Subgroups — C₃×C₅×#2541 #14275575

Order 1920.

1896 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#127	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#121	C₂	1	4	yes	maximal, complemented
4	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#392	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#390	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2541	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
10	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×D₄	C₂²	1	8	yes	—
12	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
14	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
15	C₃×C₅×#127	—	2	8	no	—
16	C₃×C₅×#127	—	2	4	no	—
17	C₃×C₅×#121	—	2	16	no	—
18	C₃×C₄×C₅×D₄	—	2	4	no	—
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×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
24	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₃×C₅×#95	C₂²	1	2	yes	—
26	C₃×#2541	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂×C₅×#127	C₂×C₃	1	2	yes	complemented
28	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×C₅×#121	C₂×C₃	1	4	yes	complemented
30	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
31	C₅×#392	C₂×C₃	1	4	yes	complemented
32	C₅×#390	C₂×C₃	1	2	yes	complemented
33	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
35	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
36	C₂×C₃×C₅×D₄	—	2	16	no	—
37	C₂×C₃×C₅×D₄	—	2	2	no	—
38	C₂×C₃×C₅×D₄	—	2	16	no	—
39	C₂×C₃×C₅×D₄	—	2	8	no	—
40	C₂×C₃×C₅×D₄	—	2	4	no	—
41	C₂×C₃×C₅×D₄	—	2	4	no	—
42	C₂×C₃×C₅×D₄	—	2	4	no	—
43	C₂×C₃×C₅×D₄	—	2	4	no	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	—	2	4	no	—
46	C₂×C₃×C₅×D₄	—	4	8	no	—
47	C₂×C₃×C₅×D₄	—	4	4	no	—
48	C₂×C₃×C₅×D₄	D₄	1	4	yes	complemented
49	C₂²×C₃×C₄×C₅	—	2	4	no	—
50	C₂²×C₃×C₄×C₅	—	2	8	no	—
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₃×C₅×C₄⋊C₄	—	2	2	no	—
57	C₃×C₅×C₄⋊C₄	D₄	1	8	yes	complemented
58	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
59	C₃×C₅×C₂²⋊C₄	—	2	16	no	—
60	C₃×C₄²×C₅	—	2	4	no	—
61	C₃×C₄²×C₅	D₄	1	4	yes	complemented
62	C₂×C₃×#127	C₂×C₅	1	2	yes	complemented
63	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic, complemented
64	C₂×C₃×#121	C₂×C₅	1	4	yes	complemented
65	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
66	C₃×#392	C₂×C₅	1	4	yes	complemented
67	C₃×#390	C₂×C₅	1	2	yes	complemented
68	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
70	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
71	C₂²×C₅×D₄	C₂²×C₃	1	8	yes	—
72	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
74	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
75	C₅×#127	—	2	8	no	—
76	C₅×#127	—	2	4	no	—
77	C₅×#121	—	2	16	no	—
78	C₄×C₅×D₄	—	2	4	no	—
79	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
81	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
82	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
83	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
84	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
85	C₅×#95	C₂²×C₃	1	2	yes	—
86	#2541	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
87	C₂³×C₃×C₅	—	2	2	no	—
88	C₂³×C₃×C₅	—	2	4	no	—
89	C₂³×C₃×C₅	—	2	2	no	—
90	C₂³×C₃×C₅	—	2	4	no	—
91	C₂³×C₃×C₅	—	2	8	no	—
92	C₂³×C₃×C₅	—	2	4	no	—
93	C₂³×C₃×C₅	—	2	4	no	—
94	C₂³×C₃×C₅	—	2	4	no	—
95	C₂³×C₃×C₅	—	2	8	no	—
96	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
