Subgroups — C₃×C₅×#3069 #14276103

Order 1920.

892 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#575	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#137	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#568	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#473	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#471	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×#430	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#413	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×C₅×#101	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3069	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×#137	—	2	2	no	—
15	C₃×C₅×#137	—	2	1	no	—
16	C₃×C₅×#137	—	2	2	no	—
17	C₃×C₅×#137	—	2	2	no	—
18	C₃×C₅×#137	C₂²	1	4	yes	—
19	C₃×C₅×#137	C₂²	1	2	yes	—
20	C₃×C₅×AGL(1,ℤ/8)	—	2	1	no	—
21	C₃×C₅×AGL(1,ℤ/8)	C₂²	1	2	yes	—
22	C₃×C₅×#135	—	2	2	no	—
23	C₂×C₃×C₅×Q₁₆	—	2	1	no	—
24	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	complemented
25	C₂×C₃×C₅×SD₁₆	—	2	1	no	—
26	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
27	C₃×C₅×#131	—	2	2	no	—
28	C₃×C₅×#131	C₂²	1	4	yes	—
29	C₂×C₃×C₅×M₁₆	—	2	2	no	—
30	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
34	C₃×C₅×#108	C₂²	1	4	yes	complemented
35	C₃×C₅×#101	C₂²	1	4	yes	complemented
36	C₃×C₅×#101	C₂²	1	2	yes	complemented
37	C₃×C₅×#100	C₂²	1	2	yes	complemented
38	C₃×#3069	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₅×#575	C₂×C₃	1	1	yes	characteristic
40	C₂×C₅×#137	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂×C₅×#137	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#568	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#473	C₂×C₃	1	4	yes	complemented
44	C₅×#471	C₂×C₃	1	4	yes	complemented
45	C₅×#430	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#413	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×C₅×#101	C₂×C₃	1	1	yes	characteristic, complemented
48	C₃×C₅×#41	—	2	1	no	—
49	C₃×C₅×#41	—	2	1	no	—
50	C₃×C₅×#41	—	2	1	no	—
51	C₃×C₅×#41	—	2	1	no	—
52	C₃×C₅×#41	—	2	1	no	—
53	C₃×C₅×#41	—	2	1	no	—
54	C₃×C₅×#41	D₄	1	2	yes	—
55	C₃×C₅×#41	C₂³	1	2	yes	—
56	C₂×C₃×C₅×Q₈	—	2	1	no	—
57	C₂×C₃×C₅×Q₈	—	2	1	no	—
58	C₂×C₃×C₅×Q₈	—	2	1	no	—
59	C₂×C₃×C₅×Q₈	—	2	1	no	—
60	C₂×C₃×C₅×Q₈	—	2	1	no	—
61	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
62	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
63	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×D₄	—	2	1	no	—
65	C₂×C₃×C₅×D₄	—	2	1	no	—
66	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
67	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	—	2	1	no	—
69	C₂²×C₃×C₄×C₅	—	2	1	no	—
70	C₂²×C₃×C₄×C₅	—	2	1	no	—
71	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₃×C₅×Q₁₆	—	2	4	no	—
73	C₃×C₅×Q₁₆	—	2	2	no	—
74	C₃×C₅×Q₁₆	—	2	4	no	—
75	C₃×C₅×SD₁₆	—	2	2	no	—
76	C₃×C₅×SD₁₆	—	2	4	no	—
77	C₃×C₅×SD₁₆	—	2	2	no	—
78	C₃×C₅×SD₁₆	—	2	4	no	—
79	C₃×C₅×D₈	—	2	2	no	—
80	C₃×C₅×M₁₆	—	2	1	no	—
81	C₃×C₅×M₁₆	—	2	1	no	—
82	C₃×C₅×M₁₆	—	2	1	no	—
