Subgroups — C₅×#75963 #14321081

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 592 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	C₂×C₅×#892	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×C₅×D₃	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4989	C₂	1	2	yes	maximal
6	C₅×#4984	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×Dic₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₅×#4972	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4928	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4668	C₂	1	2	yes	maximal
11	C₅×#4649	C₂	1	2	yes	maximal, complemented
12	C₅×#2296	—	3	1	no	maximal, Hall
13	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄²×C₅	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	2	yes	—
23	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
25	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
26	C₂×C₅×Dic₃⋊C₄	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	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
32	C₅×#892	—	2	4	no	—
33	C₅×#892	C₄	1	8	yes	complemented
34	C₄²×C₅×D₃	—	2	4	no	—
35	C₃×C₅×#95	C₂²	1	2	yes	—
36	C₅×C₃⋊#95	C₂²	1	2	yes	—
37	C₅×C₃⋊#95	C₂²	1	2	yes	—
38	C₅×C₃⋊#95	C₂²	1	2	yes	—
39	#75963	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
40	C₂×C₅×#117	—	3	1	no	—
41	C₂×C₅×#117	—	3	1	no	—
42	C₂²×C₄²×C₅	—	3	1	no	—
43	C₅×#389	—	3	1	no	—
44	C₅×#389	—	3	1	no	—
45	C₅×#389	—	3	1	no	—
46	C₅×#389	D₃	1	1	yes	characteristic, complemented
47	C₅×#385	—	3	2	no	—
48	C₅×#385	—	3	2	no	—
49	C₄×C₅×C₄⋊C₄	—	3	2	no	—
50	C₄×C₅×C₄⋊C₄	—	3	2	no	—
51	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
58	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
59	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
60	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
61	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
62	C₂×C₄×C₅×D₃	—	2	2	no	—
63	C₂×C₄×C₅×D₃	—	2	2	no	—
64	C₂×C₄×C₅×D₃	—	2	2	no	—
65	C₂×C₄×C₅×D₃	—	2	2	no	—
66	C₂×C₄×C₅×D₃	—	2	2	no	—
67	C₂×C₄×C₅×D₃	—	2	2	no	—
68	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
69	C₂×C₄×C₅×D₃	D₄	1	4	yes	—
70	C₂×C₄×C₅×D₃	Q₈	1	4	yes	—
71	C₃×C₅×C₄⋊C₄	—	2	2	no	—
72	C₃×C₅×C₄⋊C₄	—	2	4	no	—
73	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
74	C₃×C₄²×C₅	—	2	2	no	—
75	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
76	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	—
77	C₅×C₄⋊Dic₃	—	2	2	no	—
78	C₅×C₄⋊Dic₃	—	2	4	no	—
79	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	complemented
80	C₅×Dic₃⋊C₄	—	2	4	no	—
81	C₅×Dic₃⋊C₄	—	2	4	no	—
82	C₄×C₅×Dic₃	—	2	2	no	—
83	C₄×C₅×Dic₃	—	2	2	no	—
84	C₄×C₅×Dic₃	—	2	2	no	—
85	C₄×C₅×Dic₃	—	2	4	no	—
86	C₄×C₅×Dic₃	C₂×C₄	1	8	yes	complemented
87	C₂×#892	C₂×C₅	1	1	yes	characteristic
88	C₂×#892	C₂×C₅	1	1	yes	characteristic
89	C₂×C₄²×D₃	C₂×C₅	1	1	yes	characteristic
90	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
91	#4989	C₂×C₅	1	2	yes	—
