Subgroups — C₅×#10610272 #72223027

Order 3200.

1058 conjugacy classes of subgroups.

The subgroup lattice has 381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#66082	C₂	1	1	yes	maximal, characteristic
2	C₅×#66079	C₂	1	2	yes	maximal, complemented
3	C₄×C₅²×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#65414	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#3937	C₂	1	2	yes	maximal, complemented
6	C₅×#65006	C₂	1	4	yes	maximal, complemented
7	C₅×#64989	C₂	1	4	yes	maximal, complemented
8	C₂×C₅×#709	C₂²	1	2	yes	—
9	C₂×C₅²×M₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₅²×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₅²	C₂²	1	1	yes	characteristic
12	C₂×C₅×#681	C₂²	1	2	yes	—
13	C₅×#4055	C₄	1	4	yes	complemented
14	C₅×#4054	C₄	1	4	yes	complemented
15	C₅×#4053	—	2	4	no	—
16	C₅×D₅×M₁₆	—	2	4	no	—
17	C₅×#4050	C₂²	1	4	yes	—
18	C₅×#4047	C₂²	1	8	yes	complemented
19	C₅²×#97	C₂²	1	2	yes	complemented
20	C₄×C₅²×C₈	C₂²	1	2	yes	complemented
21	C₅×#3951	C₂²	1	4	yes	complemented
22	C₅×#3937	C₂²	1	4	yes	complemented
23	C₅×#3937	C₂²	1	4	yes	complemented
24	C₅×#2956	—	5	1	no	maximal
25	#10610272	C₅	1	1	yes	maximal, characteristic, direct product factor
26	C₂²×C₄×C₅²	—	2	1	no	—
27	C₂²×C₄×C₅²	C₂³	1	1	yes	characteristic
28	C₂×C₅×C₂²⋊D₅	—	2	2	no	—
29	C₅×#709	—	2	2	no	—
30	C₅×#709	—	2	2	no	—
31	C₅×#709	C₂×C₄	1	4	yes	—
32	C₅×#709	C₂³	1	4	yes	—
33	C₂×C₅×D₂₀	C₂×C₄	1	2	yes	—
34	C₂×C₄×C₅×D₅	—	2	2	no	—
35	C₂×C₅×Dic₁₀	C₂×C₄	1	2	yes	—
36	C₅²×M₁₆	C₂×C₄	1	4	yes	—
37	C₅²×M₁₆	D₄	1	4	yes	—
38	C₂×C₅²×C₈	C₂³	1	2	yes	—
39	C₂×C₅²×C₈	C₂³	1	2	yes	—
40	C₄²×C₅²	—	2	1	no	—
41	C₄²×C₅²	C₂³	1	1	yes	characteristic
42	C₄²×C₅²	C₂³	1	1	yes	characteristic
43	C₅×#681	—	2	2	no	—
44	C₅×#681	C₂³	1	4	yes	—
45	C₂×C₅×#168	—	2	2	no	—
46	C₅×Dic₂₀	C₂×C₄	1	4	yes	complemented
47	C₅×D₄₀	C₂×C₄	1	4	yes	complemented
48	C₅×#677	C₂×C₄	1	8	yes	complemented
49	C₅×#676	—	2	8	no	—
50	C₅×C₈×D₅	—	2	8	no	—
51	C₅×#575	—	5	1	no	—
52	C₅×#568	—	5	2	no	—
53	#66082	C₂×C₅	1	1	yes	characteristic
54	#66079	C₂×C₅	1	2	yes	complemented
55	C₅×#444	—	5	4	no	—
56	C₅×#443	—	5	4	no	—
57	C₅×#430	—	5	1	no	—
58	C₂×C₅×#104	—	5	2	no	—
59	C₄×C₅×M₁₆	—	2	2	no	—
60	C₄×C₅×M₁₆	D₅	1	1	yes	characteristic, complemented
