Subgroups — C₅×D₃×#560 #14495175

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	C₅×#5720	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5711	C₂	1	2	yes	maximal, complemented
5	C₅×D₃×#126	C₂	1	2	yes	maximal, complemented
6	C₅×#5666	C₂	1	3	yes	maximal, complemented
7	C₅×D₃×#123	C₂	1	3	yes	maximal, complemented
8	C₅×#5620	C₂	1	6	yes	maximal, complemented
9	C₅×D₃×#121	C₂	1	6	yes	maximal, complemented
10	C₅×#5595	C₂	1	3	yes	maximal, complemented
11	C₅×D₃×#120	C₂	1	3	yes	maximal, complemented
12	C₂×C₅×#560	—	3	1	no	maximal, Hall
13	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
14	C₂×C₅×D₃×D₄	C₂²	1	3	yes	—
15	C₂×C₅×D₃×D₄	C₂²	1	6	yes	—
16	C₂×C₅×D₃×D₄	C₂²	1	3	yes	complemented
17	C₂²×C₄×C₅×D₃	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	C₅×#953	C₂²	1	3	yes	complemented
24	C₅×#940	C₂²	1	3	yes	complemented
25	C₅×#940	C₂²	1	3	yes	complemented
26	C₅×#939	C₂²	1	6	yes	complemented
27	C₅×#939	C₂²	1	6	yes	complemented
28	C₅×#938	C₂²	1	6	yes	complemented
29	C₅×#937	C₂²	1	3	yes	complemented
30	C₅×#937	C₂²	1	6	yes	complemented
31	C₅×#935	C₂²	1	3	yes	complemented
32	C₅×#930	C₂²	1	6	yes	complemented
33	C₅×#929	C₂²	1	3	yes	complemented
34	C₅×#898	C₂²	1	6	yes	complemented
35	C₅×#895	C₂²	1	6	yes	complemented
36	C₅×#894	C₂²	1	6	yes	complemented
37	C₅×D₃×C₄⋊C₄	C₂²	1	6	yes	complemented
38	C₅×#886	C₂²	1	3	yes	complemented
39	C₅×#884	C₂²	1	6	yes	complemented
40	C₅×#884	C₂²	1	6	yes	complemented
41	C₅×#883	C₂²	1	6	yes	complemented
42	C₅×#882	C₂²	1	3	yes	complemented
43	C₅×#882	C₂²	1	6	yes	complemented
44	C₅×D₃×C₂²⋊C₄	C₂²	1	3	yes	—
45	C₅×D₃×C₂²⋊C₄	C₂²	1	6	yes	—
46	C₅×D₃×C₂²⋊C₄	C₂²	1	3	yes	complemented
47	C₅×#879	C₂²	1	6	yes	complemented
48	C₅×#876	C₂²	1	2	yes	complemented
49	C₅×#874	C₂²	1	1	yes	characteristic, complemented
50	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
51	D₃×#560	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
52	C₅×#560	—	3	1	no	—
53	C₅×#560	—	3	2	no	—
54	C₅×#560	—	3	3	no	—
55	C₅×#560	—	3	6	no	—
56	C₅×#560	—	3	3	no	—
57	C₅×#560	D₃	1	1	yes	characteristic, direct product factor
58	C₂×C₅×#127	—	3	1	no	—
59	C₂×C₅×#126	—	3	2	no	—
60	C₂×C₅×#123	—	3	3	no	—
61	C₂×C₅×#121	—	3	6	no	—
62	C₂×C₅×#120	—	3	3	no	—
63	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
64	C₂³×C₅×D₃	—	4	6	no	—
65	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
66	C₂³×C₅×D₃	C₂³	1	2	yes	—
67	C₂³×C₅×D₃	C₂³	1	3	yes	—
68	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
69	C₂³×C₅×D₃	C₂³	1	2	yes	—
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×C₅×#67	C₂³	1	3	yes	—
75	C₂×C₅×#67	C₂³	1	6	yes	—
76	C₂×C₅×#67	C₂³	1	6	yes	—
77	C₂×C₅×#67	C₂³	1	3	yes	—
78	C₂×C₅×#67	C₂³	1	6	yes	complemented
79	C₂²×C₅×Dic₃	C₂³	1	3	yes	complemented
80	C₅×D₃×D₄	—	4	12	no	—
81	C₅×D₃×D₄	—	4	6	no	—
82	C₅×D₃×D₄	—	4	6	no	—
83	C₂×C₅×D₁₂	C₂³	1	3	yes	—
