Subgroups — C₃×C₄×#4038 #14319487

Order 1920.

1504 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4038	C₂	1	2	yes	maximal
2	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄⋊C₄×Dic₅	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×#685	C₂	1	2	yes	maximal
6	C₃×C₄×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄²×Dic₅	C₂	1	2	yes	maximal, complemented
8	C₃×#64955	C₂	1	2	yes	maximal
9	C₃×#64937	C₂	1	2	yes	maximal, complemented
10	C₄×#4038	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×#685	C₂²	1	4	yes	—
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
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	4	yes	—
25	C₃×#4038	C₄	1	16	yes	direct product factor
26	C₃×C₄²×D₅	C₄	1	8	yes	complemented
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	C₂×#4038	C₂×C₃	1	2	yes	—
32	C₂×C₄²×D₅	C₂×C₃	1	1	yes	characteristic
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	—
36	C₄×C₄⋊Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
37	C₄²×Dic₅	C₂×C₃	1	2	yes	complemented
38	#64955	C₂×C₃	1	2	yes	—
39	#64937	C₂×C₃	1	2	yes	complemented
40	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
47	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
48	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
49	C₂×C₃×C₄×D₅	—	2	2	no	—
50	C₂×C₃×C₄×D₅	—	2	2	no	—
51	C₂×C₃×C₄×D₅	—	2	4	no	—
52	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
53	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
54	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
55	C₂×C₃×C₄×D₅	C₂×C₄	1	8	yes	—
56	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
57	C₃×C₄²×C₅	—	2	4	no	—
58	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
59	C₃×#685	C₂×C₄	1	16	yes	—
60	C₃×C₄⋊Dic₅	C₂×C₄	1	8	yes	complemented
61	C₃×C₄×Dic₅	—	2	4	no	—
62	C₃×C₄×Dic₅	—	2	8	no	—
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	4	yes	—
66	C₃×C₄×Dic₅	C₂×C₄	1	16	yes	complemented
67	C₂×C₃×#117	—	5	2	no	—
68	C₂²×C₃×C₄²	—	5	1	no	—
69	C₃×C₄×C₄⋊C₄	—	5	2	no	—
70	C₃×C₄×C₄⋊C₄	—	5	1	no	—
71	C₃×C₄×C₄⋊C₄	D₅	1	1	yes	characteristic, complemented
72	C₃×C₄×C₂²⋊C₄	—	5	2	no	—
73	C₃×C₄×C₂²⋊C₄	—	5	2	no	—
74	C₃×#376	—	5	2	no	—
75	C₃×C₄³	—	5	2	no	—
76	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
77	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
78	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
80	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
81	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
82	C₂×#685	C₂²×C₃	1	4	yes	—
83	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
84	C₂×C₄×Dic₅	C₂²×C₃	1	4	yes	—
85	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
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	#4038	C₃×C₄	1	16	yes	direct product factor
91	C₄²×D₅	C₃×C₄	1	8	yes	complemented
92	C₅×#95	C₂²×C₃	1	2	yes	—
93	#3963	C₂²×C₃	1	2	yes	—
94	#3963	C₂²×C₃	1	4	yes	—
95	C₄×#117	—	5	1	no	Sylow
96	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
97	C₂²×C₃×D₅	—	2	1	no	—
98	C₂²×C₃×D₅	—	2	1	no	—
99	C₂²×C₃×D₅	—	2	2	no	—
100	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
