Subgroups — C₃×C₅×#2727 #14275761

Order 1920.

952 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#126	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#399	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
5	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#389	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
10	C₅×#2727	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₃×C₅×#126	—	2	8	no	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic
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×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×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×C₄²×C₅	C₂²	1	2	yes	—
29	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
30	C₃×C₅×#95	C₂²	1	2	yes	—
31	C₃×C₅×#95	C₂²	1	2	yes	—
32	C₃×C₅×#95	C₂²	1	2	yes	—
33	C₃×#2727	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₅×#126	C₂×C₃	1	2	yes	complemented
35	C₅×#399	C₂×C₃	1	2	yes	complemented
36	C₅×#396	C₂×C₃	1	2	yes	complemented
37	C₅×#394	C₂×C₃	1	2	yes	—
38	C₅×#390	C₂×C₃	1	1	yes	characteristic
39	C₅×#389	C₂×C₃	1	2	yes	complemented
40	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#388	C₂×C₃	1	2	yes	complemented
43	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	—	4	1	no	—
46	C₂×C₃×C₅×D₄	—	4	1	no	—
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	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	1	yes	characteristic
55	C₃×C₅×C₄⋊C₄	—	2	4	no	—
56	C₃×C₅×C₄⋊C₄	—	2	4	no	—
57	C₃×C₅×C₄⋊C₄	—	2	4	no	—
58	C₃×C₅×C₄⋊C₄	—	2	2	no	—
59	C₃×C₅×C₄⋊C₄	—	4	1	no	—
60	C₃×C₅×C₄⋊C₄	—	4	1	no	—
61	C₃×C₅×C₄⋊C₄	—	4	1	no	—
62	C₃×C₅×C₄⋊C₄	—	4	2	no	—
63	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	complemented
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	—	2	4	no	—
68	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
69	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
70	C₃×C₄²×C₅	—	2	4	no	—
71	C₃×C₄²×C₅	—	4	1	no	—
72	C₂×C₃×#126	C₂×C₅	1	2	yes	complemented
73	C₃×#399	C₂×C₅	1	2	yes	complemented
74	C₃×#396	C₂×C₅	1	2	yes	complemented
75	C₃×#394	C₂×C₅	1	2	yes	—
76	C₃×#390	C₂×C₅	1	1	yes	characteristic
77	C₃×#389	C₂×C₅	1	2	yes	complemented
78	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
79	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
80	C₃×#388	C₂×C₅	1	2	yes	complemented
81	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
82	C₅×#126	—	2	8	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	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
87	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
91	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
93	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
94	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
95	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
96	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
97	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
98	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
99	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
100	C₅×#95	C₂²×C₃	1	2	yes	—
101	C₅×#95	C₂²×C₃	1	2	yes	—
102	C₅×#95	C₂²×C₃	1	2	yes	—
103	#2727	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
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	—	2	2	no	—
109	C₂³×C₃×C₅	—	2	2	no	—
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
112	C₃×C₅×D₄	—	4	4	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	1	no	—
115	C₂×C₃×C₄×C₅	—	2	1	no	—
116	C₂×C₃×C₄×C₅	—	2	1	no	—
117	C₂×C₃×C₄×C₅	—	2	1	no	—
118	C₂×C₃×C₄×C₅	—	2	1	no	—
119	C₂×C₃×C₄×C₅	—	2	1	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	2	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
134	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
135	C₂×C₃×C₄×C₅	#41	1	2	yes	—
136	C₂×C₃×C₄×C₅	#41	1	2	yes	—
137	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
138	C₃×#126	—	2	8	no	—
139	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
140	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
141	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
142	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
