Subgroups — C₃×C₅×#3244 #14276278

Order 1920.

640 conjugacy classes of subgroups.

The subgroup lattice has 640 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×#542	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#501	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#498	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#489	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#488	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#485	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#483	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#482	C₂	1	1	yes	maximal, characteristic
10	C₃×C₅×#481	C₂	1	1	yes	maximal, characteristic
11	C₃×C₅×#479	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#478	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#475	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#433	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3244	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
18	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₃×C₅×#126	—	2	1	no	—
22	C₃×C₅×#125	—	2	1	no	—
23	C₃×C₅×#125	C₂²	1	1	yes	characteristic
24	C₃×C₅×#125	C₂²	1	1	yes	characteristic
25	C₃×C₅×#124	—	2	1	no	—
26	C₃×C₅×#124	C₂²	1	1	yes	characteristic
27	C₃×C₅×#123	—	2	1	no	—
28	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
29	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
30	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
31	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₃×C₅×#121	C₂²	1	1	yes	characteristic
33	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
34	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
35	C₃×C₅×#117	C₂²	1	1	yes	characteristic
36	C₃×C₅×#117	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₃×C₅×#107	C₂²	1	1	yes	characteristic
39	C₃×C₅×#107	C₂²	1	1	yes	characteristic
40	C₃×C₅×#106	C₂²	1	1	yes	characteristic
41	C₃×C₅×#106	C₂²	1	1	yes	characteristic
42	C₃×C₅×#106	C₂²	1	1	yes	characteristic
43	C₃×C₅×#106	C₂²	1	1	yes	characteristic
44	C₃×C₅×#106	C₂²	1	1	yes	characteristic
45	C₃×C₅×#106	C₂²	1	1	yes	characteristic
46	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	C₃×C₅×#103	C₂²	1	1	yes	characteristic
49	C₃×C₅×#103	C₂²	1	1	yes	characteristic
50	C₃×C₅×#103	C₂²	1	1	yes	characteristic
51	C₃×C₅×#103	C₂²	1	1	yes	characteristic
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic
53	C₃×C₅×#102	C₂²	1	1	yes	characteristic
54	C₃×C₅×#102	C₂²	1	1	yes	characteristic
55	C₃×C₅×#102	C₂²	1	1	yes	characteristic
56	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₃×C₅×#97	C₂²	1	1	yes	characteristic
59	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
60	C₃×#3244	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#544	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#542	C₂×C₃	1	1	yes	characteristic
63	C₅×#501	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#498	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#489	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#488	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#485	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#483	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#482	C₂×C₃	1	1	yes	characteristic
70	C₅×#481	C₂×C₃	1	1	yes	characteristic
71	C₅×#479	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#478	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×#476	C₂×C₃	1	1	yes	characteristic, complemented
