Subgroups — C₃×C₅×#2356 #14275390

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#391	C₂	1	2	yes	maximal
3	C₃×C₅×#387	C₂	1	4	yes	maximal
4	C₃×C₅×#383	C₂	1	2	yes	maximal
5	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic
6	C₃×C₄×C₅×C₄⋊C₄	C₂	1	2	yes	maximal
7	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
8	C₃×C₅×#376	C₂	1	2	yes	maximal
9	C₅×#2356	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₃×C₄×C₅×Q₈	C₄	1	8	yes	complemented
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₄²×C₅	C₂²	1	4	yes	—
17	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
19	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
20	C₃×C₅×#95	C₂²	1	1	yes	characteristic
21	C₃×C₅×#95	C₂²	1	2	yes	—
22	C₃×C₅×#95	C₂²	1	4	yes	—
23	C₃×C₅×#95	C₂²	1	1	yes	characteristic
24	C₃×C₅×#95	C₂²	1	4	yes	—
25	C₃×C₅×#95	C₂²	1	2	yes	—
26	C₃×C₅×#95	C₂²	1	4	yes	—
27	C₃×#2356	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic
29	C₅×#391	C₂×C₃	1	2	yes	—
30	C₅×#387	C₂×C₃	1	4	yes	—
31	C₅×#383	C₂×C₃	1	2	yes	—
32	C₅×#382	C₂×C₃	1	1	yes	characteristic
33	C₄×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	—
34	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
35	C₅×#376	C₂×C₃	1	2	yes	—
36	C₂×C₃×C₅×Q₈	—	2	2	no	—
37	C₂×C₃×C₅×Q₈	—	2	2	no	—
38	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₃×C₅×C₄⋊C₄	—	2	4	no	—
48	C₃×C₅×C₄⋊C₄	—	2	4	no	—
49	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	—
50	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
51	C₃×C₄²×C₅	—	2	8	no	—
52	C₃×C₄²×C₅	—	2	4	no	—
53	C₃×C₄²×C₅	C₂×C₄	1	8	yes	—
54	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
55	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic
56	C₃×#391	C₂×C₅	1	2	yes	—
57	C₃×#387	C₂×C₅	1	4	yes	—
58	C₃×#383	C₂×C₅	1	2	yes	—
59	C₃×#382	C₂×C₅	1	1	yes	characteristic
60	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
61	C₃×C₄×C₄⋊C₄	C₂×C₅	1	2	yes	—
62	C₃×#376	C₂×C₅	1	2	yes	—
63	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
64	C₄×C₅×Q₈	C₃×C₄	1	8	yes	complemented
65	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
66	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
69	C₂×C₄²×C₅	C₂²×C₃	1	4	yes	—
70	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
71	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
72	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
73	C₅×#95	C₂²×C₃	1	1	yes	characteristic
74	C₅×#95	C₂²×C₃	1	2	yes	—
75	C₅×#95	C₂²×C₃	1	4	yes	—
76	C₅×#95	C₂²×C₃	1	1	yes	characteristic
77	C₅×#95	C₂²×C₃	1	4	yes	—
78	C₅×#95	C₂²×C₃	1	2	yes	—
79	C₅×#95	C₂²×C₃	1	4	yes	—
80	#2356	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
81	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
82	C₃×C₅×Q₈	—	2	8	no	—
83	C₂×C₃×C₄×C₅	—	2	4	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	2	2	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	—	2	2	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	—	2	2	no	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	2	4	no	—
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	#41	1	4	yes	—
102	C₂×C₃×C₄×C₅	#41	1	2	yes	—
103	C₂×C₃×C₄×C₅	#41	1	2	yes	—
104	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
105	C₃×C₄×Q₈	C₄×C₅	1	8	yes	complemented
106	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
107	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
108	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
109	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
110	C₂×C₃×C₄²	C₂²×C₅	1	4	yes	—
111	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
112	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
113	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
114	C₃×#95	C₂²×C₅	1	1	yes	characteristic
115	C₃×#95	C₂²×C₅	1	2	yes	—
116	C₃×#95	C₂²×C₅	1	4	yes	—
117	C₃×#95	C₂²×C₅	1	1	yes	characteristic
118	C₃×#95	C₂²×C₅	1	4	yes	—
119	C₃×#95	C₂²×C₅	1	2	yes	—
120	C₃×#95	C₂²×C₅	1	4	yes	—
121	C₂×C₅×Q₈	—	2	2	no	—
122	C₂×C₅×Q₈	—	2	2	no	—
123	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	—
124	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
125	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
126	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
127	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
130	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