84	C₂×C₅×D₁₂	C₂³	1	6	yes	—
85	C₂×C₅×D₁₂	C₂³	1	3	yes	complemented
86	C₂×C₄×C₅×D₃	—	4	6	no	—
87	C₂×C₄×C₅×D₃	C₂³	1	3	yes	—
88	C₂×C₄×C₅×D₃	C₂³	1	6	yes	—
89	C₂×C₄×C₅×D₃	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	C₅×#217	C₂³	1	6	yes	—
96	C₅×#217	C₂³	1	3	yes	—
97	C₅×#217	C₂³	1	3	yes	complemented
98	C₅×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
99	C₅×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
100	C₅×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
101	C₅×(C₂×D₃)⋊C₄	C₂³	1	6	yes	complemented
102	C₅×C₄⋊Dic₃	C₂³	1	6	yes	complemented
103	C₅×Dic₃⋊C₄	C₂³	1	6	yes	complemented
104	C₅×Dic₃⋊C₄	C₂³	1	6	yes	complemented
105	C₄×C₅×Dic₃	C₂³	1	3	yes	complemented
106	C₃×#560	C₂×C₅	1	1	yes	characteristic, complemented
107	#5720	C₂×C₅	1	1	yes	characteristic, complemented
108	D₃×#127	C₂×C₅	1	1	yes	characteristic, complemented
109	#5711	C₂×C₅	1	2	yes	complemented
110	D₃×#126	C₂×C₅	1	2	yes	complemented
111	#5666	C₂×C₅	1	3	yes	complemented
112	D₃×#123	C₂×C₅	1	3	yes	complemented
113	#5620	C₂×C₅	1	6	yes	complemented
114	D₃×#121	C₂×C₅	1	6	yes	complemented
115	#5595	C₂×C₅	1	3	yes	complemented
116	D₃×#120	C₂×C₅	1	3	yes	complemented
117	C₂⁵×C₅	—	3	1	no	—
118	C₂²×C₅×D₄	—	3	6	no	—
119	C₂²×C₅×D₄	—	3	3	no	—
120	C₂²×C₅×D₄	—	3	3	no	—
121	C₂³×C₄×C₅	—	3	3	no	—
122	C₅×#127	—	3	3	no	—
123	C₅×#127	—	3	3	no	—
124	C₅×#127	—	3	1	no	—
125	C₅×#127	C₂×D₃	1	1	yes	characteristic, complemented
126	C₅×#126	—	3	6	no	—
127	C₅×#126	—	3	6	no	—
128	C₅×#126	—	3	2	no	—
129	C₅×#126	C₂×D₃	1	2	yes	complemented
130	C₅×#123	—	3	3	no	—
131	C₅×#123	—	3	3	no	—
132	C₅×#123	—	3	6	no	—
133	C₅×#123	—	3	6	no	—
134	C₅×#123	—	3	3	no	—
135	C₅×#123	C₂×D₃	1	3	yes	complemented
136	C₅×#121	—	3	6	no	—
137	C₅×#121	—	3	6	no	—
138	C₅×#121	—	3	6	no	—
139	C₅×#121	—	3	6	no	—
140	C₅×#121	—	3	6	no	—
141	C₅×#121	—	3	6	no	—
142	C₅×#121	—	3	6	no	—
143	C₅×#121	C₂×D₃	1	6	yes	complemented
144	C₅×#120	—	3	3	no	—
145	C₅×#120	—	3	6	no	—
146	C₅×#120	—	3	3	no	—
147	C₅×#120	—	3	3	no	—
148	C₅×#120	—	3	6	no	—
149	C₅×#120	C₂×D₃	1	3	yes	complemented
150	C₂×C₅×C₄⋊C₄	—	3	6	no	—
151	C₂×C₅×C₂²⋊C₄	—	3	6	no	—
152	C₂×C₅×C₂²⋊C₄	—	3	3	no	—
153	C₂×C₅×C₂²⋊C₄	—	3	3	no	—
154	C₂×C₄²×C₅	—	3	1	no	—
155	C₂×#560	—	3	1	no	Sylow
156	C₂³×C₃×C₅	—	4	3	no	—
157	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
158	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
159	C₂³×C₃×C₅	C₂⁴	1	3	yes	—
160	C₂²×C₅×D₃	—	2	6	no	—
161	C₂²×C₅×D₃	—	2	12	no	—
162	C₂²×C₅×D₃	—	2	12	no	—
163	C₂²×C₅×D₃	—	2	6	no	—
164	C₂²×C₅×D₃	—	4	3	no	—
165	C₂²×C₅×D₃	—	4	6	no	—
166	C₂²×C₅×D₃	—	4	16	no	—
167	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
168	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
169	C₂²×C₅×D₃	C₂⁴	1	3	yes	—
170	C₂²×C₅×D₃	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	C₅×#67	—	4	6	no	—
178	C₅×#67	—	4	6	no	—
179	C₅×#67	—	4	3	no	—
