Subgroups — C₃×C₄×#4039 #14319556

Order 1920.

1848 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4039	C₂	1	2	yes	maximal
2	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄²×D₅	C₂	1	2	yes	maximal, complemented
4	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄⋊C₄×Dic₅	C₂	1	2	yes	maximal, complemented
6	C₃×C₄×#685	C₂	1	2	yes	maximal, complemented
7	C₃×C₄²×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64955	C₂	1	4	yes	maximal, complemented
9	C₄×#4039	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄×D₅	C₂²	1	4	yes	—
12	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
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	4	yes	—
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
20	C₂×C₃×C₄×Dic₅	C₂²	1	4	yes	—
21	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
23	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
24	C₃×#4039	C₄	1	16	yes	direct product factor
25	C₃×C₄×D₂₀	C₄	1	8	yes	complemented
26	C₃×C₄²×D₅	—	2	8	no	—
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₃×#3963	C₂²	1	4	yes	—
29	C₃×C₄²×D₄	—	5	1	no	maximal, Hall
30	C₂×#4039	C₂×C₃	1	2	yes	—
31	C₂×C₄×D₂₀	C₂×C₃	1	1	yes	characteristic
32	C₂×C₄²×D₅	C₂×C₃	1	2	yes	complemented
33	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
34	C₄⋊C₄×Dic₅	C₂×C₃	1	2	yes	complemented
35	C₄×#685	C₂×C₃	1	2	yes	complemented
36	C₄²×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
37	#64955	C₂×C₃	1	4	yes	complemented
38	C₂³×C₃×D₅	C₂³	1	2	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
44	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
45	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
46	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	—
47	C₂×C₃×D₂₀	C₂×C₄	1	8	yes	—
48	C₂×C₃×C₄×D₅	—	2	4	no	—
49	C₂×C₃×C₄×D₅	—	2	4	no	—
50	C₂×C₃×C₄×D₅	—	2	8	no	—
51	C₂×C₃×C₄×D₅	—	2	8	no	—
52	C₂×C₃×C₄×D₅	C₂×C₄	1	8	yes	complemented
53	C₂×C₃×C₄×D₅	C₂×C₄	1	16	yes	complemented
54	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
55	C₃×C₄²×C₅	—	2	4	no	—
56	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
57	C₃×#685	C₂×C₄	1	8	yes	complemented
58	C₃×#685	C₂×C₄	1	16	yes	complemented
59	C₃×C₄⋊Dic₅	C₂×C₄	1	4	yes	complemented
60	C₃×C₄×Dic₅	—	2	2	no	—
61	C₃×C₄×Dic₅	—	2	8	no	—
62	C₃×C₄×Dic₅	—	2	4	no	—
63	C₃×C₄×Dic₅	C₂×C₄	1	8	yes	complemented
64	C₃×C₄×Dic₅	D₄	1	4	yes	complemented
65	C₂×C₃×C₄×D₄	—	5	2	no	—
66	C₂×C₃×C₄×D₄	—	5	1	no	—
67	C₂²×C₃×C₄²	—	5	2	no	—
68	C₃×C₄×C₄⋊C₄	—	5	2	no	—
69	C₃×C₄×C₄⋊C₄	D₅	1	1	yes	characteristic, complemented
70	C₃×C₄×C₂²⋊C₄	—	5	2	no	—
71	C₃×C₄×C₂²⋊C₄	—	5	4	no	—
72	C₃×C₄³	—	5	1	no	—
73	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
74	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
75	C₂²×C₄×D₅	C₂²×C₃	1	4	yes	—
76	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
