Subgroups — C₅×#29578 #11952298

Order 1280.

732 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2859	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2293	C₂	1	1	yes	maximal, characteristic
3	C₅×#2099	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2093	C₂	1	1	yes	maximal, characteristic
5	C₅×#2084	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2071	C₂	1	1	yes	maximal, characteristic
7	C₅×#1944	C₂	1	2	yes	maximal, complemented
8	C₅×#1936	C₂	1	2	yes	maximal
9	C₅×#1921	C₂	1	2	yes	maximal, complemented
10	C₅×#1864	C₂	1	2	yes	maximal
11	C₅×#1745	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#125	—	2	1	no	—
13	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂×C₅×#117	—	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	C₂×C₅×#97	C₂²	1	2	yes	—
20	C₅×#390	C₂²	1	1	yes	characteristic
21	C₅×#390	C₂²	1	1	yes	characteristic
22	C₅×#389	—	2	1	no	—
23	C₅×#389	—	2	1	no	—
24	C₅×#389	C₂²	1	1	yes	characteristic
25	C₅×#389	C₂²	1	1	yes	characteristic
26	C₅×#389	C₂²	1	2	yes	—
27	C₅×#389	C₂²	1	2	yes	—
28	C₅×#388	—	2	1	no	—
29	C₅×#388	—	2	1	no	—
30	C₅×#384	C₂²	1	1	yes	characteristic
31	C₅×#384	C₂²	1	1	yes	characteristic
32	C₅×#382	—	2	1	no	—
33	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
35	C₄³×C₅	C₂²	1	1	yes	characteristic
36	C₅×#340	C₂²	1	2	yes	—
37	C₅×#340	C₂²	1	2	yes	—
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	1	yes	characteristic
41	C₅×#336	C₂²	1	1	yes	characteristic
42	C₅×#336	C₂²	1	2	yes	—
43	#29578	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₅	—	2	1	no	—
46	C₂²×C₅×C₈	C₂³	1	2	yes	—
47	C₂²×C₅×C₈	C₂³	1	2	yes	—
48	C₅×#125	—	4	4	no	—
49	C₄×C₅×D₄	—	2	2	no	—
50	C₄×C₅×D₄	—	2	2	no	—
51	C₅×#117	—	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	—	2	1	no	—
58	C₂×C₅×C₄⋊C₄	—	2	2	no	—
59	C₂×C₅×C₄⋊C₄	—	2	2	no	—
60	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
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	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₅×#107	—	2	4	no	—
79	C₅×#106	—	2	4	no	—
80	C₅×#102	—	2	4	no	—
81	C₅×#102	—	2	4	no	—
82	C₅×#97	—	2	4	no	—
83	C₅×#95	—	2	1	no	—
84	C₅×#95	—	2	1	no	—
85	C₅×#95	—	2	1	no	—
86	C₅×#95	—	2	2	no	—
87	C₅×#95	—	2	2	no	—
88	#2859	C₂×C₅	1	1	yes	characteristic, complemented
89	#2293	C₂×C₅	1	1	yes	characteristic
90	#2099	C₂×C₅	1	1	yes	characteristic, complemented
91	#2093	C₂×C₅	1	1	yes	characteristic
92	#2084	C₂×C₅	1	1	yes	characteristic, complemented
93	#2071	C₂×C₅	1	1	yes	characteristic
94	#1944	C₂×C₅	1	2	yes	complemented
95	#1936	C₂×C₅	1	2	yes	—
96	#1921	C₂×C₅	1	2	yes	complemented
97	#1864	C₂×C₅	1	2	yes	—
98	#1745	C₂×C₅	1	1	yes	characteristic, complemented
99	C₂⁴×C₅	—	2	1	no	—
100	C₂×C₅×D₄	—	2	2	no	—
101	C₂×C₅×D₄	—	2	1	no	—
102	C₂×C₅×D₄	—	2	2	no	—
103	C₂×C₅×D₄	#41	1	2	yes	—
104	C₂²×C₄×C₅	—	2	4	no	—
105	C₂²×C₄×C₅	—	2	1	no	—
106	C₂²×C₄×C₅	—	2	1	no	—
107	C₂²×C₄×C₅	—	2	1	no	—
108	C₂²×C₄×C₅	—	2	2	no	—
109	C₂²×C₄×C₅	—	2	2	no	—
110	C₂²×C₄×C₅	—	4	2	no	—
111	C₂²×C₄×C₅	—	4	2	no	—
112	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
119	C₂×C₅×C₈	—	2	2	no	—
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	#41	1	4	yes	—
125	C₅×C₄⋊C₄	—	2	1	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	—	4	2	no	—
133	C₅×C₄⋊C₄	—	4	2	no	—
