Subgroups — C₃×C₅×#2482 #14275516

Order 1920.

1344 conjugacy classes of subgroups.

The subgroup lattice has 436 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	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#399	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#397	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#388	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#385	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#381	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#379	C₂	1	2	yes	maximal
9	C₅×#2482	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₃×C₅×#117	—	2	4	no	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
17	C₂×C₃×C₅×C₂²⋊C₄	—	2	4	no	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	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	4	yes	—
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
24	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
25	C₃×C₅×#95	C₂²	1	2	yes	complemented
26	C₃×C₅×#95	C₂²	1	2	yes	complemented
27	C₃×C₅×#95	C₂²	1	4	yes	complemented
28	C₃×#2482	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
31	C₅×#399	C₂×C₃	1	2	yes	complemented
32	C₅×#397	C₂×C₃	1	2	yes	complemented
33	C₅×#388	C₂×C₃	1	4	yes	complemented
34	C₅×#385	C₂×C₃	1	2	yes	complemented
35	C₅×#381	C₂×C₃	1	1	yes	characteristic, complemented
36	C₅×#379	C₂×C₃	1	2	yes	—
37	C₂⁴×C₃×C₅	—	2	2	no	—
38	C₂⁴×C₃×C₅	—	2	4	no	—
39	C₂⁴×C₃×C₅	—	2	4	no	—
40	C₂⁴×C₃×C₅	—	4	2	no	—
41	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
42	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	—	2	4	no	—
44	C₂²×C₃×C₄×C₅	—	2	2	no	—
45	C₂²×C₃×C₄×C₅	—	4	2	no	—
46	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
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	4	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	1	yes	characteristic
53	C₃×C₅×C₄⋊C₄	—	2	2	no	—
54	C₃×C₅×C₄⋊C₄	—	2	2	no	—
55	C₃×C₅×C₄⋊C₄	—	4	4	no	—
56	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
57	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
58	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
59	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
60	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
61	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
62	C₃×C₄²×C₅	—	2	4	no	—
63	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
64	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
65	C₃×#399	C₂×C₅	1	2	yes	complemented
66	C₃×#397	C₂×C₅	1	2	yes	complemented
67	C₃×#388	C₂×C₅	1	4	yes	complemented
68	C₃×#385	C₂×C₅	1	2	yes	complemented
69	C₃×#381	C₂×C₅	1	1	yes	characteristic, complemented
70	C₃×#379	C₂×C₅	1	2	yes	—
71	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
72	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
73	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
74	C₅×#117	—	2	4	no	—
75	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
76	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
77	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
78	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
79	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
80	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
81	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
82	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
83	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
84	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
85	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	complemented
86	C₅×#95	C₂²×C₃	1	2	yes	complemented
87	C₅×#95	C₂²×C₃	1	2	yes	complemented
88	C₅×#95	C₂²×C₃	1	4	yes	complemented
89	#2482	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	8	no	—
93	C₂³×C₃×C₅	—	2	2	no	—
94	C₂³×C₃×C₅	—	2	2	no	—
95	C₂³×C₃×C₅	—	2	4	no	—
96	C₂³×C₃×C₅	—	2	4	no	—
97	C₂³×C₃×C₅	—	4	16	no	—
98	C₂³×C₃×C₅	—	4	4	no	—
99	C₂³×C₃×C₅	—	4	4	no	—
100	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
101	C₂³×C₃×C₅	#41	1	4	yes	—
102	C₂³×C₃×C₅	#41	1	4	yes	—
