Subgroups — C₅×#75964 #14321416

Order 1920.

1648 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#895	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#893	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄²×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4990	C₂	1	2	yes	maximal, complemented
7	C₅×#4987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×Dic₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4666	C₂	1	2	yes	maximal, complemented
11	C₅×#4665	C₂	1	2	yes	maximal, complemented
12	C₄×C₅×#121	—	3	1	no	maximal, Hall
13	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
14	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
17	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
24	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
25	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
26	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
27	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
31	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
33	C₅×#895	C₄	1	8	yes	complemented
34	C₅×#893	—	2	8	no	—
35	C₅×#893	—	2	4	no	—
36	C₄²×C₅×D₃	—	2	4	no	—
37	C₃×C₅×#95	C₂²	1	2	yes	—
38	C₅×C₃⋊#95	C₂²	1	2	yes	—
39	C₅×C₃⋊#95	C₂²	1	2	yes	—
40	#75964	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₂×C₅×#121	—	3	1	no	—
42	C₂×C₄×C₅×D₄	—	3	1	no	—
43	C₂×C₄×C₅×D₄	—	3	2	no	—
44	C₂²×C₄²×C₅	—	3	1	no	—
45	C₅×#390	—	3	1	no	—
46	C₅×#389	D₃	1	1	yes	characteristic, complemented
47	C₅×#388	—	3	2	no	—
48	C₅×#386	—	3	2	no	—
49	C₅×#380	—	3	1	no	—
50	C₄×C₅×C₄⋊C₄	—	3	1	no	—
51	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
52	C₂³×C₅×D₃	C₂³	1	2	yes	—
53	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
60	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
61	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
62	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
63	C₂×C₅×D₁₂	—	2	4	no	—
64	C₂×C₅×D₁₂	—	2	4	no	—
65	C₂×C₅×D₁₂	—	2	2	no	—
66	C₂×C₅×D₁₂	—	2	2	no	—
67	C₂×C₅×D₁₂	C₂×C₄	1	8	yes	complemented
68	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	complemented
69	C₂×C₄×C₅×D₃	—	2	2	no	—
70	C₂×C₄×C₅×D₃	—	2	2	no	—
71	C₂×C₄×C₅×D₃	—	2	2	no	—
72	C₂×C₄×C₅×D₃	—	2	2	no	—
73	C₂×C₄×C₅×D₃	—	2	2	no	—
74	C₂×C₄×C₅×D₃	—	2	2	no	—
75	C₂×C₄×C₅×D₃	—	2	2	no	—
76	C₂×C₄×C₅×D₃	—	2	4	no	—
77	C₂×C₄×C₅×D₃	—	2	4	no	—
78	C₂×C₄×C₅×D₃	—	2	4	no	—
79	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	complemented
80	C₂×C₄×C₅×D₃	D₄	1	4	yes	complemented
81	C₃×C₅×C₄⋊C₄	—	2	4	no	—
82	C₃×C₅×C₄⋊C₄	—	2	2	no	—
83	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
84	C₃×C₄²×C₅	—	2	2	no	—
85	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
86	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
87	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
88	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
89	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	complemented
90	C₅×C₄⋊Dic₃	—	2	2	no	—
91	C₄×C₅×Dic₃	—	2	2	no	—
92	C₄×C₅×Dic₃	—	2	2	no	—
93	C₄×C₅×Dic₃	—	2	4	no	—
