Subgroups — C₃×C₅×#2609 #14275643

Order 1920.

1080 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#117	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#398	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#396	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#386	C₂	1	2	yes	maximal
8	C₃×C₅×#385	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2609	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
13	C₃×C₅×#117	—	2	8	no	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
26	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₃×C₅×#95	C₂²	1	2	yes	—
29	C₃×C₅×#95	C₂²	1	1	yes	characteristic
30	C₃×C₅×#95	C₂²	1	2	yes	—
31	C₃×C₅×#95	C₂²	1	1	yes	characteristic
32	C₃×C₅×#95	C₂²	1	2	yes	—
33	C₃×#2609	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₅×#117	C₂×C₃	1	2	yes	complemented
35	C₅×#398	C₂×C₃	1	1	yes	characteristic, complemented
36	C₅×#396	C₂×C₃	1	2	yes	complemented
37	C₅×#394	C₂×C₃	1	1	yes	characteristic
38	C₅×#388	C₂×C₃	1	2	yes	complemented
39	C₅×#387	C₂×C₃	1	2	yes	complemented
40	C₅×#386	C₂×C₃	1	2	yes	—
41	C₅×#385	C₂×C₃	1	2	yes	complemented
42	C₅×#382	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
44	C₂×C₃×C₅×D₄	—	2	4	no	—
45	C₂×C₃×C₅×D₄	—	4	1	no	—
46	C₂²×C₃×C₄×C₅	—	2	4	no	—
47	C₂²×C₃×C₄×C₅	—	2	4	no	—
48	C₂²×C₃×C₄×C₅	—	2	4	no	—
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
57	C₃×C₅×C₄⋊C₄	—	2	4	no	—
58	C₃×C₅×C₄⋊C₄	—	2	4	no	—
59	C₃×C₅×C₄⋊C₄	—	2	4	no	—
60	C₃×C₅×C₄⋊C₄	—	4	1	no	—
61	C₃×C₅×C₄⋊C₄	—	4	1	no	—
62	C₃×C₅×C₄⋊C₄	—	4	1	no	—
63	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
64	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
65	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
66	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
67	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
68	C₃×C₄²×C₅	—	2	4	no	—
69	C₃×C₄²×C₅	D₄	1	4	yes	complemented
70	C₂×C₃×#117	C₂×C₅	1	2	yes	complemented
71	C₃×#398	C₂×C₅	1	1	yes	characteristic, complemented
72	C₃×#396	C₂×C₅	1	2	yes	complemented
73	C₃×#394	C₂×C₅	1	1	yes	characteristic
74	C₃×#388	C₂×C₅	1	2	yes	complemented
75	C₃×#387	C₂×C₅	1	2	yes	complemented
76	C₃×#386	C₂×C₅	1	2	yes	—
77	C₃×#385	C₂×C₅	1	2	yes	complemented
78	C₃×#382	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
80	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
81	C₅×#117	—	2	8	no	—
82	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
83	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
84	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
85	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
89	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
90	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
91	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
92	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
93	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
94	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
95	C₅×#95	C₂²×C₃	1	2	yes	—
96	C₅×#95	C₂²×C₃	1	2	yes	—
97	C₅×#95	C₂²×C₃	1	1	yes	characteristic
98	C₅×#95	C₂²×C₃	1	2	yes	—
99	C₅×#95	C₂²×C₃	1	1	yes	characteristic
100	C₅×#95	C₂²×C₃	1	2	yes	—
101	#2609	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	—	2	2	no	—
104	C₂³×C₃×C₅	—	2	2	no	—
105	C₂³×C₃×C₅	—	2	2	no	—
106	C₂³×C₃×C₅	—	2	2	no	—
107	C₂³×C₃×C₅	—	2	2	no	—
108	C₂³×C₃×C₅	#41	1	4	yes	—
109	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
110	C₃×C₅×D₄	—	4	4	no	—
111	C₂×C₃×C₄×C₅	—	2	16	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	1	no	—
117	C₂×C₃×C₄×C₅	—	2	1	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	1	no	—
129	C₂×C₃×C₄×C₅	—	2	1	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
132	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