83	C₃×C₅×M₁₆	—	2	4	no	—
84	C₃×C₅×M₁₆	D₄	1	2	yes	—
85	C₃×C₅×M₁₆	D₄	1	2	yes	—
86	C₃×C₅×M₁₆	C₂³	1	2	yes	—
87	C₃×C₅×M₁₆	C₂³	1	2	yes	—
88	C₃×C₅×M₁₆	C₂³	1	2	yes	—
89	C₂×C₃×C₅×C₈	—	2	1	no	—
90	C₂×C₃×C₅×C₈	—	2	1	no	—
91	C₂×C₃×C₅×C₈	—	2	1	no	—
92	C₂×C₃×C₅×C₈	—	2	4	no	—
93	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
94	C₃×#575	C₂×C₅	1	1	yes	characteristic
95	C₂×C₃×#137	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂×C₃×#137	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#568	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#473	C₂×C₅	1	4	yes	complemented
99	C₃×#471	C₂×C₅	1	4	yes	complemented
100	C₃×#430	C₂×C₅	1	1	yes	characteristic, complemented
101	C₃×#413	C₂×C₅	1	1	yes	characteristic, complemented
102	C₂×C₃×#101	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
105	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
106	C₅×#137	—	2	2	no	—
107	C₅×#137	—	2	1	no	—
108	C₅×#137	—	2	2	no	—
109	C₅×#137	—	2	2	no	—
110	C₅×#137	C₂²×C₃	1	4	yes	—
111	C₅×#137	C₂²×C₃	1	2	yes	—
112	C₅×AGL(1,ℤ/8)	—	2	1	no	—
113	C₅×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	—
114	C₅×#135	—	2	2	no	—
115	C₂×C₅×Q₁₆	—	2	1	no	—
116	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	complemented
117	C₂×C₅×SD₁₆	—	2	1	no	—
118	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
119	C₅×#131	—	2	2	no	—
120	C₅×#131	C₂²×C₃	1	4	yes	—
121	C₂×C₅×M₁₆	—	2	2	no	—
122	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
126	C₅×#108	C₂²×C₃	1	4	yes	complemented
127	C₅×#101	C₂²×C₃	1	4	yes	complemented
128	C₅×#101	C₂²×C₃	1	2	yes	complemented
129	C₅×#100	C₂²×C₃	1	2	yes	complemented
130	#3069	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
131	C₂³×C₃×C₅	—	2	1	no	—
132	C₂³×C₃×C₅	—	2	1	no	—
133	C₂³×C₃×C₅	#41	1	1	yes	characteristic
134	C₃×C₅×Q₈	—	2	1	no	—
135	C₃×C₅×Q₈	—	2	2	no	—
136	C₃×C₅×Q₈	—	2	2	no	—
137	C₃×C₅×Q₈	—	2	1	no	—
138	C₃×C₅×Q₈	—	2	1	no	—
139	C₃×C₅×Q₈	—	4	1	no	—
140	C₃×C₅×Q₈	—	4	1	no	—
141	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
142	C₃×C₅×D₄	—	2	2	no	—
143	C₃×C₅×D₄	—	2	2	no	—
144	C₃×C₅×D₄	—	2	1	no	—
145	C₃×C₅×D₄	—	2	1	no	—
146	C₃×C₅×D₄	—	2	1	no	—
147	C₃×C₅×D₄	—	4	1	no	—
148	C₃×C₅×D₄	—	4	1	no	—
149	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	—	2	1	no	—
154	C₂×C₃×C₄×C₅	—	2	2	no	—
155	C₂×C₃×C₄×C₅	—	4	1	no	—
156	C₂×C₃×C₄×C₅	—	4	1	no	—
157	C₂×C₃×C₄×C₅	—	4	1	no	—
158	C₂×C₃×C₄×C₅	—	4	1	no	—
159	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
161	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
162	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
164	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
165	C₃×C₅×C₈	—	2	2	no	—
166	C₃×C₅×C₈	—	2	2	no	—
167	C₃×C₅×C₈	—	2	2	no	—
168	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
169	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
170	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
171	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
172	C₃×#137	—	2	2	no	—
