Subgroups — C₃×D₅×#459 #14425804

Order 1920.

1296 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×D₈	C₂	1	2	yes	maximal, complemented
2	C₃×D₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#459	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65439	C₂	1	2	yes	maximal, complemented
6	C₃×#65361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65304	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65132	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65075	C₂	1	2	yes	maximal, complemented
11	C₃×D₅×#102	C₂	1	2	yes	maximal, complemented
12	D₅×#459	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×D₄×D₅	—	2	1	no	—
14	C₂×C₃×D₄×D₅	—	2	1	no	—
15	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
16	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₄×D₅	—	2	1	no	—
18	C₂×C₃×C₅×D₈	C₂²	1	2	yes	complemented
19	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
21	C₃×#4086	—	2	1	no	—
22	C₃×#4086	—	2	1	no	—
23	C₃×#4086	C₂²	1	2	yes	complemented
24	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×#686	C₂²	1	2	yes	complemented
26	C₂×C₃×#686	C₂²	1	2	yes	complemented
27	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
28	C₃×D₅×D₈	—	2	8	no	—
29	C₂×C₃×D₄₀	C₂²	1	2	yes	complemented
30	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
31	C₃×#4039	C₂²	1	1	yes	characteristic, complemented
32	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₃×#4027	—	2	1	no	—
34	C₃×D₅×C₂²⋊C₄	—	2	1	no	—
35	C₃×#4020	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
38	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₅×#102	C₂²	1	2	yes	complemented
40	C₃×#3964	C₂²	1	2	yes	complemented
41	C₃×#3953	C₂²	1	2	yes	complemented
42	C₃×#3946	C₂²	1	2	yes	complemented
43	C₃×#3941	C₂²	1	2	yes	complemented
44	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₃×#459	—	5	1	no	maximal, Hall
46	C₂×D₅×D₈	C₂×C₃	1	2	yes	complemented
47	D₅×#127	C₂×C₃	1	1	yes	characteristic, complemented
48	C₄×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#459	C₂×C₃	1	1	yes	characteristic, complemented
50	#65439	C₂×C₃	1	2	yes	complemented
51	#65361	C₂×C₃	1	1	yes	characteristic, complemented
52	#65304	C₂×C₃	1	1	yes	characteristic, complemented
53	#65132	C₂×C₃	1	1	yes	characteristic, complemented
54	D₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
55	#65075	C₂×C₃	1	2	yes	complemented
56	D₅×#102	C₂×C₃	1	2	yes	complemented
57	C₂³×C₃×D₅	—	2	1	no	—
58	C₂³×C₃×D₅	—	2	2	no	—
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×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	—	2	1	no	—
64	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
65	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
66	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
67	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
68	C₂²×C₃×Dic₅	—	2	1	no	—
69	C₃×D₄×D₅	—	2	4	no	—
70	C₃×D₄×D₅	—	2	2	no	—
71	C₃×D₄×D₅	—	2	4	no	—
72	C₃×D₄×D₅	—	4	4	no	—
73	C₃×D₄×D₅	—	4	4	no	—
74	C₃×D₄×D₅	D₄	1	4	yes	complemented
75	C₂×C₃×D₂₀	—	2	1	no	—
76	C₂×C₃×D₂₀	—	2	1	no	—
77	C₂×C₃×D₂₀	C₂³	1	2	yes	—