133	C₂×C₃×C₄×C₅	#41	1	4	yes	—
134	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
135	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
136	C₃×#117	—	2	8	no	—
137	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
138	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
139	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
140	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
141	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
142	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
143	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
144	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
145	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
146	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
147	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
148	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
149	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
150	C₃×#95	C₂²×C₅	1	2	yes	—
151	C₃×#95	C₂²×C₅	1	2	yes	—
152	C₃×#95	C₂²×C₅	1	1	yes	characteristic
153	C₃×#95	C₂²×C₅	1	2	yes	—
154	C₃×#95	C₂²×C₅	1	1	yes	characteristic
155	C₃×#95	C₂²×C₅	1	2	yes	—
156	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
157	C₂×C₅×D₄	—	2	4	no	—
158	C₂×C₅×D₄	—	4	1	no	—
159	C₂²×C₄×C₅	—	2	4	no	—
160	C₂²×C₄×C₅	—	2	4	no	—
161	C₂²×C₄×C₅	—	2	4	no	—
162	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
163	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
164	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
166	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
168	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
170	C₅×C₄⋊C₄	—	2	4	no	—
171	C₅×C₄⋊C₄	—	2	4	no	—
172	C₅×C₄⋊C₄	—	2	4	no	—
173	C₅×C₄⋊C₄	—	4	1	no	—
174	C₅×C₄⋊C₄	—	4	1	no	—
175	C₅×C₄⋊C₄	—	4	1	no	—
176	C₅×C₂²⋊C₄	—	2	4	no	—
177	C₅×C₂²⋊C₄	—	2	4	no	—
178	C₅×C₂²⋊C₄	—	2	4	no	—
179	C₅×C₂²⋊C₄	—	2	4	no	—
180	C₅×C₂²⋊C₄	—	4	2	no	—
181	C₄²×C₅	—	2	4	no	—
182	C₄²×C₅	C₃×D₄	1	4	yes	complemented
183	C₂×#117	C₂×C₃×C₅	1	2	yes	complemented
184	#398	C₂×C₃×C₅	1	1	yes	characteristic, complemented
185	#396	C₂×C₃×C₅	1	2	yes	complemented
186	#394	C₂×C₃×C₅	1	1	yes	characteristic
187	#388	C₂×C₃×C₅	1	2	yes	complemented
188	#387	C₂×C₃×C₅	1	2	yes	complemented
189	#386	C₂×C₃×C₅	1	2	yes	—
190	#385	C₂×C₃×C₅	1	2	yes	complemented
191	#382	C₂×C₃×C₅	1	1	yes	characteristic, complemented
192	C₂²×C₃×C₅	—	2	4	no	—
193	C₂²×C₃×C₅	—	2	4	no	—
194	C₂²×C₃×C₅	—	2	4	no	—
195	C₂²×C₃×C₅	—	4	2	no	—
196	C₂²×C₃×C₅	—	4	2	no	—
197	C₂²×C₃×C₅	—	4	2	no	—
198	C₂²×C₃×C₅	—	4	2	no	—
199	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
200	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
201	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
202	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
203	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
204	C₃×C₄×C₅	—	2	4	no	—
205	C₃×C₄×C₅	—	2	4	no	—
206	C₃×C₄×C₅	—	2	2	no	—
207	C₃×C₄×C₅	—	4	2	no	—
208	C₃×C₄×C₅	—	4	2	no	—
209	C₃×C₄×C₅	—	4	1	no	—
210	C₃×C₄×C₅	—	4	1	no	—
211	C₃×C₄×C₅	—	4	2	no	—
212	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
213	C₂×C₃×D₄	—	2	4	no	—
214	C₂×C₃×D₄	—	4	1	no	—
215	C₂²×C₃×C₄	—	2	4	no	—
216	C₂²×C₃×C₄	—	2	4	no	—
217	C₂²×C₃×C₄	—	2	4	no	—
218	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
221	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
222	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
223	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
224	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
226	C₃×C₄⋊C₄	—	2	4	no	—
227	C₃×C₄⋊C₄	—	2	4	no	—
228	C₃×C₄⋊C₄	—	2	4	no	—
229	C₃×C₄⋊C₄	—	4	1	no	—
230	C₃×C₄⋊C₄	—	4	1	no	—
231	C₃×C₄⋊C₄	—	4	1	no	—
232	C₃×C₂²⋊C₄	—	2	4	no	—
233	C₃×C₂²⋊C₄	—	2	4	no	—
234	C₃×C₂²⋊C₄	—	2	4	no	—
235	C₃×C₂²⋊C₄	—	2	4	no	—
