Subgroups — C₃×C₅×#3137 #14276171

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#491	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#489	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#488	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#487	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#419	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#417	C₂	1	1	yes	maximal, characteristic
9	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic
10	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3137	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
18	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
20	C₃×C₅×#125	—	2	1	no	—
21	C₃×C₅×#125	C₂²	1	2	yes	—
22	C₃×C₅×#124	C₂²	1	2	yes	—
23	C₃×C₅×#123	—	2	2	no	—
24	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
25	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
26	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
27	C₃×C₅×#117	C₂²	1	1	yes	characteristic
28	C₃×C₅×#117	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₅×#103	C₂²	1	1	yes	characteristic
31	C₃×C₅×#103	C₂²	1	2	yes	—
32	C₃×C₅×#103	C₂²	1	2	yes	—
33	C₃×C₅×#103	C₂²	1	2	yes	—
34	C₃×C₅×#103	C₂²	1	2	yes	—
35	C₃×C₅×#103	C₂²	1	2	yes	—
36	C₃×C₅×#103	C₂²	1	1	yes	characteristic
37	C₃×C₅×#102	C₂²	1	1	yes	characteristic
38	C₃×C₅×#102	C₂²	1	2	yes	—
39	C₃×C₅×#102	C₂²	1	1	yes	characteristic
40	C₃×C₅×#97	C₂²	1	2	yes	—
41	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
42	C₃×#3137	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#544	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#536	C₂×C₃	1	1	yes	characteristic
45	C₅×#491	C₂×C₃	1	2	yes	complemented
46	C₅×#489	C₂×C₃	1	2	yes	complemented
47	C₅×#488	C₂×C₃	1	2	yes	complemented
48	C₅×#487	C₂×C₃	1	2	yes	complemented
49	C₅×#419	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#417	C₂×C₃	1	1	yes	characteristic
51	C₅×#416	C₂×C₃	1	1	yes	characteristic
52	C₂×C₅×#103	C₂×C₃	1	1	yes	characteristic, complemented
53	C₅×#405	C₂×C₃	1	1	yes	characteristic, complemented
54	C₃×C₅×#41	—	2	2	no	—
55	C₃×C₅×#41	—	2	2	no	—
56	C₂×C₃×C₅×Q₈	—	2	1	no	—
57	C₂×C₃×C₅×Q₈	—	2	2	no	—
58	C₂×C₃×C₅×Q₈	—	2	2	no	—
59	C₂×C₃×C₅×Q₈	—	2	2	no	—
60	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
61	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×D₄	—	2	1	no	—
63	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	—	2	1	no	—
65	C₂²×C₃×C₄×C₅	—	2	1	no	—
66	C₂²×C₃×C₄×C₅	—	2	1	no	—
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₃×C₅×M₁₆	—	2	2	no	—
69	C₂×C₃×C₅×C₈	—	2	2	no	—
70	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
73	C₃×C₅×C₄⋊C₄	—	2	1	no	—
74	C₃×C₅×C₄⋊C₄	—	2	2	no	—
75	C₃×C₅×C₄⋊C₄	—	2	2	no	—
76	C₃×C₅×C₄⋊C₄	—	2	2	no	—
77	C₃×C₅×C₄⋊C₄	—	2	2	no	—
78	C₃×C₅×C₄⋊C₄	—	2	2	no	—
79	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
80	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
81	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
82	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
