Subgroups — C₃×C₅×#1881 #14274915

Order 1920.

620 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#575	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#568	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#408	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#344	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#341	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1881	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
11	C₃×C₅×#137	—	2	1	no	—
12	C₃×C₅×#137	C₄	1	2	yes	complemented
13	C₃×C₅×AGL(1,ℤ/8)	—	2	1	no	—
14	C₃×C₅×AGL(1,ℤ/8)	C₄	1	2	yes	complemented
15	C₃×C₅×#135	—	2	2	no	—
16	C₃×C₅×#131	—	2	2	no	—
17	C₃×C₅×#131	—	2	2	no	—
18	C₂×C₃×C₅×M₁₆	—	2	2	no	—
19	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×#117	C₂²	1	1	yes	characteristic
24	C₃×C₅×#104	—	2	2	no	—
25	C₃×C₅×#103	—	2	1	no	—
26	C₃×C₅×#102	—	2	1	no	—
27	C₃×C₅×C₂²⋊C₈	—	2	2	no	—
28	C₃×#1881	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₅×#575	C₂×C₃	1	1	yes	characteristic
30	C₅×#568	C₂×C₃	1	1	yes	characteristic, complemented
31	C₅×#421	C₂×C₃	1	1	yes	characteristic, complemented
32	C₅×#416	C₂×C₃	1	1	yes	characteristic, complemented
33	C₅×#408	C₂×C₃	1	1	yes	characteristic, complemented
34	C₅×#344	C₂×C₃	1	1	yes	characteristic, complemented
35	C₅×#341	C₂×C₃	1	1	yes	characteristic, complemented
36	C₃×C₅×#41	—	2	1	no	—
37	C₃×C₅×#41	—	2	1	no	—
38	C₃×C₅×#41	—	2	1	no	—
39	C₃×C₅×#41	—	2	1	no	—
40	C₃×C₅×#41	—	2	1	no	—
41	C₃×C₅×#41	—	2	1	no	—
42	C₃×C₅×#41	C₂×C₄	1	2	yes	—
43	C₃×C₅×#41	D₄	1	2	yes	—
44	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
45	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
46	C₂×C₃×C₅×D₄	—	2	1	no	—
47	C₂×C₃×C₅×D₄	—	2	1	no	—
48	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	—	2	1	no	—
51	C₂²×C₃×C₄×C₅	—	2	1	no	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₃×C₅×Q₁₆	—	2	2	no	—
54	C₃×C₅×SD₁₆	—	2	2	no	—
55	C₃×C₅×SD₁₆	—	2	2	no	—
56	C₃×C₅×D₈	—	2	2	no	—
57	C₃×C₅×M₁₆	—	2	4	no	—
58	C₃×C₅×M₁₆	—	2	1	no	—
59	C₃×C₅×M₁₆	—	2	1	no	—
60	C₃×C₅×M₁₆	—	2	1	no	—
61	C₃×C₅×M₁₆	—	2	1	no	—
62	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	—
63	C₃×C₅×M₁₆	D₄	1	2	yes	—
64	C₂×C₃×C₅×C₈	—	2	4	no	—
65	C₂×C₃×C₅×C₈	—	2	1	no	—
66	C₂×C₃×C₅×C₈	—	2	1	no	—
67	C₂×C₃×C₅×C₈	—	2	1	no	—
68	C₂×C₃×C₅×C₈	—	2	1	no	—
69	C₂×C₃×C₅×C₈	—	2	1	no	—
70	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
71	C₃×C₅×C₄⋊C₄	—	2	1	no	—
72	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
73	C₃×C₄²×C₅	—	2	1	no	—
74	C₃×#575	C₂×C₅	1	1	yes	characteristic
75	C₃×#568	C₂×C₅	1	1	yes	characteristic, complemented
76	C₃×#421	C₂×C₅	1	1	yes	characteristic, complemented
