Subgroups — C₅×D₃×#462 #14426061

Order 1920.

960 conjugacy classes of subgroups.

The subgroup lattice has 568 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	2	yes	maximal
2	C₅×D₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#462	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5182	C₂	1	2	yes	maximal, complemented
6	C₅×#5090	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5031	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4849	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
10	C₅×D₃×#103	C₂	1	2	yes	maximal
11	C₅×#4795	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#462	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
14	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
16	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
19	C₅×#944	C₂²	1	2	yes	—
20	C₂×C₅×#216	C₂²	1	2	yes	—
21	C₂×C₅×#216	C₂²	1	2	yes	—
22	C₅×D₃×Q₁₆	—	2	8	no	—
23	C₂×C₅×Dic₁₂	C₂²	1	2	yes	—
24	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
25	C₅×D₃×C₄⋊C₄	—	2	1	no	—
26	C₅×D₃×C₄⋊C₄	—	2	1	no	—
27	C₅×D₃×C₄⋊C₄	—	2	1	no	—
28	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₅×#888	—	2	1	no	—
30	C₅×#888	—	2	1	no	—
31	C₅×#887	—	2	1	no	—
32	C₅×#887	C₂²	1	1	yes	characteristic
33	C₄²×C₅×D₃	—	2	1	no	—
34	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
35	C₅×#869	C₂²	1	1	yes	characteristic
36	C₄×C₅×Dic₆	—	2	1	no	—
37	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
38	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₃×C₅×#103	C₂²	1	2	yes	—
40	C₅×#835	C₂²	1	2	yes	—
41	C₅×#816	C₂²	1	2	yes	—
42	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
43	C₅×#810	C₂²	1	2	yes	—
44	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
45	D₃×#462	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
46	C₂²×C₅×Q₁₆	—	3	2	no	—
47	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
48	C₂×C₄×C₅×Q₈	—	3	1	no	—
49	C₅×#462	—	3	1	no	—
50	C₅×#462	—	3	2	no	—
51	C₅×#462	—	3	2	no	—
52	C₅×#462	—	3	1	no	—
53	C₅×#462	—	3	1	no	—
54	C₅×#462	D₃	1	1	yes	characteristic, direct product factor
55	C₂×C₅×C₄⋊C₈	—	3	1	no	—
56	C₂×C₅×#103	—	3	2	no	—
57	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
58	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₅×D₃×Q₈	—	2	2	no	—
60	C₅×D₃×Q₈	—	2	4	no	—
61	C₅×D₃×Q₈	—	2	4	no	—
62	C₅×D₃×Q₈	D₄	1	4	yes	—
63	C₂×C₄×C₅×D₃	—	2	1	no	—
64	C₂×C₄×C₅×D₃	—	2	1	no	—
65	C₂×C₄×C₅×D₃	—	2	2	no	—
66	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
67	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
68	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
69	C₂×C₅×Dic₆	—	2	1	no	—
70	C₂×C₅×Dic₆	—	2	2	no	—
71	C₂×C₅×Dic₆	C₂³	1	2	yes	—
72	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
73	C₃×C₅×Q₁₆	—	2	4	no	—
