Subgroups — C₅×#2518 #10616113

Order 640.

454 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#397	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#396	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#394	C₂	1	1	yes	maximal, characteristic
4	C₅×#394	C₂	1	1	yes	maximal, characteristic
5	C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#387	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#386	C₂	1	1	yes	maximal, characteristic
12	C₅×#383	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic
36	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic
37	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic
38	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic
39	C₅×#95	C₂²	1	1	yes	characteristic
40	C₅×#95	C₂²	1	1	yes	characteristic
41	C₅×#95	C₂²	1	1	yes	characteristic
42	C₅×#95	C₂²	1	1	yes	characteristic
43	C₅×#95	C₂²	1	1	yes	characteristic
44	C₅×#95	C₂²	1	1	yes	characteristic
45	C₅×#95	C₂²	1	1	yes	characteristic
46	C₅×#95	C₂²	1	1	yes	characteristic
47	C₅×#95	C₂²	1	1	yes	characteristic
48	C₅×#95	C₂²	1	1	yes	characteristic
49	C₅×#95	C₂²	1	1	yes	characteristic
50	C₅×#95	C₂²	1	1	yes	characteristic
51	#2518	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
52	C₂⁴×C₅	C₂³	1	1	yes	characteristic
53	C₂⁴×C₅	C₂³	1	1	yes	characteristic
54	C₂×C₅×D₄	—	2	2	no	—
55	C₂×C₅×D₄	—	4	1	no	—
56	C₂×C₅×D₄	—	4	1	no	—
57	C₂²×C₄×C₅	—	2	2	no	—
58	C₂²×C₄×C₅	—	2	2	no	—
59	C₂²×C₄×C₅	—	4	1	no	—
60	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₅×C₄⋊C₄	—	2	2	no	—
74	C₅×C₄⋊C₄	—	2	2	no	—
75	C₅×C₄⋊C₄	—	4	1	no	—
76	C₅×C₄⋊C₄	—	4	1	no	—
77	C₅×C₄⋊C₄	—	4	1	no	—
78	C₅×C₄⋊C₄	—	4	1	no	—
79	C₅×C₂²⋊C₄	—	2	2	no	—
80	C₅×C₂²⋊C₄	—	2	2	no	—
81	C₅×C₂²⋊C₄	—	2	2	no	—
82	C₅×C₂²⋊C₄	—	2	2	no	—
83	C₅×C₂²⋊C₄	—	2	2	no	—
84	C₅×C₂²⋊C₄	—	2	2	no	—
85	C₅×C₂²⋊C₄	—	2	2	no	—
86	C₅×C₂²⋊C₄	—	2	2	no	—
87	C₅×C₂²⋊C₄	—	4	1	no	—
88	C₅×C₂²⋊C₄	—	4	1	no	—
89	C₅×C₂²⋊C₄	—	4	1	no	—
90	C₄²×C₅	—	2	2	no	—
91	C₄²×C₅	—	2	2	no	—
92	C₄²×C₅	—	4	1	no	—
93	C₄²×C₅	—	4	1	no	—
94	#397	C₂×C₅	1	1	yes	characteristic, complemented
95	#396	C₂×C₅	1	1	yes	characteristic, complemented
96	#394	C₂×C₅	1	1	yes	characteristic
97	#394	C₂×C₅	1	1	yes	characteristic
98	#389	C₂×C₅	1	1	yes	characteristic, complemented
99	#388	C₂×C₅	1	1	yes	characteristic, complemented
100	#388	C₂×C₅	1	1	yes	characteristic, complemented
101	#388	C₂×C₅	1	1	yes	characteristic, complemented
102	#388	C₂×C₅	1	1	yes	characteristic, complemented
103	#387	C₂×C₅	1	1	yes	characteristic, complemented
104	#386	C₂×C₅	1	1	yes	characteristic
105	#383	C₂×C₅	1	1	yes	characteristic, complemented
106	#382	C₂×C₅	1	1	yes	characteristic, complemented
107	C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
108	C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