77	C₃×#416	C₂×C₅	1	1	yes	characteristic, complemented
78	C₃×#408	C₂×C₅	1	1	yes	characteristic, complemented
79	C₃×#344	C₂×C₅	1	1	yes	characteristic, complemented
80	C₃×#341	C₂×C₅	1	1	yes	characteristic, complemented
81	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
83	C₅×#137	—	2	1	no	—
84	C₅×#137	C₃×C₄	1	2	yes	complemented
85	C₅×AGL(1,ℤ/8)	—	2	1	no	—
86	C₅×AGL(1,ℤ/8)	C₃×C₄	1	2	yes	complemented
87	C₅×#135	—	2	2	no	—
88	C₅×#131	—	2	2	no	—
89	C₅×#131	—	2	2	no	—
90	C₂×C₅×M₁₆	—	2	2	no	—
91	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
94	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
95	C₅×#117	C₂²×C₃	1	1	yes	characteristic
96	C₅×#104	—	2	2	no	—
97	C₅×#103	—	2	1	no	—
98	C₅×#102	—	2	1	no	—
99	C₅×C₂²⋊C₈	—	2	2	no	—
100	#1881	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
101	C₂³×C₃×C₅	—	2	1	no	—
102	C₂³×C₃×C₅	—	2	1	no	—
103	C₂³×C₃×C₅	#41	1	1	yes	characteristic
104	C₃×C₅×Q₈	—	2	1	no	—
105	C₃×C₅×Q₈	—	2	1	no	—
106	C₃×C₅×Q₈	—	2	1	no	—
107	C₃×C₅×Q₈	C₂²⋊C₄	1	2	yes	—
108	C₃×C₅×D₄	—	2	2	no	—
109	C₃×C₅×D₄	—	2	2	no	—
110	C₃×C₅×D₄	—	2	1	no	—
111	C₃×C₅×D₄	—	2	1	no	—
112	C₃×C₅×D₄	—	2	1	no	—
113	C₃×C₅×D₄	—	4	1	no	—
114	C₃×C₅×D₄	—	4	1	no	—
115	C₃×C₅×D₄	C₂²⋊C₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	—	2	1	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	1	no	—
120	C₂×C₃×C₄×C₅	—	4	1	no	—
121	C₂×C₃×C₄×C₅	—	4	1	no	—
122	C₂×C₃×C₄×C₅	—	4	1	no	—
123	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
125	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
127	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
129	C₃×C₅×C₈	—	2	2	no	—
130	C₃×C₅×C₈	—	2	2	no	—
131	C₃×C₅×C₈	—	2	2	no	—
132	C₃×C₅×C₈	—	4	1	no	—
133	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
135	C₃×#137	—	2	1	no	—
136	C₃×#137	C₄×C₅	1	2	yes	complemented
137	C₃×AGL(1,ℤ/8)	—	2	1	no	—
138	C₃×AGL(1,ℤ/8)	C₄×C₅	1	2	yes	complemented
139	C₃×#135	—	2	2	no	—
140	C₃×#131	—	2	2	no	—
141	C₃×#131	—	2	2	no	—
142	C₂×C₃×M₁₆	—	2	2	no	—
143	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
145	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
146	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
147	C₃×#117	C₂²×C₅	1	1	yes	characteristic
148	C₃×#104	—	2	2	no	—
149	C₃×#103	—	2	1	no	—
150	C₃×#102	—	2	1	no	—
151	C₃×C₂²⋊C₈	—	2	2	no	—
152	C₅×#41	—	2	1	no	—
153	C₅×#41	—	2	1	no	—
154	C₅×#41	—	2	1	no	—
155	C₅×#41	—	2	1	no	—
156	C₅×#41	—	2	1	no	—
157	C₅×#41	—	2	1	no	—
158	C₅×#41	C₂×C₃×C₄	1	2	yes	—
159	C₅×#41	C₃×D₄	1	2	yes	—
160	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
161	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
