Subgroups — C₃×C₅×#3021 #14276055

Order 1920.

1472 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#535	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#454	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#453	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#421	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#413	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#3021	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅×2₋¹⁺⁴	—	2	2	no	—
10	C₃×C₅×2₋¹⁺⁴	C₂²	1	2	yes	complemented
11	C₃×C₅×H(5,𝔽₂)	—	2	2	no	—
12	C₃×C₅×H(5,𝔽₂)	—	2	2	no	—
13	C₃×C₅×H(5,𝔽₂)	C₂²	1	2	yes	complemented
14	C₂×C₃×C₅×#41	—	2	4	no	—
15	C₂×C₃×C₅×#41	—	2	2	no	—
16	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₅×AGL(1,ℤ/8)	—	2	4	no	—
20	C₃×C₅×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
21	C₂×C₃×C₅×SD₁₆	—	2	2	no	—
22	C₂×C₃×C₅×D₈	—	2	2	no	—
23	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	complemented
24	C₃×C₅×#127	C₂²	1	2	yes	complemented
25	C₃×C₅×#124	C₂²	1	2	yes	complemented
26	C₃×C₅×#121	—	2	2	no	—
27	C₃×C₅×#120	—	2	2	no	—
28	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×#104	C₂²	1	8	yes	complemented
30	C₃×C₅×#101	C₂²	1	2	yes	complemented
31	C₃×C₅×#100	C₂²	1	2	yes	complemented
32	C₃×#3021	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₅×#585	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	2	yes	complemented
35	C₅×#535	C₂×C₃	1	1	yes	characteristic, complemented
36	C₅×#454	C₂×C₃	1	4	yes	complemented
37	C₅×#453	C₂×C₃	1	4	yes	complemented
38	C₅×#421	C₂×C₃	1	2	yes	complemented
39	C₅×#413	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂⁴×C₃×C₅	—	2	1	no	—
41	C₃×C₅×#41	—	2	4	no	—
42	C₃×C₅×#41	—	2	8	no	—
43	C₃×C₅×#41	—	2	4	no	—
44	C₃×C₅×#41	—	2	4	no	—
45	C₃×C₅×#41	—	2	4	no	—
46	C₃×C₅×#41	—	2	2	no	—
47	C₃×C₅×#41	—	2	2	no	—
48	C₃×C₅×#41	—	2	4	no	—
49	C₃×C₅×#41	—	2	2	no	—
50	C₃×C₅×#41	—	2	2	no	—
51	C₃×C₅×#41	D₄	1	4	yes	complemented
52	C₃×C₅×#41	C₂³	1	4	yes	—
53	C₂×C₃×C₅×Q₈	—	2	2	no	—
54	C₂×C₃×C₅×Q₈	—	2	4	no	—
55	C₂×C₃×C₅×Q₈	D₄	1	2	yes	complemented
56	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₅×D₄	—	2	8	no	—
58	C₂×C₃×C₅×D₄	—	2	2	no	—
59	C₂×C₃×C₅×D₄	—	2	4	no	—
60	C₂×C₃×C₅×D₄	—	2	2	no	—
61	C₂×C₃×C₅×D₄	—	2	4	no	—
62	C₂×C₃×C₅×D₄	—	2	4	no	—
63	C₂×C₃×C₅×D₄	—	2	2	no	—
64	C₂×C₃×C₅×D₄	—	2	2	no	—
65	C₂×C₃×C₅×D₄	—	2	1	no	—
66	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
67	C₂×C₃×C₅×D₄	D₄	1	2	yes	complemented
68	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
69	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	—	2	4	no	—
