Subgroups — C₃×#10605126 #14330137

Order 1920.

1120 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4021	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#376	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65229	C₂	1	2	yes	maximal, complemented
4	C₃×C₄×#685	C₂	1	2	yes	maximal, complemented
5	C₃×#65221	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64958	C₂	1	2	yes	maximal, complemented
7	C₃×#64955	C₂	1	2	yes	maximal, complemented
8	C₃×#64954	C₂	1	2	yes	maximal
9	C₃×#64935	C₂	1	2	yes	maximal, complemented
10	#10605126	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
13	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×#685	C₂²	1	2	yes	—
17	C₂×C₃×#685	C₂²	1	2	yes	—
18	C₂×C₃×#685	C₂²	1	2	yes	—
19	C₂×C₃×#685	C₂²	1	2	yes	—
20	C₂×C₃×#685	C₂²	1	2	yes	—
21	C₂×C₃×#683	C₂²	1	2	yes	—
22	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
23	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
24	C₃×#4021	C₄	1	8	yes	complemented
25	C₃×C₅×#95	C₂²	1	2	yes	—
26	C₃×C₅×#95	C₂²	1	1	yes	characteristic
27	C₃×C₅×#95	C₂²	1	1	yes	characteristic
28	C₃×#3963	C₂²	1	2	yes	—
29	C₃×#3963	C₂²	1	2	yes	—
30	C₃×#3963	C₂²	1	2	yes	—
31	C₃×#3963	C₂²	1	1	yes	characteristic
32	C₃×#3963	C₂²	1	1	yes	characteristic
33	C₃×#2372	—	5	1	no	maximal, Hall
34	C₂×#4021	C₂×C₃	1	1	yes	characteristic
35	C₅×#376	C₂×C₃	1	1	yes	characteristic, complemented
36	#65229	C₂×C₃	1	2	yes	complemented
37	C₄×#685	C₂×C₃	1	2	yes	complemented
38	#65221	C₂×C₃	1	1	yes	characteristic, complemented
39	#64958	C₂×C₃	1	2	yes	complemented
40	#64955	C₂×C₃	1	2	yes	complemented
41	#64954	C₂×C₃	1	2	yes	—
42	#64935	C₂×C₃	1	2	yes	complemented
43	C₂³×C₃×D₅	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
50	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
51	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
52	C₂×C₃×D₂₀	—	4	1	no	—
53	C₂×C₃×D₂₀	—	4	1	no	—
54	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	—
55	C₂×C₃×C₄×D₅	—	2	4	no	—
56	C₂×C₃×C₄×D₅	—	2	4	no	—
57	C₂×C₃×C₄×D₅	—	4	2	no	—
58	C₂×C₃×Dic₁₀	—	4	1	no	—
59	C₂×C₃×Dic₁₀	—	4	1	no	—
60	C₂×C₃×Dic₁₀	C₂×C₄	1	4	yes	complemented
61	C₃×C₄²×C₅	—	2	4	no	—
62	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
63	C₃×#685	—	2	4	no	—
64	C₃×#685	—	2	4	no	—
65	C₃×#685	—	4	2	no	—
66	C₃×#685	C₂×C₄	1	8	yes	complemented
67	C₃×#685	C₂×C₄	1	8	yes	complemented
68	C₃×#683	—	4	2	no	—
69	C₃×C₄×Dic₅	—	2	4	no	—
70	C₃×C₄×Dic₅	—	4	2	no	—
71	C₂×C₃×#124	—	5	1	no	—
72	C₃×#391	—	5	2	no	—
73	C₃×#388	—	5	2	no	—
74	C₃×#388	—	5	2	no	—
75	C₃×#386	—	5	2	no	—
76	C₃×C₄×C₂²⋊C₄	—	5	2	no	—
77	C₃×C₄×C₂²⋊C₄	—	5	2	no	—
