Subgroups — C₅×#76293 #14322248

Order 1920.

1848 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#940	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#67⋊C₄	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4975	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4957	C₂	1	4	yes	maximal, complemented
8	C₅×#4939	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄²×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₅×#127	—	3	1	no	maximal, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₅×#67	C₂²	1	4	yes	—
13	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
14	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₅×#217	C₂²	1	2	yes	—
20	C₅×#940	C₄	1	8	yes	complemented
21	C₅×D₄×Dic₃	—	2	4	no	—
22	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
23	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
24	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
25	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
26	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
27	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
29	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
30	C₅×#893	—	2	4	no	—
31	C₅×#67⋊C₄	—	2	16	no	—
32	#76293	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂×C₅×#127	—	3	1	no	—
34	C₂×C₄×C₅×D₄	—	3	1	no	—
35	C₂×C₄×C₅×D₄	—	3	1	no	—
36	C₂×C₄×C₅×D₄	—	3	4	no	—
37	C₅×#390	—	3	4	no	—
38	C₅×#390	—	3	1	no	—
39	C₅×#390	D₃	1	1	yes	characteristic, complemented
40	C₅×#384	—	3	1	no	—
41	C₄³×C₅	—	3	1	no	—
42	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
43	C₂³×C₅×D₃	C₂³	1	2	yes	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	—	2	2	no	—
46	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂×C₅×#67	—	2	8	no	—
51	C₂×C₅×#67	—	2	8	no	—
52	C₂×C₅×#67	C₂×C₄	1	16	yes	complemented
53	C₂²×C₅×Dic₃	—	2	8	no	—
54	C₂²×C₅×Dic₃	—	2	4	no	—
55	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
56	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
57	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
58	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
59	C₂×C₅×D₁₂	—	2	2	no	—
60	C₂×C₅×D₁₂	—	2	2	no	—
61	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	complemented
62	C₂×C₄×C₅×D₃	—	2	8	no	—
63	C₂×C₄×C₅×D₃	—	2	4	no	—
64	C₃×C₅×C₄⋊C₄	—	2	2	no	—
65	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
66	C₃×C₄²×C₅	—	2	2	no	—
67	C₅×#217	—	2	4	no	—
68	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
69	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
70	C₅×C₄⋊Dic₃	—	2	2	no	—
71	C₅×Dic₃⋊C₄	—	2	8	no	—
72	C₄×C₅×Dic₃	—	2	4	no	—
73	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
74	C₄×C₅×Dic₃	D₄	1	8	yes	complemented
75	C₄×C₅×Dic₃	D₄	1	4	yes	complemented
76	C₂×#940	C₂×C₅	1	1	yes	characteristic
77	C₂×D₄×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂×#893	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂×#67⋊C₄	C₂×C₅	1	4	yes	complemented
80	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
81	#4975	C₂×C₅	1	1	yes	characteristic, complemented
82	#4957	C₂×C₅	1	4	yes	complemented
83	#4939	C₂×C₅	1	1	yes	characteristic, complemented
