Subgroups — C₅×D₃×#479 #14430117

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×#125	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#479	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5063	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5022	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×D₃×#107	C₂	1	1	yes	maximal, characteristic
7	C₅×#4877	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×D₃×#106	C₂	1	1	yes	maximal, characteristic
9	C₅×#4857	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
11	C₅×#4829	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×D₃×#103	C₂	1	1	yes	maximal, characteristic
13	C₅×D₃×#103	C₂	1	1	yes	maximal, characteristic
14	C₅×#4799	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4796	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#479	—	3	1	no	maximal, Hall
17	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×#125	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
21	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
23	C₅×D₃×C₄⋊C₄	—	2	1	no	—
24	C₅×D₃×C₄⋊C₄	—	2	1	no	—
25	C₅×D₃×C₄⋊C₄	—	2	1	no	—
26	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₅×#890	C₂²	1	1	yes	characteristic
30	C₅×#890	C₂²	1	1	yes	characteristic
31	C₅×#889	—	2	1	no	—
32	C₅×#889	—	2	1	no	—
33	C₅×#887	—	2	1	no	—
34	C₅×#887	C₂²	1	1	yes	characteristic
35	C₄²×C₅×D₃	—	2	1	no	—
36	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
37	C₅×#870	C₂²	1	1	yes	characteristic
38	C₄×C₅×Dic₆	—	2	1	no	—
39	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
40	C₃×C₅×#107	C₂²	1	1	yes	characteristic
41	C₃×C₅×#106	C₂²	1	1	yes	characteristic
42	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₃×C₅×#103	C₂²	1	1	yes	characteristic
44	C₃×C₅×#103	C₂²	1	1	yes	characteristic
45	C₅×#835	C₂²	1	1	yes	characteristic
46	C₅×#835	C₂²	1	1	yes	characteristic
47	C₅×#818	C₂²	1	1	yes	characteristic
48	C₅×#817	C₂²	1	1	yes	characteristic
49	C₅×#816	C₂²	1	1	yes	characteristic
50	C₅×#816	C₂²	1	1	yes	characteristic
51	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
52	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
53	C₅×#810	C₂²	1	1	yes	characteristic
54	C₅×#810	C₂²	1	1	yes	characteristic
55	C₅×#808	C₂²	1	1	yes	characteristic
56	C₅×#808	C₂²	1	1	yes	characteristic
57	C₅×#807	C₂²	1	1	yes	characteristic
58	C₅×#807	C₂²	1	1	yes	characteristic
59	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
60	D₃×#479	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₂×C₅×#125	—	3	1	no	—
62	C₂×C₄×C₅×Q₈	—	3	1	no	—
63	C₅×#479	—	3	1	no	—
64	C₅×#479	—	3	1	no	—
65	C₅×#479	—	3	1	no	—
66	C₅×#479	—	3	1	no	—
67	C₅×#479	—	3	1	no	—
68	C₅×#479	—	3	1	no	—
69	C₅×#479	—	3	1	no	—
70	C₅×#479	D₃	1	1	yes	characteristic, direct product factor
71	C₂×C₅×#107	—	3	1	no	—
