Subgroups — C₅×#65920 #13106740

Order 1600.

790 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#711	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4099	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4085	C₂	1	2	yes	maximal, complemented
6	C₅×#4081	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×D₄×Dic₅	C₂	1	2	yes	maximal, complemented
8	C₅×#4032	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4027	C₂	1	2	yes	maximal, complemented
10	C₅×#4024	C₂	1	2	yes	maximal, complemented
11	C₅×#4023	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₅²	C₂²	1	1	yes	characteristic
13	C₂×C₅²×D₄	C₂²	1	2	yes	—
14	C₂×C₅²×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₂²⋊D₅	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₂²⋊D₅	C₂²	1	2	yes	—
17	C₂×C₅×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₅×Dic₅	—	2	4	no	—
19	C₂²×C₅×Dic₅	C₂²	1	1	yes	characteristic
20	C₂²×C₅×Dic₅	C₂²	1	2	yes	—
21	C₂²×C₅×Dic₅	C₂²	1	2	yes	—
22	C₂²×C₅×Dic₅	C₂²	1	1	yes	characteristic
23	C₂²×C₅×Dic₅	C₂²	1	1	yes	characteristic, complemented
24	C₅×#711	—	2	4	no	—
25	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
27	C₅²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₅²×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₅×C₂²⋊Dic₅	C₂²	1	2	yes	—
30	C₅×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
31	C₅×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
32	C₅×#685	C₂²	1	2	yes	complemented
33	C₅×C₄⋊Dic₅	C₂²	1	2	yes	complemented
34	C₅×#683	C₂²	1	2	yes	complemented
35	C₅×#683	C₂²	1	2	yes	complemented
36	C₄×C₅×Dic₅	C₂²	1	2	yes	complemented
37	C₅×#525	—	5	1	no	maximal
38	#65920	C₅	1	1	yes	maximal, characteristic, direct product factor
39	C₂³×C₅²	—	2	2	no	—
40	C₂³×C₅²	—	2	4	no	—
41	C₂³×C₅²	C₂³	1	1	yes	characteristic
42	C₂³×C₅²	C₂³	1	1	yes	characteristic
43	C₂³×C₅²	C₂³	1	2	yes	—
44	C₂²×C₅×D₅	C₂³	1	1	yes	characteristic
45	C₅²×D₄	—	2	2	no	—
46	C₅²×D₄	—	2	4	no	—
47	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
48	C₂×C₄×C₅²	C₂³	1	2	yes	—
49	C₅×C₂²⋊D₅	—	2	2	no	—
50	C₅×C₂²⋊D₅	—	2	4	no	—
51	C₅×C₂²⋊D₅	—	2	2	no	—
52	C₂×C₅×Dic₅	—	2	2	no	—
53	C₂×C₅×Dic₅	—	2	2	no	—
54	C₂×C₅×Dic₅	—	2	4	no	—
55	C₂×C₅×Dic₅	—	2	4	no	—
56	C₂×C₅×Dic₅	D₄	1	4	yes	complemented
