Subgroups — C₃×C₅×#2617 #14275651

Order 1920.

1648 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#120	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#397	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#394	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#392	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#386	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2617	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
12	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	—
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₃×C₅×#121	—	2	4	no	—
17	C₃×C₅×#120	—	2	8	no	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
20	C₂×C₃×C₅×C₂²⋊C₄	—	2	4	no	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
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	4	yes	—
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
27	C₃×C₅×#95	C₂²	1	2	yes	complemented
28	C₃×C₅×#95	C₂²	1	4	yes	complemented
29	C₃×#2617	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×C₅×#120	C₂×C₃	1	2	yes	complemented
32	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
33	C₅×#397	C₂×C₃	1	2	yes	complemented
34	C₅×#394	C₂×C₃	1	4	yes	complemented
35	C₅×#392	C₂×C₃	1	2	yes	complemented
36	C₅×#386	C₂×C₃	1	2	yes	complemented
37	C₅×#380	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂⁴×C₃×C₅	—	2	2	no	—
39	C₂⁴×C₃×C₅	—	2	2	no	—
40	C₂⁴×C₃×C₅	—	4	2	no	—
41	C₂⁴×C₃×C₅	—	4	2	no	—
42	C₂⁴×C₃×C₅	D₄	1	4	yes	complemented
43	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
44	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
45	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
46	C₂×C₃×C₅×D₄	—	2	8	no	—
47	C₂×C₃×C₅×D₄	—	2	4	no	—
48	C₂×C₃×C₅×D₄	—	2	4	no	—
49	C₂×C₃×C₅×D₄	—	2	4	no	—
50	C₂×C₃×C₅×D₄	—	2	2	no	—
51	C₂×C₃×C₅×D₄	—	4	4	no	—
52	C₂×C₃×C₅×D₄	—	4	4	no	—
53	C₂×C₃×C₅×D₄	—	4	2	no	—
54	C₂²×C₃×C₄×C₅	—	2	2	no	—
55	C₂²×C₃×C₄×C₅	—	4	2	no	—
56	C₂²×C₃×C₄×C₅	—	4	2	no	—
57	C₂²×C₃×C₄×C₅	D₄	1	4	yes	complemented
58	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
61	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₃×C₅×C₄⋊C₄	—	2	2	no	—
64	C₃×C₅×C₄⋊C₄	—	4	2	no	—
65	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
66	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
67	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
68	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
69	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
70	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
71	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×C₃×#120	C₂×C₅	1	2	yes	complemented
73	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
74	C₃×#397	C₂×C₅	1	2	yes	complemented
75	C₃×#394	C₂×C₅	1	4	yes	complemented
76	C₃×#392	C₂×C₅	1	2	yes	complemented
77	C₃×#386	C₂×C₅	1	2	yes	complemented
78	C₃×#380	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
80	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
81	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	—
82	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
83	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
84	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
85	C₅×#121	—	2	4	no	—
86	C₅×#120	—	2	8	no	—
87	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
88	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