61	C₄×C₅×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
62	#65414	C₂×C₅	1	1	yes	characteristic, complemented
63	C₂×#3937	C₂×C₅	1	2	yes	complemented
64	#65006	C₂×C₅	1	4	yes	complemented
65	#64989	C₂×C₅	1	4	yes	complemented
66	C₂³×C₅²	#41	1	1	yes	characteristic
67	C₂²×C₅×D₅	—	2	2	no	—
68	C₂×C₄×C₅²	—	2	1	no	—
69	C₂×C₄×C₅²	—	2	1	no	—
70	C₂×C₄×C₅²	—	4	2	no	—
71	C₂×C₄×C₅²	C₂²×C₄	1	2	yes	—
72	C₂×C₄×C₅²	C₂×D₄	1	2	yes	—
73	C₂×C₄×C₅²	#41	1	1	yes	characteristic
74	C₂×C₄×C₅²	C₂⁴	1	1	yes	characteristic
75	C₅×C₂²⋊D₅	—	2	4	no	—
76	C₅×C₂²⋊D₅	—	2	4	no	—
77	C₂×C₅×Dic₅	—	2	2	no	—
78	C₅×D₂₀	—	2	2	no	—
79	C₅×D₂₀	C₂²×C₄	1	4	yes	—
80	C₄×C₅×D₅	—	2	4	no	—
81	C₄×C₅×D₅	—	2	4	no	—
82	C₅×Dic₁₀	—	2	2	no	—
83	C₅×Dic₁₀	C₂²×C₄	1	4	yes	—
84	C₅²×C₈	C₂²×C₄	1	4	yes	—
85	C₅²×C₈	C₂×D₄	1	4	yes	—
86	C₅×#168	—	2	4	no	—
87	C₂×C₅×#41	—	5	2	no	—
88	C₂×#709	C₂²×C₅	1	2	yes	—
89	C₅×#137	—	5	4	no	—
90	C₅×AGL(1,ℤ/8)	—	5	4	no	—
91	C₅×#135	—	5	4	no	—
92	C₅×#131	—	5	8	no	—
93	C₅×#131	—	10	4	no	—
94	C₂×C₅×M₁₆	—	2	2	no	—
95	C₂×C₅×M₁₆	—	2	2	no	—
96	C₂×C₅×M₁₆	—	5	2	no	—
97	C₂×C₅×M₁₆	—	10	4	no	—
98	C₂×C₅×M₁₆	C₂×D₅	1	1	yes	characteristic
99	C₂×C₅×M₁₆	C₂×D₅	1	1	yes	characteristic
100	C₂×C₅×M₁₆	C₂²×C₅	1	1	yes	characteristic
101	C₂×C₅×M₁₆	C₂²×C₅	1	1	yes	characteristic
102	C₂×C₄²×C₅	—	2	2	no	—
103	C₂×C₄²×C₅	C₂×D₅	1	1	yes	characteristic
104	C₂×C₄²×C₅	C₂²×C₅	1	1	yes	characteristic
105	C₂×#681	C₂²×C₅	1	2	yes	—
106	#4055	C₄×C₅	1	4	yes	complemented
107	#4054	C₄×C₅	1	4	yes	complemented
108	#4053	—	2	4	no	—
109	D₅×M₁₆	—	2	4	no	—
110	#4050	C₂²×C₅	1	4	yes	—
111	#4047	C₂²×C₅	1	8	yes	complemented
112	C₅×#108	—	5	4	no	—
113	C₅×#104	—	5	4	no	—
114	C₅×#104	—	5	4	no	—
115	C₅×#97	—	2	4	no	—
116	C₅×#97	C₂×D₅	1	2	yes	complemented
117	C₅×#97	C₂²×C₅	1	2	yes	complemented
118	C₄×C₅×C₈	—	2	4	no	—
119	C₄×C₅×C₈	C₂×D₅	1	2	yes	complemented
120	C₄×C₅×C₈	C₂²×C₅	1	2	yes	complemented
121	#3951	C₂²×C₅	1	4	yes	complemented
122	#3937	C₂²×C₅	1	4	yes	complemented
123	#3937	C₂²×C₅	1	4	yes	complemented
124	#2956	—	5	1	no	Sylow
125	C₂²×C₅²	—	4	1	no	—
126	C₂²×C₅²	C₄×D₄	1	2	yes	—
127	C₂²×C₅²	C₂×#41	1	1	yes	characteristic
128	C₂×C₅×D₅	—	2	4	no	—
129	C₂×C₅×D₅	—	8	2	no	—
130	C₄×C₅²	—	2	2	no	—
