Subgroups — C₃×C₅×#3115 #14276149

Order 1920.

860 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#482	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#475	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#474	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#460	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#459	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#449	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#442	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#440	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#432	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3115	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	—	2	1	no	—
14	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
16	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
17	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×#127	C₂²	1	1	yes	characteristic
19	C₃×C₅×#124	—	2	1	no	—
20	C₃×C₅×#121	—	2	1	no	—
21	C₃×C₅×#121	C₂²	1	2	yes	—
22	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
24	C₃×C₄×C₅×D₄	—	2	1	no	—
25	C₃×C₄×C₅×D₄	—	2	1	no	—
26	C₃×C₄×C₅×D₄	—	2	1	no	—
27	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
28	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
30	C₃×C₅×#117	—	2	1	no	—
31	C₃×C₅×#117	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄²×C₅	—	2	1	no	—
33	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
34	C₃×C₅×#107	C₂²	1	2	yes	—
35	C₃×C₅×#106	C₂²	1	2	yes	—
36	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₃×C₅×#103	C₂²	1	2	yes	—
39	C₃×C₅×#102	C₂²	1	2	yes	—
40	C₃×C₅×#102	C₂²	1	2	yes	—
41	C₃×C₅×#102	C₂²	1	2	yes	—
42	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
43	C₃×C₅×#97	C₂²	1	2	yes	—
44	C₃×#3115	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
46	C₄×C₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#482	C₂×C₃	1	2	yes	complemented
48	C₅×#475	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#474	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#460	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#459	C₂×C₃	1	1	yes	characteristic, complemented
52	C₅×#449	C₂×C₃	1	2	yes	complemented
53	C₅×#442	C₂×C₃	1	2	yes	complemented
54	C₅×#440	C₂×C₃	1	2	yes	complemented
55	C₅×#432	C₂×C₃	1	1	yes	characteristic, complemented
56	C₃×C₅×#41	—	2	2	no	—
57	C₃×C₅×#41	—	2	2	no	—
58	C₃×C₅×#41	—	4	4	no	—
59	C₂×C₃×C₅×Q₈	—	2	1	no	—
60	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₅×D₄	—	2	1	no	—
62	C₂×C₃×C₅×D₄	—	2	2	no	—
63	C₂×C₃×C₅×D₄	—	2	1	no	—
64	C₂×C₃×C₅×D₄	—	2	1	no	—
65	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
66	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	—	2	1	no	—
68	C₂²×C₃×C₄×C₅	—	2	1	no	—
69	C₂²×C₃×C₄×C₅	—	2	1	no	—
70	C₂²×C₃×C₄×C₅	—	2	2	no	—
71	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
72	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
73	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₃×C₅×SD₁₆	—	2	4	no	—
75	C₃×C₅×D₈	—	2	4	no	—
76	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
77	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
78	C₃×C₅×C₄⋊C₄	—	2	1	no	—
79	C₃×C₅×C₄⋊C₄	—	2	1	no	—
80	C₃×C₅×C₄⋊C₄	—	2	1	no	—
81	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
84	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
85	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
86	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
87	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
88	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
89	C₃×C₄²×C₅	—	2	1	no	—
