Subgroups — C₃×#10614068 #14327676

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4072	C₂	1	2	yes	maximal, complemented
3	C₃×#65510	C₂	1	2	yes	maximal
4	C₃×#65501	C₂	1	2	yes	maximal, complemented
5	C₃×C₄⋊C₄×Dic₅	C₂	1	2	yes	maximal, complemented
6	C₃×#65240	C₂	1	4	yes	maximal, complemented
7	C₃×#65224	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
9	#10614068	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
12	C₃×C₄×C₅×D₄	C₄	1	8	yes	complemented
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₂²⋊Dic₅	C₂²	1	4	yes	—
17	C₂×C₃×C₂²⋊Dic₅	C₂²	1	4	yes	—
18	C₃×#4072	—	2	8	no	—
19	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
20	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
22	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
23	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×Dic₅	C₂²	1	4	yes	—
25	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
26	C₃×#3963	C₂²	1	2	yes	—
27	C₃×#3963	C₂²	1	4	yes	—
28	C₃×#2354	—	5	1	no	maximal, Hall
29	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic
30	C₂×#4072	C₂×C₃	1	2	yes	complemented
31	#65510	C₂×C₃	1	2	yes	—
32	#65501	C₂×C₃	1	2	yes	complemented
33	C₄⋊C₄×Dic₅	C₂×C₃	1	2	yes	complemented
34	#65240	C₂×C₃	1	4	yes	complemented
35	#65224	C₂×C₃	1	1	yes	characteristic, complemented
36	C₄×C₄⋊Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
38	C₂×C₃×C₅×D₄	—	2	2	no	—
39	C₂×C₃×C₅×D₄	—	2	2	no	—
40	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
41	C₂²×C₃×C₄×C₅	—	2	4	no	—
42	C₂²×C₃×C₄×C₅	—	2	4	no	—
43	C₂²×C₃×C₄×C₅	C₂×C₄	1	8	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
49	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
50	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
51	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
52	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
53	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
54	C₃×C₂²⋊Dic₅	—	2	8	no	—
55	C₃×C₂²⋊Dic₅	—	4	4	no	—
56	C₃×C₄⋊Dic₅	—	2	4	no	—
57	C₃×C₄⋊Dic₅	—	2	4	no	—
58	C₃×C₄⋊Dic₅	—	2	2	no	—
59	C₃×C₄⋊Dic₅	—	4	2	no	—
60	C₃×C₄⋊Dic₅	D₄	1	4	yes	complemented
61	C₃×C₄×Dic₅	—	2	4	no	—
62	C₃×C₄×Dic₅	—	2	8	no	—
63	C₂×C₃×C₄×D₄	D₅	1	1	yes	characteristic
64	C₂×C₃×#117	—	5	2	no	—
65	C₃×#390	—	5	2	no	—
66	C₃×#388	—	5	4	no	—
67	C₃×#384	—	5	1	no	—
68	C₃×#380	—	5	2	no	—
69	C₃×C₄×C₄⋊C₄	—	5	2	no	—
70	C₃×C₄×C₄⋊C₄	—	5	1	no	—
71	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
72	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
73	C₄×C₅×D₄	C₃×C₄	1	8	yes	complemented
74	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
76	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₂²⋊Dic₅	C₂²×C₃	1	4	yes	—
78	C₂×C₂²⋊Dic₅	C₂²×C₃	1	4	yes	—
79	#4072	—	2	8	no	—
80	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
81	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
83	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
84	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₄×Dic₅	C₂²×C₃	1	4	yes	—
86	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
87	#3963	C₂²×C₃	1	2	yes	—
88	#3963	C₂²×C₃	1	4	yes	—
89	#2354	—	5	1	no	Sylow
90	C₂³×C₃×C₅	—	2	2	no	—
91	C₂³×C₃×C₅	—	2	2	no	—
92	C₂³×C₃×C₅	—	2	2	no	—
93	C₂³×C₃×C₅	—	2	2	no	—
