Subgroups — C₃×#10605147 #14326414

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×#4018	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#376	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×#685	C₂	1	2	yes	maximal
4	C₃×#65225	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65222	C₂	1	2	yes	maximal, complemented
6	C₃×#64957	C₂	1	2	yes	maximal
7	C₃×#64953	C₂	1	1	yes	maximal, characteristic
8	C₃×D₅×#95	C₂	1	1	yes	maximal, characteristic
9	C₃×#64944	C₂	1	2	yes	maximal, complemented
10	C₃×#64940	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64938	C₂	1	1	yes	maximal, characteristic, complemented
12	#10605147	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
14	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×#685	C₂²	1	2	yes	—
18	C₂×C₃×#685	C₂²	1	1	yes	characteristic
19	C₂×C₃×#685	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
21	C₂×C₃×#683	C₂²	1	2	yes	—
22	C₂×C₃×#683	C₂²	1	1	yes	characteristic
23	C₂×C₃×#683	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
25	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
26	C₃×#4018	C₄	1	8	yes	complemented
27	C₃×C₅×#95	C₂²	1	1	yes	characteristic
28	C₃×C₅×#95	C₂²	1	1	yes	characteristic
29	C₃×C₅×#95	C₂²	1	2	yes	—
30	C₃×#3963	C₂²	1	1	yes	characteristic
31	C₃×#3963	C₂²	1	2	yes	—
32	C₃×#3963	C₂²	1	1	yes	characteristic
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×#4018	C₂×C₃	1	1	yes	characteristic
39	C₅×#376	C₂×C₃	1	1	yes	characteristic, complemented
40	C₄×#685	C₂×C₃	1	2	yes	—
41	#65225	C₂×C₃	1	1	yes	characteristic, complemented
42	#65222	C₂×C₃	1	2	yes	complemented
43	#64957	C₂×C₃	1	2	yes	—
44	#64953	C₂×C₃	1	1	yes	characteristic
45	D₅×#95	C₂×C₃	1	1	yes	characteristic
46	#64944	C₂×C₃	1	2	yes	complemented
47	#64940	C₂×C₃	1	1	yes	characteristic, complemented
48	#64938	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂³×C₃×D₅	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	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
55	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
56	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
57	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
58	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
59	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₄×D₅	—	2	4	no	—
61	C₂×C₃×C₄×D₅	—	2	4	no	—
62	C₂×C₃×C₄×D₅	—	2	4	no	—
63	C₂×C₃×C₄×D₅	—	4	2	no	—
64	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
65	C₃×C₄²×C₅	—	2	4	no	—
66	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
67	C₃×#685	—	2	4	no	—
68	C₃×#685	C₂×C₄	1	4	yes	—
69	C₃×#685	C₂×C₄	1	4	yes	—
70	C₃×C₄⋊Dic₅	—	4	2	no	—
71	C₃×#683	—	2	4	no	—
72	C₃×#683	C₂×C₄	1	4	yes	complemented
73	C₃×#683	C₂×C₄	1	4	yes	complemented
74	C₃×C₄×Dic₅	—	4	2	no	—
75	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	complemented
76	C₂×C₃×#117	—	5	1	no	—
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	D₅	1	1	yes	characteristic, complemented
86	C₂×C₃×#95	—	5	1	no	—
87	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
88	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
