Subgroups — C₅×#79116 #14413439

Order 1920.

952 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×#901	C₂	1	1	yes	maximal, characteristic
2	C₅×#5504	C₂	1	2	yes	maximal
3	C₂×C₃×C₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4964	C₂	1	2	yes	maximal, complemented
6	C₅×#4861	C₂	1	4	yes	maximal, complemented
7	C₅×#4860	C₂	1	2	yes	maximal, complemented
8	C₅×D₃×#106	C₂	1	2	yes	maximal, complemented
9	C₅×#2912	—	3	1	no	maximal, Hall
10	C₂×C₅×#235	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₄×C₅×#67	—	2	4	no	—
14	C₅×#926	C₂²	1	2	yes	—
15	C₂×C₅×#208	C₂²	1	1	yes	characteristic
16	C₅×#901	C₄	1	8	yes	complemented
17	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
18	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
19	C₅×#893	—	2	2	no	—
20	C₅×#892	C₂²	1	4	yes	—
21	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
22	C₅×#887	—	2	2	no	—
23	C₃×C₅×#106	C₂²	1	2	yes	—
24	C₃×C₅×#106	C₂²	1	2	yes	—
25	C₅×#818	C₂²	1	2	yes	—
26	C₅×#817	C₂²	1	1	yes	characteristic
27	C₅×#817	C₂²	1	1	yes	characteristic
28	C₅×#808	C₂²	1	4	yes	—
29	C₅×#807	C₂²	1	4	yes	—
30	#79116	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#131	—	3	1	no	—
32	C₅×#520	—	3	2	no	—
33	C₅×#428	—	3	4	no	—
34	C₅×#428	—	3	2	no	—
35	C₅×#427	—	3	2	no	—
36	C₅×#427	—	3	1	no	—
37	C₂×C₅×#106	—	3	2	no	—
38	C₂×C₅×#106	D₃	1	1	yes	characteristic, complemented
39	C₂²×C₃×C₄×C₅	—	2	2	no	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂×C₅×#67	D₄	1	2	yes	—
42	C₅×#235	C₂×C₄	1	4	yes	—
43	C₅×#235	Q₈	1	4	yes	—
44	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
45	C₂×C₄×C₅×D₃	—	2	4	no	—
46	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
47	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
48	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
49	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₃×C₅×C₄⋊C₄	—	2	2	no	—
52	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
53	C₅×#217	—	2	2	no	—
54	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
55	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
56	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
57	C₅×Dic₃⋊C₄	—	2	4	no	—
58	C₄×C₅×Dic₃	—	2	2	no	—
59	C₄×C₅×Dic₃	—	2	4	no	—
60	C₅×#208	C₂×C₄	1	4	yes	complemented
61	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
62	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	8	yes	complemented
63	C₅×D₃×C₈	C₂×C₄	1	8	yes	complemented
64	C₂×#901	C₂×C₅	1	1	yes	characteristic
65	#5504	C₂×C₅	1	2	yes	—
66	C₂×C₃×#106	C₂×C₅	1	1	yes	characteristic, complemented
67	#5106	C₂×C₅	1	1	yes	characteristic, complemented
68	#4964	C₂×C₅	1	2	yes	complemented
69	#4861	C₂×C₅	1	4	yes	complemented
70	#4860	C₂×C₅	1	2	yes	complemented
71	D₃×#106	C₂×C₅	1	2	yes	complemented
72	C₂×C₅×#41	—	3	1	no	—
73	C₅×#131	—	3	8	no	—
74	C₂×C₅×M₁₆	—	3	1	no	—
75	C₂×C₅×M₁₆	—	3	2	no	—
76	C₂²×C₅×C₈	—	3	2	no	—
77	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
78	C₄×C₅×Q₈	—	6	2	no	—
79	C₄×C₅×D₄	—	6	2	no	—
80	C₄×C₅×D₄	—	6	4	no	—
81	C₅×#117	—	3	2	no	—
82	C₅×#117	—	3	4	no	—
83	C₂×C₅×C₄⋊C₄	—	3	4	no	—
84	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
85	C₅×#107	—	3	2	no	—
86	C₅×#107	—	3	4	no	—
87	C₅×#106	—	3	1	no	—
88	C₅×#106	—	3	1	no	—
89	C₅×#106	—	3	4	no	—
90	C₅×#106	C₂×D₃	1	2	yes	—
91	C₅×#106	C₂×D₃	1	2	yes	—
92	#2912	—	3	1	no	Sylow
93	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	—	2	4	no	—
96	C₂×C₃×C₄×C₅	—	8	2	no	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
