Subgroups — C₃×C₅×#3153 #14276187

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#137	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#497	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#496	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#495	C₂	1	4	yes	maximal, complemented
8	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#3153	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₃×C₅×#137	—	2	8	no	—
14	C₃×C₅×AGL(1,ℤ/8)	—	2	8	no	—
15	C₂×C₃×C₅×Q₁₆	C₂²	1	4	yes	complemented
16	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	—
17	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	complemented
18	C₂×C₃×C₅×D₈	C₂²	1	4	yes	—
19	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
20	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₅×#124	—	2	2	no	—
23	C₃×C₅×#124	C₂²	1	2	yes	—
24	C₃×C₅×#124	C₂²	1	2	yes	—
25	C₃×C₅×#124	C₂²	1	2	yes	complemented
26	C₃×C₅×#121	—	2	2	no	—
27	C₃×C₄×C₅×D₄	—	2	2	no	—
28	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
29	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
30	C₃×C₅×#97	C₂²	1	2	yes	complemented
31	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
32	C₃×#3153	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂×C₅×#137	C₂×C₃	1	2	yes	complemented
34	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	2	yes	complemented
35	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic, complemented
37	C₅×#497	C₂×C₃	1	2	yes	complemented
38	C₅×#496	C₂×C₃	1	2	yes	complemented
39	C₅×#495	C₂×C₃	1	4	yes	complemented
40	C₄×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂⁴×C₃×C₅	—	2	1	no	—
42	C₃×C₅×#41	—	2	4	no	—
43	C₃×C₅×#41	—	2	4	no	—
44	C₂×C₃×C₅×Q₈	—	2	1	no	—
45	C₂×C₃×C₅×Q₈	—	2	4	no	—
46	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
47	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
48	C₂×C₃×C₅×D₄	—	2	2	no	—
49	C₂×C₃×C₅×D₄	—	2	4	no	—
50	C₂×C₃×C₅×D₄	—	2	2	no	—
51	C₂×C₃×C₅×D₄	—	2	1	no	—
52	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
53	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	—	2	1	no	—
55	C₂²×C₃×C₄×C₅	—	2	2	no	—
56	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₃×C₅×Q₁₆	—	2	8	no	—
59	C₃×C₅×SD₁₆	—	2	8	no	—
60	C₃×C₅×SD₁₆	—	2	8	no	—
61	C₃×C₅×D₈	—	2	8	no	—
62	C₃×C₅×M₁₆	D₄	1	8	yes	complemented
63	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
64	C₃×C₅×C₄⋊C₄	—	2	2	no	—
65	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
66	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
67	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
68	C₃×C₄²×C₅	D₄	1	2	yes	—
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₃×#137	C₂×C₅	1	2	yes	complemented
72	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	2	yes	complemented
73	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
75	C₃×#497	C₂×C₅	1	2	yes	complemented
76	C₃×#496	C₂×C₅	1	2	yes	complemented
77	C₃×#495	C₂×C₅	1	4	yes	complemented
78	C₃×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
80	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
81	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
82	C₅×#137	—	2	8	no	—
83	C₅×AGL(1,ℤ/8)	—	2	8	no	—
84	C₂×C₅×Q₁₆	C₂²×C₃	1	4	yes	complemented
85	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	—
86	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	complemented
87	C₂×C₅×D₈	C₂²×C₃	1	4	yes	—
88	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
