Subgroups — C₅×#22226 #11944946

Order 1280.

926 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#490	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×#127	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1992	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1961	C₂	1	1	yes	maximal, characteristic
6	C₅×#1926	C₂	1	2	yes	maximal, complemented
7	C₅×#1925	C₂	1	2	yes	maximal, complemented
8	C₅×#1864	C₂	1	2	yes	maximal, complemented
9	C₅×#1862	C₂	1	2	yes	maximal, complemented
10	C₅×#1847	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1745	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#127	C₂²	1	1	yes	characteristic
13	C₂×C₅×#125	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	—	2	1	no	—
15	C₂×C₄×C₅×D₄	—	2	1	no	—
16	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
17	C₅×#490	C₄	1	8	yes	complemented
18	C₂×C₅×#107	C₂²	1	2	yes	—
19	C₂×C₅×#106	C₂²	1	2	yes	—
20	C₂×C₅×#102	C₂²	1	2	yes	—
21	C₂×C₅×#102	C₂²	1	2	yes	—
22	C₂×C₅×#102	C₂²	1	2	yes	—
23	C₂×C₅×#102	C₂²	1	2	yes	—
24	C₂×C₅×#97	C₂²	1	1	yes	characteristic
25	C₂×C₅×#97	C₂²	1	1	yes	characteristic
26	C₅×#390	—	2	1	no	—
27	C₅×#390	—	2	1	no	—
28	C₅×#390	C₂²	1	2	yes	—
29	C₅×#389	C₂²	1	1	yes	characteristic
30	C₅×#389	C₂²	1	1	yes	characteristic
31	C₅×#387	—	2	1	no	—
32	C₅×#387	—	2	1	no	—
33	C₅×#384	C₂²	1	1	yes	characteristic
34	C₅×#382	C₂²	1	1	yes	characteristic
35	C₄×C₅×C₄⋊C₄	—	2	1	no	—
36	C₄×C₅×C₄⋊C₄	—	2	1	no	—
37	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₄³×C₅	C₂²	1	1	yes	characteristic
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#340	C₂²	1	2	yes	—
42	C₅×#336	C₂²	1	2	yes	—
43	C₅×#336	C₂²	1	2	yes	—
44	#22226	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂²×C₅×D₄	—	2	1	no	—
46	C₂²×C₅×D₄	—	2	1	no	—
47	C₂²×C₅×D₄	C₂³	1	2	yes	—
48	C₂³×C₄×C₅	—	2	2	no	—
49	C₂²×C₅×C₈	C₂³	1	2	yes	—
50	C₂²×C₅×C₈	C₂³	1	2	yes	—
51	C₅×#127	—	2	2	no	—
52	C₅×#127	C₂×C₄	1	4	yes	—
53	C₅×#125	—	2	2	no	—
54	C₅×#125	C₂×C₄	1	4	yes	complemented
55	C₄×C₅×D₄	—	4	2	no	—
56	C₄×C₅×D₄	—	4	2	no	—
57	C₄×C₅×D₄	—	4	4	no	—
58	C₄×C₅×D₄	—	4	4	no	—
59	C₂×C₅×C₄⋊C₄	—	2	1	no	—
60	C₂×C₅×C₄⋊C₄	—	2	1	no	—
61	C₂×C₅×C₄⋊C₄	—	2	1	no	—
62	C₂×C₅×C₄⋊C₄	—	2	1	no	—
63	C₂×C₅×C₄⋊C₄	—	2	1	no	—
64	C₂×C₅×C₄⋊C₄	—	2	1	no	—
65	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²×C₅	—	2	1	no	—
74	C₂×C₄²×C₅	—	2	1	no	—
75	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₅×#107	—	4	2	no	—
83	C₅×#106	—	4	2	no	—
84	C₅×#102	—	4	2	no	—
85	C₅×#102	—	4	2	no	—
86	C₅×#102	C₂×C₄	1	8	yes	complemented
87	C₅×#102	C₂×C₄	1	8	yes	complemented
88	C₅×#97	—	2	2	no	—
89	C₅×#97	C₂×C₄	1	4	yes	complemented
90	C₅×#95	—	2	1	no	—
91	C₅×#95	—	2	1	no	—
92	C₅×#95	—	2	1	no	—
93	C₅×#95	—	2	1	no	—
94	C₅×#95	—	2	1	no	—
95	C₅×#95	—	2	1	no	—
96	C₂×#490	C₂×C₅	1	1	yes	characteristic
97	C₄×#127	C₂×C₅	1	1	yes	characteristic
98	C₄×#125	C₂×C₅	1	1	yes	characteristic, complemented
99	#1992	C₂×C₅	1	1	yes	characteristic, complemented
100	#1961	C₂×C₅	1	1	yes	characteristic
101	#1926	C₂×C₅	1	2	yes	complemented
102	#1925	C₂×C₅	1	2	yes	complemented
103	#1864	C₂×C₅	1	2	yes	complemented
