Subgroups — C₅×D₃×#440 #14416308

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#440	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5164	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5026	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5018	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4889	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4817	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×D₃×#102	C₂	1	1	yes	maximal, characteristic
13	C₅×#4757	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4710	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×D₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#440	—	3	1	no	maximal, Hall
17	C₂×C₅×D₃×Q₈	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×SD₁₆	C₂²	1	1	yes	characteristic
21	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₅×#215	C₂²	1	1	yes	characteristic
25	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
26	C₂×C₅×#214	C₂²	1	1	yes	characteristic
27	C₄×C₅×#67	—	2	1	no	—
28	C₅×D₃×SD₁₆	C₄	1	8	yes	complemented
29	C₂×C₅×#204	C₂²	1	1	yes	characteristic
30	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
32	C₅×#893	C₂²	1	1	yes	characteristic
33	C₅×D₃×C₄⋊C₄	—	2	1	no	—
34	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₅×#887	—	2	1	no	—
37	C₅×#887	C₂²	1	1	yes	characteristic, complemented
38	C₅×#67⋊C₄	—	2	1	no	—
39	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
40	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
41	C₄²×C₅×D₃	—	2	1	no	—
42	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
43	C₄×C₅×Dic₆	—	2	1	no	—
44	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
47	C₃×C₅×#102	C₂²	1	1	yes	characteristic
48	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
49	C₅×#835	C₂²	1	1	yes	characteristic, complemented
50	C₅×#832	C₂²	1	1	yes	characteristic
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×#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×#807	C₂²	1	1	yes	characteristic, complemented
59	C₅×#807	C₂²	1	1	yes	characteristic, complemented
60	C₅×#803	C₂²	1	1	yes	characteristic, complemented
61	D₃×#440	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
62	C₂²×C₅×SD₁₆	—	3	1	no	—
63	C₂×C₄×C₅×Q₈	—	3	1	no	—
64	C₂×C₄×C₅×D₄	—	3	1	no	—
65	C₅×#440	—	3	1	no	—
66	C₅×#440	—	3	1	no	—
67	C₅×#440	—	3	1	no	—
68	C₅×#440	—	3	1	no	—
69	C₅×#440	—	3	1	no	—
70	C₅×#440	—	3	1	no	—
71	C₅×#440	—	3	1	no	—
72	C₅×#440	D₃	1	1	yes	characteristic, direct product factor
73	C₂×C₅×#107	—	3	1	no	—
74	C₂×C₅×#103	—	3	1	no	—
75	C₂×C₅×#102	—	3	1	no	—
76	C₂×C₅×#97	—	3	1	no	—
77	C₂³×C₅×D₃	—	2	1	no	—
78	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	—	2	1	no	—
81	C₂×C₅×#67	—	2	1	no	—
82	C₂²×C₅×Dic₃	—	2	1	no	—
83	C₅×D₃×Q₈	—	2	2	no	—
84	C₅×D₃×Q₈	C₂×C₄	1	4	yes	complemented
85	C₅×D₃×D₄	—	2	2	no	—
86	C₅×D₃×D₄	C₂×C₄	1	4	yes	—
87	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
88	C₂×C₄×C₅×D₃	—	2	1	no	—
89	C₂×C₄×C₅×D₃	—	2	1	no	—
90	C₂×C₄×C₅×D₃	—	2	1	no	—
91	C₂×C₄×C₅×D₃	—	2	1	no	—
92	C₂×C₄×C₅×D₃	—	2	1	no	—
93	C₂×C₄×C₅×D₃	—	4	4	no	—
94	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
95	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
96	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
97	C₂×C₅×Dic₆	—	2	1	no	—