94	C₄×C₅×Dic₃	D₄	1	4	yes	complemented
95	C₂×#895	C₂×C₅	1	1	yes	characteristic
96	C₂×#893	C₂×C₅	1	2	yes	complemented
97	C₂×#893	C₂×C₅	1	1	yes	characteristic, complemented
98	C₂×C₄²×D₃	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
100	#4990	C₂×C₅	1	2	yes	complemented
101	#4987	C₂×C₅	1	1	yes	characteristic, complemented
102	Dic₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
103	#4939	C₂×C₅	1	1	yes	characteristic, complemented
104	#4666	C₂×C₅	1	2	yes	complemented
105	#4665	C₂×C₅	1	2	yes	complemented
106	C₂²×C₅×D₄	—	3	2	no	—
107	C₂²×C₅×D₄	—	3	1	no	—
108	C₂³×C₄×C₅	—	3	1	no	—
109	C₂³×C₄×C₅	—	3	1	no	—
110	C₂³×C₄×C₅	—	3	2	no	—
111	C₂³×C₄×C₅	—	3	1	no	—
112	C₅×#121	—	3	8	no	—
113	C₄×C₅×D₄	—	6	4	no	—
114	C₄×C₅×D₄	—	6	8	no	—
115	C₂×C₅×C₄⋊C₄	—	3	1	no	—
116	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
117	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
118	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
119	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
120	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
121	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
122	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
123	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
124	C₂×C₄²×C₅	—	3	1	no	—
125	C₂×C₄²×C₅	—	3	1	no	—
126	C₂×C₄²×C₅	—	3	2	no	—
127	C₂×C₄²×C₅	—	3	1	no	—
128	C₂×C₄²×C₅	—	6	4	no	—
129	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
130	C₅×#95	—	3	2	no	—
131	C₅×#95	—	3	2	no	—
132	C₅×#95	C₂×D₃	1	2	yes	—
133	C₄×#121	—	3	1	no	Sylow
134	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
135	C₂²×C₅×D₃	—	2	1	no	—
136	C₂²×C₅×D₃	—	2	1	no	—
137	C₂²×C₅×D₃	—	2	1	no	—
138	C₂²×C₅×D₃	—	2	1	no	—
139	C₂²×C₅×D₃	—	2	2	no	—
140	C₂²×C₅×D₃	—	2	2	no	—
141	C₂²×C₅×D₃	—	2	2	no	—
142	C₂²×C₅×D₃	—	2	2	no	—
143	C₂²×C₅×D₃	—	2	2	no	—
144	C₂²×C₅×D₃	—	2	2	no	—
145	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
146	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
147	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
148	C₂²×C₅×D₃	#41	1	2	yes	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	—	2	1	no	—
153	C₂×C₃×C₄×C₅	—	2	1	no	—
154	C₂×C₃×C₄×C₅	—	2	2	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	2	2	no	—
157	C₂×C₃×C₄×C₅	—	2	2	no	—
158	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
159	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
160	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
161	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
162	C₂×C₃×C₄×C₅	#41	1	2	yes	—
163	C₂×C₃×C₄×C₅	#41	1	2	yes	—
164	C₂×C₅×Dic₃	—	2	1	no	—
165	C₂×C₅×Dic₃	—	2	1	no	—
166	C₂×C₅×Dic₃	—	2	1	no	—
167	C₂×C₅×Dic₃	—	2	1	no	—
168	C₂×C₅×Dic₃	—	2	2	no	—
169	C₂×C₅×Dic₃	—	2	2	no	—
170	C₂×C₅×Dic₃	—	2	2	no	—
171	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
172	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
173	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
174	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
175	C₂×C₅×Dic₃	#41	1	2	yes	—