77	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
78	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
79	C₂×#685	C₂²×C₃	1	2	yes	—
80	C₂×#685	C₂²×C₃	1	4	yes	—
81	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₄×Dic₅	C₂²×C₃	1	4	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	2	yes	—
86	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
87	#4039	C₃×C₄	1	16	yes	direct product factor
88	C₄×D₂₀	C₃×C₄	1	8	yes	complemented
89	C₄²×D₅	—	2	8	no	—
90	C₅×#95	C₂²×C₃	1	2	yes	—
91	#3963	C₂²×C₃	1	4	yes	—
92	C₄²×D₄	—	5	1	no	Sylow
93	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
94	C₂²×C₃×D₅	—	2	2	no	—
95	C₂²×C₃×D₅	—	2	2	no	—
96	C₂²×C₃×D₅	—	2	4	no	—
97	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
98	C₂²×C₃×D₅	C₂²×C₄	1	8	yes	—
99	C₂×C₃×C₄×C₅	—	2	4	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	4	no	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	8	yes	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	#41	1	2	yes	—
109	C₂×C₃×Dic₅	—	2	2	no	—
110	C₂×C₃×Dic₅	—	2	2	no	—
111	C₂×C₃×Dic₅	—	2	2	no	—
112	C₂×C₃×Dic₅	—	2	2	no	—
113	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
114	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
115	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
116	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
117	C₂×C₃×Dic₅	#41	1	4	yes	—
118	C₃×D₂₀	C₄²	1	16	yes	complemented
119	C₃×C₄×D₅	—	2	16	no	—
120	C₃×C₄×D₅	—	2	32	no	—
121	C₂²×C₃×D₄	—	5	1	no	—
122	C₂³×C₃×C₄	—	5	4	no	—
123	C₂³×C₃×C₄	—	5	2	no	—
124	C₃×C₄×D₄	—	5	16	no	—
125	C₃×C₄×D₄	—	5	8	no	—
126	C₂×C₃×C₄⋊C₄	—	5	1	no	—
127	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
128	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
129	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
130	C₂×C₃×C₄²	—	5	2	no	—
131	C₂×C₃×C₄²	—	5	1	no	—
132	C₂×C₃×C₄²	—	5	2	no	—
133	C₂×C₃×C₄²	—	5	4	no	—
134	C₂×C₃×C₄²	—	5	1	no	—
135	C₂×C₃×C₄²	—	10	8	no	—
136	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
137	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
138	C₃×#95	—	5	4	no	—
139	C₃×#95	C₂×D₅	1	2	yes	—
140	C₂³×D₅	C₂³×C₃	1	2	yes	—
141	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
142	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
145	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
146	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
147	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
148	C₂×D₂₀	C₂×C₃×C₄	1	4	yes	—
149	C₂×D₂₀	C₂×C₃×C₄	1	8	yes	—
150	C₂×C₄×D₅	—	2	4	no	—
151	C₂×C₄×D₅	—	2	4	no	—
152	C₂×C₄×D₅	—	2	8	no	—
153	C₂×C₄×D₅	—	2	8	no	—
154	C₂×C₄×D₅	C₂×C₃×C₄	1	8	yes	complemented
155	C₂×C₄×D₅	C₂×C₃×C₄	1	16	yes	complemented
156	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	complemented