98	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
99	C₃×C₅×SD₁₆	C₂×C₄	1	4	yes	complemented
100	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
102	C₃×C₅×C₄⋊C₄	—	2	1	no	—
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×C₄²×C₅	—	2	1	no	—
107	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
108	C₅×#217	—	2	1	no	—
109	C₅×#215	C₂×C₄	1	4	yes	complemented
110	C₅×#214	C₂×C₄	1	4	yes	complemented
111	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
112	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
113	C₅×C₄⋊Dic₃	—	2	1	no	—
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	—	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×D₃×C₈	—	2	2	no	—
130	C₅×D₃×C₈	C₂×C₄	1	4	yes	complemented
131	C₂×D₃×SD₁₆	C₂×C₅	1	1	yes	characteristic
132	C₄×D₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
133	C₄×D₃×D₄	C₂×C₅	1	1	yes	characteristic
134	C₃×#440	C₂×C₅	1	1	yes	characteristic, complemented
135	#5164	C₂×C₅	1	1	yes	characteristic, complemented
136	#5026	C₂×C₅	1	1	yes	characteristic, complemented
137	#5018	C₂×C₅	1	1	yes	characteristic, complemented
138	#4889	C₂×C₅	1	1	yes	characteristic, complemented
139	D₃×#107	C₂×C₅	1	1	yes	characteristic, complemented
140	#4817	C₂×C₅	1	1	yes	characteristic, complemented
141	D₃×#103	C₂×C₅	1	1	yes	characteristic, complemented
142	D₃×#102	C₂×C₅	1	1	yes	characteristic
143	#4757	C₂×C₅	1	1	yes	characteristic, complemented
144	#4710	C₂×C₅	1	1	yes	characteristic, complemented
145	D₃×#97	C₂×C₅	1	1	yes	characteristic, complemented
146	C₂²×C₅×Q₈	—	3	1	no	—
147	C₂²×C₅×D₄	—	3	1	no	—
148	C₂³×C₄×C₅	—	6	1	no	—
149	C₂×C₅×SD₁₆	—	3	1	no	—
150	C₂×C₅×SD₁₆	—	3	1	no	—
151	C₂×C₅×SD₁₆	—	3	8	no	—
152	C₂×C₅×SD₁₆	—	3	1	no	—
153	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
154	C₂²×C₅×C₈	—	3	1	no	—
155	C₂²×C₅×C₈	—	3	1	no	—
156	C₄×C₅×Q₈	—	3	1	no	—
157	C₄×C₅×Q₈	—	3	1	no	—
158	C₄×C₅×Q₈	—	3	1	no	—
159	C₄×C₅×Q₈	—	6	1	no	—
160	C₄×C₅×Q₈	—	6	1	no	—
161	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
162	C₄×C₅×D₄	—	3	1	no	—
163	C₄×C₅×D₄	—	3	1	no	—
164	C₄×C₅×D₄	—	3	1	no	—
165	C₄×C₅×D₄	—	6	1	no	—
166	C₄×C₅×D₄	—	6	1	no	—
167	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
168	C₂×C₅×C₄⋊C₄	—	3	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×C₄²×C₅	—	3	1	no	—
173	C₂×C₄²×C₅	—	6	1	no	—
174	C₅×#107	—	3	1	no	—
175	C₅×#107	—	3	1	no	—
176	C₅×#107	—	3	1	no	—
177	C₅×#107	C₂×D₃	1	1	yes	characteristic, complemented
178	C₅×#103	—	3	1	no	—
179	C₅×#103	—	3	1	no	—
180	C₅×#103	—	3	1	no	—
181	C₅×#103	C₂×D₃	1	1	yes	characteristic, complemented
182	C₅×#102	—	3	1	no	—
183	C₅×#102	—	3	1	no	—
184	C₅×#102	—	3	1	no	—
185	C₅×#102	C₂×D₃	1	1	yes	characteristic
186	C₅×#97	—	3	1	no	—
187	C₅×#97	—	3	1	no	—
188	C₅×#97	—	3	1	no	—
189	C₅×#97	C₂×D₃	1	1	yes	characteristic, complemented
190	C₂×#440	—	3	1	no	Sylow
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	—	4	2	no	—
195	C₂²×C₅×D₃	—	4	2	no	—
196	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
197	C₃×C₅×Q₈	—	2	1	no	—
198	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	complemented
199	C₃×C₅×D₄	—	2	1	no	—
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	—	2	1	no	—
204	C₂×C₃×C₄×C₅	—	4	2	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	C₂×C₅×Dic₃	—	2	1	no	—
