Subgroups — C₃×C₅×#2552 #14275586

Order 1920.

904 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×#125	C₂	1	2	yes	maximal
2	C₃×C₅×#398	C₂	1	4	yes	maximal
3	C₃×C₅×#389	C₂	1	2	yes	maximal
4	C₃×C₅×#389	C₂	1	2	yes	maximal
5	C₃×C₅×#384	C₂	1	2	yes	maximal
6	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic
7	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
8	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₅×#2552	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₅×#125	—	2	8	no	—
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	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×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
22	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₃×C₅×#95	C₂²	1	2	yes	—
26	C₃×C₅×#95	C₂²	1	4	yes	—
27	C₃×#2552	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂×C₅×#125	C₂×C₃	1	2	yes	—
29	C₅×#398	C₂×C₃	1	4	yes	—
30	C₅×#389	C₂×C₃	1	2	yes	—
31	C₅×#389	C₂×C₃	1	2	yes	—
32	C₅×#384	C₂×C₃	1	2	yes	—
33	C₅×#384	C₂×C₃	1	1	yes	characteristic
34	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
35	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₃×C₅×C₄⋊C₄	—	2	8	no	—
45	C₃×C₅×C₄⋊C₄	—	2	8	no	—
46	C₃×C₅×C₄⋊C₄	—	2	4	no	—
47	C₃×C₅×C₄⋊C₄	—	2	2	no	—
48	C₃×C₅×C₄⋊C₄	—	2	2	no	—
49	C₃×C₅×C₄⋊C₄	—	2	4	no	—
50	C₃×C₅×C₄⋊C₄	—	4	4	no	—
51	C₃×C₅×C₄⋊C₄	—	4	2	no	—
52	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	—
53	C₃×C₅×C₄⋊C₄	Q₈	1	4	yes	—
54	C₃×C₄²×C₅	—	2	4	no	—
55	C₃×C₄²×C₅	—	2	4	no	—
56	C₃×C₄²×C₅	Q₈	1	4	yes	—
57	C₂×C₃×#125	C₂×C₅	1	2	yes	—
58	C₃×#398	C₂×C₅	1	4	yes	—
59	C₃×#389	C₂×C₅	1	2	yes	—
60	C₃×#389	C₂×C₅	1	2	yes	—
61	C₃×#384	C₂×C₅	1	2	yes	—
62	C₃×#384	C₂×C₅	1	1	yes	characteristic
63	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
64	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
65	C₅×#125	—	2	8	no	—
66	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
67	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
69	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
70	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
71	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
72	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
73	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
74	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
77	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
78	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
79	C₅×#95	C₂²×C₃	1	2	yes	—
80	C₅×#95	C₂²×C₃	1	2	yes	—
81	C₅×#95	C₂²×C₃	1	4	yes	—
82	#2552	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
83	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	2	1	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	—	2	1	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	4	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	2	4	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	4	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
100	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
103	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
105	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
106	C₂×C₃×C₄×C₅	#41	1	2	yes	—
107	C₂×C₃×C₄×C₅	#41	1	2	yes	—
108	C₃×#125	—	2	8	no	—
109	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
110	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
111	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
112	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
113	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
114	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
115	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
116	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
117	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
118	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
119	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
120	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
121	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
122	C₃×#95	C₂²×C₅	1	2	yes	—
123	C₃×#95	C₂²×C₅	1	2	yes	—
124	C₃×#95	C₂²×C₅	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	4	yes	—
128	C₂²×C₄×C₅	C₂³×C₃	1	2	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	1	yes	characteristic
132	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
133	C₅×C₄⋊C₄	—	2	8	no	—
134	C₅×C₄⋊C₄	—	2	8	no	—
135	C₅×C₄⋊C₄	—	2	4	no	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	2	2	no	—
138	C₅×C₄⋊C₄	—	2	4	no	—
139	C₅×C₄⋊C₄	—	4	4	no	—
140	C₅×C₄⋊C₄	—	4	2	no	—
141	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	—
