Subgroups — C₅×#66138 #13106958

Order 1600.

928 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4099	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×C₂²⋊Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4085	C₂	1	4	yes	maximal, complemented
6	C₅×#4083	C₂	1	2	yes	maximal, complemented
7	C₅×#4081	C₂	1	2	yes	maximal, complemented
8	C₅×#4075	C₂	1	2	yes	maximal, complemented
9	C₂⁴×C₅²	C₂²	1	1	yes	characteristic
10	C₂⁴×C₅²	C₂²	1	1	yes	characteristic, complemented
11	C₂³×C₅×D₅	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₅²×D₄	—	2	4	no	—
13	C₂×C₅²×D₄	C₂²	1	2	yes	—
14	C₂×C₅²×D₄	C₂²	1	2	yes	complemented
15	C₂²×C₄×C₅²	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₅×C₂²⋊D₅	—	2	4	no	—
17	C₂×C₅×C₂²⋊D₅	C₂²	1	2	yes	—
18	C₂×C₅×C₂²⋊D₅	C₂²	1	2	yes	complemented
19	C₂×C₅×C₂²⋊D₅	C₂²	1	4	yes	complemented
20	C₂²×C₅×Dic₅	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₅×Dic₅	C₂²	1	2	yes	complemented
22	C₅×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
23	C₅×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
24	C₅×C₂²⋊Dic₅	C₂²	1	4	yes	complemented
25	C₅×#685	C₂²	1	4	yes	complemented
26	C₅×#683	C₂²	1	4	yes	complemented
27	C₅×#534	—	5	1	no	maximal
28	#66138	C₅	1	1	yes	maximal, characteristic, direct product factor
29	C₂³×C₅²	—	2	2	no	—
30	C₂³×C₅²	—	4	2	no	—
31	C₂³×C₅²	—	4	2	no	—
32	C₂³×C₅²	D₄	1	4	yes	complemented
33	C₂³×C₅²	C₂³	1	2	yes	—
34	C₂³×C₅²	C₂³	1	1	yes	characteristic
35	C₂³×C₅²	C₂³	1	1	yes	characteristic
36	C₂³×C₅²	C₂³	1	1	yes	characteristic
37	C₂²×C₅×D₅	—	2	2	no	—
38	C₂²×C₅×D₅	—	4	2	no	—
39	C₂²×C₅×D₅	C₂³	1	2	yes	—
40	C₅²×D₄	—	2	4	no	—
41	C₅²×D₄	—	2	4	no	—
42	C₂×C₄×C₅²	—	2	2	no	—
43	C₂×C₄×C₅²	C₂³	1	2	yes	—
44	C₅×C₂²⋊D₅	—	2	4	no	—
45	C₅×C₂²⋊D₅	—	2	4	no	—
46	C₅×C₂²⋊D₅	—	4	4	no	—
47	C₂×C₅×Dic₅	—	2	2	no	—
48	C₂×C₅×Dic₅	—	4	2	no	—
49	C₂×C₅×Dic₅	C₂³	1	2	yes	—
50	C₂×C₅×Dic₅	C₂³	1	4	yes	—
51	C₂²×C₅×D₄	—	2	2	no	—
52	C₂²×C₅×D₄	—	5	1	no	—
53	C₂²×C₅×D₄	D₅	1	1	yes	characteristic, complemented
54	C₂²×C₅×D₄	C₂×C₅	1	1	yes	characteristic, complemented
