Subgroups — C₃×C₅×#1983 #14275017

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#103	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₅×#102	C₂	1	2	yes	maximal
5	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1983	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
10	C₃×C₅×#124	—	2	2	no	—
11	C₃×C₅×#124	C₄	1	4	yes	complemented
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
14	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
15	C₂×C₃×C₄²×C₅	—	2	1	no	—
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₃×C₅×C₄⋊C₈	—	2	2	no	—
18	C₃×C₅×#103	—	2	4	no	—
19	C₃×C₅×#102	—	2	4	no	—
20	C₃×C₅×#95	—	2	1	no	—
21	C₃×#1983	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic
23	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂×C₅×#103	C₂×C₃	1	2	yes	complemented
25	C₂×C₅×#102	C₂×C₃	1	2	yes	—
26	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂⁴×C₃×C₅	—	2	1	no	—
28	C₂×C₃×C₅×Q₈	—	2	1	no	—
29	C₂×C₃×C₅×Q₈	—	2	2	no	—
30	C₂×C₃×C₅×Q₈	—	2	2	no	—
31	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
32	C₂×C₃×C₅×D₄	—	2	2	no	—
33	C₂×C₃×C₅×D₄	—	2	1	no	—
34	C₂×C₃×C₅×D₄	—	2	2	no	—
35	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
36	C₂²×C₃×C₄×C₅	—	2	2	no	—
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂×C₃×C₅×C₈	—	2	2	no	—
42	C₂×C₃×C₅×C₈	—	2	2	no	—
43	C₂×C₃×C₅×C₈	—	2	2	no	—
44	C₃×C₅×C₄⋊C₄	—	2	2	no	—
45	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	—
46	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
48	C₃×C₄²×C₅	—	4	2	no	—
49	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
50	C₃×C₄²×C₅	D₄	1	2	yes	—
51	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic
52	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
53	C₂×C₃×#103	C₂×C₅	1	2	yes	complemented
54	C₂×C₃×#102	C₂×C₅	1	2	yes	—
55	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
56	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
57	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
58	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
59	C₅×#124	—	2	2	no	—
60	C₅×#124	C₃×C₄	1	4	yes	complemented
61	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
62	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
63	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
64	C₂×C₄²×C₅	—	2	1	no	—
65	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
66	C₅×C₄⋊C₈	—	2	2	no	—
67	C₅×#103	—	2	4	no	—
68	C₅×#102	—	2	4	no	—
69	C₅×#95	—	2	1	no	—
70	#1983	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
71	C₂³×C₃×C₅	—	2	2	no	—
72	C₂³×C₃×C₅	—	4	2	no	—
73	C₂³×C₃×C₅	—	4	2	no	—
74	C₂³×C₃×C₅	—	4	1	no	—
75	C₂³×C₃×C₅	—	4	1	no	—
76	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
77	C₃×C₅×Q₈	—	2	4	no	—
78	C₃×C₅×Q₈	—	4	1	no	—
79	C₃×C₅×Q₈	—	4	1	no	—
80	C₃×C₅×D₄	—	2	4	no	—
81	C₃×C₅×D₄	—	4	1	no	—
82	C₃×C₅×D₄	—	4	1	no	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	2	1	no	—
85	C₂×C₃×C₄×C₅	—	2	1	no	—
86	C₂×C₃×C₄×C₅	—	2	2	no	—
87	C₂×C₃×C₄×C₅	—	2	4	no	—
88	C₂×C₃×C₄×C₅	—	4	2	no	—
89	C₂×C₃×C₄×C₅	—	4	2	no	—
90	C₂×C₃×C₄×C₅	—	4	2	no	—
91	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	#41	1	2	yes	—
97	C₃×C₅×C₈	—	4	2	no	—
98	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
