Subgroups — C₃×C₄×#4023 #14319481

Order 1920.

1504 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4023	C₂	1	2	yes	maximal
3	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄×C₂²⋊Dic₅	C₂	1	1	yes	maximal, characteristic
5	C₃×C₂²⋊C₄×Dic₅	C₂	1	2	yes	maximal
6	C₃×C₄×#683	C₂	1	2	yes	maximal, complemented
7	C₃×C₄²×Dic₅	C₂	1	2	yes	maximal, complemented
8	C₃×#64938	C₂	1	2	yes	maximal, complemented
9	C₃×#64937	C₂	1	2	yes	maximal, complemented
10	C₄×#4023	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
13	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
16	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
17	C₂×C₃×#683	C₂²	1	4	yes	—
18	C₂×C₃×C₄×Dic₅	C₄	1	8	yes	complemented
19	C₂×C₃×C₄×Dic₅	C₂²	1	4	yes	—
20	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
21	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄×Dic₅	C₂²	1	4	yes	—
26	C₃×#4023	C₄	1	16	yes	direct product factor
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₃×#3963	C₂²	1	2	yes	—
29	C₃×#3963	C₂²	1	4	yes	—
30	C₃×C₄×#117	—	5	1	no	maximal, Hall
31	C₂²×C₄×Dic₅	C₂×C₃	1	1	yes	characteristic
32	C₂×#4023	C₂×C₃	1	2	yes	—
33	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
34	C₄×C₂²⋊Dic₅	C₂×C₃	1	1	yes	characteristic
35	C₂²⋊C₄×Dic₅	C₂×C₃	1	2	yes	—
36	C₄×#683	C₂×C₃	1	2	yes	complemented
37	C₄²×Dic₅	C₂×C₃	1	2	yes	complemented
38	#64938	C₂×C₃	1	2	yes	complemented
39	#64937	C₂×C₃	1	2	yes	complemented
40	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	—	2	4	no	—
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×Dic₅	—	2	4	no	—
47	C₂²×C₃×Dic₅	C₂×C₄	1	4	yes	—
48	C₂²×C₃×Dic₅	C₂×C₄	1	8	yes	—
49	C₂²×C₃×Dic₅	C₂×C₄	1	4	yes	—
50	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
51	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
55	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
56	C₃×C₄²×C₅	—	2	4	no	—
57	C₃×C₂²⋊Dic₅	C₂×C₄	1	8	yes	—
58	C₃×#683	C₂×C₄	1	16	yes	complemented
59	C₃×C₄×Dic₅	—	2	4	no	—
60	C₃×C₄×Dic₅	—	2	8	no	—
61	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
62	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
63	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
64	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
65	C₃×C₄×Dic₅	C₂×C₄	1	16	yes	complemented
66	C₂×C₃×#117	—	5	2	no	—
67	C₂²×C₃×C₄²	—	5	1	no	—
68	C₃×C₄×C₄⋊C₄	—	5	2	no	—
69	C₃×C₄×C₄⋊C₄	—	5	2	no	—
70	C₃×C₄×C₂²⋊C₄	—	5	1	no	—
71	C₃×C₄×C₂²⋊C₄	—	5	2	no	—
72	C₃×C₄×C₂²⋊C₄	D₅	1	1	yes	characteristic
73	C₃×#376	—	5	2	no	—
74	C₃×C₄³	—	5	2	no	—
75	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
76	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
77	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
80	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
81	C₂×#683	C₂²×C₃	1	4	yes	—
82	C₂×C₄×Dic₅	C₃×C₄	1	8	yes	complemented
83	C₂×C₄×Dic₅	C₂²×C₃	1	4	yes	—
84	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
85	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₄×Dic₅	C₂²×C₃	1	4	yes	—
90	#4023	C₃×C₄	1	16	yes	direct product factor
91	C₅×#95	C₂²×C₃	1	2	yes	—