157	C₄²×C₅	—	2	4	no	—
158	C₄²×C₅	C₂×C₃×C₄	1	4	yes	complemented
159	#685	C₂×C₃×C₄	1	8	yes	complemented
160	#685	C₂×C₃×C₄	1	16	yes	complemented
161	C₄⋊Dic₅	C₂×C₃×C₄	1	4	yes	complemented
162	C₄×Dic₅	—	2	2	no	—
163	C₄×Dic₅	—	2	8	no	—
164	C₄×Dic₅	—	2	4	no	—
165	C₄×Dic₅	C₂×C₃×C₄	1	8	yes	complemented
166	C₄×Dic₅	C₃×D₄	1	4	yes	complemented
167	C₂×C₄×D₄	—	5	2	no	—
168	C₂×C₄×D₄	—	5	1	no	—
169	C₂²×C₄²	—	5	2	no	—
170	C₄×C₄⋊C₄	—	5	2	no	—
171	C₄×C₄⋊C₄	C₃×D₅	1	1	yes	characteristic, complemented
172	C₄×C₂²⋊C₄	—	5	2	no	—
173	C₄×C₂²⋊C₄	—	5	4	no	—
174	C₄³	—	5	1	no	—
175	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
176	C₂²×C₃×C₅	C₂³×C₄	1	2	yes	—
177	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
178	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
179	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
180	C₂×C₃×D₅	—	2	4	no	—
181	C₂×C₃×D₅	—	2	8	no	—
182	C₂×C₃×D₅	—	2	4	no	—
183	C₂×C₃×D₅	—	2	8	no	—
184	C₂×C₃×D₅	C₂×C₄²	1	8	yes	complemented
185	C₃×C₄×C₅	—	2	8	no	—
186	C₃×C₄×C₅	—	2	2	no	—
187	C₃×C₄×C₅	C₂×C₄²	1	4	yes	complemented
188	C₃×C₄×C₅	C₄×D₄	1	4	yes	complemented
189	C₃×Dic₅	—	2	4	no	—
190	C₃×Dic₅	—	2	4	no	—
191	C₃×Dic₅	C₄×D₄	1	8	yes	complemented
192	C₂⁴×C₃	—	5	2	no	—
193	C₂×C₃×D₄	—	5	8	no	—
194	C₂×C₃×D₄	—	5	4	no	—
195	C₂²×C₃×C₄	—	5	2	no	—
196	C₂²×C₃×C₄	—	5	2	no	—
197	C₂²×C₃×C₄	—	5	2	no	—
198	C₂²×C₃×C₄	—	5	16	no	—
199	C₂²×C₃×C₄	—	5	8	no	—
200	C₂²×C₃×C₄	—	10	8	no	—
201	C₂²×C₃×C₄	—	10	8	no	—
202	C₂²×C₃×C₄	—	10	4	no	—
203	C₂²×C₃×C₄	—	10	4	no	—
204	C₂²×C₃×C₄	C₂²×D₅	1	4	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	C₄×D₅	1	8	yes	complemented
210	C₃×C₂²⋊C₄	—	5	16	no	—
211	C₃×C₂²⋊C₄	—	5	8	no	—
212	C₃×C₄²	—	2	4	no	—
213	C₃×C₄²	—	5	8	no	—
214	C₃×C₄²	—	5	4	no	—
215	C₃×C₄²	—	10	4	no	—
216	C₃×C₄²	—	10	8	no	—
217	C₃×C₄²	—	10	2	no	—
218	C₃×C₄²	C₄×D₅	1	4	yes	complemented
219	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
220	C₂²×D₅	—	2	2	no	—
221	C₂²×D₅	—	2	2	no	—
222	C₂²×D₅	—	2	4	no	—
223	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
224	C₂²×D₅	C₂²×C₃×C₄	1	8	yes	—
225	C₂×C₄×C₅	—	2	4	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	2	4	no	—
228	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
229	C₂×C₄×C₅	C₂²×C₃×C₄	1	8	yes	—
230	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
231	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
232	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
233	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
234	C₂×C₄×C₅	C₃×#41	1	2	yes	—
235	C₂×Dic₅	—	2	2	no	—
236	C₂×Dic₅	—	2	2	no	—
237	C₂×Dic₅	—	2	2	no	—
238	C₂×Dic₅	—	2	2	no	—
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	4	yes	—
242	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
243	C₂×Dic₅	C₃×#41	1	4	yes	—
244	D₂₀	C₃×C₄²	1	16	yes	complemented