142	C₅×C₄⋊C₄	C₃×Q₈	1	4	yes	—
143	C₄²×C₅	—	2	4	no	—
144	C₄²×C₅	—	2	4	no	—
145	C₄²×C₅	C₃×Q₈	1	4	yes	—
146	C₂×#125	C₂×C₃×C₅	1	2	yes	—
147	#398	C₂×C₃×C₅	1	4	yes	—
148	#389	C₂×C₃×C₅	1	2	yes	—
149	#389	C₂×C₃×C₅	1	2	yes	—
150	#384	C₂×C₃×C₅	1	2	yes	—
151	#384	C₂×C₃×C₅	1	1	yes	characteristic
152	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
153	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
154	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
155	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
156	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
157	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
158	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
159	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
160	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
161	C₃×C₄×C₅	—	2	2	no	—
162	C₃×C₄×C₅	—	2	4	no	—
163	C₃×C₄×C₅	—	2	4	no	—
164	C₃×C₄×C₅	—	4	2	no	—
165	C₃×C₄×C₅	—	4	2	no	—
166	C₃×C₄×C₅	—	4	4	no	—
167	C₃×C₄×C₅	#125	1	4	yes	complemented
168	C₃×C₄×C₅	C₄⋊Q₈	1	4	yes	—
169	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
170	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
171	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
172	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
173	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
175	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
177	C₃×C₄⋊C₄	—	2	8	no	—
178	C₃×C₄⋊C₄	—	2	8	no	—
179	C₃×C₄⋊C₄	—	2	4	no	—
180	C₃×C₄⋊C₄	—	2	2	no	—
181	C₃×C₄⋊C₄	—	2	2	no	—
182	C₃×C₄⋊C₄	—	2	4	no	—
183	C₃×C₄⋊C₄	—	4	4	no	—
184	C₃×C₄⋊C₄	—	4	2	no	—
185	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	—
186	C₃×C₄⋊C₄	C₅×Q₈	1	4	yes	—
187	C₃×C₄²	—	2	4	no	—
188	C₃×C₄²	—	2	4	no	—
189	C₃×C₄²	C₅×Q₈	1	4	yes	—
190	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	1	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	1	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	4	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	4	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	4	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
207	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
208	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
209	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
210	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
211	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
212	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
213	C₂×C₄×C₅	C₃×#41	1	2	yes	—
214	C₂×C₄×C₅	C₃×#41	1	2	yes	—
215	#125	—	2	8	no	—
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	4	yes	—
219	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
220	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
221	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
222	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
223	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
224	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
226	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
227	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
228	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
229	#95	C₂²×C₃×C₅	1	2	yes	—
230	#95	C₂²×C₃×C₅	1	2	yes	—
231	#95	C₂²×C₃×C₅	1	4	yes	—
232	C₂×C₃×C₅	C₂×#125	1	1	yes	characteristic
233	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
234	C₂×C₃×C₅	#544	1	1	yes	characteristic
235	C₂×C₃×C₅	#547	1	1	yes	characteristic
236	C₂×C₃×C₅	#550	1	1	yes	characteristic
237	C₂×C₃×C₅	#554	1	1	yes	characteristic
238	C₂×C₃×C₅	#557	1	1	yes	characteristic
239	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	1	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	4	no	—
249	C₂×C₃×C₄	—	2	2	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	2	no	—
255	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
256	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
257	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
258	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
259	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
260	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
261	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
262	C₂×C₃×C₄	C₅×#41	1	2	yes	—
263	C₂×C₃×C₄	C₅×#41	1	2	yes	—
264	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
265	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
266	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
267	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
268	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