173	C₃×#137	—	2	1	no	—
174	C₃×#137	—	2	2	no	—
175	C₃×#137	—	2	2	no	—
176	C₃×#137	C₂²×C₅	1	4	yes	—
177	C₃×#137	C₂²×C₅	1	2	yes	—
178	C₃×AGL(1,ℤ/8)	—	2	1	no	—
179	C₃×AGL(1,ℤ/8)	C₂²×C₅	1	2	yes	—
180	C₃×#135	—	2	2	no	—
181	C₂×C₃×Q₁₆	—	2	1	no	—
182	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	complemented
183	C₂×C₃×SD₁₆	—	2	1	no	—
184	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
185	C₃×#131	—	2	2	no	—
186	C₃×#131	C₂²×C₅	1	4	yes	—
187	C₂×C₃×M₁₆	—	2	2	no	—
188	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
189	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
190	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
191	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
192	C₃×#108	C₂²×C₅	1	4	yes	complemented
193	C₃×#101	C₂²×C₅	1	4	yes	complemented
194	C₃×#101	C₂²×C₅	1	2	yes	complemented
195	C₃×#100	C₂²×C₅	1	2	yes	complemented
196	C₅×#41	—	2	1	no	—
197	C₅×#41	—	2	1	no	—
198	C₅×#41	—	2	1	no	—
199	C₅×#41	—	2	1	no	—
200	C₅×#41	—	2	1	no	—
201	C₅×#41	—	2	1	no	—
202	C₅×#41	C₃×D₄	1	2	yes	—
203	C₅×#41	C₂³×C₃	1	2	yes	—
204	C₂×C₅×Q₈	—	2	1	no	—
205	C₂×C₅×Q₈	—	2	1	no	—
206	C₂×C₅×Q₈	—	2	1	no	—
207	C₂×C₅×Q₈	—	2	1	no	—
208	C₂×C₅×Q₈	—	2	1	no	—
209	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
210	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
211	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
212	C₂×C₅×D₄	—	2	1	no	—
213	C₂×C₅×D₄	—	2	1	no	—
214	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
215	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
216	C₂²×C₄×C₅	—	2	1	no	—
217	C₂²×C₄×C₅	—	2	1	no	—
218	C₂²×C₄×C₅	—	2	1	no	—
219	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
220	C₅×Q₁₆	—	2	4	no	—
221	C₅×Q₁₆	—	2	2	no	—
222	C₅×Q₁₆	—	2	4	no	—
223	C₅×SD₁₆	—	2	2	no	—
224	C₅×SD₁₆	—	2	4	no	—
225	C₅×SD₁₆	—	2	2	no	—
226	C₅×SD₁₆	—	2	4	no	—
227	C₅×D₈	—	2	2	no	—
228	C₅×M₁₆	—	2	1	no	—
229	C₅×M₁₆	—	2	1	no	—
230	C₅×M₁₆	—	2	1	no	—
231	C₅×M₁₆	—	2	4	no	—
232	C₅×M₁₆	C₃×D₄	1	2	yes	—
233	C₅×M₁₆	C₃×D₄	1	2	yes	—
234	C₅×M₁₆	C₂³×C₃	1	2	yes	—
235	C₅×M₁₆	C₂³×C₃	1	2	yes	—
236	C₅×M₁₆	C₂³×C₃	1	2	yes	—
237	C₂×C₅×C₈	—	2	1	no	—
238	C₂×C₅×C₈	—	2	1	no	—
239	C₂×C₅×C₈	—	2	1	no	—
240	C₂×C₅×C₈	—	2	4	no	—
241	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
242	#575	C₂×C₃×C₅	1	1	yes	characteristic
243	C₂×#137	C₂×C₃×C₅	1	1	yes	characteristic, complemented
244	C₂×#137	C₂×C₃×C₅	1	1	yes	characteristic, complemented
245	#568	C₂×C₃×C₅	1	1	yes	characteristic, complemented
246	#473	C₂×C₃×C₅	1	4	yes	complemented
247	#471	C₂×C₃×C₅	1	4	yes	complemented
248	#430	C₂×C₃×C₅	1	1	yes	characteristic, complemented
249	#413	C₂×C₃×C₅	1	1	yes	characteristic, complemented
250	C₂×#101	C₂×C₃×C₅	1	1	yes	characteristic, complemented
251	C₂²×C₃×C₅	—	2	2	no	—
252	C₂²×C₃×C₅	—	4	1	no	—
253	C₂²×C₃×C₅	—	4	1	no	—
254	C₂²×C₃×C₅	—	8	1	no	—
255	C₂²×C₃×C₅	—	8	1	no	—
256	C₂²×C₃×C₅	#121	1	1	yes	characteristic
257	C₂²×C₃×C₅	#121	1	1	yes	characteristic
258	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