90	C₃×C₄²×C₅	—	2	1	no	—
91	C₃×C₄²×C₅	—	2	1	no	—
92	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
93	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
94	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
95	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
96	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×C₄×#41	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#482	C₂×C₅	1	2	yes	complemented
99	C₃×#475	C₂×C₅	1	1	yes	characteristic, complemented
100	C₃×#474	C₂×C₅	1	1	yes	characteristic, complemented
101	C₃×#460	C₂×C₅	1	1	yes	characteristic, complemented
102	C₃×#459	C₂×C₅	1	1	yes	characteristic, complemented
103	C₃×#449	C₂×C₅	1	2	yes	complemented
104	C₃×#442	C₂×C₅	1	2	yes	complemented
105	C₃×#440	C₂×C₅	1	2	yes	complemented
106	C₃×#432	C₂×C₅	1	1	yes	characteristic, complemented
107	C₂×C₅×#41	—	2	1	no	—
108	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
110	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
111	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
112	C₅×#127	C₂²×C₃	1	1	yes	characteristic
113	C₅×#124	—	2	1	no	—
114	C₅×#121	—	2	1	no	—
115	C₅×#121	C₂²×C₃	1	2	yes	—
116	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
117	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
118	C₄×C₅×D₄	—	2	1	no	—
119	C₄×C₅×D₄	—	2	1	no	—
120	C₄×C₅×D₄	—	2	1	no	—
121	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
122	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
123	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
124	C₅×#117	—	2	1	no	—
125	C₅×#117	C₂²×C₃	1	1	yes	characteristic
126	C₂×C₄²×C₅	—	2	1	no	—
127	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
128	C₅×#107	C₂²×C₃	1	2	yes	—
129	C₅×#106	C₂²×C₃	1	2	yes	—
130	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
131	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
132	C₅×#103	C₂²×C₃	1	2	yes	—
133	C₅×#102	C₂²×C₃	1	2	yes	—
134	C₅×#102	C₂²×C₃	1	2	yes	—
135	C₅×#102	C₂²×C₃	1	2	yes	—
136	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
137	C₅×#97	C₂²×C₃	1	2	yes	—
138	#3115	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
139	C₂³×C₃×C₅	—	2	1	no	—
140	C₂³×C₃×C₅	—	2	2	no	—
141	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
142	C₃×C₅×Q₈	—	2	1	no	—
143	C₃×C₅×Q₈	—	4	2	no	—
144	C₃×C₅×Q₈	#41	1	2	yes	complemented
145	C₃×C₅×D₄	—	2	4	no	—
146	C₃×C₅×D₄	—	2	1	no	—
147	C₃×C₅×D₄	—	2	2	no	—
148	C₃×C₅×D₄	—	2	2	no	—
149	C₃×C₅×D₄	—	4	2	no	—
150	C₃×C₅×D₄	—	4	4	no	—
151	C₃×C₅×D₄	—	4	2	no	—
152	C₃×C₅×D₄	#41	1	2	yes	complemented
153	C₂×C₃×C₄×C₅	—	2	4	no	—
154	C₂×C₃×C₄×C₅	—	2	1	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	2	1	no	—
157	C₂×C₃×C₄×C₅	—	2	1	no	—
158	C₂×C₃×C₄×C₅	—	2	1	no	—
159	C₂×C₃×C₄×C₅	—	2	1	no	—
160	C₂×C₃×C₄×C₅	—	2	2	no	—
161	C₂×C₃×C₄×C₅	—	4	1	no	—
162	C₂×C₃×C₄×C₅	—	4	2	no	—
163	C₂×C₃×C₄×C₅	—	4	4	no	—
164	C₂×C₃×C₄×C₅	—	4	2	no	—
165	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
166	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
167	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
168	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
169	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
170	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
171	C₃×C₅×C₈	—	2	2	no	—
172	C₃×C₅×C₈	—	2	2	no	—
173	C₂×C₃×#41	—	2	1	no	—
174	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
176	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
177	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
178	C₃×#127	C₂²×C₅	1	1	yes	characteristic
179	C₃×#124	—	2	1	no	—
180	C₃×#121	—	2	1	no	—
