Subgroups — C₅×#79866 #14416994

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#911	C₂	1	1	yes	maximal, characteristic
2	C₅×#5546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5545	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#442	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×Dic₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×C₅×#214	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₅×#213	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4861	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4852	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4785	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×D₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4757	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4710	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4708	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2946	—	3	1	no	maximal, Hall
17	C₂×C₅×#237	C₂²	1	1	yes	characteristic
18	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
20	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
22	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
23	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₅×#214	C₂²	1	1	yes	characteristic
25	C₂×C₅×#213	C₂²	1	1	yes	characteristic
26	C₄×C₅×#67	—	2	1	no	—
27	C₄×C₅×#67	—	2	1	no	—
28	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
29	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
30	C₅×#911	C₄	1	8	yes	complemented
31	C₂×C₅×#204	C₂²	1	1	yes	characteristic
32	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
33	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
34	C₅×#893	C₂²	1	1	yes	characteristic
35	C₅×#892	C₂²	1	1	yes	characteristic
36	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₅×#887	C₂²	1	1	yes	characteristic, complemented
38	C₅×#67⋊C₄	—	2	1	no	—
39	C₅×#67⋊C₄	—	2	1	no	—
40	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
41	C₅×#877	—	2	1	no	—
42	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
43	C₅×#872	C₂²	1	1	yes	characteristic
44	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₅×#102	C₂²	1	1	yes	characteristic
47	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
49	C₅×#832	C₂²	1	1	yes	characteristic
50	C₅×#832	C₂²	1	1	yes	characteristic, complemented
51	C₅×#821	C₂²	1	1	yes	characteristic
52	C₅×#818	C₂²	1	1	yes	characteristic, complemented
53	C₅×#816	C₂²	1	1	yes	characteristic, complemented
54	C₅×#815	C₂²	1	1	yes	characteristic, complemented
55	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
56	C₅×#810	C₂²	1	1	yes	characteristic, complemented
57	C₅×#809	C₂²	1	1	yes	characteristic
58	C₅×#808	C₂²	1	1	yes	characteristic, complemented
59	C₅×#807	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	#79866	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
62	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
63	C₅×#520	—	3	1	no	—
64	C₅×#518	—	3	1	no	—
65	C₅×#442	—	3	1	no	—
66	C₅×#442	D₃	1	1	yes	characteristic, complemented
67	C₅×#440	—	3	1	no	—
68	C₅×#440	—	3	1	no	—
69	C₄×C₅×SD₁₆	—	3	1	no	—
70	C₄×C₅×SD₁₆	—	3	1	no	—
71	C₄×C₅×D₈	—	3	1	no	—
72	C₄×C₅×D₈	—	3	1	no	—
73	C₅×#428	—	3	1	no	—
74	C₅×#416	—	3	1	no	—
75	C₂×C₅×#102	—	3	1	no	—
76	C₅×#405	—	3	1	no	—
77	C₂³×C₅×D₃	—	2	1	no	—
78	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	—	2	1	no	—
81	C₂²×C₃×C₄×C₅	—	2	1	no	—
82	C₂×C₅×#67	—	2	1	no	—
83	C₂×C₅×#67	—	2	1	no	—
84	C₂²×C₅×Dic₃	—	2	1	no	—
85	C₂²×C₅×Dic₃	—	2	1	no	—
86	C₂²×C₅×Dic₃	—	2	1	no	—
87	C₅×#237	—	2	2	no	—