89	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
90	C₅×#127	C₂²×C₃	1	1	yes	characteristic, complemented
91	C₅×#124	—	2	2	no	—
92	C₅×#124	C₂²×C₃	1	2	yes	—
93	C₅×#124	C₂²×C₃	1	2	yes	—
94	C₅×#124	C₂²×C₃	1	2	yes	complemented
95	C₅×#121	—	2	2	no	—
96	C₄×C₅×D₄	—	2	2	no	—
97	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
99	C₅×#97	C₂²×C₃	1	2	yes	complemented
100	C₄×C₅×C₈	C₂²×C₃	1	2	yes	complemented
101	#3153	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	—	2	2	no	—
104	C₂³×C₃×C₅	—	4	4	no	—
105	C₂³×C₃×C₅	—	4	2	no	—
106	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
107	C₃×C₅×Q₈	—	2	2	no	—
108	C₃×C₅×Q₈	—	2	4	no	—
109	C₃×C₅×Q₈	—	2	2	no	—
110	C₃×C₅×Q₈	—	4	2	no	—
111	C₃×C₅×D₄	—	2	2	no	—
112	C₃×C₅×D₄	—	2	4	no	—
113	C₃×C₅×D₄	—	2	2	no	—
114	C₃×C₅×D₄	—	4	4	no	—
115	C₃×C₅×D₄	—	4	4	no	—
116	C₃×C₅×D₄	—	4	2	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	4	2	no	—
120	C₂×C₃×C₄×C₅	—	4	2	no	—
121	C₂×C₃×C₄×C₅	—	4	4	no	—
122	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
124	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
125	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
126	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
127	C₃×C₅×C₈	C₂×D₄	1	8	yes	—
128	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
129	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
130	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
131	C₃×#137	—	2	8	no	—
132	C₃×AGL(1,ℤ/8)	—	2	8	no	—
133	C₂×C₃×Q₁₆	C₂²×C₅	1	4	yes	complemented
134	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	—
135	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	complemented
136	C₂×C₃×D₈	C₂²×C₅	1	4	yes	—
137	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
138	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
139	C₃×#127	C₂²×C₅	1	1	yes	characteristic, complemented
140	C₃×#124	—	2	2	no	—
141	C₃×#124	C₂²×C₅	1	2	yes	—
142	C₃×#124	C₂²×C₅	1	2	yes	—
143	C₃×#124	C₂²×C₅	1	2	yes	complemented
144	C₃×#121	—	2	2	no	—
145	C₃×C₄×D₄	—	2	2	no	—
146	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
147	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
148	C₃×#97	C₂²×C₅	1	2	yes	complemented
149	C₃×C₄×C₈	C₂²×C₅	1	2	yes	complemented
150	C₂⁴×C₅	—	2	1	no	—
151	C₅×#41	—	2	4	no	—
152	C₅×#41	—	2	4	no	—
153	C₂×C₅×Q₈	—	2	1	no	—
154	C₂×C₅×Q₈	—	2	4	no	—
155	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
156	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
157	C₂×C₅×D₄	—	2	2	no	—
158	C₂×C₅×D₄	—	2	4	no	—
159	C₂×C₅×D₄	—	2	2	no	—
160	C₂×C₅×D₄	—	2	1	no	—
161	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
162	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
163	C₂²×C₄×C₅	—	2	1	no	—
164	C₂²×C₄×C₅	—	2	2	no	—
165	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
166	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
167	C₅×Q₁₆	—	2	8	no	—
168	C₅×SD₁₆	—	2	8	no	—
169	C₅×SD₁₆	—	2	8	no	—
170	C₅×D₈	—	2	8	no	—
171	C₅×M₁₆	C₃×D₄	1	8	yes	complemented
172	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
173	C₅×C₄⋊C₄	—	2	2	no	—
174	C₅×C₂²⋊C₄	—	2	4	no	—
175	C₅×C₂²⋊C₄	—	2	4	no	—
176	C₅×C₂²⋊C₄	—	2	4	no	—
177	C₄²×C₅	C₃×D₄	1	2	yes	—
178	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
179	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
180	C₂×#137	C₂×C₃×C₅	1	2	yes	complemented
181	C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	1	2	yes	complemented
182	#532	C₂×C₃×C₅	1	1	yes	characteristic, complemented