71	C₂²×C₃×C₄×C₅	—	2	2	no	—
72	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
73	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₃×C₅×SD₁₆	—	2	8	no	—
75	C₃×C₅×D₈	—	2	8	no	—
76	C₃×C₅×M₁₆	—	2	2	no	—
77	C₃×C₅×M₁₆	C₂³	1	4	yes	—
78	C₂×C₃×C₅×C₈	—	2	2	no	—
79	C₃×C₅×C₄⋊C₄	—	2	1	no	—
80	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
81	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
82	C₃×C₄²×C₅	C₂³	1	2	yes	—
83	C₃×#585	C₂×C₅	1	1	yes	characteristic, complemented
84	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	2	yes	complemented
85	C₃×#535	C₂×C₅	1	1	yes	characteristic, complemented
86	C₃×#454	C₂×C₅	1	4	yes	complemented
87	C₃×#453	C₂×C₅	1	4	yes	complemented
88	C₃×#421	C₂×C₅	1	2	yes	complemented
89	C₃×#413	C₂×C₅	1	1	yes	characteristic, complemented
90	C₅×2₋¹⁺⁴	—	2	2	no	—
91	C₅×2₋¹⁺⁴	C₂²×C₃	1	2	yes	complemented
92	C₅×H(5,𝔽₂)	—	2	2	no	—
93	C₅×H(5,𝔽₂)	—	2	2	no	—
94	C₅×H(5,𝔽₂)	C₂²×C₃	1	2	yes	complemented
95	C₂×C₅×#41	—	2	4	no	—
96	C₂×C₅×#41	—	2	2	no	—
97	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
98	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
99	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
100	C₅×AGL(1,ℤ/8)	—	2	4	no	—
101	C₅×AGL(1,ℤ/8)	C₂²×C₃	1	8	yes	complemented
102	C₂×C₅×SD₁₆	—	2	2	no	—
103	C₂×C₅×D₈	—	2	2	no	—
104	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	complemented
105	C₅×#127	C₂²×C₃	1	2	yes	complemented
106	C₅×#124	C₂²×C₃	1	2	yes	complemented
107	C₅×#121	—	2	2	no	—
108	C₅×#120	—	2	2	no	—
109	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
110	C₅×#104	C₂²×C₃	1	8	yes	complemented
111	C₅×#101	C₂²×C₃	1	2	yes	complemented
112	C₅×#100	C₂²×C₃	1	2	yes	complemented
113	#3021	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
114	C₂³×C₃×C₅	—	2	4	no	—
115	C₂³×C₃×C₅	—	2	2	no	—
116	C₂³×C₃×C₅	—	2	2	no	—
117	C₂³×C₃×C₅	—	4	2	no	—
118	C₂³×C₃×C₅	—	8	2	no	—
119	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
120	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
121	C₃×C₅×Q₈	—	2	4	no	—
122	C₃×C₅×Q₈	—	2	2	no	—
123	C₃×C₅×Q₈	—	2	2	no	—
124	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
125	C₃×C₅×D₄	—	2	8	no	—
126	C₃×C₅×D₄	—	2	4	no	—
127	C₃×C₅×D₄	—	2	4	no	—
128	C₃×C₅×D₄	—	2	4	no	—
129	C₃×C₅×D₄	—	2	4	no	—
130	C₃×C₅×D₄	—	2	2	no	—
131	C₃×C₅×D₄	—	2	2	no	—
132	C₃×C₅×D₄	—	2	4	no	—
133	C₃×C₅×D₄	—	4	1	no	—
134	C₃×C₅×D₄	—	4	1	no	—
135	C₃×C₅×D₄	—	8	4	no	—
136	C₃×C₅×D₄	C₂×D₄	1	4	yes	—
137	C₂×C₃×C₄×C₅	—	2	4	no	—
138	C₂×C₃×C₄×C₅	—	2	8	no	—
139	C₂×C₃×C₄×C₅	—	2	2	no	—