92	#4984	C₂×C₅	1	1	yes	characteristic, complemented
93	Dic₃×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
94	#4972	C₂×C₅	1	1	yes	characteristic, complemented
95	#4928	C₂×C₅	1	1	yes	characteristic, complemented
96	#4668	C₂×C₅	1	2	yes	—
97	#4649	C₂×C₅	1	2	yes	complemented
98	C₂³×C₄×C₅	—	3	1	no	—
99	C₂³×C₄×C₅	—	3	1	no	—
100	C₂³×C₄×C₅	—	3	1	no	—
101	C₅×#117	—	3	8	no	—
102	C₅×#117	—	6	4	no	—
103	C₂×C₅×C₄⋊C₄	—	3	1	no	—
104	C₂×C₅×C₄⋊C₄	—	3	2	no	—
105	C₂×C₅×C₄⋊C₄	—	3	2	no	—
106	C₂×C₅×C₄⋊C₄	—	3	2	no	—
107	C₂×C₅×C₄⋊C₄	—	3	1	no	—
108	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
109	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
110	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
111	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
112	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
113	C₂×C₄²×C₅	—	3	2	no	—
114	C₂×C₄²×C₅	—	3	1	no	—
115	C₂×C₄²×C₅	—	3	1	no	—
116	C₂×C₄²×C₅	—	3	2	no	—
117	C₂×C₄²×C₅	—	3	1	no	—
118	C₂×C₄²×C₅	—	6	4	no	—
119	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
120	C₅×#95	—	3	2	no	—
121	C₅×#95	—	3	2	no	—
122	C₅×#95	—	3	2	no	—
123	C₅×#95	C₂×D₃	1	2	yes	—
124	#2296	—	3	1	no	Sylow
125	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
126	C₂²×C₅×D₃	—	2	1	no	—
127	C₂²×C₅×D₃	—	2	1	no	—
128	C₂²×C₅×D₃	—	2	1	no	—
129	C₂²×C₅×D₃	—	2	1	no	—
130	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
131	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
132	C₂²×C₅×D₃	C₂×Q₈	1	2	yes	—
133	C₂×C₃×C₄×C₅	—	2	1	no	—
134	C₂×C₃×C₄×C₅	—	2	1	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	1	no	—
138	C₂×C₃×C₄×C₅	—	2	1	no	—
139	C₂×C₃×C₄×C₅	—	2	2	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
143	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
144	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
146	C₂×C₃×C₄×C₅	#41	1	2	yes	—
147	C₂×C₃×C₄×C₅	#41	1	2	yes	—
148	C₂×C₅×Dic₃	—	2	1	no	—
149	C₂×C₅×Dic₃	—	2	1	no	—
150	C₂×C₅×Dic₃	—	2	2	no	—
151	C₂×C₅×Dic₃	—	2	2	no	—
152	C₂×C₅×Dic₃	—	2	1	no	—
153	C₂×C₅×Dic₃	—	2	1	no	—
154	C₂×C₅×Dic₃	—	2	2	no	—
155	C₂×C₅×Dic₃	—	2	2	no	—
156	C₂×C₅×Dic₃	—	2	2	no	—
157	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
158	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
159	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
160	C₂×C₅×Dic₃	C₂×Q₈	1	2	yes	—
161	C₂×C₅×Dic₃	#41	1	2	yes	—
162	C₂×C₅×Dic₃	#41	1	2	yes	—
163	C₄×C₅×D₃	—	2	8	no	—
164	C₄×C₅×D₃	—	2	8	no	—
165	C₄×C₅×D₃	C₄⋊C₄	1	16	yes	complemented
166	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
167	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
168	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
169	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
170	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
171	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
172	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
