Subgroups — C₃×#10613968 #14326411

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic
2	C₃×#65500	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#3963	C₂	1	1	yes	maximal, characteristic
4	C₃×#65270	C₂	1	2	yes	maximal, complemented
5	C₃×#65270	C₂	1	2	yes	maximal, complemented
6	C₃×#65239	C₂	1	2	yes	maximal
7	C₃×C₂²⋊C₄×Dic₅	C₂	1	2	yes	maximal
8	C₃×#65226	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65225	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65221	C₂	1	1	yes	maximal, characteristic, complemented
12	#10613968	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₂³×C₃×Dic₅	C₂²	1	2	yes	—
15	C₃×C₅×#117	C₄	1	8	yes	complemented
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
23	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
24	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
25	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
26	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
27	C₃×#3963	C₂²	1	1	yes	characteristic
28	C₃×#3963	C₂²	1	1	yes	characteristic
29	C₃×#3963	C₂²	1	2	yes	—
30	C₃×#3963	C₂²	1	1	yes	characteristic
31	C₃×#3963	C₂²	1	1	yes	characteristic
32	C₃×#3963	C₂²	1	2	yes	—
33	C₃×#3963	C₂²	1	2	yes	—
34	C₃×#3963	C₂²	1	2	yes	—
35	C₃×#3963	C₂²	1	2	yes	—
36	C₃×#3963	C₂²	1	2	yes	—
37	C₃×#2343	—	5	1	no	maximal, Hall
38	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic
39	#65500	C₂×C₃	1	1	yes	characteristic
40	C₂×#3963	C₂×C₃	1	1	yes	characteristic
41	#65270	C₂×C₃	1	2	yes	complemented
42	#65270	C₂×C₃	1	2	yes	complemented
43	#65239	C₂×C₃	1	2	yes	—
44	C₂²⋊C₄×Dic₅	C₂×C₃	1	2	yes	—
45	#65226	C₂×C₃	1	1	yes	characteristic, complemented
46	#65225	C₂×C₃	1	1	yes	characteristic, complemented
47	C₄×C₄⋊Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
48	#65221	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	—	2	4	no	—
51	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂²×C₃×Dic₅	—	2	4	no	—
59	C₂²×C₃×Dic₅	—	2	4	no	—
60	C₂²×C₃×Dic₅	—	4	2	no	—
61	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
62	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
63	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
64	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
65	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
66	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
67	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
68	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
69	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
70	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
71	C₃×C₂²⋊Dic₅	—	2	4	no	—
72	C₃×C₄⋊Dic₅	—	2	4	no	—
73	C₃×C₄⋊Dic₅	—	4	2	no	—
74	C₃×C₄×Dic₅	—	2	4	no	—
75	C₃×C₄×Dic₅	—	4	2	no	—
76	C₂×C₃×#117	D₅	1	1	yes	characteristic
77	C₃×#387	—	5	2	no	—
78	C₃×#387	—	5	2	no	—
79	C₃×#385	—	5	2	no	—
80	C₃×#383	—	5	1	no	—
81	C₃×#382	—	5	1	no	—
82	C₃×#381	—	5	1	no	—
83	C₃×C₄×C₄⋊C₄	—	5	1	no	—
84	C₃×C₄×C₂²⋊C₄	—	5	2	no	—
85	C₃×#376	—	5	1	no	—
86	C₂×C₃×#95	—	5	1	no	—
87	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
88	C₂³×Dic₅	C₂²×C₃	1	2	yes	—
89	C₅×#117	C₃×C₄	1	8	yes	complemented
90	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
97	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
98	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
99	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
100	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
101	#3963	C₂²×C₃	1	1	yes	characteristic
102	#3963	C₂²×C₃	1	1	yes	characteristic
