Subgroups — C₅×D₃×#464 #14426118

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₅×D₃×#124	C₂	1	1	yes	maximal, characteristic
4	C₄×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#464	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5185	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5166	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5054	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5028	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4845	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×D₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4798	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×D₃×#102	C₂	1	1	yes	maximal, characteristic
15	C₅×#4767	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#464	—	3	1	no	maximal, Hall
17	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
22	C₃×C₅×#124	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₅×#947	C₂²	1	1	yes	characteristic
25	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×#216	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×#216	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₅×#215	C₂²	1	1	yes	characteristic
29	C₅×#936	C₂²	1	1	yes	characteristic
30	C₂×C₅×#214	C₂²	1	1	yes	characteristic
31	C₅×D₃×Q₁₆	—	2	4	no	—
32	C₅×D₃×SD₁₆	—	2	4	no	—
33	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₅×#204	C₂²	1	1	yes	characteristic
35	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
36	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
37	C₅×D₃×C₄⋊C₄	—	2	1	no	—
38	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₅×#887	—	2	1	no	—
40	C₅×#887	C₂²	1	1	yes	characteristic, complemented
41	C₅×#885	—	2	1	no	—
42	C₅×#885	—	2	1	no	—
43	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
44	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
45	C₅×#875	C₂²	1	1	yes	characteristic
46	C₄²×C₅×D₃	—	2	1	no	—
47	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
48	C₄×C₅×Dic₆	—	2	1	no	—
49	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
50	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic
53	C₅×#835	C₂²	1	1	yes	characteristic, complemented
54	C₅×#832	C₂²	1	1	yes	characteristic
55	C₅×#821	C₂²	1	1	yes	characteristic
56	C₅×#816	C₂²	1	1	yes	characteristic, complemented
57	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
58	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₅×#810	C₂²	1	1	yes	characteristic, complemented
60	C₅×#809	C₂²	1	1	yes	characteristic
61	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
62	D₃×#464	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
63	C₂²×C₅×Q₁₆	—	3	1	no	—
64	C₂²×C₅×SD₁₆	—	3	1	no	—
65	C₂×C₅×#124	—	3	1	no	—
66	C₂×C₄×C₅×Q₈	—	3	1	no	—
67	C₅×#464	—	3	1	no	—
68	C₅×#464	—	3	1	no	—
69	C₅×#464	—	3	1	no	—
70	C₅×#464	—	3	1	no	—
71	C₅×#464	—	3	1	no	—
72	C₅×#464	—	3	1	no	—
73	C₅×#464	—	3	1	no	—
74	C₅×#464	D₃	1	1	yes	characteristic, direct product factor
75	C₂×C₅×C₄⋊C₈	—	3	1	no	—
76	C₂×C₅×#103	—	3	1	no	—
77	C₂×C₅×#102	—	3	1	no	—
78	C₂³×C₅×D₃	—	2	1	no	—
79	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
82	C₂×C₅×#67	—	2	1	no	—
83	C₅×D₃×Q₈	—	2	2	no	—
84	C₅×D₃×Q₈	—	2	2	no	—
85	C₅×D₃×Q₈	—	2	2	no	—
86	C₅×D₃×Q₈	D₄	1	4	yes	—
87	C₅×D₃×D₄	—	2	2	no	—
88	C₅×D₃×D₄	—	2	2	no	—
89	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
94	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
95	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