97	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
98	C₃×C₅×D₄	—	2	8	no	—
99	C₃×C₅×D₄	—	4	32	no	—
100	C₃×C₅×D₄	—	4	8	no	—
101	C₃×C₅×D₄	—	4	8	no	—
102	C₃×C₅×D₄	—	4	8	no	—
103	C₂×C₃×C₄×C₅	—	2	4	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	4	no	—
106	C₂×C₃×C₄×C₅	—	2	4	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	4	8	no	—
109	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	8	yes	—
111	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
115	C₂×C₃×C₄×C₅	#41	1	2	yes	—
116	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
117	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
118	C₂²×C₃×D₄	C₂²×C₅	1	8	yes	—
119	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
120	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
121	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
122	C₃×#127	—	2	8	no	—
123	C₃×#127	—	2	4	no	—
124	C₃×#121	—	2	16	no	—
125	C₃×C₄×D₄	—	2	4	no	—
126	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
128	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
129	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
130	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
131	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
132	C₃×#95	C₂²×C₅	1	2	yes	—
133	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
134	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
135	C₂×C₅×D₄	—	2	16	no	—
136	C₂×C₅×D₄	—	2	2	no	—
137	C₂×C₅×D₄	—	2	16	no	—
138	C₂×C₅×D₄	—	2	8	no	—
139	C₂×C₅×D₄	—	2	4	no	—
140	C₂×C₅×D₄	—	2	4	no	—
141	C₂×C₅×D₄	—	2	4	no	—
142	C₂×C₅×D₄	—	2	4	no	—
143	C₂×C₅×D₄	—	2	2	no	—
144	C₂×C₅×D₄	—	2	4	no	—
145	C₂×C₅×D₄	—	4	8	no	—
146	C₂×C₅×D₄	—	4	4	no	—
147	C₂×C₅×D₄	C₃×D₄	1	4	yes	complemented
148	C₂²×C₄×C₅	—	2	4	no	—
149	C₂²×C₄×C₅	—	2	8	no	—
150	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
151	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
152	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
155	C₅×C₄⋊C₄	—	2	2	no	—
156	C₅×C₄⋊C₄	C₃×D₄	1	8	yes	complemented
157	C₅×C₂²⋊C₄	—	2	4	no	—
158	C₅×C₂²⋊C₄	—	2	16	no	—
159	C₄²×C₅	—	2	4	no	—
160	C₄²×C₅	C₃×D₄	1	4	yes	complemented
161	C₂×#127	C₂×C₃×C₅	1	2	yes	complemented
162	C₂×#127	C₂×C₃×C₅	1	1	yes	characteristic, complemented
163	C₂×#121	C₂×C₃×C₅	1	4	yes	complemented
164	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
165	#392	C₂×C₃×C₅	1	4	yes	complemented
166	#390	C₂×C₃×C₅	1	2	yes	complemented
167	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
168	C₂²×C₃×C₅	—	2	4	no	—
169	C₂²×C₃×C₅	—	2	8	no	—
170	C₂²×C₃×C₅	—	4	2	no	—
171	C₂²×C₃×C₅	—	4	2	no	—
172	C₂²×C₃×C₅	—	4	4	no	—
173	C₂²×C₃×C₅	—	4	4	no	—
174	C₂²×C₃×C₅	—	4	4	no	—
175	C₂²×C₃×C₅	—	4	4	no	—
176	C₂²×C₃×C₅	—	4	8	no	—
177	C₂²×C₃×C₅	—	4	8	no	—
178	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
179	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
180	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
181	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
182	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
183	C₃×C₄×C₅	—	2	2	no	—
184	C₃×C₄×C₅	—	2	8	no	—
185	C₃×C₄×C₅	—	4	2	no	—
186	C₃×C₄×C₅	#121	1	4	yes	complemented
187	C₃×C₄×C₅	#127	1	4	yes	complemented
188	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
189	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
190	C₂×C₃×D₄	—	2	16	no	—
191	C₂×C₃×D₄	—	2	2	no	—
192	C₂×C₃×D₄	—	2	16	no	—
193	C₂×C₃×D₄	—	2	8	no	—
194	C₂×C₃×D₄	—	2	4	no	—
