Subgroups — C₃×C₅×#2629 #14275663

Order 1920.

944 conjugacy classes of subgroups.

The subgroup lattice has 364 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	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#398	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#396	C₂	1	4	yes	maximal
5	C₃×C₅×#389	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#380	C₂	1	2	yes	maximal
8	C₅×#2629	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₃×C₅×#125	—	2	4	no	—
11	C₃×C₅×#117	—	2	4	no	—
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	4	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₃×C₅×#95	C₂²	1	4	yes	—
23	C₃×C₅×#95	C₂²	1	4	yes	—
24	C₃×#2629	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic
27	C₅×#398	C₂×C₃	1	4	yes	complemented
28	C₅×#396	C₂×C₃	1	4	yes	—
29	C₅×#389	C₂×C₃	1	2	yes	complemented
30	C₅×#384	C₂×C₃	1	1	yes	characteristic, complemented
31	C₅×#380	C₂×C₃	1	2	yes	—
32	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	—	2	2	no	—
34	C₂²×C₃×C₄×C₅	—	2	2	no	—
35	C₂²×C₃×C₄×C₅	Q₈	1	4	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	4	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	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₃×C₅×C₄⋊C₄	—	2	4	no	—
43	C₃×C₅×C₄⋊C₄	—	2	8	no	—
44	C₃×C₅×C₄⋊C₄	—	2	4	no	—
45	C₃×C₅×C₄⋊C₄	—	2	4	no	—
46	C₃×C₅×C₄⋊C₄	—	4	4	no	—
47	C₃×C₅×C₄⋊C₄	—	4	4	no	—
48	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
49	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
50	C₃×C₄²×C₅	—	2	2	no	—
51	C₃×C₄²×C₅	D₄	1	4	yes	—
52	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
53	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic
54	C₃×#398	C₂×C₅	1	4	yes	complemented
55	C₃×#396	C₂×C₅	1	4	yes	—
56	C₃×#389	C₂×C₅	1	2	yes	complemented
57	C₃×#384	C₂×C₅	1	1	yes	characteristic, complemented
58	C₃×#380	C₂×C₅	1	2	yes	—
59	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
60	C₅×#125	—	2	4	no	—
61	C₅×#117	—	2	4	no	—
62	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
63	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
64	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
65	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
66	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
67	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
68	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
69	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
70	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
72	C₅×#95	C₂²×C₃	1	4	yes	—
73	C₅×#95	C₂²×C₃	1	4	yes	—
74	#2629	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
75	C₂³×C₃×C₅	—	2	1	no	—
76	C₂³×C₃×C₅	—	2	1	no	—
77	C₂³×C₃×C₅	—	2	2	no	—
78	C₂³×C₃×C₅	—	2	2	no	—
79	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
80	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
81	C₂×C₃×C₄×C₅	—	2	1	no	—
82	C₂×C₃×C₄×C₅	—	2	1	no	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	8	no	—
86	C₂×C₃×C₄×C₅	—	2	2	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	—	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	4	no	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
96	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
99	C₂×C₃×C₄×C₅	#41	1	2	yes	—
100	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
101	C₃×#125	—	2	4	no	—
102	C₃×#117	—	2	4	no	—
103	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
104	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
105	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
106	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
107	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
108	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
109	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
110	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
111	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
112	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
113	C₃×#95	C₂²×C₅	1	4	yes	—
114	C₃×#95	C₂²×C₅	1	4	yes	—
115	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
116	C₂²×C₄×C₅	—	2	2	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	C₃×Q₈	1	4	yes	—
119	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
120	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
121	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
122	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
123	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
125	C₅×C₄⋊C₄	—	2	4	no	—