109	C₂³×C₅	—	2	1	no	—
110	C₂³×C₅	—	2	1	no	—
111	C₂³×C₅	—	2	1	no	—
112	C₂³×C₅	—	2	1	no	—
113	C₂³×C₅	—	2	1	no	—
114	C₂³×C₅	—	2	1	no	—
115	C₂³×C₅	—	2	1	no	—
116	C₂³×C₅	—	2	1	no	—
117	C₂³×C₅	—	2	1	no	—
118	C₂³×C₅	—	2	1	no	—
119	C₂³×C₅	—	2	1	no	—
120	C₂³×C₅	—	2	1	no	—
121	C₂³×C₅	—	2	1	no	—
122	C₂³×C₅	#41	1	2	yes	—
123	C₂³×C₅	C₂⁴	1	1	yes	characteristic
124	C₅×D₄	—	4	4	no	—
125	C₂×C₄×C₅	—	2	1	no	—
126	C₂×C₄×C₅	—	2	1	no	—
127	C₂×C₄×C₅	—	2	1	no	—
128	C₂×C₄×C₅	—	2	1	no	—
129	C₂×C₄×C₅	—	2	1	no	—
130	C₂×C₄×C₅	—	2	1	no	—
131	C₂×C₄×C₅	—	2	1	no	—
132	C₂×C₄×C₅	—	2	1	no	—
133	C₂×C₄×C₅	—	2	1	no	—
134	C₂×C₄×C₅	—	2	1	no	—
135	C₂×C₄×C₅	—	2	1	no	—
136	C₂×C₄×C₅	—	2	1	no	—
137	C₂×C₄×C₅	—	2	1	no	—
138	C₂×C₄×C₅	—	2	1	no	—
139	C₂×C₄×C₅	—	2	1	no	—
140	C₂×C₄×C₅	—	2	1	no	—
141	C₂×C₄×C₅	—	2	1	no	—
142	C₂×C₄×C₅	—	2	1	no	—
143	C₂×C₄×C₅	—	2	1	no	—
144	C₂×C₄×C₅	—	2	1	no	—
145	C₂×C₄×C₅	—	2	1	no	—
146	C₂×C₄×C₅	—	2	1	no	—
147	C₂×C₄×C₅	—	2	1	no	—
148	C₂×C₄×C₅	—	2	1	no	—
149	C₂×C₄×C₅	—	2	1	no	—
150	C₂×C₄×C₅	—	2	1	no	—
151	C₂×C₄×C₅	—	2	1	no	—
152	C₂×C₄×C₅	—	2	1	no	—
153	C₂×C₄×C₅	—	2	1	no	—
154	C₂×C₄×C₅	—	2	1	no	—
155	C₂×C₄×C₅	—	2	1	no	—
156	C₂×C₄×C₅	—	2	1	no	—
157	C₂×C₄×C₅	—	2	1	no	—
158	C₂×C₄×C₅	—	2	1	no	—
159	C₂×C₄×C₅	—	2	1	no	—
160	C₂×C₄×C₅	—	4	4	no	—
161	C₂×C₄×C₅	#41	1	2	yes	—
162	C₂×C₄×C₅	#41	1	2	yes	—
163	C₂×C₄×C₅	#41	1	2	yes	—
164	C₂×C₄×C₅	#41	1	2	yes	—
165	C₂²×D₄	C₂²×C₅	1	1	yes	characteristic
166	C₂³×C₄	C₂²×C₅	1	1	yes	characteristic
167	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
168	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
169	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
170	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
171	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
172	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
173	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
174	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
176	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
179	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
180	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
181	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
182	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
184	C₂×C₄²	C₂²×C₅	1	1	yes	characteristic
185	C₂×C₄²	C₂²×C₅	1	1	yes	characteristic
186	C₂×C₄²	C₂²×C₅	1	1	yes	characteristic
187	C₂×C₄²	C₂²×C₅	1	1	yes	characteristic
188	#95	C₂²×C₅	1	1	yes	characteristic
189	#95	C₂²×C₅	1	1	yes	characteristic
190	#95	C₂²×C₅	1	1	yes	characteristic
191	#95	C₂²×C₅	1	1	yes	characteristic
192	#95	C₂²×C₅	1	1	yes	characteristic
193	#95	C₂²×C₅	1	1	yes	characteristic
194	#95	C₂²×C₅	1	1	yes	characteristic
195	#95	C₂²×C₅	1	1	yes	characteristic
196	#95	C₂²×C₅	1	1	yes	characteristic
197	#95	C₂²×C₅	1	1	yes	characteristic
