Subgroups — C₃×C₅×#2523 #14275557

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#397	C₂	1	2	yes	maximal
2	C₃×C₅×#397	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#393	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#391	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic
8	C₃×C₅×#383	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal
10	C₅×#2523	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
21	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
22	C₃×C₅×#95	C₂²	1	2	yes	—
23	C₃×C₅×#95	C₂²	1	2	yes	—
24	C₃×C₅×#95	C₂²	1	1	yes	characteristic
25	C₃×C₅×#95	C₂²	1	2	yes	—
26	C₃×C₅×#95	C₂²	1	2	yes	—
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₃×C₅×#95	C₂²	1	2	yes	—
29	C₃×C₅×#95	C₂²	1	2	yes	—
30	C₃×C₅×#95	C₂²	1	1	yes	characteristic
31	C₃×C₅×#95	C₂²	1	2	yes	—
32	C₃×#2523	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₅×#397	C₂×C₃	1	2	yes	—
34	C₅×#397	C₂×C₃	1	1	yes	characteristic
35	C₅×#393	C₂×C₃	1	1	yes	characteristic
36	C₅×#391	C₂×C₃	1	2	yes	complemented
37	C₅×#387	C₂×C₃	1	2	yes	complemented
38	C₅×#387	C₂×C₃	1	2	yes	complemented
39	C₅×#385	C₂×C₃	1	1	yes	characteristic
40	C₅×#383	C₂×C₃	1	2	yes	complemented
41	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	—
42	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
43	C₂×C₃×C₅×Q₈	—	2	4	no	—
44	C₂×C₃×C₅×Q₈	—	4	1	no	—
45	C₂²×C₃×C₄×C₅	—	2	4	no	—
46	C₂²×C₃×C₄×C₅	—	4	1	no	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
55	C₃×C₅×C₄⋊C₄	—	2	4	no	—
56	C₃×C₅×C₄⋊C₄	—	2	4	no	—
57	C₃×C₅×C₄⋊C₄	—	4	1	no	—
58	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
59	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
60	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
61	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
62	C₃×C₄²×C₅	—	2	4	no	—
63	C₃×C₄²×C₅	—	4	2	no	—
64	C₃×#397	C₂×C₅	1	2	yes	—
65	C₃×#397	C₂×C₅	1	1	yes	characteristic
66	C₃×#393	C₂×C₅	1	1	yes	characteristic
67	C₃×#391	C₂×C₅	1	2	yes	complemented
68	C₃×#387	C₂×C₅	1	2	yes	complemented
69	C₃×#387	C₂×C₅	1	2	yes	complemented
70	C₃×#385	C₂×C₅	1	1	yes	characteristic
71	C₃×#383	C₂×C₅	1	2	yes	complemented
72	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	2	yes	—
73	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
74	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
76	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
77	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
80	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
83	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
84	C₅×#95	C₂²×C₃	1	2	yes	—
85	C₅×#95	C₂²×C₃	1	2	yes	—
86	C₅×#95	C₂²×C₃	1	1	yes	characteristic
87	C₅×#95	C₂²×C₃	1	2	yes	—
88	C₅×#95	C₂²×C₃	1	2	yes	—
89	C₅×#95	C₂²×C₃	1	2	yes	—
90	C₅×#95	C₂²×C₃	1	2	yes	—
91	C₅×#95	C₂²×C₃	1	2	yes	—
92	C₅×#95	C₂²×C₃	1	1	yes	characteristic
93	C₅×#95	C₂²×C₃	1	2	yes	—
94	#2523	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
95	C₂³×C₃×C₅	—	2	2	no	—
96	C₂³×C₃×C₅	—	2	2	no	—
97	C₂³×C₃×C₅	—	2	1	no	—
98	C₂³×C₃×C₅	—	2	1	no	—
99	C₂³×C₃×C₅	#41	1	2	yes	—
100	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
101	C₃×C₅×Q₈	—	4	4	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	1	no	—
119	C₂×C₃×C₄×C₅	—	2	1	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	4	4	no	—
