Subgroups — C₃×C₅×#2354 #14275388

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#117	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#390	C₂	1	2	yes	maximal
4	C₃×C₅×#388	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#380	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×C₅×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2354	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
12	C₃×C₄×C₅×D₄	C₄	1	8	yes	complemented
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	1	yes	characteristic
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	1	yes	characteristic
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	4	yes	—
24	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₃×C₅×#95	C₂²	1	4	yes	—
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₃×#2354	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic
30	C₂×C₅×#117	C₂×C₃	1	2	yes	complemented
31	C₅×#390	C₂×C₃	1	2	yes	—
32	C₅×#388	C₂×C₃	1	4	yes	complemented
33	C₅×#384	C₂×C₃	1	1	yes	characteristic, complemented
34	C₅×#380	C₂×C₃	1	2	yes	complemented
35	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
36	C₄×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
37	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
38	C₂×C₃×C₅×D₄	—	2	2	no	—
39	C₂×C₃×C₅×D₄	—	2	2	no	—
40	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
41	C₂²×C₃×C₄×C₅	—	2	4	no	—
42	C₂²×C₃×C₄×C₅	—	2	4	no	—
43	C₂²×C₃×C₄×C₅	C₂×C₄	1	8	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	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	1	yes	characteristic
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	4	no	—
52	C₃×C₅×C₄⋊C₄	—	2	4	no	—
53	C₃×C₅×C₄⋊C₄	—	2	2	no	—
54	C₃×C₅×C₄⋊C₄	—	4	2	no	—
55	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
56	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	complemented
57	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
58	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
59	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
60	C₃×C₄²×C₅	—	2	8	no	—
61	C₃×C₄²×C₅	—	2	4	no	—
62	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
63	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
64	C₂×C₃×#117	C₂×C₅	1	2	yes	complemented
65	C₃×#390	C₂×C₅	1	2	yes	—
66	C₃×#388	C₂×C₅	1	4	yes	complemented
67	C₃×#384	C₂×C₅	1	1	yes	characteristic, complemented
68	C₃×#380	C₂×C₅	1	2	yes	complemented
69	C₃×C₄×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
70	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
72	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
73	C₄×C₅×D₄	C₃×C₄	1	8	yes	complemented
74	C₅×#117	—	2	8	no	—
75	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
77	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
78	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
82	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
83	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
84	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
85	C₂×C₄²×C₅	C₂²×C₃	1	4	yes	—
86	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
87	C₅×#95	C₂²×C₃	1	4	yes	—
88	C₅×#95	C₂²×C₃	1	2	yes	—
89	#2354	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
90	C₂³×C₃×C₅	—	2	2	no	—
91	C₂³×C₃×C₅	—	2	2	no	—
92	C₂³×C₃×C₅	—	2	2	no	—
93	C₂³×C₃×C₅	—	2	2	no	—
94	C₂³×C₃×C₅	—	2	2	no	—
95	C₂³×C₃×C₅	—	2	2	no	—
96	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
97	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
98	C₃×C₅×D₄	—	2	8	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	1	no	—
103	C₂×C₃×C₄×C₅	—	2	1	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	16	no	—
106	C₂×C₃×C₄×C₅	—	2	4	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	4	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	4	no	—
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
114	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
117	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	#41	1	2	yes	—
119	C₂×C₃×C₄×C₅	#41	1	2	yes	—
120	C₂×C₃×C₄×C₅	#41	1	2	yes	—
121	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
122	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
123	C₃×C₄×D₄	C₄×C₅	1	8	yes	complemented
124	C₃×#117	—	2	8	no	—
125	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
126	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
