Subgroups — C₃×C₅×#2501 #14275535

Order 1920.

1416 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×#123	C₂	1	4	yes	maximal, complemented
2	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#399	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#390	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#384	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2501	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₃×C₅×#123	—	2	16	no	—
14	C₃×C₅×#121	—	2	4	no	—
15	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	8	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₃×#2501	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×#123	C₂×C₃	1	4	yes	complemented
27	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic
28	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
29	C₅×#399	C₂×C₃	1	4	yes	complemented
30	C₅×#390	C₂×C₃	1	2	yes	complemented
31	C₅×#384	C₂×C₃	1	2	yes	complemented
32	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
34	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
35	C₂×C₃×C₅×D₄	—	2	4	no	—
36	C₂×C₃×C₅×D₄	—	2	8	no	—
37	C₂×C₃×C₅×D₄	—	2	2	no	—
38	C₂×C₃×C₅×D₄	—	2	4	no	—
39	C₂²×C₃×C₄×C₅	—	2	4	no	—
40	C₂²×C₃×C₄×C₅	—	2	4	no	—
41	C₂²×C₃×C₄×C₅	—	2	8	no	—
42	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₃×C₅×C₄⋊C₄	—	2	4	no	—
49	C₃×C₅×C₄⋊C₄	—	2	4	no	—
50	C₃×C₅×C₄⋊C₄	—	2	2	no	—
51	C₃×C₅×C₄⋊C₄	—	2	16	no	—
52	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
53	C₃×C₅×C₂²⋊C₄	—	2	16	no	—
54	C₃×C₅×C₂²⋊C₄	D₄	1	8	yes	complemented
55	C₃×C₄²×C₅	—	2	4	no	—
56	C₂×C₃×#123	C₂×C₅	1	4	yes	complemented
57	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic
58	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
59	C₃×#399	C₂×C₅	1	4	yes	complemented
60	C₃×#390	C₂×C₅	1	2	yes	complemented
61	C₃×#384	C₂×C₅	1	2	yes	complemented
62	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
63	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
64	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
65	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
66	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
67	C₅×#123	—	2	16	no	—
68	C₅×#121	—	2	4	no	—
69	C₂×C₅×C₄⋊C₄	—	2	4	no	—
70	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
72	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	8	yes	—
73	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
74	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
75	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
76	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
77	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
78	C₅×#95	C₂²×C₃	1	2	yes	—
79	#2501	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
80	C₂³×C₃×C₅	—	2	2	no	—
81	C₂³×C₃×C₅	—	2	2	no	—
82	C₂³×C₃×C₅	—	2	4	no	—
83	C₂³×C₃×C₅	—	2	2	no	—
84	C₂³×C₃×C₅	—	2	4	no	—
85	C₂³×C₃×C₅	—	2	4	no	—
86	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
87	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
88	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
89	C₃×C₅×D₄	—	4	8	no	—
90	C₃×C₅×D₄	—	4	4	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	8	no	—
95	C₂×C₃×C₄×C₅	—	2	8	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	4	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	—	4	8	no	—
100	C₂×C₃×C₄×C₅	C₂×D₄	1	8	yes	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	#41	1	4	yes	—
104	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
105	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
106	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
107	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
108	C₃×#123	—	2	16	no	—
109	C₃×#121	—	2	4	no	—
110	C₂×C₃×C₄⋊C₄	—	2	4	no	—
111	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
112	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
113	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	8	yes	—
114	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
115	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
116	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
117	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
118	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
119	C₃×#95	C₂²×C₅	1	2	yes	—
120	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
121	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
122	C₂×C₅×D₄	—	2	4	no	—
123	C₂×C₅×D₄	—	2	8	no	—
124	C₂×C₅×D₄	—	2	2	no	—
125	C₂×C₅×D₄	—	2	4	no	—
126	C₂²×C₄×C₅	—	2	4	no	—
127	C₂²×C₄×C₅	—	2	4	no	—
128	C₂²×C₄×C₅	—	2	8	no	—
129	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
130	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
131	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
132	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
133	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
135	C₅×C₄⋊C₄	—	2	4	no	—
136	C₅×C₄⋊C₄	—	2	4	no	—
137	C₅×C₄⋊C₄	—	2	2	no	—
138	C₅×C₄⋊C₄	—	2	16	no	—
139	C₅×C₂²⋊C₄	—	2	4	no	—
140	C₅×C₂²⋊C₄	—	2	16	no	—