88	C₅×#237	C₂×C₄	1	4	yes	complemented
89	C₅×D₃×D₄	—	2	2	no	—
90	C₅×D₃×D₄	C₂×C₄	1	4	yes	complemented
91	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
92	C₂×C₄×C₅×D₃	—	2	1	no	—
93	C₂×C₄×C₅×D₃	—	2	1	no	—
94	C₂×C₄×C₅×D₃	—	2	1	no	—
95	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
96	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
97	C₃×C₅×D₈	C₂×C₄	1	4	yes	complemented
98	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
99	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
100	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
103	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
104	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
105	C₅×#217	—	2	1	no	—
106	C₅×#217	—	2	1	no	—
107	C₅×#214	C₂×C₄	1	4	yes	complemented
108	C₅×#213	C₂×C₄	1	4	yes	complemented
109	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
110	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
111	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
112	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
113	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
114	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
115	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
116	C₅×Dic₃⋊C₄	—	2	1	no	—
117	C₅×Dic₃⋊C₄	—	2	1	no	—
118	C₅×Dic₃⋊C₄	—	2	1	no	—
119	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
120	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
121	C₄×C₅×Dic₃	—	2	1	no	—
122	C₄×C₅×Dic₃	—	2	1	no	—
123	C₄×C₅×Dic₃	—	2	1	no	—
124	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
125	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
127	C₅×#204	C₂×C₄	1	4	yes	complemented
128	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	4	yes	complemented
129	C₅×D₃×C₈	—	2	2	no	—
130	C₂×#911	C₂×C₅	1	1	yes	characteristic
131	#5546	C₂×C₅	1	1	yes	characteristic, complemented
132	#5545	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#442	C₂×C₅	1	1	yes	characteristic, complemented
134	Dic₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
135	C₄×#214	C₂×C₅	1	1	yes	characteristic, complemented
136	C₄×#213	C₂×C₅	1	1	yes	characteristic, complemented
137	#4861	C₂×C₅	1	1	yes	characteristic, complemented
138	#4852	C₂×C₅	1	1	yes	characteristic, complemented
139	#4785	C₂×C₅	1	1	yes	characteristic, complemented
140	#4772	C₂×C₅	1	1	yes	characteristic, complemented
141	D₃×#102	C₂×C₅	1	1	yes	characteristic, complemented
142	#4757	C₂×C₅	1	1	yes	characteristic, complemented
143	#4710	C₂×C₅	1	1	yes	characteristic, complemented
144	#4708	C₂×C₅	1	1	yes	characteristic, complemented
145	C₂×C₅×#41	—	3	1	no	—
146	C₂²×C₅×D₄	—	3	1	no	—
147	C₅×AGL(1,ℤ/8)	—	3	8	no	—
148	C₂×C₅×SD₁₆	—	3	1	no	—
149	C₂×C₅×SD₁₆	—	3	1	no	—
150	C₂×C₅×D₈	—	3	1	no	—
151	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
152	C₂×C₅×M₁₆	—	3	1	no	—
153	C₂²×C₅×C₈	—	3	1	no	—
154	C₄×C₅×Q₈	—	3	1	no	—
155	C₄×C₅×Q₈	—	3	1	no	—
156	C₄×C₅×D₄	—	3	1	no	—
157	C₄×C₅×D₄	—	3	1	no	—
158	C₄×C₅×D₄	—	3	1	no	—
159	C₄×C₅×D₄	—	3	1	no	—
160	C₄×C₅×D₄	—	6	1	no	—
161	C₄×C₅×D₄	—	6	1	no	—
162	C₄×C₅×D₄	—	6	1	no	—
163	C₄×C₅×D₄	—	6	1	no	—
164	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
165	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
166	C₅×#117	—	3	1	no	—
167	C₅×#117	—	3	1	no	—
168	C₅×#117	—	6	1	no	—
169	C₂×C₅×C₄⋊C₄	—	3	1	no	—
170	C₂×C₅×C₄⋊C₄	—	6	1	no	—
171	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
172	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
173	C₅×#107	—	3	1	no	—
174	C₅×#107	—	3	1	no	—
175	C₅×#106	—	3	1	no	—