55	C₂²×C₂²⋊D₅	C₂×C₅	1	1	yes	characteristic, complemented
56	C₅×#123	—	5	2	no	—
57	C₅×#123	—	5	2	no	—
58	C₅×#121	—	5	4	no	—
59	C₅×#120	—	5	2	no	—
60	C₅×#120	—	5	2	no	—
61	C₂×C₅×C₂²⋊C₄	—	5	1	no	—
62	#4099	C₂×C₅	1	2	yes	complemented
63	C₂×C₂²⋊Dic₅	C₂×C₅	1	1	yes	characteristic, complemented
64	#4085	C₂×C₅	1	4	yes	complemented
65	#4083	C₂×C₅	1	2	yes	complemented
66	#4081	C₂×C₅	1	2	yes	complemented
67	#4075	C₂×C₅	1	2	yes	complemented
68	C₂²×C₅²	—	2	2	no	—
69	C₂²×C₅²	—	2	2	no	—
70	C₂²×C₅²	—	2	2	no	—
71	C₂²×C₅²	—	2	2	no	—
72	C₂²×C₅²	—	2	4	no	—
73	C₂²×C₅²	—	4	4	no	—
74	C₂²×C₅²	—	4	4	no	—
75	C₂²×C₅²	C₂×D₄	1	2	yes	—
76	C₂²×C₅²	C₂×D₄	1	2	yes	—
77	C₂²×C₅²	C₂×D₄	1	2	yes	—
78	C₂²×C₅²	C₂⁴	1	1	yes	characteristic
79	C₂×C₅×D₅	—	2	2	no	—
80	C₂×C₅×D₅	—	2	4	no	—
81	C₂×C₅×D₅	—	4	4	no	—
82	C₄×C₅²	—	2	2	no	—
83	C₅×Dic₅	—	2	2	no	—
84	C₅×Dic₅	—	2	4	no	—
85	C₂⁴×C₅	—	2	2	no	—
86	C₂⁴×C₅	—	2	2	no	—
87	C₂⁴×C₅	—	5	1	no	—
88	C₂⁴×C₅	C₂×D₅	1	1	yes	characteristic
89	C₂⁴×C₅	C₂×D₅	1	1	yes	characteristic, complemented
90	C₂⁴×C₅	C₂²×C₅	1	1	yes	characteristic
91	C₂⁴×C₅	C₂²×C₅	1	1	yes	characteristic, complemented
92	C₂³×D₅	C₂²×C₅	1	1	yes	characteristic, complemented
93	C₂×C₅×D₄	—	2	16	no	—
94	C₂×C₅×D₄	—	2	4	no	—
95	C₂×C₅×D₄	—	2	4	no	—
96	C₂×C₅×D₄	—	2	4	no	—
97	C₂×C₅×D₄	—	2	4	no	—
98	C₂×C₅×D₄	—	5	2	no	—
99	C₂×C₅×D₄	—	5	2	no	—
100	C₂×C₅×D₄	—	5	4	no	—
101	C₂×C₅×D₄	—	10	4	no	—
102	C₂×C₅×D₄	C₂×D₅	1	2	yes	—
103	C₂×C₅×D₄	C₂×D₅	1	2	yes	complemented
104	C₂×C₅×D₄	C₂²×C₅	1	2	yes	—
105	C₂×C₅×D₄	C₂²×C₅	1	2	yes	complemented
106	C₂²×C₄×C₅	—	2	2	no	—
107	C₂²×C₄×C₅	—	5	1	no	—
108	C₂²×C₄×C₅	—	5	2	no	—
109	C₂²×C₄×C₅	C₂×D₅	1	1	yes	characteristic, complemented
110	C₂²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic, complemented
111	C₂×C₂²⋊D₅	—	2	4	no	—
112	C₂×C₂²⋊D₅	C₂²×C₅	1	2	yes	—
113	C₂×C₂²⋊D₅	C₂²×C₅	1	2	yes	complemented
114	C₂×C₂²⋊D₅	C₂²×C₅	1	4	yes	complemented
115	C₂²×Dic₅	C₂²×C₅	1	1	yes	characteristic, complemented
116	C₂²×Dic₅	C₂²×C₅	1	2	yes	complemented