84	C₄²×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂²×C₅×D₄	—	3	4	no	—
86	C₂²×C₅×D₄	—	3	1	no	—
87	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
88	C₂³×C₄×C₅	—	3	2	no	—
89	C₂³×C₄×C₅	—	3	2	no	—
90	C₅×#127	—	3	8	no	—
91	C₄×C₅×D₄	—	6	16	no	—
92	C₄×C₅×D₄	—	6	4	no	—
93	C₄×C₅×D₄	—	6	4	no	—
94	C₂×C₅×C₄⋊C₄	—	3	4	no	—
95	C₂×C₅×C₄⋊C₄	—	3	1	no	—
96	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
97	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
98	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
99	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
100	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	4	yes	—
101	C₂×C₄²×C₅	—	3	1	no	—
102	C₂×C₄²×C₅	—	3	2	no	—
103	C₂×C₄²×C₅	—	3	1	no	—
104	C₂×C₄²×C₅	—	3	2	no	—
105	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
106	C₄×#127	—	3	1	no	Sylow
107	C₂³×C₃×C₅	—	2	2	no	—
108	C₂³×C₃×C₅	—	2	4	no	—
109	C₂³×C₃×C₅	—	2	4	no	—
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
112	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
113	C₂²×C₅×D₃	—	2	2	no	—
114	C₂²×C₅×D₃	—	2	4	no	—
115	C₂²×C₅×D₃	—	2	2	no	—
116	C₂²×C₅×D₃	—	2	4	no	—
117	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
118	C₃×C₅×D₄	—	2	8	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	4	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
124	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
125	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
126	C₂×C₃×C₄×C₅	#41	1	2	yes	—
127	C₅×#67	—	2	32	no	—
128	C₂×C₅×Dic₃	—	2	2	no	—
129	C₂×C₅×Dic₃	—	2	4	no	—
130	C₂×C₅×Dic₃	—	2	2	no	—
131	C₂×C₅×Dic₃	—	4	8	no	—
132	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
133	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
134	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
135	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
136	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
137	C₂×C₅×Dic₃	#41	1	4	yes	—
138	C₅×D₁₂	—	2	8	no	—
139	C₄×C₅×D₃	—	4	8	no	—
140	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
141	C₂²×#67	C₂²×C₅	1	4	yes	—
142	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
143	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
144	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
145	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
147	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
148	C₂×#217	C₂²×C₅	1	2	yes	—
149	#940	C₄×C₅	1	8	yes	complemented
150	D₄×Dic₃	—	2	4	no	—
151	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
152	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
153	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
154	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
155	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
156	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
158	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
159	#893	—	2	4	no	—
160	#67⋊C₄	—	2	16	no	—
161	C₂⁴×C₅	—	3	2	no	—
162	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
163	C₂×C₅×D₄	—	2	2	no	—
164	C₂×C₅×D₄	—	2	2	no	—
165	C₂×C₅×D₄	—	3	16	no	—
166	C₂×C₅×D₄	—	3	4	no	—
167	C₂×C₅×D₄	—	6	8	no	—