104	#1862	C₂×C₅	1	2	yes	complemented
105	#1847	C₂×C₅	1	1	yes	characteristic, complemented
106	#1745	C₂×C₅	1	1	yes	characteristic, complemented
107	C₂⁴×C₅	—	2	2	no	—
108	C₂×C₅×D₄	—	2	4	no	—
109	C₂×C₅×D₄	—	2	4	no	—
110	C₂×C₅×D₄	—	2	2	no	—
111	C₂×C₅×D₄	—	2	2	no	—
112	C₂×C₅×D₄	—	2	2	no	—
113	C₂×C₅×D₄	—	2	2	no	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	—	4	2	no	—
116	C₂×C₅×D₄	—	4	2	no	—
117	C₂×C₅×D₄	—	4	2	no	—
118	C₂×C₅×D₄	—	4	2	no	—
119	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	—	2	1	no	—
123	C₂²×C₄×C₅	—	2	1	no	—
124	C₂²×C₄×C₅	—	2	2	no	—
125	C₂²×C₄×C₅	—	4	4	no	—
126	C₂²×C₄×C₅	—	4	4	no	—
127	C₂²×C₄×C₅	—	4	4	no	—
128	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	2	2	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
141	C₅×C₄⋊C₄	—	2	4	no	—
142	C₅×C₄⋊C₄	—	2	4	no	—
143	C₅×C₄⋊C₄	—	2	1	no	—
144	C₅×C₄⋊C₄	—	2	1	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	2	no	—
149	C₅×C₄⋊C₄	—	4	2	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	C₂²×C₄	1	2	yes	—
154	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
155	C₅×C₂²⋊C₄	—	4	4	no	—
156	C₅×C₂²⋊C₄	—	4	4	no	—
157	C₅×C₂²⋊C₄	—	4	4	no	—
158	C₄²×C₅	—	2	2	no	—
159	C₄²×C₅	—	2	2	no	—
160	C₄²×C₅	—	2	2	no	—
161	C₄²×C₅	—	2	2	no	—
162	C₄²×C₅	—	4	1	no	—
163	C₄²×C₅	—	4	1	no	—
164	C₄²×C₅	—	4	2	no	—
165	C₄²×C₅	—	4	2	no	—
166	C₄²×C₅	C₂²×C₄	1	2	yes	—
167	C₄²×C₅	#41	1	2	yes	—
168	C₂×#127	C₂²×C₅	1	1	yes	characteristic
169	C₂×#125	C₂²×C₅	1	1	yes	characteristic
170	C₂×C₄×D₄	—	2	1	no	—
171	C₂×C₄×D₄	—	2	1	no	—
172	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
173	#490	C₄×C₅	1	8	yes	complemented
174	C₂×#107	C₂²×C₅	1	2	yes	—
175	C₂×#106	C₂²×C₅	1	2	yes	—
176	C₂×#102	C₂²×C₅	1	2	yes	—
177	C₂×#102	C₂²×C₅	1	2	yes	—
178	C₂×#102	C₂²×C₅	1	2	yes	—
179	C₂×#102	C₂²×C₅	1	2	yes	—
180	C₂×#97	C₂²×C₅	1	1	yes	characteristic
181	C₂×#97	C₂²×C₅	1	1	yes	characteristic
182	#390	—	2	1	no	—
183	#390	—	2	1	no	—
184	#390	C₂²×C₅	1	2	yes	—
185	#389	C₂²×C₅	1	1	yes	characteristic
186	#389	C₂²×C₅	1	1	yes	characteristic
187	#387	—	2	1	no	—
188	#387	—	2	1	no	—
189	#384	C₂²×C₅	1	1	yes	characteristic
190	#382	C₂²×C₅	1	1	yes	characteristic
191	C₄×C₄⋊C₄	—	2	1	no	—
192	C₄×C₄⋊C₄	—	2	1	no	—
193	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
194	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
195	C₄³	C₂²×C₅	1	1	yes	characteristic
196	#340	C₂²×C₅	1	2	yes	—
197	#340	C₂²×C₅	1	2	yes	—
198	#336	C₂²×C₅	1	2	yes	—
199	#336	C₂²×C₅	1	2	yes	—
200	C₂³×C₅	—	2	4	no	—
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	C₂²×D₄	1	1	yes	characteristic
208	C₅×D₄	—	2	4	no	—
209	C₅×D₄	—	2	4	no	—
210	C₅×D₄	—	4	8	no	—
211	C₅×D₄	—	4	8	no	—
212	C₅×D₄	—	4	2	no	—
213	C₅×D₄	—	4	2	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	1	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	4	1	no	—
231	C₂×C₄×C₅	—	4	1	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	4	2	no	—
235	C₂×C₄×C₅	—	4	1	no	—
236	C₂×C₄×C₅	—	4	1	no	—
237	C₂×C₄×C₅	—	4	1	no	—
238	C₂×C₄×C₅	—	4	2	no	—
239	C₂×C₄×C₅	—	4	2	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	—	8	8	no	—