140	C₂×C₃×C₄×C₅	—	2	4	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	4	no	—
144	C₂×C₃×C₄×C₅	—	2	2	no	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
146	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
147	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
148	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
149	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
150	C₃×C₅×C₈	—	2	4	no	—
151	C₃×2₋¹⁺⁴	—	2	2	no	—
152	C₃×2₋¹⁺⁴	C₂²×C₅	1	2	yes	complemented
153	C₃×H(5,𝔽₂)	—	2	2	no	—
154	C₃×H(5,𝔽₂)	—	2	2	no	—
155	C₃×H(5,𝔽₂)	C₂²×C₅	1	2	yes	complemented
156	C₂×C₃×#41	—	2	4	no	—
157	C₂×C₃×#41	—	2	2	no	—
158	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
159	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
160	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
161	C₃×AGL(1,ℤ/8)	—	2	4	no	—
162	C₃×AGL(1,ℤ/8)	C₂²×C₅	1	8	yes	complemented
163	C₂×C₃×SD₁₆	—	2	2	no	—
164	C₂×C₃×D₈	—	2	2	no	—
165	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	complemented
166	C₃×#127	C₂²×C₅	1	2	yes	complemented
167	C₃×#124	C₂²×C₅	1	2	yes	complemented
168	C₃×#121	—	2	2	no	—
169	C₃×#120	—	2	2	no	—
170	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
171	C₃×#104	C₂²×C₅	1	8	yes	complemented
172	C₃×#101	C₂²×C₅	1	2	yes	complemented
173	C₃×#100	C₂²×C₅	1	2	yes	complemented
174	C₂⁴×C₅	—	2	1	no	—
175	C₅×#41	—	2	4	no	—
176	C₅×#41	—	2	8	no	—
177	C₅×#41	—	2	4	no	—
178	C₅×#41	—	2	4	no	—
179	C₅×#41	—	2	4	no	—
180	C₅×#41	—	2	2	no	—
181	C₅×#41	—	2	2	no	—
182	C₅×#41	—	2	4	no	—
183	C₅×#41	—	2	2	no	—
184	C₅×#41	—	2	2	no	—
185	C₅×#41	C₃×D₄	1	4	yes	complemented
186	C₅×#41	C₂³×C₃	1	4	yes	—
187	C₂×C₅×Q₈	—	2	2	no	—
188	C₂×C₅×Q₈	—	2	4	no	—
189	C₂×C₅×Q₈	C₃×D₄	1	2	yes	complemented
190	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₅×D₄	—	2	8	no	—
192	C₂×C₅×D₄	—	2	2	no	—
193	C₂×C₅×D₄	—	2	4	no	—
194	C₂×C₅×D₄	—	2	2	no	—
195	C₂×C₅×D₄	—	2	4	no	—
196	C₂×C₅×D₄	—	2	4	no	—
197	C₂×C₅×D₄	—	2	2	no	—
198	C₂×C₅×D₄	—	2	2	no	—
199	C₂×C₅×D₄	—	2	1	no	—
200	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
201	C₂×C₅×D₄	C₃×D₄	1	2	yes	complemented
202	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
203	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
204	C₂²×C₄×C₅	—	2	4	no	—
205	C₂²×C₄×C₅	—	2	2	no	—
206	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
207	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
208	C₅×SD₁₆	—	2	8	no	—
209	C₅×D₈	—	2	8	no	—
210	C₅×M₁₆	—	2	2	no	—
211	C₅×M₁₆	C₂³×C₃	1	4	yes	—
212	C₂×C₅×C₈	—	2	2	no	—
213	C₅×C₄⋊C₄	—	2	1	no	—
214	C₅×C₂²⋊C₄	—	2	1	no	—
