Subgroups — C₃×C₅×#2624 #14275658

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#399	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#397	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#394	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#390	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#389	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2624	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₃×C₅×#121	—	2	4	no	—
14	C₃×C₅×#117	—	2	4	no	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
25	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
26	C₃×C₅×#95	C₂²	1	2	yes	—
27	C₃×C₅×#95	C₂²	1	4	yes	—
28	C₃×#2624	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic
30	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
31	C₅×#399	C₂×C₃	1	2	yes	complemented
32	C₅×#397	C₂×C₃	1	2	yes	complemented
33	C₅×#394	C₂×C₃	1	4	yes	complemented
34	C₅×#390	C₂×C₃	1	2	yes	complemented
35	C₅×#389	C₂×C₃	1	2	yes	complemented
36	C₅×#380	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
38	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
39	C₂×C₃×C₅×D₄	—	2	4	no	—
40	C₂×C₃×C₅×D₄	—	2	2	no	—
41	C₂×C₃×C₅×D₄	—	2	4	no	—
42	C₂×C₃×C₅×D₄	—	4	4	no	—
43	C₂²×C₃×C₄×C₅	—	2	4	no	—
44	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₃×C₅×C₄⋊C₄	—	2	2	no	—
52	C₃×C₅×C₄⋊C₄	—	2	2	no	—
53	C₃×C₅×C₄⋊C₄	—	2	2	no	—
54	C₃×C₅×C₄⋊C₄	—	2	4	no	—
55	C₃×C₅×C₄⋊C₄	—	4	4	no	—
56	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
57	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
58	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
59	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
60	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
61	C₃×C₄²×C₅	—	2	4	no	—
62	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic
63	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
64	C₃×#399	C₂×C₅	1	2	yes	complemented
65	C₃×#397	C₂×C₅	1	2	yes	complemented
66	C₃×#394	C₂×C₅	1	4	yes	complemented
67	C₃×#390	C₂×C₅	1	2	yes	complemented
68	C₃×#389	C₂×C₅	1	2	yes	complemented
69	C₃×#380	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
71	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
72	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
73	C₅×#121	—	2	4	no	—
74	C₅×#117	—	2	4	no	—
75	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
76	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
80	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
81	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
82	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
83	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
84	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
85	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
86	C₅×#95	C₂²×C₃	1	2	yes	—
87	C₅×#95	C₂²×C₃	1	4	yes	—
88	#2624	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
89	C₂³×C₃×C₅	—	2	2	no	—
90	C₂³×C₃×C₅	—	2	1	no	—
91	C₂³×C₃×C₅	—	2	2	no	—
92	C₂³×C₃×C₅	—	2	1	no	—
93	C₂³×C₃×C₅	—	2	2	no	—
94	C₂³×C₃×C₅	—	2	4	no	—
95	C₂³×C₃×C₅	—	2	2	no	—
96	C₂³×C₃×C₅	—	2	4	no	—
97	C₂³×C₃×C₅	—	2	2	no	—
98	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
99	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
100	C₃×C₅×D₄	—	4	8	no	—
101	C₃×C₅×D₄	—	4	4	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	8	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	4	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	4	no	—
111	C₂×C₃×C₄×C₅	—	2	4	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	4	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	#41	1	4	yes	—
118	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
119	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
120	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
