂²×C₄×C₅	#41	1	2	yes	—
123	C₂²×C₄×C₅	#41	1	2	yes	—
124	C₂²×C₄×C₅	#41	1	2	yes	—
125	C₂²×C₄×C₅	#41	1	2	yes	—
126	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
127	C₅×M₁₆	—	4	4	no	—
128	C₂×C₅×C₈	—	2	8	no	—
129	C₂×C₅×C₈	—	2	1	no	—
130	C₂×C₅×C₈	—	2	1	no	—
131	C₂×C₅×C₈	—	2	1	no	—
132	C₂×C₅×C₈	—	2	1	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
137	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
138	C₅×C₄⋊C₄	—	2	4	no	—
139	C₅×C₄⋊C₄	—	2	2	no	—
140	C₅×C₄⋊C₄	—	2	2	no	—
141	C₅×C₄⋊C₄	—	2	2	no	—
142	C₅×C₄⋊C₄	—	2	1	no	—
143	C₅×C₄⋊C₄	—	2	1	no	—
144	C₅×C₄⋊C₄	—	2	1	no	—
145	C₅×C₄⋊C₄	—	2	1	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	4	2	no	—
149	C₅×C₄⋊C₄	—	8	2	no	—
150	C₅×C₄⋊C₄	—	8	2	no	—
151	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
152	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
153	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
154	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
155	C₅×C₄⋊C₄	C₂×Q₈	1	4	yes	—
156	C₅×C₂²⋊C₄	—	2	4	no	—
157	C₅×C₂²⋊C₄	—	2	4	no	—
158	C₅×C₂²⋊C₄	—	2	4	no	—
159	C₄²×C₅	—	2	4	no	—
160	C₄²×C₅	—	2	4	no	—
161	C₄²×C₅	—	2	2	no	—
162	C₄²×C₅	—	2	2	no	—
163	C₄²×C₅	—	8	2	no	—
164	C₄²×C₅	—	8	2	no	—
165	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
166	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
167	C₂×#117	C₂²×C₅	1	1	yes	characteristic
168	C₂×#117	C₂²×C₅	1	1	yes	characteristic
169	C₂×#117	C₂²×C₅	1	1	yes	characteristic
170	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
171	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
172	#427	C₄×C₅	1	8	yes	complemented
173	C₂×#107	C₂²×C₅	1	1	yes	characteristic
174	C₂×#107	C₂²×C₅	1	1	yes	characteristic
175	C₂×#106	C₂²×C₅	1	1	yes	characteristic
176	C₂×#106	C₂²×C₅	1	1	yes	characteristic
177	#389	C₂²×C₅	1	2	yes	—
178	#389	C₂²×C₅	1	2	yes	—
179	#385	—	2	2	no	—
180	#384	—	2	1	no	—
181	#382	—	2	1	no	—
182	C₄×C₄⋊C₄	—	2	1	no	—
183	C₄×C₄⋊C₄	—	2	1	no	—
184	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
185	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
186	C₄×C₂²⋊C₄	—	2	2	no	—
187	#340	C₂²×C₅	1	2	yes	—
188	#340	C₂²×C₅	1	2	yes	—
189	#340	C₂²×C₅	1	2	yes	—
190	#340	C₂²×C₅	1	2	yes	—
191	#340	C₂²×C₅	1	2	yes	—
192	#340	C₂²×C₅	1	2	yes	—
193	#336	C₂²×C₅	1	2	yes	—
194	#336	C₂²×C₅	1	2	yes	—
195	C₂³×C₅	—	2	1	no	—
196	C₂³×C₅	—	2	1	no	—
197	C₂³×C₅	—	2	1	no	—
198	C₂³×C₅	—	2	1	no	—
199	C₂³×C₅	C₄×D₄	1	2	yes	—
200	C₂³×C₅	C₂²⋊Q₈	1	2	yes	—
201	C₂³×C₅	#123	1	2	yes	—
202	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	4	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	—	4	2	no	—
216	C₂×C₄×C₅	—	4	1	no	—
217	C₂×C₄×C₅	—	4	1	no	—
218	C₂×C₄×C₅	—	4	2	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	4	1	no	—
222	C₂×C₄×C₅	—	4	1	no	—
223	C₂×C₄×C₅	—	4	1	no	—
224	C₂×C₄×C₅	—	4	2	no	—
225	C₂×C₄×C₅	—	4	2	no	—
226	C₂×C₄×C₅	—	4	2	no	—
227	C₂×C₄×C₅	—	8	4	no	—
228	C₂×C₄×C₅	—	8	4	no	—
229	C₂×C₄×C₅	#117	1	4	yes	—
230	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
231	C₂×C₄×C₅	C₄×Q₈	1	4	yes	—
232	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
233	C₂×C₄×C₅	#123	1	2	yes	—
234	C₂×C₄×C₅	#125	1	4	yes	—
235	C₂×C₄×C₅	#126	1	4	yes	—