215	C₅×C₂²⋊C₄	—	2	4	no	—
216	C₄²×C₅	C₂³×C₃	1	2	yes	—
217	#585	C₂×C₃×C₅	1	1	yes	characteristic, complemented
218	C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	1	2	yes	complemented
219	#535	C₂×C₃×C₅	1	1	yes	characteristic, complemented
220	#454	C₂×C₃×C₅	1	4	yes	complemented
221	#453	C₂×C₃×C₅	1	4	yes	complemented
222	#421	C₂×C₃×C₅	1	2	yes	complemented
223	#413	C₂×C₃×C₅	1	1	yes	characteristic, complemented
224	C₂²×C₃×C₅	—	2	2	no	—
225	C₂²×C₃×C₅	—	2	4	no	—
226	C₂²×C₃×C₅	—	4	1	no	—
227	C₂²×C₃×C₅	—	4	2	no	—
228	C₂²×C₃×C₅	—	4	4	no	—
229	C₂²×C₃×C₅	—	4	2	no	—
230	C₂²×C₃×C₅	—	8	2	no	—
231	C₂²×C₃×C₅	—	8	4	no	—
232	C₂²×C₃×C₅	—	8	4	no	—
233	C₂²×C₃×C₅	#120	1	2	yes	—
234	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
235	C₃×C₄×C₅	—	2	4	no	—
236	C₃×C₄×C₅	—	2	2	no	—
237	C₃×C₄×C₅	—	4	2	no	—
238	C₃×C₄×C₅	#120	1	1	yes	characteristic
239	C₃×C₄×C₅	#120	1	1	yes	characteristic
240	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
241	C₂⁴×C₃	—	2	1	no	—
242	C₃×#41	—	2	4	no	—
243	C₃×#41	—	2	8	no	—
244	C₃×#41	—	2	4	no	—
245	C₃×#41	—	2	4	no	—
246	C₃×#41	—	2	4	no	—
247	C₃×#41	—	2	2	no	—
248	C₃×#41	—	2	2	no	—
249	C₃×#41	—	2	4	no	—
250	C₃×#41	—	2	2	no	—
251	C₃×#41	—	2	2	no	—
252	C₃×#41	C₅×D₄	1	4	yes	complemented
253	C₃×#41	C₂³×C₅	1	4	yes	—
254	C₂×C₃×Q₈	—	2	2	no	—
255	C₂×C₃×Q₈	—	2	4	no	—
256	C₂×C₃×Q₈	C₅×D₄	1	2	yes	complemented
257	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
258	C₂×C₃×D₄	—	2	8	no	—
259	C₂×C₃×D₄	—	2	2	no	—
260	C₂×C₃×D₄	—	2	4	no	—
261	C₂×C₃×D₄	—	2	2	no	—
262	C₂×C₃×D₄	—	2	4	no	—
263	C₂×C₃×D₄	—	2	4	no	—
264	C₂×C₃×D₄	—	2	2	no	—
265	C₂×C₃×D₄	—	2	2	no	—
266	C₂×C₃×D₄	—	2	1	no	—
267	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
268	C₂×C₃×D₄	C₅×D₄	1	2	yes	complemented
269	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
270	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
271	C₂²×C₃×C₄	—	2	4	no	—
272	C₂²×C₃×C₄	—	2	2	no	—
273	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
274	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
275	C₃×SD₁₆	—	2	8	no	—
276	C₃×D₈	—	2	8	no	—
277	C₃×M₁₆	—	2	2	no	—
278	C₃×M₁₆	C₂³×C₅	1	4	yes	—
279	C₂×C₃×C₈	—	2	2	no	—
280	C₃×C₄⋊C₄	—	2	1	no	—
281	C₃×C₂²⋊C₄	—	2	1	no	—
282	C₃×C₂²⋊C₄	—	2	4	no	—
283	C₃×C₄²	C₂³×C₅	1	2	yes	—
284	C₂³×C₅	—	2	4	no	—
285	C₂³×C₅	—	2	2	no	—
286	C₂³×C₅	—	2	2	no	—
287	C₂³×C₅	—	4	2	no	—
288	C₂³×C₅	—	8	2	no	—
289	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
290	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
291	C₅×Q₈	—	2	4	no	—
292	C₅×Q₈	—	2	2	no	—
293	C₅×Q₈	—	2	2	no	—
