Subgroups — C₃×C₅×#3020 #14276054

Order 1920.

1396 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#575	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#456	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#454	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#421	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×C₅×#101	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#3020	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅×2₋¹⁺⁴	—	2	4	no	—
10	C₃×C₅×2₋¹⁺⁴	—	2	2	no	—
11	C₃×C₅×2₋¹⁺⁴	C₂²	1	4	yes	—
12	C₂×C₃×C₅×#41	—	2	2	no	—
13	C₂×C₃×C₅×#41	—	2	2	no	—
14	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
15	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×Q₈	—	2	2	no	—
17	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×#137	—	2	2	no	—
19	C₃×C₅×#137	C₂²	1	4	yes	complemented
20	C₃×C₅×AGL(1,ℤ/8)	—	2	2	no	—
21	C₃×C₅×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
22	C₃×C₅×#135	—	2	4	no	—
23	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
24	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
25	C₃×C₅×#124	C₂²	1	2	yes	complemented
26	C₃×C₅×#123	—	2	2	no	—
27	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
28	C₃×C₅×#117	C₂²	1	1	yes	characteristic
29	C₃×C₅×#104	C₂²	1	8	yes	complemented
30	C₃×C₅×#101	C₂²	1	4	yes	complemented
31	C₃×#3020	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₅×2₋¹⁺⁴	C₂×C₃	1	1	yes	characteristic, complemented
33	C₅×#575	C₂×C₃	1	2	yes	complemented
34	C₅×#536	C₂×C₃	1	1	yes	characteristic, complemented
35	C₅×#456	C₂×C₃	1	4	yes	complemented
36	C₅×#454	C₂×C₃	1	4	yes	complemented
37	C₅×#421	C₂×C₃	1	2	yes	complemented
38	C₂×C₅×#101	C₂×C₃	1	1	yes	characteristic, complemented
39	C₃×C₅×#41	—	2	8	no	—
40	C₃×C₅×#41	—	2	8	no	—
41	C₃×C₅×#41	—	2	8	no	—
42	C₃×C₅×#41	—	2	8	no	—
43	C₃×C₅×#41	—	2	2	no	—
44	C₃×C₅×#41	—	2	2	no	—
45	C₃×C₅×#41	—	2	2	no	—
46	C₃×C₅×#41	—	2	2	no	—
47	C₃×C₅×#41	D₄	1	4	yes	—
48	C₃×C₅×#41	C₂³	1	4	yes	—
49	C₂×C₃×C₅×Q₈	—	2	2	no	—
50	C₂×C₃×C₅×Q₈	—	2	8	no	—
51	C₂×C₃×C₅×Q₈	—	2	8	no	—
52	C₂×C₃×C₅×Q₈	—	2	2	no	—
53	C₂×C₃×C₅×Q₈	—	2	2	no	—
54	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
55	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
56	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
58	C₂×C₃×C₅×D₄	—	2	2	no	—
59	C₂×C₃×C₅×D₄	—	2	2	no	—
60	C₂×C₃×C₅×D₄	—	2	1	no	—
61	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
62	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	—	2	4	no	—
64	C₂²×C₃×C₄×C₅	—	2	2	no	—
65	C₂²×C₃×C₄×C₅	—	2	1	no	—
66	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₃×C₅×Q₁₆	—	2	4	no	—
69	C₃×C₅×SD₁₆	—	2	4	no	—
70	C₃×C₅×SD₁₆	—	2	4	no	—
71	C₃×C₅×D₈	—	2	4	no	—
72	C₃×C₅×M₁₆	—	2	2	no	—
73	C₃×C₅×M₁₆	C₂³	1	4	yes	—
74	C₂×C₃×C₅×C₈	—	2	2	no	—
75	C₃×C₅×C₄⋊C₄	—	2	1	no	—
76	C₃×C₅×C₄⋊C₄	—	2	4	no	—
77	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
78	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
79	C₃×C₄²×C₅	C₂³	1	2	yes	—
