Subgroups — C₅×#75979 #14326788

Order 1920.

1008 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#892	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4990	C₂	1	2	yes	maximal
4	C₅×#4987	C₂	1	1	yes	maximal, characteristic
5	C₅×#4984	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4977	C₂	1	2	yes	maximal, complemented
7	C₅×Dic₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₄×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4670	C₂	1	2	yes	maximal
11	C₅×#4648	C₂	1	2	yes	maximal, complemented
12	C₅×#2346	—	3	1	no	maximal, Hall
13	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
21	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
24	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅×Dic₃	C₂²	1	2	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	C₅×#892	C₄	1	8	yes	complemented
30	C₃×C₅×#95	C₂²	1	2	yes	—
31	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
32	C₅×C₃⋊#95	C₂²	1	2	yes	—
33	C₅×C₃⋊#95	C₂²	1	2	yes	—
34	C₅×C₃⋊#95	C₂²	1	2	yes	—
35	C₅×C₃⋊#95	C₂²	1	2	yes	—
36	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
37	#75979	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
38	C₂×C₅×#117	—	3	1	no	—
39	C₅×#389	—	3	1	no	—
40	C₅×#389	D₃	1	1	yes	characteristic, complemented
41	C₅×#388	—	3	2	no	—
42	C₅×#388	—	3	2	no	—
43	C₅×#382	—	3	2	no	—
44	C₅×#380	—	3	1	no	—
45	C₄×C₅×C₄⋊C₄	—	3	1	no	—
46	C₄×C₅×C₄⋊C₄	—	3	1	no	—
47	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
48	C₅×#376	—	3	2	no	—
49	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
60	C₂×C₄×C₅×D₃	—	2	2	no	—
61	C₂×C₄×C₅×D₃	—	2	2	no	—
62	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
63	C₃×C₅×C₄⋊C₄	—	2	2	no	—
64	C₃×C₅×C₄⋊C₄	—	4	2	no	—
65	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
66	C₃×C₄²×C₅	—	2	2	no	—
67	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
68	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
69	C₅×(C₂×D₃)⋊C₄	—	4	2	no	—
70	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	—
71	C₅×C₄⋊Dic₃	—	2	2	no	—
72	C₅×C₄⋊Dic₃	—	4	2	no	—
73	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	—
74	C₄×C₅×Dic₃	—	2	4	no	—
75	C₄×C₅×Dic₃	—	2	2	no	—
76	C₄×C₅×Dic₃	—	2	4	no	—
77	C₄×C₅×Dic₃	C₂×C₄	1	8	yes	—
78	C₂×#892	C₂×C₅	1	1	yes	characteristic
79	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
80	#4990	C₂×C₅	1	2	yes	—
81	#4987	C₂×C₅	1	1	yes	characteristic
82	#4984	C₂×C₅	1	1	yes	characteristic, complemented
83	#4977	C₂×C₅	1	2	yes	complemented
84	Dic₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
85	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic
86	C₄×C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
87	#4670	C₂×C₅	1	2	yes	—
88	#4648	C₂×C₅	1	2	yes	complemented
89	C₂³×C₄×C₅	—	3	1	no	—
90	C₅×#117	—	3	8	no	—
91	C₂×C₅×C₄⋊C₄	—	3	1	no	—
92	C₂×C₅×C₄⋊C₄	—	3	1	no	—
93	C₂×C₅×C₄⋊C₄	—	3	2	no	—
94	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
95	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
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	1	no	—
