Subgroups — C₃×C₄×#4131 #14411461

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4131	C₂	1	2	yes	maximal
2	C₃×C₄×#711	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×#704	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₄×#170	C₂	1	2	yes	maximal, complemented
5	C₃×#65701	C₂	1	2	yes	maximal, complemented
6	C₃×#65691	C₂	1	4	yes	maximal, complemented
7	C₃×C₄×#700	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×D₅⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#4131	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×#711	C₂²	1	1	yes	characteristic
11	C₂×C₃×#704	C₂²	1	4	yes	—
12	C₂²×C₃×#170	C₂²	1	4	yes	—
13	C₃×#4131	C₄	1	16	yes	direct product factor
14	C₂×C₃×#700	C₂²	1	2	yes	—
15	C₂×C₃×D₅⋊C₈	C₂²	1	2	yes	—
16	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic
17	C₃×D₄×Dic₅	C₄	1	1	yes	characteristic
18	C₃×C₄×C₂²⋊D₅	C₄	1	2	yes	—
19	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
20	C₃×#4038	C₂²	1	1	yes	characteristic
21	C₃×#4033	C₄	1	1	yes	characteristic
22	C₃×#4027	C₄	1	2	yes	—
23	C₃×#4023	C₂²	1	2	yes	—
24	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
25	C₃×C₄×Dic₁₀	C₄	1	1	yes	characteristic
26	C₃×#4002	C₂²	1	2	yes	—
27	C₃×#4002	C₂²	1	4	yes	—
28	C₃×C₄×#170	C₂²	1	2	yes	—
29	C₃×C₄×#170	C₂²	1	1	yes	characteristic
30	C₃×C₄×#170	C₂²	1	1	yes	characteristic
31	C₃×C₄×#170	C₂²	1	2	yes	—
32	C₃×C₄×#170	C₂²	1	4	yes	—
33	C₃×C₄×#131	—	5	1	no	maximal, Hall
34	C₂×#4131	C₂×C₃	1	2	yes	—
35	C₄×#711	C₂×C₃	1	1	yes	characteristic
36	C₄×#704	C₂×C₃	1	2	yes	complemented
37	C₂×C₄×#170	C₂×C₃	1	2	yes	complemented
38	#65701	C₂×C₃	1	2	yes	complemented
39	#65691	C₂×C₃	1	4	yes	complemented
40	C₄×#700	C₂×C₃	1	1	yes	characteristic, complemented
41	C₄×D₅⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
45	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
46	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
47	C₃×#711	C₂×C₄	1	8	yes	—
48	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
51	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
52	C₃×#704	C₂×C₄	1	16	yes	complemented
53	C₂×C₃×#170	C₂×C₄	1	16	yes	complemented
54	C₂×C₃×#170	C₂³	1	2	yes	—
55	C₂×C₃×#170	C₂³	1	2	yes	—
56	C₂×C₃×#170	C₂³	1	4	yes	—
57	C₃×#700	C₂×C₄	1	8	yes	complemented
58	C₃×D₅⋊C₈	C₂×C₄	1	8	yes	complemented
59	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
61	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
62	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
63	C₃×#685	C₂×C₄	1	2	yes	—
64	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
65	C₃×#683	C₂×C₄	1	2	yes	—
66	C₃×#683	C₂×C₄	1	2	yes	—
67	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
68	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
69	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
70	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
71	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
72	C₃×C₄×Dic₅	C₂³	1	2	yes	—
73	C₂×C₃×#131	—	5	2	no	—
74	C₃×C₄×#41	—	5	1	no	—
75	C₃×#405	—	5	4	no	—
76	C₃×#405	—	5	2	no	—
77	C₃×C₄×M₁₆	—	5	1	no	—
78	C₃×C₄×M₁₆	—	5	2	no	—
79	C₂×C₃×C₄×C₈	—	5	1	no	—
80	C₂×C₃×C₄×C₈	—	5	2	no	—
81	C₂×#711	C₂²×C₃	1	1	yes	characteristic
82	C₂×#704	C₂²×C₃	1	4	yes	—