176	C₅×#106	C₂×D₃	1	1	yes	characteristic, complemented
177	C₅×#103	—	3	1	no	—
178	C₅×#103	—	3	1	no	—
179	C₅×#102	—	3	1	no	—
180	C₅×#102	—	3	1	no	—
181	C₅×#102	—	3	1	no	—
182	C₅×#102	—	3	1	no	—
183	C₅×#102	C₂×D₃	1	1	yes	characteristic
184	C₅×#102	C₂×D₃	1	1	yes	characteristic, complemented
185	C₅×#97	—	3	1	no	—
186	C₅×#97	C₂×D₃	1	1	yes	characteristic, complemented
187	C₄×C₅×C₈	—	3	1	no	—
188	C₄×C₅×C₈	—	3	1	no	—
189	#2946	—	3	1	no	Sylow
190	C₂³×C₃×C₅	—	2	1	no	—
191	C₂³×C₃×C₅	—	2	1	no	—
192	C₂²×C₅×D₃	—	2	1	no	—
193	C₂²×C₅×D₃	—	2	4	no	—
194	C₂²×C₅×D₃	—	8	1	no	—
195	C₂²×C₅×D₃	—	8	1	no	—
196	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
197	C₃×C₅×D₄	—	2	1	no	—
198	C₃×C₅×D₄	—	2	1	no	—
199	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
200	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
201	C₂×C₃×C₄×C₅	—	2	1	no	—
202	C₂×C₃×C₄×C₅	—	2	1	no	—
203	C₂×C₃×C₄×C₅	—	8	1	no	—
204	C₂×C₃×C₄×C₅	—	8	1	no	—
205	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
206	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
207	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
208	C₅×#67	—	2	4	no	—
209	C₅×#67	—	2	4	no	—
210	C₂×C₅×Dic₃	—	2	1	no	—
211	C₂×C₅×Dic₃	—	2	4	no	—
212	C₂×C₅×Dic₃	—	2	1	no	—
213	C₂×C₅×Dic₃	—	2	1	no	—
214	C₂×C₅×Dic₃	—	8	1	no	—
215	C₂×C₅×Dic₃	—	8	1	no	—
216	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
217	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
218	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
219	C₅×D₁₂	—	2	1	no	—
220	C₅×D₁₂	C₂²×C₄	1	2	yes	—
221	C₄×C₅×D₃	—	8	1	no	—
222	C₄×C₅×D₃	—	8	1	no	—
223	C₄×C₅×D₃	—	8	1	no	—
224	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
225	C₄×C₅×D₃	#41	1	2	yes	—
226	C₅×Dic₆	—	2	1	no	—
227	C₅×Dic₆	C₂²×C₄	1	2	yes	—
228	C₃×C₅×C₈	—	2	1	no	—
229	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
230	C₅×C₃⋊C₈	—	2	1	no	—
231	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
232	C₂×#237	C₂²×C₅	1	1	yes	characteristic
233	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
235	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
236	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
237	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
238	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
239	C₂×#214	C₂²×C₅	1	1	yes	characteristic
240	C₂×#213	C₂²×C₅	1	1	yes	characteristic
241	C₄×#67	—	2	1	no	—
242	C₄×#67	—	2	1	no	—
243	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
244	C₂×Dic₃⋊C₄	—	2	1	no	—
245	#911	C₄×C₅	1	8	yes	complemented
246	C₂×#204	C₂²×C₅	1	1	yes	characteristic
247	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
248	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
249	#893	C₂²×C₅	1	1	yes	characteristic
250	#892	C₂²×C₅	1	1	yes	characteristic
251	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
252	#887	C₂²×C₅	1	1	yes	characteristic, complemented
253	#67⋊C₄	—	2	1	no	—
254	#67⋊C₄	—	2	1	no	—
255	D₃×C₂²⋊C₄	—	2	1	no	—
256	#877	—	2	1	no	—
257	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
258	#872	C₂²×C₅	1	1	yes	characteristic
259	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
260	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
261	C₃×#102	C₂²×C₅	1	1	yes	characteristic
262	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
264	#832	C₂²×C₅	1	1	yes	characteristic
265	#832	C₂²×C₅	1	1	yes	characteristic, complemented
266	#821	C₂²×C₅	1	1	yes	characteristic
267	#818	C₂²×C₅	1	1	yes	characteristic, complemented
268	#816	C₂²×C₅	1	1	yes	characteristic, complemented