210	C₂×C₅×Dic₃	—	2	1	no	—
211	C₂×C₅×Dic₃	—	2	1	no	—
212	C₂×C₅×Dic₃	—	4	2	no	—
213	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
214	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
215	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
216	C₅×D₁₂	—	2	1	no	—
217	C₅×D₁₂	C₂²×C₄	1	2	yes	—
218	C₄×C₅×D₃	—	2	4	no	—
219	C₄×C₅×D₃	—	2	2	no	—
220	C₄×C₅×D₃	—	2	2	no	—
221	C₄×C₅×D₃	—	4	2	no	—
222	C₄×C₅×D₃	—	4	2	no	—
223	C₄×C₅×D₃	—	4	2	no	—
224	C₄×C₅×D₃	—	4	2	no	—
225	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
226	C₄×C₅×D₃	#41	1	2	yes	—
227	C₅×Dic₆	—	2	1	no	—
228	C₅×Dic₆	—	2	4	no	—
229	C₅×Dic₆	C₂²×C₄	1	2	yes	complemented
230	C₃×C₅×C₈	—	2	1	no	—
231	C₃×C₅×C₈	C₂²×C₄	1	2	yes	complemented
232	C₅×C₃⋊C₈	—	2	1	no	—
233	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	complemented
234	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
235	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
236	C₂²×C₄×D₃	—	2	1	no	—
237	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
238	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
239	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
240	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
241	C₂×#215	C₂²×C₅	1	1	yes	characteristic
242	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
243	C₂×#214	C₂²×C₅	1	1	yes	characteristic
244	C₄×#67	—	2	1	no	—
245	D₃×SD₁₆	C₄×C₅	1	8	yes	complemented
246	C₂×#204	C₂²×C₅	1	1	yes	characteristic
247	C₂×D₃×C₈	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	D₃×C₄⋊C₄	—	2	1	no	—
251	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
252	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
253	#887	—	2	1	no	—
254	#887	C₂²×C₅	1	1	yes	characteristic, complemented
255	#67⋊C₄	—	2	1	no	—
256	D₃×C₂²⋊C₄	—	2	1	no	—
257	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
258	C₄²×D₃	—	2	1	no	—
259	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
260	C₄×Dic₆	—	2	1	no	—
261	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
262	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
264	C₃×#102	C₂²×C₅	1	1	yes	characteristic
265	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
266	#835	C₂²×C₅	1	1	yes	characteristic, complemented
267	#832	C₂²×C₅	1	1	yes	characteristic
268	#821	C₂²×C₅	1	1	yes	characteristic
269	#818	C₂²×C₅	1	1	yes	characteristic, complemented
270	#816	C₂²×C₅	1	1	yes	characteristic, complemented
271	#815	C₂²×C₅	1	1	yes	characteristic, complemented
272	#815	C₂²×C₅	1	1	yes	characteristic, complemented
273	#810	C₂²×C₅	1	1	yes	characteristic, complemented
274	#809	C₂²×C₅	1	1	yes	characteristic
275	#807	C₂²×C₅	1	1	yes	characteristic, complemented
276	#807	C₂²×C₅	1	1	yes	characteristic, complemented
277	#803	C₂²×C₅	1	1	yes	characteristic, complemented
278	C₂⁴×C₅	—	6	1	no	—
279	C₂×C₅×Q₈	—	3	4	no	—
280	C₂×C₅×Q₈	—	3	1	no	—
281	C₂×C₅×Q₈	—	6	1	no	—
282	C₂×C₅×Q₈	—	6	2	no	—
283	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
284	C₂×C₅×D₄	—	3	4	no	—
285	C₂×C₅×D₄	—	3	1	no	—
286	C₂×C₅×D₄	—	6	2	no	—
287	C₂×C₅×D₄	—	6	1	no	—
288	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
289	C₂²×C₄×C₅	—	2	1	no	—
290	C₂²×C₄×C₅	—	3	1	no	—
291	C₂²×C₄×C₅	—	3	1	no	—
292	C₂²×C₄×C₅	—	3	1	no	—
293	C₂²×C₄×C₅	—	6	1	no	—