173	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
174	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
175	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
176	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
178	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
179	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
180	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
181	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
182	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
184	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
185	#892	—	2	4	no	—
186	#892	C₄×C₅	1	8	yes	complemented
187	C₄²×D₃	—	2	4	no	—
188	C₃×#95	C₂²×C₅	1	2	yes	—
189	C₃⋊#95	C₂²×C₅	1	2	yes	—
190	C₃⋊#95	C₂²×C₅	1	2	yes	—
191	C₃⋊#95	C₂²×C₅	1	2	yes	—
192	C₂⁴×C₅	—	3	1	no	—
193	C₂²×C₄×C₅	—	3	1	no	—
194	C₂²×C₄×C₅	—	3	4	no	—
195	C₂²×C₄×C₅	—	3	4	no	—
196	C₂²×C₄×C₅	—	3	4	no	—
197	C₂²×C₄×C₅	—	3	1	no	—
198	C₂²×C₄×C₅	—	3	1	no	—
199	C₂²×C₄×C₅	—	3	2	no	—
200	C₂²×C₄×C₅	—	3	2	no	—
201	C₂²×C₄×C₅	—	6	2	no	—
202	C₂²×C₄×C₅	—	6	2	no	—
203	C₂²×C₄×C₅	—	6	2	no	—
204	C₂²×C₄×C₅	—	6	2	no	—
205	C₂²×C₄×C₅	—	6	2	no	—
206	C₂²×C₄×C₅	—	6	2	no	—
207	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
208	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
209	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
210	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
211	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
212	C₅×C₄⋊C₄	—	2	2	no	—
213	C₅×C₄⋊C₄	—	2	4	no	—
214	C₅×C₄⋊C₄	—	3	4	no	—
215	C₅×C₄⋊C₄	—	6	4	no	—
216	C₅×C₄⋊C₄	—	6	4	no	—
217	C₅×C₄⋊C₄	—	6	2	no	—
218	C₅×C₄⋊C₄	—	6	4	no	—
219	C₅×C₄⋊C₄	C₄×D₃	1	4	yes	complemented
220	C₅×C₂²⋊C₄	—	3	8	no	—
221	C₅×C₂²⋊C₄	—	6	4	no	—
222	C₄²×C₅	—	2	2	no	—
223	C₄²×C₅	—	3	8	no	—
224	C₄²×C₅	—	6	2	no	—
225	C₄²×C₅	—	6	2	no	—
226	C₄²×C₅	—	6	4	no	—
227	C₄²×C₅	—	6	2	no	—
228	C₂×#117	—	3	1	no	—
229	C₂×#117	—	3	1	no	—
230	C₂²×C₄²	—	3	1	no	—
231	#389	—	3	1	no	—
232	#389	—	3	1	no	—
233	#389	—	3	1	no	—
234	#389	C₅×D₃	1	1	yes	characteristic, complemented
235	#385	—	3	2	no	—
236	#385	—	3	2	no	—
237	C₄×C₄⋊C₄	—	3	2	no	—
238	C₄×C₄⋊C₄	—	3	2	no	—
239	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
240	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
241	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
242	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
243	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
244	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
245	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
246	C₂×C₅×D₃	—	2	2	no	—
247	C₂×C₅×D₃	—	2	2	no	—
248	C₂×C₅×D₃	—	2	2	no	—
249	C₂×C₅×D₃	—	2	2	no	—
250	C₂×C₅×D₃	—	2	2	no	—
251	C₂×C₅×D₃	—	2	2	no	—
252	C₂×C₅×D₃	C₂×C₄⋊C₄	1	4	yes	—
253	C₃×C₄×C₅	—	2	4	no	—
254	C₃×C₄×C₅	—	2	2	no	—
255	C₃×C₄×C₅	—	2	2	no	—
256	C₃×C₄×C₅	—	4	2	no	—
257	C₃×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
258	C₅×Dic₃	—	2	4	no	—
259	C₅×Dic₃	—	2	2	no	—