126	C₅×C₄⋊C₄	—	2	8	no	—
127	C₅×C₄⋊C₄	—	2	4	no	—
128	C₅×C₄⋊C₄	—	2	4	no	—
129	C₅×C₄⋊C₄	—	4	4	no	—
130	C₅×C₄⋊C₄	—	4	4	no	—
131	C₅×C₂²⋊C₄	—	2	4	no	—
132	C₅×C₂²⋊C₄	—	4	4	no	—
133	C₄²×C₅	—	2	2	no	—
134	C₄²×C₅	C₃×D₄	1	4	yes	—
135	C₂×#125	C₂×C₃×C₅	1	1	yes	characteristic, complemented
136	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic
137	#398	C₂×C₃×C₅	1	4	yes	complemented
138	#396	C₂×C₃×C₅	1	4	yes	—
139	#389	C₂×C₃×C₅	1	2	yes	complemented
140	#384	C₂×C₃×C₅	1	1	yes	characteristic, complemented
141	#380	C₂×C₃×C₅	1	2	yes	—
142	C₂²×C₃×C₅	—	2	2	no	—
143	C₂²×C₃×C₅	—	2	4	no	—
144	C₂²×C₃×C₅	—	4	2	no	—
145	C₂²×C₃×C₅	—	4	1	no	—
146	C₂²×C₃×C₅	—	4	1	no	—
147	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
148	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
149	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
150	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
151	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
152	C₃×C₄×C₅	—	2	2	no	—
153	C₃×C₄×C₅	—	2	4	no	—
154	C₃×C₄×C₅	—	4	2	no	—
155	C₃×C₄×C₅	—	4	4	no	—
156	C₃×C₄×C₅	—	4	4	no	—
157	C₃×C₄×C₅	C₂²⋊Q₈	1	4	yes	—
158	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
159	C₂²×C₃×C₄	—	2	2	no	—
160	C₂²×C₃×C₄	—	2	2	no	—
161	C₂²×C₃×C₄	C₅×Q₈	1	4	yes	—
162	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
163	C₂²×C₃×C₄	C₂³×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	1	yes	characteristic
168	C₃×C₄⋊C₄	—	2	4	no	—
169	C₃×C₄⋊C₄	—	2	8	no	—
170	C₃×C₄⋊C₄	—	2	4	no	—
171	C₃×C₄⋊C₄	—	2	4	no	—
172	C₃×C₄⋊C₄	—	4	4	no	—
173	C₃×C₄⋊C₄	—	4	4	no	—
174	C₃×C₂²⋊C₄	—	2	4	no	—
175	C₃×C₂²⋊C₄	—	4	4	no	—
176	C₃×C₄²	—	2	2	no	—
177	C₃×C₄²	C₅×D₄	1	4	yes	—
178	C₂³×C₅	—	2	1	no	—
179	C₂³×C₅	—	2	1	no	—
180	C₂³×C₅	—	2	2	no	—
181	C₂³×C₅	—	2	2	no	—
182	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
183	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
184	C₂×C₄×C₅	—	2	1	no	—
185	C₂×C₄×C₅	—	2	1	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	2	8	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	4	no	—
191	C₂×C₄×C₅	—	2	4	no	—
192	C₂×C₄×C₅	—	2	4	no	—
193	C₂×C₄×C₅	—	2	4	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	4	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	4	no	—
198	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
199	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
200	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
201	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
202	C₂×C₄×C₅	C₃×#41	1	2	yes	—
203	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
204	#125	—	2	4	no	—
205	#117	—	2	4	no	—
206	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
207	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
208	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
209	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
210	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
211	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
212	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
213	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
214	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
215	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
216	#95	C₂²×C₃×C₅	1	4	yes	—
217	#95	C₂²×C₃×C₅	1	4	yes	—
218	C₂×C₃×C₅	—	4	2	no	—
219	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
220	C₂×C₃×C₅	#537	1	2	yes	—
221	C₂×C₃×C₅	#540	1	1	yes	characteristic
222	C₂×C₃×C₅	#541	1	1	yes	characteristic
223	C₂×C₃×C₅	#544	1	2	yes	—
224	C₂³×C₃	—	2	1	no	—
225	C₂³×C₃	—	2	1	no	—
226	C₂³×C₃	—	2	2	no	—
227	C₂³×C₃	—	2	2	no	—
228	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
229	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
230	C₂×C₃×C₄	—	2	1	no	—
231	C₂×C₃×C₄	—	2	1	no	—
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	2	8	no	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	2	4	no	—
237	C₂×C₃×C₄	—	2	4	no	—
238	C₂×C₃×C₄	—	2	4	no	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	4	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	4	no	—
244	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
245	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
246	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
247	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
248	C₂×C₃×C₄	C₅×#41	1	2	yes	—
249	C₂²×C₅	—	2	2	no	—
250	C₂²×C₅	—	2	4	no	—
251	C₂²×C₅	—	4	2	no	—
252	C₂²×C₅	—	4	1	no	—
253	C₂²×C₅	—	4	1	no	—
