Subgroups — C₄×C₅×#823 #14295419

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#823	C₂	1	2	yes	maximal
4	C₄×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4554	C₂	1	2	yes	maximal, complemented
6	C₄×C₅×#100	—	3	1	no	maximal, Hall
7	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₅×D₃	C₄	1	2	yes	—
9	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
10	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
12	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
13	C₂×C₅×#208	C₂²	1	2	yes	—
14	C₄×C₅×D₁₂	—	2	1	no	—
15	C₄×C₅×D₁₂	—	2	1	no	—
16	C₄×C₅×D₁₂	—	2	1	no	—
17	C₄×C₅×D₁₂	—	2	1	no	—
18	C₃×C₅×#97	—	2	1	no	—
19	C₃×C₄×C₅×C₈	—	2	1	no	—
20	C₅×#823	C₄	1	8	yes	direct product factor
21	C₅×#803	—	2	1	no	—
22	C₄×C₅×C₃⋊C₈	—	2	1	no	—
23	C₄×#823	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₄×C₅×D₄	—	3	1	no	—
25	C₂×C₅×#100	—	3	2	no	—
26	C₄×C₅×M₁₆	—	3	1	no	—
27	C₄×C₅×M₁₆	D₃	1	1	yes	characteristic, complemented
28	C₅×#343	—	3	2	no	—
29	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
33	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
34	C₂×C₅×D₁₂	—	2	1	no	—
35	C₂×C₅×D₁₂	—	2	1	no	—
36	C₂×C₅×D₁₂	—	2	2	no	—
37	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
38	C₂×C₄×C₅×D₃	—	2	2	no	—
39	C₂×C₄×C₅×D₃	—	2	2	no	—
40	C₂×C₄×C₅×D₃	—	4	4	no	—
41	C₃×C₅×M₁₆	—	2	2	no	—
42	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
43	C₂×C₃×C₅×C₈	—	2	2	no	—
44	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
45	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
46	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
47	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
48	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
49	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
50	C₅×C₄⋊Dic₃	—	2	1	no	—
51	C₅×C₄⋊Dic₃	—	2	1	no	—
52	C₅×#208	—	2	2	no	—
53	C₅×#208	C₂×C₄	1	4	yes	complemented
54	C₂×C₅×C₃⋊C₈	—	2	2	no	—
55	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic
56	C₃×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
57	C₂×#823	C₂×C₅	1	2	yes	—
58	C₄×#208	C₂×C₅	1	1	yes	characteristic, complemented
59	#4554	C₂×C₅	1	2	yes	complemented
60	C₂²×C₅×D₄	—	3	1	no	—
61	C₂³×C₄×C₅	—	3	2	no	—
62	C₂×C₅×M₁₆	—	3	2	no	—
63	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	—
64	C₄×C₅×D₄	—	6	1	no	—
65	C₄×C₅×D₄	—	6	1	no	—
66	C₄×C₅×D₄	—	6	1	no	—
67	C₄×C₅×D₄	—	6	1	no	—
68	C₂×C₅×C₄⋊C₄	—	3	1	no	—
69	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
70	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
71	C₅×#100	—	3	8	no	—
72	C₅×#97	—	2	1	no	—
73	C₅×#97	—	6	1	no	—
74	C₄×C₅×C₈	—	2	1	no	—
75	C₄×C₅×C₈	—	6	1	no	—
76	C₄×#100	—	3	1	no	Sylow
77	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₅×D₃	—	2	2	no	—
79	C₂²×C₅×D₃	—	2	2	no	—
80	C₂²×C₅×D₃	—	4	2	no	—
81	C₂²×C₅×D₃	—	4	2	no	—
82	C₂²×C₅×D₃	C₄²	1	4	yes	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	4	1	no	—
85	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	#41	1	2	yes	—
93	C₂×C₅×Dic₃	—	2	2	no	—
94	C₂×C₅×Dic₃	—	4	2	no	—
95	C₅×D₁₂	—	2	4	no	—
96	C₅×D₁₂	—	2	4	no	—
97	C₄×C₅×D₃	—	4	4	no	—
98	C₄×C₅×D₃	—	4	4	no	—
99	C₃×C₅×C₈	—	2	4	no	—
100	C₅×C₃⋊C₈	—	2	4	no	—
101	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
102	C₂²×C₄×D₃	C₄×C₅	1	2	yes	—