57	C₂×C₅×Dic₅	C₂³	1	1	yes	characteristic
58	C₂×C₅×Dic₅	C₂³	1	2	yes	—
59	C₂×C₅×Dic₅	C₂³	1	2	yes	—
60	C₂×C₅×Dic₅	C₂³	1	1	yes	characteristic
61	C₂×C₅×Dic₅	C₂³	1	1	yes	characteristic
62	C₄×C₅×D₅	—	2	2	no	—
63	C₅×Dic₁₀	—	2	2	no	—
64	C₂×C₅×#41	—	5	1	no	—
65	C₂³×C₄×C₅	—	5	1	no	—
66	C₂³×Dic₅	C₂×C₅	1	1	yes	characteristic, complemented
67	C₂×#711	C₂×C₅	1	1	yes	characteristic, complemented
68	C₅×#123	—	5	1	no	—
69	C₅×#123	—	5	1	no	—
70	C₅×C₂²⋊Q₈	—	5	2	no	—
71	C₅×#121	—	5	2	no	—
72	C₅×#120	—	2	2	no	—
73	C₅×#120	—	5	1	no	—
74	C₅×#120	D₅	1	1	yes	characteristic, complemented
75	C₅×#120	C₂×C₅	1	1	yes	characteristic, complemented
76	C₄×C₅×D₄	—	5	2	no	—
77	C₄×C₅×D₄	—	5	2	no	—
78	C₅×#117	—	5	1	no	—
79	#4099	C₂×C₅	1	1	yes	characteristic, complemented
80	#4085	C₂×C₅	1	2	yes	complemented
81	#4081	C₂×C₅	1	1	yes	characteristic, complemented
82	D₄×Dic₅	C₂×C₅	1	2	yes	complemented
83	#4032	C₂×C₅	1	1	yes	characteristic, complemented
84	#4027	C₂×C₅	1	2	yes	complemented
85	#4024	C₂×C₅	1	2	yes	complemented
86	#4023	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂²×C₅²	—	2	8	no	—
88	C₂²×C₅²	—	2	2	no	—
89	C₂²×C₅²	—	2	2	no	—
90	C₂²×C₅²	—	2	2	no	—
91	C₂²×C₅²	—	2	1	no	—
92	C₂²×C₅²	—	2	2	no	—
93	C₂²×C₅²	C₂×D₄	1	2	yes	—
94	C₂²×C₅²	#41	1	4	yes	complemented
95	C₂²×C₅²	C₂⁴	1	1	yes	characteristic
96	C₂×C₅×D₅	—	2	1	no	—
97	C₂×C₅×D₅	—	2	2	no	—
98	C₄×C₅²	—	2	1	no	—
99	C₄×C₅²	—	2	2	no	—
100	C₅×Dic₅	—	2	1	no	—
101	C₅×Dic₅	—	2	2	no	—
102	C₅×Dic₅	—	2	2	no	—
103	C₅×Dic₅	C₂×D₄	1	2	yes	—
104	C₅×Dic₅	C₂×D₄	1	2	yes	—
105	C₂⁴×C₅	—	2	2	no	—
106	C₂⁴×C₅	C₂×D₅	1	1	yes	characteristic
107	C₂⁴×C₅	C₂²×C₅	1	1	yes	characteristic
108	C₅×#41	—	10	4	no	—
109	C₂×C₅×Q₈	—	5	1	no	—
110	C₂×C₅×D₄	—	2	4	no	—
111	C₂×C₅×D₄	—	2	2	no	—
112	C₂×C₅×D₄	—	5	2	no	—
113	C₂×C₅×D₄	—	5	1	no	—
114	C₂×C₅×D₄	—	5	1	no	—
115	C₂×C₅×D₄	C₂×D₅	1	2	yes	—
116	C₂×C₅×D₄	C₂×D₅	1	1	yes	characteristic
117	C₂×C₅×D₄	C₂²×C₅	1	1	yes	characteristic
118	C₂×C₅×D₄	C₂²×C₅	1	2	yes	—
119	C₂²×C₄×C₅	—	5	1	no	—
120	C₂²×C₄×C₅	—	5	2	no	—
121	C₂²×C₄×C₅	—	5	1	no	—
122	C₂²×C₄×C₅	—	5	2	no	—
123	C₂²×C₄×C₅	—	5	1	no	—
124	C₂²×C₄×C₅	—	5	1	no	—
125	C₂²×C₄×C₅	—	10	4	no	—
126	C₂×C₂²⋊D₅	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₂²⋊D₅	C₂²×C₅	1	2	yes	—
128	C₂×C₂²⋊D₅	C₂²×C₅	1	1	yes	characteristic, complemented
