Subgroups — C₅×#32840 #11955560

Order 1280.

648 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2862	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2860	C₂	1	1	yes	maximal, characteristic
3	C₅×#2101	C₂	1	2	yes	maximal, complemented
4	C₅×#2092	C₂	1	2	yes	maximal
5	C₅×#2085	C₂	1	2	yes	maximal, complemented
6	C₅×#2073	C₂	1	2	yes	maximal
7	C₅×#2058	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2057	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2023	C₂	1	1	yes	maximal, characteristic
10	C₅×#2023	C₂	1	1	yes	maximal, characteristic
11	C₅×#1839	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×#126	—	2	1	no	—
15	C₂×C₅×#107	C₂²	1	2	yes	—
16	C₂×C₅×#106	C₂²	1	2	yes	—
17	C₂×C₅×#102	C₂²	1	2	yes	—
18	C₂×C₅×#102	C₂²	1	2	yes	—
19	C₅×#391	—	2	1	no	—
20	C₅×#391	—	2	1	no	—
21	C₅×#391	—	2	1	no	—
22	C₅×#391	—	2	1	no	—
23	C₅×#390	C₂²	1	1	yes	characteristic
24	C₅×#390	C₂²	1	1	yes	characteristic
25	C₅×#390	C₂²	1	1	yes	characteristic
26	C₅×#389	C₂²	1	1	yes	characteristic
27	C₅×#389	C₂²	1	1	yes	characteristic
28	C₅×#389	C₂²	1	1	yes	characteristic
29	C₅×#388	—	2	1	no	—
30	C₅×#388	—	2	1	no	—
31	C₅×#388	—	2	1	no	—
32	C₅×#382	C₂²	1	2	yes	—
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	1	yes	characteristic
40	C₅×#336	C₂²	1	1	yes	characteristic
41	C₅×#336	C₂²	1	2	yes	—
42	C₅×#336	C₂²	1	2	yes	—
43	#32840	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×Q₈	—	2	1	no	—
45	C₂²×C₅×Q₈	—	2	1	no	—
46	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
47	C₂²×C₅×C₈	C₂³	1	2	yes	—
48	C₂²×C₅×C₈	C₂³	1	2	yes	—
49	C₅×C₄⋊Q₈	—	4	2	no	—
50	C₅×C₄⋊Q₈	—	4	2	no	—
51	C₅×#126	—	4	4	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	C₂³	1	2	yes	—
58	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
59	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
60	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
63	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
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×C₄²×C₅	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₅×#107	—	4	2	no	—
76	C₅×#106	—	4	2	no	—
77	C₅×#102	—	4	2	no	—
78	C₅×#102	—	4	2	no	—
79	C₅×#95	—	2	2	no	—
80	C₅×#95	—	2	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	#2862	C₂×C₅	1	1	yes	characteristic, complemented
87	#2860	C₂×C₅	1	1	yes	characteristic
88	#2101	C₂×C₅	1	2	yes	complemented
89	#2092	C₂×C₅	1	2	yes	—
90	#2085	C₂×C₅	1	2	yes	complemented
91	#2073	C₂×C₅	1	2	yes	—
92	#2058	C₂×C₅	1	1	yes	characteristic, complemented
93	#2057	C₂×C₅	1	1	yes	characteristic, complemented
94	#2023	C₂×C₅	1	1	yes	characteristic
95	#2023	C₂×C₅	1	1	yes	characteristic
96	#1839	C₂×C₅	1	1	yes	characteristic, complemented
97	C₂⁴×C₅	—	2	1	no	—
98	C₂×C₅×Q₈	—	4	2	no	—
99	C₂×C₅×Q₈	—	4	2	no	—
100	C₂×C₅×Q₈	—	4	2	no	—
101	C₂×C₅×Q₈	—	4	2	no	—
102	C₂×C₅×Q₈	—	4	2	no	—
103	C₂×C₅×Q₈	—	4	2	no	—
104	C₂×C₅×D₄	—	2	2	no	—
105	C₂×C₅×D₄	—	2	2	no	—
106	C₂×C₅×D₄	—	2	1	no	—
107	C₂×C₅×D₄	—	2	1	no	—
108	C₂²×C₄×C₅	—	2	1	no	—
109	C₂²×C₄×C₅	—	2	1	no	—
110	C₂²×C₄×C₅	—	2	1	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	—	2	2	no	—
124	C₂×C₅×C₈	—	2	2	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₅×C₄⋊C₄	—	2	2	no	—
127	C₅×C₄⋊C₄	—	2	2	no	—
128	C₅×C₄⋊C₄	—	2	2	no	—
129	C₅×C₄⋊C₄	—	2	2	no	—
130	C₅×C₄⋊C₄	—	2	2	no	—
131	C₅×C₄⋊C₄	—	2	2	no	—
132	C₅×C₄⋊C₄	—	2	1	no	—
133	C₅×C₄⋊C₄	—	2	1	no	—
134	C₅×C₄⋊C₄	—	4	2	no	—
135	C₅×C₄⋊C₄	—	4	2	no	—
