Subgroups — C₃×C₅×#3151 #14276185

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	4	yes	maximal, complemented
2	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#496	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#493	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#492	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#3151	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
10	C₂²×C₃×C₅×D₄	—	2	2	no	—
11	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
12	C₃×C₅×AGL(1,ℤ/8)	—	2	16	no	—
13	C₂×C₃×C₅×SD₁₆	C₂²	1	8	yes	complemented
14	C₂×C₃×C₅×D₈	C₂²	1	8	yes	complemented
15	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
16	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₃×C₅×#127	—	2	2	no	—
18	C₃×C₅×#127	C₂²	1	2	yes	—
19	C₃×C₅×#127	C₂²	1	2	yes	—
20	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₅×#124	C₂²	1	2	yes	complemented
22	C₃×C₅×#121	—	2	2	no	—
23	C₃×C₄×C₅×D₄	—	2	2	no	—
24	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₃×C₅×#97	C₂²	1	2	yes	complemented
26	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
27	C₃×#3151	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	4	yes	complemented
29	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic, complemented
31	C₅×#496	C₂×C₃	1	4	yes	complemented
32	C₅×#493	C₂×C₃	1	2	yes	complemented
33	C₅×#492	C₂×C₃	1	2	yes	complemented
34	C₄×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂⁴×C₃×C₅	—	2	2	no	—
36	C₃×C₅×#41	—	2	8	no	—
37	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
38	C₂×C₃×C₅×D₄	—	2	2	no	—
39	C₂×C₃×C₅×D₄	—	2	8	no	—
40	C₂×C₃×C₅×D₄	—	2	2	no	—
41	C₂×C₃×C₅×D₄	—	2	4	no	—
42	C₂×C₃×C₅×D₄	—	2	4	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	—	4	8	no	—
45	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
46	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	—	2	2	no	—
48	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₃×C₅×SD₁₆	—	2	16	no	—
51	C₃×C₅×D₈	—	2	16	no	—
52	C₃×C₅×M₁₆	D₄	1	8	yes	complemented
53	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
54	C₃×C₅×C₄⋊C₄	—	2	2	no	—
55	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
56	C₃×C₄²×C₅	D₄	1	2	yes	—
57	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
58	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	4	yes	complemented
60	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
61	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic, complemented
62	C₃×#496	C₂×C₅	1	4	yes	complemented
63	C₃×#493	C₂×C₅	1	2	yes	complemented
64	C₃×#492	C₂×C₅	1	2	yes	complemented
65	C₃×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
67	C₂²×C₅×D₄	—	2	2	no	—
68	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
69	C₅×AGL(1,ℤ/8)	—	2	16	no	—
70	C₂×C₅×SD₁₆	C₂²×C₃	1	8	yes	complemented
71	C₂×C₅×D₈	C₂²×C₃	1	8	yes	complemented
72	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
73	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
74	C₅×#127	—	2	2	no	—
75	C₅×#127	C₂²×C₃	1	2	yes	—
76	C₅×#127	C₂²×C₃	1	2	yes	—
77	C₅×#127	C₂²×C₃	1	1	yes	characteristic, complemented
78	C₅×#124	C₂²×C₃	1	2	yes	complemented