78	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₄×D₅	—	2	1	no	—
80	C₂×C₃×C₄×D₅	—	2	1	no	—
81	C₂×C₃×C₄×D₅	—	2	1	no	—
82	C₂×C₃×C₄×D₅	—	4	4	no	—
83	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
84	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
85	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
86	C₃×C₅×D₈	—	2	4	no	—
87	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
88	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
90	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
91	C₃×C₂²⋊Dic₅	—	2	1	no	—
92	C₃×#686	—	2	4	no	—
93	C₃×#686	—	2	4	no	—
94	C₃×#685	—	2	1	no	—
95	C₃×#685	—	2	1	no	—
96	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
97	C₃×#683	—	2	1	no	—
98	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
99	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
100	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
101	C₂×C₃×#168	C₂³	1	2	yes	—
102	C₃×D₄₀	—	2	4	no	—
103	C₃×C₈×D₅	—	2	4	no	—
104	C₂²×C₃×D₈	—	5	2	no	—
105	C₂×C₃×#127	—	5	1	no	—
106	C₂×C₃×C₄×D₄	—	5	1	no	—
107	C₃×#459	—	5	2	no	—
108	C₃×#459	—	5	1	no	—
109	C₃×#459	—	5	1	no	—
110	C₃×#459	—	5	1	no	—
111	C₃×#459	—	5	2	no	—
112	C₃×#459	D₅	1	1	yes	characteristic, direct product factor
113	C₂×C₃×C₄⋊C₈	—	5	1	no	—
114	C₂×C₃×#102	—	5	2	no	—
115	C₂×D₄×D₅	—	2	1	no	—
116	C₂×D₄×D₅	—	2	1	no	—
117	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
118	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
119	C₂²×C₄×D₅	—	2	1	no	—
120	C₂×C₅×D₈	C₂²×C₃	1	2	yes	complemented
121	C₅×#127	C₂²×C₃	1	1	yes	characteristic, complemented
122	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
123	#4086	—	2	1	no	—
124	#4086	—	2	1	no	—
125	#4086	C₂²×C₃	1	2	yes	complemented
126	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₂×#686	C₂²×C₃	1	2	yes	complemented
128	C₂×#686	C₂²×C₃	1	2	yes	complemented
129	C₄×C₂²⋊D₅	—	2	1	no	—
130	D₅×D₈	—	2	8	no	—
131	C₂×D₄₀	C₂²×C₃	1	2	yes	complemented
132	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
133	#4039	C₂²×C₃	1	1	yes	characteristic, complemented
134	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
135	#4027	—	2	1	no	—
136	D₅×C₂²⋊C₄	—	2	1	no	—
137	#4020	C₂²×C₃	1	1	yes	characteristic, complemented
138	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
139	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
140	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
141	C₅×#102	C₂²×C₃	1	2	yes	complemented
142	#3964	C₂²×C₃	1	2	yes	complemented
143	#3953	C₂²×C₃	1	2	yes	complemented
144	#3946	C₂²×C₃	1	2	yes	complemented
145	#3941	C₂²×C₃	1	2	yes	complemented
146	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic, complemented
147	C₂×#459	—	5	1	no	Sylow
148	C₂³×C₃×C₅	—	2	1	no	—
149	C₂³×C₃×C₅	—	2	2	no	—
150	C₂²×C₃×D₅	—	2	1	no	—
151	C₂²×C₃×D₅	—	2	4	no	—
152	C₂²×C₃×D₅	—	2	2	no	—
153	C₂²×C₃×D₅	—	4	2	no	—
154	C₂²×C₃×D₅	—	4	2	no	—
155	C₂²×C₃×D₅	—	4	4	no	—
156	C₂²×C₃×D₅	—	4	4	no	—
157	C₂²×C₃×D₅	—	4	4	no	—
158	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
159	C₃×C₅×D₄	—	2	2	no	—
160	C₃×C₅×D₄	—	2	1	no	—
161	C₃×C₅×D₄	—	2	2	no	—