244	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
245	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
246	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
247	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
248	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
251	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
252	C₅×C₈	—	2	4	no	—
253	C₅×C₈	—	4	2	no	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	C₂³×C₅	1	2	yes	—
257	C₂³×C₄	—	2	2	no	—
258	C₂²×C₈	C₂³×C₅	1	2	yes	—
259	C₂²×C₈	C₂³×C₅	1	2	yes	—
260	#127	—	2	2	no	—
261	#127	C₂×C₄×C₅	1	4	yes	—
262	#125	—	2	2	no	—
263	#125	C₂×C₄×C₅	1	4	yes	complemented
264	C₄×D₄	—	4	2	no	—
265	C₄×D₄	—	4	2	no	—
266	C₄×D₄	—	4	4	no	—
267	C₄×D₄	—	4	4	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
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	1	yes	characteristic
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
285	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
286	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
287	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
291	#107	—	4	2	no	—
292	#106	—	4	2	no	—
293	#102	—	4	2	no	—
294	#102	—	4	2	no	—
295	#102	C₂×C₄×C₅	1	8	yes	complemented
296	#102	C₂×C₄×C₅	1	8	yes	complemented
297	#97	—	2	2	no	—
298	#97	C₂×C₄×C₅	1	4	yes	complemented
299	#95	—	2	1	no	—
300	#95	—	2	1	no	—
301	#95	—	2	1	no	—
302	#95	—	2	1	no	—
303	#95	—	2	1	no	—
304	#95	—	2	1	no	—
305	C₂²×C₅	—	4	4	no	—
306	C₂²×C₅	—	4	4	no	—
307	C₂²×C₅	—	4	4	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	C₂×C₄×D₄	1	1	yes	characteristic
313	C₂²×C₅	#535	1	1	yes	characteristic
314	C₂²×C₅	#536	1	1	yes	characteristic
315	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
316	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
317	C₂²×C₅	#575	1	1	yes	characteristic
318	C₂²×C₅	#575	1	1	yes	characteristic
319	C₄×C₅	—	2	2	no	—
320	C₄×C₅	—	2	2	no	—
321	C₄×C₅	—	2	2	no	—
322	C₄×C₅	—	2	2	no	—
323	C₄×C₅	—	4	2	no	—
324	C₄×C₅	—	4	2	no	—
325	C₄×C₅	—	4	1	no	—
326	C₄×C₅	—	4	1	no	—
327	C₄×C₅	—	8	1	no	—
328	C₄×C₅	—	8	2	no	—
329	C₄×C₅	—	8	1	no	—
330	C₄×C₅	#520	1	2	yes	—
331	C₄×C₅	#542	1	2	yes	—
332	C₂⁴	—	2	2	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	4	4	no	—
351	C₂²×C₄	—	4	4	no	—
352	C₂²×C₄	—	4	4	no	—
353	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
354	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
358	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
359	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
379	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
380	C₂²⋊C₄	—	4	4	no	—
381	C₂²⋊C₄	—	4	4	no	—
382	C₂²⋊C₄	—	4	4	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	4	1	no	—
388	C₄²	—	4	1	no	—
389	C₄²	—	4	2	no	—
390	C₄²	—	4	2	no	—
391	C₄²	C₂²×C₄×C₅	1	2	yes	—
392	C₄²	C₅×#41	1	2	yes	—
393	C₂×C₅	—	8	4	no	—
394	C₂×C₅	#2326	1	1	yes	characteristic
395	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
396	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
397	C₂×C₅	#3217	1	1	yes	characteristic