136	C₅×C₄⋊C₄	—	4	2	no	—
137	C₅×C₄⋊C₄	—	4	2	no	—
138	C₅×C₄⋊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	C₅×C₂²⋊C₄	—	4	2	no	—
144	C₅×C₂²⋊C₄	—	4	2	no	—
145	C₄²×C₅	—	2	2	no	—
146	C₄²×C₅	—	2	2	no	—
147	C₄²×C₅	—	2	2	no	—
148	C₄²×C₅	—	2	2	no	—
149	C₄²×C₅	—	2	1	no	—
150	C₄²×C₅	—	2	1	no	—
151	C₄²×C₅	—	4	1	no	—
152	C₄²×C₅	—	4	1	no	—
153	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
154	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
155	C₂×#126	—	2	1	no	—
156	C₂×#107	C₂²×C₅	1	2	yes	—
157	C₂×#106	C₂²×C₅	1	2	yes	—
158	C₂×#102	C₂²×C₅	1	2	yes	—
159	C₂×#102	C₂²×C₅	1	2	yes	—
160	#391	—	2	1	no	—
161	#391	—	2	1	no	—
162	#391	—	2	1	no	—
163	#391	—	2	1	no	—
164	#390	C₂²×C₅	1	1	yes	characteristic
165	#390	C₂²×C₅	1	1	yes	characteristic
166	#390	C₂²×C₅	1	1	yes	characteristic
167	#389	C₂²×C₅	1	1	yes	characteristic
168	#389	C₂²×C₅	1	1	yes	characteristic
169	#389	C₂²×C₅	1	1	yes	characteristic
170	#388	—	2	1	no	—
171	#388	—	2	1	no	—
172	#388	—	2	1	no	—
173	#382	C₂²×C₅	1	2	yes	—
174	#382	C₂²×C₅	1	2	yes	—
175	C₄³	C₂²×C₅	1	1	yes	characteristic
176	#340	C₂²×C₅	1	2	yes	—
177	#340	C₂²×C₅	1	2	yes	—
178	#340	C₂²×C₅	1	2	yes	—
179	#340	C₂²×C₅	1	2	yes	—
180	#336	C₂²×C₅	1	1	yes	characteristic
181	#336	C₂²×C₅	1	1	yes	characteristic
182	#336	C₂²×C₅	1	2	yes	—
183	#336	C₂²×C₅	1	2	yes	—
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	—	4	1	no	—
190	C₂³×C₅	—	4	1	no	—
191	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
192	C₅×Q₈	—	8	4	no	—
193	C₅×Q₈	—	8	4	no	—
194	C₅×D₄	—	4	2	no	—
195	C₅×D₄	—	4	2	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	—	2	1	no	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	4	2	no	—
213	C₂×C₄×C₅	—	4	2	no	—
214	C₂×C₄×C₅	—	4	1	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	1	no	—
222	C₂×C₄×C₅	—	4	2	no	—
223	C₂×C₄×C₅	—	4	1	no	—
224	C₂×C₄×C₅	—	4	1	no	—
225	C₂×C₄×C₅	—	4	2	no	—
226	C₂×C₄×C₅	—	4	2	no	—
227	C₂×C₄×C₅	#135	1	2	yes	—
228	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
229	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
230	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
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	—	4	2	no	—
234	C₅×C₈	—	4	2	no	—
235	C₂²×Q₈	—	2	1	no	—
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₅	1	2	yes	—
239	C₂²×C₈	C₂³×C₅	1	2	yes	—
240	C₄⋊Q₈	—	4	2	no	—
241	C₄⋊Q₈	—	4	2	no	—
242	#126	—	4	4	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	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
249	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
250	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
258	C₂×C₂²⋊C₄	—	2	1	no	—
259	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
260	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
261	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
262	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
263	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
266	#107	—	4	2	no	—
267	#106	—	4	2	no	—
268	#102	—	4	2	no	—
269	#102	—	4	2	no	—
270	#95	—	2	2	no	—
271	#95	—	2	2	no	—
272	#95	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	—	2	1	no	—
275	#95	—	2	1	no	—
276	#95	—	2	1	no	—
277	C₂²×C₅	—	8	1	no	—
278	C₂²×C₅	—	8	1	no	—
279	C₂²×C₅	—	8	1	no	—
280	C₂²×C₅	—	8	1	no	—
281	C₂²×C₅	—	8	1	no	—
282	C₂²×C₅	—	8	1	no	—
283	C₂²×C₅	—	8	1	no	—
284	C₂²×C₅	#535	1	1	yes	characteristic
285	C₂²×C₅	#536	1	1	yes	characteristic