85	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
86	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
87	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
88	C₃×C₄²×C₅	—	2	1	no	—
89	C₃×C₄²×C₅	C₂³	1	2	yes	—
90	C₃×#544	C₂×C₅	1	1	yes	characteristic, complemented
91	C₃×#536	C₂×C₅	1	1	yes	characteristic
92	C₃×#491	C₂×C₅	1	2	yes	complemented
93	C₃×#489	C₂×C₅	1	2	yes	complemented
94	C₃×#488	C₂×C₅	1	2	yes	complemented
95	C₃×#487	C₂×C₅	1	2	yes	complemented
96	C₃×#419	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#417	C₂×C₅	1	1	yes	characteristic
98	C₃×#416	C₂×C₅	1	1	yes	characteristic
99	C₂×C₃×#103	C₂×C₅	1	1	yes	characteristic, complemented
100	C₃×#405	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
102	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
104	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
105	C₅×C₄⋊Q₈	—	2	1	no	—
106	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
107	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
108	C₅×#125	—	2	1	no	—
109	C₅×#125	C₂²×C₃	1	2	yes	—
110	C₅×#124	C₂²×C₃	1	2	yes	—
111	C₅×#123	—	2	2	no	—
112	C₅×C₂²⋊Q₈	—	2	1	no	—
113	C₅×C₂²⋊Q₈	—	2	1	no	—
114	C₅×C₂²⋊Q₈	—	2	2	no	—
115	C₅×#117	C₂²×C₃	1	1	yes	characteristic
116	C₅×#117	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
118	C₅×#103	C₂²×C₃	1	2	yes	—
119	C₅×#103	C₂²×C₃	1	2	yes	—
120	C₅×#103	C₂²×C₃	1	1	yes	characteristic
121	C₅×#103	C₂²×C₃	1	1	yes	characteristic
122	C₅×#103	C₂²×C₃	1	2	yes	—
123	C₅×#103	C₂²×C₃	1	2	yes	—
124	C₅×#103	C₂²×C₃	1	2	yes	—
125	C₅×#102	C₂²×C₃	1	1	yes	characteristic
126	C₅×#102	C₂²×C₃	1	1	yes	characteristic
127	C₅×#102	C₂²×C₃	1	2	yes	—
128	C₅×#97	C₂²×C₃	1	2	yes	—
129	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
130	#3137	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
131	C₂³×C₃×C₅	—	2	1	no	—
132	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
133	C₃×C₅×Q₈	—	2	2	no	—
134	C₃×C₅×Q₈	—	2	2	no	—
135	C₃×C₅×Q₈	—	2	1	no	—
136	C₃×C₅×Q₈	—	2	1	no	—
137	C₃×C₅×Q₈	—	4	2	no	—
138	C₃×C₅×Q₈	—	8	2	no	—
139	C₃×C₅×D₄	—	2	1	no	—
140	C₃×C₅×D₄	—	2	1	no	—
141	C₃×C₅×D₄	—	4	2	no	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	—	2	2	no	—
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	1	no	—
147	C₂×C₃×C₄×C₅	—	4	2	no	—
148	C₂×C₃×C₄×C₅	—	4	2	no	—
149	C₂×C₃×C₄×C₅	—	8	1	no	—
150	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
151	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
152	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	#41	1	2	yes	—
154	C₂×C₃×C₄×C₅	#41	1	2	yes	—
155	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
156	C₃×C₅×C₈	—	2	1	no	—
157	C₃×C₅×C₈	—	2	1	no	—
158	C₃×C₅×C₈	—	2	2	no	—
159	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
160	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
161	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
162	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
163	C₃×C₄⋊Q₈	—	2	1	no	—
164	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
165	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