260	C₅×Dic₃	—	2	2	no	—
261	C₅×Dic₃	—	4	2	no	—
262	C₅×Dic₃	C₂×C₄⋊C₄	1	4	yes	—
263	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
264	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
265	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
266	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
267	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
268	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
269	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
270	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
271	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
272	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
273	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
274	C₂×C₄×D₃	—	2	2	no	—
275	C₂×C₄×D₃	—	2	2	no	—
276	C₂×C₄×D₃	—	2	2	no	—
277	C₂×C₄×D₃	—	2	2	no	—
278	C₂×C₄×D₃	—	2	2	no	—
279	C₂×C₄×D₃	—	2	2	no	—
280	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
281	C₂×C₄×D₃	C₅×D₄	1	4	yes	—
282	C₂×C₄×D₃	C₅×Q₈	1	4	yes	—
283	C₃×C₄⋊C₄	—	2	2	no	—
284	C₃×C₄⋊C₄	—	2	4	no	—
285	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
286	C₃×C₄²	—	2	2	no	—
287	(C₂×D₃)⋊C₄	—	2	4	no	—
288	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	—
289	C₄⋊Dic₃	—	2	2	no	—
290	C₄⋊Dic₃	—	2	4	no	—
291	C₄⋊Dic₃	C₂×C₄×C₅	1	4	yes	complemented
292	Dic₃⋊C₄	—	2	4	no	—
293	Dic₃⋊C₄	—	2	4	no	—
294	C₄×Dic₃	—	2	2	no	—
295	C₄×Dic₃	—	2	2	no	—
296	C₄×Dic₃	—	2	2	no	—
297	C₄×Dic₃	—	2	4	no	—
298	C₄×Dic₃	C₂×C₄×C₅	1	8	yes	complemented
299	C₂³×C₅	—	3	2	no	—
300	C₂³×C₅	—	3	2	no	—
301	C₂³×C₅	—	3	2	no	—
302	C₂³×C₅	—	6	1	no	—
303	C₂³×C₅	—	6	1	no	—
304	C₂³×C₅	—	6	1	no	—
305	C₂³×C₅	—	6	1	no	—
306	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	2	no	—
310	C₂×C₄×C₅	—	2	2	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	2	no	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	3	2	no	—
317	C₂×C₄×C₅	—	3	2	no	—
318	C₂×C₄×C₅	—	3	2	no	—
319	C₂×C₄×C₅	—	3	16	no	—
320	C₂×C₄×C₅	—	3	4	no	—
321	C₂×C₄×C₅	—	3	2	no	—
322	C₂×C₄×C₅	—	3	2	no	—
323	C₂×C₄×C₅	—	6	8	no	—
324	C₂×C₄×C₅	—	6	8	no	—
325	C₂×C₄×C₅	—	6	1	no	—
326	C₂×C₄×C₅	—	6	1	no	—
327	C₂×C₄×C₅	—	6	1	no	—
328	C₂×C₄×C₅	—	6	2	no	—
329	C₂×C₄×C₅	—	6	1	no	—
330	C₂×C₄×C₅	—	6	2	no	—
331	C₂×C₄×C₅	—	6	2	no	—
332	C₂×C₄×C₅	—	6	2	no	—
333	C₂×C₄×C₅	—	6	2	no	—
334	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
335	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
336	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
337	C₂×C₄×C₅	#237	1	2	yes	—
338	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
339	C₂×C₄×C₅	#239	1	2	yes	—
340	C₂³×C₄	—	3	1	no	—
341	C₂³×C₄	—	3	1	no	—
342	C₂³×C₄	—	3	1	no	—
343	#117	—	3	8	no	—
344	#117	—	6	4	no	—
345	C₂×C₄⋊C₄	—	3	1	no	—
346	C₂×C₄⋊C₄	—	3	1	no	—
347	C₂×C₄⋊C₄	—	3	2	no	—
348	C₂×C₄⋊C₄	—	3	2	no	—
349	C₂×C₄⋊C₄	—	3	2	no	—
350	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
352	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
