Subgroups — C₃×D₅×#560 #14495176

Order 1920.

2688 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#560	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66054	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#66045	C₂	1	2	yes	maximal, complemented
5	C₃×D₅×#126	C₂	1	2	yes	maximal, complemented
6	C₃×#66000	C₂	1	3	yes	maximal, complemented
7	C₃×D₅×#123	C₂	1	3	yes	maximal, complemented
8	C₃×#65954	C₂	1	6	yes	maximal, complemented
9	C₃×D₅×#121	C₂	1	6	yes	maximal, complemented
10	C₃×#65929	C₂	1	3	yes	maximal, complemented
11	C₃×D₅×#120	C₂	1	3	yes	maximal, complemented
12	D₅×#560	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂⁴×C₃×D₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×D₄×D₅	C₂²	1	6	yes	—
15	C₂×C₃×D₄×D₅	C₂²	1	3	yes	—
16	C₂×C₃×D₄×D₅	C₂²	1	3	yes	complemented
17	C₂²×C₃×C₄×D₅	C₂²	1	3	yes	complemented
18	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₅×#126	C₂²	1	2	yes	complemented
20	C₃×C₅×#123	C₂²	1	3	yes	complemented
21	C₃×C₅×#121	C₂²	1	6	yes	complemented
22	C₃×C₅×#120	C₂²	1	3	yes	complemented
23	C₃×#4099	C₂²	1	3	yes	complemented
24	C₃×#4086	C₂²	1	3	yes	complemented
25	C₃×#4086	C₂²	1	3	yes	complemented
26	C₃×#4085	C₂²	1	6	yes	complemented
27	C₃×#4085	C₂²	1	6	yes	complemented
28	C₃×#4084	C₂²	1	6	yes	complemented
29	C₃×#4083	C₂²	1	6	yes	complemented
30	C₃×#4083	C₂²	1	3	yes	complemented
31	C₃×#4081	C₂²	1	3	yes	complemented
32	C₃×#4076	C₂²	1	6	yes	complemented
33	C₃×#4075	C₂²	1	3	yes	complemented
34	C₃×#4044	C₂²	1	6	yes	complemented
35	C₃×#4041	C₂²	1	6	yes	complemented
36	C₃×#4040	C₂²	1	6	yes	complemented
37	C₃×D₅×C₄⋊C₄	C₂²	1	6	yes	complemented
38	C₃×#4032	C₂²	1	3	yes	complemented
39	C₃×#4030	C₂²	1	6	yes	complemented
40	C₃×#4030	C₂²	1	6	yes	complemented
41	C₃×#4029	C₂²	1	6	yes	complemented
42	C₃×#4028	C₂²	1	6	yes	complemented
43	C₃×#4028	C₂²	1	3	yes	complemented
44	C₃×D₅×C₂²⋊C₄	C₂²	1	6	yes	—
45	C₃×D₅×C₂²⋊C₄	C₂²	1	3	yes	—
46	C₃×D₅×C₂²⋊C₄	C₂²	1	3	yes	complemented
47	C₃×#4025	C₂²	1	6	yes	complemented
48	C₃×#4022	C₂²	1	2	yes	complemented
49	C₃×#4020	C₂²	1	1	yes	characteristic, complemented
50	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₃×#560	—	5	1	no	maximal, Hall
52	C₅×#560	C₂×C₃	1	1	yes	characteristic, complemented
53	#66054	C₂×C₃	1	1	yes	characteristic, complemented
54	D₅×#127	C₂×C₃	1	1	yes	characteristic, complemented
55	#66045	C₂×C₃	1	2	yes	complemented
56	D₅×#126	C₂×C₃	1	2	yes	complemented
57	#66000	C₂×C₃	1	3	yes	complemented
58	D₅×#123	C₂×C₃	1	3	yes	complemented
59	#65954	C₂×C₃	1	6	yes	complemented
60	D₅×#121	C₂×C₃	1	6	yes	complemented
61	#65929	C₂×C₃	1	3	yes	complemented
62	D₅×#120	C₂×C₃	1	3	yes	complemented
63	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
64	C₂³×C₃×D₅	—	4	6	no	—
65	C₂³×C₃×D₅	C₂³	1	3	yes	—
66	C₂³×C₃×D₅	C₂³	1	2	yes	—
67	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
68	C₂³×C₃×D₅	C₂³	1	2	yes	—
69	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₅×D₄	C₂³	1	3	yes	—
71	C₂×C₃×C₅×D₄	C₂³	1	6	yes	—
72	C₂×C₃×C₅×D₄	C₂³	1	3	yes	complemented
