Subgroups — C₅×#78574 #14417740

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#904	C₂	1	1	yes	maximal, characteristic
2	C₅×#5523	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5133	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#817	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4716	C₂	1	2	yes	maximal, complemented
7	C₅×#4711	C₂	1	2	yes	maximal, complemented
8	C₄×C₅×#204	C₂	1	4	yes	maximal, complemented
9	C₅×#2952	—	3	1	no	maximal, Hall
10	C₂×C₅×#235	C₂²	1	2	yes	—
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₅×#117	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
15	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
16	C₅×#904	C₄	1	8	yes	complemented
17	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
18	C₂×C₅×#204	C₂²	1	2	yes	—
19	C₅×#892	—	2	2	no	—
20	C₅×D₃×C₄⋊C₄	—	2	2	no	—
21	C₅×#67⋊C₄	—	2	4	no	—
22	C₄×C₅×D₁₂	C₂²	1	4	yes	—
23	C₄×C₅×Dic₆	C₂²	1	4	yes	—
24	C₃×C₅×#97	C₂²	1	2	yes	—
25	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
26	C₅×#821	C₂²	1	4	yes	—
27	C₅×#817	C₂²	1	2	yes	—
28	C₅×#817	C₂²	1	2	yes	—
29	C₅×#816	C₂²	1	4	yes	—
30	#78574	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#135	—	3	1	no	—
32	C₅×#520	—	3	2	no	—
33	C₅×#442	—	3	2	no	—
34	C₅×#441	—	3	2	no	—
35	C₄×C₅×SD₁₆	—	3	4	no	—
36	C₂×C₅×#106	—	3	1	no	—
37	C₅×#417	—	3	2	no	—
38	C₅×#405	D₃	1	1	yes	characteristic, complemented
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂×C₅×#67	—	2	2	no	—
41	C₂²×C₅×Dic₃	—	2	2	no	—
42	C₅×#235	—	2	4	no	—
43	C₅×#235	C₂×C₄	1	8	yes	complemented
44	C₂×C₅×D₁₂	C₂³	1	2	yes	—
45	C₂×C₄×C₅×D₃	—	2	2	no	—
46	C₂×C₄×C₅×D₃	—	2	4	no	—
47	C₂×C₅×Dic₆	C₂³	1	2	yes	—
48	C₃×C₅×M₁₆	—	2	2	no	—
49	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
50	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
51	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
54	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
55	C₃×C₄²×C₅	C₂³	1	2	yes	—
56	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
57	C₅×C₄⋊Dic₃	—	2	2	no	—
58	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
59	C₅×Dic₃⋊C₄	—	2	4	no	—
60	C₄×C₅×Dic₃	—	2	4	no	—
61	C₅×Dic₁₂	C₂×C₄	1	4	yes	complemented
62	C₅×D₂₄	C₂×C₄	1	4	yes	complemented
63	C₅×#204	C₂×C₄	1	8	yes	complemented
64	C₂×#904	C₂×C₅	1	1	yes	characteristic
65	#5523	C₂×C₅	1	2	yes	complemented
66	C₃×#405	C₂×C₅	1	1	yes	characteristic, complemented
67	#5133	C₂×C₅	1	2	yes	complemented
68	C₂×#817	C₂×C₅	1	1	yes	characteristic, complemented
69	#4716	C₂×C₅	1	2	yes	complemented
70	#4711	C₂×C₅	1	2	yes	complemented
71	C₄×#204	C₂×C₅	1	4	yes	complemented
72	C₂×C₅×#41	—	3	2	no	—
73	C₅×#135	—	3	8	no	—
74	C₂×C₅×Q₁₆	—	3	1	no	—
75	C₂×C₅×SD₁₆	—	3	2	no	—
76	C₂×C₅×D₈	—	3	1	no	—
77	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
78	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
79	C₄×C₅×Q₈	—	3	4	no	—
80	C₄×C₅×D₄	—	3	4	no	—
81	C₄×C₅×D₄	—	6	4	no	—
82	C₅×#117	—	6	2	no	—
83	C₅×#117	C₂×D₃	1	1	yes	characteristic
84	C₂×C₅×C₄⋊C₄	—	3	2	no	—
85	C₂×C₅×C₄⋊C₄	—	6	2	no	—
86	C₅×#106	—	3	2	no	—
87	C₅×#106	—	3	2	no	—
88	C₅×#103	—	3	4	no	—
89	C₅×#102	—	3	4	no	—
90	C₅×#97	C₂×D₃	1	2	yes	—
91	C₄×C₅×C₈	C₂×D₃	1	2	yes	—
92	#2952	—	3	1	no	Sylow
93	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₅×D₃	—	2	2	no	—
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
97	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	#41	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
100	C₅×#67	—	2	8	no	—