353	C₂×C₂²⋊C₄	—	3	2	no	—
354	C₂×C₂²⋊C₄	—	3	2	no	—
355	C₂×C₄²	—	3	2	no	—
356	C₂×C₄²	—	3	2	no	—
357	C₂×C₄²	—	3	1	no	—
358	C₂×C₄²	—	3	1	no	—
359	C₂×C₄²	—	3	1	no	—
360	C₂×C₄²	—	6	4	no	—
361	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
362	#95	—	3	2	no	—
363	#95	—	3	2	no	—
364	#95	—	3	2	no	—
365	#95	C₂×C₅×D₃	1	2	yes	—
366	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
367	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
368	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
369	C₂×C₃×C₅	#525	1	1	yes	characteristic
370	C₂×C₃×C₅	#525	1	1	yes	characteristic
371	C₂×C₃×C₅	#533	1	1	yes	characteristic
372	C₂×C₃×C₅	#533	1	1	yes	characteristic
373	C₅×D₃	—	2	4	no	—
374	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
375	C₂²×D₃	—	2	1	no	—
376	C₂²×D₃	—	2	1	no	—
377	C₂²×D₃	—	2	1	no	—
378	C₂²×D₃	—	2	1	no	—
379	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
380	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
381	C₂²×D₃	C₂×C₅×Q₈	1	2	yes	—
382	C₂×C₃×C₄	—	2	1	no	—
383	C₂×C₃×C₄	—	2	1	no	—
384	C₂×C₃×C₄	—	2	2	no	—
385	C₂×C₃×C₄	—	2	2	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	2	1	no	—
388	C₂×C₃×C₄	—	2	2	no	—
389	C₂×C₃×C₄	—	2	2	no	—
390	C₂×C₃×C₄	—	2	2	no	—
391	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
392	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
393	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
394	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
395	C₂×C₃×C₄	C₅×#41	1	2	yes	—
396	C₂×C₃×C₄	C₅×#41	1	2	yes	—
397	C₂×Dic₃	—	2	1	no	—
398	C₂×Dic₃	—	2	1	no	—
399	C₂×Dic₃	—	2	2	no	—
400	C₂×Dic₃	—	2	2	no	—
401	C₂×Dic₃	—	2	1	no	—
402	C₂×Dic₃	—	2	1	no	—
403	C₂×Dic₃	—	2	2	no	—
404	C₂×Dic₃	—	2	2	no	—
405	C₂×Dic₃	—	2	2	no	—
406	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
407	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
408	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
409	C₂×Dic₃	C₂×C₅×Q₈	1	2	yes	—
410	C₂×Dic₃	C₅×#41	1	2	yes	—
411	C₂×Dic₃	C₅×#41	1	2	yes	—
412	C₄×D₃	—	2	8	no	—
413	C₄×D₃	—	2	8	no	—
414	C₄×D₃	C₅×C₄⋊C₄	1	16	yes	complemented
415	C₂²×C₅	—	3	4	no	—
416	C₂²×C₅	—	6	2	no	—
417	C₂²×C₅	—	6	2	no	—
418	C₂²×C₅	—	6	2	no	—
419	C₂²×C₅	—	6	2	no	—
420	C₂²×C₅	—	6	2	no	—
421	C₂²×C₅	—	6	2	no	—
422	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
423	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
424	C₂²×C₅	C₂×#237	1	1	yes	characteristic
425	C₂²×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
426	C₂²×C₅	C₂×#239	1	1	yes	characteristic
427	C₂²×C₅	D₃×#41	1	1	yes	characteristic
428	C₂²×C₅	D₃×#41	1	1	yes	characteristic
429	C₄×C₅	—	2	4	no	—
430	C₄×C₅	—	2	2	no	—
431	C₄×C₅	—	2	2	no	—
432	C₄×C₅	—	3	4	no	—
433	C₄×C₅	—	4	2	no	—
434	C₄×C₅	—	6	4	no	—
435	C₄×C₅	—	6	2	no	—
436	C₄×C₅	—	6	2	no	—
437	C₄×C₅	—	12	2	no	—
438	C₄×C₅	D₃×C₄⋊C₄	1	4	yes	—
439	C₂⁴	—	3	1	no	—
440	C₂²×C₄	—	3	1	no	—
441	C₂²×C₄	—	3	4	no	—
442	C₂²×C₄	—	3	4	no	—