123	C₂×C₃×C₄×C₅	#41	1	4	yes	—
124	C₂×C₃×C₄×C₅	#41	1	4	yes	—
125	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
126	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
128	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
129	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
130	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
131	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
132	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
133	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
135	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
136	C₃×#95	C₂²×C₅	1	2	yes	—
137	C₃×#95	C₂²×C₅	1	2	yes	—
138	C₃×#95	C₂²×C₅	1	1	yes	characteristic
139	C₃×#95	C₂²×C₅	1	2	yes	—
140	C₃×#95	C₂²×C₅	1	2	yes	—
141	C₃×#95	C₂²×C₅	1	2	yes	—
142	C₃×#95	C₂²×C₅	1	2	yes	—
143	C₃×#95	C₂²×C₅	1	2	yes	—
144	C₃×#95	C₂²×C₅	1	1	yes	characteristic
145	C₃×#95	C₂²×C₅	1	2	yes	—
146	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
147	C₂×C₅×Q₈	—	2	4	no	—
148	C₂×C₅×Q₈	—	4	1	no	—
149	C₂²×C₄×C₅	—	2	4	no	—
150	C₂²×C₄×C₅	—	4	1	no	—
151	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
152	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
153	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
154	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
156	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
158	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
159	C₅×C₄⋊C₄	—	2	4	no	—
160	C₅×C₄⋊C₄	—	2	4	no	—
161	C₅×C₄⋊C₄	—	4	1	no	—
162	C₅×C₂²⋊C₄	—	2	4	no	—
163	C₅×C₂²⋊C₄	—	2	2	no	—
164	C₅×C₂²⋊C₄	—	2	4	no	—
165	C₅×C₂²⋊C₄	—	4	1	no	—
166	C₄²×C₅	—	2	4	no	—
167	C₄²×C₅	—	4	2	no	—
168	#397	C₂×C₃×C₅	1	2	yes	—
169	#397	C₂×C₃×C₅	1	1	yes	characteristic
170	#393	C₂×C₃×C₅	1	1	yes	characteristic
171	#391	C₂×C₃×C₅	1	2	yes	complemented
172	#387	C₂×C₃×C₅	1	2	yes	complemented
173	#387	C₂×C₃×C₅	1	2	yes	complemented
174	#385	C₂×C₃×C₅	1	1	yes	characteristic
175	#383	C₂×C₃×C₅	1	2	yes	complemented
176	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	—
177	C₂²×C₃×C₅	—	2	4	no	—
178	C₂²×C₃×C₅	—	2	2	no	—
179	C₂²×C₃×C₅	—	4	1	no	—
180	C₂²×C₃×C₅	—	4	1	no	—
181	C₂²×C₃×C₅	—	4	2	no	—
182	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
183	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
184	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
185	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
187	C₃×C₄×C₅	—	2	4	no	—
188	C₃×C₄×C₅	—	2	4	no	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	—	4	2	no	—
191	C₃×C₄×C₅	—	4	2	no	—
192	C₃×C₄×C₅	—	4	1	no	—
193	C₃×C₄×C₅	—	4	1	no	—
194	C₃×C₄×C₅	—	4	2	no	—
195	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
196	C₂×C₃×Q₈	—	2	4	no	—
197	C₂×C₃×Q₈	—	4	1	no	—
198	C₂²×C₃×C₄	—	2	4	no	—
199	C₂²×C₃×C₄	—	4	1	no	—
200	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
201	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
202	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
203	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
204	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
205	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
207	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
208	C₃×C₄⋊C₄	—	2	4	no	—
