Subgroups — C₅×#17840 #11940560

Order 1280.

594 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2990	C₂	1	2	yes	maximal
2	C₅×#2965	C₂	1	1	yes	maximal, characteristic
3	C₅×#1573	C₂	1	2	yes	maximal, complemented
4	C₅×#1572	C₂	1	2	yes	maximal, complemented
5	C₅×#1571	C₂	1	2	yes	maximal, complemented
6	C₅×#1569	C₂	1	2	yes	maximal, complemented
7	C₅×#1568	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1565	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#335	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₅×#41	C₂²	1	1	yes	characteristic
11	C₅×#446	—	2	2	no	—
12	C₅×#446	C₄	1	1	yes	characteristic
13	C₅×#446	C₄	1	1	yes	characteristic
14	C₅×#436	C₄	1	1	yes	characteristic
15	C₅×#436	C₄	1	1	yes	characteristic
16	C₅×#435	—	2	2	no	—
17	C₅×#435	—	2	2	no	—
18	C₅×#435	C₄	1	2	yes	—
19	C₅×#435	C₄	1	2	yes	—
20	C₅×C₈×D₄	—	2	2	no	—
21	C₅×#432	C₂²	1	2	yes	—
22	C₅×#432	C₂²	1	2	yes	—
23	C₅×#431	C₂²	1	2	yes	—
24	C₅×#431	C₂²	1	2	yes	—
25	C₅×#431	C₂²	1	1	yes	characteristic
26	C₅×#423	C₂²	1	2	yes	—
27	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
28	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
29	C₄×C₅×M₁₆	C₂²	1	2	yes	—
30	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	C₅×#335	C₂²	1	1	yes	characteristic
32	C₅×#335	C₂²	1	1	yes	characteristic
33	C₅×#335	C₂²	1	2	yes	—
34	C₅×#335	C₂²	1	2	yes	—
35	C₅×#335	C₂²	1	1	yes	characteristic
36	C₅×#335	C₂²	1	1	yes	characteristic
37	C₅×#335	C₂²	1	2	yes	—
38	C₅×#334	C₂²	1	2	yes	—
39	C₅×#334	C₂²	1	2	yes	—
40	C₅×#334	C₂²	1	2	yes	—
41	#17840	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₅×#41	Q₈	1	1	yes	characteristic
43	C₂×C₅×M₁₆	—	2	2	no	—
44	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
45	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
46	C₂²×C₅×C₈	—	2	2	no	—
47	C₂²×C₅×C₈	—	2	2	no	—
48	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
50	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
51	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
52	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
53	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
54	C₄×C₅×D₄	D₄	1	2	yes	—
55	C₄×C₅×D₄	D₄	1	1	yes	characteristic
56	C₅×#117	Q₈	1	1	yes	characteristic
57	C₅×#117	Q₈	1	2	yes	—
58	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₅	C₂³	1	2	yes	—
60	C₅×C₄⋊C₈	—	2	2	no	—
61	C₅×C₄⋊C₈	—	2	2	no	—
62	C₅×C₄⋊C₈	—	2	2	no	—
63	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
64	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
65	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
66	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
67	C₅×C₄⋊C₈	C₂³	1	2	yes	—
68	C₅×C₄⋊C₈	C₂³	1	2	yes	—
69	C₅×C₄⋊C₈	C₂³	1	2	yes	—
70	C₅×C₄⋊C₈	C₂³	1	2	yes	—
71	C₅×C₂²⋊C₈	—	2	2	no	—
72	C₅×C₂²⋊C₈	—	2	2	no	—
73	C₅×C₂²⋊C₈	—	2	2	no	—
74	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
75	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
76	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
77	C₅×#97	—	2	2	no	—
78	C₅×#97	—	2	2	no	—
79	C₅×#97	C₂×C₄	1	2	yes	—
80	C₅×#97	C₂×C₄	1	2	yes	—
81	C₄×C₅×C₈	—	2	2	no	—
82	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
83	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
84	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
86	C₄×C₅×C₈	C₂³	1	2	yes	—
87	#2990	C₂×C₅	1	2	yes	—
88	#2965	C₂×C₅	1	1	yes	characteristic
89	#1573	C₂×C₅	1	2	yes	complemented
90	#1572	C₂×C₅	1	2	yes	complemented
91	#1571	C₂×C₅	1	2	yes	complemented
92	#1569	C₂×C₅	1	2	yes	complemented
93	#1568	C₂×C₅	1	1	yes	characteristic, complemented
94	#1565	C₂×C₅	1	2	yes	complemented
95	C₂×#335	C₂×C₅	1	1	yes	characteristic, complemented
96	C₅×#41	—	4	2	no	—
97	C₂×C₅×Q₈	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₅×D₄	C₄⋊C₄	1	2	yes	—
99	C₂×C₅×D₄	C₄⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
106	C₅×M₁₆	—	2	4	no	—
107	C₅×M₁₆	—	4	2	no	—
108	C₅×M₁₆	—	8	2	no	—
109	C₂×C₅×C₈	—	2	2	no	—
110	C₂×C₅×C₈	—	2	2	no	—
111	C₂×C₅×C₈	—	2	2	no	—
112	C₂×C₅×C₈	—	2	2	no	—
113	C₂×C₅×C₈	—	2	2	no	—
114	C₂×C₅×C₈	—	4	1	no	—
115	C₂×C₅×C₈	—	8	2	no	—
116	C₂×C₅×C₈	—	8	2	no	—
117	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
121	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
122	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
123	C₅×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
124	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
125	C₅×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