443	C₂²×C₄	—	3	4	no	—
444	C₂²×C₄	—	3	1	no	—
445	C₂²×C₄	—	3	1	no	—
446	C₂²×C₄	—	3	2	no	—
447	C₂²×C₄	—	3	2	no	—
448	C₂²×C₄	—	6	2	no	—
449	C₂²×C₄	—	6	2	no	—
450	C₂²×C₄	—	6	2	no	—
451	C₂²×C₄	—	6	2	no	—
452	C₂²×C₄	—	6	2	no	—
453	C₂²×C₄	—	6	2	no	—
454	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
455	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
456	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
457	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
458	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	3	4	no	—
462	C₄⋊C₄	—	6	4	no	—
463	C₄⋊C₄	—	6	4	no	—
464	C₄⋊C₄	—	6	2	no	—
465	C₄⋊C₄	—	6	4	no	—
466	C₄⋊C₄	C₄×C₅×D₃	1	4	yes	complemented
467	C₂²⋊C₄	—	3	8	no	—
468	C₂²⋊C₄	—	6	4	no	—
469	C₄²	—	2	2	no	—
470	C₄²	—	3	8	no	—
471	C₄²	—	6	2	no	—
472	C₄²	—	6	2	no	—
473	C₄²	—	6	4	no	—
474	C₄²	—	6	2	no	—
475	C₃×C₅	#2296	1	1	yes	characteristic, complemented, Hall
476	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
477	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
478	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
479	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
480	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
481	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
482	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
483	C₂×D₃	—	2	2	no	—
484	C₂×D₃	—	2	2	no	—
485	C₂×D₃	—	2	2	no	—
486	C₂×D₃	—	2	2	no	—
487	C₂×D₃	—	2	2	no	—
488	C₂×D₃	—	2	2	no	—
489	C₂×D₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
490	C₃×C₄	—	2	4	no	—
491	C₃×C₄	—	2	2	no	—
492	C₃×C₄	—	2	2	no	—
493	C₃×C₄	—	4	2	no	—
494	C₃×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
495	Dic₃	—	2	4	no	—
496	Dic₃	—	2	2	no	—
497	Dic₃	—	2	2	no	—
498	Dic₃	—	4	2	no	—
499	Dic₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
500	C₂×C₅	—	6	4	no	—
501	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
502	C₂×C₅	C₄×#237	1	1	yes	characteristic
503	C₂×C₅	C₄×#239	1	1	yes	characteristic
504	C₂×C₅	#5606	1	1	yes	characteristic
505	C₂×C₅	#5627	1	1	yes	characteristic
506	C₂×C₅	#5688	1	1	yes	characteristic
507	C₂×C₅	#5728	1	1	yes	characteristic
508	C₂³	—	3	2	no	—
509	C₂³	—	3	2	no	—
510	C₂³	—	3	2	no	—
511	C₂³	—	6	1	no	—
512	C₂³	—	6	1	no	—
513	C₂³	—	6	1	no	—
514	C₂³	—	6	1	no	—
515	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	3	2	no	—
526	C₂×C₄	—	3	2	no	—
527	C₂×C₄	—	3	2	no	—
528	C₂×C₄	—	3	16	no	—
529	C₂×C₄	—	3	4	no	—
530	C₂×C₄	—	3	2	no	—
531	C₂×C₄	—	3	2	no	—
532	C₂×C₄	—	6	8	no	—
533	C₂×C₄	—	6	8	no	—
534	C₂×C₄	—	6	1	no	—
535	C₂×C₄	—	6	1	no	—
536	C₂×C₄	—	6	1	no	—
537	C₂×C₄	—	6	2	no	—
538	C₂×C₄	—	6	1	no	—
539	C₂×C₄	—	6	2	no	—
540	C₂×C₄	—	6	2	no	—
541	C₂×C₄	—	6	2	no	—
542	C₂×C₄	—	6	2	no	—
543	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
544	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
545	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
546	C₂×C₄	C₅×#237	1	2	yes	—