74	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
75	C₃×C₅×C₄⋊C₄	—	2	1	no	—
76	C₃×C₅×C₄⋊C₄	—	2	1	no	—
77	C₃×C₅×C₄⋊C₄	—	2	1	no	—
78	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₃×C₄²×C₅	—	2	1	no	—
80	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₅×#216	—	2	4	no	—
82	C₅×#216	—	2	4	no	—
83	C₅×C₄⋊Dic₃	—	2	1	no	—
84	C₅×C₄⋊Dic₃	—	2	1	no	—
85	C₅×C₄⋊Dic₃	—	2	1	no	—
86	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
87	C₅×Dic₃⋊C₄	—	2	1	no	—
88	C₅×Dic₃⋊C₄	—	2	1	no	—
89	C₅×Dic₃⋊C₄	—	2	1	no	—
90	C₅×Dic₃⋊C₄	—	2	2	no	—
91	C₅×Dic₃⋊C₄	—	2	2	no	—
92	C₄×C₅×Dic₃	—	2	1	no	—
93	C₄×C₅×Dic₃	—	2	1	no	—
94	C₄×C₅×Dic₃	—	2	1	no	—
95	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
96	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
97	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
98	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
99	C₅×Dic₁₂	—	2	4	no	—
100	C₅×D₃×C₈	—	2	4	no	—
101	C₂×D₃×Q₁₆	C₂×C₅	1	2	yes	—
102	D₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
103	C₄×D₃×Q₈	C₂×C₅	1	1	yes	characteristic
104	C₃×#462	C₂×C₅	1	1	yes	characteristic, complemented
105	#5182	C₂×C₅	1	2	yes	complemented
106	#5090	C₂×C₅	1	1	yes	characteristic, complemented
107	#5031	C₂×C₅	1	1	yes	characteristic, complemented
108	#4849	C₂×C₅	1	1	yes	characteristic, complemented
109	D₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
110	D₃×#103	C₂×C₅	1	2	yes	—
111	#4795	C₂×C₅	1	2	yes	complemented
112	C₂²×C₅×Q₈	—	3	1	no	—
113	C₂²×C₅×Q₈	—	3	2	no	—
114	C₂×C₅×Q₁₆	—	3	2	no	—
115	C₂×C₅×Q₁₆	—	3	2	no	—
116	C₂×C₅×Q₁₆	—	3	2	no	—
117	C₂×C₅×Q₁₆	—	6	8	no	—
118	C₂×C₅×Q₁₆	C₂×D₃	1	2	yes	—
119	C₂²×C₅×C₈	—	3	2	no	—
120	C₅×C₄⋊Q₈	—	3	2	no	—
121	C₅×C₄⋊Q₈	—	3	1	no	—
122	C₅×C₄⋊Q₈	—	6	1	no	—
123	C₅×C₄⋊Q₈	—	6	1	no	—
124	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
125	C₄×C₅×Q₈	—	3	1	no	—
126	C₄×C₅×Q₈	—	3	1	no	—
127	C₄×C₅×Q₈	—	3	1	no	—
128	C₄×C₅×Q₈	—	6	1	no	—
129	C₄×C₅×Q₈	—	6	1	no	—
130	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
131	C₂×C₅×C₄⋊C₄	—	3	1	no	—
132	C₂×C₅×C₄⋊C₄	—	6	1	no	—
133	C₂×C₅×C₄⋊C₄	—	6	1	no	—
134	C₂×C₅×C₄⋊C₄	—	6	1	no	—
135	C₂×C₄²×C₅	—	3	1	no	—
136	C₂×C₄²×C₅	—	6	1	no	—
137	C₅×C₄⋊C₈	—	3	2	no	—
138	C₅×C₄⋊C₈	—	3	1	no	—
139	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
140	C₅×#103	—	3	2	no	—
141	C₅×#103	—	3	2	no	—
142	C₅×#103	—	3	2	no	—
143	C₅×#103	C₂×D₃	1	2	yes	—
144	C₂×#462	—	3	1	no	Sylow
145	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
146	C₃×C₅×Q₈	—	2	1	no	—
147	C₃×C₅×Q₈	—	2	2	no	—
148	C₃×C₅×Q₈	—	2	2	no	—
149	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	1	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
155	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
156	C₂×C₅×Dic₃	—	2	1	no	—
157	C₂×C₅×Dic₃	—	2	1	no	—
158	C₂×C₅×Dic₃	—	2	2	no	—
