Subgroups — C₅×#25279 #11947999

Order 1280.

878 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#486	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2548	C₂	1	1	yes	maximal, characteristic
4	C₅×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2065	C₂	1	2	yes	maximal, complemented
6	C₅×#2042	C₂	1	2	yes	maximal, complemented
7	C₅×#1983	C₂	1	2	yes	maximal, complemented
8	C₅×#1982	C₂	1	1	yes	maximal, characteristic
9	C₅×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1926	C₂	1	2	yes	maximal, complemented
11	C₄×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×#127	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×Q₈	C₂²	1	1	yes	characteristic
17	C₅×#486	—	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×#102	C₂²	1	2	yes	—
26	C₂×C₅×#102	C₂²	1	2	yes	—
27	C₂×C₅×#102	C₂²	1	2	yes	—
28	C₂×C₅×#102	C₂²	1	2	yes	—
29	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
30	C₅×#394	—	2	2	no	—
31	C₅×#391	—	2	1	no	—
32	C₅×#390	—	2	1	no	—
33	C₅×#390	—	2	1	no	—
34	C₅×#390	C₂²	1	2	yes	—
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	#25279	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×Q₈	—	2	1	no	—
45	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
46	C₂²×C₅×D₄	—	2	1	no	—
47	C₂²×C₅×D₄	—	2	1	no	—
48	C₂²×C₅×D₄	C₂³	1	2	yes	—
49	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₅×C₈	C₂³	1	2	yes	—
52	C₅×C₄⋊Q₈	—	2	2	no	—
53	C₅×C₄⋊Q₈	D₄	1	4	yes	—
54	C₅×#127	—	2	2	no	—
55	C₅×#127	—	2	2	no	—
56	C₅×#124	—	2	4	no	—
57	C₅×#124	—	4	2	no	—
58	C₄×C₅×Q₈	—	2	2	no	—
59	C₄×C₅×Q₈	—	2	2	no	—
60	C₄×C₅×Q₈	—	4	4	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	2	no	—
73	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₄²×C₅	—	2	2	no	—
75	C₂×C₄²×C₅	—	2	1	no	—
76	C₂×C₄²×C₅	—	2	1	no	—
77	C₂×C₄²×C₅	C₂³	1	2	yes	—
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₅×#106	—	2	4	no	—
80	C₅×C₄⋊C₈	—	2	2	no	—
81	C₅×C₄⋊C₈	—	4	2	no	—
82	C₅×#103	—	2	2	no	—
83	C₅×#103	—	2	4	no	—
84	C₅×#103	—	2	2	no	—
85	C₅×#102	—	2	4	no	—
86	C₅×#102	—	2	4	no	—
87	C₅×#102	—	2	4	no	—
88	C₅×#102	—	4	2	no	—
89	C₄×C₅×C₈	—	2	2	no	—
90	C₅×#95	—	2	1	no	—
91	C₅×#95	—	2	2	no	—
92	C₅×#95	—	2	2	no	—
93	C₅×#95	D₄	1	2	yes	—
94	C₂×#486	C₂×C₅	1	1	yes	characteristic
95	C₂×#475	C₂×C₅	1	1	yes	characteristic, complemented
96	#2548	C₂×C₅	1	1	yes	characteristic
97	#2365	C₂×C₅	1	1	yes	characteristic, complemented
98	#2065	C₂×C₅	1	2	yes	complemented
99	#2042	C₂×C₅	1	2	yes	complemented
100	#1983	C₂×C₅	1	2	yes	complemented
101	#1982	C₂×C₅	1	1	yes	characteristic
102	#1939	C₂×C₅	1	1	yes	characteristic, complemented
103	#1926	C₂×C₅	1	2	yes	complemented
104	C₄×#103	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂⁴×C₅	—	2	2	no	—
106	C₂×C₅×Q₈	—	2	4	no	—
107	C₂×C₅×Q₈	—	2	1	no	—
108	C₂×C₅×Q₈	—	2	1	no	—
109	C₂×C₅×Q₈	—	2	1	no	—
110	C₂×C₅×Q₈	—	2	1	no	—
111	C₂×C₅×Q₈	—	2	1	no	—
112	C₂×C₅×Q₈	—	4	2	no	—
113	C₂×C₅×Q₈	—	4	2	no	—
114	C₂×C₅×Q₈	#41	1	2	yes	—
115	C₂×C₅×D₄	—	2	2	no	—
116	C₂×C₅×D₄	—	2	2	no	—
117	C₂×C₅×D₄	—	2	2	no	—
118	C₂×C₅×D₄	—	2	2	no	—
119	C₂×C₅×D₄	—	2	2	no	—
