Subgroups — C₅×D₃×#559 #14484696

Order 1920.

2480 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×#127	C₂	1	1	yes	maximal, characteristic
3	C₅×#5713	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5681	C₂	1	4	yes	maximal, complemented
5	C₅×D₃×#124	C₂	1	4	yes	maximal, complemented
6	C₅×#5664	C₂	1	4	yes	maximal, complemented
7	C₅×D₃×#123	C₂	1	4	yes	maximal, complemented
8	C₅×#5585	C₂	1	2	yes	maximal, complemented
9	C₄×C₅×D₃×Q₈	C₂	1	2	yes	maximal, complemented
10	C₅×#5559	C₂	1	4	yes	maximal, complemented
11	C₄×C₅×D₃×D₄	C₂	1	4	yes	maximal, complemented
12	C₂×C₅×#559	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
14	C₂×C₅×D₃×D₄	C₂²	1	4	yes	—
15	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
16	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
17	C₃×C₅×#127	C₂²	1	1	yes	characteristic
18	C₃×C₅×#124	C₂²	1	4	yes	complemented
19	C₃×C₅×#123	C₂²	1	4	yes	complemented
20	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
21	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
22	C₅×#947	C₂²	1	4	yes	complemented
23	C₅×Q₈×Dic₃	C₂²	1	2	yes	complemented
24	C₅×#940	C₂²	1	2	yes	—
25	C₅×#940	C₂²	1	4	yes	—
26	C₅×#936	C₂²	1	4	yes	complemented
27	C₅×#935	C₂²	1	4	yes	complemented
28	C₅×D₄×Dic₃	C₂²	1	4	yes	complemented
29	C₅×#929	C₂²	1	4	yes	complemented
30	C₄×C₅×#67	C₂²	1	8	yes	complemented
31	C₅×#894	C₂²	1	8	yes	complemented
32	C₅×#893	C₂²	1	4	yes	complemented
33	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	—
34	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₅×#887	C₂²	1	4	yes	complemented
36	C₅×#887	C₂²	1	2	yes	complemented
37	C₅×#886	C₂²	1	4	yes	complemented
38	C₅×#885	C₂²	1	8	yes	complemented
39	C₅×#885	C₂²	1	8	yes	complemented
40	C₅×#883	C₂²	1	8	yes	complemented
41	C₅×#67⋊C₄	C₂²	1	8	yes	complemented
42	C₅×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
43	C₅×D₃×C₂²⋊C₄	C₂²	1	8	yes	—
44	C₅×#875	C₂²	1	4	yes	complemented
45	C₅×#874	C₂²	1	1	yes	characteristic
46	C₄×C₅×D₁₂	C₂²	1	4	yes	complemented
47	C₄²×C₅×D₃	C₂²	1	4	yes	—
48	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
49	C₄×C₅×Dic₆	C₂²	1	4	yes	complemented
50	C₄×C₅×Dic₆	C₂²	1	2	yes	complemented
51	D₃×#559	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
52	C₅×#559	—	3	1	no	—
53	C₅×#559	—	3	4	no	—
54	C₅×#559	—	3	4	no	—
55	C₅×#559	—	3	2	no	—
56	C₅×#559	—	3	4	no	—
57	C₅×#559	D₃	1	1	yes	characteristic, direct product factor
58	C₂×C₅×#127	—	3	1	no	—
59	C₂×C₅×#124	—	3	4	no	—
60	C₂×C₅×#123	—	3	4	no	—
61	C₂×C₄×C₅×Q₈	—	3	2	no	—
62	C₂×C₄×C₅×D₄	—	3	4	no	—
63	C₂³×C₅×D₃	C₂³	1	4	yes	—
64	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
65	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
66	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
67	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
68	C₂×C₅×#67	C₂³	1	8	yes	—