96	C₂×C₅×Dic₆	—	2	1	no	—
97	C₂×C₅×Dic₆	—	2	1	no	—
98	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
99	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
100	C₃×C₅×Q₁₆	—	2	2	no	—
101	C₃×C₅×SD₁₆	—	2	2	no	—
102	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
104	C₃×C₅×C₄⋊C₄	—	2	1	no	—
105	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
107	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
108	C₃×C₄²×C₅	—	2	1	no	—
109	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
110	C₅×#217	—	2	1	no	—
111	C₅×#217	—	2	1	no	—
112	C₅×#216	—	2	2	no	—
113	C₅×#216	—	2	2	no	—
114	C₅×#215	—	2	2	no	—
115	C₅×#214	—	2	2	no	—
116	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
117	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
118	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
119	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
120	C₅×C₄⋊Dic₃	—	2	1	no	—
121	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
122	C₅×Dic₃⋊C₄	—	2	1	no	—
123	C₅×Dic₃⋊C₄	—	2	1	no	—
124	C₅×Dic₃⋊C₄	—	2	1	no	—
125	C₄×C₅×Dic₃	—	2	1	no	—
126	C₄×C₅×Dic₃	—	2	1	no	—
127	C₄×C₅×Dic₃	—	2	1	no	—
128	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
129	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
130	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
131	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
132	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
133	C₅×Dic₁₂	—	2	2	no	—
134	C₅×#204	—	2	2	no	—
135	C₅×D₃×C₈	—	2	2	no	—
136	C₅×D₃×C₈	—	2	2	no	—
137	C₂×D₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂×D₃×SD₁₆	C₂×C₅	1	1	yes	characteristic
139	D₃×#124	C₂×C₅	1	1	yes	characteristic
140	C₄×D₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
141	C₃×#464	C₂×C₅	1	1	yes	characteristic, complemented
142	#5185	C₂×C₅	1	1	yes	characteristic, complemented
143	#5166	C₂×C₅	1	1	yes	characteristic, complemented
144	#5054	C₂×C₅	1	1	yes	characteristic, complemented
145	#5028	C₂×C₅	1	1	yes	characteristic, complemented
146	#4845	C₂×C₅	1	1	yes	characteristic, complemented
147	D₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
148	D₃×#103	C₂×C₅	1	1	yes	characteristic, complemented
149	#4798	C₂×C₅	1	1	yes	characteristic, complemented
150	D₃×#102	C₂×C₅	1	1	yes	characteristic
151	#4767	C₂×C₅	1	1	yes	characteristic, complemented
152	C₂²×C₅×Q₈	—	3	1	no	—
153	C₂²×C₅×Q₈	—	3	1	no	—
154	C₂²×C₅×D₄	—	3	1	no	—
155	C₂×C₅×Q₁₆	—	3	1	no	—
156	C₂×C₅×Q₁₆	—	3	1	no	—
157	C₂×C₅×Q₁₆	—	3	1	no	—
158	C₂×C₅×Q₁₆	—	6	4	no	—
159	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
160	C₂×C₅×SD₁₆	—	3	1	no	—
161	C₂×C₅×SD₁₆	—	3	1	no	—
162	C₂×C₅×SD₁₆	—	3	1	no	—
163	C₂×C₅×SD₁₆	—	6	4	no	—
164	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
165	C₂²×C₅×C₈	—	3	1	no	—
166	C₂²×C₅×C₈	—	3	1	no	—
167	C₅×#124	—	3	1	no	—
168	C₅×#124	—	3	1	no	—
169	C₅×#124	—	3	1	no	—
170	C₅×#124	—	6	1	no	—
171	C₅×#124	—	6	1	no	—
172	C₅×#124	C₂×D₃	1	1	yes	characteristic
173	C₄×C₅×Q₈	—	3	1	no	—
174	C₄×C₅×Q₈	—	3	1	no	—
175	C₄×C₅×Q₈	—	3	1	no	—
176	C₄×C₅×Q₈	—	6	1	no	—
177	C₄×C₅×Q₈	—	6	1	no	—
178	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
179	C₂×C₅×C₄⋊C₄	—	3	1	no	—
180	C₂×C₅×C₄⋊C₄	—	6	1	no	—
181	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
182	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
183	C₂×C₄²×C₅	—	3	1	no	—
184	C₂×C₄²×C₅	—	6	1	no	—
185	C₅×C₄⋊C₈	—	3	1	no	—
186	C₅×C₄⋊C₈	—	3	1	no	—
187	C₅×C₄⋊C₈	—	3	1	no	—