83	C₂²×#170	C₂²×C₃	1	4	yes	—
84	#4131	C₃×C₄	1	16	yes	direct product factor
85	C₂×#700	C₂²×C₃	1	2	yes	—
86	C₂×D₅⋊C₈	C₂²×C₃	1	2	yes	—
87	C₄×C₅×D₄	C₃×C₄	1	1	yes	characteristic
88	D₄×Dic₅	C₃×C₄	1	1	yes	characteristic
89	C₄×C₂²⋊D₅	C₃×C₄	1	2	yes	—
90	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
91	#4038	C₂²×C₃	1	1	yes	characteristic
92	#4033	C₃×C₄	1	1	yes	characteristic
93	#4027	C₃×C₄	1	2	yes	—
94	#4023	C₂²×C₃	1	2	yes	—
95	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
96	C₄×Dic₁₀	C₃×C₄	1	1	yes	characteristic
97	#4002	C₂²×C₃	1	2	yes	—
98	#4002	C₂²×C₃	1	4	yes	—
99	C₄×#170	C₂²×C₃	1	2	yes	—
100	C₄×#170	C₂²×C₃	1	1	yes	characteristic
101	C₄×#170	C₂²×C₃	1	1	yes	characteristic
102	C₄×#170	C₂²×C₃	1	2	yes	—
103	C₄×#170	C₂²×C₃	1	4	yes	—
104	C₄×#131	—	5	1	no	Sylow
105	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
106	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
107	C₃×C₅×D₄	C₄²	1	4	yes	—
108	C₂×C₃×C₄×C₅	—	2	4	no	—
109	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₃×C₂²⋊D₅	C₄²	1	8	yes	—
114	C₂×C₃×Dic₅	—	2	4	no	—
115	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
117	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
118	C₂×C₃×Dic₅	C₂²×C₄	1	8	yes	—
119	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
121	C₃×C₄×D₅	—	2	2	no	—
122	C₃×C₄×D₅	—	2	2	no	—
123	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
124	C₃×Dic₁₀	C₄²	1	4	yes	—
125	C₃×#170	C₂²×C₄	1	4	yes	—
126	C₃×#170	C₂²×C₄	1	4	yes	—
127	C₃×#170	C₂²×C₄	1	8	yes	—
128	C₂×C₃×#41	—	5	1	no	—
129	C₃×#131	—	5	16	no	—
130	C₂×C₃×M₁₆	—	5	2	no	—
131	C₂×C₃×M₁₆	—	5	4	no	—
132	C₂²×C₃×C₈	—	5	2	no	—
133	C₂²×C₃×C₈	—	5	4	no	—
134	C₃×C₄×Q₈	—	5	1	no	—
135	C₃×C₄×Q₈	—	5	1	no	—
136	C₃×C₄×D₄	—	5	1	no	—
137	C₃×C₄×D₄	—	5	2	no	—
138	C₃×C₄×D₄	—	5	2	no	—
139	C₃×C₄×D₄	AGL(1,𝔽₅)	1	1	yes	characteristic
140	C₃×#117	—	5	1	no	—
141	C₃×#117	—	5	2	no	—
142	C₂×C₃×C₄²	—	5	2	no	—
143	C₂×C₃×C₄²	—	5	1	no	—
144	C₃×#97	—	5	2	no	—
145	C₃×#97	—	5	4	no	—
146	C₃×C₄×C₈	—	5	1	no	—
147	C₃×C₄×C₈	—	5	1	no	—
148	C₃×C₄×C₈	—	5	2	no	—
149	C₃×C₄×C₈	—	5	2	no	—
150	C₃×C₄×C₈	—	5	4	no	—
151	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
153	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
154	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
155	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
156	#711	C₂×C₃×C₄	1	8	yes	—
157	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
158	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
159	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
160	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
161	#704	C₂×C₃×C₄	1	16	yes	complemented
162	C₂×#170	C₂×C₃×C₄	1	16	yes	complemented
163	C₂×#170	C₂³×C₃	1	2	yes	—
164	C₂×#170	C₂³×C₃	1	2	yes	—
165	C₂×#170	C₂³×C₃	1	4	yes	—
166	#700	C₂×C₃×C₄	1	8	yes	complemented
167	D₅⋊C₈	C₂×C₃×C₄	1	8	yes	complemented
168	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
169	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
170	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
171	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
172	#685	C₂×C₃×C₄	1	2	yes	—
173	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
