Subgroups — C₃×C₅×#3114 #14276148

Order 1920.

900 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#483	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#480	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#478	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#463	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#450	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#447	C₂	1	1	yes	maximal, characteristic
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×#3114	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₄×C₅	—	2	1	no	—
15	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
16	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
17	C₃×C₅×#126	—	2	1	no	—
18	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₅×#123	—	2	1	no	—
21	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₃×C₅×#121	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
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	2	yes	—
28	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
29	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₅×#117	—	2	1	no	—
31	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
33	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
34	C₃×C₅×#107	C₂²	1	2	yes	complemented
35	C₃×C₅×#106	C₂²	1	2	yes	complemented
36	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
37	C₃×C₅×#103	C₂²	1	2	yes	complemented
38	C₃×C₅×#102	C₂²	1	2	yes	—
39	C₃×C₅×#102	C₂²	1	2	yes	—
40	C₃×C₅×#102	C₂²	1	2	yes	complemented
41	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
42	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₃×C₅×#97	C₂²	1	2	yes	complemented
44	C₃×#3114	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₅×#529	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#483	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#480	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#478	C₂×C₃	1	2	yes	complemented
50	C₅×#463	C₂×C₃	1	2	yes	complemented
51	C₅×#450	C₂×C₃	1	1	yes	characteristic, complemented
52	C₅×#447	C₂×C₃	1	1	yes	characteristic
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	C₂⁴×C₃×C₅	—	2	1	no	—
57	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₅×D₄	—	2	4	no	—
59	C₂×C₃×C₅×D₄	—	2	1	no	—
60	C₂×C₃×C₅×D₄	—	2	1	no	—
61	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
63	C₂²×C₃×C₄×C₅	—	2	1	no	—
64	C₂²×C₃×C₄×C₅	—	2	1	no	—
65	C₂²×C₃×C₄×C₅	—	2	2	no	—
66	C₂²×C₃×C₄×C₅	—	2	2	no	—
67	C₂²×C₃×C₄×C₅	—	4	4	no	—
68	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₃×C₅×SD₁₆	—	2	4	no	—
72	C₃×C₅×D₈	—	2	4	no	—
73	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
74	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
75	C₃×C₅×C₄⋊C₄	—	2	1	no	—
76	C₃×C₅×C₄⋊C₄	—	2	1	no	—
77	C₃×C₅×C₄⋊C₄	—	2	1	no	—
78	C₃×C₅×C₄⋊C₄	—	2	1	no	—
79	C₃×C₅×C₄⋊C₄	—	2	1	no	—
80	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
81	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
84	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
85	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
86	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
87	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
88	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
89	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
90	C₃×C₄²×C₅	—	2	1	no	—
91	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
92	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
93	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
94	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
95	C₃×#529	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#483	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#480	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#478	C₂×C₅	1	2	yes	complemented