159	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
160	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
161	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
162	C₄×C₅×D₃	—	2	4	no	—
163	C₄×C₅×D₃	—	2	2	no	—
164	C₄×C₅×D₃	—	4	4	no	—
165	C₄×C₅×D₃	—	4	2	no	—
166	C₄×C₅×D₃	Q₁₆	1	4	yes	complemented
167	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
168	C₄×C₅×D₃	#41	1	2	yes	—
169	C₅×Dic₆	—	2	1	no	—
170	C₅×Dic₆	—	2	4	no	—
171	C₅×Dic₆	—	2	2	no	—
172	C₅×Dic₆	—	2	2	no	—
173	C₅×Dic₆	—	4	4	no	—
174	C₅×Dic₆	C₂×D₄	1	2	yes	—
175	C₃×C₅×C₈	—	2	2	no	—
176	C₅×C₃⋊C₈	—	2	2	no	—
177	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
178	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
179	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
180	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
181	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
182	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
183	#944	C₂²×C₅	1	2	yes	—
184	C₂×#216	C₂²×C₅	1	2	yes	—
185	C₂×#216	C₂²×C₅	1	2	yes	—
186	D₃×Q₁₆	—	2	8	no	—
187	C₂×Dic₁₂	C₂²×C₅	1	2	yes	—
188	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
189	D₃×C₄⋊C₄	—	2	1	no	—
190	D₃×C₄⋊C₄	—	2	1	no	—
191	D₃×C₄⋊C₄	—	2	1	no	—
192	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
193	#888	—	2	1	no	—
194	#888	—	2	1	no	—
195	#887	—	2	1	no	—
196	#887	C₂²×C₅	1	1	yes	characteristic
197	C₄²×D₃	—	2	1	no	—
198	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
199	#869	C₂²×C₅	1	1	yes	characteristic
200	C₄×Dic₆	—	2	1	no	—
201	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
202	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
203	C₃×#103	C₂²×C₅	1	2	yes	—
204	#835	C₂²×C₅	1	2	yes	—
205	#816	C₂²×C₅	1	2	yes	—
206	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
207	#810	C₂²×C₅	1	2	yes	—
208	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
209	C₂×C₅×Q₈	—	3	4	no	—
210	C₂×C₅×Q₈	—	3	1	no	—
211	C₂×C₅×Q₈	—	3	2	no	—
212	C₂×C₅×Q₈	—	6	1	no	—
213	C₂×C₅×Q₈	—	6	2	no	—
214	C₂×C₅×Q₈	—	6	2	no	—
215	C₂×C₅×Q₈	—	6	4	no	—
216	C₂×C₅×Q₈	—	6	4	no	—
217	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
218	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
219	C₂²×C₄×C₅	—	3	1	no	—
220	C₂²×C₄×C₅	—	3	1	no	—
221	C₂²×C₄×C₅	—	3	1	no	—
222	C₂²×C₄×C₅	—	6	1	no	—
223	C₂²×C₄×C₅	—	6	1	no	—
224	C₂²×C₄×C₅	—	6	2	no	—
225	C₅×Q₁₆	—	2	4	no	—
226	C₅×Q₁₆	—	6	4	no	—
227	C₅×Q₁₆	—	6	4	no	—
228	C₅×Q₁₆	—	6	4	no	—
229	C₂×C₅×C₈	—	3	2	no	—
230	C₂×C₅×C₈	—	6	4	no	—
231	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
232	C₅×C₄⋊C₄	—	2	1	no	—
233	C₅×C₄⋊C₄	—	2	1	no	—
234	C₅×C₄⋊C₄	—	2	1	no	—
235	C₅×C₄⋊C₄	—	3	1	no	—
236	C₅×C₄⋊C₄	—	6	1	no	—
237	C₅×C₄⋊C₄	—	6	1	no	—
238	C₅×C₄⋊C₄	—	6	1	no	—
239	C₅×C₄⋊C₄	—	6	2	no	—
240	C₅×C₄⋊C₄	—	6	2	no	—