176	C₅×D₁₂	—	2	16	no	—
177	C₅×D₁₂	—	2	8	no	—
178	C₄×C₅×D₃	—	2	8	no	—
179	C₄×C₅×D₃	—	2	8	no	—
180	C₄×C₅×D₃	—	2	8	no	—
181	C₄×C₅×D₃	—	4	8	no	—
182	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
183	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
184	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
185	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
186	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
187	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
188	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
189	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
190	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
191	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
192	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
193	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
194	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
195	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
196	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
197	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
198	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
199	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
200	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
201	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
202	#895	C₄×C₅	1	8	yes	complemented
203	#893	—	2	8	no	—
204	#893	—	2	4	no	—
205	C₄²×D₃	—	2	4	no	—
206	C₃×#95	C₂²×C₅	1	2	yes	—
207	C₃⋊#95	C₂²×C₅	1	2	yes	—
208	C₃⋊#95	C₂²×C₅	1	2	yes	—
209	C₂⁴×C₅	—	3	1	no	—
210	C₂⁴×C₅	—	3	2	no	—
211	C₂×C₅×D₄	—	3	8	no	—
212	C₂×C₅×D₄	—	3	4	no	—
213	C₂×C₅×D₄	—	6	4	no	—
214	C₂×C₅×D₄	—	6	4	no	—
215	C₂×C₅×D₄	—	6	2	no	—
216	C₂×C₅×D₄	—	6	2	no	—
217	C₂²×C₄×C₅	—	3	1	no	—
218	C₂²×C₄×C₅	—	3	1	no	—
219	C₂²×C₄×C₅	—	3	1	no	—
220	C₂²×C₄×C₅	—	3	4	no	—
221	C₂²×C₄×C₅	—	3	4	no	—
222	C₂²×C₄×C₅	—	3	2	no	—
223	C₂²×C₄×C₅	—	6	2	no	—
224	C₂²×C₄×C₅	—	6	2	no	—
225	C₂²×C₄×C₅	—	6	2	no	—
226	C₂²×C₄×C₅	—	6	4	no	—
227	C₂²×C₄×C₅	—	6	4	no	—
228	C₂²×C₄×C₅	—	6	4	no	—
229	C₂²×C₄×C₅	—	6	2	no	—
230	C₂²×C₄×C₅	—	6	2	no	—
231	C₂²×C₄×C₅	—	6	2	no	—
232	C₂²×C₄×C₅	—	6	2	no	—
233	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
234	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
235	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
236	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
237	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
238	C₅×C₄⋊C₄	—	2	4	no	—
239	C₅×C₄⋊C₄	—	2	2	no	—
240	C₅×C₄⋊C₄	—	6	2	no	—
241	C₅×C₄⋊C₄	C₄×D₃	1	4	yes	complemented
242	C₅×C₂²⋊C₄	—	3	8	no	—
243	C₅×C₂²⋊C₄	—	6	4	no	—
244	C₅×C₂²⋊C₄	—	6	4	no	—
245	C₅×C₂²⋊C₄	—	6	4	no	—
246	C₅×C₂²⋊C₄	—	6	4	no	—
247	C₄²×C₅	—	2	2	no	—
248	C₄²×C₅	—	3	4	no	—
249	C₄²×C₅	—	6	2	no	—
250	C₄²×C₅	—	6	2	no	—
251	C₄²×C₅	—	6	4	no	—
252	C₂×#121	—	3	1	no	—
253	C₂×C₄×D₄	—	3	1	no	—
254	C₂×C₄×D₄	—	3	2	no	—
255	C₂²×C₄²	—	3	1	no	—
256	#390	—	3	1	no	—
257	#389	C₅×D₃	1	1	yes	characteristic, complemented
258	#388	—	3	2	no	—
259	#386	—	3	2	no	—
260	#380	—	3	1	no	—