103	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	—	2	8	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	4	no	—
111	C₂×C₃×C₄×C₅	—	2	4	no	—
112	C₂×C₃×C₄×C₅	—	2	4	no	—
113	C₂×C₃×C₄×C₅	—	2	4	no	—
114	C₂×C₃×C₄×C₅	—	2	4	no	—
115	C₂×C₃×C₄×C₅	—	2	4	no	—
116	C₂×C₃×C₄×C₅	—	4	4	no	—
117	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
119	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
120	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
121	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
122	C₃×#117	—	2	4	no	—
123	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
124	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
125	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
126	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
127	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
128	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
129	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
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	4	yes	—
133	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	complemented
134	C₃×#95	C₂²×C₅	1	2	yes	complemented
135	C₃×#95	C₂²×C₅	1	2	yes	complemented
136	C₃×#95	C₂²×C₅	1	4	yes	complemented
137	C₂⁴×C₅	—	2	2	no	—
138	C₂⁴×C₅	—	2	4	no	—
139	C₂⁴×C₅	—	2	4	no	—
140	C₂⁴×C₅	—	4	2	no	—
141	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
142	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
143	C₂²×C₄×C₅	—	2	4	no	—
144	C₂²×C₄×C₅	—	2	2	no	—
145	C₂²×C₄×C₅	—	4	2	no	—
146	C₂²×C₄×C₅	C₃×D₄	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	4	yes	—
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	2	no	—
154	C₅×C₄⋊C₄	—	2	2	no	—
155	C₅×C₄⋊C₄	—	4	4	no	—
156	C₅×C₂²⋊C₄	—	2	4	no	—
157	C₅×C₂²⋊C₄	—	2	8	no	—
158	C₅×C₂²⋊C₄	—	2	4	no	—
159	C₅×C₂²⋊C₄	—	2	4	no	—
160	C₅×C₂²⋊C₄	—	2	4	no	—
161	C₅×C₂²⋊C₄	—	4	4	no	—
162	C₄²×C₅	—	2	4	no	—
163	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic, complemented
164	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
165	#399	C₂×C₃×C₅	1	2	yes	complemented
166	#397	C₂×C₃×C₅	1	2	yes	complemented
167	#388	C₂×C₃×C₅	1	4	yes	complemented
168	#385	C₂×C₃×C₅	1	2	yes	complemented
169	#381	C₂×C₃×C₅	1	1	yes	characteristic, complemented
170	#379	C₂×C₃×C₅	1	2	yes	—
171	C₂²×C₃×C₅	—	2	2	no	—
172	C₂²×C₃×C₅	—	2	2	no	—
173	C₂²×C₃×C₅	—	2	8	no	—
174	C₂²×C₃×C₅	—	2	4	no	—
175	C₂²×C₃×C₅	—	2	8	no	—
176	C₂²×C₃×C₅	—	4	16	no	—
177	C₂²×C₃×C₅	—	4	2	no	—
178	C₂²×C₃×C₅	—	4	2	no	—
179	C₂²×C₃×C₅	—	4	4	no	—
180	C₂²×C₃×C₅	#123	1	4	yes	—
181	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
182	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
183	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
184	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
185	C₃×C₄×C₅	—	2	2	no	—
186	C₃×C₄×C₅	—	2	2	no	—
187	C₃×C₄×C₅	—	4	2	no	—
188	C₃×C₄×C₅	—	4	2	no	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	—	4	4	no	—
191	C₂⁴×C₃	—	2	2	no	—
192	C₂⁴×C₃	—	2	4	no	—
193	C₂⁴×C₃	—	2	4	no	—
194	C₂⁴×C₃	—	4	2	no	—
195	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
196	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
197	C₂²×C₃×C₄	—	2	4	no	—
198	C₂²×C₃×C₄	—	2	2	no	—
199	C₂²×C₃×C₄	—	4	2	no	—
200	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
201	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
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	1	yes	characteristic
207	C₃×C₄⋊C₄	—	2	2	no	—
208	C₃×C₄⋊C₄	—	2	2	no	—
209	C₃×C₄⋊C₄	—	4	4	no	—
210	C₃×C₂²⋊C₄	—	2	4	no	—
211	C₃×C₂²⋊C₄	—	2	8	no	—
212	C₃×C₂²⋊C₄	—	2	4	no	—
213	C₃×C₂²⋊C₄	—	2	4	no	—
214	C₃×C₂²⋊C₄	—	2	4	no	—
215	C₃×C₂²⋊C₄	—	4	4	no	—
216	C₃×C₄²	—	2	4	no	—
217	C₂³×C₅	—	2	2	no	—
218	C₂³×C₅	—	2	2	no	—
219	C₂³×C₅	—	2	8	no	—
220	C₂³×C₅	—	2	2	no	—
221	C₂³×C₅	—	2	2	no	—
222	C₂³×C₅	—	2	4	no	—
223	C₂³×C₅	—	2	4	no	—
224	C₂³×C₅	—	4	16	no	—
225	C₂³×C₅	—	4	4	no	—
226	C₂³×C₅	—	4	4	no	—
227	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
228	C₂³×C₅	C₃×#41	1	4	yes	—