80	C₂×C₃×2₋¹⁺⁴	C₂×C₅	1	1	yes	characteristic, complemented
81	C₃×#575	C₂×C₅	1	2	yes	complemented
82	C₃×#536	C₂×C₅	1	1	yes	characteristic, complemented
83	C₃×#456	C₂×C₅	1	4	yes	complemented
84	C₃×#454	C₂×C₅	1	4	yes	complemented
85	C₃×#421	C₂×C₅	1	2	yes	complemented
86	C₂×C₃×#101	C₂×C₅	1	1	yes	characteristic, complemented
87	C₅×2₋¹⁺⁴	—	2	4	no	—
88	C₅×2₋¹⁺⁴	—	2	2	no	—
89	C₅×2₋¹⁺⁴	C₂²×C₃	1	4	yes	—
90	C₂×C₅×#41	—	2	2	no	—
91	C₂×C₅×#41	—	2	2	no	—
92	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
93	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
94	C₂²×C₅×Q₈	—	2	2	no	—
95	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
96	C₅×#137	—	2	2	no	—
97	C₅×#137	C₂²×C₃	1	4	yes	complemented
98	C₅×AGL(1,ℤ/8)	—	2	2	no	—
99	C₅×AGL(1,ℤ/8)	C₂²×C₃	1	4	yes	complemented
100	C₅×#135	—	2	4	no	—
101	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
102	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
103	C₅×#124	C₂²×C₃	1	2	yes	complemented
104	C₅×#123	—	2	2	no	—
105	C₅×C₂²⋊Q₈	—	2	2	no	—
106	C₅×#117	C₂²×C₃	1	1	yes	characteristic
107	C₅×#104	C₂²×C₃	1	8	yes	complemented
108	C₅×#101	C₂²×C₃	1	4	yes	complemented
109	#3020	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	—	2	1	no	—
112	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
113	C₃×C₅×Q₈	—	2	8	no	—
114	C₃×C₅×Q₈	—	2	2	no	—
115	C₃×C₅×Q₈	—	2	4	no	—
116	C₃×C₅×Q₈	—	2	4	no	—
117	C₃×C₅×Q₈	—	2	2	no	—
118	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
119	C₃×C₅×D₄	—	2	8	no	—
120	C₃×C₅×D₄	—	2	4	no	—
121	C₃×C₅×D₄	—	2	4	no	—
122	C₃×C₅×D₄	—	2	2	no	—
123	C₃×C₅×D₄	—	2	2	no	—
124	C₃×C₅×D₄	—	4	1	no	—
125	C₃×C₅×D₄	—	4	1	no	—
126	C₃×C₅×D₄	C₂×D₄	1	4	yes	—
127	C₂×C₃×C₄×C₅	—	2	16	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	4	no	—
132	C₂×C₃×C₄×C₅	—	2	4	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	2	1	no	—
135	C₂×C₃×C₄×C₅	—	4	2	no	—
136	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
137	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
139	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
140	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
141	C₃×C₅×C₈	—	2	4	no	—
142	C₃×2₋¹⁺⁴	—	2	4	no	—
143	C₃×2₋¹⁺⁴	—	2	2	no	—
144	C₃×2₋¹⁺⁴	C₂²×C₅	1	4	yes	—
145	C₂×C₃×#41	—	2	2	no	—
146	C₂×C₃×#41	—	2	2	no	—
147	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
148	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
149	C₂²×C₃×Q₈	—	2	2	no	—
150	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
151	C₃×#137	—	2	2	no	—
152	C₃×#137	C₂²×C₅	1	4	yes	complemented
153	C₃×AGL(1,ℤ/8)	—	2	2	no	—
154	C₃×AGL(1,ℤ/8)	C₂²×C₅	1	4	yes	complemented
155	C₃×#135	—	2	4	no	—
156	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
157	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
158	C₃×#124	C₂²×C₅	1	2	yes	complemented
159	C₃×#123	—	2	2	no	—
160	C₃×C₂²⋊Q₈	—	2	2	no	—
161	C₃×#117	C₂²×C₅	1	1	yes	characteristic
162	C₃×#104	C₂²×C₅	1	8	yes	complemented
163	C₃×#101	C₂²×C₅	1	4	yes	complemented