183	C₂×#124	C₂×C₃×C₅	1	1	yes	characteristic, complemented
184	#497	C₂×C₃×C₅	1	2	yes	complemented
185	#496	C₂×C₃×C₅	1	2	yes	complemented
186	#495	C₂×C₃×C₅	1	4	yes	complemented
187	C₄×M₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
188	C₂²×C₃×C₅	—	2	2	no	—
189	C₂²×C₃×C₅	—	4	2	no	—
190	C₂²×C₃×C₅	—	4	2	no	—
191	C₂²×C₃×C₅	—	4	4	no	—
192	C₂²×C₃×C₅	—	4	4	no	—
193	C₂²×C₃×C₅	—	8	4	no	—
194	C₂²×C₃×C₅	#127	1	2	yes	—
195	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
196	C₃×C₄×C₅	—	2	2	no	—
197	C₃×C₄×C₅	—	2	2	no	—
198	C₃×C₄×C₅	—	4	2	no	—
199	C₃×C₄×C₅	—	4	2	no	—
200	C₃×C₄×C₅	#127	1	2	yes	—
201	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
202	C₂⁴×C₃	—	2	1	no	—
203	C₃×#41	—	2	4	no	—
204	C₃×#41	—	2	4	no	—
205	C₂×C₃×Q₈	—	2	1	no	—
206	C₂×C₃×Q₈	—	2	4	no	—
207	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
208	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
209	C₂×C₃×D₄	—	2	2	no	—
210	C₂×C₃×D₄	—	2	4	no	—
211	C₂×C₃×D₄	—	2	2	no	—
212	C₂×C₃×D₄	—	2	1	no	—
213	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
214	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
215	C₂²×C₃×C₄	—	2	1	no	—
216	C₂²×C₃×C₄	—	2	2	no	—
217	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
218	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
219	C₃×Q₁₆	—	2	8	no	—
220	C₃×SD₁₆	—	2	8	no	—
221	C₃×SD₁₆	—	2	8	no	—
222	C₃×D₈	—	2	8	no	—
223	C₃×M₁₆	C₅×D₄	1	8	yes	complemented
224	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
225	C₃×C₄⋊C₄	—	2	2	no	—
226	C₃×C₂²⋊C₄	—	2	4	no	—
227	C₃×C₂²⋊C₄	—	2	4	no	—
228	C₃×C₂²⋊C₄	—	2	4	no	—
229	C₃×C₄²	C₅×D₄	1	2	yes	—
230	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
231	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
232	C₂³×C₅	—	2	2	no	—
233	C₂³×C₅	—	2	2	no	—
234	C₂³×C₅	—	4	4	no	—
235	C₂³×C₅	—	4	2	no	—
236	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
237	C₅×Q₈	—	2	2	no	—
238	C₅×Q₈	—	2	4	no	—
239	C₅×Q₈	—	2	2	no	—
240	C₅×Q₈	—	4	2	no	—
241	C₅×D₄	—	2	2	no	—
242	C₅×D₄	—	2	4	no	—
243	C₅×D₄	—	2	2	no	—
244	C₅×D₄	—	4	4	no	—
245	C₅×D₄	—	4	4	no	—
246	C₅×D₄	—	4	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	4	2	no	—
250	C₂×C₄×C₅	—	4	2	no	—
251	C₂×C₄×C₅	—	4	4	no	—
252	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
253	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
254	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
256	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
257	C₅×C₈	C₂×C₃×D₄	1	8	yes	—
258	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
259	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
260	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
261	#137	—	2	8	no	—
262	AGL(1,ℤ/8)	—	2	8	no	—
263	C₂×Q₁₆	C₂²×C₃×C₅	1	4	yes	complemented
264	C₂×SD₁₆	C₂²×C₃×C₅	1	4	yes	—
265	C₂×SD₁₆	C₂²×C₃×C₅	1	4	yes	complemented
266	C₂×D₈	C₂²×C₃×C₅	1	4	yes	—
267	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
268	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
269	#127	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
270	#124	—	2	2	no	—
271	#124	C₂²×C₃×C₅	1	2	yes	—
272	#124	C₂²×C₃×C₅	1	2	yes	—
273	#124	C₂²×C₃×C₅	1	2	yes	complemented
274	#121	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
278	#97	C₂²×C₃×C₅	1	2	yes	complemented
279	C₄×C₈	C₂²×C₃×C₅	1	2	yes	complemented
280	C₂×C₃×C₅	—	2	2	no	—
281	C₂×C₃×C₅	—	8	2	no	—
282	C₂×C₃×C₅	—	8	2	no	—
283	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