198	#95	C₂²×C₅	1	1	yes	characteristic
199	#95	C₂²×C₅	1	1	yes	characteristic
200	C₂²×C₅	—	2	2	no	—
201	C₂²×C₅	—	2	2	no	—
202	C₂²×C₅	—	2	2	no	—
203	C₂²×C₅	—	4	1	no	—
204	C₂²×C₅	—	4	1	no	—
205	C₂²×C₅	—	4	1	no	—
206	C₂²×C₅	—	4	1	no	—
207	C₂²×C₅	—	4	1	no	—
208	C₂²×C₅	—	4	1	no	—
209	C₂²×C₅	—	4	1	no	—
210	C₂²×C₅	—	4	1	no	—
211	C₂²×C₅	—	4	1	no	—
212	C₂²×C₅	—	4	1	no	—
213	C₂²×C₅	—	4	1	no	—
214	C₂²×C₅	C₂×#41	1	1	yes	characteristic
215	C₂²×C₅	C₂×#41	1	1	yes	characteristic
216	C₂²×C₅	C₂×#41	1	1	yes	characteristic
217	C₂²×C₅	C₂×#41	1	1	yes	characteristic
218	C₂²×C₅	C₂×#41	1	1	yes	characteristic
219	C₂²×C₅	H(5,𝔽₂)	1	1	yes	characteristic
220	C₂²×C₅	H(5,𝔽₂)	1	1	yes	characteristic
221	C₄×C₅	—	2	2	no	—
222	C₄×C₅	—	2	2	no	—
223	C₄×C₅	—	2	2	no	—
224	C₄×C₅	—	2	2	no	—
225	C₄×C₅	—	4	1	no	—
226	C₄×C₅	—	4	1	no	—
227	C₄×C₅	—	4	1	no	—
228	C₄×C₅	—	4	1	no	—
229	C₄×C₅	—	4	1	no	—
230	C₄×C₅	—	4	1	no	—
231	C₄×C₅	—	4	1	no	—
232	C₄×C₅	—	4	1	no	—
233	C₄×C₅	—	4	1	no	—
234	C₂⁴	C₂³×C₅	1	1	yes	characteristic
235	C₂⁴	C₂³×C₅	1	1	yes	characteristic
236	C₂×D₄	—	2	2	no	—
237	C₂×D₄	—	4	1	no	—
238	C₂×D₄	—	4	1	no	—
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	4	1	no	—
242	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
243	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
244	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
245	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
246	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
247	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
248	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
249	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
250	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
251	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
252	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
253	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
254	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
255	C₄⋊C₄	—	2	2	no	—
256	C₄⋊C₄	—	2	2	no	—
257	C₄⋊C₄	—	4	1	no	—
258	C₄⋊C₄	—	4	1	no	—
259	C₄⋊C₄	—	4	1	no	—
260	C₄⋊C₄	—	4	1	no	—
261	C₂²⋊C₄	—	2	2	no	—
262	C₂²⋊C₄	—	2	2	no	—
263	C₂²⋊C₄	—	2	2	no	—
264	C₂²⋊C₄	—	2	2	no	—
265	C₂²⋊C₄	—	2	2	no	—
266	C₂²⋊C₄	—	2	2	no	—
267	C₂²⋊C₄	—	2	2	no	—
268	C₂²⋊C₄	—	2	2	no	—
269	C₂²⋊C₄	—	4	1	no	—
270	C₂²⋊C₄	—	4	1	no	—
271	C₂²⋊C₄	—	4	1	no	—
272	C₄²	—	2	2	no	—
273	C₄²	—	2	2	no	—
274	C₄²	—	4	1	no	—
275	C₄²	—	4	1	no	—
276	C₂×C₅	—	4	2	no	—
277	C₂×C₅	—	8	1	no	—
278	C₂×C₅	#529	1	1	yes	characteristic
279	C₂×C₅	#529	1	1	yes	characteristic
280	C₂×C₅	#538	1	1	yes	characteristic
281	C₂×C₅	#551	1	1	yes	characteristic
282	C₂×C₅	#553	1	1	yes	characteristic
283	C₂×C₅	#553	1	1	yes	characteristic
284	C₂×C₅	#555	1	1	yes	characteristic
285	C₂³	—	2	1	no	—
286	C₂³	—	2	1	no	—
287	C₂³	—	2	1	no	—
288	C₂³	—	2	1	no	—
