Subgroups — C₃×C₅×#3230 #14276264

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#500	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#487	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#484	C₂	1	4	yes	maximal
6	C₃×C₅×#477	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×#431	C₂	1	1	yes	maximal, characteristic
8	C₅×#3230	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	—	2	1	no	—
10	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
11	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
12	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×#125	—	2	1	no	—
17	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
18	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₃×C₄×C₅×Q₈	—	2	1	no	—
20	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
21	C₃×C₅×#117	—	2	1	no	—
22	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₃×C₅×#107	C₂²	1	8	yes	—
26	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
27	C₃×C₅×#103	C₂²	1	8	yes	—
28	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
30	C₃×#3230	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₅×#533	C₂×C₃	1	1	yes	characteristic
32	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
33	C₅×#500	C₂×C₃	1	2	yes	complemented
34	C₅×#487	C₂×C₃	1	2	yes	complemented
35	C₅×#484	C₂×C₃	1	4	yes	—
36	C₅×#477	C₂×C₃	1	4	yes	complemented
37	C₅×#431	C₂×C₃	1	1	yes	characteristic
38	C₂×C₃×C₅×Q₈	—	2	1	no	—
39	C₂×C₃×C₅×Q₈	—	2	2	no	—
40	C₂×C₃×C₅×Q₈	—	2	2	no	—
41	C₂×C₃×C₅×Q₈	—	4	4	no	—
42	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
43	C₂²×C₃×C₄×C₅	—	2	2	no	—
44	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
48	C₃×C₅×C₄⋊C₄	—	2	2	no	—
49	C₃×C₅×C₄⋊C₄	—	2	2	no	—
50	C₃×C₅×C₄⋊C₄	—	2	2	no	—
51	C₃×C₅×C₄⋊C₄	—	2	1	no	—
52	C₃×C₅×C₄⋊C₄	—	2	1	no	—
53	C₃×C₅×C₄⋊C₄	—	2	1	no	—
54	C₃×C₅×C₄⋊C₄	—	2	2	no	—
55	C₃×C₅×C₄⋊C₄	—	2	2	no	—
56	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
57	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
58	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
59	C₃×C₄²×C₅	—	2	2	no	—
60	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
61	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
62	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
63	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
64	C₃×#533	C₂×C₅	1	1	yes	characteristic
65	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
66	C₃×#500	C₂×C₅	1	2	yes	complemented
67	C₃×#487	C₂×C₅	1	2	yes	complemented
68	C₃×#484	C₂×C₅	1	4	yes	—
69	C₃×#477	C₂×C₅	1	4	yes	complemented
70	C₃×#431	C₂×C₅	1	1	yes	characteristic
71	C₂²×C₅×Q₈	—	2	1	no	—
72	C₅×C₄⋊Q₈	—	2	1	no	—
73	C₅×C₄⋊Q₈	—	2	1	no	—
74	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
75	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
76	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
77	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
78	C₅×#125	—	2	1	no	—
79	C₅×C₂²⋊Q₈	—	2	1	no	—
80	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
81	C₄×C₅×Q₈	—	2	1	no	—
82	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
83	C₅×#117	—	2	1	no	—
84	C₂×C₅×C₄⋊C₄	—	2	1	no	—
85	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
86	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
87	C₅×#107	C₂²×C₃	1	8	yes	—
88	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
89	C₅×#103	C₂²×C₃	1	8	yes	—
90	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
91	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
92	#3230	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
93	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
94	C₃×C₅×Q₈	—	2	4	no	—
95	C₃×C₅×Q₈	—	4	4	no	—
96	C₃×C₅×Q₈	—	4	2	no	—
97	C₃×C₅×Q₈	—	4	4	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	4	no	—
103	C₂×C₃×C₄×C₅	—	4	4	no	—
104	C₂×C₃×C₄×C₅	Q₁₆	1	4	yes	—
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
111	C₃×C₅×C₈	—	2	4	no	—
112	C₂²×C₃×Q₈	—	2	1	no	—
113	C₃×C₄⋊Q₈	—	2	1	no	—
114	C₃×C₄⋊Q₈	—	2	1	no	—
115	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
116	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
117	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
118	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
119	C₃×#125	—	2	1	no	—
120	C₃×C₂²⋊Q₈	—	2	1	no	—
121	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
122	C₃×C₄×Q₈	—	2	1	no	—