101	C₂×C₅×Dic₃	—	2	2	no	—
102	C₂×C₅×Dic₃	—	2	4	no	—
103	C₂×C₅×Dic₃	—	8	2	no	—
104	C₅×D₁₂	—	2	2	no	—
105	C₅×D₁₂	C₂²×C₄	1	4	yes	—
106	C₄×C₅×D₃	—	2	8	no	—
107	C₄×C₅×D₃	—	8	4	no	—
108	C₅×Dic₆	—	2	2	no	—
109	C₅×Dic₆	C₂²×C₄	1	4	yes	—
110	C₃×C₅×C₈	—	2	2	no	—
111	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
112	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
113	C₂×#235	C₂²×C₅	1	2	yes	—
114	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
115	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
116	C₃×#117	C₂²×C₅	1	1	yes	characteristic
117	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
118	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
119	#904	C₄×C₅	1	8	yes	complemented
120	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
121	C₂×#204	C₂²×C₅	1	2	yes	—
122	#892	—	2	2	no	—
123	D₃×C₄⋊C₄	—	2	2	no	—
124	#67⋊C₄	—	2	4	no	—
125	C₄×D₁₂	C₂²×C₅	1	4	yes	—
126	C₄×Dic₆	C₂²×C₅	1	4	yes	—
127	C₃×#97	C₂²×C₅	1	2	yes	—
128	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
129	#821	C₂²×C₅	1	4	yes	—
130	#817	C₂²×C₅	1	2	yes	—
131	#817	C₂²×C₅	1	2	yes	—
132	#816	C₂²×C₅	1	4	yes	—
133	C₅×#41	—	3	8	no	—
134	C₅×#41	—	6	4	no	—
135	C₂×C₅×Q₈	—	3	2	no	—
136	C₂×C₅×D₄	—	3	2	no	—
137	C₂×C₅×D₄	—	6	2	no	—
138	C₂²×C₄×C₅	—	6	2	no	—
139	C₂²×C₄×C₅	—	6	2	no	—
140	C₂²×C₄×C₅	—	6	4	no	—
141	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
142	C₅×Q₁₆	—	3	4	no	—
143	C₅×SD₁₆	—	3	8	no	—
144	C₅×D₈	—	3	4	no	—
145	C₅×M₁₆	—	2	2	no	—
146	C₂×C₅×C₈	C₄×D₃	1	4	yes	complemented
147	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
148	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
149	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
150	C₅×C₄⋊C₄	—	3	4	no	—
151	C₅×C₄⋊C₄	—	6	2	no	—
152	C₅×C₄⋊C₄	—	6	4	no	—
153	C₅×C₄⋊C₄	D₁₂	1	2	yes	—
154	C₅×C₂²⋊C₄	—	6	4	no	—
155	C₅×C₂²⋊C₄	D₁₂	1	2	yes	—
156	C₄²×C₅	—	6	4	no	—
157	C₄²×C₅	C₂²×D₃	1	2	yes	—
158	C₂×#135	—	3	1	no	—
159	#520	—	3	2	no	—
160	#442	—	3	2	no	—
161	#441	—	3	2	no	—
162	C₄×SD₁₆	—	3	4	no	—
163	C₂×#106	—	3	1	no	—
164	#417	—	3	2	no	—
165	#405	C₅×D₃	1	1	yes	characteristic, complemented
166	C₂²×C₃×C₅	—	2	2	no	—
167	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
168	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₅×D₃	—	2	4	no	—
170	C₂×C₅×D₃	—	4	2	no	—
171	C₂×C₅×D₃	—	4	2	no	—
172	C₃×C₄×C₅	—	2	4	no	—
173	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
174	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
175	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
176	C₅×Dic₃	—	2	4	no	—
177	C₅×Dic₃	—	4	4	no	—
178	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
179	C₂×#67	—	2	2	no	—
180	C₂²×Dic₃	—	2	2	no	—
181	#235	—	2	4	no	—
182	#235	C₂×C₄×C₅	1	8	yes	complemented
183	C₂×D₁₂	C₂³×C₅	1	2	yes	—
184	C₂×C₄×D₃	—	2	2	no	—
185	C₂×C₄×D₃	—	2	4	no	—
186	C₂×Dic₆	C₂³×C₅	1	2	yes	—
187	C₃×M₁₆	—	2	2	no	—
188	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
189	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
190	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
191	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
192	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
193	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
194	C₃×C₄²	C₂³×C₅	1	2	yes	—
195	(C₂×D₃)⋊C₄	—	2	4	no	—
196	C₄⋊Dic₃	—	2	2	no	—
197	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
198	Dic₃⋊C₄	—	2	4	no	—
199	C₄×Dic₃	—	2	4	no	—
200	Dic₁₂	C₂×C₄×C₅	1	4	yes	complemented
201	D₂₄	C₂×C₄×C₅	1	4	yes	complemented