168	C₂×C₅×D₄	—	6	8	no	—
169	C₂×C₅×D₄	—	6	2	no	—
170	C₂×C₅×D₄	—	6	2	no	—
171	C₂×C₅×D₄	C₄×D₃	1	4	yes	complemented
172	C₂²×C₄×C₅	—	3	2	no	—
173	C₂²×C₄×C₅	—	3	1	no	—
174	C₂²×C₄×C₅	—	3	1	no	—
175	C₂²×C₄×C₅	—	3	2	no	—
176	C₂²×C₄×C₅	—	6	8	no	—
177	C₂²×C₄×C₅	—	6	4	no	—
178	C₂²×C₄×C₅	—	6	8	no	—
179	C₂²×C₄×C₅	—	6	4	no	—
180	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
181	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
182	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
183	C₅×C₄⋊C₄	—	2	2	no	—
184	C₅×C₄⋊C₄	—	6	8	no	—
185	C₅×C₄⋊C₄	—	6	2	no	—
186	C₅×C₂²⋊C₄	—	2	8	no	—
187	C₅×C₂²⋊C₄	—	6	4	no	—
188	C₅×C₂²⋊C₄	—	6	4	no	—
189	C₅×C₂²⋊C₄	—	6	8	no	—
190	C₄²×C₅	—	2	2	no	—
191	C₄²×C₅	—	3	4	no	—
192	C₄²×C₅	—	3	8	no	—
193	C₄²×C₅	—	3	4	no	—
194	C₄²×C₅	—	6	4	no	—
195	C₂×#127	—	3	1	no	—
196	C₂×C₄×D₄	—	3	1	no	—
197	C₂×C₄×D₄	—	3	1	no	—
198	C₂×C₄×D₄	—	3	4	no	—
199	#390	—	3	4	no	—
200	#390	—	3	1	no	—
201	#390	C₅×D₃	1	1	yes	characteristic, complemented
202	#384	—	3	1	no	—
203	C₄³	—	3	1	no	—
204	C₂²×C₃×C₅	—	2	8	no	—
205	C₂²×C₃×C₅	—	2	4	no	—
206	C₂²×C₃×C₅	—	4	2	no	—
207	C₂²×C₃×C₅	—	4	2	no	—
208	C₂²×C₃×C₅	—	4	4	no	—
209	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
210	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
211	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
212	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
213	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
214	C₂×C₅×D₃	—	2	4	no	—
215	C₂×C₅×D₃	—	2	8	no	—
216	C₂×C₅×D₃	—	4	2	no	—
217	C₂×C₅×D₃	—	4	2	no	—
218	C₂×C₅×D₃	—	4	4	no	—
219	C₃×C₄×C₅	—	2	4	no	—
220	C₃×C₄×C₅	—	4	2	no	—
221	C₃×C₄×C₅	C₄×D₄	1	4	yes	complemented
222	C₅×Dic₃	—	2	2	no	—
223	C₅×Dic₃	—	4	2	no	—
224	C₅×Dic₃	C₄×D₄	1	8	yes	complemented
225	C₅×Dic₃	#127	1	4	yes	complemented
226	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
227	C₂³×D₃	C₂³×C₅	1	2	yes	—
228	C₂×C₃×D₄	—	2	2	no	—
229	C₂×C₃×D₄	—	2	2	no	—
230	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
231	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
232	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
233	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
234	C₂×#67	—	2	8	no	—
235	C₂×#67	—	2	8	no	—
236	C₂×#67	C₂×C₄×C₅	1	16	yes	complemented
237	C₂²×Dic₃	—	2	8	no	—
238	C₂²×Dic₃	—	2	4	no	—
239	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
240	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
241	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
242	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
243	C₂×D₁₂	—	2	2	no	—
244	C₂×D₁₂	—	2	2	no	—
245	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	complemented
246	C₂×C₄×D₃	—	2	8	no	—
247	C₂×C₄×D₃	—	2	4	no	—
248	C₃×C₄⋊C₄	—	2	2	no	—
249	C₃×C₂²⋊C₄	—	2	8	no	—
250	C₃×C₄²	—	2	2	no	—
251	#217	—	2	4	no	—
252	(C₂×D₃)⋊C₄	—	2	8	no	—
253	(C₂×D₃)⋊C₄	—	2	4	no	—
254	C₄⋊Dic₃	—	2	2	no	—
255	Dic₃⋊C₄	—	2	8	no	—
256	C₄×Dic₃	—	2	4	no	—
257	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
258	C₄×Dic₃	C₅×D₄	1	8	yes	complemented
259	C₄×Dic₃	C₅×D₄	1	4	yes	complemented
260	C₂³×C₅	—	2	4	no	—
261	C₂³×C₅	—	2	2	no	—
262	C₂³×C₅	—	2	2	no	—