74	C₅×#475	C₂×C₃	1	1	yes	characteristic, complemented
75	C₅×#433	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂×C₃×C₅×Q₈	—	2	1	no	—
77	C₂×C₃×C₅×Q₈	—	2	1	no	—
78	C₂×C₃×C₅×Q₈	—	2	1	no	—
79	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₅×D₄	—	2	1	no	—
81	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
82	C₂²×C₃×C₄×C₅	—	2	1	no	—
83	C₂²×C₃×C₄×C₅	—	2	1	no	—
84	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×C₈	C₂³	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×C₅×C₄⋊C₄	—	2	1	no	—
90	C₃×C₅×C₄⋊C₄	—	2	1	no	—
91	C₃×C₅×C₄⋊C₄	—	2	1	no	—
92	C₃×C₅×C₄⋊C₄	—	2	1	no	—
93	C₃×C₅×C₄⋊C₄	—	2	1	no	—
94	C₃×C₅×C₄⋊C₄	—	2	1	no	—
95	C₃×C₅×C₄⋊C₄	—	2	1	no	—
96	C₃×C₅×C₄⋊C₄	—	2	1	no	—
97	C₃×C₅×C₄⋊C₄	—	2	1	no	—
98	C₃×C₅×C₄⋊C₄	—	2	1	no	—
99	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
100	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
101	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
108	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
109	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
110	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
111	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
112	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
113	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
114	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
115	C₃×C₄²×C₅	—	2	1	no	—
116	C₃×C₄²×C₅	—	2	1	no	—
117	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
118	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
119	C₃×#544	C₂×C₅	1	1	yes	characteristic, complemented
120	C₃×#542	C₂×C₅	1	1	yes	characteristic
121	C₃×#501	C₂×C₅	1	1	yes	characteristic, complemented
122	C₃×#498	C₂×C₅	1	1	yes	characteristic, complemented
123	C₃×#489	C₂×C₅	1	1	yes	characteristic, complemented
124	C₃×#488	C₂×C₅	1	1	yes	characteristic, complemented
125	C₃×#485	C₂×C₅	1	1	yes	characteristic, complemented
126	C₃×#483	C₂×C₅	1	1	yes	characteristic, complemented
127	C₃×#482	C₂×C₅	1	1	yes	characteristic
128	C₃×#481	C₂×C₅	1	1	yes	characteristic
129	C₃×#479	C₂×C₅	1	1	yes	characteristic, complemented
130	C₃×#478	C₂×C₅	1	1	yes	characteristic, complemented
131	C₃×#476	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#475	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#433	C₂×C₅	1	1	yes	characteristic, complemented
134	C₅×C₄⋊Q₈	—	2	1	no	—
135	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
136	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
137	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
138	C₅×#126	—	2	1	no	—
139	C₅×#125	—	2	1	no	—
140	C₅×#125	C₂²×C₃	1	1	yes	characteristic
141	C₅×#125	C₂²×C₃	1	1	yes	characteristic
142	C₅×#124	—	2	1	no	—
143	C₅×#124	C₂²×C₃	1	1	yes	characteristic
144	C₅×#123	—	2	1	no	—
145	C₅×C₂²⋊Q₈	—	2	1	no	—
146	C₅×C₂²⋊Q₈	—	2	1	no	—
147	C₅×C₂²⋊Q₈	—	2	1	no	—
148	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
149	C₅×#121	C₂²×C₃	1	1	yes	characteristic
150	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
151	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
152	C₅×#117	C₂²×C₃	1	1	yes	characteristic
153	C₅×#117	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
155	C₅×#107	C₂²×C₃	1	1	yes	characteristic
156	C₅×#107	C₂²×C₃	1	1	yes	characteristic
157	C₅×#106	C₂²×C₃	1	1	yes	characteristic
158	C₅×#106	C₂²×C₃	1	1	yes	characteristic
159	C₅×#106	C₂²×C₃	1	1	yes	characteristic