78	C₃×#376	—	5	1	no	—
79	C₃×#376	D₅	1	1	yes	characteristic, complemented
80	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
81	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
82	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
84	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
85	C₂×#685	C₂²×C₃	1	2	yes	—
86	C₂×#685	C₂²×C₃	1	2	yes	—
87	C₂×#685	C₂²×C₃	1	2	yes	—
88	C₂×#685	C₂²×C₃	1	2	yes	—
89	C₂×#685	C₂²×C₃	1	2	yes	—
90	C₂×#683	C₂²×C₃	1	2	yes	—
91	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
92	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
93	#4021	C₃×C₄	1	8	yes	complemented
94	C₅×#95	C₂²×C₃	1	2	yes	—
95	C₅×#95	C₂²×C₃	1	1	yes	characteristic
96	C₅×#95	C₂²×C₃	1	1	yes	characteristic
97	#3963	C₂²×C₃	1	2	yes	—
98	#3963	C₂²×C₃	1	2	yes	—
99	#3963	C₂²×C₃	1	2	yes	—
100	#3963	C₂²×C₃	1	1	yes	characteristic
101	#3963	C₂²×C₃	1	1	yes	characteristic
102	#2372	—	5	1	no	Sylow
103	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
104	C₂²×C₃×D₅	—	2	2	no	—
105	C₂²×C₃×D₅	—	2	2	no	—
106	C₂²×C₃×D₅	—	2	2	no	—
107	C₂²×C₃×D₅	—	2	2	no	—
108	C₂²×C₃×D₅	—	2	2	no	—
109	C₂²×C₃×D₅	—	2	2	no	—
110	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	1	no	—
116	C₂×C₃×C₄×C₅	—	2	1	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
123	C₂×C₃×C₄×C₅	#41	1	4	yes	—
124	C₂×C₃×Dic₅	—	2	2	no	—
125	C₂×C₃×Dic₅	—	2	2	no	—
126	C₂×C₃×Dic₅	—	2	2	no	—
127	C₂×C₃×Dic₅	—	2	2	no	—
128	C₂×C₃×Dic₅	—	2	2	no	—
129	C₂×C₃×Dic₅	—	2	2	no	—
130	C₂×C₃×Dic₅	—	2	2	no	—
131	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
132	C₂×C₃×Dic₅	#41	1	4	yes	—
133	C₃×D₂₀	—	4	4	no	—
134	C₃×C₄×D₅	—	4	8	no	—
135	C₃×Dic₁₀	—	4	4	no	—
136	C₂²×C₃×Q₈	—	5	1	no	—
137	C₂²×C₃×D₄	—	5	1	no	—
138	C₂³×C₃×C₄	—	5	2	no	—
139	C₃×#124	—	5	8	no	—
140	C₂×C₃×C₄⋊C₄	—	5	2	no	—
141	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
142	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
143	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
144	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
145	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
146	C₂×C₃×C₄²	—	5	2	no	—
147	C₂×C₃×C₄²	—	5	2	no	—
148	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
149	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
150	C₃×#95	—	5	1	no	—
151	C₃×#95	—	5	2	no	—
152	C₃×#95	—	5	1	no	—
153	C₃×#95	—	5	2	no	—
154	C₃×#95	—	5	2	no	—
155	C₃×#95	C₂×D₅	1	1	yes	characteristic
156	C₃×#95	C₂×D₅	1	2	yes	—
157	C₃×#95	C₂×D₅	1	1	yes	characteristic
158	C₂³×D₅	C₂³×C₃	1	2	yes	—
159	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
