Subgroups — C₂×C₅×#4030 #13106644

Order 1600.

984 conjugacy classes of subgroups.

The subgroup lattice has 350 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, complemented
2	C₂²×C₅×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×C₅×D₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅²×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#685	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#683	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4030	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	C₂³×C₅×D₅	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₅²	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₅²	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₂²⋊D₅	—	2	4	no	—
15	C₂×C₅×C₂²⋊D₅	—	2	4	no	—
16	C₂×C₅×C₂²⋊D₅	C₂²	1	4	yes	complemented
17	C₂×C₅×C₂²⋊D₅	C₂²	1	4	yes	complemented
18	C₂²×C₅×Dic₅	C₂²	1	1	yes	characteristic
19	C₂²×C₅×Dic₅	C₂²	1	1	yes	characteristic
20	C₂×C₅×D₂₀	—	2	4	no	—
21	C₂×C₅×D₂₀	C₂²	1	4	yes	complemented
22	C₂×C₄×C₅×D₅	—	2	4	no	—
23	C₂×C₄×C₅×D₅	C₂²	1	4	yes	complemented
24	C₅²×C₂²⋊C₄	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×#4030	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	C₂³	1	2	yes	—
33	C₂³×C₅²	C₂³	1	1	yes	characteristic
34	C₂²×C₅×D₅	—	2	2	no	—
35	C₂²×C₅×D₅	—	2	2	no	—
36	C₂²×C₅×D₅	—	2	2	no	—
37	C₂²×C₅×D₅	—	2	2	no	—
38	C₂²×C₅×D₅	—	2	2	no	—
39	C₂²×C₅×D₅	D₄	1	4	yes	complemented
40	C₂²×C₅×D₅	C₂³	1	2	yes	—
41	C₂²×C₅×D₅	C₂³	1	2	yes	—
42	C₂×C₄×C₅²	—	2	2	no	—
43	C₂×C₄×C₅²	—	2	2	no	—
44	C₂×C₄×C₅²	C₂³	1	2	yes	—
45	C₂×C₄×C₅²	C₂³	1	2	yes	—
46	C₅×C₂²⋊D₅	—	2	8	no	—
47	C₅×C₂²⋊D₅	—	2	8	no	—
48	C₂×C₅×Dic₅	—	2	2	no	—
49	C₂×C₅×Dic₅	D₄	1	4	yes	complemented
50	C₂×C₅×Dic₅	C₂³	1	2	yes	—
51	C₂×C₅×Dic₅	C₂³	1	2	yes	—
52	C₅×D₂₀	—	2	8	no	—
53	C₄×C₅×D₅	—	2	8	no	—
54	C₂²×C₅×D₄	—	5	1	no	—
55	C₂²×C₅×D₄	—	5	1	no	—
56	C₂²×C₅×D₄	—	5	1	no	—
57	C₂³×C₄×C₅	—	5	1	no	—
58	C₂²×C₂²⋊D₅	C₂×C₅	1	1	yes	characteristic, complemented
59	C₂²×C₂²⋊D₅	C₂×C₅	1	1	yes	characteristic, complemented
60	C₂²×D₂₀	C₂×C₅	1	1	yes	characteristic, complemented
61	C₂²×C₄×D₅	C₂×C₅	1	1	yes	characteristic, complemented
62	C₅×#121	—	5	8	no	—
63	C₂×C₅×C₄⋊C₄	—	5	1	no	—
64	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₅×C₂²⋊C₄	—	5	1	no	—
66	C₂×C₅×C₂²⋊C₄	D₅	1	1	yes	characteristic, complemented
67	C₂×C₅×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂×#685	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂×#683	C₂×C₅	1	1	yes	characteristic, complemented