269	#815	C₂²×C₅	1	1	yes	characteristic, complemented
270	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
271	#810	C₂²×C₅	1	1	yes	characteristic, complemented
272	#809	C₂²×C₅	1	1	yes	characteristic
273	#808	C₂²×C₅	1	1	yes	characteristic, complemented
274	#807	C₂²×C₅	1	1	yes	characteristic, complemented
275	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
276	C₂⁴×C₅	—	6	1	no	—
277	C₅×#41	—	3	4	no	—
278	C₅×#41	—	6	2	no	—
279	C₂×C₅×Q₈	—	3	1	no	—
280	C₂×C₅×D₄	—	3	4	no	—
281	C₂×C₅×D₄	—	3	1	no	—
282	C₂×C₅×D₄	—	6	2	no	—
283	C₂×C₅×D₄	—	6	1	no	—
284	C₂×C₅×D₄	—	6	1	no	—
285	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
286	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
287	C₂²×C₄×C₅	—	2	1	no	—
288	C₂²×C₄×C₅	—	2	1	no	—
289	C₂²×C₄×C₅	—	3	1	no	—
290	C₂²×C₄×C₅	—	6	1	no	—
291	C₂²×C₄×C₅	—	6	1	no	—
292	C₂²×C₄×C₅	—	6	1	no	—
293	C₂²×C₄×C₅	—	6	1	no	—
294	C₂²×C₄×C₅	—	6	1	no	—
295	C₂²×C₄×C₅	—	6	1	no	—
296	C₅×SD₁₆	—	3	4	no	—
297	C₅×SD₁₆	—	3	4	no	—
298	C₅×D₈	—	3	4	no	—
299	C₅×D₈	C₄×D₃	1	4	yes	complemented
300	C₅×M₁₆	—	3	4	no	—
301	C₂×C₅×C₈	—	3	1	no	—
302	C₂×C₅×C₈	—	3	1	no	—
303	C₂×C₅×C₈	—	6	2	no	—
304	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
305	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
306	C₅×C₄⋊C₄	—	3	1	no	—
307	C₅×C₄⋊C₄	—	3	1	no	—
308	C₅×C₄⋊C₄	—	3	1	no	—
309	C₅×C₄⋊C₄	—	3	1	no	—
310	C₅×C₄⋊C₄	—	6	1	no	—
311	C₅×C₄⋊C₄	—	6	1	no	—
312	C₅×C₄⋊C₄	—	6	1	no	—
313	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
314	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
315	C₅×C₂²⋊C₄	—	2	1	no	—
316	C₅×C₂²⋊C₄	—	2	1	no	—
317	C₅×C₂²⋊C₄	—	3	1	no	—
318	C₅×C₂²⋊C₄	—	3	1	no	—
319	C₅×C₂²⋊C₄	—	6	1	no	—
320	C₅×C₂²⋊C₄	—	6	1	no	—
321	C₅×C₂²⋊C₄	—	6	1	no	—
322	C₅×C₂²⋊C₄	—	6	1	no	—
323	C₅×C₂²⋊C₄	—	6	1	no	—
324	C₄²×C₅	—	3	1	no	—
325	C₄²×C₅	—	6	1	no	—
326	C₄²×C₅	—	6	1	no	—
327	C₄²×C₅	—	6	1	no	—
328	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
329	C₂×AGL(1,ℤ/8)	—	3	1	no	—
330	#520	—	3	1	no	—
331	#518	—	3	1	no	—
332	#442	—	3	1	no	—
333	#442	C₅×D₃	1	1	yes	characteristic, complemented
334	#440	—	3	1	no	—
335	#440	—	3	1	no	—
336	C₄×SD₁₆	—	3	1	no	—
337	C₄×SD₁₆	—	3	1	no	—
338	C₄×D₈	—	3	1	no	—
339	C₄×D₈	—	3	1	no	—
340	#428	—	3	1	no	—
341	#416	—	3	1	no	—
342	C₂×#102	—	3	1	no	—
343	#405	—	3	1	no	—
344	C₂²×C₃×C₅	—	2	2	no	—
345	C₂²×C₃×C₅	—	2	2	no	—
346	C₂²×C₃×C₅	—	4	1	no	—
347	C₂²×C₃×C₅	—	4	1	no	—
348	C₂²×C₃×C₅	—	4	1	no	—
349	C₂²×C₃×C₅	—	4	1	no	—
350	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₅×D₃	—	2	1	no	—
352	C₂×C₅×D₃	—	2	1	no	—
353	C₂×C₅×D₃	—	2	2	no	—
354	C₂×C₅×D₃	—	4	1	no	—
355	C₂×C₅×D₃	—	4	1	no	—
356	C₂×C₅×D₃	—	8	4	no	—
357	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
358	C₃×C₄×C₅	—	2	1	no	—
359	C₃×C₄×C₅	—	2	1	no	—
360	C₃×C₄×C₅	—	4	1	no	—
361	C₃×C₄×C₅	—	4	1	no	—
362	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
363	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
364	C₅×Dic₃	—	2	2	no	—
365	C₅×Dic₃	—	2	1	no	—
366	C₅×Dic₃	—	2	1	no	—
367	C₅×Dic₃	—	4	1	no	—
368	C₅×Dic₃	—	4	1	no	—
369	C₅×Dic₃	C₄×D₄	1	2	yes	—
370	C₂³×D₃	—	2	1	no	—
371	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
372	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
373	C₂²×C₃×C₄	—	2	1	no	—
374	C₂²×C₃×C₄	—	2	1	no	—
375	C₂×#67	—	2	1	no	—
376	C₂×#67	—	2	1	no	—
377	C₂²×Dic₃	—	2	1	no	—
378	C₂²×Dic₃	—	2	1	no	—
379	C₂²×Dic₃	—	2	1	no	—
380	#237	—	2	2	no	—
381	#237	C₂×C₄×C₅	1	4	yes	complemented
382	D₃×D₄	—	2	2	no	—
383	D₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
384	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