289	C₂³	—	2	1	no	—
290	C₂³	—	2	1	no	—
291	C₂³	—	2	1	no	—
292	C₂³	—	2	1	no	—
293	C₂³	—	2	1	no	—
294	C₂³	—	2	1	no	—
295	C₂³	—	2	1	no	—
296	C₂³	—	2	1	no	—
297	C₂³	—	2	1	no	—
298	C₂³	C₅×#41	1	2	yes	—
299	C₂³	C₂⁴×C₅	1	1	yes	characteristic
300	D₄	—	4	4	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	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	1	no	—
315	C₂×C₄	—	2	1	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	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	C₅×#41	1	2	yes	—
338	C₂×C₄	C₅×#41	1	2	yes	—
339	C₂×C₄	C₅×#41	1	2	yes	—
340	C₂×C₄	C₅×#41	1	2	yes	—
341	C₅	#2518	1	1	yes	characteristic, direct product factor, Sylow
342	C₂²	—	2	2	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	2	2	no	—
345	C₂²	—	4	1	no	—
346	C₂²	—	4	1	no	—
347	C₂²	—	4	1	no	—
348	C₂²	—	4	1	no	—
349	C₂²	—	4	1	no	—
350	C₂²	—	4	1	no	—
351	C₂²	—	4	1	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	C₂×C₅×#41	1	1	yes	characteristic
357	C₂²	C₂×C₅×#41	1	1	yes	characteristic
358	C₂²	C₂×C₅×#41	1	1	yes	characteristic
359	C₂²	C₂×C₅×#41	1	1	yes	characteristic
360	C₂²	C₂×C₅×#41	1	1	yes	characteristic
361	C₂²	C₅×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂²	C₅×H(5,𝔽₂)	1	1	yes	characteristic
363	C₄	—	2	2	no	—
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	4	1	no	—
368	C₄	—	4	1	no	—
369	C₄	—	4	1	no	—
370	C₄	—	4	1	no	—
371	C₄	—	4	1	no	—
372	C₄	—	4	1	no	—
373	C₄	—	4	1	no	—
374	C₄	—	4	1	no	—
375	C₄	—	4	1	no	—
376	C₂	—	4	2	no	—
377	C₂	—	8	1	no	—
378	C₂	C₅×#529	1	1	yes	characteristic
379	C₂	C₅×#529	1	1	yes	characteristic
380	C₂	C₅×#538	1	1	yes	characteristic
381	C₂	C₅×#551	1	1	yes	characteristic
382	C₂	C₅×#553	1	1	yes	characteristic
383	C₂	C₅×#553	1	1	yes	characteristic
384	C₂	C₅×#555	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#397	C₂	semidirect
2. C₅×#396	C₂	semidirect
5. C₅×#389	C₂	semidirect
6. C₅×#388	C₂	semidirect
7. C₅×#388	C₂	semidirect
8. C₅×#388	C₂	semidirect
9. C₅×#388	C₂	semidirect
10. C₅×#387	C₂	semidirect
12. C₅×#383	C₂	semidirect
13. C₅×#382	C₂	semidirect
14. C₄×C₅×C₂²⋊C₄	C₂	semidirect
15. C₄×C₅×C₂²⋊C₄	C₂	semidirect
51. #2518	C₅	direct (N × H)
94. #397	C₂×C₅	semidirect
95. #396	C₂×C₅	semidirect
98. #389	C₂×C₅	semidirect
99. #388	C₂×C₅	semidirect
100. #388	C₂×C₅	semidirect
101. #388	C₂×C₅	semidirect
102. #388	C₂×C₅	semidirect
103. #387	C₂×C₅	semidirect
105. #383	C₂×C₅	semidirect
106. #382	C₂×C₅	semidirect
107. C₄×C₂²⋊C₄	C₂×C₅	semidirect
108. C₄×C₂²⋊C₄	C₂×C₅	semidirect
341. C₅	#2518	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#397	2
C₅×#396	2
C₅×#394	2
C₅×#389	2
C₅×#388	2
C₅×#387	2
C₅×#386	2
C₅×#383	2
C₅×#382	2
C₄×C₅×C₂²⋊C₄	2
#2518	5

Subgroups — C5×#2518 #10616113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#2518 #10616113