72	C₂×C₅×#106	—	3	1	no	—
73	C₂×C₅×C₄⋊C₈	—	3	1	no	—
74	C₂×C₅×#103	—	3	1	no	—
75	C₂×C₅×#103	—	3	1	no	—
76	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
77	C₅×D₃×Q₈	—	2	2	no	—
78	C₅×D₃×Q₈	Q₈	1	4	yes	—
79	C₂×C₄×C₅×D₃	—	2	1	no	—
80	C₂×C₄×C₅×D₃	—	2	1	no	—
81	C₂×C₄×C₅×D₃	—	2	1	no	—
82	C₂×C₄×C₅×D₃	—	2	1	no	—
83	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
84	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
85	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
86	C₂×C₅×Dic₆	—	2	1	no	—
87	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
90	C₃×C₅×C₄⋊C₄	—	2	1	no	—
91	C₃×C₅×C₄⋊C₄	—	2	1	no	—
92	C₃×C₅×C₄⋊C₄	—	2	1	no	—
93	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₃×C₄²×C₅	—	2	1	no	—
97	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
98	C₅×C₄⋊Dic₃	—	2	1	no	—
99	C₅×C₄⋊Dic₃	—	2	1	no	—
100	C₅×C₄⋊Dic₃	—	2	1	no	—
101	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
102	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
103	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
104	C₅×Dic₃⋊C₄	—	2	1	no	—
105	C₅×Dic₃⋊C₄	—	2	1	no	—
106	C₅×Dic₃⋊C₄	—	2	1	no	—
107	C₅×Dic₃⋊C₄	—	2	1	no	—
108	C₅×Dic₃⋊C₄	—	2	1	no	—
109	C₅×Dic₃⋊C₄	—	2	1	no	—
110	C₅×Dic₃⋊C₄	—	2	1	no	—
111	C₅×Dic₃⋊C₄	—	2	1	no	—
112	C₅×Dic₃⋊C₄	—	2	1	no	—
113	C₄×C₅×Dic₃	—	2	1	no	—
114	C₄×C₅×Dic₃	—	2	1	no	—
115	C₄×C₅×Dic₃	—	2	1	no	—
116	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
117	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
118	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
119	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
120	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
121	C₅×D₃×C₈	—	2	2	no	—
122	C₅×D₃×C₈	—	2	2	no	—
123	D₃×#125	C₂×C₅	1	1	yes	characteristic
124	C₄×D₃×Q₈	C₂×C₅	1	1	yes	characteristic
125	C₃×#479	C₂×C₅	1	1	yes	characteristic, complemented
126	#5063	C₂×C₅	1	1	yes	characteristic, complemented
127	#5022	C₂×C₅	1	1	yes	characteristic, complemented
128	D₃×#107	C₂×C₅	1	1	yes	characteristic
129	#4877	C₂×C₅	1	1	yes	characteristic, complemented
130	D₃×#106	C₂×C₅	1	1	yes	characteristic
131	#4857	C₂×C₅	1	1	yes	characteristic, complemented
132	D₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
133	#4829	C₂×C₅	1	1	yes	characteristic, complemented
134	D₃×#103	C₂×C₅	1	1	yes	characteristic
135	D₃×#103	C₂×C₅	1	1	yes	characteristic
136	#4799	C₂×C₅	1	1	yes	characteristic, complemented
137	#4796	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂²×C₅×Q₈	—	3	1	no	—
139	C₂²×C₅×C₈	—	3	1	no	—
140	C₂²×C₅×C₈	—	3	1	no	—
141	C₅×#125	—	3	1	no	—
142	C₅×#125	—	3	1	no	—
143	C₅×#125	—	3	1	no	—
144	C₅×#125	—	6	1	no	—
145	C₅×#125	—	6	1	no	—
146	C₅×#125	C₂×D₃	1	1	yes	characteristic
147	C₄×C₅×Q₈	—	3	1	no	—
148	C₄×C₅×Q₈	—	3	1	no	—
149	C₄×C₅×Q₈	—	3	1	no	—