385	C₂×C₄×D₃	—	2	1	no	—
386	C₂×C₄×D₃	—	2	1	no	—
387	C₂×C₄×D₃	—	2	1	no	—
388	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
389	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
390	C₃×D₈	C₂×C₄×C₅	1	4	yes	complemented
391	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
392	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
393	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
394	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
395	C₃×C₂²⋊C₄	—	2	1	no	—
396	C₃×C₂²⋊C₄	—	2	1	no	—
397	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
398	#217	—	2	1	no	—
399	#217	—	2	1	no	—
400	#214	C₂×C₄×C₅	1	4	yes	complemented
401	#213	C₂×C₄×C₅	1	4	yes	complemented
402	(C₂×D₃)⋊C₄	—	2	1	no	—
403	(C₂×D₃)⋊C₄	—	2	1	no	—
404	(C₂×D₃)⋊C₄	—	2	1	no	—
405	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
406	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
407	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
408	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
409	Dic₃⋊C₄	—	2	1	no	—
410	Dic₃⋊C₄	—	2	1	no	—
411	Dic₃⋊C₄	—	2	1	no	—
412	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
413	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
414	C₄×Dic₃	—	2	1	no	—
415	C₄×Dic₃	—	2	1	no	—
416	C₄×Dic₃	—	2	1	no	—
417	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
418	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
419	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
420	#204	C₂×C₄×C₅	1	4	yes	complemented
421	ΓL(1,𝔽₂₅)	C₂×C₄×C₅	1	4	yes	complemented
422	D₃×C₈	—	2	2	no	—
423	C₂³×C₅	—	2	1	no	—
424	C₂³×C₅	—	2	1	no	—
425	C₂³×C₅	—	3	1	no	—
426	C₂³×C₅	—	6	4	no	—
427	C₂³×C₅	—	6	1	no	—
428	C₂³×C₅	—	24	1	no	—
429	C₂³×C₅	—	24	1	no	—
430	C₅×Q₈	—	3	2	no	—
431	C₅×Q₈	—	6	1	no	—
432	C₅×D₄	—	2	1	no	—
433	C₅×D₄	—	2	1	no	—
434	C₅×D₄	—	3	2	no	—
435	C₅×D₄	—	6	4	no	—
436	C₅×D₄	—	6	4	no	—
437	C₅×D₄	—	6	1	no	—
438	C₅×D₄	C₂×C₄×D₃	1	2	yes	—
439	C₅×D₄	C₂×C₄×D₃	1	2	yes	—
440	C₂×C₄×C₅	—	2	1	no	—
441	C₂×C₄×C₅	—	2	1	no	—
442	C₂×C₄×C₅	—	3	1	no	—
443	C₂×C₄×C₅	—	3	2	no	—
444	C₂×C₄×C₅	—	3	2	no	—
445	C₂×C₄×C₅	—	3	1	no	—
446	C₂×C₄×C₅	—	3	1	no	—
447	C₂×C₄×C₅	—	6	4	no	—
448	C₂×C₄×C₅	—	6	1	no	—
449	C₂×C₄×C₅	—	6	1	no	—
450	C₂×C₄×C₅	—	6	1	no	—
451	C₂×C₄×C₅	—	8	1	no	—
452	C₂×C₄×C₅	—	8	1	no	—
453	C₂×C₄×C₅	—	24	1	no	—
454	C₂×C₄×C₅	—	24	1	no	—
455	C₂×C₄×C₅	—	24	1	no	—
456	C₂×C₄×C₅	—	24	1	no	—
457	C₂×C₄×C₅	—	24	1	no	—
458	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
459	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
460	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
461	C₅×C₈	—	2	1	no	—
462	C₅×C₈	—	3	2	no	—
463	C₅×C₈	—	6	1	no	—
464	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
465	C₂×#41	—	3	1	no	—
466	C₂²×D₄	—	3	1	no	—
467	AGL(1,ℤ/8)	—	3	8	no	—
468	C₂×SD₁₆	—	3	1	no	—
469	C₂×SD₁₆	—	3	1	no	—
470	C₂×D₈	—	3	1	no	—
471	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
472	C₂×M₁₆	—	3	1	no	—
473	C₂²×C₈	—	3	1	no	—
474	C₄×Q₈	—	3	1	no	—
475	C₄×Q₈	—	3	1	no	—
476	C₄×D₄	—	3	1	no	—
477	C₄×D₄	—	3	1	no	—
478	C₄×D₄	—	3	1	no	—
479	C₄×D₄	—	3	1	no	—
480	C₄×D₄	—	6	1	no	—
481	C₄×D₄	—	6	1	no	—
482	C₄×D₄	—	6	1	no	—
483	C₄×D₄	—	6	1	no	—
484	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
485	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
486	#117	—	3	1	no	—
487	#117	—	3	1	no	—
488	#117	—	6	1	no	—
489	C₂×C₄⋊C₄	—	3	1	no	—
490	C₂×C₄⋊C₄	—	6	1	no	—
491	C₂×C₂²⋊C₄	—	6	1	no	—
492	C₂×C₂²⋊C₄	—	6	1	no	—
493	#107	—	3	1	no	—
494	#107	—	3	1	no	—
495	#106	—	3	1	no	—
