Subgroups — C₅×#66158 #13106987

Order 1600.

748 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#711	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4092	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4090	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4085	C₂	1	2	yes	maximal, complemented
6	C₅×#4081	C₂	1	2	yes	maximal, complemented
7	C₅×D₄×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4075	C₂	1	2	yes	maximal, complemented
9	C₄×C₅×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4070	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#683	C₂	1	2	yes	maximal, complemented
12	C₅²×#41	—	2	4	no	—
13	C₂×C₅²×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₅²×D₄	C₂²	1	2	yes	—
15	C₂×C₅²×D₄	C₂²	1	1	yes	characteristic
16	C₂²×C₄×C₅²	C₂²	1	2	yes	—
17	C₂²×C₄×C₅²	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₂²⋊D₅	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₂²⋊D₅	C₂²	1	2	yes	—
20	C₂²×C₅×Dic₅	C₂²	1	2	yes	—
21	C₂²×C₅×Dic₅	C₂²	1	2	yes	—
22	C₅×#711	—	2	4	no	—
23	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic
24	C₂×C₅×Dic₁₀	C₂²	1	1	yes	characteristic
25	C₅×C₂²⋊Dic₅	C₂²	1	2	yes	—
26	C₅×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
27	C₅×C₂²⋊Dic₅	C₂²	1	2	yes	—
28	C₅×#685	C₂²	1	1	yes	characteristic
29	C₅×#685	C₂²	1	2	yes	—
30	C₅×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
31	C₅×#683	C₂²	1	1	yes	characteristic
32	C₅×#683	C₂²	1	2	yes	—
33	C₅×#683	C₂²	1	2	yes	—
34	C₅×#683	C₂²	1	2	yes	—
35	C₅×#683	C₂²	1	2	yes	—
36	C₄×C₅×Dic₅	C₂²	1	1	yes	characteristic
37	C₅×#547	—	5	1	no	maximal
38	#66158	C₅	1	1	yes	maximal, characteristic, direct product factor
39	C₂³×C₅²	C₂³	1	1	yes	characteristic
40	C₂³×C₅²	C₂³	1	2	yes	—
41	C₂²×C₅×D₅	C₂³	1	1	yes	characteristic
42	C₅²×Q₈	—	2	2	no	—
43	C₅²×D₄	—	2	4	no	—
44	C₅²×D₄	D₄	1	4	yes	complemented
45	C₂×C₄×C₅²	—	2	4	no	—
46	C₂×C₄×C₅²	—	2	2	no	—
47	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
48	C₂×C₄×C₅²	C₂³	1	2	yes	—
49	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
50	C₅×C₂²⋊D₅	—	2	4	no	—
51	C₅×C₂²⋊D₅	—	2	2	no	—
52	C₂×C₅×Dic₅	—	2	4	no	—
53	C₂×C₅×Dic₅	—	2	4	no	—
54	C₂×C₅×Dic₅	C₂³	1	2	yes	—
55	C₂×C₅×Dic₅	C₂³	1	1	yes	characteristic
56	C₂×C₅×Dic₅	C₂³	1	2	yes	—
57	C₂×C₅×Dic₅	C₂³	1	1	yes	characteristic
58	C₂×C₅×Dic₅	C₂³	1	1	yes	characteristic
59	C₄×C₅×D₅	—	2	2	no	—
60	C₅×Dic₁₀	—	2	2	no	—
61	C₂×C₅×#41	—	2	2	no	—
62	C₂×C₅×#41	—	5	1	no	—
63	C₂×C₅×#41	D₅	1	1	yes	characteristic, complemented