79	C₅×#121	—	2	2	no	—
80	C₄×C₅×D₄	—	2	2	no	—
81	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
82	C₅×#97	C₂²×C₃	1	2	yes	complemented
83	C₄×C₅×C₈	C₂²×C₃	1	2	yes	complemented
84	#3151	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
85	C₂³×C₃×C₅	—	2	2	no	—
86	C₂³×C₃×C₅	—	2	4	no	—
87	C₂³×C₃×C₅	—	4	8	no	—
88	C₂³×C₃×C₅	—	4	4	no	—
89	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
90	C₃×C₅×Q₈	—	2	4	no	—
91	C₃×C₅×D₄	—	2	4	no	—
92	C₃×C₅×D₄	—	2	8	no	—
93	C₃×C₅×D₄	—	4	8	no	—
94	C₃×C₅×D₄	—	4	4	no	—
95	C₃×C₅×D₄	—	4	4	no	—
96	C₃×C₅×D₄	—	4	4	no	—
97	C₃×C₅×D₄	—	4	8	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	4	4	no	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
104	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
106	C₃×C₅×C₈	C₂×D₄	1	8	yes	complemented
107	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
108	C₂²×C₃×D₄	—	2	2	no	—
109	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
110	C₃×AGL(1,ℤ/8)	—	2	16	no	—
111	C₂×C₃×SD₁₆	C₂²×C₅	1	8	yes	complemented
112	C₂×C₃×D₈	C₂²×C₅	1	8	yes	complemented
113	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
114	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
115	C₃×#127	—	2	2	no	—
116	C₃×#127	C₂²×C₅	1	2	yes	—
117	C₃×#127	C₂²×C₅	1	2	yes	—
118	C₃×#127	C₂²×C₅	1	1	yes	characteristic, complemented
119	C₃×#124	C₂²×C₅	1	2	yes	complemented
120	C₃×#121	—	2	2	no	—
121	C₃×C₄×D₄	—	2	2	no	—
122	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
123	C₃×#97	C₂²×C₅	1	2	yes	complemented
124	C₃×C₄×C₈	C₂²×C₅	1	2	yes	complemented
125	C₂⁴×C₅	—	2	2	no	—
126	C₅×#41	—	2	8	no	—
127	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
128	C₂×C₅×D₄	—	2	2	no	—
129	C₂×C₅×D₄	—	2	8	no	—
130	C₂×C₅×D₄	—	2	2	no	—
131	C₂×C₅×D₄	—	2	2	no	—
132	C₂×C₅×D₄	—	2	4	no	—
133	C₂×C₅×D₄	—	2	4	no	—
134	C₂×C₅×D₄	—	4	8	no	—
135	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
136	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
137	C₂²×C₄×C₅	—	2	2	no	—
138	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
139	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
140	C₅×SD₁₆	—	2	16	no	—
141	C₅×D₈	—	2	16	no	—
142	C₅×M₁₆	C₃×D₄	1	8	yes	complemented
143	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₂²⋊C₄	—	2	4	no	—
146	C₄²×C₅	C₃×D₄	1	2	yes	—
147	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
148	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
149	C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	1	4	yes	complemented
150	#532	C₂×C₃×C₅	1	1	yes	characteristic, complemented
151	C₂×#127	C₂×C₃×C₅	1	1	yes	characteristic, complemented
152	#496	C₂×C₃×C₅	1	4	yes	complemented
153	#493	C₂×C₃×C₅	1	2	yes	complemented
154	#492	C₂×C₃×C₅	1	2	yes	complemented
155	C₄×M₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
156	C₂²×C₃×C₅	—	2	2	no	—
157	C₂²×C₃×C₅	—	4	2	no	—
158	C₂²×C₃×C₅	—	4	4	no	—
159	C₂²×C₃×C₅	—	4	8	no	—
160	C₂²×C₃×C₅	—	4	4	no	—
161	C₂²×C₃×C₅	—	8	8	no	—
162	C₂²×C₃×C₅	#127	1	2	yes	—
163	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
164	C₃×C₄×C₅	—	2	2	no	—
165	C₃×C₄×C₅	—	4	2	no	—
166	C₃×C₄×C₅	#127	1	2	yes	—