263	C₂³×C₅	—	2	4	no	—
264	C₂³×C₅	—	3	4	no	—
265	C₂³×C₅	—	6	2	no	—
266	C₂³×C₅	—	6	4	no	—
267	C₂³×C₅	—	6	2	no	—
268	C₂³×C₅	—	6	4	no	—
269	C₂³×C₅	C₂×C₄×D₃	1	4	yes	—
270	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
271	C₅×D₄	—	2	8	no	—
272	C₅×D₄	—	6	32	no	—
273	C₅×D₄	—	6	8	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	4	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	3	4	no	—
279	C₂×C₄×C₅	—	3	4	no	—
280	C₂×C₄×C₅	—	3	2	no	—
281	C₂×C₄×C₅	—	3	4	no	—
282	C₂×C₄×C₅	—	3	4	no	—
283	C₂×C₄×C₅	—	3	2	no	—
284	C₂×C₄×C₅	—	6	2	no	—
285	C₂×C₄×C₅	—	6	2	no	—
286	C₂×C₄×C₅	—	6	4	no	—
287	C₂×C₄×C₅	—	12	8	no	—
288	C₂×C₄×C₅	—	12	8	no	—
289	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
290	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
291	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
292	C₂×C₄×C₅	#237	1	2	yes	—
293	C₂²×D₄	—	3	4	no	—
294	C₂²×D₄	—	3	1	no	—
295	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
296	C₂³×C₄	—	3	2	no	—
297	C₂³×C₄	—	3	2	no	—
298	#127	—	3	8	no	—
299	C₄×D₄	—	6	16	no	—
300	C₄×D₄	—	6	4	no	—
301	C₄×D₄	—	6	4	no	—
302	C₂×C₄⋊C₄	—	3	4	no	—
303	C₂×C₄⋊C₄	—	3	1	no	—
304	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	—	3	2	no	—
306	C₂×C₂²⋊C₄	—	3	2	no	—
307	C₂×C₂²⋊C₄	—	3	4	no	—
308	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	4	yes	—
309	C₂×C₄²	—	3	2	no	—
310	C₂×C₄²	—	3	1	no	—
311	C₂×C₄²	—	3	1	no	—
312	C₂×C₄²	—	3	2	no	—
313	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
314	C₂×C₃×C₅	—	4	4	no	—
315	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
316	C₂×C₃×C₅	C₂×C₄×D₄	1	2	yes	—
317	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
318	C₂×C₃×C₅	#532	1	1	yes	characteristic
319	C₂×C₃×C₅	#532	1	2	yes	—
320	C₅×D₃	—	4	4	no	—
321	C₂³×C₃	—	2	2	no	—
322	C₂³×C₃	—	2	4	no	—
323	C₂³×C₃	—	2	4	no	—
324	C₂³×C₃	—	2	2	no	—
325	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
326	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
327	C₂²×D₃	—	2	2	no	—
328	C₂²×D₃	—	2	4	no	—
329	C₂²×D₃	—	2	2	no	—
330	C₂²×D₃	—	2	4	no	—
331	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
332	C₃×D₄	—	2	8	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	2	4	no	—
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
338	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
339	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
340	C₂×C₃×C₄	C₅×#41	1	2	yes	—
341	#67	—	2	32	no	—
342	C₂×Dic₃	—	2	2	no	—
343	C₂×Dic₃	—	2	4	no	—
344	C₂×Dic₃	—	2	2	no	—
345	C₂×Dic₃	—	4	8	no	—
346	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
347	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
348	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
349	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
350	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
351	C₂×Dic₃	C₅×#41	1	4	yes	—
352	D₁₂	—	2	8	no	—
353	C₄×D₃	—	4	8	no	—
354	C₂²×C₅	—	2	4	no	—
355	C₂²×C₅	—	2	8	no	—
356	C₂²×C₅	—	4	2	no	—
357	C₂²×C₅	—	4	2	no	—
358	C₂²×C₅	—	4	4	no	—
359	C₂²×C₅	—	6	4	no	—
360	C₂²×C₅	—	6	8	no	—
361	C₂²×C₅	—	12	2	no	—
362	C₂²×C₅	—	12	2	no	—
363	C₂²×C₅	—	12	4	no	—
