Subgroups — C₃×#10608023 #14321948

Order 1920.

1304 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4082	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×D₄×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#4033	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic
5	C₃×#65266	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65233	C₂	1	4	yes	maximal, complemented
7	C₃×C₂²⋊C₄×Dic₅	C₂	1	4	yes	maximal, complemented
8	C₃×C₄²×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65218	C₂	1	1	yes	maximal, characteristic, complemented
10	#10608023	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂³×C₃×Dic₅	C₂²	1	2	yes	—
13	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
18	C₂×C₃×C₂²⋊Dic₅	C₂²	1	4	yes	—
19	C₃×#4082	C₄	1	8	yes	complemented
20	C₃×D₄×Dic₅	—	2	4	no	—
21	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×#683	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	1	yes	characteristic
27	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
28	C₃×#4033	—	2	4	no	—
29	C₃×#3963	C₂²	1	4	yes	—
30	C₃×#3963	C₂²	1	4	yes	—
31	C₃×C₄×#124	—	5	1	no	maximal, Hall
32	C₂×#4082	C₂×C₃	1	1	yes	characteristic
33	C₂×D₄×Dic₅	C₂×C₃	1	1	yes	characteristic
34	C₂×#4033	C₂×C₃	1	1	yes	characteristic, complemented
35	C₅×#390	C₂×C₃	1	1	yes	characteristic
36	#65266	C₂×C₃	1	1	yes	characteristic, complemented
37	#65233	C₂×C₃	1	4	yes	complemented
38	C₂²⋊C₄×Dic₅	C₂×C₃	1	4	yes	complemented
39	C₄²×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
40	#65218	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
42	C₂×C₃×C₅×D₄	—	2	2	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂²×C₃×Dic₅	—	2	4	no	—
49	C₂²×C₃×Dic₅	—	2	8	no	—
50	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
51	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
52	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
53	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
55	C₂×C₃×Dic₁₀	—	2	2	no	—
56	C₂×C₃×Dic₁₀	—	2	2	no	—
57	C₂×C₃×Dic₁₀	C₂×C₄	1	4	yes	complemented
58	C₃×C₅×C₄⋊C₄	—	2	2	no	—
59	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
60	C₃×C₄²×C₅	—	2	2	no	—
61	C₃×C₂²⋊Dic₅	—	2	4	no	—
62	C₃×C₂²⋊Dic₅	C₂×C₄	1	16	yes	complemented
63	C₃×C₄⋊Dic₅	—	2	2	no	—
64	C₃×#683	—	2	4	no	—
65	C₃×C₄×Dic₅	—	2	4	no	—
66	C₃×C₄×Dic₅	—	2	4	no	—
67	C₃×C₄×Dic₅	—	2	4	no	—
68	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	complemented
69	C₃×C₄×Dic₅	D₄	1	4	yes	—
70	C₂×C₃×#124	—	5	1	no	—
71	C₂×C₃×C₄×Q₈	—	5	1	no	—
72	C₂×C₃×C₄×D₄	—	5	1	no	—
73	C₃×#391	—	5	1	no	—
74	C₃×#390	D₅	1	1	yes	characteristic
75	C₃×#388	—	5	4	no	—
76	C₃×#382	—	5	1	no	—
77	C₃×C₄×C₂²⋊C₄	—	5	4	no	—
78	C₃×C₄³	—	5	1	no	—
79	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
80	C₂³×Dic₅	C₂²×C₃	1	2	yes	—
81	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
84	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
86	C₂×C₂²⋊Dic₅	C₂²×C₃	1	4	yes	—
87	#4082	C₃×C₄	1	8	yes	complemented
88	D₄×Dic₅	—	2	4	no	—
89	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
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	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