160	C₅×#106	C₂²×C₃	1	1	yes	characteristic
161	C₅×#106	C₂²×C₃	1	1	yes	characteristic
162	C₅×#106	C₂²×C₃	1	1	yes	characteristic
163	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
164	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
165	C₅×#103	C₂²×C₃	1	1	yes	characteristic
166	C₅×#103	C₂²×C₃	1	1	yes	characteristic
167	C₅×#103	C₂²×C₃	1	1	yes	characteristic
168	C₅×#103	C₂²×C₃	1	1	yes	characteristic
169	C₅×#102	C₂²×C₃	1	1	yes	characteristic
170	C₅×#102	C₂²×C₃	1	1	yes	characteristic
171	C₅×#102	C₂²×C₃	1	1	yes	characteristic
172	C₅×#102	C₂²×C₃	1	1	yes	characteristic
173	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
174	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
175	C₅×#97	C₂²×C₃	1	1	yes	characteristic
176	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
177	#3244	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
178	C₂³×C₃×C₅	—	2	1	no	—
179	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
180	C₃×C₅×Q₈	—	2	1	no	—
181	C₃×C₅×Q₈	—	2	1	no	—
182	C₃×C₅×Q₈	—	8	1	no	—
183	C₃×C₅×Q₈	—	8	1	no	—
184	C₃×C₅×Q₈	—	8	1	no	—
185	C₃×C₅×D₄	—	2	1	no	—
186	C₃×C₅×D₄	—	2	1	no	—
187	C₃×C₅×D₄	—	8	1	no	—
188	C₂×C₃×C₄×C₅	—	2	1	no	—
189	C₂×C₃×C₄×C₅	—	2	1	no	—
190	C₂×C₃×C₄×C₅	—	2	1	no	—
191	C₂×C₃×C₄×C₅	—	2	1	no	—
192	C₂×C₃×C₄×C₅	—	2	1	no	—
193	C₂×C₃×C₄×C₅	—	2	1	no	—
194	C₂×C₃×C₄×C₅	—	2	1	no	—
195	C₂×C₃×C₄×C₅	—	2	1	no	—
196	C₂×C₃×C₄×C₅	—	2	1	no	—
197	C₂×C₃×C₄×C₅	—	8	1	no	—
198	C₂×C₃×C₄×C₅	—	8	1	no	—
199	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
200	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
201	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
202	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
203	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
204	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
205	C₃×C₅×C₈	—	2	1	no	—
206	C₃×C₅×C₈	—	2	1	no	—
207	C₃×C₅×C₈	—	2	1	no	—
208	C₃×C₅×C₈	—	2	1	no	—
209	C₃×C₄⋊Q₈	—	2	1	no	—
210	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
211	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
212	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
213	C₃×#126	—	2	1	no	—
214	C₃×#125	—	2	1	no	—
215	C₃×#125	C₂²×C₅	1	1	yes	characteristic
216	C₃×#125	C₂²×C₅	1	1	yes	characteristic
217	C₃×#124	—	2	1	no	—
218	C₃×#124	C₂²×C₅	1	1	yes	characteristic
219	C₃×#123	—	2	1	no	—
220	C₃×C₂²⋊Q₈	—	2	1	no	—
221	C₃×C₂²⋊Q₈	—	2	1	no	—
222	C₃×C₂²⋊Q₈	—	2	1	no	—
223	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
224	C₃×#121	C₂²×C₅	1	1	yes	characteristic
225	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
226	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
227	C₃×#117	C₂²×C₅	1	1	yes	characteristic
228	C₃×#117	C₂²×C₅	1	1	yes	characteristic
229	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
230	C₃×#107	C₂²×C₅	1	1	yes	characteristic
231	C₃×#107	C₂²×C₅	1	1	yes	characteristic
232	C₃×#106	C₂²×C₅	1	1	yes	characteristic
233	C₃×#106	C₂²×C₅	1	1	yes	characteristic
234	C₃×#106	C₂²×C₅	1	1	yes	characteristic
235	C₃×#106	C₂²×C₅	1	1	yes	characteristic
236	C₃×#106	C₂²×C₅	1	1	yes	characteristic
237	C₃×#106	C₂²×C₅	1	1	yes	characteristic
238	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
239	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
240	C₃×#103	C₂²×C₅	1	1	yes	characteristic
241	C₃×#103	C₂²×C₅	1	1	yes	characteristic
242	C₃×#103	C₂²×C₅	1	1	yes	characteristic
243	C₃×#103	C₂²×C₅	1	1	yes	characteristic
