Subgroups — C₅×D₃×#460 #14426004

Order 1920.

1168 conjugacy classes of subgroups.

The subgroup lattice has 636 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	2	yes	maximal, complemented
2	C₅×D₃×#127	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#460	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5163	C₂	1	2	yes	maximal, complemented
6	C₅×#5075	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5027	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4848	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×D₃×#102	C₂	1	2	yes	maximal, complemented
11	C₅×#4762	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#460	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×D₃×D₄	—	2	1	no	—
15	C₂×C₅×D₃×D₄	—	2	1	no	—
16	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
18	C₃×C₅×#127	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₅×#215	C₂²	1	2	yes	complemented
22	C₅×#940	—	2	1	no	—
23	C₅×#940	—	2	1	no	—
24	C₅×#940	C₂²	1	2	yes	—
25	C₂×C₅×#214	C₂²	1	2	yes	complemented
26	C₅×D₃×SD₁₆	—	2	8	no	—
27	C₂×C₅×#204	C₂²	1	2	yes	complemented
28	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
29	C₅×D₃×C₄⋊C₄	—	2	1	no	—
30	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₅×#887	—	2	1	no	—
32	C₅×#887	C₂²	1	1	yes	characteristic, complemented
33	C₅×#874	C₂²	1	1	yes	characteristic
34	C₄²×C₅×D₃	—	2	1	no	—
35	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
36	C₄×C₅×Dic₆	—	2	1	no	—
37	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₅×#102	C₂²	1	2	yes	complemented
40	C₅×#832	C₂²	1	2	yes	complemented
41	C₅×#821	C₂²	1	2	yes	complemented
42	C₅×Dic₃⋊C₈	C₂²	1	2	yes	complemented
43	C₅×#809	C₂²	1	2	yes	complemented
44	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
45	D₃×#460	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
46	C₂²×C₅×SD₁₆	—	3	2	no	—
47	C₂×C₅×#127	—	3	1	no	—
48	C₂×C₄×C₅×Q₈	—	3	1	no	—
49	C₅×#460	—	3	1	no	—
50	C₅×#460	—	3	2	no	—
51	C₅×#460	—	3	2	no	—
52	C₅×#460	—	3	1	no	—
53	C₅×#460	—	3	1	no	—
54	C₅×#460	D₃	1	1	yes	characteristic, direct product factor
55	C₂×C₅×C₄⋊C₈	—	3	1	no	—
56	C₂×C₅×#102	—	3	2	no	—
57	C₂³×C₅×D₃	—	2	2	no	—
58	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	—	2	1	no	—
60	C₂×C₃×C₅×D₄	—	2	1	no	—
61	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
62	C₂×C₅×#67	—	2	2	no	—
63	C₂×C₅×#67	—	2	2	no	—
64	C₂×C₅×#67	—	2	2	no	—
65	C₅×D₃×Q₈	—	2	2	no	—
66	C₅×D₃×Q₈	D₄	1	4	yes	complemented
67	C₅×D₃×D₄	—	2	4	no	—
68	C₅×D₃×D₄	—	2	4	no	—
69	C₅×D₃×D₄	—	4	4	no	—
70	C₅×D₃×D₄	—	4	4	no	—
71	C₂×C₅×D₁₂	—	2	1	no	—
72	C₂×C₅×D₁₂	—	2	1	no	—
73	C₂×C₅×D₁₂	C₂³	1	2	yes	—
74	C₂×C₄×C₅×D₃	—	2	1	no	—
75	C₂×C₄×C₅×D₃	—	2	1	no	—
76	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
77	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
78	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
79	C₂×C₅×Dic₆	—	2	1	no	—
