Subgroups — C₅×#25276 #11947996

Order 1280.

810 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#487	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#475	C₂	1	1	yes	maximal, characteristic
3	C₅×#2546	C₂	1	1	yes	maximal, characteristic
4	C₅×#2365	C₂	1	1	yes	maximal, characteristic
5	C₅×#2066	C₂	1	2	yes	maximal
6	C₅×#2043	C₂	1	2	yes	maximal
7	C₅×#1981	C₂	1	1	yes	maximal, characteristic
8	C₅×#1981	C₂	1	2	yes	maximal
9	C₅×#1939	C₂	1	1	yes	maximal, characteristic
10	C₅×#1927	C₂	1	2	yes	maximal
11	C₄×C₅×#103	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×Q₈	—	2	1	no	—
16	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₅×#487	—	2	4	no	—
18	C₅×#475	—	2	4	no	—
19	C₂×C₅×#106	C₂²	1	2	yes	—
20	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₅×#103	C₂²	1	1	yes	characteristic
23	C₂×C₅×#103	C₂²	1	1	yes	characteristic
24	C₂×C₅×#103	C₂²	1	2	yes	—
25	C₂×C₅×#103	C₂²	1	2	yes	—
26	C₂×C₅×#103	C₂²	1	2	yes	—
27	C₂×C₅×#103	C₂²	1	2	yes	—
28	C₂×C₅×#103	C₂²	1	2	yes	—
29	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
30	C₅×#398	—	2	2	no	—
31	C₅×#391	—	2	1	no	—
32	C₅×#391	C₂²	1	2	yes	—
33	C₅×#389	—	2	1	no	—
34	C₅×#389	—	2	1	no	—
35	C₅×#389	C₂²	1	2	yes	—
36	C₅×#387	—	2	2	no	—
37	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
39	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₅×#340	C₂²	1	1	yes	characteristic
41	C₅×#340	C₂²	1	1	yes	characteristic
42	C₅×#336	C₂²	1	2	yes	—
43	#25276	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×Q₈	—	2	1	no	—
45	C₂²×C₅×Q₈	C₂³	1	2	yes	—
46	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
47	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂³	1	2	yes	—
50	C₅×C₄⋊Q₈	—	2	4	no	—
51	C₅×C₄⋊Q₈	—	2	2	no	—
52	C₅×C₄⋊Q₈	—	2	2	no	—
53	C₅×C₄⋊Q₈	—	2	2	no	—
54	C₅×C₄⋊Q₈	—	4	2	no	—
55	C₅×C₄⋊Q₈	D₄	1	4	yes	—
56	C₄×C₅×Q₈	—	2	2	no	—
57	C₄×C₅×Q₈	—	2	2	no	—
58	C₄×C₅×Q₈	—	4	4	no	—
59	C₂×C₅×C₄⋊C₄	—	2	1	no	—
60	C₂×C₅×C₄⋊C₄	—	2	2	no	—
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	1	no	—
65	C₂×C₅×C₄⋊C₄	—	2	1	no	—
66	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
67	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₅	—	2	2	no	—
73	C₂×C₄²×C₅	—	2	1	no	—
74	C₂×C₄²×C₅	—	2	1	no	—
75	C₂×C₄²×C₅	C₂³	1	2	yes	—
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₅×#106	—	2	4	no	—
78	C₅×C₄⋊C₈	—	2	2	no	—
79	C₅×C₄⋊C₈	—	4	2	no	—
80	C₅×#103	—	2	2	no	—
81	C₅×#103	—	2	4	no	—
82	C₅×#103	—	2	4	no	—
83	C₅×#103	—	2	4	no	—
84	C₅×#103	—	2	2	no	—
85	C₅×#103	—	2	4	no	—
86	C₅×#103	—	4	2	no	—
87	C₄×C₅×C₈	—	2	2	no	—
88	C₅×#95	—	2	1	no	—
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	C₅×#95	D₄	1	2	yes	—
94	C₂×#487	C₂×C₅	1	1	yes	characteristic
95	C₂×#475	C₂×C₅	1	1	yes	characteristic
96	#2546	C₂×C₅	1	1	yes	characteristic