69	C₂×C₅×#67	C₂³	1	4	yes	—
70	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
71	C₅×D₃×Q₈	—	2	8	no	—
72	C₅×D₃×D₄	—	2	16	no	—
73	C₅×D₃×D₄	—	4	4	no	—
74	C₂×C₅×D₁₂	C₂³	1	4	yes	—
75	C₂×C₅×D₁₂	C₂³	1	2	yes	—
76	C₂×C₄×C₅×D₃	—	4	8	no	—
77	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
78	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
79	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
80	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
81	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
82	C₂×C₅×Dic₆	C₂³	1	2	yes	—
83	C₂×C₅×Dic₆	C₂³	1	4	yes	—
84	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
85	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
86	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
87	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
88	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
89	C₃×C₄²×C₅	C₂³	1	4	yes	—
90	C₅×#217	C₂³	1	8	yes	—
91	C₅×#217	C₂³	1	4	yes	—
92	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
93	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
94	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
95	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
96	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
97	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
98	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
99	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
100	C₄×C₅×Dic₃	C₂³	1	2	yes	—
101	C₄×C₅×Dic₃	C₂³	1	4	yes	—
102	C₄×C₅×Dic₃	C₂³	1	4	yes	—
103	C₄×C₅×Dic₃	C₂³	1	4	yes	—
104	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
105	C₃×#559	C₂×C₅	1	1	yes	characteristic, complemented
106	D₃×#127	C₂×C₅	1	1	yes	characteristic
107	#5713	C₂×C₅	1	1	yes	characteristic, complemented
108	#5681	C₂×C₅	1	4	yes	complemented
109	D₃×#124	C₂×C₅	1	4	yes	complemented
110	#5664	C₂×C₅	1	4	yes	complemented
111	D₃×#123	C₂×C₅	1	4	yes	complemented
112	#5585	C₂×C₅	1	2	yes	complemented
113	C₄×D₃×Q₈	C₂×C₅	1	2	yes	complemented
114	#5559	C₂×C₅	1	4	yes	complemented
115	C₄×D₃×D₄	C₂×C₅	1	4	yes	complemented
116	C₂²×C₅×Q₈	—	3	2	no	—
117	C₂²×C₅×D₄	—	3	4	no	—
118	C₂²×C₅×D₄	—	3	2	no	—
119	C₂³×C₄×C₅	—	3	4	no	—
120	C₅×#127	—	3	2	no	—
121	C₅×#127	—	3	4	no	—
122	C₅×#127	—	3	1	no	—
123	C₅×#127	C₂×D₃	1	1	yes	characteristic
124	C₅×#124	—	3	4	no	—
125	C₅×#124	—	3	4	no	—
126	C₅×#124	—	3	8	no	—
127	C₅×#124	—	3	8	no	—
128	C₅×#124	—	3	4	no	—
129	C₅×#124	C₂×D₃	1	4	yes	complemented
130	C₅×#123	—	3	4	no	—
131	C₅×#123	—	3	4	no	—
132	C₅×#123	—	3	8	no	—
133	C₅×#123	—	3	8	no	—
134	C₅×#123	—	3	4	no	—
135	C₅×#123	C₂×D₃	1	4	yes	complemented
136	C₄×C₅×Q₈	—	3	2	no	—
137	C₄×C₅×Q₈	—	3	4	no	—
138	C₄×C₅×Q₈	—	3	2	no	—
139	C₄×C₅×Q₈	—	3	2	no	—
140	C₄×C₅×Q₈	—	3	4	no	—
141	C₄×C₅×Q₈	C₂×D₃	1	2	yes	complemented
142	C₄×C₅×D₄	—	3	4	no	—
143	C₄×C₅×D₄	—	3	8	no	—