209	C₃×C₄⋊C₄	—	2	4	no	—
210	C₃×C₄⋊C₄	—	4	1	no	—
211	C₃×C₂²⋊C₄	—	2	4	no	—
212	C₃×C₂²⋊C₄	—	2	2	no	—
213	C₃×C₂²⋊C₄	—	2	4	no	—
214	C₃×C₂²⋊C₄	—	4	1	no	—
215	C₃×C₄²	—	2	4	no	—
216	C₃×C₄²	—	4	2	no	—
217	C₂³×C₅	—	2	2	no	—
218	C₂³×C₅	—	2	2	no	—
219	C₂³×C₅	—	2	1	no	—
220	C₂³×C₅	—	2	1	no	—
221	C₂³×C₅	C₃×#41	1	2	yes	—
222	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
223	C₅×Q₈	—	4	4	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	1	no	—
241	C₂×C₄×C₅	—	2	1	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	4	4	no	—
245	C₂×C₄×C₅	C₃×#41	1	4	yes	—
246	C₂×C₄×C₅	C₃×#41	1	4	yes	—
247	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
248	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
250	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
251	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
253	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
254	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
255	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
256	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
257	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
258	#95	C₂²×C₃×C₅	1	2	yes	—
259	#95	C₂²×C₃×C₅	1	2	yes	—
260	#95	C₂²×C₃×C₅	1	1	yes	characteristic
261	#95	C₂²×C₃×C₅	1	2	yes	—
262	#95	C₂²×C₃×C₅	1	2	yes	—
263	#95	C₂²×C₃×C₅	1	2	yes	—
264	#95	C₂²×C₃×C₅	1	2	yes	—
265	#95	C₂²×C₃×C₅	1	2	yes	—
266	#95	C₂²×C₃×C₅	1	1	yes	characteristic
267	#95	C₂²×C₃×C₅	1	2	yes	—
268	C₂×C₃×C₅	—	4	2	no	—
269	C₂×C₃×C₅	#529	1	2	yes	—
270	C₂×C₃×C₅	#539	1	1	yes	characteristic
271	C₂×C₃×C₅	#551	1	1	yes	characteristic
272	C₂×C₃×C₅	#551	1	1	yes	characteristic
273	C₂×C₃×C₅	#556	1	2	yes	—
274	C₂³×C₃	—	2	2	no	—
275	C₂³×C₃	—	2	2	no	—
276	C₂³×C₃	—	2	1	no	—
277	C₂³×C₃	—	2	1	no	—
278	C₂³×C₃	C₅×#41	1	2	yes	—
279	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
280	C₃×Q₈	—	4	4	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	—	2	2	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	1	no	—
298	C₂×C₃×C₄	—	2	1	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	4	4	no	—
302	C₂×C₃×C₄	C₅×#41	1	4	yes	—
303	C₂×C₃×C₄	C₅×#41	1	4	yes	—
304	C₂²×C₅	—	2	4	no	—
305	C₂²×C₅	—	2	2	no	—
306	C₂²×C₅	—	4	1	no	—
307	C₂²×C₅	—	4	1	no	—
308	C₂²×C₅	—	4	2	no	—
309	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
310	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
311	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
312	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
313	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
314	C₄×C₅	—	2	4	no	—
315	C₄×C₅	—	2	4	no	—
316	C₄×C₅	—	4	2	no	—
317	C₄×C₅	—	4	2	no	—
318	C₄×C₅	—	4	2	no	—
319	C₄×C₅	—	4	1	no	—
320	C₄×C₅	—	4	1	no	—
321	C₄×C₅	—	4	2	no	—
322	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
323	C₂×Q₈	—	2	4	no	—
324	C₂×Q₈	—	4	1	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
328	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
329	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
330	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
331	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
332	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
333	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