174	#683	C₂×C₃×C₄	1	2	yes	—
175	#683	C₂×C₃×C₄	1	2	yes	—
176	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
177	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
178	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
179	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
180	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
181	C₄×Dic₅	C₂³×C₃	1	2	yes	—
182	C₂×#131	—	5	2	no	—
183	C₄×#41	—	5	1	no	—
184	#405	—	5	4	no	—
185	#405	—	5	2	no	—
186	C₄×M₁₆	—	5	1	no	—
187	C₄×M₁₆	—	5	2	no	—
188	C₂×C₄×C₈	—	5	1	no	—
189	C₂×C₄×C₈	—	5	2	no	—
190	C₂²×C₃×C₅	—	2	2	no	—
191	C₂²×C₃×C₅	—	2	2	no	—
192	C₂²×C₃×C₅	C₂×C₄²	1	4	yes	—
193	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₃×D₅	—	2	1	no	—
195	C₂×C₃×D₅	—	2	1	no	—
196	C₂×C₃×D₅	C₂×C₄²	1	2	yes	—
197	C₃×C₄×C₅	—	2	1	no	—
198	C₃×C₄×C₅	—	2	2	no	—
199	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
200	C₃×C₄×C₅	#131	1	2	yes	complemented
201	C₃×Dic₅	—	2	1	no	—
202	C₃×Dic₅	—	2	2	no	—
203	C₃×Dic₅	C₂×C₄²	1	4	yes	—
204	C₃×Dic₅	#131	1	2	yes	complemented
205	C₃×Dic₅	C₂³×C₄	1	2	yes	—
206	C₃×#41	—	5	8	no	—
207	C₂×C₃×Q₈	—	5	1	no	—
208	C₂×C₃×D₄	—	5	2	no	—
209	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
210	C₂²×C₃×C₄	—	5	2	no	—
211	C₂²×C₃×C₄	—	5	1	no	—
212	C₂²×C₃×C₄	—	5	2	no	—
213	C₂²×C₃×C₄	—	5	1	no	—
214	C₂²×C₃×C₄	—	5	1	no	—
215	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
216	C₃×M₁₆	—	5	8	no	—
217	C₃×M₁₆	—	5	16	no	—
218	C₂×C₃×C₈	—	5	2	no	—
219	C₂×C₃×C₈	—	5	2	no	—
220	C₂×C₃×C₈	—	5	4	no	—
221	C₂×C₃×C₈	—	5	8	no	—
222	C₂×C₃×C₈	—	5	16	no	—
223	C₃×C₄⋊C₄	—	5	2	no	—
224	C₃×C₄⋊C₄	—	5	2	no	—
225	C₃×C₄⋊C₄	—	5	1	no	—
226	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
227	C₃×C₂²⋊C₄	—	5	2	no	—
228	C₃×C₂²⋊C₄	—	5	2	no	—
229	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
230	C₃×C₄²	—	5	2	no	—
231	C₃×C₄²	—	5	1	no	—
232	C₃×C₄²	—	5	2	no	—
233	C₃×C₄²	—	5	1	no	—
234	C₃×C₄²	—	5	2	no	—
235	C₃×C₄²	—	5	1	no	—
236	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
237	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
238	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
239	C₅×D₄	C₃×C₄²	1	4	yes	—
240	C₂×C₄×C₅	—	2	4	no	—
241	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
242	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
245	C₂²⋊D₅	C₃×C₄²	1	8	yes	—
246	C₂×Dic₅	—	2	4	no	—
247	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
248	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
249	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
250	C₂×Dic₅	C₂²×C₃×C₄	1	8	yes	—
251	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
252	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
253	C₄×D₅	—	2	2	no	—
254	C₄×D₅	—	2	2	no	—
255	C₄×D₅	C₂²×C₃×C₄	1	4	yes	—
256	Dic₁₀	C₃×C₄²	1	4	yes	—
257	#170	C₂²×C₃×C₄	1	4	yes	—
258	#170	C₂²×C₃×C₄	1	4	yes	—
259	#170	C₂²×C₃×C₄	1	8	yes	—
260	C₂×#41	—	5	1	no	—
261	#131	—	5	16	no	—
262	C₂×M₁₆	—	5	2	no	—
263	C₂×M₁₆	—	5	4	no	—
264	C₂²×C₈	—	5	2	no	—
265	C₂²×C₈	—	5	4	no	—
266	C₄×Q₈	—	5	1	no	—
267	C₄×Q₈	—	5	1	no	—
268	C₄×D₄	—	5	1	no	—
269	C₄×D₄	—	5	2	no	—
270	C₄×D₄	—	5	2	no	—
271	C₄×D₄	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
272	#117	—	5	1	no	—
273	#117	—	5	2	no	—
