Subgroups — C₃×C₅×#2487 #14275521

Order 1920.

1168 conjugacy classes of subgroups.

The subgroup lattice has 476 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	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#400	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#399	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#389	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#386	C₂	1	2	yes	maximal
7	C₃×C₅×#385	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#380	C₂	1	2	yes	maximal, complemented
10	C₅×#2487	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	1	yes	characteristic
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
15	C₃×C₄×C₅×D₄	—	2	4	no	—
16	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
26	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
27	C₃×C₅×#95	C₂²	1	4	yes	—
28	C₃×C₅×#95	C₂²	1	2	yes	—
29	C₃×C₅×#95	C₂²	1	4	yes	—
30	C₃×#2487	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic
32	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
33	C₅×#400	C₂×C₃	1	2	yes	complemented
34	C₅×#399	C₂×C₃	1	2	yes	complemented
35	C₅×#389	C₂×C₃	1	2	yes	complemented
36	C₅×#386	C₂×C₃	1	2	yes	—
37	C₅×#385	C₂×C₃	1	2	yes	complemented
38	C₅×#380	C₂×C₃	1	1	yes	characteristic, complemented
39	C₅×#380	C₂×C₃	1	2	yes	complemented
40	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
41	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
42	C₂×C₃×C₅×D₄	—	2	2	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	Q₈	1	4	yes	—
45	C₂²×C₃×C₄×C₅	—	2	4	no	—
46	C₂²×C₃×C₄×C₅	—	2	4	no	—
47	C₂²×C₃×C₄×C₅	—	2	2	no	—
48	C₂²×C₃×C₄×C₅	—	2	4	no	—
49	C₂²×C₃×C₄×C₅	—	4	4	no	—
50	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₃×C₅×C₄⋊C₄	—	2	4	no	—
59	C₃×C₅×C₄⋊C₄	—	2	4	no	—
60	C₃×C₅×C₄⋊C₄	—	2	2	no	—
61	C₃×C₅×C₄⋊C₄	—	2	4	no	—
62	C₃×C₅×C₄⋊C₄	—	4	4	no	—
63	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
64	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
65	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
66	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
67	C₃×C₄²×C₅	—	2	2	no	—
68	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
69	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
70	C₃×#400	C₂×C₅	1	2	yes	complemented
71	C₃×#399	C₂×C₅	1	2	yes	complemented
72	C₃×#389	C₂×C₅	1	2	yes	complemented
73	C₃×#386	C₂×C₅	1	2	yes	—
74	C₃×#385	C₂×C₅	1	2	yes	complemented
75	C₃×#380	C₂×C₅	1	2	yes	complemented
76	C₃×#380	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
78	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
79	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
80	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
81	C₄×C₅×D₄	—	2	4	no	—
82	C₂×C₅×C₄⋊C₄	—	2	4	no	—
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	2	yes	—
86	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
88	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
89	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
92	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
93	C₅×#95	C₂²×C₃	1	4	yes	—
94	C₅×#95	C₂²×C₃	1	2	yes	—
95	C₅×#95	C₂²×C₃	1	4	yes	—
96	#2487	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
97	C₂³×C₃×C₅	—	2	2	no	—
98	C₂³×C₃×C₅	—	2	2	no	—
99	C₂³×C₃×C₅	—	2	1	no	—
100	C₂³×C₃×C₅	—	2	2	no	—
101	C₂³×C₃×C₅	—	2	1	no	—
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
104	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
105	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
106	C₂³×C₃×C₅	#41	1	2	yes	—
107	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
108	C₃×C₅×D₄	—	2	8	no	—
109	C₂×C₃×C₄×C₅	—	2	1	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	1	no	—
112	C₂×C₃×C₄×C₅	—	2	8	no	—
113	C₂×C₃×C₄×C₅	—	2	1	no	—
114	C₂×C₃×C₄×C₅	—	2	1	no	—
115	C₂×C₃×C₄×C₅	—	2	4	no	—
116	C₂×C₃×C₄×C₅	—	2	4	no	—
117	C₂×C₃×C₄×C₅	—	2	4	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	4	no	—
120	C₂×C₃×C₄×C₅	—	2	4	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	4	no	—
123	C₂×C₃×C₄×C₅	—	4	8	no	—
124	C₂×C₃×C₄×C₅	—	4	4	no	—
125	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
126	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
127	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
