Subgroups — C₃×C₅×#2682 #14275716

Order 1920.

1336 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#123	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×#121	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#396	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#394	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#392	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#385	C₂	1	2	yes	maximal, complemented
10	C₅×#2682	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
12	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
16	C₃×C₅×#123	—	2	8	no	—
17	C₃×C₅×#121	—	2	8	no	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
32	C₃×C₅×#95	C₂²	1	2	yes	—
33	C₃×C₅×#95	C₂²	1	2	yes	—
34	C₃×#2682	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂×C₅×#123	C₂×C₃	1	2	yes	complemented
36	C₂×C₅×#121	C₂×C₃	1	2	yes	complemented
37	C₅×#396	C₂×C₃	1	2	yes	complemented
38	C₅×#394	C₂×C₃	1	2	yes	complemented
39	C₅×#392	C₂×C₃	1	2	yes	complemented
40	C₅×#390	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#390	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#385	C₂×C₃	1	2	yes	complemented
44	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
45	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
46	C₂×C₃×C₅×D₄	—	2	4	no	—
47	C₂×C₃×C₅×D₄	—	2	4	no	—
48	C₂×C₃×C₅×D₄	—	2	4	no	—
49	C₂×C₃×C₅×D₄	—	2	2	no	—
50	C₂×C₃×C₅×D₄	—	4	1	no	—
51	C₂×C₃×C₅×D₄	—	4	1	no	—
52	C₂×C₃×C₅×D₄	—	4	1	no	—
53	C₂×C₃×C₅×D₄	—	4	1	no	—
54	C₂×C₃×C₅×D₄	—	4	2	no	—
55	C₂×C₃×C₅×D₄	—	4	2	no	—
56	C₂×C₃×C₅×D₄	—	4	2	no	—
57	C₂×C₃×C₅×D₄	D₄	1	4	yes	complemented
58	C₂²×C₃×C₄×C₅	—	2	4	no	—
59	C₂²×C₃×C₄×C₅	—	2	4	no	—
60	C₂²×C₃×C₄×C₅	—	4	2	no	—
61	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
62	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
63	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
64	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₃×C₅×C₄⋊C₄	—	2	4	no	—
69	C₃×C₅×C₄⋊C₄	—	2	4	no	—
70	C₃×C₅×C₄⋊C₄	—	4	1	no	—
71	C₃×C₅×C₄⋊C₄	—	4	1	no	—
72	C₃×C₅×C₄⋊C₄	—	4	1	no	—
73	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	complemented
74	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
75	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
76	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
77	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
78	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
79	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
80	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
81	C₃×C₄²×C₅	—	4	1	no	—
82	C₂×C₃×#123	C₂×C₅	1	2	yes	complemented
83	C₂×C₃×#121	C₂×C₅	1	2	yes	complemented
84	C₃×#396	C₂×C₅	1	2	yes	complemented
85	C₃×#394	C₂×C₅	1	2	yes	complemented
86	C₃×#392	C₂×C₅	1	2	yes	complemented
87	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
88	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
89	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
90	C₃×#385	C₂×C₅	1	2	yes	complemented
91	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
92	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
93	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
94	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
95	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
96	C₅×#123	—	2	8	no	—
97	C₅×#121	—	2	8	no	—
98	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
99	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
100	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