94	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
96	#4033	—	2	4	no	—
97	#3963	C₂²×C₃	1	4	yes	—
98	#3963	C₂²×C₃	1	4	yes	—
99	C₄×#124	—	5	1	no	Sylow
100	C₂³×C₃×C₅	—	2	2	no	—
101	C₂³×C₃×C₅	—	2	4	no	—
102	C₂³×C₃×C₅	—	2	4	no	—
103	C₂³×C₃×C₅	—	2	2	no	—
104	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
105	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
106	C₃×C₅×D₄	—	2	8	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	4	no	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	#41	1	4	yes	—
114	C₂×C₃×C₄×C₅	#41	1	2	yes	—
115	C₂×C₃×Dic₅	—	2	2	no	—
116	C₂×C₃×Dic₅	—	2	2	no	—
117	C₂×C₃×Dic₅	—	2	2	no	—
118	C₂×C₃×Dic₅	—	2	2	no	—
119	C₂×C₃×Dic₅	—	2	2	no	—
120	C₂×C₃×Dic₅	—	2	2	no	—
121	C₂×C₃×Dic₅	—	2	4	no	—
122	C₂×C₃×Dic₅	—	4	8	no	—
123	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
124	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
125	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
126	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
127	C₂×C₃×Dic₅	#41	1	4	yes	—
128	C₃×Dic₁₀	—	2	8	no	—
129	C₂²×C₃×Q₈	—	5	1	no	—
130	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
131	C₂³×C₃×C₄	—	5	2	no	—
132	C₃×#124	—	5	8	no	—
133	C₃×C₄×Q₈	—	10	4	no	—
134	C₃×C₄×D₄	—	10	4	no	—
135	C₂×C₃×C₄⋊C₄	—	5	1	no	—
136	C₂×C₃×C₄⋊C₄	—	5	2	no	—
137	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
138	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
139	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
140	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	4	yes	—
141	C₂×C₃×C₄²	—	5	1	no	—
142	C₂×C₃×C₄²	—	5	1	no	—
143	C₂×C₃×C₄²	—	5	2	no	—
144	C₂×C₃×C₄²	—	5	2	no	—
145	C₂×C₃×C₄²	—	5	2	no	—
146	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
147	C₃×#95	—	5	4	no	—
148	C₃×#95	—	5	4	no	—
149	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
150	C₂×C₅×D₄	—	2	2	no	—
151	C₂×C₅×D₄	—	2	2	no	—
152	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
153	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
154	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
155	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
156	C₂²×Dic₅	—	2	4	no	—
157	C₂²×Dic₅	—	2	8	no	—
158	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
159	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
160	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
161	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
162	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
163	C₂×Dic₁₀	—	2	2	no	—
164	C₂×Dic₁₀	—	2	2	no	—
165	C₂×Dic₁₀	C₂×C₃×C₄	1	4	yes	complemented
166	C₅×C₄⋊C₄	—	2	2	no	—
167	C₅×C₂²⋊C₄	—	2	8	no	—
168	C₄²×C₅	—	2	2	no	—
169	C₂²⋊Dic₅	—	2	4	no	—
170	C₂²⋊Dic₅	C₂×C₃×C₄	1	16	yes	complemented
171	C₄⋊Dic₅	—	2	2	no	—
172	#683	—	2	4	no	—
173	C₄×Dic₅	—	2	4	no	—
174	C₄×Dic₅	—	2	4	no	—
175	C₄×Dic₅	—	2	4	no	—
176	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	complemented
177	C₄×Dic₅	C₃×D₄	1	4	yes	—
178	C₂×#124	—	5	1	no	—
179	C₂×C₄×Q₈	—	5	1	no	—
180	C₂×C₄×D₄	—	5	1	no	—
181	#391	—	5	1	no	—
182	#390	C₃×D₅	1	1	yes	characteristic
183	#388	—	5	4	no	—
184	#382	—	5	1	no	—