90	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
91	C₂×#685	C₂²×C₃	1	2	yes	—
92	C₂×#685	C₂²×C₃	1	1	yes	characteristic
93	C₂×#685	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
95	C₂×#683	C₂²×C₃	1	2	yes	—
96	C₂×#683	C₂²×C₃	1	1	yes	characteristic
97	C₂×#683	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
99	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
100	#4018	C₃×C₄	1	8	yes	complemented
101	C₅×#95	C₂²×C₃	1	1	yes	characteristic
102	C₅×#95	C₂²×C₃	1	1	yes	characteristic
103	C₅×#95	C₂²×C₃	1	2	yes	—
104	#3963	C₂²×C₃	1	1	yes	characteristic
105	#3963	C₂²×C₃	1	2	yes	—
106	#3963	C₂²×C₃	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
113	C₂²×C₃×D₅	—	2	2	no	—
114	C₂²×C₃×D₅	—	2	1	no	—
115	C₂²×C₃×D₅	—	2	1	no	—
116	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
117	C₂²×C₃×D₅	#41	1	4	yes	—
118	C₂×C₃×C₄×C₅	—	2	2	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	1	no	—
123	C₂×C₃×C₄×C₅	—	2	1	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	2	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	#41	1	4	yes	—
131	C₂×C₃×Dic₅	—	2	2	no	—
132	C₂×C₃×Dic₅	—	2	2	no	—
133	C₂×C₃×Dic₅	—	2	1	no	—
134	C₂×C₃×Dic₅	—	2	1	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	C₂²×C₄	1	2	yes	—
142	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
143	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
144	C₃×C₄×D₅	—	2	8	no	—
145	C₃×C₄×D₅	—	4	8	no	—
146	C₂³×C₃×C₄	—	5	1	no	—
147	C₂³×C₃×C₄	—	5	2	no	—
148	C₃×#117	—	5	8	no	—
149	C₂×C₃×C₄⋊C₄	—	5	1	no	—
150	C₂×C₃×C₄⋊C₄	—	5	1	no	—
151	C₂×C₃×C₄⋊C₄	—	5	2	no	—
152	C₂×C₃×C₄⋊C₄	—	5	2	no	—
153	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
154	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
155	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
156	C₂×C₃×C₄²	—	5	1	no	—
157	C₂×C₃×C₄²	—	5	2	no	—
158	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
159	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
160	C₃×#95	—	5	1	no	—
161	C₃×#95	—	5	2	no	—
162	C₃×#95	—	5	2	no	—
163	C₃×#95	—	5	2	no	—
164	C₃×#95	—	5	1	no	—
165	C₃×#95	—	5	2	no	—
166	C₃×#95	—	5	2	no	—
167	C₃×#95	C₂×D₅	1	1	yes	characteristic
168	C₃×#95	C₂×D₅	1	1	yes	characteristic
169	C₃×#95	C₂×D₅	1	2	yes	—
170	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
172	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
176	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
177	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
178	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
179	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
180	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
181	C₂×C₄×D₅	—	2	4	no	—
182	C₂×C₄×D₅	—	2	4	no	—
183	C₂×C₄×D₅	—	2	4	no	—
184	C₂×C₄×D₅	—	4	2	no	—
185	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
186	C₄²×C₅	—	2	4	no	—
187	C₄²×C₅	C₂×C₃×C₄	1	4	yes	complemented
188	#685	—	2	4	no	—
189	#685	C₂×C₃×C₄	1	4	yes	—
190	#685	C₂×C₃×C₄	1	4	yes	—
191	C₄⋊Dic₅	—	4	2	no	—
192	#683	—	2	4	no	—
193	#683	C₂×C₃×C₄	1	4	yes	complemented
194	#683	C₂×C₃×C₄	1	4	yes	complemented