129	C₂²×Dic₅	—	2	4	no	—
130	C₂²×Dic₅	C₂²×C₅	1	2	yes	—
131	C₂²×Dic₅	C₂²×C₅	1	2	yes	—
132	C₂²×Dic₅	C₂²×C₅	1	1	yes	characteristic
133	C₂²×Dic₅	C₂²×C₅	1	1	yes	characteristic
134	C₂²×Dic₅	C₂²×C₅	1	1	yes	characteristic, complemented
135	#711	—	2	4	no	—
136	C₂×C₄×D₅	C₂²×C₅	1	1	yes	characteristic, complemented
137	C₂×Dic₁₀	C₂²×C₅	1	1	yes	characteristic, complemented
138	C₅×C₄⋊C₄	—	5	2	no	—
139	C₅×C₄⋊C₄	—	5	2	no	—
140	C₅×C₄⋊C₄	—	5	2	no	—
141	C₅×C₂²⋊C₄	—	2	2	no	—
142	C₅×C₂²⋊C₄	—	2	4	no	—
143	C₅×C₂²⋊C₄	—	5	1	no	—
144	C₅×C₂²⋊C₄	—	5	2	no	—
145	C₅×C₂²⋊C₄	—	5	2	no	—
146	C₅×C₂²⋊C₄	—	5	2	no	—
147	C₅×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
148	C₅×C₂²⋊C₄	C₂×D₅	1	2	yes	—
149	C₅×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
150	C₅×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
151	C₄²×C₅	—	5	2	no	—
152	C₂²⋊Dic₅	C₂²×C₅	1	1	yes	characteristic
153	C₂²⋊Dic₅	C₂²×C₅	1	2	yes	—
154	C₂²⋊Dic₅	C₂²×C₅	1	2	yes	complemented
155	#685	C₂²×C₅	1	2	yes	complemented
156	C₄⋊Dic₅	C₂²×C₅	1	2	yes	complemented
157	#683	C₂²×C₅	1	2	yes	complemented
158	#683	C₂²×C₅	1	2	yes	complemented
159	C₄×Dic₅	C₂²×C₅	1	2	yes	complemented
160	#525	—	5	1	no	Sylow
161	C₂×C₅²	—	2	2	no	—
162	C₂×C₅²	—	2	4	no	—
163	C₂×C₅²	—	4	1	no	—
164	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₅²	C₂×#41	1	2	yes	—
166	C₅×D₅	—	4	1	no	—
167	C₂³×C₅	—	2	2	no	—
168	C₂³×C₅	—	2	4	no	—
169	C₂³×C₅	—	2	2	no	—
170	C₂³×C₅	—	2	4	no	—
171	C₂³×C₅	—	2	2	no	—
172	C₂³×C₅	—	2	4	no	—
173	C₂³×C₅	—	2	2	no	—
174	C₂³×C₅	—	4	4	no	—
175	C₂³×C₅	—	4	8	no	—
176	C₂³×C₅	—	5	1	no	—
177	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
178	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
179	C₂³×C₅	C₂²×D₅	1	2	yes	—
180	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
181	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
182	C₂³×C₅	C₂³×C₅	1	2	yes	—
183	C₂²×D₅	C₂³×C₅	1	1	yes	characteristic
184	C₅×Q₈	—	10	2	no	—
185	C₅×D₄	—	2	2	no	—
186	C₅×D₄	—	2	4	no	—
187	C₅×D₄	—	2	2	no	—
188	C₅×D₄	—	2	4	no	—
189	C₅×D₄	—	4	4	no	—
190	C₅×D₄	—	4	8	no	—
191	C₅×D₄	—	10	2	no	—
192	C₅×D₄	—	10	2	no	—
193	C₅×D₄	—	10	4	no	—
194	C₂×C₄×C₅	—	2	4	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	5	4	no	—
197	C₂×C₄×C₅	—	5	1	no	—
198	C₂×C₄×C₅	—	5	1	no	—