185	C₄×C₂²⋊C₄	—	5	4	no	—
186	C₄³	—	5	1	no	—
187	C₂²×C₃×C₅	—	2	4	no	—
188	C₂²×C₃×C₅	—	2	8	no	—
189	C₂²×C₃×C₅	—	4	2	no	—
190	C₂²×C₃×C₅	—	4	4	no	—
191	C₂²×C₃×C₅	—	4	2	no	—
192	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
193	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
194	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
195	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
196	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
197	C₃×C₄×C₅	—	2	4	no	—
198	C₃×C₄×C₅	—	4	2	no	—
199	C₃×C₄×C₅	C₄×D₄	1	4	yes	—
200	C₃×Dic₅	—	2	4	no	—
201	C₃×Dic₅	—	2	4	no	—
202	C₃×Dic₅	—	2	2	no	—
203	C₃×Dic₅	—	4	2	no	—
204	C₃×Dic₅	#124	1	4	yes	complemented
205	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
206	C₂×C₃×Q₈	—	5	4	no	—
207	C₂×C₃×Q₈	—	10	2	no	—
208	C₂×C₃×Q₈	—	10	2	no	—
209	C₂×C₃×D₄	—	2	2	no	—
210	C₂×C₃×D₄	—	2	2	no	—
211	C₂×C₃×D₄	C₄×D₅	1	4	yes	—
212	C₂²×C₃×C₄	—	5	1	no	—
213	C₂²×C₃×C₄	—	5	2	no	—
214	C₂²×C₃×C₄	—	5	2	no	—
215	C₂²×C₃×C₄	—	5	1	no	—
216	C₂²×C₃×C₄	—	5	2	no	—
217	C₂²×C₃×C₄	—	10	4	no	—
218	C₂²×C₃×C₄	—	10	8	no	—
219	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
220	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
221	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
222	C₃×C₄⋊C₄	—	2	2	no	—
223	C₃×C₄⋊C₄	—	10	4	no	—
224	C₃×C₄⋊C₄	—	10	2	no	—
225	C₃×C₂²⋊C₄	—	2	8	no	—
226	C₃×C₂²⋊C₄	—	5	16	no	—
227	C₃×C₂²⋊C₄	—	10	4	no	—
228	C₃×C₄²	—	2	2	no	—
229	C₃×C₄²	—	5	4	no	—
230	C₃×C₄²	—	5	4	no	—
231	C₃×C₄²	—	10	4	no	—
232	C₃×C₄²	—	10	4	no	—
233	C₃×C₄²	—	10	4	no	—
234	C₂³×C₅	—	2	2	no	—
235	C₂³×C₅	—	2	4	no	—
236	C₂³×C₅	—	2	4	no	—
237	C₂³×C₅	—	2	2	no	—
238	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
239	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
240	C₅×D₄	—	2	8	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	4	no	—
245	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
246	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
247	C₂×C₄×C₅	C₃×#41	1	4	yes	—
248	C₂×C₄×C₅	C₃×#41	1	2	yes	—
249	C₂×Dic₅	—	2	2	no	—
250	C₂×Dic₅	—	2	2	no	—
251	C₂×Dic₅	—	2	2	no	—
252	C₂×Dic₅	—	2	2	no	—
253	C₂×Dic₅	—	2	2	no	—
254	C₂×Dic₅	—	2	2	no	—
255	C₂×Dic₅	—	2	4	no	—
256	C₂×Dic₅	—	4	8	no	—
257	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
258	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
259	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
260	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
261	C₂×Dic₅	C₃×#41	1	4	yes	—
262	Dic₁₀	—	2	8	no	—
263	C₂²×Q₈	—	5	1	no	—
264	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
265	C₂³×C₄	—	5	2	no	—
266	#124	—	5	8	no	—
267	C₄×Q₈	—	10	4	no	—
268	C₄×D₄	—	10	4	no	—
269	C₂×C₄⋊C₄	—	5	1	no	—
270	C₂×C₄⋊C₄	—	5	2	no	—
271	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	—	5	4	no	—
273	C₂×C₂²⋊C₄	—	5	2	no	—
274	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	4	yes	—
275	C₂×C₄²	—	5	1	no	—
276	C₂×C₄²	—	5	1	no	—
277	C₂×C₄²	—	5	2	no	—
278	C₂×C₄²	—	5	2	no	—
279	C₂×C₄²	—	5	2	no	—
280	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
281	#95	—	5	4	no	—
282	#95	—	5	4	no	—
283	C₂×C₃×C₅	—	4	4	no	—