103	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
104	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
105	C₂×(C₂×D₃)⋊C₄	C₄×C₅	1	2	yes	—
106	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
107	C₂×#208	C₂²×C₅	1	2	yes	—
108	C₄×D₁₂	—	2	1	no	—
109	C₄×D₁₂	—	2	1	no	—
110	C₄×D₁₂	—	2	1	no	—
111	C₄×D₁₂	—	2	1	no	—
112	C₃×#97	—	2	1	no	—
113	C₃×C₄×C₈	—	2	1	no	—
114	#823	C₄×C₅	1	8	yes	direct product factor
115	#803	—	2	1	no	—
116	C₄×C₃⋊C₈	—	2	1	no	—
117	C₂⁴×C₅	—	3	2	no	—
118	C₂×C₅×D₄	—	3	4	no	—
119	C₂×C₅×D₄	—	6	1	no	—
120	C₂×C₅×D₄	—	6	2	no	—
121	C₂×C₅×D₄	—	6	1	no	—
122	C₂²×C₄×C₅	—	3	2	no	—
123	C₂²×C₄×C₅	—	6	2	no	—
124	C₂²×C₄×C₅	—	6	2	no	—
125	C₂²×C₄×C₅	—	12	4	no	—
126	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
129	C₅×M₁₆	—	2	2	no	—
130	C₅×M₁₆	—	3	4	no	—
131	C₅×M₁₆	—	6	2	no	—
132	C₅×M₁₆	C₄×D₃	1	4	yes	complemented
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	6	2	no	—
135	C₅×C₄⋊C₄	—	6	1	no	—
136	C₅×C₄⋊C₄	—	6	1	no	—
137	C₅×C₂²⋊C₄	—	6	2	no	—
138	C₅×C₂²⋊C₄	—	6	2	no	—
139	C₄²×C₅	D₁₂	1	1	yes	characteristic
140	C₄²×C₅	D₁₂	1	1	yes	characteristic
141	C₄²×C₅	#67	1	1	yes	characteristic
142	C₄²×C₅	#67	1	1	yes	characteristic
143	C₂×C₄×D₄	—	3	1	no	—
144	C₂×#100	—	3	2	no	—
145	C₄×M₁₆	—	3	1	no	—
146	C₄×M₁₆	C₅×D₃	1	1	yes	characteristic, complemented
147	#343	—	3	2	no	—
148	C₂²×C₃×C₅	—	2	1	no	—
149	C₂²×C₃×C₅	—	2	1	no	—
150	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
151	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₃×C₅	#117	1	1	yes	characteristic
153	C₂×C₅×D₃	—	2	4	no	—
154	C₂×C₅×D₃	—	4	4	no	—
155	C₂×C₅×D₃	—	4	2	no	—
156	C₂×C₅×D₃	—	4	2	no	—
157	C₂×C₅×D₃	—	4	4	no	—
158	C₃×C₄×C₅	—	2	1	no	—
159	C₃×C₄×C₅	—	2	1	no	—
160	C₃×C₄×C₅	—	2	1	no	—
161	C₃×C₄×C₅	#100	1	2	yes	complemented
162	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
163	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
164	C₅×Dic₃	—	4	2	no	—
165	C₂³×D₃	C₂×C₄×C₅	1	2	yes	—
166	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
169	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
170	C₂×D₁₂	—	2	1	no	—
171	C₂×D₁₂	—	2	1	no	—
172	C₂×D₁₂	—	2	2	no	—
173	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
174	C₂×C₄×D₃	—	2	2	no	—
175	C₂×C₄×D₃	—	2	2	no	—
176	C₂×C₄×D₃	—	4	4	no	—
177	C₃×M₁₆	—	2	2	no	—
178	C₃×M₁₆	C₂×C₄×C₅	1	4	yes	complemented
179	C₂×C₃×C₈	—	2	2	no	—
180	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
181	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
182	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
183	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
184	(C₂×D₃)⋊C₄	—	2	2	no	—
185	(C₂×D₃)⋊C₄	—	2	2	no	—
186	C₄⋊Dic₃	—	2	1	no	—
187	C₄⋊Dic₃	—	2	1	no	—
188	#208	—	2	2	no	—
189	#208	C₂×C₄×C₅	1	4	yes	complemented
190	C₂×C₃⋊C₈	—	2	2	no	—
191	C₂³×C₅	—	3	4	no	—
192	C₂³×C₅	—	6	2	no	—
193	C₂³×C₅	—	6	2	no	—
194	C₂³×C₅	—	12	2	no	—
195	C₂³×C₅	—	12	2	no	—
196	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
197	C₅×D₄	—	6	4	no	—
198	C₅×D₄	—	6	4	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	4	1	no	—
201	C₂×C₄×C₅	—	6	2	no	—
202	C₂×C₄×C₅	—	12	4	no	—
203	C₂×C₄×C₅	—	12	4	no	—
204	C₂×C₄×C₅	—	12	2	no	—
205	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
210	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