92	#3963	C₂²×C₃	1	2	yes	—
93	#3963	C₂²×C₃	1	4	yes	—
94	C₄×#117	—	5	1	no	Sylow
95	C₂³×C₃×C₅	—	2	2	no	—
96	C₂³×C₃×C₅	—	2	2	no	—
97	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
98	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
99	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	—	2	4	no	—
101	C₂×C₃×C₄×C₅	—	2	4	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	8	no	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	8	yes	—
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
107	C₂×C₃×C₄×C₅	#41	1	4	yes	—
108	C₂×C₃×Dic₅	—	2	4	no	—
109	C₂×C₃×Dic₅	—	2	4	no	—
110	C₂×C₃×Dic₅	—	2	2	no	—
111	C₂×C₃×Dic₅	—	2	8	no	—
112	C₂×C₃×Dic₅	C₄²	1	16	yes	complemented
113	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
114	C₂×C₃×Dic₅	C₂²×C₄	1	8	yes	—
115	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
116	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
117	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
118	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
119	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
120	C₂×C₃×Dic₅	#41	1	4	yes	—
121	C₂³×C₃×C₄	—	5	1	no	—
122	C₂³×C₃×C₄	—	5	1	no	—
123	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
124	C₃×#117	—	5	16	no	—
125	C₂×C₃×C₄⋊C₄	—	5	4	no	—
126	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
127	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
128	C₂×C₃×C₄²	—	5	8	no	—
129	C₂×C₃×C₄²	—	5	4	no	—
130	C₂×C₃×C₄²	—	5	1	no	—
131	C₂×C₃×C₄²	—	5	1	no	—
132	C₂×C₃×C₄²	—	5	1	no	—
133	C₂×C₃×C₄²	—	5	1	no	—
134	C₂×C₃×C₄²	—	5	4	no	—
135	C₂×C₃×C₄²	—	5	2	no	—
136	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
137	C₃×#95	—	5	4	no	—
138	C₃×#95	—	5	2	no	—
139	C₃×#95	C₂×D₅	1	2	yes	—
140	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
141	C₂²×C₄×C₅	—	2	4	no	—
142	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
143	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
144	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
146	C₂²×Dic₅	—	2	4	no	—
147	C₂²×Dic₅	C₂×C₃×C₄	1	4	yes	—
148	C₂²×Dic₅	C₂×C₃×C₄	1	8	yes	—
149	C₂²×Dic₅	C₂×C₃×C₄	1	4	yes	—
150	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
151	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
152	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
153	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
154	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
155	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
156	C₄²×C₅	—	2	4	no	—
157	C₂²⋊Dic₅	C₂×C₃×C₄	1	8	yes	—
158	#683	C₂×C₃×C₄	1	16	yes	complemented
159	C₄×Dic₅	—	2	4	no	—
160	C₄×Dic₅	—	2	8	no	—
161	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
162	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
163	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
164	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
165	C₄×Dic₅	C₂×C₃×C₄	1	16	yes	complemented
166	C₂×#117	—	5	2	no	—
167	C₂²×C₄²	—	5	1	no	—
168	C₄×C₄⋊C₄	—	5	2	no	—
169	C₄×C₄⋊C₄	—	5	2	no	—
170	C₄×C₂²⋊C₄	—	5	1	no	—
171	C₄×C₂²⋊C₄	—	5	2	no	—