131	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
132	C₅×C₄⋊C₄	—	2	4	no	—
133	C₅×C₄⋊C₄	—	2	4	no	—
134	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
135	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
136	C₄²×C₅	—	2	8	no	—
137	C₄²×C₅	—	2	4	no	—
138	C₄²×C₅	C₂×C₃×C₄	1	8	yes	—
139	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
140	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
141	#391	C₂×C₃×C₅	1	2	yes	—
142	#387	C₂×C₃×C₅	1	4	yes	—
143	#383	C₂×C₃×C₅	1	2	yes	—
144	#382	C₂×C₃×C₅	1	1	yes	characteristic
145	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
146	C₄×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	—
147	#376	C₂×C₃×C₅	1	2	yes	—
148	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
149	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
150	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
151	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
152	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
153	C₃×C₄×C₅	—	2	4	no	—
154	C₃×C₄×C₅	—	2	4	no	—
155	C₃×C₄×C₅	—	2	2	no	—
156	C₃×C₄×C₅	—	2	2	no	—
157	C₃×C₄×C₅	—	2	4	no	—
158	C₃×C₄×C₅	—	4	2	no	—
159	C₃×C₄×C₅	—	4	4	no	—
160	C₃×C₄×C₅	#117	1	4	yes	—
161	C₂×C₃×Q₈	—	2	2	no	—
162	C₂×C₃×Q₈	—	2	2	no	—
163	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	—
164	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
165	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
166	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
168	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
169	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
171	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
172	C₃×C₄⋊C₄	—	2	4	no	—
173	C₃×C₄⋊C₄	—	2	4	no	—
174	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	—
175	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
176	C₃×C₄²	—	2	8	no	—
177	C₃×C₄²	—	2	4	no	—
178	C₃×C₄²	C₂×C₄×C₅	1	8	yes	—
179	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
180	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
181	C₅×Q₈	—	2	8	no	—
182	C₂×C₄×C₅	—	2	4	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	4	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	4	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	4	no	—
195	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
196	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
197	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
198	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
199	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
200	C₂×C₄×C₅	C₃×#41	1	4	yes	—
201	C₂×C₄×C₅	C₃×#41	1	2	yes	—
202	C₂×C₄×C₅	C₃×#41	1	2	yes	—
203	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
204	C₄×Q₈	C₃×C₄×C₅	1	8	yes	complemented
205	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
206	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
207	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
208	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
209	C₂×C₄²	C₂²×C₃×C₅	1	4	yes	—
210	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
211	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
212	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
213	#95	C₂²×C₃×C₅	1	1	yes	characteristic
214	#95	C₂²×C₃×C₅	1	2	yes	—
215	#95	C₂²×C₃×C₅	1	4	yes	—
216	#95	C₂²×C₃×C₅	1	1	yes	characteristic
217	#95	C₂²×C₃×C₅	1	4	yes	—
218	#95	C₂²×C₃×C₅	1	2	yes	—
219	#95	C₂²×C₃×C₅	1	4	yes	—
220	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
221	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
222	C₂×C₃×C₅	#519	1	1	yes	characteristic
223	C₂×C₃×C₅	#552	1	2	yes	—
224	C₂×C₃×C₅	#556	1	2	yes	—
225	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
226	C₃×Q₈	—	2	8	no	—
227	C₂×C₃×C₄	—	2	4	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	2	2	no	—
230	C₂×C₃×C₄	—	2	2	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	4	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	2	4	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
241	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
242	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
243	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
244	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
245	C₂×C₃×C₄	C₅×#41	1	4	yes	—