261	C₄×C₄⋊C₄	—	3	1	no	—
262	C₄×C₂²⋊C₄	—	3	2	no	—
263	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
264	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
265	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
266	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
267	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
268	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
269	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
270	C₂×C₅×D₃	—	2	2	no	—
271	C₂×C₅×D₃	—	2	2	no	—
272	C₂×C₅×D₃	—	2	2	no	—
273	C₂×C₅×D₃	—	2	2	no	—
274	C₂×C₅×D₃	—	2	2	no	—
275	C₂×C₅×D₃	—	2	2	no	—
276	C₂×C₅×D₃	—	2	4	no	—
277	C₂×C₅×D₃	—	2	4	no	—
278	C₂×C₅×D₃	—	2	4	no	—
279	C₂×C₅×D₃	—	4	2	no	—
280	C₂×C₅×D₃	—	4	2	no	—
281	C₂×C₅×D₃	—	4	2	no	—
282	C₂×C₅×D₃	—	4	2	no	—
283	C₂×C₅×D₃	C₄×D₄	1	4	yes	complemented
284	C₃×C₄×C₅	—	2	4	no	—
285	C₃×C₄×C₅	—	2	2	no	—
286	C₃×C₄×C₅	—	2	2	no	—
287	C₃×C₄×C₅	—	4	2	no	—
288	C₃×C₄×C₅	C₄×D₄	1	4	yes	complemented
289	C₅×Dic₃	—	2	2	no	—
290	C₅×Dic₃	—	2	2	no	—
291	C₅×Dic₃	—	4	2	no	—
292	C₅×Dic₃	#121	1	4	yes	complemented
293	C₂³×D₃	C₂³×C₅	1	2	yes	—
294	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
295	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
296	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
297	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
298	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
299	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
300	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
301	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
302	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
303	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
304	C₂×D₁₂	—	2	4	no	—
305	C₂×D₁₂	—	2	4	no	—
306	C₂×D₁₂	—	2	2	no	—
307	C₂×D₁₂	—	2	2	no	—
308	C₂×D₁₂	C₂×C₄×C₅	1	8	yes	complemented
309	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	complemented
310	C₂×C₄×D₃	—	2	2	no	—
311	C₂×C₄×D₃	—	2	2	no	—
312	C₂×C₄×D₃	—	2	2	no	—
313	C₂×C₄×D₃	—	2	2	no	—
314	C₂×C₄×D₃	—	2	2	no	—
315	C₂×C₄×D₃	—	2	2	no	—
316	C₂×C₄×D₃	—	2	2	no	—
317	C₂×C₄×D₃	—	2	4	no	—
318	C₂×C₄×D₃	—	2	4	no	—
319	C₂×C₄×D₃	—	2	4	no	—
320	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	complemented
321	C₂×C₄×D₃	C₅×D₄	1	4	yes	complemented
322	C₃×C₄⋊C₄	—	2	4	no	—
323	C₃×C₄⋊C₄	—	2	2	no	—
324	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
325	C₃×C₄²	—	2	2	no	—
326	(C₂×D₃)⋊C₄	—	2	4	no	—
327	(C₂×D₃)⋊C₄	—	2	4	no	—
328	(C₂×D₃)⋊C₄	—	2	4	no	—
329	(C₂×D₃)⋊C₄	—	2	4	no	—
330	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
331	C₄⋊Dic₃	—	2	2	no	—
332	C₄×Dic₃	—	2	2	no	—
333	C₄×Dic₃	—	2	2	no	—
334	C₄×Dic₃	—	2	4	no	—
335	C₄×Dic₃	C₅×D₄	1	4	yes	complemented
336	C₂³×C₅	—	3	2	no	—
337	C₂³×C₅	—	3	2	no	—
338	C₂³×C₅	—	3	2	no	—
339	C₂³×C₅	—	3	4	no	—
340	C₂³×C₅	—	6	1	no	—
341	C₂³×C₅	—	6	1	no	—
342	C₂³×C₅	—	6	1	no	—
343	C₂³×C₅	—	6	1	no	—
344	C₂³×C₅	—	6	2	no	—
345	C₂³×C₅	—	6	2	no	—
346	C₂³×C₅	—	6	2	no	—
347	C₂³×C₅	—	6	2	no	—
348	C₂³×C₅	—	6	2	no	—
349	C₂³×C₅	—	6	2	no	—