236	C₃×C₂²⋊C₄	—	4	2	no	—
237	C₃×C₄²	—	2	4	no	—
238	C₃×C₄²	C₅×D₄	1	4	yes	complemented
239	C₂³×C₅	—	2	2	no	—
240	C₂³×C₅	—	2	2	no	—
241	C₂³×C₅	—	2	2	no	—
242	C₂³×C₅	—	2	2	no	—
243	C₂³×C₅	—	2	2	no	—
244	C₂³×C₅	—	2	2	no	—
245	C₂³×C₅	C₃×#41	1	4	yes	—
246	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
247	C₅×D₄	—	4	4	no	—
248	C₂×C₄×C₅	—	2	16	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	2	1	no	—
254	C₂×C₄×C₅	—	2	1	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	2	1	no	—
266	C₂×C₄×C₅	—	2	1	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
269	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
270	C₂×C₄×C₅	C₃×#41	1	4	yes	—
271	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
272	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
273	#117	—	2	8	no	—
274	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
275	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
276	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
277	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
281	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
282	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
283	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
284	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
285	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
286	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
287	#95	C₂²×C₃×C₅	1	2	yes	—
288	#95	C₂²×C₃×C₅	1	2	yes	—
289	#95	C₂²×C₃×C₅	1	1	yes	characteristic
290	#95	C₂²×C₃×C₅	1	2	yes	—
291	#95	C₂²×C₃×C₅	1	1	yes	characteristic
292	#95	C₂²×C₃×C₅	1	2	yes	—
293	C₂×C₃×C₅	—	4	4	no	—
294	C₂×C₃×C₅	#525	1	2	yes	—
295	C₂×C₃×C₅	#537	1	1	yes	characteristic
296	C₂×C₃×C₅	#551	1	1	yes	characteristic
297	C₂×C₃×C₅	#552	1	2	yes	—
298	C₂×C₃×C₅	#555	1	1	yes	characteristic
299	C₂³×C₃	—	2	2	no	—
300	C₂³×C₃	—	2	2	no	—
301	C₂³×C₃	—	2	2	no	—
302	C₂³×C₃	—	2	2	no	—
303	C₂³×C₃	—	2	2	no	—
304	C₂³×C₃	—	2	2	no	—
305	C₂³×C₃	C₅×#41	1	4	yes	—
306	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
307	C₃×D₄	—	4	4	no	—
308	C₂×C₃×C₄	—	2	16	no	—
309	C₂×C₃×C₄	—	2	2	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	1	no	—
314	C₂×C₃×C₄	—	2	1	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	2	no	—
322	C₂×C₃×C₄	—	2	2	no	—
323	C₂×C₃×C₄	—	2	2	no	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	2	1	no	—
326	C₂×C₃×C₄	—	2	1	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
329	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
330	C₂×C₃×C₄	C₅×#41	1	4	yes	—
331	C₂²×C₅	—	2	4	no	—
332	C₂²×C₅	—	2	4	no	—
333	C₂²×C₅	—	2	4	no	—
334	C₂²×C₅	—	4	2	no	—
335	C₂²×C₅	—	4	2	no	—
336	C₂²×C₅	—	4	2	no	—
337	C₂²×C₅	—	4	2	no	—
338	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
339	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
340	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
341	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
342	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
343	C₄×C₅	—	2	4	no	—
344	C₄×C₅	—	2	4	no	—
345	C₄×C₅	—	2	2	no	—
346	C₄×C₅	—	4	2	no	—
347	C₄×C₅	—	4	2	no	—
348	C₄×C₅	—	4	1	no	—
349	C₄×C₅	—	4	1	no	—
350	C₄×C₅	—	4	2	no	—
351	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	4	1	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
358	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
359	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
360	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
361	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
362	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
363	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
364	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	4	2	no	—
376	C₄²	—	2	4	no	—
377	C₄²	C₃×C₅×D₄	1	4	yes	complemented