236	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
242	C₅×C₈	—	2	2	no	—
243	C₅×C₈	—	2	2	no	—
244	C₅×C₈	—	4	2	no	—
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	—	2	1	no	—
247	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
248	C₂×M₁₆	—	2	2	no	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	—	2	2	no	—
253	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
254	C₂²×C₈	C₂³×C₅	1	2	yes	—
255	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
257	#117	—	2	2	no	—
258	#117	—	2	2	no	—
259	#117	—	2	2	no	—
260	#117	—	2	2	no	—
261	#117	C₂×C₄×C₅	1	4	yes	—
262	#117	C₂×C₄×C₅	1	4	yes	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₅×Q₈	1	4	yes	—
273	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
279	C₂×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	C₂³×C₅	1	2	yes	—
287	#107	C₂×C₄×C₅	1	4	yes	complemented
288	#107	C₂×C₄×C₅	1	4	yes	complemented
289	#106	C₂×C₄×C₅	1	4	yes	complemented
290	#106	C₂×C₄×C₅	1	4	yes	complemented
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	#95	—	2	2	no	—
294	#95	—	2	2	no	—
295	C₂²×C₅	—	2	2	no	—
296	C₂²×C₅	—	2	2	no	—
297	C₂²×C₅	—	2	2	no	—
298	C₂²×C₅	—	2	2	no	—
299	C₂²×C₅	—	2	2	no	—
300	C₂²×C₅	—	2	2	no	—
301	C₂²×C₅	#387	1	4	yes	—
302	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
303	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
304	C₂²×C₅	C₂×#123	1	1	yes	characteristic
305	C₂²×C₅	#576	1	1	yes	characteristic
306	C₂²×C₅	#577	1	1	yes	characteristic
307	C₂²×C₅	#577	1	1	yes	characteristic
308	C₂²×C₅	#578	1	1	yes	characteristic
309	C₄×C₅	—	4	4	no	—
310	C₄×C₅	—	4	2	no	—
311	C₄×C₅	—	4	2	no	—
312	C₄×C₅	—	4	2	no	—
313	C₄×C₅	—	4	2	no	—
314	C₄×C₅	—	4	2	no	—
315	C₄×C₅	—	4	2	no	—
316	C₄×C₅	—	8	2	no	—
317	C₄×C₅	#387	1	4	yes	—
318	C₄×C₅	C₂×#117	1	1	yes	characteristic
319	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
320	C₄×C₅	C₂×#125	1	1	yes	characteristic
321	C₄×C₅	C₂×#126	1	1	yes	characteristic
322	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	8	1	no	—
332	C₂²×C₄	—	8	1	no	—
333	C₂²×C₄	—	8	1	no	—
334	C₂²×C₄	—	8	1	no	—
335	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
336	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
337	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
338	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
340	C₂²×C₄	C₅×#41	1	2	yes	—
341	C₂²×C₄	C₅×#41	1	2	yes	—
342	C₂²×C₄	C₅×#41	1	2	yes	—
343	C₂²×C₄	C₅×#41	1	2	yes	—
344	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
345	M₁₆	—	4	4	no	—
346	C₂×C₈	—	2	8	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
355	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₄⋊C₄	—	8	2	no	—
368	C₄⋊C₄	—	8	2	no	—
369	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
370	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
371	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
372	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
373	C₄⋊C₄	C₂×C₅×Q₈	1	4	yes	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	2	4	no	—
377	C₄²	—	2	4	no	—
378	C₄²	—	2	4	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	8	2	no	—
382	C₄²	—	8	2	no	—
383	C₂×C₅	—	2	4	no	—