80	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
81	C₃×C₅×SD₁₆	—	2	4	no	—
82	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
83	C₃×C₅×C₄⋊C₄	—	2	1	no	—
84	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₃×C₄²×C₅	—	2	1	no	—
86	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
87	C₅×#215	—	2	4	no	—
88	C₅×#214	—	2	4	no	—
89	C₅×C₄⋊Dic₃	—	2	1	no	—
90	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
91	C₅×Dic₃⋊C₄	—	2	1	no	—
92	C₅×Dic₃⋊C₄	—	2	1	no	—
93	C₅×Dic₃⋊C₄	—	2	1	no	—
94	C₄×C₅×Dic₃	—	2	1	no	—
95	C₄×C₅×Dic₃	—	2	1	no	—
96	C₄×C₅×Dic₃	—	2	1	no	—
97	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
98	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
99	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
100	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
101	C₅×#204	—	2	4	no	—
102	C₅×D₃×C₈	—	2	4	no	—
103	C₂×D₃×SD₁₆	C₂×C₅	1	2	yes	complemented
104	D₃×#127	C₂×C₅	1	1	yes	characteristic
105	C₄×D₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
106	C₃×#460	C₂×C₅	1	1	yes	characteristic, complemented
107	#5163	C₂×C₅	1	2	yes	complemented
108	#5075	C₂×C₅	1	1	yes	characteristic, complemented
109	#5027	C₂×C₅	1	1	yes	characteristic, complemented
110	#4848	C₂×C₅	1	1	yes	characteristic, complemented
111	D₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
112	D₃×#102	C₂×C₅	1	2	yes	complemented
113	#4762	C₂×C₅	1	2	yes	complemented
114	C₂²×C₅×Q₈	—	3	1	no	—
115	C₂²×C₅×D₄	—	3	2	no	—
116	C₂²×C₅×D₄	—	6	1	no	—
117	C₂²×C₅×D₄	—	6	1	no	—
118	C₂×C₅×SD₁₆	—	3	2	no	—
119	C₂×C₅×SD₁₆	—	3	2	no	—
120	C₂×C₅×SD₁₆	—	3	2	no	—
121	C₂×C₅×SD₁₆	—	6	8	no	—
122	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	complemented
123	C₂²×C₅×C₈	—	3	2	no	—
124	C₅×#127	—	3	2	no	—
125	C₅×#127	—	3	1	no	—
126	C₅×#127	—	6	1	no	—
127	C₅×#127	—	6	1	no	—
128	C₅×#127	C₂×D₃	1	1	yes	characteristic
129	C₄×C₅×Q₈	—	3	1	no	—
130	C₄×C₅×Q₈	—	3	1	no	—
131	C₄×C₅×Q₈	—	3	1	no	—
132	C₄×C₅×Q₈	—	6	1	no	—
133	C₄×C₅×Q₈	—	6	1	no	—
134	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
135	C₂×C₅×C₄⋊C₄	—	3	1	no	—
136	C₂×C₅×C₄⋊C₄	—	6	1	no	—
137	C₂×C₄²×C₅	—	3	1	no	—
138	C₂×C₄²×C₅	—	6	1	no	—
139	C₅×C₄⋊C₈	—	3	2	no	—
140	C₅×C₄⋊C₈	—	3	1	no	—
141	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
142	C₅×#102	—	3	2	no	—
143	C₅×#102	—	3	2	no	—
144	C₅×#102	—	3	2	no	—
145	C₅×#102	C₂×D₃	1	2	yes	complemented
146	C₂×#460	—	3	1	no	Sylow
147	C₂³×C₃×C₅	—	2	2	no	—
148	C₂²×C₅×D₃	—	2	2	no	—
149	C₂²×C₅×D₃	—	4	4	no	—
150	C₂²×C₅×D₃	—	4	4	no	—
151	C₂²×C₅×D₃	—	4	4	no	—
152	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
153	C₃×C₅×Q₈	—	2	1	no	—
154	C₃×C₅×Q₈	C₂×D₄	1	2	yes	complemented
155	C₃×C₅×D₄	—	2	2	no	—
156	C₃×C₅×D₄	—	2	2	no	—
157	C₃×C₅×D₄	—	4	2	no	—
158	C₃×C₅×D₄	—	4	2	no	—
159	C₂×C₃×C₄×C₅	—	2	1	no	—
160	C₂×C₃×C₄×C₅	—	2	1	no	—
161	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
