Subgroups — C₃×C₅×#3067 #14276101

Order 1920.

904 conjugacy classes of subgroups.

The subgroup lattice has 532 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	2	yes	maximal, complemented
2	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#473	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#472	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#471	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×C₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#413	C₂	1	2	yes	maximal, complemented
9	C₅×#3067	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
12	C₃×C₅×#137	—	2	2	no	—
13	C₃×C₅×#137	C₂²	1	4	yes	—
14	C₃×C₅×AGL(1,ℤ/8)	—	2	2	no	—
15	C₃×C₅×AGL(1,ℤ/8)	C₂²	1	4	yes	—
16	C₃×C₅×#135	—	2	4	no	—
17	C₃×C₅×#135	—	2	1	no	—
18	C₃×C₅×#135	—	2	1	no	—
19	C₃×C₅×#135	—	2	1	no	—
20	C₃×C₅×#135	—	2	1	no	—
21	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
23	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₅×#131	—	2	1	no	—
25	C₃×C₅×#131	—	2	1	no	—
26	C₃×C₅×#131	C₂²	1	2	yes	—
27	C₃×C₅×#131	C₂²	1	2	yes	—
28	C₂×C₃×C₅×M₁₆	—	2	1	no	—
29	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
31	C₂²×C₃×C₅×C₈	—	2	1	no	—
32	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₃×C₅×#108	C₂²	1	2	yes	complemented
34	C₃×C₅×#108	C₂²	1	2	yes	complemented
35	C₃×C₅×#101	C₂²	1	4	yes	complemented
36	C₃×C₅×#100	C₂²	1	4	yes	complemented
37	C₃×#3067	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
38	C₅×#575	C₂×C₃	1	2	yes	complemented
39	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂×C₅×#131	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#473	C₂×C₃	1	2	yes	complemented
42	C₅×#472	C₂×C₃	1	2	yes	complemented
43	C₅×#471	C₂×C₃	1	4	yes	complemented
44	C₂×C₅×#108	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#413	C₂×C₃	1	2	yes	complemented
46	C₃×C₅×#41	—	2	1	no	—
47	C₃×C₅×#41	—	2	1	no	—
48	C₃×C₅×#41	—	2	2	no	—
49	C₃×C₅×#41	—	2	2	no	—
50	C₃×C₅×#41	—	2	2	no	—
51	C₃×C₅×#41	—	2	2	no	—
52	C₃×C₅×#41	D₄	1	2	yes	—
53	C₃×C₅×#41	C₂³	1	2	yes	—
54	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
55	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
56	C₂×C₃×C₅×D₄	—	2	1	no	—
57	C₂×C₃×C₅×D₄	—	2	2	no	—
58	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
60	C₂²×C₃×C₄×C₅	—	2	1	no	—
61	C₂²×C₃×C₄×C₅	—	2	2	no	—
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₃×C₅×Q₁₆	—	2	4	no	—
64	C₃×C₅×Q₁₆	—	2	1	no	—
65	C₃×C₅×Q₁₆	—	2	1	no	—
66	C₃×C₅×SD₁₆	—	2	4	no	—
67	C₃×C₅×SD₁₆	—	2	4	no	—
68	C₃×C₅×SD₁₆	—	2	2	no	—
69	C₃×C₅×SD₁₆	—	2	2	no	—
70	C₃×C₅×D₈	—	2	4	no	—
71	C₃×C₅×D₈	—	2	1	no	—
72	C₃×C₅×D₈	—	2	1	no	—
73	C₃×C₅×M₁₆	—	2	1	no	—
74	C₃×C₅×M₁₆	—	2	2	no	—
75	C₃×C₅×M₁₆	—	2	2	no	—
76	C₃×C₅×M₁₆	—	2	2	no	—
77	C₃×C₅×M₁₆	C₂³	1	2	yes	—
78	C₃×C₅×M₁₆	C₂³	1	4	yes	—
79	C₂×C₃×C₅×C₈	—	2	1	no	—
80	C₂×C₃×C₅×C₈	—	2	2	no	—
81	C₂×C₃×C₅×C₈	—	2	2	no	—
82	C₂×C₃×C₅×C₈	—	2	2	no	—
83	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
84	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
85	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
86	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
87	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₃×#575	C₂×C₅	1	2	yes	complemented
90	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×C₃×#131	C₂×C₅	1	1	yes	characteristic, complemented
92	C₃×#473	C₂×C₅	1	2	yes	complemented
93	C₃×#472	C₂×C₅	1	2	yes	complemented
94	C₃×#471	C₂×C₅	1	4	yes	complemented