73	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	complemented
74	C₂×C₃×C₂²⋊D₅	C₂³	1	6	yes	—
75	C₂×C₃×C₂²⋊D₅	C₂³	1	3	yes	—
76	C₂×C₃×C₂²⋊D₅	C₂³	1	6	yes	—
77	C₂×C₃×C₂²⋊D₅	C₂³	1	3	yes	—
78	C₂×C₃×C₂²⋊D₅	C₂³	1	6	yes	complemented
79	C₂²×C₃×Dic₅	C₂³	1	3	yes	complemented
80	C₃×D₄×D₅	—	4	12	no	—
81	C₃×D₄×D₅	—	4	6	no	—
82	C₃×D₄×D₅	—	4	6	no	—
83	C₂×C₃×D₂₀	C₂³	1	3	yes	—
84	C₂×C₃×D₂₀	C₂³	1	6	yes	—
85	C₂×C₃×D₂₀	C₂³	1	3	yes	complemented
86	C₂×C₃×C₄×D₅	—	4	6	no	—
87	C₂×C₃×C₄×D₅	C₂³	1	6	yes	—
88	C₂×C₃×C₄×D₅	C₂³	1	3	yes	—
89	C₂×C₃×C₄×D₅	C₂³	1	6	yes	complemented
90	C₃×C₅×C₄⋊C₄	C₂³	1	6	yes	complemented
91	C₃×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
92	C₃×C₅×C₂²⋊C₄	C₂³	1	3	yes	—
93	C₃×C₅×C₂²⋊C₄	C₂³	1	3	yes	complemented
94	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic, complemented
95	C₃×C₂²⋊Dic₅	C₂³	1	3	yes	—
96	C₃×C₂²⋊Dic₅	C₂³	1	6	yes	—
97	C₃×C₂²⋊Dic₅	C₂³	1	3	yes	complemented
98	C₃×#685	C₂³	1	6	yes	—
99	C₃×#685	C₂³	1	6	yes	—
100	C₃×#685	C₂³	1	6	yes	—
101	C₃×#685	C₂³	1	6	yes	complemented
102	C₃×C₄⋊Dic₅	C₂³	1	6	yes	complemented
103	C₃×#683	C₂³	1	6	yes	complemented
104	C₃×#683	C₂³	1	6	yes	complemented
105	C₃×C₄×Dic₅	C₂³	1	3	yes	complemented
106	C₃×#560	—	5	1	no	—
107	C₃×#560	—	5	2	no	—
108	C₃×#560	—	5	3	no	—
109	C₃×#560	—	5	6	no	—
110	C₃×#560	—	5	3	no	—
111	C₃×#560	D₅	1	1	yes	characteristic, direct product factor
112	C₂×C₃×#127	—	5	1	no	—
113	C₂×C₃×#126	—	5	2	no	—
114	C₂×C₃×#123	—	5	3	no	—
115	C₂×C₃×#121	—	5	6	no	—
116	C₂×C₃×#120	—	5	3	no	—
117	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic
118	C₂×D₄×D₅	C₂²×C₃	1	3	yes	—
119	C₂×D₄×D₅	C₂²×C₃	1	6	yes	—
120	C₂×D₄×D₅	C₂²×C₃	1	3	yes	complemented
121	C₂²×C₄×D₅	C₂²×C₃	1	3	yes	complemented
122	C₅×#127	C₂²×C₃	1	1	yes	characteristic, complemented
123	C₅×#126	C₂²×C₃	1	2	yes	complemented
124	C₅×#123	C₂²×C₃	1	3	yes	complemented
125	C₅×#121	C₂²×C₃	1	6	yes	complemented
126	C₅×#120	C₂²×C₃	1	3	yes	complemented
127	#4099	C₂²×C₃	1	3	yes	complemented
128	#4086	C₂²×C₃	1	3	yes	complemented
129	#4086	C₂²×C₃	1	3	yes	complemented
130	#4085	C₂²×C₃	1	6	yes	complemented
131	#4085	C₂²×C₃	1	6	yes	complemented
132	#4084	C₂²×C₃	1	6	yes	complemented
133	#4083	C₂²×C₃	1	3	yes	complemented
134	#4083	C₂²×C₃	1	6	yes	complemented
135	#4081	C₂²×C₃	1	3	yes	complemented
136	#4076	C₂²×C₃	1	6	yes	complemented
137	#4075	C₂²×C₃	1	3	yes	complemented
138	#4044	C₂²×C₃	1	6	yes	complemented
139	#4041	C₂²×C₃	1	6	yes	complemented
140	#4040	C₂²×C₃	1	6	yes	complemented
141	D₅×C₄⋊C₄	C₂²×C₃	1	6	yes	complemented
142	#4032	C₂²×C₃	1	3	yes	complemented
143	#4030	C₂²×C₃	1	6	yes	complemented
144	#4030	C₂²×C₃	1	6	yes	complemented
145	#4029	C₂²×C₃	1	6	yes	complemented
146	#4028	C₂²×C₃	1	6	yes	complemented
147	#4028	C₂²×C₃	1	3	yes	complemented
148	D₅×C₂²⋊C₄	C₂²×C₃	1	6	yes	—
149	D₅×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
150	D₅×C₂²⋊C₄	C₂²×C₃	1	3	yes	complemented
151	#4025	C₂²×C₃	1	6	yes	complemented
152	#4022	C₂²×C₃	1	2	yes	complemented
153	#4020	C₂²×C₃	1	1	yes	characteristic, complemented