162	C₂×C₅×D₄	—	2	1	no	—
163	C₂×C₅×D₄	—	2	1	no	—
164	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
165	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	—	2	1	no	—
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
169	C₅×Q₁₆	—	2	2	no	—
170	C₅×SD₁₆	—	2	2	no	—
171	C₅×SD₁₆	—	2	2	no	—
172	C₅×D₈	—	2	2	no	—
173	C₅×M₁₆	—	2	4	no	—
174	C₅×M₁₆	—	2	1	no	—
175	C₅×M₁₆	—	2	1	no	—
176	C₅×M₁₆	—	2	1	no	—
177	C₅×M₁₆	—	2	1	no	—
178	C₅×M₁₆	C₂×C₃×C₄	1	2	yes	—
179	C₅×M₁₆	C₃×D₄	1	2	yes	—
180	C₂×C₅×C₈	—	2	4	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	—	2	1	no	—
185	C₂×C₅×C₈	—	2	1	no	—
186	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
187	C₅×C₄⋊C₄	—	2	1	no	—
188	C₅×C₂²⋊C₄	—	2	1	no	—
189	C₄²×C₅	—	2	1	no	—
190	#575	C₂×C₃×C₅	1	1	yes	characteristic
191	#568	C₂×C₃×C₅	1	1	yes	characteristic, complemented
192	#421	C₂×C₃×C₅	1	1	yes	characteristic, complemented
193	#416	C₂×C₃×C₅	1	1	yes	characteristic, complemented
194	#408	C₂×C₃×C₅	1	1	yes	characteristic, complemented
195	#344	C₂×C₃×C₅	1	1	yes	characteristic, complemented
196	#341	C₂×C₃×C₅	1	1	yes	characteristic, complemented
197	C₂²×C₃×C₅	—	2	2	no	—
198	C₂²×C₃×C₅	—	4	1	no	—
199	C₂²×C₃×C₅	—	4	2	no	—
200	C₂²×C₃×C₅	—	4	1	no	—
201	C₂²×C₃×C₅	—	8	1	no	—
202	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
203	C₂²×C₃×C₅	#121	1	1	yes	characteristic
204	C₂²×C₃×C₅	#123	1	1	yes	characteristic
205	C₃×C₄×C₅	—	2	2	no	—
206	C₃×C₄×C₅	—	4	1	no	—
207	C₃×C₄×C₅	—	8	1	no	—
208	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
210	C₃×C₄×C₅	#120	1	1	yes	characteristic
211	C₃×C₄×C₅	#121	1	1	yes	characteristic
212	C₃×#41	—	2	1	no	—
213	C₃×#41	—	2	1	no	—
214	C₃×#41	—	2	1	no	—
215	C₃×#41	—	2	1	no	—
216	C₃×#41	—	2	1	no	—
217	C₃×#41	—	2	1	no	—
218	C₃×#41	C₂×C₄×C₅	1	2	yes	—
219	C₃×#41	C₅×D₄	1	2	yes	—
220	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
221	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
222	C₂×C₃×D₄	—	2	1	no	—
223	C₂×C₃×D₄	—	2	1	no	—
224	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
225	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
226	C₂²×C₃×C₄	—	2	1	no	—
227	C₂²×C₃×C₄	—	2	1	no	—
228	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
229	C₃×Q₁₆	—	2	2	no	—
230	C₃×SD₁₆	—	2	2	no	—
231	C₃×SD₁₆	—	2	2	no	—
232	C₃×D₈	—	2	2	no	—
233	C₃×M₁₆	—	2	4	no	—
234	C₃×M₁₆	—	2	1	no	—
235	C₃×M₁₆	—	2	1	no	—
236	C₃×M₁₆	—	2	1	no	—
237	C₃×M₁₆	—	2	1	no	—
238	C₃×M₁₆	C₂×C₄×C₅	1	2	yes	—
239	C₃×M₁₆	C₅×D₄	1	2	yes	—
240	C₂×C₃×C₈	—	2	4	no	—
241	C₂×C₃×C₈	—	2	1	no	—
242	C₂×C₃×C₈	—	2	1	no	—
243	C₂×C₃×C₈	—	2	1	no	—
244	C₂×C₃×C₈	—	2	1	no	—
245	C₂×C₃×C₈	—	2	1	no	—
