Subgroups — C₃×C₅×#2712 #14275746

Order 1920.

1112 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#397	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#394	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#393	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#392	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#391	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#386	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2712	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
12	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₃×C₅×#124	—	2	8	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
26	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₃×C₅×#95	C₂²	1	2	yes	—
29	C₃×C₅×#95	C₂²	1	2	yes	—
30	C₃×C₅×#95	C₂²	1	1	yes	characteristic
31	C₃×C₅×#95	C₂²	1	2	yes	—
32	C₃×C₅×#95	C₂²	1	1	yes	characteristic
33	C₃×#2712	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₅×#124	C₂×C₃	1	2	yes	complemented
35	C₅×#397	C₂×C₃	1	1	yes	characteristic, complemented
36	C₅×#394	C₂×C₃	1	2	yes	complemented
37	C₅×#393	C₂×C₃	1	2	yes	complemented
38	C₅×#392	C₂×C₃	1	1	yes	characteristic
39	C₅×#391	C₂×C₃	1	2	yes	complemented
40	C₅×#388	C₂×C₃	1	2	yes	complemented
41	C₅×#386	C₂×C₃	1	2	yes	complemented
42	C₅×#385	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
44	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
45	C₂×C₃×C₅×Q₈	—	2	4	no	—
46	C₂×C₃×C₅×Q₈	—	2	4	no	—
47	C₂×C₃×C₅×Q₈	—	4	2	no	—
48	C₂×C₃×C₅×D₄	—	2	4	no	—
49	C₂×C₃×C₅×D₄	—	2	4	no	—
50	C₂×C₃×C₅×D₄	—	4	2	no	—
51	C₂×C₃×C₅×D₄	—	4	1	no	—
52	C₂×C₃×C₅×D₄	—	4	2	no	—
53	C₂²×C₃×C₄×C₅	—	4	1	no	—
54	C₂²×C₃×C₄×C₅	—	4	2	no	—
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
58	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
61	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
62	C₃×C₅×C₄⋊C₄	—	4	2	no	—
63	C₃×C₅×C₄⋊C₄	—	4	1	no	—
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	1	no	—
70	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
71	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	complemented
72	C₃×C₄²×C₅	—	2	4	no	—
73	C₂×C₃×#124	C₂×C₅	1	2	yes	complemented
74	C₃×#397	C₂×C₅	1	1	yes	characteristic, complemented
75	C₃×#394	C₂×C₅	1	2	yes	complemented
76	C₃×#393	C₂×C₅	1	2	yes	complemented
77	C₃×#392	C₂×C₅	1	1	yes	characteristic
78	C₃×#391	C₂×C₅	1	2	yes	complemented
79	C₃×#388	C₂×C₅	1	2	yes	complemented
80	C₃×#386	C₂×C₅	1	2	yes	complemented
81	C₃×#385	C₂×C₅	1	1	yes	characteristic, complemented
82	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
83	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
84	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
85	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
86	C₅×#124	—	2	8	no	—
87	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
88	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
90	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
91	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
92	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
93	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	1	yes	characteristic
97	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
98	C₅×#95	C₂²×C₃	1	2	yes	—
99	C₅×#95	C₂²×C₃	1	2	yes	—
100	C₅×#95	C₂²×C₃	1	2	yes	—
101	C₅×#95	C₂²×C₃	1	1	yes	characteristic
102	C₅×#95	C₂²×C₃	1	2	yes	—