99	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
100	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
101	C₃×#124	—	2	2	no	—
102	C₃×#124	C₄×C₅	1	4	yes	complemented
103	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
104	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₃×C₄²	—	2	1	no	—
107	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
108	C₃×C₄⋊C₈	—	2	2	no	—
109	C₃×#103	—	2	4	no	—
110	C₃×#102	—	2	4	no	—
111	C₃×#95	—	2	1	no	—
112	C₂⁴×C₅	—	2	1	no	—
113	C₂×C₅×Q₈	—	2	1	no	—
114	C₂×C₅×Q₈	—	2	2	no	—
115	C₂×C₅×Q₈	—	2	2	no	—
116	C₂×C₅×Q₈	C₂×C₃×C₄	1	2	yes	—
117	C₂×C₅×D₄	—	2	2	no	—
118	C₂×C₅×D₄	—	2	1	no	—
119	C₂×C₅×D₄	—	2	2	no	—
120	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
121	C₂²×C₄×C₅	—	2	2	no	—
122	C₂²×C₄×C₅	—	2	1	no	—
123	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	—	2	2	no	—
128	C₂×C₅×C₈	—	2	2	no	—
129	C₅×C₄⋊C₄	—	2	2	no	—
130	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	—
131	C₅×C₂²⋊C₄	—	2	4	no	—
132	C₅×C₂²⋊C₄	—	2	4	no	—
133	C₄²×C₅	—	4	2	no	—
134	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
135	C₄²×C₅	C₃×D₄	1	2	yes	—
136	C₂×#124	C₂×C₃×C₅	1	1	yes	characteristic
137	C₂×C₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
138	C₂×#103	C₂×C₃×C₅	1	2	yes	complemented
139	C₂×#102	C₂×C₃×C₅	1	2	yes	—
140	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
141	C₂²×C₃×C₅	—	4	2	no	—
142	C₂²×C₃×C₅	—	4	2	no	—
143	C₂²×C₃×C₅	—	4	2	no	—
144	C₂²×C₃×C₅	—	8	2	no	—
145	C₂²×C₃×C₅	—	8	2	no	—
146	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂²×C₃×C₅	#121	1	2	yes	—
148	C₂²×C₃×C₅	#135	1	2	yes	—
149	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
150	C₂²×C₃×C₅	#137	1	1	yes	characteristic
151	C₃×C₄×C₅	—	2	2	no	—
152	C₃×C₄×C₅	—	2	2	no	—
153	C₃×C₄×C₅	—	4	2	no	—
154	C₃×C₄×C₅	—	4	4	no	—
155	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
156	C₃×C₄×C₅	#124	1	1	yes	characteristic
157	C₃×C₄×C₅	#127	1	1	yes	characteristic
158	C₂⁴×C₃	—	2	1	no	—
159	C₂×C₃×Q₈	—	2	1	no	—
160	C₂×C₃×Q₈	—	2	2	no	—
161	C₂×C₃×Q₈	—	2	2	no	—
162	C₂×C₃×Q₈	C₂×C₄×C₅	1	2	yes	—
163	C₂×C₃×D₄	—	2	2	no	—
164	C₂×C₃×D₄	—	2	1	no	—
165	C₂×C₃×D₄	—	2	2	no	—
166	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
167	C₂²×C₃×C₄	—	2	2	no	—
168	C₂²×C₃×C₄	—	2	1	no	—
169	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
172	C₂×C₃×C₈	—	2	2	no	—
173	C₂×C₃×C₈	—	2	2	no	—
174	C₂×C₃×C₈	—	2	2	no	—
175	C₃×C₄⋊C₄	—	2	2	no	—
176	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	—
177	C₃×C₂²⋊C₄	—	2	4	no	—
178	C₃×C₂²⋊C₄	—	2	4	no	—
179	C₃×C₄²	—	4	2	no	—
180	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
181	C₃×C₄²	C₅×D₄	1	2	yes	—
182	C₂³×C₅	—	2	2	no	—
183	C₂³×C₅	—	4	2	no	—
184	C₂³×C₅	—	4	2	no	—
185	C₂³×C₅	—	4	1	no	—
186	C₂³×C₅	—	4	1	no	—
187	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
188	C₅×Q₈	—	2	4	no	—
189	C₅×Q₈	—	4	1	no	—
190	C₅×Q₈	—	4	1	no	—
191	C₅×D₄	—	2	4	no	—
192	C₅×D₄	—	4	1	no	—
193	C₅×D₄	—	4	1	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	1	no	—
196	C₂×C₄×C₅	—	2	1	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	4	no	—
199	C₂×C₄×C₅	—	4	2	no	—
200	C₂×C₄×C₅	—	4	2	no	—
201	C₂×C₄×C₅	—	4	2	no	—
202	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