284	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
285	C₂×C₃×C₅	C₄×#41	1	2	yes	—
286	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
287	C₂×C₃×C₅	#529	1	2	yes	—
288	C₂×C₃×C₅	#532	1	1	yes	characteristic
289	C₂³×C₃	—	2	2	no	—
290	C₂³×C₃	—	2	4	no	—
291	C₂³×C₃	—	2	2	no	—
292	C₂³×C₃	—	2	4	no	—
293	C₂³×C₃	C₂×C₄×D₅	1	4	yes	—
294	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
295	C₃×Q₈	—	10	8	no	—
296	C₃×D₄	—	2	8	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	4	no	—
301	C₂×C₃×C₄	—	5	2	no	—
302	C₂×C₃×C₄	—	5	4	no	—
303	C₂×C₃×C₄	—	5	4	no	—
304	C₂×C₃×C₄	—	5	4	no	—
305	C₂×C₃×C₄	—	5	2	no	—
306	C₂×C₃×C₄	—	10	2	no	—
307	C₂×C₃×C₄	—	10	2	no	—
308	C₂×C₃×C₄	—	10	2	no	—
309	C₂×C₃×C₄	—	10	2	no	—
310	C₂×C₃×C₄	—	10	2	no	—
311	C₂×C₃×C₄	—	10	2	no	—
312	C₂×C₃×C₄	—	10	4	no	—
313	C₂×C₃×C₄	—	20	8	no	—
314	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
315	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
316	C₂×C₃×C₄	#711	1	4	yes	—
317	C₂×C₃×C₄	#711	1	2	yes	—
318	C₂²×C₅	—	2	4	no	—
319	C₂²×C₅	—	2	8	no	—
320	C₂²×C₅	—	4	2	no	—
321	C₂²×C₅	—	4	4	no	—
322	C₂²×C₅	—	4	2	no	—
323	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
324	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
325	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
326	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
327	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
328	C₄×C₅	—	2	4	no	—
329	C₄×C₅	—	4	2	no	—
330	C₄×C₅	C₃×C₄×D₄	1	4	yes	—
331	Dic₅	—	2	4	no	—
332	Dic₅	—	2	4	no	—
333	Dic₅	—	2	2	no	—
334	Dic₅	—	4	2	no	—
335	Dic₅	C₃×#124	1	4	yes	complemented
336	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
337	C₂×Q₈	—	5	4	no	—
338	C₂×Q₈	—	10	2	no	—
339	C₂×Q₈	—	10	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	C₃×C₄×D₅	1	4	yes	—
343	C₂²×C₄	—	5	1	no	—
344	C₂²×C₄	—	5	2	no	—
345	C₂²×C₄	—	5	2	no	—
346	C₂²×C₄	—	5	1	no	—
347	C₂²×C₄	—	5	2	no	—
348	C₂²×C₄	—	10	4	no	—
349	C₂²×C₄	—	10	8	no	—
350	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
351	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
352	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	10	4	no	—
355	C₄⋊C₄	—	10	2	no	—
356	C₂²⋊C₄	—	2	8	no	—
357	C₂²⋊C₄	—	5	16	no	—
358	C₂²⋊C₄	—	10	4	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	5	4	no	—
361	C₄²	—	5	4	no	—
362	C₄²	—	10	4	no	—
363	C₄²	—	10	4	no	—
364	C₄²	—	10	4	no	—
365	C₃×C₅	C₄×#124	1	1	yes	characteristic, complemented, Hall
366	C₂²×C₃	—	2	4	no	—
367	C₂²×C₃	—	2	8	no	—
368	C₂²×C₃	—	4	2	no	—
369	C₂²×C₃	—	4	4	no	—
370	C₂²×C₃	—	4	2	no	—
371	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
372	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
373	C₂²×C₃	C₂×#711	1	2	yes	—
374	C₂²×C₃	C₂×#711	1	1	yes	characteristic
375	C₂²×C₃	D₅×#41	1	2	yes	—
376	C₃×C₄	—	2	4	no	—
377	C₃×C₄	—	4	2	no	—
378	C₃×C₄	—	5	4	no	—
379	C₃×C₄	—	10	2	no	—
380	C₃×C₄	—	10	4	no	—
381	C₃×C₄	—	10	4	no	—
382	C₃×C₄	—	20	2	no	—
383	C₃×C₄	#4027	1	4	yes	—
384	C₂×C₅	—	4	4	no	—
385	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
386	C₂×C₅	C₃×C₄×#41	1	2	yes	—
387	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