121	C₃×#121	—	2	4	no	—
122	C₃×#117	—	2	4	no	—
123	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
124	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
125	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
126	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
128	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
129	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
130	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
131	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
132	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
133	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
134	C₃×#95	C₂²×C₅	1	2	yes	—
135	C₃×#95	C₂²×C₅	1	4	yes	—
136	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
137	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
138	C₂×C₅×D₄	—	2	4	no	—
139	C₂×C₅×D₄	—	2	2	no	—
140	C₂×C₅×D₄	—	2	4	no	—
141	C₂×C₅×D₄	—	4	4	no	—
142	C₂²×C₄×C₅	—	2	4	no	—
143	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
144	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
145	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
146	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
147	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
148	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
150	C₅×C₄⋊C₄	—	2	2	no	—
151	C₅×C₄⋊C₄	—	2	2	no	—
152	C₅×C₄⋊C₄	—	2	2	no	—
153	C₅×C₄⋊C₄	—	2	4	no	—
154	C₅×C₄⋊C₄	—	4	4	no	—
155	C₅×C₂²⋊C₄	—	2	4	no	—
156	C₅×C₂²⋊C₄	—	2	4	no	—
157	C₅×C₂²⋊C₄	—	4	2	no	—
158	C₅×C₂²⋊C₄	—	4	4	no	—
159	C₅×C₂²⋊C₄	—	4	4	no	—
160	C₄²×C₅	—	2	4	no	—
161	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic
162	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic, complemented
163	#399	C₂×C₃×C₅	1	2	yes	complemented
164	#397	C₂×C₃×C₅	1	2	yes	complemented
165	#394	C₂×C₃×C₅	1	4	yes	complemented
166	#390	C₂×C₃×C₅	1	2	yes	complemented
167	#389	C₂×C₃×C₅	1	2	yes	complemented
168	#380	C₂×C₃×C₅	1	1	yes	characteristic, complemented
169	C₂²×C₃×C₅	—	2	2	no	—
170	C₂²×C₃×C₅	—	2	2	no	—
171	C₂²×C₃×C₅	—	2	2	no	—
172	C₂²×C₃×C₅	—	4	2	no	—
173	C₂²×C₃×C₅	—	4	2	no	—
174	C₂²×C₃×C₅	—	4	2	no	—
175	C₂²×C₃×C₅	—	4	2	no	—
176	C₂²×C₃×C₅	—	4	2	no	—
177	C₂²×C₃×C₅	—	4	4	no	—
178	C₂²×C₃×C₅	—	4	4	no	—
179	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
180	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
181	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
182	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
184	C₃×C₄×C₅	—	2	2	no	—
185	C₃×C₄×C₅	—	4	2	no	—
186	C₃×C₄×C₅	—	4	2	no	—
187	C₃×C₄×C₅	—	4	2	no	—
188	C₃×C₄×C₅	—	4	4	no	—
189	C₃×C₄×C₅	#123	1	4	yes	—
190	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
191	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
192	C₂×C₃×D₄	—	2	4	no	—
193	C₂×C₃×D₄	—	2	2	no	—
194	C₂×C₃×D₄	—	2	4	no	—
195	C₂×C₃×D₄	—	4	4	no	—
196	C₂²×C₃×C₄	—	2	4	no	—
197	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
198	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
199	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
200	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
201	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
202	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
203	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
204	C₃×C₄⋊C₄	—	2	2	no	—
205	C₃×C₄⋊C₄	—	2	2	no	—
206	C₃×C₄⋊C₄	—	2	2	no	—
207	C₃×C₄⋊C₄	—	2	4	no	—
208	C₃×C₄⋊C₄	—	4	4	no	—
209	C₃×C₂²⋊C₄	—	2	4	no	—
210	C₃×C₂²⋊C₄	—	2	4	no	—
211	C₃×C₂²⋊C₄	—	4	2	no	—
212	C₃×C₂²⋊C₄	—	4	4	no	—
213	C₃×C₂²⋊C₄	—	4	4	no	—
214	C₃×C₄²	—	2	4	no	—
215	C₂³×C₅	—	2	2	no	—
216	C₂³×C₅	—	2	1	no	—
217	C₂³×C₅	—	2	2	no	—
218	C₂³×C₅	—	2	1	no	—
219	C₂³×C₅	—	2	2	no	—
220	C₂³×C₅	—	2	4	no	—
221	C₂³×C₅	—	2	2	no	—