144	C₄×C₅×D₄	—	3	4	no	—
145	C₄×C₅×D₄	—	3	8	no	—
146	C₄×C₅×D₄	—	3	4	no	—
147	C₄×C₅×D₄	C₂×D₃	1	4	yes	complemented
148	C₂×C₅×C₄⋊C₄	—	3	2	no	—
149	C₂×C₅×C₄⋊C₄	—	3	4	no	—
150	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
151	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
152	C₂×C₄²×C₅	—	3	4	no	—
153	C₂×C₄²×C₅	—	3	1	no	—
154	C₂×#559	—	3	1	no	Sylow
155	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
156	C₂²×C₅×D₃	—	2	16	no	—
157	C₂²×C₅×D₃	—	2	8	no	—
158	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
159	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
160	C₃×C₅×Q₈	—	2	4	no	—
161	C₃×C₅×D₄	—	2	8	no	—
162	C₃×C₅×D₄	—	4	2	no	—
163	C₂×C₃×C₄×C₅	—	4	4	no	—
164	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
165	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
166	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
167	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
168	C₅×#67	—	2	16	no	—
169	C₅×#67	—	4	4	no	—
170	C₂×C₅×Dic₃	—	4	4	no	—
171	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
173	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
174	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
175	C₅×D₁₂	—	2	8	no	—
176	C₅×D₁₂	—	4	2	no	—
177	C₄×C₅×D₃	—	2	8	no	—
178	C₄×C₅×D₃	—	2	8	no	—
179	C₄×C₅×D₃	—	2	2	no	—
180	C₄×C₅×D₃	—	4	8	no	—
181	C₄×C₅×D₃	#41	1	8	yes	—
182	C₅×Dic₆	—	2	4	no	—
183	C₅×Dic₆	—	2	8	no	—
184	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
185	C₂×D₃×D₄	C₂²×C₅	1	4	yes	—
186	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
187	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
188	C₃×#127	C₂²×C₅	1	1	yes	characteristic
189	C₃×#124	C₂²×C₅	1	4	yes	complemented
190	C₃×#123	C₂²×C₅	1	4	yes	complemented
191	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
192	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
193	#947	C₂²×C₅	1	4	yes	complemented
194	Q₈×Dic₃	C₂²×C₅	1	2	yes	complemented
195	#940	C₂²×C₅	1	2	yes	—
196	#940	C₂²×C₅	1	4	yes	—
197	#936	C₂²×C₅	1	4	yes	complemented
198	#935	C₂²×C₅	1	4	yes	complemented
199	D₄×Dic₃	C₂²×C₅	1	4	yes	complemented
200	#929	C₂²×C₅	1	4	yes	complemented
201	C₄×#67	C₂²×C₅	1	8	yes	complemented
202	#894	C₂²×C₅	1	8	yes	complemented
203	#893	C₂²×C₅	1	4	yes	complemented
204	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
205	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
206	#887	C₂²×C₅	1	4	yes	complemented
207	#887	C₂²×C₅	1	2	yes	complemented
208	#886	C₂²×C₅	1	4	yes	complemented
209	#885	C₂²×C₅	1	8	yes	complemented
210	#885	C₂²×C₅	1	8	yes	complemented
211	#883	C₂²×C₅	1	8	yes	complemented
212	#67⋊C₄	C₂²×C₅	1	8	yes	complemented
213	D₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
214	D₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
215	#875	C₂²×C₅	1	4	yes	complemented