143	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
145	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
147	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
148	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
149	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
150	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
151	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
152	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
153	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
154	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
155	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
156	C₃×#95	C₂²×C₅	1	2	yes	—
157	C₃×#95	C₂²×C₅	1	2	yes	—
158	C₃×#95	C₂²×C₅	1	2	yes	—
159	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
160	C₂×C₅×D₄	—	2	2	no	—
161	C₂×C₅×D₄	—	4	1	no	—
162	C₂×C₅×D₄	—	4	1	no	—
163	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
164	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
165	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
166	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
167	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
169	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
171	C₅×C₄⋊C₄	—	2	4	no	—
172	C₅×C₄⋊C₄	—	2	4	no	—
173	C₅×C₄⋊C₄	—	2	4	no	—
174	C₅×C₄⋊C₄	—	2	2	no	—
175	C₅×C₄⋊C₄	—	4	1	no	—
176	C₅×C₄⋊C₄	—	4	1	no	—
177	C₅×C₄⋊C₄	—	4	1	no	—
178	C₅×C₄⋊C₄	—	4	2	no	—
179	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	complemented
180	C₅×C₂²⋊C₄	—	2	4	no	—
181	C₅×C₂²⋊C₄	—	2	4	no	—
182	C₅×C₂²⋊C₄	—	2	4	no	—
183	C₅×C₂²⋊C₄	—	2	4	no	—
184	C₅×C₂²⋊C₄	—	4	2	no	—
185	C₅×C₂²⋊C₄	—	4	2	no	—
186	C₄²×C₅	—	2	4	no	—
187	C₄²×C₅	—	4	1	no	—
188	C₂×#126	C₂×C₃×C₅	1	2	yes	complemented
189	#399	C₂×C₃×C₅	1	2	yes	complemented
190	#396	C₂×C₃×C₅	1	2	yes	complemented
191	#394	C₂×C₃×C₅	1	2	yes	—
192	#390	C₂×C₃×C₅	1	1	yes	characteristic
193	#389	C₂×C₃×C₅	1	2	yes	complemented
194	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
195	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
196	#388	C₂×C₃×C₅	1	2	yes	complemented
197	C₂²×C₃×C₅	—	4	2	no	—
198	C₂²×C₃×C₅	—	4	2	no	—
199	C₂²×C₃×C₅	—	4	2	no	—
200	C₂²×C₃×C₅	—	4	2	no	—
201	C₂²×C₃×C₅	—	4	2	no	—
202	C₂²×C₃×C₅	—	4	2	no	—
203	C₂²×C₃×C₅	—	4	2	no	—
204	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
205	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
206	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
207	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
210	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
211	C₃×C₄×C₅	—	2	2	no	—
212	C₃×C₄×C₅	—	2	2	no	—
213	C₃×C₄×C₅	—	2	2	no	—
214	C₃×C₄×C₅	—	2	4	no	—
215	C₃×C₄×C₅	—	4	2	no	—
216	C₃×C₄×C₅	—	4	2	no	—
217	C₃×C₄×C₅	—	4	2	no	—
218	C₃×C₄×C₅	—	4	2	no	—
219	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
220	C₂×C₃×D₄	—	2	2	no	—
221	C₂×C₃×D₄	—	4	1	no	—
222	C₂×C₃×D₄	—	4	1	no	—
223	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
224	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
225	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
226	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
227	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
228	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
229	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
230	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
231	C₃×C₄⋊C₄	—	2	4	no	—
232	C₃×C₄⋊C₄	—	2	4	no	—
233	C₃×C₄⋊C₄	—	2	4	no	—
234	C₃×C₄⋊C₄	—	2	2	no	—
235	C₃×C₄⋊C₄	—	4	1	no	—
236	C₃×C₄⋊C₄	—	4	1	no	—
237	C₃×C₄⋊C₄	—	4	1	no	—
238	C₃×C₄⋊C₄	—	4	2	no	—
239	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	complemented
240	C₃×C₂²⋊C₄	—	2	4	no	—
241	C₃×C₂²⋊C₄	—	2	4	no	—
242	C₃×C₂²⋊C₄	—	2	4	no	—
243	C₃×C₂²⋊C₄	—	2	4	no	—
244	C₃×C₂²⋊C₄	—	4	2	no	—
245	C₃×C₂²⋊C₄	—	4	2	no	—
246	C₃×C₄²	—	2	4	no	—
247	C₃×C₄²	—	4	1	no	—
248	C₂³×C₅	—	2	2	no	—
249	C₂³×C₅	—	2	2	no	—
250	C₂³×C₅	—	2	2	no	—
251	C₂³×C₅	—	2	2	no	—
252	C₂³×C₅	—	2	2	no	—
253	C₂³×C₅	—	2	2	no	—
254	C₂³×C₅	—	2	2	no	—
255	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
