Subgroups — C₃×#10605304 #14326022

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#709	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×D₂₀	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65245	C₂	1	4	yes	maximal, complemented
6	C₃×#65218	C₂	1	2	yes	maximal, complemented
7	C₃×#64953	C₂	1	2	yes	maximal, complemented
8	C₃×D₅×#95	C₂	1	2	yes	maximal, complemented
9	#10605304	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
12	C₂×C₃×#709	—	2	8	no	—
13	C₂×C₃×#709	C₄	1	8	yes	complemented
14	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×D₅	C₂²	1	4	yes	—
16	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
17	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
20	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
21	C₂×C₃×#685	C₂²	1	4	yes	—
22	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
23	C₃×C₄×D₂₀	—	2	8	no	—
24	C₃×C₅×#95	C₂²	1	1	yes	characteristic
25	C₃×C₅×#95	C₂²	1	1	yes	characteristic
26	C₃×#3963	C₂²	1	2	yes	—
27	C₃×#3963	C₂²	1	4	yes	—
28	C₃×#3963	C₂²	1	4	yes	—
29	C₃×#2339	—	5	1	no	maximal, Hall
30	C₂²×#709	C₂×C₃	1	1	yes	characteristic
31	C₂×C₄×D₂₀	C₂×C₃	1	2	yes	complemented
32	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
33	#65501	C₂×C₃	1	1	yes	characteristic, complemented
34	#65245	C₂×C₃	1	4	yes	complemented
35	#65218	C₂×C₃	1	2	yes	complemented
36	#64953	C₂×C₃	1	2	yes	complemented
37	D₅×#95	C₂×C₃	1	2	yes	complemented
38	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
39	C₂³×C₃×D₅	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	—	2	4	no	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	complemented
42	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
47	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	8	yes	complemented
48	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
49	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
50	C₃×#709	—	2	32	no	—
51	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	—
52	C₂×C₃×D₂₀	D₄	1	8	yes	—
53	C₂×C₃×C₄×D₅	—	2	8	no	—
54	C₂×C₃×C₄×D₅	—	2	8	no	—
55	C₂×C₃×C₄×D₅	—	2	8	no	—
56	C₂×C₃×C₄×D₅	—	4	4	no	—
57	C₂×C₃×C₄×D₅	C₂×C₄	1	8	yes	complemented
58	C₂×C₃×Dic₁₀	—	2	4	no	—
59	C₂×C₃×Dic₁₀	C₂×C₄	1	4	yes	complemented
60	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
61	C₃×C₄²×C₅	—	2	4	no	—
62	C₃×C₂²⋊Dic₅	—	4	2	no	—
63	C₃×#685	—	2	8	no	—
64	C₃×C₄⋊Dic₅	—	2	4	no	—
65	C₂²×C₃×#41	—	5	1	no	—
66	C₂×C₃×C₄×D₄	—	5	2	no	—
67	C₃×#391	—	5	2	no	—
68	C₃×#386	—	5	4	no	—
69	C₃×#381	—	5	2	no	—
70	C₃×#380	—	5	1	no	—
71	C₃×C₄×C₂²⋊C₄	D₅	1	1	yes	characteristic, complemented
72	C₂×C₃×#95	—	5	2	no	—
73	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
74	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
75	C₂×#709	—	2	8	no	—
76	C₂×#709	C₃×C₄	1	8	yes	complemented
77	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
78	C₂²×C₄×D₅	C₂²×C₃	1	4	yes	—
79	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
80	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
82	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
83	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
84	C₂×#685	C₂²×C₃	1	4	yes	—
85	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
86	C₄×D₂₀	—	2	8	no	—
87	C₅×#95	C₂²×C₃	1	1	yes	characteristic
88	C₅×#95	C₂²×C₃	1	1	yes	characteristic
89	#3963	C₂²×C₃	1	2	yes	—