334	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	2	4	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	4	1	no	—
342	C₄²	—	2	4	no	—
343	C₄²	—	4	2	no	—
344	C₃×C₅	#2523	1	1	yes	characteristic, direct product factor, Hall
345	C₂²×C₃	—	2	4	no	—
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	—	4	1	no	—
348	C₂²×C₃	—	4	1	no	—
349	C₂²×C₃	—	4	2	no	—
350	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
351	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
352	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
353	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
355	C₃×C₄	—	2	4	no	—
356	C₃×C₄	—	2	4	no	—
357	C₃×C₄	—	4	2	no	—
358	C₃×C₄	—	4	2	no	—
359	C₃×C₄	—	4	2	no	—
360	C₃×C₄	—	4	1	no	—
361	C₃×C₄	—	4	1	no	—
362	C₃×C₄	—	4	2	no	—
363	C₂×C₅	—	4	2	no	—
364	C₂×C₅	C₃×#529	1	2	yes	—
365	C₂×C₅	C₃×#539	1	1	yes	characteristic
366	C₂×C₅	C₃×#551	1	1	yes	characteristic
367	C₂×C₅	C₃×#551	1	1	yes	characteristic
368	C₂×C₅	C₃×#556	1	2	yes	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	C₃×C₅×#41	1	2	yes	—
374	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
375	Q₈	—	4	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	C₃×C₅×#41	1	4	yes	—
398	C₂×C₄	C₃×C₅×#41	1	4	yes	—
399	C₂×C₃	—	4	2	no	—
400	C₂×C₃	C₅×#529	1	2	yes	—
401	C₂×C₃	C₅×#539	1	1	yes	characteristic
402	C₂×C₃	C₅×#551	1	1	yes	characteristic
403	C₂×C₃	C₅×#551	1	1	yes	characteristic
404	C₂×C₃	C₅×#556	1	2	yes	—
405	C₅	C₃×#2523	1	1	yes	characteristic, direct product factor, Sylow
406	C₂²	—	2	4	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	2	no	—
411	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
412	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
413	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
414	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
415	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
416	C₄	—	2	4	no	—
417	C₄	—	2	4	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	1	no	—
423	C₄	—	4	2	no	—
424	C₃	C₅×#2523	1	1	yes	characteristic, direct product factor, Sylow
425	C₂	—	4	2	no	—
426	C₂	C₃×C₅×#529	1	2	yes	—
427	C₂	C₃×C₅×#539	1	1	yes	characteristic
428	C₂	C₃×C₅×#551	1	1	yes	characteristic
429	C₂	C₃×C₅×#551	1	1	yes	characteristic
430	C₂	C₃×C₅×#556	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
4. C₃×C₅×#391	C₂	semidirect
5. C₃×C₅×#387	C₂	semidirect
6. C₃×C₅×#387	C₂	semidirect
8. C₃×C₅×#383	C₂	semidirect
10. C₅×#2523	C₃	direct (N × H)
32. C₃×#2523	C₅	direct (N × H)
36. C₅×#391	C₂×C₃	semidirect
37. C₅×#387	C₂×C₃	semidirect
38. C₅×#387	C₂×C₃	semidirect
40. C₅×#383	C₂×C₃	semidirect
67. C₃×#391	C₂×C₅	semidirect
68. C₃×#387	C₂×C₅	semidirect
69. C₃×#387	C₂×C₅	semidirect
71. C₃×#383	C₂×C₅	semidirect
94. #2523	C₃×C₅	direct (N × H)
171. #391	C₂×C₃×C₅	semidirect
172. #387	C₂×C₃×C₅	semidirect
173. #387	C₂×C₃×C₅	semidirect
175. #383	C₂×C₃×C₅	semidirect
344. C₃×C₅	#2523	direct (N × H)
405. C₅	C₃×#2523	direct (N × H)
424. C₃	C₅×#2523	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×#397	2
C₃×C₅×#393	2
C₃×C₅×#391	2
C₃×C₅×#387	2
C₃×C₅×#385	2
C₃×C₅×#383	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2523	3
C₃×#2523	5

Subgroups — C3×C5×#2523 #14275557

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2523 #14275557