244	C₃×#102	C₂²×C₅	1	1	yes	characteristic
245	C₃×#102	C₂²×C₅	1	1	yes	characteristic
246	C₃×#102	C₂²×C₅	1	1	yes	characteristic
247	C₃×#102	C₂²×C₅	1	1	yes	characteristic
248	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
249	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
250	C₃×#97	C₂²×C₅	1	1	yes	characteristic
251	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
252	C₂×C₅×Q₈	—	2	1	no	—
253	C₂×C₅×Q₈	—	2	1	no	—
254	C₂×C₅×Q₈	—	2	1	no	—
255	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
256	C₂×C₅×D₄	—	2	1	no	—
257	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
258	C₂²×C₄×C₅	—	2	1	no	—
259	C₂²×C₄×C₅	—	2	1	no	—
260	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
261	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
262	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
263	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
264	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
265	C₅×C₄⋊C₄	—	2	1	no	—
266	C₅×C₄⋊C₄	—	2	1	no	—
267	C₅×C₄⋊C₄	—	2	1	no	—
268	C₅×C₄⋊C₄	—	2	1	no	—
269	C₅×C₄⋊C₄	—	2	1	no	—
270	C₅×C₄⋊C₄	—	2	1	no	—
271	C₅×C₄⋊C₄	—	2	1	no	—
272	C₅×C₄⋊C₄	—	2	1	no	—
273	C₅×C₄⋊C₄	—	2	1	no	—
274	C₅×C₄⋊C₄	—	2	1	no	—
275	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
276	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
277	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
278	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
279	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
280	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
281	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
282	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
283	C₅×C₂²⋊C₄	—	2	1	no	—
284	C₅×C₂²⋊C₄	—	2	1	no	—
285	C₅×C₂²⋊C₄	—	2	1	no	—
286	C₅×C₂²⋊C₄	—	2	1	no	—
287	C₅×C₂²⋊C₄	—	2	1	no	—
288	C₅×C₂²⋊C₄	—	2	1	no	—
289	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
290	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
291	C₄²×C₅	—	2	1	no	—
292	C₄²×C₅	—	2	1	no	—
293	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
294	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
295	#544	C₂×C₃×C₅	1	1	yes	characteristic, complemented
296	#542	C₂×C₃×C₅	1	1	yes	characteristic
297	#501	C₂×C₃×C₅	1	1	yes	characteristic, complemented
298	#498	C₂×C₃×C₅	1	1	yes	characteristic, complemented
299	#489	C₂×C₃×C₅	1	1	yes	characteristic, complemented
300	#488	C₂×C₃×C₅	1	1	yes	characteristic, complemented
301	#485	C₂×C₃×C₅	1	1	yes	characteristic, complemented
302	#483	C₂×C₃×C₅	1	1	yes	characteristic, complemented
303	#482	C₂×C₃×C₅	1	1	yes	characteristic
304	#481	C₂×C₃×C₅	1	1	yes	characteristic
305	#479	C₂×C₃×C₅	1	1	yes	characteristic, complemented
306	#478	C₂×C₃×C₅	1	1	yes	characteristic, complemented
307	#476	C₂×C₃×C₅	1	1	yes	characteristic, complemented
308	#475	C₂×C₃×C₅	1	1	yes	characteristic, complemented
309	#433	C₂×C₃×C₅	1	1	yes	characteristic, complemented
310	C₂²×C₃×C₅	—	2	1	no	—
311	C₂²×C₃×C₅	—	2	1	no	—
312	C₂²×C₃×C₅	—	2	1	no	—
313	C₂²×C₃×C₅	—	4	1	no	—
314	C₂²×C₃×C₅	—	4	1	no	—
315	C₂²×C₃×C₅	—	4	1	no	—
316	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
317	C₃×C₄×C₅	—	2	1	no	—
318	C₃×C₄×C₅	—	2	1	no	—
319	C₃×C₄×C₅	—	2	1	no	—
320	C₃×C₄×C₅	—	2	1	no	—
321	C₃×C₄×C₅	—	2	1	no	—
322	C₃×C₄×C₅	—	4	1	no	—
323	C₃×C₄×C₅	—	4	1	no	—
324	C₃×C₄×C₅	—	4	1	no	—
325	C₃×C₄×C₅	—	4	1	no	—
326	C₃×C₄×C₅	—	4	1	no	—
327	C₃×C₄×C₅	—	4	1	no	—