150	C₄×C₅×Q₈	—	6	1	no	—
151	C₄×C₅×Q₈	—	6	1	no	—
152	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
153	C₂×C₅×C₄⋊C₄	—	3	1	no	—
154	C₂×C₅×C₄⋊C₄	—	3	1	no	—
155	C₂×C₅×C₄⋊C₄	—	3	1	no	—
156	C₂×C₅×C₄⋊C₄	—	6	1	no	—
157	C₂×C₅×C₄⋊C₄	—	6	1	no	—
158	C₂×C₅×C₄⋊C₄	—	6	1	no	—
159	C₂×C₄²×C₅	—	3	1	no	—
160	C₂×C₄²×C₅	—	6	1	no	—
161	C₅×#107	—	3	1	no	—
162	C₅×#107	—	3	1	no	—
163	C₅×#107	—	3	1	no	—
164	C₅×#107	C₂×D₃	1	1	yes	characteristic
165	C₅×#106	—	3	1	no	—
166	C₅×#106	—	3	1	no	—
167	C₅×#106	—	3	1	no	—
168	C₅×#106	C₂×D₃	1	1	yes	characteristic
169	C₅×C₄⋊C₈	—	3	1	no	—
170	C₅×C₄⋊C₈	—	3	1	no	—
171	C₅×C₄⋊C₈	—	3	1	no	—
172	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
173	C₅×#103	—	3	1	no	—
174	C₅×#103	—	3	1	no	—
175	C₅×#103	—	3	1	no	—
176	C₅×#103	—	3	1	no	—
177	C₅×#103	—	3	1	no	—
178	C₅×#103	—	3	1	no	—
179	C₅×#103	C₂×D₃	1	1	yes	characteristic
180	C₅×#103	C₂×D₃	1	1	yes	characteristic
181	C₂×#479	—	3	1	no	Sylow
182	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
183	C₃×C₅×Q₈	—	2	1	no	—
184	C₃×C₅×Q₈	C₂×Q₈	1	2	yes	—
185	C₂×C₃×C₄×C₅	—	2	1	no	—
186	C₂×C₃×C₄×C₅	—	2	1	no	—
187	C₂×C₃×C₄×C₅	—	2	1	no	—
188	C₂×C₃×C₄×C₅	—	2	1	no	—
189	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
190	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
191	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
192	C₂×C₅×Dic₃	—	2	1	no	—
193	C₂×C₅×Dic₃	—	2	1	no	—
194	C₂×C₅×Dic₃	—	2	1	no	—
195	C₂×C₅×Dic₃	—	2	1	no	—
196	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
197	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
198	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
199	C₄×C₅×D₃	—	2	4	no	—
200	C₄×C₅×D₃	—	2	2	no	—
201	C₄×C₅×D₃	—	2	2	no	—
202	C₄×C₅×D₃	—	4	2	no	—
203	C₄×C₅×D₃	—	4	2	no	—
204	C₄×C₅×D₃	—	4	2	no	—
205	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
206	C₄×C₅×D₃	#41	1	2	yes	—
207	C₅×Dic₆	—	2	1	no	—
208	C₅×Dic₆	—	2	4	no	—
209	C₅×Dic₆	C₂×Q₈	1	2	yes	—
210	C₃×C₅×C₈	—	2	1	no	—
211	C₃×C₅×C₈	—	2	1	no	—
212	C₅×C₃⋊C₈	—	2	1	no	—
213	C₅×C₃⋊C₈	—	2	1	no	—
214	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
215	C₃×#125	C₂²×C₅	1	1	yes	characteristic
216	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
217	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
218	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
219	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
220	D₃×C₄⋊C₄	—	2	1	no	—
221	D₃×C₄⋊C₄	—	2	1	no	—
222	D₃×C₄⋊C₄	—	2	1	no	—
223	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
224	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
225	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
226	#890	C₂²×C₅	1	1	yes	characteristic
227	#890	C₂²×C₅	1	1	yes	characteristic
228	#889	—	2	1	no	—
229	#889	—	2	1	no	—
230	#887	—	2	1	no	—