89	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
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	4	yes	—
94	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
95	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
96	C₅×#95	C₂²×C₃	1	2	yes	complemented
97	C₅×#95	C₂²×C₃	1	4	yes	complemented
98	#2617	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
99	C₂³×C₃×C₅	—	2	2	no	—
100	C₂³×C₃×C₅	—	2	2	no	—
101	C₂³×C₃×C₅	—	2	8	no	—
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	—	2	2	no	—
104	C₂³×C₃×C₅	—	2	4	no	—
105	C₂³×C₃×C₅	—	2	4	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	4	no	—
110	C₂³×C₃×C₅	—	2	4	no	—
111	C₂³×C₃×C₅	—	4	8	no	—
112	C₂³×C₃×C₅	—	4	4	no	—
113	C₂³×C₃×C₅	—	4	4	no	—
114	C₂³×C₃×C₅	—	4	8	no	—
115	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
116	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
117	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
118	C₂³×C₃×C₅	#41	1	2	yes	—
119	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
120	C₃×C₅×D₄	—	4	4	no	—
121	C₃×C₅×D₄	—	4	16	no	—
122	C₃×C₅×D₄	—	4	8	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	4	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	4	no	—
131	C₂×C₃×C₄×C₅	—	2	4	no	—
132	C₂×C₃×C₄×C₅	—	2	4	no	—
133	C₂×C₃×C₄×C₅	—	4	4	no	—
134	C₂×C₃×C₄×C₅	—	4	4	no	—
135	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
136	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
137	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
138	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
139	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	—
140	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
141	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
142	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
143	C₃×#121	—	2	4	no	—
144	C₃×#120	—	2	8	no	—
145	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
146	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
147	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
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	4	yes	—
152	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
153	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
154	C₃×#95	C₂²×C₅	1	2	yes	complemented
155	C₃×#95	C₂²×C₅	1	4	yes	complemented
156	C₂⁴×C₅	—	2	2	no	—
157	C₂⁴×C₅	—	2	2	no	—
158	C₂⁴×C₅	—	4	2	no	—
159	C₂⁴×C₅	—	4	2	no	—
160	C₂⁴×C₅	C₃×D₄	1	4	yes	complemented
161	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
162	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
163	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
164	C₂×C₅×D₄	—	2	8	no	—
165	C₂×C₅×D₄	—	2	4	no	—
166	C₂×C₅×D₄	—	2	4	no	—
167	C₂×C₅×D₄	—	2	4	no	—
168	C₂×C₅×D₄	—	2	2	no	—
169	C₂×C₅×D₄	—	4	4	no	—
170	C₂×C₅×D₄	—	4	4	no	—
171	C₂×C₅×D₄	—	4	2	no	—
172	C₂²×C₄×C₅	—	2	2	no	—
173	C₂²×C₄×C₅	—	4	2	no	—
174	C₂²×C₄×C₅	—	4	2	no	—
175	C₂²×C₄×C₅	C₃×D₄	1	4	yes	complemented
176	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
177	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
178	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
179	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
181	C₅×C₄⋊C₄	—	2	2	no	—
182	C₅×C₄⋊C₄	—	4	2	no	—
183	C₅×C₂²⋊C₄	—	2	8	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	4	no	—
189	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic, complemented
190	C₂×#120	C₂×C₃×C₅	1	2	yes	complemented
