Subgroups — C₄×C₅×#911 #14416640

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 768 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	C₄×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5152	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×#4889	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4881	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4785	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4771	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4770	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4757	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₅×#204	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₅×AGL(1,ℤ/8)	—	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	C₂²×C₄×C₅×D₃	—	2	1	no	—
20	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
21	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
23	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
24	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₅×#214	C₂²	1	1	yes	characteristic
26	C₂×C₅×#213	C₂²	1	1	yes	characteristic
27	C₄×C₅×#67	—	2	1	no	—
28	C₄×C₅×#67	—	2	1	no	—
29	C₂×C₄×C₅×Dic₃	—	2	1	no	—
30	C₅×#911	C₄	1	8	yes	direct product factor
31	C₂×C₅×#204	C₂²	1	1	yes	characteristic
32	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
33	C₂×C₅×ΓL(1,𝔽₂₅)	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	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
44	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×#107	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×C₄×C₅×C₈	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×#817	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×#815	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	C₄×#911	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
62	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
63	C₄×C₅×#41	—	3	1	no	—
64	C₂×C₄×C₅×D₄	—	3	1	no	—
65	C₅×#442	—	3	1	no	—
66	C₅×#442	—	3	1	no	—
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	D₃	1	1	yes	characteristic, complemented
73	C₅×#428	—	3	1	no	—
74	C₅×#418	—	3	1	no	—
75	C₅×#417	—	3	1	no	—
76	C₄×C₅×M₁₆	—	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	—	4	4	no	—
96	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
97	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
98	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
99	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
100	C₃×C₅×D₈	C₂×C₄	1	4	yes	complemented
101	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
102	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
103	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
106	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
107	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
108	C₅×#217	—	2	1	no	—
109	C₅×#217	—	2	1	no	—
110	C₅×#214	C₂×C₄	1	4	yes	complemented
111	C₅×#213	C₂×C₄	1	4	yes	complemented
112	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
113	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
114	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
115	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
116	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
117	C₅×Dic₃⋊C₄	—	2	1	no	—
118	C₅×Dic₃⋊C₄	—	2	1	no	—
119	C₅×Dic₃⋊C₄	—	2	1	no	—
120	C₄×C₅×Dic₃	—	2	1	no	—
121	C₄×C₅×Dic₃	—	2	1	no	—
122	C₄×C₅×Dic₃	—	2	1	no	—
123	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
124	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
