Subgroups — C₅×#5545 #11755930

Order 960.

676 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×#67	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₅×#893	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#892	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#67⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₅×D₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#872	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#518	—	3	1	no	maximal, Hall
13	C₂³×C₅×D₃	C₂²	1	2	yes	—
14	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₅	C₂²	1	2	yes	complemented
16	C₂×C₅×#67	C₂²	1	2	yes	—
17	C₂²×C₅×Dic₃	C₂²	1	2	yes	complemented
18	C₅×D₃×D₄	C₄	1	8	yes	complemented
19	C₂×C₅×D₁₂	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×D₃	C₂²	1	2	yes	complemented
22	C₂×C₄×C₅×D₃	C₂²	1	2	yes	complemented
23	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
25	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
26	C₅×#217	C₂²	1	2	yes	complemented
27	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
28	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
29	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
30	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
31	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
32	C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
33	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
34	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
35	C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
36	C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
37	#5545	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
38	C₂²×C₅×D₄	—	3	1	no	—
39	C₄×C₅×D₄	—	3	1	no	—
40	C₄×C₅×D₄	—	3	2	no	—
41	C₄×C₅×D₄	—	3	1	no	—
42	C₄×C₅×D₄	—	3	2	no	—
43	C₄×C₅×D₄	—	3	1	no	—
44	C₄×C₅×D₄	D₃	1	1	yes	characteristic, complemented
45	C₅×#117	—	3	1	no	—
46	C₅×#117	—	3	1	no	—
47	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
48	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
49	C₂³×C₃×C₅	C₂³	1	2	yes	—
50	C₂²×C₅×D₃	—	4	2	no	—
51	C₂²×C₅×D₃	—	4	2	no	—
52	C₂²×C₅×D₃	C₂×C₄	1	8	yes	complemented
53	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
54	C₂²×C₅×D₃	C₂³	1	2	yes	—
55	C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
56	C₂×C₃×C₄×C₅	—	4	2	no	—
57	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
58	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₅×#67	C₂×C₄	1	8	yes	complemented
62	C₂×C₅×Dic₃	—	4	2	no	—
63	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
64	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
65	C₂×C₅×Dic₃	C₂³	1	2	yes	—
66	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
67	C₅×D₁₂	C₂×C₄	1	4	yes	complemented
68	C₄×C₅×D₃	—	4	2	no	—
69	C₄×C₅×D₃	—	4	2	no	—
70	C₄×C₅×D₃	C₂×C₄	1	4	yes	complemented
71	C₂×D₃×D₄	C₂×C₅	1	1	yes	characteristic
72	C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