191	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
192	#397	C₂×C₃×C₅	1	2	yes	complemented
193	#394	C₂×C₃×C₅	1	4	yes	complemented
194	#392	C₂×C₃×C₅	1	2	yes	complemented
195	#386	C₂×C₃×C₅	1	2	yes	complemented
196	#380	C₂×C₃×C₅	1	1	yes	characteristic, complemented
197	C₂²×C₃×C₅	—	2	2	no	—
198	C₂²×C₃×C₅	—	2	4	no	—
199	C₂²×C₃×C₅	—	2	2	no	—
200	C₂²×C₃×C₅	—	2	4	no	—
201	C₂²×C₃×C₅	—	2	4	no	—
202	C₂²×C₃×C₅	—	2	8	no	—
203	C₂²×C₃×C₅	—	4	16	no	—
204	C₂²×C₃×C₅	—	4	2	no	—
205	C₂²×C₃×C₅	—	4	2	no	—
206	C₂²×C₃×C₅	—	4	4	no	—
207	C₂²×C₃×C₅	—	4	2	no	—
208	C₂²×C₃×C₅	—	4	2	no	—
209	C₂²×C₃×C₅	—	4	4	no	—
210	C₂²×C₃×C₅	—	4	2	no	—
211	C₂²×C₃×C₅	—	4	4	no	—
212	C₂²×C₃×C₅	#121	1	4	yes	—
213	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
215	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
216	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
217	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
218	C₃×C₄×C₅	—	2	2	no	—
219	C₃×C₄×C₅	—	2	2	no	—
220	C₃×C₄×C₅	—	4	2	no	—
221	C₃×C₄×C₅	—	4	4	no	—
222	C₃×C₄×C₅	—	4	2	no	—
223	C₂⁴×C₃	—	2	2	no	—
224	C₂⁴×C₃	—	2	2	no	—
225	C₂⁴×C₃	—	4	2	no	—
226	C₂⁴×C₃	—	4	2	no	—
227	C₂⁴×C₃	C₅×D₄	1	4	yes	complemented
228	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
229	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
230	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
231	C₂×C₃×D₄	—	2	8	no	—
232	C₂×C₃×D₄	—	2	4	no	—
233	C₂×C₃×D₄	—	2	4	no	—
234	C₂×C₃×D₄	—	2	4	no	—
235	C₂×C₃×D₄	—	2	2	no	—
236	C₂×C₃×D₄	—	4	4	no	—
237	C₂×C₃×D₄	—	4	4	no	—
238	C₂×C₃×D₄	—	4	2	no	—
239	C₂²×C₃×C₄	—	2	2	no	—
240	C₂²×C₃×C₄	—	4	2	no	—
241	C₂²×C₃×C₄	—	4	2	no	—
242	C₂²×C₃×C₄	C₅×D₄	1	4	yes	complemented
243	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
244	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
245	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
246	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
247	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
248	C₃×C₄⋊C₄	—	2	2	no	—
249	C₃×C₄⋊C₄	—	4	2	no	—
250	C₃×C₂²⋊C₄	—	2	8	no	—
251	C₃×C₂²⋊C₄	—	2	4	no	—
252	C₃×C₂²⋊C₄	—	2	4	no	—
253	C₃×C₂²⋊C₄	—	2	4	no	—
254	C₃×C₂²⋊C₄	—	2	4	no	—
255	C₃×C₂²⋊C₄	—	4	4	no	—
256	C₂³×C₅	—	2	2	no	—
257	C₂³×C₅	—	2	2	no	—
258	C₂³×C₅	—	2	8	no	—
259	C₂³×C₅	—	2	2	no	—
260	C₂³×C₅	—	2	2	no	—
261	C₂³×C₅	—	2	4	no	—
262	C₂³×C₅	—	2	4	no	—
263	C₂³×C₅	—	2	2	no	—
264	C₂³×C₅	—	2	2	no	—
265	C₂³×C₅	—	2	2	no	—
266	C₂³×C₅	—	2	4	no	—
267	C₂³×C₅	—	2	4	no	—
268	C₂³×C₅	—	4	8	no	—
269	C₂³×C₅	—	4	4	no	—
270	C₂³×C₅	—	4	4	no	—
271	C₂³×C₅	—	4	8	no	—
272	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
273	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
274	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
275	C₂³×C₅	C₃×#41	1	2	yes	—
276	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
277	C₅×D₄	—	4	4	no	—
278	C₅×D₄	—	4	16	no	—
279	C₅×D₄	—	4	8	no	—
280	C₂×C₄×C₅	—	2	2	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	4	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	4	no	—
288	C₂×C₄×C₅	—	2	4	no	—
289	C₂×C₄×C₅	—	2	4	no	—
290	C₂×C₄×C₅	—	4	4	no	—
291	C₂×C₄×C₅	—	4	4	no	—
292	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
293	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
294	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
295	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