125	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
126	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
127	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
128	C₅×#204	C₂×C₄	1	4	yes	complemented
129	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
130	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	4	yes	complemented
131	C₂×#911	C₂×C₅	1	1	yes	characteristic
132	C₄×D₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
133	C₄×#237	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×C₄×D₈	C₂×C₅	1	1	yes	characteristic, complemented
135	#5152	C₂×C₅	1	1	yes	characteristic, complemented
136	C₄×#214	C₂×C₅	1	1	yes	characteristic, complemented
137	C₄×#213	C₂×C₅	1	1	yes	characteristic, complemented
138	#4889	C₂×C₅	1	1	yes	characteristic, complemented
139	#4881	C₂×C₅	1	1	yes	characteristic, complemented
140	#4785	C₂×C₅	1	1	yes	characteristic, complemented
141	#4771	C₂×C₅	1	1	yes	characteristic, complemented
142	#4770	C₂×C₅	1	1	yes	characteristic, complemented
143	#4757	C₂×C₅	1	1	yes	characteristic, complemented
144	C₄×#204	C₂×C₅	1	1	yes	characteristic, complemented
145	C₄×ΓL(1,𝔽₂₅)	C₂×C₅	1	1	yes	characteristic, complemented
146	C₂×C₅×#41	—	3	1	no	—
147	C₂²×C₅×D₄	—	3	1	no	—
148	C₂³×C₄×C₅	—	6	1	no	—
149	C₅×AGL(1,ℤ/8)	—	3	8	no	—
150	C₂×C₅×SD₁₆	—	3	1	no	—
151	C₂×C₅×SD₁₆	—	3	1	no	—
152	C₂×C₅×D₈	—	3	1	no	—
153	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
154	C₂×C₅×M₁₆	—	3	1	no	—
155	C₂×C₅×M₁₆	—	3	1	no	—
156	C₄×C₅×Q₈	—	3	1	no	—
157	C₄×C₅×Q₈	—	3	1	no	—
158	C₄×C₅×D₄	—	3	1	no	—
159	C₄×C₅×D₄	—	3	1	no	—
160	C₄×C₅×D₄	—	3	1	no	—
161	C₄×C₅×D₄	—	3	1	no	—
162	C₄×C₅×D₄	—	6	1	no	—
163	C₄×C₅×D₄	—	6	1	no	—
164	C₄×C₅×D₄	—	6	1	no	—
165	C₄×C₅×D₄	—	6	1	no	—
166	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
167	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
168	C₅×#117	—	3	1	no	—
169	C₅×#117	—	6	1	no	—
170	C₂×C₅×C₄⋊C₄	—	3	1	no	—
171	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
172	C₂×C₄²×C₅	—	3	1	no	—
173	C₂×C₄²×C₅	—	6	1	no	—
174	C₅×#107	—	3	1	no	—
175	C₅×#107	C₂×D₃	1	1	yes	characteristic, complemented
176	C₅×#106	—	3	1	no	—
177	C₅×#106	—	3	1	no	—
178	C₅×#103	—	3	1	no	—
179	C₅×#103	—	3	1	no	—
180	C₅×#102	—	3	1	no	—
181	C₅×#102	—	3	1	no	—
182	C₅×#102	—	3	1	no	—
183	C₅×#102	—	3	1	no	—
184	C₅×#102	C₂×D₃	1	1	yes	characteristic
185	C₅×#102	C₂×D₃	1	1	yes	characteristic, complemented
186	C₅×#97	—	3	1	no	—
187	C₅×#97	—	3	1	no	—
188	C₄×C₅×C₈	—	3	1	no	—
189	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
190	C₄×AGL(1,ℤ/8)	—	3	1	no	Sylow
191	C₂³×C₃×C₅	—	2	1	no	—
192	C₂³×C₃×C₅	—	2	1	no	—
193	C₂²×C₅×D₃	—	2	1	no	—
194	C₂²×C₅×D₃	—	2	4	no	—
195	C₂²×C₅×D₃	—	4	2	no	—
196	C₂²×C₅×D₃	—	4	2	no	—
197	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
198	C₃×C₅×D₄	—	2	1	no	—
199	C₃×C₅×D₄	—	2	1	no	—
200	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
201	C₃×C₅×D₄	C₂²×C₄	1	2	yes	complemented
202	C₂×C₃×C₄×C₅	—	2	1	no	—
203	C₂×C₃×C₄×C₅	—	2	1	no	—
204	C₂×C₃×C₄×C₅	—	4	2	no	—
205	C₂×C₃×C₄×C₅	—	4	2	no	—
206	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
207	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
208	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
209	C₅×#67	—	2	4	no	—
210	C₅×#67	—	2	4	no	—
211	C₂×C₅×Dic₃	—	2	1	no	—
212	C₂×C₅×Dic₃	—	2	4	no	—
213	C₂×C₅×Dic₃	—	2	1	no	—
214	C₂×C₅×Dic₃	—	2	1	no	—
215	C₂×C₅×Dic₃	—	4	2	no	—
216	C₂×C₅×Dic₃	—	4	2	no	—
217	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