259	C₃×C₄×C₅	—	2	2	no	—
260	C₃×C₄×C₅	—	4	1	no	—
261	C₃×C₄×C₅	—	4	2	no	—
262	C₃×C₄×C₅	#121	1	1	yes	characteristic
263	C₃×C₄×C₅	#121	1	1	yes	characteristic
264	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
265	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
266	C₃×#41	—	2	1	no	—
267	C₃×#41	—	2	1	no	—
268	C₃×#41	—	2	1	no	—
269	C₃×#41	—	2	1	no	—
270	C₃×#41	—	2	1	no	—
271	C₃×#41	—	2	1	no	—
272	C₃×#41	C₅×D₄	1	2	yes	—
273	C₃×#41	C₂³×C₅	1	2	yes	—
274	C₂×C₃×Q₈	—	2	1	no	—
275	C₂×C₃×Q₈	—	2	1	no	—
276	C₂×C₃×Q₈	—	2	1	no	—
277	C₂×C₃×Q₈	—	2	1	no	—
278	C₂×C₃×Q₈	—	2	1	no	—
279	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
280	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
281	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
282	C₂×C₃×D₄	—	2	1	no	—
283	C₂×C₃×D₄	—	2	1	no	—
284	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
285	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
286	C₂²×C₃×C₄	—	2	1	no	—
287	C₂²×C₃×C₄	—	2	1	no	—
288	C₂²×C₃×C₄	—	2	1	no	—
289	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
290	C₃×Q₁₆	—	2	4	no	—
291	C₃×Q₁₆	—	2	2	no	—
292	C₃×Q₁₆	—	2	4	no	—
293	C₃×SD₁₆	—	2	2	no	—
294	C₃×SD₁₆	—	2	4	no	—
295	C₃×SD₁₆	—	2	2	no	—
296	C₃×SD₁₆	—	2	4	no	—
297	C₃×D₈	—	2	2	no	—
298	C₃×M₁₆	—	2	1	no	—
299	C₃×M₁₆	—	2	1	no	—
300	C₃×M₁₆	—	2	1	no	—
301	C₃×M₁₆	—	2	4	no	—
302	C₃×M₁₆	C₅×D₄	1	2	yes	—
303	C₃×M₁₆	C₅×D₄	1	2	yes	—
304	C₃×M₁₆	C₂³×C₅	1	2	yes	—
305	C₃×M₁₆	C₂³×C₅	1	2	yes	—
306	C₃×M₁₆	C₂³×C₅	1	2	yes	—
307	C₂×C₃×C₈	—	2	1	no	—
308	C₂×C₃×C₈	—	2	1	no	—
309	C₂×C₃×C₈	—	2	1	no	—
310	C₂×C₃×C₈	—	2	4	no	—
311	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
312	C₂³×C₅	—	2	1	no	—
313	C₂³×C₅	—	2	1	no	—
314	C₂³×C₅	C₃×#41	1	1	yes	characteristic
315	C₅×Q₈	—	2	1	no	—
316	C₅×Q₈	—	2	2	no	—
317	C₅×Q₈	—	2	2	no	—
318	C₅×Q₈	—	2	1	no	—
319	C₅×Q₈	—	2	1	no	—
320	C₅×Q₈	—	4	1	no	—
321	C₅×Q₈	—	4	1	no	—
322	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
323	C₅×D₄	—	2	2	no	—
324	C₅×D₄	—	2	2	no	—
325	C₅×D₄	—	2	1	no	—
326	C₅×D₄	—	2	1	no	—
327	C₅×D₄	—	2	1	no	—
328	C₅×D₄	—	4	1	no	—
329	C₅×D₄	—	4	1	no	—
330	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
331	C₂×C₄×C₅	—	2	1	no	—
332	C₂×C₄×C₅	—	2	2	no	—
333	C₂×C₄×C₅	—	2	2	no	—
334	C₂×C₄×C₅	—	2	1	no	—
335	C₂×C₄×C₅	—	2	2	no	—
336	C₂×C₄×C₅	—	4	1	no	—
337	C₂×C₄×C₅	—	4	1	no	—
338	C₂×C₄×C₅	—	4	1	no	—
339	C₂×C₄×C₅	—	4	1	no	—
340	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
341	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
342	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
343	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
344	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
345	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
346	C₅×C₈	—	2	2	no	—
347	C₅×C₈	—	2	2	no	—
348	C₅×C₈	—	2	2	no	—
349	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
350	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
351	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