105	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
106	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
107	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
108	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
109	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
110	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
111	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
112	C₅×#95	C₂²×C₃	1	2	yes	—
113	C₅×#95	C₂²×C₃	1	2	yes	—
114	#2682	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
115	C₂³×C₃×C₅	—	2	2	no	—
116	C₂³×C₃×C₅	—	2	2	no	—
117	C₂³×C₃×C₅	—	2	2	no	—
118	C₂³×C₃×C₅	—	2	2	no	—
119	C₂³×C₃×C₅	—	2	2	no	—
120	C₂³×C₃×C₅	—	2	2	no	—
121	C₂³×C₃×C₅	—	2	2	no	—
122	C₂³×C₃×C₅	—	2	2	no	—
123	C₂³×C₃×C₅	—	2	2	no	—
124	C₂³×C₃×C₅	—	2	2	no	—
125	C₂³×C₃×C₅	—	2	2	no	—
126	C₂³×C₃×C₅	—	2	2	no	—
127	C₂³×C₃×C₅	—	2	2	no	—
128	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
129	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
130	C₃×C₅×D₄	—	4	4	no	—
131	C₃×C₅×D₄	—	4	8	no	—
132	C₃×C₅×D₄	—	4	4	no	—
133	C₃×C₅×D₄	—	4	8	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	2	1	no	—
136	C₂×C₃×C₄×C₅	—	2	1	no	—
137	C₂×C₃×C₄×C₅	—	2	1	no	—
138	C₂×C₃×C₄×C₅	—	2	1	no	—
139	C₂×C₃×C₄×C₅	—	2	1	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	2	1	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	2	no	—
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	2	no	—
150	C₂×C₃×C₄×C₅	—	2	2	no	—
151	C₂×C₃×C₄×C₅	—	4	8	no	—
152	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
153	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
154	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
155	C₂×C₃×C₄×C₅	#41	1	2	yes	—
156	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
157	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
158	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
159	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
160	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
161	C₃×#123	—	2	8	no	—
162	C₃×#121	—	2	8	no	—
163	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
164	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
165	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
167	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
168	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
169	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
170	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
171	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
174	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
175	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
176	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
177	C₃×#95	C₂²×C₅	1	2	yes	—
178	C₃×#95	C₂²×C₅	1	2	yes	—
179	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
180	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
181	C₂×C₅×D₄	—	2	4	no	—
182	C₂×C₅×D₄	—	2	4	no	—
183	C₂×C₅×D₄	—	2	4	no	—
184	C₂×C₅×D₄	—	2	2	no	—
185	C₂×C₅×D₄	—	4	1	no	—
186	C₂×C₅×D₄	—	4	1	no	—
187	C₂×C₅×D₄	—	4	1	no	—
188	C₂×C₅×D₄	—	4	1	no	—
189	C₂×C₅×D₄	—	4	2	no	—
190	C₂×C₅×D₄	—	4	2	no	—
191	C₂×C₅×D₄	—	4	2	no	—
192	C₂×C₅×D₄	C₃×D₄	1	4	yes	complemented
193	C₂²×C₄×C₅	—	2	4	no	—
194	C₂²×C₄×C₅	—	2	4	no	—
195	C₂²×C₄×C₅	—	4	2	no	—
196	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
197	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
198	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
199	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