123	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
124	C₃×#117	—	2	1	no	—
125	C₂×C₃×C₄⋊C₄	—	2	1	no	—
126	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
127	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
128	C₃×#107	C₂²×C₅	1	8	yes	—
129	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
130	C₃×#103	C₂²×C₅	1	8	yes	—
131	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
132	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
133	C₂×C₅×Q₈	—	2	1	no	—
134	C₂×C₅×Q₈	—	2	2	no	—
135	C₂×C₅×Q₈	—	2	2	no	—
136	C₂×C₅×Q₈	—	4	4	no	—
137	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
138	C₂²×C₄×C₅	—	2	2	no	—
139	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
142	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	2	2	no	—
150	C₅×C₄⋊C₄	—	2	2	no	—
151	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
152	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
153	C₅×C₂²⋊C₄	—	2	2	no	—
154	C₄²×C₅	—	2	2	no	—
155	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
156	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
157	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
158	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
159	#533	C₂×C₃×C₅	1	1	yes	characteristic
160	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
161	#500	C₂×C₃×C₅	1	2	yes	complemented
162	#487	C₂×C₃×C₅	1	2	yes	complemented
163	#484	C₂×C₃×C₅	1	4	yes	—
164	#477	C₂×C₃×C₅	1	4	yes	complemented
165	#431	C₂×C₃×C₅	1	1	yes	characteristic
166	C₂²×C₃×C₅	—	2	1	no	—
167	C₂²×C₃×C₅	—	2	1	no	—
168	C₂²×C₃×C₅	C₂×Q₁₆	1	2	yes	—
169	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
170	C₃×C₄×C₅	—	2	1	no	—
171	C₃×C₄×C₅	—	2	1	no	—
172	C₃×C₄×C₅	—	4	2	no	—
173	C₃×C₄×C₅	—	4	4	no	—
174	C₃×C₄×C₅	—	4	2	no	—
175	C₃×C₄×C₅	C₂×Q₁₆	1	2	yes	—
176	C₃×C₄×C₅	C₂×Q₁₆	1	2	yes	—
177	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
178	C₃×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
179	C₂×C₃×Q₈	—	2	1	no	—
180	C₂×C₃×Q₈	—	2	2	no	—
181	C₂×C₃×Q₈	—	2	2	no	—
182	C₂×C₃×Q₈	—	4	4	no	—
183	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
184	C₂²×C₃×C₄	—	2	2	no	—
185	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
186	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
187	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
188	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
189	C₃×C₄⋊C₄	—	2	2	no	—
190	C₃×C₄⋊C₄	—	2	2	no	—
191	C₃×C₄⋊C₄	—	2	2	no	—
192	C₃×C₄⋊C₄	—	2	1	no	—
193	C₃×C₄⋊C₄	—	2	1	no	—
194	C₃×C₄⋊C₄	—	2	1	no	—
195	C₃×C₄⋊C₄	—	2	2	no	—
196	C₃×C₄⋊C₄	—	2	2	no	—
197	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
198	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
199	C₃×C₂²⋊C₄	—	2	2	no	—
200	C₃×C₄²	—	2	2	no	—
201	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
202	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
203	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
204	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
205	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
206	C₅×Q₈	—	2	4	no	—
207	C₅×Q₈	—	4	4	no	—
208	C₅×Q₈	—	4	2	no	—
209	C₅×Q₈	—	4	4	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	4	no	—
215	C₂×C₄×C₅	—	4	4	no	—
216	C₂×C₄×C₅	C₃×Q₁₆	1	4	yes	—
217	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
223	C₅×C₈	—	2	4	no	—
224	C₂²×Q₈	—	2	1	no	—
225	C₄⋊Q₈	—	2	1	no	—
226	C₄⋊Q₈	—	2	1	no	—
227	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
228	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
229	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
230	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
231	#125	—	2	1	no	—
232	C₂²⋊Q₈	—	2	1	no	—
233	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
234	C₄×Q₈	—	2	1	no	—
235	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
236	#117	—	2	1	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
239	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
240	#107	C₂²×C₃×C₅	1	8	yes	—
241	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
242	#103	C₂²×C₃×C₅	1	8	yes	—
243	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
244	C₄×C₈	C₂²×C₃×C₅	1	2	yes	—
245	C₂×C₃×C₅	—	2	2	no	—
246	C₂×C₃×C₅	#536	1	1	yes	characteristic
247	C₂×C₃×C₅	C₂²×Q₁₆	1	1	yes	characteristic
248	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
249	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