131	C₄×C₅²	—	4	1	no	—
132	C₄×C₅²	C₄×D₄	1	2	yes	—
133	C₄×C₅²	C₂³×C₄	1	1	yes	characteristic
134	C₄×C₅²	C₂²×D₄	1	1	yes	characteristic
135	C₅×Dic₅	—	2	4	no	—
136	C₅×#41	—	5	4	no	—
137	C₅×#41	—	5	4	no	—
138	C₅×#41	—	10	2	no	—
139	C₅×#41	—	10	2	no	—
140	C₂×C₅×Q₈	—	5	2	no	—
141	C₂×C₅×D₄	—	5	2	no	—
142	C₂×C₅×D₄	—	10	2	no	—
143	C₂²×C₄×C₅	—	2	4	no	—
144	C₂²×C₄×C₅	—	2	1	no	—
145	C₂²×C₄×C₅	—	2	1	no	—
146	C₂²×C₄×C₅	—	2	2	no	—
147	C₂²×C₄×C₅	—	10	2	no	—
148	C₂²×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
150	C₂×C₂²⋊D₅	—	2	2	no	—
151	#709	—	2	2	no	—
152	#709	—	2	2	no	—
153	#709	C₂×C₄×C₅	1	4	yes	—
154	#709	C₂³×C₅	1	4	yes	—
155	C₂×D₂₀	C₂×C₄×C₅	1	2	yes	—
156	C₂×C₄×D₅	—	2	2	no	—
157	C₂×Dic₁₀	C₂×C₄×C₅	1	2	yes	—
158	C₅×Q₁₆	—	5	4	no	—
159	C₅×SD₁₆	—	5	8	no	—
160	C₅×D₈	—	5	4	no	—
161	C₅×M₁₆	—	2	8	no	—
162	C₅×M₁₆	—	2	8	no	—
163	C₅×M₁₆	—	5	4	no	—
164	C₅×M₁₆	—	10	2	no	—
165	C₅×M₁₆	—	10	8	no	—
166	C₅×M₁₆	C₄×D₅	1	4	yes	—
167	C₅×M₁₆	D₂₀	1	4	yes	—
168	C₅×M₁₆	C₂×C₄×C₅	1	4	yes	—
169	C₅×M₁₆	C₅×D₄	1	4	yes	—
170	C₂×C₅×C₈	—	2	4	no	—
171	C₂×C₅×C₈	—	2	4	no	—
172	C₂×C₅×C₈	—	10	2	no	—
173	C₂×C₅×C₈	—	10	8	no	—
174	C₂×C₅×C₈	C₂²×D₅	1	2	yes	—
175	C₂×C₅×C₈	C₂²×D₅	1	2	yes	—
176	C₂×C₅×C₈	C₂³×C₅	1	2	yes	—
177	C₂×C₅×C₈	C₂³×C₅	1	2	yes	—
178	C₄²×C₅	—	2	4	no	—
179	C₄²×C₅	—	2	1	no	—
180	C₄²×C₅	—	2	1	no	—
181	C₄²×C₅	—	2	2	no	—
182	C₄²×C₅	—	2	2	no	—
183	C₄²×C₅	C₂²×D₅	1	1	yes	characteristic
184	C₄²×C₅	C₂²×D₅	1	1	yes	characteristic
185	C₄²×C₅	C₂³×C₅	1	1	yes	characteristic
186	C₄²×C₅	C₂³×C₅	1	1	yes	characteristic
187	#681	—	2	2	no	—
188	#681	C₂³×C₅	1	4	yes	—
189	C₂×#168	—	2	2	no	—
190	Dic₂₀	C₂×C₄×C₅	1	4	yes	complemented
191	D₄₀	C₂×C₄×C₅	1	4	yes	complemented
192	#677	C₂×C₄×C₅	1	8	yes	complemented
193	#676	—	2	8	no	—
194	C₈×D₅	—	2	8	no	—
195	#575	—	5	1	no	—
196	#568	—	5	2	no	—
197	#444	—	5	4	no	—
198	#443	—	5	4	no	—
199	#430	—	5	1	no	—
200	C₂×#104	—	5	2	no	—
201	C₄×M₁₆	C₅×D₅	1	1	yes	characteristic, complemented
202	C₂×C₅²	—	2	1	no	—
203	C₂×C₅²	—	2	2	no	—
204	C₂×C₅²	C₂×C₄×D₄	1	1	yes	characteristic
205	C₅×D₅	—	4	4	no	—
206	C₂³×C₅	—	2	2	no	—
207	C₂³×C₅	—	10	2	no	—
208	C₂³×C₅	#709	1	1	yes	characteristic
209	C₂³×C₅	C₅×#41	1	1	yes	characteristic
210	C₂²×D₅	—	2	2	no	—