200	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
201	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
202	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
203	C₅×C₄⋊C₄	—	2	4	no	—
204	C₅×C₄⋊C₄	—	2	4	no	—
205	C₅×C₄⋊C₄	—	4	1	no	—
206	C₅×C₄⋊C₄	—	4	1	no	—
207	C₅×C₄⋊C₄	—	4	1	no	—
208	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	complemented
209	C₅×C₂²⋊C₄	—	2	4	no	—
210	C₅×C₂²⋊C₄	—	2	4	no	—
211	C₅×C₂²⋊C₄	—	2	4	no	—
212	C₅×C₂²⋊C₄	—	2	4	no	—
213	C₅×C₂²⋊C₄	—	2	4	no	—
214	C₅×C₂²⋊C₄	—	2	4	no	—
215	C₅×C₂²⋊C₄	—	4	2	no	—
216	C₄²×C₅	—	4	1	no	—
217	C₂×#123	C₂×C₃×C₅	1	2	yes	complemented
218	C₂×#121	C₂×C₃×C₅	1	2	yes	complemented
219	#396	C₂×C₃×C₅	1	2	yes	complemented
220	#394	C₂×C₃×C₅	1	2	yes	complemented
221	#392	C₂×C₃×C₅	1	2	yes	complemented
222	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
223	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
224	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
225	#385	C₂×C₃×C₅	1	2	yes	complemented
226	C₂²×C₃×C₅	—	2	4	no	—
227	C₂²×C₃×C₅	—	2	4	no	—
228	C₂²×C₃×C₅	—	2	4	no	—
229	C₂²×C₃×C₅	—	4	2	no	—
230	C₂²×C₃×C₅	—	4	2	no	—
231	C₂²×C₃×C₅	—	4	2	no	—
232	C₂²×C₃×C₅	—	4	2	no	—
233	C₂²×C₃×C₅	—	4	2	no	—
234	C₂²×C₃×C₅	—	4	2	no	—
235	C₂²×C₃×C₅	—	4	2	no	—
236	C₂²×C₃×C₅	—	4	2	no	—
237	C₂²×C₃×C₅	—	4	2	no	—
238	C₂²×C₃×C₅	—	4	2	no	—
239	C₂²×C₃×C₅	—	4	2	no	—
240	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
241	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
242	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
243	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
244	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
245	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
246	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
247	C₃×C₄×C₅	—	2	2	no	—
248	C₃×C₄×C₅	—	2	2	no	—
249	C₃×C₄×C₅	—	2	2	no	—
250	C₃×C₄×C₅	—	2	4	no	—
251	C₃×C₄×C₅	—	4	2	no	—
252	C₃×C₄×C₅	—	4	2	no	—
253	C₃×C₄×C₅	—	4	2	no	—
254	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
255	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
256	C₂×C₃×D₄	—	2	4	no	—
257	C₂×C₃×D₄	—	2	4	no	—
258	C₂×C₃×D₄	—	2	4	no	—
259	C₂×C₃×D₄	—	2	2	no	—
260	C₂×C₃×D₄	—	4	1	no	—
261	C₂×C₃×D₄	—	4	1	no	—
262	C₂×C₃×D₄	—	4	1	no	—
263	C₂×C₃×D₄	—	4	1	no	—
264	C₂×C₃×D₄	—	4	2	no	—
265	C₂×C₃×D₄	—	4	2	no	—
266	C₂×C₃×D₄	—	4	2	no	—
267	C₂×C₃×D₄	C₅×D₄	1	4	yes	complemented
268	C₂²×C₃×C₄	—	2	4	no	—
269	C₂²×C₃×C₄	—	2	4	no	—
270	C₂²×C₃×C₄	—	4	2	no	—
271	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
272	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
273	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
274	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
275	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
276	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
277	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
278	C₃×C₄⋊C₄	—	2	4	no	—
279	C₃×C₄⋊C₄	—	2	4	no	—
280	C₃×C₄⋊C₄	—	4	1	no	—
281	C₃×C₄⋊C₄	—	4	1	no	—
282	C₃×C₄⋊C₄	—	4	1	no	—
283	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	complemented
284	C₃×C₂²⋊C₄	—	2	4	no	—
285	C₃×C₂²⋊C₄	—	2	4	no	—
286	C₃×C₂²⋊C₄	—	2	4	no	—
287	C₃×C₂²⋊C₄	—	2	4	no	—
288	C₃×C₂²⋊C₄	—	2	4	no	—
289	C₃×C₂²⋊C₄	—	2	4	no	—
290	C₃×C₂²⋊C₄	—	4	2	no	—
291	C₃×C₄²	—	4	1	no	—
292	C₂³×C₅	—	2	2	no	—
293	C₂³×C₅	—	2	2	no	—
294	C₂³×C₅	—	2	2	no	—
295	C₂³×C₅	—	2	2	no	—
296	C₂³×C₅	—	2	2	no	—
297	C₂³×C₅	—	2	2	no	—
298	C₂³×C₅	—	2	2	no	—
299	C₂³×C₅	—	2	2	no	—
300	C₂³×C₅	—	2	2	no	—
301	C₂³×C₅	—	2	2	no	—
302	C₂³×C₅	—	2	2	no	—