128	C₂×C₃×C₄×C₅	#41	1	4	yes	—
129	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
130	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
131	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
132	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
133	C₃×C₄×D₄	—	2	4	no	—
134	C₂×C₃×C₄⋊C₄	—	2	4	no	—
135	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
136	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
137	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
138	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
139	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
140	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
141	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
142	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
143	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
144	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
145	C₃×#95	C₂²×C₅	1	4	yes	—
146	C₃×#95	C₂²×C₅	1	2	yes	—
147	C₃×#95	C₂²×C₅	1	4	yes	—
148	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
149	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
150	C₂×C₅×D₄	—	2	2	no	—
151	C₂×C₅×D₄	—	2	2	no	—
152	C₂×C₅×D₄	C₃×Q₈	1	4	yes	—
153	C₂²×C₄×C₅	—	2	4	no	—
154	C₂²×C₄×C₅	—	2	4	no	—
155	C₂²×C₄×C₅	—	2	2	no	—
156	C₂²×C₄×C₅	—	2	4	no	—
157	C₂²×C₄×C₅	—	4	4	no	—
158	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
159	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
161	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
162	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
166	C₅×C₄⋊C₄	—	2	4	no	—
167	C₅×C₄⋊C₄	—	2	4	no	—
168	C₅×C₄⋊C₄	—	2	2	no	—
169	C₅×C₄⋊C₄	—	2	4	no	—
170	C₅×C₄⋊C₄	—	4	4	no	—
171	C₅×C₂²⋊C₄	—	2	2	no	—
172	C₅×C₂²⋊C₄	—	2	4	no	—
173	C₅×C₂²⋊C₄	—	2	2	no	—
174	C₅×C₂²⋊C₄	—	4	4	no	—
175	C₄²×C₅	—	2	2	no	—
176	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic
177	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
178	#400	C₂×C₃×C₅	1	2	yes	complemented
179	#399	C₂×C₃×C₅	1	2	yes	complemented
180	#389	C₂×C₃×C₅	1	2	yes	complemented
181	#386	C₂×C₃×C₅	1	2	yes	—
182	#385	C₂×C₃×C₅	1	2	yes	complemented
183	#380	C₂×C₃×C₅	1	2	yes	complemented
184	#380	C₂×C₃×C₅	1	1	yes	characteristic, complemented
185	C₂²×C₃×C₅	—	2	2	no	—
186	C₂²×C₃×C₅	—	2	2	no	—
187	C₂²×C₃×C₅	—	2	4	no	—
188	C₂²×C₃×C₅	—	2	4	no	—
189	C₂²×C₃×C₅	—	2	2	no	—
190	C₂²×C₃×C₅	—	2	4	no	—
191	C₂²×C₃×C₅	—	4	1	no	—
192	C₂²×C₃×C₅	—	4	1	no	—
193	C₂²×C₃×C₅	—	4	2	no	—
194	C₂²×C₃×C₅	C₂²⋊Q₈	1	4	yes	—
195	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
196	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
197	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
198	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
199	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
200	C₃×C₄×C₅	—	2	2	no	—
201	C₃×C₄×C₅	—	2	2	no	—
202	C₃×C₄×C₅	—	4	1	no	—
203	C₃×C₄×C₅	—	4	1	no	—
204	C₃×C₄×C₅	—	4	4	no	—
205	C₃×C₄×C₅	—	4	4	no	—
206	C₃×C₄×C₅	#123	1	4	yes	—
207	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
208	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
209	C₂×C₃×D₄	—	2	2	no	—
210	C₂×C₃×D₄	—	2	2	no	—
211	C₂×C₃×D₄	C₅×Q₈	1	4	yes	—
212	C₂²×C₃×C₄	—	2	4	no	—
213	C₂²×C₃×C₄	—	2	4	no	—
214	C₂²×C₃×C₄	—	2	2	no	—
215	C₂²×C₃×C₄	—	2	4	no	—
216	C₂²×C₃×C₄	—	4	4	no	—
217	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
218	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
220	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
221	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
225	C₃×C₄⋊C₄	—	2	4	no	—
226	C₃×C₄⋊C₄	—	2	4	no	—
227	C₃×C₄⋊C₄	—	2	2	no	—
228	C₃×C₄⋊C₄	—	2	4	no	—
229	C₃×C₄⋊C₄	—	4	4	no	—
230	C₃×C₂²⋊C₄	—	2	2	no	—
231	C₃×C₂²⋊C₄	—	2	4	no	—
232	C₃×C₂²⋊C₄	—	2	2	no	—
233	C₃×C₂²⋊C₄	—	4	4	no	—
234	C₃×C₄²	—	2	2	no	—
235	C₂³×C₅	—	2	2	no	—
236	C₂³×C₅	—	2	2	no	—
237	C₂³×C₅	—	2	1	no	—
238	C₂³×C₅	—	2	2	no	—
239	C₂³×C₅	—	2	1	no	—
240	C₂³×C₅	—	2	2	no	—
241	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
242	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
243	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
244	C₂³×C₅	C₃×#41	1	2	yes	—
245	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