101	C₅×#67	C₄⋊C₄	1	8	yes	—
102	C₂×C₅×Dic₃	—	2	2	no	—
103	C₂×C₅×Dic₃	—	2	2	no	—
104	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
105	C₅×D₁₂	C₄⋊C₄	1	4	yes	—
106	C₄×C₅×D₃	—	8	4	no	—
107	C₄×C₅×D₃	C₂²×C₄	1	4	yes	—
108	C₄×C₅×D₃	C₂×Q₈	1	4	yes	—
109	C₅×Dic₆	C₄⋊C₄	1	4	yes	—
110	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
111	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
112	C₅×C₃⋊C₈	C₂²×C₄	1	4	yes	—
113	C₂×#235	C₂²×C₅	1	1	yes	characteristic
114	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
115	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
116	C₄×#67	—	2	4	no	—
117	#926	C₂²×C₅	1	2	yes	—
118	C₂×#208	C₂²×C₅	1	1	yes	characteristic
119	#901	C₄×C₅	1	8	yes	complemented
120	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
121	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
122	#893	—	2	2	no	—
123	#892	C₂²×C₅	1	4	yes	—
124	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
125	#887	—	2	2	no	—
126	C₃×#106	C₂²×C₅	1	2	yes	—
127	C₃×#106	C₂²×C₅	1	2	yes	—
128	#818	C₂²×C₅	1	2	yes	—
129	#817	C₂²×C₅	1	1	yes	characteristic
130	#817	C₂²×C₅	1	1	yes	characteristic
131	#808	C₂²×C₅	1	4	yes	—
132	#807	C₂²×C₅	1	4	yes	—
133	C₅×#41	—	3	4	no	—
134	C₅×#41	—	3	4	no	—
135	C₂×C₅×Q₈	—	3	1	no	—
136	C₂×C₅×D₄	—	3	2	no	—
137	C₂×C₅×D₄	—	3	1	no	—
138	C₂²×C₄×C₅	—	2	2	no	—
139	C₂²×C₄×C₅	—	3	2	no	—
140	C₂²×C₄×C₅	—	6	4	no	—
141	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
142	C₅×M₁₆	—	3	4	no	—
143	C₅×M₁₆	—	3	8	no	—
144	C₂×C₅×C₈	—	3	2	no	—
145	C₂×C₅×C₈	—	3	8	no	—
146	C₂×C₅×C₈	C₄×D₃	1	4	yes	complemented
147	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
148	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
149	C₅×C₄⋊C₄	—	2	2	no	—
150	C₅×C₄⋊C₄	—	3	2	no	—
151	C₅×C₄⋊C₄	—	3	2	no	—
152	C₅×C₄⋊C₄	—	6	4	no	—
153	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
154	C₅×C₂²⋊C₄	—	6	4	no	—
155	C₅×C₂²⋊C₄	—	6	2	no	—
156	C₄²×C₅	—	6	4	no	—
157	C₄²×C₅	—	6	2	no	—
158	C₂×#131	—	3	1	no	—
159	#520	—	3	2	no	—
160	#428	—	3	2	no	—
161	#428	—	3	4	no	—
162	#427	—	3	1	no	—
163	#427	—	3	2	no	—
164	C₂×#106	—	3	2	no	—
165	C₂×#106	C₅×D₃	1	1	yes	characteristic, complemented
166	C₂²×C₃×C₅	—	2	2	no	—
167	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
168	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₅×D₃	—	2	4	no	—
170	C₂×C₅×D₃	C₂×C₄⋊C₄	1	4	yes	—
171	C₃×C₄×C₅	—	4	4	no	—
172	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
173	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
174	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
175	C₅×Dic₃	—	4	2	no	—
176	C₅×Dic₃	—	4	2	no	—
177	C₅×Dic₃	C₂×C₄⋊C₄	1	4	yes	—
178	C₂²×C₃×C₄	—	2	2	no	—
179	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
180	C₂×#67	C₅×D₄	1	2	yes	—
181	#235	C₂×C₄×C₅	1	4	yes	—
182	#235	C₅×Q₈	1	4	yes	—
183	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
184	C₂×C₄×D₃	—	2	4	no	—
185	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
186	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
187	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
188	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
189	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
190	C₃×C₄⋊C₄	—	2	2	no	—
191	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
192	#217	—	2	2	no	—
193	(C₂×D₃)⋊C₄	—	2	4	no	—
194	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
195	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
196	Dic₃⋊C₄	—	2	4	no	—
197	C₄×Dic₃	—	2	2	no	—
198	C₄×Dic₃	—	2	4	no	—