181	C₃×#121	C₂²×C₅	1	2	yes	—
182	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
183	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
184	C₃×C₄×D₄	—	2	1	no	—
185	C₃×C₄×D₄	—	2	1	no	—
186	C₃×C₄×D₄	—	2	1	no	—
187	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
188	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
189	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
190	C₃×#117	—	2	1	no	—
191	C₃×#117	C₂²×C₅	1	1	yes	characteristic
192	C₂×C₃×C₄²	—	2	1	no	—
193	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
194	C₃×#107	C₂²×C₅	1	2	yes	—
195	C₃×#106	C₂²×C₅	1	2	yes	—
196	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
197	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
198	C₃×#103	C₂²×C₅	1	2	yes	—
199	C₃×#102	C₂²×C₅	1	2	yes	—
200	C₃×#102	C₂²×C₅	1	2	yes	—
201	C₃×#102	C₂²×C₅	1	2	yes	—
202	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
203	C₃×#97	C₂²×C₅	1	2	yes	—
204	C₅×#41	—	2	2	no	—
205	C₅×#41	—	2	2	no	—
206	C₅×#41	—	4	4	no	—
207	C₂×C₅×Q₈	—	2	1	no	—
208	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
209	C₂×C₅×D₄	—	2	1	no	—
210	C₂×C₅×D₄	—	2	2	no	—
211	C₂×C₅×D₄	—	2	1	no	—
212	C₂×C₅×D₄	—	2	1	no	—
213	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
214	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
215	C₂²×C₄×C₅	—	2	1	no	—
216	C₂²×C₄×C₅	—	2	1	no	—
217	C₂²×C₄×C₅	—	2	1	no	—
218	C₂²×C₄×C₅	—	2	2	no	—
219	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
222	C₅×SD₁₆	—	2	4	no	—
223	C₅×D₈	—	2	4	no	—
224	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
225	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
226	C₅×C₄⋊C₄	—	2	1	no	—
227	C₅×C₄⋊C₄	—	2	1	no	—
228	C₅×C₄⋊C₄	—	2	1	no	—
229	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
230	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
231	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
232	C₅×C₂²⋊C₄	—	2	1	no	—
233	C₅×C₂²⋊C₄	—	2	1	no	—
234	C₅×C₂²⋊C₄	—	2	1	no	—
235	C₅×C₂²⋊C₄	—	2	2	no	—
236	C₅×C₂²⋊C₄	—	2	2	no	—
237	C₄²×C₅	—	2	1	no	—
238	C₄²×C₅	—	2	1	no	—
239	C₄²×C₅	—	2	1	no	—
240	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
241	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
242	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
243	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
244	#532	C₂×C₃×C₅	1	1	yes	characteristic, complemented
245	C₄×#41	C₂×C₃×C₅	1	1	yes	characteristic, complemented
246	#482	C₂×C₃×C₅	1	2	yes	complemented
247	#475	C₂×C₃×C₅	1	1	yes	characteristic, complemented
248	#474	C₂×C₃×C₅	1	1	yes	characteristic, complemented
249	#460	C₂×C₃×C₅	1	1	yes	characteristic, complemented
250	#459	C₂×C₃×C₅	1	1	yes	characteristic, complemented
251	#449	C₂×C₃×C₅	1	2	yes	complemented
252	#442	C₂×C₃×C₅	1	2	yes	complemented
253	#440	C₂×C₃×C₅	1	2	yes	complemented
254	#432	C₂×C₃×C₅	1	1	yes	characteristic, complemented
255	C₂²×C₃×C₅	—	2	1	no	—
256	C₂²×C₃×C₅	—	2	2	no	—
257	C₂²×C₃×C₅	—	2	1	no	—
258	C₂²×C₃×C₅	—	2	1	no	—
259	C₂²×C₃×C₅	—	4	1	no	—
260	C₂²×C₃×C₅	—	4	1	no	—
261	C₂²×C₃×C₅	—	4	2	no	—
262	C₂²×C₃×C₅	—	4	2	no	—
263	C₂²×C₃×C₅	—	4	2	no	—
264	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
265	C₃×C₄×C₅	—	2	1	no	—
266	C₃×C₄×C₅	—	2	2	no	—
267	C₃×C₄×C₅	—	2	1	no	—
268	C₃×C₄×C₅	—	2	1	no	—
269	C₃×C₄×C₅	—	2	1	no	—
270	C₃×C₄×C₅	—	4	1	no	—
271	C₃×C₄×C₅	—	4	2	no	—
272	C₃×C₄×C₅	—	4	1	no	—
273	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
274	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
275	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
276	C₃×#41	—	2	2	no	—