231	#887	C₂²×C₅	1	1	yes	characteristic
232	C₄²×D₃	—	2	1	no	—
233	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
234	#870	C₂²×C₅	1	1	yes	characteristic
235	C₄×Dic₆	—	2	1	no	—
236	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
237	C₃×#107	C₂²×C₅	1	1	yes	characteristic
238	C₃×#106	C₂²×C₅	1	1	yes	characteristic
239	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
240	C₃×#103	C₂²×C₅	1	1	yes	characteristic
241	C₃×#103	C₂²×C₅	1	1	yes	characteristic
242	#835	C₂²×C₅	1	1	yes	characteristic
243	#835	C₂²×C₅	1	1	yes	characteristic
244	#818	C₂²×C₅	1	1	yes	characteristic
245	#817	C₂²×C₅	1	1	yes	characteristic
246	#816	C₂²×C₅	1	1	yes	characteristic
247	#816	C₂²×C₅	1	1	yes	characteristic
248	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
249	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
250	#810	C₂²×C₅	1	1	yes	characteristic
251	#810	C₂²×C₅	1	1	yes	characteristic
252	#808	C₂²×C₅	1	1	yes	characteristic
253	#808	C₂²×C₅	1	1	yes	characteristic
254	#807	C₂²×C₅	1	1	yes	characteristic
255	#807	C₂²×C₅	1	1	yes	characteristic
256	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
257	C₂×C₅×Q₈	—	3	4	no	—
258	C₂×C₅×Q₈	—	3	1	no	—
259	C₂×C₅×Q₈	—	6	1	no	—
260	C₂×C₅×Q₈	—	6	2	no	—
261	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
262	C₂²×C₄×C₅	—	3	1	no	—
263	C₂²×C₄×C₅	—	3	1	no	—
264	C₂²×C₄×C₅	—	3	1	no	—
265	C₂²×C₄×C₅	—	6	1	no	—
266	C₂²×C₄×C₅	—	6	1	no	—
267	C₂²×C₄×C₅	—	6	1	no	—
268	C₂²×C₄×C₅	—	6	1	no	—
269	C₂×C₅×C₈	—	3	1	no	—
270	C₂×C₅×C₈	—	3	1	no	—
271	C₂×C₅×C₈	—	6	2	no	—
272	C₂×C₅×C₈	—	6	2	no	—
273	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
274	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
275	C₅×C₄⋊C₄	—	2	1	no	—
276	C₅×C₄⋊C₄	—	2	1	no	—
277	C₅×C₄⋊C₄	—	2	1	no	—
278	C₅×C₄⋊C₄	—	3	1	no	—
279	C₅×C₄⋊C₄	—	3	1	no	—
280	C₅×C₄⋊C₄	—	3	1	no	—
281	C₅×C₄⋊C₄	—	6	1	no	—
282	C₅×C₄⋊C₄	—	6	1	no	—
283	C₅×C₄⋊C₄	—	6	1	no	—
284	C₅×C₄⋊C₄	—	6	1	no	—
285	C₅×C₄⋊C₄	—	6	1	no	—
286	C₅×C₄⋊C₄	—	6	1	no	—
287	C₅×C₄⋊C₄	—	6	1	no	—
288	C₅×C₄⋊C₄	—	6	1	no	—
289	C₅×C₄⋊C₄	—	6	1	no	—
290	C₅×C₄⋊C₄	—	6	1	no	—
291	C₅×C₄⋊C₄	—	6	1	no	—
292	C₅×C₄⋊C₄	—	6	1	no	—
293	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
294	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
295	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
296	C₄²×C₅	—	2	1	no	—
297	C₄²×C₅	—	3	1	no	—
298	C₄²×C₅	—	3	1	no	—
299	C₄²×C₅	—	3	1	no	—
300	C₄²×C₅	—	6	1	no	—
301	C₄²×C₅	—	6	1	no	—
302	C₄²×C₅	—	6	1	no	—
303	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
304	C₂×#125	—	3	1	no	—
305	C₂×C₄×Q₈	—	3	1	no	—
306	#479	—	3	1	no	—
307	#479	—	3	1	no	—
308	#479	—	3	1	no	—
309	#479	—	3	1	no	—
310	#479	—	3	1	no	—
311	#479	—	3	1	no	—
312	#479	—	3	1	no	—
313	#479	C₅×D₃	1	1	yes	characteristic, direct product factor