195	C₄×Dic₅	—	4	2	no	—
196	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	complemented
197	C₂×#117	—	5	1	no	—
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	C₃×D₅	1	1	yes	characteristic, complemented
207	C₂×#95	—	5	1	no	—
208	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
209	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
210	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
211	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
213	C₂×C₃×D₅	—	2	2	no	—
214	C₂×C₃×D₅	—	2	2	no	—
215	C₂×C₃×D₅	—	2	4	no	—
216	C₂×C₃×D₅	—	2	4	no	—
217	C₂×C₃×D₅	#117	1	4	yes	—
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	4	no	—
222	C₃×C₄×C₅	—	4	2	no	—
223	C₃×Dic₅	—	2	2	no	—
224	C₃×Dic₅	—	2	2	no	—
225	C₃×Dic₅	—	2	2	no	—
226	C₃×Dic₅	—	4	2	no	—
227	C₃×Dic₅	—	4	2	no	—
228	C₂⁴×C₃	—	5	1	no	—
229	C₂²×C₃×C₄	—	5	1	no	—
230	C₂²×C₃×C₄	—	5	1	no	—
231	C₂²×C₃×C₄	—	5	1	no	—
232	C₂²×C₃×C₄	—	5	4	no	—
233	C₂²×C₃×C₄	—	5	2	no	—
234	C₂²×C₃×C₄	—	5	2	no	—
235	C₂²×C₃×C₄	—	10	4	no	—
236	C₂²×C₃×C₄	—	10	4	no	—
237	C₂²×C₃×C₄	—	10	4	no	—
238	C₂²×C₃×C₄	—	20	2	no	—
239	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
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	2	yes	—
244	C₃×C₄⋊C₄	—	5	4	no	—
245	C₃×C₄⋊C₄	—	5	4	no	—
246	C₃×C₄⋊C₄	—	10	4	no	—
247	C₃×C₄⋊C₄	—	20	2	no	—
248	C₃×C₂²⋊C₄	—	5	4	no	—
249	C₃×C₂²⋊C₄	—	5	4	no	—
250	C₃×C₂²⋊C₄	—	10	4	no	—
251	C₃×C₄²	—	2	4	no	—
252	C₃×C₄²	—	5	4	no	—
253	C₃×C₄²	—	20	2	no	—
254	C₃×C₄²	C₄×D₅	1	4	yes	complemented
255	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
256	C₂²×D₅	—	2	2	no	—
257	C₂²×D₅	—	2	1	no	—
258	C₂²×D₅	—	2	1	no	—
259	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
260	C₂²×D₅	C₃×#41	1	4	yes	—
261	C₂×C₄×C₅	—	2	2	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	1	no	—
266	C₂×C₄×C₅	—	2	1	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	2	2	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	C₃×#41	1	4	yes	—
274	C₂×Dic₅	—	2	2	no	—
275	C₂×Dic₅	—	2	2	no	—
276	C₂×Dic₅	—	2	1	no	—
277	C₂×Dic₅	—	2	1	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	C₂²×C₃×C₄	1	2	yes	—
285	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
286	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
287	C₄×D₅	—	2	8	no	—
288	C₄×D₅	—	4	8	no	—
289	C₂³×C₄	—	5	1	no	—
290	C₂³×C₄	—	5	2	no	—
291	#117	—	5	8	no	—
292	C₂×C₄⋊C₄	—	5	1	no	—
293	C₂×C₄⋊C₄	—	5	1	no	—
294	C₂×C₄⋊C₄	—	5	2	no	—
295	C₂×C₄⋊C₄	—	5	2	no	—
296	C₂×C₂²⋊C₄	—	5	1	no	—
297	C₂×C₂²⋊C₄	—	5	1	no	—
298	C₂×C₂²⋊C₄	—	5	2	no	—
299	C₂×C₄²	—	5	1	no	—
300	C₂×C₄²	—	5	2	no	—
301	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
302	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
303	#95	—	5	1	no	—
304	#95	—	5	2	no	—
305	#95	—	5	2	no	—
306	#95	—	5	2	no	—
307	#95	—	5	1	no	—
308	#95	—	5	2	no	—
309	#95	—	5	2	no	—
310	#95	C₂×C₃×D₅	1	1	yes	characteristic
311	#95	C₂×C₃×D₅	1	1	yes	characteristic
312	#95	C₂×C₃×D₅	1	2	yes	—
313	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
314	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