195	C₂×C₃×D₄	—	2	4	no	—
196	C₂×C₃×D₄	—	2	4	no	—
197	C₂×C₃×D₄	—	2	4	no	—
198	C₂×C₃×D₄	—	2	2	no	—
199	C₂×C₃×D₄	—	2	4	no	—
200	C₂×C₃×D₄	—	4	8	no	—
201	C₂×C₃×D₄	—	4	4	no	—
202	C₂×C₃×D₄	C₅×D₄	1	4	yes	complemented
203	C₂²×C₃×C₄	—	2	4	no	—
204	C₂²×C₃×C₄	—	2	8	no	—
205	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
206	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
208	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
209	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
210	C₃×C₄⋊C₄	—	2	2	no	—
211	C₃×C₄⋊C₄	C₅×D₄	1	8	yes	complemented
212	C₃×C₂²⋊C₄	—	2	4	no	—
213	C₃×C₂²⋊C₄	—	2	16	no	—
214	C₃×C₄²	—	2	4	no	—
215	C₃×C₄²	C₅×D₄	1	4	yes	complemented
216	C₂³×C₅	—	2	2	no	—
217	C₂³×C₅	—	2	4	no	—
218	C₂³×C₅	—	2	2	no	—
219	C₂³×C₅	—	2	4	no	—
220	C₂³×C₅	—	2	8	no	—
221	C₂³×C₅	—	2	4	no	—
222	C₂³×C₅	—	2	4	no	—
223	C₂³×C₅	—	2	4	no	—
224	C₂³×C₅	—	2	8	no	—
225	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
226	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
227	C₅×D₄	—	2	8	no	—
228	C₅×D₄	—	4	32	no	—
229	C₅×D₄	—	4	8	no	—
230	C₅×D₄	—	4	8	no	—
231	C₅×D₄	—	4	8	no	—
232	C₂×C₄×C₅	—	2	4	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	2	4	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	4	8	no	—
238	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
239	C₂×C₄×C₅	C₂×C₃×D₄	1	8	yes	—
240	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
241	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
242	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
243	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
244	C₂×C₄×C₅	C₃×#41	1	2	yes	—
245	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
246	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
247	C₂²×D₄	C₂²×C₃×C₅	1	8	yes	—
248	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
249	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
250	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
251	#127	—	2	8	no	—
252	#127	—	2	4	no	—
253	#121	—	2	16	no	—
254	C₄×D₄	—	2	4	no	—
255	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
256	C₂×C₄⋊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	8	yes	—
259	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
260	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
261	#95	C₂²×C₃×C₅	1	2	yes	—
262	C₂×C₃×C₅	—	4	4	no	—
263	C₂×C₃×C₅	—	8	4	no	—
264	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
265	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
266	C₂×C₃×C₅	#535	1	1	yes	characteristic
267	C₂×C₃×C₅	D₄²	1	2	yes	—
268	C₂×C₃×C₅	#550	1	2	yes	—
269	C₂³×C₃	—	2	2	no	—
270	C₂³×C₃	—	2	4	no	—
271	C₂³×C₃	—	2	2	no	—
272	C₂³×C₃	—	2	4	no	—
273	C₂³×C₃	—	2	8	no	—
274	C₂³×C₃	—	2	4	no	—
275	C₂³×C₃	—	2	4	no	—
276	C₂³×C₃	—	2	4	no	—
277	C₂³×C₃	—	2	8	no	—
278	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
279	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
280	C₃×D₄	—	2	8	no	—
281	C₃×D₄	—	4	32	no	—
282	C₃×D₄	—	4	8	no	—
283	C₃×D₄	—	4	8	no	—
284	C₃×D₄	—	4	8	no	—
285	C₂×C₃×C₄	—	2	4	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	2	4	no	—
288	C₂×C₃×C₄	—	2	4	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	4	8	no	—
291	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
292	C₂×C₃×C₄	C₂×C₅×D₄	1	8	yes	—
293	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
294	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
295	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