64	C₂×C₅×#41	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂×#711	C₂×C₅	1	1	yes	characteristic, complemented
66	C₅×C₄⋊Q₈	—	5	1	no	—
67	C₅×#123	—	5	2	no	—
68	C₅×#123	—	5	2	no	—
69	C₅×C₂²⋊Q₈	—	5	1	no	—
70	C₅×C₂²⋊Q₈	—	5	1	no	—
71	C₅×#121	—	5	2	no	—
72	C₄×C₅×D₄	—	5	1	no	—
73	C₄×C₅×D₄	—	5	1	no	—
74	C₂×C₅×C₄⋊C₄	—	5	2	no	—
75	#4092	C₂×C₅	1	1	yes	characteristic, complemented
76	#4090	C₂×C₅	1	1	yes	characteristic, complemented
77	#4085	C₂×C₅	1	2	yes	complemented
78	#4081	C₂×C₅	1	2	yes	complemented
79	D₄×Dic₅	C₂×C₅	1	1	yes	characteristic, complemented
80	#4075	C₂×C₅	1	2	yes	complemented
81	C₄×C₂²⋊D₅	C₂×C₅	1	1	yes	characteristic, complemented
82	#4070	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂×#683	C₂×C₅	1	2	yes	complemented
84	C₂²×C₅²	—	2	2	no	—
85	C₂²×C₅²	—	2	2	no	—
86	C₂²×C₅²	—	2	1	no	—
87	C₂²×C₅²	—	2	1	no	—
88	C₂²×C₅²	—	2	1	no	—
89	C₂²×C₅²	C₂×D₄	1	4	yes	—
90	C₂²×C₅²	C₂⁴	1	1	yes	characteristic
91	C₂×C₅×D₅	—	2	1	no	—
92	C₂×C₅×D₅	—	2	1	no	—
93	C₂×C₅×D₅	—	2	1	no	—
94	C₄×C₅²	—	2	1	no	—
95	C₄×C₅²	—	2	2	no	—
96	C₄×C₅²	C₂×D₄	1	2	yes	—
97	C₅×Dic₅	—	2	2	no	—
98	C₅×Dic₅	—	2	1	no	—
99	C₅×Dic₅	—	2	2	no	—
100	C₅×Dic₅	—	2	1	no	—
101	C₅×Dic₅	#41	1	2	yes	complemented
102	C₅×#41	—	2	16	no	—
103	C₅×#41	—	2	4	no	—
104	C₅×#41	—	2	4	no	—
105	C₅×#41	—	10	4	no	—
106	C₂×C₅×Q₈	—	2	2	no	—
107	C₂×C₅×Q₈	—	5	1	no	—
108	C₂×C₅×Q₈	C₂×D₅	1	1	yes	characteristic
109	C₂×C₅×Q₈	C₂²×C₅	1	1	yes	characteristic
110	C₂×C₅×D₄	—	2	4	no	—
111	C₂×C₅×D₄	—	2	2	no	—
112	C₂×C₅×D₄	—	5	1	no	—
113	C₂×C₅×D₄	—	5	2	no	—
114	C₂×C₅×D₄	C₂×D₅	1	2	yes	—
115	C₂×C₅×D₄	C₂×D₅	1	1	yes	characteristic
116	C₂×C₅×D₄	C₂²×C₅	1	2	yes	—
117	C₂×C₅×D₄	C₂²×C₅	1	1	yes	characteristic
118	C₂²×C₄×C₅	—	2	4	no	—
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	—	5	2	no	—
121	C₂²×C₄×C₅	—	5	2	no	—
122	C₂²×C₄×C₅	—	5	1	no	—
123	C₂²×C₄×C₅	C₂×D₅	1	2	yes	—
124	C₂²×C₄×C₅	C₂×D₅	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂²×C₅	1	2	yes	—
126	C₂²×C₄×C₅	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
129	C₂²×Dic₅	C₂²×C₅	1	2	yes	—
130	C₂²×Dic₅	C₂²×C₅	1	2	yes	—
131	#711	—	2	4	no	—
132	C₂×C₄×D₅	C₂²×C₅	1	1	yes	characteristic
133	C₂×Dic₁₀	C₂²×C₅	1	1	yes	characteristic
134	C₅×C₄⋊C₄	—	5	1	no	—
135	C₅×C₄⋊C₄	—	5	2	no	—
136	C₅×C₄⋊C₄	—	5	2	no	—
137	C₅×C₄⋊C₄	—	5	2	no	—
138	C₅×C₄⋊C₄	—	5	1	no	—
139	C₅×C₄⋊C₄	—	5	2	no	—
140	C₅×C₂²⋊C₄	—	5	2	no	—
141	C₅×C₂²⋊C₄	—	5	1	no	—
142	C₅×C₂²⋊C₄	—	5	2	no	—
143	C₅×C₂²⋊C₄	—	5	1	no	—
144	C₅×C₂²⋊C₄	—	5	2	no	—
145	C₄²×C₅	—	5	1	no	—
