Subgroups — C₅×#32841 #11955561

Order 1280.

632 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2860	C₂	1	1	yes	maximal, characteristic
2	C₅×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2099	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2094	C₂	1	1	yes	maximal, characteristic
6	C₅×#2093	C₂	1	1	yes	maximal, characteristic
7	C₅×#2085	C₂	1	2	yes	maximal, complemented
8	C₅×#2073	C₂	1	2	yes	maximal
9	C₅×#2059	C₂	1	2	yes	maximal, complemented
10	C₅×#2025	C₂	1	2	yes	maximal
11	C₅×#1839	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#126	—	2	1	no	—
13	C₂×C₅×#125	C₂²	1	2	yes	—
14	C₂×C₅×#107	C₂²	1	2	yes	—
15	C₂×C₅×#106	C₂²	1	2	yes	—
16	C₂×C₅×#102	C₂²	1	2	yes	—
17	C₂×C₅×#102	C₂²	1	2	yes	—
18	C₅×#390	C₂²	1	1	yes	characteristic
19	C₅×#390	C₂²	1	1	yes	characteristic
20	C₅×#390	C₂²	1	1	yes	characteristic
21	C₅×#389	—	2	1	no	—
22	C₅×#389	—	2	1	no	—
23	C₅×#389	—	2	1	no	—
24	C₅×#389	—	2	1	no	—
25	C₅×#389	C₂²	1	1	yes	characteristic
26	C₅×#389	C₂²	1	1	yes	characteristic
27	C₅×#389	C₂²	1	1	yes	characteristic
28	C₅×#388	—	2	1	no	—
29	C₅×#388	—	2	1	no	—
30	C₅×#388	—	2	1	no	—
31	C₅×#384	C₂²	1	1	yes	characteristic
32	C₅×#384	C₂²	1	1	yes	characteristic
33	C₅×#382	C₂²	1	2	yes	—
34	C₄³×C₅	C₂²	1	1	yes	characteristic
35	C₅×#340	C₂²	1	2	yes	—
36	C₅×#340	C₂²	1	2	yes	—
37	C₅×#340	C₂²	1	2	yes	—
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#336	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	1	yes	characteristic
42	C₅×#336	C₂²	1	1	yes	characteristic
43	#32841	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
45	C₂²×C₅×C₈	C₂³	1	2	yes	—
46	C₂²×C₅×C₈	C₂³	1	2	yes	—
47	C₅×#126	—	4	4	no	—
48	C₅×#125	—	4	2	no	—
49	C₅×#125	—	4	2	no	—
50	C₂×C₅×C₄⋊C₄	—	2	1	no	—
51	C₂×C₅×C₄⋊C₄	—	2	1	no	—
52	C₂×C₅×C₄⋊C₄	—	2	1	no	—
53	C₂×C₅×C₄⋊C₄	—	2	1	no	—
54	C₂×C₅×C₄⋊C₄	—	2	1	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	2	no	—
59	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
65	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
66	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₅×#107	—	4	2	no	—
78	C₅×#106	—	4	2	no	—
79	C₅×#102	—	4	2	no	—
80	C₅×#102	—	4	2	no	—
81	C₅×#95	—	2	2	no	—
82	C₅×#95	—	2	2	no	—
83	C₅×#95	—	2	1	no	—
84	C₅×#95	—	2	1	no	—
85	C₅×#95	—	2	1	no	—
86	#2860	C₂×C₅	1	1	yes	characteristic
87	#2859	C₂×C₅	1	1	yes	characteristic, complemented
88	#2100	C₂×C₅	1	1	yes	characteristic, complemented
89	#2099	C₂×C₅	1	1	yes	characteristic, complemented
90	#2094	C₂×C₅	1	1	yes	characteristic
91	#2093	C₂×C₅	1	1	yes	characteristic
92	#2085	C₂×C₅	1	2	yes	complemented
93	#2073	C₂×C₅	1	2	yes	—
94	#2059	C₂×C₅	1	2	yes	complemented
95	#2025	C₂×C₅	1	2	yes	—
96	#1839	C₂×C₅	1	1	yes	characteristic, complemented