384	C₂×C₅	C₂×#387	1	1	yes	characteristic
385	C₂×C₅	#2951	1	1	yes	characteristic
386	C₂×C₅	#2952	1	1	yes	characteristic
387	C₂×C₅	#3081	1	1	yes	characteristic
388	C₂×C₅	#3082	1	1	yes	characteristic
389	C₂×C₅	#3096	1	1	yes	characteristic
390	C₂×C₅	#3097	1	1	yes	characteristic
391	C₂³	—	2	1	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	2	1	no	—
395	C₂³	C₄×C₅×D₄	1	2	yes	—
396	C₂³	C₅×C₂²⋊Q₈	1	2	yes	—
397	C₂³	C₅×#123	1	2	yes	—
398	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	8	4	no	—
424	C₂×C₄	—	8	4	no	—
425	C₂×C₄	C₅×#117	1	4	yes	—
426	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
427	C₂×C₄	C₄×C₅×Q₈	1	4	yes	—
428	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
429	C₂×C₄	C₅×#123	1	2	yes	—
430	C₂×C₄	C₅×#125	1	4	yes	—
431	C₂×C₄	C₅×#126	1	4	yes	—
432	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
433	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
434	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
435	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
436	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
437	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
438	C₈	—	2	2	no	—
439	C₈	—	2	2	no	—
440	C₈	—	4	2	no	—
441	C₅	#21039	1	1	yes	characteristic, direct product factor, Sylow
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	C₅×#387	1	4	yes	—
449	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
450	C₂²	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
451	C₂²	C₂×C₅×#123	1	1	yes	characteristic
452	C₂²	C₅×#576	1	1	yes	characteristic
453	C₂²	C₅×#577	1	1	yes	characteristic
454	C₂²	C₅×#577	1	1	yes	characteristic
455	C₂²	C₅×#578	1	1	yes	characteristic
456	C₄	—	4	4	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	8	2	no	—
464	C₄	C₅×#387	1	4	yes	—
465	C₄	C₂×C₅×#117	1	1	yes	characteristic
466	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
467	C₄	C₂×C₅×#125	1	1	yes	characteristic
468	C₄	C₂×C₅×#126	1	1	yes	characteristic
469	C₂	—	2	4	no	—
470	C₂	C₂×C₅×#387	1	1	yes	characteristic
471	C₂	C₅×#2951	1	1	yes	characteristic
472	C₂	C₅×#2952	1	1	yes	characteristic
473	C₂	C₅×#3081	1	1	yes	characteristic
474	C₂	C₅×#3082	1	1	yes	characteristic
475	C₂	C₅×#3096	1	1	yes	characteristic
476	C₂	C₅×#3097	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 ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1921	C₂	semidirect
5. C₅×#1920	C₂	semidirect
6. C₅×#1919	C₂	semidirect
7. C₅×#1918	C₂	semidirect
19. C₅×#427	C₄	semidirect
42. #21039	C₅	direct (N × H)
85. C₅×#107	C₂×C₄	semidirect
86. C₅×#107	C₂×C₄	semidirect
87. C₅×#106	C₂×C₄	semidirect
88. C₅×#106	C₂×C₄	semidirect
96. #1921	C₂×C₅	semidirect
97. #1920	C₂×C₅	semidirect
98. #1919	C₂×C₅	semidirect
99. #1918	C₂×C₅	semidirect
172. #427	C₄×C₅	semidirect
287. #107	C₂×C₄×C₅	semidirect
288. #107	C₂×C₄×C₅	semidirect
289. #106	C₂×C₄×C₅	semidirect
290. #106	C₂×C₄×C₅	semidirect
441. C₅	#21039	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×#427	2
C₅×#2317	2
C₅×#2274	2
C₅×#1921	2
C₅×#1920	2
C₅×#1919	2
C₅×#1918	2
C₅×#1736	2
C₂×C₅×#340	2
C₅×#1729	2
#21039	5

Subgroups — C5×#21039 #11943759

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21039 #11943759