203	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
204	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
206	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
207	C₂×C₄×C₅	C₃×#41	1	2	yes	—
208	C₅×C₈	—	4	2	no	—
209	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
210	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
211	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
212	#124	—	2	2	no	—
213	#124	C₃×C₄×C₅	1	4	yes	complemented
214	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
215	C₂×C₂²⋊C₄	—	2	1	no	—
216	C₂×C₂²⋊C₄	—	2	1	no	—
217	C₂×C₄²	—	2	1	no	—
218	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
219	C₄⋊C₈	—	2	2	no	—
220	#103	—	2	4	no	—
221	#102	—	2	4	no	—
222	#95	—	2	1	no	—
223	C₂×C₃×C₅	—	8	2	no	—
224	C₂×C₃×C₅	#390	1	1	yes	characteristic
225	C₂×C₃×C₅	#416	1	1	yes	characteristic
226	C₂×C₃×C₅	#417	1	1	yes	characteristic
227	C₂×C₃×C₅	#463	1	2	yes	—
228	C₂×C₃×C₅	#464	1	2	yes	—
229	C₂³×C₃	—	2	2	no	—
230	C₂³×C₃	—	4	2	no	—
231	C₂³×C₃	—	4	2	no	—
232	C₂³×C₃	—	4	1	no	—
233	C₂³×C₃	—	4	1	no	—
234	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
235	C₃×Q₈	—	2	4	no	—
236	C₃×Q₈	—	4	1	no	—
237	C₃×Q₈	—	4	1	no	—
238	C₃×D₄	—	2	4	no	—
239	C₃×D₄	—	4	1	no	—
240	C₃×D₄	—	4	1	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	4	2	no	—
247	C₂×C₃×C₄	—	4	2	no	—
248	C₂×C₃×C₄	—	4	2	no	—
249	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
250	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
251	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
253	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
254	C₂×C₃×C₄	C₅×#41	1	2	yes	—
255	C₃×C₈	—	4	2	no	—
256	C₂²×C₅	—	4	2	no	—
257	C₂²×C₅	—	4	2	no	—
258	C₂²×C₅	—	4	2	no	—
259	C₂²×C₅	—	8	2	no	—
260	C₂²×C₅	—	8	2	no	—
261	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
262	C₂²×C₅	C₃×#121	1	2	yes	—
263	C₂²×C₅	C₃×#135	1	2	yes	—
264	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
265	C₂²×C₅	C₃×#137	1	1	yes	characteristic
266	C₄×C₅	—	2	2	no	—
267	C₄×C₅	—	2	2	no	—
268	C₄×C₅	—	4	2	no	—
269	C₄×C₅	—	4	4	no	—
270	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
271	C₄×C₅	C₃×#124	1	1	yes	characteristic
272	C₄×C₅	C₃×#127	1	1	yes	characteristic
273	C₂⁴	—	2	1	no	—
274	C₂×Q₈	—	2	1	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	C₂×C₃×C₄×C₅	1	2	yes	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	C₂×C₃×C₄×C₅	1	2	yes	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
285	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
286	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	—
292	C₂²⋊C₄	—	2	4	no	—
293	C₂²⋊C₄	—	2	4	no	—
294	C₄²	—	4	2	no	—
295	C₄²	C₂×C₃×C₄×C₅	1	2	yes	—
296	C₄²	C₃×C₅×D₄	1	2	yes	—
297	C₃×C₅	#1983	1	1	yes	characteristic, direct product factor, Hall
298	C₂²×C₃	—	4	2	no	—
299	C₂²×C₃	—	4	2	no	—
300	C₂²×C₃	—	4	2	no	—
301	C₂²×C₃	—	8	2	no	—
302	C₂²×C₃	—	8	2	no	—
303	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
304	C₂²×C₃	C₅×#121	1	2	yes	—
305	C₂²×C₃	C₅×#135	1	2	yes	—
306	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
307	C₂²×C₃	C₅×#137	1	1	yes	characteristic
308	C₃×C₄	—	2	2	no	—
309	C₃×C₄	—	2	2	no	—
310	C₃×C₄	—	4	2	no	—
311	C₃×C₄	—	4	4	no	—