296	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	—
297	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
298	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
299	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
300	#121	—	2	4	no	—
301	#120	—	2	8	no	—
302	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
303	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
304	C₂×C₂²⋊C₄	—	2	4	no	—
305	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
306	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
307	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
308	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
309	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
310	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
311	#95	C₂²×C₃×C₅	1	2	yes	complemented
312	#95	C₂²×C₃×C₅	1	4	yes	complemented
313	C₂×C₃×C₅	—	2	4	no	—
314	C₂×C₃×C₅	—	4	4	no	—
315	C₂×C₃×C₅	—	8	2	no	—
316	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
317	C₂×C₃×C₅	#534	1	1	yes	characteristic
318	C₂×C₃×C₅	#534	1	2	yes	—
319	C₂×C₃×C₅	#535	1	1	yes	characteristic
320	C₂×C₃×C₅	#538	1	2	yes	—
321	C₂³×C₃	—	2	2	no	—
322	C₂³×C₃	—	2	2	no	—
323	C₂³×C₃	—	2	8	no	—
324	C₂³×C₃	—	2	2	no	—
325	C₂³×C₃	—	2	2	no	—
326	C₂³×C₃	—	2	4	no	—
327	C₂³×C₃	—	2	4	no	—
328	C₂³×C₃	—	2	2	no	—
329	C₂³×C₃	—	2	2	no	—
330	C₂³×C₃	—	2	2	no	—
331	C₂³×C₃	—	2	4	no	—
332	C₂³×C₃	—	2	4	no	—
333	C₂³×C₃	—	4	8	no	—
334	C₂³×C₃	—	4	4	no	—
335	C₂³×C₃	—	4	4	no	—
336	C₂³×C₃	—	4	8	no	—
337	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
338	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
339	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
340	C₂³×C₃	C₅×#41	1	2	yes	—
341	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
342	C₃×D₄	—	4	4	no	—
343	C₃×D₄	—	4	16	no	—
344	C₃×D₄	—	4	8	no	—
345	C₂×C₃×C₄	—	2	2	no	—
346	C₂×C₃×C₄	—	2	2	no	—
347	C₂×C₃×C₄	—	2	2	no	—
348	C₂×C₃×C₄	—	2	2	no	—
349	C₂×C₃×C₄	—	2	4	no	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	2	2	no	—
352	C₂×C₃×C₄	—	2	4	no	—
353	C₂×C₃×C₄	—	2	4	no	—
354	C₂×C₃×C₄	—	2	4	no	—
355	C₂×C₃×C₄	—	4	4	no	—
356	C₂×C₃×C₄	—	4	4	no	—
357	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
358	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
359	C₂²×C₅	—	2	2	no	—
360	C₂²×C₅	—	2	4	no	—
361	C₂²×C₅	—	2	2	no	—
362	C₂²×C₅	—	2	4	no	—
363	C₂²×C₅	—	2	4	no	—
364	C₂²×C₅	—	2	8	no	—
365	C₂²×C₅	—	4	16	no	—
366	C₂²×C₅	—	4	2	no	—
367	C₂²×C₅	—	4	2	no	—
368	C₂²×C₅	—	4	4	no	—
369	C₂²×C₅	—	4	2	no	—
370	C₂²×C₅	—	4	2	no	—
371	C₂²×C₅	—	4	4	no	—
372	C₂²×C₅	—	4	2	no	—
373	C₂²×C₅	—	4	4	no	—
374	C₂²×C₅	C₃×#121	1	4	yes	—
375	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
376	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
377	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
378	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
379	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
380	C₄×C₅	—	2	2	no	—
381	C₄×C₅	—	2	2	no	—
382	C₄×C₅	—	4	2	no	—
383	C₄×C₅	—	4	4	no	—
384	C₄×C₅	—	4	2	no	—
385	C₂⁴	—	2	2	no	—
386	C₂⁴	—	2	2	no	—
387	C₂⁴	—	4	2	no	—
388	C₂⁴	—	4	2	no	—
389	C₂⁴	C₃×C₅×D₄	1	4	yes	complemented
390	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
391	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
392	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
393	C₂×D₄	—	2	8	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	4	4	no	—