294	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
295	C₅×D₄	—	2	8	no	—
296	C₅×D₄	—	2	4	no	—
297	C₅×D₄	—	2	4	no	—
298	C₅×D₄	—	2	4	no	—
299	C₅×D₄	—	2	4	no	—
300	C₅×D₄	—	2	2	no	—
301	C₅×D₄	—	2	2	no	—
302	C₅×D₄	—	2	4	no	—
303	C₅×D₄	—	4	1	no	—
304	C₅×D₄	—	4	1	no	—
305	C₅×D₄	—	8	4	no	—
306	C₅×D₄	C₂×C₃×D₄	1	4	yes	—
307	C₂×C₄×C₅	—	2	4	no	—
308	C₂×C₄×C₅	—	2	8	no	—
309	C₂×C₄×C₅	—	2	2	no	—
310	C₂×C₄×C₅	—	2	4	no	—
311	C₂×C₄×C₅	—	2	2	no	—
312	C₂×C₄×C₅	—	2	2	no	—
313	C₂×C₄×C₅	—	2	4	no	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
316	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
317	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
318	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
319	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
320	C₅×C₈	—	2	4	no	—
321	2₋¹⁺⁴	—	2	2	no	—
322	2₋¹⁺⁴	C₂²×C₃×C₅	1	2	yes	complemented
323	H(5,𝔽₂)	—	2	2	no	—
324	H(5,𝔽₂)	—	2	2	no	—
325	H(5,𝔽₂)	C₂²×C₃×C₅	1	2	yes	complemented
326	C₂×#41	—	2	4	no	—
327	C₂×#41	—	2	2	no	—
328	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
329	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
330	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
331	AGL(1,ℤ/8)	—	2	4	no	—
332	AGL(1,ℤ/8)	C₂²×C₃×C₅	1	8	yes	complemented
333	C₂×SD₁₆	—	2	2	no	—
334	C₂×D₈	—	2	2	no	—
335	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	complemented
336	#127	C₂²×C₃×C₅	1	2	yes	complemented
337	#124	C₂²×C₃×C₅	1	2	yes	complemented
338	#121	—	2	2	no	—
339	#120	—	2	2	no	—
340	#117	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
341	#104	C₂²×C₃×C₅	1	8	yes	complemented
342	#101	C₂²×C₃×C₅	1	2	yes	complemented
343	#100	C₂²×C₃×C₅	1	2	yes	complemented
344	C₂×C₃×C₅	—	2	1	no	—
345	C₂×C₃×C₅	—	2	2	no	—
346	C₂×C₃×C₅	—	4	2	no	—
347	C₂×C₃×C₅	—	4	4	no	—
348	C₂×C₃×C₅	—	8	2	no	—
349	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
350	C₂³×C₃	—	2	4	no	—
351	C₂³×C₃	—	2	2	no	—
352	C₂³×C₃	—	2	2	no	—
353	C₂³×C₃	—	4	2	no	—
354	C₂³×C₃	—	8	2	no	—
355	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
356	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
357	C₃×Q₈	—	2	4	no	—
358	C₃×Q₈	—	2	2	no	—
359	C₃×Q₈	—	2	2	no	—
360	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
361	C₃×D₄	—	2	8	no	—
362	C₃×D₄	—	2	4	no	—
363	C₃×D₄	—	2	4	no	—
364	C₃×D₄	—	2	4	no	—
365	C₃×D₄	—	2	4	no	—
366	C₃×D₄	—	2	2	no	—
367	C₃×D₄	—	2	2	no	—
368	C₃×D₄	—	2	4	no	—
369	C₃×D₄	—	4	1	no	—
370	C₃×D₄	—	4	1	no	—
371	C₃×D₄	—	8	4	no	—
372	C₃×D₄	C₂×C₅×D₄	1	4	yes	—
373	C₂×C₃×C₄	—	2	4	no	—
374	C₂×C₃×C₄	—	2	8	no	—
375	C₂×C₃×C₄	—	2	2	no	—