101	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	—	2	4	no	—
103	C₂×C₃×C₄×C₅	—	2	4	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	8	yes	—
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
109	C₂×C₃×C₄×C₅	C₂²×C₄	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	4	no	—
113	C₂×C₃×Dic₅	—	2	4	no	—
114	C₂×C₃×Dic₅	—	2	1	no	—
115	C₂×C₃×Dic₅	—	2	1	no	—
116	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
117	C₂×C₃×Dic₅	C₂²×C₄	1	8	yes	—
118	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
119	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
120	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
121	C₂×C₃×Dic₅	#41	1	4	yes	—
122	C₃×C₄×D₅	—	2	8	no	—
123	C₃×C₄×D₅	—	2	8	no	—
124	C₃×C₄×D₅	C₄²	1	16	yes	complemented
125	C₂³×C₃×C₄	—	5	1	no	—
126	C₂³×C₃×C₄	—	5	1	no	—
127	C₂³×C₃×C₄	—	5	1	no	—
128	C₃×#117	—	5	16	no	—
129	C₂×C₃×C₄⋊C₄	—	5	2	no	—
130	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
131	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
132	C₂×C₃×C₄²	—	5	4	no	—
133	C₂×C₃×C₄²	—	5	1	no	—
134	C₂×C₃×C₄²	—	5	1	no	—
135	C₂×C₃×C₄²	—	5	1	no	—
136	C₂×C₃×C₄²	—	5	8	no	—
137	C₂×C₃×C₄²	—	5	4	no	—
138	C₂×C₃×C₄²	—	5	2	no	—
139	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
140	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
141	C₃×#95	—	5	4	no	—
142	C₃×#95	—	5	2	no	—
143	C₃×#95	C₂×D₅	1	2	yes	—
144	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
146	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
149	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
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	C₂×C₄×D₅	—	2	2	no	—
154	C₂×C₄×D₅	—	2	2	no	—
155	C₂×C₄×D₅	—	2	4	no	—
156	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
157	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
158	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
159	C₂×C₄×D₅	C₂×C₃×C₄	1	8	yes	—
160	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	complemented
161	C₄²×C₅	—	2	4	no	—
162	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
163	#685	C₂×C₃×C₄	1	16	yes	—
164	C₄⋊Dic₅	C₂×C₃×C₄	1	8	yes	complemented
165	C₄×Dic₅	—	2	4	no	—
166	C₄×Dic₅	—	2	8	no	—
167	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
168	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
169	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
170	C₄×Dic₅	C₂×C₃×C₄	1	16	yes	complemented
171	C₂×#117	—	5	2	no	—
172	C₂²×C₄²	—	5	1	no	—
173	C₄×C₄⋊C₄	—	5	2	no	—
174	C₄×C₄⋊C₄	—	5	1	no	—
175	C₄×C₄⋊C₄	C₃×D₅	1	1	yes	characteristic, complemented
176	C₄×C₂²⋊C₄	—	5	2	no	—
177	C₄×C₂²⋊C₄	—	5	2	no	—
178	#376	—	5	2	no	—
179	C₄³	—	5	2	no	—
180	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
181	C₂²×C₃×C₅	C₂³×C₄	1	2	yes	—
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	2	yes	—
185	C₂×C₃×D₅	—	2	2	no	—
186	C₂×C₃×D₅	—	2	2	no	—
187	C₂×C₃×D₅	—	2	4	no	—
188	C₂×C₃×D₅	—	2	4	no	—
189	C₂×C₃×D₅	C₂×C₄²	1	4	yes	—
190	C₃×C₄×C₅	—	2	2	no	—
191	C₃×C₄×C₅	—	2	8	no	—
192	C₃×C₄×C₅	C₂×C₄²	1	4	yes	—
193	C₃×C₄×C₅	#117	1	4	yes	complemented
194	C₃×Dic₅	—	2	2	no	—
195	C₃×Dic₅	—	2	8	no	—
196	C₃×Dic₅	C₂×C₄²	1	4	yes	—
197	C₃×Dic₅	#117	1	4	yes	complemented