399	C₂×D₄	—	4	4	no	—
400	C₂×D₄	—	4	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	C₃×C₅×D₄	1	4	yes	complemented
405	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
406	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
407	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
408	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
409	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₂²⋊C₄	—	2	8	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	4	4	no	—
418	C₃×C₅	#2617	1	1	yes	characteristic, direct product factor, Hall
419	C₂²×C₃	—	2	2	no	—
420	C₂²×C₃	—	2	4	no	—
421	C₂²×C₃	—	2	2	no	—
422	C₂²×C₃	—	2	4	no	—
423	C₂²×C₃	—	2	4	no	—
424	C₂²×C₃	—	2	8	no	—
425	C₂²×C₃	—	4	16	no	—
426	C₂²×C₃	—	4	2	no	—
427	C₂²×C₃	—	4	2	no	—
428	C₂²×C₃	—	4	4	no	—
429	C₂²×C₃	—	4	2	no	—
430	C₂²×C₃	—	4	2	no	—
431	C₂²×C₃	—	4	4	no	—
432	C₂²×C₃	—	4	2	no	—
433	C₂²×C₃	—	4	4	no	—
434	C₂²×C₃	C₅×#121	1	4	yes	—
435	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
436	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
437	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
438	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
439	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
440	C₃×C₄	—	2	2	no	—
441	C₃×C₄	—	2	2	no	—
442	C₃×C₄	—	4	2	no	—
443	C₃×C₄	—	4	4	no	—
444	C₃×C₄	—	4	2	no	—
445	C₂×C₅	—	2	4	no	—
446	C₂×C₅	—	4	4	no	—
447	C₂×C₅	—	8	2	no	—
448	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
449	C₂×C₅	C₃×#534	1	1	yes	characteristic
450	C₂×C₅	C₃×#534	1	2	yes	—
451	C₂×C₅	C₃×#535	1	1	yes	characteristic
452	C₂×C₅	C₃×#538	1	2	yes	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	8	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	4	no	—
459	C₂³	—	2	4	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	4	no	—
464	C₂³	—	2	4	no	—
465	C₂³	—	4	8	no	—
466	C₂³	—	4	4	no	—
467	C₂³	—	4	4	no	—
468	C₂³	—	4	8	no	—
469	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
470	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
471	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
472	C₂³	C₃×C₅×#41	1	2	yes	—
473	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
474	D₄	—	4	4	no	—
475	D₄	—	4	16	no	—
476	D₄	—	4	8	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
490	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
491	C₂×C₃	—	2	4	no	—
492	C₂×C₃	—	4	4	no	—
493	C₂×C₃	—	8	2	no	—
494	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
495	C₂×C₃	C₅×#534	1	1	yes	characteristic
496	C₂×C₃	C₅×#534	1	2	yes	—
497	C₂×C₃	C₅×#535	1	1	yes	characteristic
498	C₂×C₃	C₅×#538	1	2	yes	—
499	C₅	C₃×#2617	1	1	yes	characteristic, direct product factor, Sylow
500	C₂²	—	2	2	no	—
501	C₂²	—	2	4	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	2	4	no	—
505	C₂²	—	2	8	no	—
506	C₂²	—	4	16	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	4	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	4	no	—
515	C₂²	C₃×C₅×#121	1	4	yes	—
516	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
517	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
518	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
519	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
520	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	4	no	—
525	C₄	—	4	2	no	—
526	C₃	C₅×#2617	1	1	yes	characteristic, direct product factor, Sylow