146	C₂²⋊Dic₅	C₂²×C₅	1	2	yes	—
147	C₂²⋊Dic₅	C₂²×C₅	1	1	yes	characteristic
148	C₂²⋊Dic₅	C₂²×C₅	1	2	yes	—
149	#685	C₂²×C₅	1	1	yes	characteristic
150	#685	C₂²×C₅	1	2	yes	—
151	C₄⋊Dic₅	C₂²×C₅	1	1	yes	characteristic
152	#683	C₂²×C₅	1	1	yes	characteristic
153	#683	C₂²×C₅	1	2	yes	—
154	#683	C₂²×C₅	1	2	yes	—
155	#683	C₂²×C₅	1	2	yes	—
156	#683	C₂²×C₅	1	2	yes	—
157	C₄×Dic₅	C₂²×C₅	1	1	yes	characteristic
158	#547	—	5	1	no	Sylow
159	C₂×C₅²	—	2	4	no	—
160	C₂×C₅²	—	4	1	no	—
161	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₅²	C₂×#41	1	1	yes	characteristic
163	C₂×C₅²	2₋¹⁺⁴	1	1	yes	characteristic
164	C₅×D₅	—	4	1	no	—
165	C₂³×C₅	—	2	2	no	—
166	C₂³×C₅	—	2	4	no	—
167	C₂³×C₅	—	5	1	no	—
168	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
169	C₂³×C₅	C₂²×D₅	1	2	yes	—
170	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
171	C₂³×C₅	C₂³×C₅	1	2	yes	—
172	C₂²×D₅	C₂³×C₅	1	1	yes	characteristic
173	C₅×Q₈	—	2	8	no	—
174	C₅×Q₈	—	2	2	no	—
175	C₅×Q₈	—	2	2	no	—
176	C₅×Q₈	—	10	2	no	—
177	C₅×D₄	—	2	16	no	—
178	C₅×D₄	—	2	4	no	—
179	C₅×D₄	—	2	4	no	—
180	C₅×D₄	—	2	8	no	—
181	C₅×D₄	—	10	2	no	—
182	C₅×D₄	—	10	4	no	—
183	C₅×D₄	C₂²⋊D₅	1	4	yes	complemented
184	C₅×D₄	C₅×D₄	1	4	yes	complemented
185	C₂×C₄×C₅	—	2	16	no	—
186	C₂×C₄×C₅	—	2	8	no	—
187	C₂×C₄×C₅	—	2	4	no	—
188	C₂×C₄×C₅	—	2	4	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	4	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	5	1	no	—
195	C₂×C₄×C₅	—	5	1	no	—
196	C₂×C₄×C₅	—	5	2	no	—
197	C₂×C₄×C₅	—	5	1	no	—
198	C₂×C₄×C₅	—	5	2	no	—
199	C₂×C₄×C₅	—	10	4	no	—
200	C₂×C₄×C₅	—	10	4	no	—
201	C₂×C₄×C₅	—	10	2	no	—
202	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂²×D₅	1	2	yes	—
204	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂³×C₅	1	2	yes	—
207	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
208	C₂²⋊D₅	—	2	4	no	—
209	C₂²⋊D₅	—	2	2	no	—
210	C₂×Dic₅	—	2	4	no	—
211	C₂×Dic₅	—	2	4	no	—
212	C₂×Dic₅	C₂³×C₅	1	1	yes	characteristic
213	C₂×Dic₅	C₂³×C₅	1	2	yes	—
214	C₂×Dic₅	C₂³×C₅	1	1	yes	characteristic
215	C₂×Dic₅	C₂³×C₅	1	2	yes	—
216	C₂×Dic₅	C₂³×C₅	1	1	yes	characteristic
217	C₄×D₅	—	2	2	no	—
218	Dic₁₀	—	2	2	no	—
219	C₂×#41	—	5	1	no	—
220	C₂×#41	C₅×D₅	1	1	yes	characteristic, complemented
221	C₄⋊Q₈	—	5	1	no	—
222	#123	—	5	2	no	—
223	#123	—	5	2	no	—
224	C₂²⋊Q₈	—	5	1	no	—
225	C₂²⋊Q₈	—	5	1	no	—
226	#121	—	5	2	no	—
227	C₄×D₄	—	5	1	no	—
228	C₄×D₄	—	5	1	no	—
229	C₂×C₄⋊C₄	—	5	2	no	—
230	C₅²	#547	1	1	yes	characteristic, complemented, Sylow