277	C₃×#41	—	2	2	no	—
278	C₃×#41	—	4	4	no	—
279	C₂×C₃×Q₈	—	2	1	no	—
280	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
281	C₂×C₃×D₄	—	2	1	no	—
282	C₂×C₃×D₄	—	2	2	no	—
283	C₂×C₃×D₄	—	2	1	no	—
284	C₂×C₃×D₄	—	2	1	no	—
285	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
286	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
287	C₂²×C₃×C₄	—	2	1	no	—
288	C₂²×C₃×C₄	—	2	1	no	—
289	C₂²×C₃×C₄	—	2	1	no	—
290	C₂²×C₃×C₄	—	2	2	no	—
291	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
292	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
293	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
294	C₃×SD₁₆	—	2	4	no	—
295	C₃×D₈	—	2	4	no	—
296	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
297	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
298	C₃×C₄⋊C₄	—	2	1	no	—
299	C₃×C₄⋊C₄	—	2	1	no	—
300	C₃×C₄⋊C₄	—	2	1	no	—
301	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
302	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
303	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
304	C₃×C₂²⋊C₄	—	2	1	no	—
305	C₃×C₂²⋊C₄	—	2	1	no	—
306	C₃×C₂²⋊C₄	—	2	1	no	—
307	C₃×C₂²⋊C₄	—	2	2	no	—
308	C₃×C₂²⋊C₄	—	2	2	no	—
309	C₃×C₄²	—	2	1	no	—
310	C₃×C₄²	—	2	1	no	—
311	C₃×C₄²	—	2	1	no	—
312	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
313	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
314	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
315	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
316	C₂³×C₅	—	2	1	no	—
317	C₂³×C₅	—	2	2	no	—
318	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
319	C₅×Q₈	—	2	1	no	—
320	C₅×Q₈	—	4	2	no	—
321	C₅×Q₈	C₃×#41	1	2	yes	complemented
322	C₅×D₄	—	2	4	no	—
323	C₅×D₄	—	2	1	no	—
324	C₅×D₄	—	2	2	no	—
325	C₅×D₄	—	2	2	no	—
326	C₅×D₄	—	4	2	no	—
327	C₅×D₄	—	4	4	no	—
328	C₅×D₄	—	4	2	no	—
329	C₅×D₄	C₃×#41	1	2	yes	complemented
330	C₂×C₄×C₅	—	2	4	no	—
331	C₂×C₄×C₅	—	2	1	no	—
332	C₂×C₄×C₅	—	2	2	no	—
333	C₂×C₄×C₅	—	2	1	no	—
334	C₂×C₄×C₅	—	2	1	no	—
335	C₂×C₄×C₅	—	2	1	no	—
336	C₂×C₄×C₅	—	2	1	no	—
337	C₂×C₄×C₅	—	2	2	no	—
338	C₂×C₄×C₅	—	4	1	no	—
339	C₂×C₄×C₅	—	4	2	no	—
340	C₂×C₄×C₅	—	4	4	no	—
341	C₂×C₄×C₅	—	4	2	no	—
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	C₂×C₃×D₄	1	1	yes	characteristic
345	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
346	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
347	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
348	C₅×C₈	—	2	2	no	—
349	C₅×C₈	—	2	2	no	—
350	C₂×#41	—	2	1	no	—
351	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
352	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
353	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
354	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
355	#127	C₂²×C₃×C₅	1	1	yes	characteristic
356	#124	—	2	1	no	—
357	#121	—	2	1	no	—
358	#121	C₂²×C₃×C₅	1	2	yes	—
359	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
360	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
365	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
366	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
367	#117	—	2	1	no	—
368	#117	C₂²×C₃×C₅	1	1	yes	characteristic
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
371	#107	C₂²×C₃×C₅	1	2	yes	—
372	#106	C₂²×C₃×C₅	1	2	yes	—
373	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
374	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
375	#103	C₂²×C₃×C₅	1	2	yes	—
376	#102	C₂²×C₃×C₅	1	2	yes	—
377	#102	C₂²×C₃×C₅	1	2	yes	—
378	#102	C₂²×C₃×C₅	1	2	yes	—
379	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