296	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
297	C₂×C₃×C₄	C₅×#41	1	2	yes	—
298	C₂²×C₅	—	2	4	no	—
299	C₂²×C₅	—	2	8	no	—
300	C₂²×C₅	—	4	2	no	—
301	C₂²×C₅	—	4	2	no	—
302	C₂²×C₅	—	4	4	no	—
303	C₂²×C₅	—	4	4	no	—
304	C₂²×C₅	—	4	4	no	—
305	C₂²×C₅	—	4	4	no	—
306	C₂²×C₅	—	4	8	no	—
307	C₂²×C₅	—	4	8	no	—
308	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
309	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
310	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
311	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
312	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
313	C₄×C₅	—	2	2	no	—
314	C₄×C₅	—	2	8	no	—
315	C₄×C₅	—	4	2	no	—
316	C₄×C₅	C₃×#121	1	4	yes	complemented
317	C₄×C₅	C₃×#127	1	4	yes	complemented
318	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
319	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
320	C₂×D₄	—	2	16	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	16	no	—
323	C₂×D₄	—	2	8	no	—
324	C₂×D₄	—	2	4	no	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	4	8	no	—
331	C₂×D₄	—	4	4	no	—
332	C₂×D₄	C₃×C₅×D₄	1	4	yes	complemented
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
336	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
337	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
338	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
339	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	C₃×C₅×D₄	1	8	yes	complemented
342	C₂²⋊C₄	—	2	4	no	—
343	C₂²⋊C₄	—	2	16	no	—
344	C₄²	—	2	4	no	—
345	C₄²	C₃×C₅×D₄	1	4	yes	complemented
346	C₃×C₅	#2541	1	1	yes	characteristic, direct product factor, Hall
347	C₂²×C₃	—	2	4	no	—
348	C₂²×C₃	—	2	8	no	—
349	C₂²×C₃	—	4	2	no	—
350	C₂²×C₃	—	4	2	no	—
351	C₂²×C₃	—	4	4	no	—
352	C₂²×C₃	—	4	4	no	—
353	C₂²×C₃	—	4	4	no	—
354	C₂²×C₃	—	4	4	no	—
355	C₂²×C₃	—	4	8	no	—
356	C₂²×C₃	—	4	8	no	—
357	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
358	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
359	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
360	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
361	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
362	C₃×C₄	—	2	2	no	—
363	C₃×C₄	—	2	8	no	—
364	C₃×C₄	—	4	2	no	—
365	C₃×C₄	C₅×#121	1	4	yes	complemented
366	C₃×C₄	C₅×#127	1	4	yes	complemented
367	C₂×C₅	—	4	4	no	—
368	C₂×C₅	—	8	4	no	—
369	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
370	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
371	C₂×C₅	C₃×#535	1	1	yes	characteristic
372	C₂×C₅	C₃×D₄²	1	2	yes	—
373	C₂×C₅	C₃×#550	1	2	yes	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	4	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	2	8	no	—
379	C₂³	—	2	4	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	4	no	—
382	C₂³	—	2	8	no	—
383	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
384	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
385	D₄	—	2	8	no	—
386	D₄	—	4	32	no	—
387	D₄	—	4	8	no	—
388	D₄	—	4	8	no	—
389	D₄	—	4	8	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	8	no	—
396	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
397	C₂×C₄	C₂×C₃×C₅×D₄	1	8	yes	—
398	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
399	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
400	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
401	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
402	C₂×C₄	C₃×C₅×#41	1	2	yes	—