294	C₂²×C₄×C₅	—	6	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	—	12	4	no	—
300	C₅×SD₁₆	—	3	4	no	—
301	C₅×SD₁₆	—	3	4	no	—
302	C₅×SD₁₆	—	3	4	no	—
303	C₅×SD₁₆	C₄×D₃	1	4	yes	complemented
304	C₂×C₅×C₈	—	3	1	no	—
305	C₂×C₅×C₈	—	3	4	no	—
306	C₂×C₅×C₈	—	3	1	no	—
307	C₂×C₅×C₈	—	6	2	no	—
308	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
309	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
310	C₅×C₄⋊C₄	—	2	1	no	—
311	C₅×C₄⋊C₄	—	3	1	no	—
312	C₅×C₄⋊C₄	—	3	1	no	—
313	C₅×C₄⋊C₄	—	6	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	—	6	1	no	—
318	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
319	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
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	C₄²×C₅	—	2	1	no	—
325	C₄²×C₅	—	3	1	no	—
326	C₄²×C₅	—	3	1	no	—
327	C₄²×C₅	—	3	1	no	—
328	C₄²×C₅	—	6	1	no	—
329	C₄²×C₅	—	6	1	no	—
330	C₄²×C₅	—	6	1	no	—
331	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
332	C₂²×SD₁₆	—	3	1	no	—
333	C₂×C₄×Q₈	—	3	1	no	—
334	C₂×C₄×D₄	—	3	1	no	—
335	#440	—	3	1	no	—
336	#440	—	3	1	no	—
337	#440	—	3	1	no	—
338	#440	—	3	1	no	—
339	#440	—	3	1	no	—
340	#440	—	3	1	no	—
341	#440	—	3	1	no	—
342	#440	C₅×D₃	1	1	yes	characteristic, direct product factor
343	C₂×#107	—	3	1	no	—
344	C₂×#103	—	3	1	no	—
345	C₂×#102	—	3	1	no	—
346	C₂×#97	—	3	1	no	—
347	C₂²×C₃×C₅	—	2	2	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	2	no	—
352	C₂×C₅×D₃	—	4	1	no	—
353	C₂×C₅×D₃	—	4	1	no	—
354	C₂×C₅×D₃	—	4	8	no	—
355	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
356	C₂×C₅×D₃	AGL(1,ℤ/8)	1	2	yes	—
357	C₂×C₅×D₃	#137	1	2	yes	—
358	C₃×C₄×C₅	—	2	2	no	—
359	C₃×C₄×C₅	—	2	1	no	—
360	C₃×C₄×C₅	—	2	1	no	—
361	C₃×C₄×C₅	—	4	1	no	—
362	C₃×C₄×C₅	—	4	1	no	—
363	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
364	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
365	C₅×Dic₃	—	2	2	no	—
366	C₅×Dic₃	—	2	1	no	—
367	C₅×Dic₃	—	2	1	no	—
368	C₅×Dic₃	—	4	1	no	—
369	C₅×Dic₃	—	4	1	no	—
370	C₅×Dic₃	C₄×D₄	1	2	yes	—
371	C₂³×D₃	—	2	1	no	—
372	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
373	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
374	C₂²×C₃×C₄	—	2	1	no	—
375	C₂×#67	—	2	1	no	—
376	C₂²×Dic₃	—	2	1	no	—
377	D₃×Q₈	—	2	2	no	—
378	D₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
379	D₃×D₄	—	2	2	no	—
380	D₃×D₄	C₂×C₄×C₅	1	4	yes	—
381	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
382	C₂×C₄×D₃	—	2	1	no	—
383	C₂×C₄×D₃	—	2	1	no	—
384	C₂×C₄×D₃	—	2	1	no	—
385	C₂×C₄×D₃	—	2	1	no	—
386	C₂×C₄×D₃	—	2	1	no	—
387	C₂×C₄×D₃	—	4	4	no	—
388	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
389	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
390	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
391	C₂×Dic₆	—	2	1	no	—
392	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
393	C₃×SD₁₆	C₂×C₄×C₅	1	4	yes	complemented
394	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
395	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
396	C₃×C₄⋊C₄	—	2	1	no	—
397	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
398	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
399	C₃×C₂²⋊C₄	—	2	1	no	—
400	C₃×C₄²	—	2	1	no	—
401	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
402	#217	—	2	1	no	—
403	#215	C₂×C₄×C₅	1	4	yes	complemented