328	C₃×C₄×C₅	—	4	1	no	—
329	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
330	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
331	C₂×C₃×Q₈	—	2	1	no	—
332	C₂×C₃×Q₈	—	2	1	no	—
333	C₂×C₃×Q₈	—	2	1	no	—
334	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
335	C₂×C₃×D₄	—	2	1	no	—
336	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
337	C₂²×C₃×C₄	—	2	1	no	—
338	C₂²×C₃×C₄	—	2	1	no	—
339	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
340	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
341	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
342	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
343	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
344	C₃×C₄⋊C₄	—	2	1	no	—
345	C₃×C₄⋊C₄	—	2	1	no	—
346	C₃×C₄⋊C₄	—	2	1	no	—
347	C₃×C₄⋊C₄	—	2	1	no	—
348	C₃×C₄⋊C₄	—	2	1	no	—
349	C₃×C₄⋊C₄	—	2	1	no	—
350	C₃×C₄⋊C₄	—	2	1	no	—
351	C₃×C₄⋊C₄	—	2	1	no	—
352	C₃×C₄⋊C₄	—	2	1	no	—
353	C₃×C₄⋊C₄	—	2	1	no	—
354	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
355	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
356	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
357	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
358	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
359	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
360	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
361	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
362	C₃×C₂²⋊C₄	—	2	1	no	—
363	C₃×C₂²⋊C₄	—	2	1	no	—
364	C₃×C₂²⋊C₄	—	2	1	no	—
365	C₃×C₂²⋊C₄	—	2	1	no	—
366	C₃×C₂²⋊C₄	—	2	1	no	—
367	C₃×C₂²⋊C₄	—	2	1	no	—
368	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
369	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
370	C₃×C₄²	—	2	1	no	—
371	C₃×C₄²	—	2	1	no	—
372	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
373	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
374	C₂³×C₅	—	2	1	no	—
375	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
376	C₅×Q₈	—	2	1	no	—
377	C₅×Q₈	—	2	1	no	—
378	C₅×Q₈	—	8	1	no	—
379	C₅×Q₈	—	8	1	no	—
380	C₅×Q₈	—	8	1	no	—
381	C₅×D₄	—	2	1	no	—
382	C₅×D₄	—	2	1	no	—
383	C₅×D₄	—	8	1	no	—
384	C₂×C₄×C₅	—	2	1	no	—
385	C₂×C₄×C₅	—	2	1	no	—
386	C₂×C₄×C₅	—	2	1	no	—
387	C₂×C₄×C₅	—	2	1	no	—
388	C₂×C₄×C₅	—	2	1	no	—
389	C₂×C₄×C₅	—	2	1	no	—
390	C₂×C₄×C₅	—	2	1	no	—
391	C₂×C₄×C₅	—	2	1	no	—
392	C₂×C₄×C₅	—	2	1	no	—
393	C₂×C₄×C₅	—	8	1	no	—
394	C₂×C₄×C₅	—	8	1	no	—
395	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
396	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
397	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
398	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
399	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
400	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
401	C₅×C₈	—	2	1	no	—
402	C₅×C₈	—	2	1	no	—
403	C₅×C₈	—	2	1	no	—
404	C₅×C₈	—	2	1	no	—
405	C₄⋊Q₈	—	2	1	no	—
406	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
407	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
408	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
409	#126	—	2	1	no	—
410	#125	—	2	1	no	—
411	#125	C₂²×C₃×C₅	1	1	yes	characteristic
412	#125	C₂²×C₃×C₅	1	1	yes	characteristic
413	#124	—	2	1	no	—
414	#124	C₂²×C₃×C₅	1	1	yes	characteristic
415	#123	—	2	1	no	—
416	C₂²⋊Q₈	—	2	1	no	—
417	C₂²⋊Q₈	—	2	1	no	—
418	C₂²⋊Q₈	—	2	1	no	—
419	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
420	#121	C₂²×C₃×C₅	1	1	yes	characteristic