103	C₅×#95	C₂²×C₃	1	1	yes	characteristic
104	#2712	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
105	C₂³×C₃×C₅	—	2	2	no	—
106	C₂³×C₃×C₅	—	2	1	no	—
107	C₂³×C₃×C₅	—	2	2	no	—
108	C₂³×C₃×C₅	—	2	1	no	—
109	C₂³×C₃×C₅	—	2	2	no	—
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	—	2	2	no	—
112	C₂³×C₃×C₅	—	2	2	no	—
113	C₂³×C₃×C₅	—	2	2	no	—
114	C₂³×C₃×C₅	—	2	2	no	—
115	C₂³×C₃×C₅	—	2	2	no	—
116	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
117	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
118	C₃×C₅×Q₈	—	4	8	no	—
119	C₃×C₅×D₄	—	4	8	no	—
120	C₃×C₅×D₄	—	4	4	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	1	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	1	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	4	4	no	—
139	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
140	C₂×C₃×C₄×C₅	#41	1	4	yes	—
141	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
142	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
143	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
144	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
145	C₃×#124	—	2	8	no	—
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	1	yes	characteristic
153	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
154	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
155	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
157	C₃×#95	C₂²×C₅	1	2	yes	—
158	C₃×#95	C₂²×C₅	1	2	yes	—
159	C₃×#95	C₂²×C₅	1	2	yes	—
160	C₃×#95	C₂²×C₅	1	1	yes	characteristic
161	C₃×#95	C₂²×C₅	1	2	yes	—
162	C₃×#95	C₂²×C₅	1	1	yes	characteristic
163	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
164	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
165	C₂×C₅×Q₈	—	2	4	no	—
166	C₂×C₅×Q₈	—	2	4	no	—
167	C₂×C₅×Q₈	—	4	2	no	—
168	C₂×C₅×D₄	—	2	4	no	—
169	C₂×C₅×D₄	—	2	4	no	—
170	C₂×C₅×D₄	—	4	2	no	—
171	C₂×C₅×D₄	—	4	1	no	—
172	C₂×C₅×D₄	—	4	2	no	—
173	C₂²×C₄×C₅	—	4	1	no	—
174	C₂²×C₄×C₅	—	4	2	no	—
175	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
176	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
178	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
179	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
181	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
182	C₅×C₄⋊C₄	—	4	2	no	—
183	C₅×C₄⋊C₄	—	4	1	no	—
184	C₅×C₂²⋊C₄	—	2	4	no	—
185	C₅×C₂²⋊C₄	—	2	4	no	—
186	C₅×C₂²⋊C₄	—	2	4	no	—
187	C₅×C₂²⋊C₄	—	2	4	no	—
188	C₅×C₂²⋊C₄	—	4	2	no	—
189	C₅×C₂²⋊C₄	—	4	1	no	—
190	C₅×C₂²⋊C₄	—	4	2	no	—
191	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	complemented
192	C₄²×C₅	—	2	4	no	—
193	C₂×#124	C₂×C₃×C₅	1	2	yes	complemented
194	#397	C₂×C₃×C₅	1	1	yes	characteristic, complemented
195	#394	C₂×C₃×C₅	1	2	yes	complemented
196	#393	C₂×C₃×C₅	1	2	yes	complemented
197	#392	C₂×C₃×C₅	1	1	yes	characteristic
198	#391	C₂×C₃×C₅	1	2	yes	complemented
199	#388	C₂×C₃×C₅	1	2	yes	complemented
200	#386	C₂×C₃×C₅	1	2	yes	complemented
201	#385	C₂×C₃×C₅	1	1	yes	characteristic, complemented
202	C₂²×C₃×C₅	—	2	2	no	—
203	C₂²×C₃×C₅	—	2	4	no	—
204	C₂²×C₃×C₅	—	4	2	no	—
205	C₂²×C₃×C₅	—	4	1	no	—
206	C₂²×C₃×C₅	—	4	1	no	—
207	C₂²×C₃×C₅	—	4	2	no	—
208	C₂²×C₃×C₅	—	4	2	no	—
209	C₂²×C₃×C₅	—	4	2	no	—
210	C₂²×C₃×C₅	—	4	2	no	—
211	C₂²×C₃×C₅	—	4	2	no	—
212	C₂²×C₃×C₅	—	4	2	no	—
213	C₂²×C₃×C₅	—	4	2	no	—
214	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
215	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