166	C₃×#125	—	2	1	no	—
167	C₃×#125	C₂²×C₅	1	2	yes	—
168	C₃×#124	C₂²×C₅	1	2	yes	—
169	C₃×#123	—	2	2	no	—
170	C₃×C₂²⋊Q₈	—	2	1	no	—
171	C₃×C₂²⋊Q₈	—	2	1	no	—
172	C₃×C₂²⋊Q₈	—	2	2	no	—
173	C₃×#117	C₂²×C₅	1	1	yes	characteristic
174	C₃×#117	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
176	C₃×#103	C₂²×C₅	1	2	yes	—
177	C₃×#103	C₂²×C₅	1	2	yes	—
178	C₃×#103	C₂²×C₅	1	1	yes	characteristic
179	C₃×#103	C₂²×C₅	1	1	yes	characteristic
180	C₃×#103	C₂²×C₅	1	2	yes	—
181	C₃×#103	C₂²×C₅	1	2	yes	—
182	C₃×#103	C₂²×C₅	1	2	yes	—
183	C₃×#102	C₂²×C₅	1	1	yes	characteristic
184	C₃×#102	C₂²×C₅	1	1	yes	characteristic
185	C₃×#102	C₂²×C₅	1	2	yes	—
186	C₃×#97	C₂²×C₅	1	2	yes	—
187	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
188	C₅×#41	—	2	2	no	—
189	C₅×#41	—	2	2	no	—
190	C₂×C₅×Q₈	—	2	1	no	—
191	C₂×C₅×Q₈	—	2	2	no	—
192	C₂×C₅×Q₈	—	2	2	no	—
193	C₂×C₅×Q₈	—	2	2	no	—
194	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
195	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
196	C₂×C₅×D₄	—	2	1	no	—
197	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
198	C₂²×C₄×C₅	—	2	1	no	—
199	C₂²×C₄×C₅	—	2	1	no	—
200	C₂²×C₄×C₅	—	2	1	no	—
201	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
202	C₅×M₁₆	—	2	2	no	—
203	C₂×C₅×C₈	—	2	2	no	—
204	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
205	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
206	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
207	C₅×C₄⋊C₄	—	2	1	no	—
208	C₅×C₄⋊C₄	—	2	2	no	—
209	C₅×C₄⋊C₄	—	2	2	no	—
210	C₅×C₄⋊C₄	—	2	2	no	—
211	C₅×C₄⋊C₄	—	2	2	no	—
212	C₅×C₄⋊C₄	—	2	2	no	—
213	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
214	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
215	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
216	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
217	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
218	C₅×C₂²⋊C₄	—	2	1	no	—
219	C₅×C₂²⋊C₄	—	2	2	no	—
220	C₅×C₂²⋊C₄	—	2	2	no	—
221	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
222	C₄²×C₅	—	2	1	no	—
223	C₄²×C₅	C₂³×C₃	1	2	yes	—
224	#544	C₂×C₃×C₅	1	1	yes	characteristic, complemented
225	#536	C₂×C₃×C₅	1	1	yes	characteristic
226	#491	C₂×C₃×C₅	1	2	yes	complemented
227	#489	C₂×C₃×C₅	1	2	yes	complemented
228	#488	C₂×C₃×C₅	1	2	yes	complemented
229	#487	C₂×C₃×C₅	1	2	yes	complemented
230	#419	C₂×C₃×C₅	1	1	yes	characteristic, complemented
231	#417	C₂×C₃×C₅	1	1	yes	characteristic
232	#416	C₂×C₃×C₅	1	1	yes	characteristic
233	C₂×#103	C₂×C₃×C₅	1	1	yes	characteristic, complemented
234	#405	C₂×C₃×C₅	1	1	yes	characteristic, complemented
235	C₂²×C₃×C₅	—	2	1	no	—
236	C₂²×C₃×C₅	—	2	1	no	—
237	C₂²×C₃×C₅	—	4	1	no	—
238	C₂²×C₃×C₅	—	4	1	no	—
239	C₂²×C₃×C₅	—	4	1	no	—
240	C₂²×C₃×C₅	#124	1	2	yes	—
241	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
242	C₃×C₄×C₅	—	2	2	no	—
243	C₃×C₄×C₅	—	2	2	no	—
244	C₃×C₄×C₅	—	4	1	no	—
245	C₃×C₄×C₅	—	4	2	no	—
246	C₃×C₄×C₅	—	4	2	no	—
247	C₃×C₄×C₅	—	4	1	no	—
248	C₃×C₄×C₅	—	4	1	no	—
249	C₃×C₄×C₅	#124	1	2	yes	—
250	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
