Subgroups — C₅×#23066 #11945786

Order 1280.

842 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×#474	C₂	1	1	yes	maximal, characteristic
2	C₅×#2365	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2354	C₂	1	1	yes	maximal, characteristic
4	C₅×#1990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1948	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1936	C₂	1	2	yes	maximal
7	C₅×#1926	C₂	1	2	yes	maximal
8	C₅×#1921	C₂	1	2	yes	maximal, complemented
9	C₅×#1776	C₂	1	2	yes	maximal, complemented
10	C₅×#1770	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#102	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Q₈	—	2	1	no	—
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₅×#117	—	2	1	no	—
16	C₅×#474	C₄	1	8	yes	complemented
17	C₂×C₅×#107	C₂²	1	2	yes	—
18	C₂×C₅×#106	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×#102	C₂²	1	1	yes	characteristic
21	C₂×C₅×#102	C₂²	1	1	yes	characteristic
22	C₂×C₅×#102	C₂²	1	2	yes	—
23	C₂×C₅×#97	C₂²	1	2	yes	—
24	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₅×#391	—	2	1	no	—
26	C₅×#390	C₂²	1	2	yes	—
27	C₅×#389	C₂²	1	2	yes	—
28	C₅×#388	—	2	2	no	—
29	C₅×#387	—	2	2	no	—
30	C₅×#384	C₂²	1	1	yes	characteristic
31	C₅×#380	—	2	1	no	—
32	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
34	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
35	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₅×#340	C₂²	1	1	yes	characteristic
37	C₅×#340	C₂²	1	1	yes	characteristic
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	2	yes	—
42	#23066	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×Q₈	—	2	1	no	—
44	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₅	—	2	1	no	—
46	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₅×C₈	C₂³	1	2	yes	—
48	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
49	C₅×C₄⋊Q₈	—	2	2	no	—
50	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	—
51	C₄×C₅×Q₈	—	4	4	no	—
52	C₄×C₅×D₄	—	2	2	no	—
53	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
54	C₅×#117	—	4	4	no	—
55	C₂×C₅×C₄⋊C₄	—	2	1	no	—
56	C₂×C₅×C₄⋊C₄	—	2	1	no	—
57	C₂×C₅×C₄⋊C₄	—	2	2	no	—
58	C₂×C₅×C₄⋊C₄	—	2	1	no	—
59	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
60	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
61	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₄²×C₅	—	2	2	no	—
70	C₂×C₄²×C₅	—	2	2	no	—
71	C₂×C₄²×C₅	—	2	1	no	—
72	C₂×C₄²×C₅	C₂³	1	2	yes	—
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₅×#107	C₂×C₄	1	8	yes	—
75	C₅×#106	—	2	4	no	—
76	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
77	C₅×#102	—	2	2	no	—
78	C₅×#102	—	2	2	no	—
79	C₅×#102	C₂×C₄	1	8	yes	—
80	C₅×#97	—	2	4	no	—
81	C₄×C₅×C₈	—	2	2	no	—
82	C₅×#95	—	2	2	no	—
83	C₅×#95	—	2	1	no	—
84	C₅×#95	—	2	2	no	—
85	C₅×#95	—	2	2	no	—
86	C₅×#95	D₄	1	2	yes	—
87	C₂×#474	C₂×C₅	1	1	yes	characteristic
88	#2365	C₂×C₅	1	1	yes	characteristic, complemented
89	#2354	C₂×C₅	1	1	yes	characteristic
90	#1990	C₂×C₅	1	1	yes	characteristic, complemented
91	#1948	C₂×C₅	1	1	yes	characteristic, complemented
92	#1936	C₂×C₅	1	2	yes	—
93	#1926	C₂×C₅	1	2	yes	—
94	#1921	C₂×C₅	1	2	yes	complemented
95	#1776	C₂×C₅	1	2	yes	complemented