154	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
155	C₂×#560	—	5	1	no	Sylow
156	C₂³×C₃×C₅	—	4	3	no	—
157	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
158	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
159	C₂³×C₃×C₅	C₂⁴	1	3	yes	—
160	C₂²×C₃×D₅	—	2	6	no	—
161	C₂²×C₃×D₅	—	2	12	no	—
162	C₂²×C₃×D₅	—	2	12	no	—
163	C₂²×C₃×D₅	—	2	6	no	—
164	C₂²×C₃×D₅	—	4	6	no	—
165	C₂²×C₃×D₅	—	4	3	no	—
166	C₂²×C₃×D₅	—	4	16	no	—
167	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
168	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
169	C₂²×C₃×D₅	C₂⁴	1	3	yes	—
170	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
171	C₃×C₅×D₄	—	4	6	no	—
172	C₃×C₅×D₄	—	4	3	no	—
173	C₃×C₅×D₄	—	4	3	no	—
174	C₂×C₃×C₄×C₅	—	4	3	no	—
175	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
176	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
177	C₃×C₂²⋊D₅	—	4	6	no	—
178	C₃×C₂²⋊D₅	—	4	6	no	—
179	C₃×C₂²⋊D₅	—	4	3	no	—
180	C₃×C₂²⋊D₅	—	4	3	no	—
181	C₃×C₂²⋊D₅	—	4	6	no	—
182	C₂×C₃×Dic₅	—	4	3	no	—
183	C₂×C₃×Dic₅	C₂⁴	1	3	yes	—
184	C₂×C₃×Dic₅	C₂⁴	1	6	yes	—
185	C₃×D₂₀	—	4	6	no	—
186	C₃×D₂₀	—	4	3	no	—
187	C₃×D₂₀	—	4	3	no	—
188	C₃×C₄×D₅	—	2	12	no	—
189	C₃×C₄×D₅	—	2	6	no	—
190	C₃×C₄×D₅	—	4	6	no	—
191	C₂⁵×C₃	—	5	1	no	—
192	C₂²×C₃×D₄	—	5	6	no	—
193	C₂²×C₃×D₄	—	5	3	no	—
194	C₂²×C₃×D₄	—	5	3	no	—
195	C₂³×C₃×C₄	—	5	3	no	—
196	C₃×#127	—	5	3	no	—
197	C₃×#127	—	5	3	no	—
198	C₃×#127	—	5	1	no	—
199	C₃×#127	C₂×D₅	1	1	yes	characteristic, complemented
200	C₃×#126	—	5	6	no	—
201	C₃×#126	—	5	6	no	—
202	C₃×#126	—	5	2	no	—
203	C₃×#126	C₂×D₅	1	2	yes	complemented
204	C₃×#123	—	5	3	no	—
205	C₃×#123	—	5	3	no	—
206	C₃×#123	—	5	6	no	—
207	C₃×#123	—	5	6	no	—
208	C₃×#123	—	5	3	no	—
209	C₃×#123	C₂×D₅	1	3	yes	complemented
210	C₃×#121	—	5	6	no	—
211	C₃×#121	—	5	6	no	—
212	C₃×#121	—	5	6	no	—
213	C₃×#121	—	5	6	no	—
214	C₃×#121	—	5	6	no	—
215	C₃×#121	—	5	6	no	—
216	C₃×#121	—	5	6	no	—
217	C₃×#121	C₂×D₅	1	6	yes	complemented
218	C₃×#120	—	5	3	no	—
219	C₃×#120	—	5	6	no	—
220	C₃×#120	—	5	3	no	—
221	C₃×#120	—	5	3	no	—
222	C₃×#120	—	5	6	no	—
223	C₃×#120	C₂×D₅	1	3	yes	complemented
224	C₂×C₃×C₄⋊C₄	—	5	6	no	—
225	C₂×C₃×C₂²⋊C₄	—	5	6	no	—
226	C₂×C₃×C₂²⋊C₄	—	5	3	no	—
227	C₂×C₃×C₂²⋊C₄	—	5	3	no	—
228	C₂×C₃×C₄²	—	5	1	no	—
229	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
230	C₂³×D₅	—	4	6	no	—
231	C₂³×D₅	C₂³×C₃	1	3	yes	—
232	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
233	C₂³×D₅	C₂³×C₃	1	2	yes	—
234	C₂³×D₅	C₂³×C₃	1	2	yes	—
235	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
236	C₂×C₅×D₄	C₂³×C₃	1	6	yes	—
237	C₂×C₅×D₄	C₂³×C₃	1	3	yes	—
238	C₂×C₅×D₄	C₂³×C₃	1	3	yes	complemented
239	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	complemented
240	C₂×C₂²⋊D₅	C₂³×C₃	1	3	yes	—
241	C₂×C₂²⋊D₅	C₂³×C₃	1	6	yes	—
242	C₂×C₂²⋊D₅	C₂³×C₃	1	6	yes	—
243	C₂×C₂²⋊D₅	C₂³×C₃	1	3	yes	—
244	C₂×C₂²⋊D₅	C₂³×C₃	1	6	yes	complemented
245	C₂²×Dic₅	C₂³×C₃	1	3	yes	complemented
246	D₄×D₅	—	4	12	no	—
247	D₄×D₅	—	4	6	no	—
248	D₄×D₅	—	4	6	no	—
249	C₂×D₂₀	C₂³×C₃	1	3	yes	—
250	C₂×D₂₀	C₂³×C₃	1	6	yes	—