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×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
132	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
133	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
134	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
135	C₂×C₃×C₄²	C₂²×C₅	1	4	yes	—
136	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
137	C₃×#95	C₂²×C₅	1	4	yes	—
138	C₃×#95	C₂²×C₅	1	2	yes	—
139	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
140	C₂×C₅×D₄	—	2	2	no	—
141	C₂×C₅×D₄	—	2	2	no	—
142	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
143	C₂²×C₄×C₅	—	2	4	no	—
144	C₂²×C₄×C₅	—	2	4	no	—
145	C₂²×C₄×C₅	C₂×C₃×C₄	1	8	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	2	yes	—
149	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
151	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
153	C₅×C₄⋊C₄	—	2	4	no	—
154	C₅×C₄⋊C₄	—	2	4	no	—
155	C₅×C₄⋊C₄	—	2	2	no	—
156	C₅×C₄⋊C₄	—	4	2	no	—
157	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
158	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	complemented
159	C₅×C₂²⋊C₄	—	2	8	no	—
160	C₅×C₂²⋊C₄	—	4	4	no	—
161	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
162	C₄²×C₅	—	2	8	no	—
163	C₄²×C₅	—	2	4	no	—
164	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
165	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic
166	C₂×#117	C₂×C₃×C₅	1	2	yes	complemented
167	#390	C₂×C₃×C₅	1	2	yes	—
168	#388	C₂×C₃×C₅	1	4	yes	complemented
169	#384	C₂×C₃×C₅	1	1	yes	characteristic, complemented
170	#380	C₂×C₃×C₅	1	2	yes	complemented
171	C₄×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
172	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
173	C₂²×C₃×C₅	—	2	4	no	—
174	C₂²×C₃×C₅	—	2	4	no	—
175	C₂²×C₃×C₅	—	2	4	no	—
176	C₂²×C₃×C₅	—	4	2	no	—
177	C₂²×C₃×C₅	—	4	2	no	—
178	C₂²×C₃×C₅	—	4	2	no	—
179	C₂²×C₃×C₅	—	4	2	no	—
180	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
181	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
182	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
183	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
184	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
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	2	no	—
189	C₃×C₄×C₅	—	2	4	no	—
190	C₃×C₄×C₅	—	4	4	no	—
191	C₃×C₄×C₅	—	4	2	no	—
192	C₃×C₄×C₅	#117	1	4	yes	complemented
193	C₃×C₄×C₅	C₄×D₄	1	4	yes	—
194	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
195	C₂×C₃×D₄	—	2	2	no	—
196	C₂×C₃×D₄	—	2	2	no	—
197	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
198	C₂²×C₃×C₄	—	2	4	no	—
199	C₂²×C₃×C₄	—	2	4	no	—
200	C₂²×C₃×C₄	C₂×C₄×C₅	1	8	yes	—
201	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
202	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
203	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
204	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
205	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
206	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
208	C₃×C₄⋊C₄	—	2	4	no	—
209	C₃×C₄⋊C₄	—	2	4	no	—
210	C₃×C₄⋊C₄	—	2	2	no	—
211	C₃×C₄⋊C₄	—	4	2	no	—
212	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
213	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	complemented
214	C₃×C₂²⋊C₄	—	2	8	no	—
215	C₃×C₂²⋊C₄	—	4	4	no	—
216	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	—
217	C₃×C₄²	—	2	8	no	—
218	C₃×C₄²	—	2	4	no	—
219	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
220	C₂³×C₅	—	2	2	no	—
221	C₂³×C₅	—	2	2	no	—
222	C₂³×C₅	—	2	2	no	—
223	C₂³×C₅	—	2	2	no	—
224	C₂³×C₅	—	2	2	no	—
225	C₂³×C₅	—	2	2	no	—
226	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
227	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
228	C₅×D₄	—	2	8	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	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	16	no	—
236	C₂×C₄×C₅	—	2	4	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	4	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	4	no	—
242	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
243	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
244	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
245	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
246	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
247	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
248	C₂×C₄×C₅	C₃×#41	1	2	yes	—
249	C₂×C₄×C₅	C₃×#41	1	2	yes	—
250	C₂×C₄×C₅	C₃×#41	1	2	yes	—