103	#3963	C₂²×C₃	1	2	yes	—
104	#3963	C₂²×C₃	1	1	yes	characteristic
105	#3963	C₂²×C₃	1	1	yes	characteristic
106	#3963	C₂²×C₃	1	2	yes	—
107	#3963	C₂²×C₃	1	2	yes	—
108	#3963	C₂²×C₃	1	2	yes	—
109	#3963	C₂²×C₃	1	2	yes	—
110	#3963	C₂²×C₃	1	2	yes	—
111	#2343	—	5	1	no	Sylow
112	C₂³×C₃×C₅	—	2	2	no	—
113	C₂³×C₃×C₅	—	2	1	no	—
114	C₂³×C₃×C₅	—	2	1	no	—
115	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
116	C₂³×C₃×C₅	#41	1	4	yes	—
117	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
118	C₂×C₃×C₄×C₅	—	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	2	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	1	no	—
124	C₂×C₃×C₄×C₅	—	2	1	no	—
125	C₂×C₃×C₄×C₅	—	2	1	no	—
126	C₂×C₃×C₄×C₅	—	2	1	no	—
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
133	C₂×C₃×Dic₅	—	2	2	no	—
134	C₂×C₃×Dic₅	—	2	2	no	—
135	C₂×C₃×Dic₅	—	2	2	no	—
136	C₂×C₃×Dic₅	—	2	2	no	—
137	C₂×C₃×Dic₅	—	2	2	no	—
138	C₂×C₃×Dic₅	—	2	2	no	—
139	C₂×C₃×Dic₅	—	2	2	no	—
140	C₂×C₃×Dic₅	—	2	2	no	—
141	C₂×C₃×Dic₅	—	2	2	no	—
142	C₂×C₃×Dic₅	—	2	2	no	—
143	C₂×C₃×Dic₅	—	2	2	no	—
144	C₂×C₃×Dic₅	—	4	8	no	—
145	C₂×C₃×Dic₅	#41	1	4	yes	—
146	C₂³×C₃×C₄	—	5	2	no	—
147	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
148	C₃×#117	Dic₅	1	8	yes	complemented
149	C₂×C₃×C₄⋊C₄	—	5	2	no	—
150	C₂×C₃×C₄⋊C₄	—	5	2	no	—
151	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
152	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
153	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
154	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
155	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
156	C₂×C₃×C₄²	—	5	2	no	—
157	C₂×C₃×C₄²	—	5	2	no	—
158	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
159	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
160	C₃×#95	—	5	1	no	—
161	C₃×#95	—	5	1	no	—
162	C₃×#95	—	5	2	no	—
163	C₃×#95	—	5	1	no	—
164	C₃×#95	—	5	2	no	—
165	C₃×#95	—	5	2	no	—
166	C₃×#95	—	5	2	no	—
167	C₃×#95	—	5	1	no	—
168	C₃×#95	—	5	2	no	—
169	C₃×#95	—	5	2	no	—
170	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
171	C₂²×C₄×C₅	—	2	4	no	—
172	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
173	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
175	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
176	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
179	C₂²×Dic₅	—	2	4	no	—
180	C₂²×Dic₅	—	2	4	no	—
181	C₂²×Dic₅	—	4	2	no	—
182	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
183	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
184	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
185	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
186	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	complemented
187	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	complemented
188	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
189	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
190	C₄²×C₅	C₂×C₃×C₄	1	4	yes	complemented
191	C₄²×C₅	C₂×C₃×C₄	1	4	yes	complemented
192	C₂²⋊Dic₅	—	2	4	no	—
193	C₄⋊Dic₅	—	2	4	no	—
194	C₄⋊Dic₅	—	4	2	no	—
195	C₄×Dic₅	—	2	4	no	—
196	C₄×Dic₅	—	4	2	no	—
197	C₂×#117	C₃×D₅	1	1	yes	characteristic
198	#387	—	5	2	no	—
199	#387	—	5	2	no	—
200	#385	—	5	2	no	—
201	#383	—	5	1	no	—
202	#382	—	5	1	no	—
203	#381	—	5	1	no	—
204	C₄×C₄⋊C₄	—	5	1	no	—
205	C₄×C₂²⋊C₄	—	5	2	no	—
206	#376	—	5	1	no	—
207	C₂×#95	—	5	1	no	—
208	C₂²×C₃×C₅	—	2	2	no	—
209	C₂²×C₃×C₅	—	2	2	no	—
210	C₂²×C₃×C₅	—	2	4	no	—
211	C₂²×C₃×C₅	—	2	4	no	—
212	C₂²×C₃×C₅	#117	1	4	yes	—