216	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
218	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
219	C₃×C₄×C₅	—	2	4	no	—
220	C₃×C₄×C₅	—	2	4	no	—
221	C₃×C₄×C₅	—	4	2	no	—
222	C₃×C₄×C₅	—	4	2	no	—
223	C₃×C₄×C₅	—	4	1	no	—
224	C₃×C₄×C₅	—	4	2	no	—
225	C₃×C₄×C₅	—	4	1	no	—
226	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
227	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
228	C₂×C₃×Q₈	—	2	4	no	—
229	C₂×C₃×Q₈	—	2	4	no	—
230	C₂×C₃×Q₈	—	4	2	no	—
231	C₂×C₃×D₄	—	2	4	no	—
232	C₂×C₃×D₄	—	2	4	no	—
233	C₂×C₃×D₄	—	4	2	no	—
234	C₂×C₃×D₄	—	4	1	no	—
235	C₂×C₃×D₄	—	4	2	no	—
236	C₂²×C₃×C₄	—	4	1	no	—
237	C₂²×C₃×C₄	—	4	2	no	—
238	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
239	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
240	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
241	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
242	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
243	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
244	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
245	C₃×C₄⋊C₄	—	4	2	no	—
246	C₃×C₄⋊C₄	—	4	1	no	—
247	C₃×C₂²⋊C₄	—	2	4	no	—
248	C₃×C₂²⋊C₄	—	2	4	no	—
249	C₃×C₂²⋊C₄	—	2	4	no	—
250	C₃×C₂²⋊C₄	—	2	4	no	—
251	C₃×C₂²⋊C₄	—	4	2	no	—
252	C₃×C₂²⋊C₄	—	4	1	no	—
253	C₃×C₂²⋊C₄	—	4	2	no	—
254	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	complemented
255	C₃×C₄²	—	2	4	no	—
256	C₂³×C₅	—	2	2	no	—
257	C₂³×C₅	—	2	1	no	—
258	C₂³×C₅	—	2	2	no	—
259	C₂³×C₅	—	2	1	no	—
260	C₂³×C₅	—	2	2	no	—
261	C₂³×C₅	—	2	2	no	—
262	C₂³×C₅	—	2	2	no	—
263	C₂³×C₅	—	2	2	no	—
264	C₂³×C₅	—	2	2	no	—
265	C₂³×C₅	—	2	2	no	—
266	C₂³×C₅	—	2	2	no	—
267	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
268	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
269	C₅×Q₈	—	4	8	no	—
270	C₅×D₄	—	4	8	no	—
271	C₅×D₄	—	4	4	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	—	2	2	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	1	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	4	4	no	—
290	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
291	C₂×C₄×C₅	C₃×#41	1	4	yes	—
292	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
293	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
294	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
295	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
296	#124	—	2	8	no	—
297	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
298	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
300	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
301	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
302	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
303	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
305	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
306	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
307	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
308	#95	C₂²×C₃×C₅	1	2	yes	—
309	#95	C₂²×C₃×C₅	1	2	yes	—
310	#95	C₂²×C₃×C₅	1	2	yes	—
311	#95	C₂²×C₃×C₅	1	1	yes	characteristic
312	#95	C₂²×C₃×C₅	1	2	yes	—
313	#95	C₂²×C₃×C₅	1	1	yes	characteristic
314	C₂×C₃×C₅	—	4	2	no	—
315	C₂×C₃×C₅	—	8	2	no	—
316	C₂×C₃×C₅	#537	1	1	yes	characteristic
317	C₂×C₃×C₅	#542	1	2	yes	—
318	C₂×C₃×C₅	#546	1	2	yes	—
319	C₂×C₃×C₅	#559	1	1	yes	characteristic
320	C₂×C₃×C₅	H(3,𝔽₄)	1	1	yes	characteristic
