Subgroups — C₂×C₄×C₅×C₂²⋊D₅ #13106942

Order 1600.

1088 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₅²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₅×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₂²⋊Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₅×C₂²⋊D₅	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#685	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#683	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×C₅×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁴×C₅²	C₂²	1	1	yes	characteristic
10	C₂³×C₅×D₅	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₅²	—	2	4	no	—
12	C₂²×C₄×C₅²	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₅²	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₅²	C₂²	1	4	yes	complemented
15	C₂×C₅×C₂²⋊D₅	C₄	1	8	yes	direct product factor
16	C₂×C₅×C₂²⋊D₅	C₂²	1	4	yes	—
17	C₂²×C₅×Dic₅	C₂²	1	1	yes	characteristic
18	C₂²×C₅×Dic₅	C₂²	1	1	yes	characteristic
19	C₂²×C₅×Dic₅	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×D₅	—	2	4	no	—
21	C₂×C₄×C₅×D₅	C₂²	1	4	yes	complemented
22	C₅×C₂²⋊Dic₅	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×C₄×C₂²⋊D₅	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	8	no	—
39	C₂×C₄×C₅²	D₄	1	4	yes	complemented
40	C₂×C₄×C₅²	C₂³	1	2	yes	—
41	C₂×C₄×C₅²	C₂³	1	2	yes	—
42	C₅×C₂²⋊D₅	C₂×C₄	1	16	yes	direct product factor
43	C₂×C₅×Dic₅	—	2	2	no	—
44	C₂×C₅×Dic₅	—	2	2	no	—
45	C₂×C₅×Dic₅	C₂×C₄	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	—	2	2	no	—
52	C₂³×C₄×C₅	—	5	1	no	—
53	C₂³×C₄×C₅	D₅	1	1	yes	characteristic, complemented
54	C₂³×C₄×C₅	C₂×C₅	1	1	yes	characteristic, complemented
55	C₂²×C₂²⋊D₅	C₂×C₅	1	1	yes	characteristic
56	C₂²×C₄×D₅	C₂×C₅	1	1	yes	characteristic, complemented
57	C₄×C₅×D₄	—	5	8	no	—
58	C₂×C₅×C₄⋊C₄	—	5	1	no	—
59	C₂×C₅×C₂²⋊C₄	—	5	1	no	—
60	C₂×C₅×C₂²⋊C₄	—	5	1	no	—
61	C₂×C₄²×C₅	—	5	1	no	—
62	C₂×C₂²⋊Dic₅	C₂×C₅	1	1	yes	characteristic, complemented
63	C₄×C₂²⋊D₅	C₂×C₅	1	8	yes	direct product factor
64	C₂×#685	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂×#683	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂×C₄×Dic₅	C₂×C₅	1	1	yes	characteristic, complemented
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	C₂×D₄	1	4	yes	complemented
81	C₅×Dic₅	—	2	2	no	—
82	C₅×Dic₅	—	2	2	no	—