245	C₄×D₅	—	2	16	no	—
246	C₄×D₅	—	2	32	no	—
247	C₂²×D₄	—	5	1	no	—
248	C₂³×C₄	—	5	4	no	—
249	C₂³×C₄	—	5	2	no	—
250	C₄×D₄	—	5	16	no	—
251	C₄×D₄	—	5	8	no	—
252	C₂×C₄⋊C₄	—	5	1	no	—
253	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
254	C₂×C₂²⋊C₄	—	5	4	no	—
255	C₂×C₂²⋊C₄	—	5	2	no	—
256	C₂×C₄²	—	5	2	no	—
257	C₂×C₄²	—	5	1	no	—
258	C₂×C₄²	—	5	2	no	—
259	C₂×C₄²	—	5	1	no	—
260	C₂×C₄²	—	5	4	no	—
261	C₂×C₄²	—	10	8	no	—
262	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
263	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
264	#95	—	5	4	no	—
265	#95	C₂×C₃×D₅	1	2	yes	—
266	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
267	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
268	C₂×C₃×C₅	C₂×C₄×D₄	1	2	yes	—
269	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
270	C₂×C₃×C₅	C₄×#41	1	2	yes	—
271	C₃×D₅	—	2	8	no	—
272	C₂³×C₃	—	5	4	no	—
273	C₂³×C₃	—	5	8	no	—
274	C₂³×C₃	—	10	2	no	—
275	C₂³×C₃	—	10	2	no	—
276	C₂³×C₃	—	10	4	no	—
277	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
278	C₃×D₄	—	5	16	no	—
279	C₂×C₃×C₄	—	2	4	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	4	no	—
282	C₂×C₃×C₄	—	5	4	no	—
283	C₂×C₃×C₄	—	5	4	no	—
284	C₂×C₃×C₄	—	5	4	no	—
285	C₂×C₃×C₄	—	5	4	no	—
286	C₂×C₃×C₄	—	5	4	no	—
287	C₂×C₃×C₄	—	10	32	no	—
288	C₂×C₃×C₄	—	10	2	no	—
289	C₂×C₃×C₄	—	10	2	no	—
290	C₂×C₃×C₄	—	10	2	no	—
291	C₂×C₃×C₄	—	10	2	no	—
292	C₂×C₃×C₄	—	10	16	no	—
293	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
294	C₂×C₃×C₄	C₂×C₄×D₅	1	8	yes	—
295	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
296	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
297	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
298	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
299	C₂×C₃×C₄	#713	1	2	yes	—
300	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
301	C₂²×C₅	C₂³×C₃×C₄	1	2	yes	—
302	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
303	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
304	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
305	C₂×D₅	—	2	8	no	—
306	C₂×D₅	—	2	4	no	—
307	C₂×D₅	—	2	4	no	—
308	C₂×D₅	—	2	8	no	—
309	C₂×D₅	C₂×C₃×C₄²	1	8	yes	complemented
310	C₄×C₅	—	2	8	no	—
311	C₄×C₅	—	2	2	no	—
312	C₄×C₅	C₂×C₃×C₄²	1	4	yes	complemented
313	C₄×C₅	C₃×C₄×D₄	1	4	yes	complemented
314	Dic₅	—	2	4	no	—
315	Dic₅	—	2	4	no	—
316	Dic₅	C₃×C₄×D₄	1	8	yes	complemented
317	C₂⁴	—	5	2	no	—
318	C₂×D₄	—	5	8	no	—
319	C₂×D₄	—	5	4	no	—
320	C₂²×C₄	—	5	2	no	—
321	C₂²×C₄	—	5	2	no	—
322	C₂²×C₄	—	5	2	no	—
323	C₂²×C₄	—	5	16	no	—
324	C₂²×C₄	—	5	8	no	—
325	C₂²×C₄	—	10	8	no	—
326	C₂²×C₄	—	10	8	no	—
327	C₂²×C₄	—	10	4	no	—
328	C₂²×C₄	—	10	4	no	—
329	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
330	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