284	C₂×C₃×C₅	#575	1	2	yes	—
285	C₂³×C₃	—	2	2	no	—
286	C₂³×C₃	—	2	2	no	—
287	C₂³×C₃	—	4	4	no	—
288	C₂³×C₃	—	4	2	no	—
289	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
290	C₃×Q₈	—	2	2	no	—
291	C₃×Q₈	—	2	4	no	—
292	C₃×Q₈	—	2	2	no	—
293	C₃×Q₈	—	4	2	no	—
294	C₃×D₄	—	2	2	no	—
295	C₃×D₄	—	2	4	no	—
296	C₃×D₄	—	2	2	no	—
297	C₃×D₄	—	4	4	no	—
298	C₃×D₄	—	4	4	no	—
299	C₃×D₄	—	4	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	4	2	no	—
303	C₂×C₃×C₄	—	4	2	no	—
304	C₂×C₃×C₄	—	4	4	no	—
305	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
306	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
307	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
308	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
309	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
310	C₃×C₈	C₂×C₅×D₄	1	8	yes	—
311	C₂²×C₅	—	2	2	no	—
312	C₂²×C₅	—	4	4	no	—
313	C₂²×C₅	—	4	4	no	—
314	C₂²×C₅	—	4	2	no	—
315	C₂²×C₅	—	4	2	no	—
316	C₂²×C₅	—	8	4	no	—
317	C₂²×C₅	C₃×#127	1	2	yes	—
318	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
319	C₄×C₅	—	2	2	no	—
320	C₄×C₅	—	2	2	no	—
321	C₄×C₅	—	4	2	no	—
322	C₄×C₅	—	4	2	no	—
323	C₄×C₅	C₃×#127	1	2	yes	—
324	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
325	C₂⁴	—	2	1	no	—
326	#41	—	2	4	no	—
327	#41	—	2	4	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	4	no	—
330	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
331	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
337	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
341	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
342	Q₁₆	—	2	8	no	—
343	SD₁₆	—	2	8	no	—
344	SD₁₆	—	2	8	no	—
345	D₈	—	2	8	no	—
346	M₁₆	C₃×C₅×D₄	1	8	yes	complemented
347	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
348	C₄⋊C₄	—	2	2	no	—
349	C₂²⋊C₄	—	2	4	no	—
350	C₂²⋊C₄	—	2	4	no	—
351	C₂²⋊C₄	—	2	4	no	—
352	C₄²	C₃×C₅×D₄	1	2	yes	—
353	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
354	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
355	C₃×C₅	#3153	1	1	yes	characteristic, direct product factor, Hall
356	C₂²×C₃	—	2	2	no	—
357	C₂²×C₃	—	4	2	no	—
358	C₂²×C₃	—	4	2	no	—
359	C₂²×C₃	—	4	4	no	—
360	C₂²×C₃	—	4	4	no	—
361	C₂²×C₃	—	8	4	no	—
362	C₂²×C₃	C₅×#127	1	2	yes	—
363	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
364	C₃×C₄	—	2	2	no	—
365	C₃×C₄	—	2	2	no	—
366	C₃×C₄	—	4	2	no	—
367	C₃×C₄	—	4	2	no	—
368	C₃×C₄	C₅×#127	1	2	yes	—
369	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
370	C₂×C₅	—	2	2	no	—
371	C₂×C₅	—	8	2	no	—
372	C₂×C₅	—	8	2	no	—
373	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
374	C₂×C₅	C₃×#575	1	2	yes	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	4	4	no	—
378	C₂³	—	4	2	no	—
379	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	2	4	no	—
382	Q₈	—	2	2	no	—
383	Q₈	—	4	2	no	—
384	D₄	—	2	2	no	—
385	D₄	—	2	4	no	—
386	D₄	—	2	2	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	4	no	—
389	D₄	—	4	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
396	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
397	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
398	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
399	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
400	C₈	C₂×C₃×C₅×D₄	1	8	yes	—
401	C₂×C₃	—	2	2	no	—
402	C₂×C₃	—	8	2	no	—
403	C₂×C₃	—	8	2	no	—
404	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
405	C₂×C₃	C₅×#575	1	2	yes	—