404	#214	C₂×C₄×C₅	1	4	yes	complemented
405	(C₂×D₃)⋊C₄	—	2	1	no	—
406	(C₂×D₃)⋊C₄	—	2	1	no	—
407	C₄⋊Dic₃	—	2	1	no	—
408	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
409	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
410	Dic₃⋊C₄	—	2	1	no	—
411	Dic₃⋊C₄	—	2	1	no	—
412	Dic₃⋊C₄	—	2	1	no	—
413	Dic₃⋊C₄	—	2	1	no	—
414	C₄×Dic₃	—	2	1	no	—
415	C₄×Dic₃	—	2	1	no	—
416	C₄×Dic₃	—	2	1	no	—
417	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
418	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
419	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
420	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
421	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
422	#204	C₂×C₄×C₅	1	4	yes	complemented
423	D₃×C₈	—	2	2	no	—
424	D₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
425	C₂³×C₅	—	2	1	no	—
426	C₂³×C₅	—	3	1	no	—
427	C₂³×C₅	—	6	4	no	—
428	C₂³×C₅	—	6	1	no	—
429	C₂³×C₅	—	12	2	no	—
430	C₂³×C₅	—	12	2	no	—
431	C₅×Q₈	—	2	1	no	—
432	C₅×Q₈	—	3	2	no	—
433	C₅×Q₈	—	6	4	no	—
434	C₅×Q₈	—	6	1	no	—
435	C₅×Q₈	C₂×C₄×D₃	1	2	yes	complemented
436	C₅×D₄	—	2	1	no	—
437	C₅×D₄	—	3	2	no	—
438	C₅×D₄	—	6	4	no	—
439	C₅×D₄	—	6	1	no	—
440	C₅×D₄	C₂×C₄×D₃	1	2	yes	—
441	C₂×C₄×C₅	—	2	1	no	—
442	C₂×C₄×C₅	—	2	1	no	—
443	C₂×C₄×C₅	—	2	1	no	—
444	C₂×C₄×C₅	—	3	1	no	—
445	C₂×C₄×C₅	—	3	2	no	—
446	C₂×C₄×C₅	—	3	2	no	—
447	C₂×C₄×C₅	—	3	1	no	—
448	C₂×C₄×C₅	—	3	1	no	—
449	C₂×C₄×C₅	—	4	2	no	—
450	C₂×C₄×C₅	—	6	2	no	—
451	C₂×C₄×C₅	—	6	2	no	—
452	C₂×C₄×C₅	—	6	4	no	—
453	C₂×C₄×C₅	—	6	1	no	—
454	C₂×C₄×C₅	—	6	1	no	—
455	C₂×C₄×C₅	—	6	1	no	—
456	C₂×C₄×C₅	—	12	2	no	—
457	C₂×C₄×C₅	—	12	2	no	—
458	C₂×C₄×C₅	—	12	2	no	—
459	C₂×C₄×C₅	—	12	2	no	—
460	C₂×C₄×C₅	—	12	2	no	—
461	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
462	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
463	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
464	C₅×C₈	—	2	1	no	—
465	C₅×C₈	—	3	2	no	—
466	C₅×C₈	—	6	1	no	—
467	C₅×C₈	C₂×C₄×D₃	1	2	yes	complemented
468	C₂²×Q₈	—	3	1	no	—
469	C₂²×D₄	—	3	1	no	—
470	C₂³×C₄	—	6	1	no	—
471	C₂×SD₁₆	—	3	1	no	—
472	C₂×SD₁₆	—	3	1	no	—
473	C₂×SD₁₆	—	3	8	no	—
474	C₂×SD₁₆	—	3	1	no	—
475	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
476	C₂²×C₈	—	3	1	no	—
477	C₂²×C₈	—	3	1	no	—
478	C₄×Q₈	—	3	1	no	—
479	C₄×Q₈	—	3	1	no	—
480	C₄×Q₈	—	3	1	no	—
481	C₄×Q₈	—	6	1	no	—
482	C₄×Q₈	—	6	1	no	—
483	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
484	C₄×D₄	—	3	1	no	—
485	C₄×D₄	—	3	1	no	—
486	C₄×D₄	—	3	1	no	—
487	C₄×D₄	—	6	1	no	—
488	C₄×D₄	—	6	1	no	—
489	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
490	C₂×C₄⋊C₄	—	3	1	no	—
491	C₂×C₄⋊C₄	—	3	1	no	—
492	C₂×C₄⋊C₄	—	6	1	no	—
493	C₂×C₂²⋊C₄	—	6	1	no	—
494	C₂×C₄²	—	3	1	no	—
495	C₂×C₄²	—	6	1	no	—
496	#107	—	3	1	no	—
497	#107	—	3	1	no	—
498	#107	—	3	1	no	—
499	#107	C₂×C₅×D₃	1	1	yes	characteristic, complemented
500	#103	—	3	1	no	—
501	#103	—	3	1	no	—
502	#103	—	3	1	no	—
503	#103	C₂×C₅×D₃	1	1	yes	characteristic, complemented
504	#102	—	3	1	no	—
505	#102	—	3	1	no	—
506	#102	—	3	1	no	—
507	#102	C₂×C₅×D₃	1	1	yes	characteristic
508	#97	—	3	1	no	—
509	#97	—	3	1	no	—
510	#97	—	3	1	no	—
511	#97	C₂×C₅×D₃	1	1	yes	characteristic, complemented
512	C₂×C₃×C₅	—	4	2	no	—
513	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
