Subgroups — C₅×#22246 #11944966

Order 1280.

790 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#498	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₅×#1990	C₂	1	1	yes	maximal, characteristic
5	C₅×#1990	C₂	1	1	yes	maximal, characteristic
6	C₅×#1920	C₂	1	4	yes	maximal
7	C₅×#1919	C₂	1	4	yes	maximal
8	C₅×#1834	C₂	1	1	yes	maximal, characteristic
9	C₅×#1744	C₂	1	1	yes	maximal, characteristic
10	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₅×Q₈	—	2	1	no	—
13	C₂×C₄×C₅×Q₈	—	2	1	no	—
14	C₅×#498	C₄	1	8	yes	complemented
15	C₂×C₅×#106	C₂²	1	4	yes	—
16	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₅×#391	—	2	1	no	—
19	C₅×#391	—	2	1	no	—
20	C₅×#389	—	2	1	no	—
21	C₅×#389	—	2	1	no	—
22	C₅×#389	C₂²	1	2	yes	—
23	C₅×#389	C₂²	1	2	yes	—
24	C₅×#384	C₂²	1	1	yes	characteristic
25	C₅×#384	C₂²	1	1	yes	characteristic
26	C₄×C₅×C₄⋊C₄	—	2	1	no	—
27	C₄×C₅×C₄⋊C₄	—	2	1	no	—
28	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
29	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
30	C₄³×C₅	C₂²	1	1	yes	characteristic
31	C₅×#340	C₂²	1	4	yes	—
32	C₅×#340	C₂²	1	4	yes	—
33	C₅×#340	C₂²	1	4	yes	—
34	C₅×#336	C₂²	1	2	yes	—
35	C₅×#336	C₂²	1	2	yes	—
36	#22246	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂²×C₅×Q₈	—	2	1	no	—
38	C₂²×C₅×Q₈	—	2	1	no	—
39	C₂²×C₅×C₈	C₂³	1	2	yes	—
40	C₂²×C₅×C₈	C₂³	1	2	yes	—
41	C₅×C₄⋊Q₈	—	2	2	no	—
42	C₅×C₄⋊Q₈	—	2	2	no	—
43	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	—
44	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	—
45	C₄×C₅×Q₈	—	4	4	no	—
46	C₄×C₅×Q₈	—	4	4	no	—
47	C₂×C₅×C₄⋊C₄	—	2	1	no	—
48	C₂×C₅×C₄⋊C₄	—	2	1	no	—
49	C₂×C₅×C₄⋊C₄	—	2	1	no	—
50	C₂×C₅×C₄⋊C₄	—	2	1	no	—
51	C₂×C₅×C₄⋊C₄	—	2	1	no	—
52	C₂×C₅×C₄⋊C₄	—	2	1	no	—
53	C₂×C₅×C₄⋊C₄	—	2	2	no	—
54	C₂×C₅×C₄⋊C₄	—	2	2	no	—
55	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
56	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
57	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
58	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
59	C₂×C₄²×C₅	—	2	2	no	—
60	C₂×C₄²×C₅	—	2	2	no	—
61	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₅×#106	C₂×C₄	1	16	yes	—
69	C₄×C₅×C₈	—	2	2	no	—
70	C₄×C₅×C₈	C₂×C₄	1	4	yes	—
71	C₅×#95	—	2	2	no	—
72	C₅×#95	—	2	2	no	—
73	C₅×#95	—	2	2	no	—
74	C₅×#95	—	2	2	no	—
75	C₂×#498	C₂×C₅	1	1	yes	characteristic
76	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
77	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
78	#1990	C₂×C₅	1	1	yes	characteristic
79	#1990	C₂×C₅	1	1	yes	characteristic
80	#1920	C₂×C₅	1	4	yes	—
81	#1919	C₂×C₅	1	4	yes	—
82	#1834	C₂×C₅	1	1	yes	characteristic
83	#1744	C₂×C₅	1	1	yes	characteristic
84	C₂×C₅×Q₈	—	2	4	no	—
85	C₂×C₅×Q₈	—	2	4	no	—
86	C₂×C₅×Q₈	—	4	2	no	—
87	C₂×C₅×Q₈	—	4	2	no	—
88	C₂×C₅×Q₈	—	4	2	no	—
89	C₂×C₅×Q₈	—	4	2	no	—
90	C₂²×C₄×C₅	—	2	2	no	—
91	C₂²×C₄×C₅	—	2	2	no	—