213	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
214	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
215	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
216	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
218	C₃×C₄×C₅	—	2	2	no	—
219	C₃×C₄×C₅	—	2	2	no	—
220	C₃×C₄×C₅	—	2	2	no	—
221	C₃×C₄×C₅	—	2	2	no	—
222	C₃×C₄×C₅	—	2	2	no	—
223	C₃×C₄×C₅	—	2	2	no	—
224	C₃×Dic₅	—	2	4	no	—
225	C₃×Dic₅	—	4	2	no	—
226	C₃×Dic₅	—	4	2	no	—
227	C₃×Dic₅	—	4	2	no	—
228	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
229	C₂²×C₃×C₄	—	2	4	no	—
230	C₂²×C₃×C₄	—	5	2	no	—
231	C₂²×C₃×C₄	—	5	2	no	—
232	C₂²×C₃×C₄	—	5	2	no	—
233	C₂²×C₃×C₄	—	5	2	no	—
234	C₂²×C₃×C₄	—	10	4	no	—
235	C₂²×C₃×C₄	—	10	4	no	—
236	C₂²×C₃×C₄	—	20	2	no	—
237	C₂²×C₃×C₄	C₂×Dic₅	1	4	yes	—
238	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
239	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
240	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
241	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
242	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
243	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
244	C₃×C₄⋊C₄	—	10	4	no	—
245	C₃×C₄⋊C₄	—	20	2	no	—
246	C₃×C₄⋊C₄	C₂×Dic₅	1	4	yes	complemented
247	C₃×C₄⋊C₄	C₂×Dic₅	1	4	yes	complemented
248	C₃×C₂²⋊C₄	—	10	4	no	—
249	C₃×C₂²⋊C₄	C₂×Dic₅	1	4	yes	—
250	C₃×C₂²⋊C₄	C₂×Dic₅	1	4	yes	—
251	C₃×C₄²	—	10	4	no	—
252	C₃×C₄²	—	20	2	no	—
253	C₃×C₄²	C₂×Dic₅	1	4	yes	complemented
254	C₃×C₄²	C₂×Dic₅	1	4	yes	complemented
255	C₂³×C₅	—	2	2	no	—
256	C₂³×C₅	—	2	1	no	—
257	C₂³×C₅	—	2	1	no	—
258	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
259	C₂³×C₅	C₃×#41	1	4	yes	—
260	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
261	C₂×C₄×C₅	—	2	8	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	2	1	no	—
267	C₂×C₄×C₅	—	2	1	no	—
268	C₂×C₄×C₅	—	2	1	no	—
269	C₂×C₄×C₅	—	2	1	no	—
270	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
271	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
272	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
273	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
274	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
275	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
276	C₂×Dic₅	—	2	2	no	—
277	C₂×Dic₅	—	2	2	no	—
278	C₂×Dic₅	—	2	2	no	—
279	C₂×Dic₅	—	2	2	no	—
280	C₂×Dic₅	—	2	2	no	—
281	C₂×Dic₅	—	2	2	no	—
282	C₂×Dic₅	—	2	2	no	—
283	C₂×Dic₅	—	2	2	no	—
284	C₂×Dic₅	—	2	2	no	—
285	C₂×Dic₅	—	2	2	no	—
286	C₂×Dic₅	—	2	2	no	—
287	C₂×Dic₅	—	4	8	no	—
288	C₂×Dic₅	C₃×#41	1	4	yes	—
289	C₂³×C₄	—	5	2	no	—
290	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
291	#117	C₃×Dic₅	1	8	yes	complemented
292	C₂×C₄⋊C₄	—	5	2	no	—
293	C₂×C₄⋊C₄	—	5	2	no	—
294	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	—	5	2	no	—
297	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
299	C₂×C₄²	—	5	2	no	—
300	C₂×C₄²	—	5	2	no	—
301	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
302	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
303	#95	—	5	1	no	—
304	#95	—	5	1	no	—
305	#95	—	5	2	no	—
306	#95	—	5	1	no	—
307	#95	—	5	2	no	—
308	#95	—	5	2	no	—
309	#95	—	5	2	no	—
310	#95	—	5	1	no	—
311	#95	—	5	2	no	—
312	#95	—	5	2	no	—
313	C₂×C₃×C₅	—	2	4	no	—
314	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
315	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
316	C₂×C₃×C₅	#520	1	1	yes	characteristic
317	C₂×C₃×C₅	#551	1	2	yes	—
318	C₂×C₃×C₅	#552	1	2	yes	—
319	C₂³×C₃	—	2	2	no	—
320	C₂³×C₃	—	2	1	no	—
321	C₂³×C₃	—	2	1	no	—