198	C₂⁴×C₃	—	5	1	no	—
199	C₂²×C₃×C₄	—	5	1	no	—
200	C₂²×C₃×C₄	—	5	1	no	—
201	C₂²×C₃×C₄	—	5	4	no	—
202	C₂²×C₃×C₄	—	5	8	no	—
203	C₂²×C₃×C₄	—	5	1	no	—
204	C₂²×C₃×C₄	—	5	4	no	—
205	C₂²×C₃×C₄	—	5	4	no	—
206	C₂²×C₃×C₄	—	5	4	no	—
207	C₂²×C₃×C₄	—	10	4	no	—
208	C₂²×C₃×C₄	—	10	2	no	—
209	C₂²×C₃×C₄	—	10	2	no	—
210	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
211	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
212	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
213	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
214	C₃×C₄⋊C₄	—	5	8	no	—
215	C₃×C₄⋊C₄	C₄×D₅	1	8	yes	complemented
216	C₃×C₂²⋊C₄	—	5	16	no	—
217	C₃×C₄²	—	2	4	no	—
218	C₃×C₄²	—	5	4	no	—
219	C₃×C₄²	—	5	4	no	—
220	C₃×C₄²	—	5	4	no	—
221	C₃×C₄²	—	5	16	no	—
222	C₃×C₄²	—	10	8	no	—
223	C₃×C₄²	—	10	4	no	—
224	C₃×C₄²	C₄×D₅	1	4	yes	—
225	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
226	C₂²×D₅	—	2	1	no	—
227	C₂²×D₅	—	2	1	no	—
228	C₂²×D₅	—	2	2	no	—
229	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
230	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
231	C₂×C₄×C₅	—	2	4	no	—
232	C₂×C₄×C₅	—	2	4	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
235	C₂×C₄×C₅	C₂²×C₃×C₄	1	8	yes	—
236	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
237	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
238	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
239	C₂×C₄×C₅	C₃×#41	1	2	yes	—
240	C₂×C₄×C₅	C₃×#41	1	2	yes	—
241	C₂×Dic₅	—	2	4	no	—
242	C₂×Dic₅	—	2	4	no	—
243	C₂×Dic₅	—	2	1	no	—
244	C₂×Dic₅	—	2	1	no	—
245	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
246	C₂×Dic₅	C₂²×C₃×C₄	1	8	yes	—
247	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
248	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
249	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
250	C₂×Dic₅	C₃×#41	1	4	yes	—
251	C₄×D₅	—	2	8	no	—
252	C₄×D₅	—	2	8	no	—
253	C₄×D₅	C₃×C₄²	1	16	yes	complemented
254	C₂³×C₄	—	5	1	no	—
255	C₂³×C₄	—	5	1	no	—
256	C₂³×C₄	—	5	1	no	—
257	#117	—	5	16	no	—
258	C₂×C₄⋊C₄	—	5	2	no	—
259	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
260	C₂×C₂²⋊C₄	—	5	4	no	—
261	C₂×C₄²	—	5	4	no	—
262	C₂×C₄²	—	5	1	no	—
263	C₂×C₄²	—	5	1	no	—
264	C₂×C₄²	—	5	1	no	—
265	C₂×C₄²	—	5	8	no	—
266	C₂×C₄²	—	5	4	no	—
267	C₂×C₄²	—	5	2	no	—
268	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
269	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
270	#95	—	5	4	no	—
271	#95	—	5	2	no	—
272	#95	C₂×C₃×D₅	1	2	yes	—
273	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
274	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
275	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
276	C₂×C₃×C₅	C₄×#41	1	2	yes	—
277	C₂×C₃×C₅	C₄×#41	1	2	yes	—
278	C₃×D₅	—	2	4	no	—
279	C₂³×C₃	—	5	4	no	—
280	C₂³×C₃	—	5	2	no	—
281	C₂³×C₃	—	10	1	no	—
282	C₂³×C₃	—	10	1	no	—
283	C₂³×C₃	—	10	2	no	—
284	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
285	C₂×C₃×C₄	—	2	4	no	—
286	C₂×C₃×C₄	—	2	4	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	5	2	no	—
289	C₂×C₃×C₄	—	5	4	no	—
290	C₂×C₃×C₄	—	5	2	no	—
291	C₂×C₃×C₄	—	5	4	no	—
292	C₂×C₃×C₄	—	5	16	no	—