164	C₅×#41	—	2	8	no	—
165	C₅×#41	—	2	8	no	—
166	C₅×#41	—	2	8	no	—
167	C₅×#41	—	2	8	no	—
168	C₅×#41	—	2	2	no	—
169	C₅×#41	—	2	2	no	—
170	C₅×#41	—	2	2	no	—
171	C₅×#41	—	2	2	no	—
172	C₅×#41	C₃×D₄	1	4	yes	—
173	C₅×#41	C₂³×C₃	1	4	yes	—
174	C₂×C₅×Q₈	—	2	2	no	—
175	C₂×C₅×Q₈	—	2	8	no	—
176	C₂×C₅×Q₈	—	2	8	no	—
177	C₂×C₅×Q₈	—	2	2	no	—
178	C₂×C₅×Q₈	—	2	2	no	—
179	C₂×C₅×Q₈	C₃×D₄	1	2	yes	—
180	C₂×C₅×Q₈	C₃×D₄	1	2	yes	—
181	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
182	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
183	C₂×C₅×D₄	—	2	2	no	—
184	C₂×C₅×D₄	—	2	2	no	—
185	C₂×C₅×D₄	—	2	1	no	—
186	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
187	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
188	C₂²×C₄×C₅	—	2	4	no	—
189	C₂²×C₄×C₅	—	2	2	no	—
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
192	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
193	C₅×Q₁₆	—	2	4	no	—
194	C₅×SD₁₆	—	2	4	no	—
195	C₅×SD₁₆	—	2	4	no	—
196	C₅×D₈	—	2	4	no	—
197	C₅×M₁₆	—	2	2	no	—
198	C₅×M₁₆	C₂³×C₃	1	4	yes	—
199	C₂×C₅×C₈	—	2	2	no	—
200	C₅×C₄⋊C₄	—	2	1	no	—
201	C₅×C₄⋊C₄	—	2	4	no	—
202	C₅×C₂²⋊C₄	—	2	1	no	—
203	C₅×C₂²⋊C₄	—	2	4	no	—
204	C₄²×C₅	C₂³×C₃	1	2	yes	—
205	C₂×2₋¹⁺⁴	C₂×C₃×C₅	1	1	yes	characteristic, complemented
206	#575	C₂×C₃×C₅	1	2	yes	complemented
207	#536	C₂×C₃×C₅	1	1	yes	characteristic, complemented
208	#456	C₂×C₃×C₅	1	4	yes	complemented
209	#454	C₂×C₃×C₅	1	4	yes	complemented
210	#421	C₂×C₃×C₅	1	2	yes	complemented
211	C₂×#101	C₂×C₃×C₅	1	1	yes	characteristic, complemented
212	C₂²×C₃×C₅	—	2	4	no	—
213	C₂²×C₃×C₅	—	4	1	no	—
214	C₂²×C₃×C₅	—	4	4	no	—
215	C₂²×C₃×C₅	—	4	2	no	—
216	C₂²×C₃×C₅	—	4	1	no	—
217	C₂²×C₃×C₅	#120	1	1	yes	characteristic
218	C₂²×C₃×C₅	#120	1	1	yes	characteristic
219	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
220	C₃×C₄×C₅	—	2	4	no	—
221	C₃×C₄×C₅	—	2	4	no	—
222	C₃×C₄×C₅	—	4	2	no	—
223	C₃×C₄×C₅	—	4	1	no	—
224	C₃×C₄×C₅	#120	1	2	yes	—
225	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
226	C₃×#41	—	2	8	no	—
227	C₃×#41	—	2	8	no	—
228	C₃×#41	—	2	8	no	—
229	C₃×#41	—	2	8	no	—
230	C₃×#41	—	2	2	no	—
231	C₃×#41	—	2	2	no	—
232	C₃×#41	—	2	2	no	—
233	C₃×#41	—	2	2	no	—
234	C₃×#41	C₅×D₄	1	4	yes	—
235	C₃×#41	C₂³×C₅	1	4	yes	—
236	C₂×C₃×Q₈	—	2	2	no	—
237	C₂×C₃×Q₈	—	2	8	no	—
238	C₂×C₃×Q₈	—	2	8	no	—
239	C₂×C₃×Q₈	—	2	2	no	—
240	C₂×C₃×Q₈	—	2	2	no	—
241	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
242	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
243	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
244	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
245	C₂×C₃×D₄	—	2	2	no	—
246	C₂×C₃×D₄	—	2	2	no	—
247	C₂×C₃×D₄	—	2	1	no	—
248	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
249	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
250	C₂²×C₃×C₄	—	2	4	no	—
251	C₂²×C₃×C₄	—	2	2	no	—
252	C₂²×C₃×C₄	—	2	1	no	—
253	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
254	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