231	C₂²×C₅	—	2	2	no	—
232	C₂²×C₅	—	2	2	no	—
233	C₂²×C₅	—	2	2	no	—
234	C₂²×C₅	—	2	2	no	—
235	C₂²×C₅	—	2	4	no	—
236	C₂²×C₅	—	2	1	no	—
237	C₂²×C₅	—	2	1	no	—
238	C₂²×C₅	—	2	1	no	—
239	C₂²×C₅	—	2	1	no	—
240	C₂²×C₅	—	2	1	no	—
241	C₂²×C₅	—	2	1	no	—
242	C₂²×C₅	—	2	8	no	—
243	C₂²×C₅	—	2	2	no	—
244	C₂²×C₅	—	4	4	no	—
245	C₂²×C₅	—	4	4	no	—
246	C₂²×C₅	—	4	2	no	—
247	C₂²×C₅	—	4	2	no	—
248	C₂²×C₅	—	10	1	no	—
249	C₂²×C₅	—	10	1	no	—
250	C₂²×C₅	—	10	1	no	—
251	C₂²×C₅	C₂×C₂²⋊D₅	1	4	yes	—
252	C₂²×C₅	C₂×C₅×D₄	1	4	yes	—
253	C₂²×C₅	C₂³×D₅	1	1	yes	characteristic
254	C₂²×C₅	C₂⁴×C₅	1	1	yes	characteristic
255	C₂×D₅	—	2	1	no	—
256	C₂×D₅	—	2	1	no	—
257	C₂×D₅	—	2	1	no	—
258	C₄×C₅	—	2	4	no	—
259	C₄×C₅	—	2	8	no	—
260	C₄×C₅	—	2	1	no	—
261	C₄×C₅	—	2	2	no	—
262	C₄×C₅	—	2	1	no	—
263	C₄×C₅	—	2	2	no	—
264	C₄×C₅	—	2	4	no	—
265	C₄×C₅	—	5	2	no	—
266	C₄×C₅	—	10	2	no	—
267	C₄×C₅	—	10	1	no	—
268	C₄×C₅	—	10	1	no	—
269	C₄×C₅	—	10	2	no	—
270	C₄×C₅	C₂×C₂²⋊D₅	1	2	yes	—
271	C₄×C₅	C₂×C₅×D₄	1	2	yes	—
272	Dic₅	—	2	2	no	—
273	Dic₅	—	2	1	no	—
274	Dic₅	—	2	2	no	—
275	Dic₅	—	2	1	no	—
276	Dic₅	C₅×#41	1	2	yes	complemented
277	#41	—	2	4	no	—
278	#41	—	10	4	no	—
279	C₂×Q₈	—	5	1	no	—
280	C₂×Q₈	C₂×C₅×D₅	1	1	yes	characteristic
281	C₂×D₄	—	5	1	no	—
282	C₂×D₄	—	5	2	no	—
283	C₂×D₄	C₂×C₅×D₅	1	2	yes	—
284	C₂×D₄	C₂×C₅×D₅	1	1	yes	characteristic
285	C₂²×C₄	—	5	2	no	—
286	C₂²×C₄	—	5	2	no	—
287	C₂²×C₄	—	5	1	no	—
288	C₂²×C₄	C₂×C₅×D₅	1	2	yes	—
289	C₂²×C₄	C₂×C₅×D₅	1	1	yes	characteristic
290	C₄⋊C₄	—	5	1	no	—
291	C₄⋊C₄	—	5	2	no	—
292	C₄⋊C₄	—	5	2	no	—
293	C₄⋊C₄	—	5	2	no	—
294	C₄⋊C₄	—	5	1	no	—
295	C₄⋊C₄	—	5	2	no	—
296	C₂²⋊C₄	—	5	2	no	—
297	C₂²⋊C₄	—	5	1	no	—
298	C₂²⋊C₄	—	5	2	no	—
299	C₂²⋊C₄	—	5	1	no	—
300	C₂²⋊C₄	—	5	2	no	—
301	C₄²	—	5	1	no	—
302	C₂×C₅	—	2	4	no	—
303	C₂×C₅	—	2	4	no	—
304	C₂×C₅	—	2	2	no	—
305	C₂×C₅	—	2	2	no	—
306	C₂×C₅	—	2	2	no	—
307	C₂×C₅	—	4	8	no	—
308	C₂×C₅	—	4	4	no	—
309	C₂×C₅	—	4	1	no	—
310	C₂×C₅	—	4	1	no	—
311	C₂×C₅	—	20	1	no	—
312	C₂×C₅	D₅×#41	1	1	yes	characteristic
313	C₂×C₅	#4150	1	1	yes	characteristic
314	C₂×C₅	C₂²×C₂²⋊D₅	1	1	yes	characteristic
315	C₂×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
316	C₂×C₅	C₂×C₅×#41	1	1	yes	characteristic
317	C₂×C₅	C₅×2₋¹⁺⁴	1	1	yes	characteristic
318	D₅	—	4	1	no	—
319	C₂³	—	5	1	no	—
320	C₂³	C₂²×C₅×D₅	1	1	yes	characteristic
321	C₂³	C₂²×C₅×D₅	1	2	yes	—
322	Q₈	—	2	2	no	—
323	Q₈	—	10	2	no	—
324	D₄	—	2	4	no	—
325	D₄	—	10	2	no	—
326	D₄	—	10	4	no	—
327	D₄	C₅×C₂²⋊D₅	1	4	yes	complemented