199	C₂×C₄×C₅	—	5	2	no	—
200	C₂×C₄×C₅	—	5	2	no	—
201	C₂×C₄×C₅	—	5	1	no	—
202	C₂×C₄×C₅	—	10	2	no	—
203	C₂×C₄×C₅	—	10	4	no	—
204	C₂×C₄×C₅	—	10	4	no	—
205	C₂×C₄×C₅	—	10	2	no	—
206	C₂×C₄×C₅	—	10	2	no	—
207	C₂×C₄×C₅	C₂²×D₅	1	2	yes	—
208	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂³×C₅	1	2	yes	—
210	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
211	C₂²⋊D₅	—	2	2	no	—
212	C₂²⋊D₅	—	2	4	no	—
213	C₂²⋊D₅	—	2	2	no	—
214	C₂×Dic₅	—	2	2	no	—
215	C₂×Dic₅	—	2	2	no	—
216	C₂×Dic₅	—	2	4	no	—
217	C₂×Dic₅	—	2	4	no	—
218	C₂×Dic₅	C₅×D₄	1	4	yes	complemented
219	C₂×Dic₅	C₂³×C₅	1	2	yes	—
220	C₂×Dic₅	C₂³×C₅	1	2	yes	—
221	C₂×Dic₅	C₂³×C₅	1	1	yes	characteristic
222	C₂×Dic₅	C₂³×C₅	1	1	yes	characteristic
223	C₂×Dic₅	C₂³×C₅	1	1	yes	characteristic
224	C₄×D₅	—	2	2	no	—
225	Dic₁₀	—	2	2	no	—
226	C₂×#41	—	5	1	no	—
227	C₂³×C₄	—	5	1	no	—
228	#123	—	5	1	no	—
229	#123	—	5	1	no	—
230	C₂²⋊Q₈	—	5	2	no	—
231	#121	—	5	2	no	—
232	#120	—	5	1	no	—
233	#120	C₅×D₅	1	1	yes	characteristic, complemented
234	C₄×D₄	—	5	2	no	—
235	C₄×D₄	—	5	2	no	—
236	#117	—	5	1	no	—
237	C₅²	#525	1	1	yes	characteristic, complemented, Sylow
238	C₂²×C₅	—	2	8	no	—
239	C₂²×C₅	—	2	8	no	—
240	C₂²×C₅	—	2	2	no	—
241	C₂²×C₅	—	2	2	no	—
242	C₂²×C₅	—	2	2	no	—
243	C₂²×C₅	—	2	2	no	—
244	C₂²×C₅	—	2	2	no	—
245	C₂²×C₅	—	2	2	no	—
246	C₂²×C₅	—	2	1	no	—
247	C₂²×C₅	—	2	2	no	—
248	C₂²×C₅	—	2	1	no	—
249	C₂²×C₅	—	2	2	no	—
250	C₂²×C₅	—	2	4	no	—
251	C₂²×C₅	—	2	8	no	—
252	C₂²×C₅	—	2	2	no	—
253	C₂²×C₅	—	4	4	no	—
254	C₂²×C₅	—	4	4	no	—
255	C₂²×C₅	—	4	4	no	—
256	C₂²×C₅	—	4	2	no	—
257	C₂²×C₅	—	4	4	no	—
258	C₂²×C₅	—	4	16	no	—
259	C₂²×C₅	—	10	1	no	—
260	C₂²×C₅	—	10	2	no	—
261	C₂²×C₅	D₄×D₅	1	2	yes	—
262	C₂²×C₅	#711	1	4	yes	complemented
263	C₂²×C₅	C₂×C₅×D₄	1	2	yes	—
264	C₂²×C₅	C₅×#41	1	4	yes	complemented
265	C₂²×C₅	C₂³×D₅	1	1	yes	characteristic
266	C₂²×C₅	C₂⁴×C₅	1	1	yes	characteristic
267	C₂×D₅	—	2	1	no	—
268	C₂×D₅	—	2	2	no	—
269	C₄×C₅	—	2	1	no	—
270	C₄×C₅	—	2	2	no	—
271	C₄×C₅	—	2	1	no	—
272	C₄×C₅	—	2	2	no	—
273	C₄×C₅	—	4	2	no	—
274	C₄×C₅	—	4	4	no	—
275	C₄×C₅	—	5	2	no	—
276	C₄×C₅	—	5	2	no	—
277	C₄×C₅	—	10	2	no	—
278	C₄×C₅	—	10	1	no	—
279	C₄×C₅	—	10	2	no	—
280	Dic₅	—	2	1	no	—
281	Dic₅	—	2	2	no	—
282	Dic₅	—	2	2	no	—
283	Dic₅	C₂×C₅×D₄	1	2	yes	—
284	Dic₅	C₂×C₅×D₄	1	2	yes	—