246	C₂×C₃×C₄	C₅×#41	1	2	yes	—
247	C₂×C₃×C₄	C₅×#41	1	2	yes	—
248	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
249	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
250	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
251	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
252	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
253	C₄×C₅	—	2	4	no	—
254	C₄×C₅	—	2	4	no	—
255	C₄×C₅	—	2	2	no	—
256	C₄×C₅	—	2	2	no	—
257	C₄×C₅	—	2	4	no	—
258	C₄×C₅	—	4	2	no	—
259	C₄×C₅	—	4	4	no	—
260	C₄×C₅	C₃×#117	1	4	yes	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	C₂×C₃×C₄×C₅	1	4	yes	—
264	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
265	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
266	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
267	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
268	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
269	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
270	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
271	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
272	C₄⋊C₄	—	2	4	no	—
273	C₄⋊C₄	—	2	4	no	—
274	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
275	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
276	C₄²	—	2	8	no	—
277	C₄²	—	2	4	no	—
278	C₄²	C₂×C₃×C₄×C₅	1	8	yes	—
279	C₄²	C₂×C₃×C₄×C₅	1	4	yes	—
280	C₃×C₅	#2356	1	1	yes	characteristic, direct product factor, Hall
281	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
282	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
283	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
284	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
285	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
286	C₃×C₄	—	2	4	no	—
287	C₃×C₄	—	2	4	no	—
288	C₃×C₄	—	2	2	no	—
289	C₃×C₄	—	2	2	no	—
290	C₃×C₄	—	2	4	no	—
291	C₃×C₄	—	4	2	no	—
292	C₃×C₄	—	4	4	no	—
293	C₃×C₄	C₅×#117	1	4	yes	—
294	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
295	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
296	C₂×C₅	C₃×#519	1	1	yes	characteristic
297	C₂×C₅	C₃×#552	1	2	yes	—
298	C₂×C₅	C₃×#556	1	2	yes	—
299	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
300	Q₈	—	2	8	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
315	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
316	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
317	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
318	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
319	C₂×C₄	C₃×C₅×#41	1	4	yes	—
320	C₂×C₄	C₃×C₅×#41	1	2	yes	—
321	C₂×C₄	C₃×C₅×#41	1	2	yes	—
322	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
323	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
324	C₂×C₃	C₅×#519	1	1	yes	characteristic
325	C₂×C₃	C₅×#552	1	2	yes	—
326	C₂×C₃	C₅×#556	1	2	yes	—
327	C₅	C₃×#2356	1	1	yes	characteristic, direct product factor, Sylow
328	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
329	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
330	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
331	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
332	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
333	C₄	—	2	4	no	—
334	C₄	—	2	4	no	—
335	C₄	—	2	2	no	—
336	C₄	—	2	2	no	—
337	C₄	—	2	4	no	—
338	C₄	—	4	2	no	—
339	C₄	—	4	4	no	—
340	C₄	C₃×C₅×#117	1	4	yes	—
341	C₃	C₅×#2356	1	1	yes	characteristic, direct product factor, Sylow
342	C₂	C₂×C₃×C₅×#117	1	1	yes	characteristic
343	C₂	C₃×C₄×C₅×#41	1	1	yes	characteristic
344	C₂	C₃×C₅×#519	1	1	yes	characteristic
345	C₂	C₃×C₅×#552	1	2	yes	—
346	C₂	C₃×C₅×#556	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂⁴
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
9. C₅×#2356	C₃	direct (N × H)
11. C₃×C₄×C₅×Q₈	C₄	semidirect
27. C₃×#2356	C₅	direct (N × H)
64. C₄×C₅×Q₈	C₃×C₄	semidirect
80. #2356	C₃×C₅	direct (N × H)
105. C₃×C₄×Q₈	C₄×C₅	semidirect
204. C₄×Q₈	C₃×C₄×C₅	semidirect
280. C₃×C₅	#2356	direct (N × H)
327. C₅	C₃×#2356	direct (N × H)
341. C₃	C₅×#2356	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×C₄×C₅×Q₈	2
C₃×C₅×#391	2
C₃×C₅×#387	2
C₃×C₅×#383	2
C₃×C₅×#382	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₅×#376	2
C₅×#2356	3
C₃×#2356	5

Subgroups — C3×C5×#2356 #14275390

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2356 #14275390