350	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
351	C₅×D₄	—	6	16	no	—
352	C₅×D₄	—	6	8	no	—
353	C₂×C₄×C₅	—	2	1	no	—
354	C₂×C₄×C₅	—	2	1	no	—
355	C₂×C₄×C₅	—	2	2	no	—
356	C₂×C₄×C₅	—	2	1	no	—
357	C₂×C₄×C₅	—	2	1	no	—
358	C₂×C₄×C₅	—	2	2	no	—
359	C₂×C₄×C₅	—	2	2	no	—
360	C₂×C₄×C₅	—	2	2	no	—
361	C₂×C₄×C₅	—	2	2	no	—
362	C₂×C₄×C₅	—	3	2	no	—
363	C₂×C₄×C₅	—	3	2	no	—
364	C₂×C₄×C₅	—	3	2	no	—
365	C₂×C₄×C₅	—	3	2	no	—
366	C₂×C₄×C₅	—	3	2	no	—
367	C₂×C₄×C₅	—	6	8	no	—
368	C₂×C₄×C₅	—	6	8	no	—
369	C₂×C₄×C₅	—	6	1	no	—
370	C₂×C₄×C₅	—	6	1	no	—
371	C₂×C₄×C₅	—	6	1	no	—
372	C₂×C₄×C₅	—	6	1	no	—
373	C₂×C₄×C₅	—	6	8	no	—
374	C₂×C₄×C₅	—	6	2	no	—
375	C₂×C₄×C₅	—	6	2	no	—
376	C₂×C₄×C₅	—	6	2	no	—
377	C₂×C₄×C₅	—	12	8	no	—
378	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
379	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
380	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
381	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
382	C₂×C₄×C₅	#239	1	2	yes	—
383	C₂×C₄×C₅	#239	1	2	yes	—
384	C₂²×D₄	—	3	2	no	—
385	C₂²×D₄	—	3	1	no	—
386	C₂³×C₄	—	3	1	no	—
387	C₂³×C₄	—	3	1	no	—
388	C₂³×C₄	—	3	2	no	—
389	C₂³×C₄	—	3	1	no	—
390	#121	—	3	8	no	—
391	C₄×D₄	—	6	4	no	—
392	C₄×D₄	—	6	8	no	—
393	C₂×C₄⋊C₄	—	3	1	no	—
394	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
396	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
397	C₂×C₂²⋊C₄	—	3	2	no	—
398	C₂×C₂²⋊C₄	—	3	2	no	—
399	C₂×C₂²⋊C₄	—	3	2	no	—
400	C₂×C₂²⋊C₄	—	3	2	no	—
401	C₂×C₂²⋊C₄	—	3	2	no	—
402	C₂×C₄²	—	3	1	no	—
403	C₂×C₄²	—	3	2	no	—
404	C₂×C₄²	—	3	1	no	—
405	C₂×C₄²	—	3	1	no	—
406	C₂×C₄²	—	6	4	no	—
407	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
408	#95	—	3	2	no	—
409	#95	—	3	2	no	—
410	#95	C₂×C₅×D₃	1	2	yes	—
411	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
412	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
413	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
414	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
415	C₂×C₃×C₅	#525	1	1	yes	characteristic
416	C₂×C₃×C₅	#529	1	1	yes	characteristic
417	C₂×C₃×C₅	#532	1	1	yes	characteristic
418	C₅×D₃	—	2	4	no	—
419	C₅×D₃	—	4	4	no	—
420	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
421	C₂²×D₃	—	2	1	no	—
422	C₂²×D₃	—	2	1	no	—
423	C₂²×D₃	—	2	1	no	—
424	C₂²×D₃	—	2	1	no	—
425	C₂²×D₃	—	2	2	no	—
426	C₂²×D₃	—	2	2	no	—
427	C₂²×D₃	—	2	2	no	—
428	C₂²×D₃	—	2	2	no	—
429	C₂²×D₃	—	2	2	no	—
430	C₂²×D₃	—	2	2	no	—
431	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
432	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
433	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
434	C₂²×D₃	C₅×#41	1	2	yes	—
435	C₂×C₃×C₄	—	2	1	no	—
436	C₂×C₃×C₄	—	2	1	no	—
437	C₂×C₃×C₄	—	2	2	no	—
438	C₂×C₃×C₄	—	2	1	no	—
439	C₂×C₃×C₄	—	2	1	no	—
440	C₂×C₃×C₄	—	2	2	no	—
441	C₂×C₃×C₄	—	2	2	no	—
442	C₂×C₃×C₄	—	2	2	no	—
443	C₂×C₃×C₄	—	2	2	no	—
444	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
445	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
446	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