218	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
219	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
220	C₅×D₁₂	—	2	1	no	—
221	C₅×D₁₂	C₂²×C₄	1	2	yes	—
222	C₄×C₅×D₃	—	2	2	no	—
223	C₄×C₅×D₃	—	4	1	no	—
224	C₄×C₅×D₃	—	4	2	no	—
225	C₄×C₅×D₃	—	4	2	no	—
226	C₄×C₅×D₃	—	4	2	no	—
227	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
228	C₄×C₅×D₃	#41	1	2	yes	—
229	C₅×Dic₆	—	2	1	no	—
230	C₅×Dic₆	C₂²×C₄	1	2	yes	complemented
231	C₃×C₅×C₈	—	2	1	no	—
232	C₃×C₅×C₈	C₂²×C₄	1	2	yes	complemented
233	C₅×C₃⋊C₈	—	2	1	no	—
234	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	complemented
235	C₂×#237	C₂²×C₅	1	1	yes	characteristic
236	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
237	C₂²×C₄×D₃	—	2	1	no	—
238	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
239	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
240	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
241	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
242	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
243	C₂×#214	C₂²×C₅	1	1	yes	characteristic
244	C₂×#213	C₂²×C₅	1	1	yes	characteristic
245	C₄×#67	—	2	1	no	—
246	C₄×#67	—	2	1	no	—
247	C₂×C₄×Dic₃	—	2	1	no	—
248	#911	C₄×C₅	1	8	yes	direct product factor
249	C₂×#204	C₂²×C₅	1	1	yes	characteristic
250	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
251	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
252	#893	C₂²×C₅	1	1	yes	characteristic
253	#892	C₂²×C₅	1	1	yes	characteristic
254	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
255	#887	C₂²×C₅	1	1	yes	characteristic, complemented
256	#67⋊C₄	—	2	1	no	—
257	#67⋊C₄	—	2	1	no	—
258	D₃×C₂²⋊C₄	—	2	1	no	—
259	#877	—	2	1	no	—
260	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
261	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
262	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
264	C₃×#102	C₂²×C₅	1	1	yes	characteristic
265	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
266	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
267	#832	C₂²×C₅	1	1	yes	characteristic
268	#832	C₂²×C₅	1	1	yes	characteristic, complemented
269	#821	C₂²×C₅	1	1	yes	characteristic
270	#817	C₂²×C₅	1	1	yes	characteristic, complemented
271	#816	C₂²×C₅	1	1	yes	characteristic, complemented
272	#815	C₂²×C₅	1	1	yes	characteristic, complemented
273	#815	C₂²×C₅	1	1	yes	characteristic, complemented
274	#810	C₂²×C₅	1	1	yes	characteristic, complemented
275	#809	C₂²×C₅	1	1	yes	characteristic
276	#808	C₂²×C₅	1	1	yes	characteristic, complemented
277	#807	C₂²×C₅	1	1	yes	characteristic, complemented
278	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
279	C₂⁴×C₅	—	6	1	no	—
280	C₅×#41	—	3	4	no	—
281	C₅×#41	—	6	2	no	—
282	C₂×C₅×Q₈	—	3	1	no	—
283	C₂×C₅×D₄	—	3	4	no	—
284	C₂×C₅×D₄	—	3	1	no	—
285	C₂×C₅×D₄	—	6	2	no	—
286	C₂×C₅×D₄	—	6	1	no	—
287	C₂×C₅×D₄	—	6	1	no	—
288	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
289	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
290	C₂²×C₄×C₅	—	2	1	no	—
291	C₂²×C₄×C₅	—	2	1	no	—
292	C₂²×C₄×C₅	—	3	1	no	—
293	C₂²×C₄×C₅	—	3	1	no	—
294	C₂²×C₄×C₅	—	3	1	no	—
295	C₂²×C₄×C₅	—	6	1	no	—
296	C₂²×C₄×C₅	—	6	1	no	—
297	C₂²×C₄×C₅	—	6	1	no	—
298	C₂²×C₄×C₅	—	6	1	no	—
299	C₂²×C₄×C₅	—	6	1	no	—
300	C₂²×C₄×C₅	—	6	1	no	—
301	C₂²×C₄×C₅	—	12	4	no	—
302	C₅×SD₁₆	—	3	4	no	—
303	C₅×SD₁₆	—	3	4	no	—
304	C₅×D₈	—	3	4	no	—
305	C₅×D₈	C₄×D₃	1	4	yes	complemented
306	C₅×M₁₆	—	3	4	no	—
307	C₅×M₁₆	—	6	2	no	—
308	C₂×C₅×C₈	—	3	1	no	—
309	C₂×C₅×C₈	—	3	1	no	—
310	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