514	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
515	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
516	C₅×D₃	—	4	2	no	—
517	C₅×D₃	#440	1	4	yes	direct product factor
518	C₂³×C₃	—	2	1	no	—
519	C₂²×D₃	—	2	1	no	—
520	C₂²×D₃	—	2	4	no	—
521	C₂²×D₃	—	4	2	no	—
522	C₂²×D₃	—	4	2	no	—
523	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
524	C₃×Q₈	—	2	1	no	—
525	C₃×Q₈	C₂²×C₄×C₅	1	2	yes	complemented
526	C₃×D₄	—	2	1	no	—
527	C₃×D₄	C₂²×C₄×C₅	1	2	yes	—
528	C₂×C₃×C₄	—	2	1	no	—
529	C₂×C₃×C₄	—	2	1	no	—
530	C₂×C₃×C₄	—	2	1	no	—
531	C₂×C₃×C₄	—	4	2	no	—
532	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
533	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
534	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
535	#67	—	2	4	no	—
536	C₂×Dic₃	—	2	1	no	—
537	C₂×Dic₃	—	2	1	no	—
538	C₂×Dic₃	—	2	1	no	—
539	C₂×Dic₃	—	4	2	no	—
540	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
541	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
542	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
543	D₁₂	—	2	1	no	—
544	D₁₂	C₂²×C₄×C₅	1	2	yes	—
545	C₄×D₃	—	2	4	no	—
546	C₄×D₃	—	2	2	no	—
547	C₄×D₃	—	2	2	no	—
548	C₄×D₃	—	4	2	no	—
549	C₄×D₃	—	4	2	no	—
550	C₄×D₃	—	4	2	no	—
551	C₄×D₃	—	4	2	no	—
552	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
553	C₄×D₃	C₅×#41	1	2	yes	—
554	Dic₆	—	2	1	no	—
555	Dic₆	—	2	4	no	—
556	Dic₆	C₂²×C₄×C₅	1	2	yes	complemented
557	C₃×C₈	—	2	1	no	—
558	C₃×C₈	C₂²×C₄×C₅	1	2	yes	complemented
559	C₃⋊C₈	—	2	1	no	—
560	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	complemented
561	C₂²×C₅	—	2	2	no	—
562	C₂²×C₅	—	3	2	no	—
563	C₂²×C₅	—	3	2	no	—
564	C₂²×C₅	—	3	2	no	—
565	C₂²×C₅	—	4	1	no	—
566	C₂²×C₅	—	4	1	no	—
567	C₂²×C₅	—	6	2	no	—
568	C₂²×C₅	—	12	8	no	—
569	C₂²×C₅	—	12	1	no	—
570	C₂²×C₅	—	12	1	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	—	2	2	no	—
575	C₄×C₅	—	3	2	no	—
576	C₄×C₅	—	4	1	no	—
577	C₄×C₅	—	4	1	no	—
578	C₄×C₅	—	6	1	no	—
579	C₄×C₅	—	6	1	no	—
580	C₄×C₅	—	6	2	no	—
581	C₄×C₅	—	12	1	no	—
582	C₄×C₅	—	12	1	no	—
583	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
584	C₄×C₅	D₃×#41	1	1	yes	characteristic
585	C₂⁴	—	6	1	no	—
586	C₂×Q₈	—	3	4	no	—
587	C₂×Q₈	—	3	1	no	—
588	C₂×Q₈	—	6	1	no	—
589	C₂×Q₈	—	6	2	no	—
590	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
591	C₂×D₄	—	3	4	no	—
592	C₂×D₄	—	3	1	no	—
593	C₂×D₄	—	6	2	no	—
594	C₂×D₄	—	6	1	no	—
595	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	3	1	no	—
598	C₂²×C₄	—	3	1	no	—
599	C₂²×C₄	—	3	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	C₂²×C₄	—	6	1	no	—
605	C₂²×C₄	—	6	1	no	—
606	C₂²×C₄	—	12	4	no	—
607	SD₁₆	—	3	4	no	—
608	SD₁₆	—	3	4	no	—
609	SD₁₆	—	3	4	no	—
610	SD₁₆	C₄×C₅×D₃	1	4	yes	complemented
611	C₂×C₈	—	3	1	no	—
612	C₂×C₈	—	3	4	no	—
613	C₂×C₈	—	3	1	no	—
614	C₂×C₈	—	6	2	no	—
615	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
616	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	3	1	no	—
619	C₄⋊C₄	—	3	1	no	—
620	C₄⋊C₄	—	6	1	no	—
621	C₄⋊C₄	—	6	1	no	—
622	C₄⋊C₄	—	6	1	no	—
623	C₄⋊C₄	—	6	1	no	—
624	C₄⋊C₄	—	6	1	no	—
625	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
626	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	6	1	no	—
629	C₂²⋊C₄	—	6	1	no	—
630	C₂²⋊C₄	—	6	1	no	—
631	C₄²	—	2	1	no	—
632	C₄²	—	3	1	no	—
633	C₄²	—	3	1	no	—
634	C₄²	—	3	1	no	—