70	#4030	C₂×C₅	1	8	yes	direct product factor
71	C₂²×C₅²	—	2	2	no	—
72	C₂²×C₅²	—	2	2	no	—
73	C₂²×C₅²	—	2	2	no	—
74	C₂²×C₅²	—	4	4	no	—
75	C₂²×C₅²	C₂×D₄	1	2	yes	—
76	C₂²×C₅²	C₂×D₄	1	2	yes	—
77	C₂²×C₅²	#41	1	2	yes	—
78	C₂²×C₅²	C₂⁴	1	1	yes	characteristic
79	C₂×C₅×D₅	—	2	8	no	—
80	C₂×C₅×D₅	—	2	2	no	—
81	C₂×C₅×D₅	—	2	2	no	—
82	C₂×C₅×D₅	—	2	2	no	—
83	C₂×C₅×D₅	—	2	2	no	—
84	C₂×C₅×D₅	—	2	2	no	—
85	C₂×C₅×D₅	—	4	4	no	—
86	C₂×C₅×D₅	C₂×D₄	1	4	yes	complemented
87	C₄×C₅²	—	2	2	no	—
88	C₄×C₅²	—	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	—	5	1	no	—
93	C₂⁴×C₅	—	5	1	no	—
94	C₂⁴×C₅	C₂×D₅	1	1	yes	characteristic
95	C₂⁴×C₅	C₂²×C₅	1	1	yes	characteristic
96	C₂³×D₅	C₂²×C₅	1	1	yes	characteristic
97	C₂³×D₅	C₂²×C₅	1	1	yes	characteristic
98	C₂×C₅×D₄	—	5	4	no	—
99	C₂×C₅×D₄	—	5	4	no	—
100	C₂×C₅×D₄	—	5	4	no	—
101	C₂×C₅×D₄	—	10	4	no	—
102	C₂×C₅×D₄	—	10	4	no	—
103	C₂×C₅×D₄	—	10	4	no	—
104	C₂²×C₄×C₅	—	2	2	no	—
105	C₂²×C₄×C₅	—	2	2	no	—
106	C₂²×C₄×C₅	—	5	1	no	—
107	C₂²×C₄×C₅	—	5	1	no	—
108	C₂²×C₄×C₅	—	5	4	no	—
109	C₂²×C₄×C₅	—	10	4	no	—
110	C₂²×C₄×C₅	C₂×D₅	1	1	yes	characteristic
111	C₂²×C₄×C₅	C₂×D₅	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
114	C₂×C₂²⋊D₅	—	2	4	no	—
115	C₂×C₂²⋊D₅	—	2	4	no	—
116	C₂×C₂²⋊D₅	C₂²×C₅	1	4	yes	complemented
117	C₂×C₂²⋊D₅	C₂²×C₅	1	4	yes	complemented
118	C₂²×Dic₅	C₂²×C₅	1	1	yes	characteristic
119	C₂²×Dic₅	C₂²×C₅	1	1	yes	characteristic
120	C₂×D₂₀	—	2	4	no	—
121	C₂×D₂₀	C₂²×C₅	1	4	yes	complemented
122	C₂×C₄×D₅	—	2	4	no	—
123	C₂×C₄×D₅	C₂²×C₅	1	4	yes	complemented
124	C₅×C₄⋊C₄	—	5	4	no	—
125	C₅×C₂²⋊C₄	—	2	8	no	—
126	C₅×C₂²⋊C₄	—	5	4	no	—
127	C₅×C₂²⋊C₄	C₂×D₅	1	4	yes	complemented
128	C₅×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
129	#685	C₂²×C₅	1	4	yes	complemented
130	#683	C₂²×C₅	1	4	yes	complemented
131	C₂×#121	—	5	1	no	Sylow
132	C₂×C₅²	—	4	2	no	—
133	C₂×C₅²	#121	1	4	yes	complemented
134	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
135	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
136	C₂×C₅²	C₂×#41	1	1	yes	characteristic
137	C₅×D₅	—	2	4	no	—
138	C₅×D₅	—	4	2	no	—
139	C₂³×C₅	—	2	8	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	2	no	—
145	C₂³×C₅	—	2	2	no	—
146	C₂³×C₅	—	2	2	no	—
147	C₂³×C₅	—	2	4	no	—
148	C₂³×C₅	—	4	4	no	—
149	C₂³×C₅	—	4	4	no	—
150	C₂³×C₅	—	5	4	no	—
151	C₂³×C₅	—	5	2	no	—
152	C₂³×C₅	—	5	2	no	—