256	C₅×D₄	—	4	4	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	1	no	—
259	C₂×C₄×C₅	—	2	1	no	—
260	C₂×C₄×C₅	—	2	1	no	—
261	C₂×C₄×C₅	—	2	1	no	—
262	C₂×C₄×C₅	—	2	1	no	—
263	C₂×C₄×C₅	—	2	1	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	2	2	no	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
278	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
279	C₂×C₄×C₅	C₃×#41	1	2	yes	—
280	C₂×C₄×C₅	C₃×#41	1	2	yes	—
281	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
282	#126	—	2	8	no	—
283	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
284	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
285	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
286	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
291	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
293	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
294	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
295	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
296	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
297	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
298	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
299	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
300	#95	C₂²×C₃×C₅	1	2	yes	—
301	#95	C₂²×C₃×C₅	1	2	yes	—
302	#95	C₂²×C₃×C₅	1	2	yes	—
303	C₂×C₃×C₅	—	8	2	no	—
304	C₂×C₃×C₅	#537	1	1	yes	characteristic
305	C₂×C₃×C₅	#538	1	1	yes	characteristic
306	C₂×C₃×C₅	#539	1	1	yes	characteristic
307	C₂×C₃×C₅	#547	1	1	yes	characteristic
308	C₂×C₃×C₅	#550	1	1	yes	characteristic
309	C₂×C₃×C₅	#556	1	1	yes	characteristic
310	C₂×C₃×C₅	#563	1	1	yes	characteristic
311	C₂³×C₃	—	2	2	no	—
312	C₂³×C₃	—	2	2	no	—
313	C₂³×C₃	—	2	2	no	—
314	C₂³×C₃	—	2	2	no	—
315	C₂³×C₃	—	2	2	no	—
316	C₂³×C₃	—	2	2	no	—
317	C₂³×C₃	—	2	2	no	—
318	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
319	C₃×D₄	—	4	4	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	1	no	—
322	C₂×C₃×C₄	—	2	1	no	—
323	C₂×C₃×C₄	—	2	1	no	—
324	C₂×C₃×C₄	—	2	1	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	—	2	2	no	—
329	C₂×C₃×C₄	—	2	2	no	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	2	2	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	—	2	2	no	—
338	C₂×C₃×C₄	—	2	2	no	—
339	C₂×C₃×C₄	—	2	2	no	—
340	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
341	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
342	C₂×C₃×C₄	C₅×#41	1	2	yes	—
343	C₂×C₃×C₄	C₅×#41	1	2	yes	—
344	C₂²×C₅	—	4	2	no	—
345	C₂²×C₅	—	4	2	no	—
346	C₂²×C₅	—	4	2	no	—
347	C₂²×C₅	—	4	2	no	—
348	C₂²×C₅	—	4	2	no	—
349	C₂²×C₅	—	4	2	no	—
350	C₂²×C₅	—	4	2	no	—
351	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
352	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
353	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
354	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
355	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
356	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
357	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
358	C₄×C₅	—	2	2	no	—
359	C₄×C₅	—	2	2	no	—
360	C₄×C₅	—	2	2	no	—
361	C₄×C₅	—	2	4	no	—
362	C₄×C₅	—	4	2	no	—
363	C₄×C₅	—	4	2	no	—
364	C₄×C₅	—	4	2	no	—
365	C₄×C₅	—	4	2	no	—
366	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	4	1	no	—
369	C₂×D₄	—	4	1	no	—
370	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
371	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
372	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
373	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
374	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
375	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
376	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
377	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	4	1	no	—
383	C₄⋊C₄	—	4	1	no	—
384	C₄⋊C₄	—	4	1	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
387	C₂²⋊C₄	—	2	4	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	2	4	no	—
391	C₂²⋊C₄	—	4	2	no	—
392	C₂²⋊C₄	—	4	2	no	—
393	C₄²	—	2	4	no	—
394	C₄²	—	4	1	no	—
395	C₃×C₅	#2727	1	1	yes	characteristic, direct product factor, Hall
396	C₂²×C₃	—	4	2	no	—
