Subgroups — C₅×#19280 #11942000

Order 1280.

766 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3169	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3036	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1701	C₂	1	4	yes	maximal, complemented
5	C₅×#1693	C₂	1	2	yes	maximal, complemented
6	C₅×#1687	C₂	1	2	yes	maximal, complemented
7	C₅×#1566	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1547	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×AGL(1,ℤ/8)	—	2	2	no	—
10	C₂²×C₅×M₁₆	—	2	1	no	—
11	C₅×#532	C₂²	1	2	yes	—
12	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₅×#500	C₂²	1	1	yes	characteristic, complemented
14	C₅×#493	C₂²	1	1	yes	characteristic, complemented
15	C₅×#486	C₂²	1	2	yes	complemented
16	C₅×#466	—	2	1	no	—
17	C₅×#466	—	2	1	no	—
18	C₅×#463	—	2	4	no	—
19	C₅×#461	C₂²	1	4	yes	—
20	C₅×#459	C₂²	1	4	yes	—
21	C₄×C₅×D₈	—	2	1	no	—
22	C₄×C₅×D₈	—	2	1	no	—
23	C₅×#436	—	2	1	no	—
24	C₅×#436	—	2	1	no	—
25	C₅×#436	C₂²	1	2	yes	—
26	C₅×#436	C₂²	1	2	yes	—
27	C₅×#423	C₂²	1	2	yes	—
28	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₅×#417	—	2	2	no	—
30	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
31	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₅×#334	C₂²	1	2	yes	complemented
33	C₅×#334	C₂²	1	2	yes	complemented
34	C₅×#332	C₂²	1	4	yes	complemented
35	C₅×#331	C₂²	1	4	yes	complemented
36	#19280	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂×C₅×#41	—	2	2	no	—
38	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₅	—	2	1	no	—
40	C₅×AGL(1,ℤ/8)	—	4	8	no	—
41	C₂×C₅×SD₁₆	—	2	4	no	—
42	C₂×C₅×D₈	—	2	4	no	—
43	C₂×C₅×D₈	—	2	1	no	—
44	C₂×C₅×D₈	—	2	1	no	—
45	C₂×C₅×M₁₆	—	2	2	no	—
46	C₂×C₅×M₁₆	—	2	2	no	—
47	C₂×C₅×M₁₆	—	2	2	no	—
48	C₂×C₅×M₁₆	—	4	4	no	—
49	C₂²×C₅×C₈	—	2	1	no	—
50	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
51	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
52	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
53	C₅×#127	C₂³	1	2	yes	—
54	C₅×#124	—	2	2	no	—
55	C₅×#121	—	2	2	no	—
56	C₅×#121	—	2	2	no	—
57	C₄×C₅×D₄	—	2	1	no	—
58	C₄×C₅×D₄	—	2	2	no	—
59	C₄×C₅×D₄	—	2	1	no	—
60	C₄×C₅×D₄	—	2	2	no	—
61	C₄×C₅×D₄	D₄	1	2	yes	—
62	C₄×C₅×D₄	C₂³	1	2	yes	—
63	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
64	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
65	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₅×#107	—	2	1	no	—
67	C₅×#107	—	2	1	no	—
68	C₅×C₄⋊C₈	—	2	1	no	—
69	C₅×C₄⋊C₈	—	2	2	no	—
70	C₅×C₄⋊C₈	C₂³	1	2	yes	—
71	C₅×C₄⋊C₈	C₂³	1	4	yes	—
72	C₅×#103	—	2	4	no	—
73	C₅×#102	—	2	2	no	—
74	C₅×#102	—	2	2	no	—
75	C₅×#102	—	2	4	no	—
76	C₅×C₂²⋊C₈	—	2	2	no	—
77	C₅×C₂²⋊C₈	—	2	2	no	—
78	C₄×C₅×C₈	D₄	1	1	yes	characteristic
79	C₄×C₅×C₈	D₄	1	1	yes	characteristic
80	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
81	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
82	#3169	C₂×C₅	1	1	yes	characteristic, complemented
83	#3036	C₂×C₅	1	2	yes	complemented
84	C₂×#436	C₂×C₅	1	1	yes	characteristic, complemented
85	#1701	C₂×C₅	1	4	yes	complemented