120	C₂×C₅×D₄	—	2	2	no	—
121	C₂×C₅×D₄	—	4	2	no	—
122	C₂×C₅×D₄	—	4	2	no	—
123	C₂×C₅×D₄	—	4	2	no	—
124	C₂×C₅×D₄	—	4	2	no	—
125	C₂×C₅×D₄	—	8	1	no	—
126	C₂×C₅×D₄	—	8	1	no	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	—	2	1	no	—
131	C₂²×C₄×C₅	—	2	1	no	—
132	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	2	1	no	—
145	C₂×C₅×C₈	—	2	1	no	—
146	C₅×C₄⋊C₄	—	2	4	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	2	no	—
149	C₅×C₄⋊C₄	—	2	2	no	—
150	C₅×C₄⋊C₄	—	2	1	no	—
151	C₅×C₄⋊C₄	—	2	1	no	—
152	C₅×C₄⋊C₄	—	2	1	no	—
153	C₅×C₄⋊C₄	—	2	1	no	—
154	C₅×C₄⋊C₄	—	2	1	no	—
155	C₅×C₄⋊C₄	—	4	4	no	—
156	C₅×C₄⋊C₄	—	4	2	no	—
157	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
158	C₅×C₄⋊C₄	#41	1	2	yes	—
159	C₅×C₂²⋊C₄	—	4	4	no	—
160	C₅×C₂²⋊C₄	—	4	4	no	—
161	C₅×C₂²⋊C₄	—	8	2	no	—
162	C₅×C₂²⋊C₄	—	8	2	no	—
163	C₄²×C₅	—	2	2	no	—
164	C₄²×C₅	—	2	2	no	—
165	C₄²×C₅	—	4	4	no	—
166	C₄²×C₅	—	4	2	no	—
167	C₄²×C₅	—	4	2	no	—
168	C₄²×C₅	C₂×D₄	1	2	yes	—
169	C₄²×C₅	#41	1	2	yes	—
170	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
171	C₂×#127	C₂²×C₅	1	1	yes	characteristic
172	C₂×#124	C₂²×C₅	1	2	yes	—
173	C₂×C₄×Q₈	—	2	1	no	—
174	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
175	#486	—	2	4	no	—
176	#475	—	2	4	no	—
177	C₂×#106	C₂²×C₅	1	2	yes	—
178	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
179	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
180	C₂×#103	C₂²×C₅	1	2	yes	—
181	C₂×#103	C₂²×C₅	1	1	yes	characteristic
182	C₂×#103	C₂²×C₅	1	1	yes	characteristic
183	C₂×#102	C₂²×C₅	1	2	yes	—
184	C₂×#102	C₂²×C₅	1	2	yes	—
185	C₂×#102	C₂²×C₅	1	2	yes	—
186	C₂×#102	C₂²×C₅	1	2	yes	—
187	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
188	#394	—	2	2	no	—
189	#391	—	2	1	no	—
190	#390	—	2	1	no	—
191	#390	—	2	1	no	—
192	#390	C₂²×C₅	1	2	yes	—
193	#389	C₂²×C₅	1	2	yes	—
194	#387	—	2	2	no	—
195	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
196	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
197	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
198	#340	C₂²×C₅	1	1	yes	characteristic
199	#340	C₂²×C₅	1	1	yes	characteristic
200	#336	C₂²×C₅	1	2	yes	—
201	C₂³×C₅	—	4	2	no	—
202	C₂³×C₅	—	4	2	no	—
203	C₂³×C₅	—	4	2	no	—
204	C₂³×C₅	—	4	2	no	—
205	C₂³×C₅	—	4	2	no	—
206	C₂³×C₅	—	4	2	no	—
207	C₂³×C₅	—	4	2	no	—
208	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
209	C₅×Q₈	—	2	2	no	—
210	C₅×Q₈	—	2	2	no	—
211	C₅×Q₈	—	4	1	no	—
212	C₅×Q₈	—	4	1	no	—
213	C₅×Q₈	—	4	8	no	—
214	C₅×D₄	—	4	2	no	—
215	C₅×D₄	—	4	2	no	—
216	C₅×D₄	—	4	2	no	—
217	C₅×D₄	—	4	2	no	—
218	C₅×D₄	—	8	4	no	—
219	C₅×D₄	—	8	4	no	—
220	C₂×C₄×C₅	—	2	1	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	4	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	4	1	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	4	2	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	4	2	no	—
236	C₂×C₄×C₅	—	4	1	no	—
237	C₂×C₄×C₅	—	4	1	no	—
238	C₂×C₄×C₅	—	4	1	no	—
239	C₂×C₄×C₅	—	4	1	no	—
240	C₂×C₄×C₅	—	4	1	no	—
241	C₂×C₄×C₅	—	4	1	no	—
242	C₂×C₄×C₅	—	4	1	no	—
243	C₂×C₄×C₅	#121	1	2	yes	—