388	C₂×C₅	C₃×#529	1	2	yes	—
389	C₂×C₅	C₃×#532	1	1	yes	characteristic
390	C₂³	—	2	2	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	4	no	—
394	C₂³	C₂×C₃×C₄×D₅	1	4	yes	—
395	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
396	Q₈	—	10	8	no	—
397	D₄	—	2	8	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	5	2	no	—
403	C₂×C₄	—	5	4	no	—
404	C₂×C₄	—	5	4	no	—
405	C₂×C₄	—	5	4	no	—
406	C₂×C₄	—	5	2	no	—
407	C₂×C₄	—	10	2	no	—
408	C₂×C₄	—	10	2	no	—
409	C₂×C₄	—	10	2	no	—
410	C₂×C₄	—	10	2	no	—
411	C₂×C₄	—	10	2	no	—
412	C₂×C₄	—	10	2	no	—
413	C₂×C₄	—	10	4	no	—
414	C₂×C₄	—	20	8	no	—
415	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
416	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
417	C₂×C₄	C₃×#711	1	4	yes	—
418	C₂×C₄	C₃×#711	1	2	yes	—
419	C₂×C₃	—	4	4	no	—
420	C₂×C₃	C₂×#4027	1	1	yes	characteristic
421	C₂×C₃	C₄×#711	1	2	yes	—
422	C₂×C₃	#65934	1	2	yes	—
423	C₂×C₃	D₅×#124	1	1	yes	characteristic
424	C₂×C₃	#66050	1	1	yes	characteristic
425	C₅	C₃×C₄×#124	1	1	yes	characteristic, complemented, Sylow
426	C₂²	—	2	8	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
432	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
433	C₂²	C₂×C₃×#711	1	2	yes	—
434	C₂²	C₂×C₃×#711	1	1	yes	characteristic
435	C₂²	C₃×D₅×#41	1	2	yes	—
436	C₄	—	2	4	no	—
437	C₄	—	4	2	no	—
438	C₄	—	5	4	no	—
439	C₄	—	10	4	no	—
440	C₄	—	10	2	no	—
441	C₄	—	10	4	no	—
442	C₄	—	20	2	no	—
443	C₄	C₃×#4027	1	4	yes	—
444	C₃	#10608023	1	1	yes	characteristic, direct product factor, Sylow
445	C₂	—	4	4	no	—
446	C₂	C₂×C₃×#4027	1	1	yes	characteristic
447	C₂	C₃×C₄×#711	1	2	yes	—
448	C₂	C₃×#65934	1	2	yes	—
449	C₂	C₃×D₅×#124	1	1	yes	characteristic
450	C₂	C₃×#66050	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₃×C₅×#390	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₃×C₅×D₄	C₂²
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×#390	D₅
hypocenter	C₅	C₃×C₄×#124
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×#390

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×#4033	C₂	semidirect
5. C₃×#65266	C₂	semidirect
6. C₃×#65233	C₂	semidirect
7. C₃×C₂²⋊C₄×Dic₅	C₂	semidirect
8. C₃×C₄²×Dic₅	C₂	semidirect
9. C₃×#65218	C₂	semidirect
10. #10608023	C₃	direct (N × H)
19. C₃×#4082	C₄	semidirect
34. C₂×#4033	C₂×C₃	semidirect
36. #65266	C₂×C₃	semidirect
37. #65233	C₂×C₃	semidirect
38. C₂²⋊C₄×Dic₅	C₂×C₃	semidirect
39. C₄²×Dic₅	C₂×C₃	semidirect
40. #65218	C₂×C₃	semidirect
57. C₂×C₃×Dic₁₀	C₂×C₄	semidirect
62. C₃×C₂²⋊Dic₅	C₂×C₄	semidirect
68. C₃×C₄×Dic₅	C₂×C₄	semidirect
87. #4082	C₃×C₄	semidirect
165. C₂×Dic₁₀	C₂×C₃×C₄	semidirect
170. C₂²⋊Dic₅	C₂×C₃×C₄	semidirect
176. C₄×Dic₅	C₂×C₃×C₄	semidirect
204. C₃×Dic₅	#124	semidirect
335. Dic₅	C₃×#124	semidirect
365. C₃×C₅	C₄×#124	semidirect
425. C₅	C₃×C₄×#124	semidirect
444. C₃	#10608023	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×#4082	2
C₂×C₃×D₄×Dic₅	2
C₂×C₃×#4033	2
C₃×C₅×#390	2
C₃×#65266	2
C₃×#65233	2
C₃×C₂²⋊C₄×Dic₅	2
C₃×C₄²×Dic₅	2
C₃×#65218	2
#10608023	3
C₃×C₄×#124	5

Subgroups — C3×#10608023 #14321948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10608023 #14321948