96	#1770	C₂×C₅	1	1	yes	characteristic, complemented
97	C₄×#102	C₂×C₅	1	1	yes	characteristic
98	C₂⁴×C₅	—	2	1	no	—
99	C₂×C₅×Q₈	—	2	4	no	—
100	C₂×C₅×Q₈	—	4	2	no	—
101	C₂×C₅×Q₈	—	4	2	no	—
102	C₂×C₅×D₄	—	2	1	no	—
103	C₂×C₅×D₄	—	2	1	no	—
104	C₂×C₅×D₄	—	2	1	no	—
105	C₂×C₅×D₄	—	2	1	no	—
106	C₂×C₅×D₄	—	2	1	no	—
107	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₅	—	2	1	no	—
109	C₂²×C₄×C₅	—	2	1	no	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	2	4	no	—
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	—	2	1	no	—
114	C₂²×C₄×C₅	—	4	2	no	—
115	C₂²×C₄×C₅	—	4	2	no	—
116	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
121	C₂×C₅×C₈	—	2	1	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	—	2	2	no	—
124	C₂×C₅×C₈	—	2	1	no	—
125	C₂×C₅×C₈	—	2	1	no	—
126	C₂×C₅×C₈	—	2	1	no	—
127	C₂×C₅×C₈	—	2	1	no	—
128	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
129	C₂×C₅×C₈	#41	1	2	yes	—
130	C₅×C₄⋊C₄	—	2	4	no	—
131	C₅×C₄⋊C₄	—	2	2	no	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₄⋊C₄	—	2	1	no	—
134	C₅×C₄⋊C₄	—	2	2	no	—
135	C₅×C₄⋊C₄	—	2	1	no	—
136	C₅×C₄⋊C₄	—	2	1	no	—
137	C₅×C₄⋊C₄	—	2	2	no	—
138	C₅×C₄⋊C₄	—	2	1	no	—
139	C₅×C₄⋊C₄	—	2	2	no	—
140	C₅×C₄⋊C₄	—	4	4	no	—
141	C₅×C₄⋊C₄	—	4	2	no	—
142	C₅×C₄⋊C₄	—	8	1	no	—
143	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
144	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
145	C₅×C₄⋊C₄	#41	1	2	yes	—
146	C₅×C₂²⋊C₄	—	2	4	no	—
147	C₅×C₂²⋊C₄	—	4	4	no	—
148	C₅×C₂²⋊C₄	—	8	2	no	—
149	C₄²×C₅	—	2	2	no	—
150	C₄²×C₅	—	2	2	no	—
151	C₄²×C₅	—	4	4	no	—
152	C₄²×C₅	—	4	4	no	—
153	C₄²×C₅	—	4	2	no	—
154	C₄²×C₅	C₂²×C₄	1	2	yes	—
155	C₄²×C₅	#41	1	2	yes	—
156	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₄×Q₈	—	2	1	no	—
158	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
159	C₂×#117	—	2	1	no	—
160	#474	C₄×C₅	1	8	yes	complemented
161	C₂×#107	C₂²×C₅	1	2	yes	—
162	C₂×#106	C₂²×C₅	1	2	yes	—
163	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
164	C₂×#102	C₂²×C₅	1	1	yes	characteristic
165	C₂×#102	C₂²×C₅	1	1	yes	characteristic
166	C₂×#102	C₂²×C₅	1	2	yes	—
167	C₂×#97	C₂²×C₅	1	2	yes	—
168	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
169	#391	—	2	1	no	—
170	#390	C₂²×C₅	1	2	yes	—
171	#389	C₂²×C₅	1	2	yes	—
172	#388	—	2	2	no	—
173	#387	—	2	2	no	—
174	#384	C₂²×C₅	1	1	yes	characteristic
175	#380	—	2	1	no	—
176	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
177	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
178	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
179	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
180	#340	C₂²×C₅	1	1	yes	characteristic
181	#340	C₂²×C₅	1	2	yes	—
182	#340	C₂²×C₅	1	2	yes	—
183	#340	C₂²×C₅	1	2	yes	—
184	#340	C₂²×C₅	1	1	yes	characteristic
185	#336	C₂²×C₅	1	2	yes	—
186	C₂³×C₅	—	2	2	no	—
187	C₂³×C₅	—	4	1	no	—
188	C₂³×C₅	—	4	1	no	—
189	C₂³×C₅	—	4	1	no	—
190	C₂³×C₅	—	4	1	no	—
191	C₂³×C₅	—	4	1	no	—
192	C₂³×C₅	—	4	1	no	—
193	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
194	C₅×Q₈	—	4	8	no	—
195	C₅×D₄	—	2	2	no	—
196	C₅×D₄	—	2	2	no	—
197	C₅×D₄	—	4	1	no	—
198	C₅×D₄	—	4	1	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	4	no	—