321	C₂³×C₃	—	2	2	no	—
322	C₂³×C₃	—	2	1	no	—
323	C₂³×C₃	—	2	2	no	—
324	C₂³×C₃	—	2	1	no	—
325	C₂³×C₃	—	2	2	no	—
326	C₂³×C₃	—	2	2	no	—
327	C₂³×C₃	—	2	2	no	—
328	C₂³×C₃	—	2	2	no	—
329	C₂³×C₃	—	2	2	no	—
330	C₂³×C₃	—	2	2	no	—
331	C₂³×C₃	—	2	2	no	—
332	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
333	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
334	C₃×Q₈	—	4	8	no	—
335	C₃×D₄	—	4	8	no	—
336	C₃×D₄	—	4	4	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	—	2	2	no	—
341	C₂×C₃×C₄	—	2	2	no	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	—	2	2	no	—
344	C₂×C₃×C₄	—	2	2	no	—
345	C₂×C₃×C₄	—	2	2	no	—
346	C₂×C₃×C₄	—	2	1	no	—
347	C₂×C₃×C₄	—	2	2	no	—
348	C₂×C₃×C₄	—	2	2	no	—
349	C₂×C₃×C₄	—	2	1	no	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	2	2	no	—
352	C₂×C₃×C₄	—	2	2	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	4	4	no	—
355	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
356	C₂×C₃×C₄	C₅×#41	1	4	yes	—
357	C₂²×C₅	—	2	2	no	—
358	C₂²×C₅	—	2	4	no	—
359	C₂²×C₅	—	4	1	no	—
360	C₂²×C₅	—	4	1	no	—
361	C₂²×C₅	—	4	2	no	—
362	C₂²×C₅	—	4	2	no	—
363	C₂²×C₅	—	4	2	no	—
364	C₂²×C₅	—	4	2	no	—
365	C₂²×C₅	—	4	2	no	—
366	C₂²×C₅	—	4	2	no	—
367	C₂²×C₅	—	4	2	no	—
368	C₂²×C₅	—	4	2	no	—
369	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
370	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
371	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
372	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
373	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
374	C₄×C₅	—	2	4	no	—
375	C₄×C₅	—	2	4	no	—
376	C₄×C₅	—	4	1	no	—
377	C₄×C₅	—	4	2	no	—
378	C₄×C₅	—	4	1	no	—
379	C₄×C₅	—	4	2	no	—
380	C₄×C₅	—	4	2	no	—
381	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
382	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
383	C₂×Q₈	—	2	4	no	—
384	C₂×Q₈	—	2	4	no	—
385	C₂×Q₈	—	4	2	no	—
386	C₂×D₄	—	2	4	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	4	2	no	—
389	C₂×D₄	—	4	1	no	—
390	C₂×D₄	—	4	2	no	—
391	C₂²×C₄	—	4	1	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
394	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
395	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
396	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
397	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
398	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
399	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
400	C₄⋊C₄	—	4	2	no	—
401	C₄⋊C₄	—	4	1	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	2	4	no	—
406	C₂²⋊C₄	—	4	2	no	—
407	C₂²⋊C₄	—	4	1	no	—
408	C₂²⋊C₄	—	4	2	no	—
409	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
410	C₄²	—	2	4	no	—
411	C₃×C₅	#2712	1	1	yes	characteristic, direct product factor, Hall
412	C₂²×C₃	—	2	2	no	—
413	C₂²×C₃	—	2	4	no	—
414	C₂²×C₃	—	4	2	no	—
415	C₂²×C₃	—	4	1	no	—
416	C₂²×C₃	—	4	1	no	—
417	C₂²×C₃	—	4	2	no	—
418	C₂²×C₃	—	4	2	no	—
419	C₂²×C₃	—	4	2	no	—
420	C₂²×C₃	—	4	2	no	—
421	C₂²×C₃	—	4	2	no	—
422	C₂²×C₃	—	4	2	no	—
423	C₂²×C₃	—	4	2	no	—
424	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
425	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
426	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
428	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
429	C₃×C₄	—	2	4	no	—
430	C₃×C₄	—	2	4	no	—
431	C₃×C₄	—	4	2	no	—
432	C₃×C₄	—	4	2	no	—
433	C₃×C₄	—	4	1	no	—