188	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
189	C₅×#103	—	3	1	no	—
190	C₅×#103	—	3	1	no	—
191	C₅×#103	—	3	1	no	—
192	C₅×#103	C₂×D₃	1	1	yes	characteristic, complemented
193	C₅×#102	—	3	1	no	—
194	C₅×#102	—	3	1	no	—
195	C₅×#102	—	3	1	no	—
196	C₅×#102	C₂×D₃	1	1	yes	characteristic
197	C₂×#464	—	3	1	no	Sylow
198	C₂³×C₃×C₅	—	2	1	no	—
199	C₂²×C₅×D₃	—	2	1	no	—
200	C₂²×C₅×D₃	—	4	2	no	—
201	C₂²×C₅×D₃	—	4	2	no	—
202	C₂²×C₅×D₃	—	4	2	no	—
203	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
204	C₃×C₅×Q₈	—	2	1	no	—
205	C₃×C₅×Q₈	—	2	1	no	—
206	C₃×C₅×Q₈	—	2	1	no	—
207	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
208	C₃×C₅×D₄	—	2	1	no	—
209	C₃×C₅×D₄	—	2	1	no	—
210	C₂×C₃×C₄×C₅	—	2	1	no	—
211	C₂×C₃×C₄×C₅	—	2	1	no	—
212	C₂×C₃×C₄×C₅	—	2	1	no	—
213	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
214	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
215	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
216	C₅×#67	—	4	2	no	—
217	C₂×C₅×Dic₃	—	2	1	no	—
218	C₂×C₅×Dic₃	—	2	1	no	—
219	C₂×C₅×Dic₃	—	2	1	no	—
220	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
221	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
222	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
223	C₅×D₁₂	—	2	1	no	—
224	C₅×D₁₂	—	2	1	no	—
225	C₄×C₅×D₃	—	2	4	no	—
226	C₄×C₅×D₃	—	2	2	no	—
227	C₄×C₅×D₃	—	2	2	no	—
228	C₄×C₅×D₃	—	4	2	no	—
229	C₄×C₅×D₃	—	4	2	no	—
230	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
231	C₄×C₅×D₃	#41	1	2	yes	—
232	C₅×Dic₆	—	2	1	no	—
233	C₅×Dic₆	—	2	4	no	—
234	C₅×Dic₆	—	2	1	no	—
235	C₅×Dic₆	—	2	1	no	—
236	C₅×Dic₆	—	4	2	no	—
237	C₅×Dic₆	C₂×D₄	1	2	yes	—
238	C₃×C₅×C₈	—	2	1	no	—
239	C₃×C₅×C₈	—	2	1	no	—
240	C₅×C₃⋊C₈	—	2	1	no	—
241	C₅×C₃⋊C₈	—	2	1	no	—
242	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
243	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
244	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
245	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
246	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
247	C₃×#124	C₂²×C₅	1	1	yes	characteristic
248	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
249	#947	C₂²×C₅	1	1	yes	characteristic
250	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
251	C₂×#216	C₂²×C₅	1	1	yes	characteristic, complemented
252	C₂×#216	C₂²×C₅	1	1	yes	characteristic, complemented
253	C₂×#215	C₂²×C₅	1	1	yes	characteristic
254	#936	C₂²×C₅	1	1	yes	characteristic
255	C₂×#214	C₂²×C₅	1	1	yes	characteristic
256	D₃×Q₁₆	—	2	4	no	—
257	D₃×SD₁₆	—	2	4	no	—
258	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
259	C₂×#204	C₂²×C₅	1	1	yes	characteristic
260	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
261	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
262	D₃×C₄⋊C₄	—	2	1	no	—
263	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
264	#887	—	2	1	no	—
265	#887	C₂²×C₅	1	1	yes	characteristic, complemented
266	#885	—	2	1	no	—
267	#885	—	2	1	no	—
268	D₃×C₂²⋊C₄	—	2	1	no	—
269	D₃×C₂²⋊C₄	—	2	1	no	—
270	#875	C₂²×C₅	1	1	yes	characteristic
271	C₄²×D₃	—	2	1	no	—
272	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
273	C₄×Dic₆	—	2	1	no	—
274	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
275	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
276	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
277	C₃×#102	C₂²×C₅	1	1	yes	characteristic
278	#835	C₂²×C₅	1	1	yes	characteristic, complemented