90	#3963	C₂²×C₃	1	4	yes	—
91	#3963	C₂²×C₃	1	4	yes	—
92	#2339	—	5	1	no	Sylow
93	C₂³×C₃×C₅	—	2	2	no	—
94	C₂³×C₃×C₅	—	2	2	no	—
95	C₂³×C₃×C₅	—	2	1	no	—
96	C₂³×C₃×C₅	—	2	1	no	—
97	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
98	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
99	C₂²×C₃×D₅	—	2	4	no	—
100	C₂²×C₃×D₅	—	2	2	no	—
101	C₂²×C₃×D₅	—	2	2	no	—
102	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
103	C₂²×C₃×D₅	C₂×D₄	1	8	yes	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	8	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
114	C₂×C₃×C₄×C₅	#41	1	4	yes	complemented
115	C₃×C₂²⋊D₅	—	2	16	no	—
116	C₂×C₃×Dic₅	—	2	4	no	—
117	C₂×C₃×Dic₅	—	2	4	no	—
118	C₂×C₃×Dic₅	—	2	4	no	—
119	C₂×C₃×Dic₅	—	2	4	no	—
120	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
121	C₃×D₂₀	C₂²⋊C₄	1	16	yes	complemented
122	C₃×C₄×D₅	—	2	16	no	—
123	C₃×C₄×D₅	—	4	16	no	—
124	C₃×Dic₁₀	—	2	8	no	—
125	C₂×C₃×#41	—	5	8	no	—
126	C₂×C₃×#41	—	10	8	no	—
127	C₂²×C₃×Q₈	—	5	1	no	—
128	C₂²×C₃×D₄	—	5	2	no	—
129	C₂²×C₃×D₄	—	5	1	no	—
130	C₂³×C₃×C₄	—	5	2	no	—
131	C₂³×C₃×C₄	—	5	4	no	—
132	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
133	C₃×C₄×D₄	—	10	8	no	—
134	C₂×C₃×C₄⋊C₄	—	5	2	no	—
135	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
136	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
137	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
138	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
139	C₃×#95	—	5	2	no	—
140	C₃×#95	—	5	4	no	—
141	C₃×#95	—	5	4	no	—
142	C₃×#95	C₂×D₅	1	1	yes	characteristic
143	C₃×#95	C₂×D₅	1	1	yes	characteristic
144	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
145	C₂³×D₅	C₂³×C₃	1	2	yes	—
146	C₂²×C₄×C₅	—	2	4	no	—
147	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	complemented
148	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
149	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
151	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
152	C₂×C₂²⋊D₅	—	2	8	no	—
153	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	8	yes	complemented
154	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
155	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
156	#709	—	2	32	no	—
157	C₂×D₂₀	C₂×C₃×C₄	1	4	yes	—
158	C₂×D₂₀	C₃×D₄	1	8	yes	—
159	C₂×C₄×D₅	—	2	8	no	—
160	C₂×C₄×D₅	—	2	8	no	—
161	C₂×C₄×D₅	—	2	8	no	—
162	C₂×C₄×D₅	—	4	4	no	—
163	C₂×C₄×D₅	C₂×C₃×C₄	1	8	yes	complemented
164	C₂×Dic₁₀	—	2	4	no	—
165	C₂×Dic₁₀	C₂×C₃×C₄	1	4	yes	complemented
166	C₅×C₂²⋊C₄	—	2	4	no	—
167	C₄²×C₅	—	2	4	no	—
168	C₂²⋊Dic₅	—	4	2	no	—
169	#685	—	2	8	no	—
170	C₄⋊Dic₅	—	2	4	no	—
171	C₂²×#41	—	5	1	no	—
172	C₂×C₄×D₄	—	5	2	no	—
173	#391	—	5	2	no	—
174	#386	—	5	4	no	—
175	#381	—	5	2	no	—
176	#380	—	5	1	no	—
177	C₄×C₂²⋊C₄	C₃×D₅	1	1	yes	characteristic, complemented
178	C₂×#95	—	5	2	no	—
179	C₂²×C₃×C₅	—	2	2	no	—
180	C₂²×C₃×C₅	—	2	2	no	—
181	C₂²×C₃×C₅	—	2	2	no	—
182	C₂²×C₃×C₅	—	4	2	no	—
183	C₂²×C₃×C₅	—	4	2	no	—
184	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
185	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
186	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
187	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
189	C₂×C₃×D₅	—	2	4	no	—
190	C₂×C₃×D₅	—	2	4	no	—
191	C₂×C₃×D₅	—	2	8	no	—
192	C₂×C₃×D₅	—	2	8	no	—
193	C₂×C₃×D₅	C₂×C₂²⋊C₄	1	8	yes	—