162	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
164	C₅×#67	—	4	4	no	—
165	C₅×#67	—	4	4	no	—
166	C₅×#67	—	4	4	no	—
167	C₂×C₅×Dic₃	—	2	1	no	—
168	C₂×C₅×Dic₃	—	2	1	no	—
169	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
170	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
171	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
172	C₅×D₁₂	—	2	2	no	—
173	C₅×D₁₂	—	2	2	no	—
174	C₅×D₁₂	—	4	2	no	—
175	C₅×D₁₂	—	4	2	no	—
176	C₄×C₅×D₃	—	2	4	no	—
177	C₄×C₅×D₃	—	2	2	no	—
178	C₄×C₅×D₃	—	4	2	no	—
179	C₄×C₅×D₃	SD₁₆	1	4	yes	complemented
180	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
181	C₄×C₅×D₃	#41	1	2	yes	—
182	C₅×Dic₆	—	2	1	no	—
183	C₅×Dic₆	—	2	4	no	—
184	C₅×Dic₆	C₂×D₄	1	2	yes	complemented
185	C₃×C₅×C₈	—	2	2	no	—
186	C₅×C₃⋊C₈	—	2	2	no	—
187	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
188	C₂×D₃×D₄	—	2	1	no	—
189	C₂×D₃×D₄	—	2	1	no	—
190	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
191	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
192	C₃×#127	C₂²×C₅	1	1	yes	characteristic
193	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
194	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
195	C₂×#215	C₂²×C₅	1	2	yes	complemented
196	#940	—	2	1	no	—
197	#940	—	2	1	no	—
198	#940	C₂²×C₅	1	2	yes	—
199	C₂×#214	C₂²×C₅	1	2	yes	complemented
200	D₃×SD₁₆	—	2	8	no	—
201	C₂×#204	C₂²×C₅	1	2	yes	complemented
202	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
203	D₃×C₄⋊C₄	—	2	1	no	—
204	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
205	#887	—	2	1	no	—
206	#887	C₂²×C₅	1	1	yes	characteristic, complemented
207	#874	C₂²×C₅	1	1	yes	characteristic
208	C₄²×D₃	—	2	1	no	—
209	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
210	C₄×Dic₆	—	2	1	no	—
211	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
212	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
213	C₃×#102	C₂²×C₅	1	2	yes	complemented
214	#832	C₂²×C₅	1	2	yes	complemented
215	#821	C₂²×C₅	1	2	yes	complemented
216	Dic₃⋊C₈	C₂²×C₅	1	2	yes	complemented
217	#809	C₂²×C₅	1	2	yes	complemented
218	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
219	C₂⁴×C₅	—	6	2	no	—
220	C₂×C₅×Q₈	—	3	4	no	—
221	C₂×C₅×Q₈	—	3	1	no	—
222	C₂×C₅×Q₈	—	6	1	no	—
223	C₂×C₅×Q₈	—	6	2	no	—
224	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
225	C₂×C₅×D₄	—	2	1	no	—
226	C₂×C₅×D₄	—	2	1	no	—
227	C₂×C₅×D₄	—	3	2	no	—
228	C₂×C₅×D₄	—	6	4	no	—
229	C₂×C₅×D₄	—	6	4	no	—
230	C₂×C₅×D₄	—	6	2	no	—
231	C₂×C₅×D₄	—	6	2	no	—
232	C₂×C₅×D₄	—	6	2	no	—
233	C₂×C₅×D₄	—	6	1	no	—
234	C₂×C₅×D₄	—	6	1	no	—
235	C₂×C₅×D₄	—	12	4	no	—
236	C₂×C₅×D₄	—	12	4	no	—
237	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
238	C₂²×C₄×C₅	—	3	1	no	—
239	C₂²×C₄×C₅	—	3	1	no	—
240	C₂²×C₄×C₅	—	3	1	no	—
241	C₂²×C₄×C₅	—	6	1	no	—
242	C₂²×C₄×C₅	—	6	1	no	—
243	C₅×SD₁₆	—	2	4	no	—
244	C₅×SD₁₆	—	6	4	no	—
245	C₅×SD₁₆	—	6	4	no	—
246	C₅×SD₁₆	—	6	4	no	—
