Subgroups — C₅×#25275 #11947995

Order 1280.

842 conjugacy classes of subgroups.

The subgroup lattice has 488 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, complemented
2	C₂×C₅×#474	C₂	1	1	yes	maximal, characteristic
3	C₅×#2547	C₂	1	1	yes	maximal, characteristic
4	C₅×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2068	C₂	1	2	yes	maximal, complemented
6	C₅×#2042	C₂	1	2	yes	maximal
7	C₅×#1983	C₂	1	2	yes	maximal
8	C₅×#1981	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1928	C₂	1	2	yes	maximal, complemented
11	C₄×C₅×#102	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×#124	C₂²	1	2	yes	—
15	C₂×C₄×C₅×Q₈	—	2	1	no	—
16	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₅×#487	—	2	4	no	—
18	C₅×#474	—	2	4	no	—
19	C₂×C₅×#107	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	2	yes	—
23	C₂×C₅×#103	C₂²	1	2	yes	—
24	C₂×C₅×#103	C₂²	1	2	yes	—
25	C₂×C₅×#103	C₂²	1	2	yes	—
26	C₂×C₅×#102	C₂²	1	1	yes	characteristic
27	C₂×C₅×#102	C₂²	1	1	yes	characteristic
28	C₂×C₅×#102	C₂²	1	2	yes	—
29	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
30	C₅×#397	—	2	2	no	—
31	C₅×#391	—	2	1	no	—
32	C₅×#391	C₂²	1	2	yes	—
33	C₅×#389	C₂²	1	2	yes	—
34	C₅×#387	—	2	2	no	—
35	C₅×#380	—	2	1	no	—
36	C₅×#380	—	2	1	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	#25275	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×D₄	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₅	—	2	1	no	—
48	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₅×C₈	C₂³	1	2	yes	—
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	D₄	1	4	yes	—
55	C₅×#124	—	2	4	no	—
56	C₅×#124	—	4	2	no	—
57	C₄×C₅×Q₈	—	4	4	no	—
58	C₄×C₅×D₄	—	2	2	no	—
59	C₄×C₅×D₄	—	2	2	no	—
60	C₂×C₅×C₄⋊C₄	—	2	1	no	—
61	C₂×C₅×C₄⋊C₄	—	2	1	no	—
62	C₂×C₅×C₄⋊C₄	—	2	2	no	—
63	C₂×C₅×C₄⋊C₄	—	2	1	no	—
64	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₄²×C₅	—	2	2	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×#107	—	2	4	no	—
78	C₅×C₄⋊C₈	—	2	2	no	—
79	C₅×C₄⋊C₈	—	4	2	no	—
80	C₅×#103	—	2	4	no	—
81	C₅×#103	—	2	4	no	—
82	C₅×#103	—	2	4	no	—
83	C₅×#103	—	4	2	no	—
84	C₅×#102	—	2	2	no	—
85	C₅×#102	—	2	4	no	—
86	C₅×#102	—	2	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, complemented
95	C₂×#474	C₂×C₅	1	1	yes	characteristic
96	#2547	C₂×C₅	1	1	yes	characteristic
97	#2365	C₂×C₅	1	1	yes	characteristic, complemented
98	#2068	C₂×C₅	1	2	yes	complemented
99	#2042	C₂×C₅	1	2	yes	—
100	#1983	C₂×C₅	1	2	yes	—
101	#1981	C₂×C₅	1	1	yes	characteristic, complemented
102	#1939	C₂×C₅	1	1	yes	characteristic, complemented
103	#1928	C₂×C₅	1	2	yes	complemented
104	C₄×#102	C₂×C₅	1	1	yes	characteristic
105	C₂⁴×C₅	—	2	1	no	—
106	C₂×C₅×Q₈	—	2	4	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	—	2	2	no	—
110	C₂×C₅×Q₈	—	2	2	no	—
111	C₂×C₅×Q₈	—	2	2	no	—
112	C₂×C₅×Q₈	—	2	2	no	—
113	C₂×C₅×Q₈	—	4	2	no	—
114	C₂×C₅×Q₈	—	4	2	no	—
115	C₂×C₅×D₄	—	2	1	no	—