194	C₃×C₄×C₅	—	2	2	no	—
195	C₃×C₄×C₅	—	2	4	no	—
196	C₃×C₄×C₅	—	4	2	no	—
197	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
198	C₃×Dic₅	—	2	4	no	—
199	C₃×Dic₅	—	4	4	no	—
200	C₂⁴×C₃	—	5	2	no	—
201	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
202	C₃×#41	—	10	32	no	—
203	C₂×C₃×Q₈	—	5	4	no	—
204	C₂×C₃×Q₈	—	10	4	no	—
205	C₂×C₃×D₄	—	5	8	no	—
206	C₂×C₃×D₄	—	5	4	no	—
207	C₂×C₃×D₄	—	5	8	no	—
208	C₂×C₃×D₄	—	10	8	no	—
209	C₂²×C₃×C₄	—	2	4	no	—
210	C₂²×C₃×C₄	—	5	2	no	—
211	C₂²×C₃×C₄	—	5	8	no	—
212	C₂²×C₃×C₄	—	5	4	no	—
213	C₂²×C₃×C₄	—	10	8	no	—
214	C₂²×C₃×C₄	—	10	8	no	—
215	C₂²×C₃×C₄	—	10	8	no	—
216	C₂²×C₃×C₄	—	20	4	no	—
217	C₂²×C₃×C₄	C₄×D₅	1	4	yes	complemented
218	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
219	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
221	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
222	C₃×C₄⋊C₄	—	10	4	no	—
223	C₃×C₂²⋊C₄	—	2	4	no	—
224	C₃×C₂²⋊C₄	—	10	8	no	—
225	C₃×C₂²⋊C₄	—	20	2	no	—
226	C₃×C₄²	—	2	4	no	—
227	C₂³×C₅	—	2	2	no	—
228	C₂³×C₅	—	2	2	no	—
229	C₂³×C₅	—	2	1	no	—
230	C₂³×C₅	—	2	1	no	—
231	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
232	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
233	C₂²×D₅	—	2	4	no	—
234	C₂²×D₅	—	2	2	no	—
235	C₂²×D₅	—	2	2	no	—
236	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
237	C₂²×D₅	C₂×C₃×D₄	1	8	yes	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	8	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
246	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
247	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
248	C₂×C₄×C₅	C₃×#41	1	4	yes	complemented
249	C₂²⋊D₅	—	2	16	no	—
250	C₂×Dic₅	—	2	4	no	—
251	C₂×Dic₅	—	2	4	no	—
252	C₂×Dic₅	—	2	4	no	—
253	C₂×Dic₅	—	2	4	no	—
254	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
255	D₂₀	C₃×C₂²⋊C₄	1	16	yes	complemented
256	C₄×D₅	—	2	16	no	—
257	C₄×D₅	—	4	16	no	—
258	Dic₁₀	—	2	8	no	—
259	C₂×#41	—	5	8	no	—
260	C₂×#41	—	10	8	no	—
261	C₂²×Q₈	—	5	1	no	—
262	C₂²×D₄	—	5	2	no	—
263	C₂²×D₄	—	5	1	no	—
264	C₂³×C₄	—	5	2	no	—
265	C₂³×C₄	—	5	4	no	—
266	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
267	C₄×D₄	—	10	8	no	—
268	C₂×C₄⋊C₄	—	5	2	no	—
269	C₂×C₂²⋊C₄	—	5	4	no	—
270	C₂×C₂²⋊C₄	—	5	2	no	—
271	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
272	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
273	#95	—	5	2	no	—
274	#95	—	5	4	no	—
275	#95	—	5	4	no	—
276	#95	C₂×C₃×D₅	1	1	yes	characteristic
277	#95	C₂×C₃×D₅	1	1	yes	characteristic
278	C₂×C₃×C₅	—	4	2	no	—
279	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
281	C₂×C₃×C₅	#520	1	1	yes	characteristic
282	C₂×C₃×C₅	#546	1	2	yes	—
283	C₂×C₃×C₅	#547	1	2	yes	—
284	C₃×D₅	—	2	8	no	—
285	C₂³×C₃	—	2	2	no	—
286	C₂³×C₃	—	2	2	no	—
287	C₂³×C₃	—	2	1	no	—
288	C₂³×C₃	—	2	1	no	—
289	C₂³×C₃	—	5	4	no	—
290	C₂³×C₃	—	5	8	no	—
291	C₂³×C₃	—	10	4	no	—
292	C₂³×C₃	—	10	2	no	—
293	C₂³×C₃	—	10	2	no	—
294	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
295	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
296	C₃×Q₈	—	10	8	no	—
297	C₃×D₄	—	5	16	no	—
298	C₃×D₄	—	10	16	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	8	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	2	2	no	—
305	C₂×C₃×C₄	—	2	2	no	—
306	C₂×C₃×C₄	—	5	4	no	—
307	C₂×C₃×C₄	—	10	16	no	—