160	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
164	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
165	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
166	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
167	C₂×D₂₀	—	4	1	no	—
168	C₂×D₂₀	—	4	1	no	—
169	C₂×D₂₀	C₂×C₃×C₄	1	4	yes	—
170	C₂×C₄×D₅	—	2	4	no	—
171	C₂×C₄×D₅	—	2	4	no	—
172	C₂×C₄×D₅	—	4	2	no	—
173	C₂×Dic₁₀	—	4	1	no	—
174	C₂×Dic₁₀	—	4	1	no	—
175	C₂×Dic₁₀	C₂×C₃×C₄	1	4	yes	complemented
176	C₄²×C₅	—	2	4	no	—
177	C₄²×C₅	C₂×C₃×C₄	1	4	yes	complemented
178	#685	—	2	4	no	—
179	#685	—	2	4	no	—
180	#685	—	4	2	no	—
181	#685	C₂×C₃×C₄	1	8	yes	complemented
182	#685	C₂×C₃×C₄	1	8	yes	complemented
183	#683	—	4	2	no	—
184	C₄×Dic₅	—	2	4	no	—
185	C₄×Dic₅	—	4	2	no	—
186	C₂×#124	—	5	1	no	—
187	#391	—	5	2	no	—
188	#388	—	5	2	no	—
189	#388	—	5	2	no	—
190	#386	—	5	2	no	—
191	C₄×C₂²⋊C₄	—	5	2	no	—
192	C₄×C₂²⋊C₄	—	5	2	no	—
193	#376	—	5	1	no	—
194	#376	C₃×D₅	1	1	yes	characteristic, complemented
195	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
196	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
197	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
198	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
200	C₂×C₃×D₅	—	2	4	no	—
201	C₂×C₃×D₅	—	2	4	no	—
202	C₂×C₃×D₅	—	2	4	no	—
203	C₂×C₃×D₅	—	4	2	no	—
204	C₂×C₃×D₅	—	4	2	no	—
205	C₂×C₃×D₅	—	4	2	no	—
206	C₂×C₃×D₅	—	4	2	no	—
207	C₃×C₄×C₅	—	2	2	no	—
208	C₃×C₄×C₅	—	2	2	no	—
209	C₃×C₄×C₅	—	2	2	no	—
210	C₃×C₄×C₅	—	2	4	no	—
211	C₃×C₄×C₅	—	4	2	no	—
212	C₃×Dic₅	—	2	4	no	—
213	C₃×Dic₅	—	2	4	no	—
214	C₃×Dic₅	—	4	2	no	—
215	C₂⁴×C₃	—	5	2	no	—
216	C₂×C₃×Q₈	—	5	4	no	—
217	C₂×C₃×Q₈	—	20	1	no	—
218	C₂×C₃×Q₈	—	20	1	no	—
219	C₂×C₃×D₄	—	5	4	no	—
220	C₂×C₃×D₄	—	20	1	no	—
221	C₂×C₃×D₄	—	20	1	no	—
222	C₂²×C₃×C₄	—	5	2	no	—
223	C₂²×C₃×C₄	—	5	2	no	—
224	C₂²×C₃×C₄	—	5	2	no	—
225	C₂²×C₃×C₄	—	10	4	no	—
226	C₂²×C₃×C₄	—	10	4	no	—
227	C₂²×C₃×C₄	—	20	2	no	—
228	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
229	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
230	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
232	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
233	C₃×C₄⋊C₄	—	20	2	no	—
234	C₃×C₂²⋊C₄	—	5	8	no	—
235	C₃×C₂²⋊C₄	—	5	8	no	—
236	C₃×C₂²⋊C₄	—	10	4	no	—
237	C₃×C₂²⋊C₄	—	10	4	no	—
238	C₃×C₂²⋊C₄	—	20	2	no	—
239	C₃×C₄²	—	2	4	no	—
240	C₃×C₄²	—	10	4	no	—
241	C₃×C₄²	—	20	2	no	—
242	C₃×C₄²	C₄×D₅	1	4	yes	complemented
243	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
244	C₂²×D₅	—	2	2	no	—
245	C₂²×D₅	—	2	2	no	—
246	C₂²×D₅	—	2	2	no	—
247	C₂²×D₅	—	2	2	no	—
248	C₂²×D₅	—	2	2	no	—
249	C₂²×D₅	—	2	2	no	—