97	#2365	C₂×C₅	1	1	yes	characteristic
98	#2066	C₂×C₅	1	2	yes	—
99	#2043	C₂×C₅	1	2	yes	—
100	#1981	C₂×C₅	1	1	yes	characteristic
101	#1981	C₂×C₅	1	2	yes	—
102	#1939	C₂×C₅	1	1	yes	characteristic
103	#1927	C₂×C₅	1	2	yes	—
104	C₄×#103	C₂×C₅	1	1	yes	characteristic
105	C₂×C₅×Q₈	—	2	4	no	—
106	C₂×C₅×Q₈	—	2	1	no	—
107	C₂×C₅×Q₈	—	2	1	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	—	2	1	no	—
110	C₂×C₅×Q₈	—	2	1	no	—
111	C₂×C₅×Q₈	—	2	2	no	—
112	C₂×C₅×Q₈	—	2	2	no	—
113	C₂×C₅×Q₈	—	2	2	no	—
114	C₂×C₅×Q₈	—	2	2	no	—
115	C₂×C₅×Q₈	—	2	1	no	—
116	C₂×C₅×Q₈	—	2	2	no	—
117	C₂×C₅×Q₈	—	4	2	no	—
118	C₂×C₅×Q₈	—	4	2	no	—
119	C₂×C₅×Q₈	#41	1	2	yes	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	—	2	2	no	—
123	C₂²×C₄×C₅	—	2	1	no	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	1	no	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	2	1	no	—
140	C₅×C₄⋊C₄	—	2	4	no	—
141	C₅×C₄⋊C₄	—	2	2	no	—
142	C₅×C₄⋊C₄	—	2	2	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	1	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	4	4	no	—
149	C₅×C₄⋊C₄	—	4	4	no	—
150	C₅×C₄⋊C₄	—	4	2	no	—
151	C₅×C₄⋊C₄	—	4	2	no	—
152	C₅×C₄⋊C₄	—	4	2	no	—
153	C₅×C₄⋊C₄	—	4	4	no	—
154	C₅×C₄⋊C₄	SD₁₆	1	4	yes	—
155	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
156	C₅×C₄⋊C₄	#41	1	2	yes	—
157	C₄²×C₅	—	2	2	no	—
158	C₄²×C₅	—	2	2	no	—
159	C₄²×C₅	—	4	2	no	—
160	C₄²×C₅	—	4	4	no	—
161	C₄²×C₅	—	4	2	no	—
162	C₄²×C₅	C₂×D₄	1	2	yes	—
163	C₄²×C₅	#41	1	2	yes	—
164	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
166	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
167	C₂×C₄×Q₈	—	2	1	no	—
168	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
169	#487	—	2	4	no	—
170	#475	—	2	4	no	—
171	C₂×#106	C₂²×C₅	1	2	yes	—
172	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
173	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
174	C₂×#103	C₂²×C₅	1	2	yes	—
175	C₂×#103	C₂²×C₅	1	2	yes	—
176	C₂×#103	C₂²×C₅	1	2	yes	—
177	C₂×#103	C₂²×C₅	1	2	yes	—
178	C₂×#103	C₂²×C₅	1	1	yes	characteristic
179	C₂×#103	C₂²×C₅	1	1	yes	characteristic
180	C₂×#103	C₂²×C₅	1	2	yes	—
181	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
182	#398	—	2	2	no	—
183	#391	—	2	1	no	—
184	#391	C₂²×C₅	1	2	yes	—
185	#389	—	2	1	no	—
186	#389	—	2	1	no	—
187	#389	C₂²×C₅	1	2	yes	—
188	#387	—	2	2	no	—
189	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
190	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
191	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
192	#340	C₂²×C₅	1	1	yes	characteristic
193	#340	C₂²×C₅	1	1	yes	characteristic
194	#336	C₂²×C₅	1	2	yes	—
195	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
196	C₅×Q₈	—	2	2	no	—
197	C₅×Q₈	—	2	2	no	—
198	C₅×Q₈	—	4	1	no	—
199	C₅×Q₈	—	4	1	no	—
200	C₅×Q₈	—	4	8	no	—
201	C₅×Q₈	—	4	2	no	—
202	C₅×Q₈	—	4	2	no	—