246	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
247	C₃×C₄⋊C₄	—	2	1	no	—
248	C₃×C₂²⋊C₄	—	2	1	no	—
249	C₃×C₄²	—	2	1	no	—
250	C₂³×C₅	—	2	1	no	—
251	C₂³×C₅	—	2	1	no	—
252	C₂³×C₅	C₃×#41	1	1	yes	characteristic
253	C₅×Q₈	—	2	1	no	—
254	C₅×Q₈	—	2	1	no	—
255	C₅×Q₈	—	2	1	no	—
256	C₅×Q₈	C₃×C₂²⋊C₄	1	2	yes	—
257	C₅×D₄	—	2	2	no	—
258	C₅×D₄	—	2	2	no	—
259	C₅×D₄	—	2	1	no	—
260	C₅×D₄	—	2	1	no	—
261	C₅×D₄	—	2	1	no	—
262	C₅×D₄	—	4	1	no	—
263	C₅×D₄	—	4	1	no	—
264	C₅×D₄	C₃×C₂²⋊C₄	1	2	yes	—
265	C₂×C₄×C₅	—	2	1	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	2	1	no	—
269	C₂×C₄×C₅	—	4	1	no	—
270	C₂×C₄×C₅	—	4	1	no	—
271	C₂×C₄×C₅	—	4	1	no	—
272	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
275	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
277	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
278	C₅×C₈	—	2	2	no	—
279	C₅×C₈	—	2	2	no	—
280	C₅×C₈	—	2	2	no	—
281	C₅×C₈	—	4	1	no	—
282	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
283	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
284	#137	—	2	1	no	—
285	#137	C₃×C₄×C₅	1	2	yes	complemented
286	AGL(1,ℤ/8)	—	2	1	no	—
287	AGL(1,ℤ/8)	C₃×C₄×C₅	1	2	yes	complemented
288	#135	—	2	2	no	—
289	#131	—	2	2	no	—
290	#131	—	2	2	no	—
291	C₂×M₁₆	—	2	2	no	—
292	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
293	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
294	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
295	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
296	#117	C₂²×C₃×C₅	1	1	yes	characteristic
297	#104	—	2	2	no	—
298	#103	—	2	1	no	—
299	#102	—	2	1	no	—
300	C₂²⋊C₈	—	2	2	no	—
301	C₂×C₃×C₅	—	2	1	no	—
302	C₂×C₃×C₅	—	2	1	no	—
303	C₂×C₃×C₅	—	2	1	no	—
304	C₂×C₃×C₅	—	4	2	no	—
305	C₂×C₃×C₅	—	8	1	no	—
306	C₂×C₃×C₅	#386	1	1	yes	characteristic
307	C₂³×C₃	—	2	1	no	—
308	C₂³×C₃	—	2	1	no	—
309	C₂³×C₃	C₅×#41	1	1	yes	characteristic
310	C₃×Q₈	—	2	1	no	—
311	C₃×Q₈	—	2	1	no	—
312	C₃×Q₈	—	2	1	no	—
313	C₃×Q₈	C₅×C₂²⋊C₄	1	2	yes	—
314	C₃×D₄	—	2	2	no	—
315	C₃×D₄	—	2	2	no	—
316	C₃×D₄	—	2	1	no	—
317	C₃×D₄	—	2	1	no	—
318	C₃×D₄	—	2	1	no	—
319	C₃×D₄	—	4	1	no	—
320	C₃×D₄	—	4	1	no	—
321	C₃×D₄	C₅×C₂²⋊C₄	1	2	yes	—
322	C₂×C₃×C₄	—	2	1	no	—
323	C₂×C₃×C₄	—	2	2	no	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	2	1	no	—
326	C₂×C₃×C₄	—	4	1	no	—
327	C₂×C₃×C₄	—	4	1	no	—
328	C₂×C₃×C₄	—	4	1	no	—
329	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
331	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
334	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
335	C₃×C₈	—	2	2	no	—
336	C₃×C₈	—	2	2	no	—
337	C₃×C₈	—	2	2	no	—
338	C₃×C₈	—	4	1	no	—
339	C₂²×C₅	—	2	2	no	—