153	C₂³×C₅	—	10	2	no	—
154	C₂³×C₅	—	10	2	no	—
155	C₂³×C₅	—	10	2	no	—
156	C₂³×C₅	—	10	2	no	—
157	C₂³×C₅	—	10	2	no	—
158	C₂³×C₅	C₂²×D₅	1	2	yes	—
159	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
160	C₂³×C₅	C₂³×C₅	1	2	yes	—
161	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
162	C₂²×D₅	—	2	2	no	—
163	C₂²×D₅	—	2	2	no	—
164	C₂²×D₅	—	2	2	no	—
165	C₂²×D₅	—	2	2	no	—
166	C₂²×D₅	—	2	2	no	—
167	C₂²×D₅	C₅×D₄	1	4	yes	complemented
168	C₂²×D₅	C₂³×C₅	1	2	yes	—
169	C₂²×D₅	C₂³×C₅	1	2	yes	—
170	C₅×D₄	—	10	8	no	—
171	C₅×D₄	—	10	8	no	—
172	C₅×D₄	—	10	8	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	2	2	no	—
176	C₂×C₄×C₅	—	2	2	no	—
177	C₂×C₄×C₅	—	2	4	no	—
178	C₂×C₄×C₅	—	2	4	no	—
179	C₂×C₄×C₅	—	4	4	no	—
180	C₂×C₄×C₅	—	4	4	no	—
181	C₂×C₄×C₅	—	5	4	no	—
182	C₂×C₄×C₅	—	5	2	no	—
183	C₂×C₄×C₅	—	5	2	no	—
184	C₂×C₄×C₅	—	10	8	no	—
185	C₂×C₄×C₅	—	10	2	no	—
186	C₂×C₄×C₅	C₂²×D₅	1	2	yes	—
187	C₂×C₄×C₅	C₂²×D₅	1	2	yes	—
188	C₂×C₄×C₅	C₂³×C₅	1	2	yes	—
189	C₂×C₄×C₅	C₂³×C₅	1	2	yes	—
190	C₂²⋊D₅	—	2	8	no	—
191	C₂²⋊D₅	—	2	8	no	—
192	C₂×Dic₅	—	2	2	no	—
193	C₂×Dic₅	C₅×D₄	1	4	yes	complemented
194	C₂×Dic₅	C₂³×C₅	1	2	yes	—
195	C₂×Dic₅	C₂³×C₅	1	2	yes	—
196	D₂₀	—	2	8	no	—
197	C₄×D₅	—	2	8	no	—
198	C₂²×D₄	—	5	1	no	—
199	C₂²×D₄	—	5	1	no	—
200	C₂²×D₄	—	5	1	no	—
201	C₂³×C₄	—	5	1	no	—
202	#121	—	5	8	no	—
203	C₂×C₄⋊C₄	—	5	1	no	—
204	C₂×C₂²⋊C₄	—	5	1	no	—
205	C₂×C₂²⋊C₄	C₅×D₅	1	1	yes	characteristic, complemented
206	C₅²	C₂×#121	1	1	yes	characteristic, complemented, Sylow
207	C₂²×C₅	—	2	8	no	—
208	C₂²×C₅	—	2	2	no	—
209	C₂²×C₅	—	2	2	no	—
210	C₂²×C₅	—	2	2	no	—
211	C₂²×C₅	—	2	2	no	—
212	C₂²×C₅	—	2	2	no	—
213	C₂²×C₅	—	2	2	no	—
214	C₂²×C₅	—	2	4	no	—
215	C₂²×C₅	—	2	4	no	—
216	C₂²×C₅	—	2	4	no	—
217	C₂²×C₅	—	2	2	no	—
218	C₂²×C₅	—	4	4	no	—
219	C₂²×C₅	—	4	4	no	—
220	C₂²×C₅	—	4	16	no	—
221	C₂²×C₅	—	4	4	no	—
222	C₂²×C₅	—	4	4	no	—
223	C₂²×C₅	—	5	4	no	—
224	C₂²×C₅	—	10	2	no	—
225	C₂²×C₅	—	10	2	no	—
226	C₂²×C₅	—	10	8	no	—
227	C₂²×C₅	—	10	2	no	—
228	C₂²×C₅	—	10	2	no	—
229	C₂²×C₅	—	10	2	no	—
230	C₂²×C₅	—	20	4	no	—
231	C₂²×C₅	#709	1	2	yes	—
232	C₂²×C₅	D₄×D₅	1	2	yes	—
233	C₂²×C₅	D₄×D₅	1	2	yes	—
234	C₂²×C₅	C₂×C₅×D₄	1	2	yes	—
235	C₂²×C₅	C₂×C₅×D₄	1	2	yes	—
236	C₂²×C₅	C₅×#41	1	2	yes	—
237	C₂²×C₅	C₂³×D₅	1	1	yes	characteristic
238	C₂²×C₅	C₂⁴×C₅	1	1	yes	characteristic
239	C₂×D₅	—	2	8	no	—
240	C₂×D₅	—	2	2	no	—
241	C₂×D₅	—	2	2	no	—
242	C₂×D₅	—	2	2	no	—
243	C₂×D₅	—	2	2	no	—
244	C₂×D₅	—	2	2	no	—