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	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	4	1	no	—
212	C₂×C₄×C₅	—	4	2	no	—
213	C₂×C₄×C₅	—	4	1	no	—
214	C₂×C₄×C₅	—	4	2	no	—
215	C₂×C₄×C₅	—	4	1	no	—
216	C₂×C₄×C₅	—	4	8	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	2	no	—
222	C₂×C₄×C₅	—	4	1	no	—
223	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
224	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
225	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
226	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
227	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
232	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
233	C₅×C₈	—	2	4	no	—
234	C₅×C₈	—	2	2	no	—
235	C₅×C₈	—	4	1	no	—
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
238	C₂³×C₄	—	2	1	no	—
239	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
240	C₂²×C₈	C₂³×C₅	1	2	yes	—
241	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
242	C₄⋊Q₈	—	2	2	no	—
243	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	—
244	C₄×Q₈	—	4	4	no	—
245	C₄×D₄	—	2	2	no	—
246	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
247	#117	—	4	4	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	C₂³×C₅	1	2	yes	—
266	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
267	#107	C₂×C₄×C₅	1	8	yes	—
268	#106	—	2	4	no	—
269	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
270	#102	—	2	2	no	—
271	#102	—	2	2	no	—
272	#102	C₂×C₄×C₅	1	8	yes	—
273	#97	—	2	4	no	—
274	C₄×C₈	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	—	2	1	no	—
277	#95	—	2	2	no	—
278	#95	—	2	2	no	—
279	#95	C₅×D₄	1	2	yes	—
280	C₂²×C₅	—	4	2	no	—
281	C₂²×C₅	—	4	2	no	—
282	C₂²×C₅	—	4	2	no	—
283	C₂²×C₅	—	8	1	no	—
284	C₂²×C₅	—	8	1	no	—
285	C₂²×C₅	—	8	1	no	—
286	C₂²×C₅	—	8	1	no	—
287	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
288	C₂²×C₅	#547	1	1	yes	characteristic
289	C₂²×C₅	#548	1	1	yes	characteristic
290	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
291	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
292	C₂²×C₅	#577	1	1	yes	characteristic
293	C₂²×C₅	#578	1	1	yes	characteristic
294	C₄×C₅	—	2	2	no	—
295	C₄×C₅	—	4	2	no	—
296	C₄×C₅	—	4	2	no	—
297	C₄×C₅	—	4	2	no	—
298	C₄×C₅	—	4	2	no	—
299	C₄×C₅	—	4	4	no	—
300	C₄×C₅	—	8	1	no	—
301	C₄×C₅	—	8	2	no	—
302	C₄×C₅	#442	1	4	yes	—
303	C₄×C₅	C₄×#41	1	1	yes	characteristic
304	C₄×C₅	#519	1	1	yes	characteristic
305	C₄×C₅	#552	1	1	yes	characteristic
306	C₄×C₅	#556	1	1	yes	characteristic
307	C₂⁴	—	2	1	no	—
308	C₂×Q₈	—	2	4	no	—
309	C₂×Q₈	—	4	2	no	—
310	C₂×Q₈	—	4	2	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
326	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
327	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
328	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
329	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
338	C₂×C₈	C₅×#41	1	2	yes	—
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	4	4	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	8	1	no	—
352	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
353	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
354	C₄⋊C₄	C₅×#41	1	2	yes	—
355	C₂²⋊C₄	—	2	4	no	—