314	C₂×#107	—	3	1	no	—
315	C₂×#106	—	3	1	no	—
316	C₂×C₄⋊C₈	—	3	1	no	—
317	C₂×#103	—	3	1	no	—
318	C₂×#103	—	3	1	no	—
319	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₅×D₃	C₂²⋊Q₈	1	2	yes	—
321	C₂×C₅×D₃	#135	1	2	yes	—
322	C₂×C₅×D₃	#137	1	2	yes	—
323	C₃×C₄×C₅	—	2	2	no	—
324	C₃×C₄×C₅	—	2	1	no	—
325	C₃×C₄×C₅	—	2	1	no	—
326	C₃×C₄×C₅	—	4	1	no	—
327	C₃×C₄×C₅	—	4	1	no	—
328	C₃×C₄×C₅	—	4	1	no	—
329	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
330	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
331	C₅×Dic₃	—	2	2	no	—
332	C₅×Dic₃	—	2	1	no	—
333	C₅×Dic₃	—	2	1	no	—
334	C₅×Dic₃	—	4	1	no	—
335	C₅×Dic₃	—	4	1	no	—
336	C₅×Dic₃	—	4	1	no	—
337	C₅×Dic₃	C₂²⋊Q₈	1	2	yes	—
338	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
339	D₃×Q₈	—	2	2	no	—
340	D₃×Q₈	C₅×Q₈	1	4	yes	—
341	C₂×C₄×D₃	—	2	1	no	—
342	C₂×C₄×D₃	—	2	1	no	—
343	C₂×C₄×D₃	—	2	1	no	—
344	C₂×C₄×D₃	—	2	1	no	—
345	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
346	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
347	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
348	C₂×Dic₆	—	2	1	no	—
349	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
350	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
351	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
352	C₃×C₄⋊C₄	—	2	1	no	—
353	C₃×C₄⋊C₄	—	2	1	no	—
354	C₃×C₄⋊C₄	—	2	1	no	—
355	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
356	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
357	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
358	C₃×C₄²	—	2	1	no	—
359	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
360	C₄⋊Dic₃	—	2	1	no	—
361	C₄⋊Dic₃	—	2	1	no	—
362	C₄⋊Dic₃	—	2	1	no	—
363	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
364	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
365	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
366	Dic₃⋊C₄	—	2	1	no	—
367	Dic₃⋊C₄	—	2	1	no	—
368	Dic₃⋊C₄	—	2	1	no	—
369	Dic₃⋊C₄	—	2	1	no	—
370	Dic₃⋊C₄	—	2	1	no	—
371	Dic₃⋊C₄	—	2	1	no	—
372	Dic₃⋊C₄	—	2	1	no	—
373	Dic₃⋊C₄	—	2	1	no	—
374	Dic₃⋊C₄	—	2	1	no	—
375	C₄×Dic₃	—	2	1	no	—
376	C₄×Dic₃	—	2	1	no	—
377	C₄×Dic₃	—	2	1	no	—
378	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
379	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
380	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
381	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
382	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
383	D₃×C₈	—	2	2	no	—
384	D₃×C₈	—	2	2	no	—
385	C₂³×C₅	—	3	1	no	—
386	C₅×Q₈	—	2	1	no	—
387	C₅×Q₈	—	3	2	no	—
388	C₅×Q₈	—	6	4	no	—
389	C₅×Q₈	—	6	1	no	—
390	C₅×Q₈	D₃×Q₈	1	2	yes	—
391	C₂×C₄×C₅	—	2	1	no	—
392	C₂×C₄×C₅	—	2	1	no	—
393	C₂×C₄×C₅	—	2	1	no	—
394	C₂×C₄×C₅	—	2	1	no	—
395	C₂×C₄×C₅	—	3	1	no	—
396	C₂×C₄×C₅	—	3	2	no	—
397	C₂×C₄×C₅	—	3	2	no	—