94	C₂³×C₃×C₅	—	2	2	no	—
95	C₂³×C₃×C₅	—	2	2	no	—
96	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
97	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
98	C₃×C₅×D₄	—	2	8	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	1	no	—
102	C₂×C₃×C₄×C₅	—	2	1	no	—
103	C₂×C₃×C₄×C₅	—	2	16	no	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
109	C₂×C₃×C₄×C₅	#41	1	2	yes	—
110	C₂×C₃×C₄×C₅	#41	1	2	yes	—
111	C₂×C₃×C₄×C₅	#41	1	2	yes	—
112	C₂×C₃×Dic₅	—	2	2	no	—
113	C₂×C₃×Dic₅	—	2	2	no	—
114	C₂×C₃×Dic₅	—	2	4	no	—
115	C₂×C₃×Dic₅	—	2	2	no	—
116	C₂×C₃×Dic₅	—	2	4	no	—
117	C₂×C₃×Dic₅	—	2	2	no	—
118	C₂×C₃×Dic₅	—	2	4	no	—
119	C₂×C₃×Dic₅	—	2	2	no	—
120	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
121	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
122	C₂³×C₃×C₄	C₂×D₅	1	2	yes	—
123	C₃×C₄×D₄	Dic₅	1	8	yes	complemented
124	C₃×#117	—	10	8	no	—
125	C₂×C₃×C₄⋊C₄	—	5	1	no	—
126	C₂×C₃×C₄⋊C₄	—	5	1	no	—
127	C₂×C₃×C₄⋊C₄	—	5	2	no	—
128	C₂×C₃×C₄⋊C₄	—	5	2	no	—
129	C₂×C₃×C₄⋊C₄	—	5	2	no	—
130	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
131	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
132	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
133	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
134	C₂×C₃×C₄²	—	5	2	no	—
135	C₂×C₃×C₄²	—	5	4	no	—
136	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
137	C₃×#95	—	5	4	no	—
138	C₃×#95	—	5	2	no	—
139	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
140	C₂×C₅×D₄	—	2	2	no	—
141	C₂×C₅×D₄	—	2	2	no	—
142	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
143	C₂²×C₄×C₅	—	2	4	no	—
144	C₂²×C₄×C₅	—	2	4	no	—
145	C₂²×C₄×C₅	C₂×C₃×C₄	1	8	yes	—
146	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
148	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
150	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
151	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
152	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
153	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
154	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
155	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
156	C₂²⋊Dic₅	—	2	8	no	—
157	C₂²⋊Dic₅	—	4	4	no	—
158	C₄⋊Dic₅	—	2	4	no	—
159	C₄⋊Dic₅	—	2	4	no	—
160	C₄⋊Dic₅	—	2	2	no	—
161	C₄⋊Dic₅	—	4	2	no	—
162	C₄⋊Dic₅	C₃×D₄	1	4	yes	complemented
163	C₄×Dic₅	—	2	4	no	—
164	C₄×Dic₅	—	2	8	no	—
165	C₂×C₄×D₄	C₃×D₅	1	1	yes	characteristic
166	C₂×#117	—	5	2	no	—
167	#390	—	5	2	no	—
168	#388	—	5	4	no	—
169	#384	—	5	1	no	—
170	#380	—	5	2	no	—
171	C₄×C₄⋊C₄	—	5	2	no	—
172	C₄×C₄⋊C₄	—	5	1	no	—
173	C₂²×C₃×C₅	—	2	4	no	—
174	C₂²×C₃×C₅	—	2	4	no	—
175	C₂²×C₃×C₅	—	2	4	no	—
176	C₂²×C₃×C₅	—	4	2	no	—
177	C₂²×C₃×C₅	—	4	2	no	—
178	C₂²×C₃×C₅	—	4	2	no	—
179	C₂²×C₃×C₅	—	4	2	no	—
180	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
181	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
182	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
183	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
184	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
185	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
187	C₃×C₄×C₅	—	2	4	no	—
188	C₃×C₄×C₅	—	2	2	no	—
189	C₃×C₄×C₅	#117	1	4	yes	complemented
190	C₃×C₄×C₅	C₄×D₄	1	4	yes	—