83	C₅×Dic₅	C₂²×C₄	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	16	no	—
92	C₂²×C₄×C₅	—	2	4	no	—
93	C₂²×C₄×C₅	—	2	4	no	—
94	C₂²×C₄×C₅	—	2	2	no	—
95	C₂²×C₄×C₅	—	2	2	no	—
96	C₂²×C₄×C₅	—	2	8	no	—
97	C₂²×C₄×C₅	—	5	1	no	—
98	C₂²×C₄×C₅	—	5	1	no	—
99	C₂²×C₄×C₅	—	5	1	no	—
100	C₂²×C₄×C₅	—	5	4	no	—
101	C₂²×C₄×C₅	—	10	4	no	—
102	C₂²×C₄×C₅	C₂×D₅	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂×D₅	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂×D₅	1	4	yes	complemented
105	C₂²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₂²×C₅	1	4	yes	complemented
108	C₂×C₂²⋊D₅	C₄×C₅	1	8	yes	direct product factor
109	C₂×C₂²⋊D₅	C₂²×C₅	1	4	yes	—
110	C₂²×Dic₅	C₂²×C₅	1	1	yes	characteristic
111	C₂²×Dic₅	C₂²×C₅	1	1	yes	characteristic
112	C₂²×Dic₅	C₂²×C₅	1	1	yes	characteristic
113	C₂×C₄×D₅	—	2	4	no	—
114	C₂×C₄×D₅	C₂²×C₅	1	4	yes	complemented
115	C₅×C₄⋊C₄	—	5	4	no	—
116	C₅×C₂²⋊C₄	—	5	4	no	—
117	C₅×C₂²⋊C₄	—	5	4	no	—
118	C₄²×C₅	—	5	4	no	—
119	C₂²⋊Dic₅	C₂²×C₅	1	4	yes	complemented
120	#685	C₂²×C₅	1	4	yes	complemented
121	#683	C₂²×C₅	1	4	yes	complemented
122	C₄×Dic₅	C₂²×C₅	1	4	yes	complemented
123	C₂×C₄×D₄	—	5	1	no	Sylow
124	C₂×C₅²	—	2	4	no	—
125	C₂×C₅²	C₄×D₄	1	4	yes	complemented
126	C₂×C₅²	C₂³×C₄	1	1	yes	characteristic
127	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
128	C₂×C₅²	C₂×#41	1	1	yes	characteristic
129	C₅×D₅	—	2	4	no	—
130	C₂³×C₅	—	2	8	no	—
131	C₂³×C₅	—	2	8	no	—
132	C₂³×C₅	—	2	2	no	—
133	C₂³×C₅	—	2	2	no	—
134	C₂³×C₅	—	2	2	no	—
135	C₂³×C₅	—	2	2	no	—
136	C₂³×C₅	—	2	8	no	—
137	C₂³×C₅	—	2	4	no	—
138	C₂³×C₅	—	2	2	no	—
139	C₂³×C₅	—	5	4	no	—
140	C₂³×C₅	—	5	2	no	—
141	C₂³×C₅	—	10	2	no	—
142	C₂³×C₅	—	10	2	no	—
143	C₂³×C₅	C₄×D₅	1	4	yes	complemented
144	C₂³×C₅	C₂×C₄×C₅	1	4	yes	complemented
145	C₂³×C₅	C₂²×D₅	1	2	yes	—
146	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
147	C₂³×C₅	C₂³×C₅	1	2	yes	—
148	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
149	C₂²×D₅	—	2	2	no	—
150	C₂²×D₅	—	2	2	no	—
151	C₂²×D₅	C₂×C₄×C₅	1	4	yes	complemented
152	C₂²×D₅	C₂³×C₅	1	2	yes	—
153	C₅×D₄	—	5	16	no	—
154	C₂×C₄×C₅	—	2	8	no	—
155	C₂×C₄×C₅	—	2	32	no	—
156	C₂×C₄×C₅	—	2	2	no	—
157	C₂×C₄×C₅	—	2	2	no	—
158	C₂×C₄×C₅	—	2	8	no	—
159	C₂×C₄×C₅	—	2	8	no	—
160	C₂×C₄×C₅	—	2	8	no	—
161	C₂×C₄×C₅	—	2	4	no	—
162	C₂×C₄×C₅	—	2	4	no	—
163	C₂×C₄×C₅	—	5	4	no	—