251	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
252	C₃×#41	—	2	2	no	—
253	C₃×#41	—	2	2	no	—
254	C₂×C₃×Q₈	—	2	1	no	—
255	C₂×C₃×Q₈	—	2	2	no	—
256	C₂×C₃×Q₈	—	2	2	no	—
257	C₂×C₃×Q₈	—	2	2	no	—
258	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
259	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
260	C₂×C₃×D₄	—	2	1	no	—
261	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
262	C₂²×C₃×C₄	—	2	1	no	—
263	C₂²×C₃×C₄	—	2	1	no	—
264	C₂²×C₃×C₄	—	2	1	no	—
265	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
266	C₃×M₁₆	—	2	2	no	—
267	C₂×C₃×C₈	—	2	2	no	—
268	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
269	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
270	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
271	C₃×C₄⋊C₄	—	2	1	no	—
272	C₃×C₄⋊C₄	—	2	2	no	—
273	C₃×C₄⋊C₄	—	2	2	no	—
274	C₃×C₄⋊C₄	—	2	2	no	—
275	C₃×C₄⋊C₄	—	2	2	no	—
276	C₃×C₄⋊C₄	—	2	2	no	—
277	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
278	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
279	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
280	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
281	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
282	C₃×C₂²⋊C₄	—	2	1	no	—
283	C₃×C₂²⋊C₄	—	2	2	no	—
284	C₃×C₂²⋊C₄	—	2	2	no	—
285	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
286	C₃×C₄²	—	2	1	no	—
287	C₃×C₄²	C₂³×C₅	1	2	yes	—
288	C₂³×C₅	—	2	1	no	—
289	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
290	C₅×Q₈	—	2	2	no	—
291	C₅×Q₈	—	2	2	no	—
292	C₅×Q₈	—	2	1	no	—
293	C₅×Q₈	—	2	1	no	—
294	C₅×Q₈	—	4	2	no	—
295	C₅×Q₈	—	8	2	no	—
296	C₅×D₄	—	2	1	no	—
297	C₅×D₄	—	2	1	no	—
298	C₅×D₄	—	4	2	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	4	2	no	—
305	C₂×C₄×C₅	—	4	2	no	—
306	C₂×C₄×C₅	—	8	1	no	—
307	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
308	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
309	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
310	C₂×C₄×C₅	C₃×#41	1	2	yes	—
311	C₂×C₄×C₅	C₃×#41	1	2	yes	—
312	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
313	C₅×C₈	—	2	1	no	—
314	C₅×C₈	—	2	1	no	—
315	C₅×C₈	—	2	2	no	—
316	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
317	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
318	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
319	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
320	C₄⋊Q₈	—	2	1	no	—
321	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
322	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
323	#125	—	2	1	no	—
324	#125	C₂²×C₃×C₅	1	2	yes	—
325	#124	C₂²×C₃×C₅	1	2	yes	—
326	#123	—	2	2	no	—
327	C₂²⋊Q₈	—	2	1	no	—
328	C₂²⋊Q₈	—	2	1	no	—
329	C₂²⋊Q₈	—	2	2	no	—
330	#117	C₂²×C₃×C₅	1	1	yes	characteristic
331	#117	C₂²×C₃×C₅	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
333	#103	C₂²×C₃×C₅	1	2	yes	—
334	#103	C₂²×C₃×C₅	1	2	yes	—
335	#103	C₂²×C₃×C₅	1	1	yes	characteristic
336	#103	C₂²×C₃×C₅	1	1	yes	characteristic
337	#103	C₂²×C₃×C₅	1	2	yes	—
338	#103	C₂²×C₃×C₅	1	2	yes	—
339	#103	C₂²×C₃×C₅	1	2	yes	—