406	C₅	C₃×#3153	1	1	yes	characteristic, direct product factor, Sylow
407	C₂²	—	2	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	4	4	no	—
412	C₂²	—	8	4	no	—
413	C₂²	C₃×C₅×#127	1	2	yes	—
414	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	2	no	—
419	C₄	C₃×C₅×#127	1	2	yes	—
420	C₄	C₂²×C₃×C₅×D₄	1	2	yes	—
421	C₃	C₅×#3153	1	1	yes	characteristic, direct product factor, Sylow
422	C₂	—	2	2	no	—
423	C₂	—	8	2	no	—
424	C₂	—	8	2	no	—
425	C₂	C₂×C₃×C₅×#127	1	1	yes	characteristic
426	C₂	C₃×C₅×#575	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×#137	C₂	semidirect
2. C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
3. C₃×C₅×#532	C₂	semidirect
4. C₂×C₃×C₅×#124	C₂	semidirect
5. C₃×C₅×#497	C₂	semidirect
6. C₃×C₅×#496	C₂	semidirect
7. C₃×C₅×#495	C₂	semidirect
8. C₃×C₄×C₅×M₁₆	C₂	semidirect
9. C₅×#3153	C₃	direct (N × H)
15. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
17. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
20. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
21. C₃×C₅×#127	C₂²	semidirect
25. C₃×C₅×#124	C₂²	semidirect
30. C₃×C₅×#97	C₂²	semidirect
31. C₃×C₄×C₅×C₈	C₂²	semidirect
32. C₃×#3153	C₅	direct (N × H)
33. C₂×C₅×#137	C₂×C₃	semidirect
34. C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
35. C₅×#532	C₂×C₃	semidirect
36. C₂×C₅×#124	C₂×C₃	semidirect
37. C₅×#497	C₂×C₃	semidirect
38. C₅×#496	C₂×C₃	semidirect
39. C₅×#495	C₂×C₃	semidirect
40. C₄×C₅×M₁₆	C₂×C₃	semidirect
62. C₃×C₅×M₁₆	D₄	semidirect
71. C₂×C₃×#137	C₂×C₅	semidirect
72. C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
73. C₃×#532	C₂×C₅	semidirect
74. C₂×C₃×#124	C₂×C₅	semidirect
75. C₃×#497	C₂×C₅	semidirect
76. C₃×#496	C₂×C₅	semidirect
77. C₃×#495	C₂×C₅	semidirect
78. C₃×C₄×M₁₆	C₂×C₅	semidirect
84. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
86. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
89. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
90. C₅×#127	C₂²×C₃	semidirect
94. C₅×#124	C₂²×C₃	semidirect
99. C₅×#97	C₂²×C₃	semidirect
100. C₄×C₅×C₈	C₂²×C₃	semidirect
101. #3153	C₃×C₅	direct (N × H)
133. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
135. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
138. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
139. C₃×#127	C₂²×C₅	semidirect
143. C₃×#124	C₂²×C₅	semidirect
148. C₃×#97	C₂²×C₅	semidirect
149. C₃×C₄×C₈	C₂²×C₅	semidirect
171. C₅×M₁₆	C₃×D₄	semidirect
180. C₂×#137	C₂×C₃×C₅	semidirect
181. C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	semidirect
182. #532	C₂×C₃×C₅	semidirect
183. C₂×#124	C₂×C₃×C₅	semidirect
184. #497	C₂×C₃×C₅	semidirect
185. #496	C₂×C₃×C₅	semidirect
186. #495	C₂×C₃×C₅	semidirect
187. C₄×M₁₆	C₂×C₃×C₅	semidirect
223. C₃×M₁₆	C₅×D₄	semidirect
263. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
265. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
268. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
269. #127	C₂²×C₃×C₅	semidirect
273. #124	C₂²×C₃×C₅	semidirect
278. #97	C₂²×C₃×C₅	semidirect
279. C₄×C₈	C₂²×C₃×C₅	semidirect
346. M₁₆	C₃×C₅×D₄	semidirect
355. C₃×C₅	#3153	direct (N × H)
406. C₅	C₃×#3153	direct (N × H)
421. C₃	C₅×#3153	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×#137	2
C₂×C₃×C₅×AGL(1,ℤ/8)	2
C₃×C₅×#532	2
C₂×C₃×C₅×#124	2
C₃×C₅×#497	2
C₃×C₅×#496	2
C₃×C₅×#495	2
C₃×C₄×C₅×M₁₆	2
C₅×#3153	3
C₃×#3153	5

Subgroups — C3×C5×#3153 #14276187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3153 #14276187