244	C₂×C₄×C₅	#121	1	2	yes	—
245	C₂×C₄×C₅	#135	1	2	yes	—
246	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
247	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
252	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
253	C₅×C₈	—	4	1	no	—
254	C₅×C₈	—	4	1	no	—
255	C₅×C₈	—	4	2	no	—
256	C₂²×Q₈	—	2	1	no	—
257	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
258	C₂²×D₄	—	2	1	no	—
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	C₂³×C₅	1	2	yes	—
261	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₅	1	2	yes	—
263	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
264	C₄⋊Q₈	—	2	2	no	—
265	C₄⋊Q₈	C₅×D₄	1	4	yes	—
266	#127	—	2	2	no	—
267	#127	—	2	2	no	—
268	#124	—	2	4	no	—
269	#124	—	4	2	no	—
270	C₄×Q₈	—	2	2	no	—
271	C₄×Q₈	—	2	2	no	—
272	C₄×Q₈	—	4	4	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	C₂³×C₅	1	2	yes	—
290	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
291	#106	—	2	4	no	—
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	—	4	2	no	—
294	#103	—	2	2	no	—
295	#103	—	2	4	no	—
296	#103	—	2	2	no	—
297	#102	—	2	4	no	—
298	#102	—	2	4	no	—
299	#102	—	2	4	no	—
300	#102	—	4	2	no	—
301	C₄×C₈	—	2	2	no	—
302	#95	—	2	1	no	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	C₅×D₄	1	2	yes	—
306	C₂²×C₅	—	8	2	no	—
307	C₂²×C₅	—	8	2	no	—
308	C₂²×C₅	—	8	2	no	—
309	C₂²×C₅	—	8	2	no	—
310	C₂²×C₅	—	8	2	no	—
311	C₂²×C₅	—	8	2	no	—
312	C₂²×C₅	—	8	2	no	—
313	C₂²×C₅	C₂×#121	1	1	yes	characteristic
314	C₂²×C₅	#546	1	1	yes	characteristic
315	C₂²×C₅	#548	1	1	yes	characteristic
316	C₂²×C₅	C₂×#135	1	1	yes	characteristic
317	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
318	C₂²×C₅	#577	1	1	yes	characteristic
319	C₂²×C₅	#577	1	1	yes	characteristic
320	C₄×C₅	—	2	2	no	—
321	C₄×C₅	—	4	2	no	—
322	C₄×C₅	—	4	2	no	—
323	C₄×C₅	—	4	2	no	—
324	C₄×C₅	—	4	4	no	—
325	C₄×C₅	—	4	2	no	—
326	C₄×C₅	—	8	1	no	—
327	C₄×C₅	—	8	1	no	—
328	C₄×C₅	#463	1	4	yes	—
329	C₄×C₅	#529	1	1	yes	characteristic
330	C₄×C₅	#542	1	1	yes	characteristic
331	C₄×C₅	#548	1	1	yes	characteristic
332	C₄×C₅	#550	1	1	yes	characteristic
333	C₂⁴	—	2	2	no	—
334	C₂×Q₈	—	2	4	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	4	2	no	—
341	C₂×Q₈	—	4	2	no	—
342	C₂×Q₈	C₅×#41	1	2	yes	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	4	2	no	—
350	C₂×D₄	—	4	2	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	8	1	no	—
354	C₂×D₄	—	8	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
361	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
362	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
363	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	4	4	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
386	C₄⋊C₄	C₅×#41	1	2	yes	—
387	C₂²⋊C₄	—	4	4	no	—
388	C₂²⋊C₄	—	4	4	no	—
389	C₂²⋊C₄	—	8	2	no	—
390	C₂²⋊C₄	—	8	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	4	4	no	—
394	C₄²	—	4	2	no	—
395	C₄²	—	4	2	no	—
396	C₄²	C₂×C₅×D₄	1	2	yes	—
397	C₄²	C₅×#41	1	2	yes	—
398	C₂×C₅	—	16	2	no	—
399	C₂×C₅	#2426	1	1	yes	characteristic
400	C₂×C₅	C₂×#463	1	1	yes	characteristic