447	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
448	C₂×C₃×C₄	C₅×#41	1	2	yes	—
449	C₂×C₃×C₄	C₅×#41	1	2	yes	—
450	C₂×Dic₃	—	2	1	no	—
451	C₂×Dic₃	—	2	1	no	—
452	C₂×Dic₃	—	2	1	no	—
453	C₂×Dic₃	—	2	1	no	—
454	C₂×Dic₃	—	2	2	no	—
455	C₂×Dic₃	—	2	2	no	—
456	C₂×Dic₃	—	2	2	no	—
457	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
458	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
459	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
460	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
461	C₂×Dic₃	C₅×#41	1	2	yes	—
462	D₁₂	—	2	16	no	—
463	D₁₂	—	2	8	no	—
464	C₄×D₃	—	2	8	no	—
465	C₄×D₃	—	2	8	no	—
466	C₄×D₃	—	2	8	no	—
467	C₄×D₃	—	4	8	no	—
468	C₂²×C₅	—	3	4	no	—
469	C₂²×C₅	—	6	2	no	—
470	C₂²×C₅	—	6	2	no	—
471	C₂²×C₅	—	6	2	no	—
472	C₂²×C₅	—	6	2	no	—
473	C₂²×C₅	—	6	2	no	—
474	C₂²×C₅	—	6	2	no	—
475	C₂²×C₅	—	6	4	no	—
476	C₂²×C₅	—	6	4	no	—
477	C₂²×C₅	—	6	4	no	—
478	C₂²×C₅	—	12	2	no	—
479	C₂²×C₅	—	12	2	no	—
480	C₂²×C₅	—	12	2	no	—
481	C₂²×C₅	—	12	2	no	—
482	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
483	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
484	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
485	C₂²×C₅	C₂×#239	1	1	yes	characteristic
486	C₂²×C₅	C₂×#239	1	1	yes	characteristic
487	C₂²×C₅	D₃×#41	1	1	yes	characteristic
488	C₂²×C₅	D₃×#41	1	1	yes	characteristic
489	C₄×C₅	—	2	4	no	—
490	C₄×C₅	—	2	2	no	—
491	C₄×C₅	—	2	2	no	—
492	C₄×C₅	—	3	4	no	—
493	C₄×C₅	—	4	2	no	—
494	C₄×C₅	—	6	2	no	—
495	C₄×C₅	—	6	2	no	—
496	C₄×C₅	—	12	2	no	—
497	C₄×C₅	#893	1	4	yes	complemented
498	C₂⁴	—	3	1	no	—
499	C₂⁴	—	3	2	no	—
500	C₂×D₄	—	3	8	no	—
501	C₂×D₄	—	3	4	no	—
502	C₂×D₄	—	6	4	no	—
503	C₂×D₄	—	6	4	no	—
504	C₂×D₄	—	6	2	no	—
505	C₂×D₄	—	6	2	no	—
506	C₂²×C₄	—	3	1	no	—
507	C₂²×C₄	—	3	1	no	—
508	C₂²×C₄	—	3	1	no	—
509	C₂²×C₄	—	3	4	no	—
510	C₂²×C₄	—	3	4	no	—
511	C₂²×C₄	—	3	2	no	—
512	C₂²×C₄	—	6	2	no	—
513	C₂²×C₄	—	6	2	no	—
514	C₂²×C₄	—	6	2	no	—
515	C₂²×C₄	—	6	4	no	—
516	C₂²×C₄	—	6	4	no	—
517	C₂²×C₄	—	6	4	no	—
518	C₂²×C₄	—	6	2	no	—
519	C₂²×C₄	—	6	2	no	—
520	C₂²×C₄	—	6	2	no	—
521	C₂²×C₄	—	6	2	no	—
522	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
523	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
524	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
525	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
526	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
527	C₄⋊C₄	—	2	4	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	6	2	no	—
530	C₄⋊C₄	C₄×C₅×D₃	1	4	yes	complemented
531	C₂²⋊C₄	—	3	8	no	—
532	C₂²⋊C₄	—	6	4	no	—
533	C₂²⋊C₄	—	6	4	no	—
534	C₂²⋊C₄	—	6	4	no	—
535	C₂²⋊C₄	—	6	4	no	—
536	C₄²	—	2	2	no	—
537	C₄²	—	3	4	no	—
538	C₄²	—	6	2	no	—
539	C₄²	—	6	2	no	—
540	C₄²	—	6	4	no	—
541	C₃×C₅	C₄×#121	1	1	yes	characteristic, complemented, Hall
542	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
543	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
544	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
545	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