116	C₂×C₅×D₄	—	2	1	no	—
117	C₂×C₅×D₄	—	2	1	no	—
118	C₂×C₅×D₄	—	2	1	no	—
119	C₂×C₅×D₄	—	2	1	no	—
120	C₂×C₅×D₄	#41	1	2	yes	—
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	2	no	—
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	—	4	2	no	—
127	C₂²×C₄×C₅	—	4	2	no	—
128	C₂²×C₄×C₅	—	4	2	no	—
129	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	1	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₅×C₄⋊C₄	—	2	4	no	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	2	1	no	—
150	C₅×C₄⋊C₄	—	2	1	no	—
151	C₅×C₄⋊C₄	—	2	1	no	—
152	C₅×C₄⋊C₄	—	4	4	no	—
153	C₅×C₄⋊C₄	—	4	2	no	—
154	C₅×C₄⋊C₄	—	4	2	no	—
155	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
156	C₅×C₄⋊C₄	#41	1	2	yes	—
157	C₅×C₂²⋊C₄	—	4	4	no	—
158	C₅×C₂²⋊C₄	—	4	4	no	—
159	C₅×C₂²⋊C₄	—	4	2	no	—
160	C₄²×C₅	—	2	2	no	—
161	C₄²×C₅	—	2	2	no	—
162	C₄²×C₅	—	4	4	no	—
163	C₄²×C₅	—	4	2	no	—
164	C₄²×C₅	C₂×D₄	1	2	yes	—
165	C₄²×C₅	#41	1	2	yes	—
166	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
167	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
168	C₂×#124	C₂²×C₅	1	2	yes	—
169	C₂×C₄×Q₈	—	2	1	no	—
170	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
171	#487	—	2	4	no	—
172	#474	—	2	4	no	—
173	C₂×#107	C₂²×C₅	1	2	yes	—
174	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₄⋊C₈	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	2	yes	—
179	C₂×#103	C₂²×C₅	1	2	yes	—
180	C₂×#102	C₂²×C₅	1	1	yes	characteristic
181	C₂×#102	C₂²×C₅	1	2	yes	—
182	C₂×#102	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
184	#397	—	2	2	no	—
185	#391	—	2	1	no	—
186	#391	C₂²×C₅	1	2	yes	—
187	#389	C₂²×C₅	1	2	yes	—
188	#387	—	2	2	no	—
189	#380	—	2	1	no	—
190	#380	—	2	1	no	—
191	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
192	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
193	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
194	#340	C₂²×C₅	1	1	yes	characteristic
195	#340	C₂²×C₅	1	1	yes	characteristic
196	#336	C₂²×C₅	1	2	yes	—
197	C₂³×C₅	—	2	2	no	—
198	C₂³×C₅	—	4	1	no	—
199	C₂³×C₅	—	4	1	no	—
200	C₂³×C₅	—	4	1	no	—
201	C₂³×C₅	—	4	1	no	—
202	C₂³×C₅	—	4	1	no	—
203	C₂³×C₅	—	4	1	no	—
204	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
205	C₅×Q₈	—	4	8	no	—
206	C₅×Q₈	—	4	2	no	—
207	C₅×Q₈	—	4	2	no	—
208	C₅×Q₈	—	4	2	no	—
209	C₅×Q₈	—	4	2	no	—
210	C₅×D₄	—	2	2	no	—
211	C₅×D₄	—	2	2	no	—
212	C₅×D₄	—	4	1	no	—
213	C₅×D₄	—	4	1	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	4	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	4	2	no	—
225	C₂×C₄×C₅	—	4	1	no	—
226	C₂×C₄×C₅	—	4	2	no	—
227	C₂×C₄×C₅	—	4	1	no	—
228	C₂×C₄×C₅	—	4	1	no	—
229	C₂×C₄×C₅	—	4	2	no	—
230	C₂×C₄×C₅	—	4	2	no	—
231	C₂×C₄×C₅	—	4	1	no	—
232	C₂×C₄×C₅	—	4	2	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	4	1	no	—
236	C₂×C₄×C₅	—	4	1	no	—
237	C₂×C₄×C₅	—	8	4	no	—
238	C₂×C₄×C₅	#121	1	2	yes	—
239	C₂×C₄×C₅	#121	1	2	yes	—