279	#832	C₂²×C₅	1	1	yes	characteristic
280	#821	C₂²×C₅	1	1	yes	characteristic
281	#816	C₂²×C₅	1	1	yes	characteristic, complemented
282	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
283	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
284	#810	C₂²×C₅	1	1	yes	characteristic, complemented
285	#809	C₂²×C₅	1	1	yes	characteristic
286	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
287	C₂⁴×C₅	—	6	1	no	—
288	C₂×C₅×Q₈	—	3	4	no	—
289	C₂×C₅×Q₈	—	3	1	no	—
290	C₂×C₅×Q₈	—	3	1	no	—
291	C₂×C₅×Q₈	—	6	1	no	—
292	C₂×C₅×Q₈	—	6	1	no	—
293	C₂×C₅×Q₈	—	6	2	no	—
294	C₂×C₅×Q₈	—	6	2	no	—
295	C₂×C₅×Q₈	—	6	2	no	—
296	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
297	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
298	C₂×C₅×D₄	—	3	1	no	—
299	C₂×C₅×D₄	—	6	2	no	—
300	C₂×C₅×D₄	—	6	2	no	—
301	C₂×C₅×D₄	—	6	1	no	—
302	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
303	C₂²×C₄×C₅	—	3	1	no	—
304	C₂²×C₄×C₅	—	3	1	no	—
305	C₂²×C₄×C₅	—	3	1	no	—
306	C₂²×C₄×C₅	—	6	1	no	—
307	C₂²×C₄×C₅	—	6	1	no	—
308	C₂²×C₄×C₅	—	6	1	no	—
309	C₅×Q₁₆	—	2	2	no	—
310	C₅×Q₁₆	—	6	2	no	—
311	C₅×Q₁₆	—	6	2	no	—
312	C₅×Q₁₆	—	6	2	no	—
313	C₅×SD₁₆	—	2	2	no	—
314	C₅×SD₁₆	—	6	2	no	—
315	C₅×SD₁₆	—	6	2	no	—
316	C₅×SD₁₆	—	6	2	no	—
317	C₂×C₅×C₈	—	3	1	no	—
318	C₂×C₅×C₈	—	3	1	no	—
319	C₂×C₅×C₈	—	6	2	no	—
320	C₂×C₅×C₈	—	6	2	no	—
321	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
322	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
323	C₅×C₄⋊C₄	—	2	1	no	—
324	C₅×C₄⋊C₄	—	3	1	no	—
325	C₅×C₄⋊C₄	—	6	1	no	—
326	C₅×C₄⋊C₄	—	6	1	no	—
327	C₅×C₄⋊C₄	—	6	1	no	—
328	C₅×C₄⋊C₄	—	6	1	no	—
329	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
330	C₅×C₂²⋊C₄	—	2	1	no	—
331	C₅×C₂²⋊C₄	—	2	1	no	—
332	C₅×C₂²⋊C₄	—	6	1	no	—
333	C₅×C₂²⋊C₄	—	6	1	no	—
334	C₅×C₂²⋊C₄	—	6	1	no	—
335	C₅×C₂²⋊C₄	—	6	1	no	—
336	C₅×C₂²⋊C₄	—	6	1	no	—
337	C₅×C₂²⋊C₄	—	6	1	no	—
338	C₄²×C₅	—	2	1	no	—
339	C₄²×C₅	—	3	1	no	—
340	C₄²×C₅	—	3	1	no	—
341	C₄²×C₅	—	3	1	no	—
342	C₄²×C₅	—	6	1	no	—
343	C₄²×C₅	—	6	1	no	—
344	C₄²×C₅	—	6	1	no	—
345	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
346	C₂²×Q₁₆	—	3	1	no	—
347	C₂²×SD₁₆	—	3	1	no	—
348	C₂×#124	—	3	1	no	—
349	C₂×C₄×Q₈	—	3	1	no	—
350	#464	—	3	1	no	—
351	#464	—	3	1	no	—
352	#464	—	3	1	no	—
353	#464	—	3	1	no	—
354	#464	—	3	1	no	—
355	#464	—	3	1	no	—
356	#464	—	3	1	no	—
357	#464	C₅×D₃	1	1	yes	characteristic, direct product factor
358	C₂×C₄⋊C₈	—	3	1	no	—
359	C₂×#103	—	3	1	no	—
360	C₂×#102	—	3	1	no	—
361	C₂²×C₃×C₅	—	4	1	no	—
362	C₂²×C₃×C₅	—	4	1	no	—
363	C₂²×C₃×C₅	—	4	1	no	—
364	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₅×D₃	—	4	1	no	—
366	C₂×C₅×D₃	—	4	1	no	—
367	C₂×C₅×D₃	—	4	1	no	—
368	C₂×C₅×D₃	—	8	4	no	—
369	C₂×C₅×D₃	#121	1	2	yes	—
370	C₂×C₅×D₃	#135	1	2	yes	—
371	C₂×C₅×D₃	#137	1	2	yes	—
372	C₃×C₄×C₅	—	2	2	no	—
373	C₃×C₄×C₅	—	2	1	no	—
374	C₃×C₄×C₅	—	2	1	no	—
375	C₃×C₄×C₅	—	4	1	no	—
376	C₃×C₄×C₅	—	4	1	no	—
377	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
378	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
379	C₅×Dic₃	—	2	2	no	—
380	C₅×Dic₃	—	2	1	no	—
381	C₅×Dic₃	—	2	1	no	—
382	C₅×Dic₃	—	4	1	no	—
383	C₅×Dic₃	—	4	1	no	—
384	C₅×Dic₃	#121	1	2	yes	—
385	C₂³×D₃	—	2	1	no	—
386	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
387	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
388	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
389	C₂×#67	—	2	1	no	—
390	D₃×Q₈	—	2	2	no	—
391	D₃×Q₈	—	2	2	no	—
392	D₃×Q₈	—	2	2	no	—