97	C₂⁴×C₅	—	2	1	no	—
98	C₂×C₅×D₄	—	2	2	no	—
99	C₂×C₅×D₄	—	2	2	no	—
100	C₂×C₅×D₄	—	2	1	no	—
101	C₂×C₅×D₄	—	2	1	no	—
102	C₂²×C₄×C₅	—	2	1	no	—
103	C₂²×C₄×C₅	—	2	1	no	—
104	C₂²×C₄×C₅	—	2	1	no	—
105	C₂²×C₄×C₅	—	2	2	no	—
106	C₂²×C₄×C₅	—	2	2	no	—
107	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
114	C₂×C₅×C₈	—	2	2	no	—
115	C₂×C₅×C₈	—	2	2	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	—	2	2	no	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₅×C₄⋊C₄	—	2	2	no	—
121	C₅×C₄⋊C₄	—	2	2	no	—
122	C₅×C₄⋊C₄	—	2	2	no	—
123	C₅×C₄⋊C₄	—	2	2	no	—
124	C₅×C₄⋊C₄	—	2	2	no	—
125	C₅×C₄⋊C₄	—	2	2	no	—
126	C₅×C₄⋊C₄	—	2	1	no	—
127	C₅×C₄⋊C₄	—	2	1	no	—
128	C₅×C₄⋊C₄	—	4	2	no	—
129	C₅×C₄⋊C₄	—	4	2	no	—
130	C₅×C₄⋊C₄	—	4	4	no	—
131	C₅×C₄⋊C₄	—	4	4	no	—
132	C₅×C₄⋊C₄	—	4	2	no	—
133	C₅×C₄⋊C₄	—	4	2	no	—
134	C₅×C₄⋊C₄	—	4	2	no	—
135	C₅×C₄⋊C₄	—	4	2	no	—
136	C₅×C₄⋊C₄	—	4	2	no	—
137	C₅×C₂²⋊C₄	—	4	2	no	—
138	C₅×C₂²⋊C₄	—	4	2	no	—
139	C₅×C₂²⋊C₄	—	4	2	no	—
140	C₅×C₂²⋊C₄	—	4	2	no	—
141	C₅×C₂²⋊C₄	—	4	2	no	—
142	C₅×C₂²⋊C₄	—	4	2	no	—
143	C₄²×C₅	—	2	2	no	—
144	C₄²×C₅	—	2	2	no	—
145	C₄²×C₅	—	2	2	no	—
146	C₄²×C₅	—	2	2	no	—
147	C₄²×C₅	—	2	1	no	—
148	C₄²×C₅	—	2	1	no	—
149	C₄²×C₅	—	4	1	no	—
150	C₄²×C₅	—	4	1	no	—
151	C₂×#126	—	2	1	no	—
152	C₂×#125	C₂²×C₅	1	2	yes	—
153	C₂×#107	C₂²×C₅	1	2	yes	—
154	C₂×#106	C₂²×C₅	1	2	yes	—
155	C₂×#102	C₂²×C₅	1	2	yes	—
156	C₂×#102	C₂²×C₅	1	2	yes	—
157	#390	C₂²×C₅	1	1	yes	characteristic
158	#390	C₂²×C₅	1	1	yes	characteristic
159	#390	C₂²×C₅	1	1	yes	characteristic
160	#389	—	2	1	no	—
161	#389	—	2	1	no	—
162	#389	—	2	1	no	—
163	#389	—	2	1	no	—
164	#389	C₂²×C₅	1	1	yes	characteristic
165	#389	C₂²×C₅	1	1	yes	characteristic
166	#389	C₂²×C₅	1	1	yes	characteristic
167	#388	—	2	1	no	—
168	#388	—	2	1	no	—
169	#388	—	2	1	no	—
170	#384	C₂²×C₅	1	1	yes	characteristic
171	#384	C₂²×C₅	1	1	yes	characteristic
172	#382	C₂²×C₅	1	2	yes	—
173	C₄³	C₂²×C₅	1	1	yes	characteristic
174	#340	C₂²×C₅	1	2	yes	—
175	#340	C₂²×C₅	1	2	yes	—
176	#340	C₂²×C₅	1	2	yes	—
177	#340	C₂²×C₅	1	2	yes	—
178	#336	C₂²×C₅	1	2	yes	—
179	#336	C₂²×C₅	1	2	yes	—
180	#336	C₂²×C₅	1	1	yes	characteristic
181	#336	C₂²×C₅	1	1	yes	characteristic
182	C₂³×C₅	—	4	1	no	—
183	C₂³×C₅	—	4	1	no	—
184	C₂³×C₅	—	4	1	no	—
185	C₂³×C₅	—	4	1	no	—
186	C₂³×C₅	—	4	1	no	—
187	C₂³×C₅	—	4	1	no	—
188	C₂³×C₅	—	4	1	no	—
189	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
190	C₅×D₄	—	4	2	no	—
191	C₅×D₄	—	4	2	no	—
192	C₂×C₄×C₅	—	2	1	no	—
193	C₂×C₄×C₅	—	2	1	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	1	no	—
196	C₂×C₄×C₅	—	2	1	no	—
197	C₂×C₄×C₅	—	2	1	no	—
198	C₂×C₄×C₅	—	2	1	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	2	1	no	—