172	C₄×C₂²⋊C₄	C₃×D₅	1	1	yes	characteristic
173	#376	—	5	2	no	—
174	C₄³	—	5	2	no	—
175	C₂²×C₃×C₅	—	2	2	no	—
176	C₂²×C₃×C₅	—	2	2	no	—
177	C₂²×C₃×C₅	—	2	8	no	—
178	C₂²×C₃×C₅	C₂×C₄²	1	4	yes	—
179	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
180	C₂²×C₃×C₅	C₂³×C₄	1	2	yes	—
181	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
182	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
183	C₃×C₄×C₅	—	2	2	no	—
184	C₃×C₄×C₅	—	2	8	no	—
185	C₃×C₄×C₅	#117	1	4	yes	complemented
186	C₃×Dic₅	—	2	2	no	—
187	C₃×Dic₅	—	2	8	no	—
188	C₃×Dic₅	C₂×C₄²	1	4	yes	—
189	C₃×Dic₅	C₂×C₄²	1	4	yes	—
190	C₃×Dic₅	#117	1	4	yes	complemented
191	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
192	C₂²×C₃×C₄	—	2	4	no	—
193	C₂²×C₃×C₄	—	5	4	no	—
194	C₂²×C₃×C₄	—	5	8	no	—
195	C₂²×C₃×C₄	—	5	1	no	—
196	C₂²×C₃×C₄	—	5	1	no	—
197	C₂²×C₃×C₄	—	5	1	no	—
198	C₂²×C₃×C₄	—	5	4	no	—
199	C₂²×C₃×C₄	—	5	1	no	—
200	C₂²×C₃×C₄	—	5	4	no	—
201	C₂²×C₃×C₄	—	10	4	no	—
202	C₂²×C₃×C₄	C₄×D₅	1	4	yes	—
203	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
204	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
205	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
206	C₃×C₄⋊C₄	—	5	16	no	—
207	C₃×C₂²⋊C₄	—	5	8	no	—
208	C₃×C₂²⋊C₄	C₄×D₅	1	8	yes	—
209	C₃×C₄²	—	2	4	no	—
210	C₃×C₄²	—	5	4	no	—
211	C₃×C₄²	—	5	4	no	—
212	C₃×C₄²	—	5	4	no	—
213	C₃×C₄²	—	5	4	no	—
214	C₃×C₄²	—	5	16	no	—
215	C₃×C₄²	—	10	8	no	—
216	C₃×C₄²	—	10	4	no	—
217	C₂³×C₅	—	2	2	no	—
218	C₂³×C₅	—	2	2	no	—
219	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
220	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
221	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
222	C₂×C₄×C₅	—	2	4	no	—
223	C₂×C₄×C₅	—	2	4	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	8	no	—
226	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
227	C₂×C₄×C₅	C₂²×C₃×C₄	1	8	yes	—
228	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
229	C₂×C₄×C₅	C₃×#41	1	4	yes	—
230	C₂×Dic₅	—	2	4	no	—
231	C₂×Dic₅	—	2	4	no	—
232	C₂×Dic₅	—	2	2	no	—
233	C₂×Dic₅	—	2	8	no	—
234	C₂×Dic₅	C₃×C₄²	1	16	yes	complemented
235	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
236	C₂×Dic₅	C₂²×C₃×C₄	1	8	yes	—
237	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
238	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
239	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
240	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
241	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
242	C₂×Dic₅	C₃×#41	1	4	yes	—
243	C₂³×C₄	—	5	1	no	—
244	C₂³×C₄	—	5	1	no	—
245	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
246	#117	—	5	16	no	—
247	C₂×C₄⋊C₄	—	5	4	no	—
248	C₂×C₂²⋊C₄	—	5	2	no	—
249	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
250	C₂×C₄²	—	5	8	no	—
251	C₂×C₄²	—	5	4	no	—
252	C₂×C₄²	—	5	1	no	—
253	C₂×C₄²	—	5	1	no	—
254	C₂×C₄²	—	5	1	no	—
255	C₂×C₄²	—	5	1	no	—
256	C₂×C₄²	—	5	4	no	—
257	C₂×C₄²	—	5	2	no	—
258	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
259	#95	—	5	4	no	—
260	#95	—	5	2	no	—
261	#95	C₂×C₃×D₅	1	2	yes	—
262	C₂×C₃×C₅	—	2	4	no	—