251	C₂×D₂₀	C₂³×C₃	1	3	yes	complemented
252	C₂×C₄×D₅	—	4	6	no	—
253	C₂×C₄×D₅	C₂³×C₃	1	6	yes	—
254	C₂×C₄×D₅	C₂³×C₃	1	3	yes	—
255	C₂×C₄×D₅	C₂³×C₃	1	6	yes	complemented
256	C₅×C₄⋊C₄	C₂³×C₃	1	6	yes	complemented
257	C₅×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
258	C₅×C₂²⋊C₄	C₂³×C₃	1	3	yes	—
259	C₅×C₂²⋊C₄	C₂³×C₃	1	3	yes	complemented
260	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic, complemented
261	C₂²⋊Dic₅	C₂³×C₃	1	6	yes	—
262	C₂²⋊Dic₅	C₂³×C₃	1	3	yes	—
263	C₂²⋊Dic₅	C₂³×C₃	1	3	yes	complemented
264	#685	C₂³×C₃	1	6	yes	—
265	#685	C₂³×C₃	1	6	yes	—
266	#685	C₂³×C₃	1	6	yes	—
267	#685	C₂³×C₃	1	6	yes	complemented
268	C₄⋊Dic₅	C₂³×C₃	1	6	yes	complemented
269	#683	C₂³×C₃	1	6	yes	complemented
270	#683	C₂³×C₃	1	6	yes	complemented
271	C₄×Dic₅	C₂³×C₃	1	3	yes	complemented
272	#560	—	5	1	no	—
273	#560	—	5	2	no	—
274	#560	—	5	3	no	—
275	#560	—	5	6	no	—
276	#560	—	5	3	no	—
277	#560	C₃×D₅	1	1	yes	characteristic, direct product factor
278	C₂×#127	—	5	1	no	—
279	C₂×#126	—	5	2	no	—
280	C₂×#123	—	5	3	no	—
281	C₂×#121	—	5	6	no	—
282	C₂×#120	—	5	3	no	—
283	C₂²×C₃×C₅	—	2	3	no	—
284	C₂²×C₃×C₅	—	2	6	no	—
285	C₂²×C₃×C₅	—	2	6	no	—
286	C₂²×C₃×C₅	—	2	3	no	—
287	C₂²×C₃×C₅	—	4	4	no	—
288	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
289	C₂×C₃×D₅	—	2	3	no	—
290	C₂×C₃×D₅	—	2	6	no	—
291	C₂×C₃×D₅	—	2	6	no	—
292	C₂×C₃×D₅	—	2	3	no	—
293	C₂×C₃×D₅	—	4	8	no	—
294	C₂×C₃×D₅	—	4	4	no	—
295	C₂×C₃×D₅	—	4	12	no	—
296	C₂×C₃×D₅	—	4	8	no	—
297	C₂×C₃×D₅	—	4	4	no	—
298	C₂×C₃×D₅	H(5,𝔽₂)	1	6	yes	—
299	C₃×C₄×C₅	—	2	6	no	—
300	C₃×C₄×C₅	—	2	3	no	—
301	C₃×Dic₅	—	2	6	no	—
302	C₃×Dic₅	—	2	3	no	—
303	C₂⁴×C₃	—	5	2	no	—
304	C₂⁴×C₃	—	5	1	no	—
305	C₂⁴×C₃	—	5	3	no	—
306	C₂⁴×C₃	—	5	1	no	—
307	C₂⁴×C₃	—	5	2	no	—
308	C₂⁴×C₃	—	20	6	no	—
309	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
310	C₂×C₃×D₄	—	5	6	no	—
311	C₂×C₃×D₄	—	5	6	no	—
312	C₂×C₃×D₄	—	5	3	no	—
313	C₂×C₃×D₄	—	5	3	no	—
314	C₂×C₃×D₄	—	5	6	no	—
315	C₂×C₃×D₄	—	5	6	no	—
316	C₂×C₃×D₄	—	5	3	no	—
317	C₂×C₃×D₄	—	5	3	no	—
318	C₂×C₃×D₄	—	20	12	no	—
319	C₂×C₃×D₄	—	20	6	no	—
320	C₂×C₃×D₄	—	20	6	no	—
321	C₂×C₃×D₄	C₂²×D₅	1	6	yes	—
322	C₂×C₃×D₄	C₂²×D₅	1	3	yes	—
323	C₂×C₃×D₄	C₂²×D₅	1	3	yes	complemented
324	C₂²×C₃×C₄	—	5	3	no	—
325	C₂²×C₃×C₄	—	5	3	no	—
326	C₂²×C₃×C₄	—	5	6	no	—
327	C₂²×C₃×C₄	—	5	6	no	—
328	C₂²×C₃×C₄	—	20	6	no	—
329	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	complemented
330	C₃×C₄⋊C₄	—	5	6	no	—
331	C₃×C₄⋊C₄	—	5	6	no	—
332	C₃×C₄⋊C₄	—	5	6	no	—
333	C₃×C₄⋊C₄	C₂²×D₅	1	6	yes	complemented
334	C₃×C₂²⋊C₄	—	5	6	no	—
335	C₃×C₂²⋊C₄	—	5	3	no	—
336	C₃×C₂²⋊C₄	—	5	3	no	—
337	C₃×C₂²⋊C₄	—	5	6	no	—
338	C₃×C₂²⋊C₄	—	5	6	no	—
339	C₃×C₂²⋊C₄	—	5	6	no	—
340	C₃×C₂²⋊C₄	—	5	6	no	—
341	C₃×C₂²⋊C₄	C₂²×D₅	1	6	yes	—
342	C₃×C₂²⋊C₄	C₂²×D₅	1	3	yes	—
343	C₃×C₂²⋊C₄	C₂²×D₅	1	3	yes	complemented
344	C₃×C₄²	—	5	3	no	—
345	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic, complemented
346	C₂³×C₅	—	4	3	no	—
347	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
348	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