100	C₃×#463	C₂×C₅	1	2	yes	complemented
101	C₃×#450	C₂×C₅	1	1	yes	characteristic, complemented
102	C₃×#447	C₂×C₅	1	1	yes	characteristic
103	C₃×#442	C₂×C₅	1	2	yes	complemented
104	C₃×#440	C₂×C₅	1	2	yes	complemented
105	C₃×#432	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
107	C₂³×C₄×C₅	—	2	1	no	—
108	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
109	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
110	C₅×#126	—	2	1	no	—
111	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
112	C₅×#124	C₂²×C₃	1	1	yes	characteristic, complemented
113	C₅×#123	—	2	1	no	—
114	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
115	C₅×#121	C₂²×C₃	1	1	yes	characteristic
116	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
117	C₄×C₅×D₄	—	2	1	no	—
118	C₄×C₅×D₄	—	2	1	no	—
119	C₄×C₅×D₄	—	2	1	no	—
120	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
121	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
122	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
123	C₅×#117	—	2	1	no	—
124	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
126	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
127	C₅×#107	C₂²×C₃	1	2	yes	complemented
128	C₅×#106	C₂²×C₃	1	2	yes	complemented
129	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
130	C₅×#103	C₂²×C₃	1	2	yes	complemented
131	C₅×#102	C₂²×C₃	1	2	yes	—
132	C₅×#102	C₂²×C₃	1	2	yes	—
133	C₅×#102	C₂²×C₃	1	2	yes	complemented
134	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
135	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
136	C₅×#97	C₂²×C₃	1	2	yes	complemented
137	#3114	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
138	C₂³×C₃×C₅	—	2	4	no	—
139	C₂³×C₃×C₅	—	2	2	no	—
140	C₂³×C₃×C₅	—	2	1	no	—
141	C₂³×C₃×C₅	—	4	2	no	—
142	C₂³×C₃×C₅	—	4	2	no	—
143	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
144	C₃×C₅×Q₈	—	2	2	no	—
145	C₃×C₅×D₄	—	2	4	no	—
146	C₃×C₅×D₄	—	2	2	no	—
147	C₃×C₅×D₄	—	2	2	no	—
148	C₃×C₅×D₄	—	4	2	no	—
149	C₃×C₅×D₄	#41	1	4	yes	—
150	C₂×C₃×C₄×C₅	—	2	2	no	—
151	C₂×C₃×C₄×C₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	—	2	1	no	—
153	C₂×C₃×C₄×C₅	—	2	1	no	—
154	C₂×C₃×C₄×C₅	—	2	1	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	4	1	no	—
157	C₂×C₃×C₄×C₅	—	4	2	no	—
158	C₂×C₃×C₄×C₅	—	4	4	no	—
159	C₂×C₃×C₄×C₅	—	4	4	no	—
160	C₂×C₃×C₄×C₅	—	4	2	no	—
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	C₂×D₄	1	1	yes	characteristic
164	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
165	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
166	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
167	C₃×C₅×C₈	—	2	2	no	—
168	C₃×C₅×C₈	—	2	2	no	—
169	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
170	C₂³×C₃×C₄	—	2	1	no	—
171	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
172	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
173	C₃×#126	—	2	1	no	—
174	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
175	C₃×#124	C₂²×C₅	1	1	yes	characteristic, complemented
176	C₃×#123	—	2	1	no	—
177	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
178	C₃×#121	C₂²×C₅	1	1	yes	characteristic
179	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
180	C₃×C₄×D₄	—	2	1	no	—
181	C₃×C₄×D₄	—	2	1	no	—
182	C₃×C₄×D₄	—	2	1	no	—
183	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
184	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
185	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
186	C₃×#117	—	2	1	no	—
187	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
188	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
189	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