398	C₂×C₄×C₅	—	3	1	no	—
399	C₂×C₄×C₅	—	3	1	no	—
400	C₂×C₄×C₅	—	6	2	no	—
401	C₂×C₄×C₅	—	6	2	no	—
402	C₂×C₄×C₅	—	6	4	no	—
403	C₂×C₄×C₅	—	6	1	no	—
404	C₂×C₄×C₅	—	6	1	no	—
405	C₂×C₄×C₅	—	6	1	no	—
406	C₂×C₄×C₅	—	6	1	no	—
407	C₂×C₄×C₅	—	12	2	no	—
408	C₂×C₄×C₅	—	12	2	no	—
409	C₂×C₄×C₅	—	12	2	no	—
410	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
411	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
412	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
413	C₅×C₈	—	2	1	no	—
414	C₅×C₈	—	2	1	no	—
415	C₅×C₈	—	6	1	no	—
416	C₅×C₈	—	6	1	no	—
417	C₂²×Q₈	—	3	1	no	—
418	C₂²×C₈	—	3	1	no	—
419	C₂²×C₈	—	3	1	no	—
420	#125	—	3	1	no	—
421	#125	—	3	1	no	—
422	#125	—	3	1	no	—
423	#125	—	6	1	no	—
424	#125	—	6	1	no	—
425	#125	C₂×C₅×D₃	1	1	yes	characteristic
426	C₄×Q₈	—	3	1	no	—
427	C₄×Q₈	—	3	1	no	—
428	C₄×Q₈	—	3	1	no	—
429	C₄×Q₈	—	6	1	no	—
430	C₄×Q₈	—	6	1	no	—
431	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
432	C₂×C₄⋊C₄	—	3	1	no	—
433	C₂×C₄⋊C₄	—	3	1	no	—
434	C₂×C₄⋊C₄	—	3	1	no	—
435	C₂×C₄⋊C₄	—	6	1	no	—
436	C₂×C₄⋊C₄	—	6	1	no	—
437	C₂×C₄⋊C₄	—	6	1	no	—
438	C₂×C₄²	—	3	1	no	—
439	C₂×C₄²	—	6	1	no	—
440	#107	—	3	1	no	—
441	#107	—	3	1	no	—
442	#107	—	3	1	no	—
443	#107	C₂×C₅×D₃	1	1	yes	characteristic
444	#106	—	3	1	no	—
445	#106	—	3	1	no	—
446	#106	—	3	1	no	—
447	#106	C₂×C₅×D₃	1	1	yes	characteristic
448	C₄⋊C₈	—	3	1	no	—
449	C₄⋊C₈	—	3	1	no	—
450	C₄⋊C₈	—	3	1	no	—
451	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
452	#103	—	3	1	no	—
453	#103	—	3	1	no	—
454	#103	—	3	1	no	—
455	#103	—	3	1	no	—
456	#103	—	3	1	no	—
457	#103	—	3	1	no	—
458	#103	C₂×C₅×D₃	1	1	yes	characteristic
459	#103	C₂×C₅×D₃	1	1	yes	characteristic
460	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
461	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
462	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
463	C₅×D₃	#479	1	4	yes	direct product factor
464	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
465	C₃×Q₈	—	2	1	no	—
466	C₃×Q₈	C₂×C₅×Q₈	1	2	yes	—
467	C₂×C₃×C₄	—	2	1	no	—
468	C₂×C₃×C₄	—	2	1	no	—
469	C₂×C₃×C₄	—	2	1	no	—
470	C₂×C₃×C₄	—	2	1	no	—
471	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
472	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
473	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
474	C₂×Dic₃	—	2	1	no	—
475	C₂×Dic₃	—	2	1	no	—
476	C₂×Dic₃	—	2	1	no	—
477	C₂×Dic₃	—	2	1	no	—
478	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
479	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
480	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
481	C₄×D₃	—	2	4	no	—
482	C₄×D₃	—	2	2	no	—
483	C₄×D₃	—	2	2	no	—
484	C₄×D₃	—	4	2	no	—
485	C₄×D₃	—	4	2	no	—
486	C₄×D₃	—	4	2	no	—
487	C₄×D₃	C₂×C₅×Q₈	1	2	yes	—
488	C₄×D₃	C₅×#41	1	2	yes	—
489	Dic₆	—	2	1	no	—
490	Dic₆	—	2	4	no	—