349	C₂³×C₅	C₂⁴×C₃	1	3	yes	—
350	C₂²×D₅	—	2	6	no	—
351	C₂²×D₅	—	2	12	no	—
352	C₂²×D₅	—	2	12	no	—
353	C₂²×D₅	—	2	6	no	—
354	C₂²×D₅	—	4	6	no	—
355	C₂²×D₅	—	4	3	no	—
356	C₂²×D₅	—	4	16	no	—
357	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
358	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
359	C₂²×D₅	C₂⁴×C₃	1	3	yes	—
360	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
361	C₅×D₄	—	4	6	no	—
362	C₅×D₄	—	4	3	no	—
363	C₅×D₄	—	4	3	no	—
364	C₂×C₄×C₅	—	4	3	no	—
365	C₂×C₄×C₅	C₂⁴×C₃	1	3	yes	—
366	C₂×C₄×C₅	C₂⁴×C₃	1	6	yes	—
367	C₂²⋊D₅	—	4	6	no	—
368	C₂²⋊D₅	—	4	6	no	—
369	C₂²⋊D₅	—	4	3	no	—
370	C₂²⋊D₅	—	4	3	no	—
371	C₂²⋊D₅	—	4	6	no	—
372	C₂×Dic₅	—	4	3	no	—
373	C₂×Dic₅	C₂⁴×C₃	1	3	yes	—
374	C₂×Dic₅	C₂⁴×C₃	1	6	yes	—
375	D₂₀	—	4	6	no	—
376	D₂₀	—	4	3	no	—
377	D₂₀	—	4	3	no	—
378	C₄×D₅	—	2	12	no	—
379	C₄×D₅	—	2	6	no	—
380	C₄×D₅	—	4	6	no	—
381	C₂⁵	—	5	1	no	—
382	C₂²×D₄	—	5	6	no	—
383	C₂²×D₄	—	5	3	no	—
384	C₂²×D₄	—	5	3	no	—
385	C₂³×C₄	—	5	3	no	—
386	#127	—	5	3	no	—
387	#127	—	5	3	no	—
388	#127	—	5	1	no	—
389	#127	C₂×C₃×D₅	1	1	yes	characteristic, complemented
390	#126	—	5	6	no	—
391	#126	—	5	6	no	—
392	#126	—	5	2	no	—
393	#126	C₂×C₃×D₅	1	2	yes	complemented
394	#123	—	5	3	no	—
395	#123	—	5	3	no	—
396	#123	—	5	6	no	—
397	#123	—	5	6	no	—
398	#123	—	5	3	no	—
399	#123	C₂×C₃×D₅	1	3	yes	complemented
400	#121	—	5	6	no	—
401	#121	—	5	6	no	—
402	#121	—	5	6	no	—
403	#121	—	5	6	no	—
404	#121	—	5	6	no	—
405	#121	—	5	6	no	—
406	#121	—	5	6	no	—
407	#121	C₂×C₃×D₅	1	6	yes	complemented
408	#120	—	5	3	no	—
409	#120	—	5	6	no	—
410	#120	—	5	3	no	—
411	#120	—	5	3	no	—
412	#120	—	5	6	no	—
413	#120	C₂×C₃×D₅	1	3	yes	complemented
414	C₂×C₄⋊C₄	—	5	6	no	—
415	C₂×C₂²⋊C₄	—	5	6	no	—
416	C₂×C₂²⋊C₄	—	5	3	no	—
417	C₂×C₂²⋊C₄	—	5	3	no	—
418	C₂×C₄²	—	5	1	no	—
419	C₂×C₃×C₅	—	4	2	no	—
420	C₂×C₃×C₅	—	4	1	no	—
421	C₂×C₃×C₅	—	4	3	no	—
422	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	3	yes	—
423	C₃×D₅	—	4	3	no	—
424	C₃×D₅	—	4	2	no	—
425	C₃×D₅	—	4	1	no	—
426	C₃×D₅	#560	1	4	yes	direct product factor
427	C₂³×C₃	—	4	3	no	—
428	C₂³×C₃	—	5	1	no	—
429	C₂³×C₃	—	5	2	no	—
430	C₂³×C₃	—	5	1	no	—
431	C₂³×C₃	—	5	3	no	—
432	C₂³×C₃	—	10	6	no	—
433	C₂³×C₃	—	10	12	no	—
434	C₂³×C₃	—	10	12	no	—
435	C₂³×C₃	—	10	6	no	—
436	C₂³×C₃	—	20	6	no	—
437	C₂³×C₃	—	20	3	no	—
438	C₂³×C₃	—	20	16	no	—
439	C₂³×C₃	C₂³×D₅	1	2	yes	—
440	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
441	C₂³×C₃	C₂³×D₅	1	3	yes	—
442	C₃×D₄	—	4	6	no	—
443	C₃×D₄	—	4	3	no	—
444	C₃×D₄	—	4	3	no	—
445	C₃×D₄	—	20	6	no	—
446	C₃×D₄	—	20	3	no	—
447	C₃×D₄	—	20	3	no	—
448	C₃×D₄	—	20	6	no	—
449	C₃×D₄	—	20	6	no	—
450	C₃×D₄	—	20	3	no	—
451	C₃×D₄	—	20	6	no	—
452	C₃×D₄	—	20	3	no	—
453	C₂×C₃×C₄	—	4	3	no	—
454	C₂×C₃×C₄	—	5	3	no	—
455	C₂×C₃×C₄	—	5	6	no	—
456	C₂×C₃×C₄	—	10	12	no	—
457	C₂×C₃×C₄	—	10	6	no	—
458	C₂×C₃×C₄	—	20	6	no	—
459	C₂×C₃×C₄	—	20	3	no	—
460	C₂×C₃×C₄	C₂³×D₅	1	3	yes	—
461	C₂×C₃×C₄	C₂³×D₅	1	6	yes	—
462	C₂²×C₅	—	2	3	no	—
463	C₂²×C₅	—	2	6	no	—
464	C₂²×C₅	—	2	6	no	—
465	C₂²×C₅	—	2	3	no	—
466	C₂²×C₅	—	4	4	no	—