134	C₅×C₄⋊C₄	—	4	4	no	—
135	C₅×C₄⋊C₄	—	4	4	no	—
136	C₅×C₄⋊C₄	—	4	2	no	—
137	C₅×C₄⋊C₄	—	4	2	no	—
138	C₅×C₄⋊C₄	—	4	2	no	—
139	C₅×C₄⋊C₄	—	4	2	no	—
140	C₅×C₄⋊C₄	#41	1	2	yes	—
141	C₅×C₂²⋊C₄	—	2	4	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	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	—	2	2	no	—
152	C₄²×C₅	—	2	2	no	—
153	C₄²×C₅	—	4	1	no	—
154	C₄²×C₅	—	4	2	no	—
155	C₂×#125	—	2	1	no	—
156	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
157	C₂×#117	—	2	1	no	—
158	C₂×#107	C₂²×C₅	1	2	yes	—
159	C₂×#106	C₂²×C₅	1	2	yes	—
160	C₂×#102	C₂²×C₅	1	2	yes	—
161	C₂×#102	C₂²×C₅	1	2	yes	—
162	C₂×#97	C₂²×C₅	1	2	yes	—
163	#390	C₂²×C₅	1	1	yes	characteristic
164	#390	C₂²×C₅	1	1	yes	characteristic
165	#389	—	2	1	no	—
166	#389	—	2	1	no	—
167	#389	C₂²×C₅	1	1	yes	characteristic
168	#389	C₂²×C₅	1	2	yes	—
169	#389	C₂²×C₅	1	2	yes	—
170	#389	C₂²×C₅	1	1	yes	characteristic
171	#388	—	2	1	no	—
172	#388	—	2	1	no	—
173	#384	C₂²×C₅	1	1	yes	characteristic
174	#384	C₂²×C₅	1	1	yes	characteristic
175	#382	—	2	1	no	—
176	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
177	C₄×C₂²⋊C₄	—	2	1	no	—
178	C₄³	C₂²×C₅	1	1	yes	characteristic
179	#340	C₂²×C₅	1	2	yes	—
180	#340	C₂²×C₅	1	2	yes	—
181	#340	C₂²×C₅	1	2	yes	—
182	#340	C₂²×C₅	1	2	yes	—
183	#336	C₂²×C₅	1	1	yes	characteristic
184	#336	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×D₄	—	2	4	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	2	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	8	no	—
213	C₂×C₄×C₅	—	4	1	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	—	4	2	no	—
216	C₂×C₄×C₅	—	4	2	no	—
217	C₂×C₄×C₅	—	4	1	no	—
218	C₂×C₄×C₅	—	4	1	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	2	no	—
224	C₂×C₄×C₅	—	4	2	no	—
225	C₂×C₄×C₅	—	4	1	no	—
226	C₂×C₄×C₅	—	4	2	no	—
227	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
228	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
229	C₂×C₄×C₅	#137	1	2	yes	—
230	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂×#41	1	2	yes	—
233	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
234	C₅×C₈	—	2	4	no	—
235	C₅×C₈	—	4	2	no	—
236	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
237	C₂³×C₄	—	2	1	no	—
238	C₂²×C₈	C₂³×C₅	1	2	yes	—
239	C₂²×C₈	C₂³×C₅	1	2	yes	—
240	#125	—	4	4	no	—
241	C₄×D₄	—	2	2	no	—
242	C₄×D₄	—	2	2	no	—
243	#117	—	4	4	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	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	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×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	—	2	1	no	—
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	C₅×D₄	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
270	#107	—	2	4	no	—
271	#106	—	2	4	no	—
272	#102	—	2	4	no	—
273	#102	—	2	4	no	—
274	#97	—	2	4	no	—
275	#95	—	2	1	no	—
276	#95	—	2	1	no	—
277	#95	—	2	1	no	—
278	#95	—	2	2	no	—
279	#95	—	2	2	no	—
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	#525	1	1	yes	characteristic
288	C₂²×C₅	#532	1	1	yes	characteristic
289	C₂²×C₅	#536	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	C₂×#137	1	1	yes	characteristic
293	C₂²×C₅	#575	1	1	yes	characteristic
294	C₄×C₅	—	2	2	no	—
295	C₄×C₅	—	2	2	no	—
296	C₄×C₅	—	2	2	no	—
297	C₄×C₅	—	4	2	no	—