222	C₂³×C₅	—	2	4	no	—
223	C₂³×C₅	—	2	2	no	—
224	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
225	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
226	C₅×D₄	—	4	8	no	—
227	C₅×D₄	—	4	4	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	8	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	4	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	4	no	—
237	C₂×C₄×C₅	—	2	4	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	4	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
242	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
243	C₂×C₄×C₅	C₃×#41	1	4	yes	—
244	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
245	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
246	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
247	#121	—	2	4	no	—
248	#117	—	2	4	no	—
249	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
253	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
254	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
255	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
256	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
257	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
258	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
259	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
260	#95	C₂²×C₃×C₅	1	2	yes	—
261	#95	C₂²×C₃×C₅	1	4	yes	—
262	C₂×C₃×C₅	—	4	2	no	—
263	C₂×C₃×C₅	—	8	2	no	—
264	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
265	C₂×C₃×C₅	#535	1	1	yes	characteristic
266	C₂×C₃×C₅	#537	1	1	yes	characteristic
267	C₂×C₃×C₅	#540	1	2	yes	—
268	C₂×C₃×C₅	#542	1	2	yes	—
269	C₂³×C₃	—	2	2	no	—
270	C₂³×C₃	—	2	1	no	—
271	C₂³×C₃	—	2	2	no	—
272	C₂³×C₃	—	2	1	no	—
273	C₂³×C₃	—	2	2	no	—
274	C₂³×C₃	—	2	4	no	—
275	C₂³×C₃	—	2	2	no	—
276	C₂³×C₃	—	2	4	no	—
277	C₂³×C₃	—	2	2	no	—
278	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
279	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
280	C₃×D₄	—	4	8	no	—
281	C₃×D₄	—	4	4	no	—
282	C₂×C₃×C₄	—	2	2	no	—
283	C₂×C₃×C₄	—	2	8	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	4	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	4	no	—
291	C₂×C₃×C₄	—	2	4	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	2	4	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
296	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
297	C₂×C₃×C₄	C₅×#41	1	4	yes	—
298	C₂²×C₅	—	2	2	no	—
299	C₂²×C₅	—	2	2	no	—
300	C₂²×C₅	—	2	2	no	—
301	C₂²×C₅	—	4	2	no	—
302	C₂²×C₅	—	4	2	no	—
303	C₂²×C₅	—	4	2	no	—
304	C₂²×C₅	—	4	2	no	—
305	C₂²×C₅	—	4	2	no	—
306	C₂²×C₅	—	4	4	no	—
307	C₂²×C₅	—	4	4	no	—
308	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
309	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
310	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
311	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
312	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
313	C₄×C₅	—	2	2	no	—
314	C₄×C₅	—	4	2	no	—
315	C₄×C₅	—	4	2	no	—
316	C₄×C₅	—	4	2	no	—
317	C₄×C₅	—	4	4	no	—
318	C₄×C₅	C₃×#123	1	4	yes	—
319	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
320	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	4	no	—
324	C₂×D₄	—	4	4	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
327	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
328	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
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	1	yes	characteristic
332	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	4	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	4	no	—
342	C₂²⋊C₄	—	4	4	no	—
343	C₄²	—	2	4	no	—
344	C₃×C₅	#2624	1	1	yes	characteristic, direct product factor, Hall
345	C₂²×C₃	—	2	2	no	—
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	—	2	2	no	—
348	C₂²×C₃	—	4	2	no	—