398	C₂×C₅	#3219	1	1	yes	characteristic
399	C₂×C₅	#3234	1	1	yes	characteristic
400	C₂×C₅	#3235	1	1	yes	characteristic
401	C₂³	—	2	4	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
409	D₄	—	2	4	no	—
410	D₄	—	2	4	no	—
411	D₄	—	4	8	no	—
412	D₄	—	4	8	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	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	—	8	8	no	—
445	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
446	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
447	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
448	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
449	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
450	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
451	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
452	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
453	C₈	—	2	4	no	—
454	C₈	—	4	2	no	—
455	C₅	#22226	1	1	yes	characteristic, direct product factor, Sylow
456	C₂²	—	4	4	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	8	2	no	—
462	C₂²	—	8	2	no	—
463	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
464	C₂²	C₅×#535	1	1	yes	characteristic
465	C₂²	C₅×#536	1	1	yes	characteristic
466	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
467	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
468	C₂²	C₅×#575	1	1	yes	characteristic
469	C₂²	C₅×#575	1	1	yes	characteristic
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	1	no	—
477	C₄	—	4	1	no	—
478	C₄	—	8	2	no	—
479	C₄	—	8	1	no	—
480	C₄	—	8	1	no	—
481	C₄	C₅×#520	1	2	yes	—
482	C₄	C₅×#542	1	2	yes	—
483	C₂	—	8	4	no	—
484	C₂	C₅×#2326	1	1	yes	characteristic
485	C₂	C₄×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
486	C₂	C₄×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
487	C₂	C₅×#3217	1	1	yes	characteristic
488	C₂	C₅×#3219	1	1	yes	characteristic
489	C₂	C₅×#3234	1	1	yes	characteristic
490	C₂	C₅×#3235	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	C₂×C₅×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×C₅×#125	C₂	semidirect
4. C₅×#1992	C₂	semidirect
6. C₅×#1926	C₂	semidirect
7. C₅×#1925	C₂	semidirect
8. C₅×#1864	C₂	semidirect
9. C₅×#1862	C₂	semidirect
10. C₅×#1847	C₂	semidirect
11. C₅×#1745	C₂	semidirect
17. C₅×#490	C₄	semidirect
44. #22226	C₅	direct (N × H)
54. C₅×#125	C₂×C₄	semidirect
86. C₅×#102	C₂×C₄	semidirect
87. C₅×#102	C₂×C₄	semidirect
89. C₅×#97	C₂×C₄	semidirect
98. C₄×#125	C₂×C₅	semidirect
99. #1992	C₂×C₅	semidirect
101. #1926	C₂×C₅	semidirect
102. #1925	C₂×C₅	semidirect
103. #1864	C₂×C₅	semidirect
104. #1862	C₂×C₅	semidirect
105. #1847	C₂×C₅	semidirect
106. #1745	C₂×C₅	semidirect
173. #490	C₄×C₅	semidirect
263. #125	C₂×C₄×C₅	semidirect
295. #102	C₂×C₄×C₅	semidirect
296. #102	C₂×C₄×C₅	semidirect
298. #97	C₂×C₄×C₅	semidirect
455. C₅	#22226	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×#490	2
C₄×C₅×#127	2
C₄×C₅×#125	2
C₅×#1992	2
C₅×#1961	2
C₅×#1926	2
C₅×#1925	2
C₅×#1864	2
C₅×#1862	2
C₅×#1847	2
C₅×#1745	2
#22226	5

Subgroups — C5×#22226 #11944946

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22226 #11944946