376	C₂×C₃×C₄	—	2	4	no	—
377	C₂×C₃×C₄	—	2	2	no	—
378	C₂×C₃×C₄	—	2	2	no	—
379	C₂×C₃×C₄	—	2	4	no	—
380	C₂×C₃×C₄	—	2	2	no	—
381	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
382	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
383	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
384	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
385	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
386	C₃×C₈	—	2	4	no	—
387	C₂²×C₅	—	2	2	no	—
388	C₂²×C₅	—	2	4	no	—
389	C₂²×C₅	—	4	1	no	—
390	C₂²×C₅	—	4	2	no	—
391	C₂²×C₅	—	4	4	no	—
392	C₂²×C₅	—	4	2	no	—
393	C₂²×C₅	—	8	2	no	—
394	C₂²×C₅	—	8	4	no	—
395	C₂²×C₅	—	8	4	no	—
396	C₂²×C₅	C₃×#120	1	2	yes	—
397	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
398	C₄×C₅	—	2	4	no	—
399	C₄×C₅	—	2	2	no	—
400	C₄×C₅	—	4	2	no	—
401	C₄×C₅	C₃×#120	1	1	yes	characteristic
402	C₄×C₅	C₃×#120	1	1	yes	characteristic
403	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
404	C₂⁴	—	2	1	no	—
405	#41	—	2	4	no	—
406	#41	—	2	8	no	—
407	#41	—	2	4	no	—
408	#41	—	2	4	no	—
409	#41	—	2	4	no	—
410	#41	—	2	2	no	—
411	#41	—	2	2	no	—
412	#41	—	2	4	no	—
413	#41	—	2	2	no	—
414	#41	—	2	2	no	—
415	#41	C₃×C₅×D₄	1	4	yes	complemented
416	#41	C₂³×C₃×C₅	1	4	yes	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	4	no	—
419	C₂×Q₈	C₃×C₅×D₄	1	2	yes	complemented
420	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
431	C₂×D₄	C₃×C₅×D₄	1	2	yes	complemented
432	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
433	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
437	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
438	SD₁₆	—	2	8	no	—
439	D₈	—	2	8	no	—
440	M₁₆	—	2	2	no	—
441	M₁₆	C₂³×C₃×C₅	1	4	yes	—
442	C₂×C₈	—	2	2	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	2	4	no	—
446	C₄²	C₂³×C₃×C₅	1	2	yes	—
447	C₃×C₅	#3021	1	1	yes	characteristic, direct product factor, Hall
448	C₂²×C₃	—	2	2	no	—
449	C₂²×C₃	—	2	4	no	—
450	C₂²×C₃	—	4	1	no	—
451	C₂²×C₃	—	4	2	no	—
452	C₂²×C₃	—	4	4	no	—
453	C₂²×C₃	—	4	2	no	—
454	C₂²×C₃	—	8	2	no	—
455	C₂²×C₃	—	8	4	no	—
456	C₂²×C₃	—	8	4	no	—
457	C₂²×C₃	C₅×#120	1	2	yes	—
458	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
459	C₃×C₄	—	2	4	no	—
460	C₃×C₄	—	2	2	no	—
461	C₃×C₄	—	4	2	no	—
462	C₃×C₄	C₅×#120	1	1	yes	characteristic
463	C₃×C₄	C₅×#120	1	1	yes	characteristic
464	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
465	C₂×C₅	—	2	1	no	—
466	C₂×C₅	—	2	2	no	—
467	C₂×C₅	—	4	2	no	—
468	C₂×C₅	—	4	4	no	—
469	C₂×C₅	—	8	2	no	—
470	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
471	C₂³	—	2	4	no	—