203	C₂×C₄×C₅	—	2	1	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	4	2	no	—
209	C₂×C₄×C₅	—	4	2	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	4	1	no	—
212	C₂×C₄×C₅	—	4	1	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	1	no	—
217	C₂×C₄×C₅	—	4	1	no	—
218	C₂×C₄×C₅	—	4	2	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	4	2	no	—
222	C₂×C₄×C₅	—	4	2	no	—
223	C₂×C₄×C₅	#135	1	2	yes	—
224	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
225	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
226	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
227	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
228	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
229	C₅×C₈	—	4	2	no	—
230	C₅×C₈	—	4	2	no	—
231	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₅	1	2	yes	—
233	C₂²×C₈	C₂³×C₅	1	2	yes	—
234	#126	—	4	4	no	—
235	#125	—	4	2	no	—
236	#125	—	4	2	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
247	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
248	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₂²⋊C₄	—	2	1	no	—
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₂²⋊C₄	—	2	1	no	—
256	C₂×C₂²⋊C₄	—	2	1	no	—
257	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
258	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
259	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
260	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
263	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
264	#107	—	4	2	no	—
265	#106	—	4	2	no	—
266	#102	—	4	2	no	—
267	#102	—	4	2	no	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	#95	—	2	1	no	—
271	#95	—	2	1	no	—
272	#95	—	2	1	no	—
273	C₂²×C₅	—	8	1	no	—
274	C₂²×C₅	—	8	1	no	—
275	C₂²×C₅	—	8	1	no	—
276	C₂²×C₅	—	8	1	no	—
277	C₂²×C₅	—	8	1	no	—
278	C₂²×C₅	—	8	1	no	—
279	C₂²×C₅	—	8	1	no	—
280	C₂²×C₅	#535	1	1	yes	characteristic
281	C₂²×C₅	#536	1	1	yes	characteristic
282	C₂²×C₅	#536	1	1	yes	characteristic
283	C₂²×C₅	C₂×#135	1	1	yes	characteristic
284	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
285	C₂²×C₅	#575	1	1	yes	characteristic
286	C₂²×C₅	#575	1	1	yes	characteristic
287	C₄×C₅	—	2	2	no	—
288	C₄×C₅	—	2	2	no	—
289	C₄×C₅	—	4	1	no	—
290	C₄×C₅	—	4	1	no	—
291	C₄×C₅	—	4	1	no	—
292	C₄×C₅	—	4	1	no	—
293	C₄×C₅	—	8	2	no	—
294	C₄×C₅	—	8	1	no	—
295	C₄×C₅	—	8	2	no	—
296	C₄×C₅	—	8	1	no	—
297	C₄×C₅	—	8	1	no	—
298	C₄×C₅	#563	1	2	yes	—
299	C₄×C₅	#563	1	2	yes	—
300	C₂⁴	—	2	1	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
316	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	4	4	no	—
332	C₄⋊C₄	—	4	4	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₄⋊C₄	—	4	2	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	—	4	2	no	—
343	C₂²⋊C₄	—	4	2	no	—
