Subgroups — C₃×C₅×#2346 #14275380

Order 1920.

1008 conjugacy classes of subgroups.

The subgroup lattice has 380 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×#389	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#388	C₂	1	4	yes	maximal
4	C₃×C₅×#382	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic
6	C₃×C₄×C₅×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
8	C₃×C₅×#376	C₂	1	2	yes	maximal, complemented
9	C₅×#2346	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₃×C₅×#117	C₄	1	8	yes	complemented
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	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₄²×C₅	C₂²	1	4	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
21	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
22	C₃×C₅×#95	C₂²	1	1	yes	characteristic
23	C₃×C₅×#95	C₂²	1	2	yes	—
24	C₃×C₅×#95	C₂²	1	4	yes	—
25	C₃×C₅×#95	C₂²	1	1	yes	characteristic
26	C₃×C₅×#95	C₂²	1	4	yes	—
27	C₃×#2346	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic
29	C₅×#389	C₂×C₃	1	2	yes	complemented
30	C₅×#388	C₂×C₃	1	4	yes	—
31	C₅×#382	C₂×C₃	1	2	yes	complemented
32	C₅×#380	C₂×C₃	1	1	yes	characteristic
33	C₄×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
34	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
35	C₅×#376	C₂×C₃	1	2	yes	complemented
36	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	—	2	4	no	—
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	4	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	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₃×C₅×C₄⋊C₄	—	2	4	no	—
47	C₃×C₅×C₄⋊C₄	—	4	4	no	—
48	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
49	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
50	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
51	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
52	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
53	C₃×C₄²×C₅	—	2	8	no	—
54	C₃×C₄²×C₅	—	2	4	no	—
55	C₃×C₄²×C₅	C₂×C₄	1	8	yes	—
56	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic
57	C₃×#389	C₂×C₅	1	2	yes	complemented
58	C₃×#388	C₂×C₅	1	4	yes	—
59	C₃×#382	C₂×C₅	1	2	yes	complemented
60	C₃×#380	C₂×C₅	1	1	yes	characteristic
61	C₃×C₄×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
62	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
63	C₃×#376	C₂×C₅	1	2	yes	complemented
64	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
65	C₅×#117	C₃×C₄	1	8	yes	complemented
66	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
68	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
71	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
72	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
73	C₂×C₄²×C₅	C₂²×C₃	1	4	yes	—
74	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
75	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
76	C₅×#95	C₂²×C₃	1	1	yes	characteristic
77	C₅×#95	C₂²×C₃	1	2	yes	—
78	C₅×#95	C₂²×C₃	1	4	yes	—
79	C₅×#95	C₂²×C₃	1	1	yes	characteristic
80	C₅×#95	C₂²×C₃	1	4	yes	—
81	#2346	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
82	C₂³×C₃×C₅	—	2	2	no	—
83	C₂³×C₃×C₅	—	2	2	no	—
84	C₂³×C₃×C₅	—	2	1	no	—
85	C₂³×C₃×C₅	—	2	1	no	—
86	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
87	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	—	2	4	no	—
89	C₂×C₃×C₄×C₅	—	2	2	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	2	2	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	—	2	8	no	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	4	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	—	2	4	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	#41	1	4	yes	—
106	C₂×C₃×C₄×C₅	#41	1	4	yes	—
107	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
108	C₃×#117	C₄×C₅	1	8	yes	complemented
109	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
110	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
111	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
112	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
113	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
114	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
115	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
116	C₂×C₃×C₄²	C₂²×C₅	1	4	yes	—
117	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
118	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
119	C₃×#95	C₂²×C₅	1	1	yes	characteristic
120	C₃×#95	C₂²×C₅	1	2	yes	—
121	C₃×#95	C₂²×C₅	1	4	yes	—
122	C₃×#95	C₂²×C₅	1	1	yes	characteristic
123	C₃×#95	C₂²×C₅	1	4	yes	—
124	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
125	C₂²×C₄×C₅	—	2	4	no	—
126	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
127	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
128	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
129	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