180	C₅×#67	—	4	3	no	—
181	C₅×#67	—	4	6	no	—
182	C₂×C₅×Dic₃	—	4	3	no	—
183	C₂×C₅×Dic₃	C₂⁴	1	3	yes	—
184	C₂×C₅×Dic₃	C₂⁴	1	6	yes	—
185	C₅×D₁₂	—	4	6	no	—
186	C₅×D₁₂	—	4	3	no	—
187	C₅×D₁₂	—	4	3	no	—
188	C₄×C₅×D₃	—	2	12	no	—
189	C₄×C₅×D₃	—	2	6	no	—
190	C₄×C₅×D₃	—	4	6	no	—
191	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
192	C₂×D₃×D₄	C₂²×C₅	1	3	yes	—
193	C₂×D₃×D₄	C₂²×C₅	1	6	yes	—
194	C₂×D₃×D₄	C₂²×C₅	1	3	yes	complemented
195	C₂²×C₄×D₃	C₂²×C₅	1	3	yes	complemented
196	C₃×#127	C₂²×C₅	1	1	yes	characteristic, complemented
197	C₃×#126	C₂²×C₅	1	2	yes	complemented
198	C₃×#123	C₂²×C₅	1	3	yes	complemented
199	C₃×#121	C₂²×C₅	1	6	yes	complemented
200	C₃×#120	C₂²×C₅	1	3	yes	complemented
201	#953	C₂²×C₅	1	3	yes	complemented
202	#940	C₂²×C₅	1	3	yes	complemented
203	#940	C₂²×C₅	1	3	yes	complemented
204	#939	C₂²×C₅	1	6	yes	complemented
205	#939	C₂²×C₅	1	6	yes	complemented
206	#938	C₂²×C₅	1	6	yes	complemented
207	#937	C₂²×C₅	1	3	yes	complemented
208	#937	C₂²×C₅	1	6	yes	complemented
209	#935	C₂²×C₅	1	3	yes	complemented
210	#930	C₂²×C₅	1	6	yes	complemented
211	#929	C₂²×C₅	1	3	yes	complemented
212	#898	C₂²×C₅	1	6	yes	complemented
213	#895	C₂²×C₅	1	6	yes	complemented
214	#894	C₂²×C₅	1	6	yes	complemented
215	D₃×C₄⋊C₄	C₂²×C₅	1	6	yes	complemented
216	#886	C₂²×C₅	1	3	yes	complemented
217	#884	C₂²×C₅	1	6	yes	complemented
218	#884	C₂²×C₅	1	6	yes	complemented
219	#883	C₂²×C₅	1	6	yes	complemented
220	#882	C₂²×C₅	1	3	yes	complemented
221	#882	C₂²×C₅	1	6	yes	complemented
222	D₃×C₂²⋊C₄	C₂²×C₅	1	3	yes	—
223	D₃×C₂²⋊C₄	C₂²×C₅	1	6	yes	—
224	D₃×C₂²⋊C₄	C₂²×C₅	1	3	yes	complemented
225	#879	C₂²×C₅	1	6	yes	complemented
226	#876	C₂²×C₅	1	2	yes	complemented
227	#874	C₂²×C₅	1	1	yes	characteristic, complemented
228	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
229	C₂⁴×C₅	—	3	2	no	—
230	C₂⁴×C₅	—	3	1	no	—
231	C₂⁴×C₅	—	3	3	no	—
232	C₂⁴×C₅	—	3	1	no	—
233	C₂⁴×C₅	—	3	2	no	—
234	C₂⁴×C₅	—	12	6	no	—
235	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
236	C₂×C₅×D₄	—	3	6	no	—
237	C₂×C₅×D₄	—	3	6	no	—
238	C₂×C₅×D₄	—	3	3	no	—
239	C₂×C₅×D₄	—	3	3	no	—
240	C₂×C₅×D₄	—	3	6	no	—
241	C₂×C₅×D₄	—	3	6	no	—
242	C₂×C₅×D₄	—	3	3	no	—
243	C₂×C₅×D₄	—	3	3	no	—
244	C₂×C₅×D₄	—	12	12	no	—
245	C₂×C₅×D₄	—	12	6	no	—
246	C₂×C₅×D₄	—	12	6	no	—
247	C₂×C₅×D₄	C₂²×D₃	1	6	yes	—
248	C₂×C₅×D₄	C₂²×D₃	1	3	yes	—
249	C₂×C₅×D₄	C₂²×D₃	1	3	yes	complemented
250	C₂²×C₄×C₅	—	3	3	no	—
251	C₂²×C₄×C₅	—	3	3	no	—
252	C₂²×C₄×C₅	—	3	6	no	—
253	C₂²×C₄×C₅	—	3	6	no	—
254	C₂²×C₄×C₅	—	12	6	no	—
255	C₂²×C₄×C₅	C₂²×D₃	1	3	yes	complemented
256	C₅×C₄⋊C₄	—	3	6	no	—
257	C₅×C₄⋊C₄	—	3	6	no	—
258	C₅×C₄⋊C₄	—	3	6	no	—
259	C₅×C₄⋊C₄	C₂²×D₃	1	6	yes	complemented
260	C₅×C₂²⋊C₄	—	3	6	no	—
261	C₅×C₂²⋊C₄	—	3	3	no	—
262	C₅×C₂²⋊C₄	—	3	3	no	—
263	C₅×C₂²⋊C₄	—	3	6	no	—
264	C₅×C₂²⋊C₄	—	3	6	no	—
265	C₅×C₂²⋊C₄	—	3	6	no	—
266	C₅×C₂²⋊C₄	—	3	6	no	—
267	C₅×C₂²⋊C₄	C₂²×D₃	1	6	yes	—