322	C₂³×C₃	#709	1	4	yes	—
323	C₂³×C₃	C₂²×Dic₅	1	2	yes	—
324	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
325	C₂×C₃×C₄	—	2	2	no	—
326	C₂×C₃×C₄	—	2	2	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	2	2	no	—
329	C₂×C₃×C₄	—	2	1	no	—
330	C₂×C₃×C₄	—	2	1	no	—
331	C₂×C₃×C₄	—	2	1	no	—
332	C₂×C₃×C₄	—	2	1	no	—
333	C₂×C₃×C₄	—	2	8	no	—
334	C₂×C₃×C₄	—	5	4	no	—
335	C₂×C₃×C₄	—	10	2	no	—
336	C₂×C₃×C₄	—	10	2	no	—
337	C₂×C₃×C₄	—	10	2	no	—
338	C₂×C₃×C₄	—	10	2	no	—
339	C₂×C₃×C₄	—	10	2	no	—
340	C₂×C₃×C₄	—	10	2	no	—
341	C₂×C₃×C₄	—	10	2	no	—
342	C₂×C₃×C₄	—	10	2	no	—
343	C₂×C₃×C₄	—	10	2	no	—
344	C₂×C₃×C₄	—	10	2	no	—
345	C₂×C₃×C₄	—	10	2	no	—
346	C₂×C₃×C₄	—	20	8	no	—
347	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
348	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
349	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
350	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
351	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
352	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
353	C₂²×C₅	—	2	2	no	—
354	C₂²×C₅	—	2	2	no	—
355	C₂²×C₅	—	2	4	no	—
356	C₂²×C₅	—	2	4	no	—
357	C₂²×C₅	C₃×#117	1	4	yes	—
358	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
359	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
360	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
361	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
363	C₄×C₅	—	2	2	no	—
364	C₄×C₅	—	2	2	no	—
365	C₄×C₅	—	2	2	no	—
366	C₄×C₅	—	2	2	no	—
367	C₄×C₅	—	2	2	no	—
368	C₄×C₅	—	2	2	no	—
369	Dic₅	—	2	4	no	—
370	Dic₅	—	4	2	no	—
371	Dic₅	—	4	2	no	—
372	Dic₅	—	4	2	no	—
373	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	5	2	no	—
376	C₂²×C₄	—	5	2	no	—
377	C₂²×C₄	—	5	2	no	—
378	C₂²×C₄	—	5	2	no	—
379	C₂²×C₄	—	10	4	no	—
380	C₂²×C₄	—	10	4	no	—
381	C₂²×C₄	—	20	2	no	—
382	C₂²×C₄	C₂×C₃×Dic₅	1	4	yes	—
383	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
384	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
385	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
386	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
387	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
388	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
389	C₄⋊C₄	—	10	4	no	—
390	C₄⋊C₄	—	20	2	no	—
391	C₄⋊C₄	C₂×C₃×Dic₅	1	4	yes	complemented
392	C₄⋊C₄	C₂×C₃×Dic₅	1	4	yes	complemented
393	C₂²⋊C₄	—	10	4	no	—
394	C₂²⋊C₄	C₂×C₃×Dic₅	1	4	yes	—
395	C₂²⋊C₄	C₂×C₃×Dic₅	1	4	yes	—
396	C₄²	—	10	4	no	—
397	C₄²	—	20	2	no	—
398	C₄²	C₂×C₃×Dic₅	1	4	yes	complemented
399	C₄²	C₂×C₃×Dic₅	1	4	yes	complemented
400	C₃×C₅	#2343	1	1	yes	characteristic, complemented, Hall
401	C₂²×C₃	—	2	4	no	—
402	C₂²×C₃	—	2	4	no	—
403	C₂²×C₃	—	2	2	no	—
404	C₂²×C₃	—	2	2	no	—
405	C₂²×C₃	#4072	1	4	yes	—
406	C₂²×C₃	C₂×#709	1	2	yes	—
407	C₂²×C₃	D₅×#41	1	2	yes	—
408	C₂²×C₃	#4149	1	1	yes	characteristic
409	C₂²×C₃	#4150	1	1	yes	characteristic
410	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
411	C₃×C₄	—	2	2	no	—
412	C₃×C₄	—	2	2	no	—
413	C₃×C₄	—	2	2	no	—
414	C₃×C₄	—	2	2	no	—
415	C₃×C₄	—	2	2	no	—
416	C₃×C₄	—	2	2	no	—
417	C₃×C₄	—	10	4	no	—
418	C₃×C₄	—	20	2	no	—
419	C₃×C₄	—	20	2	no	—
420	C₃×C₄	—	20	2	no	—
421	C₂×C₅	—	2	4	no	—
422	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
423	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
424	C₂×C₅	C₃×#520	1	1	yes	characteristic
425	C₂×C₅	C₃×#551	1	2	yes	—
426	C₂×C₅	C₃×#552	1	2	yes	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	2	1	no	—
430	C₂³	C₃×#709	1	4	yes	—
431	C₂³	C₂²×C₃×Dic₅	1	2	yes	—