211	C₅×Q₈	—	5	4	no	—
212	C₅×Q₈	—	10	2	no	—
213	C₅×D₄	—	5	4	no	—
214	C₅×D₄	—	10	4	no	—
215	C₅×D₄	—	10	4	no	—
216	C₅×D₄	—	10	2	no	—
217	C₂×C₄×C₅	—	2	4	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	4	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	2	4	no	—
224	C₂×C₄×C₅	—	2	4	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	4	2	no	—
228	C₂×C₄×C₅	—	4	2	no	—
229	C₂×C₄×C₅	—	4	8	no	—
230	C₂×C₄×C₅	—	10	2	no	—
231	C₂×C₄×C₅	—	10	4	no	—
232	C₂×C₄×C₅	—	10	4	no	—
233	C₂×C₄×C₅	C₂×C₄×D₅	1	2	yes	—
234	C₂×C₄×C₅	C₂×D₂₀	1	2	yes	—
235	C₂×C₄×C₅	#709	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂²×C₄×C₅	1	2	yes	—
237	C₂×C₄×C₅	C₂×C₅×D₄	1	2	yes	—
238	C₂×C₄×C₅	C₅×#41	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂³×D₅	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂⁴×C₅	1	1	yes	characteristic
241	C₂²⋊D₅	—	2	4	no	—
242	C₂²⋊D₅	—	2	4	no	—
243	C₂×Dic₅	—	2	2	no	—
244	D₂₀	—	2	2	no	—
245	D₂₀	C₂²×C₄×C₅	1	4	yes	—
246	C₄×D₅	—	2	4	no	—
247	C₄×D₅	—	2	4	no	—
248	Dic₁₀	—	2	2	no	—
249	Dic₁₀	C₂²×C₄×C₅	1	4	yes	—
250	C₅×C₈	—	2	8	no	—
251	C₅×C₈	—	2	8	no	—
252	C₅×C₈	—	10	4	no	—
253	C₅×C₈	C₂×C₄×D₅	1	4	yes	—
254	C₅×C₈	C₂×D₂₀	1	4	yes	—
255	C₅×C₈	C₂²×C₄×C₅	1	4	yes	—
256	C₅×C₈	C₂×C₅×D₄	1	4	yes	—
257	#168	—	2	4	no	—
258	C₂×#41	—	5	2	no	—
259	#137	—	5	4	no	—
260	AGL(1,ℤ/8)	—	5	4	no	—
261	#135	—	5	4	no	—
262	#131	—	5	8	no	—
263	#131	—	10	4	no	—
264	C₂×M₁₆	—	5	2	no	—
265	C₂×M₁₆	—	10	4	no	—
266	C₂×M₁₆	C₂×C₅×D₅	1	1	yes	characteristic
267	C₂×M₁₆	C₂×C₅×D₅	1	1	yes	characteristic
268	C₂×C₄²	C₂×C₅×D₅	1	1	yes	characteristic
269	#108	—	5	4	no	—
270	#104	—	5	4	no	—
271	#104	—	5	4	no	—
272	#97	C₂×C₅×D₅	1	2	yes	complemented
273	C₄×C₈	C₂×C₅×D₅	1	2	yes	complemented
274	C₅²	#2956	1	1	yes	characteristic, complemented, Sylow
275	C₂²×C₅	—	2	2	no	—
276	C₂²×C₅	—	2	4	no	—
277	C₂²×C₅	—	4	1	no	—
278	C₂²×C₅	—	4	1	no	—
279	C₂²×C₅	—	4	4	no	—
280	C₂²×C₅	—	10	4	no	—
281	C₂²×C₅	—	40	2	no	—
282	C₂²×C₅	C₄×D₂₀	1	2	yes	—
283	C₂²×C₅	C₄×C₅×D₄	1	2	yes	—
284	C₂²×C₅	C₂×#709	1	1	yes	characteristic
285	C₂²×C₅	C₂×C₅×#41	1	1	yes	characteristic
286	C₂×D₅	—	2	4	no	—
287	C₂×D₅	—	8	2	no	—
288	C₄×C₅	—	2	8	no	—
289	C₄×C₅	—	2	2	no	—
290	C₄×C₅	—	2	2	no	—
291	C₄×C₅	—	2	2	no	—