126	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
127	C₅×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
128	C₅×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
129	C₅×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
130	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₅	C₂²×C₄	1	2	yes	—
132	C₄²×C₅	C₂×D₄	1	2	yes	—
133	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
135	C₄²×C₅	C₂×Q₈	1	2	yes	—
136	C₄²×C₅	C₂⁴	1	1	yes	characteristic
137	C₄×#41	C₂²×C₅	1	1	yes	characteristic
138	#446	—	2	2	no	—
139	#446	C₄×C₅	1	1	yes	characteristic
140	#446	C₄×C₅	1	1	yes	characteristic
141	#436	C₄×C₅	1	1	yes	characteristic
142	#436	C₄×C₅	1	1	yes	characteristic
143	#435	—	2	2	no	—
144	#435	—	2	2	no	—
145	#435	C₄×C₅	1	2	yes	—
146	#435	C₄×C₅	1	2	yes	—
147	C₈×D₄	—	2	2	no	—
148	#432	C₂²×C₅	1	2	yes	—
149	#432	C₂²×C₅	1	2	yes	—
150	#431	C₂²×C₅	1	2	yes	—
151	#431	C₂²×C₅	1	2	yes	—
152	#431	C₂²×C₅	1	1	yes	characteristic
153	#423	C₂²×C₅	1	2	yes	—
154	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
155	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
156	C₄×M₁₆	C₂²×C₅	1	2	yes	—
157	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
158	#335	C₂²×C₅	1	1	yes	characteristic
159	#335	C₂²×C₅	1	1	yes	characteristic
160	#335	C₂²×C₅	1	2	yes	—
161	#335	C₂²×C₅	1	2	yes	—
162	#335	C₂²×C₅	1	1	yes	characteristic
163	#335	C₂²×C₅	1	1	yes	characteristic
164	#335	C₂²×C₅	1	2	yes	—
165	#334	C₂²×C₅	1	2	yes	—
166	#334	C₂²×C₅	1	2	yes	—
167	#334	C₂²×C₅	1	2	yes	—
168	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
169	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₅×Q₈	—	4	1	no	—
171	C₅×D₄	—	2	4	no	—
172	C₅×D₄	—	4	1	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	1	no	—
175	C₂×C₄×C₅	—	2	2	no	—
176	C₂×C₄×C₅	—	2	1	no	—
177	C₂×C₄×C₅	—	2	2	no	—
178	C₂×C₄×C₅	—	2	1	no	—
179	C₂×C₄×C₅	—	2	2	no	—
180	C₂×C₄×C₅	—	2	1	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	4	2	no	—
183	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
185	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
187	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
188	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
192	C₅×C₈	—	2	1	no	—
193	C₅×C₈	—	2	2	no	—
194	C₅×C₈	—	2	1	no	—
195	C₅×C₈	—	2	1	no	—
196	C₅×C₈	—	2	2	no	—
197	C₅×C₈	—	4	2	no	—
198	C₅×C₈	—	4	2	no	—
199	C₅×C₈	—	4	2	no	—
200	C₅×C₈	—	4	2	no	—
201	C₅×C₈	#131	1	2	yes	—
202	C₂×#41	C₅×Q₈	1	1	yes	characteristic
203	C₂×M₁₆	—	2	2	no	—
204	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
205	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
206	C₂²×C₈	—	2	2	no	—
207	C₂²×C₈	—	2	2	no	—
208	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
209	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
210	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
211	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
212	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
213	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
214	C₄×D₄	C₅×D₄	1	2	yes	—
215	C₄×D₄	C₅×D₄	1	1	yes	characteristic
216	#117	C₅×Q₈	1	1	yes	characteristic
217	#117	C₅×Q₈	1	2	yes	—
218	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
219	C₂×C₄²	C₂³×C₅	1	2	yes	—
220	C₄⋊C₈	—	2	2	no	—
221	C₄⋊C₈	—	2	2	no	—
222	C₄⋊C₈	—	2	2	no	—
223	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
224	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
225	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
226	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
227	C₄⋊C₈	C₂³×C₅	1	2	yes	—
228	C₄⋊C₈	C₂³×C₅	1	2	yes	—
229	C₄⋊C₈	C₂³×C₅	1	2	yes	—
230	C₄⋊C₈	C₂³×C₅	1	2	yes	—
231	C₂²⋊C₈	—	2	2	no	—
232	C₂²⋊C₈	—	2	2	no	—
233	C₂²⋊C₈	—	2	2	no	—
234	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
235	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
236	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
237	#97	—	2	2	no	—
238	#97	—	2	2	no	—
239	#97	C₂×C₄×C₅	1	2	yes	—
240	#97	C₂×C₄×C₅	1	2	yes	—
241	C₄×C₈	—	2	2	no	—
242	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
243	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
244	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
245	C₄×C₈	C₂³×C₅	1	2	yes	—
246	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
247	C₂²×C₅	—	2	1	no	—
248	C₂²×C₅	—	2	1	no	—
249	C₂²×C₅	—	2	2	no	—
250	C₂²×C₅	—	2	2	no	—
251	C₂²×C₅	—	2	2	no	—
252	C₂²×C₅	#430	1	2	yes	—