229	C₂³×C₅	C₃×#41	1	4	yes	—
230	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
231	C₂×C₄×C₅	—	2	8	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	4	no	—
238	C₂×C₄×C₅	—	2	4	no	—
239	C₂×C₄×C₅	—	2	4	no	—
240	C₂×C₄×C₅	—	2	4	no	—
241	C₂×C₄×C₅	—	2	4	no	—
242	C₂×C₄×C₅	—	2	4	no	—
243	C₂×C₄×C₅	—	4	4	no	—
244	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
245	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
246	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
247	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
248	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
249	#117	—	2	4	no	—
250	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
251	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
252	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
253	C₂×C₂²⋊C₄	—	2	4	no	—
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	2	yes	—
258	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
259	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
260	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	complemented
261	#95	C₂²×C₃×C₅	1	2	yes	complemented
262	#95	C₂²×C₃×C₅	1	2	yes	complemented
263	#95	C₂²×C₃×C₅	1	4	yes	complemented
264	C₂×C₃×C₅	—	2	4	no	—
265	C₂×C₃×C₅	—	4	4	no	—
266	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
267	C₂×C₃×C₅	#525	1	1	yes	characteristic
268	C₂×C₃×C₅	#535	1	1	yes	characteristic
269	C₂×C₃×C₅	#551	1	4	yes	—
270	C₂³×C₃	—	2	2	no	—
271	C₂³×C₃	—	2	2	no	—
272	C₂³×C₃	—	2	8	no	—
273	C₂³×C₃	—	2	2	no	—
274	C₂³×C₃	—	2	2	no	—
275	C₂³×C₃	—	2	4	no	—
276	C₂³×C₃	—	2	4	no	—
277	C₂³×C₃	—	4	16	no	—
278	C₂³×C₃	—	4	4	no	—
279	C₂³×C₃	—	4	4	no	—
280	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
281	C₂³×C₃	C₅×#41	1	4	yes	—
282	C₂³×C₃	C₅×#41	1	4	yes	—
283	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
284	C₂×C₃×C₄	—	2	8	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	4	no	—
291	C₂×C₃×C₄	—	2	4	no	—
292	C₂×C₃×C₄	—	2	4	no	—
293	C₂×C₃×C₄	—	2	4	no	—
294	C₂×C₃×C₄	—	2	4	no	—
295	C₂×C₃×C₄	—	2	4	no	—
296	C₂×C₃×C₄	—	4	4	no	—
297	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
298	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
299	C₂²×C₅	—	2	2	no	—
300	C₂²×C₅	—	2	2	no	—
301	C₂²×C₅	—	2	8	no	—
302	C₂²×C₅	—	2	4	no	—
303	C₂²×C₅	—	2	8	no	—
304	C₂²×C₅	—	4	16	no	—
305	C₂²×C₅	—	4	2	no	—
306	C₂²×C₅	—	4	2	no	—
307	C₂²×C₅	—	4	4	no	—
308	C₂²×C₅	C₃×#123	1	4	yes	—
309	C₂²×C₅	C₂²×C₃×D₄	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	2	yes	—
313	C₄×C₅	—	2	2	no	—
314	C₄×C₅	—	2	2	no	—
315	C₄×C₅	—	4	2	no	—
316	C₄×C₅	—	4	2	no	—
317	C₄×C₅	—	4	2	no	—
318	C₄×C₅	—	4	4	no	—
319	C₂⁴	—	2	2	no	—
320	C₂⁴	—	2	4	no	—
321	C₂⁴	—	2	4	no	—
322	C₂⁴	—	4	2	no	—
323	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
324	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
329	C₂²×C₄	C₂³×C₃×C₅	1	4	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	2	yes	—
333	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
334	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	2	8	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	2	4	no	—
343	C₂²⋊C₄	—	4	4	no	—
344	C₄²	—	2	4	no	—
345	C₃×C₅	#2482	1	1	yes	characteristic, direct product factor, Hall
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	—	2	2	no	—
348	C₂²×C₃	—	2	8	no	—
349	C₂²×C₃	—	2	4	no	—
350	C₂²×C₃	—	2	8	no	—
351	C₂²×C₃	—	4	16	no	—
352	C₂²×C₃	—	4	2	no	—
353	C₂²×C₃	—	4	2	no	—
354	C₂²×C₃	—	4	4	no	—
355	C₂²×C₃	C₅×#123	1	4	yes	—
356	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
357	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
358	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
359	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
360	C₃×C₄	—	2	2	no	—
361	C₃×C₄	—	2	2	no	—
362	C₃×C₄	—	4	2	no	—
363	C₃×C₄	—	4	2	no	—
364	C₃×C₄	—	4	2	no	—
365	C₃×C₄	—	4	4	no	—
366	C₂×C₅	—	2	4	no	—
367	C₂×C₅	—	4	4	no	—
368	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
369	C₂×C₅	C₃×#525	1	1	yes	characteristic