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	5	1	no	—
331	C₂×C₄	—	5	1	no	—
332	C₂×C₄	—	5	2	no	—
333	C₂×C₄	—	5	1	no	—
334	C₂×C₄	—	5	2	no	—
335	C₂×C₄	—	10	4	no	—
336	C₂×C₄	—	10	4	no	—
337	C₂×C₄	—	10	2	no	—
338	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
339	C₂×C₄	C₂²×C₅×D₅	1	2	yes	—
340	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
341	C₅	—	2	2	no	—
342	C₅	#66158	1	1	yes	characteristic, direct product factor
343	C₅	C₅×#547	1	1	yes	characteristic, complemented
344	C₂²	—	2	2	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	10	1	no	—
350	C₂²	—	10	1	no	—
351	C₂²	—	10	1	no	—
352	C₂²	C₂×C₅×C₂²⋊D₅	1	4	yes	—
353	C₂²	C₂³×C₅×D₅	1	1	yes	characteristic
354	C₄	—	2	1	no	—
355	C₄	—	2	2	no	—
356	C₄	—	5	2	no	—
357	C₄	—	10	2	no	—
358	C₄	—	10	1	no	—
359	C₄	—	10	1	no	—
360	C₄	—	10	2	no	—
361	C₄	C₂×C₅×C₂²⋊D₅	1	2	yes	—
362	C₂	—	2	4	no	—
363	C₂	—	4	1	no	—
364	C₂	—	20	1	no	—
365	C₂	C₅×D₅×#41	1	1	yes	characteristic
366	C₂	C₅×#4150	1	1	yes	characteristic
367	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	C₂×C₅²×#41	C₂
socle	C₂²×C₅²	C₂⁴
hypercenter	C₂×C₅×#41	D₅
hypocenter	C₅	C₅×#547
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₅×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₅²×#41	C₂	semidirect
2. C₂×C₅×#711	C₂	semidirect
3. C₅×#4092	C₂	semidirect
4. C₅×#4090	C₂	semidirect
5. C₅×#4085	C₂	semidirect
6. C₅×#4081	C₂	semidirect
7. C₅×D₄×Dic₅	C₂	semidirect
8. C₅×#4075	C₂	semidirect
9. C₄×C₅×C₂²⋊D₅	C₂	semidirect
10. C₅×#4070	C₂	semidirect
11. C₂×C₅×#683	C₂	semidirect
38. #66158	C₅	direct (N × H)
44. C₅²×D₄	D₄	semidirect
63. C₂×C₅×#41	D₅	semidirect
64. C₂×C₅×#41	C₂×C₅	semidirect
65. C₂×#711	C₂×C₅	semidirect
75. #4092	C₂×C₅	semidirect
76. #4090	C₂×C₅	semidirect
77. #4085	C₂×C₅	semidirect
78. #4081	C₂×C₅	semidirect
79. D₄×Dic₅	C₂×C₅	semidirect
80. #4075	C₂×C₅	semidirect
81. C₄×C₂²⋊D₅	C₂×C₅	semidirect
82. #4070	C₂×C₅	semidirect
83. C₂×#683	C₂×C₅	semidirect
101. C₅×Dic₅	#41	semidirect
183. C₅×D₄	C₂²⋊D₅	semidirect
184. C₅×D₄	C₅×D₄	semidirect
220. C₂×#41	C₅×D₅	semidirect
230. C₅²	#547	semidirect
276. Dic₅	C₅×#41	semidirect
327. D₄	C₅×C₂²⋊D₅	semidirect
342. C₅	#66158	direct (N × H)
343. C₅	C₅×#547	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅²×#41	2
C₂×C₅×#711	2
C₅×#4092	2
C₅×#4090	2
C₅×#4085	2
C₅×#4081	2
C₅×D₄×Dic₅	2
C₅×#4075	2
C₄×C₅×C₂²⋊D₅	2
C₅×#4070	2
C₂×C₅×#683	2
C₅×#547	5
#66158	5

Subgroups — C5×#66158 #13106987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#66158 #13106987