211	C₂×C₄×C₅	#235	1	2	yes	—
212	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
213	C₅×C₈	—	2	4	no	—
214	C₅×C₈	—	6	4	no	—
215	C₂²×D₄	—	3	1	no	—
216	C₂³×C₄	—	3	2	no	—
217	C₂×M₁₆	—	3	2	no	—
218	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	—
219	C₄×D₄	—	6	1	no	—
220	C₄×D₄	—	6	1	no	—
221	C₄×D₄	—	6	1	no	—
222	C₄×D₄	—	6	1	no	—
223	C₂×C₄⋊C₄	—	3	1	no	—
224	C₂×C₂²⋊C₄	—	3	2	no	—
225	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
226	#100	—	3	8	no	—
227	#97	—	2	1	no	—
228	#97	—	6	1	no	—
229	C₄×C₈	—	2	1	no	—
230	C₄×C₈	—	6	1	no	—
231	C₂×C₃×C₅	—	2	1	no	—
232	C₂×C₃×C₅	—	2	1	no	—
233	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
234	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
235	C₂×C₃×C₅	#413	1	1	yes	characteristic
236	C₅×D₃	—	4	4	no	—
237	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
238	C₂²×D₃	—	2	2	no	—
239	C₂²×D₃	—	2	2	no	—
240	C₂²×D₃	—	4	2	no	—
241	C₂²×D₃	—	4	2	no	—
242	C₂²×D₃	C₄²×C₅	1	4	yes	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	4	1	no	—
245	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
250	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
252	C₂×C₃×C₄	C₅×#41	1	2	yes	—
253	C₂×Dic₃	—	2	2	no	—
254	C₂×Dic₃	—	4	2	no	—
255	D₁₂	—	2	4	no	—
256	D₁₂	—	2	4	no	—
257	C₄×D₃	—	4	4	no	—
258	C₄×D₃	—	4	4	no	—
259	C₃×C₈	—	2	4	no	—
260	C₃⋊C₈	—	2	4	no	—
261	C₂²×C₅	—	2	1	no	—
262	C₂²×C₅	—	2	1	no	—
263	C₂²×C₅	—	6	4	no	—
264	C₂²×C₅	—	12	4	no	—
265	C₂²×C₅	—	12	4	no	—
266	C₂²×C₅	—	12	2	no	—
267	C₂²×C₅	—	12	2	no	—
268	C₂²×C₅	C₄²×D₃	1	1	yes	characteristic
269	C₂²×C₅	#872	1	1	yes	characteristic
270	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
271	C₄×C₅	—	2	1	no	—
272	C₄×C₅	—	2	1	no	—
273	C₄×C₅	—	2	1	no	—
274	C₄×C₅	—	12	2	no	—
275	C₄×C₅	#823	1	2	yes	direct product factor
276	C₄×C₅	C₄×D₁₂	1	2	yes	—
277	C₄×C₅	C₄×#67	1	2	yes	—
278	C₂⁴	—	3	2	no	—
279	C₂×D₄	—	3	4	no	—
280	C₂×D₄	—	6	1	no	—
281	C₂×D₄	—	6	2	no	—
282	C₂×D₄	—	6	1	no	—
283	C₂²×C₄	—	3	2	no	—
284	C₂²×C₄	—	6	2	no	—
285	C₂²×C₄	—	6	2	no	—
286	C₂²×C₄	—	12	4	no	—
287	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
288	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
289	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
290	M₁₆	—	2	2	no	—
291	M₁₆	—	3	4	no	—
292	M₁₆	—	6	2	no	—
293	M₁₆	C₄×C₅×D₃	1	4	yes	complemented
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	6	2	no	—
296	C₄⋊C₄	—	6	1	no	—
297	C₄⋊C₄	—	6	1	no	—
298	C₂²⋊C₄	—	6	2	no	—
299	C₂²⋊C₄	—	6	2	no	—
300	C₄²	C₅×D₁₂	1	1	yes	characteristic
301	C₄²	C₅×D₁₂	1	1	yes	characteristic
302	C₄²	C₅×#67	1	1	yes	characteristic
303	C₄²	C₅×#67	1	1	yes	characteristic
304	C₃×C₅	C₄×#100	1	1	yes	characteristic, complemented, Hall
305	C₂²×C₃	—	2	1	no	—
306	C₂²×C₃	—	2	1	no	—
307	C₂²×C₃	C₂×C₄²×C₅	1	1	yes	characteristic
308	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
309	C₂²×C₃	C₅×#117	1	1	yes	characteristic
310	C₂×D₃	—	2	4	no	—
311	C₂×D₃	—	4	4	no	—
312	C₂×D₃	—	4	2	no	—
313	C₂×D₃	—	4	2	no	—
314	C₂×D₃	—	4	4	no	—
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	2	1	no	—
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	C₅×#100	1	2	yes	complemented
319	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
320	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