268	C₅×C₂²⋊C₄	C₂²×D₃	1	3	yes	—
269	C₅×C₂²⋊C₄	C₂²×D₃	1	3	yes	complemented
270	C₄²×C₅	—	3	3	no	—
271	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic, complemented
272	#560	—	3	1	no	—
273	#560	—	3	2	no	—
274	#560	—	3	3	no	—
275	#560	—	3	6	no	—
276	#560	—	3	3	no	—
277	#560	C₅×D₃	1	1	yes	characteristic, direct product factor
278	C₂×#127	—	3	1	no	—
279	C₂×#126	—	3	2	no	—
280	C₂×#123	—	3	3	no	—
281	C₂×#121	—	3	6	no	—
282	C₂×#120	—	3	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×C₅×D₃	—	2	3	no	—
290	C₂×C₅×D₃	—	2	6	no	—
291	C₂×C₅×D₃	—	2	6	no	—
292	C₂×C₅×D₃	—	2	3	no	—
293	C₂×C₅×D₃	—	4	4	no	—
294	C₂×C₅×D₃	—	4	8	no	—
295	C₂×C₅×D₃	—	4	12	no	—
296	C₂×C₅×D₃	—	4	8	no	—
297	C₂×C₅×D₃	—	4	4	no	—
298	C₂×C₅×D₃	H(5,𝔽₂)	1	6	yes	—
299	C₃×C₄×C₅	—	2	6	no	—
300	C₃×C₄×C₅	—	2	3	no	—
301	C₅×Dic₃	—	2	6	no	—
302	C₅×Dic₃	—	2	3	no	—
303	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
304	C₂³×D₃	—	4	6	no	—
305	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
306	C₂³×D₃	C₂³×C₅	1	2	yes	—
307	C₂³×D₃	C₂³×C₅	1	3	yes	—
308	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
309	C₂³×D₃	C₂³×C₅	1	2	yes	—
310	C₂×C₃×D₄	C₂³×C₅	1	3	yes	—
311	C₂×C₃×D₄	C₂³×C₅	1	6	yes	—
312	C₂×C₃×D₄	C₂³×C₅	1	3	yes	complemented
313	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	complemented
314	C₂×#67	C₂³×C₅	1	3	yes	—
315	C₂×#67	C₂³×C₅	1	6	yes	—
316	C₂×#67	C₂³×C₅	1	6	yes	—
317	C₂×#67	C₂³×C₅	1	3	yes	—
318	C₂×#67	C₂³×C₅	1	6	yes	complemented
319	C₂²×Dic₃	C₂³×C₅	1	3	yes	complemented
320	D₃×D₄	—	4	12	no	—
321	D₃×D₄	—	4	6	no	—
322	D₃×D₄	—	4	6	no	—
323	C₂×D₁₂	C₂³×C₅	1	3	yes	—
324	C₂×D₁₂	C₂³×C₅	1	6	yes	—
325	C₂×D₁₂	C₂³×C₅	1	3	yes	complemented
326	C₂×C₄×D₃	—	4	6	no	—
327	C₂×C₄×D₃	C₂³×C₅	1	3	yes	—
328	C₂×C₄×D₃	C₂³×C₅	1	6	yes	—
329	C₂×C₄×D₃	C₂³×C₅	1	6	yes	complemented
330	C₃×C₄⋊C₄	C₂³×C₅	1	6	yes	complemented
331	C₃×C₂²⋊C₄	C₂³×C₅	1	6	yes	—
332	C₃×C₂²⋊C₄	C₂³×C₅	1	3	yes	—
333	C₃×C₂²⋊C₄	C₂³×C₅	1	3	yes	complemented
334	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic, complemented
335	#217	C₂³×C₅	1	6	yes	—
336	#217	C₂³×C₅	1	3	yes	—
337	#217	C₂³×C₅	1	3	yes	complemented
338	(C₂×D₃)⋊C₄	C₂³×C₅	1	6	yes	—
339	(C₂×D₃)⋊C₄	C₂³×C₅	1	6	yes	—
340	(C₂×D₃)⋊C₄	C₂³×C₅	1	6	yes	—
341	(C₂×D₃)⋊C₄	C₂³×C₅	1	6	yes	complemented
342	C₄⋊Dic₃	C₂³×C₅	1	6	yes	complemented
343	Dic₃⋊C₄	C₂³×C₅	1	6	yes	complemented
344	Dic₃⋊C₄	C₂³×C₅	1	6	yes	complemented
345	C₄×Dic₃	C₂³×C₅	1	3	yes	complemented
346	C₂³×C₅	—	3	1	no	—
347	C₂³×C₅	—	3	2	no	—
348	C₂³×C₅	—	3	1	no	—
349	C₂³×C₅	—	3	3	no	—
350	C₂³×C₅	—	4	3	no	—
351	C₂³×C₅	—	6	6	no	—
352	C₂³×C₅	—	6	12	no	—
353	C₂³×C₅	—	6	12	no	—
354	C₂³×C₅	—	6	6	no	—
355	C₂³×C₅	—	12	6	no	—
356	C₂³×C₅	—	12	3	no	—
357	C₂³×C₅	—	12	16	no	—
358	C₂³×C₅	C₂³×D₃	1	2	yes	—
359	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
360	C₂³×C₅	C₂³×D₃	1	3	yes	—
361	C₅×D₄	—	4	6	no	—