190	C₃×#107	C₂²×C₅	1	2	yes	complemented
191	C₃×#106	C₂²×C₅	1	2	yes	complemented
192	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
193	C₃×#103	C₂²×C₅	1	2	yes	complemented
194	C₃×#102	C₂²×C₅	1	2	yes	—
195	C₃×#102	C₂²×C₅	1	2	yes	—
196	C₃×#102	C₂²×C₅	1	2	yes	complemented
197	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
198	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
199	C₃×#97	C₂²×C₅	1	2	yes	complemented
200	C₂⁴×C₅	—	2	1	no	—
201	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
202	C₂×C₅×D₄	—	2	4	no	—
203	C₂×C₅×D₄	—	2	1	no	—
204	C₂×C₅×D₄	—	2	1	no	—
205	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
206	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
207	C₂²×C₄×C₅	—	2	1	no	—
208	C₂²×C₄×C₅	—	2	1	no	—
209	C₂²×C₄×C₅	—	2	2	no	—
210	C₂²×C₄×C₅	—	2	2	no	—
211	C₂²×C₄×C₅	—	4	4	no	—
212	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
215	C₅×SD₁₆	—	2	4	no	—
216	C₅×D₈	—	2	4	no	—
217	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
218	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
219	C₅×C₄⋊C₄	—	2	1	no	—
220	C₅×C₄⋊C₄	—	2	1	no	—
221	C₅×C₄⋊C₄	—	2	1	no	—
222	C₅×C₄⋊C₄	—	2	1	no	—
223	C₅×C₄⋊C₄	—	2	1	no	—
224	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
225	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
226	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
227	C₅×C₂²⋊C₄	—	2	1	no	—
228	C₅×C₂²⋊C₄	—	2	2	no	—
229	C₅×C₂²⋊C₄	—	2	2	no	—
230	C₅×C₂²⋊C₄	—	2	1	no	—
231	C₅×C₂²⋊C₄	—	2	1	no	—
232	C₅×C₂²⋊C₄	—	2	1	no	—
233	C₅×C₂²⋊C₄	—	2	1	no	—
234	C₄²×C₅	—	2	1	no	—
235	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
236	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
237	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
238	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
239	#529	C₂×C₃×C₅	1	1	yes	characteristic, complemented
240	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
241	#483	C₂×C₃×C₅	1	1	yes	characteristic, complemented
242	#480	C₂×C₃×C₅	1	1	yes	characteristic, complemented
243	#478	C₂×C₃×C₅	1	2	yes	complemented
244	#463	C₂×C₃×C₅	1	2	yes	complemented
245	#450	C₂×C₃×C₅	1	1	yes	characteristic, complemented
246	#447	C₂×C₃×C₅	1	1	yes	characteristic
247	#442	C₂×C₃×C₅	1	2	yes	complemented
248	#440	C₂×C₃×C₅	1	2	yes	complemented
249	#432	C₂×C₃×C₅	1	1	yes	characteristic, complemented
250	C₂²×C₃×C₅	—	2	1	no	—
251	C₂²×C₃×C₅	—	2	1	no	—
252	C₂²×C₃×C₅	—	2	4	no	—
253	C₂²×C₃×C₅	—	4	8	no	—
254	C₂²×C₃×C₅	—	4	2	no	—
255	C₂²×C₃×C₅	—	4	2	no	—
256	C₂²×C₃×C₅	—	4	1	no	—
257	C₂²×C₃×C₅	—	4	1	no	—
258	C₂²×C₃×C₅	—	4	1	no	—
259	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
260	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
261	C₃×C₄×C₅	—	2	1	no	—
262	C₃×C₄×C₅	—	2	1	no	—
263	C₃×C₄×C₅	—	2	1	no	—
264	C₃×C₄×C₅	—	2	1	no	—
265	C₃×C₄×C₅	—	2	1	no	—
266	C₃×C₄×C₅	—	4	1	no	—
267	C₃×C₄×C₅	—	4	2	no	—
268	C₃×C₄×C₅	—	4	1	no	—
269	C₃×C₄×C₅	—	4	1	no	—
270	C₃×C₄×C₅	C₂×#41	1	2	yes	—
271	C₂⁴×C₃	—	2	1	no	—
272	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
273	C₂×C₃×D₄	—	2	4	no	—
274	C₂×C₃×D₄	—	2	1	no	—
275	C₂×C₃×D₄	—	2	1	no	—
276	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
277	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
278	C₂²×C₃×C₄	—	2	1	no	—
279	C₂²×C₃×C₄	—	2	1	no	—
280	C₂²×C₃×C₄	—	2	2	no	—
281	C₂²×C₃×C₄	—	2	2	no	—
282	C₂²×C₃×C₄	—	4	4	no	—
283	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
284	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
285	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
286	C₃×SD₁₆	—	2	4	no	—
287	C₃×D₈	—	2	4	no	—
288	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
289	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