247	C₂×C₅×C₈	—	3	2	no	—
248	C₂×C₅×C₈	—	6	4	no	—
249	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
250	C₅×C₄⋊C₄	—	2	1	no	—
251	C₅×C₄⋊C₄	—	3	1	no	—
252	C₅×C₄⋊C₄	—	6	1	no	—
253	C₅×C₄⋊C₄	—	6	1	no	—
254	C₅×C₄⋊C₄	—	6	1	no	—
255	C₅×C₄⋊C₄	—	6	1	no	—
256	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
257	C₄²×C₅	—	2	1	no	—
258	C₄²×C₅	—	3	1	no	—
259	C₄²×C₅	—	3	1	no	—
260	C₄²×C₅	—	3	1	no	—
261	C₄²×C₅	—	6	1	no	—
262	C₄²×C₅	—	6	1	no	—
263	C₄²×C₅	—	6	1	no	—
264	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
265	C₂²×SD₁₆	—	3	2	no	—
266	C₂×#127	—	3	1	no	—
267	C₂×C₄×Q₈	—	3	1	no	—
268	#460	—	3	2	no	—
269	#460	—	3	1	no	—
270	#460	—	3	1	no	—
271	#460	—	3	1	no	—
272	#460	—	3	2	no	—
273	#460	C₅×D₃	1	1	yes	characteristic, direct product factor
274	C₂×C₄⋊C₈	—	3	1	no	—
275	C₂×#102	—	3	2	no	—
276	C₂²×C₃×C₅	—	4	2	no	—
277	C₂²×C₃×C₅	—	4	2	no	—
278	C₂²×C₃×C₅	—	4	2	no	—
279	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₅×D₃	—	4	2	no	—
281	C₂×C₅×D₃	—	4	2	no	—
282	C₂×C₅×D₃	—	4	2	no	—
283	C₂×C₅×D₃	—	8	8	no	—
284	C₂×C₅×D₃	#121	1	2	yes	—
285	C₂×C₅×D₃	C₂×SD₁₆	1	2	yes	—
286	C₂×C₅×D₃	AGL(1,ℤ/8)	1	2	yes	—
287	C₃×C₄×C₅	—	2	2	no	—
288	C₃×C₄×C₅	—	2	1	no	—
289	C₃×C₄×C₅	—	4	1	no	—
290	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	complemented
291	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
292	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
293	C₅×Dic₃	—	2	2	no	—
294	C₅×Dic₃	—	2	1	no	—
295	C₅×Dic₃	—	4	1	no	—
296	C₅×Dic₃	#121	1	2	yes	—
297	C₅×Dic₃	C₂×SD₁₆	1	2	yes	complemented
298	C₂³×D₃	—	2	2	no	—
299	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
300	C₂×C₃×D₄	—	2	1	no	—
301	C₂×C₃×D₄	—	2	1	no	—
302	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
303	C₂×#67	—	2	2	no	—
304	C₂×#67	—	2	2	no	—
305	C₂×#67	—	2	2	no	—
306	D₃×Q₈	—	2	2	no	—
307	D₃×Q₈	C₅×D₄	1	4	yes	complemented
308	D₃×D₄	—	2	4	no	—
309	D₃×D₄	—	2	4	no	—
310	D₃×D₄	—	4	4	no	—
311	D₃×D₄	—	4	4	no	—
312	C₂×D₁₂	—	2	1	no	—
313	C₂×D₁₂	—	2	1	no	—
314	C₂×D₁₂	C₂³×C₅	1	2	yes	—
315	C₂×C₄×D₃	—	2	1	no	—
316	C₂×C₄×D₃	—	2	1	no	—
317	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
318	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
319	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
320	C₂×Dic₆	—	2	1	no	—
321	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
322	C₃×SD₁₆	—	2	4	no	—
323	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
324	C₃×C₄⋊C₄	—	2	1	no	—
325	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
326	C₃×C₄²	—	2	1	no	—
327	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
328	#215	—	2	4	no	—
329	#214	—	2	4	no	—
330	C₄⋊Dic₃	—	2	1	no	—
331	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
332	Dic₃⋊C₄	—	2	1	no	—
333	Dic₃⋊C₄	—	2	1	no	—
334	Dic₃⋊C₄	—	2	1	no	—
335	C₄×Dic₃	—	2	1	no	—
336	C₄×Dic₃	—	2	1	no	—
337	C₄×Dic₃	—	2	1	no	—