308	C₂×C₃×C₄	—	10	4	no	—
309	C₂×C₃×C₄	—	10	4	no	—
310	C₂×C₃×C₄	—	10	4	no	—
311	C₂×C₃×C₄	—	10	4	no	—
312	C₂×C₃×C₄	—	20	16	no	—
313	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
314	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
315	C₂×C₃×C₄	#709	1	4	yes	complemented
316	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
317	C₂²×C₅	—	2	2	no	—
318	C₂²×C₅	—	2	2	no	—
319	C₂²×C₅	—	2	2	no	—
320	C₂²×C₅	—	4	2	no	—
321	C₂²×C₅	—	4	2	no	—
322	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
323	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
324	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
325	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
326	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
327	C₂×D₅	—	2	4	no	—
328	C₂×D₅	—	2	4	no	—
329	C₂×D₅	—	2	8	no	—
330	C₂×D₅	—	2	8	no	—
331	C₂×D₅	C₂×C₃×C₂²⋊C₄	1	8	yes	—
332	C₄×C₅	—	2	2	no	—
333	C₄×C₅	—	2	4	no	—
334	C₄×C₅	—	4	2	no	—
335	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
336	Dic₅	—	2	4	no	—
337	Dic₅	—	4	4	no	—
338	C₂⁴	—	5	2	no	—
339	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
340	#41	—	10	32	no	—
341	C₂×Q₈	—	5	4	no	—
342	C₂×Q₈	—	10	4	no	—
343	C₂×D₄	—	5	8	no	—
344	C₂×D₄	—	5	4	no	—
345	C₂×D₄	—	5	8	no	—
346	C₂×D₄	—	10	8	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	5	2	no	—
349	C₂²×C₄	—	5	8	no	—
350	C₂²×C₄	—	5	4	no	—
351	C₂²×C₄	—	10	8	no	—
352	C₂²×C₄	—	10	8	no	—
353	C₂²×C₄	—	10	8	no	—
354	C₂²×C₄	—	20	4	no	—
355	C₂²×C₄	C₃×C₄×D₅	1	4	yes	complemented
356	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
357	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
358	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
359	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
360	C₄⋊C₄	—	10	4	no	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	10	8	no	—
363	C₂²⋊C₄	—	20	2	no	—
364	C₄²	—	2	4	no	—
365	C₃×C₅	#2339	1	1	yes	characteristic, complemented, Hall
366	C₂²×C₃	—	2	2	no	—
367	C₂²×C₃	—	2	2	no	—
368	C₂²×C₃	—	2	2	no	—
369	C₂²×C₃	—	4	2	no	—
370	C₂²×C₃	—	4	2	no	—
371	C₂²×C₃	—	5	8	no	—
372	C₂²×C₃	—	10	4	no	—
373	C₂²×C₃	—	10	4	no	—
374	C₂²×C₃	—	10	8	no	—
375	C₂²×C₃	—	10	8	no	—
376	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
377	C₂²×C₃	C₂×#709	1	2	yes	—
378	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
379	C₂²×C₃	#4149	1	1	yes	characteristic
380	C₂²×C₃	#4150	1	1	yes	characteristic
381	C₃×C₄	—	2	2	no	—
382	C₃×C₄	—	2	4	no	—
383	C₃×C₄	—	4	2	no	—
384	C₃×C₄	—	10	4	no	—
385	C₃×C₄	—	20	4	no	—
386	C₃×C₄	D₅×C₂²⋊C₄	1	4	yes	—
387	C₂×C₅	—	4	2	no	—
388	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
389	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
390	C₂×C₅	C₃×#520	1	1	yes	characteristic
391	C₂×C₅	C₃×#546	1	2	yes	—
392	C₂×C₅	C₃×#547	1	2	yes	—
393	D₅	—	2	8	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	2	1	no	—
398	C₂³	—	5	4	no	—
399	C₂³	—	5	8	no	—
400	C₂³	—	10	4	no	—
401	C₂³	—	10	2	no	—
402	C₂³	—	10	2	no	—
403	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
404	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
405	Q₈	—	10	8	no	—
406	D₄	—	5	16	no	—
407	D₄	—	10	16	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	8	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	5	4	no	—
416	C₂×C₄	—	10	16	no	—
417	C₂×C₄	—	10	4	no	—