293	C₂×C₃×C₄	—	5	2	no	—
294	C₂×C₃×C₄	—	5	8	no	—
295	C₂×C₃×C₄	—	10	8	no	—
296	C₂×C₃×C₄	—	10	1	no	—
297	C₂×C₃×C₄	—	10	4	no	—
298	C₂×C₃×C₄	—	10	1	no	—
299	C₂×C₃×C₄	—	10	4	no	—
300	C₂×C₃×C₄	—	10	8	no	—
301	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
302	C₂×C₃×C₄	C₂×C₄×D₅	1	8	yes	—
303	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
304	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
305	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
306	C₂×C₃×C₄	#711	1	2	yes	—
307	C₂×C₃×C₄	#713	1	2	yes	—
308	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
309	C₂²×C₅	C₂³×C₃×C₄	1	2	yes	—
310	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
311	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
312	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
313	C₂×D₅	—	2	2	no	—
314	C₂×D₅	—	2	2	no	—
315	C₂×D₅	—	2	4	no	—
316	C₂×D₅	—	2	4	no	—
317	C₂×D₅	C₂×C₃×C₄²	1	4	yes	—
318	C₄×C₅	—	2	2	no	—
319	C₄×C₅	—	2	8	no	—
320	C₄×C₅	C₂×C₃×C₄²	1	4	yes	—
321	C₄×C₅	C₃×#117	1	4	yes	complemented
322	Dic₅	—	2	2	no	—
323	Dic₅	—	2	8	no	—
324	Dic₅	C₂×C₃×C₄²	1	4	yes	—
325	Dic₅	C₃×#117	1	4	yes	complemented
326	C₂⁴	—	5	1	no	—
327	C₂²×C₄	—	5	1	no	—
328	C₂²×C₄	—	5	1	no	—
329	C₂²×C₄	—	5	4	no	—
330	C₂²×C₄	—	5	8	no	—
331	C₂²×C₄	—	5	1	no	—
332	C₂²×C₄	—	5	4	no	—
333	C₂²×C₄	—	5	4	no	—
334	C₂²×C₄	—	5	4	no	—
335	C₂²×C₄	—	10	4	no	—
336	C₂²×C₄	—	10	2	no	—
337	C₂²×C₄	—	10	2	no	—
338	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
339	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
340	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
341	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
342	C₄⋊C₄	—	5	8	no	—
343	C₄⋊C₄	C₃×C₄×D₅	1	8	yes	complemented
344	C₂²⋊C₄	—	5	16	no	—
345	C₄²	—	2	4	no	—
346	C₄²	—	5	4	no	—
347	C₄²	—	5	4	no	—
348	C₄²	—	5	4	no	—
349	C₄²	—	5	16	no	—
350	C₄²	—	10	8	no	—
351	C₄²	—	10	4	no	—
352	C₄²	C₃×C₄×D₅	1	4	yes	—
353	C₃×C₅	C₄×#117	1	1	yes	characteristic, complemented, Hall
354	C₂²×C₃	—	5	4	no	—
355	C₂²×C₃	—	10	2	no	—
356	C₂²×C₃	—	10	2	no	—
357	C₂²×C₃	—	10	4	no	—
358	C₂²×C₃	—	10	4	no	—
359	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
360	C₂²×C₃	C₂²×C₄×D₅	1	2	yes	—
361	C₂²×C₃	C₂×#711	1	1	yes	characteristic
362	C₂²×C₃	C₂×#713	1	1	yes	characteristic
363	C₂²×C₃	D₅×#41	1	2	yes	—
364	C₃×C₄	—	2	2	no	—
365	C₃×C₄	—	2	8	no	—
366	C₃×C₄	—	5	4	no	—
367	C₃×C₄	—	5	4	no	—
368	C₃×C₄	—	10	2	no	—
369	C₃×C₄	—	10	8	no	—
370	C₃×C₄	C₄²×D₅	1	4	yes	—
371	C₃×C₄	#4038	1	4	yes	direct product factor
372	C₂×C₅	C₂²×C₃×C₄²	1	1	yes	characteristic
373	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
374	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
375	C₂×C₅	C₃×C₄×#41	1	2	yes	—
376	C₂×C₅	C₃×C₄×#41	1	2	yes	—
377	D₅	—	2	4	no	—
378	C₂³	—	5	4	no	—
379	C₂³	—	5	2	no	—
380	C₂³	—	10	1	no	—
381	C₂³	—	10	1	no	—
382	C₂³	—	10	2	no	—
383	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	5	2	no	—
388	C₂×C₄	—	5	2	no	—
389	C₂×C₄	—	5	4	no	—
390	C₂×C₄	—	5	4	no	—
391	C₂×C₄	—	5	16	no	—
392	C₂×C₄	—	5	2	no	—
393	C₂×C₄	—	5	8	no	—
394	C₂×C₄	—	10	8	no	—
395	C₂×C₄	—	10	1	no	—
396	C₂×C₄	—	10	4	no	—
397	C₂×C₄	—	10	1	no	—