496	#106	C₂×C₅×D₃	1	1	yes	characteristic, complemented
497	#103	—	3	1	no	—
498	#103	—	3	1	no	—
499	#102	—	3	1	no	—
500	#102	—	3	1	no	—
501	#102	—	3	1	no	—
502	#102	—	3	1	no	—
503	#102	C₂×C₅×D₃	1	1	yes	characteristic
504	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
505	#97	—	3	1	no	—
506	#97	C₂×C₅×D₃	1	1	yes	characteristic, complemented
507	C₄×C₈	—	3	1	no	—
508	C₄×C₈	—	3	1	no	—
509	C₂×C₃×C₅	—	4	2	no	—
510	C₂×C₃×C₅	—	4	2	no	—
511	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
512	C₂×C₃×C₅	#576	1	1	yes	characteristic
513	C₂×C₃×C₅	#577	1	1	yes	characteristic
514	C₅×D₃	—	2	2	no	—
515	C₅×D₃	—	4	2	no	—
516	C₂³×C₃	—	2	1	no	—
517	C₂³×C₃	—	2	1	no	—
518	C₂²×D₃	—	2	1	no	—
519	C₂²×D₃	—	2	4	no	—
520	C₂²×D₃	—	8	1	no	—
521	C₂²×D₃	—	8	1	no	—
522	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
523	C₃×D₄	—	2	1	no	—
524	C₃×D₄	—	2	1	no	—
525	C₃×D₄	C₂²×C₄×C₅	1	2	yes	—
526	C₃×D₄	C₂²×C₄×C₅	1	2	yes	—
527	C₂×C₃×C₄	—	2	1	no	—
528	C₂×C₃×C₄	—	2	1	no	—
529	C₂×C₃×C₄	—	8	1	no	—
530	C₂×C₃×C₄	—	8	1	no	—
531	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
532	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
533	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
534	#67	—	2	4	no	—
535	#67	—	2	4	no	—
536	C₂×Dic₃	—	2	1	no	—
537	C₂×Dic₃	—	2	4	no	—
538	C₂×Dic₃	—	2	1	no	—
539	C₂×Dic₃	—	2	1	no	—
540	C₂×Dic₃	—	8	1	no	—
541	C₂×Dic₃	—	8	1	no	—
542	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
543	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
544	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
545	D₁₂	—	2	1	no	—
546	D₁₂	C₂²×C₄×C₅	1	2	yes	—
547	C₄×D₃	—	8	1	no	—
548	C₄×D₃	—	8	1	no	—
549	C₄×D₃	—	8	1	no	—
550	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
551	C₄×D₃	C₅×#41	1	2	yes	—
552	Dic₆	—	2	1	no	—
553	Dic₆	C₂²×C₄×C₅	1	2	yes	—
554	C₃×C₈	—	2	1	no	—
555	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
556	C₃⋊C₈	—	2	1	no	—
557	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
558	C₂²×C₅	—	2	2	no	—
559	C₂²×C₅	—	2	2	no	—
560	C₂²×C₅	—	3	2	no	—
561	C₂²×C₅	—	4	1	no	—
562	C₂²×C₅	—	4	1	no	—
563	C₂²×C₅	—	4	1	no	—
564	C₂²×C₅	—	4	1	no	—
565	C₂²×C₅	—	6	1	no	—
566	C₂²×C₅	—	6	1	no	—
567	C₂²×C₅	—	6	2	no	—
568	C₂²×C₅	—	12	1	no	—
569	C₂²×C₅	—	12	1	no	—
570	C₂²×C₅	—	24	4	no	—
571	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
572	C₄×C₅	—	2	1	no	—
573	C₄×C₅	—	2	1	no	—
574	C₄×C₅	—	3	2	no	—
575	C₄×C₅	—	4	1	no	—
576	C₄×C₅	—	4	1	no	—
577	C₄×C₅	—	6	1	no	—
578	C₄×C₅	—	6	1	no	—
579	C₄×C₅	—	6	2	no	—
580	C₄×C₅	—	12	1	no	—
581	C₄×C₅	—	12	1	no	—
582	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
583	C₄×C₅	D₃×#41	1	1	yes	characteristic
584	C₂⁴	—	6	1	no	—
585	#41	—	3	4	no	—
586	#41	—	6	2	no	—
587	C₂×Q₈	—	3	1	no	—
588	C₂×D₄	—	3	4	no	—
589	C₂×D₄	—	3	1	no	—
590	C₂×D₄	—	6	2	no	—
591	C₂×D₄	—	6	1	no	—
592	C₂×D₄	—	6	1	no	—
593	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
594	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	3	1	no	—
598	C₂²×C₄	—	6	1	no	—
599	C₂²×C₄	—	6	1	no	—
600	C₂²×C₄	—	6	1	no	—
601	C₂²×C₄	—	6	1	no	—
602	C₂²×C₄	—	6	1	no	—
603	C₂²×C₄	—	6	1	no	—
604	SD₁₆	—	3	4	no	—
605	SD₁₆	—	3	4	no	—
606	D₈	—	3	4	no	—
607	D₈	C₄×C₅×D₃	1	4	yes	complemented
608	M₁₆	—	3	4	no	—
609	C₂×C₈	—	3	1	no	—
610	C₂×C₈	—	3	1	no	—
611	C₂×C₈	—	6	2	no	—
612	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
613	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
614	C₄⋊C₄	—	3	1	no	—
615	C₄⋊C₄	—	3	1	no	—
616	C₄⋊C₄	—	3	1	no	—
617	C₄⋊C₄	—	3	1	no	—
618	C₄⋊C₄	—	6	1	no	—
619	C₄⋊C₄	—	6	1	no	—
620	C₄⋊C₄	—	6	1	no	—