216	#874	C₂²×C₅	1	1	yes	characteristic
217	C₄×D₁₂	C₂²×C₅	1	4	yes	complemented
218	C₄²×D₃	C₂²×C₅	1	4	yes	—
219	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
220	C₄×Dic₆	C₂²×C₅	1	4	yes	complemented
221	C₄×Dic₆	C₂²×C₅	1	2	yes	complemented
222	C₂⁴×C₅	—	3	4	no	—
223	C₂×C₅×Q₈	—	3	4	no	—
224	C₂×C₅×Q₈	—	3	2	no	—
225	C₂×C₅×Q₈	—	6	8	no	—
226	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
227	C₂×C₅×D₄	—	3	8	no	—
228	C₂×C₅×D₄	—	3	4	no	—
229	C₂×C₅×D₄	—	3	4	no	—
230	C₂×C₅×D₄	—	3	2	no	—
231	C₂×C₅×D₄	—	6	16	no	—
232	C₂×C₅×D₄	—	12	4	no	—
233	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
234	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
235	C₂²×C₄×C₅	—	3	2	no	—
236	C₂²×C₄×C₅	—	3	4	no	—
237	C₂²×C₄×C₅	—	3	4	no	—
238	C₂²×C₄×C₅	—	3	4	no	—
239	C₂²×C₄×C₅	—	3	1	no	—
240	C₂²×C₄×C₅	—	3	8	no	—
241	C₂²×C₄×C₅	—	12	8	no	—
242	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
243	C₅×C₄⋊C₄	—	3	4	no	—
244	C₅×C₄⋊C₄	—	3	2	no	—
245	C₅×C₄⋊C₄	—	3	4	no	—
246	C₅×C₄⋊C₄	—	3	4	no	—
247	C₅×C₄⋊C₄	—	3	4	no	—
248	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
249	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
250	C₅×C₂²⋊C₄	—	3	8	no	—
251	C₅×C₂²⋊C₄	—	3	4	no	—
252	C₅×C₂²⋊C₄	—	3	8	no	—
253	C₅×C₂²⋊C₄	—	3	8	no	—
254	C₅×C₂²⋊C₄	—	3	8	no	—
255	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
256	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
257	C₄²×C₅	—	3	4	no	—
258	C₄²×C₅	—	3	4	no	—
259	C₄²×C₅	—	3	4	no	—
260	C₄²×C₅	—	3	1	no	—
261	C₄²×C₅	—	3	2	no	—
262	C₄²×C₅	C₂²×D₃	1	4	yes	—
263	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
264	#559	—	3	1	no	—
265	#559	—	3	4	no	—
266	#559	—	3	4	no	—
267	#559	—	3	2	no	—
268	#559	—	3	4	no	—
269	#559	C₅×D₃	1	1	yes	characteristic, direct product factor
270	C₂×#127	—	3	1	no	—
271	C₂×#124	—	3	4	no	—
272	C₂×#123	—	3	4	no	—
273	C₂×C₄×Q₈	—	3	2	no	—
274	C₂×C₄×D₄	—	3	4	no	—
275	C₂²×C₃×C₅	—	2	8	no	—
276	C₂²×C₃×C₅	—	2	4	no	—
277	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
278	C₂×C₅×D₃	—	2	8	no	—
279	C₂×C₅×D₃	—	2	4	no	—
280	C₂×C₅×D₃	—	4	16	no	—
281	C₂×C₅×D₃	C₂×#41	1	4	yes	—
282	C₂×C₅×D₃	H(5,𝔽₂)	1	2	yes	—
283	C₃×C₄×C₅	—	2	4	no	—
284	C₃×C₄×C₅	—	2	4	no	—
285	C₃×C₄×C₅	—	2	1	no	—
286	C₃×C₄×C₅	C₂×#41	1	4	yes	—
287	C₅×Dic₃	—	2	4	no	—
288	C₅×Dic₃	—	2	4	no	—
289	C₅×Dic₃	—	2	1	no	—
290	C₅×Dic₃	C₂×#41	1	4	yes	—
291	C₂³×D₃	C₂³×C₅	1	4	yes	—
292	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
293	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
294	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
295	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
296	C₂×#67	C₂³×C₅	1	8	yes	—
297	C₂×#67	C₂³×C₅	1	4	yes	—
298	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
299	D₃×Q₈	—	2	8	no	—
300	D₃×D₄	—	2	16	no	—
301	D₃×D₄	—	4	4	no	—
302	C₂×D₁₂	C₂³×C₅	1	4	yes	—
