Subgroups — C₅×#71568 #14280235

Order 1920.

1216 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×Dic₃⋊C₄	C₂	1	2	yes	maximal
3	C₂×C₅×C₃⋊#95	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×C₃⋊#95	C₂	1	2	yes	maximal
5	C₂×C₅×C₃⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₅×#1444	—	3	1	no	maximal, Hall
7	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
10	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
11	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
12	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
13	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
14	C₂×C₅×Dic₃⋊C₄	—	2	4	no	—
15	C₂×C₅×Dic₃⋊C₄	—	2	4	no	—
16	C₂×C₅×Dic₃⋊C₄	—	2	4	no	—
17	C₅×C₃⋊#95	—	2	2	no	—
18	C₅×C₃⋊#95	—	2	4	no	—
19	C₅×C₃⋊#95	C₄	1	4	yes	complemented
20	#71568	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂²×C₅×C₄⋊C₄	—	3	2	no	—
22	C₂²×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic
23	C₂×C₅×#95	—	3	1	no	—
24	C₂×C₅×#95	—	3	2	no	—
25	C₂×C₅×#95	—	3	1	no	—
26	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
27	C₂²×C₃×C₄×C₅	—	2	2	no	—
28	C₂²×C₃×C₄×C₅	—	2	2	no	—
29	C₂²×C₃×C₄×C₅	—	2	2	no	—
30	C₂²×C₃×C₄×C₅	—	2	2	no	—
31	C₂²×C₃×C₄×C₅	—	2	2	no	—
32	C₂²×C₃×C₄×C₅	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	—	2	2	no	—
34	C₂²×C₃×C₄×C₅	—	2	2	no	—
35	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
36	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
37	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
38	C₂²×C₃×C₄×C₅	Q₈	1	2	yes	—
39	C₂²×C₅×Dic₃	—	2	2	no	—
40	C₂²×C₅×Dic₃	—	2	2	no	—
41	C₂²×C₅×Dic₃	—	2	2	no	—
42	C₂²×C₅×Dic₃	—	2	2	no	—
43	C₂²×C₅×Dic₃	—	2	2	no	—
44	C₂²×C₅×Dic₃	—	2	2	no	—
45	C₂²×C₅×Dic₃	—	2	1	no	—
46	C₂²×C₅×Dic₃	—	2	2	no	—
47	C₂²×C₅×Dic₃	—	2	1	no	—
48	C₂²×C₅×Dic₃	—	2	1	no	—
49	C₂²×C₅×Dic₃	—	2	2	no	—
50	C₂²×C₅×Dic₃	—	2	1	no	—
51	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	—
52	C₂²×C₅×Dic₃	D₄	1	2	yes	—
53	C₂²×C₅×Dic₃	D₄	1	4	yes	—
54	C₂²×C₅×Dic₃	Q₈	1	2	yes	—
55	C₂²×C₅×Dic₃	Q₈	1	4	yes	—
56	C₃×C₅×C₄⋊C₄	—	2	8	no	—
57	C₅×Dic₃⋊C₄	—	2	16	no	—
58	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
59	C₂²×Dic₃⋊C₄	C₂×C₅	1	2	yes	—
60	C₂×C₃⋊#95	C₂×C₅	1	1	yes	characteristic
61	C₂×C₃⋊#95	C₂×C₅	1	2	yes	—
62	C₂×C₃⋊#95	C₂×C₅	1	1	yes	characteristic
63	C₂³×C₄×C₅	—	3	2	no	—
64	C₂³×C₄×C₅	—	3	1	no	—
65	C₂³×C₄×C₅	—	3	1	no	—
66	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
67	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	—	2	4	no	—
69	C₂×C₅×C₄⋊C₄	—	2	2	no	—
70	C₂×C₅×C₄⋊C₄	—	6	4	no	—