344	C₂²⋊C₄	—	4	2	no	—
345	C₂²⋊C₄	—	4	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	4	1	no	—
353	C₄²	—	4	1	no	—
354	C₂×C₅	—	16	1	no	—
355	C₂×C₅	#2821	1	1	yes	characteristic
356	C₂×C₅	#3207	1	1	yes	characteristic
357	C₂×C₅	#3219	1	1	yes	characteristic
358	C₂×C₅	#3232	1	1	yes	characteristic
359	C₂×C₅	#3233	1	1	yes	characteristic
360	C₂×C₅	#3234	1	1	yes	characteristic
361	C₂×C₅	#3235	1	1	yes	characteristic
362	C₂³	—	4	1	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	C₅×#135	1	2	yes	—
404	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
405	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
406	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
407	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
408	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
409	C₈	—	4	2	no	—
410	C₈	—	4	2	no	—
411	C₅	#32841	1	1	yes	characteristic, direct product factor, Sylow
412	C₂²	—	8	1	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	1	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	1	no	—
417	C₂²	—	8	1	no	—
418	C₂²	—	8	1	no	—
419	C₂²	C₅×#535	1	1	yes	characteristic
420	C₂²	C₅×#536	1	1	yes	characteristic
421	C₂²	C₅×#536	1	1	yes	characteristic
422	C₂²	C₂×C₅×#135	1	1	yes	characteristic
423	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
424	C₂²	C₅×#575	1	1	yes	characteristic
425	C₂²	C₅×#575	1	1	yes	characteristic
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	4	1	no	—
429	C₄	—	4	1	no	—
430	C₄	—	4	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	8	2	no	—
433	C₄	—	8	1	no	—
434	C₄	—	8	2	no	—
435	C₄	—	8	1	no	—
436	C₄	—	8	1	no	—
437	C₄	C₅×#563	1	2	yes	—
438	C₄	C₅×#563	1	2	yes	—
439	C₂	—	16	1	no	—
440	C₂	C₅×#2821	1	1	yes	characteristic
441	C₂	C₅×#3207	1	1	yes	characteristic
442	C₂	C₅×#3219	1	1	yes	characteristic
443	C₂	C₅×#3232	1	1	yes	characteristic
444	C₂	C₅×#3233	1	1	yes	characteristic
445	C₂	C₅×#3234	1	1	yes	characteristic
446	C₂	C₅×#3235	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 ◁ C₄³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2859	C₂	semidirect
3. C₅×#2100	C₂	semidirect
4. C₅×#2099	C₂	semidirect
7. C₅×#2085	C₂	semidirect
9. C₅×#2059	C₂	semidirect
11. C₅×#1839	C₂	semidirect
43. #32841	C₅	direct (N × H)
87. #2859	C₂×C₅	semidirect
88. #2100	C₂×C₅	semidirect
89. #2099	C₂×C₅	semidirect
92. #2085	C₂×C₅	semidirect
94. #2059	C₂×C₅	semidirect
96. #1839	C₂×C₅	semidirect
411. C₅	#32841	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×#2860	2
C₅×#2859	2
C₅×#2100	2
C₅×#2099	2
C₅×#2094	2
C₅×#2093	2
C₅×#2085	2
C₅×#2073	2
C₅×#2059	2
C₅×#2025	2
C₅×#1839	2
#32841	5

Subgroups — C5×#32841 #11955561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#32841 #11955561