546	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
547	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
548	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
549	C₂×D₃	—	2	2	no	—
550	C₂×D₃	—	2	2	no	—
551	C₂×D₃	—	2	2	no	—
552	C₂×D₃	—	2	2	no	—
553	C₂×D₃	—	2	2	no	—
554	C₂×D₃	—	2	2	no	—
555	C₂×D₃	—	2	4	no	—
556	C₂×D₃	—	2	4	no	—
557	C₂×D₃	—	2	4	no	—
558	C₂×D₃	—	4	2	no	—
559	C₂×D₃	—	4	2	no	—
560	C₂×D₃	—	4	2	no	—
561	C₂×D₃	—	4	2	no	—
562	C₂×D₃	C₄×C₅×D₄	1	4	yes	complemented
563	C₃×C₄	—	2	4	no	—
564	C₃×C₄	—	2	2	no	—
565	C₃×C₄	—	2	2	no	—
566	C₃×C₄	—	4	2	no	—
567	C₃×C₄	C₄×C₅×D₄	1	4	yes	complemented
568	Dic₃	—	2	2	no	—
569	Dic₃	—	2	2	no	—
570	Dic₃	—	4	2	no	—
571	Dic₃	C₅×#121	1	4	yes	complemented
572	C₂×C₅	—	6	4	no	—
573	C₂×C₅	—	12	4	no	—
574	C₂×C₅	C₂×#893	1	1	yes	characteristic
575	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
576	C₂×C₅	C₄×#239	1	1	yes	characteristic
577	C₂×C₅	D₃×#121	1	1	yes	characteristic
578	C₂×C₅	#5627	1	1	yes	characteristic
579	C₂×C₅	#5691	1	1	yes	characteristic
580	C₂×C₅	#5725	1	1	yes	characteristic
581	C₂³	—	3	2	no	—
582	C₂³	—	3	2	no	—
583	C₂³	—	3	2	no	—
584	C₂³	—	3	4	no	—
585	C₂³	—	6	1	no	—
586	C₂³	—	6	1	no	—
587	C₂³	—	6	1	no	—
588	C₂³	—	6	1	no	—
589	C₂³	—	6	2	no	—
590	C₂³	—	6	2	no	—
591	C₂³	—	6	2	no	—
592	C₂³	—	6	2	no	—
593	C₂³	—	6	2	no	—
594	C₂³	—	6	2	no	—
595	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
596	D₄	—	6	16	no	—
597	D₄	—	6	8	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	3	2	no	—
608	C₂×C₄	—	3	2	no	—
609	C₂×C₄	—	3	2	no	—
610	C₂×C₄	—	3	2	no	—
611	C₂×C₄	—	3	2	no	—
612	C₂×C₄	—	6	8	no	—
613	C₂×C₄	—	6	8	no	—
614	C₂×C₄	—	6	1	no	—
615	C₂×C₄	—	6	1	no	—
616	C₂×C₄	—	6	1	no	—
617	C₂×C₄	—	6	1	no	—
618	C₂×C₄	—	6	8	no	—
619	C₂×C₄	—	6	2	no	—
620	C₂×C₄	—	6	2	no	—
621	C₂×C₄	—	6	2	no	—
622	C₂×C₄	—	12	8	no	—
623	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
624	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
625	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
626	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
627	C₂×C₄	C₅×#239	1	2	yes	—
628	C₂×C₄	C₅×#239	1	2	yes	—
629	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
630	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
631	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
632	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
633	C₂×C₃	C₅×#525	1	1	yes	characteristic
634	C₂×C₃	C₅×#529	1	1	yes	characteristic
635	C₂×C₃	C₅×#532	1	1	yes	characteristic
636	D₃	—	2	4	no	—
637	D₃	—	4	4	no	—
638	C₅	#75964	1	1	yes	characteristic, direct product factor, Sylow
639	C₂²	—	3	4	no	—
640	C₂²	—	6	2	no	—
641	C₂²	—	6	2	no	—
642	C₂²	—	6	2	no	—
643	C₂²	—	6	2	no	—
644	C₂²	—	6	2	no	—
645	C₂²	—	6	2	no	—
646	C₂²	—	6	4	no	—
647	C₂²	—	6	4	no	—
648	C₂²	—	6	4	no	—
649	C₂²	—	12	2	no	—
650	C₂²	—	12	2	no	—
651	C₂²	—	12	2	no	—
652	C₂²	—	12	2	no	—
653	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
654	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