71	C₂×C₅×C₄⋊C₄	—	6	4	no	—
72	C₂×C₅×C₄⋊C₄	—	6	4	no	—
73	C₅×#95	—	3	4	no	—
74	C₅×#95	—	6	4	no	—
75	C₅×#95	—	6	2	no	—
76	#1444	—	3	1	no	Sylow
77	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
78	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
79	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
80	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
81	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
82	C₂³×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
83	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
84	C₂³×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
85	C₂³×C₃×C₅	#41	1	2	yes	—
86	C₂³×C₃×C₅	#41	1	1	yes	characteristic
87	C₂³×C₃×C₅	#41	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	—	2	4	no	—
89	C₂×C₃×C₄×C₅	—	2	2	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	—	2	4	no	—
95	C₂×C₃×C₄×C₅	—	4	2	no	—
96	C₂×C₃×C₄×C₅	—	4	2	no	—
97	C₂×C₃×C₄×C₅	—	4	2	no	—
98	C₂×C₃×C₄×C₅	—	4	2	no	—
99	C₂×C₃×C₄×C₅	C₄⋊C₄	1	4	yes	complemented
100	C₂×C₅×Dic₃	—	2	4	no	—
101	C₂×C₅×Dic₃	—	2	4	no	—
102	C₂×C₅×Dic₃	—	2	4	no	—
103	C₂×C₅×Dic₃	—	2	4	no	—
104	C₂×C₅×Dic₃	—	2	4	no	—
105	C₂×C₅×Dic₃	—	2	4	no	—
106	C₂×C₅×Dic₃	—	2	4	no	—
107	C₂×C₅×Dic₃	—	2	2	no	—
108	C₂×C₅×Dic₃	—	2	4	no	—
109	C₂×C₅×Dic₃	—	2	2	no	—
110	C₂×C₅×Dic₃	—	4	1	no	—
111	C₂×C₅×Dic₃	—	4	2	no	—
112	C₂×C₅×Dic₃	—	4	2	no	—
113	C₂×C₅×Dic₃	—	4	1	no	—
114	C₂×C₅×Dic₃	—	4	1	no	—
115	C₂×C₅×Dic₃	—	4	1	no	—
116	C₂×C₅×Dic₃	C₄⋊C₄	1	8	yes	complemented
117	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
118	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
119	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
120	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
121	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
122	C₂×C₃×C₄⋊C₄	—	2	4	no	—
123	C₂×C₃×C₄⋊C₄	—	2	2	no	—
124	C₂×Dic₃⋊C₄	—	2	4	no	—
125	C₂×Dic₃⋊C₄	—	2	4	no	—
126	C₂×Dic₃⋊C₄	—	2	4	no	—
127	C₃⋊#95	—	2	2	no	—
128	C₃⋊#95	—	2	4	no	—
129	C₃⋊#95	C₄×C₅	1	4	yes	complemented
130	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
131	C₂²×C₄×C₅	—	2	2	no	—
132	C₂²×C₄×C₅	—	2	2	no	—
133	C₂²×C₄×C₅	—	2	2	no	—
134	C₂²×C₄×C₅	—	2	2	no	—
135	C₂²×C₄×C₅	—	2	2	no	—
136	C₂²×C₄×C₅	—	2	2	no	—
137	C₂²×C₄×C₅	—	2	2	no	—
138	C₂²×C₄×C₅	—	2	2	no	—
139	C₂²×C₄×C₅	—	3	4	no	—
140	C₂²×C₄×C₅	—	3	4	no	—
141	C₂²×C₄×C₅	—	3	4	no	—
142	C₂²×C₄×C₅	—	3	2	no	—
143	C₂²×C₄×C₅	—	3	2	no	—
144	C₂²×C₄×C₅	—	6	2	no	—
145	C₂²×C₄×C₅	—	6	2	no	—
146	C₂²×C₄×C₅	—	6	2	no	—
147	C₂²×C₄×C₅	—	6	2	no	—
148	C₂²×C₄×C₅	—	6	2	no	—
149	C₂²×C₄×C₅	—	6	2	no	—