86	#1693	C₂×C₅	1	2	yes	complemented
87	#1687	C₂×C₅	1	2	yes	complemented
88	#1566	C₂×C₅	1	1	yes	characteristic, complemented
89	#1547	C₂×C₅	1	2	yes	complemented
90	C₂⁴×C₅	—	2	1	no	—
91	C₅×#41	—	4	4	no	—
92	C₅×#41	—	4	4	no	—
93	C₂×C₅×Q₈	—	2	2	no	—
94	C₂×C₅×D₄	—	2	1	no	—
95	C₂×C₅×D₄	—	2	4	no	—
96	C₂×C₅×D₄	—	2	2	no	—
97	C₂×C₅×D₄	—	2	2	no	—
98	C₂×C₅×D₄	—	2	2	no	—
99	C₂×C₅×D₄	—	4	2	no	—
100	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₅	—	2	1	no	—
102	C₂²×C₄×C₅	—	2	2	no	—
103	C₂²×C₄×C₅	—	2	2	no	—
104	C₂²×C₄×C₅	—	4	2	no	—
105	C₂²×C₄×C₅	—	4	2	no	—
106	C₂²×C₄×C₅	—	4	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	#41	1	1	yes	characteristic
110	C₅×SD₁₆	—	4	8	no	—
111	C₅×D₈	—	4	2	no	—
112	C₅×D₈	—	4	8	no	—
113	C₅×D₈	—	4	2	no	—
114	C₅×M₁₆	—	4	4	no	—
115	C₅×M₁₆	—	4	4	no	—
116	C₅×M₁₆	—	4	4	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	—	2	2	no	—
119	C₂×C₅×C₈	—	2	4	no	—
120	C₂×C₅×C₈	—	4	1	no	—
121	C₂×C₅×C₈	—	4	2	no	—
122	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
123	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
124	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
125	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
126	C₅×C₄⋊C₄	—	2	1	no	—
127	C₅×C₄⋊C₄	—	2	2	no	—
128	C₅×C₄⋊C₄	—	2	2	no	—
129	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
130	C₅×C₂²⋊C₄	—	2	2	no	—
131	C₅×C₂²⋊C₄	—	2	2	no	—
132	C₅×C₂²⋊C₄	—	4	2	no	—
133	C₅×C₂²⋊C₄	—	4	2	no	—
134	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₅	#41	1	1	yes	characteristic
137	C₄²×C₅	C₂⁴	1	1	yes	characteristic
138	C₂×AGL(1,ℤ/8)	—	2	2	no	—
139	C₂²×M₁₆	—	2	1	no	—
140	#532	C₂²×C₅	1	2	yes	—
141	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
142	#500	C₂²×C₅	1	1	yes	characteristic, complemented
143	#493	C₂²×C₅	1	1	yes	characteristic, complemented
144	#486	C₂²×C₅	1	2	yes	complemented
145	#466	—	2	1	no	—
146	#466	—	2	1	no	—
147	#463	—	2	4	no	—
148	#461	C₂²×C₅	1	4	yes	—
149	#459	C₂²×C₅	1	4	yes	—
150	C₄×D₈	—	2	1	no	—
151	C₄×D₈	—	2	1	no	—
152	#436	—	2	1	no	—
153	#436	—	2	1	no	—
154	#436	C₂²×C₅	1	2	yes	—
155	#436	C₂²×C₅	1	2	yes	—
156	#423	C₂²×C₅	1	2	yes	—
157	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
158	#417	—	2	2	no	—
159	C₂×C₂²⋊C₈	—	2	1	no	—
160	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
161	#334	C₂²×C₅	1	2	yes	complemented
162	#334	C₂²×C₅	1	2	yes	complemented
163	#332	C₂²×C₅	1	4	yes	complemented
164	#331	C₂²×C₅	1	4	yes	complemented
165	C₂³×C₅	—	2	2	no	—
166	C₂³×C₅	—	4	2	no	—
167	C₂³×C₅	—	4	2	no	—
168	C₂³×C₅	—	4	2	no	—
169	C₂³×C₅	—	4	2	no	—
170	C₂³×C₅	#121	1	1	yes	characteristic
171	C₅×Q₈	—	4	2	no	—
172	C₅×Q₈	—	4	2	no	—
173	C₅×D₄	—	2	4	no	—
174	C₅×D₄	—	4	2	no	—
175	C₅×D₄	—	4	2	no	—
176	C₅×D₄	—	4	2	no	—
177	C₅×D₄	—	4	2	no	—
178	C₅×D₄	—	4	2	no	—
179	C₅×D₄	—	8	2	no	—
180	C₅×D₄	—	8	4	no	—
181	C₂×C₄×C₅	—	2	1	no	—
182	C₂×C₄×C₅	—	2	1	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	4	1	no	—
185	C₂×C₄×C₅	—	4	4	no	—
186	C₂×C₄×C₅	—	4	2	no	—
187	C₂×C₄×C₅	—	4	2	no	—
188	C₂×C₄×C₅	—	4	2	no	—
189	C₂×C₄×C₅	—	4	2	no	—
190	C₂×C₄×C₅	—	8	4	no	—