418	C₂×C₄	—	10	4	no	—
419	C₂×C₄	—	10	4	no	—
420	C₂×C₄	—	10	4	no	—
421	C₂×C₄	—	20	16	no	—
422	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
423	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
424	C₂×C₄	C₃×#709	1	4	yes	complemented
425	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
426	C₂×C₃	—	4	2	no	—
427	C₂×C₃	—	10	8	no	—
428	C₂×C₃	C₄×#709	1	1	yes	characteristic
429	C₂×C₃	C₂×D₅×C₂²⋊C₄	1	1	yes	characteristic
430	C₂×C₃	#65857	1	1	yes	characteristic
431	C₂×C₃	#65884	1	2	yes	—
432	C₂×C₃	#65885	1	2	yes	—
433	C₅	C₃×#2339	1	1	yes	characteristic, complemented, Sylow
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	5	8	no	—
440	C₂²	—	10	4	no	—
441	C₂²	—	10	8	no	—
442	C₂²	—	10	8	no	—
443	C₂²	—	10	4	no	—
444	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
445	C₂²	C₂×C₃×#709	1	2	yes	—
446	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
447	C₂²	C₃×#4149	1	1	yes	characteristic
448	C₂²	C₃×#4150	1	1	yes	characteristic
449	C₄	—	2	4	no	—
450	C₄	—	2	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	10	4	no	—
453	C₄	—	20	4	no	—
454	C₄	C₃×D₅×C₂²⋊C₄	1	4	yes	—
455	C₃	#10605304	1	1	yes	characteristic, direct product factor, Sylow
456	C₂	—	4	2	no	—
457	C₂	—	10	8	no	—
458	C₂	C₃×C₄×#709	1	1	yes	characteristic
459	C₂	C₂×C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
460	C₂	C₃×#65857	1	1	yes	characteristic
461	C₂	C₃×#65884	1	2	yes	—
462	C₂	C₃×#65885	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×C₂²⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₃×#709	C₂
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×C₂²⋊C₄	D₅
hypocenter	C₅	C₃×#2339
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×C₄×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄×D₂₀	C₂	semidirect
3. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
4. C₃×#65501	C₂	semidirect
5. C₃×#65245	C₂	semidirect
6. C₃×#65218	C₂	semidirect
7. C₃×#64953	C₂	semidirect
8. C₃×D₅×#95	C₂	semidirect
9. #10605304	C₃	direct (N × H)
13. C₂×C₃×#709	C₄	semidirect
31. C₂×C₄×D₂₀	C₂×C₃	semidirect
32. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
33. #65501	C₂×C₃	semidirect
34. #65245	C₂×C₃	semidirect
35. #65218	C₂×C₃	semidirect
36. #64953	C₂×C₃	semidirect
37. D₅×#95	C₂×C₃	semidirect
41. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
47. C₂×C₃×C₂²⋊D₅	C₂×C₄	semidirect
57. C₂×C₃×C₄×D₅	C₂×C₄	semidirect
59. C₂×C₃×Dic₁₀	C₂×C₄	semidirect
71. C₃×C₄×C₂²⋊C₄	D₅	semidirect
76. C₂×#709	C₃×C₄	semidirect
114. C₂×C₃×C₄×C₅	#41	semidirect
121. C₃×D₂₀	C₂²⋊C₄	semidirect
147. C₂²×C₄×C₅	C₂×C₃×C₄	semidirect
153. C₂×C₂²⋊D₅	C₂×C₃×C₄	semidirect
163. C₂×C₄×D₅	C₂×C₃×C₄	semidirect
165. C₂×Dic₁₀	C₂×C₃×C₄	semidirect
177. C₄×C₂²⋊C₄	C₃×D₅	semidirect
217. C₂²×C₃×C₄	C₄×D₅	semidirect
248. C₂×C₄×C₅	C₃×#41	semidirect
255. D₂₀	C₃×C₂²⋊C₄	semidirect
315. C₂×C₃×C₄	#709	semidirect
355. C₂²×C₄	C₃×C₄×D₅	semidirect
365. C₃×C₅	#2339	semidirect
424. C₂×C₄	C₃×#709	semidirect
433. C₅	C₃×#2339	semidirect
455. C₃	#10605304	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×#709	2
C₂×C₃×C₄×D₂₀	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₃×#65501	2
C₃×#65245	2
C₃×#65218	2
C₃×#64953	2
C₃×D₅×#95	2
#10605304	3
C₃×#2339	5

Subgroups — C3×#10605304 #14326022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10605304 #14326022