255	C₃×Q₁₆	—	2	4	no	—
256	C₃×SD₁₆	—	2	4	no	—
257	C₃×SD₁₆	—	2	4	no	—
258	C₃×D₈	—	2	4	no	—
259	C₃×M₁₆	—	2	2	no	—
260	C₃×M₁₆	C₂³×C₅	1	4	yes	—
261	C₂×C₃×C₈	—	2	2	no	—
262	C₃×C₄⋊C₄	—	2	1	no	—
263	C₃×C₄⋊C₄	—	2	4	no	—
264	C₃×C₂²⋊C₄	—	2	1	no	—
265	C₃×C₂²⋊C₄	—	2	4	no	—
266	C₃×C₄²	C₂³×C₅	1	2	yes	—
267	C₂³×C₅	—	2	2	no	—
268	C₂³×C₅	—	2	1	no	—
269	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
270	C₅×Q₈	—	2	8	no	—
271	C₅×Q₈	—	2	2	no	—
272	C₅×Q₈	—	2	4	no	—
273	C₅×Q₈	—	2	4	no	—
274	C₅×Q₈	—	2	2	no	—
275	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
276	C₅×D₄	—	2	8	no	—
277	C₅×D₄	—	2	4	no	—
278	C₅×D₄	—	2	4	no	—
279	C₅×D₄	—	2	2	no	—
280	C₅×D₄	—	2	2	no	—
281	C₅×D₄	—	4	1	no	—
282	C₅×D₄	—	4	1	no	—
283	C₅×D₄	C₂×C₃×D₄	1	4	yes	—
284	C₂×C₄×C₅	—	2	16	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	4	no	—
289	C₂×C₄×C₅	—	2	4	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	4	2	no	—
293	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
294	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
295	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
296	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
297	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
298	C₅×C₈	—	2	4	no	—
299	2₋¹⁺⁴	—	2	4	no	—
300	2₋¹⁺⁴	—	2	2	no	—
301	2₋¹⁺⁴	C₂²×C₃×C₅	1	4	yes	—
302	C₂×#41	—	2	2	no	—
303	C₂×#41	—	2	2	no	—
304	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
305	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
306	C₂²×Q₈	—	2	2	no	—
307	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
308	#137	—	2	2	no	—
309	#137	C₂²×C₃×C₅	1	4	yes	complemented
310	AGL(1,ℤ/8)	—	2	2	no	—
311	AGL(1,ℤ/8)	C₂²×C₃×C₅	1	4	yes	complemented
312	#135	—	2	4	no	—
313	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
314	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
315	#124	C₂²×C₃×C₅	1	2	yes	complemented
316	#123	—	2	2	no	—
317	C₂²⋊Q₈	—	2	2	no	—
318	#117	C₂²×C₃×C₅	1	1	yes	characteristic
319	#104	C₂²×C₃×C₅	1	8	yes	complemented
320	#101	C₂²×C₃×C₅	1	4	yes	complemented
321	C₂×C₃×C₅	—	2	1	no	—
322	C₂×C₃×C₅	—	2	1	no	—
323	C₂×C₃×C₅	—	2	1	no	—
324	C₂×C₃×C₅	—	4	4	no	—
325	C₂×C₃×C₅	—	8	1	no	—
326	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
327	C₂³×C₃	—	2	2	no	—
328	C₂³×C₃	—	2	1	no	—
329	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
330	C₃×Q₈	—	2	8	no	—
331	C₃×Q₈	—	2	2	no	—
332	C₃×Q₈	—	2	4	no	—
333	C₃×Q₈	—	2	4	no	—
334	C₃×Q₈	—	2	2	no	—
335	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
336	C₃×D₄	—	2	8	no	—
337	C₃×D₄	—	2	4	no	—
338	C₃×D₄	—	2	4	no	—
339	C₃×D₄	—	2	2	no	—
340	C₃×D₄	—	2	2	no	—
341	C₃×D₄	—	4	1	no	—
342	C₃×D₄	—	4	1	no	—
343	C₃×D₄	C₂×C₅×D₄	1	4	yes	—
344	C₂×C₃×C₄	—	2	16	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	4	no	—
349	C₂×C₃×C₄	—	2	4	no	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	2	1	no	—
352	C₂×C₃×C₄	—	4	2	no	—
353	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