191	C₂×C₄×C₅	#121	1	1	yes	characteristic
192	C₂×C₄×C₅	#121	1	1	yes	characteristic
193	C₂×C₄×C₅	#121	1	1	yes	characteristic
194	C₂×C₄×C₅	AGL(1,ℤ/8)	1	4	yes	—
195	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
198	C₅×C₈	—	2	1	no	—
199	C₅×C₈	—	2	1	no	—
200	C₅×C₈	—	2	1	no	—
201	C₅×C₈	—	4	2	no	—
202	C₅×C₈	—	4	4	no	—
203	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	complemented
204	C₂×#41	—	2	2	no	—
205	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
206	C₂³×C₄	—	2	1	no	—
207	AGL(1,ℤ/8)	—	4	8	no	—
208	C₂×SD₁₆	—	2	4	no	—
209	C₂×D₈	—	2	4	no	—
210	C₂×D₈	—	2	1	no	—
211	C₂×D₈	—	2	1	no	—
212	C₂×M₁₆	—	2	2	no	—
213	C₂×M₁₆	—	2	2	no	—
214	C₂×M₁₆	—	2	2	no	—
215	C₂×M₁₆	—	4	4	no	—
216	C₂²×C₈	—	2	1	no	—
217	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
218	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
219	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
220	#127	C₂³×C₅	1	2	yes	—
221	#124	—	2	2	no	—
222	#121	—	2	2	no	—
223	#121	—	2	2	no	—
224	C₄×D₄	—	2	1	no	—
225	C₄×D₄	—	2	2	no	—
226	C₄×D₄	—	2	1	no	—
227	C₄×D₄	—	2	2	no	—
228	C₄×D₄	C₅×D₄	1	2	yes	—
229	C₄×D₄	C₂³×C₅	1	2	yes	—
230	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
231	C₂×C₂²⋊C₄	—	2	1	no	—
232	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
233	#107	—	2	1	no	—
234	#107	—	2	1	no	—
235	C₄⋊C₈	—	2	1	no	—
236	C₄⋊C₈	—	2	2	no	—
237	C₄⋊C₈	C₂³×C₅	1	2	yes	—
238	C₄⋊C₈	C₂³×C₅	1	4	yes	—
239	#103	—	2	4	no	—
240	#102	—	2	2	no	—
241	#102	—	2	2	no	—
242	#102	—	2	4	no	—
243	C₂²⋊C₈	—	2	2	no	—
244	C₂²⋊C₈	—	2	2	no	—
245	C₄×C₈	C₅×D₄	1	1	yes	characteristic
246	C₄×C₈	C₅×D₄	1	1	yes	characteristic
247	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
248	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
249	C₂²×C₅	—	2	1	no	—
250	C₂²×C₅	—	2	1	no	—
251	C₂²×C₅	—	4	2	no	—
252	C₂²×C₅	—	4	2	no	—
253	C₂²×C₅	—	4	2	no	—
254	C₂²×C₅	—	8	4	no	—
255	C₂²×C₅	—	8	2	no	—
256	C₂²×C₅	—	8	2	no	—
257	C₂²×C₅	—	8	2	no	—
258	C₂²×C₅	#469	1	2	yes	—
259	C₂²×C₅	C₂×#121	1	1	yes	characteristic
260	C₄×C₅	—	2	1	no	—
261	C₄×C₅	—	2	1	no	—
262	C₄×C₅	—	2	1	no	—
263	C₄×C₅	—	4	2	no	—
264	C₄×C₅	—	8	2	no	—
265	C₄×C₅	#469	1	2	yes	—
266	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
267	C₄×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
268	C₄×C₅	#575	1	1	yes	characteristic
269	C₂⁴	—	2	1	no	—
270	#41	—	4	4	no	—
271	#41	—	4	4	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
288	C₂²×C₄	C₅×#41	1	1	yes	characteristic
289	SD₁₆	—	4	8	no	—
290	D₈	—	4	2	no	—
291	D₈	—	4	8	no	—
292	D₈	—	4	2	no	—
293	M₁₆	—	4	4	no	—
294	M₁₆	—	4	4	no	—
295	M₁₆	—	4	4	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	2	no	—
301	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
302	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
303	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
304	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₂²⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	4	2	no	—
313	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