467	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
468	C₂×D₅	—	2	3	no	—
469	C₂×D₅	—	2	6	no	—
470	C₂×D₅	—	2	6	no	—
471	C₂×D₅	—	2	3	no	—
472	C₂×D₅	—	4	8	no	—
473	C₂×D₅	—	4	4	no	—
474	C₂×D₅	—	4	12	no	—
475	C₂×D₅	—	4	8	no	—
476	C₂×D₅	—	4	4	no	—
477	C₂×D₅	C₃×H(5,𝔽₂)	1	6	yes	—
478	C₄×C₅	—	2	6	no	—
479	C₄×C₅	—	2	3	no	—
480	Dic₅	—	2	6	no	—
481	Dic₅	—	2	3	no	—
482	C₂⁴	—	5	2	no	—
483	C₂⁴	—	5	1	no	—
484	C₂⁴	—	5	3	no	—
485	C₂⁴	—	5	1	no	—
486	C₂⁴	—	5	2	no	—
487	C₂⁴	—	20	6	no	—
488	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
489	C₂×D₄	—	5	6	no	—
490	C₂×D₄	—	5	6	no	—
491	C₂×D₄	—	5	3	no	—
492	C₂×D₄	—	5	3	no	—
493	C₂×D₄	—	5	6	no	—
494	C₂×D₄	—	5	6	no	—
495	C₂×D₄	—	5	3	no	—
496	C₂×D₄	—	5	3	no	—
497	C₂×D₄	—	20	12	no	—
498	C₂×D₄	—	20	6	no	—
499	C₂×D₄	—	20	6	no	—
500	C₂×D₄	C₂²×C₃×D₅	1	6	yes	—
501	C₂×D₄	C₂²×C₃×D₅	1	3	yes	—
502	C₂×D₄	C₂²×C₃×D₅	1	3	yes	complemented
503	C₂²×C₄	—	5	3	no	—
504	C₂²×C₄	—	5	3	no	—
505	C₂²×C₄	—	5	6	no	—
506	C₂²×C₄	—	5	6	no	—
507	C₂²×C₄	—	20	6	no	—
508	C₂²×C₄	C₂²×C₃×D₅	1	3	yes	complemented
509	C₄⋊C₄	—	5	6	no	—
510	C₄⋊C₄	—	5	6	no	—
511	C₄⋊C₄	—	5	6	no	—
512	C₄⋊C₄	C₂²×C₃×D₅	1	6	yes	complemented
513	C₂²⋊C₄	—	5	6	no	—
514	C₂²⋊C₄	—	5	3	no	—
515	C₂²⋊C₄	—	5	3	no	—
516	C₂²⋊C₄	—	5	6	no	—
517	C₂²⋊C₄	—	5	6	no	—
518	C₂²⋊C₄	—	5	6	no	—
519	C₂²⋊C₄	—	5	6	no	—
520	C₂²⋊C₄	C₂²×C₃×D₅	1	6	yes	—
521	C₂²⋊C₄	C₂²×C₃×D₅	1	3	yes	—
522	C₂²⋊C₄	C₂²×C₃×D₅	1	3	yes	complemented
523	C₄²	—	5	3	no	—
524	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic, complemented
525	C₃×C₅	C₂×#560	1	1	yes	characteristic, complemented, Hall
526	C₂²×C₃	—	2	3	no	—
527	C₂²×C₃	—	2	6	no	—
528	C₂²×C₃	—	2	6	no	—
529	C₂²×C₃	—	2	3	no	—
530	C₂²×C₃	—	4	4	no	—
531	C₂²×C₃	—	5	6	no	—
532	C₂²×C₃	—	10	3	no	—
533	C₂²×C₃	—	10	6	no	—
534	C₂²×C₃	—	10	6	no	—
535	C₂²×C₃	—	10	3	no	—
536	C₂²×C₃	—	20	12	no	—
537	C₂²×C₃	—	20	8	no	—
538	C₂²×C₃	—	20	4	no	—
539	C₂²×C₃	—	20	8	no	—
540	C₂²×C₃	—	20	4	no	—
541	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
542	C₃×C₄	—	2	6	no	—
543	C₃×C₄	—	2	3	no	—
544	C₃×C₄	—	10	6	no	—
545	C₃×C₄	—	10	3	no	—
546	C₂×C₅	—	4	2	no	—
547	C₂×C₅	—	4	1	no	—
548	C₂×C₅	—	4	3	no	—
549	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	3	yes	—
550	D₅	—	4	2	no	—
551	D₅	—	4	1	no	—
552	D₅	—	4	3	no	—
553	D₅	C₃×#560	1	4	yes	direct product factor
554	C₂³	—	4	3	no	—
555	C₂³	—	5	1	no	—
556	C₂³	—	5	2	no	—
557	C₂³	—	5	1	no	—
558	C₂³	—	5	3	no	—
559	C₂³	—	10	6	no	—
560	C₂³	—	10	12	no	—
561	C₂³	—	10	12	no	—
562	C₂³	—	10	6	no	—
563	C₂³	—	20	6	no	—
564	C₂³	—	20	3	no	—
565	C₂³	—	20	16	no	—
566	C₂³	C₂³×C₃×D₅	1	2	yes	—
567	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
568	C₂³	C₂³×C₃×D₅	1	3	yes	—
569	D₄	—	4	6	no	—
570	D₄	—	4	3	no	—
571	D₄	—	4	3	no	—
572	D₄	—	20	6	no	—
573	D₄	—	20	3	no	—
574	D₄	—	20	3	no	—
575	D₄	—	20	6	no	—
576	D₄	—	20	6	no	—
577	D₄	—	20	3	no	—
578	D₄	—	20	6	no	—
579	D₄	—	20	3	no	—
580	C₂×C₄	—	4	3	no	—
581	C₂×C₄	—	5	3	no	—
582	C₂×C₄	—	5	6	no	—
583	C₂×C₄	—	10	12	no	—
584	C₂×C₄	—	10	6	no	—
585	C₂×C₄	—	20	6	no	—
586	C₂×C₄	—	20	3	no	—