362	C₅×D₄	—	4	3	no	—
363	C₅×D₄	—	4	3	no	—
364	C₅×D₄	—	12	6	no	—
365	C₅×D₄	—	12	3	no	—
366	C₅×D₄	—	12	3	no	—
367	C₅×D₄	—	12	6	no	—
368	C₅×D₄	—	12	6	no	—
369	C₅×D₄	—	12	3	no	—
370	C₅×D₄	—	12	6	no	—
371	C₅×D₄	—	12	3	no	—
372	C₂×C₄×C₅	—	3	3	no	—
373	C₂×C₄×C₅	—	3	6	no	—
374	C₂×C₄×C₅	—	4	3	no	—
375	C₂×C₄×C₅	—	6	12	no	—
376	C₂×C₄×C₅	—	6	6	no	—
377	C₂×C₄×C₅	—	12	6	no	—
378	C₂×C₄×C₅	—	12	3	no	—
379	C₂×C₄×C₅	C₂³×D₃	1	3	yes	—
380	C₂×C₄×C₅	C₂³×D₃	1	6	yes	—
381	C₂⁵	—	3	1	no	—
382	C₂²×D₄	—	3	6	no	—
383	C₂²×D₄	—	3	3	no	—
384	C₂²×D₄	—	3	3	no	—
385	C₂³×C₄	—	3	3	no	—
386	#127	—	3	3	no	—
387	#127	—	3	3	no	—
388	#127	—	3	1	no	—
389	#127	C₂×C₅×D₃	1	1	yes	characteristic, complemented
390	#126	—	3	6	no	—
391	#126	—	3	6	no	—
392	#126	—	3	2	no	—
393	#126	C₂×C₅×D₃	1	2	yes	complemented
394	#123	—	3	3	no	—
395	#123	—	3	3	no	—
396	#123	—	3	6	no	—
397	#123	—	3	6	no	—
398	#123	—	3	3	no	—
399	#123	C₂×C₅×D₃	1	3	yes	complemented
400	#121	—	3	6	no	—
401	#121	—	3	6	no	—
402	#121	—	3	6	no	—
403	#121	—	3	6	no	—
404	#121	—	3	6	no	—
405	#121	—	3	6	no	—
406	#121	—	3	6	no	—
407	#121	C₂×C₅×D₃	1	6	yes	complemented
408	#120	—	3	3	no	—
409	#120	—	3	6	no	—
410	#120	—	3	3	no	—
411	#120	—	3	3	no	—
412	#120	—	3	6	no	—
413	#120	C₂×C₅×D₃	1	3	yes	complemented
414	C₂×C₄⋊C₄	—	3	6	no	—
415	C₂×C₂²⋊C₄	—	3	6	no	—
416	C₂×C₂²⋊C₄	—	3	3	no	—
417	C₂×C₂²⋊C₄	—	3	3	no	—
418	C₂×C₄²	—	3	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	C₅×D₃	—	4	3	no	—
424	C₅×D₃	—	4	2	no	—
425	C₅×D₃	—	4	1	no	—
426	C₅×D₃	#560	1	4	yes	direct product factor
427	C₂³×C₃	—	4	3	no	—
428	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
429	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
430	C₂³×C₃	C₂⁴×C₅	1	3	yes	—
431	C₂²×D₃	—	2	6	no	—
432	C₂²×D₃	—	2	12	no	—
433	C₂²×D₃	—	2	12	no	—
434	C₂²×D₃	—	2	6	no	—
435	C₂²×D₃	—	4	3	no	—
436	C₂²×D₃	—	4	6	no	—
437	C₂²×D₃	—	4	16	no	—
438	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
439	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
440	C₂²×D₃	C₂⁴×C₅	1	3	yes	—
441	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
442	C₃×D₄	—	4	6	no	—
443	C₃×D₄	—	4	3	no	—
444	C₃×D₄	—	4	3	no	—
445	C₂×C₃×C₄	—	4	3	no	—
446	C₂×C₃×C₄	C₂⁴×C₅	1	3	yes	—
447	C₂×C₃×C₄	C₂⁴×C₅	1	6	yes	—
448	#67	—	4	6	no	—
449	#67	—	4	6	no	—
450	#67	—	4	3	no	—
451	#67	—	4	3	no	—
452	#67	—	4	6	no	—
453	C₂×Dic₃	—	4	3	no	—
454	C₂×Dic₃	C₂⁴×C₅	1	3	yes	—
455	C₂×Dic₃	C₂⁴×C₅	1	6	yes	—
456	D₁₂	—	4	6	no	—
457	D₁₂	—	4	3	no	—
458	D₁₂	—	4	3	no	—
459	C₄×D₃	—	2	12	no	—
460	C₄×D₃	—	2	6	no	—
461	C₄×D₃	—	4	6	no	—
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	—	3	6	no	—
467	C₂²×C₅	—	4	4	no	—
468	C₂²×C₅	—	6	3	no	—
469	C₂²×C₅	—	6	6	no	—
470	C₂²×C₅	—	6	6	no	—
471	C₂²×C₅	—	6	3	no	—
472	C₂²×C₅	—	12	12	no	—
473	C₂²×C₅	—	12	8	no	—
474	C₂²×C₅	—	12	4	no	—
475	C₂²×C₅	—	12	8	no	—
476	C₂²×C₅	—	12	4	no	—
477	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