349	C₂²×C₃	—	4	2	no	—
350	C₂²×C₃	—	4	2	no	—
351	C₂²×C₃	—	4	2	no	—
352	C₂²×C₃	—	4	2	no	—
353	C₂²×C₃	—	4	4	no	—
354	C₂²×C₃	—	4	4	no	—
355	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
356	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
357	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
358	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
359	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
360	C₃×C₄	—	2	2	no	—
361	C₃×C₄	—	4	2	no	—
362	C₃×C₄	—	4	2	no	—
363	C₃×C₄	—	4	2	no	—
364	C₃×C₄	—	4	4	no	—
365	C₃×C₄	C₅×#123	1	4	yes	—
366	C₂×C₅	—	4	2	no	—
367	C₂×C₅	—	8	2	no	—
368	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
369	C₂×C₅	C₃×#535	1	1	yes	characteristic
370	C₂×C₅	C₃×#537	1	1	yes	characteristic
371	C₂×C₅	C₃×#540	1	2	yes	—
372	C₂×C₅	C₃×#542	1	2	yes	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	4	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	2	no	—
382	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
383	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
384	D₄	—	4	8	no	—
385	D₄	—	4	4	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	8	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
400	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
401	C₂×C₄	C₃×C₅×#41	1	4	yes	—
402	C₂×C₃	—	4	2	no	—
403	C₂×C₃	—	8	2	no	—
404	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
405	C₂×C₃	C₅×#535	1	1	yes	characteristic
406	C₂×C₃	C₅×#537	1	1	yes	characteristic
407	C₂×C₃	C₅×#540	1	2	yes	—
408	C₂×C₃	C₅×#542	1	2	yes	—
409	C₅	C₃×#2624	1	1	yes	characteristic, direct product factor, Sylow
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	4	4	no	—
420	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
421	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
422	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
423	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
424	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
425	C₄	—	2	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	4	no	—
430	C₄	C₃×C₅×#123	1	4	yes	—
431	C₃	C₅×#2624	1	1	yes	characteristic, direct product factor, Sylow
432	C₂	—	4	2	no	—
433	C₂	—	8	2	no	—
434	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
435	C₂	C₃×C₅×#535	1	1	yes	characteristic
436	C₂	C₃×C₅×#537	1	1	yes	characteristic
437	C₂	C₃×C₅×#540	1	2	yes	—
438	C₂	C₃×C₅×#542	1	2	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
2. C₂×C₃×C₅×#117	C₂	semidirect
3. C₃×C₅×#399	C₂	semidirect
4. C₃×C₅×#397	C₂	semidirect
5. C₃×C₅×#394	C₂	semidirect
6. C₃×C₅×#390	C₂	semidirect
7. C₃×C₅×#389	C₂	semidirect
8. C₃×C₅×#380	C₂	semidirect
9. C₅×#2624	C₃	direct (N × H)
28. C₃×#2624	C₅	direct (N × H)
30. C₂×C₅×#117	C₂×C₃	semidirect
31. C₅×#399	C₂×C₃	semidirect
32. C₅×#397	C₂×C₃	semidirect
33. C₅×#394	C₂×C₃	semidirect
34. C₅×#390	C₂×C₃	semidirect
35. C₅×#389	C₂×C₃	semidirect
36. C₅×#380	C₂×C₃	semidirect
63. C₂×C₃×#117	C₂×C₅	semidirect
64. C₃×#399	C₂×C₅	semidirect
65. C₃×#397	C₂×C₅	semidirect
66. C₃×#394	C₂×C₅	semidirect
67. C₃×#390	C₂×C₅	semidirect
68. C₃×#389	C₂×C₅	semidirect
69. C₃×#380	C₂×C₅	semidirect
88. #2624	C₃×C₅	direct (N × H)
162. C₂×#117	C₂×C₃×C₅	semidirect
163. #399	C₂×C₃×C₅	semidirect
164. #397	C₂×C₃×C₅	semidirect
165. #394	C₂×C₃×C₅	semidirect
166. #390	C₂×C₃×C₅	semidirect
167. #389	C₂×C₃×C₅	semidirect
168. #380	C₂×C₃×C₅	semidirect
344. C₃×C₅	#2624	direct (N × H)
409. C₅	C₃×#2624	direct (N × H)
431. C₃	C₅×#2624	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×#121	2
C₂×C₃×C₅×#117	2
C₃×C₅×#399	2
C₃×C₅×#397	2
C₃×C₅×#394	2
C₃×C₅×#390	2
C₃×C₅×#389	2
C₃×C₅×#380	2
C₅×#2624	3
C₃×#2624	5

Subgroups — C3×C5×#2624 #14275658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2624 #14275658