245	C₂×D₅	—	4	4	no	—
246	C₂×D₅	C₂×C₅×D₄	1	4	yes	complemented
247	C₄×C₅	—	2	2	no	—
248	C₄×C₅	—	2	2	no	—
249	C₄×C₅	—	2	2	no	—
250	C₄×C₅	—	2	2	no	—
251	C₄×C₅	—	4	4	no	—
252	C₄×C₅	—	4	4	no	—
253	C₄×C₅	—	5	4	no	—
254	C₄×C₅	—	10	2	no	—
255	Dic₅	—	2	2	no	—
256	Dic₅	C₂×C₅×D₄	1	4	yes	complemented
257	C₂⁴	—	5	1	no	—
258	C₂⁴	—	5	1	no	—
259	C₂⁴	C₂×C₅×D₅	1	1	yes	characteristic
260	C₂×D₄	—	5	4	no	—
261	C₂×D₄	—	5	4	no	—
262	C₂×D₄	—	5	4	no	—
263	C₂×D₄	—	10	4	no	—
264	C₂×D₄	—	10	4	no	—
265	C₂×D₄	—	10	4	no	—
266	C₂²×C₄	—	5	1	no	—
267	C₂²×C₄	—	5	1	no	—
268	C₂²×C₄	—	5	4	no	—
269	C₂²×C₄	—	10	4	no	—
270	C₂²×C₄	C₂×C₅×D₅	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₅×D₅	1	1	yes	characteristic
272	C₄⋊C₄	—	5	4	no	—
273	C₂²⋊C₄	—	5	4	no	—
274	C₂²⋊C₄	C₂×C₅×D₅	1	4	yes	complemented
275	C₂×C₅	—	2	2	no	—
276	C₂×C₅	—	2	2	no	—
277	C₂×C₅	—	2	2	no	—
278	C₂×C₅	—	2	8	no	—
279	C₂×C₅	—	4	8	no	—
280	C₂×C₅	—	4	2	no	—
281	C₂×C₅	—	4	2	no	—
282	C₂×C₅	—	10	4	no	—
283	C₂×C₅	—	20	2	no	—
284	C₂×C₅	#4030	1	4	yes	direct product factor
285	C₂×C₅	C₅×#121	1	4	yes	complemented
286	C₂×C₅	C₂×#709	1	1	yes	characteristic
287	C₂×C₅	C₂×D₄×D₅	1	1	yes	characteristic
288	C₂×C₅	C₂×D₄×D₅	1	1	yes	characteristic
289	C₂×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
290	C₂×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
291	C₂×C₅	C₂×C₅×#41	1	1	yes	characteristic
292	D₅	—	2	4	no	—
293	D₅	—	4	2	no	—
294	C₂³	—	2	2	no	—
295	C₂³	—	2	2	no	—
296	C₂³	—	2	2	no	—
297	C₂³	—	5	4	no	—
298	C₂³	—	5	2	no	—
299	C₂³	—	5	2	no	—
300	C₂³	—	10	2	no	—
301	C₂³	—	10	2	no	—
302	C₂³	—	10	2	no	—
303	C₂³	—	10	2	no	—
304	C₂³	—	10	2	no	—
305	C₂³	C₂²×C₅×D₅	1	2	yes	—
306	C₂³	C₂²×C₅×D₅	1	1	yes	characteristic
307	D₄	—	10	8	no	—
308	D₄	—	10	8	no	—
309	D₄	—	10	8	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	5	4	no	—
313	C₂×C₄	—	5	2	no	—
314	C₂×C₄	—	5	2	no	—
315	C₂×C₄	—	10	8	no	—
316	C₂×C₄	—	10	2	no	—
317	C₂×C₄	C₂²×C₅×D₅	1	2	yes	—
318	C₂×C₄	C₂²×C₅×D₅	1	2	yes	—
319	C₅	—	2	2	no	—
320	C₅	C₂×#4030	1	1	yes	characteristic, direct product factor
321	C₅	C₂×C₅×#121	1	1	yes	characteristic, complemented
322	C₂²	—	2	2	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	4	4	no	—
326	C₂²	—	5	4	no	—
327	C₂²	—	10	2	no	—
328	C₂²	—	10	2	no	—
329	C₂²	—	10	8	no	—
330	C₂²	—	10	2	no	—
331	C₂²	—	10	2	no	—
332	C₂²	—	10	2	no	—
333	C₂²	—	20	4	no	—
334	C₂²	C₅×#709	1	2	yes	—
335	C₂²	C₅×D₄×D₅	1	2	yes	—