250	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	1	no	—
256	C₂×C₄×C₅	—	2	1	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
261	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
262	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
263	C₂×C₄×C₅	C₃×#41	1	4	yes	—
264	C₂×Dic₅	—	2	2	no	—
265	C₂×Dic₅	—	2	2	no	—
266	C₂×Dic₅	—	2	2	no	—
267	C₂×Dic₅	—	2	2	no	—
268	C₂×Dic₅	—	2	2	no	—
269	C₂×Dic₅	—	2	2	no	—
270	C₂×Dic₅	—	2	2	no	—
271	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
272	C₂×Dic₅	C₃×#41	1	4	yes	—
273	D₂₀	—	4	4	no	—
274	C₄×D₅	—	4	8	no	—
275	Dic₁₀	—	4	4	no	—
276	C₂²×Q₈	—	5	1	no	—
277	C₂²×D₄	—	5	1	no	—
278	C₂³×C₄	—	5	2	no	—
279	#124	—	5	8	no	—
280	C₂×C₄⋊C₄	—	5	2	no	—
281	C₂×C₂²⋊C₄	—	5	2	no	—
282	C₂×C₂²⋊C₄	—	5	2	no	—
283	C₂×C₂²⋊C₄	—	5	2	no	—
284	C₂×C₂²⋊C₄	—	5	2	no	—
285	C₂×C₂²⋊C₄	—	5	2	no	—
286	C₂×C₄²	—	5	2	no	—
287	C₂×C₄²	—	5	2	no	—
288	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
289	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
290	#95	—	5	1	no	—
291	#95	—	5	2	no	—
292	#95	—	5	1	no	—
293	#95	—	5	2	no	—
294	#95	—	5	2	no	—
295	#95	C₂×C₃×D₅	1	1	yes	characteristic
296	#95	C₂×C₃×D₅	1	2	yes	—
297	#95	C₂×C₃×D₅	1	1	yes	characteristic
298	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
299	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
300	C₂×C₃×C₅	#518	1	1	yes	characteristic
301	C₂×C₃×C₅	#551	1	2	yes	—
302	C₂×C₃×C₅	#555	1	2	yes	—
303	C₃×D₅	—	4	4	no	—
304	C₂³×C₃	—	5	4	no	—
305	C₂³×C₃	—	10	2	no	—
306	C₂³×C₃	—	10	2	no	—
307	C₂³×C₃	—	10	2	no	—
308	C₂³×C₃	—	10	2	no	—
309	C₂³×C₃	—	10	2	no	—
310	C₂³×C₃	—	10	2	no	—
311	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
312	C₃×Q₈	—	20	4	no	—
313	C₃×D₄	—	20	4	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	1	no	—
319	C₂×C₃×C₄	—	2	1	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	2	no	—
322	C₂×C₃×C₄	—	2	2	no	—
323	C₂×C₃×C₄	—	5	4	no	—
324	C₂×C₃×C₄	—	5	4	no	—
325	C₂×C₃×C₄	—	10	2	no	—
326	C₂×C₃×C₄	—	10	2	no	—
327	C₂×C₃×C₄	—	10	2	no	—
328	C₂×C₃×C₄	—	10	2	no	—
329	C₂×C₃×C₄	—	10	2	no	—
330	C₂×C₃×C₄	—	10	2	no	—
331	C₂×C₃×C₄	—	10	2	no	—
332	C₂×C₃×C₄	—	20	8	no	—
333	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
334	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
335	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
336	C₂×C₃×C₄	#709	1	4	yes	—
337	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
338	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
339	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
340	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