99	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
100	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
101	C₂×C₄²×C₅	—	3	2	no	—
102	C₂×C₄²×C₅	—	3	2	no	—
103	C₂×C₄²×C₅	—	3	2	no	—
104	C₂×C₄²×C₅	—	3	1	no	—
105	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
106	C₅×#95	—	3	1	no	—
107	C₅×#95	—	3	2	no	—
108	C₅×#95	—	3	2	no	—
109	C₅×#95	—	3	1	no	—
110	C₅×#95	—	3	2	no	—
111	C₅×#95	—	3	2	no	—
112	C₅×#95	C₂×D₃	1	2	yes	—
113	#2346	—	3	1	no	Sylow
114	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
115	C₂²×C₅×D₃	—	2	1	no	—
116	C₂²×C₅×D₃	—	2	1	no	—
117	C₂²×C₅×D₃	—	2	1	no	—
118	C₂²×C₅×D₃	—	2	1	no	—
119	C₂²×C₅×D₃	—	2	1	no	—
120	C₂²×C₅×D₃	—	2	1	no	—
121	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	—	2	1	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	2	1	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	1	no	—
128	C₂×C₃×C₄×C₅	—	2	1	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	1	no	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
133	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
134	C₂×C₃×C₄×C₅	#41	1	2	yes	—
135	C₂×C₃×C₄×C₅	#41	1	2	yes	—
136	C₂×C₃×C₄×C₅	#41	1	2	yes	—
137	C₂×C₅×Dic₃	—	2	2	no	—
138	C₂×C₅×Dic₃	—	2	2	no	—
139	C₂×C₅×Dic₃	—	2	1	no	—
140	C₂×C₅×Dic₃	—	2	1	no	—
141	C₂×C₅×Dic₃	—	2	1	no	—
142	C₂×C₅×Dic₃	—	2	1	no	—
143	C₂×C₅×Dic₃	—	2	1	no	—
144	C₂×C₅×Dic₃	—	2	2	no	—
145	C₂×C₅×Dic₃	—	2	2	no	—
146	C₂×C₅×Dic₃	—	2	1	no	—
147	C₂×C₅×Dic₃	—	2	1	no	—
148	C₂×C₅×Dic₃	—	2	2	no	—
149	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
150	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
151	C₂×C₅×Dic₃	#41	1	2	yes	—
152	C₄×C₅×D₃	—	2	8	no	—
153	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
154	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
155	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
156	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
158	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
159	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
160	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
161	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
162	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
163	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
164	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
166	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
167	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
168	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
169	#892	C₄×C₅	1	8	yes	complemented
170	C₃×#95	C₂²×C₅	1	2	yes	—
171	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
172	C₃⋊#95	C₂²×C₅	1	2	yes	—
173	C₃⋊#95	C₂²×C₅	1	2	yes	—
174	C₃⋊#95	C₂²×C₅	1	2	yes	—
175	C₃⋊#95	C₂²×C₅	1	2	yes	—
176	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
177	C₂⁴×C₅	—	3	1	no	—
178	C₂²×C₄×C₅	—	3	2	no	—
179	C₂²×C₄×C₅	—	3	1	no	—
180	C₂²×C₄×C₅	—	3	1	no	—
181	C₂²×C₄×C₅	—	3	4	no	—
182	C₂²×C₄×C₅	—	3	2	no	—
183	C₂²×C₄×C₅	—	3	1	no	—
184	C₂²×C₄×C₅	—	6	2	no	—