421	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
422	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
423	#117	C₂²×C₃×C₅	1	1	yes	characteristic
424	#117	C₂²×C₃×C₅	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
426	#107	C₂²×C₃×C₅	1	1	yes	characteristic
427	#107	C₂²×C₃×C₅	1	1	yes	characteristic
428	#106	C₂²×C₃×C₅	1	1	yes	characteristic
429	#106	C₂²×C₃×C₅	1	1	yes	characteristic
430	#106	C₂²×C₃×C₅	1	1	yes	characteristic
431	#106	C₂²×C₃×C₅	1	1	yes	characteristic
432	#106	C₂²×C₃×C₅	1	1	yes	characteristic
433	#106	C₂²×C₃×C₅	1	1	yes	characteristic
434	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
435	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
436	#103	C₂²×C₃×C₅	1	1	yes	characteristic
437	#103	C₂²×C₃×C₅	1	1	yes	characteristic
438	#103	C₂²×C₃×C₅	1	1	yes	characteristic
439	#103	C₂²×C₃×C₅	1	1	yes	characteristic
440	#102	C₂²×C₃×C₅	1	1	yes	characteristic
441	#102	C₂²×C₃×C₅	1	1	yes	characteristic
442	#102	C₂²×C₃×C₅	1	1	yes	characteristic
443	#102	C₂²×C₃×C₅	1	1	yes	characteristic
444	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
445	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
446	#97	C₂²×C₃×C₅	1	1	yes	characteristic
447	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
448	C₂×C₃×C₅	—	4	1	no	—
449	C₂×C₃×C₅	—	8	1	no	—
450	C₂×C₃×C₅	#536	1	1	yes	characteristic
451	C₂×C₃×C₅	#577	1	1	yes	characteristic
452	C₂×C₃×C₅	#577	1	1	yes	characteristic
453	C₂³×C₃	—	2	1	no	—
454	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
455	C₃×Q₈	—	2	1	no	—
456	C₃×Q₈	—	2	1	no	—
457	C₃×Q₈	—	8	1	no	—
458	C₃×Q₈	—	8	1	no	—
459	C₃×Q₈	—	8	1	no	—
460	C₃×D₄	—	2	1	no	—
461	C₃×D₄	—	2	1	no	—
462	C₃×D₄	—	8	1	no	—
463	C₂×C₃×C₄	—	2	1	no	—
464	C₂×C₃×C₄	—	2	1	no	—
465	C₂×C₃×C₄	—	2	1	no	—
466	C₂×C₃×C₄	—	2	1	no	—
467	C₂×C₃×C₄	—	2	1	no	—
468	C₂×C₃×C₄	—	2	1	no	—
469	C₂×C₃×C₄	—	2	1	no	—
470	C₂×C₃×C₄	—	2	1	no	—
471	C₂×C₃×C₄	—	2	1	no	—
472	C₂×C₃×C₄	—	8	1	no	—
473	C₂×C₃×C₄	—	8	1	no	—
474	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
475	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
476	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
477	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
478	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
479	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
480	C₃×C₈	—	2	1	no	—
481	C₃×C₈	—	2	1	no	—
482	C₃×C₈	—	2	1	no	—
483	C₃×C₈	—	2	1	no	—
484	C₂²×C₅	—	2	1	no	—
485	C₂²×C₅	—	2	1	no	—
486	C₂²×C₅	—	2	1	no	—
487	C₂²×C₅	—	4	1	no	—
488	C₂²×C₅	—	4	1	no	—
489	C₂²×C₅	—	4	1	no	—
490	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
491	C₄×C₅	—	2	1	no	—
492	C₄×C₅	—	2	1	no	—
493	C₄×C₅	—	2	1	no	—
494	C₄×C₅	—	2	1	no	—
495	C₄×C₅	—	2	1	no	—
496	C₄×C₅	—	4	1	no	—
497	C₄×C₅	—	4	1	no	—
498	C₄×C₅	—	4	1	no	—
499	C₄×C₅	—	4	1	no	—
500	C₄×C₅	—	4	1	no	—
501	C₄×C₅	—	4	1	no	—
502	C₄×C₅	—	4	1	no	—
503	C₄×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
504	C₄×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
514	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
515	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
516	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
517	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
529	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
530	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
531	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