393	D₃×Q₈	C₅×D₄	1	4	yes	—
394	D₃×D₄	—	2	2	no	—
395	D₃×D₄	—	2	2	no	—
396	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
397	C₂×C₄×D₃	—	2	1	no	—
398	C₂×C₄×D₃	—	2	1	no	—
399	C₂×C₄×D₃	—	2	1	no	—
400	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
401	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
402	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
403	C₂×Dic₆	—	2	1	no	—
404	C₂×Dic₆	—	2	1	no	—
405	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
406	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
407	C₃×Q₁₆	—	2	2	no	—
408	C₃×SD₁₆	—	2	2	no	—
409	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
410	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
411	C₃×C₄⋊C₄	—	2	1	no	—
412	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
413	C₃×C₂²⋊C₄	—	2	1	no	—
414	C₃×C₂²⋊C₄	—	2	1	no	—
415	C₃×C₄²	—	2	1	no	—
416	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
417	#217	—	2	1	no	—
418	#217	—	2	1	no	—
419	#216	—	2	2	no	—
420	#216	—	2	2	no	—
421	#215	—	2	2	no	—
422	#214	—	2	2	no	—
423	(C₂×D₃)⋊C₄	—	2	1	no	—
424	(C₂×D₃)⋊C₄	—	2	1	no	—
425	(C₂×D₃)⋊C₄	—	2	1	no	—
426	(C₂×D₃)⋊C₄	—	2	1	no	—
427	C₄⋊Dic₃	—	2	1	no	—
428	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
429	Dic₃⋊C₄	—	2	1	no	—
430	Dic₃⋊C₄	—	2	1	no	—
431	Dic₃⋊C₄	—	2	1	no	—
432	C₄×Dic₃	—	2	1	no	—
433	C₄×Dic₃	—	2	1	no	—
434	C₄×Dic₃	—	2	1	no	—
435	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
436	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
437	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
438	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
439	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
440	Dic₁₂	—	2	2	no	—
441	#204	—	2	2	no	—
442	D₃×C₈	—	2	2	no	—
443	D₃×C₈	—	2	2	no	—
444	C₂³×C₅	—	2	1	no	—
445	C₂³×C₅	—	3	1	no	—
446	C₂³×C₅	—	6	1	no	—
447	C₂³×C₅	—	12	2	no	—
448	C₂³×C₅	—	12	2	no	—
449	C₂³×C₅	—	12	2	no	—
450	C₅×Q₈	—	2	1	no	—
451	C₅×Q₈	—	2	1	no	—
452	C₅×Q₈	—	2	1	no	—
453	C₅×Q₈	—	3	2	no	—
454	C₅×Q₈	—	6	4	no	—
455	C₅×Q₈	—	6	1	no	—
456	C₅×Q₈	—	6	1	no	—
457	C₅×Q₈	—	6	1	no	—
458	C₅×Q₈	—	12	2	no	—
459	C₅×Q₈	D₃×D₄	1	2	yes	—
460	C₅×D₄	—	2	1	no	—
461	C₅×D₄	—	2	1	no	—
462	C₅×D₄	—	6	1	no	—
463	C₅×D₄	—	6	1	no	—
464	C₅×D₄	—	12	2	no	—
465	C₂×C₄×C₅	—	2	1	no	—
466	C₂×C₄×C₅	—	2	1	no	—
467	C₂×C₄×C₅	—	2	1	no	—
468	C₂×C₄×C₅	—	3	1	no	—
469	C₂×C₄×C₅	—	3	2	no	—
470	C₂×C₄×C₅	—	3	2	no	—
471	C₂×C₄×C₅	—	3	1	no	—
472	C₂×C₄×C₅	—	3	1	no	—
473	C₂×C₄×C₅	—	6	2	no	—
474	C₂×C₄×C₅	—	6	2	no	—
475	C₂×C₄×C₅	—	6	4	no	—
476	C₂×C₄×C₅	—	6	1	no	—
477	C₂×C₄×C₅	—	6	1	no	—
478	C₂×C₄×C₅	—	6	1	no	—
479	C₂×C₄×C₅	—	12	2	no	—
480	C₂×C₄×C₅	—	12	2	no	—
481	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
482	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
483	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
484	C₅×C₈	—	2	1	no	—
485	C₅×C₈	—	2	1	no	—
486	C₅×C₈	—	6	1	no	—
487	C₅×C₈	—	6	1	no	—
488	C₂²×Q₈	—	3	1	no	—
489	C₂²×Q₈	—	3	1	no	—
490	C₂²×D₄	—	3	1	no	—
491	C₂×Q₁₆	—	3	1	no	—
492	C₂×Q₁₆	—	3	1	no	—
493	C₂×Q₁₆	—	3	1	no	—
494	C₂×Q₁₆	—	6	4	no	—
495	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
496	C₂×SD₁₆	—	3	1	no	—
497	C₂×SD₁₆	—	3	1	no	—
498	C₂×SD₁₆	—	3	1	no	—
499	C₂×SD₁₆	—	6	4	no	—
500	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
501	C₂²×C₈	—	3	1	no	—
502	C₂²×C₈	—	3	1	no	—
503	#124	—	3	1	no	—
504	#124	—	3	1	no	—
505	#124	—	3	1	no	—
506	#124	—	6	1	no	—
507	#124	—	6	1	no	—