199	#208	C₂×C₄×C₅	1	4	yes	complemented
200	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
201	ΓL(1,𝔽₂₅)	C₂×C₄×C₅	1	8	yes	complemented
202	D₃×C₈	C₂×C₄×C₅	1	8	yes	complemented
203	C₂³×C₅	—	3	2	no	—
204	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
205	C₅×Q₈	—	3	4	no	—
206	C₅×D₄	—	3	8	no	—
207	C₅×D₄	—	3	4	no	—
208	C₂×C₄×C₅	—	2	4	no	—
209	C₂×C₄×C₅	—	3	2	no	—
210	C₂×C₄×C₅	—	3	4	no	—
211	C₂×C₄×C₅	—	3	4	no	—
212	C₂×C₄×C₅	—	6	2	no	—
213	C₂×C₄×C₅	—	6	2	no	—
214	C₂×C₄×C₅	—	8	2	no	—
215	C₂×C₄×C₅	—	24	4	no	—
216	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
217	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
218	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
219	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
220	C₅×C₈	—	3	4	no	—
221	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
222	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
223	C₂×#41	—	3	1	no	—
224	#131	—	3	8	no	—
225	C₂×M₁₆	—	3	1	no	—
226	C₂×M₁₆	—	3	2	no	—
227	C₂²×C₈	—	3	2	no	—
228	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
229	C₄×Q₈	—	6	2	no	—
230	C₄×D₄	—	6	2	no	—
231	C₄×D₄	—	6	4	no	—
232	#117	—	3	2	no	—
233	#117	—	3	4	no	—
234	C₂×C₄⋊C₄	—	3	4	no	—
235	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
236	#107	—	3	2	no	—
237	#107	—	3	4	no	—
238	#106	—	3	1	no	—
239	#106	—	3	1	no	—
240	#106	—	3	4	no	—
241	#106	C₂×C₅×D₃	1	2	yes	—
242	#106	C₂×C₅×D₃	1	2	yes	—
243	C₂×C₃×C₅	—	2	2	no	—
244	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
245	C₂×C₃×C₅	#577	1	2	yes	—
246	C₅×D₃	—	2	4	no	—
247	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
248	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	—	8	2	no	—
251	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
252	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
254	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
255	#67	C₅×C₄⋊C₄	1	8	yes	—
256	C₂×Dic₃	—	2	2	no	—
257	C₂×Dic₃	—	2	2	no	—
258	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
259	D₁₂	C₅×C₄⋊C₄	1	4	yes	—
260	C₄×D₃	—	8	4	no	—
261	C₄×D₃	C₂²×C₄×C₅	1	4	yes	—
262	C₄×D₃	C₂×C₅×Q₈	1	4	yes	—
263	Dic₆	C₅×C₄⋊C₄	1	4	yes	—
264	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
265	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
266	C₃⋊C₈	C₂²×C₄×C₅	1	4	yes	—
267	C₂²×C₅	—	2	2	no	—
268	C₂²×C₅	—	3	4	no	—
269	C₂²×C₅	—	6	4	no	—
270	C₂²×C₅	D₃×C₄⋊C₄	1	2	yes	—
271	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
272	C₄×C₅	—	3	4	no	—
273	C₄×C₅	—	4	4	no	—
274	C₄×C₅	—	12	2	no	—
275	C₄×C₅	—	12	2	no	—
276	C₄×C₅	D₃×C₄⋊C₄	1	2	yes	—
277	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
278	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
279	#41	—	3	4	no	—
280	#41	—	3	4	no	—
281	C₂×Q₈	—	3	1	no	—
282	C₂×D₄	—	3	2	no	—
283	C₂×D₄	—	3	1	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	3	2	no	—
286	C₂²×C₄	—	6	4	no	—
287	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
288	M₁₆	—	3	4	no	—
289	M₁₆	—	3	8	no	—
290	C₂×C₈	—	3	2	no	—
291	C₂×C₈	—	3	8	no	—
292	C₂×C₈	C₄×C₅×D₃	1	4	yes	complemented
293	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
294	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	3	2	no	—
297	C₄⋊C₄	—	3	2	no	—
298	C₄⋊C₄	—	6	4	no	—
299	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
300	C₂²⋊C₄	—	6	4	no	—
301	C₂²⋊C₄	—	6	2	no	—
302	C₄²	—	6	4	no	—
303	C₄²	—	6	2	no	—
304	C₃×C₅	#2912	1	1	yes	characteristic, complemented, Hall
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	2	yes	—