587	C₂×C₄	C₂³×C₃×D₅	1	3	yes	—
588	C₂×C₄	C₂³×C₃×D₅	1	6	yes	—
589	C₂×C₃	—	4	2	no	—
590	C₂×C₃	—	4	1	no	—
591	C₂×C₃	—	4	3	no	—
592	C₂×C₃	—	5	4	no	—
593	C₂×C₃	—	20	2	no	—
594	C₂×C₃	—	20	1	no	—
595	C₂×C₃	—	20	3	no	—
596	C₂×C₃	D₅×H(5,𝔽₂)	1	3	yes	—
597	C₅	C₂×C₃×#560	1	1	yes	characteristic, complemented, Sylow
598	C₂²	—	2	3	no	—
599	C₂²	—	2	6	no	—
600	C₂²	—	2	6	no	—
601	C₂²	—	2	3	no	—
602	C₂²	—	4	4	no	—
603	C₂²	—	5	6	no	—
604	C₂²	—	10	3	no	—
605	C₂²	—	10	6	no	—
606	C₂²	—	10	6	no	—
607	C₂²	—	10	3	no	—
608	C₂²	—	20	8	no	—
609	C₂²	—	20	4	no	—
610	C₂²	—	20	12	no	—
611	C₂²	—	20	8	no	—
612	C₂²	—	20	4	no	—
613	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
614	C₄	—	2	6	no	—
615	C₄	—	2	3	no	—
616	C₄	—	10	6	no	—
617	C₄	—	10	3	no	—
618	C₃	D₅×#560	1	1	yes	characteristic, direct product factor, Sylow
619	C₂	—	4	2	no	—
620	C₂	—	4	1	no	—
621	C₂	—	4	3	no	—
622	C₂	—	5	4	no	—
623	C₂	—	20	2	no	—
624	C₂	—	20	1	no	—
625	C₂	—	20	3	no	—
626	C₂	C₃×D₅×H(5,𝔽₂)	1	3	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₅×#560	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×#560	D₅
hypocenter	C₅	C₂×C₃×#560
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#560

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#560	C₂	semidirect
2. C₃×#66054	C₂	semidirect
3. C₃×D₅×#127	C₂	semidirect
4. C₃×#66045	C₂	semidirect
5. C₃×D₅×#126	C₂	semidirect
6. C₃×#66000	C₂	semidirect
7. C₃×D₅×#123	C₂	semidirect
8. C₃×#65954	C₂	semidirect
9. C₃×D₅×#121	C₂	semidirect
10. C₃×#65929	C₂	semidirect
11. C₃×D₅×#120	C₂	semidirect
12. D₅×#560	C₃	direct (N × H)
16. C₂×C₃×D₄×D₅	C₂²	semidirect
17. C₂²×C₃×C₄×D₅	C₂²	semidirect
18. C₃×C₅×#127	C₂²	semidirect
19. C₃×C₅×#126	C₂²	semidirect
20. C₃×C₅×#123	C₂²	semidirect
21. C₃×C₅×#121	C₂²	semidirect
22. C₃×C₅×#120	C₂²	semidirect
23. C₃×#4099	C₂²	semidirect
24. C₃×#4086	C₂²	semidirect
25. C₃×#4086	C₂²	semidirect
26. C₃×#4085	C₂²	semidirect
27. C₃×#4085	C₂²	semidirect
28. C₃×#4084	C₂²	semidirect
29. C₃×#4083	C₂²	semidirect
30. C₃×#4083	C₂²	semidirect
31. C₃×#4081	C₂²	semidirect
32. C₃×#4076	C₂²	semidirect
33. C₃×#4075	C₂²	semidirect
34. C₃×#4044	C₂²	semidirect
35. C₃×#4041	C₂²	semidirect
36. C₃×#4040	C₂²	semidirect
37. C₃×D₅×C₄⋊C₄	C₂²	semidirect
38. C₃×#4032	C₂²	semidirect
39. C₃×#4030	C₂²	semidirect
40. C₃×#4030	C₂²	semidirect
41. C₃×#4029	C₂²	semidirect
42. C₃×#4028	C₂²	semidirect
43. C₃×#4028	C₂²	semidirect
46. C₃×D₅×C₂²⋊C₄	C₂²	semidirect
47. C₃×#4025	C₂²	semidirect
48. C₃×#4022	C₂²	semidirect
49. C₃×#4020	C₂²	semidirect
50. C₃×C₄²×D₅	C₂²	semidirect
52. C₅×#560	C₂×C₃	semidirect
53. #66054	C₂×C₃	semidirect
54. D₅×#127	C₂×C₃	semidirect
55. #66045	C₂×C₃	semidirect
56. D₅×#126	C₂×C₃	semidirect
57. #66000	C₂×C₃	semidirect
58. D₅×#123	C₂×C₃	semidirect
59. #65954	C₂×C₃	semidirect
60. D₅×#121	C₂×C₃	semidirect
61. #65929	C₂×C₃	semidirect
62. D₅×#120	C₂×C₃	semidirect
72. C₂×C₃×C₅×D₄	C₂³	semidirect
73. C₂²×C₃×C₄×C₅	C₂³	semidirect
78. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
79. C₂²×C₃×Dic₅	C₂³	semidirect
85. C₂×C₃×D₂₀	C₂³	semidirect