340	C₂²×C₅	—	4	1	no	—
341	C₂²×C₅	—	4	2	no	—
342	C₂²×C₅	—	4	1	no	—
343	C₂²×C₅	—	8	1	no	—
344	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
345	C₂²×C₅	C₃×#121	1	1	yes	characteristic
346	C₂²×C₅	C₃×#123	1	1	yes	characteristic
347	C₄×C₅	—	2	2	no	—
348	C₄×C₅	—	4	1	no	—
349	C₄×C₅	—	8	1	no	—
350	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
351	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
352	C₄×C₅	C₃×#120	1	1	yes	characteristic
353	C₄×C₅	C₃×#121	1	1	yes	characteristic
354	#41	—	2	1	no	—
355	#41	—	2	1	no	—
356	#41	—	2	1	no	—
357	#41	—	2	1	no	—
358	#41	—	2	1	no	—
359	#41	—	2	1	no	—
360	#41	C₂×C₃×C₄×C₅	1	2	yes	—
361	#41	C₃×C₅×D₄	1	2	yes	—
362	C₂×Q₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
363	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
367	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
371	Q₁₆	—	2	2	no	—
372	SD₁₆	—	2	2	no	—
373	SD₁₆	—	2	2	no	—
374	D₈	—	2	2	no	—
375	M₁₆	—	2	4	no	—
376	M₁₆	—	2	1	no	—
377	M₁₆	—	2	1	no	—
378	M₁₆	—	2	1	no	—
379	M₁₆	—	2	1	no	—
380	M₁₆	C₂×C₃×C₄×C₅	1	2	yes	—
381	M₁₆	C₃×C₅×D₄	1	2	yes	—
382	C₂×C₈	—	2	4	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
389	C₄⋊C₄	—	2	1	no	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₄²	—	2	1	no	—
392	C₃×C₅	#1881	1	1	yes	characteristic, direct product factor, Hall
393	C₂²×C₃	—	2	2	no	—
394	C₂²×C₃	—	4	1	no	—
395	C₂²×C₃	—	4	2	no	—
396	C₂²×C₃	—	4	1	no	—
397	C₂²×C₃	—	8	1	no	—
398	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
399	C₂²×C₃	C₅×#121	1	1	yes	characteristic
400	C₂²×C₃	C₅×#123	1	1	yes	characteristic
401	C₃×C₄	—	2	2	no	—
402	C₃×C₄	—	4	1	no	—
403	C₃×C₄	—	8	1	no	—
404	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
405	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
406	C₃×C₄	C₅×#120	1	1	yes	characteristic
407	C₃×C₄	C₅×#121	1	1	yes	characteristic
408	C₂×C₅	—	2	1	no	—
409	C₂×C₅	—	2	1	no	—
410	C₂×C₅	—	2	1	no	—
411	C₂×C₅	—	4	2	no	—
412	C₂×C₅	—	8	1	no	—
413	C₂×C₅	C₃×#386	1	1	yes	characteristic
414	C₂³	—	2	1	no	—
415	C₂³	—	2	1	no	—
416	C₂³	C₃×C₅×#41	1	1	yes	characteristic
417	Q₈	—	2	1	no	—
418	Q₈	—	2	1	no	—
419	Q₈	—	2	1	no	—
420	Q₈	C₃×C₅×C₂²⋊C₄	1	2	yes	—
421	D₄	—	2	2	no	—
422	D₄	—	2	2	no	—
423	D₄	—	2	1	no	—
424	D₄	—	2	1	no	—
425	D₄	—	2	1	no	—
426	D₄	—	4	1	no	—
427	D₄	—	4	1	no	—
428	D₄	C₃×C₅×C₂²⋊C₄	1	2	yes	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
437	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
438	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
439	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
440	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
