Subgroups — C₅×#32825 #11955545

Order 1280.

662 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	C₅×#2861	C₂	1	1	yes	maximal, characteristic
2	C₅×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2096	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2093	C₂	1	1	yes	maximal, characteristic
5	C₅×#2072	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2071	C₂	1	1	yes	maximal, characteristic
7	C₅×#2068	C₂	1	2	yes	maximal, complemented
8	C₅×#2065	C₂	1	2	yes	maximal
9	C₅×#2059	C₂	1	2	yes	maximal, complemented
10	C₅×#2042	C₂	1	2	yes	maximal
11	C₅×#1831	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#125	—	2	1	no	—
13	C₂×C₅×#125	C₂²	1	1	yes	characteristic
14	C₂×C₅×#124	C₂²	1	1	yes	characteristic
15	C₂×C₅×#107	C₂²	1	2	yes	—
16	C₂×C₅×#106	C₂²	1	2	yes	—
17	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₅×#103	C₂²	1	2	yes	—
19	C₂×C₅×#103	C₂²	1	2	yes	—
20	C₂×C₅×#102	C₂²	1	2	yes	—
21	C₂×C₅×#102	C₂²	1	2	yes	—
22	C₅×#391	C₂²	1	1	yes	characteristic
23	C₅×#391	C₂²	1	1	yes	characteristic
24	C₅×#390	C₂²	1	1	yes	characteristic
25	C₅×#390	C₂²	1	1	yes	characteristic
26	C₅×#389	—	2	1	no	—
27	C₅×#389	—	2	1	no	—
28	C₅×#389	C₂²	1	2	yes	—
29	C₅×#389	C₂²	1	2	yes	—
30	C₅×#388	—	2	1	no	—
31	C₅×#388	—	2	1	no	—
32	C₅×#388	—	2	1	no	—
33	C₅×#388	—	2	1	no	—
34	C₅×#384	C₂²	1	1	yes	characteristic
35	C₅×#384	C₂²	1	1	yes	characteristic
36	C₅×#382	—	2	1	no	—
37	C₄³×C₅	C₂²	1	1	yes	characteristic
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	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	#32825	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
45	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
46	C₂²×C₅×C₈	C₂³	1	2	yes	—
47	C₂²×C₅×C₈	C₂³	1	2	yes	—
48	C₅×#125	—	4	2	no	—
49	C₅×#125	—	4	4	no	—
50	C₅×#124	—	4	2	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×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×C₅×C₂²⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₅×#107	—	4	2	no	—
77	C₅×#106	—	4	2	no	—
78	C₅×C₄⋊C₈	—	4	2	no	—
79	C₅×#103	—	4	2	no	—
80	C₅×#103	—	4	2	no	—
81	C₅×#102	—	4	2	no	—
82	C₅×#102	—	4	2	no	—
83	C₅×#95	—	2	2	no	—
84	C₅×#95	—	2	2	no	—
85	C₅×#95	—	2	1	no	—
86	C₅×#95	—	2	1	no	—
87	C₅×#95	—	2	1	no	—
88	C₅×#95	—	2	1	no	—
89	#2861	C₂×C₅	1	1	yes	characteristic
90	#2859	C₂×C₅	1	1	yes	characteristic, complemented
91	#2096	C₂×C₅	1	1	yes	characteristic, complemented
92	#2093	C₂×C₅	1	1	yes	characteristic
93	#2072	C₂×C₅	1	1	yes	characteristic, complemented
94	#2071	C₂×C₅	1	1	yes	characteristic
95	#2068	C₂×C₅	1	2	yes	complemented
96	#2065	C₂×C₅	1	2	yes	—
97	#2059	C₂×C₅	1	2	yes	complemented
98	#2042	C₂×C₅	1	2	yes	—
99	#1831	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂⁴×C₅	—	2	1	no	—
101	C₂×C₅×Q₈	—	2	2	no	—
102	C₂×C₅×Q₈	—	2	1	no	—
103	C₂×C₅×Q₈	—	2	2	no	—
104	C₂×C₅×Q₈	—	2	1	no	—
105	C₂×C₅×D₄	—	2	2	no	—
106	C₂×C₅×D₄	—	2	1	no	—
107	C₂×C₅×D₄	—	2	2	no	—
108	C₂×C₅×D₄	—	2	1	no	—
109	C₂²×C₄×C₅	—	2	1	no	—
110	C₂²×C₄×C₅	—	2	1	no	—
111	C₂²×C₄×C₅	—	2	1	no	—
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	C₂×C₅×C₈	—	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	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	4	no	—
137	C₅×C₄⋊C₄	—	4	4	no	—
138	C₅×C₄⋊C₄	—	4	2	no	—
139	C₅×C₄⋊C₄	—	4	2	no	—
140	C₅×C₄⋊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	C₅×C₂²⋊C₄	—	4	2	no	—
146	C₅×C₂²⋊C₄	—	4	2	no	—
147	C₄²×C₅	—	2	2	no	—
148	C₄²×C₅	—	2	2	no	—
149	C₄²×C₅	—	2	2	no	—
150	C₄²×C₅	—	2	2	no	—
151	C₄²×C₅	—	2	1	no	—
152	C₄²×C₅	—	2	2	no	—