303	C₂×D₁₂	C₂³×C₅	1	2	yes	—
304	C₂×C₄×D₃	—	4	8	no	—
305	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
306	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
307	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
308	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
309	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
310	C₂×Dic₆	C₂³×C₅	1	2	yes	—
311	C₂×Dic₆	C₂³×C₅	1	4	yes	—
312	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
313	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
314	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
315	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
316	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
317	C₃×C₄²	C₂³×C₅	1	4	yes	—
318	#217	C₂³×C₅	1	8	yes	—
319	#217	C₂³×C₅	1	4	yes	—
320	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
321	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
322	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
323	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
324	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
325	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
326	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
327	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
328	C₄×Dic₃	C₂³×C₅	1	2	yes	—
329	C₄×Dic₃	C₂³×C₅	1	4	yes	—
330	C₄×Dic₃	C₂³×C₅	1	4	yes	—
331	C₄×Dic₃	C₂³×C₅	1	4	yes	—
332	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
333	C₂³×C₅	—	3	1	no	—
334	C₂³×C₅	—	3	4	no	—
335	C₂³×C₅	—	6	8	no	—
336	C₂³×C₅	—	6	16	no	—
337	C₂³×C₅	C₂³×D₃	1	4	yes	—
338	C₅×Q₈	—	2	4	no	—
339	C₅×Q₈	—	6	8	no	—
340	C₅×Q₈	—	6	4	no	—
341	C₅×D₄	—	2	8	no	—
342	C₅×D₄	—	4	2	no	—
343	C₅×D₄	—	6	16	no	—
344	C₅×D₄	—	6	8	no	—
345	C₅×D₄	—	12	2	no	—
346	C₅×D₄	—	12	4	no	—
347	C₂×C₄×C₅	—	3	2	no	—
348	C₂×C₄×C₅	—	3	8	no	—
349	C₂×C₄×C₅	—	3	4	no	—
350	C₂×C₄×C₅	—	3	4	no	—
351	C₂×C₄×C₅	—	3	1	no	—
352	C₂×C₄×C₅	—	4	4	no	—
353	C₂×C₄×C₅	—	6	8	no	—
354	C₂×C₄×C₅	—	6	2	no	—
355	C₂×C₄×C₅	—	6	8	no	—
356	C₂×C₄×C₅	—	12	8	no	—
357	C₂×C₄×C₅	—	12	4	no	—
358	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
359	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
360	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
361	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
362	C₂²×Q₈	—	3	2	no	—
363	C₂²×D₄	—	3	4	no	—
364	C₂²×D₄	—	3	2	no	—
365	C₂³×C₄	—	3	4	no	—
366	#127	—	3	2	no	—
367	#127	—	3	4	no	—
368	#127	—	3	1	no	—
369	#127	C₂×C₅×D₃	1	1	yes	characteristic
370	#124	—	3	4	no	—
371	#124	—	3	4	no	—
372	#124	—	3	8	no	—
373	#124	—	3	8	no	—
374	#124	—	3	4	no	—
375	#124	C₂×C₅×D₃	1	4	yes	complemented
376	#123	—	3	4	no	—
377	#123	—	3	4	no	—
378	#123	—	3	8	no	—
379	#123	—	3	8	no	—
380	#123	—	3	4	no	—
381	#123	C₂×C₅×D₃	1	4	yes	complemented
382	C₄×Q₈	—	3	2	no	—
383	C₄×Q₈	—	3	4	no	—
384	C₄×Q₈	—	3	2	no	—
385	C₄×Q₈	—	3	2	no	—