286	C₂²×C₅	#536	1	1	yes	characteristic
287	C₂²×C₅	C₂×#135	1	1	yes	characteristic
288	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
289	C₂²×C₅	#575	1	1	yes	characteristic
290	C₂²×C₅	#575	1	1	yes	characteristic
291	C₄×C₅	—	2	2	no	—
292	C₄×C₅	—	2	2	no	—
293	C₄×C₅	—	4	1	no	—
294	C₄×C₅	—	4	1	no	—
295	C₄×C₅	—	4	1	no	—
296	C₄×C₅	—	4	1	no	—
297	C₄×C₅	—	8	2	no	—
298	C₄×C₅	—	8	1	no	—
299	C₄×C₅	—	8	2	no	—
300	C₄×C₅	—	8	1	no	—
301	C₄×C₅	—	8	1	no	—
302	C₄×C₅	#563	1	2	yes	—
303	C₄×C₅	#563	1	2	yes	—
304	C₂⁴	—	2	1	no	—
305	C₂×Q₈	—	4	2	no	—
306	C₂×Q₈	—	4	2	no	—
307	C₂×Q₈	—	4	2	no	—
308	C₂×Q₈	—	4	2	no	—
309	C₂×Q₈	—	4	2	no	—
310	C₂×Q₈	—	4	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
321	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
326	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₂²⋊C₄	—	4	2	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	4	1	no	—
359	C₄²	—	4	1	no	—
360	C₂×C₅	—	16	1	no	—
361	C₂×C₅	#2821	1	1	yes	characteristic
362	C₂×C₅	#3211	1	1	yes	characteristic
363	C₂×C₅	#3213	1	1	yes	characteristic
364	C₂×C₅	#3228	1	1	yes	characteristic
365	C₂×C₅	#3233	1	1	yes	characteristic
366	C₂×C₅	#3235	1	1	yes	characteristic
367	C₂×C₅	#3240	1	1	yes	characteristic
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
376	Q₈	—	8	4	no	—
377	Q₈	—	8	4	no	—
378	D₄	—	4	2	no	—
379	D₄	—	4	2	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	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	C₅×#135	1	2	yes	—
412	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
413	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
414	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
415	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
416	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
417	C₈	—	4	2	no	—
418	C₈	—	4	2	no	—
419	C₅	#32840	1	1	yes	characteristic, direct product factor, Sylow
420	C₂²	—	8	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	C₅×#535	1	1	yes	characteristic
428	C₂²	C₅×#536	1	1	yes	characteristic
429	C₂²	C₅×#536	1	1	yes	characteristic
430	C₂²	C₂×C₅×#135	1	1	yes	characteristic
431	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
432	C₂²	C₅×#575	1	1	yes	characteristic
433	C₂²	C₅×#575	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	8	2	no	—
441	C₄	—	8	2	no	—
442	C₄	—	8	1	no	—
443	C₄	—	8	1	no	—
444	C₄	—	8	1	no	—
445	C₄	C₅×#563	1	2	yes	—
446	C₄	C₅×#563	1	2	yes	—
447	C₂	—	16	1	no	—
448	C₂	C₅×#2821	1	1	yes	characteristic
449	C₂	C₅×#3211	1	1	yes	characteristic
450	C₂	C₅×#3213	1	1	yes	characteristic
451	C₂	C₅×#3228	1	1	yes	characteristic
452	C₂	C₅×#3233	1	1	yes	characteristic
453	C₂	C₅×#3235	1	1	yes	characteristic
454	C₂	C₅×#3240	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
1. C₅×#2862	C₂	semidirect
3. C₅×#2101	C₂	semidirect
5. C₅×#2085	C₂	semidirect
7. C₅×#2058	C₂	semidirect
8. C₅×#2057	C₂	semidirect
11. C₅×#1839	C₂	semidirect
43. #32840	C₅	direct (N × H)
86. #2862	C₂×C₅	semidirect
88. #2101	C₂×C₅	semidirect
90. #2085	C₂×C₅	semidirect
92. #2058	C₂×C₅	semidirect
93. #2057	C₂×C₅	semidirect
96. #1839	C₂×C₅	semidirect
419. C₅	#32840	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×#2862	2
C₅×#2860	2
C₅×#2101	2
C₅×#2092	2
C₅×#2085	2
C₅×#2073	2
C₅×#2058	2
C₅×#2057	2
C₅×#2023	2
C₅×#1839	2
#32840	5

Subgroups — C5×#32840 #11955560

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#32840 #11955560