203	C₅×Q₈	—	4	2	no	—
204	C₅×Q₈	—	4	2	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	4	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	—	2	2	no	—
215	C₂×C₄×C₅	—	4	1	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	2	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	4	1	no	—
222	C₂×C₄×C₅	—	4	2	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	1	no	—
227	C₂×C₄×C₅	—	4	1	no	—
228	C₂×C₄×C₅	—	4	1	no	—
229	C₂×C₄×C₅	—	4	1	no	—
230	C₂×C₄×C₅	#121	1	2	yes	—
231	C₂×C₄×C₅	#121	1	2	yes	—
232	C₂×C₄×C₅	C₂×SD₁₆	1	4	yes	—
233	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
234	C₂×C₄×C₅	#137	1	2	yes	—
235	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
240	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
241	C₅×C₈	—	4	1	no	—
242	C₅×C₈	—	4	1	no	—
243	C₅×C₈	—	4	2	no	—
244	C₂²×Q₈	—	2	1	no	—
245	C₂²×Q₈	C₂³×C₅	1	2	yes	—
246	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₅	1	2	yes	—
249	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
250	C₄⋊Q₈	—	2	4	no	—
251	C₄⋊Q₈	—	2	2	no	—
252	C₄⋊Q₈	—	2	2	no	—
253	C₄⋊Q₈	—	2	2	no	—
254	C₄⋊Q₈	—	4	2	no	—
255	C₄⋊Q₈	C₅×D₄	1	4	yes	—
256	C₄×Q₈	—	2	2	no	—
257	C₄×Q₈	—	2	2	no	—
258	C₄×Q₈	—	4	4	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	C₂³×C₅	1	2	yes	—
276	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
277	#106	—	2	4	no	—
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	—	4	2	no	—
280	#103	—	2	2	no	—
281	#103	—	2	4	no	—
282	#103	—	2	4	no	—
283	#103	—	2	4	no	—
284	#103	—	2	2	no	—
285	#103	—	2	4	no	—
286	#103	—	4	2	no	—
287	C₄×C₈	—	2	2	no	—
288	#95	—	2	1	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	#95	C₅×D₄	1	2	yes	—
294	C₂²×C₅	C₂×#121	1	1	yes	characteristic
295	C₂²×C₅	#546	1	1	yes	characteristic
296	C₂²×C₅	#548	1	1	yes	characteristic
297	C₂²×C₅	C₂²×SD₁₆	1	1	yes	characteristic
298	C₂²×C₅	C₂×#137	1	1	yes	characteristic
299	C₂²×C₅	#578	1	1	yes	characteristic
300	C₂²×C₅	#578	1	1	yes	characteristic
301	C₄×C₅	—	2	4	no	—
302	C₄×C₅	—	2	2	no	—
303	C₄×C₅	—	4	2	no	—
304	C₄×C₅	—	4	2	no	—
305	C₄×C₅	—	4	2	no	—
306	C₄×C₅	—	4	4	no	—
307	C₄×C₅	—	8	2	no	—
308	C₄×C₅	—	8	1	no	—
309	C₄×C₅	—	8	1	no	—
310	C₄×C₅	#461	1	4	yes	—
311	C₄×C₅	#529	1	1	yes	characteristic
312	C₄×C₅	#542	1	1	yes	characteristic
313	C₄×C₅	#548	1	1	yes	characteristic
314	C₄×C₅	#550	1	1	yes	characteristic
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	C₅×#41	1	2	yes	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
337	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
339	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
340	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	4	4	no	—
359	C₄⋊C₄	—	4	4	no	—
360	C₄⋊C₄	—	4	2	no	—
361	C₄⋊C₄	—	4	2	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	—	4	4	no	—