117	C₅×C₄⋊C₄	—	5	4	no	—
118	C₅×C₂²⋊C₄	—	5	2	no	—
119	C₅×C₂²⋊C₄	—	5	2	no	—
120	C₅×C₂²⋊C₄	—	5	4	no	—
121	C₅×C₂²⋊C₄	—	5	4	no	—
122	C₂²⋊Dic₅	C₂²×C₅	1	2	yes	complemented
123	C₂²⋊Dic₅	C₂²×C₅	1	2	yes	complemented
124	C₂²⋊Dic₅	C₂²×C₅	1	4	yes	complemented
125	#685	C₂²×C₅	1	4	yes	complemented
126	#683	C₂²×C₅	1	4	yes	complemented
127	#534	—	5	1	no	Sylow
128	C₂×C₅²	—	2	2	no	—
129	C₂×C₅²	—	2	2	no	—
130	C₂×C₅²	—	2	2	no	—
131	C₂×C₅²	—	4	2	no	—
132	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
133	C₂×C₅²	H(5,𝔽₂)	1	2	yes	—
134	C₅×D₅	—	4	2	no	—
135	C₂³×C₅	—	2	8	no	—
136	C₂³×C₅	—	2	2	no	—
137	C₂³×C₅	—	2	2	no	—
138	C₂³×C₅	—	2	8	no	—
139	C₂³×C₅	—	2	2	no	—
140	C₂³×C₅	—	2	4	no	—
141	C₂³×C₅	—	2	2	no	—
142	C₂³×C₅	—	2	2	no	—
143	C₂³×C₅	—	4	2	no	—
144	C₂³×C₅	—	4	2	no	—
145	C₂³×C₅	—	4	2	no	—
146	C₂³×C₅	—	4	2	no	—
147	C₂³×C₅	—	4	8	no	—
148	C₂³×C₅	—	4	8	no	—
149	C₂³×C₅	—	5	2	no	—
150	C₂³×C₅	—	10	2	no	—
151	C₂³×C₅	—	20	2	no	—
152	C₂³×C₅	C₂²⋊D₅	1	4	yes	complemented
153	C₂³×C₅	C₅×D₄	1	4	yes	complemented
154	C₂³×C₅	C₂²×D₅	1	2	yes	—
155	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
156	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
157	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
158	C₂³×C₅	C₂³×C₅	1	2	yes	—
159	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
160	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
161	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
162	C₂²×D₅	—	2	2	no	—
163	C₂²×D₅	—	4	2	no	—
164	C₂²×D₅	C₂³×C₅	1	2	yes	—
165	C₅×D₄	—	2	16	no	—
166	C₅×D₄	—	2	16	no	—
167	C₅×D₄	—	2	4	no	—
168	C₅×D₄	—	2	4	no	—
169	C₅×D₄	—	2	4	no	—
170	C₅×D₄	—	2	4	no	—
171	C₅×D₄	—	10	4	no	—
172	C₅×D₄	—	10	4	no	—
173	C₅×D₄	—	20	4	no	—
174	C₂×C₄×C₅	—	2	8	no	—
175	C₂×C₄×C₅	—	2	2	no	—
176	C₂×C₄×C₅	—	2	2	no	—
177	C₂×C₄×C₅	—	2	4	no	—
178	C₂×C₄×C₅	—	5	4	no	—
179	C₂×C₄×C₅	—	5	2	no	—
180	C₂×C₄×C₅	—	10	2	no	—
181	C₂×C₄×C₅	—	20	2	no	—
182	C₂×C₄×C₅	C₂²×D₅	1	2	yes	—
183	C₂×C₄×C₅	C₂³×C₅	1	2	yes	—
184	C₂²⋊D₅	—	2	4	no	—
185	C₂²⋊D₅	—	2	4	no	—
186	C₂²⋊D₅	—	4	4	no	—