153	C₄²×C₅	—	2	1	no	—
154	C₄²×C₅	—	4	1	no	—
155	C₂×#125	—	2	1	no	—
156	C₂×#125	C₂²×C₅	1	1	yes	characteristic
157	C₂×#124	C₂²×C₅	1	1	yes	characteristic
158	C₂×#107	C₂²×C₅	1	2	yes	—
159	C₂×#106	C₂²×C₅	1	2	yes	—
160	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
161	C₂×#103	C₂²×C₅	1	2	yes	—
162	C₂×#103	C₂²×C₅	1	2	yes	—
163	C₂×#102	C₂²×C₅	1	2	yes	—
164	C₂×#102	C₂²×C₅	1	2	yes	—
165	#391	C₂²×C₅	1	1	yes	characteristic
166	#391	C₂²×C₅	1	1	yes	characteristic
167	#390	C₂²×C₅	1	1	yes	characteristic
168	#390	C₂²×C₅	1	1	yes	characteristic
169	#389	—	2	1	no	—
170	#389	—	2	1	no	—
171	#389	C₂²×C₅	1	2	yes	—
172	#389	C₂²×C₅	1	2	yes	—
173	#388	—	2	1	no	—
174	#388	—	2	1	no	—
175	#388	—	2	1	no	—
176	#388	—	2	1	no	—
177	#384	C₂²×C₅	1	1	yes	characteristic
178	#384	C₂²×C₅	1	1	yes	characteristic
179	#382	—	2	1	no	—
180	C₄³	C₂²×C₅	1	1	yes	characteristic
181	#340	C₂²×C₅	1	2	yes	—
182	#340	C₂²×C₅	1	2	yes	—
183	#336	C₂²×C₅	1	2	yes	—
184	#336	C₂²×C₅	1	1	yes	characteristic
185	#336	C₂²×C₅	1	1	yes	characteristic
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	—	4	1	no	—
192	C₂³×C₅	—	4	1	no	—
193	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
194	C₅×Q₈	—	4	2	no	—
195	C₅×Q₈	—	4	2	no	—
196	C₅×D₄	—	4	2	no	—
197	C₅×D₄	—	4	2	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	—	2	1	no	—
213	C₂×C₄×C₅	—	4	1	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	—	4	1	no	—
216	C₂×C₄×C₅	—	4	2	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	1	no	—
223	C₂×C₄×C₅	—	4	2	no	—
224	C₂×C₄×C₅	—	4	2	no	—
225	C₂×C₄×C₅	—	4	1	no	—
226	C₂×C₄×C₅	—	4	1	no	—
227	C₂×C₄×C₅	—	4	2	no	—
228	C₂×C₄×C₅	#135	1	2	yes	—
229	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
230	C₂×C₄×C₅	#137	1	2	yes	—
231	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
232	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
233	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
234	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
235	C₅×C₈	—	4	2	no	—
236	C₅×C₈	—	4	2	no	—
237	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
238	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
239	C₂²×C₈	C₂³×C₅	1	2	yes	—
240	C₂²×C₈	C₂³×C₅	1	2	yes	—
241	#125	—	4	2	no	—
242	#125	—	4	4	no	—
243	#124	—	4	2	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
256	C₂×C₂²⋊C₄	—	2	1	no	—
257	C₂×C₂²⋊C₄	—	2	1	no	—
258	C₂×C₂²⋊C₄	—	2	1	no	—
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	C₂×C₂²⋊C₄	—	2	1	no	—
261	C₂×C₂²⋊C₄	—	2	1	no	—
262	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
263	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
264	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
265	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
269	#107	—	4	2	no	—
270	#106	—	4	2	no	—
271	C₄⋊C₈	—	4	2	no	—
272	#103	—	4	2	no	—
273	#103	—	4	2	no	—
274	#102	—	4	2	no	—
275	#102	—	4	2	no	—
276	#95	—	2	2	no	—
277	#95	—	2	2	no	—
278	#95	—	2	1	no	—
279	#95	—	2	1	no	—
280	#95	—	2	1	no	—
281	#95	—	2	1	no	—
282	C₂²×C₅	—	8	1	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	—	8	1	no	—
288	C₂²×C₅	—	8	1	no	—
289	C₂²×C₅	#535	1	1	yes	characteristic
290	C₂²×C₅	#536	1	1	yes	characteristic
291	C₂²×C₅	#537	1	1	yes	characteristic
292	C₂²×C₅	C₂×#135	1	1	yes	characteristic
293	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
294	C₂²×C₅	C₂×#137	1	1	yes	characteristic
295	C₂²×C₅	#575	1	1	yes	characteristic
296	C₄×C₅	—	2	2	no	—
297	C₄×C₅	—	2	2	no	—
298	C₄×C₅	—	2	2	no	—
299	C₄×C₅	—	4	1	no	—
300	C₄×C₅	—	4	1	no	—
301	C₄×C₅	—	4	1	no	—