164	C₂×C₄×C₅	—	5	2	no	—
165	C₂×C₄×C₅	—	5	2	no	—
166	C₂×C₄×C₅	—	5	2	no	—
167	C₂×C₄×C₅	—	10	2	no	—
168	C₂×C₄×C₅	—	10	2	no	—
169	C₂×C₄×C₅	—	10	8	no	—
170	C₂×C₄×C₅	C₂²⋊D₅	1	4	yes	direct product factor
171	C₂×C₄×C₅	C₅×D₄	1	4	yes	complemented
172	C₂×C₄×C₅	C₂²×D₅	1	2	yes	—
173	C₂×C₄×C₅	C₂²×D₅	1	2	yes	—
174	C₂×C₄×C₅	C₂³×C₅	1	2	yes	—
175	C₂×C₄×C₅	C₂³×C₅	1	2	yes	—
176	C₂²⋊D₅	C₂×C₄×C₅	1	16	yes	direct product factor
177	C₂×Dic₅	—	2	2	no	—
178	C₂×Dic₅	—	2	2	no	—
179	C₂×Dic₅	C₂×C₄×C₅	1	4	yes	complemented
180	C₂×Dic₅	C₂³×C₅	1	2	yes	—
181	C₂×Dic₅	C₂³×C₅	1	2	yes	—
182	C₂×Dic₅	C₂³×C₅	1	2	yes	—
183	C₄×D₅	—	2	8	no	—
184	C₂²×D₄	—	5	1	no	—
185	C₂³×C₄	—	5	1	no	—
186	C₂³×C₄	C₅×D₅	1	1	yes	characteristic, complemented
187	C₄×D₄	—	5	8	no	—
188	C₂×C₄⋊C₄	—	5	1	no	—
189	C₂×C₂²⋊C₄	—	5	1	no	—
190	C₂×C₂²⋊C₄	—	5	1	no	—
191	C₂×C₄²	—	5	1	no	—
192	C₅²	C₂×C₄×D₄	1	1	yes	characteristic, complemented, Sylow
193	C₂²×C₅	—	2	8	no	—
194	C₂²×C₅	—	2	32	no	—
195	C₂²×C₅	—	2	8	no	—
196	C₂²×C₅	—	2	8	no	—
197	C₂²×C₅	—	2	2	no	—
198	C₂²×C₅	—	2	2	no	—
199	C₂²×C₅	—	2	2	no	—
200	C₂²×C₅	—	2	2	no	—
201	C₂²×C₅	—	2	8	no	—
202	C₂²×C₅	—	2	4	no	—
203	C₂²×C₅	—	2	8	no	—
204	C₂²×C₅	—	2	4	no	—
205	C₂²×C₅	—	2	4	no	—
206	C₂²×C₅	—	2	2	no	—
207	C₂²×C₅	—	5	4	no	—
208	C₂²×C₅	—	10	2	no	—
209	C₂²×C₅	—	10	2	no	—
210	C₂²×C₅	—	10	8	no	—
211	C₂²×C₅	C₂×C₄×D₅	1	2	yes	—
212	C₂²×C₅	C₂×C₄×D₅	1	4	yes	complemented
213	C₂²×C₅	#709	1	2	yes	—
214	C₂²×C₅	C₂×C₂²⋊D₅	1	2	yes	—
215	C₂²×C₅	C₂²×C₄×C₅	1	2	yes	—
216	C₂²×C₅	C₂²×C₄×C₅	1	4	yes	complemented
217	C₂²×C₅	C₂×C₅×D₄	1	2	yes	—
218	C₂²×C₅	C₅×#41	1	2	yes	—
219	C₂²×C₅	C₂³×D₅	1	1	yes	characteristic
220	C₂²×C₅	C₂⁴×C₅	1	1	yes	characteristic
221	C₂×D₅	—	2	8	no	—
222	C₂×D₅	—	2	2	no	—
223	C₂×D₅	—	2	2	no	—
224	C₂×D₅	C₂²×C₄×C₅	1	4	yes	complemented
225	C₄×C₅	—	2	8	no	—
226	C₄×C₅	—	2	2	no	—
227	C₄×C₅	—	2	2	no	—
228	C₄×C₅	—	2	8	no	—
229	C₄×C₅	—	5	4	no	—
230	C₄×C₅	—	10	2	no	—
231	C₄×C₅	—	10	2	no	—
232	C₄×C₅	C₂×C₂²⋊D₅	1	4	yes	direct product factor
233	C₄×C₅	C₂×C₅×D₄	1	4	yes	complemented
234	Dic₅	—	2	2	no	—
235	Dic₅	—	2	2	no	—
236	Dic₅	C₂²×C₄×C₅	1	4	yes	complemented
237	C₂⁴	—	5	1	no	—
238	C₂⁴	C₂×C₅×D₅	1	1	yes	characteristic
239	C₂×D₄	—	5	8	no	—
240	C₂×D₄	—	5	4	no	—
241	C₂²×C₄	—	2	4	no	—
242	C₂²×C₄	—	5	1	no	—
243	C₂²×C₄	—	5	1	no	—
244	C₂²×C₄	—	5	1	no	—
245	C₂²×C₄	—	5	4	no	—