241	C₅×C₄⋊C₄	—	6	1	no	—
242	C₅×C₄⋊C₄	—	6	1	no	—
243	C₅×C₄⋊C₄	—	6	1	no	—
244	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
245	C₄²×C₅	—	2	1	no	—
246	C₄²×C₅	—	3	1	no	—
247	C₄²×C₅	—	3	1	no	—
248	C₄²×C₅	—	3	1	no	—
249	C₄²×C₅	—	6	1	no	—
250	C₄²×C₅	—	6	1	no	—
251	C₄²×C₅	—	6	1	no	—
252	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
253	C₂²×Q₁₆	—	3	2	no	—
254	C₂×C₄⋊Q₈	—	3	1	no	—
255	C₂×C₄×Q₈	—	3	1	no	—
256	#462	—	3	2	no	—
257	#462	—	3	1	no	—
258	#462	—	3	1	no	—
259	#462	—	3	1	no	—
260	#462	—	3	2	no	—
261	#462	C₅×D₃	1	1	yes	characteristic, direct product factor
262	C₂×C₄⋊C₈	—	3	1	no	—
263	C₂×#103	—	3	2	no	—
264	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₅×D₃	#121	1	2	yes	—
266	C₂×C₅×D₃	C₂×Q₁₆	1	2	yes	—
267	C₂×C₅×D₃	#137	1	2	yes	—
268	C₃×C₄×C₅	—	2	2	no	—
269	C₃×C₄×C₅	—	2	1	no	—
270	C₃×C₄×C₅	—	4	2	no	—
271	C₃×C₄×C₅	—	4	1	no	—
272	C₃×C₄×C₅	C₂×Q₁₆	1	2	yes	complemented
273	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
274	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
275	C₅×Dic₃	—	2	2	no	—
276	C₅×Dic₃	—	2	1	no	—
277	C₅×Dic₃	—	4	2	no	—
278	C₅×Dic₃	—	4	1	no	—
279	C₅×Dic₃	#121	1	2	yes	—
280	C₅×Dic₃	C₂×Q₁₆	1	2	yes	complemented
281	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
282	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
283	D₃×Q₈	—	2	2	no	—
284	D₃×Q₈	—	2	4	no	—
285	D₃×Q₈	—	2	4	no	—
286	D₃×Q₈	C₅×D₄	1	4	yes	—
287	C₂×C₄×D₃	—	2	1	no	—
288	C₂×C₄×D₃	—	2	1	no	—
289	C₂×C₄×D₃	—	2	2	no	—
290	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
291	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
292	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
293	C₂×Dic₆	—	2	1	no	—
294	C₂×Dic₆	—	2	2	no	—
295	C₂×Dic₆	C₂³×C₅	1	2	yes	—
296	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
297	C₃×Q₁₆	—	2	4	no	—
298	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
299	C₃×C₄⋊C₄	—	2	1	no	—
300	C₃×C₄⋊C₄	—	2	1	no	—
301	C₃×C₄⋊C₄	—	2	1	no	—
302	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
303	C₃×C₄²	—	2	1	no	—
304	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
305	#216	—	2	4	no	—
306	#216	—	2	4	no	—
307	C₄⋊Dic₃	—	2	1	no	—
308	C₄⋊Dic₃	—	2	1	no	—
309	C₄⋊Dic₃	—	2	1	no	—
310	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
311	Dic₃⋊C₄	—	2	1	no	—
312	Dic₃⋊C₄	—	2	1	no	—
313	Dic₃⋊C₄	—	2	1	no	—
314	Dic₃⋊C₄	—	2	2	no	—
315	Dic₃⋊C₄	—	2	2	no	—
316	C₄×Dic₃	—	2	1	no	—
317	C₄×Dic₃	—	2	1	no	—
318	C₄×Dic₃	—	2	1	no	—
319	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
320	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
321	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
322	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
323	Dic₁₂	—	2	4	no	—
324	D₃×C₈	—	2	4	no	—
325	C₂³×C₅	—	3	1	no	—