635	C₄²	—	6	1	no	—
636	C₄²	—	6	1	no	—
637	C₄²	—	6	1	no	—
638	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
639	C₃×C₅	C₂×#440	1	1	yes	characteristic, complemented, Hall
640	C₂²×C₃	—	2	2	no	—
641	C₂²×C₃	—	4	1	no	—
642	C₂²×C₃	—	4	1	no	—
643	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
644	C₂×D₃	—	2	2	no	—
645	C₂×D₃	—	4	1	no	—
646	C₂×D₃	—	4	1	no	—
647	C₂×D₃	—	4	8	no	—
648	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
649	C₂×D₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
650	C₂×D₃	C₅×#137	1	2	yes	—
651	C₃×C₄	—	2	2	no	—
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	—	3	4	no	—
665	C₂×C₅	—	4	2	no	—
666	C₂×C₅	—	12	2	no	—
667	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
668	C₂×C₅	D₃×AGL(1,ℤ/8)	1	1	yes	characteristic
669	C₂×C₅	D₃×#137	1	1	yes	characteristic
670	C₂³	—	2	1	no	—
671	C₂³	—	3	1	no	—
672	C₂³	—	6	4	no	—
673	C₂³	—	6	1	no	—
674	C₂³	—	12	2	no	—
675	C₂³	—	12	2	no	—
676	Q₈	—	2	1	no	—
677	Q₈	—	3	2	no	—
678	Q₈	—	6	4	no	—
679	Q₈	—	6	1	no	—
680	Q₈	C₂×C₄×C₅×D₃	1	2	yes	complemented
681	D₄	—	2	1	no	—
682	D₄	—	3	2	no	—
683	D₄	—	6	4	no	—
684	D₄	—	6	1	no	—
685	D₄	C₂×C₄×C₅×D₃	1	2	yes	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	3	1	no	—
690	C₂×C₄	—	3	2	no	—
691	C₂×C₄	—	3	2	no	—
692	C₂×C₄	—	3	1	no	—
693	C₂×C₄	—	3	1	no	—
694	C₂×C₄	—	4	2	no	—
695	C₂×C₄	—	6	2	no	—
696	C₂×C₄	—	6	2	no	—
697	C₂×C₄	—	6	4	no	—
698	C₂×C₄	—	6	1	no	—
699	C₂×C₄	—	6	1	no	—
700	C₂×C₄	—	6	1	no	—
701	C₂×C₄	—	12	2	no	—
702	C₂×C₄	—	12	2	no	—
703	C₂×C₄	—	12	2	no	—
704	C₂×C₄	—	12	2	no	—
705	C₂×C₄	—	12	2	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	complemented
713	C₂×C₃	—	4	2	no	—
714	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
715	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
716	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
717	D₃	—	4	2	no	—
718	D₃	C₅×#440	1	4	yes	direct product factor
719	C₅	D₃×#440	1	1	yes	characteristic, direct product factor, Sylow
720	C₂²	—	2	2	no	—
721	C₂²	—	3	2	no	—
722	C₂²	—	3	2	no	—
723	C₂²	—	3	2	no	—
724	C₂²	—	4	1	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	6	2	no	—
727	C₂²	—	12	8	no	—
728	C₂²	—	12	1	no	—
729	C₂²	—	12	1	no	—
730	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
731	C₄	—	2	1	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	2	no	—
734	C₄	—	3	2	no	—
735	C₄	—	4	1	no	—
736	C₄	—	4	1	no	—
737	C₄	—	6	1	no	—
738	C₄	—	6	1	no	—
739	C₄	—	6	2	no	—
740	C₄	—	12	1	no	—
741	C₄	—	12	1	no	—
742	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
743	C₄	C₅×D₃×#41	1	1	yes	characteristic
744	C₃	C₂×C₅×#440	1	1	yes	characteristic, complemented, Sylow
745	C₂	—	3	4	no	—
746	C₂	—	4	2	no	—
747	C₂	—	12	2	no	—
748	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
749	C₂	C₅×D₃×AGL(1,ℤ/8)	1	1	yes	characteristic
750	C₂	C₅×D₃×#137	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×#440	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×D₃×D₄	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#440	D₃
hypocenter	C₃	C₂×C₅×#440
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#440

Complements

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

N	H ≅ G/N	type
2. C₄×C₅×D₃×Q₈	C₂	semidirect
4. C₃×C₅×#440	C₂	semidirect
5. C₅×#5164	C₂	semidirect
