Subgroups — C₅×#78516 #14411528

Order 1920.

1112 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#907	C₂	1	2	yes	maximal
2	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5122	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#803	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4707	C₂	1	2	yes	maximal, complemented
7	C₅×D₃×#97	C₂	1	2	yes	maximal, complemented
8	C₅×#4689	C₂	1	4	yes	maximal, complemented
9	C₅×#2875	—	3	1	no	maximal, Hall
10	C₂×C₅×#235	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₄×C₅×#67	C₄	1	4	yes	—
14	C₅×#926	C₂²	1	1	yes	characteristic
15	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
16	C₅×#907	C₄	1	16	yes	complemented
17	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
18	C₂×C₅×D₃×C₈	C₂²	1	4	yes	—
19	C₄×C₅×D₁₂	C₄	1	2	yes	—
20	C₅×#872	C₂²	1	2	yes	—
21	C₄²×C₅×D₃	C₂²	1	2	yes	—
22	C₄×C₅×Dic₆	C₄	1	2	yes	—
23	C₃×C₅×#97	C₂²	1	2	yes	—
24	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
25	C₅×#815	C₂²	1	4	yes	—
26	C₅×C₈×Dic₃	C₂²	1	4	yes	—
27	C₅×#803	C₂²	1	2	yes	—
28	C₅×#803	C₂²	1	1	yes	characteristic
29	C₅×#803	C₂²	1	1	yes	characteristic
30	#78516	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#131	—	3	2	no	—
32	C₄×C₅×#41	—	3	1	no	—
33	C₅×#405	—	3	4	no	—
34	C₅×#405	—	3	2	no	—
35	C₄×C₅×M₁₆	—	3	2	no	—
36	C₄×C₅×M₁₆	D₃	1	1	yes	characteristic, complemented
37	C₂×C₅×#97	—	3	2	no	—
38	C₂×C₅×#97	—	3	1	no	—
39	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂×C₅×#67	C₂×C₄	1	2	yes	—
42	C₅×#235	C₂×C₄	1	8	yes	—
43	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
45	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
46	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
47	C₃×C₅×M₁₆	C₂×C₄	1	8	yes	complemented
48	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
49	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
50	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
51	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
52	C₅×#217	C₂×C₄	1	2	yes	—
53	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
54	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
55	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
56	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
57	C₄×C₅×Dic₃	C₂³	1	2	yes	—
58	C₂×C₅×C₃⋊C₈	C₂×C₄	1	8	yes	complemented
59	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
60	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
61	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	16	yes	complemented
62	C₅×D₃×C₈	C₂×C₄	1	16	yes	complemented
63	C₂×#907	C₂×C₅	1	2	yes	—
64	C₄×#235	C₂×C₅	1	1	yes	characteristic
65	C₃×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
66	#5122	C₂×C₅	1	2	yes	complemented
67	C₂×#803	C₂×C₅	1	1	yes	characteristic, complemented
68	#4707	C₂×C₅	1	2	yes	complemented
69	D₃×#97	C₂×C₅	1	2	yes	complemented
70	#4689	C₂×C₅	1	4	yes	complemented
71	C₂×C₅×#41	—	3	1	no	—
72	C₅×#131	—	3	16	no	—
73	C₂×C₅×M₁₆	—	3	4	no	—
74	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	—
75	C₂²×C₅×C₈	—	3	2	no	—
76	C₂²×C₅×C₈	—	3	4	no	—
77	C₄×C₅×Q₈	—	3	2	no	—
78	C₄×C₅×D₄	—	3	4	no	—
79	C₄×C₅×D₄	—	3	2	no	—
80	C₅×#117	—	3	1	no	—
81	C₅×#117	—	3	2	no	—
82	C₂×C₄²×C₅	—	3	2	no	—
83	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
84	C₅×#97	—	3	4	no	—
85	C₅×#97	—	3	1	no	—
86	C₅×#97	—	3	1	no	—
87	C₅×#97	—	3	2	no	—
88	C₅×#97	C₂×D₃	1	2	yes	—
89	C₄×C₅×C₈	—	3	4	no	—