338	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
339	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
340	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
341	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
342	#204	—	2	4	no	—
343	D₃×C₈	—	2	4	no	—
344	C₂³×C₅	—	2	2	no	—
345	C₂³×C₅	—	3	1	no	—
346	C₂³×C₅	—	6	2	no	—
347	C₂³×C₅	—	12	4	no	—
348	C₂³×C₅	—	12	4	no	—
349	C₂³×C₅	—	12	4	no	—
350	C₅×Q₈	—	2	1	no	—
351	C₅×Q₈	—	3	2	no	—
352	C₅×Q₈	—	6	4	no	—
353	C₅×Q₈	—	6	1	no	—
354	C₅×Q₈	D₃×D₄	1	2	yes	complemented
355	C₅×D₄	—	2	2	no	—
356	C₅×D₄	—	2	2	no	—
357	C₅×D₄	—	4	2	no	—
358	C₅×D₄	—	4	2	no	—
359	C₅×D₄	—	6	2	no	—
360	C₅×D₄	—	6	2	no	—
361	C₅×D₄	—	12	2	no	—
362	C₅×D₄	—	12	4	no	—
363	C₅×D₄	—	12	4	no	—
364	C₅×D₄	—	12	4	no	—
365	C₅×D₄	—	12	2	no	—
366	C₂×C₄×C₅	—	2	1	no	—
367	C₂×C₄×C₅	—	2	1	no	—
368	C₂×C₄×C₅	—	3	1	no	—
369	C₂×C₄×C₅	—	3	1	no	—
370	C₂×C₄×C₅	—	3	4	no	—
371	C₂×C₄×C₅	—	3	2	no	—
372	C₂×C₄×C₅	—	3	2	no	—
373	C₂×C₄×C₅	—	3	1	no	—
374	C₂×C₄×C₅	—	6	2	no	—
375	C₂×C₄×C₅	—	6	4	no	—
376	C₂×C₄×C₅	—	6	1	no	—
377	C₂×C₄×C₅	—	6	1	no	—
378	C₂×C₄×C₅	—	12	2	no	—
379	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
380	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
381	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
382	C₅×C₈	—	2	2	no	—
383	C₅×C₈	—	6	2	no	—
384	C₂²×Q₈	—	3	1	no	—
385	C₂²×D₄	—	3	2	no	—
386	C₂²×D₄	—	6	1	no	—
387	C₂²×D₄	—	6	1	no	—
388	C₂×SD₁₆	—	3	2	no	—
389	C₂×SD₁₆	—	3	2	no	—
390	C₂×SD₁₆	—	3	2	no	—
391	C₂×SD₁₆	—	6	8	no	—
392	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	complemented
393	C₂²×C₈	—	3	2	no	—
394	#127	—	3	2	no	—
395	#127	—	3	1	no	—
396	#127	—	6	1	no	—
397	#127	—	6	1	no	—
398	#127	C₂×C₅×D₃	1	1	yes	characteristic
399	C₄×Q₈	—	3	1	no	—
400	C₄×Q₈	—	3	1	no	—
401	C₄×Q₈	—	3	1	no	—
402	C₄×Q₈	—	6	1	no	—
403	C₄×Q₈	—	6	1	no	—
404	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
405	C₂×C₄⋊C₄	—	3	1	no	—
406	C₂×C₄⋊C₄	—	6	1	no	—
407	C₂×C₄²	—	3	1	no	—
408	C₂×C₄²	—	6	1	no	—
409	C₄⋊C₈	—	3	2	no	—
410	C₄⋊C₈	—	3	1	no	—
411	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
412	#102	—	3	2	no	—
413	#102	—	3	2	no	—
414	#102	—	3	2	no	—
415	#102	C₂×C₅×D₃	1	2	yes	complemented
416	C₂×C₃×C₅	—	8	2	no	—
417	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
418	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
419	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
420	C₅×D₃	—	8	2	no	—
421	C₅×D₃	#460	1	4	yes	direct product factor
422	C₂³×C₃	—	2	2	no	—
423	C₂²×D₃	—	2	2	no	—
424	C₂²×D₃	—	4	4	no	—
425	C₂²×D₃	—	4	4	no	—
426	C₂²×D₃	—	4	4	no	—
427	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
428	C₃×Q₈	—	2	1	no	—
429	C₃×Q₈	C₂×C₅×D₄	1	2	yes	complemented
430	C₃×D₄	—	2	2	no	—
431	C₃×D₄	—	2	2	no	—
432	C₃×D₄	—	4	2	no	—
433	C₃×D₄	—	4	2	no	—
434	C₂×C₃×C₄	—	2	1	no	—
435	C₂×C₃×C₄	—	2	1	no	—
436	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