303	C₂³×C₅	—	2	2	no	—
304	C₂³×C₅	—	2	2	no	—
305	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
306	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
307	C₅×D₄	—	4	4	no	—
308	C₅×D₄	—	4	8	no	—
309	C₅×D₄	—	4	4	no	—
310	C₅×D₄	—	4	8	no	—
311	C₂×C₄×C₅	—	2	2	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	2	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	2	2	no	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	2	2	no	—
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	2	2	no	—
326	C₂×C₄×C₅	—	2	2	no	—
327	C₂×C₄×C₅	—	2	2	no	—
328	C₂×C₄×C₅	—	4	8	no	—
329	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
330	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
331	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
332	C₂×C₄×C₅	C₃×#41	1	2	yes	—
333	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
334	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
335	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
336	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
337	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
338	#123	—	2	8	no	—
339	#121	—	2	8	no	—
340	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
341	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
342	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
346	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
347	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
348	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
349	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
350	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
351	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
352	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
353	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
354	#95	C₂²×C₃×C₅	1	2	yes	—
355	#95	C₂²×C₃×C₅	1	2	yes	—
356	C₂×C₃×C₅	—	4	4	no	—
357	C₂×C₃×C₅	—	8	2	no	—
358	C₂×C₃×C₅	#534	1	1	yes	characteristic
359	C₂×C₃×C₅	#537	1	1	yes	characteristic
360	C₂×C₃×C₅	#538	1	1	yes	characteristic
361	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
362	C₂×C₃×C₅	#547	1	1	yes	characteristic
363	C₂×C₃×C₅	#550	1	1	yes	characteristic
364	C₂×C₃×C₅	#562	1	1	yes	characteristic
365	C₂³×C₃	—	2	2	no	—
366	C₂³×C₃	—	2	2	no	—
367	C₂³×C₃	—	2	2	no	—
368	C₂³×C₃	—	2	2	no	—
369	C₂³×C₃	—	2	2	no	—
370	C₂³×C₃	—	2	2	no	—
371	C₂³×C₃	—	2	2	no	—
372	C₂³×C₃	—	2	2	no	—
373	C₂³×C₃	—	2	2	no	—
374	C₂³×C₃	—	2	2	no	—
375	C₂³×C₃	—	2	2	no	—
376	C₂³×C₃	—	2	2	no	—
377	C₂³×C₃	—	2	2	no	—
378	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
379	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
380	C₃×D₄	—	4	4	no	—
381	C₃×D₄	—	4	8	no	—
382	C₃×D₄	—	4	4	no	—
383	C₃×D₄	—	4	8	no	—
384	C₂×C₃×C₄	—	2	2	no	—
385	C₂×C₃×C₄	—	2	1	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	2	1	no	—
388	C₂×C₃×C₄	—	2	1	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	2	no	—
391	C₂×C₃×C₄	—	2	1	no	—
392	C₂×C₃×C₄	—	2	2	no	—
393	C₂×C₃×C₄	—	2	2	no	—
394	C₂×C₃×C₄	—	2	2	no	—
395	C₂×C₃×C₄	—	2	2	no	—
396	C₂×C₃×C₄	—	2	2	no	—
397	C₂×C₃×C₄	—	2	2	no	—
398	C₂×C₃×C₄	—	2	2	no	—
399	C₂×C₃×C₄	—	2	2	no	—
400	C₂×C₃×C₄	—	2	2	no	—
401	C₂×C₃×C₄	—	4	8	no	—
402	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
403	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
404	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
405	C₂×C₃×C₄	C₅×#41	1	2	yes	—
406	C₂²×C₅	—	2	4	no	—
407	C₂²×C₅	—	2	4	no	—
408	C₂²×C₅	—	2	4	no	—
409	C₂²×C₅	—	4	2	no	—
410	C₂²×C₅	—	4	2	no	—