95	C₂×C₃×#108	C₂×C₅	1	1	yes	characteristic, complemented
96	C₃×#413	C₂×C₅	1	2	yes	complemented
97	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
99	C₅×#137	—	2	2	no	—
100	C₅×#137	C₂²×C₃	1	4	yes	—
101	C₅×AGL(1,ℤ/8)	—	2	2	no	—
102	C₅×AGL(1,ℤ/8)	C₂²×C₃	1	4	yes	—
103	C₅×#135	—	2	4	no	—
104	C₅×#135	—	2	1	no	—
105	C₅×#135	—	2	1	no	—
106	C₅×#135	—	2	1	no	—
107	C₅×#135	—	2	1	no	—
108	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
109	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
110	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
111	C₅×#131	—	2	1	no	—
112	C₅×#131	—	2	1	no	—
113	C₅×#131	C₂²×C₃	1	2	yes	—
114	C₅×#131	C₂²×C₃	1	2	yes	—
115	C₂×C₅×M₁₆	—	2	1	no	—
116	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
118	C₂²×C₅×C₈	—	2	1	no	—
119	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
120	C₅×#108	C₂²×C₃	1	2	yes	complemented
121	C₅×#108	C₂²×C₃	1	2	yes	complemented
122	C₅×#101	C₂²×C₃	1	4	yes	complemented
123	C₅×#100	C₂²×C₃	1	4	yes	complemented
124	#3067	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
125	C₂³×C₃×C₅	—	2	1	no	—
126	C₂³×C₃×C₅	—	2	2	no	—
127	C₂³×C₃×C₅	#41	1	1	yes	characteristic
128	C₃×C₅×Q₈	—	2	1	no	—
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₃×C₅×Q₈	—	2	2	no	—
131	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
132	C₃×C₅×D₄	—	2	2	no	—
133	C₃×C₅×D₄	—	2	2	no	—
134	C₃×C₅×D₄	—	2	1	no	—
135	C₃×C₅×D₄	—	2	2	no	—
136	C₃×C₅×D₄	—	2	2	no	—
137	C₃×C₅×D₄	—	4	2	no	—
138	C₃×C₅×D₄	—	4	2	no	—
139	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
140	C₂×C₃×C₄×C₅	—	2	1	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	4	2	no	—
145	C₂×C₃×C₄×C₅	—	4	2	no	—
146	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
147	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
148	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
149	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
152	C₃×C₅×C₈	—	2	2	no	—
153	C₃×C₅×C₈	—	2	4	no	—
154	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
155	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
156	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
157	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
158	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
159	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
160	C₃×#137	—	2	2	no	—
161	C₃×#137	C₂²×C₅	1	4	yes	—
162	C₃×AGL(1,ℤ/8)	—	2	2	no	—
163	C₃×AGL(1,ℤ/8)	C₂²×C₅	1	4	yes	—
164	C₃×#135	—	2	4	no	—
165	C₃×#135	—	2	1	no	—
166	C₃×#135	—	2	1	no	—
167	C₃×#135	—	2	1	no	—
168	C₃×#135	—	2	1	no	—
169	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
170	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
171	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
172	C₃×#131	—	2	1	no	—
173	C₃×#131	—	2	1	no	—
174	C₃×#131	C₂²×C₅	1	2	yes	—
175	C₃×#131	C₂²×C₅	1	2	yes	—
176	C₂×C₃×M₁₆	—	2	1	no	—
177	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
179	C₂²×C₃×C₈	—	2	1	no	—
180	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
181	C₃×#108	C₂²×C₅	1	2	yes	complemented
182	C₃×#108	C₂²×C₅	1	2	yes	complemented
183	C₃×#101	C₂²×C₅	1	4	yes	complemented
184	C₃×#100	C₂²×C₅	1	4	yes	complemented
185	C₅×#41	—	2	1	no	—
186	C₅×#41	—	2	1	no	—
187	C₅×#41	—	2	2	no	—
188	C₅×#41	—	2	2	no	—
189	C₅×#41	—	2	2	no	—
190	C₅×#41	—	2	2	no	—
191	C₅×#41	C₃×D₄	1	2	yes	—
192	C₅×#41	C₂³×C₃	1	2	yes	—
193	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
194	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