386	C₄×Q₈	—	3	4	no	—
387	C₄×Q₈	C₂×C₅×D₃	1	2	yes	complemented
388	C₄×D₄	—	3	4	no	—
389	C₄×D₄	—	3	8	no	—
390	C₄×D₄	—	3	4	no	—
391	C₄×D₄	—	3	8	no	—
392	C₄×D₄	—	3	4	no	—
393	C₄×D₄	C₂×C₅×D₃	1	4	yes	complemented
394	C₂×C₄⋊C₄	—	3	2	no	—
395	C₂×C₄⋊C₄	—	3	4	no	—
396	C₂×C₂²⋊C₄	—	3	8	no	—
397	C₂×C₂²⋊C₄	—	3	4	no	—
398	C₂×C₄²	—	3	4	no	—
399	C₂×C₄²	—	3	1	no	—
400	C₂×C₃×C₅	—	4	4	no	—
401	C₂×C₃×C₅	C₂²×#41	1	2	yes	—
402	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
403	C₅×D₃	—	4	4	no	—
404	C₅×D₃	#559	1	4	yes	direct product factor
405	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
406	C₂²×D₃	—	2	16	no	—
407	C₂²×D₃	—	2	8	no	—
408	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
409	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
410	C₃×Q₈	—	2	4	no	—
411	C₃×D₄	—	2	8	no	—
412	C₃×D₄	—	4	2	no	—
413	C₂×C₃×C₄	—	4	4	no	—
414	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
415	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
416	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
417	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
418	#67	—	2	16	no	—
419	#67	—	4	4	no	—
420	C₂×Dic₃	—	4	4	no	—
421	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
422	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
423	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
424	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
425	D₁₂	—	2	8	no	—
426	D₁₂	—	4	2	no	—
427	C₄×D₃	—	2	8	no	—
428	C₄×D₃	—	2	8	no	—
429	C₄×D₃	—	2	2	no	—
430	C₄×D₃	—	4	8	no	—
431	C₄×D₃	C₅×#41	1	8	yes	—
432	Dic₆	—	2	4	no	—
433	Dic₆	—	2	8	no	—
434	C₂²×C₅	—	2	8	no	—
435	C₂²×C₅	—	2	4	no	—
436	C₂²×C₅	—	3	4	no	—
437	C₂²×C₅	—	3	2	no	—
438	C₂²×C₅	—	6	8	no	—
439	C₂²×C₅	—	6	4	no	—
440	C₂²×C₅	—	12	16	no	—
441	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
442	C₄×C₅	—	2	4	no	—
443	C₄×C₅	—	2	4	no	—
444	C₄×C₅	—	2	1	no	—
445	C₄×C₅	—	3	4	no	—
446	C₄×C₅	—	6	4	no	—
447	C₄×C₅	—	6	4	no	—
448	C₄×C₅	—	6	1	no	—
449	C₄×C₅	D₃×#41	1	4	yes	—
450	C₂⁴	—	3	4	no	—
451	C₂×Q₈	—	3	4	no	—
452	C₂×Q₈	—	3	2	no	—
453	C₂×Q₈	—	6	8	no	—
454	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
455	C₂×D₄	—	3	8	no	—
456	C₂×D₄	—	3	4	no	—
457	C₂×D₄	—	3	4	no	—
458	C₂×D₄	—	3	2	no	—
459	C₂×D₄	—	6	16	no	—
460	C₂×D₄	—	12	4	no	—
461	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
462	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
463	C₂²×C₄	—	3	2	no	—
464	C₂²×C₄	—	3	4	no	—
465	C₂²×C₄	—	3	4	no	—
466	C₂²×C₄	—	3	4	no	—
467	C₂²×C₄	—	3	1	no	—
468	C₂²×C₄	—	3	8	no	—
469	C₂²×C₄	—	12	8	no	—
470	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
471	C₄⋊C₄	—	3	4	no	—
472	C₄⋊C₄	—	3	2	no	—
473	C₄⋊C₄	—	3	4	no	—
474	C₄⋊C₄	—	3	4	no	—
475	C₄⋊C₄	—	3	4	no	—
476	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
477	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