141	C₅×C₂²⋊C₄	C₃×D₄	1	8	yes	complemented
142	C₄²×C₅	—	2	4	no	—
143	C₂×#123	C₂×C₃×C₅	1	4	yes	complemented
144	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic
145	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
146	#399	C₂×C₃×C₅	1	4	yes	complemented
147	#390	C₂×C₃×C₅	1	2	yes	complemented
148	#384	C₂×C₃×C₅	1	2	yes	complemented
149	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
150	C₂²×C₃×C₅	—	2	2	no	—
151	C₂²×C₃×C₅	—	2	2	no	—
152	C₂²×C₃×C₅	—	2	8	no	—
153	C₂²×C₃×C₅	—	4	2	no	—
154	C₂²×C₃×C₅	—	4	2	no	—
155	C₂²×C₃×C₅	—	4	2	no	—
156	C₂²×C₃×C₅	—	4	8	no	—
157	C₂²×C₃×C₅	#127	1	4	yes	—
158	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
159	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
160	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
161	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
162	C₃×C₄×C₅	—	2	2	no	—
163	C₃×C₄×C₅	—	2	8	no	—
164	C₃×C₄×C₅	—	4	4	no	—
165	C₃×C₄×C₅	—	4	2	no	—
166	C₃×C₄×C₅	#123	1	4	yes	complemented
167	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
168	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
169	C₂×C₃×D₄	—	2	4	no	—
170	C₂×C₃×D₄	—	2	8	no	—
171	C₂×C₃×D₄	—	2	2	no	—
172	C₂×C₃×D₄	—	2	4	no	—
173	C₂²×C₃×C₄	—	2	4	no	—
174	C₂²×C₃×C₄	—	2	4	no	—
175	C₂²×C₃×C₄	—	2	8	no	—
176	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
177	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
178	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
179	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
180	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
181	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
182	C₃×C₄⋊C₄	—	2	4	no	—
183	C₃×C₄⋊C₄	—	2	4	no	—
184	C₃×C₄⋊C₄	—	2	2	no	—
185	C₃×C₄⋊C₄	—	2	16	no	—
186	C₃×C₂²⋊C₄	—	2	4	no	—
187	C₃×C₂²⋊C₄	—	2	16	no	—
188	C₃×C₂²⋊C₄	C₅×D₄	1	8	yes	complemented
189	C₃×C₄²	—	2	4	no	—
190	C₂³×C₅	—	2	2	no	—
191	C₂³×C₅	—	2	2	no	—
192	C₂³×C₅	—	2	4	no	—
193	C₂³×C₅	—	2	2	no	—
194	C₂³×C₅	—	2	4	no	—
195	C₂³×C₅	—	2	4	no	—
196	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
197	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
198	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
199	C₅×D₄	—	4	8	no	—
200	C₅×D₄	—	4	4	no	—
201	C₂×C₄×C₅	—	2	4	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	4	no	—
204	C₂×C₄×C₅	—	2	8	no	—
205	C₂×C₄×C₅	—	2	8	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	4	no	—
208	C₂×C₄×C₅	—	2	4	no	—
209	C₂×C₄×C₅	—	4	8	no	—
210	C₂×C₄×C₅	C₂×C₃×D₄	1	8	yes	—
211	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
212	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
213	C₂×C₄×C₅	C₃×#41	1	4	yes	—
214	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
215	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
216	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
217	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
218	#123	—	2	16	no	—
219	#121	—	2	4	no	—
220	C₂×C₄⋊C₄	—	2	4	no	—
221	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
222	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
223	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
224	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	8	yes	—
225	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
226	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	8	yes	—
227	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
228	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
229	#95	C₂²×C₃×C₅	1	2	yes	—
230	C₂×C₃×C₅	—	2	4	no	—
231	C₂×C₃×C₅	—	8	2	no	—
232	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
233	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
234	C₂×C₃×C₅	#536	1	1	yes	characteristic
235	C₂×C₃×C₅	#547	1	4	yes	—
236	C₂³×C₃	—	2	2	no	—
237	C₂³×C₃	—	2	2	no	—
238	C₂³×C₃	—	2	4	no	—
239	C₂³×C₃	—	2	2	no	—
240	C₂³×C₃	—	2	4	no	—
241	C₂³×C₃	—	2	4	no	—
242	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
243	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
244	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
245	C₃×D₄	—	4	8	no	—
246	C₃×D₄	—	4	4	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	—	2	8	no	—
251	C₂×C₃×C₄	—	2	8	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	—	4	8	no	—
256	C₂×C₃×C₄	C₂×C₅×D₄	1	8	yes	—
257	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
258	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
259	C₂×C₃×C₄	C₅×#41	1	4	yes	—
260	C₂²×C₅	—	2	2	no	—
261	C₂²×C₅	—	2	2	no	—
262	C₂²×C₅	—	2	8	no	—
263	C₂²×C₅	—	4	2	no	—
264	C₂²×C₅	—	4	2	no	—
265	C₂²×C₅	—	4	2	no	—
266	C₂²×C₅	—	4	8	no	—
267	C₂²×C₅	C₃×#127	1	4	yes	—
268	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
269	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
270	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
271	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
272	C₄×C₅	—	2	2	no	—
273	C₄×C₅	—	2	8	no	—
274	C₄×C₅	—	4	4	no	—
275	C₄×C₅	—	4	2	no	—
276	C₄×C₅	C₃×#123	1	4	yes	complemented