73	D₄×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
74	C₄×#67	C₂×C₅	1	2	yes	complemented
75	C₂×(C₂×D₃)⋊C₄	C₂×C₅	1	2	yes	complemented
76	#893	C₂×C₅	1	1	yes	characteristic, complemented
77	#892	C₂×C₅	1	1	yes	characteristic, complemented
78	#67⋊C₄	C₂×C₅	1	2	yes	complemented
79	D₃×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
80	C₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
81	#872	C₂×C₅	1	1	yes	characteristic, complemented
82	C₂⁴×C₅	—	3	2	no	—
83	C₂×C₅×D₄	—	3	2	no	—
84	C₂×C₅×D₄	—	3	8	no	—
85	C₂×C₅×D₄	—	3	1	no	—
86	C₂×C₅×D₄	C₂×D₃	1	1	yes	characteristic
87	C₂²×C₄×C₅	—	3	1	no	—
88	C₂²×C₄×C₅	—	3	2	no	—
89	C₂²×C₄×C₅	—	3	2	no	—
90	C₂²×C₄×C₅	—	3	2	no	—
91	C₂²×C₄×C₅	C₂×D₃	1	2	yes	complemented
92	C₅×C₄⋊C₄	—	3	1	no	—
93	C₅×C₄⋊C₄	—	3	1	no	—
94	C₅×C₄⋊C₄	—	3	1	no	—
95	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
96	C₅×C₂²⋊C₄	—	3	2	no	—
97	C₅×C₂²⋊C₄	—	3	2	no	—
98	C₅×C₂²⋊C₄	—	3	1	no	—
99	C₅×C₂²⋊C₄	—	3	1	no	—
100	C₅×C₂²⋊C₄	—	3	2	no	—
101	C₅×C₂²⋊C₄	—	3	2	no	—
102	C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
103	C₄²×C₅	—	3	2	no	—
104	C₄²×C₅	—	3	1	no	—
105	C₄²×C₅	C₂×D₃	1	1	yes	characteristic, complemented
106	#518	—	3	1	no	Sylow
107	C₂²×C₃×C₅	—	2	2	no	—
108	C₂²×C₃×C₅	—	2	2	no	—
109	C₂²×C₃×C₅	C₂²×C₄	1	4	yes	—
110	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
111	C₂×C₅×D₃	—	2	2	no	—
112	C₂×C₅×D₃	—	2	2	no	—
113	C₂×C₅×D₃	—	2	1	no	—
114	C₂×C₅×D₃	—	2	1	no	—
115	C₂×C₅×D₃	—	4	8	no	—
116	C₂×C₅×D₃	C₂²×C₄	1	2	yes	—
117	C₂×C₅×D₃	C₂²×C₄	1	4	yes	—
118	C₃×C₄×C₅	—	2	1	no	—
119	C₃×C₄×C₅	—	2	2	no	—
120	C₃×C₄×C₅	—	2	1	no	—
121	C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
122	C₅×Dic₃	—	2	1	no	—
123	C₅×Dic₃	—	2	2	no	—
124	C₅×Dic₃	—	2	1	no	—
125	C₅×Dic₃	C₂²×C₄	1	2	yes	—
126	C₂³×D₃	C₂²×C₅	1	2	yes	—
127	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
128	C₂²×C₃×C₄	C₂²×C₅	1	2	yes	complemented
129	C₂×#67	C₂²×C₅	1	2	yes	—
130	C₂²×Dic₃	C₂²×C₅	1	2	yes	complemented
131	D₃×D₄	C₄×C₅	1	8	yes	complemented
132	C₂×D₁₂	C₂²×C₅	1	1	yes	characteristic
133	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₄×D₃	C₂²×C₅	1	2	yes	complemented
135	C₂×C₄×D₃	C₂²×C₅	1	2	yes	complemented
136	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
137	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
138	C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
139	#217	C₂²×C₅	1	2	yes	complemented
140	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
141	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
142	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
143	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
144	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
145	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
146	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
147	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