162	C₃×C₅×D₄	—	4	2	no	—
163	C₃×C₅×D₄	—	4	2	no	—
164	C₃×C₅×D₄	C₂×D₄	1	2	yes	complemented
165	C₂×C₃×C₄×C₅	—	2	1	no	—
166	C₂×C₃×C₄×C₅	—	4	2	no	—
167	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
168	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
169	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
170	C₃×C₂²⋊D₅	—	2	4	no	—
171	C₃×C₂²⋊D₅	—	4	4	no	—
172	C₃×C₂²⋊D₅	—	4	4	no	—
173	C₃×C₂²⋊D₅	—	4	4	no	—
174	C₂×C₃×Dic₅	—	2	1	no	—
175	C₂×C₃×Dic₅	—	4	2	no	—
176	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
177	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
178	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
179	C₃×D₂₀	—	2	2	no	—
180	C₃×D₂₀	—	2	1	no	—
181	C₃×D₂₀	—	2	2	no	—
182	C₃×D₂₀	—	4	2	no	—
183	C₃×D₂₀	—	4	2	no	—
184	C₃×D₂₀	C₂×D₄	1	2	yes	complemented
185	C₃×C₄×D₅	—	2	2	no	—
186	C₃×C₄×D₅	—	4	2	no	—
187	C₃×C₄×D₅	—	4	2	no	—
188	C₃×C₄×D₅	—	4	2	no	—
189	C₃×C₄×D₅	D₈	1	4	yes	complemented
190	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
191	C₃×C₄×D₅	#41	1	2	yes	—
192	C₃×C₅×C₈	—	2	2	no	—
193	C₃×#168	—	2	2	no	—
194	C₂²×C₃×D₄	—	5	1	no	—
195	C₂²×C₃×D₄	—	5	2	no	—
196	C₂²×C₃×D₄	—	10	1	no	—
197	C₂²×C₃×D₄	—	10	1	no	—
198	C₂³×C₃×C₄	—	10	1	no	—
199	C₂×C₃×D₈	—	5	2	no	—
200	C₂×C₃×D₈	—	5	2	no	—
201	C₂×C₃×D₈	—	5	2	no	—
202	C₂×C₃×D₈	—	10	8	no	—
203	C₂×C₃×D₈	C₂×D₅	1	2	yes	complemented
204	C₂²×C₃×C₈	—	5	2	no	—
205	C₃×#127	—	5	2	no	—
206	C₃×#127	—	5	1	no	—
207	C₃×#127	—	10	1	no	—
208	C₃×#127	—	10	1	no	—
209	C₃×#127	C₂×D₅	1	1	yes	characteristic, complemented
210	C₃×C₄×D₄	—	5	1	no	—
211	C₃×C₄×D₄	—	5	1	no	—
212	C₃×C₄×D₄	—	5	1	no	—
213	C₃×C₄×D₄	—	10	1	no	—
214	C₃×C₄×D₄	—	10	1	no	—
215	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
216	C₂×C₃×C₄⋊C₄	—	5	1	no	—
217	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
218	C₂×C₃×C₄²	—	5	1	no	—
219	C₃×C₄⋊C₈	—	5	2	no	—
220	C₃×C₄⋊C₈	—	5	1	no	—
221	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
222	C₃×#102	—	5	2	no	—
223	C₃×#102	—	5	2	no	—
224	C₃×#102	—	5	2	no	—
225	C₃×#102	C₂×D₅	1	2	yes	complemented
226	C₂³×D₅	—	2	1	no	—
227	C₂³×D₅	—	2	2	no	—
228	C₂×C₅×D₄	—	2	1	no	—
229	C₂×C₅×D₄	—	2	1	no	—
230	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
231	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
232	C₂²×C₄×C₅	—	2	1	no	—
233	C₂×C₂²⋊D₅	—	2	1	no	—
234	C₂×C₂²⋊D₅	—	2	2	no	—
235	C₂×C₂²⋊D₅	—	2	2	no	—
236	C₂×C₂²⋊D₅	—	2	2	no	—
237	C₂²×Dic₅	—	2	1	no	—
238	D₄×D₅	—	2	4	no	—
239	D₄×D₅	—	2	2	no	—
240	D₄×D₅	—	2	4	no	—
241	D₄×D₅	—	4	4	no	—
242	D₄×D₅	—	4	4	no	—
243	D₄×D₅	C₃×D₄	1	4	yes	complemented
244	C₂×D₂₀	—	2	1	no	—
245	C₂×D₂₀	—	2	1	no	—
246	C₂×D₂₀	C₂³×C₃	1	2	yes	—
247	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
248	C₂×C₄×D₅	—	2	1	no	—
249	C₂×C₄×D₅	—	2	1	no	—
250	C₂×C₄×D₅	—	2	1	no	—
251	C₂×C₄×D₅	—	4	4	no	—
252	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
253	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
254	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
255	C₅×D₈	—	2	4	no	—
256	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
257	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