290	C₃×C₄⋊C₄	—	2	1	no	—
291	C₃×C₄⋊C₄	—	2	1	no	—
292	C₃×C₄⋊C₄	—	2	1	no	—
293	C₃×C₄⋊C₄	—	2	1	no	—
294	C₃×C₄⋊C₄	—	2	1	no	—
295	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
296	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
297	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
298	C₃×C₂²⋊C₄	—	2	1	no	—
299	C₃×C₂²⋊C₄	—	2	2	no	—
300	C₃×C₂²⋊C₄	—	2	2	no	—
301	C₃×C₂²⋊C₄	—	2	1	no	—
302	C₃×C₂²⋊C₄	—	2	1	no	—
303	C₃×C₂²⋊C₄	—	2	1	no	—
304	C₃×C₂²⋊C₄	—	2	1	no	—
305	C₃×C₄²	—	2	1	no	—
306	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
307	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
308	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
309	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
310	C₂³×C₅	—	2	4	no	—
311	C₂³×C₅	—	2	2	no	—
312	C₂³×C₅	—	2	1	no	—
313	C₂³×C₅	—	4	2	no	—
314	C₂³×C₅	—	4	2	no	—
315	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
316	C₅×Q₈	—	2	2	no	—
317	C₅×D₄	—	2	4	no	—
318	C₅×D₄	—	2	2	no	—
319	C₅×D₄	—	2	2	no	—
320	C₅×D₄	—	4	2	no	—
321	C₅×D₄	C₃×#41	1	4	yes	—
322	C₂×C₄×C₅	—	2	2	no	—
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	—	2	1	no	—
325	C₂×C₄×C₅	—	2	1	no	—
326	C₂×C₄×C₅	—	2	1	no	—
327	C₂×C₄×C₅	—	2	2	no	—
328	C₂×C₄×C₅	—	4	1	no	—
329	C₂×C₄×C₅	—	4	2	no	—
330	C₂×C₄×C₅	—	4	4	no	—
331	C₂×C₄×C₅	—	4	4	no	—
332	C₂×C₄×C₅	—	4	2	no	—
333	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
334	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
335	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
336	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
337	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
338	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
339	C₅×C₈	—	2	2	no	—
340	C₅×C₈	—	2	2	no	—
341	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
342	C₂³×C₄	—	2	1	no	—
343	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
344	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
345	#126	—	2	1	no	—
346	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
347	#124	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
348	#123	—	2	1	no	—
349	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
350	#121	C₂²×C₃×C₅	1	1	yes	characteristic
351	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
352	C₄×D₄	—	2	1	no	—
353	C₄×D₄	—	2	1	no	—
354	C₄×D₄	—	2	1	no	—
355	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
356	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
357	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
358	#117	—	2	1	no	—
359	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
362	#107	C₂²×C₃×C₅	1	2	yes	complemented
363	#106	C₂²×C₃×C₅	1	2	yes	complemented
364	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
365	#103	C₂²×C₃×C₅	1	2	yes	complemented
366	#102	C₂²×C₃×C₅	1	2	yes	—
367	#102	C₂²×C₃×C₅	1	2	yes	—
368	#102	C₂²×C₃×C₅	1	2	yes	complemented
369	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
370	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
371	#97	C₂²×C₃×C₅	1	2	yes	complemented
372	C₂×C₃×C₅	—	2	2	no	—
373	C₂×C₃×C₅	—	4	4	no	—
374	C₂×C₃×C₅	—	8	1	no	—
375	C₂×C₃×C₅	#525	1	1	yes	characteristic
376	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
377	C₂×C₃×C₅	#575	1	1	yes	characteristic
378	C₂³×C₃	—	2	4	no	—
379	C₂³×C₃	—	2	2	no	—
380	C₂³×C₃	—	2	1	no	—
381	C₂³×C₃	—	4	2	no	—
382	C₂³×C₃	—	4	2	no	—
383	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
384	C₃×Q₈	—	2	2	no	—
385	C₃×D₄	—	2	4	no	—
386	C₃×D₄	—	2	2	no	—
387	C₃×D₄	—	2	2	no	—
388	C₃×D₄	—	4	2	no	—
389	C₃×D₄	C₅×#41	1	4	yes	—
390	C₂×C₃×C₄	—	2	2	no	—
391	C₂×C₃×C₄	—	2	2	no	—
392	C₂×C₃×C₄	—	2	1	no	—
393	C₂×C₃×C₄	—	2	1	no	—
394	C₂×C₃×C₄	—	2	1	no	—