246	C₅×D₄	—	2	8	no	—
247	C₂×C₄×C₅	—	2	1	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	1	no	—
250	C₂×C₄×C₅	—	2	8	no	—
251	C₂×C₄×C₅	—	2	1	no	—
252	C₂×C₄×C₅	—	2	1	no	—
253	C₂×C₄×C₅	—	2	4	no	—
254	C₂×C₄×C₅	—	2	4	no	—
255	C₂×C₄×C₅	—	2	4	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	4	no	—
258	C₂×C₄×C₅	—	2	4	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	4	no	—
261	C₂×C₄×C₅	—	4	8	no	—
262	C₂×C₄×C₅	—	4	4	no	—
263	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
264	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
265	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
266	C₂×C₄×C₅	C₃×#41	1	4	yes	—
267	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
268	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
269	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
270	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
271	C₄×D₄	—	2	4	no	—
272	C₂×C₄⋊C₄	—	2	4	no	—
273	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
274	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
275	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
277	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
278	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
279	C₂×C₂²⋊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	4	yes	—
282	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
283	#95	C₂²×C₃×C₅	1	4	yes	—
284	#95	C₂²×C₃×C₅	1	2	yes	—
285	#95	C₂²×C₃×C₅	1	4	yes	—
286	C₂×C₃×C₅	—	2	4	no	—
287	C₂×C₃×C₅	—	4	2	no	—
288	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
289	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
290	C₂×C₃×C₅	#535	1	1	yes	characteristic
291	C₂×C₃×C₅	#553	1	2	yes	—
292	C₂×C₃×C₅	#554	1	2	yes	—
293	C₂³×C₃	—	2	2	no	—
294	C₂³×C₃	—	2	2	no	—
295	C₂³×C₃	—	2	1	no	—
296	C₂³×C₃	—	2	2	no	—
297	C₂³×C₃	—	2	1	no	—
298	C₂³×C₃	—	2	2	no	—
299	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
300	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
301	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
302	C₂³×C₃	C₅×#41	1	2	yes	—
303	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
304	C₃×D₄	—	2	8	no	—
305	C₂×C₃×C₄	—	2	1	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	2	1	no	—
308	C₂×C₃×C₄	—	2	8	no	—
309	C₂×C₃×C₄	—	2	1	no	—
310	C₂×C₃×C₄	—	2	1	no	—
311	C₂×C₃×C₄	—	2	4	no	—
312	C₂×C₃×C₄	—	2	4	no	—
313	C₂×C₃×C₄	—	2	4	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	4	no	—
316	C₂×C₃×C₄	—	2	4	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	4	no	—
319	C₂×C₃×C₄	—	4	8	no	—
320	C₂×C₃×C₄	—	4	4	no	—
321	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
322	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
323	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
324	C₂×C₃×C₄	C₅×#41	1	4	yes	—
325	C₂²×C₅	—	2	2	no	—
326	C₂²×C₅	—	2	2	no	—
327	C₂²×C₅	—	2	4	no	—
328	C₂²×C₅	—	2	4	no	—
329	C₂²×C₅	—	2	2	no	—
330	C₂²×C₅	—	2	4	no	—
331	C₂²×C₅	—	4	1	no	—
332	C₂²×C₅	—	4	1	no	—
333	C₂²×C₅	—	4	2	no	—
334	C₂²×C₅	C₃×C₂²⋊Q₈	1	4	yes	—
335	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
336	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
337	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
338	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
339	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
340	C₄×C₅	—	2	2	no	—
341	C₄×C₅	—	2	2	no	—
342	C₄×C₅	—	4	1	no	—
343	C₄×C₅	—	4	1	no	—
344	C₄×C₅	—	4	4	no	—
345	C₄×C₅	—	4	4	no	—
346	C₄×C₅	C₃×#123	1	4	yes	—
347	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
348	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	C₃×C₅×Q₈	1	4	yes	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	4	4	no	—
357	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
358	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
359	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
360	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
361	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
362	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
363	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
364	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	4	4	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₄²	—	2	2	no	—