292	C₄×C₅	—	2	2	no	—
293	C₄×C₅	—	2	4	no	—
294	C₄×C₅	—	4	4	no	—
295	C₄×C₅	—	4	1	no	—
296	C₄×C₅	—	4	1	no	—
297	C₄×C₅	—	10	4	no	—
298	C₄×C₅	C₄×D₂₀	1	2	yes	—
299	C₄×C₅	C₄×C₅×D₄	1	2	yes	—
300	C₄×C₅	C₂²×C₄×D₅	1	1	yes	characteristic
301	C₄×C₅	C₂²×D₂₀	1	1	yes	characteristic
302	C₄×C₅	C₂³×C₄×C₅	1	1	yes	characteristic
303	C₄×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
304	Dic₅	—	2	4	no	—
305	#41	—	5	4	no	—
306	#41	—	5	4	no	—
307	#41	—	10	2	no	—
308	#41	—	10	2	no	—
309	C₂×Q₈	—	5	2	no	—
310	C₂×D₄	—	5	2	no	—
311	C₂×D₄	—	10	2	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	10	2	no	—
314	C₂²×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
315	Q₁₆	—	5	4	no	—
316	SD₁₆	—	5	8	no	—
317	D₈	—	5	4	no	—
318	M₁₆	—	5	4	no	—
319	M₁₆	—	10	2	no	—
320	M₁₆	—	10	8	no	—
321	M₁₆	C₄×C₅×D₅	1	4	yes	—
322	M₁₆	C₅×D₂₀	1	4	yes	—
323	C₂×C₈	—	10	2	no	—
324	C₂×C₈	—	10	8	no	—
325	C₂×C₈	C₂²×C₅×D₅	1	2	yes	—
326	C₂×C₈	C₂²×C₅×D₅	1	2	yes	—
327	C₄²	—	2	1	no	—
328	C₄²	C₂²×C₅×D₅	1	1	yes	characteristic
329	C₄²	C₂²×C₅×D₅	1	1	yes	characteristic
330	C₂×C₅	—	2	4	no	—
331	C₂×C₅	—	2	1	no	—
332	C₂×C₅	—	2	2	no	—
333	C₂×C₅	—	2	1	no	—
334	C₂×C₅	—	2	2	no	—
335	C₂×C₅	—	2	2	no	—
336	C₂×C₅	—	4	4	no	—
337	C₂×C₅	—	20	4	no	—
338	C₂×C₅	C₂×C₄×D₂₀	1	1	yes	characteristic
339	C₂×C₅	C₂×C₄×C₅×D₄	1	1	yes	characteristic
340	D₅	—	4	4	no	—
341	C₂³	—	10	2	no	—
342	C₂³	C₅×#709	1	1	yes	characteristic
343	Q₈	—	5	4	no	—
344	Q₈	—	10	2	no	—
345	D₄	—	5	4	no	—
346	D₄	—	10	4	no	—
347	D₄	—	10	4	no	—
348	D₄	—	10	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	10	2	no	—
353	C₂×C₄	—	10	4	no	—
354	C₂×C₄	—	10	4	no	—
355	C₂×C₄	C₂×C₄×C₅×D₅	1	2	yes	—
356	C₂×C₄	C₂×C₅×D₂₀	1	2	yes	—
357	C₂×C₄	C₅×#709	1	1	yes	characteristic
358	C₂×C₄	C₂³×C₅×D₅	1	1	yes	characteristic
359	C₈	—	10	4	no	—
360	C₈	C₂×C₄×C₅×D₅	1	4	yes	—
361	C₈	C₂×C₅×D₂₀	1	4	yes	—
362	C₅	—	2	2	no	—
363	C₅	#10610272	1	1	yes	characteristic, direct product factor
364	C₅	C₅×#2956	1	1	yes	characteristic, complemented
365	C₂²	—	4	1	no	—
366	C₂²	—	10	4	no	—
367	C₂²	—	40	2	no	—
368	C₂²	C₄×C₅×D₂₀	1	2	yes	—
369	C₂²	C₂×C₅×#709	1	1	yes	characteristic
370	C₄	—	2	2	no	—
371	C₄	—	4	1	no	—
372	C₄	—	10	4	no	—
373	C₄	C₄×C₅×D₂₀	1	2	yes	—