191	C₃×Dic₅	—	2	4	no	—
192	C₃×Dic₅	—	4	4	no	—
193	C₃×Dic₅	—	4	2	no	—
194	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
195	C₂×C₃×D₄	—	2	2	no	—
196	C₂×C₃×D₄	—	2	2	no	—
197	C₂×C₃×D₄	C₂×Dic₅	1	4	yes	—
198	C₂²×C₃×C₄	—	2	4	no	—
199	C₂²×C₃×C₄	—	2	4	no	—
200	C₂²×C₃×C₄	—	5	2	no	—
201	C₂²×C₃×C₄	—	5	2	no	—
202	C₂²×C₃×C₄	—	5	4	no	—
203	C₂²×C₃×C₄	C₂×Dic₅	1	8	yes	—
204	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
205	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
208	C₃×C₄⋊C₄	—	5	4	no	—
209	C₃×C₄⋊C₄	—	10	4	no	—
210	C₃×C₄⋊C₄	—	10	4	no	—
211	C₃×C₄⋊C₄	—	10	2	no	—
212	C₃×C₄⋊C₄	—	20	2	no	—
213	C₃×C₄⋊C₄	C₂×Dic₅	1	4	yes	—
214	C₃×C₂²⋊C₄	—	10	8	no	—
215	C₃×C₂²⋊C₄	—	20	4	no	—
216	C₃×C₂²⋊C₄	C₂×Dic₅	1	8	yes	—
217	C₃×C₄²	—	10	8	no	—
218	C₃×C₄²	—	10	4	no	—
219	C₃×C₄²	C₂×Dic₅	1	4	yes	—
220	C₂³×C₅	—	2	2	no	—
221	C₂³×C₅	—	2	2	no	—
222	C₂³×C₅	—	2	2	no	—
223	C₂³×C₅	—	2	2	no	—
224	C₂³×C₅	—	2	2	no	—
225	C₂³×C₅	—	2	2	no	—
226	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
227	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
228	C₅×D₄	—	2	8	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	16	no	—
234	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
235	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
236	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
237	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
238	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
239	C₂×C₄×C₅	C₃×#41	1	2	yes	—
240	C₂×C₄×C₅	C₃×#41	1	2	yes	—
241	C₂×C₄×C₅	C₃×#41	1	2	yes	—
242	C₂×Dic₅	—	2	2	no	—
243	C₂×Dic₅	—	2	2	no	—
244	C₂×Dic₅	—	2	4	no	—
245	C₂×Dic₅	—	2	2	no	—
246	C₂×Dic₅	—	2	4	no	—
247	C₂×Dic₅	—	2	2	no	—
248	C₂×Dic₅	—	2	4	no	—
249	C₂×Dic₅	—	2	2	no	—
250	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
251	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
252	C₂³×C₄	C₂×C₃×D₅	1	2	yes	—
253	C₄×D₄	C₃×Dic₅	1	8	yes	complemented
254	#117	—	10	8	no	—
255	C₂×C₄⋊C₄	—	5	1	no	—
256	C₂×C₄⋊C₄	—	5	2	no	—
257	C₂×C₄⋊C₄	—	5	1	no	—
258	C₂×C₄⋊C₄	—	5	2	no	—
259	C₂×C₄⋊C₄	—	5	2	no	—
260	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
261	C₂×C₂²⋊C₄	—	5	4	no	—
262	C₂×C₂²⋊C₄	—	5	4	no	—
263	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
264	C₂×C₄²	—	5	4	no	—
265	C₂×C₄²	—	5	2	no	—
266	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
267	#95	—	5	4	no	—
268	#95	—	5	2	no	—
269	C₂×C₃×C₅	—	4	4	no	—
270	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
271	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
272	C₂×C₃×C₅	#520	1	1	yes	characteristic
273	C₂×C₃×C₅	#547	1	1	yes	characteristic
274	C₂×C₃×C₅	#550	1	1	yes	characteristic
275	C₂×C₃×C₅	#555	1	1	yes	characteristic
276	C₂×C₃×C₅	#556	1	1	yes	characteristic
277	C₂³×C₃	—	2	2	no	—
278	C₂³×C₃	—	2	2	no	—
279	C₂³×C₃	—	2	2	no	—
280	C₂³×C₃	—	2	2	no	—
281	C₂³×C₃	—	2	2	no	—
282	C₂³×C₃	—	2	2	no	—
283	C₂³×C₃	C₂²×Dic₅	1	4	yes	—
284	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
285	C₃×D₄	—	2	8	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	1	no	—
289	C₂×C₃×C₄	—	2	1	no	—
290	C₂×C₃×C₄	—	2	16	no	—
291	C₂×C₃×C₄	—	5	4	no	—
292	C₂×C₃×C₄	—	10	2	no	—
293	C₂×C₃×C₄	—	10	2	no	—
294	C₂×C₃×C₄	—	10	2	no	—
295	C₂×C₃×C₄	—	10	4	no	—