254	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
255	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
256	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
257	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
258	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
259	C₄×C₅	—	2	2	no	—
260	C₄×C₅	—	2	4	no	—
261	C₄×C₅	—	4	2	no	—
262	C₄×C₅	—	4	4	no	—
263	C₄×C₅	—	4	4	no	—
264	C₄×C₅	C₃×C₂²⋊Q₈	1	4	yes	—
265	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	C₃×C₅×Q₈	1	4	yes	—
269	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
270	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
271	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
272	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
273	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
274	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
275	C₄⋊C₄	—	2	4	no	—
276	C₄⋊C₄	—	2	8	no	—
277	C₄⋊C₄	—	2	4	no	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	—	4	4	no	—
280	C₄⋊C₄	—	4	4	no	—
281	C₂²⋊C₄	—	2	4	no	—
282	C₂²⋊C₄	—	4	4	no	—
283	C₄²	—	2	2	no	—
284	C₄²	C₃×C₅×D₄	1	4	yes	—
285	C₃×C₅	#2629	1	1	yes	characteristic, direct product factor, Hall
286	C₂²×C₃	—	2	2	no	—
287	C₂²×C₃	—	2	4	no	—
288	C₂²×C₃	—	4	2	no	—
289	C₂²×C₃	—	4	1	no	—
290	C₂²×C₃	—	4	1	no	—
291	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
292	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
293	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
294	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
295	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
296	C₃×C₄	—	2	2	no	—
297	C₃×C₄	—	2	4	no	—
298	C₃×C₄	—	4	2	no	—
299	C₃×C₄	—	4	4	no	—
300	C₃×C₄	—	4	4	no	—
301	C₃×C₄	C₅×C₂²⋊Q₈	1	4	yes	—
302	C₂×C₅	—	4	2	no	—
303	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
304	C₂×C₅	C₃×#537	1	2	yes	—
305	C₂×C₅	C₃×#540	1	1	yes	characteristic
306	C₂×C₅	C₃×#541	1	1	yes	characteristic
307	C₂×C₅	C₃×#544	1	2	yes	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	2	2	no	—
312	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
313	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
329	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
330	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
331	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
332	C₂×C₄	C₃×C₅×#41	1	2	yes	—
333	C₂×C₃	—	4	2	no	—
334	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
335	C₂×C₃	C₅×#537	1	2	yes	—
336	C₂×C₃	C₅×#540	1	1	yes	characteristic
337	C₂×C₃	C₅×#541	1	1	yes	characteristic
338	C₂×C₃	C₅×#544	1	2	yes	—
339	C₅	C₃×#2629	1	1	yes	characteristic, direct product factor, Sylow
340	C₂²	—	2	2	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	1	no	—
344	C₂²	—	4	1	no	—
345	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
346	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
347	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
348	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
349	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
350	C₄	—	2	2	no	—
351	C₄	—	2	4	no	—
352	C₄	—	4	2	no	—
353	C₄	—	4	4	no	—
354	C₄	—	4	4	no	—
355	C₄	C₃×C₅×C₂²⋊Q₈	1	4	yes	—
356	C₃	C₅×#2629	1	1	yes	characteristic, direct product factor, Sylow
357	C₂	—	4	2	no	—
358	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
359	C₂	C₃×C₅×#537	1	2	yes	—
360	C₂	C₃×C₅×#540	1	1	yes	characteristic
361	C₂	C₃×C₅×#541	1	1	yes	characteristic
362	C₂	C₃×C₅×#544	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
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×#125	C₂	semidirect
3. C₃×C₅×#398	C₂	semidirect
5. C₃×C₅×#389	C₂	semidirect
6. C₃×C₅×#384	C₂	semidirect
8. C₅×#2629	C₃	direct (N × H)
24. C₃×#2629	C₅	direct (N × H)
25. C₂×C₅×#125	C₂×C₃	semidirect
27. C₅×#398	C₂×C₃	semidirect
29. C₅×#389	C₂×C₃	semidirect
30. C₅×#384	C₂×C₃	semidirect
52. C₂×C₃×#125	C₂×C₅	semidirect
54. C₃×#398	C₂×C₅	semidirect
56. C₃×#389	C₂×C₅	semidirect
57. C₃×#384	C₂×C₅	semidirect
74. #2629	C₃×C₅	direct (N × H)
135. C₂×#125	C₂×C₃×C₅	semidirect
137. #398	C₂×C₃×C₅	semidirect
139. #389	C₂×C₃×C₅	semidirect
140. #384	C₂×C₃×C₅	semidirect
285. C₃×C₅	#2629	direct (N × H)
339. C₅	C₃×#2629	direct (N × H)
356. C₃	C₅×#2629	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
C₂×C₃×C₅×#117	2
C₃×C₅×#398	2
C₃×C₅×#396	2
C₃×C₅×#389	2
C₃×C₅×#384	2
C₃×C₅×#380	2
C₅×#2629	3
C₃×#2629	5

Subgroups — C3×C5×#2629 #14275663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2629 #14275663