Subgroups — C₃×C₅×#1948 #14274982

Order 1920.

512 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#106	C₂	1	2	yes	maximal
2	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#340	C₂	1	2	yes	maximal
6	C₅×#1948	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
8	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
9	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
10	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄²×C₅	—	2	1	no	—
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₃×C₅×#106	—	2	4	no	—
16	C₃×C₅×C₄⋊C₈	C₄	1	4	yes	complemented
17	C₃×C₅×#95	—	2	1	no	—
18	C₃×#1948	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₅×#106	C₂×C₃	1	2	yes	—
20	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
21	C₅×#384	C₂×C₃	1	1	yes	characteristic
22	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
23	C₅×#340	C₂×C₃	1	2	yes	—
24	C₂²×C₃×C₄×C₅	—	2	1	no	—
25	C₂²×C₃×C₄×C₅	—	2	1	no	—
26	C₂²×C₃×C₄×C₅	—	2	2	no	—
27	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
29	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
30	C₂×C₃×C₅×C₈	—	2	2	no	—
31	C₂×C₃×C₅×C₈	—	2	2	no	—
32	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	—
33	C₃×C₅×C₄⋊C₄	—	2	1	no	—
34	C₃×C₅×C₄⋊C₄	—	2	1	no	—
35	C₃×C₅×C₄⋊C₄	—	2	2	no	—
36	C₃×C₅×C₄⋊C₄	—	2	2	no	—
37	C₃×C₅×C₄⋊C₄	—	4	2	no	—
38	C₃×C₅×C₄⋊C₄	—	4	2	no	—
39	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
40	C₃×C₅×C₄⋊C₄	Q₈	1	2	yes	—
41	C₃×C₄²×C₅	—	4	2	no	—
42	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
43	C₃×C₄²×C₅	Q₈	1	2	yes	—
44	C₂×C₃×#106	C₂×C₅	1	2	yes	—
45	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
46	C₃×#384	C₂×C₅	1	1	yes	characteristic
47	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
48	C₃×#340	C₂×C₅	1	2	yes	—
49	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
50	C₂×C₅×C₄⋊C₄	—	2	1	no	—
51	C₂×C₅×C₄⋊C₄	—	2	1	no	—
52	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
53	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
54	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
55	C₂×C₄²×C₅	—	2	1	no	—
56	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
57	C₅×#106	—	2	4	no	—
58	C₅×C₄⋊C₈	C₃×C₄	1	4	yes	complemented
59	C₅×#95	—	2	1	no	—
60	#1948	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
61	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
62	C₂×C₃×C₄×C₅	—	2	1	no	—
63	C₂×C₃×C₄×C₅	—	2	1	no	—
64	C₂×C₃×C₄×C₅	—	2	2	no	—
65	C₂×C₃×C₄×C₅	—	2	2	no	—
66	C₂×C₃×C₄×C₅	—	4	1	no	—
67	C₂×C₃×C₄×C₅	—	4	1	no	—
68	C₂×C₃×C₄×C₅	—	4	1	no	—
69	C₂×C₃×C₄×C₅	—	4	1	no	—
70	C₂×C₃×C₄×C₅	—	4	2	no	—
71	C₂×C₃×C₄×C₅	—	4	2	no	—
72	C₂×C₃×C₄×C₅	—	4	2	no	—
73	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
74	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
75	C₂×C₃×C₄×C₅	SD₁₆	1	2	yes	—
76	C₂×C₃×C₄×C₅	SD₁₆	1	2	yes	—
77	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
79	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
80	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
81	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
82	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
83	C₃×C₅×C₈	—	2	4	no	—
84	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
85	C₂×C₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
88	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
89	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
90	C₂×C₃×C₄²	—	2	1	no	—