185	C₂²×C₄×C₅	—	6	2	no	—
186	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
187	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
189	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
190	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
191	C₅×C₄⋊C₄	—	2	2	no	—
192	C₅×C₄⋊C₄	—	3	4	no	—
193	C₅×C₄⋊C₄	—	4	2	no	—
194	C₅×C₄⋊C₄	—	6	2	no	—
195	C₅×C₄⋊C₄	—	12	2	no	—
196	C₅×C₄⋊C₄	C₄×D₃	1	4	yes	—
197	C₅×C₂²⋊C₄	—	3	8	no	—
198	C₅×C₂²⋊C₄	—	6	2	no	—
199	C₅×C₂²⋊C₄	—	6	2	no	—
200	C₅×C₂²⋊C₄	—	12	2	no	—
201	C₄²×C₅	—	2	2	no	—
202	C₄²×C₅	—	3	8	no	—
203	C₄²×C₅	—	6	4	no	—
204	C₄²×C₅	—	6	4	no	—
205	C₄²×C₅	—	6	2	no	—
206	C₂×#117	—	3	1	no	—
207	#389	—	3	1	no	—
208	#389	C₅×D₃	1	1	yes	characteristic, complemented
209	#388	—	3	2	no	—
210	#388	—	3	2	no	—
211	#382	—	3	2	no	—
212	#380	—	3	1	no	—
213	C₄×C₄⋊C₄	—	3	1	no	—
214	C₄×C₄⋊C₄	—	3	1	no	—
215	C₄×C₂²⋊C₄	—	3	1	no	—
216	#376	—	3	2	no	—
217	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
218	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
219	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
220	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
221	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
222	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
224	C₂×C₅×D₃	—	2	2	no	—
225	C₂×C₅×D₃	—	2	2	no	—
226	C₂×C₅×D₃	—	2	2	no	—
227	C₂×C₅×D₃	—	4	1	no	—
228	C₂×C₅×D₃	—	4	1	no	—
229	C₂×C₅×D₃	—	4	1	no	—
230	C₂×C₅×D₃	—	4	1	no	—
231	C₃×C₄×C₅	—	2	4	no	—
232	C₃×C₄×C₅	—	2	2	no	—
233	C₃×C₄×C₅	—	4	2	no	—
234	C₃×C₄×C₅	—	4	1	no	—
235	C₃×C₄×C₅	#117	1	4	yes	—
236	C₅×Dic₃	—	2	2	no	—
237	C₅×Dic₃	—	2	4	no	—
238	C₅×Dic₃	—	2	2	no	—
239	C₅×Dic₃	—	4	2	no	—
240	C₅×Dic₃	—	4	1	no	—
241	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
242	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
243	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
244	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
245	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
246	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
247	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
248	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
249	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
250	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
251	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
252	C₂×C₄×D₃	—	2	2	no	—
253	C₂×C₄×D₃	—	2	2	no	—
254	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
255	C₃×C₄⋊C₄	—	2	2	no	—
256	C₃×C₄⋊C₄	—	4	2	no	—
257	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
258	C₃×C₄²	—	2	2	no	—
259	(C₂×D₃)⋊C₄	—	2	2	no	—
260	(C₂×D₃)⋊C₄	—	2	2	no	—
261	(C₂×D₃)⋊C₄	—	4	2	no	—
262	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	—
263	C₄⋊Dic₃	—	2	2	no	—
264	C₄⋊Dic₃	—	4	2	no	—
265	C₄⋊Dic₃	C₂×C₄×C₅	1	4	yes	—
266	C₄×Dic₃	—	2	4	no	—
267	C₄×Dic₃	—	2	2	no	—
268	C₄×Dic₃	—	2	4	no	—
269	C₄×Dic₃	C₂×C₄×C₅	1	8	yes	—
270	C₂³×C₅	—	3	2	no	—
271	C₂³×C₅	—	6	1	no	—
272	C₂³×C₅	—	6	1	no	—
273	C₂³×C₅	—	6	1	no	—
274	C₂³×C₅	—	6	1	no	—