296	C₂×C₃×C₄	—	10	4	no	—
297	C₂×C₃×C₄	—	10	2	no	—
298	C₂×C₃×C₄	—	10	2	no	—
299	C₂×C₃×C₄	—	10	4	no	—
300	C₂×C₃×C₄	#709	1	2	yes	—
301	C₂×C₃×C₄	#709	1	2	yes	—
302	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
303	C₂×C₃×C₄	#711	1	2	yes	—
304	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
305	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
306	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
307	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
308	C₂²×C₅	—	2	4	no	—
309	C₂²×C₅	—	2	4	no	—
310	C₂²×C₅	—	2	4	no	—
311	C₂²×C₅	—	4	2	no	—
312	C₂²×C₅	—	4	2	no	—
313	C₂²×C₅	—	4	2	no	—
314	C₂²×C₅	—	4	2	no	—
315	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
316	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
317	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
318	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
319	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
320	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
321	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
322	C₄×C₅	—	2	4	no	—
323	C₄×C₅	—	2	2	no	—
324	C₄×C₅	C₃×#117	1	4	yes	complemented
325	C₄×C₅	C₃×C₄×D₄	1	4	yes	—
326	Dic₅	—	2	4	no	—
327	Dic₅	—	4	4	no	—
328	Dic₅	—	4	2	no	—
329	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	C₂×C₃×Dic₅	1	4	yes	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	5	2	no	—
336	C₂²×C₄	—	5	2	no	—
337	C₂²×C₄	—	5	4	no	—
338	C₂²×C₄	C₂×C₃×Dic₅	1	8	yes	—
339	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
340	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
341	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
342	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
343	C₄⋊C₄	—	5	4	no	—
344	C₄⋊C₄	—	10	4	no	—
345	C₄⋊C₄	—	10	4	no	—
346	C₄⋊C₄	—	10	2	no	—
347	C₄⋊C₄	—	20	2	no	—
348	C₄⋊C₄	C₂×C₃×Dic₅	1	4	yes	—
349	C₂²⋊C₄	—	10	8	no	—
350	C₂²⋊C₄	—	20	4	no	—
351	C₂²⋊C₄	C₂×C₃×Dic₅	1	8	yes	—
352	C₄²	—	10	8	no	—
353	C₄²	—	10	4	no	—
354	C₄²	C₂×C₃×Dic₅	1	4	yes	—
355	C₃×C₅	#2354	1	1	yes	characteristic, complemented, Hall
356	C₂²×C₃	—	2	4	no	—
357	C₂²×C₃	—	2	4	no	—
358	C₂²×C₃	—	2	4	no	—
359	C₂²×C₃	—	4	2	no	—
360	C₂²×C₃	—	4	2	no	—
361	C₂²×C₃	—	4	2	no	—
362	C₂²×C₃	—	4	2	no	—
363	C₂²×C₃	C₂×#709	1	1	yes	characteristic
364	C₂²×C₃	C₂×#709	1	1	yes	characteristic
365	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
366	C₂²×C₃	C₂×#711	1	1	yes	characteristic
367	C₂²×C₃	#4149	1	1	yes	characteristic
368	C₂²×C₃	#4150	1	1	yes	characteristic
369	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
370	C₃×C₄	—	2	4	no	—
371	C₃×C₄	—	2	2	no	—
372	C₃×C₄	—	10	4	no	—
373	C₃×C₄	—	20	4	no	—
374	C₃×C₄	—	20	2	no	—
375	C₃×C₄	#4072	1	4	yes	complemented
376	C₃×C₄	D₄×Dic₅	1	4	yes	—
377	C₂×C₅	—	4	4	no	—
378	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
379	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
380	C₂×C₅	C₃×#520	1	1	yes	characteristic
381	C₂×C₅	C₃×#547	1	1	yes	characteristic
382	C₂×C₅	C₃×#550	1	1	yes	characteristic
383	C₂×C₅	C₃×#555	1	1	yes	characteristic
384	C₂×C₅	C₃×#556	1	1	yes	characteristic
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	C₂²×C₃×Dic₅	1	4	yes	—
392	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