91	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
92	C₃×#106	—	2	4	no	—
93	C₃×C₄⋊C₈	C₄×C₅	1	4	yes	complemented
94	C₃×#95	—	2	1	no	—
95	C₂²×C₄×C₅	—	2	1	no	—
96	C₂²×C₄×C₅	—	2	1	no	—
97	C₂²×C₄×C₅	—	2	2	no	—
98	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
101	C₂×C₅×C₈	—	2	2	no	—
102	C₂×C₅×C₈	—	2	2	no	—
103	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	—
104	C₅×C₄⋊C₄	—	2	1	no	—
105	C₅×C₄⋊C₄	—	2	1	no	—
106	C₅×C₄⋊C₄	—	2	2	no	—
107	C₅×C₄⋊C₄	—	2	2	no	—
108	C₅×C₄⋊C₄	—	4	2	no	—
109	C₅×C₄⋊C₄	—	4	2	no	—
110	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
111	C₅×C₄⋊C₄	C₃×Q₈	1	2	yes	—
112	C₄²×C₅	—	4	2	no	—
113	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
114	C₄²×C₅	C₃×Q₈	1	2	yes	—
115	C₂×#106	C₂×C₃×C₅	1	2	yes	—
116	C₂×C₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic
117	#384	C₂×C₃×C₅	1	1	yes	characteristic
118	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
119	#340	C₂×C₃×C₅	1	2	yes	—
120	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂²×C₃×C₅	#121	1	1	yes	characteristic
122	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
123	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
124	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
125	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
126	C₂²×C₃×C₅	#137	1	1	yes	characteristic
127	C₃×C₄×C₅	—	2	2	no	—
128	C₃×C₄×C₅	—	4	2	no	—
129	C₃×C₄×C₅	—	4	2	no	—
130	C₃×C₄×C₅	—	8	2	no	—
131	C₃×C₄×C₅	#106	1	4	yes	complemented
132	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
133	C₃×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
134	C₃×C₄×C₅	#125	1	1	yes	characteristic
135	C₃×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
136	C₂²×C₃×C₄	—	2	1	no	—
137	C₂²×C₃×C₄	—	2	1	no	—
138	C₂²×C₃×C₄	—	2	2	no	—
139	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
140	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
141	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
142	C₂×C₃×C₈	—	2	2	no	—
143	C₂×C₃×C₈	—	2	2	no	—
144	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	—
145	C₃×C₄⋊C₄	—	2	1	no	—
146	C₃×C₄⋊C₄	—	2	1	no	—
147	C₃×C₄⋊C₄	—	2	2	no	—
148	C₃×C₄⋊C₄	—	2	2	no	—
149	C₃×C₄⋊C₄	—	4	2	no	—
150	C₃×C₄⋊C₄	—	4	2	no	—
151	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
152	C₃×C₄⋊C₄	C₅×Q₈	1	2	yes	—
153	C₃×C₄²	—	4	2	no	—
154	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
155	C₃×C₄²	C₅×Q₈	1	2	yes	—
156	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
157	C₂×C₄×C₅	—	2	1	no	—
158	C₂×C₄×C₅	—	2	1	no	—
159	C₂×C₄×C₅	—	2	2	no	—
160	C₂×C₄×C₅	—	2	2	no	—
161	C₂×C₄×C₅	—	4	1	no	—
162	C₂×C₄×C₅	—	4	1	no	—
163	C₂×C₄×C₅	—	4	1	no	—
164	C₂×C₄×C₅	—	4	1	no	—
165	C₂×C₄×C₅	—	4	2	no	—
166	C₂×C₄×C₅	—	4	2	no	—
167	C₂×C₄×C₅	—	4	2	no	—
168	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
169	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
170	C₂×C₄×C₅	C₃×SD₁₆	1	2	yes	—
171	C₂×C₄×C₅	C₃×SD₁₆	1	2	yes	—
172	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
173	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
174	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
176	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
177	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
178	C₅×C₈	—	2	4	no	—
179	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
180	C₂×C₄⋊C₄	—	2	1	no	—
181	C₂×C₄⋊C₄	—	2	1	no	—
182	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