250	C₃×Q₈	—	2	4	no	—
251	C₃×Q₈	—	4	4	no	—
252	C₃×Q₈	—	4	2	no	—
253	C₃×Q₈	—	4	4	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	2	4	no	—
259	C₂×C₃×C₄	—	4	4	no	—
260	C₂×C₃×C₄	C₅×Q₁₆	1	4	yes	—
261	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
267	C₃×C₈	—	2	4	no	—
268	C₂²×C₅	—	2	1	no	—
269	C₂²×C₅	—	2	1	no	—
270	C₂²×C₅	C₂×C₃×Q₁₆	1	2	yes	—
271	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
272	C₄×C₅	—	2	1	no	—
273	C₄×C₅	—	2	1	no	—
274	C₄×C₅	—	4	4	no	—
275	C₄×C₅	—	4	2	no	—
276	C₄×C₅	—	4	2	no	—
277	C₄×C₅	C₂×C₃×Q₁₆	1	2	yes	—
278	C₄×C₅	C₂×C₃×Q₁₆	1	2	yes	—
279	C₄×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
280	C₄×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	4	4	no	—
285	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
288	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
289	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
290	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	1	no	—
295	C₄⋊C₄	—	2	1	no	—
296	C₄⋊C₄	—	2	1	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
300	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
301	C₂²⋊C₄	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
304	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
305	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
306	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
307	C₃×C₅	#3230	1	1	yes	characteristic, direct product factor, Hall
308	C₂²×C₃	—	2	1	no	—
309	C₂²×C₃	—	2	1	no	—
310	C₂²×C₃	C₂×C₅×Q₁₆	1	2	yes	—
311	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
312	C₃×C₄	—	2	1	no	—
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	4	2	no	—
315	C₃×C₄	—	4	4	no	—
316	C₃×C₄	—	4	2	no	—
317	C₃×C₄	C₂×C₅×Q₁₆	1	2	yes	—
318	C₃×C₄	C₂×C₅×Q₁₆	1	2	yes	—
319	C₃×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
320	C₃×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
321	C₂×C₅	—	2	2	no	—
322	C₂×C₅	C₃×#536	1	1	yes	characteristic
323	C₂×C₅	C₂²×C₃×Q₁₆	1	1	yes	characteristic
324	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
325	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
326	Q₈	—	2	4	no	—
327	Q₈	—	4	4	no	—
328	Q₈	—	4	4	no	—
329	Q₈	—	4	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	C₃×C₅×Q₁₆	1	4	yes	—
337	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
338	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
339	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
340	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
341	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
342	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
343	C₈	—	2	4	no	—
344	C₂×C₃	—	2	2	no	—
345	C₂×C₃	C₅×#536	1	1	yes	characteristic
346	C₂×C₃	C₂²×C₅×Q₁₆	1	1	yes	characteristic
347	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
348	C₅	C₃×#3230	1	1	yes	characteristic, direct product factor, Sylow
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	C₂×C₃×C₅×Q₁₆	1	2	yes	—
352	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	4	2	no	—
356	C₄	—	4	4	no	—
357	C₄	—	4	2	no	—
358	C₄	C₂×C₃×C₅×Q₁₆	1	2	yes	—
359	C₄	C₂×C₃×C₅×Q₁₆	1	2	yes	—
360	C₄	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
361	C₄	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
362	C₃	C₅×#3230	1	1	yes	characteristic, direct product factor, Sylow
363	C₂	—	2	2	no	—
364	C₂	C₃×C₅×#536	1	1	yes	characteristic
365	C₂	C₂²×C₃×C₅×Q₁₆	1	1	yes	characteristic
366	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂³×C₃×C₅	C₂×D₄
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
3. C₃×C₅×#500	C₂	semidirect
4. C₃×C₅×#487	C₂	semidirect
6. C₃×C₅×#477	C₂	semidirect
8. C₅×#3230	C₃	direct (N × H)
30. C₃×#3230	C₅	direct (N × H)
33. C₅×#500	C₂×C₃	semidirect
34. C₅×#487	C₂×C₃	semidirect
36. C₅×#477	C₂×C₃	semidirect
66. C₃×#500	C₂×C₅	semidirect
67. C₃×#487	C₂×C₅	semidirect
69. C₃×#477	C₂×C₅	semidirect
92. #3230	C₃×C₅	direct (N × H)
161. #500	C₂×C₃×C₅	semidirect
162. #487	C₂×C₃×C₅	semidirect
164. #477	C₂×C₃×C₅	semidirect
307. C₃×C₅	#3230	direct (N × H)
348. C₅	C₃×#3230	direct (N × H)
362. C₃	C₅×#3230	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×#533	2
C₂×C₃×C₅×C₄⋊Q₈	2
C₃×C₅×#500	2
C₃×C₅×#487	2
C₃×C₅×#484	2
C₃×C₅×#477	2
C₃×C₅×#431	2
C₅×#3230	3
C₃×#3230	5

Subgroups — C3×C5×#3230 #14276264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3230 #14276264