269	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
270	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
271	C₄×C₅	—	2	2	no	—
272	C₄×C₅	—	2	4	no	—
273	C₄×C₅	—	2	4	no	—
274	C₄×C₅	—	4	2	no	—
275	C₄×C₅	—	4	2	no	—
276	C₄×C₅	—	4	4	no	—
277	C₄×C₅	C₃×#125	1	4	yes	complemented
278	C₄×C₅	C₃×C₄⋊Q₈	1	4	yes	—
279	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
280	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
281	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
282	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
283	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
284	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
285	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
286	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
287	C₄⋊C₄	—	2	8	no	—
288	C₄⋊C₄	—	2	8	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	4	4	no	—
294	C₄⋊C₄	—	4	2	no	—
295	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	—
296	C₄⋊C₄	C₃×C₅×Q₈	1	4	yes	—
297	C₄²	—	2	4	no	—
298	C₄²	—	2	4	no	—
299	C₄²	C₃×C₅×Q₈	1	4	yes	—
300	C₃×C₅	#2552	1	1	yes	characteristic, direct product factor, Hall
301	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
302	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
303	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
304	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
305	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
306	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
307	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
308	C₃×C₄	—	2	2	no	—
309	C₃×C₄	—	2	4	no	—
310	C₃×C₄	—	2	4	no	—
311	C₃×C₄	—	4	2	no	—
312	C₃×C₄	—	4	2	no	—
313	C₃×C₄	—	4	4	no	—
314	C₃×C₄	C₅×#125	1	4	yes	complemented
315	C₃×C₄	C₅×C₄⋊Q₈	1	4	yes	—
316	C₂×C₅	C₂×C₃×#125	1	1	yes	characteristic
317	C₂×C₅	C₂×C₃×C₄⋊Q₈	1	1	yes	characteristic
318	C₂×C₅	C₃×#544	1	1	yes	characteristic
319	C₂×C₅	C₃×#547	1	1	yes	characteristic
320	C₂×C₅	C₃×#550	1	1	yes	characteristic
321	C₂×C₅	C₃×#554	1	1	yes	characteristic
322	C₂×C₅	C₃×#557	1	1	yes	characteristic
323	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
340	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
341	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
342	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
343	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
344	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
345	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
346	C₂×C₄	C₃×C₅×#41	1	2	yes	—
347	C₂×C₄	C₃×C₅×#41	1	2	yes	—
348	C₂×C₃	C₂×C₅×#125	1	1	yes	characteristic
349	C₂×C₃	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
350	C₂×C₃	C₅×#544	1	1	yes	characteristic
351	C₂×C₃	C₅×#547	1	1	yes	characteristic
352	C₂×C₃	C₅×#550	1	1	yes	characteristic
353	C₂×C₃	C₅×#554	1	1	yes	characteristic
354	C₂×C₃	C₅×#557	1	1	yes	characteristic
355	C₅	C₃×#2552	1	1	yes	characteristic, direct product factor, Sylow
356	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
357	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
358	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
359	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
360	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
361	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
363	C₄	—	2	2	no	—
364	C₄	—	2	4	no	—
365	C₄	—	2	4	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	4	no	—
369	C₄	C₃×C₅×#125	1	4	yes	complemented
370	C₄	C₃×C₅×C₄⋊Q₈	1	4	yes	—
371	C₃	C₅×#2552	1	1	yes	characteristic, direct product factor, Sylow
372	C₂	C₂×C₃×C₅×#125	1	1	yes	characteristic
373	C₂	C₂×C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
374	C₂	C₃×C₅×#544	1	1	yes	characteristic
375	C₂	C₃×C₅×#547	1	1	yes	characteristic
376	C₂	C₃×C₅×#550	1	1	yes	characteristic
377	C₂	C₃×C₅×#554	1	1	yes	characteristic
378	C₂	C₃×C₅×#557	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
LCS	G ▷ C₂³ ▷ 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×#2552	C₃	direct (N × H)
27. C₃×#2552	C₅	direct (N × H)
82. #2552	C₃×C₅	direct (N × H)
167. C₃×C₄×C₅	#125	semidirect
277. C₄×C₅	C₃×#125	semidirect
300. C₃×C₅	#2552	direct (N × H)
314. C₃×C₄	C₅×#125	semidirect
355. C₅	C₃×#2552	direct (N × H)
369. C₄	C₃×C₅×#125	semidirect
371. C₃	C₅×#2552	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×#125	2
C₃×C₅×#398	2
C₃×C₅×#389	2
C₃×C₅×#384	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2552	3
C₃×#2552	5

Subgroups — C3×C5×#2552 #14275586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2552 #14275586