150	C₂²×C₄×C₅	—	6	2	no	—
151	C₂²×C₄×C₅	—	6	1	no	—
152	C₂²×C₄×C₅	—	6	1	no	—
153	C₂²×C₄×C₅	—	6	2	no	—
154	C₂²×C₄×C₅	—	6	1	no	—
155	C₂²×C₄×C₅	—	6	1	no	—
156	C₂²×C₄×C₅	Dic₆	1	2	yes	—
157	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
158	C₂²×C₄×C₅	#67	1	4	yes	—
159	C₂²×C₄×C₅	#67	1	2	yes	—
160	C₅×C₄⋊C₄	—	2	8	no	—
161	C₅×C₄⋊C₄	—	6	16	no	—
162	C₂²×C₄⋊C₄	—	3	2	no	—
163	C₂²×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic
164	C₂×#95	—	3	1	no	—
165	C₂×#95	—	3	2	no	—
166	C₂×#95	—	3	1	no	—
167	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
168	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
170	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
171	C₂²×C₃×C₅	C₄×Q₈	1	1	yes	characteristic
172	C₂²×C₃×C₅	#120	1	2	yes	—
173	C₂²×C₃×C₅	#120	1	1	yes	characteristic
174	C₂²×C₃×C₅	#121	1	1	yes	characteristic
175	C₂²×C₃×C₅	#121	1	2	yes	—
176	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
177	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
178	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
179	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
180	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
181	C₂²×C₃×C₅	#123	1	2	yes	—
182	C₂²×C₃×C₅	#123	1	1	yes	characteristic
183	C₂²×C₃×C₅	#125	1	2	yes	—
184	C₂²×C₃×C₅	#125	1	1	yes	characteristic
185	C₂²×C₃×C₅	#127	1	1	yes	characteristic
186	C₂²×C₃×C₅	C₄⋊Q₈	1	2	yes	—
187	C₂²×C₃×C₅	C₄⋊Q₈	1	1	yes	characteristic
188	C₂²×C₃×C₅	C₄⋊Q₈	1	1	yes	characteristic
189	C₂²×C₃×C₅	C₄⋊Q₈	1	2	yes	—
190	C₃×C₄×C₅	—	2	4	no	—
191	C₃×C₄×C₅	—	4	4	no	—
192	C₅×Dic₃	—	2	8	no	—
193	C₅×Dic₃	—	4	2	no	—
194	C₅×Dic₃	—	4	2	no	—
195	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
196	C₂²×C₃×C₄	—	2	2	no	—
197	C₂²×C₃×C₄	—	2	2	no	—
198	C₂²×C₃×C₄	—	2	2	no	—
199	C₂²×C₃×C₄	—	2	2	no	—
200	C₂²×C₃×C₄	—	2	2	no	—
201	C₂²×C₃×C₄	—	2	2	no	—
202	C₂²×C₃×C₄	—	2	2	no	—
203	C₂²×C₃×C₄	—	2	2	no	—
204	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
205	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
206	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
207	C₂²×C₃×C₄	C₅×Q₈	1	2	yes	—
208	C₂²×Dic₃	—	2	2	no	—
209	C₂²×Dic₃	—	2	2	no	—
210	C₂²×Dic₃	—	2	2	no	—
211	C₂²×Dic₃	—	2	2	no	—
212	C₂²×Dic₃	—	2	2	no	—
213	C₂²×Dic₃	—	2	1	no	—
214	C₂²×Dic₃	—	2	1	no	—
215	C₂²×Dic₃	—	2	2	no	—
216	C₂²×Dic₃	—	2	2	no	—
217	C₂²×Dic₃	—	2	2	no	—
218	C₂²×Dic₃	—	2	1	no	—
219	C₂²×Dic₃	—	2	1	no	—
220	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	—
221	C₂²×Dic₃	C₅×D₄	1	2	yes	—
222	C₂²×Dic₃	C₅×D₄	1	4	yes	—
223	C₂²×Dic₃	C₅×Q₈	1	2	yes	—