315	C₂×C₃×C₅	#520	1	1	yes	characteristic
316	C₂×C₃×C₅	#551	1	2	yes	—
317	C₂×C₃×C₅	#552	1	2	yes	—
318	C₃×D₅	—	2	4	no	—
319	C₂³×C₃	—	5	2	no	—
320	C₂³×C₃	—	5	4	no	—
321	C₂³×C₃	—	10	2	no	—
322	C₂³×C₃	—	10	1	no	—
323	C₂³×C₃	—	10	1	no	—
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	2	no	—
332	C₂×C₃×C₄	—	2	2	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	5	2	no	—
335	C₂×C₃×C₄	—	5	2	no	—
336	C₂×C₃×C₄	—	5	2	no	—
337	C₂×C₃×C₄	—	10	8	no	—
338	C₂×C₃×C₄	—	10	2	no	—
339	C₂×C₃×C₄	—	10	2	no	—
340	C₂×C₃×C₄	—	10	1	no	—
341	C₂×C₃×C₄	—	10	1	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	—	10	2	no	—
347	C₂×C₃×C₄	—	10	2	no	—
348	C₂×C₃×C₄	—	20	8	no	—
349	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
350	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
351	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
352	C₂×C₃×C₄	#709	1	4	yes	—
353	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
354	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
355	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
356	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
357	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
358	C₂×D₅	—	2	2	no	—
359	C₂×D₅	—	2	2	no	—
360	C₂×D₅	—	2	4	no	—
361	C₂×D₅	—	2	4	no	—
362	C₂×D₅	C₃×#117	1	4	yes	—
363	C₄×C₅	—	2	2	no	—
364	C₄×C₅	—	2	2	no	—
365	C₄×C₅	—	2	2	no	—
366	C₄×C₅	—	2	4	no	—
367	C₄×C₅	—	4	2	no	—
368	Dic₅	—	2	2	no	—
369	Dic₅	—	2	2	no	—
370	Dic₅	—	2	2	no	—
371	Dic₅	—	4	2	no	—
372	Dic₅	—	4	2	no	—
373	C₂⁴	—	5	1	no	—
374	C₂²×C₄	—	5	1	no	—
375	C₂²×C₄	—	5	1	no	—
376	C₂²×C₄	—	5	1	no	—
377	C₂²×C₄	—	5	4	no	—
378	C₂²×C₄	—	5	2	no	—
379	C₂²×C₄	—	5	2	no	—
380	C₂²×C₄	—	10	4	no	—
381	C₂²×C₄	—	10	4	no	—
382	C₂²×C₄	—	10	4	no	—
383	C₂²×C₄	—	20	2	no	—
384	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
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	2	yes	—
389	C₄⋊C₄	—	5	4	no	—
390	C₄⋊C₄	—	5	4	no	—
391	C₄⋊C₄	—	10	4	no	—
392	C₄⋊C₄	—	20	2	no	—
393	C₂²⋊C₄	—	5	4	no	—
394	C₂²⋊C₄	—	5	4	no	—
395	C₂²⋊C₄	—	10	4	no	—
396	C₄²	—	2	4	no	—
397	C₄²	—	5	4	no	—
398	C₄²	—	20	2	no	—
399	C₄²	C₃×C₄×D₅	1	4	yes	complemented
400	C₃×C₅	#2343	1	1	yes	characteristic, complemented, Hall
401	C₂²×C₃	—	5	4	no	—
402	C₂²×C₃	—	10	2	no	—
403	C₂²×C₃	—	10	2	no	—
404	C₂²×C₃	—	10	4	no	—
405	C₂²×C₃	—	10	4	no	—
406	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
407	C₂²×C₃	C₂×#709	1	2	yes	—
408	C₂²×C₃	D₅×#41	1	2	yes	—
409	C₂²×C₃	#4149	1	1	yes	characteristic
410	C₂²×C₃	#4150	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	4	no	—
415	C₃×C₄	—	4	2	no	—
416	C₃×C₄	—	10	2	no	—
417	C₃×C₄	—	10	2	no	—
418	C₃×C₄	—	10	2	no	—
419	C₃×C₄	—	20	2	no	—
420	C₃×C₄	—	20	2	no	—
421	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
422	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
423	C₂×C₅	C₃×#520	1	1	yes	characteristic
424	C₂×C₅	C₃×#551	1	2	yes	—
425	C₂×C₅	C₃×#552	1	2	yes	—
426	D₅	—	2	4	no	—
427	C₂³	—	5	2	no	—
428	C₂³	—	5	4	no	—
429	C₂³	—	10	2	no	—
430	C₂³	—	10	1	no	—
431	C₂³	—	10	1	no	—