167	C₃×C₄×C₅	AGL(1,ℤ/8)	1	4	yes	complemented
168	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
169	C₂⁴×C₃	—	2	2	no	—
170	C₃×#41	—	2	8	no	—
171	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
172	C₂×C₃×D₄	—	2	2	no	—
173	C₂×C₃×D₄	—	2	8	no	—
174	C₂×C₃×D₄	—	2	2	no	—
175	C₂×C₃×D₄	—	2	2	no	—
176	C₂×C₃×D₄	—	2	4	no	—
177	C₂×C₃×D₄	—	2	4	no	—
178	C₂×C₃×D₄	—	4	8	no	—
179	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
180	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
181	C₂²×C₃×C₄	—	2	2	no	—
182	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
183	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
184	C₃×SD₁₆	—	2	16	no	—
185	C₃×D₈	—	2	16	no	—
186	C₃×M₁₆	C₅×D₄	1	8	yes	complemented
187	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
188	C₃×C₄⋊C₄	—	2	2	no	—
189	C₃×C₂²⋊C₄	—	2	4	no	—
190	C₃×C₄²	C₅×D₄	1	2	yes	—
191	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
192	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
193	C₂³×C₅	—	2	2	no	—
194	C₂³×C₅	—	2	4	no	—
195	C₂³×C₅	—	4	8	no	—
196	C₂³×C₅	—	4	4	no	—
197	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
198	C₅×Q₈	—	2	4	no	—
199	C₅×D₄	—	2	4	no	—
200	C₅×D₄	—	2	8	no	—
201	C₅×D₄	—	4	8	no	—
202	C₅×D₄	—	4	4	no	—
203	C₅×D₄	—	4	4	no	—
204	C₅×D₄	—	4	4	no	—
205	C₅×D₄	—	4	8	no	—
206	C₂×C₄×C₅	—	2	4	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	4	4	no	—
209	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
210	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
212	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
213	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
214	C₅×C₈	C₂×C₃×D₄	1	8	yes	complemented
215	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
216	C₂²×D₄	—	2	2	no	—
217	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
218	AGL(1,ℤ/8)	—	2	16	no	—
219	C₂×SD₁₆	C₂²×C₃×C₅	1	8	yes	complemented
220	C₂×D₈	C₂²×C₃×C₅	1	8	yes	complemented
221	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
222	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
223	#127	—	2	2	no	—
224	#127	C₂²×C₃×C₅	1	2	yes	—
225	#127	C₂²×C₃×C₅	1	2	yes	—
226	#127	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
227	#124	C₂²×C₃×C₅	1	2	yes	complemented
228	#121	—	2	2	no	—
229	C₄×D₄	—	2	2	no	—
230	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
231	#97	C₂²×C₃×C₅	1	2	yes	complemented
232	C₄×C₈	C₂²×C₃×C₅	1	2	yes	complemented
233	C₂×C₃×C₅	—	2	2	no	—
234	C₂×C₃×C₅	—	8	2	no	—
235	C₂×C₃×C₅	—	8	4	no	—
236	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
237	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
238	C₂³×C₃	—	2	2	no	—
239	C₂³×C₃	—	2	4	no	—
240	C₂³×C₃	—	4	8	no	—
241	C₂³×C₃	—	4	4	no	—
242	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
243	C₃×Q₈	—	2	4	no	—
244	C₃×D₄	—	2	4	no	—
245	C₃×D₄	—	2	8	no	—
246	C₃×D₄	—	4	8	no	—
247	C₃×D₄	—	4	4	no	—
248	C₃×D₄	—	4	4	no	—
249	C₃×D₄	—	4	4	no	—
250	C₃×D₄	—	4	8	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	4	4	no	—
254	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
255	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
