Subgroups — C₃×C₅×#3168 #14276202

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 476 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	2	yes	maximal, complemented
2	C₃×C₅×#499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#495	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#488	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#467	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#466	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#465	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×C₅×SD₁₆	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3168	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
15	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×#126	—	2	2	no	—
19	C₃×C₅×#125	C₂²	1	2	yes	—
20	C₃×C₅×#124	C₂²	1	2	yes	—
21	C₃×C₅×#123	—	2	2	no	—
22	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₃×C₅×#121	C₂²	1	2	yes	—
24	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
25	C₃×C₄×C₅×D₄	—	2	2	no	—
26	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
27	C₃×C₅×#117	—	2	2	no	—
28	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
29	C₃×C₅×#107	C₂²	1	1	yes	characteristic
30	C₃×C₅×#107	C₂²	1	1	yes	characteristic
31	C₃×C₅×#106	C₂²	1	2	yes	—
32	C₃×C₅×#103	C₂²	1	2	yes	—
33	C₃×C₅×#103	C₂²	1	2	yes	—
34	C₃×C₅×#102	C₂²	1	2	yes	—
35	C₃×C₅×#102	C₂²	1	2	yes	—
36	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
37	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
38	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
39	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
40	C₃×#3168	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₅×#529	C₂×C₃	1	2	yes	complemented
42	C₅×#499	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#495	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#488	C₂×C₃	1	2	yes	complemented
45	C₅×#467	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#466	C₂×C₃	1	1	yes	characteristic
47	C₅×#465	C₂×C₃	1	2	yes	complemented
48	C₄×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
49	C₄×C₅×SD₁₆	C₂×C₃	1	2	yes	complemented
50	C₄×C₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
51	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
53	C₂×C₃×C₅×D₄	—	2	2	no	—
54	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	—	2	2	no	—
56	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₃×C₅×Q₁₆	—	2	2	no	—
60	C₃×C₅×SD₁₆	—	2	4	no	—
61	C₃×C₅×D₈	—	2	2	no	—
62	C₂×C₃×C₅×C₈	—	2	2	no	—
63	C₂×C₃×C₅×C₈	—	2	2	no	—
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₃×C₅×C₄⋊C₄	—	2	2	no	—
69	C₃×C₅×C₄⋊C₄	—	2	2	no	—
70	C₃×C₅×C₄⋊C₄	—	2	2	no	—
71	C₃×C₅×C₄⋊C₄	—	2	2	no	—
72	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
73	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
74	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
75	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
76	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
77	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
78	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
79	C₃×C₄²×C₅	—	2	2	no	—
80	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
81	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
82	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
83	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₃×#529	C₂×C₅	1	2	yes	complemented
85	C₃×#499	C₂×C₅	1	1	yes	characteristic, complemented
86	C₃×#495	C₂×C₅	1	1	yes	characteristic, complemented
87	C₃×#488	C₂×C₅	1	2	yes	complemented
88	C₃×#467	C₂×C₅	1	1	yes	characteristic, complemented
89	C₃×#466	C₂×C₅	1	1	yes	characteristic
90	C₃×#465	C₂×C₅	1	2	yes	complemented
91	C₃×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
92	C₃×C₄×SD₁₆	C₂×C₅	1	2	yes	complemented
93	C₃×C₄×D₈	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
97	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
98	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
99	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
100	C₅×#126	—	2	2	no	—
101	C₅×#125	C₂²×C₃	1	2	yes	—
102	C₅×#124	C₂²×C₃	1	2	yes	—
103	C₅×#123	—	2	2	no	—
104	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
105	C₅×#121	C₂²×C₃	1	2	yes	—
106	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
107	C₄×C₅×D₄	—	2	2	no	—
108	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
109	C₅×#117	—	2	2	no	—
110	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
111	C₅×#107	C₂²×C₃	1	1	yes	characteristic
112	C₅×#107	C₂²×C₃	1	1	yes	characteristic
113	C₅×#106	C₂²×C₃	1	2	yes	—