274	C₂×C₄²	—	5	2	no	—
275	C₂×C₄²	—	5	1	no	—
276	#97	—	5	2	no	—
277	#97	—	5	4	no	—
278	C₄×C₈	—	5	1	no	—
279	C₄×C₈	—	5	1	no	—
280	C₄×C₈	—	5	2	no	—
281	C₄×C₈	—	5	2	no	—
282	C₄×C₈	—	5	4	no	—
283	C₂×C₃×C₅	—	2	4	no	—
284	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
285	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
286	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
287	C₃×D₅	—	2	2	no	—
288	C₂³×C₃	—	5	1	no	—
289	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
290	C₃×Q₈	—	5	4	no	—
291	C₃×D₄	—	5	8	no	—
292	C₃×D₄	C₄×AGL(1,𝔽₅)	1	4	yes	—
293	C₂×C₃×C₄	—	2	4	no	—
294	C₂×C₃×C₄	—	5	8	no	—
295	C₂×C₃×C₄	—	5	1	no	—
296	C₂×C₃×C₄	—	5	2	no	—
297	C₂×C₃×C₄	—	5	1	no	—
298	C₂×C₃×C₄	—	5	4	no	—
299	C₂×C₃×C₄	—	5	1	no	—
300	C₂×C₃×C₄	—	5	2	no	—
301	C₂×C₃×C₄	—	10	2	no	—
302	C₂×C₃×C₄	—	10	4	no	—
303	C₂×C₃×C₄	—	10	2	no	—
304	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
305	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
306	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
307	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
308	C₃×C₈	—	5	4	no	—
309	C₃×C₈	—	5	4	no	—
310	C₃×C₈	—	5	8	no	—
311	C₂²×C₅	—	2	2	no	—
312	C₂²×C₅	—	2	2	no	—
313	C₂²×C₅	C₂×C₃×C₄²	1	4	yes	—
314	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
315	C₂×D₅	—	2	1	no	—
316	C₂×D₅	—	2	1	no	—
317	C₂×D₅	C₂×C₃×C₄²	1	2	yes	—
318	C₄×C₅	—	2	1	no	—
319	C₄×C₅	—	2	2	no	—
320	C₄×C₅	C₂×C₃×C₄²	1	2	yes	—
321	C₄×C₅	C₃×#131	1	2	yes	complemented
322	Dic₅	—	2	1	no	—
323	Dic₅	—	2	2	no	—
324	Dic₅	C₂×C₃×C₄²	1	4	yes	—
325	Dic₅	C₃×#131	1	2	yes	complemented
326	Dic₅	C₂³×C₃×C₄	1	2	yes	—
327	#41	—	5	8	no	—
328	C₂×Q₈	—	5	1	no	—
329	C₂×D₄	—	5	2	no	—
330	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
331	C₂²×C₄	—	5	2	no	—
332	C₂²×C₄	—	5	1	no	—
333	C₂²×C₄	—	5	2	no	—
334	C₂²×C₄	—	5	1	no	—
335	C₂²×C₄	—	5	1	no	—
336	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
337	M₁₆	—	5	8	no	—
338	M₁₆	—	5	16	no	—
339	C₂×C₈	—	5	2	no	—
340	C₂×C₈	—	5	2	no	—
341	C₂×C₈	—	5	4	no	—
342	C₂×C₈	—	5	8	no	—
343	C₂×C₈	—	5	16	no	—
344	C₄⋊C₄	—	5	2	no	—
345	C₄⋊C₄	—	5	2	no	—
346	C₄⋊C₄	—	5	1	no	—
347	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
348	C₂²⋊C₄	—	5	2	no	—
349	C₂²⋊C₄	—	5	2	no	—
350	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
351	C₄²	—	5	1	no	—
352	C₄²	—	5	2	no	—
353	C₄²	—	5	1	no	—
354	C₄²	—	5	2	no	—
355	C₄²	—	5	1	no	—
356	C₄²	—	5	2	no	—
357	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
358	C₃×C₅	C₄×#131	1	1	yes	characteristic, complemented, Hall
359	C₂²×C₃	—	2	2	no	—
360	C₂²×C₃	—	2	2	no	—
361	C₂²×C₃	—	5	2	no	—
362	C₂²×C₃	—	10	1	no	—
363	C₂²×C₃	—	10	1	no	—
364	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	4	yes	—
365	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
366	C₃×C₄	—	2	2	no	—
367	C₃×C₄	—	2	1	no	—
368	C₃×C₄	—	5	4	no	—
369	C₃×C₄	—	5	2	no	—
370	C₃×C₄	—	5	2	no	—
371	C₃×C₄	—	10	1	no	—
372	C₃×C₄	—	10	2	no	—
373	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
374	C₃×C₄	#4131	1	2	yes	direct product factor
375	C₂×C₅	—	2	4	no	—
376	C₂×C₅	C₂²×C₃×C₄²	1	1	yes	characteristic
377	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
378	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