403	C₂×C₃	—	4	4	no	—
404	C₂×C₃	—	8	4	no	—
405	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
406	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
407	C₂×C₃	C₅×#535	1	1	yes	characteristic
408	C₂×C₃	C₅×D₄²	1	2	yes	—
409	C₂×C₃	C₅×#550	1	2	yes	—
410	C₅	C₃×#2541	1	1	yes	characteristic, direct product factor, Sylow
411	C₂²	—	2	4	no	—
412	C₂²	—	2	8	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	4	8	no	—
420	C₂²	—	4	8	no	—
421	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
422	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
423	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
424	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
425	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
426	C₄	—	2	2	no	—
427	C₄	—	2	8	no	—
428	C₄	—	4	2	no	—
429	C₄	C₃×C₅×#121	1	4	yes	complemented
430	C₄	C₃×C₅×#127	1	4	yes	complemented
431	C₃	C₅×#2541	1	1	yes	characteristic, direct product factor, Sylow
432	C₂	—	4	4	no	—
433	C₂	—	8	4	no	—
434	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
435	C₂	C₂×C₃×C₅×#127	1	1	yes	characteristic
436	C₂	C₃×C₅×#535	1	1	yes	characteristic
437	C₂	C₃×C₅×D₄²	1	2	yes	—
438	C₂	C₃×C₅×#550	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×#127	C₂	semidirect
2. C₂×C₃×C₅×#127	C₂	semidirect
3. C₂×C₃×C₅×#121	C₂	semidirect
4. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
5. C₃×C₅×#392	C₂	semidirect
6. C₃×C₅×#390	C₂	semidirect
7. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
8. C₅×#2541	C₃	direct (N × H)
26. C₃×#2541	C₅	direct (N × H)
27. C₂×C₅×#127	C₂×C₃	semidirect
28. C₂×C₅×#127	C₂×C₃	semidirect
29. C₂×C₅×#121	C₂×C₃	semidirect
30. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
31. C₅×#392	C₂×C₃	semidirect
32. C₅×#390	C₂×C₃	semidirect
33. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
48. C₂×C₃×C₅×D₄	D₄	semidirect
57. C₃×C₅×C₄⋊C₄	D₄	semidirect
61. C₃×C₄²×C₅	D₄	semidirect
62. C₂×C₃×#127	C₂×C₅	semidirect
63. C₂×C₃×#127	C₂×C₅	semidirect
64. C₂×C₃×#121	C₂×C₅	semidirect
65. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
66. C₃×#392	C₂×C₅	semidirect
67. C₃×#390	C₂×C₅	semidirect
68. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
86. #2541	C₃×C₅	direct (N × H)
147. C₂×C₅×D₄	C₃×D₄	semidirect
156. C₅×C₄⋊C₄	C₃×D₄	semidirect
160. C₄²×C₅	C₃×D₄	semidirect
161. C₂×#127	C₂×C₃×C₅	semidirect
162. C₂×#127	C₂×C₃×C₅	semidirect
163. C₂×#121	C₂×C₃×C₅	semidirect
164. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
165. #392	C₂×C₃×C₅	semidirect
166. #390	C₂×C₃×C₅	semidirect
167. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
186. C₃×C₄×C₅	#121	semidirect
187. C₃×C₄×C₅	#127	semidirect
202. C₂×C₃×D₄	C₅×D₄	semidirect
211. C₃×C₄⋊C₄	C₅×D₄	semidirect
215. C₃×C₄²	C₅×D₄	semidirect
316. C₄×C₅	C₃×#121	semidirect
317. C₄×C₅	C₃×#127	semidirect
332. C₂×D₄	C₃×C₅×D₄	semidirect
341. C₄⋊C₄	C₃×C₅×D₄	semidirect
345. C₄²	C₃×C₅×D₄	semidirect
346. C₃×C₅	#2541	direct (N × H)
365. C₃×C₄	C₅×#121	semidirect
366. C₃×C₄	C₅×#127	semidirect
410. C₅	C₃×#2541	direct (N × H)
429. C₄	C₃×C₅×#121	semidirect
430. C₄	C₃×C₅×#127	semidirect
431. C₃	C₅×#2541	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×#127	2
C₂×C₃×C₅×#121	2
C₂×C₃×C₄×C₅×D₄	2
C₃×C₅×#392	2
C₃×C₅×#390	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2541	3
C₃×#2541	5

Subgroups — C3×C5×#2541 #14275575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2541 #14275575