434	C₃×C₄	—	4	2	no	—
435	C₃×C₄	—	4	1	no	—
436	C₂×C₅	—	4	2	no	—
437	C₂×C₅	—	8	2	no	—
438	C₂×C₅	C₃×#537	1	1	yes	characteristic
439	C₂×C₅	C₃×#542	1	2	yes	—
440	C₂×C₅	C₃×#546	1	2	yes	—
441	C₂×C₅	C₃×#559	1	1	yes	characteristic
442	C₂×C₅	C₃×H(3,𝔽₄)	1	1	yes	characteristic
443	C₂³	—	2	2	no	—
444	C₂³	—	2	1	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
455	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
456	Q₈	—	4	8	no	—
457	D₄	—	4	8	no	—
458	D₄	—	4	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
478	C₂×C₄	C₃×C₅×#41	1	4	yes	—
479	C₂×C₃	—	4	2	no	—
480	C₂×C₃	—	8	2	no	—
481	C₂×C₃	C₅×#537	1	1	yes	characteristic
482	C₂×C₃	C₅×#542	1	2	yes	—
483	C₂×C₃	C₅×#546	1	2	yes	—
484	C₂×C₃	C₅×#559	1	1	yes	characteristic
485	C₂×C₃	C₅×H(3,𝔽₄)	1	1	yes	characteristic
486	C₅	C₃×#2712	1	1	yes	characteristic, direct product factor, Sylow
487	C₂²	—	2	2	no	—
488	C₂²	—	2	4	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	1	no	—
491	C₂²	—	4	1	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
500	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
501	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
502	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
503	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
504	C₄	—	2	4	no	—
505	C₄	—	2	4	no	—
506	C₄	—	4	2	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	1	no	—
509	C₄	—	4	2	no	—
510	C₄	—	4	1	no	—
511	C₃	C₅×#2712	1	1	yes	characteristic, direct product factor, Sylow
512	C₂	—	4	2	no	—
513	C₂	—	8	2	no	—
514	C₂	C₃×C₅×#537	1	1	yes	characteristic
515	C₂	C₃×C₅×#542	1	2	yes	—
516	C₂	C₃×C₅×#546	1	2	yes	—
517	C₂	C₃×C₅×#559	1	1	yes	characteristic
518	C₂	C₃×C₅×H(3,𝔽₄)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₃×C₅×#392	C₂
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×#124	C₂	semidirect
2. C₃×C₅×#397	C₂	semidirect
3. C₃×C₅×#394	C₂	semidirect
4. C₃×C₅×#393	C₂	semidirect
6. C₃×C₅×#391	C₂	semidirect
7. C₃×C₅×#388	C₂	semidirect
8. C₃×C₅×#386	C₂	semidirect
9. C₃×C₅×#385	C₂	semidirect
10. C₅×#2712	C₃	direct (N × H)
33. C₃×#2712	C₅	direct (N × H)
34. C₂×C₅×#124	C₂×C₃	semidirect
35. C₅×#397	C₂×C₃	semidirect
36. C₅×#394	C₂×C₃	semidirect
37. C₅×#393	C₂×C₃	semidirect
39. C₅×#391	C₂×C₃	semidirect
40. C₅×#388	C₂×C₃	semidirect
41. C₅×#386	C₂×C₃	semidirect
42. C₅×#385	C₂×C₃	semidirect
71. C₃×C₅×C₂²⋊C₄	D₄	semidirect
73. C₂×C₃×#124	C₂×C₅	semidirect
74. C₃×#397	C₂×C₅	semidirect
75. C₃×#394	C₂×C₅	semidirect
76. C₃×#393	C₂×C₅	semidirect
78. C₃×#391	C₂×C₅	semidirect
79. C₃×#388	C₂×C₅	semidirect
80. C₃×#386	C₂×C₅	semidirect
81. C₃×#385	C₂×C₅	semidirect
104. #2712	C₃×C₅	direct (N × H)
191. C₅×C₂²⋊C₄	C₃×D₄	semidirect
193. C₂×#124	C₂×C₃×C₅	semidirect
194. #397	C₂×C₃×C₅	semidirect
195. #394	C₂×C₃×C₅	semidirect
196. #393	C₂×C₃×C₅	semidirect
198. #391	C₂×C₃×C₅	semidirect
199. #388	C₂×C₃×C₅	semidirect
200. #386	C₂×C₃×C₅	semidirect
201. #385	C₂×C₃×C₅	semidirect
254. C₃×C₂²⋊C₄	C₅×D₄	semidirect
409. C₂²⋊C₄	C₃×C₅×D₄	semidirect
411. C₃×C₅	#2712	direct (N × H)
486. C₅	C₃×#2712	direct (N × H)
511. C₃	C₅×#2712	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×#124	2
C₃×C₅×#397	2
C₃×C₅×#394	2
C₃×C₅×#393	2
C₃×C₅×#392	2
C₃×C₅×#391	2
C₃×C₅×#388	2
C₃×C₅×#386	2
C₃×C₅×#385	2
C₅×#2712	3
C₃×#2712	5

Subgroups — C3×C5×#2712 #14275746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2712 #14275746