263	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
264	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
265	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
266	C₂×C₃×C₅	C₄×#41	1	4	yes	—
267	C₂³×C₃	—	2	2	no	—
268	C₂³×C₃	—	2	2	no	—
269	C₂³×C₃	C₂×C₄×D₅	1	4	yes	—
270	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
271	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
272	C₂×C₃×C₄	—	2	4	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	2	4	no	—
275	C₂×C₃×C₄	—	2	8	no	—
276	C₂×C₃×C₄	—	5	2	no	—
277	C₂×C₃×C₄	—	5	2	no	—
278	C₂×C₃×C₄	—	5	4	no	—
279	C₂×C₃×C₄	—	5	2	no	—
280	C₂×C₃×C₄	—	5	4	no	—
281	C₂×C₃×C₄	—	5	4	no	—
282	C₂×C₃×C₄	—	5	16	no	—
283	C₂×C₃×C₄	—	5	2	no	—
284	C₂×C₃×C₄	—	5	8	no	—
285	C₂×C₃×C₄	—	10	8	no	—
286	C₂×C₃×C₄	—	10	4	no	—
287	C₂×C₃×C₄	—	10	4	no	—
288	C₂×C₃×C₄	—	10	2	no	—
289	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
290	C₂×C₃×C₄	C₂×C₄×D₅	1	8	yes	—
291	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
292	C₂×C₃×C₄	#711	1	4	yes	—
293	C₂²×C₅	—	2	2	no	—
294	C₂²×C₅	—	2	2	no	—
295	C₂²×C₅	—	2	8	no	—
296	C₂²×C₅	C₂×C₃×C₄²	1	4	yes	—
297	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
298	C₂²×C₅	C₂³×C₃×C₄	1	2	yes	—
299	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
300	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
301	C₄×C₅	—	2	2	no	—
302	C₄×C₅	—	2	8	no	—
303	C₄×C₅	C₃×#117	1	4	yes	complemented
304	Dic₅	—	2	2	no	—
305	Dic₅	—	2	8	no	—
306	Dic₅	C₂×C₃×C₄²	1	4	yes	—
307	Dic₅	C₂×C₃×C₄²	1	4	yes	—
308	Dic₅	C₃×#117	1	4	yes	complemented
309	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	5	4	no	—
312	C₂²×C₄	—	5	8	no	—
313	C₂²×C₄	—	5	1	no	—
314	C₂²×C₄	—	5	1	no	—
315	C₂²×C₄	—	5	1	no	—
316	C₂²×C₄	—	5	4	no	—
317	C₂²×C₄	—	5	1	no	—
318	C₂²×C₄	—	5	4	no	—
319	C₂²×C₄	—	10	4	no	—
320	C₂²×C₄	C₃×C₄×D₅	1	4	yes	—
321	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
322	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
323	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
324	C₄⋊C₄	—	5	16	no	—
325	C₂²⋊C₄	—	5	8	no	—
326	C₂²⋊C₄	C₃×C₄×D₅	1	8	yes	—
327	C₄²	—	2	4	no	—
328	C₄²	—	5	4	no	—
329	C₄²	—	5	4	no	—
330	C₄²	—	5	4	no	—
331	C₄²	—	5	4	no	—
332	C₄²	—	5	16	no	—
333	C₄²	—	10	8	no	—
334	C₄²	—	10	4	no	—
335	C₃×C₅	C₄×#117	1	1	yes	characteristic, complemented, Hall
336	C₂²×C₃	—	2	2	no	—
337	C₂²×C₃	—	2	2	no	—
338	C₂²×C₃	—	2	8	no	—
339	C₂²×C₃	C₄²×D₅	1	4	yes	—
340	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
341	C₂²×C₃	C₂²×C₄×D₅	1	2	yes	—
342	C₂²×C₃	C₂×#711	1	2	yes	—
343	C₂²×C₃	D₅×#41	1	2	yes	—
344	C₃×C₄	—	2	2	no	—
345	C₃×C₄	—	2	8	no	—
346	C₃×C₄	—	5	4	no	—
347	C₃×C₄	—	5	4	no	—
348	C₃×C₄	—	5	4	no	—
349	C₃×C₄	—	10	2	no	—
350	C₃×C₄	—	10	8	no	—
351	C₃×C₄	#4023	1	4	yes	direct product factor
352	C₂×C₅	—	2	4	no	—
353	C₂×C₅	C₂²×C₃×C₄²	1	1	yes	characteristic
354	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
355	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
356	C₂×C₅	C₃×C₄×#41	1	4	yes	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	C₂×C₃×C₄×D₅	1	4	yes	—