397	C₂²×C₃	—	4	2	no	—
398	C₂²×C₃	—	4	2	no	—
399	C₂²×C₃	—	4	2	no	—
400	C₂²×C₃	—	4	2	no	—
401	C₂²×C₃	—	4	2	no	—
402	C₂²×C₃	—	4	2	no	—
403	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
404	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
405	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
406	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
407	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
408	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
409	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
410	C₃×C₄	—	2	2	no	—
411	C₃×C₄	—	2	2	no	—
412	C₃×C₄	—	2	2	no	—
413	C₃×C₄	—	2	4	no	—
414	C₃×C₄	—	4	2	no	—
415	C₃×C₄	—	4	2	no	—
416	C₃×C₄	—	4	2	no	—
417	C₃×C₄	—	4	2	no	—
418	C₂×C₅	—	8	2	no	—
419	C₂×C₅	C₃×#537	1	1	yes	characteristic
420	C₂×C₅	C₃×#538	1	1	yes	characteristic
421	C₂×C₅	C₃×#539	1	1	yes	characteristic
422	C₂×C₅	C₃×#547	1	1	yes	characteristic
423	C₂×C₅	C₃×#550	1	1	yes	characteristic
424	C₂×C₅	C₃×#556	1	1	yes	characteristic
425	C₂×C₅	C₃×#563	1	1	yes	characteristic
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	2	no	—
433	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
434	D₄	—	4	4	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
456	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
457	C₂×C₄	C₃×C₅×#41	1	2	yes	—
458	C₂×C₄	C₃×C₅×#41	1	2	yes	—
459	C₂×C₃	—	8	2	no	—
460	C₂×C₃	C₅×#537	1	1	yes	characteristic
461	C₂×C₃	C₅×#538	1	1	yes	characteristic
462	C₂×C₃	C₅×#539	1	1	yes	characteristic
463	C₂×C₃	C₅×#547	1	1	yes	characteristic
464	C₂×C₃	C₅×#550	1	1	yes	characteristic
465	C₂×C₃	C₅×#556	1	1	yes	characteristic
466	C₂×C₃	C₅×#563	1	1	yes	characteristic
467	C₅	C₃×#2727	1	1	yes	characteristic, direct product factor, Sylow
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
476	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
477	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
478	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
479	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
480	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
481	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
482	C₄	—	2	2	no	—
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	2	4	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₃	C₅×#2727	1	1	yes	characteristic, direct product factor, Sylow
491	C₂	—	8	2	no	—
492	C₂	C₃×C₅×#537	1	1	yes	characteristic
493	C₂	C₃×C₅×#538	1	1	yes	characteristic
494	C₂	C₃×C₅×#539	1	1	yes	characteristic
495	C₂	C₃×C₅×#547	1	1	yes	characteristic
496	C₂	C₃×C₅×#550	1	1	yes	characteristic
497	C₂	C₃×C₅×#556	1	1	yes	characteristic
498	C₂	C₃×C₅×#563	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×#126	C₂	semidirect
2. C₃×C₅×#399	C₂	semidirect
3. C₃×C₅×#396	C₂	semidirect
6. C₃×C₅×#389	C₂	semidirect
7. C₃×C₅×#389	C₂	semidirect
8. C₃×C₅×#389	C₂	semidirect
9. C₃×C₅×#388	C₂	semidirect
10. C₅×#2727	C₃	direct (N × H)
33. C₃×#2727	C₅	direct (N × H)
34. C₂×C₅×#126	C₂×C₃	semidirect
35. C₅×#399	C₂×C₃	semidirect
36. C₅×#396	C₂×C₃	semidirect
39. C₅×#389	C₂×C₃	semidirect
40. C₅×#389	C₂×C₃	semidirect
41. C₅×#389	C₂×C₃	semidirect
42. C₅×#388	C₂×C₃	semidirect
63. C₃×C₅×C₄⋊C₄	D₄	semidirect
72. C₂×C₃×#126	C₂×C₅	semidirect
73. C₃×#399	C₂×C₅	semidirect
74. C₃×#396	C₂×C₅	semidirect
77. C₃×#389	C₂×C₅	semidirect
78. C₃×#389	C₂×C₅	semidirect
79. C₃×#389	C₂×C₅	semidirect
80. C₃×#388	C₂×C₅	semidirect
103. #2727	C₃×C₅	direct (N × H)
179. C₅×C₄⋊C₄	C₃×D₄	semidirect
188. C₂×#126	C₂×C₃×C₅	semidirect
189. #399	C₂×C₃×C₅	semidirect
190. #396	C₂×C₃×C₅	semidirect
193. #389	C₂×C₃×C₅	semidirect
194. #389	C₂×C₃×C₅	semidirect
195. #389	C₂×C₃×C₅	semidirect
196. #388	C₂×C₃×C₅	semidirect
239. C₃×C₄⋊C₄	C₅×D₄	semidirect
386. C₄⋊C₄	C₃×C₅×D₄	semidirect
395. C₃×C₅	#2727	direct (N × H)
467. C₅	C₃×#2727	direct (N × H)
490. C₃	C₅×#2727	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×#126	2
C₃×C₅×#399	2
C₃×C₅×#396	2
C₃×C₅×#394	2
C₃×C₅×#390	2
C₃×C₅×#389	2
C₃×C₅×#388	2
C₅×#2727	3
C₃×#2727	5

Subgroups — C3×C5×#2727 #14275761

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2727 #14275761