374	C₄	C₂²×C₄×C₅×D₅	1	1	yes	characteristic
375	C₄	C₂²×C₅×D₂₀	1	1	yes	characteristic
376	C₂	—	2	1	no	—
377	C₂	—	2	2	no	—
378	C₂	—	20	4	no	—
379	C₂	C₂×C₄×C₅×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	C₂²×D₂₀
commutator	C₄×C₅	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₅
Fitting	C₄×C₅²×M₁₆	C₂
socle	C₂×C₅²	C₂×C₄×D₄
prime radical	C₅×#66082	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₅
hypercenter	C₄×C₅×M₁₆	D₅
hypocenter	C₅	C₅×#2956
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄×C₅ ◁ C₂×C₅×M₁₆ ◁ C₄×C₅×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₅×#66079	C₂	semidirect
3. C₄×C₅²×M₁₆	C₂	semidirect
4. C₅×#65414	C₂	semidirect
5. C₂×C₅×#3937	C₂	semidirect
6. C₅×#65006	C₂	semidirect
7. C₅×#64989	C₂	semidirect
13. C₅×#4055	C₄	semidirect
14. C₅×#4054	C₄	semidirect
18. C₅×#4047	C₂²	semidirect
19. C₅²×#97	C₂²	semidirect
20. C₄×C₅²×C₈	C₂²	semidirect
21. C₅×#3951	C₂²	semidirect
22. C₅×#3937	C₂²	semidirect
23. C₅×#3937	C₂²	semidirect
25. #10610272	C₅	direct (N × H)
46. C₅×Dic₂₀	C₂×C₄	semidirect
47. C₅×D₄₀	C₂×C₄	semidirect
48. C₅×#677	C₂×C₄	semidirect
54. #66079	C₂×C₅	semidirect
60. C₄×C₅×M₁₆	D₅	semidirect
61. C₄×C₅×M₁₆	C₂×C₅	semidirect
62. #65414	C₂×C₅	semidirect
63. C₂×#3937	C₂×C₅	semidirect
64. #65006	C₂×C₅	semidirect
65. #64989	C₂×C₅	semidirect
106. #4055	C₄×C₅	semidirect
107. #4054	C₄×C₅	semidirect
111. #4047	C₂²×C₅	semidirect
116. C₅×#97	C₂×D₅	semidirect
117. C₅×#97	C₂²×C₅	semidirect
119. C₄×C₅×C₈	C₂×D₅	semidirect
120. C₄×C₅×C₈	C₂²×C₅	semidirect
121. #3951	C₂²×C₅	semidirect
122. #3937	C₂²×C₅	semidirect
123. #3937	C₂²×C₅	semidirect
190. Dic₂₀	C₂×C₄×C₅	semidirect
191. D₄₀	C₂×C₄×C₅	semidirect
192. #677	C₂×C₄×C₅	semidirect
201. C₄×M₁₆	C₅×D₅	semidirect
272. #97	C₂×C₅×D₅	semidirect
273. C₄×C₈	C₂×C₅×D₅	semidirect
274. C₅²	#2956	semidirect
363. C₅	#10610272	direct (N × H)
364. C₅	C₅×#2956	semidirect

Maximal subgroups

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

subgroup	index
C₅×#66082	2
C₅×#66079	2
C₄×C₅²×M₁₆	2
C₅×#65414	2
C₂×C₅×#3937	2
C₅×#65006	2
C₅×#64989	2
C₅×#2956	5
#10610272	5

Subgroups — C5×#10610272 #72223027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10610272 #72223027