352	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
353	#137	—	2	2	no	—
354	#137	—	2	1	no	—
355	#137	—	2	2	no	—
356	#137	—	2	2	no	—
357	#137	C₂²×C₃×C₅	1	4	yes	—
358	#137	C₂²×C₃×C₅	1	2	yes	—
359	AGL(1,ℤ/8)	—	2	1	no	—
360	AGL(1,ℤ/8)	C₂²×C₃×C₅	1	2	yes	—
361	#135	—	2	2	no	—
362	C₂×Q₁₆	—	2	1	no	—
363	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	complemented
364	C₂×SD₁₆	—	2	1	no	—
365	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
366	#131	—	2	2	no	—
367	#131	C₂²×C₃×C₅	1	4	yes	—
368	C₂×M₁₆	—	2	2	no	—
369	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
370	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
371	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
372	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
373	#108	C₂²×C₃×C₅	1	4	yes	complemented
374	#101	C₂²×C₃×C₅	1	4	yes	complemented
375	#101	C₂²×C₃×C₅	1	2	yes	complemented
376	#100	C₂²×C₃×C₅	1	2	yes	complemented
377	C₂×C₃×C₅	—	2	1	no	—
378	C₂×C₃×C₅	—	2	1	no	—
379	C₂×C₃×C₅	—	2	1	no	—
380	C₂×C₃×C₅	—	4	2	no	—
381	C₂×C₃×C₅	—	8	1	no	—
382	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
383	C₂³×C₃	—	2	1	no	—
384	C₂³×C₃	—	2	1	no	—
385	C₂³×C₃	C₅×#41	1	1	yes	characteristic
386	C₃×Q₈	—	2	1	no	—
387	C₃×Q₈	—	2	2	no	—
388	C₃×Q₈	—	2	2	no	—
389	C₃×Q₈	—	2	1	no	—
390	C₃×Q₈	—	2	1	no	—
391	C₃×Q₈	—	4	1	no	—
392	C₃×Q₈	—	4	1	no	—
393	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
394	C₃×D₄	—	2	2	no	—
395	C₃×D₄	—	2	2	no	—
396	C₃×D₄	—	2	1	no	—
397	C₃×D₄	—	2	1	no	—
398	C₃×D₄	—	2	1	no	—
399	C₃×D₄	—	4	1	no	—
400	C₃×D₄	—	4	1	no	—
401	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
402	C₂×C₃×C₄	—	2	1	no	—
403	C₂×C₃×C₄	—	2	2	no	—
404	C₂×C₃×C₄	—	2	2	no	—
405	C₂×C₃×C₄	—	2	1	no	—
406	C₂×C₃×C₄	—	2	2	no	—
407	C₂×C₃×C₄	—	4	1	no	—
408	C₂×C₃×C₄	—	4	1	no	—
409	C₂×C₃×C₄	—	4	1	no	—
410	C₂×C₃×C₄	—	4	1	no	—
411	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
412	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
413	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
414	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
415	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
416	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
417	C₃×C₈	—	2	2	no	—
418	C₃×C₈	—	2	2	no	—
419	C₃×C₈	—	2	2	no	—
420	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
421	C₂²×C₅	—	2	2	no	—
422	C₂²×C₅	—	4	1	no	—
423	C₂²×C₅	—	4	1	no	—
424	C₂²×C₅	—	8	1	no	—
425	C₂²×C₅	—	8	1	no	—
426	C₂²×C₅	C₃×#121	1	1	yes	characteristic
427	C₂²×C₅	C₃×#121	1	1	yes	characteristic
428	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
429	C₄×C₅	—	2	2	no	—
430	C₄×C₅	—	4	1	no	—
431	C₄×C₅	—	4	2	no	—
432	C₄×C₅	C₃×#121	1	1	yes	characteristic
433	C₄×C₅	C₃×#121	1	1	yes	characteristic
434	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
435	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
436	#41	—	2	1	no	—
437	#41	—	2	1	no	—
438	#41	—	2	1	no	—
439	#41	—	2	1	no	—
440	#41	—	2	1	no	—
441	#41	—	2	1	no	—