380	#97	C₂²×C₃×C₅	1	2	yes	—
381	C₂×C₃×C₅	—	4	1	no	—
382	C₂×C₃×C₅	—	4	2	no	—
383	C₂×C₃×C₅	—	8	2	no	—
384	C₂×C₃×C₅	#525	1	1	yes	characteristic
385	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
386	C₂×C₃×C₅	#575	1	1	yes	characteristic
387	C₂³×C₃	—	2	1	no	—
388	C₂³×C₃	—	2	2	no	—
389	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
390	C₃×Q₈	—	2	1	no	—
391	C₃×Q₈	—	4	2	no	—
392	C₃×Q₈	C₅×#41	1	2	yes	complemented
393	C₃×D₄	—	2	4	no	—
394	C₃×D₄	—	2	1	no	—
395	C₃×D₄	—	2	2	no	—
396	C₃×D₄	—	2	2	no	—
397	C₃×D₄	—	4	2	no	—
398	C₃×D₄	—	4	4	no	—
399	C₃×D₄	—	4	2	no	—
400	C₃×D₄	C₅×#41	1	2	yes	complemented
401	C₂×C₃×C₄	—	2	4	no	—
402	C₂×C₃×C₄	—	2	1	no	—
403	C₂×C₃×C₄	—	2	2	no	—
404	C₂×C₃×C₄	—	2	1	no	—
405	C₂×C₃×C₄	—	2	1	no	—
406	C₂×C₃×C₄	—	2	1	no	—
407	C₂×C₃×C₄	—	2	1	no	—
408	C₂×C₃×C₄	—	2	2	no	—
409	C₂×C₃×C₄	—	4	1	no	—
410	C₂×C₃×C₄	—	4	2	no	—
411	C₂×C₃×C₄	—	4	4	no	—
412	C₂×C₃×C₄	—	4	2	no	—
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	C₂×C₅×D₄	1	1	yes	characteristic
416	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
417	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
418	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
419	C₃×C₈	—	2	2	no	—
420	C₃×C₈	—	2	2	no	—
421	C₂²×C₅	—	2	1	no	—
422	C₂²×C₅	—	2	1	no	—
423	C₂²×C₅	—	2	1	no	—
424	C₂²×C₅	—	2	2	no	—
425	C₂²×C₅	—	4	1	no	—
426	C₂²×C₅	—	4	1	no	—
427	C₂²×C₅	—	4	2	no	—
428	C₂²×C₅	—	4	2	no	—
429	C₂²×C₅	—	4	2	no	—
430	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
431	C₄×C₅	—	2	1	no	—
432	C₄×C₅	—	2	1	no	—
433	C₄×C₅	—	2	1	no	—
434	C₄×C₅	—	2	1	no	—
435	C₄×C₅	—	2	2	no	—
436	C₄×C₅	—	4	1	no	—
437	C₄×C₅	—	4	2	no	—
438	C₄×C₅	—	4	1	no	—
439	C₄×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
440	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
441	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
442	#41	—	2	2	no	—
443	#41	—	2	2	no	—
444	#41	—	4	4	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
452	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
458	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
459	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
460	SD₁₆	—	2	4	no	—
461	D₈	—	2	4	no	—
462	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
463	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
468	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
469	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
479	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
480	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
481	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
482	C₃×C₅	#3115	1	1	yes	characteristic, direct product factor, Hall
483	C₂²×C₃	—	2	1	no	—
484	C₂²×C₃	—	2	2	no	—
485	C₂²×C₃	—	2	1	no	—
486	C₂²×C₃	—	2	1	no	—
487	C₂²×C₃	—	4	1	no	—
488	C₂²×C₃	—	4	1	no	—
489	C₂²×C₃	—	4	2	no	—
490	C₂²×C₃	—	4	2	no	—
491	C₂²×C₃	—	4	2	no	—
492	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
493	C₃×C₄	—	2	1	no	—
494	C₃×C₄	—	2	2	no	—
495	C₃×C₄	—	2	1	no	—
496	C₃×C₄	—	2	1	no	—
497	C₃×C₄	—	2	1	no	—
498	C₃×C₄	—	4	1	no	—
499	C₃×C₄	—	4	2	no	—
500	C₃×C₄	—	4	1	no	—
501	C₃×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
502	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
503	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
504	C₂×C₅	—	4	1	no	—
505	C₂×C₅	—	4	2	no	—
506	C₂×C₅	—	8	2	no	—
507	C₂×C₅	C₃×#525	1	1	yes	characteristic
508	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
509	C₂×C₅	C₃×#575	1	1	yes	characteristic
510	C₂³	—	2	1	no	—
511	C₂³	—	2	2	no	—
512	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