398	C₂×C₄	—	10	4	no	—
399	C₂×C₄	—	10	8	no	—
400	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
401	C₂×C₄	C₂×C₃×C₄×D₅	1	8	yes	—
402	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
403	C₂×C₄	C₂×C₃×C₄×D₅	1	4	yes	—
404	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
405	C₂×C₄	C₃×#711	1	2	yes	—
406	C₂×C₄	C₃×#713	1	2	yes	—
407	C₂×C₃	—	10	4	no	—
408	C₂×C₃	C₂×C₄²×D₅	1	1	yes	characteristic
409	C₂×C₃	C₂×#4038	1	1	yes	characteristic
410	C₂×C₃	D₅×#117	1	1	yes	characteristic
411	C₂×C₃	C₄×#711	1	2	yes	—
412	C₂×C₃	C₄×#713	1	2	yes	—
413	C₅	C₃×C₄×#117	1	1	yes	characteristic, complemented, Sylow
414	C₂²	—	5	4	no	—
415	C₂²	—	10	2	no	—
416	C₂²	—	10	4	no	—
417	C₂²	—	10	4	no	—
418	C₂²	—	10	2	no	—
419	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
420	C₂²	C₂²×C₃×C₄×D₅	1	2	yes	—
421	C₂²	C₂×C₃×#711	1	1	yes	characteristic
422	C₂²	C₂×C₃×#713	1	1	yes	characteristic
423	C₂²	C₃×D₅×#41	1	2	yes	—
424	C₄	—	2	2	no	—
425	C₄	—	2	8	no	—
426	C₄	—	5	4	no	—
427	C₄	—	5	4	no	—
428	C₄	—	10	8	no	—
429	C₄	—	10	2	no	—
430	C₄	C₃×C₄²×D₅	1	4	yes	—
431	C₄	C₃×#4038	1	4	yes	direct product factor
432	C₃	C₄×#4038	1	1	yes	characteristic, direct product factor, Sylow
433	C₂	—	10	4	no	—
434	C₂	C₂×C₃×C₄²×D₅	1	1	yes	characteristic
435	C₂	C₂×C₃×#4038	1	1	yes	characteristic
436	C₂	C₃×D₅×#117	1	1	yes	characteristic
437	C₂	C₃×C₄×#711	1	2	yes	—
438	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	C₂³×C₃×D₅	C₂³
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×C₄⋊C₄	D₅
hypocenter	C₅	C₃×C₄×#117
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. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
4. C₃×C₄⋊C₄×Dic₅	C₂	semidirect
6. C₃×C₄×C₄⋊Dic₅	C₂	semidirect
7. C₃×C₄²×Dic₅	C₂	semidirect
9. C₃×#64937	C₂	semidirect
10. C₄×#4038	C₃	direct (N × H)
25. C₃×#4038	C₄	direct (N × H)
26. C₃×C₄²×D₅	C₄	semidirect
33. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
34. C₄⋊C₄×Dic₅	C₂×C₃	semidirect
36. C₄×C₄⋊Dic₅	C₂×C₃	semidirect
37. C₄²×Dic₅	C₂×C₃	semidirect
39. #64937	C₂×C₃	semidirect
56. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
60. C₃×C₄⋊Dic₅	C₂×C₄	semidirect
66. C₃×C₄×Dic₅	C₂×C₄	semidirect
71. C₃×C₄×C₄⋊C₄	D₅	semidirect
90. #4038	C₃×C₄	direct (N × H)
91. C₄²×D₅	C₃×C₄	semidirect
124. C₃×C₄×D₅	C₄²	semidirect
160. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
164. C₄⋊Dic₅	C₂×C₃×C₄	semidirect
170. C₄×Dic₅	C₂×C₃×C₄	semidirect
175. C₄×C₄⋊C₄	C₃×D₅	semidirect
193. C₃×C₄×C₅	#117	semidirect
197. C₃×Dic₅	#117	semidirect
215. C₃×C₄⋊C₄	C₄×D₅	semidirect
253. C₄×D₅	C₃×C₄²	semidirect
321. C₄×C₅	C₃×#117	semidirect
325. Dic₅	C₃×#117	semidirect
343. C₄⋊C₄	C₃×C₄×D₅	semidirect
353. C₃×C₅	C₄×#117	semidirect
371. C₃×C₄	#4038	direct (N × H)
413. C₅	C₃×C₄×#117	semidirect
431. C₄	C₃×#4038	direct (N × H)
432. C₃	C₄×#4038	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×#4038	2
C₂×C₃×C₄²×D₅	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄⋊C₄×Dic₅	2
C₃×C₄×#685	2
C₃×C₄×C₄⋊Dic₅	2
C₃×C₄²×Dic₅	2
C₃×#64955	2
C₃×#64937	2
C₄×#4038	3
C₃×C₄×#117	5

Subgroups — C3×C4×#4038 #14319487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#4038 #14319487