326	C₅×Q₈	—	2	1	no	—
327	C₅×Q₈	—	2	2	no	—
328	C₅×Q₈	—	2	2	no	—
329	C₅×Q₈	—	3	2	no	—
330	C₅×Q₈	—	6	4	no	—
331	C₅×Q₈	—	6	1	no	—
332	C₅×Q₈	—	6	2	no	—
333	C₅×Q₈	—	6	2	no	—
334	C₅×Q₈	—	12	4	no	—
335	C₅×Q₈	D₃×D₄	1	2	yes	—
336	C₂×C₄×C₅	—	2	1	no	—
337	C₂×C₄×C₅	—	2	1	no	—
338	C₂×C₄×C₅	—	2	2	no	—
339	C₂×C₄×C₅	—	3	1	no	—
340	C₂×C₄×C₅	—	3	1	no	—
341	C₂×C₄×C₅	—	3	4	no	—
342	C₂×C₄×C₅	—	3	2	no	—
343	C₂×C₄×C₅	—	3	2	no	—
344	C₂×C₄×C₅	—	3	1	no	—
345	C₂×C₄×C₅	—	6	2	no	—
346	C₂×C₄×C₅	—	6	4	no	—
347	C₂×C₄×C₅	—	6	1	no	—
348	C₂×C₄×C₅	—	6	1	no	—
349	C₂×C₄×C₅	—	6	2	no	—
350	C₂×C₄×C₅	—	12	2	no	—
351	C₂×C₄×C₅	—	12	4	no	—
352	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
353	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
354	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
355	C₅×C₈	—	2	2	no	—
356	C₅×C₈	—	6	2	no	—
357	C₂²×Q₈	—	3	1	no	—
358	C₂²×Q₈	—	3	2	no	—
359	C₂×Q₁₆	—	3	2	no	—
360	C₂×Q₁₆	—	3	2	no	—
361	C₂×Q₁₆	—	3	2	no	—
362	C₂×Q₁₆	—	6	8	no	—
363	C₂×Q₁₆	C₂×C₅×D₃	1	2	yes	—
364	C₂²×C₈	—	3	2	no	—
365	C₄⋊Q₈	—	3	2	no	—
366	C₄⋊Q₈	—	3	1	no	—
367	C₄⋊Q₈	—	6	1	no	—
368	C₄⋊Q₈	—	6	1	no	—
369	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
370	C₄×Q₈	—	3	1	no	—
371	C₄×Q₈	—	3	1	no	—
372	C₄×Q₈	—	3	1	no	—
373	C₄×Q₈	—	6	1	no	—
374	C₄×Q₈	—	6	1	no	—
375	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
376	C₂×C₄⋊C₄	—	3	1	no	—
377	C₂×C₄⋊C₄	—	6	1	no	—
378	C₂×C₄⋊C₄	—	6	1	no	—
379	C₂×C₄⋊C₄	—	6	1	no	—
380	C₂×C₄²	—	3	1	no	—
381	C₂×C₄²	—	6	1	no	—
382	C₄⋊C₈	—	3	2	no	—
383	C₄⋊C₈	—	3	1	no	—
384	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
385	#103	—	3	2	no	—
386	#103	—	3	2	no	—
387	#103	—	3	2	no	—
388	#103	C₂×C₅×D₃	1	2	yes	—
389	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
390	C₂×C₃×C₅	C₂²×Q₁₆	1	1	yes	characteristic
391	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
392	C₅×D₃	#462	1	4	yes	direct product factor
393	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
394	C₃×Q₈	—	2	1	no	—
395	C₃×Q₈	—	2	2	no	—
396	C₃×Q₈	—	2	2	no	—
397	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
398	C₂×C₃×C₄	—	2	1	no	—
399	C₂×C₃×C₄	—	2	1	no	—
400	C₂×C₃×C₄	—	2	2	no	—
401	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
402	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
403	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
404	C₂×Dic₃	—	2	1	no	—
405	C₂×Dic₃	—	2	1	no	—
406	C₂×Dic₃	—	2	2	no	—
407	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
408	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
409	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
410	C₄×D₃	—	2	4	no	—
411	C₄×D₃	—	2	2	no	—
412	C₄×D₃	—	4	4	no	—
413	C₄×D₃	—	4	2	no	—
414	C₄×D₃	C₅×Q₁₆	1	4	yes	complemented
415	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
416	C₄×D₃	C₅×#41	1	2	yes	—