275	C₂³×C₅	—	6	1	no	—
276	C₂³×C₅	—	6	1	no	—
277	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
278	C₂×C₄×C₅	—	2	1	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	1	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	3	2	no	—
289	C₂×C₄×C₅	—	3	4	no	—
290	C₂×C₄×C₅	—	3	2	no	—
291	C₂×C₄×C₅	—	6	1	no	—
292	C₂×C₄×C₅	—	6	1	no	—
293	C₂×C₄×C₅	—	6	2	no	—
294	C₂×C₄×C₅	—	6	1	no	—
295	C₂×C₄×C₅	—	6	2	no	—
296	C₂×C₄×C₅	—	6	1	no	—
297	C₂×C₄×C₅	—	6	8	no	—
298	C₂×C₄×C₅	—	6	2	no	—
299	C₂×C₄×C₅	—	6	1	no	—
300	C₂×C₄×C₅	—	6	2	no	—
301	C₂×C₄×C₅	—	6	1	no	—
302	C₂×C₄×C₅	—	6	1	no	—
303	C₂×C₄×C₅	—	6	2	no	—
304	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
305	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
306	C₂×C₄×C₅	#237	1	2	yes	—
307	C₂×C₄×C₅	#239	1	2	yes	—
308	C₂×C₄×C₅	#239	1	2	yes	—
309	C₂³×C₄	—	3	1	no	—
310	#117	—	3	8	no	—
311	C₂×C₄⋊C₄	—	3	1	no	—
312	C₂×C₄⋊C₄	—	3	1	no	—
313	C₂×C₄⋊C₄	—	3	2	no	—
314	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
316	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	—	3	2	no	—
318	C₂×C₂²⋊C₄	—	3	1	no	—
319	C₂×C₂²⋊C₄	—	3	1	no	—
320	C₂×C₂²⋊C₄	—	3	2	no	—
321	C₂×C₄²	—	3	2	no	—
322	C₂×C₄²	—	3	2	no	—
323	C₂×C₄²	—	3	2	no	—
324	C₂×C₄²	—	3	1	no	—
325	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
326	#95	—	3	1	no	—
327	#95	—	3	2	no	—
328	#95	—	3	2	no	—
329	#95	—	3	1	no	—
330	#95	—	3	2	no	—
331	#95	—	3	2	no	—
332	#95	C₂×C₅×D₃	1	2	yes	—
333	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
334	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
335	C₂×C₃×C₅	#520	1	1	yes	characteristic
336	C₂×C₃×C₅	#552	1	1	yes	characteristic
337	C₂×C₃×C₅	#552	1	1	yes	characteristic
338	C₂×C₃×C₅	#555	1	1	yes	characteristic
339	C₂×C₃×C₅	#555	1	1	yes	characteristic
340	C₅×D₃	—	4	2	no	—
341	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
342	C₂²×D₃	—	2	1	no	—
343	C₂²×D₃	—	2	1	no	—
344	C₂²×D₃	—	2	1	no	—
345	C₂²×D₃	—	2	1	no	—
346	C₂²×D₃	—	2	1	no	—
347	C₂²×D₃	—	2	1	no	—
348	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
349	C₂×C₃×C₄	—	2	1	no	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	2	2	no	—
352	C₂×C₃×C₄	—	2	1	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	2	1	no	—
355	C₂×C₃×C₄	—	2	1	no	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	2	1	no	—
359	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
360	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
361	C₂×C₃×C₄	C₅×#41	1	2	yes	—
362	C₂×C₃×C₄	C₅×#41	1	2	yes	—
363	C₂×C₃×C₄	C₅×#41	1	2	yes	—
364	C₂×Dic₃	—	2	2	no	—
365	C₂×Dic₃	—	2	1	no	—
366	C₂×Dic₃	—	2	2	no	—
367	C₂×Dic₃	—	2	1	no	—
368	C₂×Dic₃	—	2	1	no	—
369	C₂×Dic₃	—	2	1	no	—
370	C₂×Dic₃	—	2	1	no	—
371	C₂×Dic₃	—	2	2	no	—
372	C₂×Dic₃	—	2	2	no	—
373	C₂×Dic₃	—	2	1	no	—
374	C₂×Dic₃	—	2	1	no	—
375	C₂×Dic₃	—	2	2	no	—
376	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
377	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
378	C₂×Dic₃	C₅×#41	1	2	yes	—
379	C₄×D₃	—	2	8	no	—
380	C₂²×C₅	—	6	2	no	—
381	C₂²×C₅	—	6	2	no	—