314	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
315	C₄²	C₅×#41	1	1	yes	characteristic
316	C₄²	C₂⁴×C₅	1	1	yes	characteristic
317	C₂×C₅	—	2	2	no	—
318	C₂×C₅	—	8	2	no	—
319	C₂×C₅	—	16	2	no	—
320	C₂×C₅	#3036	1	1	yes	characteristic
321	C₂×C₅	C₂×#469	1	1	yes	characteristic
322	C₂×C₅	#3067	1	1	yes	characteristic
323	C₂³	—	2	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	C₅×#121	1	1	yes	characteristic
329	Q₈	—	4	2	no	—
330	Q₈	—	4	2	no	—
331	D₄	—	2	4	no	—
332	D₄	—	4	2	no	—
333	D₄	—	4	2	no	—
334	D₄	—	4	2	no	—
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	8	2	no	—
338	D₄	—	8	4	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	8	4	no	—
349	C₂×C₄	C₅×#121	1	1	yes	characteristic
350	C₂×C₄	C₅×#121	1	1	yes	characteristic
351	C₂×C₄	C₅×#121	1	1	yes	characteristic
352	C₂×C₄	C₅×AGL(1,ℤ/8)	1	4	yes	—
353	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
354	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
355	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
356	C₈	—	2	1	no	—
357	C₈	—	2	1	no	—
358	C₈	—	2	1	no	—
359	C₈	—	4	2	no	—
360	C₈	—	4	4	no	—
361	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	complemented
362	C₅	#19280	1	1	yes	characteristic, direct product factor, Sylow
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	8	4	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	C₅×#469	1	2	yes	—
373	C₂²	C₂×C₅×#121	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	8	2	no	—
379	C₄	C₅×#469	1	2	yes	—
380	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
381	C₄	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
382	C₄	C₅×#575	1	1	yes	characteristic
383	C₂	—	2	2	no	—
384	C₂	—	8	2	no	—
385	C₂	—	16	2	no	—
386	C₂	C₅×#3036	1	1	yes	characteristic
387	C₂	C₂×C₅×#469	1	1	yes	characteristic
388	C₂	C₅×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3169	C₂	semidirect
2. C₅×#3036	C₂	semidirect
3. C₂×C₅×#436	C₂	semidirect
4. C₅×#1701	C₂	semidirect
5. C₅×#1693	C₂	semidirect
6. C₅×#1687	C₂	semidirect
7. C₅×#1566	C₂	semidirect
8. C₅×#1547	C₂	semidirect
13. C₅×#500	C₂²	semidirect
14. C₅×#493	C₂²	semidirect
15. C₅×#486	C₂²	semidirect
32. C₅×#334	C₂²	semidirect
33. C₅×#334	C₂²	semidirect
34. C₅×#332	C₂²	semidirect
35. C₅×#331	C₂²	semidirect
36. #19280	C₅	direct (N × H)
82. #3169	C₂×C₅	semidirect
83. #3036	C₂×C₅	semidirect
84. C₂×#436	C₂×C₅	semidirect
85. #1701	C₂×C₅	semidirect
86. #1693	C₂×C₅	semidirect
87. #1687	C₂×C₅	semidirect
88. #1566	C₂×C₅	semidirect
89. #1547	C₂×C₅	semidirect
142. #500	C₂²×C₅	semidirect
143. #493	C₂²×C₅	semidirect
144. #486	C₂²×C₅	semidirect
161. #334	C₂²×C₅	semidirect
162. #334	C₂²×C₅	semidirect
163. #332	C₂²×C₅	semidirect
164. #331	C₂²×C₅	semidirect
203. C₅×C₈	AGL(1,ℤ/8)	semidirect
361. C₈	C₅×AGL(1,ℤ/8)	semidirect
362. C₅	#19280	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×#3169	2
C₅×#3036	2
C₂×C₅×#436	2
C₅×#1701	2
C₅×#1693	2
C₅×#1687	2
C₅×#1566	2
C₅×#1547	2
#19280	5

Subgroups — C5×#19280 #11942000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19280 #11942000