508	#124	C₂×C₅×D₃	1	1	yes	characteristic
509	C₄×Q₈	—	3	1	no	—
510	C₄×Q₈	—	3	1	no	—
511	C₄×Q₈	—	3	1	no	—
512	C₄×Q₈	—	6	1	no	—
513	C₄×Q₈	—	6	1	no	—
514	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
515	C₂×C₄⋊C₄	—	3	1	no	—
516	C₂×C₄⋊C₄	—	6	1	no	—
517	C₂×C₂²⋊C₄	—	6	1	no	—
518	C₂×C₂²⋊C₄	—	6	1	no	—
519	C₂×C₄²	—	3	1	no	—
520	C₂×C₄²	—	6	1	no	—
521	C₄⋊C₈	—	3	1	no	—
522	C₄⋊C₈	—	3	1	no	—
523	C₄⋊C₈	—	3	1	no	—
524	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
525	#103	—	3	1	no	—
526	#103	—	3	1	no	—
527	#103	—	3	1	no	—
528	#103	C₂×C₅×D₃	1	1	yes	characteristic, complemented
529	#102	—	3	1	no	—
530	#102	—	3	1	no	—
531	#102	—	3	1	no	—
532	#102	C₂×C₅×D₃	1	1	yes	characteristic
533	C₂×C₃×C₅	—	8	1	no	—
534	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
535	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
536	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
537	C₅×D₃	—	8	1	no	—
538	C₅×D₃	#464	1	4	yes	direct product factor
539	C₂³×C₃	—	2	1	no	—
540	C₂²×D₃	—	2	1	no	—
541	C₂²×D₃	—	4	2	no	—
542	C₂²×D₃	—	4	2	no	—
543	C₂²×D₃	—	4	2	no	—
544	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
545	C₃×Q₈	—	2	1	no	—
546	C₃×Q₈	—	2	1	no	—
547	C₃×Q₈	—	2	1	no	—
548	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
549	C₃×D₄	—	2	1	no	—
550	C₃×D₄	—	2	1	no	—
551	C₂×C₃×C₄	—	2	1	no	—
552	C₂×C₃×C₄	—	2	1	no	—
553	C₂×C₃×C₄	—	2	1	no	—
554	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
555	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
556	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
557	#67	—	4	2	no	—
558	C₂×Dic₃	—	2	1	no	—
559	C₂×Dic₃	—	2	1	no	—
560	C₂×Dic₃	—	2	1	no	—
561	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
562	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
563	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
564	D₁₂	—	2	1	no	—
565	D₁₂	—	2	1	no	—
566	C₄×D₃	—	2	4	no	—
567	C₄×D₃	—	2	2	no	—
568	C₄×D₃	—	2	2	no	—
569	C₄×D₃	—	4	2	no	—
570	C₄×D₃	—	4	2	no	—
571	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
572	C₄×D₃	C₅×#41	1	2	yes	—
573	Dic₆	—	2	1	no	—
574	Dic₆	—	2	4	no	—
575	Dic₆	—	2	1	no	—
576	Dic₆	—	2	1	no	—
577	Dic₆	—	4	2	no	—
578	Dic₆	C₂×C₅×D₄	1	2	yes	—
579	C₃×C₈	—	2	1	no	—
580	C₃×C₈	—	2	1	no	—
581	C₃⋊C₈	—	2	1	no	—
582	C₃⋊C₈	—	2	1	no	—
583	C₂²×C₅	—	3	2	no	—
584	C₂²×C₅	—	3	2	no	—
585	C₂²×C₅	—	3	2	no	—
586	C₂²×C₅	—	4	1	no	—
587	C₂²×C₅	—	4	1	no	—
588	C₂²×C₅	—	4	1	no	—
589	C₂²×C₅	—	12	1	no	—
590	C₂²×C₅	—	12	1	no	—
591	C₂²×C₅	—	12	1	no	—
592	C₂²×C₅	—	24	4	no	—
593	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
594	C₄×C₅	—	2	1	no	—
595	C₄×C₅	—	2	1	no	—
596	C₄×C₅	—	2	2	no	—
597	C₄×C₅	—	3	2	no	—
598	C₄×C₅	—	4	1	no	—
599	C₄×C₅	—	4	1	no	—
600	C₄×C₅	—	6	1	no	—
601	C₄×C₅	—	6	1	no	—
602	C₄×C₅	—	6	2	no	—
603	C₄×C₅	—	12	1	no	—
604	C₄×C₅	—	12	1	no	—
605	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
606	C₄×C₅	D₃×#41	1	1	yes	characteristic
607	C₂⁴	—	6	1	no	—
608	C₂×Q₈	—	3	4	no	—
609	C₂×Q₈	—	3	1	no	—
610	C₂×Q₈	—	3	1	no	—
611	C₂×Q₈	—	6	1	no	—
612	C₂×Q₈	—	6	1	no	—
613	C₂×Q₈	—	6	2	no	—
614	C₂×Q₈	—	6	2	no	—
615	C₂×Q₈	—	6	2	no	—
616	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
617	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
618	C₂×D₄	—	3	1	no	—
619	C₂×D₄	—	6	2	no	—
620	C₂×D₄	—	6	2	no	—
621	C₂×D₄	—	6	1	no	—
622	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
623	C₂²×C₄	—	3	1	no	—
624	C₂²×C₄	—	3	1	no	—
625	C₂²×C₄	—	3	1	no	—
626	C₂²×C₄	—	6	1	no	—