442	#41	C₃×C₅×D₄	1	2	yes	—
443	#41	C₂³×C₃×C₅	1	2	yes	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
450	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
451	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
455	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
460	Q₁₆	—	2	4	no	—
461	Q₁₆	—	2	2	no	—
462	Q₁₆	—	2	4	no	—
463	SD₁₆	—	2	2	no	—
464	SD₁₆	—	2	4	no	—
465	SD₁₆	—	2	2	no	—
466	SD₁₆	—	2	4	no	—
467	D₈	—	2	2	no	—
468	M₁₆	—	2	1	no	—
469	M₁₆	—	2	1	no	—
470	M₁₆	—	2	1	no	—
471	M₁₆	—	2	4	no	—
472	M₁₆	C₃×C₅×D₄	1	2	yes	—
473	M₁₆	C₃×C₅×D₄	1	2	yes	—
474	M₁₆	C₂³×C₃×C₅	1	2	yes	—
475	M₁₆	C₂³×C₃×C₅	1	2	yes	—
476	M₁₆	C₂³×C₃×C₅	1	2	yes	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	4	no	—
481	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
482	C₃×C₅	#3069	1	1	yes	characteristic, direct product factor, Hall
483	C₂²×C₃	—	2	2	no	—
484	C₂²×C₃	—	4	1	no	—
485	C₂²×C₃	—	4	1	no	—
486	C₂²×C₃	—	8	1	no	—
487	C₂²×C₃	—	8	1	no	—
488	C₂²×C₃	C₅×#121	1	1	yes	characteristic
489	C₂²×C₃	C₅×#121	1	1	yes	characteristic
490	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
491	C₃×C₄	—	2	2	no	—
492	C₃×C₄	—	4	1	no	—
493	C₃×C₄	—	4	2	no	—
494	C₃×C₄	C₅×#121	1	1	yes	characteristic
495	C₃×C₄	C₅×#121	1	1	yes	characteristic
496	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
497	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
498	C₂×C₅	—	2	1	no	—
499	C₂×C₅	—	2	1	no	—
500	C₂×C₅	—	2	1	no	—
501	C₂×C₅	—	4	2	no	—
502	C₂×C₅	—	8	1	no	—
503	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
504	C₂³	—	2	1	no	—
505	C₂³	—	2	1	no	—
506	C₂³	C₃×C₅×#41	1	1	yes	characteristic
507	Q₈	—	2	1	no	—
508	Q₈	—	2	2	no	—
509	Q₈	—	2	2	no	—
510	Q₈	—	2	1	no	—
511	Q₈	—	2	1	no	—
512	Q₈	—	4	1	no	—
513	Q₈	—	4	1	no	—
514	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
515	D₄	—	2	2	no	—
516	D₄	—	2	2	no	—
517	D₄	—	2	1	no	—
518	D₄	—	2	1	no	—
519	D₄	—	2	1	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	1	no	—
522	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
533	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
534	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
535	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
536	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
537	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
538	C₈	—	2	2	no	—
539	C₈	—	2	2	no	—
540	C₈	—	2	2	no	—
541	C₈	C₂×C₃×C₅×D₄	1	4	yes	—
542	C₂×C₃	—	2	1	no	—
543	C₂×C₃	—	2	1	no	—
544	C₂×C₃	—	2	1	no	—
545	C₂×C₃	—	4	2	no	—
546	C₂×C₃	—	8	1	no	—
547	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
548	C₅	C₃×#3069	1	1	yes	characteristic, direct product factor, Sylow
549	C₂²	—	2	2	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	8	1	no	—
553	C₂²	—	8	1	no	—
554	C₂²	C₃×C₅×#121	1	1	yes	characteristic
555	C₂²	C₃×C₅×#121	1	1	yes	characteristic
556	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
557	C₄	—	2	2	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	2	no	—