513	Q₈	—	2	1	no	—
514	Q₈	—	4	2	no	—
515	Q₈	C₃×C₅×#41	1	2	yes	complemented
516	D₄	—	2	4	no	—
517	D₄	—	2	1	no	—
518	D₄	—	2	2	no	—
519	D₄	—	2	2	no	—
520	D₄	—	4	2	no	—
521	D₄	—	4	4	no	—
522	D₄	—	4	2	no	—
523	D₄	C₃×C₅×#41	1	2	yes	complemented
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	4	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
537	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
538	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
539	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
540	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
541	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
542	C₈	—	2	2	no	—
543	C₈	—	2	2	no	—
544	C₂×C₃	—	4	1	no	—
545	C₂×C₃	—	4	2	no	—
546	C₂×C₃	—	8	2	no	—
547	C₂×C₃	C₅×#525	1	1	yes	characteristic
548	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
549	C₂×C₃	C₅×#575	1	1	yes	characteristic
550	C₅	C₃×#3115	1	1	yes	characteristic, direct product factor, Sylow
551	C₂²	—	2	1	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	2	2	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
570	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
571	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
572	C₃	C₅×#3115	1	1	yes	characteristic, direct product factor, Sylow
573	C₂	—	4	1	no	—
574	C₂	—	4	2	no	—
575	C₂	—	8	2	no	—
576	C₂	C₃×C₅×#525	1	1	yes	characteristic
577	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
578	C₂	C₃×C₅×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#532	C₂	semidirect
2. C₃×C₄×C₅×#41	C₂	semidirect
3. C₃×C₅×#482	C₂	semidirect
4. C₃×C₅×#475	C₂	semidirect
5. C₃×C₅×#474	C₂	semidirect
6. C₃×C₅×#460	C₂	semidirect
7. C₃×C₅×#459	C₂	semidirect
8. C₃×C₅×#449	C₂	semidirect
9. C₃×C₅×#442	C₂	semidirect
10. C₃×C₅×#440	C₂	semidirect
11. C₃×C₅×#432	C₂	semidirect
12. C₅×#3115	C₃	direct (N × H)
44. C₃×#3115	C₅	direct (N × H)
45. C₅×#532	C₂×C₃	semidirect
46. C₄×C₅×#41	C₂×C₃	semidirect
47. C₅×#482	C₂×C₃	semidirect
48. C₅×#475	C₂×C₃	semidirect
49. C₅×#474	C₂×C₃	semidirect
50. C₅×#460	C₂×C₃	semidirect
51. C₅×#459	C₂×C₃	semidirect
52. C₅×#449	C₂×C₃	semidirect
53. C₅×#442	C₂×C₃	semidirect
54. C₅×#440	C₂×C₃	semidirect
55. C₅×#432	C₂×C₃	semidirect
96. C₃×#532	C₂×C₅	semidirect
97. C₃×C₄×#41	C₂×C₅	semidirect
98. C₃×#482	C₂×C₅	semidirect
99. C₃×#475	C₂×C₅	semidirect
100. C₃×#474	C₂×C₅	semidirect
101. C₃×#460	C₂×C₅	semidirect
102. C₃×#459	C₂×C₅	semidirect
103. C₃×#449	C₂×C₅	semidirect
104. C₃×#442	C₂×C₅	semidirect
105. C₃×#440	C₂×C₅	semidirect
106. C₃×#432	C₂×C₅	semidirect
138. #3115	C₃×C₅	direct (N × H)
144. C₃×C₅×Q₈	#41	semidirect
152. C₃×C₅×D₄	#41	semidirect
244. #532	C₂×C₃×C₅	semidirect
245. C₄×#41	C₂×C₃×C₅	semidirect
246. #482	C₂×C₃×C₅	semidirect
247. #475	C₂×C₃×C₅	semidirect
248. #474	C₂×C₃×C₅	semidirect
249. #460	C₂×C₃×C₅	semidirect
250. #459	C₂×C₃×C₅	semidirect
251. #449	C₂×C₃×C₅	semidirect
252. #442	C₂×C₃×C₅	semidirect
253. #440	C₂×C₃×C₅	semidirect
254. #432	C₂×C₃×C₅	semidirect
321. C₅×Q₈	C₃×#41	semidirect
329. C₅×D₄	C₃×#41	semidirect
392. C₃×Q₈	C₅×#41	semidirect
400. C₃×D₄	C₅×#41	semidirect
482. C₃×C₅	#3115	direct (N × H)
515. Q₈	C₃×C₅×#41	semidirect
523. D₄	C₃×C₅×#41	semidirect
550. C₅	C₃×#3115	direct (N × H)
572. C₃	C₅×#3115	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×#532	2
C₃×C₄×C₅×#41	2
C₃×C₅×#482	2
C₃×C₅×#475	2
C₃×C₅×#474	2
C₃×C₅×#460	2
C₃×C₅×#459	2
C₃×C₅×#449	2
C₃×C₅×#442	2
C₃×C₅×#440	2
C₃×C₅×#432	2
C₅×#3115	3
C₃×#3115	5

Subgroups — C3×C5×#3115 #14276149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3115 #14276149