195	C₂×C₅×D₄	—	2	1	no	—
196	C₂×C₅×D₄	—	2	2	no	—
197	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
198	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
199	C₂²×C₄×C₅	—	2	1	no	—
200	C₂²×C₄×C₅	—	2	2	no	—
201	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
202	C₅×Q₁₆	—	2	4	no	—
203	C₅×Q₁₆	—	2	1	no	—
204	C₅×Q₁₆	—	2	1	no	—
205	C₅×SD₁₆	—	2	4	no	—
206	C₅×SD₁₆	—	2	4	no	—
207	C₅×SD₁₆	—	2	2	no	—
208	C₅×SD₁₆	—	2	2	no	—
209	C₅×D₈	—	2	4	no	—
210	C₅×D₈	—	2	1	no	—
211	C₅×D₈	—	2	1	no	—
212	C₅×M₁₆	—	2	1	no	—
213	C₅×M₁₆	—	2	2	no	—
214	C₅×M₁₆	—	2	2	no	—
215	C₅×M₁₆	—	2	2	no	—
216	C₅×M₁₆	C₂³×C₃	1	2	yes	—
217	C₅×M₁₆	C₂³×C₃	1	4	yes	—
218	C₂×C₅×C₈	—	2	1	no	—
219	C₂×C₅×C₈	—	2	2	no	—
220	C₂×C₅×C₈	—	2	2	no	—
221	C₂×C₅×C₈	—	2	2	no	—
222	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
223	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
224	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
225	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
226	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
227	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
228	#575	C₂×C₃×C₅	1	2	yes	complemented
229	C₂×#135	C₂×C₃×C₅	1	1	yes	characteristic, complemented
230	C₂×#131	C₂×C₃×C₅	1	1	yes	characteristic, complemented
231	#473	C₂×C₃×C₅	1	2	yes	complemented
232	#472	C₂×C₃×C₅	1	2	yes	complemented
233	#471	C₂×C₃×C₅	1	4	yes	complemented
234	C₂×#108	C₂×C₃×C₅	1	1	yes	characteristic, complemented
235	#413	C₂×C₃×C₅	1	2	yes	complemented
236	C₂²×C₃×C₅	—	2	2	no	—
237	C₂²×C₃×C₅	—	4	1	no	—
238	C₂²×C₃×C₅	—	4	2	no	—
239	C₂²×C₃×C₅	—	4	2	no	—
240	C₂²×C₃×C₅	—	8	2	no	—
241	C₂²×C₃×C₅	#121	1	1	yes	characteristic
242	C₂²×C₃×C₅	#121	1	1	yes	characteristic
243	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
244	C₃×C₄×C₅	—	2	2	no	—
245	C₃×C₄×C₅	—	4	2	no	—
246	C₃×C₄×C₅	#121	1	1	yes	characteristic
247	C₃×C₄×C₅	#121	1	1	yes	characteristic
248	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
249	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₃×#41	—	2	1	no	—
251	C₃×#41	—	2	1	no	—
252	C₃×#41	—	2	2	no	—
253	C₃×#41	—	2	2	no	—
254	C₃×#41	—	2	2	no	—
255	C₃×#41	—	2	2	no	—
256	C₃×#41	C₅×D₄	1	2	yes	—
257	C₃×#41	C₂³×C₅	1	2	yes	—
258	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
259	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
260	C₂×C₃×D₄	—	2	1	no	—
261	C₂×C₃×D₄	—	2	2	no	—
262	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
263	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
264	C₂²×C₃×C₄	—	2	1	no	—
265	C₂²×C₃×C₄	—	2	2	no	—
266	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
267	C₃×Q₁₆	—	2	4	no	—
268	C₃×Q₁₆	—	2	1	no	—
269	C₃×Q₁₆	—	2	1	no	—
270	C₃×SD₁₆	—	2	4	no	—
271	C₃×SD₁₆	—	2	4	no	—
272	C₃×SD₁₆	—	2	2	no	—
273	C₃×SD₁₆	—	2	2	no	—
274	C₃×D₈	—	2	4	no	—
275	C₃×D₈	—	2	1	no	—
276	C₃×D₈	—	2	1	no	—
277	C₃×M₁₆	—	2	1	no	—
278	C₃×M₁₆	—	2	2	no	—
279	C₃×M₁₆	—	2	2	no	—
280	C₃×M₁₆	—	2	2	no	—
281	C₃×M₁₆	C₂³×C₅	1	2	yes	—
282	C₃×M₁₆	C₂³×C₅	1	4	yes	—
283	C₂×C₃×C₈	—	2	1	no	—
284	C₂×C₃×C₈	—	2	2	no	—
285	C₂×C₃×C₈	—	2	2	no	—
286	C₂×C₃×C₈	—	2	2	no	—
287	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
288	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
289	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
290	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
291	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
292	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