257	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
258	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
259	C₃×C₈	C₂×C₅×D₄	1	8	yes	complemented
260	C₂²×C₅	—	2	2	no	—
261	C₂²×C₅	—	4	8	no	—
262	C₂²×C₅	—	4	4	no	—
263	C₂²×C₅	—	4	2	no	—
264	C₂²×C₅	—	4	4	no	—
265	C₂²×C₅	—	8	8	no	—
266	C₂²×C₅	C₃×#127	1	2	yes	—
267	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
268	C₄×C₅	—	2	2	no	—
269	C₄×C₅	—	4	2	no	—
270	C₄×C₅	C₃×#127	1	2	yes	—
271	C₄×C₅	C₃×AGL(1,ℤ/8)	1	4	yes	complemented
272	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
273	C₂⁴	—	2	2	no	—
274	#41	—	2	8	no	—
275	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	8	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	4	8	no	—
283	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
284	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
287	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
288	SD₁₆	—	2	16	no	—
289	D₈	—	2	16	no	—
290	M₁₆	C₃×C₅×D₄	1	8	yes	complemented
291	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
292	C₄⋊C₄	—	2	2	no	—
293	C₂²⋊C₄	—	2	4	no	—
294	C₄²	C₃×C₅×D₄	1	2	yes	—
295	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
296	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
297	C₃×C₅	#3151	1	1	yes	characteristic, direct product factor, Hall
298	C₂²×C₃	—	2	2	no	—
299	C₂²×C₃	—	4	2	no	—
300	C₂²×C₃	—	4	4	no	—
301	C₂²×C₃	—	4	8	no	—
302	C₂²×C₃	—	4	4	no	—
303	C₂²×C₃	—	8	8	no	—
304	C₂²×C₃	C₅×#127	1	2	yes	—
305	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
306	C₃×C₄	—	2	2	no	—
307	C₃×C₄	—	4	2	no	—
308	C₃×C₄	C₅×#127	1	2	yes	—
309	C₃×C₄	C₅×AGL(1,ℤ/8)	1	4	yes	complemented
310	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
311	C₂×C₅	—	2	2	no	—
312	C₂×C₅	—	8	4	no	—
313	C₂×C₅	—	8	2	no	—
314	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
315	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
316	C₂³	—	2	2	no	—
317	C₂³	—	2	4	no	—
318	C₂³	—	4	8	no	—
319	C₂³	—	4	4	no	—
320	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
321	Q₈	—	2	4	no	—
322	D₄	—	2	4	no	—
323	D₄	—	2	8	no	—
324	D₄	—	4	8	no	—
325	D₄	—	4	4	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	8	no	—
328	D₄	—	4	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
333	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
334	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
335	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
336	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
337	C₈	C₂×C₃×C₅×D₄	1	8	yes	complemented
338	C₂×C₃	—	2	2	no	—
339	C₂×C₃	—	8	4	no	—
340	C₂×C₃	—	8	2	no	—
341	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
342	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
343	C₅	C₃×#3151	1	1	yes	characteristic, direct product factor, Sylow
344	C₂²	—	2	2	no	—
345	C₂²	—	4	2	no	—
346	C₂²	—	4	4	no	—
347	C₂²	—	4	8	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	8	8	no	—
350	C₂²	C₃×C₅×#127	1	2	yes	—
351	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
352	C₄	—	2	2	no	—
353	C₄	—	4	2	no	—
354	C₄	C₃×C₅×#127	1	2	yes	—
355	C₄	C₃×C₅×AGL(1,ℤ/8)	1	4	yes	complemented
356	C₄	C₂²×C₃×C₅×D₄	1	2	yes	—