312	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
313	C₃×C₄	C₅×#124	1	1	yes	characteristic
314	C₃×C₄	C₅×#127	1	1	yes	characteristic
315	C₂×C₅	—	8	2	no	—
316	C₂×C₅	C₃×#390	1	1	yes	characteristic
317	C₂×C₅	C₃×#416	1	1	yes	characteristic
318	C₂×C₅	C₃×#417	1	1	yes	characteristic
319	C₂×C₅	C₃×#463	1	2	yes	—
320	C₂×C₅	C₃×#464	1	2	yes	—
321	C₂³	—	2	2	no	—
322	C₂³	—	4	2	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	1	no	—
325	C₂³	—	4	1	no	—
326	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
327	Q₈	—	2	4	no	—
328	Q₈	—	4	1	no	—
329	Q₈	—	4	1	no	—
330	D₄	—	2	4	no	—
331	D₄	—	4	1	no	—
332	D₄	—	4	1	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	2	yes	—
342	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	2	yes	—
343	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
344	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
345	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
346	C₂×C₄	C₃×C₅×#41	1	2	yes	—
347	C₈	—	4	2	no	—
348	C₂×C₃	—	8	2	no	—
349	C₂×C₃	C₅×#390	1	1	yes	characteristic
350	C₂×C₃	C₅×#416	1	1	yes	characteristic
351	C₂×C₃	C₅×#417	1	1	yes	characteristic
352	C₂×C₃	C₅×#463	1	2	yes	—
353	C₂×C₃	C₅×#464	1	2	yes	—
354	C₅	C₃×#1983	1	1	yes	characteristic, direct product factor, Sylow
355	C₂²	—	4	2	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	8	2	no	—
359	C₂²	—	8	2	no	—
360	C₂²	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
361	C₂²	C₃×C₅×#121	1	2	yes	—
362	C₂²	C₃×C₅×#135	1	2	yes	—
363	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
364	C₂²	C₃×C₅×#137	1	1	yes	characteristic
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	4	4	no	—
368	C₄	—	4	2	no	—
369	C₄	C₃×C₄×C₅×D₄	1	2	yes	—
370	C₄	C₃×C₅×#124	1	1	yes	characteristic
371	C₄	C₃×C₅×#127	1	1	yes	characteristic
372	C₃	C₅×#1983	1	1	yes	characteristic, direct product factor, Sylow
373	C₂	—	8	2	no	—
374	C₂	C₃×C₅×#390	1	1	yes	characteristic
375	C₂	C₃×C₅×#416	1	1	yes	characteristic
376	C₂	C₃×C₅×#417	1	1	yes	characteristic
377	C₂	C₃×C₅×#463	1	2	yes	—
378	C₂	C₃×C₅×#464	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂×D₄
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
3. C₂×C₃×C₅×#103	C₂	semidirect
5. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
6. C₅×#1983	C₃	direct (N × H)
11. C₃×C₅×#124	C₄	semidirect
21. C₃×#1983	C₅	direct (N × H)
23. C₂×C₅×C₄⋊C₈	C₂×C₃	semidirect
24. C₂×C₅×#103	C₂×C₃	semidirect
26. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
52. C₂×C₃×C₄⋊C₈	C₂×C₅	semidirect
53. C₂×C₃×#103	C₂×C₅	semidirect
55. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
60. C₅×#124	C₃×C₄	semidirect
70. #1983	C₃×C₅	direct (N × H)
102. C₃×#124	C₄×C₅	semidirect
137. C₂×C₄⋊C₈	C₂×C₃×C₅	semidirect
138. C₂×#103	C₂×C₃×C₅	semidirect
140. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
213. #124	C₃×C₄×C₅	semidirect
297. C₃×C₅	#1983	direct (N × H)
354. C₅	C₃×#1983	direct (N × H)
372. C₃	C₅×#1983	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×C₅×#124	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₃×C₅×#103	2
C₂×C₃×C₅×#102	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#1983	3
C₃×#1983	5

Subgroups — C3×C5×#1983 #14275017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1983 #14275017