379	D₅	—	2	2	no	—
380	C₂³	—	5	1	no	—
381	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
382	Q₈	—	5	4	no	—
383	D₄	—	5	8	no	—
384	D₄	C₃×C₄×AGL(1,𝔽₅)	1	4	yes	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	5	8	no	—
387	C₂×C₄	—	5	1	no	—
388	C₂×C₄	—	5	1	no	—
389	C₂×C₄	—	5	2	no	—
390	C₂×C₄	—	5	4	no	—
391	C₂×C₄	—	5	1	no	—
392	C₂×C₄	—	5	2	no	—
393	C₂×C₄	—	10	2	no	—
394	C₂×C₄	—	10	4	no	—
395	C₂×C₄	—	10	2	no	—
396	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
397	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
398	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
400	C₈	—	5	4	no	—
401	C₈	—	5	4	no	—
402	C₈	—	5	8	no	—
403	C₂×C₃	—	2	4	no	—
404	C₂×C₃	—	10	2	no	—
405	C₂×C₃	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
406	C₂×C₃	C₂×#4131	1	1	yes	characteristic
407	C₂×C₃	D₅⋊#131	1	1	yes	characteristic
408	C₅	C₃×C₄×#131	1	1	yes	characteristic, complemented, Sylow
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	5	2	no	—
412	C₂²	—	10	1	no	—
413	C₂²	—	10	1	no	—
414	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	4	yes	—
415	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	1	no	—
418	C₄	—	5	2	no	—
419	C₄	—	5	4	no	—
420	C₄	—	5	2	no	—
421	C₄	—	10	1	no	—
422	C₄	—	10	2	no	—
423	C₄	C₂×C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
424	C₄	C₃×#4131	1	2	yes	direct product factor
425	C₃	C₄×#4131	1	1	yes	characteristic, direct product factor, Sylow
426	C₂	—	2	4	no	—
427	C₂	—	10	2	no	—
428	C₂	C₂²×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
429	C₂	C₂×C₃×#4131	1	1	yes	characteristic
430	C₂	C₃×D₅⋊#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂²×C₃×C₄²
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₄×C₅×D₄	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₃×#711	C₂²
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×C₄×D₄	AGL(1,𝔽₅)
hypocenter	C₅	C₃×C₄×#131
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
3. C₃×C₄×#704	C₂	semidirect
4. C₂×C₃×C₄×#170	C₂	semidirect
5. C₃×#65701	C₂	semidirect
6. C₃×#65691	C₂	semidirect
7. C₃×C₄×#700	C₂	semidirect
8. C₃×C₄×D₅⋊C₈	C₂	semidirect
9. C₄×#4131	C₃	direct (N × H)
13. C₃×#4131	C₄	direct (N × H)
36. C₄×#704	C₂×C₃	semidirect
37. C₂×C₄×#170	C₂×C₃	semidirect
38. #65701	C₂×C₃	semidirect
39. #65691	C₂×C₃	semidirect
40. C₄×#700	C₂×C₃	semidirect
41. C₄×D₅⋊C₈	C₂×C₃	semidirect
52. C₃×#704	C₂×C₄	semidirect
53. C₂×C₃×#170	C₂×C₄	semidirect
57. C₃×#700	C₂×C₄	semidirect
58. C₃×D₅⋊C₈	C₂×C₄	semidirect
84. #4131	C₃×C₄	direct (N × H)
161. #704	C₂×C₃×C₄	semidirect
162. C₂×#170	C₂×C₃×C₄	semidirect
166. #700	C₂×C₃×C₄	semidirect
167. D₅⋊C₈	C₂×C₃×C₄	semidirect
200. C₃×C₄×C₅	#131	semidirect
204. C₃×Dic₅	#131	semidirect
321. C₄×C₅	C₃×#131	semidirect
325. Dic₅	C₃×#131	semidirect
358. C₃×C₅	C₄×#131	semidirect
374. C₃×C₄	#4131	direct (N × H)
408. C₅	C₃×C₄×#131	semidirect
424. C₄	C₃×#4131	direct (N × H)
425. C₃	C₄×#4131	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×#4131	2
C₃×C₄×#711	2
C₃×C₄×#704	2
C₂×C₃×C₄×#170	2
C₃×#65701	2
C₃×#65691	2
C₃×C₄×#700	2
C₃×C₄×D₅⋊C₈	2
C₄×#4131	3
C₃×C₄×#131	5

Subgroups — C3×C4×#4131 #14411461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#4131 #14411461