340	#102	C₂²×C₃×C₅	1	1	yes	characteristic
341	#102	C₂²×C₃×C₅	1	1	yes	characteristic
342	#102	C₂²×C₃×C₅	1	2	yes	—
343	#97	C₂²×C₃×C₅	1	2	yes	—
344	C₄×C₈	C₂²×C₃×C₅	1	2	yes	—
345	C₂×C₃×C₅	—	2	2	no	—
346	C₂×C₃×C₅	—	8	1	no	—
347	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
348	C₂×C₃×C₅	#577	1	1	yes	characteristic
349	C₂×C₃×C₅	#578	1	1	yes	characteristic
350	C₂³×C₃	—	2	1	no	—
351	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
352	C₃×Q₈	—	2	2	no	—
353	C₃×Q₈	—	2	2	no	—
354	C₃×Q₈	—	2	1	no	—
355	C₃×Q₈	—	2	1	no	—
356	C₃×Q₈	—	4	2	no	—
357	C₃×Q₈	—	8	2	no	—
358	C₃×D₄	—	2	1	no	—
359	C₃×D₄	—	2	1	no	—
360	C₃×D₄	—	4	2	no	—
361	C₂×C₃×C₄	—	2	1	no	—
362	C₂×C₃×C₄	—	2	1	no	—
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	2	1	no	—
366	C₂×C₃×C₄	—	4	2	no	—
367	C₂×C₃×C₄	—	4	2	no	—
368	C₂×C₃×C₄	—	8	1	no	—
369	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
370	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
371	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
372	C₂×C₃×C₄	C₅×#41	1	2	yes	—
373	C₂×C₃×C₄	C₅×#41	1	2	yes	—
374	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
375	C₃×C₈	—	2	1	no	—
376	C₃×C₈	—	2	1	no	—
377	C₃×C₈	—	2	2	no	—
378	C₂²×C₅	—	2	1	no	—
379	C₂²×C₅	—	2	1	no	—
380	C₂²×C₅	—	4	1	no	—
381	C₂²×C₅	—	4	1	no	—
382	C₂²×C₅	—	4	1	no	—
383	C₂²×C₅	C₃×#124	1	2	yes	—
384	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
385	C₄×C₅	—	2	2	no	—
386	C₄×C₅	—	2	2	no	—
387	C₄×C₅	—	4	2	no	—
388	C₄×C₅	—	4	1	no	—
389	C₄×C₅	—	4	1	no	—
390	C₄×C₅	—	4	1	no	—
391	C₄×C₅	—	4	2	no	—
392	C₄×C₅	C₃×#124	1	2	yes	—
393	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
394	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
395	#41	—	2	2	no	—
396	#41	—	2	2	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
402	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
409	M₁₆	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
412	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
413	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
421	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
422	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
423	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
424	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
429	C₄²	—	2	1	no	—
430	C₄²	C₂³×C₃×C₅	1	2	yes	—
431	C₃×C₅	#3137	1	1	yes	characteristic, direct product factor, Hall
432	C₂²×C₃	—	2	1	no	—
433	C₂²×C₃	—	2	1	no	—
434	C₂²×C₃	—	4	1	no	—
435	C₂²×C₃	—	4	1	no	—
436	C₂²×C₃	—	4	1	no	—
437	C₂²×C₃	C₅×#124	1	2	yes	—
438	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
439	C₃×C₄	—	2	2	no	—
440	C₃×C₄	—	2	2	no	—
441	C₃×C₄	—	4	1	no	—
442	C₃×C₄	—	4	2	no	—
443	C₃×C₄	—	4	2	no	—
444	C₃×C₄	—	4	1	no	—
445	C₃×C₄	—	4	1	no	—
446	C₃×C₄	C₅×#124	1	2	yes	—
447	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
448	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
449	C₂×C₅	—	2	2	no	—
450	C₂×C₅	—	8	1	no	—
451	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
452	C₂×C₅	C₃×#577	1	1	yes	characteristic