432	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	5	4	no	—
443	C₂×C₄	—	10	2	no	—
444	C₂×C₄	—	10	2	no	—
445	C₂×C₄	—	10	2	no	—
446	C₂×C₄	—	10	2	no	—
447	C₂×C₄	—	10	2	no	—
448	C₂×C₄	—	10	2	no	—
449	C₂×C₄	—	10	2	no	—
450	C₂×C₄	—	10	2	no	—
451	C₂×C₄	—	10	2	no	—
452	C₂×C₄	—	10	2	no	—
453	C₂×C₄	—	10	2	no	—
454	C₂×C₄	—	20	8	no	—
455	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
456	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
457	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
458	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
459	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
460	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
461	C₂×C₃	—	2	4	no	—
462	C₂×C₃	#65861	1	2	yes	—
463	C₂×C₃	#65865	1	2	yes	—
464	C₂×C₃	C₂×#4072	1	1	yes	characteristic
465	C₂×C₃	#41×Dic₅	1	1	yes	characteristic
466	C₂×C₃	#66161	1	1	yes	characteristic
467	C₅	C₃×#2343	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	2	4	no	—
469	C₂²	—	2	4	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	C₃×#4072	1	4	yes	—
473	C₂²	C₂×C₃×#709	1	2	yes	—
474	C₂²	C₃×D₅×#41	1	2	yes	—
475	C₂²	C₃×#4149	1	1	yes	characteristic
476	C₂²	C₃×#4150	1	1	yes	characteristic
477	C₂²	C₂³×C₃×Dic₅	1	1	yes	characteristic
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	2	no	—
483	C₄	—	2	2	no	—
484	C₄	—	10	4	no	—
485	C₄	—	20	2	no	—
486	C₄	—	20	2	no	—
487	C₄	—	20	2	no	—
488	C₃	#10613968	1	1	yes	characteristic, direct product factor, Sylow
489	C₂	—	2	4	no	—
490	C₂	C₃×#65861	1	2	yes	—
491	C₂	C₃×#65865	1	2	yes	—
492	C₂	C₂×C₃×#4072	1	1	yes	characteristic
493	C₂	C₃×#41×Dic₅	1	1	yes	characteristic
494	C₂	C₃×#66161	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×C₅	C₂³
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×#117	D₅
hypocenter	C₅	C₃×#2343
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#117

Complements

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

N	H ≅ G/N	type
4. C₃×#65270	C₂	semidirect
5. C₃×#65270	C₂	semidirect
8. C₃×#65226	C₂	semidirect
9. C₃×#65225	C₂	semidirect
10. C₃×C₄×C₄⋊Dic₅	C₂	semidirect
11. C₃×#65221	C₂	semidirect
12. #10613968	C₃	direct (N × H)
15. C₃×C₅×#117	C₄	semidirect
41. #65270	C₂×C₃	semidirect
42. #65270	C₂×C₃	semidirect
45. #65226	C₂×C₃	semidirect
46. #65225	C₂×C₃	semidirect
47. C₄×C₄⋊Dic₅	C₂×C₃	semidirect
48. #65221	C₂×C₃	semidirect
65. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
66. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
69. C₃×C₄²×C₅	C₂×C₄	semidirect
70. C₃×C₄²×C₅	C₂×C₄	semidirect
89. C₅×#117	C₃×C₄	semidirect
148. C₃×#117	Dic₅	semidirect
186. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
187. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
190. C₄²×C₅	C₂×C₃×C₄	semidirect
191. C₄²×C₅	C₂×C₃×C₄	semidirect
246. C₃×C₄⋊C₄	C₂×Dic₅	semidirect
247. C₃×C₄⋊C₄	C₂×Dic₅	semidirect
253. C₃×C₄²	C₂×Dic₅	semidirect
254. C₃×C₄²	C₂×Dic₅	semidirect
291. #117	C₃×Dic₅	semidirect
391. C₄⋊C₄	C₂×C₃×Dic₅	semidirect
392. C₄⋊C₄	C₂×C₃×Dic₅	semidirect
398. C₄²	C₂×C₃×Dic₅	semidirect
399. C₄²	C₂×C₃×Dic₅	semidirect
400. C₃×C₅	#2343	semidirect
467. C₅	C₃×#2343	semidirect
488. C₃	#10613968	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#117	2
C₃×#65500	2
C₂×C₃×#3963	2
C₃×#65270	2
C₃×#65239	2
C₃×C₂²⋊C₄×Dic₅	2
C₃×#65226	2
C₃×#65225	2
C₃×C₄×C₄⋊Dic₅	2
C₃×#65221	2
#10613968	3
C₃×#2343	5

Subgroups — C3×#10613968 #14326411

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613968 #14326411