478	C₄×C₅	—	2	6	no	—
479	C₄×C₅	—	2	3	no	—
480	C₄×C₅	—	6	6	no	—
481	C₄×C₅	—	6	3	no	—
482	C₂⁴	—	3	2	no	—
483	C₂⁴	—	3	1	no	—
484	C₂⁴	—	3	3	no	—
485	C₂⁴	—	3	1	no	—
486	C₂⁴	—	3	2	no	—
487	C₂⁴	—	12	6	no	—
488	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
489	C₂×D₄	—	3	6	no	—
490	C₂×D₄	—	3	6	no	—
491	C₂×D₄	—	3	3	no	—
492	C₂×D₄	—	3	3	no	—
493	C₂×D₄	—	3	6	no	—
494	C₂×D₄	—	3	6	no	—
495	C₂×D₄	—	3	3	no	—
496	C₂×D₄	—	3	3	no	—
497	C₂×D₄	—	12	12	no	—
498	C₂×D₄	—	12	6	no	—
499	C₂×D₄	—	12	6	no	—
500	C₂×D₄	C₂²×C₅×D₃	1	6	yes	—
501	C₂×D₄	C₂²×C₅×D₃	1	3	yes	—
502	C₂×D₄	C₂²×C₅×D₃	1	3	yes	complemented
503	C₂²×C₄	—	3	3	no	—
504	C₂²×C₄	—	3	3	no	—
505	C₂²×C₄	—	3	6	no	—
506	C₂²×C₄	—	3	6	no	—
507	C₂²×C₄	—	12	6	no	—
508	C₂²×C₄	C₂²×C₅×D₃	1	3	yes	complemented
509	C₄⋊C₄	—	3	6	no	—
510	C₄⋊C₄	—	3	6	no	—
511	C₄⋊C₄	—	3	6	no	—
512	C₄⋊C₄	C₂²×C₅×D₃	1	6	yes	complemented
513	C₂²⋊C₄	—	3	6	no	—
514	C₂²⋊C₄	—	3	3	no	—
515	C₂²⋊C₄	—	3	3	no	—
516	C₂²⋊C₄	—	3	6	no	—
517	C₂²⋊C₄	—	3	6	no	—
518	C₂²⋊C₄	—	3	6	no	—
519	C₂²⋊C₄	—	3	6	no	—
520	C₂²⋊C₄	C₂²×C₅×D₃	1	6	yes	—
521	C₂²⋊C₄	C₂²×C₅×D₃	1	3	yes	—
522	C₂²⋊C₄	C₂²×C₅×D₃	1	3	yes	complemented
523	C₄²	—	3	3	no	—
524	C₄²	C₂²×C₅×D₃	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	C₂⁵×C₅	1	1	yes	characteristic
532	C₂×D₃	—	2	3	no	—
533	C₂×D₃	—	2	6	no	—
534	C₂×D₃	—	2	6	no	—
535	C₂×D₃	—	2	3	no	—
536	C₂×D₃	—	4	4	no	—
537	C₂×D₃	—	4	8	no	—
538	C₂×D₃	—	4	12	no	—
539	C₂×D₃	—	4	8	no	—
540	C₂×D₃	—	4	4	no	—
541	C₂×D₃	C₅×H(5,𝔽₂)	1	6	yes	—
542	C₃×C₄	—	2	6	no	—
543	C₃×C₄	—	2	3	no	—
544	Dic₃	—	2	6	no	—
545	Dic₃	—	2	3	no	—
546	C₂×C₅	—	3	4	no	—
547	C₂×C₅	—	4	2	no	—
548	C₂×C₅	—	4	1	no	—
549	C₂×C₅	—	4	3	no	—
550	C₂×C₅	—	12	2	no	—
551	C₂×C₅	—	12	1	no	—
552	C₂×C₅	—	12	3	no	—
553	C₂×C₅	D₃×H(5,𝔽₂)	1	3	yes	—
554	C₂³	—	3	1	no	—
555	C₂³	—	3	2	no	—
556	C₂³	—	3	1	no	—
557	C₂³	—	3	3	no	—
558	C₂³	—	4	3	no	—
559	C₂³	—	6	6	no	—
560	C₂³	—	6	12	no	—
561	C₂³	—	6	12	no	—
562	C₂³	—	6	6	no	—
563	C₂³	—	12	6	no	—
564	C₂³	—	12	3	no	—
565	C₂³	—	12	16	no	—
566	C₂³	C₂³×C₅×D₃	1	2	yes	—
567	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
568	C₂³	C₂³×C₅×D₃	1	3	yes	—
569	D₄	—	4	6	no	—
570	D₄	—	4	3	no	—
571	D₄	—	4	3	no	—
572	D₄	—	12	6	no	—
573	D₄	—	12	3	no	—
574	D₄	—	12	3	no	—
575	D₄	—	12	6	no	—
576	D₄	—	12	6	no	—
577	D₄	—	12	3	no	—
578	D₄	—	12	6	no	—
579	D₄	—	12	3	no	—
580	C₂×C₄	—	3	3	no	—
581	C₂×C₄	—	3	6	no	—
582	C₂×C₄	—	4	3	no	—
583	C₂×C₄	—	6	12	no	—
584	C₂×C₄	—	6	6	no	—
585	C₂×C₄	—	12	6	no	—
586	C₂×C₄	—	12	3	no	—
587	C₂×C₄	C₂³×C₅×D₃	1	3	yes	—
588	C₂×C₄	C₂³×C₅×D₃	1	6	yes	—
589	C₂×C₃	—	4	2	no	—
590	C₂×C₃	—	4	1	no	—
591	C₂×C₃	—	4	3	no	—
592	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	3	yes	—
593	D₃	—	4	2	no	—
594	D₃	—	4	1	no	—
595	D₃	—	4	3	no	—
596	D₃	C₅×#560	1	4	yes	direct product factor
597	C₅	D₃×#560	1	1	yes	characteristic, direct product factor, Sylow