311	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
312	C₅×C₄⋊C₄	—	3	1	no	—
313	C₅×C₄⋊C₄	—	3	1	no	—
314	C₅×C₄⋊C₄	—	6	1	no	—
315	C₅×C₄⋊C₄	—	6	1	no	—
316	C₅×C₄⋊C₄	—	6	1	no	—
317	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
318	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
319	C₅×C₂²⋊C₄	—	2	1	no	—
320	C₅×C₂²⋊C₄	—	2	1	no	—
321	C₅×C₂²⋊C₄	—	6	1	no	—
322	C₅×C₂²⋊C₄	—	6	1	no	—
323	C₅×C₂²⋊C₄	—	6	1	no	—
324	C₅×C₂²⋊C₄	—	6	1	no	—
325	C₅×C₂²⋊C₄	—	6	1	no	—
326	C₄²×C₅	—	3	1	no	—
327	C₄²×C₅	—	3	1	no	—
328	C₄²×C₅	—	3	1	no	—
329	C₄²×C₅	—	6	1	no	—
330	C₄²×C₅	—	6	1	no	—
331	C₄²×C₅	—	6	1	no	—
332	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
333	C₂×AGL(1,ℤ/8)	—	3	1	no	—
334	C₄×#41	—	3	1	no	—
335	C₂×C₄×D₄	—	3	1	no	—
336	#442	—	3	1	no	—
337	#442	—	3	1	no	—
338	#440	—	3	1	no	—
339	#440	—	3	1	no	—
340	C₄×SD₁₆	—	3	1	no	—
341	C₄×SD₁₆	—	3	1	no	—
342	C₄×D₈	—	3	1	no	—
343	C₄×D₈	C₅×D₃	1	1	yes	characteristic, complemented
344	#428	—	3	1	no	—
345	#418	—	3	1	no	—
346	#417	—	3	1	no	—
347	C₄×M₁₆	—	3	1	no	—
348	C₂²×C₃×C₅	—	2	2	no	—
349	C₂²×C₃×C₅	—	2	2	no	—
350	C₂²×C₃×C₅	—	4	1	no	—
351	C₂²×C₃×C₅	—	4	1	no	—
352	C₂²×C₃×C₅	—	4	1	no	—
353	C₂²×C₃×C₅	—	4	1	no	—
354	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₅×D₃	—	2	1	no	—
356	C₂×C₅×D₃	—	2	1	no	—
357	C₂×C₅×D₃	—	2	2	no	—
358	C₂×C₅×D₃	—	4	8	no	—
359	C₂×C₅×D₃	—	4	1	no	—
360	C₂×C₅×D₃	—	4	1	no	—
361	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
362	C₃×C₄×C₅	—	2	1	no	—
363	C₃×C₄×C₅	—	4	1	no	—
364	C₃×C₄×C₅	—	4	1	no	—
365	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	complemented
366	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
367	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
368	C₅×Dic₃	—	2	2	no	—
369	C₅×Dic₃	—	2	1	no	—
370	C₅×Dic₃	—	2	1	no	—
371	C₅×Dic₃	—	4	1	no	—
372	C₅×Dic₃	—	4	1	no	—
373	C₅×Dic₃	C₄×D₄	1	2	yes	—
374	C₂³×D₃	—	2	1	no	—
375	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
376	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
377	C₂²×C₃×C₄	—	2	1	no	—
378	C₂²×C₃×C₄	—	2	1	no	—
379	C₂×#67	—	2	1	no	—
380	C₂×#67	—	2	1	no	—
381	C₂²×Dic₃	—	2	1	no	—
382	C₂²×Dic₃	—	2	1	no	—
383	C₂²×Dic₃	—	2	1	no	—
384	#237	—	2	2	no	—
385	#237	C₂×C₄×C₅	1	4	yes	complemented
386	D₃×D₄	—	2	2	no	—
387	D₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
388	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
389	C₂×C₄×D₃	—	2	1	no	—
390	C₂×C₄×D₃	—	2	1	no	—
391	C₂×C₄×D₃	—	2	1	no	—
392	C₂×C₄×D₃	—	4	4	no	—
393	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
394	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
395	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
396	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
397	C₃×D₈	C₂×C₄×C₅	1	4	yes	complemented
398	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
399	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
400	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
401	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
402	C₃×C₂²⋊C₄	—	2	1	no	—
403	C₃×C₂²⋊C₄	—	2	1	no	—
404	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
405	#217	—	2	1	no	—
406	#217	—	2	1	no	—
407	#214	C₂×C₄×C₅	1	4	yes	complemented
408	#213	C₂×C₄×C₅	1	4	yes	complemented
409	(C₂×D₃)⋊C₄	—	2	1	no	—
410	(C₂×D₃)⋊C₄	—	2	1	no	—
411	(C₂×D₃)⋊C₄	—	2	1	no	—
412	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
413	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
414	Dic₃⋊C₄	—	2	1	no	—
415	Dic₃⋊C₄	—	2	1	no	—