341	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
342	C₂×D₅	—	2	4	no	—
343	C₂×D₅	—	2	4	no	—
344	C₂×D₅	—	2	4	no	—
345	C₂×D₅	—	4	2	no	—
346	C₂×D₅	—	4	2	no	—
347	C₂×D₅	—	4	2	no	—
348	C₂×D₅	—	4	2	no	—
349	C₄×C₅	—	2	2	no	—
350	C₄×C₅	—	2	2	no	—
351	C₄×C₅	—	2	2	no	—
352	C₄×C₅	—	2	4	no	—
353	C₄×C₅	—	4	2	no	—
354	Dic₅	—	2	4	no	—
355	Dic₅	—	2	4	no	—
356	Dic₅	—	4	2	no	—
357	C₂⁴	—	5	2	no	—
358	C₂×Q₈	—	5	4	no	—
359	C₂×Q₈	—	20	1	no	—
360	C₂×Q₈	—	20	1	no	—
361	C₂×D₄	—	5	4	no	—
362	C₂×D₄	—	20	1	no	—
363	C₂×D₄	—	20	1	no	—
364	C₂²×C₄	—	5	2	no	—
365	C₂²×C₄	—	5	2	no	—
366	C₂²×C₄	—	5	2	no	—
367	C₂²×C₄	—	10	4	no	—
368	C₂²×C₄	—	10	4	no	—
369	C₂²×C₄	—	20	2	no	—
370	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
371	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
372	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
373	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
374	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
375	C₄⋊C₄	—	20	2	no	—
376	C₂²⋊C₄	—	5	8	no	—
377	C₂²⋊C₄	—	5	8	no	—
378	C₂²⋊C₄	—	10	4	no	—
379	C₂²⋊C₄	—	10	4	no	—
380	C₂²⋊C₄	—	20	2	no	—
381	C₄²	—	2	4	no	—
382	C₄²	—	10	4	no	—
383	C₄²	—	20	2	no	—
384	C₄²	C₃×C₄×D₅	1	4	yes	complemented
385	C₃×C₅	#2372	1	1	yes	characteristic, complemented, Hall
386	C₂²×C₃	—	10	4	no	—
387	C₂²×C₃	—	10	4	no	—
388	C₂²×C₃	—	10	4	no	—
389	C₂²×C₃	—	20	2	no	—
390	C₂²×C₃	—	20	2	no	—
391	C₂²×C₃	—	20	2	no	—
392	C₂²×C₃	—	20	2	no	—
393	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
394	C₂²×C₃	C₂×#709	1	2	yes	—
395	C₂²×C₃	D₅×#41	1	2	yes	—
396	C₂²×C₃	#4149	1	1	yes	characteristic
397	C₂²×C₃	#4149	1	1	yes	characteristic
398	C₃×C₄	—	2	2	no	—
399	C₃×C₄	—	2	2	no	—
400	C₃×C₄	—	2	2	no	—
401	C₃×C₄	—	2	4	no	—
402	C₃×C₄	—	4	2	no	—
403	C₃×C₄	—	10	4	no	—
404	C₃×C₄	—	10	4	no	—
405	C₃×C₄	—	20	2	no	—
406	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
407	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
408	C₂×C₅	C₃×#518	1	1	yes	characteristic
409	C₂×C₅	C₃×#551	1	2	yes	—
410	C₂×C₅	C₃×#555	1	2	yes	—
411	D₅	—	4	4	no	—
412	C₂³	—	5	4	no	—
413	C₂³	—	10	2	no	—
414	C₂³	—	10	2	no	—
415	C₂³	—	10	2	no	—
416	C₂³	—	10	2	no	—
417	C₂³	—	10	2	no	—
418	C₂³	—	10	2	no	—
419	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
420	Q₈	—	20	4	no	—
421	D₄	—	20	4	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	5	4	no	—
432	C₂×C₄	—	5	4	no	—
433	C₂×C₄	—	10	2	no	—
434	C₂×C₄	—	10	2	no	—
435	C₂×C₄	—	10	2	no	—
436	C₂×C₄	—	10	2	no	—
437	C₂×C₄	—	10	2	no	—
438	C₂×C₄	—	10	2	no	—
439	C₂×C₄	—	10	2	no	—
440	C₂×C₄	—	20	8	no	—
441	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