92	C₂²×C₄×C₅	—	2	2	no	—
93	C₂²×C₄×C₅	—	2	2	no	—
94	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
101	C₂×C₅×C₈	—	2	2	no	—
102	C₂×C₅×C₈	—	2	2	no	—
103	C₂×C₅×C₈	—	2	2	no	—
104	C₂×C₅×C₈	—	2	2	no	—
105	C₂×C₅×C₈	—	2	2	no	—
106	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
107	C₅×C₄⋊C₄	—	2	4	no	—
108	C₅×C₄⋊C₄	—	2	4	no	—
109	C₅×C₄⋊C₄	—	2	2	no	—
110	C₅×C₄⋊C₄	—	2	2	no	—
111	C₅×C₄⋊C₄	—	2	4	no	—
112	C₅×C₄⋊C₄	—	2	4	no	—
113	C₅×C₄⋊C₄	—	4	4	no	—
114	C₅×C₄⋊C₄	—	4	4	no	—
115	C₅×C₄⋊C₄	—	4	2	no	—
116	C₅×C₄⋊C₄	—	4	2	no	—
117	C₅×C₄⋊C₄	—	4	2	no	—
118	C₅×C₄⋊C₄	—	4	2	no	—
119	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
120	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
121	C₄²×C₅	—	2	2	no	—
122	C₄²×C₅	—	2	2	no	—
123	C₄²×C₅	—	2	2	no	—
124	C₄²×C₅	—	2	2	no	—
125	C₄²×C₅	—	2	2	no	—
126	C₄²×C₅	—	4	4	no	—
127	C₄²×C₅	—	4	4	no	—
128	C₄²×C₅	SD₁₆	1	4	yes	—
129	C₄²×C₅	C₂²×C₄	1	2	yes	—
130	C₄²×C₅	#41	1	2	yes	—
131	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
132	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
133	C₂×C₄×Q₈	—	2	1	no	—
134	C₂×C₄×Q₈	—	2	1	no	—
135	#498	C₄×C₅	1	8	yes	complemented
136	C₂×#106	C₂²×C₅	1	4	yes	—
137	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
138	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
139	#391	—	2	1	no	—
140	#391	—	2	1	no	—
141	#389	—	2	1	no	—
142	#389	—	2	1	no	—
143	#389	C₂²×C₅	1	2	yes	—
144	#389	C₂²×C₅	1	2	yes	—
145	#384	C₂²×C₅	1	1	yes	characteristic
146	#384	C₂²×C₅	1	1	yes	characteristic
147	C₄×C₄⋊C₄	—	2	1	no	—
148	C₄×C₄⋊C₄	—	2	1	no	—
149	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
150	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
151	C₄³	C₂²×C₅	1	1	yes	characteristic
152	#340	C₂²×C₅	1	4	yes	—
153	#340	C₂²×C₅	1	4	yes	—
154	#340	C₂²×C₅	1	4	yes	—
155	#336	C₂²×C₅	1	2	yes	—
156	#336	C₂²×C₅	1	2	yes	—
157	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
158	C₅×Q₈	—	4	8	no	—
159	C₅×Q₈	—	4	8	no	—
160	C₂×C₄×C₅	—	2	1	no	—
161	C₂×C₄×C₅	—	2	1	no	—
162	C₂×C₄×C₅	—	2	1	no	—
163	C₂×C₄×C₅	—	2	1	no	—
164	C₂×C₄×C₅	—	2	4	no	—
165	C₂×C₄×C₅	—	2	4	no	—
166	C₂×C₄×C₅	—	2	1	no	—
167	C₂×C₄×C₅	—	2	1	no	—
168	C₂×C₄×C₅	—	2	1	no	—
169	C₂×C₄×C₅	—	2	1	no	—
170	C₂×C₄×C₅	—	2	1	no	—
171	C₂×C₄×C₅	—	2	1	no	—
172	C₂×C₄×C₅	—	4	2	no	—
173	C₂×C₄×C₅	—	4	2	no	—
174	C₂×C₄×C₅	—	4	2	no	—
175	C₂×C₄×C₅	—	4	2	no	—
176	C₂×C₄×C₅	—	4	2	no	—
177	C₂×C₄×C₅	—	4	2	no	—
178	C₂×C₄×C₅	—	4	2	no	—
179	C₂×C₄×C₅	—	4	2	no	—
180	C₂×C₄×C₅	—	4	2	no	—
181	C₂×C₄×C₅	—	4	2	no	—
182	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
183	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
184	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
185	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
186	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
187	C₂×C₄×C₅	#135	1	2	yes	—