293	C₂³×C₅	—	2	1	no	—
294	C₂³×C₅	—	2	2	no	—
295	C₂³×C₅	C₃×#41	1	1	yes	characteristic
296	C₅×Q₈	—	2	1	no	—
297	C₅×Q₈	—	2	2	no	—
298	C₅×Q₈	—	2	2	no	—
299	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
300	C₅×D₄	—	2	2	no	—
301	C₅×D₄	—	2	2	no	—
302	C₅×D₄	—	2	1	no	—
303	C₅×D₄	—	2	2	no	—
304	C₅×D₄	—	2	2	no	—
305	C₅×D₄	—	4	2	no	—
306	C₅×D₄	—	4	2	no	—
307	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	2	no	—
310	C₂×C₄×C₅	—	2	2	no	—
311	C₂×C₄×C₅	—	2	2	no	—
312	C₂×C₄×C₅	—	4	2	no	—
313	C₂×C₄×C₅	—	4	2	no	—
314	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
315	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
316	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
317	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
318	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
319	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
320	C₅×C₈	—	2	2	no	—
321	C₅×C₈	—	2	4	no	—
322	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
323	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
324	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
325	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
326	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
327	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
328	#137	—	2	2	no	—
329	#137	C₂²×C₃×C₅	1	4	yes	—
330	AGL(1,ℤ/8)	—	2	2	no	—
331	AGL(1,ℤ/8)	C₂²×C₃×C₅	1	4	yes	—
332	#135	—	2	4	no	—
333	#135	—	2	1	no	—
334	#135	—	2	1	no	—
335	#135	—	2	1	no	—
336	#135	—	2	1	no	—
337	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
338	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
339	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
340	#131	—	2	1	no	—
341	#131	—	2	1	no	—
342	#131	C₂²×C₃×C₅	1	2	yes	—
343	#131	C₂²×C₃×C₅	1	2	yes	—
344	C₂×M₁₆	—	2	1	no	—
345	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
346	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
347	C₂²×C₈	—	2	1	no	—
348	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
349	#108	C₂²×C₃×C₅	1	2	yes	complemented
350	#108	C₂²×C₃×C₅	1	2	yes	complemented
351	#101	C₂²×C₃×C₅	1	4	yes	complemented
352	#100	C₂²×C₃×C₅	1	4	yes	complemented
353	C₂×C₃×C₅	—	2	1	no	—
354	C₂×C₃×C₅	—	2	1	no	—
355	C₂×C₃×C₅	—	2	1	no	—
356	C₂×C₃×C₅	—	4	2	no	—
357	C₂×C₃×C₅	—	8	2	no	—
358	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
359	C₂³×C₃	—	2	1	no	—
360	C₂³×C₃	—	2	2	no	—
361	C₂³×C₃	C₅×#41	1	1	yes	characteristic
362	C₃×Q₈	—	2	1	no	—
363	C₃×Q₈	—	2	2	no	—
364	C₃×Q₈	—	2	2	no	—
365	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
366	C₃×D₄	—	2	2	no	—
367	C₃×D₄	—	2	2	no	—
368	C₃×D₄	—	2	1	no	—
369	C₃×D₄	—	2	2	no	—
370	C₃×D₄	—	2	2	no	—
371	C₃×D₄	—	4	2	no	—
372	C₃×D₄	—	4	2	no	—
373	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
374	C₂×C₃×C₄	—	2	1	no	—
375	C₂×C₃×C₄	—	2	2	no	—
376	C₂×C₃×C₄	—	2	2	no	—
377	C₂×C₃×C₄	—	2	2	no	—
378	C₂×C₃×C₄	—	4	2	no	—
379	C₂×C₃×C₄	—	4	2	no	—
380	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
382	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
383	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
384	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
385	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
386	C₃×C₈	—	2	2	no	—
387	C₃×C₈	—	2	4	no	—
388	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
389	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
390	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