302	C₄×C₅	—	8	1	no	—
303	C₄×C₅	—	8	1	no	—
304	C₄×C₅	—	8	2	no	—
305	C₄×C₅	—	8	1	no	—
306	C₄×C₅	—	8	2	no	—
307	C₄×C₅	#562	1	2	yes	—
308	C₄×C₅	#563	1	2	yes	—
309	C₂⁴	—	2	1	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
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	C₂×C₅×D₄	1	1	yes	characteristic
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	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	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	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₄⋊C₄	—	4	4	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₂²⋊C₄	—	4	2	no	—
353	C₂²⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	4	2	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	4	1	no	—
364	C₂×C₅	—	16	1	no	—
365	C₂×C₅	#2820	1	1	yes	characteristic
366	C₂×C₅	#3207	1	1	yes	characteristic
367	C₂×C₅	#3216	1	1	yes	characteristic
368	C₂×C₅	#3232	1	1	yes	characteristic
369	C₂×C₅	#3238	1	1	yes	characteristic
370	C₂×C₅	#3248	1	1	yes	characteristic
371	C₂×C₅	#3251	1	1	yes	characteristic
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	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	C₂²×C₅×D₄	1	1	yes	characteristic
380	Q₈	—	4	2	no	—
381	Q₈	—	4	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	2	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	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	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	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	C₅×#135	1	2	yes	—
415	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
416	C₂×C₄	C₅×#137	1	2	yes	—
417	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
418	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
419	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
420	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
421	C₈	—	4	2	no	—
422	C₈	—	4	2	no	—
423	C₅	#32825	1	1	yes	characteristic, direct product factor, Sylow
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	C₅×#535	1	1	yes	characteristic
432	C₂²	C₅×#536	1	1	yes	characteristic
433	C₂²	C₅×#537	1	1	yes	characteristic
434	C₂²	C₂×C₅×#135	1	1	yes	characteristic
435	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
436	C₂²	C₂×C₅×#137	1	1	yes	characteristic
437	C₂²	C₅×#575	1	1	yes	characteristic
438	C₄	—	2	2	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	4	1	no	—
442	C₄	—	4	1	no	—
443	C₄	—	4	1	no	—
444	C₄	—	8	2	no	—
445	C₄	—	8	1	no	—
446	C₄	—	8	1	no	—
447	C₄	—	8	2	no	—
448	C₄	—	8	1	no	—
449	C₄	C₅×#562	1	2	yes	—
450	C₄	C₅×#563	1	2	yes	—
451	C₂	—	16	1	no	—
452	C₂	C₅×#2820	1	1	yes	characteristic
453	C₂	C₅×#3207	1	1	yes	characteristic
454	C₂	C₅×#3216	1	1	yes	characteristic
455	C₂	C₅×#3232	1	1	yes	characteristic
456	C₂	C₅×#3238	1	1	yes	characteristic
457	C₂	C₅×#3248	1	1	yes	characteristic
458	C₂	C₅×#3251	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×#2096	C₂	semidirect
5. C₅×#2072	C₂	semidirect
7. C₅×#2068	C₂	semidirect
9. C₅×#2059	C₂	semidirect
11. C₅×#1831	C₂	semidirect
43. #32825	C₅	direct (N × H)
90. #2859	C₂×C₅	semidirect
91. #2096	C₂×C₅	semidirect
93. #2072	C₂×C₅	semidirect
95. #2068	C₂×C₅	semidirect
97. #2059	C₂×C₅	semidirect
99. #1831	C₂×C₅	semidirect
423. C₅	#32825	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×#2861	2
C₅×#2859	2
C₅×#2096	2
C₅×#2093	2
C₅×#2072	2
C₅×#2071	2
C₅×#2068	2
C₅×#2065	2
C₅×#2059	2
C₅×#2042	2
C₅×#1831	2
#32825	5

Subgroups — C5×#32825 #11955545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#32825 #11955545