417	Dic₆	—	2	1	no	—
418	Dic₆	—	2	4	no	—
419	Dic₆	—	2	2	no	—
420	Dic₆	—	2	2	no	—
421	Dic₆	—	4	4	no	—
422	Dic₆	C₂×C₅×D₄	1	2	yes	—
423	C₃×C₈	—	2	2	no	—
424	C₃⋊C₈	—	2	2	no	—
425	C₂²×C₅	—	3	2	no	—
426	C₂²×C₅	—	3	2	no	—
427	C₂²×C₅	—	3	2	no	—
428	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
429	C₄×C₅	—	2	1	no	—
430	C₄×C₅	—	2	2	no	—
431	C₄×C₅	—	3	2	no	—
432	C₄×C₅	—	3	2	no	—
433	C₄×C₅	—	4	1	no	—
434	C₄×C₅	—	4	2	no	—
435	C₄×C₅	—	6	1	no	—
436	C₄×C₅	—	6	2	no	—
437	C₄×C₅	—	12	1	no	—
438	C₄×C₅	—	12	2	no	—
439	C₄×C₅	D₃×Q₁₆	1	2	yes	complemented
440	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
441	C₄×C₅	D₃×#41	1	1	yes	characteristic
442	C₂×Q₈	—	3	4	no	—
443	C₂×Q₈	—	3	1	no	—
444	C₂×Q₈	—	3	2	no	—
445	C₂×Q₈	—	6	1	no	—
446	C₂×Q₈	—	6	2	no	—
447	C₂×Q₈	—	6	2	no	—
448	C₂×Q₈	—	6	4	no	—
449	C₂×Q₈	—	6	4	no	—
450	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
451	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
452	C₂²×C₄	—	3	1	no	—
453	C₂²×C₄	—	3	1	no	—
454	C₂²×C₄	—	3	1	no	—
455	C₂²×C₄	—	6	1	no	—
456	C₂²×C₄	—	6	1	no	—
457	C₂²×C₄	—	6	2	no	—
458	Q₁₆	—	2	4	no	—
459	Q₁₆	—	6	4	no	—
460	Q₁₆	—	6	4	no	—
461	Q₁₆	—	6	4	no	—
462	C₂×C₈	—	3	2	no	—
463	C₂×C₈	—	6	4	no	—
464	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	3	1	no	—
469	C₄⋊C₄	—	6	1	no	—
470	C₄⋊C₄	—	6	1	no	—
471	C₄⋊C₄	—	6	1	no	—
472	C₄⋊C₄	—	6	2	no	—
473	C₄⋊C₄	—	6	2	no	—
474	C₄⋊C₄	—	6	1	no	—
475	C₄⋊C₄	—	6	1	no	—
476	C₄⋊C₄	—	6	1	no	—
477	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
478	C₄²	—	2	1	no	—
479	C₄²	—	3	1	no	—
480	C₄²	—	3	1	no	—
481	C₄²	—	3	1	no	—
482	C₄²	—	6	1	no	—
483	C₄²	—	6	1	no	—
484	C₄²	—	6	1	no	—
485	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
486	C₃×C₅	C₂×#462	1	1	yes	characteristic, complemented, Hall
487	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
488	C₂×D₃	C₅×#121	1	2	yes	—
489	C₂×D₃	C₂×C₅×Q₁₆	1	2	yes	—
490	C₂×D₃	C₅×#137	1	2	yes	—
491	C₃×C₄	—	2	2	no	—
492	C₃×C₄	—	2	1	no	—
493	C₃×C₄	—	4	2	no	—
494	C₃×C₄	—	4	1	no	—
495	C₃×C₄	C₂×C₅×Q₁₆	1	2	yes	complemented
496	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
497	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
498	Dic₃	—	2	2	no	—
499	Dic₃	—	2	1	no	—
500	Dic₃	—	4	2	no	—
501	Dic₃	—	4	1	no	—
502	Dic₃	C₅×#121	1	2	yes	—
503	Dic₃	C₂×C₅×Q₁₆	1	2	yes	complemented
504	C₂×C₅	—	3	4	no	—
505	C₂×C₅	D₃×#121	1	1	yes	characteristic
506	C₂×C₅	C₂×D₃×Q₁₆	1	1	yes	characteristic
507	C₂×C₅	D₃×#137	1	1	yes	characteristic
508	C₂³	—	3	1	no	—
509	Q₈	—	2	1	no	—
510	Q₈	—	2	2	no	—
511	Q₈	—	2	2	no	—
512	Q₈	—	3	2	no	—
513	Q₈	—	6	4	no	—
514	Q₈	—	6	1	no	—
515	Q₈	—	6	2	no	—
516	Q₈	—	6	2	no	—
517	Q₈	—	12	4	no	—
518	Q₈	C₅×D₃×D₄	1	2	yes	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	3	1	no	—
523	C₂×C₄	—	3	1	no	—
524	C₂×C₄	—	3	4	no	—