441	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
442	C₈	—	2	2	no	—
443	C₈	—	2	2	no	—
444	C₈	—	2	2	no	—
445	C₈	—	4	1	no	—
446	C₂×C₃	—	2	1	no	—
447	C₂×C₃	—	2	1	no	—
448	C₂×C₃	—	2	1	no	—
449	C₂×C₃	—	4	2	no	—
450	C₂×C₃	—	8	1	no	—
451	C₂×C₃	C₅×#386	1	1	yes	characteristic
452	C₅	C₃×#1881	1	1	yes	characteristic, direct product factor, Sylow
453	C₂²	—	2	2	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	8	1	no	—
458	C₂²	C₃×C₄×C₅×D₄	1	1	yes	characteristic
459	C₂²	C₃×C₅×#121	1	1	yes	characteristic
460	C₂²	C₃×C₅×#123	1	1	yes	characteristic
461	C₄	—	2	2	no	—
462	C₄	—	4	1	no	—
463	C₄	—	8	1	no	—
464	C₄	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
465	C₄	C₃×C₄×C₅×D₄	1	1	yes	characteristic
466	C₄	C₃×C₅×#120	1	1	yes	characteristic
467	C₄	C₃×C₅×#121	1	1	yes	characteristic
468	C₃	C₅×#1881	1	1	yes	characteristic, direct product factor, Sylow
469	C₂	—	2	1	no	—
470	C₂	—	2	1	no	—
471	C₂	—	2	1	no	—
472	C₂	—	4	2	no	—
473	C₂	—	8	1	no	—
474	C₂	C₃×C₅×#386	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄×C₅	#120
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
socle	C₂×C₃×C₅	#386
prime radical	C₃×C₅×#575	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#568	C₂	semidirect
3. C₃×C₅×#421	C₂	semidirect
4. C₃×C₅×#416	C₂	semidirect
5. C₃×C₅×#408	C₂	semidirect
6. C₃×C₅×#344	C₂	semidirect
7. C₃×C₅×#341	C₂	semidirect
8. C₅×#1881	C₃	direct (N × H)
12. C₃×C₅×#137	C₄	semidirect
14. C₃×C₅×AGL(1,ℤ/8)	C₄	semidirect
28. C₃×#1881	C₅	direct (N × H)
30. C₅×#568	C₂×C₃	semidirect
31. C₅×#421	C₂×C₃	semidirect
32. C₅×#416	C₂×C₃	semidirect
33. C₅×#408	C₂×C₃	semidirect
34. C₅×#344	C₂×C₃	semidirect
35. C₅×#341	C₂×C₃	semidirect
75. C₃×#568	C₂×C₅	semidirect
76. C₃×#421	C₂×C₅	semidirect
77. C₃×#416	C₂×C₅	semidirect
78. C₃×#408	C₂×C₅	semidirect
79. C₃×#344	C₂×C₅	semidirect
80. C₃×#341	C₂×C₅	semidirect
84. C₅×#137	C₃×C₄	semidirect
86. C₅×AGL(1,ℤ/8)	C₃×C₄	semidirect
100. #1881	C₃×C₅	direct (N × H)
136. C₃×#137	C₄×C₅	semidirect
138. C₃×AGL(1,ℤ/8)	C₄×C₅	semidirect
191. #568	C₂×C₃×C₅	semidirect
192. #421	C₂×C₃×C₅	semidirect
193. #416	C₂×C₃×C₅	semidirect
194. #408	C₂×C₃×C₅	semidirect
195. #344	C₂×C₃×C₅	semidirect
196. #341	C₂×C₃×C₅	semidirect
285. #137	C₃×C₄×C₅	semidirect
287. AGL(1,ℤ/8)	C₃×C₄×C₅	semidirect
392. C₃×C₅	#1881	direct (N × H)
452. C₅	C₃×#1881	direct (N × H)
468. C₃	C₅×#1881	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#575	2
C₃×C₅×#568	2
C₃×C₅×#421	2
C₃×C₅×#416	2
C₃×C₅×#408	2
C₃×C₅×#344	2
C₃×C₅×#341	2
C₅×#1881	3
C₃×#1881	5

Subgroups — C3×C5×#1881 #14274915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1881 #14274915