148	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
149	C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
150	C₂³×C₅	—	3	1	no	—
151	C₂³×C₅	—	3	2	no	—
152	C₂³×C₅	—	3	8	no	—
153	C₂³×C₅	—	12	2	no	—
154	C₂³×C₅	—	12	2	no	—
155	C₂³×C₅	C₂²×D₃	1	2	yes	—
156	C₅×D₄	—	3	8	no	—
157	C₅×D₄	—	3	4	no	—
158	C₅×D₄	C₄×D₃	1	4	yes	complemented
159	C₂×C₄×C₅	—	3	1	no	—
160	C₂×C₄×C₅	—	3	4	no	—
161	C₂×C₄×C₅	—	3	1	no	—
162	C₂×C₄×C₅	—	3	2	no	—
163	C₂×C₄×C₅	—	3	1	no	—
164	C₂×C₄×C₅	—	4	2	no	—
165	C₂×C₄×C₅	—	12	2	no	—
166	C₂×C₄×C₅	—	12	2	no	—
167	C₂×C₄×C₅	—	12	2	no	—
168	C₂×C₄×C₅	C₂²×D₃	1	2	yes	—
169	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
170	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
171	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
172	C₂²×D₄	—	3	1	no	—
173	C₄×D₄	—	3	1	no	—
174	C₄×D₄	—	3	2	no	—
175	C₄×D₄	—	3	1	no	—
176	C₄×D₄	—	3	2	no	—
177	C₄×D₄	—	3	1	no	—
178	C₄×D₄	C₅×D₃	1	1	yes	characteristic, complemented
179	#117	—	3	1	no	—
180	#117	—	3	1	no	—
181	C₂×C₂²⋊C₄	—	3	2	no	—
182	C₂×C₂²⋊C₄	—	3	2	no	—
183	C₂×C₃×C₅	—	2	4	no	—
184	C₂×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
187	C₅×D₃	—	2	2	no	—
188	C₅×D₃	—	2	4	no	—
189	C₂³×C₃	C₂³×C₅	1	2	yes	—
190	C₂²×D₃	—	4	2	no	—
191	C₂²×D₃	—	4	2	no	—
192	C₂²×D₃	C₂×C₄×C₅	1	8	yes	complemented
193	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
194	C₂²×D₃	C₂³×C₅	1	2	yes	—
195	C₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
196	C₂×C₃×C₄	—	4	2	no	—
197	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
198	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
199	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
200	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
201	#67	C₂×C₄×C₅	1	8	yes	complemented
202	C₂×Dic₃	—	4	2	no	—
203	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
204	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
205	C₂×Dic₃	C₂³×C₅	1	2	yes	—
206	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
207	D₁₂	C₂×C₄×C₅	1	4	yes	complemented
208	C₄×D₃	—	4	2	no	—
209	C₄×D₃	—	4	2	no	—
210	C₄×D₃	C₂×C₄×C₅	1	4	yes	complemented
211	C₂²×C₅	—	2	2	no	—
212	C₂²×C₅	—	2	2	no	—
213	C₂²×C₅	—	3	2	no	—
214	C₂²×C₅	—	3	4	no	—
215	C₂²×C₅	—	6	2	no	—
216	C₂²×C₅	—	6	1	no	—
217	C₂²×C₅	—	6	2	no	—
218	C₂²×C₅	—	6	1	no	—
219	C₂²×C₅	—	12	8	no	—
220	C₂²×C₅	C₂×C₄×D₃	1	4	yes	—
221	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
222	C₄×C₅	—	2	1	no	—
223	C₄×C₅	—	2	2	no	—
224	C₄×C₅	—	2	1	no	—
225	C₄×C₅	—	3	2	no	—
226	C₄×C₅	—	6	1	no	—
227	C₄×C₅	—	6	2	no	—
228	C₄×C₅	—	6	1	no	—
229	C₄×C₅	C₂×C₄×D₃	1	2	yes	—
230	C₂⁴	—	3	2	no	—
231	C₂×D₄	—	3	2	no	—
232	C₂×D₄	—	3	8	no	—
233	C₂×D₄	—	3	1	no	—
234	C₂×D₄	C₂×C₅×D₃	1	1	yes	characteristic
235	C₂²×C₄	—	3	1	no	—
236	C₂²×C₄	—	3	2	no	—
237	C₂²×C₄	—	3	2	no	—
238	C₂²×C₄	—	3	2	no	—
239	C₂²×C₄	C₂×C₅×D₃	1	2	yes	complemented
240	C₄⋊C₄	—	3	1	no	—
241	C₄⋊C₄	—	3	1	no	—
242	C₄⋊C₄	—	3	1	no	—