188	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
189	C₂×C₄×C₅	#137	1	2	yes	—
190	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
193	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
194	C₅×C₈	—	2	4	no	—
195	C₅×C₈	—	4	2	no	—
196	C₂²×Q₈	—	2	1	no	—
197	C₂²×Q₈	—	2	1	no	—
198	C₂²×C₈	C₂³×C₅	1	2	yes	—
199	C₂²×C₈	C₂³×C₅	1	2	yes	—
200	C₄⋊Q₈	—	2	2	no	—
201	C₄⋊Q₈	—	2	2	no	—
202	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	—
203	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	—
204	C₄×Q₈	—	4	4	no	—
205	C₄×Q₈	—	4	4	no	—
206	C₂×C₄⋊C₄	—	2	1	no	—
207	C₂×C₄⋊C₄	—	2	1	no	—
208	C₂×C₄⋊C₄	—	2	1	no	—
209	C₂×C₄⋊C₄	—	2	1	no	—
210	C₂×C₄⋊C₄	—	2	2	no	—
211	C₂×C₄⋊C₄	—	2	2	no	—
212	C₂×C₄⋊C₄	—	2	1	no	—
213	C₂×C₄⋊C₄	—	2	1	no	—
214	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
215	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
216	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
217	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
218	C₂×C₄²	—	2	2	no	—
219	C₂×C₄²	—	2	2	no	—
220	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
221	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
222	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
223	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
224	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
225	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
226	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
227	#106	C₂×C₄×C₅	1	16	yes	—
228	C₄×C₈	—	2	2	no	—
229	C₄×C₈	C₂×C₄×C₅	1	4	yes	—
230	#95	—	2	2	no	—
231	#95	—	2	2	no	—
232	#95	—	2	2	no	—
233	#95	—	2	2	no	—
234	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
235	C₂²×C₅	#536	1	1	yes	characteristic
236	C₂²×C₅	#536	1	1	yes	characteristic
237	C₂²×C₅	C₂²×SD₁₆	1	1	yes	characteristic
238	C₂²×C₅	C₂×#135	1	1	yes	characteristic
239	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
240	C₂²×C₅	C₂×#137	1	1	yes	characteristic
241	C₄×C₅	—	2	2	no	—
242	C₄×C₅	—	2	2	no	—
243	C₄×C₅	—	4	4	no	—
244	C₄×C₅	—	4	4	no	—
245	C₄×C₅	—	4	1	no	—
246	C₄×C₅	—	4	1	no	—
247	C₄×C₅	—	8	2	no	—
248	C₄×C₅	—	8	2	no	—
249	C₄×C₅	C₄×SD₁₆	1	4	yes	—
250	C₄×C₅	#440	1	4	yes	—
251	C₄×C₅	#519	1	2	yes	—
252	C₄×C₅	#541	1	2	yes	—
253	C₂×Q₈	—	2	4	no	—
254	C₂×Q₈	—	2	4	no	—
255	C₂×Q₈	—	4	2	no	—
256	C₂×Q₈	—	4	2	no	—
257	C₂×Q₈	—	4	2	no	—
258	C₂×Q₈	—	4	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
264	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
265	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
266	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
269	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	—	2	4	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	—	2	4	no	—
281	C₄⋊C₄	—	2	4	no	—
282	C₄⋊C₄	—	4	4	no	—
283	C₄⋊C₄	—	4	4	no	—
284	C₄⋊C₄	—	4	2	no	—
285	C₄⋊C₄	—	4	2	no	—
286	C₄⋊C₄	—	4	2	no	—