331	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
332	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
333	C₄⋊C₄	—	5	4	no	—
334	C₄⋊C₄	C₃×C₄×D₅	1	8	yes	complemented
335	C₂²⋊C₄	—	5	16	no	—
336	C₂²⋊C₄	—	5	8	no	—
337	C₄²	—	2	4	no	—
338	C₄²	—	5	8	no	—
339	C₄²	—	5	4	no	—
340	C₄²	—	10	8	no	—
341	C₄²	—	10	4	no	—
342	C₄²	—	10	2	no	—
343	C₄²	C₃×C₄×D₅	1	4	yes	complemented
344	C₃×C₅	C₄²×D₄	1	1	yes	characteristic, complemented, Hall
345	C₂²×C₃	—	5	8	no	—
346	C₂²×C₃	—	10	4	no	—
347	C₂²×C₃	—	10	4	no	—
348	C₂²×C₃	—	10	8	no	—
349	C₂²×C₃	—	10	8	no	—
350	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
351	C₂²×C₃	C₂²×C₄×D₅	1	2	yes	—
352	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
353	C₂²×C₃	C₂×#713	1	1	yes	characteristic
354	C₂²×C₃	D₅×#41	1	2	yes	—
355	C₃×C₄	—	2	2	no	—
356	C₃×C₄	—	2	8	no	—
357	C₃×C₄	—	5	8	no	—
358	C₃×C₄	—	10	4	no	—
359	C₃×C₄	—	10	4	no	—
360	C₃×C₄	C₄²×D₅	1	4	yes	complemented
361	C₃×C₄	#4039	1	4	yes	direct product factor
362	C₂×C₅	C₂²×C₃×C₄²	1	1	yes	characteristic
363	C₂×C₅	C₂×C₃×C₄×D₄	1	2	yes	—
364	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
365	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
366	C₂×C₅	C₃×C₄×#41	1	2	yes	—
367	D₅	—	2	8	no	—
368	C₂³	—	5	4	no	—
369	C₂³	—	5	8	no	—
370	C₂³	—	10	2	no	—
371	C₂³	—	10	2	no	—
372	C₂³	—	10	4	no	—
373	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
374	D₄	—	5	16	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	5	4	no	—
379	C₂×C₄	—	5	4	no	—
380	C₂×C₄	—	5	4	no	—
381	C₂×C₄	—	5	4	no	—
382	C₂×C₄	—	5	4	no	—
383	C₂×C₄	—	10	32	no	—
384	C₂×C₄	—	10	2	no	—
385	C₂×C₄	—	10	2	no	—
386	C₂×C₄	—	10	2	no	—
387	C₂×C₄	—	10	2	no	—
388	C₂×C₄	—	10	16	no	—
389	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
390	C₂×C₄	C₂×C₃×C₄×D₅	1	8	yes	—
391	C₂×C₄	C₂×C₃×C₄×D₅	1	4	yes	—
392	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
393	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
394	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
395	C₂×C₄	C₃×#713	1	2	yes	—
396	C₂×C₃	—	10	8	no	—
397	C₂×C₃	C₂×C₄²×D₅	1	1	yes	characteristic
398	C₂×C₃	C₂×#4039	1	1	yes	characteristic
399	C₂×C₃	#65856	1	1	yes	characteristic
400	C₂×C₃	C₄×D₄×D₅	1	2	yes	—
401	C₂×C₃	C₄×#713	1	2	yes	—
402	C₅	C₃×C₄²×D₄	1	1	yes	characteristic, complemented, Sylow
403	C₂²	—	5	8	no	—
404	C₂²	—	10	4	no	—
405	C₂²	—	10	8	no	—
406	C₂²	—	10	8	no	—
407	C₂²	—	10	4	no	—
408	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
409	C₂²	C₂²×C₃×C₄×D₅	1	2	yes	—
410	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
411	C₂²	C₂×C₃×#713	1	1	yes	characteristic
412	C₂²	C₃×D₅×#41	1	2	yes	—
413	C₄	—	2	2	no	—
414	C₄	—	2	8	no	—
415	C₄	—	5	8	no	—
416	C₄	—	10	4	no	—
417	C₄	—	10	4	no	—
418	C₄	C₃×C₄²×D₅	1	4	yes	complemented
419	C₄	C₃×#4039	1	4	yes	direct product factor