187	C₂×Dic₅	—	2	2	no	—
188	C₂×Dic₅	—	4	2	no	—
189	C₂×Dic₅	C₂³×C₅	1	2	yes	—
190	C₂×Dic₅	C₂³×C₅	1	4	yes	—
191	C₂²×D₄	—	5	1	no	—
192	C₂²×D₄	C₅×D₅	1	1	yes	characteristic, complemented
193	#123	—	5	2	no	—
194	#123	—	5	2	no	—
195	#121	—	5	4	no	—
196	#120	—	5	2	no	—
197	#120	—	5	2	no	—
198	C₂×C₂²⋊C₄	—	5	1	no	—
199	C₅²	#534	1	1	yes	characteristic, complemented, Sylow
200	C₂²×C₅	—	2	8	no	—
201	C₂²×C₅	—	2	2	no	—
202	C₂²×C₅	—	2	2	no	—
203	C₂²×C₅	—	2	2	no	—
204	C₂²×C₅	—	2	2	no	—
205	C₂²×C₅	—	2	2	no	—
206	C₂²×C₅	—	2	2	no	—
207	C₂²×C₅	—	2	8	no	—
208	C₂²×C₅	—	2	4	no	—
209	C₂²×C₅	—	2	2	no	—
210	C₂²×C₅	—	2	2	no	—
211	C₂²×C₅	—	2	4	no	—
212	C₂²×C₅	—	2	4	no	—
213	C₂²×C₅	—	2	4	no	—
214	C₂²×C₅	—	2	4	no	—
215	C₂²×C₅	—	2	2	no	—
216	C₂²×C₅	—	4	4	no	—
217	C₂²×C₅	—	4	4	no	—
218	C₂²×C₅	—	4	8	no	—
219	C₂²×C₅	—	4	4	no	—
220	C₂²×C₅	—	4	4	no	—
221	C₂²×C₅	—	4	16	no	—
222	C₂²×C₅	—	4	16	no	—
223	C₂²×C₅	—	4	4	no	—
224	C₂²×C₅	—	4	4	no	—
225	C₂²×C₅	—	10	4	no	—
226	C₂²×C₅	—	10	2	no	—
227	C₂²×C₅	—	20	4	no	—
228	C₂²×C₅	C₂×C₂²⋊D₅	1	2	yes	—
229	C₂²×C₅	C₂×C₂²⋊D₅	1	2	yes	—
230	C₂²×C₅	C₂×C₂²⋊D₅	1	2	yes	—
231	C₂²×C₅	C₂×C₅×D₄	1	2	yes	—
232	C₂²×C₅	C₂×C₅×D₄	1	2	yes	—
233	C₂²×C₅	C₂×C₅×D₄	1	2	yes	—
234	C₂²×C₅	C₂³×D₅	1	1	yes	characteristic
235	C₂²×C₅	C₂⁴×C₅	1	1	yes	characteristic
236	C₂×D₅	—	2	2	no	—
237	C₂×D₅	—	2	4	no	—
238	C₂×D₅	—	4	4	no	—
239	C₄×C₅	—	2	8	no	—
240	C₄×C₅	—	2	2	no	—
241	C₄×C₅	—	2	2	no	—
242	C₄×C₅	—	10	4	no	—
243	C₄×C₅	—	10	2	no	—
244	Dic₅	—	2	2	no	—
245	Dic₅	—	2	4	no	—
246	C₂⁴	—	5	1	no	—
247	C₂⁴	C₂×C₅×D₅	1	1	yes	characteristic
248	C₂⁴	C₂×C₅×D₅	1	1	yes	characteristic, complemented
249	C₂×D₄	—	2	4	no	—
250	C₂×D₄	—	5	2	no	—
251	C₂×D₄	—	5	2	no	—
252	C₂×D₄	—	5	4	no	—
253	C₂×D₄	—	10	4	no	—
254	C₂×D₄	C₂×C₅×D₅	1	2	yes	—
255	C₂×D₄	C₂×C₅×D₅	1	2	yes	complemented
256	C₂²×C₄	—	5	1	no	—
257	C₂²×C₄	—	5	2	no	—
258	C₂²×C₄	C₂×C₅×D₅	1	1	yes	characteristic, complemented
259	C₄⋊C₄	—	5	4	no	—
260	C₂²⋊C₄	—	5	2	no	—
261	C₂²⋊C₄	—	5	2	no	—
262	C₂²⋊C₄	—	5	4	no	—
263	C₂²⋊C₄	—	5	4	no	—