437	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
438	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
439	#67	—	4	4	no	—
440	#67	—	4	4	no	—
441	#67	—	4	4	no	—
442	C₂×Dic₃	—	2	1	no	—
443	C₂×Dic₃	—	2	1	no	—
444	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
445	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
446	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
447	D₁₂	—	2	2	no	—
448	D₁₂	—	2	2	no	—
449	D₁₂	—	4	2	no	—
450	D₁₂	—	4	2	no	—
451	C₄×D₃	—	2	4	no	—
452	C₄×D₃	—	2	2	no	—
453	C₄×D₃	—	4	2	no	—
454	C₄×D₃	C₅×SD₁₆	1	4	yes	complemented
455	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
456	C₄×D₃	C₅×#41	1	2	yes	—
457	Dic₆	—	2	1	no	—
458	Dic₆	—	2	4	no	—
459	Dic₆	C₂×C₅×D₄	1	2	yes	complemented
460	C₃×C₈	—	2	2	no	—
461	C₃⋊C₈	—	2	2	no	—
462	C₂²×C₅	—	3	2	no	—
463	C₂²×C₅	—	3	2	no	—
464	C₂²×C₅	—	3	2	no	—
465	C₂²×C₅	—	4	2	no	—
466	C₂²×C₅	—	4	2	no	—
467	C₂²×C₅	—	4	2	no	—
468	C₂²×C₅	—	12	2	no	—
469	C₂²×C₅	—	12	2	no	—
470	C₂²×C₅	—	12	2	no	—
471	C₂²×C₅	—	24	8	no	—
472	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
473	C₄×C₅	—	2	1	no	—
474	C₄×C₅	—	2	2	no	—
475	C₄×C₅	—	3	2	no	—
476	C₄×C₅	—	3	2	no	—
477	C₄×C₅	—	4	1	no	—
478	C₄×C₅	—	6	1	no	—
479	C₄×C₅	—	6	2	no	—
480	C₄×C₅	—	12	1	no	—
481	C₄×C₅	D₃×SD₁₆	1	2	yes	complemented
482	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
483	C₄×C₅	D₃×#41	1	1	yes	characteristic
484	C₂⁴	—	6	2	no	—
485	C₂×Q₈	—	3	4	no	—
486	C₂×Q₈	—	3	1	no	—
487	C₂×Q₈	—	6	1	no	—
488	C₂×Q₈	—	6	2	no	—
489	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	3	2	no	—
493	C₂×D₄	—	6	4	no	—
494	C₂×D₄	—	6	4	no	—
495	C₂×D₄	—	6	2	no	—
496	C₂×D₄	—	6	2	no	—
497	C₂×D₄	—	6	2	no	—
498	C₂×D₄	—	6	1	no	—
499	C₂×D₄	—	6	1	no	—
500	C₂×D₄	—	12	4	no	—
501	C₂×D₄	—	12	4	no	—
502	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
503	C₂²×C₄	—	3	1	no	—
504	C₂²×C₄	—	3	1	no	—
505	C₂²×C₄	—	3	1	no	—
506	C₂²×C₄	—	6	1	no	—
507	C₂²×C₄	—	6	1	no	—
508	SD₁₆	—	2	4	no	—
509	SD₁₆	—	6	4	no	—
510	SD₁₆	—	6	4	no	—
511	SD₁₆	—	6	4	no	—
512	C₂×C₈	—	3	2	no	—
513	C₂×C₈	—	6	4	no	—
514	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	3	1	no	—
517	C₄⋊C₄	—	6	1	no	—
518	C₄⋊C₄	—	6	1	no	—
519	C₄⋊C₄	—	6	1	no	—
520	C₄⋊C₄	—	6	1	no	—
521	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
522	C₄²	—	2	1	no	—
523	C₄²	—	3	1	no	—
524	C₄²	—	3	1	no	—
525	C₄²	—	3	1	no	—
526	C₄²	—	6	1	no	—
527	C₄²	—	6	1	no	—
528	C₄²	—	6	1	no	—
529	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
530	C₃×C₅	C₂×#460	1	1	yes	characteristic, complemented, Hall
531	C₂²×C₃	—	4	2	no	—
532	C₂²×C₃	—	4	2	no	—
533	C₂²×C₃	—	4	2	no	—
534	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
535	C₂×D₃	—	4	2	no	—
536	C₂×D₃	—	4	2	no	—
537	C₂×D₃	—	4	2	no	—
538	C₂×D₃	—	8	8	no	—
539	C₂×D₃	C₅×#121	1	2	yes	—
540	C₂×D₃	C₂×C₅×SD₁₆	1	2	yes	—
541	C₂×D₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