224	C₂²×Dic₃	C₅×Q₈	1	4	yes	—
225	C₃×C₄⋊C₄	—	2	8	no	—
226	Dic₃⋊C₄	—	2	16	no	—
227	C₂³×C₅	C₂×Dic₆	1	1	yes	characteristic
228	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
229	C₂³×C₅	#235	1	2	yes	—
230	C₂³×C₅	D₃×D₄	1	2	yes	—
231	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
232	C₂³×C₅	#237	1	1	yes	characteristic
233	C₂³×C₅	D₃×Q₈	1	1	yes	characteristic
234	C₂³×C₅	D₃×Q₈	1	2	yes	—
235	C₂³×C₅	#239	1	1	yes	characteristic
236	C₂³×C₅	C₂×#67	1	1	yes	characteristic
237	C₂³×C₅	C₂×#67	1	2	yes	—
238	C₂×C₄×C₅	—	2	4	no	—
239	C₂×C₄×C₅	—	2	4	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	4	no	—
243	C₂×C₄×C₅	—	2	4	no	—
244	C₂×C₄×C₅	—	2	4	no	—
245	C₂×C₄×C₅	—	3	8	no	—
246	C₂×C₄×C₅	—	4	2	no	—
247	C₂×C₄×C₅	—	4	2	no	—
248	C₂×C₄×C₅	—	4	2	no	—
249	C₂×C₄×C₅	—	4	2	no	—
250	C₂×C₄×C₅	—	6	4	no	—
251	C₂×C₄×C₅	—	6	4	no	—
252	C₂×C₄×C₅	—	6	4	no	—
253	C₂×C₄×C₅	—	6	4	no	—
254	C₂×C₄×C₅	—	6	4	no	—
255	C₂×C₄×C₅	—	6	4	no	—
256	C₂×C₄×C₅	—	6	4	no	—
257	C₂×C₄×C₅	—	6	4	no	—
258	C₂×C₄×C₅	—	6	2	no	—
259	C₂×C₄×C₅	—	6	2	no	—
260	C₂×C₄×C₅	—	12	2	no	—
261	C₂×C₄×C₅	—	12	1	no	—
262	C₂×C₄×C₅	—	12	2	no	—
263	C₂×C₄×C₅	—	12	1	no	—
264	C₂×C₄×C₅	—	12	1	no	—
265	C₂×C₄×C₅	—	12	1	no	—
266	C₂×C₄×C₅	Dic₃⋊C₄	1	4	yes	complemented
267	C₂³×C₄	—	3	2	no	—
268	C₂³×C₄	—	3	1	no	—
269	C₂³×C₄	—	3	1	no	—
270	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
271	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
272	C₂×C₄⋊C₄	—	2	4	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	6	4	no	—
275	C₂×C₄⋊C₄	—	6	4	no	—
276	C₂×C₄⋊C₄	—	6	4	no	—
277	#95	—	3	4	no	—
278	#95	—	6	4	no	—
279	#95	—	6	2	no	—
280	C₂×C₃×C₅	#384	1	1	yes	characteristic
281	C₂×C₃×C₅	#385	1	1	yes	characteristic
282	C₂×C₃×C₅	#385	1	2	yes	—
283	C₂×C₃×C₅	#389	1	1	yes	characteristic
284	C₂×C₃×C₅	#389	1	2	yes	—
285	C₂×C₃×C₅	#392	1	1	yes	characteristic
286	C₂×C₃×C₅	#395	1	1	yes	characteristic
287	C₂×C₃×C₅	#395	1	2	yes	—
288	C₂×C₃×C₅	#398	1	2	yes	—
289	C₂×C₃×C₅	#398	1	1	yes	characteristic
290	C₂×C₃×C₅	#399	1	1	yes	characteristic
291	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
292	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
293	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
294	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
295	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
296	C₂³×C₃	C₂×C₅×Q₈	1	1	yes	characteristic
297	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
298	C₂³×C₃	C₂×C₅×Q₈	1	1	yes	characteristic
299	C₂³×C₃	C₅×#41	1	2	yes	—
300	C₂³×C₃	C₅×#41	1	1	yes	characteristic