285	C₂⁴	C₂×C₅×D₅	1	1	yes	characteristic
286	#41	—	10	4	no	—
287	C₂×Q₈	—	5	1	no	—
288	C₂×D₄	—	5	2	no	—
289	C₂×D₄	—	5	1	no	—
290	C₂×D₄	—	5	1	no	—
291	C₂×D₄	C₂×C₅×D₅	1	2	yes	—
292	C₂×D₄	C₂×C₅×D₅	1	1	yes	characteristic
293	C₂²×C₄	—	5	1	no	—
294	C₂²×C₄	—	5	2	no	—
295	C₂²×C₄	—	5	1	no	—
296	C₂²×C₄	—	5	2	no	—
297	C₂²×C₄	—	5	1	no	—
298	C₂²×C₄	—	5	1	no	—
299	C₂²×C₄	—	10	4	no	—
300	C₄⋊C₄	—	5	2	no	—
301	C₄⋊C₄	—	5	2	no	—
302	C₄⋊C₄	—	5	2	no	—
303	C₂²⋊C₄	—	5	1	no	—
304	C₂²⋊C₄	—	5	2	no	—
305	C₂²⋊C₄	—	5	2	no	—
306	C₂²⋊C₄	—	5	2	no	—
307	C₂²⋊C₄	C₂×C₅×D₅	1	1	yes	characteristic
308	C₂²⋊C₄	C₂×C₅×D₅	1	2	yes	—
309	C₄²	—	5	2	no	—
310	C₂×C₅	—	2	2	no	—
311	C₂×C₅	—	2	4	no	—
312	C₂×C₅	—	2	2	no	—
313	C₂×C₅	—	2	4	no	—
314	C₂×C₅	—	2	2	no	—
315	C₂×C₅	—	2	4	no	—
316	C₂×C₅	—	4	4	no	—
317	C₂×C₅	—	4	8	no	—
318	C₂×C₅	—	4	1	no	—
319	C₂×C₅	—	4	1	no	—
320	C₂×C₅	—	8	2	no	—
321	C₂×C₅	—	20	1	no	—
322	C₂×C₅	C₂×D₄×D₅	1	1	yes	characteristic
323	C₂×C₅	C₂×#711	1	2	yes	—
324	C₂×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
325	C₂×C₅	C₂×C₅×#41	1	2	yes	—
326	D₅	—	4	1	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	4	no	—
329	C₂³	—	5	1	no	—
330	C₂³	C₂²×C₅×D₅	1	1	yes	characteristic
331	C₂³	C₂²×C₅×D₅	1	1	yes	characteristic
332	C₂³	C₂²×C₅×D₅	1	2	yes	—
333	Q₈	—	10	2	no	—
334	D₄	—	2	2	no	—
335	D₄	—	2	4	no	—
336	D₄	—	10	2	no	—
337	D₄	—	10	2	no	—
338	D₄	—	10	4	no	—
339	C₂×C₄	—	5	4	no	—
340	C₂×C₄	—	5	1	no	—
341	C₂×C₄	—	5	1	no	—
342	C₂×C₄	—	5	2	no	—
343	C₂×C₄	—	5	2	no	—
344	C₂×C₄	—	5	1	no	—
345	C₂×C₄	—	10	2	no	—
346	C₂×C₄	—	10	4	no	—
347	C₂×C₄	—	10	4	no	—
348	C₂×C₄	—	10	2	no	—
349	C₂×C₄	—	10	2	no	—
350	C₂×C₄	C₂²×C₅×D₅	1	2	yes	—
351	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
352	C₅	—	2	2	no	—
353	C₅	#65920	1	1	yes	characteristic, direct product factor
354	C₅	C₅×#525	1	1	yes	characteristic, complemented
355	C₂²	—	2	8	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	10	1	no	—
362	C₂²	—	10	2	no	—
363	C₂²	C₅×D₄×D₅	1	2	yes	—
364	C₂²	C₅×#711	1	4	yes	complemented
365	C₂²	C₂³×C₅×D₅	1	1	yes	characteristic
366	C₄	—	2	1	no	—
367	C₄	—	2	2	no	—
368	C₄	—	5	2	no	—
369	C₄	—	5	2	no	—
370	C₄	—	10	2	no	—
371	C₄	—	10	1	no	—
372	C₄	—	10	2	no	—
373	C₂	—	2	2	no	—
374	C₂	—	2	4	no	—
375	C₂	—	4	1	no	—
376	C₂	—	20	1	no	—