240	C₂×C₄×C₅	#135	1	2	yes	—
241	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
242	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
247	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
248	C₅×C₈	—	4	1	no	—
249	C₅×C₈	—	4	1	no	—
250	C₅×C₈	—	4	2	no	—
251	C₂²×Q₈	—	2	1	no	—
252	C₂²×Q₈	C₂³×C₅	1	2	yes	—
253	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
254	C₂³×C₄	—	2	1	no	—
255	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₅	1	2	yes	—
257	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
258	C₄⋊Q₈	—	2	2	no	—
259	C₄⋊Q₈	—	2	2	no	—
260	C₄⋊Q₈	—	2	2	no	—
261	C₄⋊Q₈	C₅×D₄	1	4	yes	—
262	#124	—	2	4	no	—
263	#124	—	4	2	no	—
264	C₄×Q₈	—	4	4	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₄²	—	2	2	no	—
281	C₂×C₄²	—	2	1	no	—
282	C₂×C₄²	C₂³×C₅	1	2	yes	—
283	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
284	#107	—	2	4	no	—
285	C₄⋊C₈	—	2	2	no	—
286	C₄⋊C₈	—	4	2	no	—
287	#103	—	2	4	no	—
288	#103	—	2	4	no	—
289	#103	—	2	4	no	—
290	#103	—	4	2	no	—
291	#102	—	2	2	no	—
292	#102	—	2	4	no	—
293	#102	—	2	2	no	—
294	C₄×C₈	—	2	2	no	—
295	#95	—	2	1	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	#95	—	2	2	no	—
299	#95	—	2	2	no	—
300	#95	C₅×D₄	1	2	yes	—
301	C₂²×C₅	—	4	2	no	—
302	C₂²×C₅	—	4	2	no	—
303	C₂²×C₅	—	4	2	no	—
304	C₂²×C₅	—	8	1	no	—
305	C₂²×C₅	—	8	1	no	—
306	C₂²×C₅	—	8	1	no	—
307	C₂²×C₅	—	8	1	no	—
308	C₂²×C₅	C₂×#121	1	1	yes	characteristic
309	C₂²×C₅	#546	1	1	yes	characteristic
310	C₂²×C₅	#548	1	1	yes	characteristic
311	C₂²×C₅	C₂×#135	1	1	yes	characteristic
312	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
313	C₂²×C₅	#578	1	1	yes	characteristic
314	C₂²×C₅	#578	1	1	yes	characteristic
315	C₄×C₅	—	2	2	no	—
316	C₄×C₅	—	4	2	no	—
317	C₄×C₅	—	4	2	no	—
318	C₄×C₅	—	4	4	no	—
319	C₄×C₅	—	4	2	no	—
320	C₄×C₅	—	8	1	no	—
321	C₄×C₅	—	8	2	no	—
322	C₄×C₅	—	8	1	no	—
323	C₄×C₅	#463	1	4	yes	—
324	C₄×C₅	#529	1	1	yes	characteristic
325	C₄×C₅	#542	1	1	yes	characteristic
326	C₄×C₅	#548	1	1	yes	characteristic
327	C₄×C₅	#550	1	1	yes	characteristic
328	C₂⁴	—	2	1	no	—
329	C₂×Q₈	—	2	4	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	4	2	no	—
337	C₂×Q₈	—	4	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	C₅×#41	1	2	yes	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
353	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
354	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
356	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	4	4	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
379	C₄⋊C₄	C₅×#41	1	2	yes	—
380	C₂²⋊C₄	—	4	4	no	—
381	C₂²⋊C₄	—	4	4	no	—
382	C₂²⋊C₄	—	4	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	4	4	no	—
386	C₄²	—	4	2	no	—
387	C₄²	C₂×C₅×D₄	1	2	yes	—
388	C₄²	C₅×#41	1	2	yes	—
389	C₂×C₅	—	8	2	no	—
390	C₂×C₅	#2426	1	1	yes	characteristic
391	C₂×C₅	C₂×#463	1	1	yes	characteristic
392	C₂×C₅	#3044	1	1	yes	characteristic