264	C₂×C₅	—	2	8	no	—
265	C₂×C₅	—	2	2	no	—
266	C₂×C₅	—	2	2	no	—
267	C₂×C₅	—	2	2	no	—
268	C₂×C₅	—	2	2	no	—
269	C₂×C₅	—	2	2	no	—
270	C₂×C₅	—	2	2	no	—
271	C₂×C₅	—	2	4	no	—
272	C₂×C₅	—	2	2	no	—
273	C₂×C₅	—	4	4	no	—
274	C₂×C₅	—	4	4	no	—
275	C₂×C₅	—	4	8	no	—
276	C₂×C₅	—	4	2	no	—
277	C₂×C₅	—	4	2	no	—
278	C₂×C₅	—	20	2	no	—
279	C₂×C₅	#4144	1	2	yes	—
280	C₂×C₅	C₂²×C₂²⋊D₅	1	1	yes	characteristic
281	C₂×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
282	C₂×C₅	C₅×H(5,𝔽₂)	1	2	yes	—
283	D₅	—	4	2	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	4	2	no	—
286	C₂³	—	4	2	no	—
287	C₂³	—	5	2	no	—
288	C₂³	—	10	2	no	—
289	C₂³	—	20	2	no	—
290	C₂³	C₅×C₂²⋊D₅	1	4	yes	complemented
291	C₂³	C₂²×C₅×D₅	1	2	yes	—
292	C₂³	C₂²×C₅×D₅	1	1	yes	characteristic
293	C₂³	C₂²×C₅×D₅	1	1	yes	characteristic
294	C₂³	C₂²×C₅×D₅	1	1	yes	characteristic
295	D₄	—	2	4	no	—
296	D₄	—	2	4	no	—
297	D₄	—	10	4	no	—
298	D₄	—	10	4	no	—
299	D₄	—	20	4	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	5	4	no	—
302	C₂×C₄	—	5	2	no	—
303	C₂×C₄	—	10	2	no	—
304	C₂×C₄	—	20	2	no	—
305	C₂×C₄	C₂²×C₅×D₅	1	2	yes	—
306	C₅	—	2	2	no	—
307	C₅	#66138	1	1	yes	characteristic, direct product factor
308	C₅	C₅×#534	1	1	yes	characteristic, complemented
309	C₂²	—	2	2	no	—
310	C₂²	—	2	2	no	—
311	C₂²	—	2	2	no	—
312	C₂²	—	2	4	no	—
313	C₂²	—	2	2	no	—
314	C₂²	—	4	4	no	—
315	C₂²	—	4	4	no	—
316	C₂²	—	10	4	no	—
317	C₂²	—	10	2	no	—
318	C₂²	—	20	4	no	—
319	C₂²	C₂×C₅×C₂²⋊D₅	1	2	yes	—
320	C₂²	C₂×C₅×C₂²⋊D₅	1	2	yes	—
321	C₂²	C₂×C₅×C₂²⋊D₅	1	2	yes	—
322	C₂²	C₂³×C₅×D₅	1	1	yes	characteristic
323	C₄	—	2	2	no	—
324	C₄	—	10	4	no	—
325	C₄	—	10	2	no	—
326	C₂	—	2	2	no	—
327	C₂	—	2	2	no	—
328	C₂	—	2	2	no	—
329	C₂	—	4	2	no	—
330	C₂	—	20	2	no	—
331	C₂	C₅×#4144	1	2	yes	—
332	C₂	C₂²×C₅×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁴×C₅
Frattini	C₂²	C₂³×C₅×D₅
Fitting	C₂²×C₅²×D₄	C₂
socle	C₂²×C₅²	C₂⁴
hypercenter	C₂²×C₅×D₄	D₅
hypocenter	C₅	C₅×#534
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅²×D₄	C₂	semidirect
2. C₂²×C₅×C₂²⋊D₅	C₂	semidirect