243	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
244	C₂²⋊C₄	—	3	2	no	—
245	C₂²⋊C₄	—	3	2	no	—
246	C₂²⋊C₄	—	3	1	no	—
247	C₂²⋊C₄	—	3	1	no	—
248	C₂²⋊C₄	—	3	2	no	—
249	C₂²⋊C₄	—	3	2	no	—
250	C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
251	C₄²	—	3	2	no	—
252	C₄²	—	3	1	no	—
253	C₄²	C₂×C₅×D₃	1	1	yes	characteristic, complemented
254	C₃×C₅	#518	1	1	yes	characteristic, complemented, Hall
255	C₂²×C₃	—	2	2	no	—
256	C₂²×C₃	—	2	2	no	—
257	C₂²×C₃	C₂²×C₄×C₅	1	4	yes	—
258	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
259	C₂×D₃	—	2	2	no	—
260	C₂×D₃	—	2	2	no	—
261	C₂×D₃	—	2	1	no	—
262	C₂×D₃	—	2	1	no	—
263	C₂×D₃	—	4	8	no	—
264	C₂×D₃	C₂²×C₄×C₅	1	2	yes	—
265	C₂×D₃	C₂²×C₄×C₅	1	4	yes	—
266	C₃×C₄	—	2	1	no	—
267	C₃×C₄	—	2	2	no	—
268	C₃×C₄	—	2	1	no	—
269	C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
270	Dic₃	—	2	1	no	—
271	Dic₃	—	2	2	no	—
272	Dic₃	—	2	1	no	—
273	Dic₃	C₂²×C₄×C₅	1	2	yes	—
274	C₂×C₅	—	2	4	no	—
275	C₂×C₅	—	6	2	no	—
276	C₂×C₅	—	6	4	no	—
277	C₂×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
278	C₂×C₅	#1004	1	1	yes	characteristic
279	C₂×C₅	#1009	1	1	yes	characteristic
280	C₂³	—	3	1	no	—
281	C₂³	—	3	2	no	—
282	C₂³	—	3	8	no	—
283	C₂³	—	12	2	no	—
284	C₂³	—	12	2	no	—
285	C₂³	C₂²×C₅×D₃	1	2	yes	—
286	D₄	—	3	8	no	—
287	D₄	—	3	4	no	—
288	D₄	C₄×C₅×D₃	1	4	yes	complemented
289	C₂×C₄	—	3	1	no	—
290	C₂×C₄	—	3	4	no	—
291	C₂×C₄	—	3	1	no	—
292	C₂×C₄	—	3	2	no	—
293	C₂×C₄	—	3	1	no	—
294	C₂×C₄	—	4	2	no	—
295	C₂×C₄	—	12	2	no	—
296	C₂×C₄	—	12	2	no	—
297	C₂×C₄	—	12	2	no	—
298	C₂×C₄	C₂²×C₅×D₃	1	2	yes	—
299	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
300	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
301	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
302	C₂×C₃	—	2	4	no	—
303	C₂×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
304	C₂×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
305	C₂×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
306	D₃	—	2	2	no	—
307	D₃	—	2	4	no	—
308	C₅	#5545	1	1	yes	characteristic, direct product factor, Sylow
309	C₂²	—	2	2	no	—
310	C₂²	—	2	2	no	—
311	C₂²	—	3	2	no	—
312	C₂²	—	3	4	no	—
313	C₂²	—	6	2	no	—
314	C₂²	—	6	1	no	—
315	C₂²	—	6	2	no	—
316	C₂²	—	6	1	no	—
317	C₂²	—	12	8	no	—
318	C₂²	C₂×C₄×C₅×D₃	1	4	yes	—
319	C₂²	C₂³×C₅×D₃	1	1	yes	characteristic
320	C₄	—	2	1	no	—
321	C₄	—	2	2	no	—
322	C₄	—	2	1	no	—
323	C₄	—	3	2	no	—
324	C₄	—	6	1	no	—
325	C₄	—	6	2	no	—
326	C₄	—	6	1	no	—
327	C₄	C₂×C₄×C₅×D₃	1	2	yes	—
328	C₃	C₅×#518	1	1	yes	characteristic, complemented, Sylow
329	C₂	—	2	4	no	—
330	C₂	—	6	2	no	—
331	C₂	—	6	4	no	—
332	C₂	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
333	C₂	C₅×#1004	1	1	yes	characteristic
334	C₂	C₅×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂³×D₃
commutator	C₂×C₃	C₂³×C₄×C₅
Frattini	C₂²	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×D₄	C₂
socle	C₂²×C₃×C₅	C₂⁴
prime radical	C₂×C₅×D₃×D₄	C₂
cosocle	C₂²×C₃	C₂⁴×C₅