393	D₄	—	2	8	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	16	no	—
399	C₂×C₄	—	5	4	no	—
400	C₂×C₄	—	10	2	no	—
401	C₂×C₄	—	10	2	no	—
402	C₂×C₄	—	10	2	no	—
403	C₂×C₄	—	10	4	no	—
404	C₂×C₄	—	10	4	no	—
405	C₂×C₄	—	10	2	no	—
406	C₂×C₄	—	10	2	no	—
407	C₂×C₄	—	10	4	no	—
408	C₂×C₄	C₃×#709	1	2	yes	—
409	C₂×C₄	C₃×#709	1	2	yes	—
410	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
411	C₂×C₄	C₃×#711	1	2	yes	—
412	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
413	C₂×C₄	C₂²×C₃×Dic₅	1	4	yes	—
414	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
415	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
416	C₂×C₃	—	4	4	no	—
417	C₂×C₃	#65876	1	1	yes	characteristic
418	C₂×C₃	#65885	1	1	yes	characteristic
419	C₂×C₃	#65887	1	1	yes	characteristic
420	C₂×C₃	#65897	1	1	yes	characteristic
421	C₂×C₃	C₂×#4072	1	1	yes	characteristic
422	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
423	C₂×C₃	#66161	1	1	yes	characteristic
424	C₅	C₃×#2354	1	1	yes	characteristic, complemented, Sylow
425	C₂²	—	2	4	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	C₂×C₃×#709	1	1	yes	characteristic
433	C₂²	C₂×C₃×#709	1	1	yes	characteristic
434	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
435	C₂²	C₂×C₃×#711	1	1	yes	characteristic
436	C₂²	C₃×#4149	1	1	yes	characteristic
437	C₂²	C₃×#4150	1	1	yes	characteristic
438	C₂²	C₂³×C₃×Dic₅	1	1	yes	characteristic
439	C₄	—	2	4	no	—
440	C₄	—	2	2	no	—
441	C₄	—	10	4	no	—
442	C₄	—	20	4	no	—
443	C₄	—	20	2	no	—
444	C₄	C₃×#4072	1	4	yes	complemented
445	C₄	C₃×D₄×Dic₅	1	4	yes	—
446	C₃	#10614068	1	1	yes	characteristic, direct product factor, Sylow
447	C₂	—	4	4	no	—
448	C₂	C₃×#65876	1	1	yes	characteristic
449	C₂	C₃×#65885	1	1	yes	characteristic
450	C₂	C₃×#65887	1	1	yes	characteristic
451	C₂	C₃×#65897	1	1	yes	characteristic
452	C₂	C₂×C₃×#4072	1	1	yes	characteristic
453	C₂	C₂×C₃×D₄×Dic₅	1	1	yes	characteristic
454	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×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₃×C₅×D₄	C₂²
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×C₄×D₄	D₅
hypocenter	C₅	C₃×#2354
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4072	C₂	semidirect
4. C₃×#65501	C₂	semidirect
5. C₃×C₄⋊C₄×Dic₅	C₂	semidirect
6. C₃×#65240	C₂	semidirect
7. C₃×#65224	C₂	semidirect
8. C₃×C₄×C₄⋊Dic₅	C₂	semidirect
9. #10614068	C₃	direct (N × H)
12. C₃×C₄×C₅×D₄	C₄	semidirect
30. C₂×#4072	C₂×C₃	semidirect
32. #65501	C₂×C₃	semidirect
33. C₄⋊C₄×Dic₅	C₂×C₃	semidirect
34. #65240	C₂×C₃	semidirect
35. #65224	C₂×C₃	semidirect
36. C₄×C₄⋊Dic₅	C₂×C₃	semidirect
60. C₃×C₄⋊Dic₅	D₄	semidirect
73. C₄×C₅×D₄	C₃×C₄	semidirect
123. C₃×C₄×D₄	Dic₅	semidirect
162. C₄⋊Dic₅	C₃×D₄	semidirect
189. C₃×C₄×C₅	#117	semidirect
253. C₄×D₄	C₃×Dic₅	semidirect
324. C₄×C₅	C₃×#117	semidirect
355. C₃×C₅	#2354	semidirect
375. C₃×C₄	#4072	semidirect
424. C₅	C₃×#2354	semidirect
444. C₄	C₃×#4072	semidirect
446. C₃	#10614068	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×C₄×C₅×D₄	2
C₂×C₃×#4072	2
C₃×#65510	2
C₃×#65501	2
C₃×C₄⋊C₄×Dic₅	2
C₃×#65240	2
C₃×#65224	2
C₃×C₄×C₄⋊Dic₅	2
#10614068	3
C₃×#2354	5

Subgroups — C3×#10614068 #14327676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10614068 #14327676