420	C₃	C₄×#4039	1	1	yes	characteristic, direct product factor, Sylow
421	C₂	—	10	8	no	—
422	C₂	C₂×C₃×C₄²×D₅	1	1	yes	characteristic
423	C₂	C₂×C₃×#4039	1	1	yes	characteristic
424	C₂	C₃×#65856	1	1	yes	characteristic
425	C₂	C₃×C₄×D₄×D₅	1	2	yes	—
426	C₂	C₃×C₄×#713	1	2	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×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₃×D₂₀	C₂²
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×C₄⋊C₄	D₅
hypocenter	C₅	C₃×C₄²×D₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₃×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×C₄²×D₅	C₂	semidirect
4. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
5. C₃×C₄⋊C₄×Dic₅	C₂	semidirect
6. C₃×C₄×#685	C₂	semidirect
7. C₃×C₄²×Dic₅	C₂	semidirect
8. C₃×#64955	C₂	semidirect
9. C₄×#4039	C₃	direct (N × H)
24. C₃×#4039	C₄	direct (N × H)
25. C₃×C₄×D₂₀	C₄	semidirect
32. C₂×C₄²×D₅	C₂×C₃	semidirect
33. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
34. C₄⋊C₄×Dic₅	C₂×C₃	semidirect
35. C₄×#685	C₂×C₃	semidirect
36. C₄²×Dic₅	C₂×C₃	semidirect
37. #64955	C₂×C₃	semidirect
52. C₂×C₃×C₄×D₅	C₂×C₄	semidirect
53. C₂×C₃×C₄×D₅	C₂×C₄	semidirect
54. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
56. C₃×C₄²×C₅	C₂×C₄	semidirect
57. C₃×#685	C₂×C₄	semidirect
58. C₃×#685	C₂×C₄	semidirect
59. C₃×C₄⋊Dic₅	C₂×C₄	semidirect
63. C₃×C₄×Dic₅	C₂×C₄	semidirect
64. C₃×C₄×Dic₅	D₄	semidirect
69. C₃×C₄×C₄⋊C₄	D₅	semidirect
87. #4039	C₃×C₄	direct (N × H)
88. C₄×D₂₀	C₃×C₄	semidirect
118. C₃×D₂₀	C₄²	semidirect
154. C₂×C₄×D₅	C₂×C₃×C₄	semidirect
155. C₂×C₄×D₅	C₂×C₃×C₄	semidirect
156. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
158. C₄²×C₅	C₂×C₃×C₄	semidirect
159. #685	C₂×C₃×C₄	semidirect
160. #685	C₂×C₃×C₄	semidirect
161. C₄⋊Dic₅	C₂×C₃×C₄	semidirect
165. C₄×Dic₅	C₂×C₃×C₄	semidirect
166. C₄×Dic₅	C₃×D₄	semidirect
171. C₄×C₄⋊C₄	C₃×D₅	semidirect
184. C₂×C₃×D₅	C₂×C₄²	semidirect
187. C₃×C₄×C₅	C₂×C₄²	semidirect
188. C₃×C₄×C₅	C₄×D₄	semidirect
191. C₃×Dic₅	C₄×D₄	semidirect
209. C₃×C₄⋊C₄	C₄×D₅	semidirect
218. C₃×C₄²	C₄×D₅	semidirect
244. D₂₀	C₃×C₄²	semidirect
309. C₂×D₅	C₂×C₃×C₄²	semidirect
312. C₄×C₅	C₂×C₃×C₄²	semidirect
313. C₄×C₅	C₃×C₄×D₄	semidirect
316. Dic₅	C₃×C₄×D₄	semidirect
334. C₄⋊C₄	C₃×C₄×D₅	semidirect
343. C₄²	C₃×C₄×D₅	semidirect
344. C₃×C₅	C₄²×D₄	semidirect
360. C₃×C₄	C₄²×D₅	semidirect
361. C₃×C₄	#4039	direct (N × H)
402. C₅	C₃×C₄²×D₄	semidirect
418. C₄	C₃×C₄²×D₅	semidirect
419. C₄	C₃×#4039	direct (N × H)
420. C₃	C₄×#4039	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×#4039	2
C₂×C₃×C₄×D₂₀	2
C₂×C₃×C₄²×D₅	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄⋊C₄×Dic₅	2
C₃×C₄×#685	2
C₃×C₄²×Dic₅	2
C₃×#64955	2
C₄×#4039	3
C₃×C₄²×D₄	5

Subgroups — C3×C4×#4039 #14319556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#4039 #14319556