598	C₂²	—	2	3	no	—
599	C₂²	—	2	6	no	—
600	C₂²	—	2	6	no	—
601	C₂²	—	2	3	no	—
602	C₂²	—	3	6	no	—
603	C₂²	—	4	4	no	—
604	C₂²	—	6	3	no	—
605	C₂²	—	6	6	no	—
606	C₂²	—	6	6	no	—
607	C₂²	—	6	3	no	—
608	C₂²	—	12	8	no	—
609	C₂²	—	12	4	no	—
610	C₂²	—	12	12	no	—
611	C₂²	—	12	8	no	—
612	C₂²	—	12	4	no	—
613	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
614	C₄	—	2	6	no	—
615	C₄	—	2	3	no	—
616	C₄	—	6	6	no	—
617	C₄	—	6	3	no	—
618	C₃	C₂×C₅×#560	1	1	yes	characteristic, complemented, Sylow
619	C₂	—	3	4	no	—
620	C₂	—	4	2	no	—
621	C₂	—	4	1	no	—
622	C₂	—	4	3	no	—
623	C₂	—	12	2	no	—
624	C₂	—	12	1	no	—
625	C₂	—	12	3	no	—
626	C₂	C₅×D₃×H(5,𝔽₂)	1	3	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#560	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#560	D₃
hypocenter	C₃	C₂×C₅×#560
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#560

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#560	C₂	semidirect
2. C₅×#5720	C₂	semidirect
3. C₅×D₃×#127	C₂	semidirect
4. C₅×#5711	C₂	semidirect
5. C₅×D₃×#126	C₂	semidirect
6. C₅×#5666	C₂	semidirect
7. C₅×D₃×#123	C₂	semidirect
8. C₅×#5620	C₂	semidirect
9. C₅×D₃×#121	C₂	semidirect
10. C₅×#5595	C₂	semidirect
11. C₅×D₃×#120	C₂	semidirect
16. C₂×C₅×D₃×D₄	C₂²	semidirect
17. C₂²×C₄×C₅×D₃	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. C₅×#953	C₂²	semidirect
24. C₅×#940	C₂²	semidirect
25. C₅×#940	C₂²	semidirect
26. C₅×#939	C₂²	semidirect
27. C₅×#939	C₂²	semidirect
28. C₅×#938	C₂²	semidirect
29. C₅×#937	C₂²	semidirect
30. C₅×#937	C₂²	semidirect
31. C₅×#935	C₂²	semidirect
32. C₅×#930	C₂²	semidirect
33. C₅×#929	C₂²	semidirect
34. C₅×#898	C₂²	semidirect
35. C₅×#895	C₂²	semidirect
36. C₅×#894	C₂²	semidirect
37. C₅×D₃×C₄⋊C₄	C₂²	semidirect
38. C₅×#886	C₂²	semidirect
39. C₅×#884	C₂²	semidirect
40. C₅×#884	C₂²	semidirect
41. C₅×#883	C₂²	semidirect
42. C₅×#882	C₂²	semidirect
43. C₅×#882	C₂²	semidirect
46. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
47. C₅×#879	C₂²	semidirect
48. C₅×#876	C₂²	semidirect
49. C₅×#874	C₂²	semidirect
50. C₄²×C₅×D₃	C₂²	semidirect
51. D₃×#560	C₅	direct (N × H)
57. C₅×#560	D₃	direct (N × H)
72. C₂×C₃×C₅×D₄	C₂³	semidirect
73. C₂²×C₃×C₄×C₅	C₂³	semidirect
78. C₂×C₅×#67	C₂³	semidirect
79. C₂²×C₅×Dic₃	C₂³	semidirect
85. C₂×C₅×D₁₂	C₂³	semidirect
89. C₂×C₄×C₅×D₃	C₂³	semidirect
90. C₃×C₅×C₄⋊C₄	C₂³	semidirect
93. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
94. C₃×C₄²×C₅	C₂³	semidirect
97. C₅×#217	C₂³	semidirect
101. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
102. C₅×C₄⋊Dic₃	C₂³	semidirect
103. C₅×Dic₃⋊C₄	C₂³	semidirect
104. C₅×Dic₃⋊C₄	C₂³	semidirect
105. C₄×C₅×Dic₃	C₂³	semidirect
106. C₃×#560	C₂×C₅	semidirect
107. #5720	C₂×C₅	semidirect
108. D₃×#127	C₂×C₅	semidirect
109. #5711	C₂×C₅	semidirect
110. D₃×#126	C₂×C₅	semidirect
111. #5666	C₂×C₅	semidirect
