Subgroups — C₃×C₅×#2314 #14275348

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#388	C₂	1	4	yes	maximal
3	C₃×C₅×#387	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#380	C₂	1	2	yes	maximal
7	C₃×C₄×C₅×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₅×#2314	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₃×C₅×#117	C₄	1	8	yes	complemented
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
16	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₄²×C₅	C₂²	1	4	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
20	C₃×C₅×#95	C₂²	1	4	yes	—
21	C₃×C₅×#95	C₂²	1	4	yes	—
22	C₃×C₅×#95	C₂²	1	4	yes	—
23	C₃×#2314	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic
25	C₅×#388	C₂×C₃	1	4	yes	—
26	C₅×#387	C₂×C₃	1	4	yes	complemented
27	C₅×#384	C₂×C₃	1	1	yes	characteristic, complemented
28	C₅×#382	C₂×C₃	1	1	yes	characteristic, complemented
29	C₅×#380	C₂×C₃	1	2	yes	—
30	C₄×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
31	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	—	2	2	no	—
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
35	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₃×C₅×C₄⋊C₄	—	2	4	no	—
42	C₃×C₅×C₄⋊C₄	—	2	4	no	—
43	C₃×C₅×C₄⋊C₄	—	4	4	no	—
44	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	—
45	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
46	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
47	C₃×C₄²×C₅	—	4	4	no	—
48	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
49	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
50	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic
51	C₃×#388	C₂×C₅	1	4	yes	—
52	C₃×#387	C₂×C₅	1	4	yes	complemented
53	C₃×#384	C₂×C₅	1	1	yes	characteristic, complemented
54	C₃×#382	C₂×C₅	1	1	yes	characteristic, complemented
55	C₃×#380	C₂×C₅	1	2	yes	—
56	C₃×C₄×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
57	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
58	C₅×#117	C₃×C₄	1	8	yes	complemented
59	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
60	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
61	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
62	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
63	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
64	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
65	C₂×C₄²×C₅	C₂²×C₃	1	4	yes	—
66	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
68	C₅×#95	C₂²×C₃	1	4	yes	—
69	C₅×#95	C₂²×C₃	1	4	yes	—
70	C₅×#95	C₂²×C₃	1	4	yes	—
71	#2314	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
72	C₂³×C₃×C₅	—	2	1	no	—
73	C₂³×C₃×C₅	—	2	1	no	—
74	C₂³×C₃×C₅	—	2	2	no	—
75	C₂³×C₃×C₅	—	2	2	no	—
76	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
77	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
78	C₂×C₃×C₄×C₅	—	2	1	no	—
79	C₂×C₃×C₄×C₅	—	2	1	no	—
80	C₂×C₃×C₄×C₅	—	2	2	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	2	2	no	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	2	8	no	—
85	C₂×C₃×C₄×C₅	—	2	4	no	—
86	C₂×C₃×C₄×C₅	—	2	4	no	—
87	C₂×C₃×C₄×C₅	—	2	4	no	—
88	C₂×C₃×C₄×C₅	—	2	4	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
93	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	#41	1	2	yes	—
96	C₂×C₃×C₄×C₅	#41	1	2	yes	—
97	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
98	C₃×#117	C₄×C₅	1	8	yes	complemented
99	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
100	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
101	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
102	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
103	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
104	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
105	C₂×C₃×C₄²	C₂²×C₅	1	4	yes	—
106	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
107	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
108	C₃×#95	C₂²×C₅	1	4	yes	—
109	C₃×#95	C₂²×C₅	1	4	yes	—
110	C₃×#95	C₂²×C₅	1	4	yes	—
111	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
115	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
116	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
117	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
118	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
119	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
121	C₅×C₄⋊C₄	—	2	4	no	—
122	C₅×C₄⋊C₄	—	2	4	no	—
123	C₅×C₄⋊C₄	—	4	4	no	—
124	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
125	C₅×C₂²⋊C₄	—	4	4	no	—
126	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
127	C₄²×C₅	—	4	4	no	—
128	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