183	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
184	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
185	C₂×C₄²	—	2	1	no	—
186	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
187	#106	—	2	4	no	—
188	C₄⋊C₈	C₃×C₄×C₅	1	4	yes	complemented
189	#95	—	2	1	no	—
190	C₂×C₃×C₅	#389	1	1	yes	characteristic
191	C₂×C₃×C₅	C₂×#106	1	1	yes	characteristic
192	C₂×C₃×C₅	#428	1	1	yes	characteristic
193	C₂×C₃×C₅	#460	1	1	yes	characteristic
194	C₂×C₃×C₅	#461	1	1	yes	characteristic
195	C₂×C₃×C₅	#475	1	1	yes	characteristic
196	C₂×C₃×C₅	#476	1	1	yes	characteristic
197	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
198	C₂×C₃×C₄	—	2	1	no	—
199	C₂×C₃×C₄	—	2	1	no	—
200	C₂×C₃×C₄	—	2	2	no	—
201	C₂×C₃×C₄	—	2	2	no	—
202	C₂×C₃×C₄	—	4	1	no	—
203	C₂×C₃×C₄	—	4	1	no	—
204	C₂×C₃×C₄	—	4	1	no	—
205	C₂×C₃×C₄	—	4	1	no	—
206	C₂×C₃×C₄	—	4	2	no	—
207	C₂×C₃×C₄	—	4	2	no	—
208	C₂×C₃×C₄	—	4	2	no	—
209	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
210	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
211	C₂×C₃×C₄	C₅×SD₁₆	1	2	yes	—
212	C₂×C₃×C₄	C₅×SD₁₆	1	2	yes	—
213	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
214	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
215	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
216	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
217	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
218	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
219	C₃×C₈	—	2	4	no	—
220	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
221	C₂²×C₅	C₃×#121	1	1	yes	characteristic
222	C₂²×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
223	C₂²×C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
224	C₂²×C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
225	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
226	C₂²×C₅	C₃×#137	1	1	yes	characteristic
227	C₄×C₅	—	2	2	no	—
228	C₄×C₅	—	4	2	no	—
229	C₄×C₅	—	4	2	no	—
230	C₄×C₅	—	8	2	no	—
231	C₄×C₅	C₃×#106	1	4	yes	complemented
232	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
233	C₄×C₅	C₃×C₄×Q₈	1	1	yes	characteristic
234	C₄×C₅	C₃×#125	1	1	yes	characteristic
235	C₄×C₅	C₃×C₄⋊Q₈	1	1	yes	characteristic
236	C₂²×C₄	—	2	1	no	—
237	C₂²×C₄	—	2	1	no	—
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
240	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
241	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
242	C₂×C₈	—	2	2	no	—
243	C₂×C₈	—	2	2	no	—
244	C₂×C₈	C₂×C₃×C₄×C₅	1	4	yes	—
245	C₄⋊C₄	—	2	1	no	—
246	C₄⋊C₄	—	2	1	no	—
247	C₄⋊C₄	—	2	2	no	—
248	C₄⋊C₄	—	2	2	no	—
249	C₄⋊C₄	—	4	2	no	—
250	C₄⋊C₄	—	4	2	no	—
251	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
252	C₄⋊C₄	C₃×C₅×Q₈	1	2	yes	—
253	C₄²	—	4	2	no	—
254	C₄²	C₂×C₃×C₄×C₅	1	2	yes	—
255	C₄²	C₃×C₅×Q₈	1	2	yes	—
256	C₃×C₅	#1948	1	1	yes	characteristic, direct product factor, Hall
257	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
258	C₂²×C₃	C₅×#121	1	1	yes	characteristic
259	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
260	C₂²×C₃	C₂×C₅×SD₁₆	1	1	yes	characteristic
261	C₂²×C₃	C₂×C₅×SD₁₆	1	1	yes	characteristic
262	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
263	C₂²×C₃	C₅×#137	1	1	yes	characteristic
264	C₃×C₄	—	2	2	no	—
265	C₃×C₄	—	4	2	no	—
266	C₃×C₄	—	4	2	no	—
267	C₃×C₄	—	8	2	no	—
268	C₃×C₄	C₅×#106	1	4	yes	complemented
269	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
270	C₃×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