114	C₅×#103	C₂²×C₃	1	2	yes	—
115	C₅×#103	C₂²×C₃	1	2	yes	—
116	C₅×#102	C₂²×C₃	1	2	yes	—
117	C₅×#102	C₂²×C₃	1	2	yes	—
118	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
119	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
120	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
121	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
122	#3168	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
123	C₂³×C₃×C₅	—	2	2	no	—
124	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
125	C₃×C₅×Q₈	—	2	2	no	—
126	C₃×C₅×Q₈	—	2	2	no	—
127	C₃×C₅×D₄	—	2	2	no	—
128	C₃×C₅×D₄	—	2	2	no	—
129	C₃×C₅×D₄	—	4	4	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	1	no	—
133	C₂×C₃×C₄×C₅	—	2	1	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	4	4	no	—
138	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
143	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
144	C₃×C₅×C₈	—	2	1	no	—
145	C₃×C₅×C₈	—	2	1	no	—
146	C₃×C₅×C₈	#41	1	2	yes	—
147	C₃×C₅×C₈	#41	1	2	yes	—
148	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
149	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
150	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
151	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
152	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
153	C₃×#126	—	2	2	no	—
154	C₃×#125	C₂²×C₅	1	2	yes	—
155	C₃×#124	C₂²×C₅	1	2	yes	—
156	C₃×#123	—	2	2	no	—
157	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
158	C₃×#121	C₂²×C₅	1	2	yes	—
159	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
160	C₃×C₄×D₄	—	2	2	no	—
161	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
162	C₃×#117	—	2	2	no	—
163	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
164	C₃×#107	C₂²×C₅	1	1	yes	characteristic
165	C₃×#107	C₂²×C₅	1	1	yes	characteristic
166	C₃×#106	C₂²×C₅	1	2	yes	—
167	C₃×#103	C₂²×C₅	1	2	yes	—
168	C₃×#103	C₂²×C₅	1	2	yes	—
169	C₃×#102	C₂²×C₅	1	2	yes	—
170	C₃×#102	C₂²×C₅	1	2	yes	—
171	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
172	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
173	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
174	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
176	C₂×C₅×D₄	—	2	2	no	—
177	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
178	C₂²×C₄×C₅	—	2	2	no	—
179	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
182	C₅×Q₁₆	—	2	2	no	—
183	C₅×SD₁₆	—	2	4	no	—
184	C₅×D₈	—	2	2	no	—
185	C₂×C₅×C₈	—	2	2	no	—
186	C₂×C₅×C₈	—	2	2	no	—
187	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
188	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
190	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
191	C₅×C₄⋊C₄	—	2	2	no	—
192	C₅×C₄⋊C₄	—	2	2	no	—
193	C₅×C₄⋊C₄	—	2	2	no	—
194	C₅×C₄⋊C₄	—	2	2	no	—
195	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
196	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
197	C₅×C₂²⋊C₄	—	2	2	no	—
198	C₅×C₂²⋊C₄	—	2	2	no	—
199	C₅×C₂²⋊C₄	—	2	2	no	—
200	C₅×C₂²⋊C₄	—	2	2	no	—
201	C₅×C₂²⋊C₄	—	2	2	no	—
202	C₄²×C₅	—	2	2	no	—
203	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
204	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
205	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
206	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
207	#529	C₂×C₃×C₅	1	2	yes	complemented
208	#499	C₂×C₃×C₅	1	1	yes	characteristic, complemented
209	#495	C₂×C₃×C₅	1	1	yes	characteristic, complemented
210	#488	C₂×C₃×C₅	1	2	yes	complemented
211	#467	C₂×C₃×C₅	1	1	yes	characteristic, complemented
212	#466	C₂×C₃×C₅	1	1	yes	characteristic
213	#465	C₂×C₃×C₅	1	2	yes	complemented
214	C₄×Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
215	C₄×SD₁₆	C₂×C₃×C₅	1	2	yes	complemented
216	C₄×D₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
217	C₂×C₄×C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
218	C₂²×C₃×C₅	—	2	1	no	—
219	C₂²×C₃×C₅	—	2	1	no	—
220	C₂²×C₃×C₅	—	4	2	no	—
221	C₂²×C₃×C₅	—	4	2	no	—
222	C₂²×C₃×C₅	—	4	2	no	—
223	C₂²×C₃×C₅	#135	1	2	yes	—
224	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
225	C₃×C₄×C₅	—	2	1	no	—
226	C₃×C₄×C₅	—	2	1	no	—
227	C₃×C₄×C₅	—	2	1	no	—
228	C₃×C₄×C₅	—	2	1	no	—
229	C₃×C₄×C₅	—	4	2	no	—
230	C₃×C₄×C₅	—	4	2	no	—
231	C₃×C₄×C₅	—	4	2	no	—
232	C₃×C₄×C₅	#135	1	2	yes	—
233	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
234	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
235	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
236	C₂×C₃×D₄	—	2	2	no	—
237	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