411	C₂²×C₅	—	4	2	no	—
412	C₂²×C₅	—	4	2	no	—
413	C₂²×C₅	—	4	2	no	—
414	C₂²×C₅	—	4	2	no	—
415	C₂²×C₅	—	4	2	no	—
416	C₂²×C₅	—	4	2	no	—
417	C₂²×C₅	—	4	2	no	—
418	C₂²×C₅	—	4	2	no	—
419	C₂²×C₅	—	4	2	no	—
420	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
421	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
422	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
423	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
424	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
425	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
427	C₄×C₅	—	2	2	no	—
428	C₄×C₅	—	2	2	no	—
429	C₄×C₅	—	2	2	no	—
430	C₄×C₅	—	2	4	no	—
431	C₄×C₅	—	4	2	no	—
432	C₄×C₅	—	4	2	no	—
433	C₄×C₅	—	4	2	no	—
434	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
435	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	4	1	no	—
441	C₂×D₄	—	4	1	no	—
442	C₂×D₄	—	4	1	no	—
443	C₂×D₄	—	4	1	no	—
444	C₂×D₄	—	4	2	no	—
445	C₂×D₄	—	4	2	no	—
446	C₂×D₄	—	4	2	no	—
447	C₂×D₄	C₃×C₅×D₄	1	4	yes	complemented
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	4	2	no	—
451	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
452	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
453	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
454	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
455	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
456	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
457	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	4	2	no	—
471	C₄²	—	4	1	no	—
472	C₃×C₅	#2682	1	1	yes	characteristic, direct product factor, Hall
473	C₂²×C₃	—	2	4	no	—
474	C₂²×C₃	—	2	4	no	—
475	C₂²×C₃	—	2	4	no	—
476	C₂²×C₃	—	4	2	no	—
477	C₂²×C₃	—	4	2	no	—
478	C₂²×C₃	—	4	2	no	—
479	C₂²×C₃	—	4	2	no	—
480	C₂²×C₃	—	4	2	no	—
481	C₂²×C₃	—	4	2	no	—
482	C₂²×C₃	—	4	2	no	—
483	C₂²×C₃	—	4	2	no	—
484	C₂²×C₃	—	4	2	no	—
485	C₂²×C₃	—	4	2	no	—
486	C₂²×C₃	—	4	2	no	—
487	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
488	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
489	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
490	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
491	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
492	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
493	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
494	C₃×C₄	—	2	2	no	—
495	C₃×C₄	—	2	2	no	—
496	C₃×C₄	—	2	2	no	—
497	C₃×C₄	—	2	4	no	—
498	C₃×C₄	—	4	2	no	—
499	C₃×C₄	—	4	2	no	—
500	C₃×C₄	—	4	2	no	—
501	C₂×C₅	—	4	4	no	—
502	C₂×C₅	—	8	2	no	—
503	C₂×C₅	C₃×#534	1	1	yes	characteristic
504	C₂×C₅	C₃×#537	1	1	yes	characteristic
505	C₂×C₅	C₃×#538	1	1	yes	characteristic
506	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
507	C₂×C₅	C₃×#547	1	1	yes	characteristic
508	C₂×C₅	C₃×#550	1	1	yes	characteristic
509	C₂×C₅	C₃×#562	1	1	yes	characteristic
510	C₂³	—	2	2	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	2	2	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	2	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	2	no	—
519	C₂³	—	2	2	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	2	2	no	—
522	C₂³	—	2	2	no	—
523	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
524	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
525	D₄	—	4	4	no	—
526	D₄	—	4	8	no	—
527	D₄	—	4	4	no	—
528	D₄	—	4	8	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	4	8	no	—
547	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
548	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