202	#204	C₂×C₄×C₅	1	8	yes	complemented
203	C₂³×C₅	—	6	2	no	—
204	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
205	C₅×Q₈	—	3	4	no	—
206	C₅×Q₈	—	6	2	no	—
207	C₅×D₄	—	3	4	no	—
208	C₅×D₄	—	6	8	no	—
209	C₅×D₄	—	6	2	no	—
210	C₂×C₄×C₅	—	6	2	no	—
211	C₂×C₄×C₅	—	6	8	no	—
212	C₂×C₄×C₅	—	6	4	no	—
213	C₂×C₄×C₅	—	24	4	no	—
214	C₂×C₄×C₅	—	24	2	no	—
215	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
216	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
217	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
218	C₂×C₄×C₅	#235	1	2	yes	—
219	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
220	C₅×C₈	—	2	2	no	—
221	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
222	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
223	C₂×#41	—	3	2	no	—
224	#135	—	3	8	no	—
225	C₂×Q₁₆	—	3	1	no	—
226	C₂×SD₁₆	—	3	2	no	—
227	C₂×D₈	—	3	1	no	—
228	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
229	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
230	C₄×Q₈	—	3	4	no	—
231	C₄×D₄	—	3	4	no	—
232	C₄×D₄	—	6	4	no	—
233	#117	—	6	2	no	—
234	#117	C₂×C₅×D₃	1	1	yes	characteristic
235	C₂×C₄⋊C₄	—	3	2	no	—
236	C₂×C₄⋊C₄	—	6	2	no	—
237	#106	—	3	2	no	—
238	#106	—	3	2	no	—
239	#103	—	3	4	no	—
240	#102	—	3	4	no	—
241	#97	C₂×C₅×D₃	1	2	yes	—
242	C₄×C₈	C₂×C₅×D₃	1	2	yes	—
243	C₂×C₃×C₅	—	2	2	no	—
244	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
245	C₂×C₃×C₅	#577	1	2	yes	—
246	C₅×D₃	—	4	4	no	—
247	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
248	C₂²×D₃	—	2	2	no	—
249	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
250	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
251	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
252	C₂×C₃×C₄	C₅×#41	1	2	yes	—
253	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
254	#67	—	2	8	no	—
255	C₂×Dic₃	—	2	2	no	—
256	C₂×Dic₃	—	2	4	no	—
257	C₂×Dic₃	—	8	2	no	—
258	D₁₂	—	2	2	no	—
259	D₁₂	C₂²×C₄×C₅	1	4	yes	—
260	C₄×D₃	—	2	8	no	—
261	C₄×D₃	—	8	4	no	—
262	Dic₆	—	2	2	no	—
263	Dic₆	C₂²×C₄×C₅	1	4	yes	—
264	C₃×C₈	—	2	2	no	—
265	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
266	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
267	C₂²×C₅	—	2	2	no	—
268	C₂²×C₅	—	6	4	no	—
269	C₂²×C₅	—	12	2	no	—
270	C₂²×C₅	—	12	2	no	—
271	C₂²×C₅	C₄×D₁₂	1	2	yes	—
272	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
273	C₄×C₅	—	2	4	no	—
274	C₄×C₅	—	6	4	no	—
275	C₄×C₅	—	12	4	no	—
276	C₄×C₅	C₄×D₁₂	1	2	yes	—
277	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
278	C₄×C₅	C₂×#235	1	1	yes	characteristic
279	#41	—	3	8	no	—
280	#41	—	6	4	no	—
281	C₂×Q₈	—	3	2	no	—
282	C₂×D₄	—	3	2	no	—
283	C₂×D₄	—	6	2	no	—
284	C₂²×C₄	—	6	2	no	—
285	C₂²×C₄	—	6	2	no	—
286	C₂²×C₄	—	6	4	no	—
287	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
288	Q₁₆	—	3	4	no	—
289	SD₁₆	—	3	8	no	—
290	D₈	—	3	4	no	—
291	M₁₆	—	2	2	no	—
292	C₂×C₈	C₄×C₅×D₃	1	4	yes	complemented
293	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
294	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
295	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
296	C₄⋊C₄	—	3	4	no	—
297	C₄⋊C₄	—	6	2	no	—
298	C₄⋊C₄	—	6	4	no	—
299	C₄⋊C₄	C₅×D₁₂	1	2	yes	—
300	C₂²⋊C₄	—	6	4	no	—
301	C₂²⋊C₄	C₅×D₁₂	1	2	yes	—
302	C₄²	—	6	4	no	—
303	C₄²	C₂²×C₅×D₃	1	2	yes	—
304	C₃×C₅	#2952	1	1	yes	characteristic, complemented, Hall
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
307	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
308	C₂×D₃	—	2	4	no	—
309	C₂×D₃	—	4	2	no	—