271	C₃×C₄	C₅×#125	1	1	yes	characteristic
272	C₃×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
273	C₂×C₅	C₃×#389	1	1	yes	characteristic
274	C₂×C₅	C₂×C₃×#106	1	1	yes	characteristic
275	C₂×C₅	C₃×#428	1	1	yes	characteristic
276	C₂×C₅	C₃×#460	1	1	yes	characteristic
277	C₂×C₅	C₃×#461	1	1	yes	characteristic
278	C₂×C₅	C₃×#475	1	1	yes	characteristic
279	C₂×C₅	C₃×#476	1	1	yes	characteristic
280	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	1	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	4	1	no	—
286	C₂×C₄	—	4	1	no	—
287	C₂×C₄	—	4	1	no	—
288	C₂×C₄	—	4	1	no	—
289	C₂×C₄	—	4	2	no	—
290	C₂×C₄	—	4	2	no	—
291	C₂×C₄	—	4	2	no	—
292	C₂×C₄	C₃×C₅×C₄⋊C₄	1	2	yes	—
293	C₂×C₄	C₃×C₅×C₄⋊C₄	1	2	yes	—
294	C₂×C₄	C₃×C₅×SD₁₆	1	2	yes	—
295	C₂×C₄	C₃×C₅×SD₁₆	1	2	yes	—
296	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
297	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
298	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
299	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
300	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
301	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
302	C₈	—	2	4	no	—
303	C₂×C₃	C₅×#389	1	1	yes	characteristic
304	C₂×C₃	C₂×C₅×#106	1	1	yes	characteristic
305	C₂×C₃	C₅×#428	1	1	yes	characteristic
306	C₂×C₃	C₅×#460	1	1	yes	characteristic
307	C₂×C₃	C₅×#461	1	1	yes	characteristic
308	C₂×C₃	C₅×#475	1	1	yes	characteristic
309	C₂×C₃	C₅×#476	1	1	yes	characteristic
310	C₅	C₃×#1948	1	1	yes	characteristic, direct product factor, Sylow
311	C₂²	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
312	C₂²	C₃×C₅×#121	1	1	yes	characteristic
313	C₂²	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
314	C₂²	C₂×C₃×C₅×SD₁₆	1	1	yes	characteristic
315	C₂²	C₂×C₃×C₅×SD₁₆	1	1	yes	characteristic
316	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
317	C₂²	C₃×C₅×#137	1	1	yes	characteristic
318	C₄	—	2	2	no	—
319	C₄	—	4	2	no	—
320	C₄	—	4	2	no	—
321	C₄	—	8	2	no	—
322	C₄	C₃×C₅×#106	1	4	yes	complemented
323	C₄	C₃×C₄×C₅×D₄	1	1	yes	characteristic
324	C₄	C₃×C₄×C₅×Q₈	1	1	yes	characteristic
325	C₄	C₃×C₅×#125	1	1	yes	characteristic
326	C₄	C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
327	C₃	C₅×#1948	1	1	yes	characteristic, direct product factor, Sylow
328	C₂	C₃×C₅×#389	1	1	yes	characteristic
329	C₂	C₂×C₃×C₅×#106	1	1	yes	characteristic
330	C₂	C₃×C₅×#428	1	1	yes	characteristic
331	C₂	C₃×C₅×#460	1	1	yes	characteristic
332	C₂	C₃×C₅×#461	1	1	yes	characteristic
333	C₂	C₃×C₅×#475	1	1	yes	characteristic
334	C₂	C₃×C₅×#476	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂×D₄
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
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
6. C₅×#1948	C₃	direct (N × H)
16. C₃×C₅×C₄⋊C₈	C₄	semidirect
18. C₃×#1948	C₅	direct (N × H)
58. C₅×C₄⋊C₈	C₃×C₄	semidirect
60. #1948	C₃×C₅	direct (N × H)
93. C₃×C₄⋊C₈	C₄×C₅	semidirect
131. C₃×C₄×C₅	#106	semidirect
188. C₄⋊C₈	C₃×C₄×C₅	semidirect
231. C₄×C₅	C₃×#106	semidirect
256. C₃×C₅	#1948	direct (N × H)
268. C₃×C₄	C₅×#106	semidirect
310. C₅	C₃×#1948	direct (N × H)
322. C₄	C₃×C₅×#106	semidirect
327. C₃	C₅×#1948	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×#106	2
C₂×C₃×C₅×C₄⋊C₈	2
C₃×C₅×#384	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₅×#340	2
C₅×#1948	3
C₃×#1948	5

Subgroups — C3×C5×#1948 #14274982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1948 #14274982