89. C₂×C₃×C₄×D₅	C₂³	semidirect
90. C₃×C₅×C₄⋊C₄	C₂³	semidirect
93. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
94. C₃×C₄²×C₅	C₂³	semidirect
97. C₃×C₂²⋊Dic₅	C₂³	semidirect
101. C₃×#685	C₂³	semidirect
102. C₃×C₄⋊Dic₅	C₂³	semidirect
103. C₃×#683	C₂³	semidirect
104. C₃×#683	C₂³	semidirect
105. C₃×C₄×Dic₅	C₂³	semidirect
111. C₃×#560	D₅	direct (N × H)
120. C₂×D₄×D₅	C₂²×C₃	semidirect
121. C₂²×C₄×D₅	C₂²×C₃	semidirect
122. C₅×#127	C₂²×C₃	semidirect
123. C₅×#126	C₂²×C₃	semidirect
124. C₅×#123	C₂²×C₃	semidirect
125. C₅×#121	C₂²×C₃	semidirect
126. C₅×#120	C₂²×C₃	semidirect
127. #4099	C₂²×C₃	semidirect
128. #4086	C₂²×C₃	semidirect
129. #4086	C₂²×C₃	semidirect
130. #4085	C₂²×C₃	semidirect
131. #4085	C₂²×C₃	semidirect
132. #4084	C₂²×C₃	semidirect
133. #4083	C₂²×C₃	semidirect
134. #4083	C₂²×C₃	semidirect
135. #4081	C₂²×C₃	semidirect
136. #4076	C₂²×C₃	semidirect
137. #4075	C₂²×C₃	semidirect
138. #4044	C₂²×C₃	semidirect
139. #4041	C₂²×C₃	semidirect
140. #4040	C₂²×C₃	semidirect
141. D₅×C₄⋊C₄	C₂²×C₃	semidirect
142. #4032	C₂²×C₃	semidirect
143. #4030	C₂²×C₃	semidirect
144. #4030	C₂²×C₃	semidirect
145. #4029	C₂²×C₃	semidirect
146. #4028	C₂²×C₃	semidirect
147. #4028	C₂²×C₃	semidirect
150. D₅×C₂²⋊C₄	C₂²×C₃	semidirect
151. #4025	C₂²×C₃	semidirect
152. #4022	C₂²×C₃	semidirect
153. #4020	C₂²×C₃	semidirect
154. C₄²×D₅	C₂²×C₃	semidirect
199. C₃×#127	C₂×D₅	semidirect
203. C₃×#126	C₂×D₅	semidirect
209. C₃×#123	C₂×D₅	semidirect
217. C₃×#121	C₂×D₅	semidirect
223. C₃×#120	C₂×D₅	semidirect
238. C₂×C₅×D₄	C₂³×C₃	semidirect
239. C₂²×C₄×C₅	C₂³×C₃	semidirect
244. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
245. C₂²×Dic₅	C₂³×C₃	semidirect
251. C₂×D₂₀	C₂³×C₃	semidirect
255. C₂×C₄×D₅	C₂³×C₃	semidirect
256. C₅×C₄⋊C₄	C₂³×C₃	semidirect
259. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
260. C₄²×C₅	C₂³×C₃	semidirect
263. C₂²⋊Dic₅	C₂³×C₃	semidirect
267. #685	C₂³×C₃	semidirect
268. C₄⋊Dic₅	C₂³×C₃	semidirect
269. #683	C₂³×C₃	semidirect
270. #683	C₂³×C₃	semidirect
271. C₄×Dic₅	C₂³×C₃	semidirect
277. #560	C₃×D₅	direct (N × H)
323. C₂×C₃×D₄	C₂²×D₅	semidirect
329. C₂²×C₃×C₄	C₂²×D₅	semidirect
333. C₃×C₄⋊C₄	C₂²×D₅	semidirect
343. C₃×C₂²⋊C₄	C₂²×D₅	semidirect
345. C₃×C₄²	C₂²×D₅	semidirect
389. #127	C₂×C₃×D₅	semidirect
393. #126	C₂×C₃×D₅	semidirect
399. #123	C₂×C₃×D₅	semidirect
407. #121	C₂×C₃×D₅	semidirect
413. #120	C₂×C₃×D₅	semidirect
426. C₃×D₅	#560	direct (N × H)
502. C₂×D₄	C₂²×C₃×D₅	semidirect
508. C₂²×C₄	C₂²×C₃×D₅	semidirect
512. C₄⋊C₄	C₂²×C₃×D₅	semidirect
522. C₂²⋊C₄	C₂²×C₃×D₅	semidirect
524. C₄²	C₂²×C₃×D₅	semidirect
525. C₃×C₅	C₂×#560	semidirect
553. D₅	C₃×#560	direct (N × H)
597. C₅	C₂×C₃×#560	semidirect
618. C₃	D₅×#560	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#560	2
C₃×#66054	2
C₃×D₅×#127	2
C₃×#66045	2
C₃×D₅×#126	2
C₃×#66000	2
C₃×D₅×#123	2
C₃×#65954	2
C₃×D₅×#121	2
C₃×#65929	2
C₃×D₅×#120	2
D₅×#560	3
C₂×C₃×#560	5

Subgroups — C3×D5×#560 #14495176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#560 #14495176