258	C₅×C₂²⋊C₄	—	2	1	no	—
259	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
260	C₂²⋊Dic₅	—	2	1	no	—
261	#686	—	2	4	no	—
262	#686	—	2	4	no	—
263	#685	—	2	1	no	—
264	#685	—	2	1	no	—
265	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
266	#683	—	2	1	no	—
267	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
268	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
269	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
270	C₂×#168	C₂³×C₃	1	2	yes	—
271	D₄₀	—	2	4	no	—
272	C₈×D₅	—	2	4	no	—
273	C₂²×D₈	—	5	2	no	—
274	C₂×#127	—	5	1	no	—
275	C₂×C₄×D₄	—	5	1	no	—
276	#459	—	5	2	no	—
277	#459	—	5	1	no	—
278	#459	—	5	1	no	—
279	#459	—	5	1	no	—
280	#459	—	5	2	no	—
281	#459	C₃×D₅	1	1	yes	characteristic, direct product factor
282	C₂×C₄⋊C₈	—	5	1	no	—
283	C₂×#102	—	5	2	no	—
284	C₂²×C₃×C₅	—	2	2	no	—
285	C₂²×C₃×C₅	—	4	1	no	—
286	C₂²×C₃×C₅	—	4	1	no	—
287	C₂²×C₃×C₅	—	4	2	no	—
288	C₂²×C₃×C₅	—	4	2	no	—
289	C₂²×C₃×C₅	—	4	2	no	—
290	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₃×D₅	—	2	2	no	—
292	C₂×C₃×D₅	—	4	1	no	—
293	C₂×C₃×D₅	—	4	1	no	—
294	C₂×C₃×D₅	—	4	8	no	—
295	C₂×C₃×D₅	—	4	2	no	—
296	C₂×C₃×D₅	—	4	2	no	—
297	C₂×C₃×D₅	—	4	2	no	—
298	C₂×C₃×D₅	—	8	8	no	—
299	C₂×C₃×D₅	#121	1	2	yes	—
300	C₂×C₃×D₅	C₂×D₈	1	2	yes	—
301	C₂×C₃×D₅	AGL(1,ℤ/8)	1	2	yes	—
302	C₃×C₄×C₅	—	2	1	no	—
303	C₃×C₄×C₅	—	4	1	no	—
304	C₃×C₄×C₅	C₂×D₈	1	2	yes	complemented
305	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
306	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
307	C₃×Dic₅	—	2	1	no	—
308	C₃×Dic₅	—	4	1	no	—
309	C₃×Dic₅	#121	1	2	yes	—
310	C₃×Dic₅	C₂×D₈	1	2	yes	complemented
311	C₂⁴×C₃	—	10	1	no	—
312	C₂⁴×C₃	—	10	2	no	—
313	C₂×C₃×D₄	—	2	1	no	—
314	C₂×C₃×D₄	—	2	1	no	—
315	C₂×C₃×D₄	—	5	4	no	—
316	C₂×C₃×D₄	—	5	1	no	—
317	C₂×C₃×D₄	—	5	2	no	—
318	C₂×C₃×D₄	—	10	2	no	—
319	C₂×C₃×D₄	—	10	4	no	—
320	C₂×C₃×D₄	—	10	4	no	—
321	C₂×C₃×D₄	—	10	1	no	—
322	C₂×C₃×D₄	—	10	2	no	—
323	C₂×C₃×D₄	—	10	2	no	—
324	C₂×C₃×D₄	—	10	2	no	—
325	C₂×C₃×D₄	—	10	1	no	—
326	C₂×C₃×D₄	—	10	1	no	—
327	C₂×C₃×D₄	—	20	4	no	—
328	C₂×C₃×D₄	—	20	4	no	—
329	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
330	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
331	C₂²×C₃×C₄	—	2	1	no	—
332	C₂²×C₃×C₄	—	5	1	no	—
333	C₂²×C₃×C₄	—	5	1	no	—
334	C₂²×C₃×C₄	—	5	1	no	—
335	C₂²×C₃×C₄	—	10	1	no	—
336	C₂²×C₃×C₄	—	10	1	no	—
337	C₂²×C₃×C₄	—	10	1	no	—
338	C₂²×C₃×C₄	—	10	1	no	—
339	C₂²×C₃×C₄	—	20	4	no	—
340	C₃×D₈	—	2	4	no	—
341	C₃×D₈	—	10	4	no	—
342	C₃×D₈	—	10	4	no	—
343	C₃×D₈	—	10	4	no	—
344	C₂×C₃×C₈	—	5	2	no	—
345	C₂×C₃×C₈	—	10	4	no	—
346	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
347	C₃×C₄⋊C₄	—	5	1	no	—
348	C₃×C₄⋊C₄	—	10	1	no	—
349	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
350	C₃×C₂²⋊C₄	—	2	1	no	—
351	C₃×C₂²⋊C₄	—	10	1	no	—
352	C₃×C₂²⋊C₄	—	10	1	no	—
353	C₃×C₂²⋊C₄	—	10	1	no	—
354	C₃×C₄²	—	5	1	no	—
355	C₃×C₄²	—	5	1	no	—
356	C₃×C₄²	—	5	1	no	—
357	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
358	C₂³×C₅	—	2	1	no	—
359	C₂³×C₅	—	2	2	no	—
360	C₂²×D₅	—	2	1	no	—
361	C₂²×D₅	—	2	4	no	—
362	C₂²×D₅	—	2	2	no	—