251	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
252	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
253	C₄×D₄	C₃×C₄×C₅	1	8	yes	complemented
254	#117	—	2	8	no	—
255	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
256	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
258	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
259	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
261	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
262	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
263	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
264	C₂×C₄²	C₂²×C₃×C₅	1	4	yes	—
265	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
266	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
267	#95	C₂²×C₃×C₅	1	4	yes	—
268	#95	C₂²×C₃×C₅	1	2	yes	—
269	C₂×C₃×C₅	—	4	4	no	—
270	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
271	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
272	C₂×C₃×C₅	#520	1	1	yes	characteristic
273	C₂×C₃×C₅	#547	1	1	yes	characteristic
274	C₂×C₃×C₅	#550	1	1	yes	characteristic
275	C₂×C₃×C₅	#555	1	1	yes	characteristic
276	C₂×C₃×C₅	#556	1	1	yes	characteristic
277	C₂³×C₃	—	2	2	no	—
278	C₂³×C₃	—	2	2	no	—
279	C₂³×C₃	—	2	2	no	—
280	C₂³×C₃	—	2	2	no	—
281	C₂³×C₃	—	2	2	no	—
282	C₂³×C₃	—	2	2	no	—
283	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
284	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
285	C₃×D₄	—	2	8	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	1	no	—
290	C₂×C₃×C₄	—	2	1	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	16	no	—
293	C₂×C₃×C₄	—	2	4	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	4	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	4	no	—
299	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
300	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
301	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
302	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
303	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
304	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
305	C₂×C₃×C₄	C₅×#41	1	2	yes	—
306	C₂×C₃×C₄	C₅×#41	1	2	yes	—
307	C₂×C₃×C₄	C₅×#41	1	2	yes	—
308	C₂²×C₅	—	2	4	no	—
309	C₂²×C₅	—	2	4	no	—
310	C₂²×C₅	—	2	4	no	—
311	C₂²×C₅	—	4	2	no	—
312	C₂²×C₅	—	4	2	no	—
313	C₂²×C₅	—	4	2	no	—
314	C₂²×C₅	—	4	2	no	—
315	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
316	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
317	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
318	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
319	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
320	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
321	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
322	C₄×C₅	—	2	4	no	—
323	C₄×C₅	—	2	2	no	—
324	C₄×C₅	—	2	4	no	—
325	C₄×C₅	—	4	4	no	—
326	C₄×C₅	—	4	2	no	—
327	C₄×C₅	C₃×#117	1	4	yes	complemented
328	C₄×C₅	C₃×C₄×D₄	1	4	yes	—
329	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	C₂×C₃×C₄×C₅	1	4	yes	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	C₂×C₃×C₄×C₅	1	8	yes	—
336	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
337	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
338	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
339	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
340	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
341	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
342	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
348	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
349	C₂²⋊C₄	—	2	8	no	—
350	C₂²⋊C₄	—	4	4	no	—
351	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
352	C₄²	—	2	8	no	—
353	C₄²	—	2	4	no	—
354	C₄²	C₂×C₃×C₄×C₅	1	4	yes	—
355	C₃×C₅	#2354	1	1	yes	characteristic, direct product factor, Hall
356	C₂²×C₃	—	2	4	no	—
357	C₂²×C₃	—	2	4	no	—
358	C₂²×C₃	—	2	4	no	—
359	C₂²×C₃	—	4	2	no	—
360	C₂²×C₃	—	4	2	no	—
361	C₂²×C₃	—	4	2	no	—
362	C₂²×C₃	—	4	2	no	—
363	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
364	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
365	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
366	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
367	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
368	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
369	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
370	C₃×C₄	—	2	4	no	—
371	C₃×C₄	—	2	2	no	—