360	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
361	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	8	no	—
366	C₂×C₄	—	5	2	no	—
367	C₂×C₄	—	5	2	no	—
368	C₂×C₄	—	5	2	no	—
369	C₂×C₄	—	5	4	no	—
370	C₂×C₄	—	5	4	no	—
371	C₂×C₄	—	5	4	no	—
372	C₂×C₄	—	5	16	no	—
373	C₂×C₄	—	5	2	no	—
374	C₂×C₄	—	5	8	no	—
375	C₂×C₄	—	10	8	no	—
376	C₂×C₄	—	10	4	no	—
377	C₂×C₄	—	10	4	no	—
378	C₂×C₄	—	10	2	no	—
379	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
380	C₂×C₄	C₂×C₃×C₄×D₅	1	8	yes	—
381	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
382	C₂×C₄	C₃×#711	1	4	yes	—
383	C₂×C₃	—	2	4	no	—
384	C₂×C₃	C₂×C₄²×D₅	1	1	yes	characteristic
385	C₂×C₃	C₂×#4023	1	1	yes	characteristic
386	C₂×C₃	D₅×#117	1	1	yes	characteristic
387	C₂×C₃	C₄×#711	1	4	yes	—
388	C₅	C₃×C₄×#117	1	1	yes	characteristic, complemented, Sylow
389	C₂²	—	2	2	no	—
390	C₂²	—	2	8	no	—
391	C₂²	—	2	2	no	—
392	C₂²	C₃×C₄²×D₅	1	4	yes	—
393	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
394	C₂²	C₂²×C₃×C₄×D₅	1	2	yes	—
395	C₂²	C₂×C₃×#711	1	2	yes	—
396	C₂²	C₃×D₅×#41	1	2	yes	—
397	C₄	—	2	8	no	—
398	C₄	—	2	2	no	—
399	C₄	—	5	4	no	—
400	C₄	—	5	4	no	—
401	C₄	—	5	4	no	—
402	C₄	—	10	2	no	—
403	C₄	—	10	8	no	—
404	C₄	C₃×#4023	1	4	yes	direct product factor
405	C₃	C₄×#4023	1	1	yes	characteristic, direct product factor, Sylow
406	C₂	—	2	4	no	—
407	C₂	C₂×C₃×C₄²×D₅	1	1	yes	characteristic
408	C₂	C₂×C₃×#4023	1	1	yes	characteristic
409	C₂	C₃×D₅×#117	1	1	yes	characteristic
410	C₂	C₃×C₄×#711	1	4	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator	C₂×C₅	C₂²×C₃×C₄²
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×C₂²⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×C₅	C₂³
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×C₂²⋊C₄	D₅
hypocenter	C₅	C₃×C₄×#117
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₃×C₄×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
6. C₃×C₄×#683	C₂	semidirect
7. C₃×C₄²×Dic₅	C₂	semidirect
8. C₃×#64938	C₂	semidirect
9. C₃×#64937	C₂	semidirect
10. C₄×#4023	C₃	direct (N × H)
18. C₂×C₃×C₄×Dic₅	C₄	semidirect
26. C₃×#4023	C₄	direct (N × H)
36. C₄×#683	C₂×C₃	semidirect
37. C₄²×Dic₅	C₂×C₃	semidirect
38. #64938	C₂×C₃	semidirect
39. #64937	C₂×C₃	semidirect
58. C₃×#683	C₂×C₄	semidirect
65. C₃×C₄×Dic₅	C₂×C₄	semidirect
82. C₂×C₄×Dic₅	C₃×C₄	semidirect
90. #4023	C₃×C₄	direct (N × H)
112. C₂×C₃×Dic₅	C₄²	semidirect
158. #683	C₂×C₃×C₄	semidirect
165. C₄×Dic₅	C₂×C₃×C₄	semidirect
185. C₃×C₄×C₅	#117	semidirect
190. C₃×Dic₅	#117	semidirect
234. C₂×Dic₅	C₃×C₄²	semidirect
303. C₄×C₅	C₃×#117	semidirect
308. Dic₅	C₃×#117	semidirect
335. C₃×C₅	C₄×#117	semidirect
351. C₃×C₄	#4023	direct (N × H)
388. C₅	C₃×C₄×#117	semidirect
404. C₄	C₃×#4023	direct (N × H)
405. C₃	C₄×#4023	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×C₄×Dic₅	2
C₂×C₃×#4023	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₃×C₄×C₂²⋊Dic₅	2
C₃×C₂²⋊C₄×Dic₅	2
C₃×C₄×#683	2
C₃×C₄²×Dic₅	2
C₃×#64938	2
C₃×#64937	2
C₄×#4023	3
C₃×C₄×#117	5

Subgroups — C3×C4×#4023 #14319481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#4023 #14319481