627	C₂²×C₄	—	6	1	no	—
628	C₂²×C₄	—	6	1	no	—
629	Q₁₆	—	2	2	no	—
630	Q₁₆	—	6	2	no	—
631	Q₁₆	—	6	2	no	—
632	Q₁₆	—	6	2	no	—
633	SD₁₆	—	2	2	no	—
634	SD₁₆	—	6	2	no	—
635	SD₁₆	—	6	2	no	—
636	SD₁₆	—	6	2	no	—
637	C₂×C₈	—	3	1	no	—
638	C₂×C₈	—	3	1	no	—
639	C₂×C₈	—	6	2	no	—
640	C₂×C₈	—	6	2	no	—
641	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
642	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	3	1	no	—
645	C₄⋊C₄	—	6	1	no	—
646	C₄⋊C₄	—	6	1	no	—
647	C₄⋊C₄	—	6	1	no	—
648	C₄⋊C₄	—	6	1	no	—
649	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
650	C₂²⋊C₄	—	2	1	no	—
651	C₂²⋊C₄	—	2	1	no	—
652	C₂²⋊C₄	—	6	1	no	—
653	C₂²⋊C₄	—	6	1	no	—
654	C₂²⋊C₄	—	6	1	no	—
655	C₂²⋊C₄	—	6	1	no	—
656	C₂²⋊C₄	—	6	1	no	—
657	C₂²⋊C₄	—	6	1	no	—
658	C₄²	—	2	1	no	—
659	C₄²	—	3	1	no	—
660	C₄²	—	3	1	no	—
661	C₄²	—	3	1	no	—
662	C₄²	—	6	1	no	—
663	C₄²	—	6	1	no	—
664	C₄²	—	6	1	no	—
665	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
666	C₃×C₅	C₂×#464	1	1	yes	characteristic, complemented, Hall
667	C₂²×C₃	—	4	1	no	—
668	C₂²×C₃	—	4	1	no	—
669	C₂²×C₃	—	4	1	no	—
670	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
671	C₂×D₃	—	4	1	no	—
672	C₂×D₃	—	4	1	no	—
673	C₂×D₃	—	4	1	no	—
674	C₂×D₃	—	8	4	no	—
675	C₂×D₃	C₅×#121	1	2	yes	—
676	C₂×D₃	C₅×#135	1	2	yes	—
677	C₂×D₃	C₅×#137	1	2	yes	—
678	C₃×C₄	—	2	2	no	—
679	C₃×C₄	—	2	1	no	—
680	C₃×C₄	—	2	1	no	—
681	C₃×C₄	—	4	1	no	—
682	C₃×C₄	—	4	1	no	—
683	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
684	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
685	Dic₃	—	2	2	no	—
686	Dic₃	—	2	1	no	—
687	Dic₃	—	2	1	no	—
688	Dic₃	—	4	1	no	—
689	Dic₃	—	4	1	no	—
690	Dic₃	C₅×#121	1	2	yes	—
691	C₂×C₅	—	3	4	no	—
692	C₂×C₅	—	8	1	no	—
693	C₂×C₅	—	24	1	no	—
694	C₂×C₅	D₃×#121	1	1	yes	characteristic
695	C₂×C₅	D₃×#135	1	1	yes	characteristic
696	C₂×C₅	D₃×#137	1	1	yes	characteristic
697	C₂³	—	2	1	no	—
698	C₂³	—	3	1	no	—
699	C₂³	—	6	1	no	—
700	C₂³	—	12	2	no	—
701	C₂³	—	12	2	no	—
702	C₂³	—	12	2	no	—
703	Q₈	—	2	1	no	—
704	Q₈	—	2	1	no	—
705	Q₈	—	2	1	no	—
706	Q₈	—	3	2	no	—
707	Q₈	—	6	4	no	—
708	Q₈	—	6	1	no	—
709	Q₈	—	6	1	no	—
710	Q₈	—	6	1	no	—
711	Q₈	—	12	2	no	—
712	Q₈	C₅×D₃×D₄	1	2	yes	—
713	D₄	—	2	1	no	—
714	D₄	—	2	1	no	—
715	D₄	—	6	1	no	—
716	D₄	—	6	1	no	—
717	D₄	—	12	2	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	3	1	no	—
722	C₂×C₄	—	3	2	no	—
723	C₂×C₄	—	3	2	no	—
724	C₂×C₄	—	3	1	no	—
725	C₂×C₄	—	3	1	no	—
726	C₂×C₄	—	6	2	no	—
727	C₂×C₄	—	6	2	no	—
728	C₂×C₄	—	6	4	no	—
729	C₂×C₄	—	6	1	no	—
730	C₂×C₄	—	6	1	no	—
731	C₂×C₄	—	6	1	no	—
732	C₂×C₄	—	12	2	no	—
733	C₂×C₄	—	12	2	no	—
734	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
735	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
736	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
737	C₈	—	2	1	no	—
738	C₈	—	2	1	no	—
739	C₈	—	6	1	no	—
740	C₈	—	6	1	no	—
741	C₂×C₃	—	8	1	no	—
742	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
743	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
744	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
745	D₃	—	8	1	no	—
746	D₃	C₅×#464	1	4	yes	direct product factor
747	C₅	D₃×#464	1	1	yes	characteristic, direct product factor, Sylow
748	C₂²	—	3	2	no	—
749	C₂²	—	3	2	no	—
750	C₂²	—	3	2	no	—
751	C₂²	—	4	1	no	—
752	C₂²	—	4	1	no	—
753	C₂²	—	4	1	no	—
754	C₂²	—	12	1	no	—
755	C₂²	—	12	1	no	—
756	C₂²	—	12	1	no	—
757	C₂²	—	24	4	no	—
758	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
759	C₄	—	2	1	no	—