491	Dic₆	C₂×C₅×Q₈	1	2	yes	—
492	C₃×C₈	—	2	1	no	—
493	C₃×C₈	—	2	1	no	—
494	C₃⋊C₈	—	2	1	no	—
495	C₃⋊C₈	—	2	1	no	—
496	C₂²×C₅	—	3	2	no	—
497	C₂²×C₅	—	3	2	no	—
498	C₂²×C₅	—	3	2	no	—
499	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
500	C₄×C₅	—	2	1	no	—
501	C₄×C₅	—	2	1	no	—
502	C₄×C₅	—	2	2	no	—
503	C₄×C₅	—	3	2	no	—
504	C₄×C₅	—	4	1	no	—
505	C₄×C₅	—	4	1	no	—
506	C₄×C₅	—	4	1	no	—
507	C₄×C₅	—	6	1	no	—
508	C₄×C₅	—	6	1	no	—
509	C₄×C₅	—	6	2	no	—
510	C₄×C₅	—	12	1	no	—
511	C₄×C₅	—	12	1	no	—
512	C₄×C₅	—	12	1	no	—
513	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
514	C₄×C₅	D₃×#41	1	1	yes	characteristic
515	C₂×Q₈	—	3	4	no	—
516	C₂×Q₈	—	3	1	no	—
517	C₂×Q₈	—	6	1	no	—
518	C₂×Q₈	—	6	2	no	—
519	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
520	C₂²×C₄	—	3	1	no	—
521	C₂²×C₄	—	3	1	no	—
522	C₂²×C₄	—	3	1	no	—
523	C₂²×C₄	—	6	1	no	—
524	C₂²×C₄	—	6	1	no	—
525	C₂²×C₄	—	6	1	no	—
526	C₂²×C₄	—	6	1	no	—
527	C₂×C₈	—	3	1	no	—
528	C₂×C₈	—	3	1	no	—
529	C₂×C₈	—	6	2	no	—
530	C₂×C₈	—	6	2	no	—
531	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
532	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	3	1	no	—
537	C₄⋊C₄	—	3	1	no	—
538	C₄⋊C₄	—	3	1	no	—
539	C₄⋊C₄	—	6	1	no	—
540	C₄⋊C₄	—	6	1	no	—
541	C₄⋊C₄	—	6	1	no	—
542	C₄⋊C₄	—	6	1	no	—
543	C₄⋊C₄	—	6	1	no	—
544	C₄⋊C₄	—	6	1	no	—
545	C₄⋊C₄	—	6	1	no	—
546	C₄⋊C₄	—	6	1	no	—
547	C₄⋊C₄	—	6	1	no	—
548	C₄⋊C₄	—	6	1	no	—
549	C₄⋊C₄	—	6	1	no	—
550	C₄⋊C₄	—	6	1	no	—
551	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
552	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
553	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
554	C₄²	—	2	1	no	—
555	C₄²	—	3	1	no	—
556	C₄²	—	3	1	no	—
557	C₄²	—	3	1	no	—
558	C₄²	—	6	1	no	—
559	C₄²	—	6	1	no	—
560	C₄²	—	6	1	no	—
561	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
562	C₃×C₅	C₂×#479	1	1	yes	characteristic, complemented, Hall
563	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
564	C₂×D₃	C₅×C₂²⋊Q₈	1	2	yes	—
565	C₂×D₃	C₅×#135	1	2	yes	—
566	C₂×D₃	C₅×#137	1	2	yes	—
567	C₃×C₄	—	2	2	no	—
568	C₃×C₄	—	2	1	no	—
569	C₃×C₄	—	2	1	no	—
570	C₃×C₄	—	4	1	no	—
571	C₃×C₄	—	4	1	no	—
572	C₃×C₄	—	4	1	no	—
573	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
574	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
575	Dic₃	—	2	2	no	—
576	Dic₃	—	2	1	no	—
577	Dic₃	—	2	1	no	—
578	Dic₃	—	4	1	no	—
579	Dic₃	—	4	1	no	—
580	Dic₃	—	4	1	no	—
581	Dic₃	C₅×C₂²⋊Q₈	1	2	yes	—
582	C₂×C₅	—	3	4	no	—
583	C₂×C₅	D₃×C₂²⋊Q₈	1	1	yes	characteristic
584	C₂×C₅	D₃×#135	1	1	yes	characteristic
585	C₂×C₅	D₃×#137	1	1	yes	characteristic
586	C₂³	—	3	1	no	—
587	Q₈	—	2	1	no	—
588	Q₈	—	3	2	no	—
589	Q₈	—	6	4	no	—
590	Q₈	—	6	1	no	—
591	Q₈	C₅×D₃×Q₈	1	2	yes	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	3	1	no	—
597	C₂×C₄	—	3	2	no	—