310	C₂×D₃	—	4	2	no	—
311	C₃×C₄	—	2	4	no	—
312	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
313	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
314	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
315	Dic₃	—	2	4	no	—
316	Dic₃	—	4	4	no	—
317	C₂×C₅	—	2	2	no	—
318	C₂×C₅	—	12	4	no	—
319	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
320	C₂×C₅	#5751	1	2	yes	—
321	C₂³	—	6	2	no	—
322	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
323	Q₈	—	3	4	no	—
324	Q₈	—	6	2	no	—
325	D₄	—	3	4	no	—
326	D₄	—	6	8	no	—
327	D₄	—	6	2	no	—
328	C₂×C₄	—	6	2	no	—
329	C₂×C₄	—	6	8	no	—
330	C₂×C₄	—	6	4	no	—
331	C₂×C₄	—	24	4	no	—
332	C₂×C₄	—	24	2	no	—
333	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
334	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
335	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
336	C₂×C₄	C₅×#235	1	2	yes	—
337	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
338	C₈	—	2	2	no	—
339	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
340	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
341	C₂×C₃	—	2	2	no	—
342	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
343	C₂×C₃	C₅×#577	1	2	yes	—
344	D₃	—	4	4	no	—
345	C₅	#78574	1	1	yes	characteristic, direct product factor, Sylow
346	C₂²	—	2	2	no	—
347	C₂²	—	6	4	no	—
348	C₂²	—	12	2	no	—
349	C₂²	—	12	2	no	—
350	C₂²	C₄×C₅×D₁₂	1	2	yes	—
351	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
352	C₄	—	2	4	no	—
353	C₄	—	6	4	no	—
354	C₄	—	12	4	no	—
355	C₄	C₄×C₅×D₁₂	1	2	yes	—
356	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
357	C₄	C₂×C₅×#235	1	1	yes	characteristic
358	C₃	C₅×#2952	1	1	yes	characteristic, complemented, Sylow
359	C₂	—	2	2	no	—
360	C₂	—	12	4	no	—
361	C₂	C₂×C₄×C₅×D₁₂	1	1	yes	characteristic
362	C₂	C₅×#5751	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂²×D₁₂
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#405	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#904	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#405	D₃
hypocenter	C₃	C₅×#2952
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#117 ◁ C₅×#405

Complements

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

N	H ≅ G/N	type
2. C₅×#5523	C₂	semidirect
3. C₃×C₅×#405	C₂	semidirect
4. C₅×#5133	C₂	semidirect
5. C₂×C₅×#817	C₂	semidirect
6. C₅×#4716	C₂	semidirect
7. C₅×#4711	C₂	semidirect
8. C₄×C₅×#204	C₂	semidirect
16. C₅×#904	C₄	semidirect
30. #78574	C₅	direct (N × H)
38. C₅×#405	D₃	semidirect
43. C₅×#235	C₂×C₄	semidirect
49. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
61. C₅×Dic₁₂	C₂×C₄	semidirect
62. C₅×D₂₄	C₂×C₄	semidirect
63. C₅×#204	C₂×C₄	semidirect
65. #5523	C₂×C₅	semidirect
66. C₃×#405	C₂×C₅	semidirect
67. #5133	C₂×C₅	semidirect
68. C₂×#817	C₂×C₅	semidirect
69. #4716	C₂×C₅	semidirect
70. #4711	C₂×C₅	semidirect
71. C₄×#204	C₂×C₅	semidirect
119. #904	C₄×C₅	semidirect
146. C₂×C₅×C₈	C₄×D₃	semidirect
165. #405	C₅×D₃	semidirect
182. #235	C₂×C₄×C₅	semidirect
188. C₂×C₃×C₈	C₂×C₄×C₅	semidirect
200. Dic₁₂	C₂×C₄×C₅	semidirect
201. D₂₄	C₂×C₄×C₅	semidirect
202. #204	C₂×C₄×C₅	semidirect
292. C₂×C₈	C₄×C₅×D₃	semidirect
304. C₃×C₅	#2952	semidirect
345. C₅	#78574	direct (N × H)
358. C₃	C₅×#2952	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#904	2
C₅×#5523	2
C₃×C₅×#405	2
C₅×#5133	2
C₂×C₅×#817	2
C₅×#4716	2
C₅×#4711	2
C₄×C₅×#204	2
C₅×#2952	3
#78574	5

Subgroups — C5×#78574 #14417740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78574 #14417740