130	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
132	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
133	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
134	C₅×C₄⋊C₄	—	2	4	no	—
135	C₅×C₄⋊C₄	—	4	4	no	—
136	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
137	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
138	C₅×C₂²⋊C₄	—	2	4	no	—
139	C₅×C₂²⋊C₄	—	4	2	no	—
140	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
141	C₄²×C₅	—	2	8	no	—
142	C₄²×C₅	—	2	4	no	—
143	C₄²×C₅	C₂×C₃×C₄	1	8	yes	—
144	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic
145	#389	C₂×C₃×C₅	1	2	yes	complemented
146	#388	C₂×C₃×C₅	1	4	yes	—
147	#382	C₂×C₃×C₅	1	2	yes	complemented
148	#380	C₂×C₃×C₅	1	1	yes	characteristic
149	C₄×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
150	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
151	#376	C₂×C₃×C₅	1	2	yes	complemented
152	C₂²×C₃×C₅	—	2	2	no	—
153	C₂²×C₃×C₅	—	2	2	no	—
154	C₂²×C₃×C₅	—	2	2	no	—
155	C₂²×C₃×C₅	—	4	2	no	—
156	C₂²×C₃×C₅	—	4	2	no	—
157	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
158	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
159	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
160	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
162	C₃×C₄×C₅	—	2	2	no	—
163	C₃×C₄×C₅	—	2	4	no	—
164	C₃×C₄×C₅	—	2	4	no	—
165	C₃×C₄×C₅	—	2	4	no	—
166	C₃×C₄×C₅	—	4	2	no	—
167	C₃×C₄×C₅	—	4	4	no	—
168	C₃×C₄×C₅	#117	1	4	yes	—
169	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
170	C₂²×C₃×C₄	—	2	4	no	—
171	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
172	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
173	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
174	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
176	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
177	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
178	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
179	C₃×C₄⋊C₄	—	2	4	no	—
180	C₃×C₄⋊C₄	—	4	4	no	—
181	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
182	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
183	C₃×C₂²⋊C₄	—	2	4	no	—
184	C₃×C₂²⋊C₄	—	4	2	no	—
185	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	—
186	C₃×C₄²	—	2	8	no	—
187	C₃×C₄²	—	2	4	no	—
188	C₃×C₄²	C₂×C₄×C₅	1	8	yes	—
189	C₂³×C₅	—	2	2	no	—
190	C₂³×C₅	—	2	2	no	—
191	C₂³×C₅	—	2	1	no	—
192	C₂³×C₅	—	2	1	no	—
193	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
194	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
195	C₂×C₄×C₅	—	2	4	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	8	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	4	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	4	no	—
206	C₂×C₄×C₅	—	2	4	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
209	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
210	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
211	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
212	C₂×C₄×C₅	C₃×#41	1	4	yes	—
213	C₂×C₄×C₅	C₃×#41	1	4	yes	—
214	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
215	#117	C₃×C₄×C₅	1	8	yes	complemented
216	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
217	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
218	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
219	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
220	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
221	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
222	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
223	C₂×C₄²	C₂²×C₃×C₅	1	4	yes	—
224	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
225	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
226	#95	C₂²×C₃×C₅	1	1	yes	characteristic
227	#95	C₂²×C₃×C₅	1	2	yes	—
228	#95	C₂²×C₃×C₅	1	4	yes	—
229	#95	C₂²×C₃×C₅	1	1	yes	characteristic
230	#95	C₂²×C₃×C₅	1	4	yes	—
231	C₂×C₃×C₅	—	4	2	no	—
232	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
233	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
234	C₂×C₃×C₅	#520	1	1	yes	characteristic
235	C₂×C₃×C₅	#552	1	2	yes	—
236	C₂×C₃×C₅	#555	1	2	yes	—
237	C₂³×C₃	—	2	2	no	—
238	C₂³×C₃	—	2	2	no	—
239	C₂³×C₃	—	2	1	no	—
240	C₂³×C₃	—	2	1	no	—
241	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
242	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
243	C₂×C₃×C₄	—	2	4	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	2	8	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
257	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
258	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
259	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
260	C₂×C₃×C₄	C₅×#41	1	4	yes	—
261	C₂×C₃×C₄	C₅×#41	1	4	yes	—
262	C₂²×C₅	—	2	2	no	—
263	C₂²×C₅	—	2	2	no	—
264	C₂²×C₅	—	2	2	no	—
265	C₂²×C₅	—	4	2	no	—
266	C₂²×C₅	—	4	2	no	—
267	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