277	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
278	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	—	2	8	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	8	no	—
286	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
287	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
288	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
289	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
290	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
291	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	16	no	—
296	C₂²⋊C₄	—	2	4	no	—
297	C₂²⋊C₄	—	2	16	no	—
298	C₂²⋊C₄	C₃×C₅×D₄	1	8	yes	complemented
299	C₄²	—	2	4	no	—
300	C₃×C₅	#2501	1	1	yes	characteristic, direct product factor, Hall
301	C₂²×C₃	—	2	2	no	—
302	C₂²×C₃	—	2	2	no	—
303	C₂²×C₃	—	2	8	no	—
304	C₂²×C₃	—	4	2	no	—
305	C₂²×C₃	—	4	2	no	—
306	C₂²×C₃	—	4	2	no	—
307	C₂²×C₃	—	4	8	no	—
308	C₂²×C₃	C₅×#127	1	4	yes	—
309	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
310	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
311	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
312	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
313	C₃×C₄	—	2	2	no	—
314	C₃×C₄	—	2	8	no	—
315	C₃×C₄	—	4	4	no	—
316	C₃×C₄	—	4	2	no	—
317	C₃×C₄	C₅×#123	1	4	yes	complemented
318	C₂×C₅	—	2	4	no	—
319	C₂×C₅	—	8	2	no	—
320	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
321	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
322	C₂×C₅	C₃×#536	1	1	yes	characteristic
323	C₂×C₅	C₃×#547	1	4	yes	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	4	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	4	no	—
329	C₂³	—	2	4	no	—
330	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
331	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
332	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
333	D₄	—	4	8	no	—
334	D₄	—	4	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	8	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	4	8	no	—
344	C₂×C₄	C₂×C₃×C₅×D₄	1	8	yes	—
345	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
346	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
347	C₂×C₄	C₃×C₅×#41	1	4	yes	—
348	C₂×C₃	—	2	4	no	—
349	C₂×C₃	—	8	2	no	—
350	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
351	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
352	C₂×C₃	C₅×#536	1	1	yes	characteristic
353	C₂×C₃	C₅×#547	1	4	yes	—
354	C₅	C₃×#2501	1	1	yes	characteristic, direct product factor, Sylow
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	8	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	8	no	—
362	C₂²	C₃×C₅×#127	1	4	yes	—
363	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
364	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
365	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
366	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
367	C₄	—	2	2	no	—
368	C₄	—	2	8	no	—
369	C₄	—	4	4	no	—
370	C₄	—	4	2	no	—
371	C₄	C₃×C₅×#123	1	4	yes	complemented
372	C₃	C₅×#2501	1	1	yes	characteristic, direct product factor, Sylow
373	C₂	—	2	4	no	—
374	C₂	—	8	2	no	—
375	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
376	C₂	C₂×C₃×C₅×#127	1	1	yes	characteristic
377	C₂	C₃×C₅×#536	1	1	yes	characteristic
378	C₂	C₃×C₅×#547	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#121	C₂
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
1. C₂×C₃×C₅×#123	C₂	semidirect
3. C₂²×C₃×C₅×C₄⋊C₄	C₂	semidirect
4. C₃×C₅×#399	C₂	semidirect
5. C₃×C₅×#390	C₂	semidirect
6. C₃×C₅×#384	C₂	semidirect
7. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
8. C₅×#2501	C₃	direct (N × H)
25. C₃×#2501	C₅	direct (N × H)
26. C₂×C₅×#123	C₂×C₃	semidirect
28. C₂²×C₅×C₄⋊C₄	C₂×C₃	semidirect
29. C₅×#399	C₂×C₃	semidirect
30. C₅×#390	C₂×C₃	semidirect
31. C₅×#384	C₂×C₃	semidirect
32. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
54. C₃×C₅×C₂²⋊C₄	D₄	semidirect
56. C₂×C₃×#123	C₂×C₅	semidirect
58. C₂²×C₃×C₄⋊C₄	C₂×C₅	semidirect
59. C₃×#399	C₂×C₅	semidirect
60. C₃×#390	C₂×C₅	semidirect
61. C₃×#384	C₂×C₅	semidirect
62. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
79. #2501	C₃×C₅	direct (N × H)
141. C₅×C₂²⋊C₄	C₃×D₄	semidirect
143. C₂×#123	C₂×C₃×C₅	semidirect
145. C₂²×C₄⋊C₄	C₂×C₃×C₅	semidirect
146. #399	C₂×C₃×C₅	semidirect
147. #390	C₂×C₃×C₅	semidirect
148. #384	C₂×C₃×C₅	semidirect
149. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
166. C₃×C₄×C₅	#123	semidirect
188. C₃×C₂²⋊C₄	C₅×D₄	semidirect
276. C₄×C₅	C₃×#123	semidirect
298. C₂²⋊C₄	C₃×C₅×D₄	semidirect
300. C₃×C₅	#2501	direct (N × H)
317. C₃×C₄	C₅×#123	semidirect
354. C₅	C₃×#2501	direct (N × H)
371. C₄	C₃×C₅×#123	semidirect
372. C₃	C₅×#2501	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×#123	2
C₂×C₃×C₅×#121	2
C₂²×C₃×C₅×C₄⋊C₄	2
C₃×C₅×#399	2
C₃×C₅×#390	2
C₃×C₅×#384	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2501	3
C₃×#2501	5

Subgroups — C3×C5×#2501 #14275535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2501 #14275535