301	C₂³×C₃	C₅×#41	1	1	yes	characteristic
302	C₂×C₃×C₄	—	2	4	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	2	4	no	—
305	C₂×C₃×C₄	—	2	2	no	—
306	C₂×C₃×C₄	—	2	4	no	—
307	C₂×C₃×C₄	—	2	4	no	—
308	C₂×C₃×C₄	—	2	4	no	—
309	C₂×C₃×C₄	—	4	2	no	—
310	C₂×C₃×C₄	—	4	2	no	—
311	C₂×C₃×C₄	—	4	2	no	—
312	C₂×C₃×C₄	—	4	2	no	—
313	C₂×C₃×C₄	C₅×C₄⋊C₄	1	4	yes	complemented
314	C₂×Dic₃	—	2	4	no	—
315	C₂×Dic₃	—	2	4	no	—
316	C₂×Dic₃	—	2	4	no	—
317	C₂×Dic₃	—	2	4	no	—
318	C₂×Dic₃	—	2	4	no	—
319	C₂×Dic₃	—	2	4	no	—
320	C₂×Dic₃	—	2	4	no	—
321	C₂×Dic₃	—	2	2	no	—
322	C₂×Dic₃	—	2	4	no	—
323	C₂×Dic₃	—	2	2	no	—
324	C₂×Dic₃	—	4	1	no	—
325	C₂×Dic₃	—	4	2	no	—
326	C₂×Dic₃	—	4	2	no	—
327	C₂×Dic₃	—	4	1	no	—
328	C₂×Dic₃	—	4	1	no	—
329	C₂×Dic₃	—	4	1	no	—
330	C₂×Dic₃	C₅×C₄⋊C₄	1	8	yes	complemented
331	C₂²×C₅	#887	1	1	yes	characteristic
332	C₂²×C₅	#888	1	1	yes	characteristic
333	C₂²×C₅	#888	1	2	yes	—
334	C₂²×C₅	#889	1	2	yes	—
335	C₂²×C₅	#890	1	1	yes	characteristic
336	C₂²×C₅	D₃×C₄⋊C₄	1	2	yes	—
337	C₂²×C₅	#893	1	1	yes	characteristic
338	C₂²×C₅	#894	1	2	yes	—
339	C₂²×C₅	#896	1	2	yes	—
340	C₂²×C₅	#896	1	2	yes	—
341	C₂²×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
342	C₂²×C₅	#924	1	2	yes	—
343	C₂²×C₅	C₄×#67	1	2	yes	—
344	C₂²×C₅	#929	1	1	yes	characteristic
345	C₂²×C₅	#937	1	2	yes	—
346	C₂²×C₅	#938	1	1	yes	characteristic
347	C₂²×C₅	#939	1	2	yes	—
348	C₂²×C₅	#940	1	1	yes	characteristic
349	C₂²×C₅	#944	1	1	yes	characteristic
350	C₂²×C₅	#944	1	2	yes	—
351	C₂²×C₅	#946	1	1	yes	characteristic
352	C₂²×C₅	#946	1	2	yes	—
353	C₂²×C₅	#953	1	1	yes	characteristic
354	C₄×C₅	—	2	4	no	—
355	C₄×C₅	—	4	4	no	—
356	C₄×C₅	—	6	8	no	—
357	C₄×C₅	—	12	2	no	—
358	C₄×C₅	—	12	2	no	—
359	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	3	4	no	—
369	C₂²×C₄	—	3	4	no	—
370	C₂²×C₄	—	3	4	no	—
371	C₂²×C₄	—	3	2	no	—
372	C₂²×C₄	—	3	2	no	—
373	C₂²×C₄	—	6	2	no	—
374	C₂²×C₄	—	6	2	no	—
375	C₂²×C₄	—	6	2	no	—
376	C₂²×C₄	—	6	2	no	—
377	C₂²×C₄	—	6	2	no	—
378	C₂²×C₄	—	6	2	no	—
379	C₂²×C₄	—	6	2	no	—
380	C₂²×C₄	—	6	1	no	—
381	C₂²×C₄	—	6	1	no	—
382	C₂²×C₄	—	6	1	no	—
383	C₂²×C₄	—	6	1	no	—
384	C₂²×C₄	—	6	2	no	—
385	C₂²×C₄	C₅×Dic₆	1	2	yes	—
386	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
387	C₂²×C₄	C₅×#67	1	4	yes	—
388	C₂²×C₄	C₅×#67	1	2	yes	—
389	C₄⋊C₄	—	2	8	no	—
390	C₄⋊C₄	—	6	16	no	—
391	C₃×C₅	#1444	1	1	yes	characteristic, complemented, Hall
392	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	2	yes	—
393	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
394	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