598	C₂×C₄	—	3	2	no	—
599	C₂×C₄	—	3	1	no	—
600	C₂×C₄	—	3	1	no	—
601	C₂×C₄	—	6	2	no	—
602	C₂×C₄	—	6	2	no	—
603	C₂×C₄	—	6	4	no	—
604	C₂×C₄	—	6	1	no	—
605	C₂×C₄	—	6	1	no	—
606	C₂×C₄	—	6	1	no	—
607	C₂×C₄	—	6	1	no	—
608	C₂×C₄	—	12	2	no	—
609	C₂×C₄	—	12	2	no	—
610	C₂×C₄	—	12	2	no	—
611	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
612	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
613	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
614	C₈	—	2	1	no	—
615	C₈	—	2	1	no	—
616	C₈	—	6	1	no	—
617	C₈	—	6	1	no	—
618	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
619	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
620	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
621	D₃	C₅×#479	1	4	yes	direct product factor
622	C₅	D₃×#479	1	1	yes	characteristic, direct product factor, Sylow
623	C₂²	—	3	2	no	—
624	C₂²	—	3	2	no	—
625	C₂²	—	3	2	no	—
626	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
627	C₄	—	2	1	no	—
628	C₄	—	2	1	no	—
629	C₄	—	2	2	no	—
630	C₄	—	3	2	no	—
631	C₄	—	4	1	no	—
632	C₄	—	4	1	no	—
633	C₄	—	4	1	no	—
634	C₄	—	6	1	no	—
635	C₄	—	6	1	no	—
636	C₄	—	6	2	no	—
637	C₄	—	12	1	no	—
638	C₄	—	12	1	no	—
639	C₄	—	12	1	no	—
640	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
641	C₄	C₅×D₃×#41	1	1	yes	characteristic
642	C₃	C₂×C₅×#479	1	1	yes	characteristic, complemented, Sylow
643	C₂	—	3	4	no	—
644	C₂	C₅×D₃×C₂²⋊Q₈	1	1	yes	characteristic
645	C₂	C₅×D₃×#135	1	1	yes	characteristic
646	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×#479	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₅×D₃	C₂×D₄
hypercenter	C₅×#479	D₃
hypocenter	C₃	C₂×C₅×#479
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#479

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#479	C₂	semidirect
4. C₅×#5063	C₂	semidirect
5. C₅×#5022	C₂	semidirect
7. C₅×#4877	C₂	semidirect
9. C₅×#4857	C₂	semidirect
11. C₅×#4829	C₂	semidirect
14. C₅×#4799	C₂	semidirect
15. C₅×#4796	C₂	semidirect
60. D₃×#479	C₅	direct (N × H)
70. C₅×#479	D₃	direct (N × H)
125. C₃×#479	C₂×C₅	semidirect
126. #5063	C₂×C₅	semidirect
127. #5022	C₂×C₅	semidirect
129. #4877	C₂×C₅	semidirect
131. #4857	C₂×C₅	semidirect
133. #4829	C₂×C₅	semidirect
136. #4799	C₂×C₅	semidirect
137. #4796	C₂×C₅	semidirect
313. #479	C₅×D₃	direct (N × H)
463. C₅×D₃	#479	direct (N × H)
562. C₃×C₅	C₂×#479	semidirect
621. D₃	C₅×#479	direct (N × H)
622. C₅	D₃×#479	direct (N × H)
642. C₃	C₂×C₅×#479	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×#125	2
C₄×C₅×D₃×Q₈	2
C₃×C₅×#479	2
C₅×#5063	2
C₅×#5022	2
C₅×D₃×#107	2
C₅×#4877	2
C₅×D₃×#106	2
C₅×#4857	2
C₅×D₃×C₄⋊C₈	2
C₅×#4829	2
C₅×D₃×#103	2
C₅×#4799	2
C₅×#4796	2
C₂×C₅×#479	3
D₃×#479	5

Subgroups — C5×D3×#479 #14430117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#479 #14430117