472	C₂³	—	2	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	4	2	no	—
475	C₂³	—	8	2	no	—
476	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
477	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
478	Q₈	—	2	4	no	—
479	Q₈	—	2	2	no	—
480	Q₈	—	2	2	no	—
481	Q₈	C₂×C₃×C₅×D₄	1	4	yes	—
482	D₄	—	2	8	no	—
483	D₄	—	2	4	no	—
484	D₄	—	2	4	no	—
485	D₄	—	2	4	no	—
486	D₄	—	2	4	no	—
487	D₄	—	2	2	no	—
488	D₄	—	2	2	no	—
489	D₄	—	2	4	no	—
490	D₄	—	4	1	no	—
491	D₄	—	4	1	no	—
492	D₄	—	8	4	no	—
493	D₄	C₂×C₃×C₅×D₄	1	4	yes	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	8	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
503	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
504	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
505	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
506	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
507	C₈	—	2	4	no	—
508	C₂×C₃	—	2	1	no	—
509	C₂×C₃	—	2	2	no	—
510	C₂×C₃	—	4	2	no	—
511	C₂×C₃	—	4	4	no	—
512	C₂×C₃	—	8	2	no	—
513	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
514	C₅	C₃×#3021	1	1	yes	characteristic, direct product factor, Sylow
515	C₂²	—	2	2	no	—
516	C₂²	—	2	4	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	4	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	8	2	no	—
522	C₂²	—	8	4	no	—
523	C₂²	—	8	4	no	—
524	C₂²	C₃×C₅×#120	1	2	yes	—
525	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
526	C₄	—	2	4	no	—
527	C₄	—	2	2	no	—
528	C₄	—	4	2	no	—
529	C₄	C₃×C₅×#120	1	1	yes	characteristic
530	C₄	C₃×C₅×#120	1	1	yes	characteristic
531	C₄	C₂²×C₃×C₅×D₄	1	2	yes	—
532	C₃	C₅×#3021	1	1	yes	characteristic, direct product factor, Sylow
533	C₂	—	2	1	no	—
534	C₂	—	2	2	no	—
535	C₂	—	4	2	no	—
536	C₂	—	4	4	no	—
537	C₂	—	8	2	no	—
538	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃×C₅	C₂×#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₅×#585	C₂	semidirect
2. C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
3. C₃×C₅×#535	C₂	semidirect
4. C₃×C₅×#454	C₂	semidirect
5. C₃×C₅×#453	C₂	semidirect
6. C₃×C₅×#421	C₂	semidirect
7. C₃×C₅×#413	C₂	semidirect
8. C₅×#3021	C₃	direct (N × H)
10. C₃×C₅×2₋¹⁺⁴	C₂²	semidirect
13. C₃×C₅×H(5,𝔽₂)	C₂²	semidirect
18. C₂²×C₃×C₅×D₄	C₂²	semidirect
20. C₃×C₅×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂×C₃×C₅×M₁₆	C₂²	semidirect
24. C₃×C₅×#127	C₂²	semidirect
25. C₃×C₅×#124	C₂²	semidirect
28. C₃×C₅×#117	C₂²	semidirect
29. C₃×C₅×#104	C₂²	semidirect
30. C₃×C₅×#101	C₂²	semidirect
31. C₃×C₅×#100	C₂²	semidirect
32. C₃×#3021	C₅	direct (N × H)
33. C₅×#585	C₂×C₃	semidirect