395	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
396	C₂²×C₃	C₄×C₅×Q₈	1	1	yes	characteristic
397	C₂²×C₃	C₅×#120	1	2	yes	—
398	C₂²×C₃	C₅×#120	1	1	yes	characteristic
399	C₂²×C₃	C₅×#121	1	1	yes	characteristic
400	C₂²×C₃	C₅×#121	1	2	yes	—
401	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
402	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
403	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
404	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
405	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
406	C₂²×C₃	C₅×#123	1	2	yes	—
407	C₂²×C₃	C₅×#123	1	1	yes	characteristic
408	C₂²×C₃	C₅×#125	1	2	yes	—
409	C₂²×C₃	C₅×#125	1	1	yes	characteristic
410	C₂²×C₃	C₅×#127	1	1	yes	characteristic
411	C₂²×C₃	C₅×C₄⋊Q₈	1	2	yes	—
412	C₂²×C₃	C₅×C₄⋊Q₈	1	1	yes	characteristic
413	C₂²×C₃	C₅×C₄⋊Q₈	1	1	yes	characteristic
414	C₂²×C₃	C₅×C₄⋊Q₈	1	2	yes	—
415	C₃×C₄	—	2	4	no	—
416	C₃×C₄	—	4	4	no	—
417	Dic₃	—	2	8	no	—
418	Dic₃	—	4	2	no	—
419	Dic₃	—	4	2	no	—
420	C₂×C₅	#4972	1	1	yes	characteristic
421	C₂×C₅	#4975	1	1	yes	characteristic
422	C₂×C₅	#4976	1	2	yes	—
423	C₂×C₅	#4979	1	2	yes	—
424	C₂×C₅	#4982	1	2	yes	—
425	C₂×C₅	#4983	1	1	yes	characteristic
426	C₂×C₅	#4989	1	2	yes	—
427	C₂×C₅	#4993	1	1	yes	characteristic
428	C₂×C₅	#5210	1	1	yes	characteristic
429	C₂×C₅	#5223	1	1	yes	characteristic
430	C₂×C₅	#5230	1	1	yes	characteristic
431	C₂³	C₂×C₅×Dic₆	1	1	yes	characteristic
432	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
433	C₂³	C₅×#235	1	2	yes	—
434	C₂³	C₅×D₃×D₄	1	2	yes	—
435	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
436	C₂³	C₅×#237	1	1	yes	characteristic
437	C₂³	C₅×D₃×Q₈	1	1	yes	characteristic
438	C₂³	C₅×D₃×Q₈	1	2	yes	—
439	C₂³	C₅×#239	1	1	yes	characteristic
440	C₂³	C₂×C₅×#67	1	1	yes	characteristic
441	C₂³	C₂×C₅×#67	1	2	yes	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	3	8	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	6	4	no	—
455	C₂×C₄	—	6	4	no	—
456	C₂×C₄	—	6	4	no	—
457	C₂×C₄	—	6	4	no	—
458	C₂×C₄	—	6	4	no	—
459	C₂×C₄	—	6	4	no	—
460	C₂×C₄	—	6	4	no	—
461	C₂×C₄	—	6	4	no	—
462	C₂×C₄	—	6	2	no	—
463	C₂×C₄	—	6	2	no	—
464	C₂×C₄	—	12	2	no	—
465	C₂×C₄	—	12	1	no	—
466	C₂×C₄	—	12	2	no	—
467	C₂×C₄	—	12	1	no	—
468	C₂×C₄	—	12	1	no	—
469	C₂×C₄	—	12	1	no	—
470	C₂×C₄	C₅×Dic₃⋊C₄	1	4	yes	complemented
471	C₂×C₃	C₅×#384	1	1	yes	characteristic
472	C₂×C₃	C₅×#385	1	1	yes	characteristic
473	C₂×C₃	C₅×#385	1	2	yes	—
474	C₂×C₃	C₅×#389	1	1	yes	characteristic
475	C₂×C₃	C₅×#389	1	2	yes	—
476	C₂×C₃	C₅×#392	1	1	yes	characteristic