129	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
130	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic
131	#388	C₂×C₃×C₅	1	4	yes	—
132	#387	C₂×C₃×C₅	1	4	yes	complemented
133	#384	C₂×C₃×C₅	1	1	yes	characteristic, complemented
134	#382	C₂×C₃×C₅	1	1	yes	characteristic, complemented
135	#380	C₂×C₃×C₅	1	2	yes	—
136	C₄×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
137	C₂²×C₃×C₅	—	2	2	no	—
138	C₂²×C₃×C₅	—	2	4	no	—
139	C₂²×C₃×C₅	—	4	1	no	—
140	C₂²×C₃×C₅	—	4	1	no	—
141	C₂²×C₃×C₅	—	4	2	no	—
142	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
143	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
144	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
145	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
146	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
147	C₃×C₄×C₅	—	2	2	no	—
148	C₃×C₄×C₅	—	2	4	no	—
149	C₃×C₄×C₅	—	2	4	no	—
150	C₃×C₄×C₅	—	4	4	no	—
151	C₃×C₄×C₅	—	4	4	no	—
152	C₃×C₄×C₅	#117	1	4	yes	—
153	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
154	C₂²×C₃×C₄	—	2	2	no	—
155	C₂²×C₃×C₄	—	2	2	no	—
156	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
157	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
158	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
159	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
161	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
162	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
163	C₃×C₄⋊C₄	—	2	4	no	—
164	C₃×C₄⋊C₄	—	2	4	no	—
165	C₃×C₄⋊C₄	—	4	4	no	—
166	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	—
167	C₃×C₂²⋊C₄	—	4	4	no	—
168	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	—
169	C₃×C₄²	—	4	4	no	—
170	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
171	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
172	C₂³×C₅	—	2	1	no	—
173	C₂³×C₅	—	2	1	no	—
174	C₂³×C₅	—	2	2	no	—
175	C₂³×C₅	—	2	2	no	—
176	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
177	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
178	C₂×C₄×C₅	—	2	1	no	—
179	C₂×C₄×C₅	—	2	1	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	8	no	—
185	C₂×C₄×C₅	—	2	4	no	—
186	C₂×C₄×C₅	—	2	4	no	—
187	C₂×C₄×C₅	—	2	4	no	—
188	C₂×C₄×C₅	—	2	4	no	—
189	C₂×C₄×C₅	—	2	4	no	—
190	C₂×C₄×C₅	—	2	4	no	—
191	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
192	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
193	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
194	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
195	C₂×C₄×C₅	C₃×#41	1	2	yes	—
196	C₂×C₄×C₅	C₃×#41	1	2	yes	—
197	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
198	#117	C₃×C₄×C₅	1	8	yes	complemented
199	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
200	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
201	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
202	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
203	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
204	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
205	C₂×C₄²	C₂²×C₃×C₅	1	4	yes	—
206	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
207	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
208	#95	C₂²×C₃×C₅	1	4	yes	—
209	#95	C₂²×C₃×C₅	1	4	yes	—
210	#95	C₂²×C₃×C₅	1	4	yes	—
211	C₂×C₃×C₅	—	4	2	no	—
212	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
213	C₂×C₃×C₅	#520	1	2	yes	—
214	C₂×C₃×C₅	#540	1	1	yes	characteristic
215	C₂×C₃×C₅	#541	1	1	yes	characteristic
216	C₂×C₃×C₅	#542	1	2	yes	—
217	C₂³×C₃	—	2	1	no	—
218	C₂³×C₃	—	2	1	no	—
219	C₂³×C₃	—	2	2	no	—
220	C₂³×C₃	—	2	2	no	—
221	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
222	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
223	C₂×C₃×C₄	—	2	1	no	—
224	C₂×C₃×C₄	—	2	1	no	—
225	C₂×C₃×C₄	—	2	2	no	—
226	C₂×C₃×C₄	—	2	2	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	2	8	no	—
230	C₂×C₃×C₄	—	2	4	no	—
231	C₂×C₃×C₄	—	2	4	no	—
232	C₂×C₃×C₄	—	2	4	no	—
233	C₂×C₃×C₄	—	2	4	no	—
234	C₂×C₃×C₄	—	2	4	no	—
235	C₂×C₃×C₄	—	2	4	no	—
236	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
237	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
238	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
239	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
240	C₂×C₃×C₄	C₅×#41	1	2	yes	—
241	C₂×C₃×C₄	C₅×#41	1	2	yes	—
242	C₂²×C₅	—	2	2	no	—
243	C₂²×C₅	—	2	4	no	—
244	C₂²×C₅	—	4	1	no	—
245	C₂²×C₅	—	4	1	no	—
246	C₂²×C₅	—	4	2	no	—
247	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
248	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
249	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