453	C₂×C₅	C₃×#578	1	1	yes	characteristic
454	C₂³	—	2	1	no	—
455	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
456	Q₈	—	2	2	no	—
457	Q₈	—	2	2	no	—
458	Q₈	—	2	1	no	—
459	Q₈	—	2	1	no	—
460	Q₈	—	4	2	no	—
461	Q₈	—	8	2	no	—
462	D₄	—	2	1	no	—
463	D₄	—	2	1	no	—
464	D₄	—	4	2	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	8	1	no	—
473	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
474	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
475	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
476	C₂×C₄	C₃×C₅×#41	1	2	yes	—
477	C₂×C₄	C₃×C₅×#41	1	2	yes	—
478	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
479	C₈	—	2	1	no	—
480	C₈	—	2	1	no	—
481	C₈	—	2	2	no	—
482	C₂×C₃	—	2	2	no	—
483	C₂×C₃	—	8	1	no	—
484	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
485	C₂×C₃	C₅×#577	1	1	yes	characteristic
486	C₂×C₃	C₅×#578	1	1	yes	characteristic
487	C₅	C₃×#3137	1	1	yes	characteristic, direct product factor, Sylow
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	4	1	no	—
491	C₂²	—	4	1	no	—
492	C₂²	—	4	1	no	—
493	C₂²	C₃×C₅×#124	1	2	yes	—
494	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	1	no	—
501	C₄	—	4	1	no	—
502	C₄	C₃×C₅×#124	1	2	yes	—
503	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
504	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
505	C₃	C₅×#3137	1	1	yes	characteristic, direct product factor, Sylow
506	C₂	—	2	2	no	—
507	C₂	—	8	1	no	—
508	C₂	C₂×C₃×C₅×#124	1	1	yes	characteristic
509	C₂	C₃×C₅×#577	1	1	yes	characteristic
510	C₂	C₃×C₅×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#544	C₂	semidirect
3. C₃×C₅×#491	C₂	semidirect
4. C₃×C₅×#489	C₂	semidirect
5. C₃×C₅×#488	C₂	semidirect
6. C₃×C₅×#487	C₂	semidirect
7. C₃×C₅×#419	C₂	semidirect
10. C₂×C₃×C₅×#103	C₂	semidirect
11. C₃×C₅×#405	C₂	semidirect
12. C₅×#3137	C₃	direct (N × H)
42. C₃×#3137	C₅	direct (N × H)
43. C₅×#544	C₂×C₃	semidirect
45. C₅×#491	C₂×C₃	semidirect
46. C₅×#489	C₂×C₃	semidirect
47. C₅×#488	C₂×C₃	semidirect
48. C₅×#487	C₂×C₃	semidirect
49. C₅×#419	C₂×C₃	semidirect
52. C₂×C₅×#103	C₂×C₃	semidirect
53. C₅×#405	C₂×C₃	semidirect
90. C₃×#544	C₂×C₅	semidirect
92. C₃×#491	C₂×C₅	semidirect
93. C₃×#489	C₂×C₅	semidirect
94. C₃×#488	C₂×C₅	semidirect
95. C₃×#487	C₂×C₅	semidirect
96. C₃×#419	C₂×C₅	semidirect
99. C₂×C₃×#103	C₂×C₅	semidirect
100. C₃×#405	C₂×C₅	semidirect
130. #3137	C₃×C₅	direct (N × H)
224. #544	C₂×C₃×C₅	semidirect
226. #491	C₂×C₃×C₅	semidirect
227. #489	C₂×C₃×C₅	semidirect
228. #488	C₂×C₃×C₅	semidirect
229. #487	C₂×C₃×C₅	semidirect
230. #419	C₂×C₃×C₅	semidirect
233. C₂×#103	C₂×C₃×C₅	semidirect
234. #405	C₂×C₃×C₅	semidirect
431. C₃×C₅	#3137	direct (N × H)
487. C₅	C₃×#3137	direct (N × H)
505. C₃	C₅×#3137	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×#544	2
C₃×C₅×#536	2
C₃×C₅×#491	2
C₃×C₅×#489	2
C₃×C₅×#488	2
C₃×C₅×#487	2
C₃×C₅×#419	2
C₃×C₅×#417	2
C₃×C₅×#416	2
C₂×C₃×C₅×#103	2
C₃×C₅×#405	2
C₅×#3137	3
C₃×#3137	5

Subgroups — C3×C5×#3137 #14276171

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3137 #14276171