238	C₂²×C₃×C₄	—	2	2	no	—
239	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
240	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
241	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
242	C₃×Q₁₆	—	2	2	no	—
243	C₃×SD₁₆	—	2	4	no	—
244	C₃×D₈	—	2	2	no	—
245	C₂×C₃×C₈	—	2	2	no	—
246	C₂×C₃×C₈	—	2	2	no	—
247	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
248	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
249	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
250	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
251	C₃×C₄⋊C₄	—	2	2	no	—
252	C₃×C₄⋊C₄	—	2	2	no	—
253	C₃×C₄⋊C₄	—	2	2	no	—
254	C₃×C₄⋊C₄	—	2	2	no	—
255	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
256	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
257	C₃×C₂²⋊C₄	—	2	2	no	—
258	C₃×C₂²⋊C₄	—	2	2	no	—
259	C₃×C₂²⋊C₄	—	2	2	no	—
260	C₃×C₂²⋊C₄	—	2	2	no	—
261	C₃×C₂²⋊C₄	—	2	2	no	—
262	C₃×C₄²	—	2	2	no	—
263	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
264	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
265	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
266	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
267	C₂³×C₅	—	2	2	no	—
268	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
269	C₅×Q₈	—	2	2	no	—
270	C₅×Q₈	—	2	2	no	—
271	C₅×D₄	—	2	2	no	—
272	C₅×D₄	—	2	2	no	—
273	C₅×D₄	—	4	4	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	1	no	—
277	C₂×C₄×C₅	—	2	1	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	4	4	no	—
282	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
283	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
288	C₅×C₈	—	2	1	no	—
289	C₅×C₈	—	2	1	no	—
290	C₅×C₈	C₃×#41	1	2	yes	—
291	C₅×C₈	C₃×#41	1	2	yes	—
292	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
293	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
294	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
295	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
296	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
297	#126	—	2	2	no	—
298	#125	C₂²×C₃×C₅	1	2	yes	—
299	#124	C₂²×C₃×C₅	1	2	yes	—
300	#123	—	2	2	no	—
301	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
302	#121	C₂²×C₃×C₅	1	2	yes	—
303	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
306	#117	—	2	2	no	—
307	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
308	#107	C₂²×C₃×C₅	1	1	yes	characteristic
309	#107	C₂²×C₃×C₅	1	1	yes	characteristic
310	#106	C₂²×C₃×C₅	1	2	yes	—
311	#103	C₂²×C₃×C₅	1	2	yes	—
312	#103	C₂²×C₃×C₅	1	2	yes	—
313	#102	C₂²×C₃×C₅	1	2	yes	—
314	#102	C₂²×C₃×C₅	1	2	yes	—
315	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
316	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
317	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
318	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
319	C₂×C₃×C₅	—	2	2	no	—
320	C₂×C₃×C₅	—	8	2	no	—
321	C₂×C₃×C₅	#532	1	1	yes	characteristic
322	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
323	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
324	C₂³×C₃	—	2	2	no	—
325	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
326	C₃×Q₈	—	2	2	no	—
327	C₃×Q₈	—	2	2	no	—
328	C₃×D₄	—	2	2	no	—
329	C₃×D₄	—	2	2	no	—
330	C₃×D₄	—	4	4	no	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	2	2	no	—
333	C₂×C₃×C₄	—	2	1	no	—
334	C₂×C₃×C₄	—	2	1	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	—	2	2	no	—
338	C₂×C₃×C₄	—	4	4	no	—
339	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
341	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
343	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
344	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
345	C₃×C₈	—	2	1	no	—
346	C₃×C₈	—	2	1	no	—
347	C₃×C₈	C₅×#41	1	2	yes	—
348	C₃×C₈	C₅×#41	1	2	yes	—
349	C₂²×C₅	—	2	1	no	—
350	C₂²×C₅	—	2	1	no	—
351	C₂²×C₅	—	4	2	no	—
352	C₂²×C₅	—	4	2	no	—
353	C₂²×C₅	—	4	2	no	—
354	C₂²×C₅	C₃×#135	1	2	yes	—
355	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
356	C₄×C₅	—	2	1	no	—
357	C₄×C₅	—	2	1	no	—
358	C₄×C₅	—	2	1	no	—
359	C₄×C₅	—	2	1	no	—
360	C₄×C₅	—	4	2	no	—
361	C₄×C₅	—	4	2	no	—
362	C₄×C₅	—	4	2	no	—
363	C₄×C₅	C₃×#135	1	2	yes	—
364	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
365	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
366	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
371	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
372	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
373	Q₁₆	—	2	2	no	—
374	SD₁₆	—	2	4	no	—
375	D₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