391	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
392	C₂²×C₅	—	2	2	no	—
393	C₂²×C₅	—	4	1	no	—
394	C₂²×C₅	—	4	2	no	—
395	C₂²×C₅	—	4	2	no	—
396	C₂²×C₅	—	8	2	no	—
397	C₂²×C₅	C₃×#121	1	1	yes	characteristic
398	C₂²×C₅	C₃×#121	1	1	yes	characteristic
399	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
400	C₄×C₅	—	2	2	no	—
401	C₄×C₅	—	4	2	no	—
402	C₄×C₅	C₃×#121	1	1	yes	characteristic
403	C₄×C₅	C₃×#121	1	1	yes	characteristic
404	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
405	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
406	#41	—	2	1	no	—
407	#41	—	2	1	no	—
408	#41	—	2	2	no	—
409	#41	—	2	2	no	—
410	#41	—	2	2	no	—
411	#41	—	2	2	no	—
412	#41	C₃×C₅×D₄	1	2	yes	—
413	#41	C₂³×C₃×C₅	1	2	yes	—
414	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
415	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
419	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
423	Q₁₆	—	2	4	no	—
424	Q₁₆	—	2	1	no	—
425	Q₁₆	—	2	1	no	—
426	SD₁₆	—	2	4	no	—
427	SD₁₆	—	2	4	no	—
428	SD₁₆	—	2	2	no	—
429	SD₁₆	—	2	2	no	—
430	D₈	—	2	4	no	—
431	D₈	—	2	1	no	—
432	D₈	—	2	1	no	—
433	M₁₆	—	2	1	no	—
434	M₁₆	—	2	2	no	—
435	M₁₆	—	2	2	no	—
436	M₁₆	—	2	2	no	—
437	M₁₆	C₂³×C₃×C₅	1	2	yes	—
438	M₁₆	C₂³×C₃×C₅	1	4	yes	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
444	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
445	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
446	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
447	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
448	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
449	C₃×C₅	#3067	1	1	yes	characteristic, direct product factor, Hall
450	C₂²×C₃	—	2	2	no	—
451	C₂²×C₃	—	4	1	no	—
452	C₂²×C₃	—	4	2	no	—
453	C₂²×C₃	—	4	2	no	—
454	C₂²×C₃	—	8	2	no	—
455	C₂²×C₃	C₅×#121	1	1	yes	characteristic
456	C₂²×C₃	C₅×#121	1	1	yes	characteristic
457	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
458	C₃×C₄	—	2	2	no	—
459	C₃×C₄	—	4	2	no	—
460	C₃×C₄	C₅×#121	1	1	yes	characteristic
461	C₃×C₄	C₅×#121	1	1	yes	characteristic
462	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
463	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
464	C₂×C₅	—	2	1	no	—
465	C₂×C₅	—	2	1	no	—
466	C₂×C₅	—	2	1	no	—
467	C₂×C₅	—	4	2	no	—
468	C₂×C₅	—	8	2	no	—
469	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
470	C₂³	—	2	1	no	—
471	C₂³	—	2	2	no	—
472	C₂³	C₃×C₅×#41	1	1	yes	characteristic
473	Q₈	—	2	1	no	—
474	Q₈	—	2	2	no	—
475	Q₈	—	2	2	no	—
476	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
477	D₄	—	2	2	no	—
478	D₄	—	2	2	no	—
479	D₄	—	2	2	no	—
480	D₄	—	2	2	no	—
481	D₄	—	2	1	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	2	no	—
484	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
492	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
493	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
494	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
495	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
496	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	2	4	no	—
499	C₈	C₂×C₃×C₅×D₄	1	1	yes	characteristic
500	C₈	C₂×C₃×C₅×D₄	1	1	yes	characteristic
501	C₈	C₂×C₃×C₅×D₄	1	1	yes	characteristic
502	C₈	C₂×C₃×C₅×D₄	1	1	yes	characteristic
503	C₂×C₃	—	2	1	no	—
504	C₂×C₃	—	2	1	no	—
505	C₂×C₃	—	2	1	no	—
506	C₂×C₃	—	4	2	no	—
507	C₂×C₃	—	8	2	no	—
508	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
509	C₅	C₃×#3067	1	1	yes	characteristic, direct product factor, Sylow