307	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
308	C₂×D₃	—	2	4	no	—
309	C₂×D₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
310	C₃×C₄	—	4	4	no	—
311	C₃×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
312	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
313	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
314	Dic₃	—	4	2	no	—
315	Dic₃	—	4	2	no	—
316	Dic₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
317	C₂×C₅	—	2	2	no	—
318	C₂×C₅	—	6	4	no	—
319	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
320	C₂×C₅	#5762	1	2	yes	—
321	C₂³	—	3	2	no	—
322	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
323	Q₈	—	3	4	no	—
324	D₄	—	3	8	no	—
325	D₄	—	3	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	3	2	no	—
328	C₂×C₄	—	3	4	no	—
329	C₂×C₄	—	3	4	no	—
330	C₂×C₄	—	6	2	no	—
331	C₂×C₄	—	6	2	no	—
332	C₂×C₄	—	8	2	no	—
333	C₂×C₄	—	24	4	no	—
334	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
335	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
336	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
337	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
338	C₈	—	3	4	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	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
343	C₂×C₃	C₅×#577	1	2	yes	—
344	D₃	—	2	4	no	—
345	C₅	#79116	1	1	yes	characteristic, direct product factor, Sylow
346	C₂²	—	2	2	no	—
347	C₂²	—	3	4	no	—
348	C₂²	—	6	4	no	—
349	C₂²	C₅×D₃×C₄⋊C₄	1	2	yes	—
350	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
351	C₄	—	3	4	no	—
352	C₄	—	4	4	no	—
353	C₄	—	12	2	no	—
354	C₄	—	12	2	no	—
355	C₄	C₅×D₃×C₄⋊C₄	1	2	yes	—
356	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
357	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
358	C₃	C₅×#2912	1	1	yes	characteristic, complemented, Sylow
359	C₂	—	2	2	no	—
360	C₂	—	6	4	no	—
361	C₂	C₂×C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
362	C₂	C₅×#5762	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#106	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#235	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×#106	D₃
hypocenter	C₃	C₅×#2912
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#106

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×C₅×#106	C₂	semidirect
4. C₅×#5106	C₂	semidirect
5. C₅×#4964	C₂	semidirect
6. C₅×#4861	C₂	semidirect
7. C₅×#4860	C₂	semidirect
8. C₅×D₃×#106	C₂	semidirect
16. C₅×#901	C₄	semidirect
30. #79116	C₅	direct (N × H)
38. C₂×C₅×#106	D₃	semidirect
48. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
60. C₅×#208	C₂×C₄	semidirect
62. C₅×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
63. C₅×D₃×C₈	C₂×C₄	semidirect
66. C₂×C₃×#106	C₂×C₅	semidirect
67. #5106	C₂×C₅	semidirect
68. #4964	C₂×C₅	semidirect
69. #4861	C₂×C₅	semidirect
70. #4860	C₂×C₅	semidirect
71. D₃×#106	C₂×C₅	semidirect
119. #901	C₄×C₅	semidirect
146. C₂×C₅×C₈	C₄×D₃	semidirect
165. C₂×#106	C₅×D₃	semidirect
187. C₂×C₃×C₈	C₂×C₄×C₅	semidirect
199. #208	C₂×C₄×C₅	semidirect
201. ΓL(1,𝔽₂₅)	C₂×C₄×C₅	semidirect
202. D₃×C₈	C₂×C₄×C₅	semidirect
292. C₂×C₈	C₄×C₅×D₃	semidirect
304. C₃×C₅	#2912	semidirect
345. C₅	#79116	direct (N × H)
358. C₃	C₅×#2912	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#901	2
C₅×#5504	2
C₂×C₃×C₅×#106	2
C₅×#5106	2
C₅×#4964	2
C₅×#4861	2
C₅×#4860	2
C₅×D₃×#106	2
C₅×#2912	3
#79116	5

Subgroups — C5×#79116 #14413439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79116 #14413439