382	C₂²×C₅	—	6	2	no	—
383	C₂²×C₅	—	12	1	no	—
384	C₂²×C₅	—	12	1	no	—
385	C₂²×C₅	—	12	1	no	—
386	C₂²×C₅	—	12	1	no	—
387	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
388	C₂²×C₅	C₂×#237	1	1	yes	characteristic
389	C₂²×C₅	#1004	1	1	yes	characteristic
390	C₂²×C₅	C₂×#239	1	1	yes	characteristic
391	C₂²×C₅	C₂×#239	1	1	yes	characteristic
392	C₂²×C₅	D₃×#41	1	1	yes	characteristic
393	C₂²×C₅	#1010	1	1	yes	characteristic
394	C₄×C₅	—	2	2	no	—
395	C₄×C₅	—	2	4	no	—
396	C₄×C₅	—	4	1	no	—
397	C₄×C₅	—	4	2	no	—
398	C₄×C₅	—	6	2	no	—
399	C₄×C₅	—	6	2	no	—
400	C₄×C₅	—	6	4	no	—
401	C₄×C₅	—	12	2	no	—
402	C₄×C₅	—	12	1	no	—
403	C₄×C₅	#892	1	4	yes	—
404	C₂⁴	—	3	1	no	—
405	C₂²×C₄	—	3	1	no	—
406	C₂²×C₄	—	3	1	no	—
407	C₂²×C₄	—	3	2	no	—
408	C₂²×C₄	—	3	4	no	—
409	C₂²×C₄	—	3	2	no	—
410	C₂²×C₄	—	3	1	no	—
411	C₂²×C₄	—	6	2	no	—
412	C₂²×C₄	—	6	2	no	—
413	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
414	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
415	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
416	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
417	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	3	4	no	—
420	C₄⋊C₄	—	4	2	no	—
421	C₄⋊C₄	—	6	2	no	—
422	C₄⋊C₄	—	12	2	no	—
423	C₄⋊C₄	C₄×C₅×D₃	1	4	yes	—
424	C₂²⋊C₄	—	3	8	no	—
425	C₂²⋊C₄	—	6	2	no	—
426	C₂²⋊C₄	—	6	2	no	—
427	C₂²⋊C₄	—	12	2	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	3	8	no	—
430	C₄²	—	6	4	no	—
431	C₄²	—	6	4	no	—
432	C₄²	—	6	2	no	—
433	C₃×C₅	#2346	1	1	yes	characteristic, complemented, Hall
434	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
435	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
436	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
437	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
438	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
439	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
440	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
441	C₂×D₃	—	2	2	no	—
442	C₂×D₃	—	2	2	no	—
443	C₂×D₃	—	2	2	no	—
444	C₂×D₃	—	4	1	no	—
445	C₂×D₃	—	4	1	no	—
446	C₂×D₃	—	4	1	no	—
447	C₂×D₃	—	4	1	no	—
448	C₃×C₄	—	2	4	no	—
449	C₃×C₄	—	2	2	no	—
450	C₃×C₄	—	4	2	no	—
451	C₃×C₄	—	4	1	no	—
452	C₃×C₄	C₅×#117	1	4	yes	—
453	Dic₃	—	2	2	no	—
454	Dic₃	—	2	4	no	—
455	Dic₃	—	2	2	no	—
456	Dic₃	—	4	2	no	—
457	Dic₃	—	4	1	no	—
458	C₂×C₅	—	12	2	no	—
459	C₂×C₅	C₂×#892	1	1	yes	characteristic
460	C₂×C₅	#5546	1	1	yes	characteristic
461	C₂×C₅	C₄×#239	1	1	yes	characteristic
462	C₂×C₅	#5616	1	1	yes	characteristic
463	C₂×C₅	#5642	1	1	yes	characteristic
464	C₂×C₅	#5694	1	1	yes	characteristic
465	C₂×C₅	#5734	1	1	yes	characteristic
466	C₂³	—	3	2	no	—
467	C₂³	—	6	1	no	—
468	C₂³	—	6	1	no	—
469	C₂³	—	6	1	no	—
470	C₂³	—	6	1	no	—
471	C₂³	—	6	1	no	—
472	C₂³	—	6	1	no	—
473	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	3	2	no	—
485	C₂×C₄	—	3	4	no	—
486	C₂×C₄	—	3	2	no	—
487	C₂×C₄	—	6	1	no	—
488	C₂×C₄	—	6	1	no	—
489	C₂×C₄	—	6	2	no	—
490	C₂×C₄	—	6	1	no	—
491	C₂×C₄	—	6	2	no	—
492	C₂×C₄	—	6	1	no	—