760	C₄	—	2	1	no	—
761	C₄	—	2	2	no	—
762	C₄	—	3	2	no	—
763	C₄	—	4	1	no	—
764	C₄	—	4	1	no	—
765	C₄	—	6	1	no	—
766	C₄	—	6	1	no	—
767	C₄	—	6	2	no	—
768	C₄	—	12	1	no	—
769	C₄	—	12	1	no	—
770	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
771	C₄	C₅×D₃×#41	1	1	yes	characteristic
772	C₃	C₂×C₅×#464	1	1	yes	characteristic, complemented, Sylow
773	C₂	—	3	4	no	—
774	C₂	—	8	1	no	—
775	C₂	—	24	1	no	—
776	C₂	C₅×D₃×#121	1	1	yes	characteristic
777	C₂	C₅×D₃×#135	1	1	yes	characteristic
778	C₂	C₅×D₃×#137	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#464	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×D₃×D₄	C₂²
hypercenter	C₅×#464	D₃
hypocenter	C₃	C₂×C₅×#464
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#464

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×Q₁₆	C₂	semidirect
4. C₄×C₅×D₃×Q₈	C₂	semidirect
5. C₃×C₅×#464	C₂	semidirect
6. C₅×#5185	C₂	semidirect
7. C₅×#5166	C₂	semidirect
8. C₅×#5054	C₂	semidirect
9. C₅×#5028	C₂	semidirect
10. C₅×#4845	C₂	semidirect
11. C₅×D₃×C₄⋊C₈	C₂	semidirect
12. C₅×D₃×#103	C₂	semidirect
13. C₅×#4798	C₂	semidirect
15. C₅×#4767	C₂	semidirect
20. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
23. C₃×C₄×C₅×Q₈	C₂²	semidirect
25. C₅×Q₈×Dic₃	C₂²	semidirect
26. C₂×C₅×#216	C₂²	semidirect
27. C₂×C₅×#216	C₂²	semidirect
33. C₂×C₅×Dic₁₂	C₂²	semidirect
40. C₅×#887	C₂²	semidirect
49. C₄×C₅×Dic₆	C₂²	semidirect
50. C₃×C₅×C₄⋊C₈	C₂²	semidirect
51. C₃×C₅×#103	C₂²	semidirect
53. C₅×#835	C₂²	semidirect
56. C₅×#816	C₂²	semidirect
57. C₅×Dic₃⋊C₈	C₂²	semidirect
58. C₅×Dic₃⋊C₈	C₂²	semidirect
59. C₅×#810	C₂²	semidirect
61. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
62. D₃×#464	C₅	direct (N × H)
74. C₅×#464	D₃	direct (N × H)
137. C₂×D₃×Q₁₆	C₂×C₅	semidirect
140. C₄×D₃×Q₈	C₂×C₅	semidirect
141. C₃×#464	C₂×C₅	semidirect
142. #5185	C₂×C₅	semidirect
143. #5166	C₂×C₅	semidirect
144. #5054	C₂×C₅	semidirect
145. #5028	C₂×C₅	semidirect
146. #4845	C₂×C₅	semidirect
147. D₃×C₄⋊C₈	C₂×C₅	semidirect
148. D₃×#103	C₂×C₅	semidirect
149. #4798	C₂×C₅	semidirect
151. #4767	C₂×C₅	semidirect
159. C₂×C₅×Q₁₆	C₂×D₃	semidirect
178. C₄×C₅×Q₈	C₂×D₃	semidirect
188. C₅×C₄⋊C₈	C₂×D₃	semidirect
192. C₅×#103	C₂×D₃	semidirect
245. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
248. C₃×C₄×Q₈	C₂²×C₅	semidirect
250. Q₈×Dic₃	C₂²×C₅	semidirect
251. C₂×#216	C₂²×C₅	semidirect
252. C₂×#216	C₂²×C₅	semidirect
258. C₂×Dic₁₂	C₂²×C₅	semidirect
265. #887	C₂²×C₅	semidirect
274. C₄×Dic₆	C₂²×C₅	semidirect
275. C₃×C₄⋊C₈	C₂²×C₅	semidirect
276. C₃×#103	C₂²×C₅	semidirect
278. #835	C₂²×C₅	semidirect
281. #816	C₂²×C₅	semidirect
282. Dic₃⋊C₈	C₂²×C₅	semidirect
283. Dic₃⋊C₈	C₂²×C₅	semidirect
284. #810	C₂²×C₅	semidirect
286. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
357. #464	C₅×D₃	direct (N × H)
495. C₂×Q₁₆	C₂×C₅×D₃	semidirect
514. C₄×Q₈	C₂×C₅×D₃	semidirect
524. C₄⋊C₈	C₂×C₅×D₃	semidirect
528. #103	C₂×C₅×D₃	semidirect
538. C₅×D₃	#464	direct (N × H)
666. C₃×C₅	C₂×#464	semidirect
746. D₃	C₅×#464	direct (N × H)
747. C₅	D₃×#464	direct (N × H)
772. C₃	C₂×C₅×#464	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×Q₁₆	2
C₂×C₅×D₃×SD₁₆	2
C₅×D₃×#124	2
C₄×C₅×D₃×Q₈	2
C₃×C₅×#464	2
C₅×#5185	2
C₅×#5166	2
C₅×#5054	2
C₅×#5028	2
C₅×#4845	2
C₅×D₃×C₄⋊C₈	2
C₅×D₃×#103	2
C₅×#4798	2
C₅×D₃×#102	2
C₅×#4767	2
C₂×C₅×#464	3
D₃×#464	5

Subgroups — C5×D3×#464 #14426118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#464 #14426118