442	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
443	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
444	C₂×C₄	C₃×#709	1	4	yes	—
445	C₂×C₃	—	20	4	no	—
446	C₂×C₃	C₄×#709	1	1	yes	characteristic
447	C₂×C₃	#65855	1	1	yes	characteristic
448	C₂×C₃	#65856	1	1	yes	characteristic
449	C₂×C₃	#65861	1	2	yes	—
450	C₂×C₃	#65866	1	2	yes	—
451	C₅	C₃×#2372	1	1	yes	characteristic, complemented, Sylow
452	C₂²	—	10	4	no	—
453	C₂²	—	10	4	no	—
454	C₂²	—	10	4	no	—
455	C₂²	—	20	2	no	—
456	C₂²	—	20	2	no	—
457	C₂²	—	20	2	no	—
458	C₂²	—	20	2	no	—
459	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
460	C₂²	C₂×C₃×#709	1	2	yes	—
461	C₂²	C₃×D₅×#41	1	2	yes	—
462	C₂²	C₃×#4149	1	1	yes	characteristic
463	C₂²	C₃×#4149	1	1	yes	characteristic
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	2	4	no	—
467	C₄	—	2	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	10	4	no	—
470	C₄	—	10	4	no	—
471	C₄	—	20	2	no	—
472	C₃	#10605126	1	1	yes	characteristic, direct product factor, Sylow
473	C₂	—	20	4	no	—
474	C₂	C₃×C₄×#709	1	1	yes	characteristic
475	C₂	C₃×#65855	1	1	yes	characteristic
476	C₂	C₃×#65856	1	1	yes	characteristic
477	C₂	C₃×#65861	1	2	yes	—
478	C₂	C₃×#65866	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	C₂²×C₃×D₂₀	C₂²
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×#376	D₅
hypocenter	C₅	C₃×#2372
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
3. C₃×#65229	C₂	semidirect
4. C₃×C₄×#685	C₂	semidirect
5. C₃×#65221	C₂	semidirect
6. C₃×#64958	C₂	semidirect
7. C₃×#64955	C₂	semidirect
9. C₃×#64935	C₂	semidirect
10. #10605126	C₃	direct (N × H)
24. C₃×#4021	C₄	semidirect
35. C₅×#376	C₂×C₃	semidirect
36. #65229	C₂×C₃	semidirect
37. C₄×#685	C₂×C₃	semidirect
38. #65221	C₂×C₃	semidirect
39. #64958	C₂×C₃	semidirect
40. #64955	C₂×C₃	semidirect
42. #64935	C₂×C₃	semidirect
60. C₂×C₃×Dic₁₀	C₂×C₄	semidirect
62. C₃×C₄²×C₅	C₂×C₄	semidirect
66. C₃×#685	C₂×C₄	semidirect
67. C₃×#685	C₂×C₄	semidirect
79. C₃×#376	D₅	semidirect
93. #4021	C₃×C₄	semidirect
175. C₂×Dic₁₀	C₂×C₃×C₄	semidirect
177. C₄²×C₅	C₂×C₃×C₄	semidirect
181. #685	C₂×C₃×C₄	semidirect
182. #685	C₂×C₃×C₄	semidirect
194. #376	C₃×D₅	semidirect
242. C₃×C₄²	C₄×D₅	semidirect
384. C₄²	C₃×C₄×D₅	semidirect
385. C₃×C₅	#2372	semidirect
451. C₅	C₃×#2372	semidirect
472. C₃	#10605126	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×#4021	2
C₃×C₅×#376	2
C₃×#65229	2
C₃×C₄×#685	2
C₃×#65221	2
C₃×#64958	2
C₃×#64955	2
C₃×#64954	2
C₃×#64935	2
#10605126	3
C₃×#2372	5

Subgroups — C3×#10605126 #14330137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10605126 #14330137