416	Dic₃⋊C₄	—	2	1	no	—
417	C₄×Dic₃	—	2	1	no	—
418	C₄×Dic₃	—	2	1	no	—
419	C₄×Dic₃	—	2	1	no	—
420	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
421	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
422	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
423	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
424	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
425	#204	C₂×C₄×C₅	1	4	yes	complemented
426	ΓL(1,𝔽₂₅)	—	2	2	no	—
427	ΓL(1,𝔽₂₅)	C₂×C₄×C₅	1	4	yes	complemented
428	C₂³×C₅	—	2	1	no	—
429	C₂³×C₅	—	2	1	no	—
430	C₂³×C₅	—	3	1	no	—
431	C₂³×C₅	—	6	4	no	—
432	C₂³×C₅	—	6	1	no	—
433	C₂³×C₅	—	12	2	no	—
434	C₂³×C₅	—	12	2	no	—
435	C₅×Q₈	—	3	2	no	—
436	C₅×Q₈	—	6	1	no	—
437	C₅×D₄	—	2	1	no	—
438	C₅×D₄	—	2	1	no	—
439	C₅×D₄	—	3	2	no	—
440	C₅×D₄	—	6	4	no	—
441	C₅×D₄	—	6	4	no	—
442	C₅×D₄	—	6	1	no	—
443	C₅×D₄	C₂×C₄×D₃	1	2	yes	—
444	C₅×D₄	C₂×C₄×D₃	1	2	yes	complemented
445	C₂×C₄×C₅	—	2	1	no	—
446	C₂×C₄×C₅	—	2	1	no	—
447	C₂×C₄×C₅	—	3	1	no	—
448	C₂×C₄×C₅	—	3	2	no	—
449	C₂×C₄×C₅	—	3	2	no	—
450	C₂×C₄×C₅	—	3	1	no	—
451	C₂×C₄×C₅	—	3	1	no	—
452	C₂×C₄×C₅	—	4	2	no	—
453	C₂×C₄×C₅	—	4	2	no	—
454	C₂×C₄×C₅	—	6	4	no	—
455	C₂×C₄×C₅	—	6	1	no	—
456	C₂×C₄×C₅	—	6	2	no	—
457	C₂×C₄×C₅	—	6	1	no	—
458	C₂×C₄×C₅	—	6	1	no	—
459	C₂×C₄×C₅	—	12	1	no	—
460	C₂×C₄×C₅	—	12	2	no	—
461	C₂×C₄×C₅	—	12	2	no	—
462	C₂×C₄×C₅	—	12	2	no	—
463	C₂×C₄×C₅	—	12	2	no	—
464	C₂×C₄×C₅	—	12	2	no	—
465	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
466	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
467	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
468	C₅×C₈	—	2	1	no	—
469	C₅×C₈	—	3	2	no	—
470	C₅×C₈	—	6	1	no	—
471	C₅×C₈	C₂×C₄×D₃	1	2	yes	complemented
472	C₂×#41	—	3	1	no	—
473	C₂²×D₄	—	3	1	no	—
474	C₂³×C₄	—	6	1	no	—
475	AGL(1,ℤ/8)	—	3	8	no	—
476	C₂×SD₁₆	—	3	1	no	—
477	C₂×SD₁₆	—	3	1	no	—
478	C₂×D₈	—	3	1	no	—
479	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
480	C₂×M₁₆	—	3	1	no	—
481	C₂×M₁₆	—	3	1	no	—
482	C₄×Q₈	—	3	1	no	—
483	C₄×Q₈	—	3	1	no	—
484	C₄×D₄	—	3	1	no	—
485	C₄×D₄	—	3	1	no	—
486	C₄×D₄	—	3	1	no	—
487	C₄×D₄	—	3	1	no	—
488	C₄×D₄	—	6	1	no	—
489	C₄×D₄	—	6	1	no	—
490	C₄×D₄	—	6	1	no	—
491	C₄×D₄	—	6	1	no	—
492	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
493	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
494	#117	—	3	1	no	—
495	#117	—	6	1	no	—
496	C₂×C₄⋊C₄	—	3	1	no	—
497	C₂×C₂²⋊C₄	—	6	1	no	—
498	C₂×C₄²	—	3	1	no	—
499	C₂×C₄²	—	6	1	no	—
500	#107	—	3	1	no	—
501	#107	C₂×C₅×D₃	1	1	yes	characteristic, complemented
502	#106	—	3	1	no	—
503	#106	—	3	1	no	—
504	#103	—	3	1	no	—
505	#103	—	3	1	no	—
506	#102	—	3	1	no	—
507	#102	—	3	1	no	—
508	#102	—	3	1	no	—
509	#102	—	3	1	no	—
510	#102	C₂×C₅×D₃	1	1	yes	characteristic
511	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
512	#97	—	3	1	no	—
513	#97	—	3	1	no	—
514	C₄×C₈	—	3	1	no	—
515	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
516	C₂×C₃×C₅	—	4	2	no	—
517	C₂×C₃×C₅	—	4	2	no	—
518	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
519	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
520	C₂×C₃×C₅	#575	1	1	yes	characteristic
521	C₅×D₃	—	2	2	no	—
522	C₅×D₃	—	4	2	no	—
523	C₂³×C₃	—	2	1	no	—
524	C₂³×C₃	—	2	1	no	—
525	C₂²×D₃	—	2	1	no	—
526	C₂²×D₃	—	2	4	no	—
527	C₂²×D₃	—	4	2	no	—
528	C₂²×D₃	—	4	2	no	—
529	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
530	C₃×D₄	—	2	1	no	—
531	C₃×D₄	—	2	1	no	—
532	C₃×D₄	C₂²×C₄×C₅	1	2	yes	—
533	C₃×D₄	C₂²×C₄×C₅	1	2	yes	complemented
534	C₂×C₃×C₄	—	2	1	no	—
535	C₂×C₃×C₄	—	2	1	no	—