336	C₂²	C₅×D₄×D₅	1	2	yes	—
337	C₂²	C₂³×C₅×D₅	1	1	yes	characteristic
338	C₄	—	2	2	no	—
339	C₄	—	2	2	no	—
340	C₄	—	5	4	no	—
341	C₄	—	10	2	no	—
342	C₂	—	4	2	no	—
343	C₂	—	10	4	no	—
344	C₂	—	20	2	no	—
345	C₂	C₅×#4030	1	4	yes	direct product factor
346	C₂	C₂×C₅×#709	1	1	yes	characteristic
347	C₂	C₂×C₅×D₄×D₅	1	1	yes	characteristic
348	C₂	C₂×C₅×D₄×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	C₂×C₅²×C₂²⋊C₄	C₂
socle	C₂³×C₅²	C₂³
hypercenter	C₂×C₅×C₂²⋊C₄	D₅
hypocenter	C₅	C₂×C₅×#121
LCS	G ▷ C₂²×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
1. C₂²×C₅×C₂²⋊D₅	C₂	semidirect
2. C₂²×C₅×C₂²⋊D₅	C₂	semidirect
3. C₂²×C₅×D₂₀	C₂	semidirect
4. C₂²×C₄×C₅×D₅	C₂	semidirect
5. C₂×C₅²×C₂²⋊C₄	C₂	semidirect
6. C₂×C₅×#685	C₂	semidirect
7. C₂×C₅×#683	C₂	semidirect
8. C₅×#4030	C₂	direct (N × H)
16. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
17. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
21. C₂×C₅×D₂₀	C₂²	semidirect
23. C₂×C₄×C₅×D₅	C₂²	semidirect
24. C₅²×C₂²⋊C₄	C₂²	semidirect
25. C₅×#685	C₂²	semidirect
26. C₅×#683	C₂²	semidirect
28. C₂×#4030	C₅	direct (N × H)
39. C₂²×C₅×D₅	D₄	semidirect
49. C₂×C₅×Dic₅	D₄	semidirect
58. C₂²×C₂²⋊D₅	C₂×C₅	semidirect
59. C₂²×C₂²⋊D₅	C₂×C₅	semidirect
60. C₂²×D₂₀	C₂×C₅	semidirect
61. C₂²×C₄×D₅	C₂×C₅	semidirect
66. C₂×C₅×C₂²⋊C₄	D₅	semidirect
67. C₂×C₅×C₂²⋊C₄	C₂×C₅	semidirect
68. C₂×#685	C₂×C₅	semidirect
69. C₂×#683	C₂×C₅	semidirect
70. #4030	C₂×C₅	direct (N × H)
86. C₂×C₅×D₅	C₂×D₄	semidirect
90. C₅×Dic₅	C₂×D₄	semidirect
116. C₂×C₂²⋊D₅	C₂²×C₅	semidirect
117. C₂×C₂²⋊D₅	C₂²×C₅	semidirect
121. C₂×D₂₀	C₂²×C₅	semidirect
123. C₂×C₄×D₅	C₂²×C₅	semidirect
127. C₅×C₂²⋊C₄	C₂×D₅	semidirect
128. C₅×C₂²⋊C₄	C₂²×C₅	semidirect
129. #685	C₂²×C₅	semidirect
130. #683	C₂²×C₅	semidirect
133. C₂×C₅²	#121	semidirect
167. C₂²×D₅	C₅×D₄	semidirect
193. C₂×Dic₅	C₅×D₄	semidirect
205. C₂×C₂²⋊C₄	C₅×D₅	semidirect
206. C₅²	C₂×#121	semidirect
246. C₂×D₅	C₂×C₅×D₄	semidirect
256. Dic₅	C₂×C₅×D₄	semidirect
274. C₂²⋊C₄	C₂×C₅×D₅	semidirect
284. C₂×C₅	#4030	direct (N × H)
285. C₂×C₅	C₅×#121	semidirect
320. C₅	C₂×#4030	direct (N × H)
321. C₅	C₂×C₅×#121	semidirect
345. C₂	C₅×#4030	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
C₂²×C₅×D₂₀	2
C₂²×C₄×C₅×D₅	2
C₂×C₅²×C₂²⋊C₄	2
C₂×C₅×#685	2
C₂×C₅×#683	2
C₅×#4030	2
C₂×C₅×#121	5
C₂×#4030	5

Subgroups — C2×C5×#4030 #13106644

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4030 #13106644