364	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
365	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
366	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
367	C₂²×C₅	C₂×#237	1	1	yes	characteristic
368	C₂²×C₅	D₃×#41	1	2	yes	—
369	C₄×C₅	—	2	4	no	—
370	C₄×C₅	—	3	4	no	—
371	C₄×C₅	—	3	8	no	—
372	C₄×C₅	—	4	2	no	—
373	C₄×C₅	—	6	2	no	—
374	C₄×C₅	—	12	2	no	—
375	C₄×C₅	#67⋊C₄	1	4	yes	complemented
376	C₂⁴	—	3	2	no	—
377	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	3	16	no	—
381	C₂×D₄	—	3	4	no	—
382	C₂×D₄	—	6	8	no	—
383	C₂×D₄	—	6	8	no	—
384	C₂×D₄	—	6	2	no	—
385	C₂×D₄	—	6	2	no	—
386	C₂×D₄	C₄×C₅×D₃	1	4	yes	complemented
387	C₂²×C₄	—	3	2	no	—
388	C₂²×C₄	—	3	1	no	—
389	C₂²×C₄	—	3	1	no	—
390	C₂²×C₄	—	3	2	no	—
391	C₂²×C₄	—	6	8	no	—
392	C₂²×C₄	—	6	4	no	—
393	C₂²×C₄	—	6	8	no	—
394	C₂²×C₄	—	6	4	no	—
395	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
396	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
397	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	6	8	no	—
400	C₄⋊C₄	—	6	2	no	—
401	C₂²⋊C₄	—	2	8	no	—
402	C₂²⋊C₄	—	6	4	no	—
403	C₂²⋊C₄	—	6	4	no	—
404	C₂²⋊C₄	—	6	8	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	3	4	no	—
407	C₄²	—	3	8	no	—
408	C₄²	—	3	4	no	—
409	C₄²	—	6	4	no	—
410	C₃×C₅	C₄×#127	1	1	yes	characteristic, complemented, Hall
411	C₂²×C₃	—	2	8	no	—
412	C₂²×C₃	—	2	4	no	—
413	C₂²×C₃	—	4	2	no	—
414	C₂²×C₃	—	4	2	no	—
415	C₂²×C₃	—	4	4	no	—
416	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
417	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
418	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
419	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
420	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
421	C₂×D₃	—	2	4	no	—
422	C₂×D₃	—	2	8	no	—
423	C₂×D₃	—	4	2	no	—
424	C₂×D₃	—	4	2	no	—
425	C₂×D₃	—	4	4	no	—
426	C₃×C₄	—	2	4	no	—
427	C₃×C₄	—	4	2	no	—
428	C₃×C₄	C₄×C₅×D₄	1	4	yes	complemented
429	Dic₃	—	2	2	no	—
430	Dic₃	—	4	2	no	—
431	Dic₃	C₄×C₅×D₄	1	8	yes	complemented
432	Dic₃	C₅×#127	1	4	yes	complemented
433	C₂×C₅	—	4	4	no	—
434	C₂×C₅	—	12	4	no	—
435	C₂×C₅	C₂×#67⋊C₄	1	1	yes	characteristic
436	C₂×C₅	C₄×D₃×D₄	1	2	yes	—
437	C₂×C₅	#5596	1	2	yes	—
438	C₂×C₅	#5668	1	1	yes	characteristic
439	C₂×C₅	D₃×#127	1	1	yes	characteristic
440	C₂³	—	2	4	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	4	no	—
444	C₂³	—	3	4	no	—
445	C₂³	—	6	2	no	—
446	C₂³	—	6	4	no	—
447	C₂³	—	6	2	no	—
448	C₂³	—	6	4	no	—
449	C₂³	C₂×C₄×C₅×D₃	1	4	yes	—
450	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
451	D₄	—	2	8	no	—
452	D₄	—	6	32	no	—
453	D₄	—	6	8	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	3	4	no	—
459	C₂×C₄	—	3	4	no	—
460	C₂×C₄	—	3	2	no	—
461	C₂×C₄	—	3	4	no	—
462	C₂×C₄	—	3	4	no	—
463	C₂×C₄	—	3	2	no	—
464	C₂×C₄	—	6	2	no	—
465	C₂×C₄	—	6	2	no	—
466	C₂×C₄	—	6	4	no	—
467	C₂×C₄	—	12	8	no	—
468	C₂×C₄	—	12	8	no	—
469	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
470	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
471	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
472	C₂×C₄	C₅×#237	1	2	yes	—
473	C₂×C₃	—	4	4	no	—
474	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