34. C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
35. C₅×#535	C₂×C₃	semidirect
36. C₅×#454	C₂×C₃	semidirect
37. C₅×#453	C₂×C₃	semidirect
38. C₅×#421	C₂×C₃	semidirect
39. C₅×#413	C₂×C₃	semidirect
51. C₃×C₅×#41	D₄	semidirect
55. C₂×C₃×C₅×Q₈	D₄	semidirect
67. C₂×C₃×C₅×D₄	D₄	semidirect
83. C₃×#585	C₂×C₅	semidirect
84. C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
85. C₃×#535	C₂×C₅	semidirect
86. C₃×#454	C₂×C₅	semidirect
87. C₃×#453	C₂×C₅	semidirect
88. C₃×#421	C₂×C₅	semidirect
89. C₃×#413	C₂×C₅	semidirect
91. C₅×2₋¹⁺⁴	C₂²×C₃	semidirect
94. C₅×H(5,𝔽₂)	C₂²×C₃	semidirect
99. C₂²×C₅×D₄	C₂²×C₃	semidirect
101. C₅×AGL(1,ℤ/8)	C₂²×C₃	semidirect
104. C₂×C₅×M₁₆	C₂²×C₃	semidirect
105. C₅×#127	C₂²×C₃	semidirect
106. C₅×#124	C₂²×C₃	semidirect
109. C₅×#117	C₂²×C₃	semidirect
110. C₅×#104	C₂²×C₃	semidirect
111. C₅×#101	C₂²×C₃	semidirect
112. C₅×#100	C₂²×C₃	semidirect
113. #3021	C₃×C₅	direct (N × H)
152. C₃×2₋¹⁺⁴	C₂²×C₅	semidirect
155. C₃×H(5,𝔽₂)	C₂²×C₅	semidirect
160. C₂²×C₃×D₄	C₂²×C₅	semidirect
162. C₃×AGL(1,ℤ/8)	C₂²×C₅	semidirect
165. C₂×C₃×M₁₆	C₂²×C₅	semidirect
166. C₃×#127	C₂²×C₅	semidirect
167. C₃×#124	C₂²×C₅	semidirect
170. C₃×#117	C₂²×C₅	semidirect
171. C₃×#104	C₂²×C₅	semidirect
172. C₃×#101	C₂²×C₅	semidirect
173. C₃×#100	C₂²×C₅	semidirect
185. C₅×#41	C₃×D₄	semidirect
189. C₂×C₅×Q₈	C₃×D₄	semidirect
201. C₂×C₅×D₄	C₃×D₄	semidirect
217. #585	C₂×C₃×C₅	semidirect
218. C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	semidirect
219. #535	C₂×C₃×C₅	semidirect
220. #454	C₂×C₃×C₅	semidirect
221. #453	C₂×C₃×C₅	semidirect
222. #421	C₂×C₃×C₅	semidirect
223. #413	C₂×C₃×C₅	semidirect
252. C₃×#41	C₅×D₄	semidirect
256. C₂×C₃×Q₈	C₅×D₄	semidirect
268. C₂×C₃×D₄	C₅×D₄	semidirect
322. 2₋¹⁺⁴	C₂²×C₃×C₅	semidirect
325. H(5,𝔽₂)	C₂²×C₃×C₅	semidirect
330. C₂²×D₄	C₂²×C₃×C₅	semidirect
332. AGL(1,ℤ/8)	C₂²×C₃×C₅	semidirect
335. C₂×M₁₆	C₂²×C₃×C₅	semidirect
336. #127	C₂²×C₃×C₅	semidirect
337. #124	C₂²×C₃×C₅	semidirect
340. #117	C₂²×C₃×C₅	semidirect
341. #104	C₂²×C₃×C₅	semidirect
342. #101	C₂²×C₃×C₅	semidirect
343. #100	C₂²×C₃×C₅	semidirect
415. #41	C₃×C₅×D₄	semidirect
419. C₂×Q₈	C₃×C₅×D₄	semidirect
431. C₂×D₄	C₃×C₅×D₄	semidirect
447. C₃×C₅	#3021	direct (N × H)
514. C₅	C₃×#3021	direct (N × H)
532. C₃	C₅×#3021	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×#585	2
C₂×C₃×C₅×AGL(1,ℤ/8)	2
C₃×C₅×#535	2
C₃×C₅×#454	2
C₃×C₅×#453	2
C₃×C₅×#421	2
C₃×C₅×#413	2
C₅×#3021	3
C₃×#3021	5

Subgroups — C3×C5×#3021 #14276055

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3021 #14276055