375	C₃×C₅	#2487	1	1	yes	characteristic, direct product factor, Hall
376	C₂²×C₃	—	2	2	no	—
377	C₂²×C₃	—	2	2	no	—
378	C₂²×C₃	—	2	4	no	—
379	C₂²×C₃	—	2	4	no	—
380	C₂²×C₃	—	2	2	no	—
381	C₂²×C₃	—	2	4	no	—
382	C₂²×C₃	—	4	1	no	—
383	C₂²×C₃	—	4	1	no	—
384	C₂²×C₃	—	4	2	no	—
385	C₂²×C₃	C₅×C₂²⋊Q₈	1	4	yes	—
386	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
387	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
388	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
389	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
390	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
391	C₃×C₄	—	2	2	no	—
392	C₃×C₄	—	2	2	no	—
393	C₃×C₄	—	4	1	no	—
394	C₃×C₄	—	4	1	no	—
395	C₃×C₄	—	4	4	no	—
396	C₃×C₄	—	4	4	no	—
397	C₃×C₄	C₅×#123	1	4	yes	—
398	C₂×C₅	—	2	4	no	—
399	C₂×C₅	—	4	2	no	—
400	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
401	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
402	C₂×C₅	C₃×#535	1	1	yes	characteristic
403	C₂×C₅	C₃×#553	1	2	yes	—
404	C₂×C₅	C₃×#554	1	2	yes	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	2	no	—
411	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
412	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
413	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
414	C₂³	C₃×C₅×#41	1	2	yes	—
415	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
416	D₄	—	2	8	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	8	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	4	8	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
434	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
435	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
436	C₂×C₄	C₃×C₅×#41	1	4	yes	—
437	C₂×C₃	—	2	4	no	—
438	C₂×C₃	—	4	2	no	—
439	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
440	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
441	C₂×C₃	C₅×#535	1	1	yes	characteristic
442	C₂×C₃	C₅×#553	1	2	yes	—
443	C₂×C₃	C₅×#554	1	2	yes	—
444	C₅	C₃×#2487	1	1	yes	characteristic, direct product factor, Sylow
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	4	2	no	—
454	C₂²	C₃×C₅×C₂²⋊Q₈	1	4	yes	—
455	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
456	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
457	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
458	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
459	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	4	no	—
464	C₄	—	4	1	no	—
465	C₄	—	4	4	no	—
466	C₄	C₃×C₅×#123	1	4	yes	—
467	C₃	C₅×#2487	1	1	yes	characteristic, direct product factor, Sylow
468	C₂	—	2	4	no	—
469	C₂	—	4	2	no	—
470	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
471	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
472	C₂	C₃×C₅×#535	1	1	yes	characteristic
473	C₂	C₃×C₅×#553	1	2	yes	—
474	C₂	C₃×C₅×#554	1	2	yes	—

	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
2. C₂²×C₃×C₅×C₄⋊C₄	C₂	semidirect
3. C₃×C₅×#400	C₂	semidirect
4. C₃×C₅×#399	C₂	semidirect
5. C₃×C₅×#389	C₂	semidirect
7. C₃×C₅×#385	C₂	semidirect
8. C₃×C₅×#380	C₂	semidirect
9. C₃×C₅×#380	C₂	semidirect
10. C₅×#2487	C₃	direct (N × H)
30. C₃×#2487	C₅	direct (N × H)
32. C₂²×C₅×C₄⋊C₄	C₂×C₃	semidirect
33. C₅×#400	C₂×C₃	semidirect
34. C₅×#399	C₂×C₃	semidirect
35. C₅×#389	C₂×C₃	semidirect
37. C₅×#385	C₂×C₃	semidirect
38. C₅×#380	C₂×C₃	semidirect
39. C₅×#380	C₂×C₃	semidirect
69. C₂²×C₃×C₄⋊C₄	C₂×C₅	semidirect
70. C₃×#400	C₂×C₅	semidirect
71. C₃×#399	C₂×C₅	semidirect
72. C₃×#389	C₂×C₅	semidirect
74. C₃×#385	C₂×C₅	semidirect
75. C₃×#380	C₂×C₅	semidirect
76. C₃×#380	C₂×C₅	semidirect
96. #2487	C₃×C₅	direct (N × H)
177. C₂²×C₄⋊C₄	C₂×C₃×C₅	semidirect
178. #400	C₂×C₃×C₅	semidirect
179. #399	C₂×C₃×C₅	semidirect
180. #389	C₂×C₃×C₅	semidirect
182. #385	C₂×C₃×C₅	semidirect
183. #380	C₂×C₃×C₅	semidirect
184. #380	C₂×C₃×C₅	semidirect
375. C₃×C₅	#2487	direct (N × H)
444. C₅	C₃×#2487	direct (N × H)
467. C₃	C₅×#2487	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
C₂²×C₃×C₅×C₄⋊C₄	2
C₃×C₅×#400	2
C₃×C₅×#399	2
C₃×C₅×#389	2
C₃×C₅×#386	2
C₃×C₅×#385	2
C₃×C₅×#380	2
C₅×#2487	3
C₃×#2487	5

Subgroups — C3×C5×#2487 #14275521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2487 #14275521