525	C₂×C₄	—	3	2	no	—
526	C₂×C₄	—	3	2	no	—
527	C₂×C₄	—	3	1	no	—
528	C₂×C₄	—	6	2	no	—
529	C₂×C₄	—	6	4	no	—
530	C₂×C₄	—	6	1	no	—
531	C₂×C₄	—	6	1	no	—
532	C₂×C₄	—	6	2	no	—
533	C₂×C₄	—	12	4	no	—
534	C₂×C₄	—	12	2	no	—
535	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
536	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
537	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
538	C₈	—	2	2	no	—
539	C₈	—	6	2	no	—
540	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
541	C₂×C₃	C₂²×C₅×Q₁₆	1	1	yes	characteristic
542	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
543	D₃	C₅×#462	1	4	yes	direct product factor
544	C₅	D₃×#462	1	1	yes	characteristic, direct product factor, Sylow
545	C₂²	—	3	2	no	—
546	C₂²	—	3	2	no	—
547	C₂²	—	3	2	no	—
548	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
549	C₄	—	2	1	no	—
550	C₄	—	2	2	no	—
551	C₄	—	3	2	no	—
552	C₄	—	3	2	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	2	no	—
555	C₄	—	6	1	no	—
556	C₄	—	6	2	no	—
557	C₄	—	12	1	no	—
558	C₄	—	12	2	no	—
559	C₄	C₅×D₃×Q₁₆	1	2	yes	complemented
560	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
561	C₄	C₅×D₃×#41	1	1	yes	characteristic
562	C₃	C₂×C₅×#462	1	1	yes	characteristic, complemented, Sylow
563	C₂	—	3	4	no	—
564	C₂	C₅×D₃×#121	1	1	yes	characteristic
565	C₂	C₂×C₅×D₃×Q₁₆	1	1	yes	characteristic
566	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×#462	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₅×D₃	C₂×D₄
hypercenter	C₅×#462	D₃
hypocenter	C₃	C₂×C₅×#462
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#462

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#462	C₂	semidirect
5. C₅×#5182	C₂	semidirect
6. C₅×#5090	C₂	semidirect
7. C₅×#5031	C₂	semidirect
8. C₅×#4849	C₂	semidirect
11. C₅×#4795	C₂	semidirect
45. D₃×#462	C₅	direct (N × H)
54. C₅×#462	D₃	direct (N × H)
104. C₃×#462	C₂×C₅	semidirect
105. #5182	C₂×C₅	semidirect
106. #5090	C₂×C₅	semidirect
107. #5031	C₂×C₅	semidirect
108. #4849	C₂×C₅	semidirect
111. #4795	C₂×C₅	semidirect
166. C₄×C₅×D₃	Q₁₆	semidirect
261. #462	C₅×D₃	direct (N × H)
272. C₃×C₄×C₅	C₂×Q₁₆	semidirect
280. C₅×Dic₃	C₂×Q₁₆	semidirect
392. C₅×D₃	#462	direct (N × H)
414. C₄×D₃	C₅×Q₁₆	semidirect
439. C₄×C₅	D₃×Q₁₆	semidirect
486. C₃×C₅	C₂×#462	semidirect
495. C₃×C₄	C₂×C₅×Q₁₆	semidirect
503. Dic₃	C₂×C₅×Q₁₆	semidirect
543. D₃	C₅×#462	direct (N × H)
544. C₅	D₃×#462	direct (N × H)
559. C₄	C₅×D₃×Q₁₆	semidirect
562. C₃	C₂×C₅×#462	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
C₅×D₃×C₄⋊Q₈	2
C₄×C₅×D₃×Q₈	2
C₃×C₅×#462	2
C₅×#5182	2
C₅×#5090	2
C₅×#5031	2
C₅×#4849	2
C₅×D₃×C₄⋊C₈	2
C₅×D₃×#103	2
C₅×#4795	2
C₂×C₅×#462	3
D₃×#462	5

Subgroups — C5×D3×#462 #14426061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#462 #14426061