298	C₄×C₅	—	4	1	no	—
299	C₄×C₅	—	4	1	no	—
300	C₄×C₅	—	4	1	no	—
301	C₄×C₅	—	8	2	no	—
302	C₄×C₅	—	8	1	no	—
303	C₄×C₅	—	8	2	no	—
304	C₄×C₅	—	8	1	no	—
305	C₄×C₅	#552	1	2	yes	—
306	C₄×C₅	#552	1	2	yes	—
307	C₂⁴	—	2	1	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	C₅×#41	1	2	yes	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	4	2	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	C₅×#41	1	4	yes	—
333	C₄⋊C₄	—	2	1	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	2	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	—	4	4	no	—
342	C₄⋊C₄	—	4	4	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	C₅×#41	1	2	yes	—
349	C₂²⋊C₄	—	2	4	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	C₄²	—	2	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	4	1	no	—
362	C₄²	—	4	2	no	—
363	C₂×C₅	—	8	2	no	—
364	C₂×C₅	#2611	1	1	yes	characteristic
365	C₂×C₅	#3110	1	1	yes	characteristic
366	C₂×C₅	#3115	1	1	yes	characteristic
367	C₂×C₅	#3172	1	1	yes	characteristic
368	C₂×C₅	#3184	1	1	yes	characteristic
369	C₂×C₅	#3234	1	1	yes	characteristic
370	C₂×C₅	#3238	1	1	yes	characteristic
371	C₂³	—	2	2	no	—
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	C₂²×C₅×D₄	1	1	yes	characteristic
379	D₄	—	2	4	no	—
380	D₄	—	4	2	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	2	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	—	4	8	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
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	C₅×#137	1	2	yes	—
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	2	yes	—
418	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
419	C₈	—	2	4	no	—
420	C₈	—	4	2	no	—
421	C₅	#29578	1	1	yes	characteristic, direct product factor, Sylow
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	C₅×#525	1	1	yes	characteristic
430	C₂²	C₅×#532	1	1	yes	characteristic
431	C₂²	C₅×#536	1	1	yes	characteristic
432	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
433	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
434	C₂²	C₂×C₅×#137	1	1	yes	characteristic
435	C₂²	C₅×#575	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	—	4	1	no	—
443	C₄	—	8	2	no	—
444	C₄	—	8	1	no	—
445	C₄	—	8	2	no	—
446	C₄	—	8	1	no	—
447	C₄	C₅×#552	1	2	yes	—
448	C₄	C₅×#552	1	2	yes	—
449	C₂	—	8	2	no	—
450	C₂	C₅×#2611	1	1	yes	characteristic
451	C₂	C₅×#3110	1	1	yes	characteristic
452	C₂	C₅×#3115	1	1	yes	characteristic
453	C₂	C₅×#3172	1	1	yes	characteristic
454	C₂	C₅×#3184	1	1	yes	characteristic
455	C₂	C₅×#3234	1	1	yes	characteristic
456	C₂	C₅×#3238	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×#2859	C₂	semidirect
3. C₅×#2099	C₂	semidirect
5. C₅×#2084	C₂	semidirect
7. C₅×#1944	C₂	semidirect
9. C₅×#1921	C₂	semidirect
11. C₅×#1745	C₂	semidirect
43. #29578	C₅	direct (N × H)
88. #2859	C₂×C₅	semidirect
90. #2099	C₂×C₅	semidirect
92. #2084	C₂×C₅	semidirect
94. #1944	C₂×C₅	semidirect
96. #1921	C₂×C₅	semidirect
98. #1745	C₂×C₅	semidirect
421. C₅	#29578	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×#2859	2
C₅×#2293	2
C₅×#2099	2
C₅×#2093	2
C₅×#2084	2
C₅×#2071	2
C₅×#1944	2
C₅×#1936	2
C₅×#1921	2
C₅×#1864	2
C₅×#1745	2
#29578	5

Subgroups — C5×#29578 #11952298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#29578 #11952298