401	C₂×C₅	#3043	1	1	yes	characteristic
402	C₂×C₅	#3304	1	1	yes	characteristic
403	C₂×C₅	#3332	1	1	yes	characteristic
404	C₂×C₅	#3365	1	1	yes	characteristic
405	C₂×C₅	#3373	1	1	yes	characteristic
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
414	Q₈	—	2	2	no	—
415	Q₈	—	2	2	no	—
416	Q₈	—	4	8	no	—
417	Q₈	—	4	1	no	—
418	Q₈	—	4	1	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	2	no	—
423	D₄	—	8	4	no	—
424	D₄	—	8	4	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	C₅×#121	1	2	yes	—
449	C₂×C₄	C₅×#121	1	2	yes	—
450	C₂×C₄	C₅×#135	1	2	yes	—
451	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
452	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
453	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
454	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
455	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
456	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
457	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
458	C₈	—	4	1	no	—
459	C₈	—	4	1	no	—
460	C₈	—	4	2	no	—
461	C₅	#25279	1	1	yes	characteristic, direct product factor, Sylow
462	C₂²	—	8	2	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	2	no	—
466	C₂²	—	8	2	no	—
467	C₂²	—	8	2	no	—
468	C₂²	—	8	2	no	—
469	C₂²	C₂×C₅×#121	1	1	yes	characteristic
470	C₂²	C₅×#546	1	1	yes	characteristic
471	C₂²	C₅×#548	1	1	yes	characteristic
472	C₂²	C₂×C₅×#135	1	1	yes	characteristic
473	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
474	C₂²	C₅×#577	1	1	yes	characteristic
475	C₂²	C₅×#577	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	4	4	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	—	8	1	no	—
483	C₄	—	8	1	no	—
484	C₄	C₅×#463	1	4	yes	—
485	C₄	C₅×#529	1	1	yes	characteristic
486	C₄	C₅×#542	1	1	yes	characteristic
487	C₄	C₅×#548	1	1	yes	characteristic
488	C₄	C₅×#550	1	1	yes	characteristic
489	C₂	—	16	2	no	—
490	C₂	C₅×#2426	1	1	yes	characteristic
491	C₂	C₂×C₅×#463	1	1	yes	characteristic
492	C₂	C₅×#3043	1	1	yes	characteristic
493	C₂	C₅×#3304	1	1	yes	characteristic
494	C₂	C₅×#3332	1	1	yes	characteristic
495	C₂	C₅×#3365	1	1	yes	characteristic
496	C₂	C₅×#3373	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#127	C₂²
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
2. C₂×C₅×#475	C₂	semidirect
4. C₅×#2365	C₂	semidirect
5. C₅×#2065	C₂	semidirect
6. C₅×#2042	C₂	semidirect
7. C₅×#1983	C₂	semidirect
9. C₅×#1939	C₂	semidirect
10. C₅×#1926	C₂	semidirect
11. C₄×C₅×#103	C₂	semidirect
43. #25279	C₅	direct (N × H)
95. C₂×#475	C₂×C₅	semidirect
97. #2365	C₂×C₅	semidirect
98. #2065	C₂×C₅	semidirect
99. #2042	C₂×C₅	semidirect
100. #1983	C₂×C₅	semidirect
102. #1939	C₂×C₅	semidirect
103. #1926	C₂×C₅	semidirect
104. C₄×#103	C₂×C₅	semidirect
461. C₅	#25279	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×#486	2
C₂×C₅×#475	2
C₅×#2548	2
C₅×#2365	2
C₅×#2065	2
C₅×#2042	2
C₅×#1983	2
C₅×#1982	2
C₅×#1939	2
C₅×#1926	2
C₄×C₅×#103	2
#25279	5

Subgroups — C5×#25279 #11947999

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#25279 #11947999