370	C₂×C₅	C₃×#535	1	1	yes	characteristic
371	C₂×C₅	C₃×#551	1	4	yes	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	8	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	2	4	no	—
379	C₂³	—	4	16	no	—
380	C₂³	—	4	4	no	—
381	C₂³	—	4	4	no	—
382	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
383	C₂³	C₃×C₅×#41	1	4	yes	—
384	C₂³	C₃×C₅×#41	1	4	yes	—
385	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
400	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
401	C₂×C₃	—	2	4	no	—
402	C₂×C₃	—	4	4	no	—
403	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
404	C₂×C₃	C₅×#525	1	1	yes	characteristic
405	C₂×C₃	C₅×#535	1	1	yes	characteristic
406	C₂×C₃	C₅×#551	1	4	yes	—
407	C₅	C₃×#2482	1	1	yes	characteristic, direct product factor, Sylow
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	8	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	2	8	no	—
413	C₂²	—	4	16	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	4	no	—
417	C₂²	C₃×C₅×#123	1	4	yes	—
418	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
419	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
420	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
421	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	4	no	—
428	C₃	C₅×#2482	1	1	yes	characteristic, direct product factor, Sylow
429	C₂	—	2	4	no	—
430	C₂	—	4	4	no	—
431	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
432	C₂	C₃×C₅×#525	1	1	yes	characteristic
433	C₂	C₃×C₅×#535	1	1	yes	characteristic
434	C₂	C₃×C₅×#551	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁵×C₃×C₅	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
3. C₃×C₅×#399	C₂	semidirect
4. C₃×C₅×#397	C₂	semidirect
5. C₃×C₅×#388	C₂	semidirect
6. C₃×C₅×#385	C₂	semidirect
7. C₃×C₅×#381	C₂	semidirect
9. C₅×#2482	C₃	direct (N × H)
14. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
15. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
16. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
24. C₂×C₃×C₄²×C₅	C₂²	semidirect
25. C₃×C₅×#95	C₂²	semidirect
26. C₃×C₅×#95	C₂²	semidirect
27. C₃×C₅×#95	C₂²	semidirect
28. C₃×#2482	C₅	direct (N × H)
29. C₂×C₅×#117	C₂×C₃	semidirect
31. C₅×#399	C₂×C₃	semidirect
32. C₅×#397	C₂×C₃	semidirect
33. C₅×#388	C₂×C₃	semidirect
34. C₅×#385	C₂×C₃	semidirect
35. C₅×#381	C₂×C₃	semidirect
63. C₂×C₃×#117	C₂×C₅	semidirect
65. C₃×#399	C₂×C₅	semidirect
66. C₃×#397	C₂×C₅	semidirect
67. C₃×#388	C₂×C₅	semidirect
68. C₃×#385	C₂×C₅	semidirect
69. C₃×#381	C₂×C₅	semidirect
75. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
76. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
77. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
85. C₂×C₄²×C₅	C₂²×C₃	semidirect
86. C₅×#95	C₂²×C₃	semidirect
87. C₅×#95	C₂²×C₃	semidirect
88. C₅×#95	C₂²×C₃	semidirect
89. #2482	C₃×C₅	direct (N × H)
123. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
124. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
125. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
133. C₂×C₃×C₄²	C₂²×C₅	semidirect
134. C₃×#95	C₂²×C₅	semidirect
135. C₃×#95	C₂²×C₅	semidirect
136. C₃×#95	C₂²×C₅	semidirect
163. C₂×#117	C₂×C₃×C₅	semidirect
165. #399	C₂×C₃×C₅	semidirect
166. #397	C₂×C₃×C₅	semidirect
167. #388	C₂×C₃×C₅	semidirect
168. #385	C₂×C₃×C₅	semidirect
169. #381	C₂×C₃×C₅	semidirect
250. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
251. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
252. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
260. C₂×C₄²	C₂²×C₃×C₅	semidirect
261. #95	C₂²×C₃×C₅	semidirect
262. #95	C₂²×C₃×C₅	semidirect
263. #95	C₂²×C₃×C₅	semidirect
345. C₃×C₅	#2482	direct (N × H)
407. C₅	C₃×#2482	direct (N × H)
428. C₃	C₅×#2482	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
C₂²×C₃×C₅×C₂²⋊C₄	2
C₃×C₅×#399	2
C₃×C₅×#397	2
C₃×C₅×#388	2
C₃×C₅×#385	2
C₃×C₅×#381	2
C₃×C₅×#379	2
C₅×#2482	3
C₃×#2482	5

Subgroups — C3×C5×#2482 #14275516

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2482 #14275516