655	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
656	C₂²	C₂×C₅×#239	1	1	yes	characteristic
657	C₂²	C₂×C₅×#239	1	1	yes	characteristic
658	C₂²	C₅×D₃×#41	1	1	yes	characteristic
659	C₂²	C₅×D₃×#41	1	1	yes	characteristic
660	C₄	—	2	4	no	—
661	C₄	—	2	2	no	—
662	C₄	—	2	2	no	—
663	C₄	—	3	4	no	—
664	C₄	—	4	2	no	—
665	C₄	—	6	2	no	—
666	C₄	—	6	2	no	—
667	C₄	—	12	2	no	—
668	C₄	C₅×#893	1	4	yes	complemented
669	C₃	C₄×C₅×#121	1	1	yes	characteristic, complemented, Sylow
670	C₂	—	6	4	no	—
671	C₂	—	12	4	no	—
672	C₂	C₂×C₅×#893	1	1	yes	characteristic
673	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
674	C₂	C₄×C₅×#239	1	1	yes	characteristic
675	C₂	C₅×D₃×#121	1	1	yes	characteristic
676	C₂	C₅×#5627	1	1	yes	characteristic
677	C₂	C₅×#5691	1	1	yes	characteristic
678	C₂	C₅×#5725	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	C₂×C₅×#895	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#389	D₃
hypocenter	C₃	C₄×C₅×#121
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. C₂×C₅×#893	C₂	semidirect
3. C₂×C₅×#893	C₂	semidirect
4. C₂×C₄²×C₅×D₃	C₂	semidirect
5. C₃×C₅×#389	C₂	semidirect
6. C₅×#4990	C₂	semidirect
7. C₅×#4987	C₂	semidirect
8. C₅×Dic₃×C₄⋊C₄	C₂	semidirect
9. C₅×#4939	C₂	semidirect
10. C₅×#4666	C₂	semidirect
11. C₅×#4665	C₂	semidirect
33. C₅×#895	C₄	semidirect
40. #75964	C₅	direct (N × H)
46. C₅×#389	D₃	semidirect
67. C₂×C₅×D₁₂	C₂×C₄	semidirect
68. C₂×C₅×D₁₂	C₂×C₄	semidirect
79. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
80. C₂×C₄×C₅×D₃	D₄	semidirect
83. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
89. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
94. C₄×C₅×Dic₃	D₄	semidirect
96. C₂×#893	C₂×C₅	semidirect
97. C₂×#893	C₂×C₅	semidirect
98. C₂×C₄²×D₃	C₂×C₅	semidirect
99. C₃×#389	C₂×C₅	semidirect
100. #4990	C₂×C₅	semidirect
101. #4987	C₂×C₅	semidirect
102. Dic₃×C₄⋊C₄	C₂×C₅	semidirect
103. #4939	C₂×C₅	semidirect
104. #4666	C₂×C₅	semidirect
105. #4665	C₂×C₅	semidirect
202. #895	C₄×C₅	semidirect
241. C₅×C₄⋊C₄	C₄×D₃	semidirect
257. #389	C₅×D₃	semidirect
283. C₂×C₅×D₃	C₄×D₄	semidirect
288. C₃×C₄×C₅	C₄×D₄	semidirect
292. C₅×Dic₃	#121	semidirect
308. C₂×D₁₂	C₂×C₄×C₅	semidirect
309. C₂×D₁₂	C₂×C₄×C₅	semidirect
320. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
321. C₂×C₄×D₃	C₅×D₄	semidirect
324. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
330. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
335. C₄×Dic₃	C₅×D₄	semidirect
497. C₄×C₅	#893	semidirect
530. C₄⋊C₄	C₄×C₅×D₃	semidirect
541. C₃×C₅	C₄×#121	semidirect
562. C₂×D₃	C₄×C₅×D₄	semidirect
567. C₃×C₄	C₄×C₅×D₄	semidirect
571. Dic₃	C₅×#121	semidirect
638. C₅	#75964	direct (N × H)
668. C₄	C₅×#893	semidirect
669. C₃	C₄×C₅×#121	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#895	2
C₂×C₅×#893	2
C₂×C₄²×C₅×D₃	2
C₃×C₅×#389	2
C₅×#4990	2
C₅×#4987	2
C₅×Dic₃×C₄⋊C₄	2
C₅×#4939	2
C₅×#4666	2
C₅×#4665	2
C₄×C₅×#121	3
#75964	5

Subgroups — C5×#75964 #14321416

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#75964 #14321416