287	C₄⋊C₄	—	4	2	no	—
288	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
289	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
290	C₄²	—	2	2	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	2	2	no	—
293	C₄²	—	2	2	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	4	4	no	—
296	C₄²	—	4	4	no	—
297	C₄²	C₅×SD₁₆	1	4	yes	—
298	C₄²	C₂²×C₄×C₅	1	2	yes	—
299	C₄²	C₅×#41	1	2	yes	—
300	C₂×C₅	#2327	1	1	yes	characteristic
301	C₂×C₅	C₂×C₄×SD₁₆	1	1	yes	characteristic
302	C₂×C₅	C₂×#440	1	1	yes	characteristic
303	C₂×C₅	#3227	1	1	yes	characteristic
304	C₂×C₅	#3228	1	1	yes	characteristic
305	C₂×C₅	#3229	1	1	yes	characteristic
306	C₂×C₅	#3231	1	1	yes	characteristic
307	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
308	Q₈	—	4	8	no	—
309	Q₈	—	4	8	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
333	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
334	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
335	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
336	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
337	C₂×C₄	C₅×#135	1	2	yes	—
338	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
339	C₂×C₄	C₅×#137	1	2	yes	—
340	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
341	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
342	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
343	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
344	C₈	—	2	4	no	—
345	C₈	—	4	2	no	—
346	C₅	#22246	1	1	yes	characteristic, direct product factor, Sylow
347	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
348	C₂²	C₅×#536	1	1	yes	characteristic
349	C₂²	C₅×#536	1	1	yes	characteristic
350	C₂²	C₂²×C₅×SD₁₆	1	1	yes	characteristic
351	C₂²	C₂×C₅×#135	1	1	yes	characteristic
352	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
353	C₂²	C₂×C₅×#137	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	—	4	4	no	—
357	C₄	—	4	4	no	—
358	C₄	—	4	1	no	—
359	C₄	—	4	1	no	—
360	C₄	—	8	2	no	—
361	C₄	—	8	2	no	—
362	C₄	C₄×C₅×SD₁₆	1	4	yes	—
363	C₄	C₅×#440	1	4	yes	—
364	C₄	C₅×#519	1	2	yes	—
365	C₄	C₅×#541	1	2	yes	—
366	C₂	C₅×#2327	1	1	yes	characteristic
367	C₂	C₂×C₄×C₅×SD₁₆	1	1	yes	characteristic
368	C₂	C₂×C₅×#440	1	1	yes	characteristic
369	C₂	C₅×#3227	1	1	yes	characteristic
370	C₂	C₅×#3228	1	1	yes	characteristic
371	C₂	C₅×#3229	1	1	yes	characteristic
372	C₂	C₅×#3231	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
LCS	G ▷ C₂×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
14. C₅×#498	C₄	semidirect
36. #22246	C₅	direct (N × H)
135. #498	C₄×C₅	semidirect
346. C₅	#22246	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×#498	2
C₄×C₅×C₄⋊Q₈	2
C₅×#1990	2
C₅×#1920	2
C₅×#1919	2
C₅×#1834	2
C₅×#1744	2
#22246	5

Subgroups — C5×#22246 #11944966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22246 #11944966