536	C₂×C₃×C₄	—	4	2	no	—
537	C₂×C₃×C₄	—	4	2	no	—
538	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
539	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
540	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
541	#67	—	2	4	no	—
542	#67	—	2	4	no	—
543	C₂×Dic₃	—	2	1	no	—
544	C₂×Dic₃	—	2	4	no	—
545	C₂×Dic₃	—	2	1	no	—
546	C₂×Dic₃	—	2	1	no	—
547	C₂×Dic₃	—	4	2	no	—
548	C₂×Dic₃	—	4	2	no	—
549	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
550	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
551	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
552	D₁₂	—	2	1	no	—
553	D₁₂	C₂²×C₄×C₅	1	2	yes	—
554	C₄×D₃	—	2	2	no	—
555	C₄×D₃	—	4	1	no	—
556	C₄×D₃	—	4	2	no	—
557	C₄×D₃	—	4	2	no	—
558	C₄×D₃	—	4	2	no	—
559	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
560	C₄×D₃	C₅×#41	1	2	yes	—
561	Dic₆	—	2	1	no	—
562	Dic₆	C₂²×C₄×C₅	1	2	yes	complemented
563	C₃×C₈	—	2	1	no	—
564	C₃×C₈	C₂²×C₄×C₅	1	2	yes	complemented
565	C₃⋊C₈	—	2	1	no	—
566	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	complemented
567	C₂²×C₅	—	2	2	no	—
568	C₂²×C₅	—	2	2	no	—
569	C₂²×C₅	—	3	2	no	—
570	C₂²×C₅	—	4	1	no	—
571	C₂²×C₅	—	4	1	no	—
572	C₂²×C₅	—	4	1	no	—
573	C₂²×C₅	—	4	1	no	—
574	C₂²×C₅	—	6	1	no	—
575	C₂²×C₅	—	6	1	no	—
576	C₂²×C₅	—	6	2	no	—
577	C₂²×C₅	—	12	8	no	—
578	C₂²×C₅	—	12	1	no	—
579	C₂²×C₅	—	12	1	no	—
580	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
581	C₄×C₅	—	2	1	no	—
582	C₄×C₅	—	3	2	no	—
583	C₄×C₅	—	4	1	no	—
584	C₄×C₅	—	4	1	no	—
585	C₄×C₅	—	6	1	no	—
586	C₄×C₅	—	6	1	no	—
587	C₄×C₅	—	6	2	no	—
588	C₄×C₅	—	12	1	no	—
589	C₄×C₅	—	12	1	no	—
590	C₄×C₅	#911	1	2	yes	direct product factor
591	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
592	C₄×C₅	D₃×#41	1	1	yes	characteristic
593	C₂⁴	—	6	1	no	—
594	#41	—	3	4	no	—
595	#41	—	6	2	no	—
596	C₂×Q₈	—	3	1	no	—
597	C₂×D₄	—	3	4	no	—
598	C₂×D₄	—	3	1	no	—
599	C₂×D₄	—	6	2	no	—
600	C₂×D₄	—	6	1	no	—
601	C₂×D₄	—	6	1	no	—
602	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
603	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	3	1	no	—
607	C₂²×C₄	—	3	1	no	—
608	C₂²×C₄	—	3	1	no	—
609	C₂²×C₄	—	6	1	no	—
610	C₂²×C₄	—	6	1	no	—
611	C₂²×C₄	—	6	1	no	—
612	C₂²×C₄	—	6	1	no	—
613	C₂²×C₄	—	6	1	no	—
614	C₂²×C₄	—	6	1	no	—
615	C₂²×C₄	—	12	4	no	—
616	SD₁₆	—	3	4	no	—
617	SD₁₆	—	3	4	no	—
618	D₈	—	3	4	no	—
619	D₈	C₄×C₅×D₃	1	4	yes	complemented
620	M₁₆	—	3	4	no	—
621	M₁₆	—	6	2	no	—
622	C₂×C₈	—	3	1	no	—
623	C₂×C₈	—	3	1	no	—
624	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
625	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
626	C₄⋊C₄	—	3	1	no	—
627	C₄⋊C₄	—	3	1	no	—
628	C₄⋊C₄	—	6	1	no	—
629	C₄⋊C₄	—	6	1	no	—
630	C₄⋊C₄	—	6	1	no	—
631	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
632	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
633	C₂²⋊C₄	—	2	1	no	—
634	C₂²⋊C₄	—	2	1	no	—
635	C₂²⋊C₄	—	6	1	no	—
636	C₂²⋊C₄	—	6	1	no	—
637	C₂²⋊C₄	—	6	1	no	—
638	C₂²⋊C₄	—	6	1	no	—
639	C₂²⋊C₄	—	6	1	no	—
640	C₄²	—	3	1	no	—
641	C₄²	—	3	1	no	—
642	C₄²	—	3	1	no	—
643	C₄²	—	6	1	no	—
644	C₄²	—	6	1	no	—
645	C₄²	—	6	1	no	—
646	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
647	C₃×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Hall
648	C₂²×C₃	—	2	2	no	—
649	C₂²×C₃	—	2	2	no	—
650	C₂²×C₃	—	4	1	no	—
651	C₂²×C₃	—	4	1	no	—
652	C₂²×C₃	—	4	1	no	—
653	C₂²×C₃	—	4	1	no	—
654	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
655	C₂×D₃	—	2	1	no	—
656	C₂×D₃	—	2	1	no	—
657	C₂×D₃	—	2	2	no	—
658	C₂×D₃	—	4	8	no	—
659	C₂×D₃	—	4	1	no	—