112. D₃×#123	C₂×C₅	semidirect
113. #5620	C₂×C₅	semidirect
114. D₃×#121	C₂×C₅	semidirect
115. #5595	C₂×C₅	semidirect
116. D₃×#120	C₂×C₅	semidirect
125. C₅×#127	C₂×D₃	semidirect
129. C₅×#126	C₂×D₃	semidirect
135. C₅×#123	C₂×D₃	semidirect
143. C₅×#121	C₂×D₃	semidirect
149. C₅×#120	C₂×D₃	semidirect
194. C₂×D₃×D₄	C₂²×C₅	semidirect
195. C₂²×C₄×D₃	C₂²×C₅	semidirect
196. C₃×#127	C₂²×C₅	semidirect
197. C₃×#126	C₂²×C₅	semidirect
198. C₃×#123	C₂²×C₅	semidirect
199. C₃×#121	C₂²×C₅	semidirect
200. C₃×#120	C₂²×C₅	semidirect
201. #953	C₂²×C₅	semidirect
202. #940	C₂²×C₅	semidirect
203. #940	C₂²×C₅	semidirect
204. #939	C₂²×C₅	semidirect
205. #939	C₂²×C₅	semidirect
206. #938	C₂²×C₅	semidirect
207. #937	C₂²×C₅	semidirect
208. #937	C₂²×C₅	semidirect
209. #935	C₂²×C₅	semidirect
210. #930	C₂²×C₅	semidirect
211. #929	C₂²×C₅	semidirect
212. #898	C₂²×C₅	semidirect
213. #895	C₂²×C₅	semidirect
214. #894	C₂²×C₅	semidirect
215. D₃×C₄⋊C₄	C₂²×C₅	semidirect
216. #886	C₂²×C₅	semidirect
217. #884	C₂²×C₅	semidirect
218. #884	C₂²×C₅	semidirect
219. #883	C₂²×C₅	semidirect
220. #882	C₂²×C₅	semidirect
221. #882	C₂²×C₅	semidirect
224. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
225. #879	C₂²×C₅	semidirect
226. #876	C₂²×C₅	semidirect
227. #874	C₂²×C₅	semidirect
228. C₄²×D₃	C₂²×C₅	semidirect
249. C₂×C₅×D₄	C₂²×D₃	semidirect
255. C₂²×C₄×C₅	C₂²×D₃	semidirect
259. C₅×C₄⋊C₄	C₂²×D₃	semidirect
269. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
271. C₄²×C₅	C₂²×D₃	semidirect
277. #560	C₅×D₃	direct (N × H)
312. C₂×C₃×D₄	C₂³×C₅	semidirect
313. C₂²×C₃×C₄	C₂³×C₅	semidirect
318. C₂×#67	C₂³×C₅	semidirect
319. C₂²×Dic₃	C₂³×C₅	semidirect
325. C₂×D₁₂	C₂³×C₅	semidirect
329. C₂×C₄×D₃	C₂³×C₅	semidirect
330. C₃×C₄⋊C₄	C₂³×C₅	semidirect
333. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
334. C₃×C₄²	C₂³×C₅	semidirect
337. #217	C₂³×C₅	semidirect
341. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
342. C₄⋊Dic₃	C₂³×C₅	semidirect
343. Dic₃⋊C₄	C₂³×C₅	semidirect
344. Dic₃⋊C₄	C₂³×C₅	semidirect
345. C₄×Dic₃	C₂³×C₅	semidirect
389. #127	C₂×C₅×D₃	semidirect
393. #126	C₂×C₅×D₃	semidirect
399. #123	C₂×C₅×D₃	semidirect
407. #121	C₂×C₅×D₃	semidirect
413. #120	C₂×C₅×D₃	semidirect
426. C₅×D₃	#560	direct (N × H)
502. C₂×D₄	C₂²×C₅×D₃	semidirect
508. C₂²×C₄	C₂²×C₅×D₃	semidirect
512. C₄⋊C₄	C₂²×C₅×D₃	semidirect
522. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
524. C₄²	C₂²×C₅×D₃	semidirect
525. C₃×C₅	C₂×#560	semidirect
596. D₃	C₅×#560	direct (N × H)
597. C₅	D₃×#560	direct (N × H)
618. C₃	C₂×C₅×#560	semidirect

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
C₅×#5720	2
C₅×D₃×#127	2
C₅×#5711	2
C₅×D₃×#126	2
C₅×#5666	2
C₅×D₃×#123	2
C₅×#5620	2
C₅×D₃×#121	2
C₅×#5595	2
C₅×D₃×#120	2
C₂×C₅×#560	3
D₃×#560	5

Subgroups — C5×D3×#560 #14495175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#560 #14495175