hypercenter	C₄×C₅×D₄	D₃
hypocenter	C₃	C₅×#518
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅×D₄	C₂	semidirect
3. C₅×D₄×Dic₃	C₂	semidirect
4. C₄×C₅×#67	C₂	semidirect
5. C₂×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₅×#893	C₂	semidirect
7. C₅×#892	C₂	semidirect
8. C₅×#67⋊C₄	C₂	semidirect
9. C₅×D₃×C₂²⋊C₄	C₂	semidirect
10. C₄×C₅×D₁₂	C₂	semidirect
11. C₅×#872	C₂	semidirect
15. C₂²×C₃×C₄×C₅	C₂²	semidirect
17. C₂²×C₅×Dic₃	C₂²	semidirect
18. C₅×D₃×D₄	C₄	semidirect
21. C₂×C₄×C₅×D₃	C₂²	semidirect
22. C₂×C₄×C₅×D₃	C₂²	semidirect
23. C₃×C₅×C₄⋊C₄	C₂²	semidirect
24. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
25. C₃×C₄²×C₅	C₂²	semidirect
26. C₅×#217	C₂²	semidirect
30. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
31. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
32. C₅×C₄⋊Dic₃	C₂²	semidirect
33. C₅×Dic₃⋊C₄	C₂²	semidirect
34. C₅×Dic₃⋊C₄	C₂²	semidirect
35. C₄×C₅×Dic₃	C₂²	semidirect
36. C₄×C₅×Dic₃	C₂²	semidirect
37. #5545	C₅	direct (N × H)
44. C₄×C₅×D₄	D₃	semidirect
52. C₂²×C₅×D₃	C₂×C₄	semidirect
55. C₃×C₅×D₄	C₂×C₄	semidirect
61. C₅×#67	C₂×C₄	semidirect
67. C₅×D₁₂	C₂×C₄	semidirect
70. C₄×C₅×D₃	C₂×C₄	semidirect
72. C₃×C₄×D₄	C₂×C₅	semidirect
73. D₄×Dic₃	C₂×C₅	semidirect
74. C₄×#67	C₂×C₅	semidirect
75. C₂×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
76. #893	C₂×C₅	semidirect
77. #892	C₂×C₅	semidirect
78. #67⋊C₄	C₂×C₅	semidirect
79. D₃×C₂²⋊C₄	C₂×C₅	semidirect
80. C₄×D₁₂	C₂×C₅	semidirect
81. #872	C₂×C₅	semidirect
91. C₂²×C₄×C₅	C₂×D₃	semidirect
95. C₅×C₄⋊C₄	C₂×D₃	semidirect
102. C₅×C₂²⋊C₄	C₂×D₃	semidirect
105. C₄²×C₅	C₂×D₃	semidirect
128. C₂²×C₃×C₄	C₂²×C₅	semidirect
130. C₂²×Dic₃	C₂²×C₅	semidirect
131. D₃×D₄	C₄×C₅	semidirect
134. C₂×C₄×D₃	C₂²×C₅	semidirect
135. C₂×C₄×D₃	C₂²×C₅	semidirect
136. C₃×C₄⋊C₄	C₂²×C₅	semidirect
137. C₃×C₂²⋊C₄	C₂²×C₅	semidirect
138. C₃×C₄²	C₂²×C₅	semidirect
139. #217	C₂²×C₅	semidirect
143. (C₂×D₃)⋊C₄	C₂²×C₅	semidirect
144. (C₂×D₃)⋊C₄	C₂²×C₅	semidirect
145. C₄⋊Dic₃	C₂²×C₅	semidirect
146. Dic₃⋊C₄	C₂²×C₅	semidirect
147. Dic₃⋊C₄	C₂²×C₅	semidirect
148. C₄×Dic₃	C₂²×C₅	semidirect
149. C₄×Dic₃	C₂²×C₅	semidirect
158. C₅×D₄	C₄×D₃	semidirect
178. C₄×D₄	C₅×D₃	semidirect
192. C₂²×D₃	C₂×C₄×C₅	semidirect
195. C₃×D₄	C₂×C₄×C₅	semidirect
201. #67	C₂×C₄×C₅	semidirect
207. D₁₂	C₂×C₄×C₅	semidirect
210. C₄×D₃	C₂×C₄×C₅	semidirect
239. C₂²×C₄	C₂×C₅×D₃	semidirect
243. C₄⋊C₄	C₂×C₅×D₃	semidirect
250. C₂²⋊C₄	C₂×C₅×D₃	semidirect
253. C₄²	C₂×C₅×D₃	semidirect
254. C₃×C₅	#518	semidirect
288. D₄	C₄×C₅×D₃	semidirect
308. C₅	#5545	direct (N × H)
328. C₃	C₅×#518	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×D₄	2
C₃×C₄×C₅×D₄	2
C₅×D₄×Dic₃	2
C₄×C₅×#67	2
C₂×C₅×(C₂×D₃)⋊C₄	2
C₅×#893	2
C₅×#892	2
C₅×#67⋊C₄	2
C₅×D₃×C₂²⋊C₄	2
C₄×C₅×D₁₂	2
C₅×#872	2
C₅×#518	3
#5545	5

Subgroups — C5×#5545 #11755930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5545 #11755930