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	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	5	2	no	—
443	C₂×C₄	—	5	2	no	—
444	C₂×C₄	—	5	2	no	—
445	C₂×C₄	—	10	8	no	—
446	C₂×C₄	—	10	2	no	—
447	C₂×C₄	—	10	2	no	—
448	C₂×C₄	—	10	1	no	—
449	C₂×C₄	—	10	1	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	—	10	2	no	—
455	C₂×C₄	—	10	2	no	—
456	C₂×C₄	—	20	8	no	—
457	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
458	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
459	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
460	C₂×C₄	C₃×#709	1	4	yes	—
461	C₂×C₃	—	10	4	no	—
462	C₂×C₃	C₄×#709	1	1	yes	characteristic
463	C₂×C₃	D₅×#117	1	1	yes	characteristic
464	C₂×C₃	#65857	1	1	yes	characteristic
465	C₂×C₃	#65861	1	2	yes	—
466	C₂×C₃	#65863	1	2	yes	—
467	C₅	C₃×#2343	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	5	4	no	—
469	C₂²	—	10	2	no	—
470	C₂²	—	10	4	no	—
471	C₂²	—	10	4	no	—
472	C₂²	—	10	2	no	—
473	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
474	C₂²	C₂×C₃×#709	1	2	yes	—
475	C₂²	C₃×D₅×#41	1	2	yes	—
476	C₂²	C₃×#4149	1	1	yes	characteristic
477	C₂²	C₃×#4150	1	1	yes	characteristic
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	4	no	—
481	C₄	—	2	2	no	—
482	C₄	—	4	2	no	—
483	C₄	—	10	2	no	—
484	C₄	—	10	2	no	—
485	C₄	—	10	2	no	—
486	C₄	—	20	2	no	—
487	C₄	—	20	2	no	—
488	C₃	#10605147	1	1	yes	characteristic, direct product factor, Sylow
489	C₂	—	10	4	no	—
490	C₂	C₃×C₄×#709	1	1	yes	characteristic
491	C₂	C₃×D₅×#117	1	1	yes	characteristic
492	C₂	C₃×#65857	1	1	yes	characteristic
493	C₂	C₃×#65861	1	2	yes	—
494	C₂	C₃×#65863	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₃×C₅×#376	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₃×D₅	C₂³
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×#376	D₅
hypocenter	C₅	C₃×#2343
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×#376

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#376	C₂	semidirect
4. C₃×#65225	C₂	semidirect
5. C₃×#65222	C₂	semidirect
9. C₃×#64944	C₂	semidirect
10. C₃×#64940	C₂	semidirect
11. C₃×#64938	C₂	semidirect
12. #10605147	C₃	direct (N × H)
26. C₃×#4018	C₄	semidirect
39. C₅×#376	C₂×C₃	semidirect
41. #65225	C₂×C₃	semidirect
42. #65222	C₂×C₃	semidirect
46. #64944	C₂×C₃	semidirect
47. #64940	C₂×C₃	semidirect
48. #64938	C₂×C₃	semidirect
66. C₃×C₄²×C₅	C₂×C₄	semidirect
72. C₃×#683	C₂×C₄	semidirect
73. C₃×#683	C₂×C₄	semidirect
75. C₃×C₄×Dic₅	C₂×C₄	semidirect
85. C₃×#376	D₅	semidirect
100. #4018	C₃×C₄	semidirect
187. C₄²×C₅	C₂×C₃×C₄	semidirect
193. #683	C₂×C₃×C₄	semidirect
194. #683	C₂×C₃×C₄	semidirect
196. C₄×Dic₅	C₂×C₃×C₄	semidirect
206. #376	C₃×D₅	semidirect
254. C₃×C₄²	C₄×D₅	semidirect
399. C₄²	C₃×C₄×D₅	semidirect
400. C₃×C₅	#2343	semidirect
467. C₅	C₃×#2343	semidirect
488. C₃	#10605147	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×#4018	2
C₃×C₅×#376	2
C₃×C₄×#685	2
C₃×#65225	2
C₃×#65222	2
C₃×#64957	2
C₃×#64953	2
C₃×D₅×#95	2
C₃×#64944	2
C₃×#64940	2
C₃×#64938	2
#10605147	3
C₃×#2343	5

Subgroups — C3×#10605147 #14326414

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10605147 #14326414