250	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
251	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
252	C₄×C₅	—	2	2	no	—
253	C₄×C₅	—	2	4	no	—
254	C₄×C₅	—	2	4	no	—
255	C₄×C₅	—	4	4	no	—
256	C₄×C₅	—	4	4	no	—
257	C₄×C₅	C₃×#117	1	4	yes	—
258	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
262	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
263	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
264	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
265	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
266	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
267	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
268	C₄⋊C₄	—	2	4	no	—
269	C₄⋊C₄	—	2	4	no	—
270	C₄⋊C₄	—	4	4	no	—
271	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
272	C₂²⋊C₄	—	4	4	no	—
273	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
274	C₄²	—	4	4	no	—
275	C₄²	C₂×C₃×C₄×C₅	1	4	yes	—
276	C₄²	C₂×C₃×C₄×C₅	1	4	yes	—
277	C₃×C₅	#2314	1	1	yes	characteristic, direct product factor, Hall
278	C₂²×C₃	—	2	2	no	—
279	C₂²×C₃	—	2	4	no	—
280	C₂²×C₃	—	4	1	no	—
281	C₂²×C₃	—	4	1	no	—
282	C₂²×C₃	—	4	2	no	—
283	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
284	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
285	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
286	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
287	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
288	C₃×C₄	—	2	2	no	—
289	C₃×C₄	—	2	4	no	—
290	C₃×C₄	—	2	4	no	—
291	C₃×C₄	—	4	4	no	—
292	C₃×C₄	—	4	4	no	—
293	C₃×C₄	C₅×#117	1	4	yes	—
294	C₂×C₅	—	4	2	no	—
295	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
296	C₂×C₅	C₃×#520	1	2	yes	—
297	C₂×C₅	C₃×#540	1	1	yes	characteristic
298	C₂×C₅	C₃×#541	1	1	yes	characteristic
299	C₂×C₅	C₃×#542	1	2	yes	—
300	C₂³	—	2	1	no	—
301	C₂³	—	2	1	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
305	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
320	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
321	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
322	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
323	C₂×C₄	C₃×C₅×#41	1	2	yes	—
324	C₂×C₄	C₃×C₅×#41	1	2	yes	—
325	C₂×C₃	—	4	2	no	—
326	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
327	C₂×C₃	C₅×#520	1	2	yes	—
328	C₂×C₃	C₅×#540	1	1	yes	characteristic
329	C₂×C₃	C₅×#541	1	1	yes	characteristic
330	C₂×C₃	C₅×#542	1	2	yes	—
331	C₅	C₃×#2314	1	1	yes	characteristic, direct product factor, Sylow
332	C₂²	—	2	2	no	—
333	C₂²	—	2	4	no	—
334	C₂²	—	4	1	no	—
335	C₂²	—	4	1	no	—
336	C₂²	—	4	2	no	—
337	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
338	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
339	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
340	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
341	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
342	C₄	—	2	2	no	—
343	C₄	—	2	4	no	—
344	C₄	—	2	4	no	—
345	C₄	—	4	4	no	—
346	C₄	—	4	4	no	—
347	C₄	C₃×C₅×#117	1	4	yes	—
348	C₃	C₅×#2314	1	1	yes	characteristic, direct product factor, Sylow
349	C₂	—	4	2	no	—
350	C₂	C₂×C₃×C₅×#117	1	1	yes	characteristic
351	C₂	C₃×C₅×#520	1	2	yes	—
352	C₂	C₃×C₅×#540	1	1	yes	characteristic
353	C₂	C₃×C₅×#541	1	1	yes	characteristic
354	C₂	C₃×C₅×#542	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
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
3. C₃×C₅×#387	C₂	semidirect
4. C₃×C₅×#384	C₂	semidirect
5. C₃×C₅×#382	C₂	semidirect
7. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
8. C₅×#2314	C₃	direct (N × H)
10. C₃×C₅×#117	C₄	semidirect
23. C₃×#2314	C₅	direct (N × H)
26. C₅×#387	C₂×C₃	semidirect
27. C₅×#384	C₂×C₃	semidirect
28. C₅×#382	C₂×C₃	semidirect
30. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
52. C₃×#387	C₂×C₅	semidirect
53. C₃×#384	C₂×C₅	semidirect
54. C₃×#382	C₂×C₅	semidirect
56. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
58. C₅×#117	C₃×C₄	semidirect
71. #2314	C₃×C₅	direct (N × H)
98. C₃×#117	C₄×C₅	semidirect
132. #387	C₂×C₃×C₅	semidirect
133. #384	C₂×C₃×C₅	semidirect
134. #382	C₂×C₃×C₅	semidirect
136. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
198. #117	C₃×C₄×C₅	semidirect
277. C₃×C₅	#2314	direct (N × H)
331. C₅	C₃×#2314	direct (N × H)
348. C₃	C₅×#2314	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×#117	2
C₃×C₅×#388	2
C₃×C₅×#387	2
C₃×C₅×#384	2
C₃×C₅×#382	2
C₃×C₅×#380	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2314	3
C₃×#2314	5

Subgroups — C3×C5×#2314 #14275348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2314 #14275348