Subgroups — C₂×C₅×#4085 #13106947

Order 1600.

1088 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂³×C₅	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂⁴×C₅
Frattini	C₂²	C₂³×C₅×D₅
Fitting	C₂²×C₅²×D₄	C₂
socle	C₂³×C₅²	C₂³
hypercenter	C₂²×C₅×D₄	D₅
hypocenter	C₅	C₂×C₅×#121
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅²×D₄	C₂	semidirect
2. C₂²×C₅×C₂²⋊D₅	C₂	semidirect
3. C₂²×C₅×C₂²⋊D₅	C₂	semidirect
4. C₂³×C₅×Dic₅	C₂	semidirect
5. C₂×C₅×C₂²⋊Dic₅	C₂	semidirect
6. C₅×#4085	C₂	direct (N × H)
7. C₂×C₅×#685	C₂	semidirect
8. C₂×C₅×#683	C₂	semidirect
13. C₂×C₅²×D₄	C₂²	semidirect
17. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
18. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
23. C₂²×C₅×Dic₅	C₂²	semidirect
24. C₅×C₂²⋊Dic₅	C₂²	semidirect
25. C₅×#685	C₂²	semidirect
26. C₅×#683	C₂²	semidirect
28. C₂×#4085	C₅	direct (N × H)
34. C₂³×C₅²	D₄	semidirect
50. C₂×C₅×Dic₅	D₄	semidirect
57. C₂²×C₅×D₄	D₅	semidirect
58. C₂²×C₅×D₄	C₂×C₅	semidirect
60. C₂²×C₂²⋊D₅	C₂×C₅	semidirect
61. C₂²×C₂²⋊D₅	C₂×C₅	semidirect
62. C₂³×Dic₅	C₂×C₅	semidirect
67. C₂×C₂²⋊Dic₅	C₂×C₅	semidirect
68. #4085	C₂×C₅	direct (N × H)
69. C₂×#685	C₂×C₅	semidirect
70. C₂×#683	C₂×C₅	semidirect
80. C₂²×C₅²	C₂×D₄	semidirect
90. C₅×Dic₅	C₂×D₄	semidirect
107. C₂×C₅×D₄	C₂×D₅	semidirect
108. C₂×C₅×D₄	C₂²×C₅	semidirect
119. C₂×C₂²⋊D₅	C₂²×C₅	semidirect
120. C₂×C₂²⋊D₅	C₂²×C₅	semidirect
125. C₂²×Dic₅	C₂²×C₅	semidirect
129. C₂²⋊Dic₅	C₂²×C₅	semidirect
130. #685	C₂²×C₅	semidirect
131. #683	C₂²×C₅	semidirect
135. C₂×C₅²	#121	semidirect
163. C₂³×C₅	C₂²⋊D₅	semidirect
164. C₂³×C₅	C₅×D₄	semidirect
198. C₂×Dic₅	C₅×D₄	semidirect
204. C₂²×D₄	C₅×D₅	semidirect
210. C₅²	C₂×#121	semidirect
244. C₂²×C₅	C₂×C₂²⋊D₅	semidirect
247. C₂²×C₅	C₂×C₅×D₄	semidirect
263. Dic₅	C₂×C₅×D₄	semidirect
272. C₂×D₄	C₂×C₅×D₅	semidirect
293. C₂×C₅	#4085	direct (N × H)
294. C₂×C₅	C₅×#121	semidirect
311. C₂³	C₅×C₂²⋊D₅	semidirect
328. C₅	C₂×#4085	direct (N × H)
329. C₅	C₂×C₅×#121	semidirect
344. C₂²	C₂×C₅×C₂²⋊D₅	semidirect
353. C₂	C₅×#4085	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×C₅²×D₄	2
C₂²×C₅×C₂²⋊D₅	2
C₂³×C₅×Dic₅	2
C₂×C₅×C₂²⋊Dic₅	2
C₅×#4085	2
C₂×C₅×#685	2
C₂×C₅×#683	2
C₂×C₅×#121	5
C₂×#4085	5

Subgroups — C2×C5×#4085 #13106947

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4085 #13106947