549	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
550	C₂×C₄	C₃×C₅×#41	1	2	yes	—
551	C₂×C₃	—	4	4	no	—
552	C₂×C₃	—	8	2	no	—
553	C₂×C₃	C₅×#534	1	1	yes	characteristic
554	C₂×C₃	C₅×#537	1	1	yes	characteristic
555	C₂×C₃	C₅×#538	1	1	yes	characteristic
556	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
557	C₂×C₃	C₅×#547	1	1	yes	characteristic
558	C₂×C₃	C₅×#550	1	1	yes	characteristic
559	C₂×C₃	C₅×#562	1	1	yes	characteristic
560	C₅	C₃×#2682	1	1	yes	characteristic, direct product factor, Sylow
561	C₂²	—	2	4	no	—
562	C₂²	—	2	4	no	—
563	C₂²	—	2	4	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	2	no	—
575	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
576	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
577	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
578	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
579	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
580	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
581	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
582	C₄	—	2	2	no	—
583	C₄	—	2	2	no	—
584	C₄	—	2	2	no	—
585	C₄	—	2	4	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	2	no	—
588	C₄	—	4	2	no	—
589	C₃	C₅×#2682	1	1	yes	characteristic, direct product factor, Sylow
590	C₂	—	4	4	no	—
591	C₂	—	8	2	no	—
592	C₂	C₃×C₅×#534	1	1	yes	characteristic
593	C₂	C₃×C₅×#537	1	1	yes	characteristic
594	C₂	C₃×C₅×#538	1	1	yes	characteristic
595	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
596	C₂	C₃×C₅×#547	1	1	yes	characteristic
597	C₂	C₃×C₅×#550	1	1	yes	characteristic
598	C₂	C₃×C₅×#562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
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×#123	C₂	semidirect
2. C₂×C₃×C₅×#121	C₂	semidirect
3. C₃×C₅×#396	C₂	semidirect
4. C₃×C₅×#394	C₂	semidirect
5. C₃×C₅×#392	C₂	semidirect
6. C₃×C₅×#390	C₂	semidirect
7. C₃×C₅×#390	C₂	semidirect
8. C₃×C₅×#389	C₂	semidirect
9. C₃×C₅×#385	C₂	semidirect
10. C₅×#2682	C₃	direct (N × H)
34. C₃×#2682	C₅	direct (N × H)
35. C₂×C₅×#123	C₂×C₃	semidirect
36. C₂×C₅×#121	C₂×C₃	semidirect
37. C₅×#396	C₂×C₃	semidirect
38. C₅×#394	C₂×C₃	semidirect
39. C₅×#392	C₂×C₃	semidirect
40. C₅×#390	C₂×C₃	semidirect
41. C₅×#390	C₂×C₃	semidirect
42. C₅×#389	C₂×C₃	semidirect
43. C₅×#385	C₂×C₃	semidirect
57. C₂×C₃×C₅×D₄	D₄	semidirect
73. C₃×C₅×C₄⋊C₄	D₄	semidirect
82. C₂×C₃×#123	C₂×C₅	semidirect
83. C₂×C₃×#121	C₂×C₅	semidirect
84. C₃×#396	C₂×C₅	semidirect
85. C₃×#394	C₂×C₅	semidirect
86. C₃×#392	C₂×C₅	semidirect
87. C₃×#390	C₂×C₅	semidirect
88. C₃×#390	C₂×C₅	semidirect
89. C₃×#389	C₂×C₅	semidirect
90. C₃×#385	C₂×C₅	semidirect
114. #2682	C₃×C₅	direct (N × H)
192. C₂×C₅×D₄	C₃×D₄	semidirect
208. C₅×C₄⋊C₄	C₃×D₄	semidirect
217. C₂×#123	C₂×C₃×C₅	semidirect
218. C₂×#121	C₂×C₃×C₅	semidirect
219. #396	C₂×C₃×C₅	semidirect
220. #394	C₂×C₃×C₅	semidirect
221. #392	C₂×C₃×C₅	semidirect
222. #390	C₂×C₃×C₅	semidirect
223. #390	C₂×C₃×C₅	semidirect
224. #389	C₂×C₃×C₅	semidirect
225. #385	C₂×C₃×C₅	semidirect
267. C₂×C₃×D₄	C₅×D₄	semidirect
283. C₃×C₄⋊C₄	C₅×D₄	semidirect
447. C₂×D₄	C₃×C₅×D₄	semidirect
463. C₄⋊C₄	C₃×C₅×D₄	semidirect
472. C₃×C₅	#2682	direct (N × H)
560. C₅	C₃×#2682	direct (N × H)
589. C₃	C₅×#2682	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×#123	2
C₂×C₃×C₅×#121	2
C₃×C₅×#396	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₅×#390	2
C₃×C₅×#389	2
C₃×C₅×#385	2
C₅×#2682	3
C₃×#2682	5

Subgroups — C3×C5×#2682 #14275716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2682 #14275716