321	Dic₃	—	4	2	no	—
322	C₂×C₅	—	2	1	no	—
323	C₂×C₅	—	2	1	no	—
324	C₂×C₅	—	12	4	no	—
325	C₂×C₅	C₄×(C₂×D₃)⋊C₄	1	1	yes	characteristic
326	C₂×C₅	C₂×#823	1	1	yes	characteristic
327	C₂×C₅	#5132	1	1	yes	characteristic
328	C₂³	—	3	4	no	—
329	C₂³	—	6	2	no	—
330	C₂³	—	6	2	no	—
331	C₂³	—	12	2	no	—
332	C₂³	—	12	2	no	—
333	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
334	D₄	—	6	4	no	—
335	D₄	—	6	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	6	2	no	—
339	C₂×C₄	—	12	4	no	—
340	C₂×C₄	—	12	4	no	—
341	C₂×C₄	—	12	2	no	—
342	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
343	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
344	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
345	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
346	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
347	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
348	C₂×C₄	C₅×#235	1	2	yes	—
349	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
350	C₈	—	2	4	no	—
351	C₈	—	6	4	no	—
352	C₂×C₃	—	2	1	no	—
353	C₂×C₃	—	2	1	no	—
354	C₂×C₃	C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
355	C₂×C₃	C₂×C₅×#100	1	1	yes	characteristic
356	C₂×C₃	C₅×#413	1	1	yes	characteristic
357	D₃	—	4	4	no	—
358	C₅	C₄×#823	1	1	yes	characteristic, direct product factor, Sylow
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	6	4	no	—
362	C₂²	—	12	4	no	—
363	C₂²	—	12	4	no	—
364	C₂²	—	12	2	no	—
365	C₂²	—	12	2	no	—
366	C₂²	C₄²×C₅×D₃	1	1	yes	characteristic
367	C₂²	C₅×#872	1	1	yes	characteristic
368	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	12	2	no	—
373	C₄	C₅×#823	1	2	yes	direct product factor
374	C₄	C₄×C₅×D₁₂	1	2	yes	—
375	C₄	C₄×C₅×#67	1	2	yes	—
376	C₃	C₄×C₅×#100	1	1	yes	characteristic, complemented, Sylow
377	C₂	—	2	1	no	—
378	C₂	—	2	1	no	—
379	C₂	—	12	4	no	—
380	C₂	C₄×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
381	C₂	C₂×C₅×#823	1	1	yes	characteristic
382	C₂	C₅×#5132	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	(C₂×D₃)⋊C₄
commutator	C₂²×C₃	C₂×C₄²×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₄×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₄×C₅×M₁₆	D₃
hypocenter	C₃	C₄×C₅×#100
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₄×C₅×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅×M₁₆	C₂	semidirect
4. C₄×C₅×#208	C₂	semidirect
5. C₅×#4554	C₂	semidirect
20. C₅×#823	C₄	direct (N × H)
23. C₄×#823	C₅	direct (N × H)
27. C₄×C₅×M₁₆	D₃	semidirect
42. C₃×C₅×M₁₆	C₂×C₄	semidirect
53. C₅×#208	C₂×C₄	semidirect
56. C₃×C₄×M₁₆	C₂×C₅	semidirect
58. C₄×#208	C₂×C₅	semidirect
59. #4554	C₂×C₅	semidirect
114. #823	C₄×C₅	direct (N × H)
132. C₅×M₁₆	C₄×D₃	semidirect
146. C₄×M₁₆	C₅×D₃	semidirect
161. C₃×C₄×C₅	#100	semidirect
178. C₃×M₁₆	C₂×C₄×C₅	semidirect
189. #208	C₂×C₄×C₅	semidirect
275. C₄×C₅	#823	direct (N × H)
293. M₁₆	C₄×C₅×D₃	semidirect
304. C₃×C₅	C₄×#100	semidirect
318. C₃×C₄	C₅×#100	semidirect
358. C₅	C₄×#823	direct (N × H)
373. C₄	C₅×#823	direct (N × H)
376. C₃	C₄×C₅×#100	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄×C₅×D₁₂	2
C₃×C₄×C₅×M₁₆	2
C₂×C₅×#823	2
C₄×C₅×#208	2
C₅×#4554	2
C₄×C₅×#100	3
C₄×#823	5

Subgroups — C4×C5×#823 #14295419

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#823 #14295419