547	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
548	C₂×C₄	C₅×#239	1	2	yes	—
549	C₂×C₃	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
550	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
551	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
552	C₂×C₃	C₅×#525	1	1	yes	characteristic
553	C₂×C₃	C₅×#525	1	1	yes	characteristic
554	C₂×C₃	C₅×#533	1	1	yes	characteristic
555	C₂×C₃	C₅×#533	1	1	yes	characteristic
556	D₃	—	2	4	no	—
557	C₅	#75963	1	1	yes	characteristic, direct product factor, Sylow
558	C₂²	—	3	4	no	—
559	C₂²	—	6	2	no	—
560	C₂²	—	6	2	no	—
561	C₂²	—	6	2	no	—
562	C₂²	—	6	2	no	—
563	C₂²	—	6	2	no	—
564	C₂²	—	6	2	no	—
565	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
566	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
567	C₂²	C₂×C₅×#237	1	1	yes	characteristic
568	C₂²	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
569	C₂²	C₂×C₅×#239	1	1	yes	characteristic
570	C₂²	C₅×D₃×#41	1	1	yes	characteristic
571	C₂²	C₅×D₃×#41	1	1	yes	characteristic
572	C₄	—	2	4	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	3	4	no	—
576	C₄	—	4	2	no	—
577	C₄	—	6	4	no	—
578	C₄	—	6	2	no	—
579	C₄	—	6	2	no	—
580	C₄	—	12	2	no	—
581	C₄	C₅×D₃×C₄⋊C₄	1	4	yes	—
582	C₃	C₅×#2296	1	1	yes	characteristic, complemented, Sylow
583	C₂	—	6	4	no	—
584	C₂	C₂×C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
585	C₂	C₄×C₅×#237	1	1	yes	characteristic
586	C₂	C₄×C₅×#239	1	1	yes	characteristic
587	C₂	C₅×#5606	1	1	yes	characteristic
588	C₂	C₅×#5627	1	1	yes	characteristic
589	C₂	C₅×#5688	1	1	yes	characteristic
590	C₂	C₅×#5728	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×#2296
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
4. C₃×C₅×#389	C₂	semidirect
6. C₅×#4984	C₂	semidirect
7. C₅×Dic₃×C₄⋊C₄	C₂	semidirect
8. C₅×#4972	C₂	semidirect
9. C₅×#4928	C₂	semidirect
11. C₅×#4649	C₂	semidirect
33. C₅×#892	C₄	semidirect
39. #75963	C₅	direct (N × H)
46. C₅×#389	D₃	semidirect
73. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
79. C₅×C₄⋊Dic₃	C₂×C₄	semidirect
86. C₄×C₅×Dic₃	C₂×C₄	semidirect
90. C₃×#389	C₂×C₅	semidirect
92. #4984	C₂×C₅	semidirect
93. Dic₃×C₄⋊C₄	C₂×C₅	semidirect
94. #4972	C₂×C₅	semidirect
95. #4928	C₂×C₅	semidirect
97. #4649	C₂×C₅	semidirect
165. C₄×C₅×D₃	C₄⋊C₄	semidirect
186. #892	C₄×C₅	semidirect
219. C₅×C₄⋊C₄	C₄×D₃	semidirect
234. #389	C₅×D₃	semidirect
285. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
291. C₄⋊Dic₃	C₂×C₄×C₅	semidirect
298. C₄×Dic₃	C₂×C₄×C₅	semidirect
414. C₄×D₃	C₅×C₄⋊C₄	semidirect
466. C₄⋊C₄	C₄×C₅×D₃	semidirect
475. C₃×C₅	#2296	semidirect
557. C₅	#75963	direct (N × H)
582. C₃	C₅×#2296	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
C₂×C₄²×C₅×D₃	2
C₃×C₅×#389	2
C₅×#4989	2
C₅×#4984	2
C₅×Dic₃×C₄⋊C₄	2
C₅×#4972	2
C₅×#4928	2
C₅×#4668	2
C₅×#4649	2
C₅×#2296	3
#75963	5

Subgroups — C5×#75963 #14321081

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#75963 #14321081