246	C₂²×C₄	—	10	4	no	—
247	C₂²×C₄	C₂×C₅×D₅	1	1	yes	characteristic
248	C₂²×C₄	C₂×C₅×D₅	1	1	yes	characteristic
249	C₂²×C₄	C₂×C₅×D₅	1	4	yes	complemented
250	C₄⋊C₄	—	5	4	no	—
251	C₂²⋊C₄	—	5	4	no	—
252	C₂²⋊C₄	—	5	4	no	—
253	C₄²	—	5	4	no	—
254	C₂×C₅	—	2	16	no	—
255	C₂×C₅	—	2	4	no	—
256	C₂×C₅	—	2	4	no	—
257	C₂×C₅	—	2	8	no	—
258	C₂×C₅	—	2	2	no	—
259	C₂×C₅	—	2	2	no	—
260	C₂×C₅	—	2	2	no	—
261	C₂×C₅	—	10	4	no	—
262	C₂×C₅	C₄×C₂²⋊D₅	1	4	yes	direct product factor
263	C₂×C₅	C₄×C₅×D₄	1	4	yes	complemented
264	C₂×C₅	C₂²×C₄×D₅	1	1	yes	characteristic
265	C₂×C₅	C₂×#709	1	1	yes	characteristic
266	C₂×C₅	C₂²×C₂²⋊D₅	1	1	yes	characteristic
267	C₂×C₅	C₂³×C₄×C₅	1	1	yes	characteristic
268	C₂×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
269	C₂×C₅	C₂×C₅×#41	1	1	yes	characteristic
270	D₅	—	2	4	no	—
271	C₂³	—	2	2	no	—
272	C₂³	—	2	2	no	—
273	C₂³	—	5	4	no	—
274	C₂³	—	5	2	no	—
275	C₂³	—	10	2	no	—
276	C₂³	—	10	2	no	—
277	C₂³	C₄×C₅×D₅	1	4	yes	complemented
278	C₂³	C₂²×C₅×D₅	1	2	yes	—
279	C₂³	C₂²×C₅×D₅	1	1	yes	characteristic
280	D₄	—	5	16	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	2	8	no	—
283	C₂×C₄	—	5	4	no	—
284	C₂×C₄	—	5	2	no	—
285	C₂×C₄	—	5	2	no	—
286	C₂×C₄	—	5	2	no	—
287	C₂×C₄	—	10	2	no	—
288	C₂×C₄	—	10	2	no	—
289	C₂×C₄	—	10	8	no	—
290	C₂×C₄	C₅×C₂²⋊D₅	1	4	yes	direct product factor
291	C₂×C₄	C₂²×C₅×D₅	1	2	yes	—
292	C₂×C₄	C₂²×C₅×D₅	1	2	yes	—
293	C₅	—	2	2	no	—
294	C₅	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic, direct product factor
295	C₅	C₂×C₄×C₅×D₄	1	1	yes	characteristic, complemented
296	C₂²	—	2	8	no	—
297	C₂²	—	2	2	no	—
298	C₂²	—	2	2	no	—
299	C₂²	—	5	4	no	—
300	C₂²	—	10	8	no	—
301	C₂²	—	10	2	no	—
302	C₂²	—	10	2	no	—
303	C₂²	C₂×C₄×C₅×D₅	1	2	yes	—
304	C₂²	C₂×C₄×C₅×D₅	1	4	yes	complemented
305	C₂²	C₅×#709	1	2	yes	—
306	C₂²	C₂×C₅×C₂²⋊D₅	1	2	yes	—
307	C₂²	C₂³×C₅×D₅	1	1	yes	characteristic
308	C₄	—	2	2	no	—
309	C₄	—	5	4	no	—
310	C₄	—	10	2	no	—
311	C₄	—	10	2	no	—
312	C₄	C₂×C₅×C₂²⋊D₅	1	4	yes	direct product factor
313	C₂	—	2	4	no	—
314	C₂	—	10	4	no	—
315	C₂	C₄×C₅×C₂²⋊D₅	1	4	yes	direct product factor
316	C₂	C₂²×C₄×C₅×D₅	1	1	yes	characteristic
317	C₂	C₂×C₅×#709	1	1	yes	characteristic
318	C₂	C₂²×C₅×C₂²⋊D₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂³×C₄×C₅²	C₂	semidirect
3. C₂²×C₄×C₅×D₅	C₂	semidirect