363	C₂²×D₅	—	4	2	no	—
364	C₂²×D₅	—	4	2	no	—
365	C₂²×D₅	—	4	4	no	—
366	C₂²×D₅	—	4	4	no	—
367	C₂²×D₅	—	4	4	no	—
368	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
369	C₅×D₄	—	2	2	no	—
370	C₅×D₄	—	2	1	no	—
371	C₅×D₄	—	2	2	no	—
372	C₅×D₄	—	4	2	no	—
373	C₅×D₄	—	4	2	no	—
374	C₅×D₄	C₂×C₃×D₄	1	2	yes	complemented
375	C₂×C₄×C₅	—	2	1	no	—
376	C₂×C₄×C₅	—	4	2	no	—
377	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
378	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
379	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
380	C₂²⋊D₅	—	2	4	no	—
381	C₂²⋊D₅	—	4	4	no	—
382	C₂²⋊D₅	—	4	4	no	—
383	C₂²⋊D₅	—	4	4	no	—
384	C₂×Dic₅	—	2	1	no	—
385	C₂×Dic₅	—	4	2	no	—
386	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
387	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
388	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
389	D₂₀	—	2	2	no	—
390	D₂₀	—	2	1	no	—
391	D₂₀	—	2	2	no	—
392	D₂₀	—	4	2	no	—
393	D₂₀	—	4	2	no	—
394	D₂₀	C₂×C₃×D₄	1	2	yes	complemented
395	C₄×D₅	—	2	2	no	—
396	C₄×D₅	—	4	2	no	—
397	C₄×D₅	—	4	2	no	—
398	C₄×D₅	—	4	2	no	—
399	C₄×D₅	C₃×D₈	1	4	yes	complemented
400	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
401	C₄×D₅	C₃×#41	1	2	yes	—
402	C₅×C₈	—	2	2	no	—
403	#168	—	2	2	no	—
404	C₂²×D₄	—	5	1	no	—
405	C₂²×D₄	—	5	2	no	—
406	C₂²×D₄	—	10	1	no	—
407	C₂²×D₄	—	10	1	no	—
408	C₂³×C₄	—	10	1	no	—
409	C₂×D₈	—	5	2	no	—
410	C₂×D₈	—	5	2	no	—
411	C₂×D₈	—	5	2	no	—
412	C₂×D₈	—	10	8	no	—
413	C₂×D₈	C₂×C₃×D₅	1	2	yes	complemented
414	C₂²×C₈	—	5	2	no	—
415	#127	—	5	2	no	—
416	#127	—	5	1	no	—
417	#127	—	10	1	no	—
418	#127	—	10	1	no	—
419	#127	C₂×C₃×D₅	1	1	yes	characteristic, complemented
420	C₄×D₄	—	5	1	no	—
421	C₄×D₄	—	5	1	no	—
422	C₄×D₄	—	5	1	no	—
423	C₄×D₄	—	10	1	no	—
424	C₄×D₄	—	10	1	no	—
425	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
426	C₂×C₄⋊C₄	—	5	1	no	—
427	C₂×C₂²⋊C₄	—	10	1	no	—
428	C₂×C₄²	—	5	1	no	—
429	C₄⋊C₈	—	5	2	no	—
430	C₄⋊C₈	—	5	1	no	—
431	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
432	#102	—	5	2	no	—
433	#102	—	5	2	no	—
434	#102	—	5	2	no	—
435	#102	C₂×C₃×D₅	1	2	yes	complemented
436	C₂×C₃×C₅	—	4	2	no	—
437	C₂×C₃×C₅	—	8	2	no	—
438	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
439	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
440	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
441	C₃×D₅	—	4	2	no	—
442	C₃×D₅	—	8	2	no	—
443	C₃×D₅	#459	1	4	yes	direct product factor
444	C₂³×C₃	—	2	1	no	—
445	C₂³×C₃	—	2	2	no	—
446	C₂³×C₃	—	5	1	no	—
447	C₂³×C₃	—	10	4	no	—
448	C₂³×C₃	—	10	1	no	—
449	C₂³×C₃	—	10	2	no	—
450	C₂³×C₃	—	20	2	no	—
451	C₂³×C₃	—	20	2	no	—
452	C₂³×C₃	—	20	4	no	—
453	C₂³×C₃	—	20	4	no	—
454	C₂³×C₃	—	20	4	no	—
455	C₃×D₄	—	2	2	no	—
456	C₃×D₄	—	2	1	no	—
457	C₃×D₄	—	2	2	no	—
458	C₃×D₄	—	4	2	no	—
459	C₃×D₄	—	4	2	no	—
460	C₃×D₄	—	5	2	no	—
461	C₃×D₄	—	10	4	no	—
462	C₃×D₄	—	10	2	no	—
463	C₃×D₄	—	10	1	no	—
464	C₃×D₄	—	10	2	no	—
465	C₃×D₄	—	20	2	no	—
466	C₃×D₄	—	20	4	no	—
467	C₃×D₄	—	20	4	no	—
468	C₃×D₄	—	20	4	no	—
469	C₃×D₄	—	20	2	no	—
470	C₃×D₄	D₄×D₅	1	2	yes	complemented
471	C₂×C₃×C₄	—	2	1	no	—
472	C₂×C₃×C₄	—	4	2	no	—