621	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
622	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
623	C₂²⋊C₄	—	2	1	no	—
624	C₂²⋊C₄	—	2	1	no	—
625	C₂²⋊C₄	—	3	1	no	—
626	C₂²⋊C₄	—	3	1	no	—
627	C₂²⋊C₄	—	6	1	no	—
628	C₂²⋊C₄	—	6	1	no	—
629	C₂²⋊C₄	—	6	1	no	—
630	C₂²⋊C₄	—	6	1	no	—
631	C₂²⋊C₄	—	6	1	no	—
632	C₄²	—	3	1	no	—
633	C₄²	—	6	1	no	—
634	C₄²	—	6	1	no	—
635	C₄²	—	6	1	no	—
636	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
637	C₃×C₅	#2946	1	1	yes	characteristic, complemented, Hall
638	C₂²×C₃	—	2	2	no	—
639	C₂²×C₃	—	2	2	no	—
640	C₂²×C₃	—	4	1	no	—
641	C₂²×C₃	—	4	1	no	—
642	C₂²×C₃	—	4	1	no	—
643	C₂²×C₃	—	4	1	no	—
644	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
645	C₂×D₃	—	2	1	no	—
646	C₂×D₃	—	2	1	no	—
647	C₂×D₃	—	2	2	no	—
648	C₂×D₃	—	4	1	no	—
649	C₂×D₃	—	4	1	no	—
650	C₂×D₃	—	8	4	no	—
651	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
652	C₃×C₄	—	2	1	no	—
653	C₃×C₄	—	2	1	no	—
654	C₃×C₄	—	4	1	no	—
655	C₃×C₄	—	4	1	no	—
656	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
657	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
658	Dic₃	—	2	2	no	—
659	Dic₃	—	2	1	no	—
660	Dic₃	—	2	1	no	—
661	Dic₃	—	4	1	no	—
662	Dic₃	—	4	1	no	—
663	Dic₃	C₄×C₅×D₄	1	2	yes	—
664	C₂×C₅	—	4	2	no	—
665	C₂×C₅	—	4	2	no	—
666	C₂×C₅	—	6	2	no	—
667	C₂×C₅	—	12	2	no	—
668	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
669	C₂×C₅	#5774	1	1	yes	characteristic
670	C₂×C₅	#5775	1	1	yes	characteristic
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	3	1	no	—
674	C₂³	—	6	4	no	—
675	C₂³	—	6	1	no	—
676	C₂³	—	24	1	no	—
677	C₂³	—	24	1	no	—
678	Q₈	—	3	2	no	—
679	Q₈	—	6	1	no	—
680	D₄	—	2	1	no	—
681	D₄	—	2	1	no	—
682	D₄	—	3	2	no	—
683	D₄	—	6	4	no	—
684	D₄	—	6	4	no	—
685	D₄	—	6	1	no	—
686	D₄	C₂×C₄×C₅×D₃	1	2	yes	—
687	D₄	C₂×C₄×C₅×D₃	1	2	yes	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	3	1	no	—
691	C₂×C₄	—	3	2	no	—
692	C₂×C₄	—	3	2	no	—
693	C₂×C₄	—	3	1	no	—
694	C₂×C₄	—	3	1	no	—
695	C₂×C₄	—	6	4	no	—
696	C₂×C₄	—	6	1	no	—
697	C₂×C₄	—	6	1	no	—
698	C₂×C₄	—	6	1	no	—
699	C₂×C₄	—	8	1	no	—
700	C₂×C₄	—	8	1	no	—
701	C₂×C₄	—	24	1	no	—
702	C₂×C₄	—	24	1	no	—
703	C₂×C₄	—	24	1	no	—
704	C₂×C₄	—	24	1	no	—
705	C₂×C₄	—	24	1	no	—
706	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
707	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
708	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
709	C₈	—	2	1	no	—
710	C₈	—	3	2	no	—
711	C₈	—	6	1	no	—
712	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
713	C₂×C₃	—	4	2	no	—
714	C₂×C₃	—	4	2	no	—
715	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
716	C₂×C₃	C₅×#576	1	1	yes	characteristic
717	C₂×C₃	C₅×#577	1	1	yes	characteristic
718	D₃	—	2	2	no	—
719	D₃	—	4	2	no	—
720	C₅	#79866	1	1	yes	characteristic, direct product factor, Sylow
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	3	2	no	—
724	C₂²	—	4	1	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	6	1	no	—
729	C₂²	—	6	1	no	—
730	C₂²	—	6	2	no	—
731	C₂²	—	12	1	no	—
732	C₂²	—	12	1	no	—
733	C₂²	—	24	4	no	—
734	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
735	C₄	—	2	1	no	—
736	C₄	—	2	1	no	—
737	C₄	—	3	2	no	—
738	C₄	—	4	1	no	—
739	C₄	—	4	1	no	—
740	C₄	—	6	1	no	—
741	C₄	—	6	1	no	—
742	C₄	—	6	2	no	—
743	C₄	—	12	1	no	—
744	C₄	—	12	1	no	—
745	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
746	C₄	C₅×D₃×#41	1	1	yes	characteristic
747	C₃	C₅×#2946	1	1	yes	characteristic, complemented, Sylow
748	C₂	—	4	2	no	—
749	C₂	—	4	2	no	—
750	C₂	—	6	2	no	—
751	C₂	—	12	2	no	—