377	C₂	C₂×C₅×D₄×D₅	1	1	yes	characteristic
378	C₂	C₂×C₅×#711	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁴×C₅
Frattini	C₂²	C₂³×C₅×D₅
Fitting	C₅²×#120	C₂
socle	C₂²×C₅²	C₂⁴
hypercenter	C₅×#120	D₅
hypocenter	C₅	C₅×#525
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#120

Complements

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

N	H ≅ G/N	type
1. C₂³×C₅×Dic₅	C₂	semidirect
2. C₂×C₅×#711	C₂	semidirect
3. C₅²×#120	C₂	semidirect
4. C₅×#4099	C₂	semidirect
5. C₅×#4085	C₂	semidirect
6. C₅×#4081	C₂	semidirect
7. C₅×D₄×Dic₅	C₂	semidirect
8. C₅×#4032	C₂	semidirect
9. C₅×#4027	C₂	semidirect
10. C₅×#4024	C₂	semidirect
11. C₅×#4023	C₂	semidirect
17. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
23. C₂²×C₅×Dic₅	C₂²	semidirect
25. C₂×C₄×C₅×D₅	C₂²	semidirect
26. C₂×C₅×Dic₁₀	C₂²	semidirect
31. C₅×C₂²⋊Dic₅	C₂²	semidirect
32. C₅×#685	C₂²	semidirect
33. C₅×C₄⋊Dic₅	C₂²	semidirect
34. C₅×#683	C₂²	semidirect
35. C₅×#683	C₂²	semidirect
36. C₄×C₅×Dic₅	C₂²	semidirect
38. #65920	C₅	direct (N × H)
56. C₂×C₅×Dic₅	D₄	semidirect
66. C₂³×Dic₅	C₂×C₅	semidirect
67. C₂×#711	C₂×C₅	semidirect
74. C₅×#120	D₅	semidirect
75. C₅×#120	C₂×C₅	semidirect
79. #4099	C₂×C₅	semidirect
80. #4085	C₂×C₅	semidirect
81. #4081	C₂×C₅	semidirect
82. D₄×Dic₅	C₂×C₅	semidirect
83. #4032	C₂×C₅	semidirect
84. #4027	C₂×C₅	semidirect
85. #4024	C₂×C₅	semidirect
86. #4023	C₂×C₅	semidirect
94. C₂²×C₅²	#41	semidirect
128. C₂×C₂²⋊D₅	C₂²×C₅	semidirect
134. C₂²×Dic₅	C₂²×C₅	semidirect
136. C₂×C₄×D₅	C₂²×C₅	semidirect
137. C₂×Dic₁₀	C₂²×C₅	semidirect
154. C₂²⋊Dic₅	C₂²×C₅	semidirect
155. #685	C₂²×C₅	semidirect
156. C₄⋊Dic₅	C₂²×C₅	semidirect
157. #683	C₂²×C₅	semidirect
158. #683	C₂²×C₅	semidirect
159. C₄×Dic₅	C₂²×C₅	semidirect
218. C₂×Dic₅	C₅×D₄	semidirect
233. #120	C₅×D₅	semidirect
237. C₅²	#525	semidirect
262. C₂²×C₅	#711	semidirect
264. C₂²×C₅	C₅×#41	semidirect
353. C₅	#65920	direct (N × H)
354. C₅	C₅×#525	semidirect
364. C₂²	C₅×#711	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₅×Dic₅	2
C₂×C₅×#711	2
C₅²×#120	2
C₅×#4099	2
C₅×#4085	2
C₅×#4081	2
C₅×D₄×Dic₅	2
C₅×#4032	2
C₅×#4027	2
C₅×#4024	2
C₅×#4023	2
C₅×#525	5
#65920	5

Subgroups — C5×#65920 #13106740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#65920 #13106740