473	C₂×C₃×C₄	—	5	1	no	—
474	C₂×C₃×C₄	—	5	1	no	—
475	C₂×C₃×C₄	—	5	2	no	—
476	C₂×C₃×C₄	—	5	2	no	—
477	C₂×C₃×C₄	—	5	4	no	—
478	C₂×C₃×C₄	—	5	1	no	—
479	C₂×C₃×C₄	—	10	2	no	—
480	C₂×C₃×C₄	—	10	1	no	—
481	C₂×C₃×C₄	—	20	2	no	—
482	C₂×C₃×C₄	—	20	2	no	—
483	C₂×C₃×C₄	—	20	2	no	—
484	C₂×C₃×C₄	—	20	2	no	—
485	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
486	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
487	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
488	C₃×C₈	—	2	2	no	—
489	C₃×C₈	—	10	2	no	—
490	C₂²×C₅	—	2	2	no	—
491	C₂²×C₅	—	4	1	no	—
492	C₂²×C₅	—	4	1	no	—
493	C₂²×C₅	—	4	2	no	—
494	C₂²×C₅	—	4	2	no	—
495	C₂²×C₅	—	4	2	no	—
496	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
497	C₂×D₅	—	2	2	no	—
498	C₂×D₅	—	4	1	no	—
499	C₂×D₅	—	4	1	no	—
500	C₂×D₅	—	4	8	no	—
501	C₂×D₅	—	4	2	no	—
502	C₂×D₅	—	4	2	no	—
503	C₂×D₅	—	4	2	no	—
504	C₂×D₅	—	8	8	no	—
505	C₂×D₅	C₃×#121	1	2	yes	—
506	C₂×D₅	C₂×C₃×D₈	1	2	yes	—
507	C₂×D₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
508	C₄×C₅	—	2	1	no	—
509	C₄×C₅	—	4	1	no	—
510	C₄×C₅	C₂×C₃×D₈	1	2	yes	complemented
511	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
512	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
513	Dic₅	—	2	1	no	—
514	Dic₅	—	4	1	no	—
515	Dic₅	C₃×#121	1	2	yes	—
516	Dic₅	C₂×C₃×D₈	1	2	yes	complemented
517	C₂⁴	—	10	1	no	—
518	C₂⁴	—	10	2	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	5	4	no	—
522	C₂×D₄	—	5	1	no	—
523	C₂×D₄	—	5	2	no	—
524	C₂×D₄	—	10	2	no	—
525	C₂×D₄	—	10	4	no	—
526	C₂×D₄	—	10	4	no	—
527	C₂×D₄	—	10	1	no	—
528	C₂×D₄	—	10	2	no	—
529	C₂×D₄	—	10	2	no	—
530	C₂×D₄	—	10	2	no	—
531	C₂×D₄	—	10	1	no	—
532	C₂×D₄	—	10	1	no	—
533	C₂×D₄	—	20	4	no	—
534	C₂×D₄	—	20	4	no	—
535	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
536	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	5	1	no	—
539	C₂²×C₄	—	5	1	no	—
540	C₂²×C₄	—	5	1	no	—
541	C₂²×C₄	—	10	1	no	—
542	C₂²×C₄	—	10	1	no	—
543	C₂²×C₄	—	10	1	no	—
544	C₂²×C₄	—	10	1	no	—
545	C₂²×C₄	—	20	4	no	—
546	D₈	—	2	4	no	—
547	D₈	—	10	4	no	—
548	D₈	—	10	4	no	—
549	D₈	—	10	4	no	—
550	C₂×C₈	—	5	2	no	—
551	C₂×C₈	—	10	4	no	—
552	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
553	C₄⋊C₄	—	5	1	no	—
554	C₄⋊C₄	—	10	1	no	—
555	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
556	C₂²⋊C₄	—	2	1	no	—
557	C₂²⋊C₄	—	10	1	no	—
558	C₂²⋊C₄	—	10	1	no	—
559	C₂²⋊C₄	—	10	1	no	—
560	C₄²	—	5	1	no	—
561	C₄²	—	5	1	no	—
562	C₄²	—	5	1	no	—
563	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
564	C₃×C₅	C₂×#459	1	1	yes	characteristic, complemented, Hall
565	C₂²×C₃	—	2	2	no	—
566	C₂²×C₃	—	4	1	no	—
567	C₂²×C₃	—	4	1	no	—
568	C₂²×C₃	—	4	2	no	—
569	C₂²×C₃	—	4	2	no	—
570	C₂²×C₃	—	4	2	no	—
571	C₂²×C₃	—	5	2	no	—
572	C₂²×C₃	—	5	2	no	—
573	C₂²×C₃	—	5	2	no	—
574	C₂²×C₃	—	10	2	no	—
575	C₂²×C₃	—	20	8	no	—
576	C₂²×C₃	—	20	1	no	—
577	C₂²×C₃	—	20	1	no	—
578	C₂²×C₃	—	20	2	no	—
579	C₂²×C₃	—	20	2	no	—
580	C₂²×C₃	—	20	2	no	—
581	C₂²×C₃	—	40	8	no	—
582	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
583	C₃×C₄	—	2	1	no	—
584	C₃×C₄	—	4	1	no	—
585	C₃×C₄	—	5	2	no	—