6. C₅×#5026	C₂	semidirect
7. C₅×#5018	C₂	semidirect
8. C₅×#4889	C₂	semidirect
9. C₅×D₃×#107	C₂	semidirect
10. C₅×#4817	C₂	semidirect
11. C₅×D₃×#103	C₂	semidirect
13. C₅×#4757	C₂	semidirect
14. C₅×#4710	C₂	semidirect
15. C₅×D₃×#97	C₂	semidirect
21. C₃×C₄×C₅×Q₈	C₂²	semidirect
23. C₅×Q₈×Dic₃	C₂²	semidirect
28. C₅×D₃×SD₁₆	C₄	semidirect
37. C₅×#887	C₂²	semidirect
44. C₄×C₅×Dic₆	C₂²	semidirect
45. C₃×C₅×#107	C₂²	semidirect
46. C₃×C₅×#103	C₂²	semidirect
48. C₃×C₅×#97	C₂²	semidirect
49. C₅×#835	C₂²	semidirect
52. C₅×#818	C₂²	semidirect
53. C₅×#816	C₂²	semidirect
54. C₅×#815	C₂²	semidirect
55. C₅×#815	C₂²	semidirect
56. C₅×#810	C₂²	semidirect
58. C₅×#807	C₂²	semidirect
59. C₅×#807	C₂²	semidirect
60. C₅×#803	C₂²	semidirect
61. D₃×#440	C₅	direct (N × H)
72. C₅×#440	D₃	direct (N × H)
84. C₅×D₃×Q₈	C₂×C₄	semidirect
99. C₃×C₅×SD₁₆	C₂×C₄	semidirect
109. C₅×#215	C₂×C₄	semidirect
110. C₅×#214	C₂×C₄	semidirect
128. C₅×#204	C₂×C₄	semidirect
130. C₅×D₃×C₈	C₂×C₄	semidirect
132. C₄×D₃×Q₈	C₂×C₅	semidirect
134. C₃×#440	C₂×C₅	semidirect
135. #5164	C₂×C₅	semidirect
136. #5026	C₂×C₅	semidirect
137. #5018	C₂×C₅	semidirect
138. #4889	C₂×C₅	semidirect
139. D₃×#107	C₂×C₅	semidirect
140. #4817	C₂×C₅	semidirect
141. D₃×#103	C₂×C₅	semidirect
143. #4757	C₂×C₅	semidirect
144. #4710	C₂×C₅	semidirect
145. D₃×#97	C₂×C₅	semidirect
161. C₄×C₅×Q₈	C₂×D₃	semidirect
177. C₅×#107	C₂×D₃	semidirect
181. C₅×#103	C₂×D₃	semidirect
189. C₅×#97	C₂×D₃	semidirect
198. C₃×C₅×Q₈	C₂²×C₄	semidirect
229. C₅×Dic₆	C₂²×C₄	semidirect
231. C₃×C₅×C₈	C₂²×C₄	semidirect
233. C₅×C₃⋊C₈	C₂²×C₄	semidirect
238. C₃×C₄×Q₈	C₂²×C₅	semidirect
240. Q₈×Dic₃	C₂²×C₅	semidirect
245. D₃×SD₁₆	C₄×C₅	semidirect
254. #887	C₂²×C₅	semidirect
261. C₄×Dic₆	C₂²×C₅	semidirect
262. C₃×#107	C₂²×C₅	semidirect
263. C₃×#103	C₂²×C₅	semidirect
265. C₃×#97	C₂²×C₅	semidirect
266. #835	C₂²×C₅	semidirect
269. #818	C₂²×C₅	semidirect
270. #816	C₂²×C₅	semidirect
271. #815	C₂²×C₅	semidirect
272. #815	C₂²×C₅	semidirect
273. #810	C₂²×C₅	semidirect
275. #807	C₂²×C₅	semidirect
276. #807	C₂²×C₅	semidirect
277. #803	C₂²×C₅	semidirect
303. C₅×SD₁₆	C₄×D₃	semidirect
342. #440	C₅×D₃	direct (N × H)
378. D₃×Q₈	C₂×C₄×C₅	semidirect
393. C₃×SD₁₆	C₂×C₄×C₅	semidirect
403. #215	C₂×C₄×C₅	semidirect
404. #214	C₂×C₄×C₅	semidirect
422. #204	C₂×C₄×C₅	semidirect
424. D₃×C₈	C₂×C₄×C₅	semidirect
435. C₅×Q₈	C₂×C₄×D₃	semidirect
467. C₅×C₈	C₂×C₄×D₃	semidirect
483. C₄×Q₈	C₂×C₅×D₃	semidirect
499. #107	C₂×C₅×D₃	semidirect
503. #103	C₂×C₅×D₃	semidirect
511. #97	C₂×C₅×D₃	semidirect
517. C₅×D₃	#440	direct (N × H)
525. C₃×Q₈	C₂²×C₄×C₅	semidirect
556. Dic₆	C₂²×C₄×C₅	semidirect
558. C₃×C₈	C₂²×C₄×C₅	semidirect
560. C₃⋊C₈	C₂²×C₄×C₅	semidirect
610. SD₁₆	C₄×C₅×D₃	semidirect
639. C₃×C₅	C₂×#440	semidirect
680. Q₈	C₂×C₄×C₅×D₃	semidirect
712. C₈	C₂×C₄×C₅×D₃	semidirect
718. D₃	C₅×#440	direct (N × H)
719. C₅	D₃×#440	direct (N × H)
744. C₃	C₂×C₅×#440	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×SD₁₆	2
C₄×C₅×D₃×Q₈	2
C₄×C₅×D₃×D₄	2
C₃×C₅×#440	2
C₅×#5164	2
C₅×#5026	2
C₅×#5018	2
C₅×#4889	2
C₅×D₃×#107	2
C₅×#4817	2
C₅×D₃×#103	2
C₅×D₃×#102	2
C₅×#4757	2
C₅×#4710	2
C₅×D₃×#97	2
C₂×C₅×#440	3
D₃×#440	5

Subgroups — C5×D3×#440 #14416308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#440 #14416308