90	C₄×C₅×C₈	C₂×D₃	1	2	yes	—
91	#2875	—	3	1	no	Sylow
92	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	—	4	2	no	—
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
99	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
100	C₅×#67	C₄²	1	8	yes	—
101	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
102	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
103	C₅×D₁₂	C₄²	1	4	yes	—
104	C₄×C₅×D₃	—	4	4	no	—
105	C₄×C₅×D₃	C₂²×C₄	1	8	yes	—
106	C₅×Dic₆	C₄²	1	4	yes	—
107	C₃×C₅×C₈	C₂²×C₄	1	8	yes	—
108	C₅×C₃⋊C₈	C₂²×C₄	1	4	yes	—
109	C₅×C₃⋊C₈	C₂²×C₄	1	4	yes	—
110	C₂×#235	C₂²×C₅	1	1	yes	characteristic
111	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
112	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
113	C₄×#67	C₄×C₅	1	4	yes	—
114	#926	C₂²×C₅	1	1	yes	characteristic
115	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
116	#907	C₄×C₅	1	16	yes	complemented
117	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	4	yes	—
118	C₂×D₃×C₈	C₂²×C₅	1	4	yes	—
119	C₄×D₁₂	C₄×C₅	1	2	yes	—
120	#872	C₂²×C₅	1	2	yes	—
121	C₄²×D₃	C₂²×C₅	1	2	yes	—
122	C₄×Dic₆	C₄×C₅	1	2	yes	—
123	C₃×#97	C₂²×C₅	1	2	yes	—
124	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
125	#815	C₂²×C₅	1	4	yes	—
126	C₈×Dic₃	C₂²×C₅	1	4	yes	—
127	#803	C₂²×C₅	1	2	yes	—
128	#803	C₂²×C₅	1	1	yes	characteristic
129	#803	C₂²×C₅	1	1	yes	characteristic
130	C₅×#41	—	3	8	no	—
131	C₂×C₅×Q₈	—	3	1	no	—
132	C₂×C₅×D₄	—	3	2	no	—
133	C₂×C₅×D₄	—	3	1	no	—
134	C₂²×C₄×C₅	—	3	2	no	—
135	C₂²×C₄×C₅	—	3	4	no	—
136	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
137	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
138	C₅×M₁₆	—	3	16	no	—
139	C₅×M₁₆	C₄×D₃	1	8	yes	complemented
140	C₂×C₅×C₈	—	3	8	no	—
141	C₂×C₅×C₈	—	3	2	no	—
142	C₂×C₅×C₈	—	3	2	no	—
143	C₂×C₅×C₈	—	3	16	no	—
144	C₂×C₅×C₈	C₂²×D₃	1	4	yes	—
145	C₅×C₄⋊C₄	—	3	4	no	—
146	C₅×C₄⋊C₄	—	3	2	no	—
147	C₅×C₂²⋊C₄	—	3	2	no	—
148	C₅×C₂²⋊C₄	—	3	4	no	—
149	C₄²×C₅	—	3	4	no	—
150	C₄²×C₅	—	3	2	no	—
151	C₄²×C₅	C₄×D₃	1	2	yes	—
152	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
153	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
154	C₂×#131	—	3	2	no	—
155	C₄×#41	—	3	1	no	—
156	#405	—	3	2	no	—
157	#405	—	3	4	no	—
158	C₄×M₁₆	—	3	2	no	—
159	C₄×M₁₆	C₅×D₃	1	1	yes	characteristic, complemented
160	C₂×#97	—	3	1	no	—
161	C₂×#97	—	3	2	no	—
162	C₂²×C₃×C₅	—	2	2	no	—
163	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
164	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₅×D₃	—	2	4	no	—
166	C₂×C₅×D₃	C₂×C₄²	1	4	yes	—
167	C₃×C₄×C₅	—	2	2	no	—
168	C₃×C₄×C₅	—	2	2	no	—
169	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
170	C₃×C₄×C₅	C₂³×C₄	1	2	yes	—
171	C₅×Dic₃	—	2	4	no	—
172	C₅×Dic₃	C₂×C₄²	1	4	yes	—
173	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
174	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
175	C₂×#67	C₂×C₄×C₅	1	2	yes	—
176	#235	C₂×C₄×C₅	1	8	yes	—
177	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
178	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
179	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
180	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
181	C₃×M₁₆	C₂×C₄×C₅	1	8	yes	complemented
182	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
183	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
184	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
185	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