378	C₃×C₅	#2609	1	1	yes	characteristic, direct product factor, Hall
379	C₂²×C₃	—	2	4	no	—
380	C₂²×C₃	—	2	4	no	—
381	C₂²×C₃	—	2	4	no	—
382	C₂²×C₃	—	4	2	no	—
383	C₂²×C₃	—	4	2	no	—
384	C₂²×C₃	—	4	2	no	—
385	C₂²×C₃	—	4	2	no	—
386	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
387	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
388	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
389	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
390	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
391	C₃×C₄	—	2	4	no	—
392	C₃×C₄	—	2	4	no	—
393	C₃×C₄	—	2	2	no	—
394	C₃×C₄	—	4	2	no	—
395	C₃×C₄	—	4	2	no	—
396	C₃×C₄	—	4	1	no	—
397	C₃×C₄	—	4	1	no	—
398	C₃×C₄	—	4	2	no	—
399	C₂×C₅	—	4	4	no	—
400	C₂×C₅	C₃×#525	1	2	yes	—
401	C₂×C₅	C₃×#537	1	1	yes	characteristic
402	C₂×C₅	C₃×#551	1	1	yes	characteristic
403	C₂×C₅	C₃×#552	1	2	yes	—
404	C₂×C₅	C₃×#555	1	1	yes	characteristic
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	C₃×C₅×#41	1	4	yes	—
412	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
413	D₄	—	4	4	no	—
414	C₂×C₄	—	2	16	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
435	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
436	C₂×C₄	C₃×C₅×#41	1	4	yes	—
437	C₂×C₃	—	4	4	no	—
438	C₂×C₃	C₅×#525	1	2	yes	—
439	C₂×C₃	C₅×#537	1	1	yes	characteristic
440	C₂×C₃	C₅×#551	1	1	yes	characteristic
441	C₂×C₃	C₅×#552	1	2	yes	—
442	C₂×C₃	C₅×#555	1	1	yes	characteristic
443	C₅	C₃×#2609	1	1	yes	characteristic, direct product factor, Sylow
444	C₂²	—	2	4	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
452	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
453	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
454	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
455	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
456	C₄	—	2	4	no	—
457	C₄	—	2	4	no	—
458	C₄	—	2	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	1	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	2	no	—
464	C₃	C₅×#2609	1	1	yes	characteristic, direct product factor, Sylow
465	C₂	—	4	4	no	—
466	C₂	C₃×C₅×#525	1	2	yes	—
467	C₂	C₃×C₅×#537	1	1	yes	characteristic
468	C₂	C₃×C₅×#551	1	1	yes	characteristic
469	C₂	C₃×C₅×#552	1	2	yes	—
470	C₂	C₃×C₅×#555	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
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×#117	C₂	semidirect
2. C₃×C₅×#398	C₂	semidirect
3. C₃×C₅×#396	C₂	semidirect
5. C₃×C₅×#388	C₂	semidirect
6. C₃×C₅×#387	C₂	semidirect
8. C₃×C₅×#385	C₂	semidirect
9. C₃×C₅×#382	C₂	semidirect
10. C₅×#2609	C₃	direct (N × H)
33. C₃×#2609	C₅	direct (N × H)
34. C₂×C₅×#117	C₂×C₃	semidirect
35. C₅×#398	C₂×C₃	semidirect
36. C₅×#396	C₂×C₃	semidirect
38. C₅×#388	C₂×C₃	semidirect
39. C₅×#387	C₂×C₃	semidirect
41. C₅×#385	C₂×C₃	semidirect
42. C₅×#382	C₂×C₃	semidirect
69. C₃×C₄²×C₅	D₄	semidirect
70. C₂×C₃×#117	C₂×C₅	semidirect
71. C₃×#398	C₂×C₅	semidirect
72. C₃×#396	C₂×C₅	semidirect
74. C₃×#388	C₂×C₅	semidirect
75. C₃×#387	C₂×C₅	semidirect
77. C₃×#385	C₂×C₅	semidirect
78. C₃×#382	C₂×C₅	semidirect
101. #2609	C₃×C₅	direct (N × H)
182. C₄²×C₅	C₃×D₄	semidirect
183. C₂×#117	C₂×C₃×C₅	semidirect
184. #398	C₂×C₃×C₅	semidirect
185. #396	C₂×C₃×C₅	semidirect
187. #388	C₂×C₃×C₅	semidirect
188. #387	C₂×C₃×C₅	semidirect
190. #385	C₂×C₃×C₅	semidirect
191. #382	C₂×C₃×C₅	semidirect
238. C₃×C₄²	C₅×D₄	semidirect
377. C₄²	C₃×C₅×D₄	semidirect
378. C₃×C₅	#2609	direct (N × H)
443. C₅	C₃×#2609	direct (N × H)
464. C₃	C₅×#2609	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×#117	2
C₃×C₅×#398	2
C₃×C₅×#396	2
C₃×C₅×#394	2
C₃×C₅×#388	2
C₃×C₅×#387	2
C₃×C₅×#386	2
C₃×C₅×#385	2
C₃×C₅×#382	2
C₅×#2609	3
C₃×#2609	5

Subgroups — C3×C5×#2609 #14275643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2609 #14275643