364	C₄⋊C₄	C₅×SD₁₆	1	4	yes	—
365	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
366	C₄⋊C₄	C₅×#41	1	2	yes	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	4	2	no	—
370	C₄²	—	4	4	no	—
371	C₄²	—	4	2	no	—
372	C₄²	C₂×C₅×D₄	1	2	yes	—
373	C₄²	C₅×#41	1	2	yes	—
374	C₂×C₅	#2426	1	1	yes	characteristic
375	C₂×C₅	C₂×#461	1	1	yes	characteristic
376	C₂×C₅	#3044	1	1	yes	characteristic
377	C₂×C₅	#3298	1	1	yes	characteristic
378	C₂×C₅	#3328	1	1	yes	characteristic
379	C₂×C₅	#3359	1	1	yes	characteristic
380	C₂×C₅	#3374	1	1	yes	characteristic
381	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
382	Q₈	—	2	2	no	—
383	Q₈	—	2	2	no	—
384	Q₈	—	4	8	no	—
385	Q₈	—	4	1	no	—
386	Q₈	—	4	1	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	4	2	no	—
389	Q₈	—	4	2	no	—
390	Q₈	—	4	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	C₅×#121	1	2	yes	—
417	C₂×C₄	C₅×#121	1	2	yes	—
418	C₂×C₄	C₂×C₅×SD₁₆	1	4	yes	—
419	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
420	C₂×C₄	C₅×#137	1	2	yes	—
421	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
422	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
423	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
424	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
425	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
427	C₈	—	4	1	no	—
428	C₈	—	4	1	no	—
429	C₈	—	4	2	no	—
430	C₅	#25276	1	1	yes	characteristic, direct product factor, Sylow
431	C₂²	C₂×C₅×#121	1	1	yes	characteristic
432	C₂²	C₅×#546	1	1	yes	characteristic
433	C₂²	C₅×#548	1	1	yes	characteristic
434	C₂²	C₂²×C₅×SD₁₆	1	1	yes	characteristic
435	C₂²	C₂×C₅×#137	1	1	yes	characteristic
436	C₂²	C₅×#578	1	1	yes	characteristic
437	C₂²	C₅×#578	1	1	yes	characteristic
438	C₄	—	2	4	no	—
439	C₄	—	2	2	no	—
440	C₄	—	4	4	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	8	1	no	—
445	C₄	—	8	1	no	—
446	C₄	—	8	2	no	—
447	C₄	C₅×#461	1	4	yes	—
448	C₄	C₅×#529	1	1	yes	characteristic
449	C₄	C₅×#542	1	1	yes	characteristic
450	C₄	C₅×#548	1	1	yes	characteristic
451	C₄	C₅×#550	1	1	yes	characteristic
452	C₂	C₅×#2426	1	1	yes	characteristic
453	C₂	C₂×C₅×#461	1	1	yes	characteristic
454	C₂	C₅×#3044	1	1	yes	characteristic
455	C₂	C₅×#3298	1	1	yes	characteristic
456	C₂	C₅×#3328	1	1	yes	characteristic
457	C₂	C₅×#3359	1	1	yes	characteristic
458	C₂	C₅×#3374	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
LCS	G ▷ C₂²×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
43. #25276	C₅	direct (N × H)
430. C₅	#25276	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×#487	2
C₂×C₅×#475	2
C₅×#2546	2
C₅×#2365	2
C₅×#2066	2
C₅×#2043	2
C₅×#1981	2
C₅×#1939	2
C₅×#1927	2
C₄×C₅×#103	2
#25276	5

Subgroups — C5×#25276 #11947996

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#25276 #11947996