354	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
355	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
356	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
357	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
358	C₃×C₈	—	2	4	no	—
359	C₂²×C₅	—	2	4	no	—
360	C₂²×C₅	—	4	1	no	—
361	C₂²×C₅	—	4	4	no	—
362	C₂²×C₅	—	4	2	no	—
363	C₂²×C₅	—	4	1	no	—
364	C₂²×C₅	C₃×#120	1	1	yes	characteristic
365	C₂²×C₅	C₃×#120	1	1	yes	characteristic
366	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
367	C₄×C₅	—	2	4	no	—
368	C₄×C₅	—	2	4	no	—
369	C₄×C₅	—	4	2	no	—
370	C₄×C₅	—	4	1	no	—
371	C₄×C₅	C₃×#120	1	2	yes	—
372	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
373	#41	—	2	8	no	—
374	#41	—	2	8	no	—
375	#41	—	2	8	no	—
376	#41	—	2	8	no	—
377	#41	—	2	2	no	—
378	#41	—	2	2	no	—
379	#41	—	2	2	no	—
380	#41	—	2	2	no	—
381	#41	C₃×C₅×D₄	1	4	yes	—
382	#41	C₂³×C₃×C₅	1	4	yes	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	8	no	—
385	C₂×Q₈	—	2	8	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	C₃×C₅×D₄	1	2	yes	—
389	C₂×Q₈	C₃×C₅×D₄	1	2	yes	—
390	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
391	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
396	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
401	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
402	Q₁₆	—	2	4	no	—
403	SD₁₆	—	2	4	no	—
404	SD₁₆	—	2	4	no	—
405	D₈	—	2	4	no	—
406	M₁₆	—	2	2	no	—
407	M₁₆	C₂³×C₃×C₅	1	4	yes	—
408	C₂×C₈	—	2	2	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₄²	C₂³×C₃×C₅	1	2	yes	—
414	C₃×C₅	#3020	1	1	yes	characteristic, direct product factor, Hall
415	C₂²×C₃	—	2	4	no	—
416	C₂²×C₃	—	4	1	no	—
417	C₂²×C₃	—	4	4	no	—
418	C₂²×C₃	—	4	2	no	—
419	C₂²×C₃	—	4	1	no	—
420	C₂²×C₃	C₅×#120	1	1	yes	characteristic
421	C₂²×C₃	C₅×#120	1	1	yes	characteristic
422	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
423	C₃×C₄	—	2	4	no	—
424	C₃×C₄	—	2	4	no	—
425	C₃×C₄	—	4	2	no	—
426	C₃×C₄	—	4	1	no	—
427	C₃×C₄	C₅×#120	1	2	yes	—
428	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
429	C₂×C₅	—	2	1	no	—
430	C₂×C₅	—	2	1	no	—
431	C₂×C₅	—	2	1	no	—
432	C₂×C₅	—	4	4	no	—
433	C₂×C₅	—	8	1	no	—
434	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
435	C₂³	—	2	2	no	—
436	C₂³	—	2	1	no	—
437	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
438	Q₈	—	2	8	no	—
439	Q₈	—	2	2	no	—
440	Q₈	—	2	4	no	—
441	Q₈	—	2	4	no	—
442	Q₈	—	2	2	no	—
443	Q₈	C₂×C₃×C₅×D₄	1	4	yes	—
444	D₄	—	2	8	no	—
445	D₄	—	2	4	no	—
446	D₄	—	2	4	no	—
447	D₄	—	2	2	no	—
448	D₄	—	2	2	no	—
449	D₄	—	4	1	no	—
450	D₄	—	4	1	no	—
451	D₄	C₂×C₃×C₅×D₄	1	4	yes	—
452	C₂×C₄	—	2	16	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
462	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
463	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
464	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
465	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
466	C₈	—	2	4	no	—
467	C₂×C₃	—	2	1	no	—
468	C₂×C₃	—	2	1	no	—
469	C₂×C₃	—	2	1	no	—