542	C₃×C₄	—	2	2	no	—
543	C₃×C₄	—	2	1	no	—
544	C₃×C₄	—	4	1	no	—
545	C₃×C₄	C₂×C₅×SD₁₆	1	2	yes	complemented
546	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
547	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
548	Dic₃	—	2	2	no	—
549	Dic₃	—	2	1	no	—
550	Dic₃	—	4	1	no	—
551	Dic₃	C₅×#121	1	2	yes	—
552	Dic₃	C₂×C₅×SD₁₆	1	2	yes	complemented
553	C₂×C₅	—	3	4	no	—
554	C₂×C₅	—	8	2	no	—
555	C₂×C₅	—	24	2	no	—
556	C₂×C₅	D₃×#121	1	1	yes	characteristic
557	C₂×C₅	C₂×D₃×SD₁₆	1	1	yes	characteristic
558	C₂×C₅	D₃×AGL(1,ℤ/8)	1	1	yes	characteristic
559	C₂³	—	2	2	no	—
560	C₂³	—	3	1	no	—
561	C₂³	—	6	2	no	—
562	C₂³	—	12	4	no	—
563	C₂³	—	12	4	no	—
564	C₂³	—	12	4	no	—
565	Q₈	—	2	1	no	—
566	Q₈	—	3	2	no	—
567	Q₈	—	6	4	no	—
568	Q₈	—	6	1	no	—
569	Q₈	C₅×D₃×D₄	1	2	yes	complemented
570	D₄	—	2	2	no	—
571	D₄	—	2	2	no	—
572	D₄	—	4	2	no	—
573	D₄	—	4	2	no	—
574	D₄	—	6	2	no	—
575	D₄	—	6	2	no	—
576	D₄	—	12	2	no	—
577	D₄	—	12	4	no	—
578	D₄	—	12	4	no	—
579	D₄	—	12	4	no	—
580	D₄	—	12	2	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	3	1	no	—
584	C₂×C₄	—	3	1	no	—
585	C₂×C₄	—	3	4	no	—
586	C₂×C₄	—	3	2	no	—
587	C₂×C₄	—	3	2	no	—
588	C₂×C₄	—	3	1	no	—
589	C₂×C₄	—	6	2	no	—
590	C₂×C₄	—	6	4	no	—
591	C₂×C₄	—	6	1	no	—
592	C₂×C₄	—	6	1	no	—
593	C₂×C₄	—	12	2	no	—
594	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
595	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
596	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
597	C₈	—	2	2	no	—
598	C₈	—	6	2	no	—
599	C₂×C₃	—	8	2	no	—
600	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
601	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
602	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
603	D₃	—	8	2	no	—
604	D₃	C₅×#460	1	4	yes	direct product factor
605	C₅	D₃×#460	1	1	yes	characteristic, direct product factor, Sylow
606	C₂²	—	3	2	no	—
607	C₂²	—	3	2	no	—
608	C₂²	—	3	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	12	2	no	—
613	C₂²	—	12	2	no	—
614	C₂²	—	12	2	no	—
615	C₂²	—	24	8	no	—
616	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	2	no	—
619	C₄	—	3	2	no	—
620	C₄	—	3	2	no	—
621	C₄	—	4	1	no	—
622	C₄	—	6	1	no	—
623	C₄	—	6	2	no	—
624	C₄	—	12	1	no	—
625	C₄	C₅×D₃×SD₁₆	1	2	yes	complemented
626	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
627	C₄	C₅×D₃×#41	1	1	yes	characteristic
628	C₃	C₂×C₅×#460	1	1	yes	characteristic, complemented, Sylow
629	C₂	—	3	4	no	—
630	C₂	—	8	2	no	—
631	C₂	—	24	2	no	—
632	C₂	C₅×D₃×#121	1	1	yes	characteristic
633	C₂	C₂×C₅×D₃×SD₁₆	1	1	yes	characteristic
634	C₂	C₅×D₃×AGL(1,ℤ/8)	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×#460	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×D₃×#127	C₂
hypercenter	C₅×#460	D₃
hypocenter	C₃	C₂×C₅×#460
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#460

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×SD₁₆	C₂	semidirect