475	C₂×C₃	C₂×C₄×C₅×D₄	1	2	yes	—
476	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
477	C₂×C₃	C₅×#532	1	1	yes	characteristic
478	C₂×C₃	C₅×#532	1	2	yes	—
479	D₃	—	4	4	no	—
480	C₅	#76293	1	1	yes	characteristic, direct product factor, Sylow
481	C₂²	—	2	4	no	—
482	C₂²	—	2	8	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	6	4	no	—
487	C₂²	—	6	8	no	—
488	C₂²	—	12	2	no	—
489	C₂²	—	12	2	no	—
490	C₂²	—	12	4	no	—
491	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
492	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
493	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
494	C₂²	C₂×C₅×#237	1	1	yes	characteristic
495	C₂²	C₅×D₃×#41	1	2	yes	—
496	C₄	—	2	4	no	—
497	C₄	—	3	4	no	—
498	C₄	—	3	8	no	—
499	C₄	—	4	2	no	—
500	C₄	—	6	2	no	—
501	C₄	—	12	2	no	—
502	C₄	C₅×#67⋊C₄	1	4	yes	complemented
503	C₃	C₄×C₅×#127	1	1	yes	characteristic, complemented, Sylow
504	C₂	—	4	4	no	—
505	C₂	—	12	4	no	—
506	C₂	C₂×C₅×#67⋊C₄	1	1	yes	characteristic
507	C₂	C₄×C₅×D₃×D₄	1	2	yes	—
508	C₂	C₅×#5596	1	2	yes	—
509	C₂	C₅×#5668	1	1	yes	characteristic
510	C₂	C₅×D₃×#127	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#390	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₅×#940	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#390	D₃
hypocenter	C₃	C₄×C₅×#127
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#390

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×D₄×Dic₃	C₂	semidirect
3. C₂×C₅×#893	C₂	semidirect
4. C₂×C₅×#67⋊C₄	C₂	semidirect
5. C₃×C₅×#390	C₂	semidirect
6. C₅×#4975	C₂	semidirect
7. C₅×#4957	C₂	semidirect
8. C₅×#4939	C₂	semidirect
9. C₄²×C₅×Dic₃	C₂	semidirect
20. C₅×#940	C₄	semidirect
32. #76293	C₅	direct (N × H)
39. C₅×#390	D₃	semidirect
46. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
52. C₂×C₅×#67	C₂×C₄	semidirect
61. C₂×C₅×D₁₂	C₂×C₄	semidirect
73. C₄×C₅×Dic₃	C₂×C₄	semidirect
74. C₄×C₅×Dic₃	D₄	semidirect
75. C₄×C₅×Dic₃	D₄	semidirect
77. C₂×D₄×Dic₃	C₂×C₅	semidirect
78. C₂×#893	C₂×C₅	semidirect
79. C₂×#67⋊C₄	C₂×C₅	semidirect
80. C₃×#390	C₂×C₅	semidirect
81. #4975	C₂×C₅	semidirect
82. #4957	C₂×C₅	semidirect
83. #4939	C₂×C₅	semidirect
84. C₄²×Dic₃	C₂×C₅	semidirect
149. #940	C₄×C₅	semidirect
171. C₂×C₅×D₄	C₄×D₃	semidirect
201. #390	C₅×D₃	semidirect
221. C₃×C₄×C₅	C₄×D₄	semidirect
224. C₅×Dic₃	C₄×D₄	semidirect
225. C₅×Dic₃	#127	semidirect
230. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
236. C₂×#67	C₂×C₄×C₅	semidirect
245. C₂×D₁₂	C₂×C₄×C₅	semidirect
257. C₄×Dic₃	C₂×C₄×C₅	semidirect
258. C₄×Dic₃	C₅×D₄	semidirect
259. C₄×Dic₃	C₅×D₄	semidirect
375. C₄×C₅	#67⋊C₄	semidirect
386. C₂×D₄	C₄×C₅×D₃	semidirect
410. C₃×C₅	C₄×#127	semidirect
428. C₃×C₄	C₄×C₅×D₄	semidirect
431. Dic₃	C₄×C₅×D₄	semidirect
432. Dic₃	C₅×#127	semidirect
480. C₅	#76293	direct (N × H)
502. C₄	C₅×#67⋊C₄	semidirect
503. C₃	C₄×C₅×#127	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#940	2
C₂×C₅×D₄×Dic₃	2
C₂×C₅×#893	2
C₂×C₅×#67⋊C₄	2
C₃×C₅×#390	2
C₅×#4975	2
C₅×#4957	2
C₅×#4939	2
C₄²×C₅×Dic₃	2
C₄×C₅×#127	3
#76293	5

Subgroups — C5×#76293 #14322248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#76293 #14322248