493	C₂×C₄	—	6	8	no	—
494	C₂×C₄	—	6	2	no	—
495	C₂×C₄	—	6	1	no	—
496	C₂×C₄	—	6	1	no	—
497	C₂×C₄	—	6	2	no	—
498	C₂×C₄	—	6	1	no	—
499	C₂×C₄	—	6	2	no	—
500	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
501	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
502	C₂×C₄	C₅×#237	1	2	yes	—
503	C₂×C₄	C₅×#239	1	2	yes	—
504	C₂×C₄	C₅×#239	1	2	yes	—
505	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
506	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
507	C₂×C₃	C₅×#520	1	1	yes	characteristic
508	C₂×C₃	C₅×#552	1	1	yes	characteristic
509	C₂×C₃	C₅×#552	1	1	yes	characteristic
510	C₂×C₃	C₅×#555	1	1	yes	characteristic
511	C₂×C₃	C₅×#555	1	1	yes	characteristic
512	D₃	—	4	2	no	—
513	C₅	#75979	1	1	yes	characteristic, direct product factor, Sylow
514	C₂²	—	6	2	no	—
515	C₂²	—	6	2	no	—
516	C₂²	—	6	2	no	—
517	C₂²	—	12	1	no	—
518	C₂²	—	12	1	no	—
519	C₂²	—	12	1	no	—
520	C₂²	—	12	1	no	—
521	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
522	C₂²	C₂×C₅×#237	1	1	yes	characteristic
523	C₂²	C₅×#1004	1	1	yes	characteristic
524	C₂²	C₂×C₅×#239	1	1	yes	characteristic
525	C₂²	C₂×C₅×#239	1	1	yes	characteristic
526	C₂²	C₅×D₃×#41	1	1	yes	characteristic
527	C₂²	C₅×#1010	1	1	yes	characteristic
528	C₄	—	2	4	no	—
529	C₄	—	2	2	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	2	no	—
532	C₄	—	6	2	no	—
533	C₄	—	6	2	no	—
534	C₄	—	6	4	no	—
535	C₄	—	12	2	no	—
536	C₄	—	12	1	no	—
537	C₄	C₅×#892	1	4	yes	—
538	C₃	C₅×#2346	1	1	yes	characteristic, complemented, Sylow
539	C₂	—	12	2	no	—
540	C₂	C₂×C₅×#892	1	1	yes	characteristic
541	C₂	C₅×#5546	1	1	yes	characteristic
542	C₂	C₄×C₅×#239	1	1	yes	characteristic
543	C₂	C₅×#5616	1	1	yes	characteristic
544	C₂	C₅×#5642	1	1	yes	characteristic
545	C₂	C₅×#5694	1	1	yes	characteristic
546	C₂	C₅×#5734	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×#389	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₅×D₃	C₂³
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#389	D₃
hypocenter	C₃	C₅×#2346
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#389

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#389	C₂	semidirect
5. C₅×#4984	C₂	semidirect
6. C₅×#4977	C₂	semidirect
7. C₅×Dic₃×C₄⋊C₄	C₂	semidirect
9. C₄×C₅×C₄⋊Dic₃	C₂	semidirect
11. C₅×#4648	C₂	semidirect
29. C₅×#892	C₄	semidirect
37. #75979	C₅	direct (N × H)
40. C₅×#389	D₃	semidirect
79. C₃×#389	C₂×C₅	semidirect
82. #4984	C₂×C₅	semidirect
83. #4977	C₂×C₅	semidirect
84. Dic₃×C₄⋊C₄	C₂×C₅	semidirect
86. C₄×C₄⋊Dic₃	C₂×C₅	semidirect
88. #4648	C₂×C₅	semidirect
169. #892	C₄×C₅	semidirect
208. #389	C₅×D₃	semidirect
433. C₃×C₅	#2346	semidirect
513. C₅	#75979	direct (N × H)
538. C₃	C₅×#2346	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#892	2
C₃×C₅×#389	2
C₅×#4990	2
C₅×#4987	2
C₅×#4984	2
C₅×#4977	2
C₅×Dic₃×C₄⋊C₄	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₄×C₅×C₄⋊Dic₃	2
C₅×#4670	2
C₅×#4648	2
C₅×#2346	3
#75979	5

Subgroups — C5×#75979 #14326788

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#75979 #14326788