527	C₂	—	2	4	no	—
528	C₂	—	4	4	no	—
529	C₂	—	8	2	no	—
530	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
531	C₂	C₃×C₅×#534	1	1	yes	characteristic
532	C₂	C₃×C₅×#534	1	2	yes	—
533	C₂	C₃×C₅×#535	1	1	yes	characteristic
534	C₂	C₃×C₅×#538	1	2	yes	—

	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×#121	C₂	semidirect
2. C₂×C₃×C₅×#120	C₂	semidirect
3. C₂²×C₃×C₅×C₂²⋊C₄	C₂	semidirect
4. C₃×C₅×#397	C₂	semidirect
5. C₃×C₅×#394	C₂	semidirect
6. C₃×C₅×#392	C₂	semidirect
7. C₃×C₅×#386	C₂	semidirect
8. C₃×C₅×#380	C₂	semidirect
9. C₅×#2617	C₃	direct (N × H)
13. C₂²×C₃×C₅×D₄	C₂²	semidirect
18. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
19. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
25. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
26. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
27. C₃×C₅×#95	C₂²	semidirect
28. C₃×C₅×#95	C₂²	semidirect
29. C₃×#2617	C₅	direct (N × H)
30. C₂×C₅×#121	C₂×C₃	semidirect
31. C₂×C₅×#120	C₂×C₃	semidirect
32. C₂²×C₅×C₂²⋊C₄	C₂×C₃	semidirect
33. C₅×#397	C₂×C₃	semidirect
34. C₅×#394	C₂×C₃	semidirect
35. C₅×#392	C₂×C₃	semidirect
36. C₅×#386	C₂×C₃	semidirect
37. C₅×#380	C₂×C₃	semidirect
42. C₂⁴×C₃×C₅	D₄	semidirect
57. C₂²×C₃×C₄×C₅	D₄	semidirect
71. C₂×C₃×#121	C₂×C₅	semidirect
72. C₂×C₃×#120	C₂×C₅	semidirect
73. C₂²×C₃×C₂²⋊C₄	C₂×C₅	semidirect
74. C₃×#397	C₂×C₅	semidirect
75. C₃×#394	C₂×C₅	semidirect
76. C₃×#392	C₂×C₅	semidirect
77. C₃×#386	C₂×C₅	semidirect
78. C₃×#380	C₂×C₅	semidirect
82. C₂²×C₅×D₄	C₂²×C₃	semidirect
87. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
88. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
94. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
95. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
96. C₅×#95	C₂²×C₃	semidirect
97. C₅×#95	C₂²×C₃	semidirect
98. #2617	C₃×C₅	direct (N × H)
140. C₂²×C₃×D₄	C₂²×C₅	semidirect
145. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
146. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
152. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
153. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
154. C₃×#95	C₂²×C₅	semidirect
155. C₃×#95	C₂²×C₅	semidirect
160. C₂⁴×C₅	C₃×D₄	semidirect
175. C₂²×C₄×C₅	C₃×D₄	semidirect
189. C₂×#121	C₂×C₃×C₅	semidirect
190. C₂×#120	C₂×C₃×C₅	semidirect
191. C₂²×C₂²⋊C₄	C₂×C₃×C₅	semidirect
192. #397	C₂×C₃×C₅	semidirect
193. #394	C₂×C₃×C₅	semidirect
194. #392	C₂×C₃×C₅	semidirect
195. #386	C₂×C₃×C₅	semidirect
196. #380	C₂×C₃×C₅	semidirect
227. C₂⁴×C₃	C₅×D₄	semidirect
242. C₂²×C₃×C₄	C₅×D₄	semidirect
297. C₂²×D₄	C₂²×C₃×C₅	semidirect
302. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
303. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
309. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
310. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
311. #95	C₂²×C₃×C₅	semidirect
312. #95	C₂²×C₃×C₅	semidirect
389. C₂⁴	C₃×C₅×D₄	semidirect
404. C₂²×C₄	C₃×C₅×D₄	semidirect
418. C₃×C₅	#2617	direct (N × H)
499. C₅	C₃×#2617	direct (N × H)
526. C₃	C₅×#2617	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×#121	2
C₂×C₃×C₅×#120	2
C₂²×C₃×C₅×C₂²⋊C₄	2
C₃×C₅×#397	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₅×#386	2
C₃×C₅×#380	2
C₅×#2617	3
C₃×#2617	5

Subgroups — C3×C5×#2617 #14275651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2617 #14275651