186	#217	C₂×C₄×C₅	1	2	yes	—
187	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
188	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
189	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	—
190	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
191	C₄×Dic₃	C₂³×C₅	1	2	yes	—
192	C₂×C₃⋊C₈	C₂×C₄×C₅	1	8	yes	complemented
193	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
194	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
195	ΓL(1,𝔽₂₅)	C₂×C₄×C₅	1	16	yes	complemented
196	D₃×C₈	C₂×C₄×C₅	1	16	yes	complemented
197	C₂³×C₅	—	3	2	no	—
198	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
199	C₅×Q₈	—	3	4	no	—
200	C₅×D₄	—	3	8	no	—
201	C₅×D₄	—	3	4	no	—
202	C₂×C₄×C₅	—	3	2	no	—
203	C₂×C₄×C₅	—	3	8	no	—
204	C₂×C₄×C₅	—	3	4	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	12	4	no	—
207	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
208	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
209	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
211	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
212	C₅×C₈	—	3	4	no	—
213	C₅×C₈	—	3	4	no	—
214	C₅×C₈	C₂×C₄×D₃	1	8	yes	—
215	C₂×#41	—	3	1	no	—
216	#131	—	3	16	no	—
217	C₂×M₁₆	—	3	4	no	—
218	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	—
219	C₂²×C₈	—	3	2	no	—
220	C₂²×C₈	—	3	4	no	—
221	C₄×Q₈	—	3	2	no	—
222	C₄×D₄	—	3	4	no	—
223	C₄×D₄	—	3	2	no	—
224	#117	—	3	1	no	—
225	#117	—	3	2	no	—
226	C₂×C₄²	—	3	2	no	—
227	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
228	#97	—	3	4	no	—
229	#97	—	3	1	no	—
230	#97	—	3	1	no	—
231	#97	—	3	2	no	—
232	#97	C₂×C₅×D₃	1	2	yes	—
233	C₄×C₈	—	3	4	no	—
234	C₄×C₈	C₂×C₅×D₃	1	2	yes	—
235	C₂×C₃×C₅	—	2	2	no	—
236	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
237	C₂×C₃×C₅	#568	1	2	yes	—
238	C₅×D₃	—	2	4	no	—
239	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
240	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
241	C₂×C₃×C₄	—	4	2	no	—
242	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
243	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
244	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
246	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
247	#67	C₄²×C₅	1	8	yes	—
248	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
249	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
250	D₁₂	C₄²×C₅	1	4	yes	—
251	C₄×D₃	—	4	4	no	—
252	C₄×D₃	C₂²×C₄×C₅	1	8	yes	—
253	Dic₆	C₄²×C₅	1	4	yes	—
254	C₃×C₈	C₂²×C₄×C₅	1	8	yes	—
255	C₃⋊C₈	C₂²×C₄×C₅	1	4	yes	—
256	C₃⋊C₈	C₂²×C₄×C₅	1	4	yes	—
257	C₂²×C₅	—	2	2	no	—
258	C₂²×C₅	—	3	4	no	—
259	C₂²×C₅	—	6	4	no	—
260	C₂²×C₅	C₄²×D₃	1	2	yes	—
261	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
262	C₄×C₅	—	2	2	no	—
263	C₄×C₅	—	2	2	no	—
264	C₄×C₅	—	3	4	no	—
265	C₄×C₅	—	6	4	no	—
266	C₄×C₅	C₄²×D₃	1	2	yes	—
267	C₄×C₅	C₂²×C₄×D₃	1	2	yes	—
268	#41	—	3	8	no	—
269	C₂×Q₈	—	3	1	no	—
270	C₂×D₄	—	3	2	no	—
271	C₂×D₄	—	3	1	no	—
272	C₂²×C₄	—	3	2	no	—
273	C₂²×C₄	—	3	4	no	—
274	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
275	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
276	M₁₆	—	3	16	no	—
277	M₁₆	C₄×C₅×D₃	1	8	yes	complemented
278	C₂×C₈	—	3	8	no	—
279	C₂×C₈	—	3	2	no	—
280	C₂×C₈	—	3	2	no	—
281	C₂×C₈	—	3	16	no	—
282	C₂×C₈	C₂²×C₅×D₃	1	4	yes	—
283	C₄⋊C₄	—	3	4	no	—
284	C₄⋊C₄	—	3	2	no	—
285	C₂²⋊C₄	—	3	2	no	—
286	C₂²⋊C₄	—	3	4	no	—
287	C₄²	—	3	4	no	—
288	C₄²	—	3	2	no	—
289	C₄²	C₄×C₅×D₃	1	2	yes	—