3. C₄×C₅×D₃×Q₈	C₂	semidirect
4. C₃×C₅×#460	C₂	semidirect
5. C₅×#5163	C₂	semidirect
6. C₅×#5075	C₂	semidirect
7. C₅×#5027	C₂	semidirect
8. C₅×#4848	C₂	semidirect
9. C₅×D₃×C₄⋊C₈	C₂	semidirect
10. C₅×D₃×#102	C₂	semidirect
11. C₅×#4762	C₂	semidirect
17. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
19. C₃×C₄×C₅×Q₈	C₂²	semidirect
20. C₅×Q₈×Dic₃	C₂²	semidirect
21. C₂×C₅×#215	C₂²	semidirect
25. C₂×C₅×#214	C₂²	semidirect
27. C₂×C₅×#204	C₂²	semidirect
32. C₅×#887	C₂²	semidirect
37. C₄×C₅×Dic₆	C₂²	semidirect
38. C₃×C₅×C₄⋊C₈	C₂²	semidirect
39. C₃×C₅×#102	C₂²	semidirect
40. C₅×#832	C₂²	semidirect
41. C₅×#821	C₂²	semidirect
42. C₅×Dic₃⋊C₈	C₂²	semidirect
43. C₅×#809	C₂²	semidirect
44. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
45. D₃×#460	C₅	direct (N × H)
54. C₅×#460	D₃	direct (N × H)
66. C₅×D₃×Q₈	D₄	semidirect
103. C₂×D₃×SD₁₆	C₂×C₅	semidirect
105. C₄×D₃×Q₈	C₂×C₅	semidirect
106. C₃×#460	C₂×C₅	semidirect
107. #5163	C₂×C₅	semidirect
108. #5075	C₂×C₅	semidirect
109. #5027	C₂×C₅	semidirect
110. #4848	C₂×C₅	semidirect
111. D₃×C₄⋊C₈	C₂×C₅	semidirect
112. D₃×#102	C₂×C₅	semidirect
113. #4762	C₂×C₅	semidirect
122. C₂×C₅×SD₁₆	C₂×D₃	semidirect
134. C₄×C₅×Q₈	C₂×D₃	semidirect
141. C₅×C₄⋊C₈	C₂×D₃	semidirect
145. C₅×#102	C₂×D₃	semidirect
154. C₃×C₅×Q₈	C₂×D₄	semidirect
179. C₄×C₅×D₃	SD₁₆	semidirect
184. C₅×Dic₆	C₂×D₄	semidirect
191. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
193. C₃×C₄×Q₈	C₂²×C₅	semidirect
194. Q₈×Dic₃	C₂²×C₅	semidirect
195. C₂×#215	C₂²×C₅	semidirect
199. C₂×#214	C₂²×C₅	semidirect
201. C₂×#204	C₂²×C₅	semidirect
206. #887	C₂²×C₅	semidirect
211. C₄×Dic₆	C₂²×C₅	semidirect
212. C₃×C₄⋊C₈	C₂²×C₅	semidirect
213. C₃×#102	C₂²×C₅	semidirect
214. #832	C₂²×C₅	semidirect
215. #821	C₂²×C₅	semidirect
216. Dic₃⋊C₈	C₂²×C₅	semidirect
217. #809	C₂²×C₅	semidirect
218. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
273. #460	C₅×D₃	direct (N × H)
290. C₃×C₄×C₅	C₂×SD₁₆	semidirect
297. C₅×Dic₃	C₂×SD₁₆	semidirect
307. D₃×Q₈	C₅×D₄	semidirect
354. C₅×Q₈	D₃×D₄	semidirect
392. C₂×SD₁₆	C₂×C₅×D₃	semidirect
404. C₄×Q₈	C₂×C₅×D₃	semidirect
411. C₄⋊C₈	C₂×C₅×D₃	semidirect
415. #102	C₂×C₅×D₃	semidirect
421. C₅×D₃	#460	direct (N × H)
429. C₃×Q₈	C₂×C₅×D₄	semidirect
454. C₄×D₃	C₅×SD₁₆	semidirect
459. Dic₆	C₂×C₅×D₄	semidirect
481. C₄×C₅	D₃×SD₁₆	semidirect
530. C₃×C₅	C₂×#460	semidirect
545. C₃×C₄	C₂×C₅×SD₁₆	semidirect
552. Dic₃	C₂×C₅×SD₁₆	semidirect
569. Q₈	C₅×D₃×D₄	semidirect
604. D₃	C₅×#460	direct (N × H)
605. C₅	D₃×#460	direct (N × H)
625. C₄	C₅×D₃×SD₁₆	semidirect
628. C₃	C₂×C₅×#460	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
C₅×D₃×#127	2
C₄×C₅×D₃×Q₈	2
C₃×C₅×#460	2
C₅×#5163	2
C₅×#5075	2
C₅×#5027	2
C₅×#4848	2
C₅×D₃×C₄⋊C₈	2
C₅×D₃×#102	2
C₅×#4762	2
C₂×C₅×#460	3
D₃×#460	5

Subgroups — C5×D3×#460 #14426004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#460 #14426004