357	C₃	C₅×#3151	1	1	yes	characteristic, direct product factor, Sylow
358	C₂	—	2	2	no	—
359	C₂	—	8	4	no	—
360	C₂	—	8	2	no	—
361	C₂	C₂×C₃×C₅×#127	1	1	yes	characteristic
362	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
2. C₃×C₅×#532	C₂	semidirect
3. C₂×C₃×C₅×#127	C₂	semidirect
4. C₃×C₅×#496	C₂	semidirect
5. C₃×C₅×#493	C₂	semidirect
6. C₃×C₅×#492	C₂	semidirect
7. C₃×C₄×C₅×M₁₆	C₂	semidirect
8. C₅×#3151	C₃	direct (N × H)
13. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
14. C₂×C₃×C₅×D₈	C₂²	semidirect
16. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
20. C₃×C₅×#127	C₂²	semidirect
21. C₃×C₅×#124	C₂²	semidirect
25. C₃×C₅×#97	C₂²	semidirect
26. C₃×C₄×C₅×C₈	C₂²	semidirect
27. C₃×#3151	C₅	direct (N × H)
28. C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
29. C₅×#532	C₂×C₃	semidirect
30. C₂×C₅×#127	C₂×C₃	semidirect
31. C₅×#496	C₂×C₃	semidirect
32. C₅×#493	C₂×C₃	semidirect
33. C₅×#492	C₂×C₃	semidirect
34. C₄×C₅×M₁₆	C₂×C₃	semidirect
52. C₃×C₅×M₁₆	D₄	semidirect
59. C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
60. C₃×#532	C₂×C₅	semidirect
61. C₂×C₃×#127	C₂×C₅	semidirect
62. C₃×#496	C₂×C₅	semidirect
63. C₃×#493	C₂×C₅	semidirect
64. C₃×#492	C₂×C₅	semidirect
65. C₃×C₄×M₁₆	C₂×C₅	semidirect
70. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
71. C₂×C₅×D₈	C₂²×C₃	semidirect
73. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
77. C₅×#127	C₂²×C₃	semidirect
78. C₅×#124	C₂²×C₃	semidirect
82. C₅×#97	C₂²×C₃	semidirect
83. C₄×C₅×C₈	C₂²×C₃	semidirect
84. #3151	C₃×C₅	direct (N × H)
106. C₃×C₅×C₈	C₂×D₄	semidirect
111. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
112. C₂×C₃×D₈	C₂²×C₅	semidirect
114. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
118. C₃×#127	C₂²×C₅	semidirect
119. C₃×#124	C₂²×C₅	semidirect
123. C₃×#97	C₂²×C₅	semidirect
124. C₃×C₄×C₈	C₂²×C₅	semidirect
142. C₅×M₁₆	C₃×D₄	semidirect
149. C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	semidirect
150. #532	C₂×C₃×C₅	semidirect
151. C₂×#127	C₂×C₃×C₅	semidirect
152. #496	C₂×C₃×C₅	semidirect
153. #493	C₂×C₃×C₅	semidirect
154. #492	C₂×C₃×C₅	semidirect
155. C₄×M₁₆	C₂×C₃×C₅	semidirect
167. C₃×C₄×C₅	AGL(1,ℤ/8)	semidirect
186. C₃×M₁₆	C₅×D₄	semidirect
214. C₅×C₈	C₂×C₃×D₄	semidirect
219. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
220. C₂×D₈	C₂²×C₃×C₅	semidirect
222. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
226. #127	C₂²×C₃×C₅	semidirect
227. #124	C₂²×C₃×C₅	semidirect
231. #97	C₂²×C₃×C₅	semidirect
232. C₄×C₈	C₂²×C₃×C₅	semidirect
259. C₃×C₈	C₂×C₅×D₄	semidirect
271. C₄×C₅	C₃×AGL(1,ℤ/8)	semidirect
290. M₁₆	C₃×C₅×D₄	semidirect
297. C₃×C₅	#3151	direct (N × H)
309. C₃×C₄	C₅×AGL(1,ℤ/8)	semidirect
337. C₈	C₂×C₃×C₅×D₄	semidirect
343. C₅	C₃×#3151	direct (N × H)
355. C₄	C₃×C₅×AGL(1,ℤ/8)	semidirect
357. C₃	C₅×#3151	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×AGL(1,ℤ/8)	2
C₃×C₅×#532	2
C₂×C₃×C₅×#127	2
C₃×C₅×#496	2
C₃×C₅×#493	2
C₃×C₅×#492	2
C₃×C₄×C₅×M₁₆	2
C₅×#3151	3
C₃×#3151	5

Subgroups — C3×C5×#3151 #14276185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3151 #14276185