290	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
291	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
292	C₃×C₅	#2875	1	1	yes	characteristic, complemented, Hall
293	C₂²×C₃	—	2	2	no	—
294	C₂²×C₃	C₂×C₄²×C₅	1	2	yes	—
295	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
296	C₂×D₃	—	2	4	no	—
297	C₂×D₃	C₂×C₄²×C₅	1	4	yes	—
298	C₃×C₄	—	2	2	no	—
299	C₃×C₄	—	2	2	no	—
300	C₃×C₄	C₂×C₄²×C₅	1	2	yes	—
301	C₃×C₄	C₂³×C₄×C₅	1	2	yes	—
302	Dic₃	—	2	4	no	—
303	Dic₃	C₂×C₄²×C₅	1	4	yes	—
304	C₂×C₅	—	2	2	no	—
305	C₂×C₅	—	6	4	no	—
306	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
307	C₂×C₅	#5745	1	2	yes	—
308	C₂³	—	3	2	no	—
309	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
310	Q₈	—	3	4	no	—
311	D₄	—	3	8	no	—
312	D₄	—	3	4	no	—
313	C₂×C₄	—	3	2	no	—
314	C₂×C₄	—	3	8	no	—
315	C₂×C₄	—	3	4	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	12	4	no	—
318	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
319	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
320	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
321	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
322	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
323	C₈	—	3	4	no	—
324	C₈	—	3	4	no	—
325	C₈	C₂×C₄×C₅×D₃	1	8	yes	—
326	C₂×C₃	—	2	2	no	—
327	C₂×C₃	C₂²×C₄²×C₅	1	1	yes	characteristic
328	C₂×C₃	C₅×#568	1	2	yes	—
329	D₃	—	2	4	no	—
330	C₅	#78516	1	1	yes	characteristic, direct product factor, Sylow
331	C₂²	—	2	2	no	—
332	C₂²	—	3	4	no	—
333	C₂²	—	6	4	no	—
334	C₂²	C₄²×C₅×D₃	1	2	yes	—
335	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
336	C₄	—	2	2	no	—
337	C₄	—	2	2	no	—
338	C₄	—	3	4	no	—
339	C₄	—	6	4	no	—
340	C₄	C₄²×C₅×D₃	1	2	yes	—
341	C₄	C₂²×C₄×C₅×D₃	1	2	yes	—
342	C₃	C₅×#2875	1	1	yes	characteristic, complemented, Sylow
343	C₂	—	2	2	no	—
344	C₂	—	6	4	no	—
345	C₂	C₂×C₄²×C₅×D₃	1	1	yes	characteristic
346	C₂	C₅×#5745	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂×C₃	C₂²×C₄²×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₅×#235	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₄×C₅×M₁₆	D₃
hypocenter	C₃	C₅×#2875
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄×C₅×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₃×C₄×C₅×M₁₆	C₂	semidirect
4. C₅×#5122	C₂	semidirect
5. C₂×C₅×#803	C₂	semidirect
6. C₅×#4707	C₂	semidirect
7. C₅×D₃×#97	C₂	semidirect
8. C₅×#4689	C₂	semidirect
16. C₅×#907	C₄	semidirect
30. #78516	C₅	direct (N × H)
36. C₄×C₅×M₁₆	D₃	semidirect
47. C₃×C₅×M₁₆	C₂×C₄	semidirect
58. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
61. C₅×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
62. C₅×D₃×C₈	C₂×C₄	semidirect
65. C₃×C₄×M₁₆	C₂×C₅	semidirect
66. #5122	C₂×C₅	semidirect
67. C₂×#803	C₂×C₅	semidirect
68. #4707	C₂×C₅	semidirect
69. D₃×#97	C₂×C₅	semidirect
70. #4689	C₂×C₅	semidirect
116. #907	C₄×C₅	semidirect
139. C₅×M₁₆	C₄×D₃	semidirect
159. C₄×M₁₆	C₅×D₃	semidirect
181. C₃×M₁₆	C₂×C₄×C₅	semidirect
192. C₂×C₃⋊C₈	C₂×C₄×C₅	semidirect
195. ΓL(1,𝔽₂₅)	C₂×C₄×C₅	semidirect
196. D₃×C₈	C₂×C₄×C₅	semidirect
277. M₁₆	C₄×C₅×D₃	semidirect
292. C₃×C₅	#2875	semidirect
330. C₅	#78516	direct (N × H)
342. C₃	C₅×#2875	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#907	2
C₄×C₅×#235	2
C₃×C₄×C₅×M₁₆	2
C₅×#5122	2
C₂×C₅×#803	2
C₅×#4707	2
C₅×D₃×#97	2
C₅×#4689	2
C₅×#2875	3
#78516	5

Subgroups — C5×#78516 #14411528

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78516 #14411528