4. C₂×C₅×C₂²⋊Dic₅	C₂	semidirect
5. C₄×C₅×C₂²⋊D₅	C₂	direct (N × H)
6. C₂×C₅×#685	C₂	semidirect
7. C₂×C₅×#683	C₂	semidirect
8. C₂×C₄×C₅×Dic₅	C₂	semidirect
14. C₂²×C₄×C₅²	C₂²	semidirect
15. C₂×C₅×C₂²⋊D₅	C₄	direct (N × H)
21. C₂×C₄×C₅×D₅	C₂²	semidirect
22. C₅×C₂²⋊Dic₅	C₂²	semidirect
23. C₅×#685	C₂²	semidirect
24. C₅×#683	C₂²	semidirect
25. C₄×C₅×Dic₅	C₂²	semidirect
27. C₂×C₄×C₂²⋊D₅	C₅	direct (N × H)
30. C₂³×C₅²	C₂×C₄	semidirect
35. C₂²×C₅×D₅	C₂×C₄	semidirect
39. C₂×C₄×C₅²	D₄	semidirect
42. C₅×C₂²⋊D₅	C₂×C₄	direct (N × H)
45. C₂×C₅×Dic₅	C₂×C₄	semidirect
53. C₂³×C₄×C₅	D₅	semidirect
54. C₂³×C₄×C₅	C₂×C₅	semidirect
56. C₂²×C₄×D₅	C₂×C₅	semidirect
62. C₂×C₂²⋊Dic₅	C₂×C₅	semidirect
63. C₄×C₂²⋊D₅	C₂×C₅	direct (N × H)
64. C₂×#685	C₂×C₅	semidirect
65. C₂×#683	C₂×C₅	semidirect
66. C₂×C₄×Dic₅	C₂×C₅	semidirect
71. C₂²×C₅²	C₂²×C₄	semidirect
78. C₂×C₅×D₅	C₂²×C₄	semidirect
80. C₄×C₅²	C₂×D₄	semidirect
83. C₅×Dic₅	C₂²×C₄	semidirect
104. C₂²×C₄×C₅	C₂×D₅	semidirect
107. C₂²×C₄×C₅	C₂²×C₅	semidirect
108. C₂×C₂²⋊D₅	C₄×C₅	direct (N × H)
114. C₂×C₄×D₅	C₂²×C₅	semidirect
119. C₂²⋊Dic₅	C₂²×C₅	semidirect
120. #685	C₂²×C₅	semidirect
121. #683	C₂²×C₅	semidirect
122. C₄×Dic₅	C₂²×C₅	semidirect
125. C₂×C₅²	C₄×D₄	semidirect
143. C₂³×C₅	C₄×D₅	semidirect
144. C₂³×C₅	C₂×C₄×C₅	semidirect
151. C₂²×D₅	C₂×C₄×C₅	semidirect
170. C₂×C₄×C₅	C₂²⋊D₅	direct (N × H)
171. C₂×C₄×C₅	C₅×D₄	semidirect
176. C₂²⋊D₅	C₂×C₄×C₅	direct (N × H)
179. C₂×Dic₅	C₂×C₄×C₅	semidirect
186. C₂³×C₄	C₅×D₅	semidirect
192. C₅²	C₂×C₄×D₄	semidirect
212. C₂²×C₅	C₂×C₄×D₅	semidirect
216. C₂²×C₅	C₂²×C₄×C₅	semidirect
224. C₂×D₅	C₂²×C₄×C₅	semidirect
232. C₄×C₅	C₂×C₂²⋊D₅	direct (N × H)
233. C₄×C₅	C₂×C₅×D₄	semidirect
236. Dic₅	C₂²×C₄×C₅	semidirect
249. C₂²×C₄	C₂×C₅×D₅	semidirect
262. C₂×C₅	C₄×C₂²⋊D₅	direct (N × H)
263. C₂×C₅	C₄×C₅×D₄	semidirect
277. C₂³	C₄×C₅×D₅	semidirect
290. C₂×C₄	C₅×C₂²⋊D₅	direct (N × H)
294. C₅	C₂×C₄×C₂²⋊D₅	direct (N × H)
295. C₅	C₂×C₄×C₅×D₄	semidirect
304. C₂²	C₂×C₄×C₅×D₅	semidirect
312. C₄	C₂×C₅×C₂²⋊D₅	direct (N × H)
315. C₂	C₄×C₅×C₂²⋊D₅	direct (N × H)

Maximal subgroups

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

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

Subgroups — C2×C4×C5×C22⋊D5 #13106942

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₅×C₂²⋊D₅ #13106942