660	C₂×D₃	—	4	1	no	—
661	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
662	C₃×C₄	—	2	1	no	—
663	C₃×C₄	—	4	1	no	—
664	C₃×C₄	—	4	1	no	—
665	C₃×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	complemented
666	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
667	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
668	Dic₃	—	2	2	no	—
669	Dic₃	—	2	1	no	—
670	Dic₃	—	2	1	no	—
671	Dic₃	—	4	1	no	—
672	Dic₃	—	4	1	no	—
673	Dic₃	C₄×C₅×D₄	1	2	yes	—
674	C₂×C₅	—	4	2	no	—
675	C₂×C₅	—	4	2	no	—
676	C₂×C₅	—	6	2	no	—
677	C₂×C₅	—	12	2	no	—
678	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
679	C₂×C₅	C₂×#911	1	1	yes	characteristic
680	C₂×C₅	#5768	1	1	yes	characteristic
681	C₂³	—	2	1	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	3	1	no	—
684	C₂³	—	6	4	no	—
685	C₂³	—	6	1	no	—
686	C₂³	—	12	2	no	—
687	C₂³	—	12	2	no	—
688	Q₈	—	3	2	no	—
689	Q₈	—	6	1	no	—
690	D₄	—	2	1	no	—
691	D₄	—	2	1	no	—
692	D₄	—	3	2	no	—
693	D₄	—	6	4	no	—
694	D₄	—	6	4	no	—
695	D₄	—	6	1	no	—
696	D₄	C₂×C₄×C₅×D₃	1	2	yes	—
697	D₄	C₂×C₄×C₅×D₃	1	2	yes	complemented
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	3	1	no	—
701	C₂×C₄	—	3	2	no	—
702	C₂×C₄	—	3	2	no	—
703	C₂×C₄	—	3	1	no	—
704	C₂×C₄	—	3	1	no	—
705	C₂×C₄	—	4	2	no	—
706	C₂×C₄	—	4	2	no	—
707	C₂×C₄	—	6	4	no	—
708	C₂×C₄	—	6	1	no	—
709	C₂×C₄	—	6	2	no	—
710	C₂×C₄	—	6	1	no	—
711	C₂×C₄	—	6	1	no	—
712	C₂×C₄	—	12	1	no	—
713	C₂×C₄	—	12	2	no	—
714	C₂×C₄	—	12	2	no	—
715	C₂×C₄	—	12	2	no	—
716	C₂×C₄	—	12	2	no	—
717	C₂×C₄	—	12	2	no	—
718	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
719	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
720	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
721	C₈	—	2	1	no	—
722	C₈	—	3	2	no	—
723	C₈	—	6	1	no	—
724	C₈	C₂×C₄×C₅×D₃	1	2	yes	complemented
725	C₂×C₃	—	4	2	no	—
726	C₂×C₃	—	4	2	no	—
727	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
728	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
729	C₂×C₃	C₅×#575	1	1	yes	characteristic
730	D₃	—	2	2	no	—
731	D₃	—	4	2	no	—
732	C₅	C₄×#911	1	1	yes	characteristic, direct product factor, Sylow
733	C₂²	—	2	2	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	3	2	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	1	no	—
740	C₂²	—	6	1	no	—
741	C₂²	—	6	1	no	—
742	C₂²	—	6	2	no	—
743	C₂²	—	12	8	no	—
744	C₂²	—	12	1	no	—
745	C₂²	—	12	1	no	—
746	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
747	C₄	—	2	1	no	—
748	C₄	—	3	2	no	—
749	C₄	—	4	1	no	—
750	C₄	—	4	1	no	—
751	C₄	—	6	1	no	—
752	C₄	—	6	1	no	—
753	C₄	—	6	2	no	—
754	C₄	—	12	1	no	—
755	C₄	—	12	1	no	—
756	C₄	C₅×#911	1	2	yes	direct product factor
757	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
758	C₄	C₅×D₃×#41	1	1	yes	characteristic
759	C₃	C₄×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
760	C₂	—	4	2	no	—
761	C₂	—	4	2	no	—
762	C₂	—	6	2	no	—
763	C₂	—	12	2	no	—
764	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
765	C₂	C₂×C₅×#911	1	1	yes	characteristic
766	C₂	C₅×#5768	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×D₈	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#911	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₄×C₅×D₈	D₃
hypocenter	C₃	C₄×C₅×AGL(1,ℤ/8)
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄²×C₅ ◁ C₄×C₅×D₈

Complements

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

N	H ≅ G/N	type
2. C₄×C₅×D₃×D₄	C₂	semidirect
3. C₄×C₅×#237	C₂	semidirect
4. C₃×C₄×C₅×D₈	C₂	semidirect
5. C₅×#5152	C₂	semidirect
6. C₄×C₅×#214	C₂	semidirect