586	C₃×C₄	—	5	2	no	—
587	C₃×C₄	—	10	1	no	—
588	C₃×C₄	—	20	1	no	—
589	C₃×C₄	D₅×D₈	1	2	yes	complemented
590	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
591	C₃×C₄	D₅×#41	1	1	yes	characteristic
592	C₂×C₅	—	4	2	no	—
593	C₂×C₅	—	8	2	no	—
594	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
595	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
596	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
597	D₅	—	4	2	no	—
598	D₅	—	8	2	no	—
599	D₅	C₃×#459	1	4	yes	direct product factor
600	C₂³	—	2	1	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	5	1	no	—
603	C₂³	—	10	4	no	—
604	C₂³	—	10	1	no	—
605	C₂³	—	10	2	no	—
606	C₂³	—	20	2	no	—
607	C₂³	—	20	2	no	—
608	C₂³	—	20	4	no	—
609	C₂³	—	20	4	no	—
610	C₂³	—	20	4	no	—
611	D₄	—	2	2	no	—
612	D₄	—	2	1	no	—
613	D₄	—	2	2	no	—
614	D₄	—	4	2	no	—
615	D₄	—	4	2	no	—
616	D₄	—	5	2	no	—
617	D₄	—	10	4	no	—
618	D₄	—	10	2	no	—
619	D₄	—	10	1	no	—
620	D₄	—	10	2	no	—
621	D₄	—	20	2	no	—
622	D₄	—	20	4	no	—
623	D₄	—	20	4	no	—
624	D₄	—	20	4	no	—
625	D₄	—	20	2	no	—
626	D₄	C₃×D₄×D₅	1	2	yes	complemented
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	5	1	no	—
630	C₂×C₄	—	5	1	no	—
631	C₂×C₄	—	5	2	no	—
632	C₂×C₄	—	5	2	no	—
633	C₂×C₄	—	5	4	no	—
634	C₂×C₄	—	5	1	no	—
635	C₂×C₄	—	10	2	no	—
636	C₂×C₄	—	10	1	no	—
637	C₂×C₄	—	20	2	no	—
638	C₂×C₄	—	20	2	no	—
639	C₂×C₄	—	20	2	no	—
640	C₂×C₄	—	20	2	no	—
641	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
642	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
643	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
644	C₈	—	2	2	no	—
645	C₈	—	10	2	no	—
646	C₂×C₃	—	4	2	no	—
647	C₂×C₃	—	5	4	no	—
648	C₂×C₃	—	8	2	no	—
649	C₂×C₃	—	20	2	no	—
650	C₂×C₃	—	40	2	no	—
651	C₂×C₃	D₅×#121	1	1	yes	characteristic
652	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
653	C₂×C₃	D₅×AGL(1,ℤ/8)	1	1	yes	characteristic
654	C₅	C₂×C₃×#459	1	1	yes	characteristic, complemented, Sylow
655	C₂²	—	2	2	no	—
656	C₂²	—	4	1	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	2	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	5	2	no	—
662	C₂²	—	5	2	no	—
663	C₂²	—	5	2	no	—
664	C₂²	—	10	2	no	—
665	C₂²	—	20	8	no	—
666	C₂²	—	20	1	no	—
667	C₂²	—	20	1	no	—
668	C₂²	—	20	2	no	—
669	C₂²	—	20	2	no	—
670	C₂²	—	20	2	no	—
671	C₂²	—	40	8	no	—
672	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
673	C₄	—	2	1	no	—
674	C₄	—	4	1	no	—
675	C₄	—	5	2	no	—
676	C₄	—	5	2	no	—
677	C₄	—	10	1	no	—
678	C₄	—	20	1	no	—
679	C₄	C₃×D₅×D₈	1	2	yes	complemented
680	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
681	C₄	C₃×D₅×#41	1	1	yes	characteristic
682	C₃	D₅×#459	1	1	yes	characteristic, direct product factor, Sylow
683	C₂	—	4	2	no	—
684	C₂	—	5	4	no	—
685	C₂	—	8	2	no	—
686	C₂	—	20	2	no	—
687	C₂	—	40	2	no	—
688	C₂	C₃×D₅×#121	1	1	yes	characteristic
689	C₂	C₂×C₃×D₅×D₈	1	1	yes	characteristic
690	C₂	C₃×D₅×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#459	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#459	D₅
hypocenter	C₅	C₂×C₃×#459
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#459