752	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
753	C₂	C₅×#5774	1	1	yes	characteristic
754	C₂	C₅×#5775	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#442	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#911	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#442	D₃
hypocenter	C₃	C₅×#2946
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#442

Complements

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

N	H ≅ G/N	type
2. C₅×#5546	C₂	semidirect
3. C₅×#5545	C₂	semidirect
4. C₃×C₅×#442	C₂	semidirect
5. C₅×Dic₃×D₈	C₂	semidirect
6. C₄×C₅×#214	C₂	semidirect
7. C₄×C₅×#213	C₂	semidirect
8. C₅×#4861	C₂	semidirect
9. C₅×#4852	C₂	semidirect
10. C₅×#4785	C₂	semidirect
11. C₅×#4772	C₂	semidirect
12. C₅×D₃×#102	C₂	semidirect
13. C₅×#4757	C₂	semidirect
14. C₅×#4710	C₂	semidirect
15. C₅×#4708	C₂	semidirect
21. C₃×C₄×C₅×D₄	C₂²	semidirect
23. C₅×D₄×Dic₃	C₂²	semidirect
30. C₅×#911	C₄	semidirect
37. C₅×#887	C₂²	semidirect
44. C₄×C₅×Dic₆	C₂²	semidirect
45. C₃×C₅×#106	C₂²	semidirect
47. C₃×C₅×#102	C₂²	semidirect
48. C₃×C₅×#97	C₂²	semidirect
50. C₅×#832	C₂²	semidirect
52. C₅×#818	C₂²	semidirect
53. C₅×#816	C₂²	semidirect
54. C₅×#815	C₂²	semidirect
55. C₅×C₈×Dic₃	C₂²	semidirect
56. C₅×#810	C₂²	semidirect
58. C₅×#808	C₂²	semidirect
59. C₅×#807	C₂²	semidirect
60. C₄×C₅×C₃⋊C₈	C₂²	semidirect
61. #79866	C₅	direct (N × H)
66. C₅×#442	D₃	semidirect
88. C₅×#237	C₂×C₄	semidirect
90. C₅×D₃×D₄	C₂×C₄	semidirect
97. C₃×C₅×D₈	C₂×C₄	semidirect
107. C₅×#214	C₂×C₄	semidirect
108. C₅×#213	C₂×C₄	semidirect
127. C₅×#204	C₂×C₄	semidirect
128. C₅×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
131. #5546	C₂×C₅	semidirect
132. #5545	C₂×C₅	semidirect
133. C₃×#442	C₂×C₅	semidirect
134. Dic₃×D₈	C₂×C₅	semidirect
135. C₄×#214	C₂×C₅	semidirect
136. C₄×#213	C₂×C₅	semidirect
137. #4861	C₂×C₅	semidirect
138. #4852	C₂×C₅	semidirect
139. #4785	C₂×C₅	semidirect
140. #4772	C₂×C₅	semidirect
141. D₃×#102	C₂×C₅	semidirect
142. #4757	C₂×C₅	semidirect
143. #4710	C₂×C₅	semidirect
144. #4708	C₂×C₅	semidirect
165. C₄×C₅×D₄	C₂×D₃	semidirect
176. C₅×#106	C₂×D₃	semidirect
184. C₅×#102	C₂×D₃	semidirect
186. C₅×#97	C₂×D₃	semidirect
236. C₃×C₄×D₄	C₂²×C₅	semidirect
238. D₄×Dic₃	C₂²×C₅	semidirect
245. #911	C₄×C₅	semidirect
252. #887	C₂²×C₅	semidirect
259. C₄×Dic₆	C₂²×C₅	semidirect
260. C₃×#106	C₂²×C₅	semidirect
262. C₃×#102	C₂²×C₅	semidirect
263. C₃×#97	C₂²×C₅	semidirect
265. #832	C₂²×C₅	semidirect
267. #818	C₂²×C₅	semidirect
268. #816	C₂²×C₅	semidirect
269. #815	C₂²×C₅	semidirect
270. C₈×Dic₃	C₂²×C₅	semidirect
271. #810	C₂²×C₅	semidirect
273. #808	C₂²×C₅	semidirect
274. #807	C₂²×C₅	semidirect
275. C₄×C₃⋊C₈	C₂²×C₅	semidirect
299. C₅×D₈	C₄×D₃	semidirect
333. #442	C₅×D₃	semidirect
381. #237	C₂×C₄×C₅	semidirect
383. D₃×D₄	C₂×C₄×C₅	semidirect
390. C₃×D₈	C₂×C₄×C₅	semidirect
400. #214	C₂×C₄×C₅	semidirect
401. #213	C₂×C₄×C₅	semidirect
420. #204	C₂×C₄×C₅	semidirect
421. ΓL(1,𝔽₂₅)	C₂×C₄×C₅	semidirect
485. C₄×D₄	C₂×C₅×D₃	semidirect
496. #106	C₂×C₅×D₃	semidirect
504. #102	C₂×C₅×D₃	semidirect
506. #97	C₂×C₅×D₃	semidirect
607. D₈	C₄×C₅×D₃	semidirect
637. C₃×C₅	#2946	semidirect
720. C₅	#79866	direct (N × H)
747. C₃	C₅×#2946	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#911	2
C₅×#5546	2
C₅×#5545	2
C₃×C₅×#442	2
C₅×Dic₃×D₈	2
C₄×C₅×#214	2
C₄×C₅×#213	2
C₅×#4861	2
C₅×#4852	2
C₅×#4785	2
C₅×#4772	2
C₅×D₃×#102	2
C₅×#4757	2
C₅×#4710	2
C₅×#4708	2
C₅×#2946	3
#79866	5

Subgroups — C5×#79866 #14416994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79866 #14416994