560	C₄	C₃×C₅×#121	1	1	yes	characteristic
561	C₄	C₃×C₅×#121	1	1	yes	characteristic
562	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
563	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
564	C₃	C₅×#3069	1	1	yes	characteristic, direct product factor, Sylow
565	C₂	—	2	1	no	—
566	C₂	—	2	1	no	—
567	C₂	—	2	1	no	—
568	C₂	—	4	2	no	—
569	C₂	—	8	1	no	—
570	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃×C₅	C₂×#121
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₃×C₅×#575	C₂
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
2. C₂×C₃×C₅×#137	C₂	semidirect
3. C₂×C₃×C₅×#137	C₂	semidirect
4. C₃×C₅×#568	C₂	semidirect
5. C₃×C₅×#473	C₂	semidirect
6. C₃×C₅×#471	C₂	semidirect
7. C₃×C₅×#430	C₂	semidirect
8. C₃×C₅×#413	C₂	semidirect
9. C₂×C₃×C₅×#101	C₂	semidirect
10. C₅×#3069	C₃	direct (N × H)
24. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
26. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
34. C₃×C₅×#108	C₂²	semidirect
35. C₃×C₅×#101	C₂²	semidirect
36. C₃×C₅×#101	C₂²	semidirect
37. C₃×C₅×#100	C₂²	semidirect
38. C₃×#3069	C₅	direct (N × H)
40. C₂×C₅×#137	C₂×C₃	semidirect
41. C₂×C₅×#137	C₂×C₃	semidirect
42. C₅×#568	C₂×C₃	semidirect
43. C₅×#473	C₂×C₃	semidirect
44. C₅×#471	C₂×C₃	semidirect
45. C₅×#430	C₂×C₃	semidirect
46. C₅×#413	C₂×C₃	semidirect
47. C₂×C₅×#101	C₂×C₃	semidirect
95. C₂×C₃×#137	C₂×C₅	semidirect
96. C₂×C₃×#137	C₂×C₅	semidirect
97. C₃×#568	C₂×C₅	semidirect
98. C₃×#473	C₂×C₅	semidirect
99. C₃×#471	C₂×C₅	semidirect
100. C₃×#430	C₂×C₅	semidirect
101. C₃×#413	C₂×C₅	semidirect
102. C₂×C₃×#101	C₂×C₅	semidirect
116. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
118. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
126. C₅×#108	C₂²×C₃	semidirect
127. C₅×#101	C₂²×C₃	semidirect
128. C₅×#101	C₂²×C₃	semidirect
129. C₅×#100	C₂²×C₃	semidirect
130. #3069	C₃×C₅	direct (N × H)
182. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
184. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
192. C₃×#108	C₂²×C₅	semidirect
193. C₃×#101	C₂²×C₅	semidirect
194. C₃×#101	C₂²×C₅	semidirect
195. C₃×#100	C₂²×C₅	semidirect
243. C₂×#137	C₂×C₃×C₅	semidirect
244. C₂×#137	C₂×C₃×C₅	semidirect
245. #568	C₂×C₃×C₅	semidirect
246. #473	C₂×C₃×C₅	semidirect
247. #471	C₂×C₃×C₅	semidirect
248. #430	C₂×C₃×C₅	semidirect
249. #413	C₂×C₃×C₅	semidirect
250. C₂×#101	C₂×C₃×C₅	semidirect
363. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
365. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
373. #108	C₂²×C₃×C₅	semidirect
374. #101	C₂²×C₃×C₅	semidirect
375. #101	C₂²×C₃×C₅	semidirect
376. #100	C₂²×C₃×C₅	semidirect
482. C₃×C₅	#3069	direct (N × H)
548. C₅	C₃×#3069	direct (N × H)
564. C₃	C₅×#3069	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×#575	2
C₂×C₃×C₅×#137	2
C₃×C₅×#568	2
C₃×C₅×#473	2
C₃×C₅×#471	2
C₃×C₅×#430	2
C₃×C₅×#413	2
C₂×C₃×C₅×#101	2
C₅×#3069	3
C₃×#3069	5

Subgroups — C3×C5×#3069 #14276103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3069 #14276103