393	C₂×C₅	#3302	1	1	yes	characteristic
394	C₂×C₅	#3330	1	1	yes	characteristic
395	C₂×C₅	#3364	1	1	yes	characteristic
396	C₂×C₅	#3367	1	1	yes	characteristic
397	C₂³	—	2	2	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	1	no	—
404	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
405	Q₈	—	4	8	no	—
406	Q₈	—	4	2	no	—
407	Q₈	—	4	2	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	4	2	no	—
410	D₄	—	2	2	no	—
411	D₄	—	2	2	no	—
412	D₄	—	4	1	no	—
413	D₄	—	4	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	8	4	no	—
438	C₂×C₄	C₅×#121	1	2	yes	—
439	C₂×C₄	C₅×#121	1	2	yes	—
440	C₂×C₄	C₅×#135	1	2	yes	—
441	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
442	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
443	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
444	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
445	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
446	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
447	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
448	C₈	—	4	1	no	—
449	C₈	—	4	1	no	—
450	C₈	—	4	2	no	—
451	C₅	#25275	1	1	yes	characteristic, direct product factor, Sylow
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	C₂×C₅×#121	1	1	yes	characteristic
460	C₂²	C₅×#546	1	1	yes	characteristic
461	C₂²	C₅×#548	1	1	yes	characteristic
462	C₂²	C₂×C₅×#135	1	1	yes	characteristic
463	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
464	C₂²	C₅×#578	1	1	yes	characteristic
465	C₂²	C₅×#578	1	1	yes	characteristic
466	C₄	—	2	2	no	—
467	C₄	—	4	4	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	8	1	no	—
472	C₄	—	8	1	no	—
473	C₄	—	8	2	no	—
474	C₄	C₅×#463	1	4	yes	—
475	C₄	C₅×#529	1	1	yes	characteristic
476	C₄	C₅×#542	1	1	yes	characteristic
477	C₄	C₅×#548	1	1	yes	characteristic
478	C₄	C₅×#550	1	1	yes	characteristic
479	C₂	—	8	2	no	—
480	C₂	C₅×#2426	1	1	yes	characteristic
481	C₂	C₂×C₅×#463	1	1	yes	characteristic
482	C₂	C₅×#3044	1	1	yes	characteristic
483	C₂	C₅×#3302	1	1	yes	characteristic
484	C₂	C₅×#3330	1	1	yes	characteristic
485	C₂	C₅×#3364	1	1	yes	characteristic
486	C₂	C₅×#3367	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	C₂³
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
1. C₂×C₅×#487	C₂	semidirect
4. C₅×#2365	C₂	semidirect
5. C₅×#2068	C₂	semidirect
8. C₅×#1981	C₂	semidirect
9. C₅×#1939	C₂	semidirect
10. C₅×#1928	C₂	semidirect
43. #25275	C₅	direct (N × H)
94. C₂×#487	C₂×C₅	semidirect
97. #2365	C₂×C₅	semidirect
98. #2068	C₂×C₅	semidirect
101. #1981	C₂×C₅	semidirect
102. #1939	C₂×C₅	semidirect
103. #1928	C₂×C₅	semidirect
451. C₅	#25275	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×#474	2
C₅×#2547	2
C₅×#2365	2
C₅×#2068	2
C₅×#2042	2
C₅×#1983	2
C₅×#1981	2
C₅×#1939	2
C₅×#1928	2
C₄×C₅×#102	2
#25275	5

Subgroups — C5×#25275 #11947995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#25275 #11947995