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₅×D₈	C₂	semidirect
2. C₃×D₅×#127	C₂	semidirect
3. C₃×C₄×D₄×D₅	C₂	semidirect
4. C₃×C₅×#459	C₂	semidirect
5. C₃×#65439	C₂	semidirect
6. C₃×#65361	C₂	semidirect
7. C₃×#65304	C₂	semidirect
8. C₃×#65132	C₂	semidirect
9. C₃×D₅×C₄⋊C₈	C₂	semidirect
10. C₃×#65075	C₂	semidirect
11. C₃×D₅×#102	C₂	semidirect
12. D₅×#459	C₃	direct (N × H)
18. C₂×C₃×C₅×D₈	C₂²	semidirect
19. C₃×C₅×#127	C₂²	semidirect
20. C₃×C₄×C₅×D₄	C₂²	semidirect
23. C₃×#4086	C₂²	semidirect
24. C₃×D₄×Dic₅	C₂²	semidirect
25. C₂×C₃×#686	C₂²	semidirect
26. C₂×C₃×#686	C₂²	semidirect
29. C₂×C₃×D₄₀	C₂²	semidirect
31. C₃×#4039	C₂²	semidirect
35. C₃×#4020	C₂²	semidirect
36. C₃×C₄×D₂₀	C₂²	semidirect
38. C₃×C₅×C₄⋊C₈	C₂²	semidirect
39. C₃×C₅×#102	C₂²	semidirect
40. C₃×#3964	C₂²	semidirect
41. C₃×#3953	C₂²	semidirect
42. C₃×#3946	C₂²	semidirect
43. C₃×#3941	C₂²	semidirect
44. C₃×C₄⋊#168	C₂²	semidirect
46. C₂×D₅×D₈	C₂×C₃	semidirect
47. D₅×#127	C₂×C₃	semidirect
48. C₄×D₄×D₅	C₂×C₃	semidirect
49. C₅×#459	C₂×C₃	semidirect
50. #65439	C₂×C₃	semidirect
51. #65361	C₂×C₃	semidirect
52. #65304	C₂×C₃	semidirect
53. #65132	C₂×C₃	semidirect
54. D₅×C₄⋊C₈	C₂×C₃	semidirect
55. #65075	C₂×C₃	semidirect
56. D₅×#102	C₂×C₃	semidirect
74. C₃×D₄×D₅	D₄	semidirect
112. C₃×#459	D₅	direct (N × H)
120. C₂×C₅×D₈	C₂²×C₃	semidirect
121. C₅×#127	C₂²×C₃	semidirect
122. C₄×C₅×D₄	C₂²×C₃	semidirect
125. #4086	C₂²×C₃	semidirect
126. D₄×Dic₅	C₂²×C₃	semidirect
127. C₂×#686	C₂²×C₃	semidirect
128. C₂×#686	C₂²×C₃	semidirect
131. C₂×D₄₀	C₂²×C₃	semidirect
133. #4039	C₂²×C₃	semidirect
137. #4020	C₂²×C₃	semidirect
138. C₄×D₂₀	C₂²×C₃	semidirect
140. C₅×C₄⋊C₈	C₂²×C₃	semidirect
141. C₅×#102	C₂²×C₃	semidirect
142. #3964	C₂²×C₃	semidirect
143. #3953	C₂²×C₃	semidirect
144. #3946	C₂²×C₃	semidirect
145. #3941	C₂²×C₃	semidirect
146. C₄⋊#168	C₂²×C₃	semidirect
164. C₃×C₅×D₄	C₂×D₄	semidirect
184. C₃×D₂₀	C₂×D₄	semidirect
189. C₃×C₄×D₅	D₈	semidirect
203. C₂×C₃×D₈	C₂×D₅	semidirect
209. C₃×#127	C₂×D₅	semidirect
215. C₃×C₄×D₄	C₂×D₅	semidirect
221. C₃×C₄⋊C₈	C₂×D₅	semidirect
225. C₃×#102	C₂×D₅	semidirect
243. D₄×D₅	C₃×D₄	semidirect
281. #459	C₃×D₅	direct (N × H)
304. C₃×C₄×C₅	C₂×D₈	semidirect
310. C₃×Dic₅	C₂×D₈	semidirect
374. C₅×D₄	C₂×C₃×D₄	semidirect
394. D₂₀	C₂×C₃×D₄	semidirect
399. C₄×D₅	C₃×D₈	semidirect
413. C₂×D₈	C₂×C₃×D₅	semidirect
419. #127	C₂×C₃×D₅	semidirect
425. C₄×D₄	C₂×C₃×D₅	semidirect
431. C₄⋊C₈	C₂×C₃×D₅	semidirect
435. #102	C₂×C₃×D₅	semidirect
443. C₃×D₅	#459	direct (N × H)
470. C₃×D₄	D₄×D₅	semidirect
510. C₄×C₅	C₂×C₃×D₈	semidirect
516. Dic₅	C₂×C₃×D₈	semidirect
564. C₃×C₅	C₂×#459	semidirect
589. C₃×C₄	D₅×D₈	semidirect
599. D₅	C₃×#459	direct (N × H)
626. D₄	C₃×D₄×D₅	semidirect
654. C₅	C₂×C₃×#459	semidirect
679. C₄	C₃×D₅×D₈	semidirect
682. C₃	D₅×#459	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×D₅×D₈	2
C₃×D₅×#127	2
C₃×C₄×D₄×D₅	2
C₃×C₅×#459	2
C₃×#65439	2
C₃×#65361	2
C₃×#65304	2
C₃×#65132	2
C₃×D₅×C₄⋊C₈	2
C₃×#65075	2
C₃×D₅×#102	2
D₅×#459	3
C₂×C₃×#459	5

Subgroups — C3×D5×#459 #14425804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#459 #14425804