477	C₂×C₃	C₅×#395	1	1	yes	characteristic
478	C₂×C₃	C₅×#395	1	2	yes	—
479	C₂×C₃	C₅×#398	1	2	yes	—
480	C₂×C₃	C₅×#398	1	1	yes	characteristic
481	C₂×C₃	C₅×#399	1	1	yes	characteristic
482	C₅	#71568	1	1	yes	characteristic, direct product factor, Sylow
483	C₂²	C₅×#887	1	1	yes	characteristic
484	C₂²	C₅×#888	1	1	yes	characteristic
485	C₂²	C₅×#888	1	2	yes	—
486	C₂²	C₅×#889	1	2	yes	—
487	C₂²	C₅×#890	1	1	yes	characteristic
488	C₂²	C₅×D₃×C₄⋊C₄	1	2	yes	—
489	C₂²	C₅×#893	1	1	yes	characteristic
490	C₂²	C₅×#894	1	2	yes	—
491	C₂²	C₅×#896	1	2	yes	—
492	C₂²	C₅×#896	1	2	yes	—
493	C₂²	C₂×C₅×Dic₃⋊C₄	1	1	yes	characteristic
494	C₂²	C₅×#924	1	2	yes	—
495	C₂²	C₄×C₅×#67	1	2	yes	—
496	C₂²	C₅×#929	1	1	yes	characteristic
497	C₂²	C₅×#937	1	2	yes	—
498	C₂²	C₅×#938	1	1	yes	characteristic
499	C₂²	C₅×#939	1	2	yes	—
500	C₂²	C₅×#940	1	1	yes	characteristic
501	C₂²	C₅×#944	1	1	yes	characteristic
502	C₂²	C₅×#944	1	2	yes	—
503	C₂²	C₅×#946	1	1	yes	characteristic
504	C₂²	C₅×#946	1	2	yes	—
505	C₂²	C₅×#953	1	1	yes	characteristic
506	C₄	—	2	4	no	—
507	C₄	—	4	4	no	—
508	C₄	—	6	8	no	—
509	C₄	—	12	2	no	—
510	C₄	—	12	2	no	—
511	C₃	C₅×#1444	1	1	yes	characteristic, complemented, Sylow
512	C₂	C₅×#4972	1	1	yes	characteristic
513	C₂	C₅×#4975	1	1	yes	characteristic
514	C₂	C₅×#4976	1	2	yes	—
515	C₂	C₅×#4979	1	2	yes	—
516	C₂	C₅×#4982	1	2	yes	—
517	C₂	C₅×#4983	1	1	yes	characteristic
518	C₂	C₅×#4989	1	2	yes	—
519	C₂	C₅×#4993	1	1	yes	characteristic
520	C₂	C₅×#5210	1	1	yes	characteristic
521	C₂	C₅×#5223	1	1	yes	characteristic
522	C₂	C₅×#5230	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₅	C₂²×D₃
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂⁴	C₂²×C₅×D₃
Fitting	C₂²×C₃×C₅×C₄⋊C₄	C₂
socle, prime radical	C₂⁴×C₃×C₅	C₂³
cosocle	C₂⁴×C₃	C₂³×C₅
hypercenter	C₂²×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₅×#1444
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₅ ◁ C₂²×C₅×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
19. C₅×C₃⋊#95	C₄	semidirect
20. #71568	C₅	direct (N × H)
99. C₂×C₃×C₄×C₅	C₄⋊C₄	semidirect
116. C₂×C₅×Dic₃	C₄⋊C₄	semidirect
129. C₃⋊#95	C₄×C₅	semidirect
266. C₂×C₄×C₅	Dic₃⋊C₄	semidirect
313. C₂×C₃×C₄	C₅×C₄⋊C₄	semidirect
330. C₂×Dic₃	C₅×C₄⋊C₄	semidirect
391. C₃×C₅	#1444	semidirect
470. C₂×C₄	C₅×Dic₃⋊C₄	semidirect
482. C₅	#71568	direct (N × H)
511. C₃	C₅×#1444	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×C₄⋊C₄	2
C₂²×C₅×Dic₃⋊C₄	2
C₂×C₅×C₃⋊#95	2
C₅×#1444	3
#71568	5

Subgroups — C5×#71568 #14280235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71568 #14280235