379	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
380	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
381	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
387	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
395	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
396	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
397	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
398	C₃×C₅	#3168	1	1	yes	characteristic, direct product factor, Hall
399	C₂²×C₃	—	2	1	no	—
400	C₂²×C₃	—	2	1	no	—
401	C₂²×C₃	—	4	2	no	—
402	C₂²×C₃	—	4	2	no	—
403	C₂²×C₃	—	4	2	no	—
404	C₂²×C₃	C₅×#135	1	2	yes	—
405	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
406	C₃×C₄	—	2	1	no	—
407	C₃×C₄	—	2	1	no	—
408	C₃×C₄	—	2	1	no	—
409	C₃×C₄	—	2	1	no	—
410	C₃×C₄	—	4	2	no	—
411	C₃×C₄	—	4	2	no	—
412	C₃×C₄	—	4	2	no	—
413	C₃×C₄	C₅×#135	1	2	yes	—
414	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
415	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
416	C₂×C₅	—	2	2	no	—
417	C₂×C₅	—	8	2	no	—
418	C₂×C₅	C₃×#532	1	1	yes	characteristic
419	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
420	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
421	C₂³	—	2	2	no	—
422	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
423	Q₈	—	2	2	no	—
424	Q₈	—	2	2	no	—
425	D₄	—	2	2	no	—
426	D₄	—	2	2	no	—
427	D₄	—	4	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
437	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
438	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
439	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
440	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
441	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
442	C₈	—	2	1	no	—
443	C₈	—	2	1	no	—
444	C₈	C₃×C₅×#41	1	2	yes	—
445	C₈	C₃×C₅×#41	1	2	yes	—
446	C₂×C₃	—	2	2	no	—
447	C₂×C₃	—	8	2	no	—
448	C₂×C₃	C₅×#532	1	1	yes	characteristic
449	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
450	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
451	C₅	C₃×#3168	1	1	yes	characteristic, direct product factor, Sylow
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	C₃×C₅×#135	1	2	yes	—
458	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	2	no	—
466	C₄	C₃×C₅×#135	1	2	yes	—
467	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
468	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
469	C₃	C₅×#3168	1	1	yes	characteristic, direct product factor, Sylow
470	C₂	—	2	2	no	—
471	C₂	—	8	2	no	—
472	C₂	C₃×C₅×#532	1	1	yes	characteristic
473	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
474	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₃×C₅×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄×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. C₃×C₅×#499	C₂	semidirect
3. C₃×C₅×#495	C₂	semidirect
4. C₃×C₅×#488	C₂	semidirect
5. C₃×C₅×#467	C₂	semidirect
7. C₃×C₅×#465	C₂	semidirect
8. C₃×C₄×C₅×Q₁₆	C₂	semidirect
9. C₃×C₄×C₅×SD₁₆	C₂	semidirect
10. C₃×C₄×C₅×D₈	C₂	semidirect
11. C₂×C₃×C₄×C₅×C₈	C₂	semidirect
12. C₅×#3168	C₃	direct (N × H)
40. C₃×#3168	C₅	direct (N × H)
41. C₅×#529	C₂×C₃	semidirect
42. C₅×#499	C₂×C₃	semidirect
43. C₅×#495	C₂×C₃	semidirect
44. C₅×#488	C₂×C₃	semidirect
45. C₅×#467	C₂×C₃	semidirect
47. C₅×#465	C₂×C₃	semidirect
48. C₄×C₅×Q₁₆	C₂×C₃	semidirect
49. C₄×C₅×SD₁₆	C₂×C₃	semidirect
50. C₄×C₅×D₈	C₂×C₃	semidirect
51. C₂×C₄×C₅×C₈	C₂×C₃	semidirect
84. C₃×#529	C₂×C₅	semidirect
85. C₃×#499	C₂×C₅	semidirect
86. C₃×#495	C₂×C₅	semidirect
87. C₃×#488	C₂×C₅	semidirect
88. C₃×#467	C₂×C₅	semidirect
90. C₃×#465	C₂×C₅	semidirect
91. C₃×C₄×Q₁₆	C₂×C₅	semidirect
92. C₃×C₄×SD₁₆	C₂×C₅	semidirect
93. C₃×C₄×D₈	C₂×C₅	semidirect
94. C₂×C₃×C₄×C₈	C₂×C₅	semidirect
122. #3168	C₃×C₅	direct (N × H)
207. #529	C₂×C₃×C₅	semidirect
208. #499	C₂×C₃×C₅	semidirect
209. #495	C₂×C₃×C₅	semidirect
210. #488	C₂×C₃×C₅	semidirect
211. #467	C₂×C₃×C₅	semidirect
213. #465	C₂×C₃×C₅	semidirect
214. C₄×Q₁₆	C₂×C₃×C₅	semidirect
215. C₄×SD₁₆	C₂×C₃×C₅	semidirect
216. C₄×D₈	C₂×C₃×C₅	semidirect
217. C₂×C₄×C₈	C₂×C₃×C₅	semidirect
398. C₃×C₅	#3168	direct (N × H)
451. C₅	C₃×#3168	direct (N × H)
469. C₃	C₅×#3168	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
C₃×C₅×#499	2
C₃×C₅×#495	2
C₃×C₅×#488	2
C₃×C₅×#467	2
C₃×C₅×#466	2
C₃×C₅×#465	2
C₃×C₄×C₅×Q₁₆	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₄×C₅×D₈	2
C₂×C₃×C₄×C₅×C₈	2
C₅×#3168	3
C₃×#3168	5

Subgroups — C3×C5×#3168 #14276202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3168 #14276202