268	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
269	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
270	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
271	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
272	C₄×C₅	—	2	2	no	—
273	C₄×C₅	—	2	4	no	—
274	C₄×C₅	—	2	4	no	—
275	C₄×C₅	—	2	4	no	—
276	C₄×C₅	—	4	2	no	—
277	C₄×C₅	—	4	4	no	—
278	C₄×C₅	C₃×#117	1	4	yes	—
279	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
282	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
283	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
284	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
285	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
286	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
287	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
288	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	4	4	no	—
291	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
292	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
293	C₂²⋊C₄	—	2	4	no	—
294	C₂²⋊C₄	—	4	2	no	—
295	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
296	C₄²	—	2	8	no	—
297	C₄²	—	2	4	no	—
298	C₄²	C₂×C₃×C₄×C₅	1	8	yes	—
299	C₃×C₅	#2346	1	1	yes	characteristic, direct product factor, Hall
300	C₂²×C₃	—	2	2	no	—
301	C₂²×C₃	—	2	2	no	—
302	C₂²×C₃	—	2	2	no	—
303	C₂²×C₃	—	4	2	no	—
304	C₂²×C₃	—	4	2	no	—
305	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
306	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
307	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
308	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
309	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
310	C₃×C₄	—	2	2	no	—
311	C₃×C₄	—	2	4	no	—
312	C₃×C₄	—	2	4	no	—
313	C₃×C₄	—	2	4	no	—
314	C₃×C₄	—	4	2	no	—
315	C₃×C₄	—	4	4	no	—
316	C₃×C₄	C₅×#117	1	4	yes	—
317	C₂×C₅	—	4	2	no	—
318	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
319	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
320	C₂×C₅	C₃×#520	1	1	yes	characteristic
321	C₂×C₅	C₃×#552	1	2	yes	—
322	C₂×C₅	C₃×#555	1	2	yes	—
323	C₂³	—	2	2	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
328	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
329	C₂×C₄	—	2	4	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	2	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
343	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
344	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
345	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
346	C₂×C₄	C₃×C₅×#41	1	4	yes	—
347	C₂×C₄	C₃×C₅×#41	1	4	yes	—
348	C₂×C₃	—	4	2	no	—
349	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
350	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
351	C₂×C₃	C₅×#520	1	1	yes	characteristic
352	C₂×C₃	C₅×#552	1	2	yes	—
353	C₂×C₃	C₅×#555	1	2	yes	—
354	C₅	C₃×#2346	1	1	yes	characteristic, direct product factor, Sylow
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
361	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
362	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
363	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
364	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
365	C₄	—	2	2	no	—
366	C₄	—	2	4	no	—
367	C₄	—	2	4	no	—
368	C₄	—	2	4	no	—
369	C₄	—	4	2	no	—
370	C₄	—	4	4	no	—
371	C₄	C₃×C₅×#117	1	4	yes	—
372	C₃	C₅×#2346	1	1	yes	characteristic, direct product factor, Sylow
373	C₂	—	4	2	no	—
374	C₂	C₂×C₃×C₅×#117	1	1	yes	characteristic
375	C₂	C₃×C₄×C₅×#41	1	1	yes	characteristic
376	C₂	C₃×C₅×#520	1	1	yes	characteristic
377	C₂	C₃×C₅×#552	1	2	yes	—
378	C₂	C₃×C₅×#555	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
2. C₃×C₅×#389	C₂	semidirect
4. C₃×C₅×#382	C₂	semidirect
6. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
8. C₃×C₅×#376	C₂	semidirect
9. C₅×#2346	C₃	direct (N × H)
11. C₃×C₅×#117	C₄	semidirect
27. C₃×#2346	C₅	direct (N × H)
29. C₅×#389	C₂×C₃	semidirect
31. C₅×#382	C₂×C₃	semidirect
33. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
35. C₅×#376	C₂×C₃	semidirect
57. C₃×#389	C₂×C₅	semidirect
59. C₃×#382	C₂×C₅	semidirect
61. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
63. C₃×#376	C₂×C₅	semidirect
65. C₅×#117	C₃×C₄	semidirect
81. #2346	C₃×C₅	direct (N × H)
108. C₃×#117	C₄×C₅	semidirect
145. #389	C₂×C₃×C₅	semidirect
147. #382	C₂×C₃×C₅	semidirect
149. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
151. #376	C₂×C₃×C₅	semidirect
215. #117	C₃×C₄×C₅	semidirect
299. C₃×C₅	#2346	direct (N × H)
354. C₅	C₃×#2346	direct (N × H)
372. C₃	C₅×#2346	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×#389	2
C₃×C₅×#388	2
C₃×C₅×#382	2
C₃×C₅×#380	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₃×C₅×#376	2
C₅×#2346	3
C₃×#2346	5

Subgroups — C3×C5×#2346 #14275380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2346 #14275380