253	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
254	C₄×C₅	—	2	1	no	—
255	C₄×C₅	—	2	2	no	—
256	C₄×C₅	—	2	1	no	—
257	C₄×C₅	—	2	2	no	—
258	C₄×C₅	—	2	1	no	—
259	C₄×C₅	—	2	1	no	—
260	C₄×C₅	—	2	2	no	—
261	C₄×C₅	C₂×#131	1	1	yes	characteristic
262	C₄×C₅	#568	1	1	yes	characteristic
263	C₄×C₅	#576	1	1	yes	characteristic
264	C₄×C₅	#578	1	1	yes	characteristic
265	#41	—	4	2	no	—
266	C₂×Q₈	C₅×C₄⋊C₄	1	1	yes	characteristic
267	C₂×D₄	C₅×C₄⋊C₄	1	2	yes	—
268	C₂×D₄	C₅×C₄⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
270	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
271	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
273	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
275	M₁₆	—	2	4	no	—
276	M₁₆	—	4	2	no	—
277	M₁₆	—	8	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	4	1	no	—
284	C₂×C₈	—	8	2	no	—
285	C₂×C₈	—	8	2	no	—
286	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
287	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
288	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
289	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
290	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
291	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
292	C₄⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
293	C₄⋊C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
294	C₄⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
295	C₄⋊C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
296	C₂²⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
297	C₂²⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
298	C₂²⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
299	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
300	C₄²	C₂²×C₄×C₅	1	2	yes	—
301	C₄²	C₂×C₅×D₄	1	2	yes	—
302	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
303	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
304	C₄²	C₂×C₅×Q₈	1	2	yes	—
305	C₄²	C₂⁴×C₅	1	1	yes	characteristic
306	C₂×C₅	—	2	2	no	—
307	C₂×C₅	—	4	2	no	—
308	C₂×C₅	#2906	1	1	yes	characteristic
309	C₂×C₅	#2913	1	1	yes	characteristic
310	C₂×C₅	C₂×#430	1	1	yes	characteristic
311	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
312	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
313	Q₈	—	4	1	no	—
314	D₄	—	2	4	no	—
315	D₄	—	4	1	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
327	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
328	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
329	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
330	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
331	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
332	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
333	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
334	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
335	C₈	—	2	1	no	—
336	C₈	—	2	2	no	—
337	C₈	—	2	1	no	—
338	C₈	—	2	1	no	—
339	C₈	—	2	2	no	—
340	C₈	—	4	2	no	—
341	C₈	—	4	2	no	—
342	C₈	—	4	2	no	—
343	C₈	—	4	2	no	—
344	C₈	C₅×#131	1	2	yes	—
345	C₅	#17840	1	1	yes	characteristic, direct product factor, Sylow
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	C₅×#430	1	2	yes	—
352	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
353	C₄	—	2	1	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	2	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	2	no	—
360	C₄	C₂×C₅×#131	1	1	yes	characteristic
361	C₄	C₅×#568	1	1	yes	characteristic
362	C₄	C₅×#576	1	1	yes	characteristic
363	C₄	C₅×#578	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	4	2	no	—
366	C₂	C₅×#2906	1	1	yes	characteristic
367	C₂	C₅×#2913	1	1	yes	characteristic
368	C₂	C₂×C₅×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂×C₅×#41	Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#1573	C₂	semidirect
4. C₅×#1572	C₂	semidirect
5. C₅×#1571	C₂	semidirect
6. C₅×#1569	C₂	semidirect
7. C₅×#1568	C₂	semidirect
8. C₅×#1565	C₂	semidirect
9. C₂×C₅×#335	C₂	semidirect
41. #17840	C₅	direct (N × H)
89. #1573	C₂×C₅	semidirect
90. #1572	C₂×C₅	semidirect
91. #1571	C₂×C₅	semidirect
92. #1569	C₂×C₅	semidirect
93. #1568	C₂×C₅	semidirect
94. #1565	C₂×C₅	semidirect
95. C₂×#335	C₂×C₅	semidirect
345. C₅	#17840	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×#2990	2
C₅×#2965	2
C₅×#1573	2
C₅×#1572	2
C₅×#1571	2
C₅×#1569	2
C₅×#1568	2
C₅×#1565	2
C₂×C₅×#335	2
#17840	5

Subgroups — C5×#17840 #11940560

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17840 #11940560