395	C₂×C₃×C₄	—	2	2	no	—
396	C₂×C₃×C₄	—	4	1	no	—
397	C₂×C₃×C₄	—	4	2	no	—
398	C₂×C₃×C₄	—	4	4	no	—
399	C₂×C₃×C₄	—	4	4	no	—
400	C₂×C₃×C₄	—	4	2	no	—
401	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
402	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
403	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
404	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
405	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
406	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
407	C₃×C₈	—	2	2	no	—
408	C₃×C₈	—	2	2	no	—
409	C₂²×C₅	—	2	1	no	—
410	C₂²×C₅	—	2	1	no	—
411	C₂²×C₅	—	2	4	no	—
412	C₂²×C₅	—	4	8	no	—
413	C₂²×C₅	—	4	2	no	—
414	C₂²×C₅	—	4	2	no	—
415	C₂²×C₅	—	4	1	no	—
416	C₂²×C₅	—	4	1	no	—
417	C₂²×C₅	—	4	1	no	—
418	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
419	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
420	C₄×C₅	—	2	1	no	—
421	C₄×C₅	—	2	1	no	—
422	C₄×C₅	—	2	1	no	—
423	C₄×C₅	—	2	1	no	—
424	C₄×C₅	—	2	1	no	—
425	C₄×C₅	—	4	2	no	—
426	C₄×C₅	—	4	1	no	—
427	C₄×C₅	—	4	1	no	—
428	C₄×C₅	—	4	1	no	—
429	C₄×C₅	C₂×C₃×#41	1	2	yes	—
430	C₂⁴	—	2	1	no	—
431	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
436	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	4	4	no	—
442	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
443	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
444	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
445	SD₁₆	—	2	4	no	—
446	D₈	—	2	4	no	—
447	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
448	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
455	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
456	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
457	C₂²⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
466	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
467	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
468	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
469	C₃×C₅	#3114	1	1	yes	characteristic, direct product factor, Hall
470	C₂²×C₃	—	2	1	no	—
471	C₂²×C₃	—	2	1	no	—
472	C₂²×C₃	—	2	4	no	—
473	C₂²×C₃	—	4	8	no	—
474	C₂²×C₃	—	4	2	no	—
475	C₂²×C₃	—	4	2	no	—
476	C₂²×C₃	—	4	1	no	—
477	C₂²×C₃	—	4	1	no	—
478	C₂²×C₃	—	4	1	no	—
479	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
480	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
481	C₃×C₄	—	2	1	no	—
482	C₃×C₄	—	2	1	no	—
483	C₃×C₄	—	2	1	no	—
484	C₃×C₄	—	2	1	no	—
485	C₃×C₄	—	2	1	no	—
486	C₃×C₄	—	4	1	no	—
487	C₃×C₄	—	4	2	no	—
488	C₃×C₄	—	4	1	no	—
489	C₃×C₄	—	4	1	no	—
490	C₃×C₄	C₂×C₅×#41	1	2	yes	—
491	C₂×C₅	—	2	2	no	—
492	C₂×C₅	—	4	4	no	—
493	C₂×C₅	—	8	1	no	—
494	C₂×C₅	C₃×#525	1	1	yes	characteristic
495	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
496	C₂×C₅	C₃×#575	1	1	yes	characteristic
497	C₂³	—	2	4	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	1	no	—
500	C₂³	—	4	2	no	—
501	C₂³	—	4	2	no	—
502	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
503	Q₈	—	2	2	no	—
504	D₄	—	2	4	no	—
505	D₄	—	2	2	no	—
506	D₄	—	2	2	no	—
507	D₄	—	4	2	no	—
508	D₄	C₃×C₅×#41	1	4	yes	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
521	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
522	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
523	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
524	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
525	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
526	C₈	—	2	2	no	—
527	C₈	—	2	2	no	—
528	C₂×C₃	—	2	2	no	—
529	C₂×C₃	—	4	4	no	—
530	C₂×C₃	—	8	1	no	—
531	C₂×C₃	C₅×#525	1	1	yes	characteristic
532	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
533	C₂×C₃	C₅×#575	1	1	yes	characteristic
534	C₅	C₃×#3114	1	1	yes	characteristic, direct product factor, Sylow
