Subgroups — C₂×C₅×#4027 #13106640

Order 1600.

984 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
2. C₂³×C₅×Dic₅	C₂	semidirect
3. C₂²×C₄×C₅×D₅	C₂	semidirect
4. C₂×C₅²×C₂²⋊C₄	C₂	semidirect
5. C₂×C₅×#685	C₂	semidirect
6. C₂×C₅×#683	C₂	semidirect
7. C₂×C₄×C₅×Dic₅	C₂	semidirect
8. C₅×#4027	C₂	direct (N × H)
13. C₂×C₅×C₂²⋊D₅	C₄	semidirect
19. C₂²×C₅×Dic₅	C₂²	semidirect
21. C₂×C₄×C₅×D₅	C₂²	semidirect
22. C₅²×C₂²⋊C₄	C₂²	semidirect
23. C₅×#685	C₂²	semidirect
24. C₅×#683	C₂²	semidirect
25. C₄×C₅×Dic₅	C₂²	semidirect
27. C₂×#4027	C₅	direct (N × H)
30. C₂³×C₅²	C₂×C₄	semidirect
35. C₂²×C₅×D₅	C₂×C₄	semidirect
41. C₅×C₂²⋊D₅	C₂×C₄	semidirect
44. C₂×C₅×Dic₅	C₂×C₄	semidirect
45. C₂×C₅×Dic₅	D₄	semidirect
54. C₂³×Dic₅	C₂×C₅	semidirect
55. C₂²×C₄×D₅	C₂×C₅	semidirect
60. C₂×C₅×C₂²⋊C₄	D₅	semidirect
61. C₂×C₅×C₂²⋊C₄	C₂×C₅	semidirect
63. C₂×#685	C₂×C₅	semidirect
64. C₂×#683	C₂×C₅	semidirect
65. C₂×C₄×Dic₅	C₂×C₅	semidirect
66. #4027	C₂×C₅	direct (N × H)
71. C₂²×C₅²	C₂²×C₄	semidirect
78. C₂×C₅×D₅	C₂²×C₄	semidirect
82. C₅×Dic₅	C₂²×C₄	semidirect
83. C₅×Dic₅	C₂×D₄	semidirect
104. C₂×C₂²⋊D₅	C₄×C₅	semidirect
110. C₂²×Dic₅	C₂²×C₅	semidirect
112. C₂×C₄×D₅	C₂²×C₅	semidirect
116. C₅×C₂²⋊C₄	C₂×D₅	semidirect
117. C₅×C₂²⋊C₄	C₂²×C₅	semidirect
119. #685	C₂²×C₅	semidirect
120. #683	C₂²×C₅	semidirect
121. C₄×Dic₅	C₂²×C₅	semidirect
124. C₂×C₅²	C₄×D₄	semidirect
142. C₂³×C₅	C₄×D₅	semidirect
143. C₂³×C₅	C₂×C₄×C₅	semidirect
150. C₂²×D₅	C₂×C₄×C₅	semidirect
173. C₂²⋊D₅	C₂×C₄×C₅	semidirect
176. C₂×Dic₅	C₂×C₄×C₅	semidirect
177. C₂×Dic₅	C₅×D₄	semidirect
188. C₂×C₂²⋊C₄	C₅×D₅	semidirect
190. C₅²	C₂×C₄×D₄	semidirect
210. C₂²×C₅	C₂×C₄×D₅	semidirect
214. C₂²×C₅	C₂²×C₄×C₅	semidirect
222. C₂×D₅	C₂²×C₄×C₅	semidirect
233. Dic₅	C₂²×C₄×C₅	semidirect
234. Dic₅	C₂×C₅×D₄	semidirect
250. C₂²⋊C₄	C₂×C₅×D₅	semidirect
260. C₂×C₅	#4027	direct (N × H)
261. C₂×C₅	C₄×C₅×D₄	semidirect
275. C₂³	C₄×C₅×D₅	semidirect
292. C₅	C₂×#4027	direct (N × H)
293. C₅	C₂×C₄×C₅×D₄	semidirect
302. C₂²	C₂×C₄×C₅×D₅	semidirect
313. C₂	C₅×#4027	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×C₂²⋊D₅	2
C₂³×C₅×Dic₅	2
C₂²×C₄×C₅×D₅	2
C₂×C₅²×C₂²⋊C₄	2
C₂×C₅×#685	2
C₂×C₅×#683	2
C₂×C₄×C₅×Dic₅	2
C₅×#4027	2
C₂×C₄×C₅×D₄	5
C₂×#4027	5

Subgroups — C2×C5×#4027 #13106640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4027 #13106640