7. C₄×C₅×#213	C₂	semidirect
8. C₅×#4889	C₂	semidirect
9. C₅×#4881	C₂	semidirect
10. C₅×#4785	C₂	semidirect
11. C₅×#4771	C₂	semidirect
12. C₅×#4770	C₂	semidirect
13. C₅×#4757	C₂	semidirect
14. C₄×C₅×#204	C₂	semidirect
15. C₄×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
22. C₃×C₄×C₅×D₄	C₂²	semidirect
24. C₅×D₄×Dic₃	C₂²	semidirect
30. C₅×#911	C₄	direct (N × H)
37. C₅×#887	C₂²	semidirect
44. C₄×C₅×Dic₆	C₂²	semidirect
45. C₃×C₅×#107	C₂²	semidirect
47. C₃×C₅×#102	C₂²	semidirect
48. C₃×C₄×C₅×C₈	C₂²	semidirect
50. C₅×#832	C₂²	semidirect
52. C₅×#817	C₂²	semidirect
53. C₅×#816	C₂²	semidirect
54. C₅×#815	C₂²	semidirect
55. C₅×#815	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. C₄×#911	C₅	direct (N × H)
72. C₄×C₅×D₈	D₃	semidirect
88. C₅×#237	C₂×C₄	semidirect
90. C₅×D₃×D₄	C₂×C₄	semidirect
100. C₃×C₅×D₈	C₂×C₄	semidirect
110. C₅×#214	C₂×C₄	semidirect
111. C₅×#213	C₂×C₄	semidirect
128. C₅×#204	C₂×C₄	semidirect
130. C₅×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
132. C₄×D₃×D₄	C₂×C₅	semidirect
133. C₄×#237	C₂×C₅	semidirect
134. C₃×C₄×D₈	C₂×C₅	semidirect
135. #5152	C₂×C₅	semidirect
136. C₄×#214	C₂×C₅	semidirect
137. C₄×#213	C₂×C₅	semidirect
138. #4889	C₂×C₅	semidirect
139. #4881	C₂×C₅	semidirect
140. #4785	C₂×C₅	semidirect
141. #4771	C₂×C₅	semidirect
142. #4770	C₂×C₅	semidirect
143. #4757	C₂×C₅	semidirect
144. C₄×#204	C₂×C₅	semidirect
145. C₄×ΓL(1,𝔽₂₅)	C₂×C₅	semidirect
167. C₄×C₅×D₄	C₂×D₃	semidirect
175. C₅×#107	C₂×D₃	semidirect
185. C₅×#102	C₂×D₃	semidirect
189. C₄×C₅×C₈	C₂×D₃	semidirect
201. C₃×C₅×D₄	C₂²×C₄	semidirect
230. C₅×Dic₆	C₂²×C₄	semidirect
232. C₃×C₅×C₈	C₂²×C₄	semidirect
234. C₅×C₃⋊C₈	C₂²×C₄	semidirect
240. C₃×C₄×D₄	C₂²×C₅	semidirect
242. D₄×Dic₃	C₂²×C₅	semidirect
248. #911	C₄×C₅	direct (N × H)
255. #887	C₂²×C₅	semidirect
262. C₄×Dic₆	C₂²×C₅	semidirect
263. C₃×#107	C₂²×C₅	semidirect
265. C₃×#102	C₂²×C₅	semidirect
266. C₃×C₄×C₈	C₂²×C₅	semidirect
268. #832	C₂²×C₅	semidirect
270. #817	C₂²×C₅	semidirect
271. #816	C₂²×C₅	semidirect
272. #815	C₂²×C₅	semidirect
273. #815	C₂²×C₅	semidirect
274. #810	C₂²×C₅	semidirect
276. #808	C₂²×C₅	semidirect
277. #807	C₂²×C₅	semidirect
278. C₄×C₃⋊C₈	C₂²×C₅	semidirect
305. C₅×D₈	C₄×D₃	semidirect
343. C₄×D₈	C₅×D₃	semidirect
365. C₃×C₄×C₅	AGL(1,ℤ/8)	semidirect
385. #237	C₂×C₄×C₅	semidirect
387. D₃×D₄	C₂×C₄×C₅	semidirect
397. C₃×D₈	C₂×C₄×C₅	semidirect
407. #214	C₂×C₄×C₅	semidirect
408. #213	C₂×C₄×C₅	semidirect
425. #204	C₂×C₄×C₅	semidirect
427. ΓL(1,𝔽₂₅)	C₂×C₄×C₅	semidirect
444. C₅×D₄	C₂×C₄×D₃	semidirect
471. C₅×C₈	C₂×C₄×D₃	semidirect
493. C₄×D₄	C₂×C₅×D₃	semidirect
501. #107	C₂×C₅×D₃	semidirect
511. #102	C₂×C₅×D₃	semidirect
515. C₄×C₈	C₂×C₅×D₃	semidirect
533. C₃×D₄	C₂²×C₄×C₅	semidirect
562. Dic₆	C₂²×C₄×C₅	semidirect
564. C₃×C₈	C₂²×C₄×C₅	semidirect
566. C₃⋊C₈	C₂²×C₄×C₅	semidirect
590. C₄×C₅	#911	direct (N × H)
619. D₈	C₄×C₅×D₃	semidirect
647. C₃×C₅	C₄×AGL(1,ℤ/8)	semidirect
665. C₃×C₄	C₅×AGL(1,ℤ/8)	semidirect
697. D₄	C₂×C₄×C₅×D₃	semidirect
724. C₈	C₂×C₄×C₅×D₃	semidirect
732. C₅	C₄×#911	direct (N × H)
756. C₄	C₅×#911	direct (N × H)
759. C₃	C₄×C₅×AGL(1,ℤ/8)	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
C₄×C₅×D₃×D₄	2
C₄×C₅×#237	2
C₃×C₄×C₅×D₈	2
C₅×#5152	2
C₄×C₅×#214	2
C₄×C₅×#213	2
C₅×#4889	2
C₅×#4881	2
C₅×#4785	2
C₅×#4771	2
C₅×#4770	2
C₅×#4757	2
C₄×C₅×#204	2
C₄×C₅×ΓL(1,𝔽₂₅)	2
C₄×C₅×AGL(1,ℤ/8)	3
C₄×#911	5

Subgroups — C4×C5×#911 #14416640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#911 #14416640