478	C₂²⋊C₄	—	3	8	no	—
479	C₂²⋊C₄	—	3	4	no	—
480	C₂²⋊C₄	—	3	8	no	—
481	C₂²⋊C₄	—	3	8	no	—
482	C₂²⋊C₄	—	3	8	no	—
483	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
484	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
485	C₄²	—	3	4	no	—
486	C₄²	—	3	4	no	—
487	C₄²	—	3	4	no	—
488	C₄²	—	3	1	no	—
489	C₄²	—	3	2	no	—
490	C₄²	C₂²×C₅×D₃	1	4	yes	—
491	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
492	C₃×C₅	C₂×#559	1	1	yes	characteristic, complemented, Hall
493	C₂²×C₃	—	2	8	no	—
494	C₂²×C₃	—	2	4	no	—
495	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
496	C₂×D₃	—	2	8	no	—
497	C₂×D₃	—	2	4	no	—
498	C₂×D₃	—	4	16	no	—
499	C₂×D₃	C₂×C₅×#41	1	4	yes	—
500	C₂×D₃	C₅×H(5,𝔽₂)	1	2	yes	—
501	C₃×C₄	—	2	4	no	—
502	C₃×C₄	—	2	4	no	—
503	C₃×C₄	—	2	1	no	—
504	C₃×C₄	C₂×C₅×#41	1	4	yes	—
505	Dic₃	—	2	4	no	—
506	Dic₃	—	2	4	no	—
507	Dic₃	—	2	1	no	—
508	Dic₃	C₂×C₅×#41	1	4	yes	—
509	C₂×C₅	—	3	4	no	—
510	C₂×C₅	—	4	4	no	—
511	C₂×C₅	—	12	4	no	—
512	C₂×C₅	C₂×D₃×#41	1	2	yes	—
513	C₂×C₅	D₃×H(5,𝔽₂)	1	1	yes	characteristic
514	C₂³	—	3	1	no	—
515	C₂³	—	3	4	no	—
516	C₂³	—	6	8	no	—
517	C₂³	—	6	16	no	—
518	C₂³	C₂³×C₅×D₃	1	4	yes	—
519	Q₈	—	2	4	no	—
520	Q₈	—	6	8	no	—
521	Q₈	—	6	4	no	—
522	D₄	—	2	8	no	—
523	D₄	—	4	2	no	—
524	D₄	—	6	16	no	—
525	D₄	—	6	8	no	—
526	D₄	—	12	2	no	—
527	D₄	—	12	4	no	—
528	C₂×C₄	—	3	2	no	—
529	C₂×C₄	—	3	8	no	—
530	C₂×C₄	—	3	4	no	—
531	C₂×C₄	—	3	4	no	—
532	C₂×C₄	—	3	1	no	—
533	C₂×C₄	—	4	4	no	—
534	C₂×C₄	—	6	8	no	—
535	C₂×C₄	—	6	2	no	—
536	C₂×C₄	—	6	8	no	—
537	C₂×C₄	—	12	8	no	—
538	C₂×C₄	—	12	4	no	—
539	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
540	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
541	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
542	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
543	C₂×C₃	—	4	4	no	—
544	C₂×C₃	C₂²×C₅×#41	1	2	yes	—
545	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
546	D₃	—	4	4	no	—
547	D₃	C₅×#559	1	4	yes	direct product factor
548	C₅	D₃×#559	1	1	yes	characteristic, direct product factor, Sylow
549	C₂²	—	2	8	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	3	4	no	—
552	C₂²	—	3	2	no	—
553	C₂²	—	6	8	no	—
554	C₂²	—	6	4	no	—
555	C₂²	—	12	16	no	—
556	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
557	C₄	—	2	4	no	—
558	C₄	—	2	4	no	—
559	C₄	—	2	1	no	—
560	C₄	—	3	4	no	—
561	C₄	—	6	4	no	—
562	C₄	—	6	4	no	—
563	C₄	—	6	1	no	—
564	C₄	C₅×D₃×#41	1	4	yes	—
565	C₃	C₂×C₅×#559	1	1	yes	characteristic, complemented, Sylow
566	C₂	—	3	4	no	—
567	C₂	—	4	4	no	—
568	C₂	—	12	4	no	—
569	C₂	C₂×C₅×D₃×#41	1	2	yes	—
570	C₂	C₅×D₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#559	C₂
socle	C₂²×C₃×C₅	C₂⁵
prime radical	C₅×D₃×#127	C₂
hypercenter	C₅×#559	D₃
hypocenter	C₃	C₂×C₅×#559
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#559