3. C₅×#4099	C₂	semidirect
4. C₂×C₅×C₂²⋊Dic₅	C₂	semidirect
5. C₅×#4085	C₂	semidirect
6. C₅×#4083	C₂	semidirect
7. C₅×#4081	C₂	semidirect
8. C₅×#4075	C₂	semidirect
10. C₂⁴×C₅²	C₂²	semidirect
11. C₂³×C₅×D₅	C₂²	semidirect
14. C₂×C₅²×D₄	C₂²	semidirect
15. C₂²×C₄×C₅²	C₂²	semidirect
18. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
19. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
20. C₂²×C₅×Dic₅	C₂²	semidirect
21. C₂²×C₅×Dic₅	C₂²	semidirect
22. C₅×C₂²⋊Dic₅	C₂²	semidirect
23. C₅×C₂²⋊Dic₅	C₂²	semidirect
24. C₅×C₂²⋊Dic₅	C₂²	semidirect
25. C₅×#685	C₂²	semidirect
26. C₅×#683	C₂²	semidirect
28. #66138	C₅	direct (N × H)
32. C₂³×C₅²	D₄	semidirect
53. C₂²×C₅×D₄	D₅	semidirect
54. C₂²×C₅×D₄	C₂×C₅	semidirect
55. C₂²×C₂²⋊D₅	C₂×C₅	semidirect
62. #4099	C₂×C₅	semidirect
63. C₂×C₂²⋊Dic₅	C₂×C₅	semidirect
64. #4085	C₂×C₅	semidirect
65. #4083	C₂×C₅	semidirect
66. #4081	C₂×C₅	semidirect
67. #4075	C₂×C₅	semidirect
89. C₂⁴×C₅	C₂×D₅	semidirect
91. C₂⁴×C₅	C₂²×C₅	semidirect
92. C₂³×D₅	C₂²×C₅	semidirect
103. C₂×C₅×D₄	C₂×D₅	semidirect
105. C₂×C₅×D₄	C₂²×C₅	semidirect
109. C₂²×C₄×C₅	C₂×D₅	semidirect
110. C₂²×C₄×C₅	C₂²×C₅	semidirect
113. C₂×C₂²⋊D₅	C₂²×C₅	semidirect
114. C₂×C₂²⋊D₅	C₂²×C₅	semidirect
115. C₂²×Dic₅	C₂²×C₅	semidirect
116. C₂²×Dic₅	C₂²×C₅	semidirect
122. C₂²⋊Dic₅	C₂²×C₅	semidirect
123. C₂²⋊Dic₅	C₂²×C₅	semidirect
124. C₂²⋊Dic₅	C₂²×C₅	semidirect
125. #685	C₂²×C₅	semidirect
126. #683	C₂²×C₅	semidirect
152. C₂³×C₅	C₂²⋊D₅	semidirect
153. C₂³×C₅	C₅×D₄	semidirect
192. C₂²×D₄	C₅×D₅	semidirect
199. C₅²	#534	semidirect
248. C₂⁴	C₂×C₅×D₅	semidirect
255. C₂×D₄	C₂×C₅×D₅	semidirect
258. C₂²×C₄	C₂×C₅×D₅	semidirect
290. C₂³	C₅×C₂²⋊D₅	semidirect
307. C₅	#66138	direct (N × H)
308. C₅	C₅×#534	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅²×D₄	2
C₂²×C₅×C₂²⋊D₅	2
C₅×#4099	2
C₂×C₅×C₂²⋊Dic₅	2
C₅×#4085	2
C₅×#4083	2
C₅×#4081	2
C₅×#4075	2
C₅×#534	5
#66138	5

Subgroups — C5×#66138 #13106958

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#66138 #13106958