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	4	no	—
538	C₂²	—	4	8	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
545	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	C₂×C₃×C₅×#41	1	2	yes	—
556	C₃	C₅×#3114	1	1	yes	characteristic, direct product factor, Sylow
557	C₂	—	2	2	no	—
558	C₂	—	4	4	no	—
559	C₂	—	8	1	no	—
560	C₂	C₃×C₅×#525	1	1	yes	characteristic
561	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
562	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
prime radical	C₃×C₅×#447	C₂
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×#529	C₂	semidirect
2. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
3. C₃×C₅×#483	C₂	semidirect
4. C₃×C₅×#480	C₂	semidirect
5. C₃×C₅×#478	C₂	semidirect
6. C₃×C₅×#463	C₂	semidirect
7. C₃×C₅×#450	C₂	semidirect
9. C₃×C₅×#442	C₂	semidirect
10. C₃×C₅×#440	C₂	semidirect
11. C₃×C₅×#432	C₂	semidirect
12. C₅×#3114	C₃	direct (N × H)
18. C₃×C₅×#125	C₂²	semidirect
19. C₃×C₅×#124	C₂²	semidirect
23. C₃×C₄×C₅×Q₈	C₂²	semidirect
29. C₃×C₄×C₅×D₄	C₂²	semidirect
34. C₃×C₅×#107	C₂²	semidirect
35. C₃×C₅×#106	C₂²	semidirect
36. C₃×C₅×C₄⋊C₈	C₂²	semidirect
37. C₃×C₅×#103	C₂²	semidirect
40. C₃×C₅×#102	C₂²	semidirect
43. C₃×C₅×#97	C₂²	semidirect
44. C₃×#3114	C₅	direct (N × H)
45. C₅×#529	C₂×C₃	semidirect
46. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
47. C₅×#483	C₂×C₃	semidirect
48. C₅×#480	C₂×C₃	semidirect
49. C₅×#478	C₂×C₃	semidirect
50. C₅×#463	C₂×C₃	semidirect
51. C₅×#450	C₂×C₃	semidirect
53. C₅×#442	C₂×C₃	semidirect
54. C₅×#440	C₂×C₃	semidirect
55. C₅×#432	C₂×C₃	semidirect
95. C₃×#529	C₂×C₅	semidirect
96. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
97. C₃×#483	C₂×C₅	semidirect
98. C₃×#480	C₂×C₅	semidirect
99. C₃×#478	C₂×C₅	semidirect
100. C₃×#463	C₂×C₅	semidirect
101. C₃×#450	C₂×C₅	semidirect
103. C₃×#442	C₂×C₅	semidirect
104. C₃×#440	C₂×C₅	semidirect
105. C₃×#432	C₂×C₅	semidirect
111. C₅×#125	C₂²×C₃	semidirect
112. C₅×#124	C₂²×C₃	semidirect
116. C₄×C₅×Q₈	C₂²×C₃	semidirect
122. C₄×C₅×D₄	C₂²×C₃	semidirect
127. C₅×#107	C₂²×C₃	semidirect
128. C₅×#106	C₂²×C₃	semidirect
129. C₅×C₄⋊C₈	C₂²×C₃	semidirect
130. C₅×#103	C₂²×C₃	semidirect
133. C₅×#102	C₂²×C₃	semidirect
136. C₅×#97	C₂²×C₃	semidirect
137. #3114	C₃×C₅	direct (N × H)
174. C₃×#125	C₂²×C₅	semidirect
175. C₃×#124	C₂²×C₅	semidirect
179. C₃×C₄×Q₈	C₂²×C₅	semidirect
185. C₃×C₄×D₄	C₂²×C₅	semidirect
190. C₃×#107	C₂²×C₅	semidirect
191. C₃×#106	C₂²×C₅	semidirect
192. C₃×C₄⋊C₈	C₂²×C₅	semidirect
193. C₃×#103	C₂²×C₅	semidirect
196. C₃×#102	C₂²×C₅	semidirect
199. C₃×#97	C₂²×C₅	semidirect
239. #529	C₂×C₃×C₅	semidirect
240. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
241. #483	C₂×C₃×C₅	semidirect
242. #480	C₂×C₃×C₅	semidirect
243. #478	C₂×C₃×C₅	semidirect
244. #463	C₂×C₃×C₅	semidirect
245. #450	C₂×C₃×C₅	semidirect
247. #442	C₂×C₃×C₅	semidirect
248. #440	C₂×C₃×C₅	semidirect
249. #432	C₂×C₃×C₅	semidirect
346. #125	C₂²×C₃×C₅	semidirect
347. #124	C₂²×C₃×C₅	semidirect
351. C₄×Q₈	C₂²×C₃×C₅	semidirect
357. C₄×D₄	C₂²×C₃×C₅	semidirect
362. #107	C₂²×C₃×C₅	semidirect
363. #106	C₂²×C₃×C₅	semidirect
364. C₄⋊C₈	C₂²×C₃×C₅	semidirect
365. #103	C₂²×C₃×C₅	semidirect
368. #102	C₂²×C₃×C₅	semidirect
371. #97	C₂²×C₃×C₅	semidirect
469. C₃×C₅	#3114	direct (N × H)
534. C₅	C₃×#3114	direct (N × H)
556. C₃	C₅×#3114	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×#529	2
C₂×C₃×C₄×C₅×D₄	2
C₃×C₅×#483	2
C₃×C₅×#480	2
C₃×C₅×#478	2
C₃×C₅×#463	2
C₃×C₅×#450	2
C₃×C₅×#447	2
C₃×C₅×#442	2
C₃×C₅×#440	2
C₃×C₅×#432	2
C₅×#3114	3
C₃×#3114	5

Subgroups — C3×C5×#3114 #14276148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3114 #14276148