372	C₃×C₄	—	2	4	no	—
373	C₃×C₄	—	4	4	no	—
374	C₃×C₄	—	4	2	no	—
375	C₃×C₄	C₅×#117	1	4	yes	complemented
376	C₃×C₄	C₄×C₅×D₄	1	4	yes	—
377	C₂×C₅	—	4	4	no	—
378	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
379	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
380	C₂×C₅	C₃×#520	1	1	yes	characteristic
381	C₂×C₅	C₃×#547	1	1	yes	characteristic
382	C₂×C₅	C₃×#550	1	1	yes	characteristic
383	C₂×C₅	C₃×#555	1	1	yes	characteristic
384	C₂×C₅	C₃×#556	1	1	yes	characteristic
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	C₂²×C₃×C₄×C₅	1	4	yes	—
392	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
393	D₄	—	2	8	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	16	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
408	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
409	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
410	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
411	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
412	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
413	C₂×C₄	C₃×C₅×#41	1	2	yes	—
414	C₂×C₄	C₃×C₅×#41	1	2	yes	—
415	C₂×C₄	C₃×C₅×#41	1	2	yes	—
416	C₂×C₃	—	4	4	no	—
417	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
418	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
419	C₂×C₃	C₅×#520	1	1	yes	characteristic
420	C₂×C₃	C₅×#547	1	1	yes	characteristic
421	C₂×C₃	C₅×#550	1	1	yes	characteristic
422	C₂×C₃	C₅×#555	1	1	yes	characteristic
423	C₂×C₃	C₅×#556	1	1	yes	characteristic
424	C₅	C₃×#2354	1	1	yes	characteristic, direct product factor, Sylow
425	C₂²	—	2	4	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
433	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
434	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
435	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
436	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
437	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
439	C₄	—	2	4	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	4	no	—
442	C₄	—	4	4	no	—
443	C₄	—	4	2	no	—
444	C₄	C₃×C₅×#117	1	4	yes	complemented
445	C₄	C₃×C₄×C₅×D₄	1	4	yes	—
446	C₃	C₅×#2354	1	1	yes	characteristic, direct product factor, Sylow
447	C₂	—	4	4	no	—
448	C₂	C₂×C₃×C₅×#117	1	1	yes	characteristic
449	C₂	C₂×C₃×C₄×C₅×D₄	1	1	yes	characteristic
450	C₂	C₃×C₅×#520	1	1	yes	characteristic
451	C₂	C₃×C₅×#547	1	1	yes	characteristic
452	C₂	C₃×C₅×#550	1	1	yes	characteristic
453	C₂	C₃×C₅×#555	1	1	yes	characteristic
454	C₂	C₃×C₅×#556	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
LCS	G ▷ C₂² ▷ 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
4. C₃×C₅×#388	C₂	semidirect
5. C₃×C₅×#384	C₂	semidirect
6. C₃×C₅×#380	C₂	semidirect
7. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
8. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
9. C₅×#2354	C₃	direct (N × H)
12. C₃×C₄×C₅×D₄	C₄	semidirect
28. C₃×#2354	C₅	direct (N × H)
30. C₂×C₅×#117	C₂×C₃	semidirect
32. C₅×#388	C₂×C₃	semidirect
33. C₅×#384	C₂×C₃	semidirect
34. C₅×#380	C₂×C₃	semidirect
35. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
36. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
56. C₃×C₅×C₄⋊C₄	D₄	semidirect
64. C₂×C₃×#117	C₂×C₅	semidirect
66. C₃×#388	C₂×C₅	semidirect
67. C₃×#384	C₂×C₅	semidirect
68. C₃×#380	C₂×C₅	semidirect
69. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
70. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
73. C₄×C₅×D₄	C₃×C₄	semidirect
89. #2354	C₃×C₅	direct (N × H)
123. C₃×C₄×D₄	C₄×C₅	semidirect
158. C₅×C₄⋊C₄	C₃×D₄	semidirect
166. C₂×#117	C₂×C₃×C₅	semidirect
168. #388	C₂×C₃×C₅	semidirect
169. #384	C₂×C₃×C₅	semidirect
170. #380	C₂×C₃×C₅	semidirect
171. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
172. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
192. C₃×C₄×C₅	#117	semidirect
213. C₃×C₄⋊C₄	C₅×D₄	semidirect
253. C₄×D₄	C₃×C₄×C₅	semidirect
327. C₄×C₅	C₃×#117	semidirect
348. C₄⋊C₄	C₃×C₅×D₄	semidirect
355. C₃×C₅	#2354	direct (N × H)
375. C₃×C₄	C₅×#117	semidirect
424. C₅	C₃×#2354	direct (N × H)
444. C₄	C₃×C₅×#117	semidirect
446. C₃	C₅×#2354	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×C₄×C₅×D₄	2
C₂×C₃×C₅×#117	2
C₃×C₅×#390	2
C₃×C₅×#388	2
C₃×C₅×#384	2
C₃×C₅×#380	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2354	3
C₃×#2354	5

Subgroups — C3×C5×#2354 #14275388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2354 #14275388