356	C₂²⋊C₄	—	4	4	no	—
357	C₂²⋊C₄	—	8	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	4	4	no	—
361	C₄²	—	4	4	no	—
362	C₄²	—	4	2	no	—
363	C₄²	C₂²×C₄×C₅	1	2	yes	—
364	C₄²	C₅×#41	1	2	yes	—
365	C₂×C₅	—	8	2	no	—
366	C₂×C₅	#2362	1	1	yes	characteristic
367	C₂×C₅	C₂×#442	1	1	yes	characteristic
368	C₂×C₅	#2947	1	1	yes	characteristic
369	C₂×C₅	#3353	1	1	yes	characteristic
370	C₂×C₅	#3354	1	1	yes	characteristic
371	C₂×C₅	#3367	1	1	yes	characteristic
372	C₂×C₅	#3368	1	1	yes	characteristic
373	C₂³	—	2	2	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
381	Q₈	—	4	8	no	—
382	D₄	—	2	2	no	—
383	D₄	—	2	2	no	—
384	D₄	—	4	1	no	—
385	D₄	—	4	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	8	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
411	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
412	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
413	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
414	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
415	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
416	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
417	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
418	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
419	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
420	C₈	—	2	4	no	—
421	C₈	—	2	2	no	—
422	C₈	—	4	1	no	—
423	C₅	#23066	1	1	yes	characteristic, direct product factor, Sylow
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
432	C₂²	C₅×#547	1	1	yes	characteristic
433	C₂²	C₅×#548	1	1	yes	characteristic
434	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
435	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
436	C₂²	C₅×#577	1	1	yes	characteristic
437	C₂²	C₅×#578	1	1	yes	characteristic
438	C₄	—	2	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	4	no	—
444	C₄	—	8	1	no	—
445	C₄	—	8	2	no	—
446	C₄	C₅×#442	1	4	yes	—
447	C₄	C₄×C₅×#41	1	1	yes	characteristic
448	C₄	C₅×#519	1	1	yes	characteristic
449	C₄	C₅×#552	1	1	yes	characteristic
450	C₄	C₅×#556	1	1	yes	characteristic
451	C₂	—	8	2	no	—
452	C₂	C₅×#2362	1	1	yes	characteristic
453	C₂	C₂×C₅×#442	1	1	yes	characteristic
454	C₂	C₅×#2947	1	1	yes	characteristic
455	C₂	C₅×#3353	1	1	yes	characteristic
456	C₂	C₅×#3354	1	1	yes	characteristic
457	C₂	C₅×#3367	1	1	yes	characteristic
458	C₂	C₅×#3368	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	C₂²×C₅×D₄	C₂³
LCS	G ▷ C₂×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. C₅×#2365	C₂	semidirect
4. C₅×#1990	C₂	semidirect
5. C₅×#1948	C₂	semidirect
8. C₅×#1921	C₂	semidirect
9. C₅×#1776	C₂	semidirect
10. C₅×#1770	C₂	semidirect
16. C₅×#474	C₄	semidirect
42. #23066	C₅	direct (N × H)
88. #2365	C₂×C₅	semidirect
90. #1990	C₂×C₅	semidirect
91. #1948	C₂×C₅	semidirect
94. #1921	C₂×C₅	semidirect
95. #1776	C₂×C₅	semidirect
96. #1770	C₂×C₅	semidirect
160. #474	C₄×C₅	semidirect
423. C₅	#23066	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×#474	2
C₅×#2365	2
C₅×#2354	2
C₅×#1990	2
C₅×#1948	2
C₅×#1936	2
C₅×#1926	2
C₅×#1921	2
C₅×#1776	2
C₅×#1770	2
C₄×C₅×#102	2
#23066	5

Subgroups — C5×#23066 #11945786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23066 #11945786