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#559	C₂	semidirect
3. C₅×#5713	C₂	semidirect
4. C₅×#5681	C₂	semidirect
5. C₅×D₃×#124	C₂	semidirect
6. C₅×#5664	C₂	semidirect
7. C₅×D₃×#123	C₂	semidirect
8. C₅×#5585	C₂	semidirect
9. C₄×C₅×D₃×Q₈	C₂	semidirect
10. C₅×#5559	C₂	semidirect
11. C₄×C₅×D₃×D₄	C₂	semidirect
18. C₃×C₅×#124	C₂²	semidirect
19. C₃×C₅×#123	C₂²	semidirect
20. C₃×C₄×C₅×Q₈	C₂²	semidirect
21. C₃×C₄×C₅×D₄	C₂²	semidirect
22. C₅×#947	C₂²	semidirect
23. C₅×Q₈×Dic₃	C₂²	semidirect
26. C₅×#936	C₂²	semidirect
27. C₅×#935	C₂²	semidirect
28. C₅×D₄×Dic₃	C₂²	semidirect
29. C₅×#929	C₂²	semidirect
30. C₄×C₅×#67	C₂²	semidirect
31. C₅×#894	C₂²	semidirect
32. C₅×#893	C₂²	semidirect
35. C₅×#887	C₂²	semidirect
36. C₅×#887	C₂²	semidirect
37. C₅×#886	C₂²	semidirect
38. C₅×#885	C₂²	semidirect
39. C₅×#885	C₂²	semidirect
40. C₅×#883	C₂²	semidirect
41. C₅×#67⋊C₄	C₂²	semidirect
44. C₅×#875	C₂²	semidirect
46. C₄×C₅×D₁₂	C₂²	semidirect
49. C₄×C₅×Dic₆	C₂²	semidirect
50. C₄×C₅×Dic₆	C₂²	semidirect
51. D₃×#559	C₅	direct (N × H)
57. C₅×#559	D₃	direct (N × H)
105. C₃×#559	C₂×C₅	semidirect
107. #5713	C₂×C₅	semidirect
108. #5681	C₂×C₅	semidirect
109. D₃×#124	C₂×C₅	semidirect
110. #5664	C₂×C₅	semidirect
111. D₃×#123	C₂×C₅	semidirect
112. #5585	C₂×C₅	semidirect
113. C₄×D₃×Q₈	C₂×C₅	semidirect
114. #5559	C₂×C₅	semidirect
115. C₄×D₃×D₄	C₂×C₅	semidirect
129. C₅×#124	C₂×D₃	semidirect
135. C₅×#123	C₂×D₃	semidirect
141. C₄×C₅×Q₈	C₂×D₃	semidirect
147. C₄×C₅×D₄	C₂×D₃	semidirect
189. C₃×#124	C₂²×C₅	semidirect
190. C₃×#123	C₂²×C₅	semidirect
191. C₃×C₄×Q₈	C₂²×C₅	semidirect
192. C₃×C₄×D₄	C₂²×C₅	semidirect
193. #947	C₂²×C₅	semidirect
194. Q₈×Dic₃	C₂²×C₅	semidirect
197. #936	C₂²×C₅	semidirect
198. #935	C₂²×C₅	semidirect
199. D₄×Dic₃	C₂²×C₅	semidirect
200. #929	C₂²×C₅	semidirect
201. C₄×#67	C₂²×C₅	semidirect
202. #894	C₂²×C₅	semidirect
203. #893	C₂²×C₅	semidirect
206. #887	C₂²×C₅	semidirect
207. #887	C₂²×C₅	semidirect
208. #886	C₂²×C₅	semidirect
209. #885	C₂²×C₅	semidirect
210. #885	C₂²×C₅	semidirect
211. #883	C₂²×C₅	semidirect
212. #67⋊C₄	C₂²×C₅	semidirect
215. #875	C₂²×C₅	semidirect
217. C₄×D₁₂	C₂²×C₅	semidirect
220. C₄×Dic₆	C₂²×C₅	semidirect
221. C₄×Dic₆	C₂²×C₅	semidirect
269. #559	C₅×D₃	direct (N × H)
375. #124	C₂×C₅×D₃	semidirect
381. #123	C₂×C₅×D₃	semidirect
387. C₄×Q₈	C₂×C₅×D₃	semidirect
393. C₄×D₄	C₂×C₅×D₃	semidirect
404. C₅×D₃	#559	direct (N × H)
492. C₃×C₅	C₂×#559	semidirect
547. D₃	C₅×#559	direct (N × H)
548. C₅	D₃×#559	direct (N × H)
565. C₃	C₂×C₅×#559	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#559	2
C₅×D₃×#127	2
C₅×#5713	2
C₅×#5681	2
C₅×D₃×#124	2
C₅×#5664	2
C₅×D₃×#123	2
C₅×#5585	2
C₄×C₅×D₃×Q₈	2
C₅×#5559	2
C₄×C₅×D₃×D₄	2
C₂×C₅×#559	3
D₃×#559	5

Subgroups — C5×D3×#559 #14484696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#559 #14484696