510	C₂²	—	2	2	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	8	2	no	—
515	C₂²	C₃×C₅×#121	1	1	yes	characteristic
516	C₂²	C₃×C₅×#121	1	1	yes	characteristic
517	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
518	C₄	—	2	2	no	—
519	C₄	—	4	2	no	—
520	C₄	C₃×C₅×#121	1	1	yes	characteristic
521	C₄	C₃×C₅×#121	1	1	yes	characteristic
522	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
523	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
524	C₃	C₅×#3067	1	1	yes	characteristic, direct product factor, Sylow
525	C₂	—	2	1	no	—
526	C₂	—	2	1	no	—
527	C₂	—	2	1	no	—
528	C₂	—	4	2	no	—
529	C₂	—	8	2	no	—
530	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄×C₅	#121
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
socle	C₂×C₃×C₅	C₂×#121
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄×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×#575	C₂	semidirect
2. C₂×C₃×C₅×#135	C₂	semidirect
3. C₂×C₃×C₅×#131	C₂	semidirect
4. C₃×C₅×#473	C₂	semidirect
5. C₃×C₅×#472	C₂	semidirect
6. C₃×C₅×#471	C₂	semidirect
7. C₂×C₃×C₅×#108	C₂	semidirect
8. C₃×C₅×#413	C₂	semidirect
9. C₅×#3067	C₃	direct (N × H)
21. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
22. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
23. C₂×C₃×C₅×D₈	C₂²	semidirect
33. C₃×C₅×#108	C₂²	semidirect
34. C₃×C₅×#108	C₂²	semidirect
35. C₃×C₅×#101	C₂²	semidirect
36. C₃×C₅×#100	C₂²	semidirect
37. C₃×#3067	C₅	direct (N × H)
38. C₅×#575	C₂×C₃	semidirect
39. C₂×C₅×#135	C₂×C₃	semidirect
40. C₂×C₅×#131	C₂×C₃	semidirect
41. C₅×#473	C₂×C₃	semidirect
42. C₅×#472	C₂×C₃	semidirect
43. C₅×#471	C₂×C₃	semidirect
44. C₂×C₅×#108	C₂×C₃	semidirect
45. C₅×#413	C₂×C₃	semidirect
89. C₃×#575	C₂×C₅	semidirect
90. C₂×C₃×#135	C₂×C₅	semidirect
91. C₂×C₃×#131	C₂×C₅	semidirect
92. C₃×#473	C₂×C₅	semidirect
93. C₃×#472	C₂×C₅	semidirect
94. C₃×#471	C₂×C₅	semidirect
95. C₂×C₃×#108	C₂×C₅	semidirect
96. C₃×#413	C₂×C₅	semidirect
108. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
109. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
110. C₂×C₅×D₈	C₂²×C₃	semidirect
120. C₅×#108	C₂²×C₃	semidirect
121. C₅×#108	C₂²×C₃	semidirect
122. C₅×#101	C₂²×C₃	semidirect
123. C₅×#100	C₂²×C₃	semidirect
124. #3067	C₃×C₅	direct (N × H)
169. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
170. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
171. C₂×C₃×D₈	C₂²×C₅	semidirect
181. C₃×#108	C₂²×C₅	semidirect
182. C₃×#108	C₂²×C₅	semidirect
183. C₃×#101	C₂²×C₅	semidirect
184. C₃×#100	C₂²×C₅	semidirect
228. #575	C₂×C₃×C₅	semidirect
229. C₂×#135	C₂×C₃×C₅	semidirect
230. C₂×#131	C₂×C₃×C₅	semidirect
231. #473	C₂×C₃×C₅	semidirect
232. #472	C₂×C₃×C₅	semidirect
233. #471	C₂×C₃×C₅	semidirect
234. C₂×#108	C₂×C₃×C₅	semidirect
235. #413	C₂×C₃×C₅	semidirect
337. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
338. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
339. C₂×D₈	C₂²×C₃×C₅	semidirect
349. #108	C₂²×C₃×C₅	semidirect
350. #108	C₂²×C₃×C₅	semidirect
351. #101	C₂²×C₃×C₅	semidirect
352. #100	C₂²×C₃×C₅	semidirect
449. C₃×C₅	#3067	direct (N × H)
509. C₅	C₃×#3067	direct (N × H)
524. C₃	C₅×#3067	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×#135	2
C₂×C₃×C₅×#131	2
C₃×C₅×#473	2
C₃×C₅×#472	2
C₃×C₅×#471	2
C₂×C₃×C₅×#108	2
C₃×C₅×#413	2
C₅×#3067	3
C₃×#3067	5

Subgroups — C3×C5×#3067 #14276101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3067 #14276101