470	C₂×C₃	—	4	4	no	—
471	C₂×C₃	—	8	1	no	—
472	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
473	C₅	C₃×#3020	1	1	yes	characteristic, direct product factor, Sylow
474	C₂²	—	2	4	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	1	no	—
479	C₂²	C₃×C₅×#120	1	1	yes	characteristic
480	C₂²	C₃×C₅×#120	1	1	yes	characteristic
481	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
482	C₄	—	2	4	no	—
483	C₄	—	2	4	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	1	no	—
486	C₄	C₃×C₅×#120	1	2	yes	—
487	C₄	C₂²×C₃×C₅×D₄	1	2	yes	—
488	C₃	C₅×#3020	1	1	yes	characteristic, direct product factor, Sylow
489	C₂	—	2	1	no	—
490	C₂	—	2	1	no	—
491	C₂	—	2	1	no	—
492	C₂	—	4	4	no	—
493	C₂	—	8	1	no	—
494	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. C₂×C₃×C₅×2₋¹⁺⁴	C₂	semidirect
2. C₃×C₅×#575	C₂	semidirect
3. C₃×C₅×#536	C₂	semidirect
4. C₃×C₅×#456	C₂	semidirect
5. C₃×C₅×#454	C₂	semidirect
6. C₃×C₅×#421	C₂	semidirect
7. C₂×C₃×C₅×#101	C₂	semidirect
8. C₅×#3020	C₃	direct (N × H)
19. C₃×C₅×#137	C₂²	semidirect
21. C₃×C₅×AGL(1,ℤ/8)	C₂²	semidirect
24. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
25. C₃×C₅×#124	C₂²	semidirect
29. C₃×C₅×#104	C₂²	semidirect
30. C₃×C₅×#101	C₂²	semidirect
31. C₃×#3020	C₅	direct (N × H)
32. C₂×C₅×2₋¹⁺⁴	C₂×C₃	semidirect
33. C₅×#575	C₂×C₃	semidirect
34. C₅×#536	C₂×C₃	semidirect
35. C₅×#456	C₂×C₃	semidirect
36. C₅×#454	C₂×C₃	semidirect
37. C₅×#421	C₂×C₃	semidirect
38. C₂×C₅×#101	C₂×C₃	semidirect
80. C₂×C₃×2₋¹⁺⁴	C₂×C₅	semidirect
81. C₃×#575	C₂×C₅	semidirect
82. C₃×#536	C₂×C₅	semidirect
83. C₃×#456	C₂×C₅	semidirect
84. C₃×#454	C₂×C₅	semidirect
85. C₃×#421	C₂×C₅	semidirect
86. C₂×C₃×#101	C₂×C₅	semidirect
97. C₅×#137	C₂²×C₃	semidirect
99. C₅×AGL(1,ℤ/8)	C₂²×C₃	semidirect
102. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
103. C₅×#124	C₂²×C₃	semidirect
107. C₅×#104	C₂²×C₃	semidirect
108. C₅×#101	C₂²×C₃	semidirect
109. #3020	C₃×C₅	direct (N × H)
152. C₃×#137	C₂²×C₅	semidirect
154. C₃×AGL(1,ℤ/8)	C₂²×C₅	semidirect
157. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
158. C₃×#124	C₂²×C₅	semidirect
162. C₃×#104	C₂²×C₅	semidirect
163. C₃×#101	C₂²×C₅	semidirect
205. C₂×2₋¹⁺⁴	C₂×C₃×C₅	semidirect
206. #575	C₂×C₃×C₅	semidirect
207. #536	C₂×C₃×C₅	semidirect
208. #456	C₂×C₃×C₅	semidirect
209. #454	C₂×C₃×C₅	semidirect
210. #421	C₂×C₃×C₅	semidirect
211. C₂×#101	C₂×C₃×C₅	semidirect
309. #137	C₂²×C₃×C₅	semidirect
311. AGL(1,ℤ/8)	C₂²×C₃×C₅	semidirect
314. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
315. #124	C₂²×C₃×C₅	semidirect
319. #104	C₂²×C₃×C₅	semidirect
320. #101	C₂²×C₃×C₅	semidirect
414. C₃×C₅	#3020	direct (N × H)
473. C₅	C₃×#3020	direct (N × H)
488. C₃	C₅×#3020	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×C₅×2₋¹⁺⁴	2
C₃×C₅×#575	2
C₃×C₅×#536	2
C₃×C₅×#456	2
C₃×C₅×#454	2
C₃×C₅×#421	2
C₂×C₃×C₅×#101	2
C₅×#3020	3
C₃×#3020	5

Subgroups — C3×C5×#3020 #14276054

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3020 #14276054