532	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
533	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
534	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
535	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
536	C₂²⋊C₄	—	2	1	no	—
537	C₂²⋊C₄	—	2	1	no	—
538	C₂²⋊C₄	—	2	1	no	—
539	C₂²⋊C₄	—	2	1	no	—
540	C₂²⋊C₄	—	2	1	no	—
541	C₂²⋊C₄	—	2	1	no	—
542	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
543	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
547	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
548	C₃×C₅	#3244	1	1	yes	characteristic, direct product factor, Hall
549	C₂²×C₃	—	2	1	no	—
550	C₂²×C₃	—	2	1	no	—
551	C₂²×C₃	—	2	1	no	—
552	C₂²×C₃	—	4	1	no	—
553	C₂²×C₃	—	4	1	no	—
554	C₂²×C₃	—	4	1	no	—
555	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
556	C₃×C₄	—	2	1	no	—
557	C₃×C₄	—	2	1	no	—
558	C₃×C₄	—	2	1	no	—
559	C₃×C₄	—	2	1	no	—
560	C₃×C₄	—	2	1	no	—
561	C₃×C₄	—	4	1	no	—
562	C₃×C₄	—	4	1	no	—
563	C₃×C₄	—	4	1	no	—
564	C₃×C₄	—	4	1	no	—
565	C₃×C₄	—	4	1	no	—
566	C₃×C₄	—	4	1	no	—
567	C₃×C₄	—	4	1	no	—
568	C₃×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
569	C₃×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
570	C₂×C₅	—	4	1	no	—
571	C₂×C₅	—	8	1	no	—
572	C₂×C₅	C₃×#536	1	1	yes	characteristic
573	C₂×C₅	C₃×#577	1	1	yes	characteristic
574	C₂×C₅	C₃×#577	1	1	yes	characteristic
575	C₂³	—	2	1	no	—
576	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
577	Q₈	—	2	1	no	—
578	Q₈	—	2	1	no	—
579	Q₈	—	8	1	no	—
580	Q₈	—	8	1	no	—
581	Q₈	—	8	1	no	—
582	D₄	—	2	1	no	—
583	D₄	—	2	1	no	—
584	D₄	—	8	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	8	1	no	—
595	C₂×C₄	—	8	1	no	—
596	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
597	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
598	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
599	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
600	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
601	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
602	C₈	—	2	1	no	—
603	C₈	—	2	1	no	—
604	C₈	—	2	1	no	—
605	C₈	—	2	1	no	—
606	C₂×C₃	—	4	1	no	—
607	C₂×C₃	—	8	1	no	—
608	C₂×C₃	C₅×#536	1	1	yes	characteristic
609	C₂×C₃	C₅×#577	1	1	yes	characteristic
610	C₂×C₃	C₅×#577	1	1	yes	characteristic
611	C₅	C₃×#3244	1	1	yes	characteristic, direct product factor, Sylow
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	4	1	no	—
617	C₂²	—	4	1	no	—
618	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	1	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	1	no	—
628	C₄	—	4	1	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
632	C₄	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
633	C₃	C₅×#3244	1	1	yes	characteristic, direct product factor, Sylow
634	C₂	—	4	1	no	—
635	C₂	—	8	1	no	—
636	C₂	C₃×C₅×#536	1	1	yes	characteristic
637	C₂	C₃×C₅×#577	1	1	yes	characteristic
638	C₂	C₃×C₅×#577	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×#121	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×#501	C₂	semidirect
4. C₃×C₅×#498	C₂	semidirect
5. C₃×C₅×#489	C₂	semidirect
6. C₃×C₅×#488	C₂	semidirect
7. C₃×C₅×#485	C₂	semidirect
8. C₃×C₅×#483	C₂	semidirect
11. C₃×C₅×#479	C₂	semidirect
12. C₃×C₅×#478	C₂	semidirect
13. C₃×C₅×#476	C₂	semidirect
14. C₃×C₅×#475	C₂	semidirect
15. C₃×C₅×#433	C₂	semidirect
16. C₅×#3244	C₃	direct (N × H)
60. C₃×#3244	C₅	direct (N × H)
61. C₅×#544	C₂×C₃	semidirect
63. C₅×#501	C₂×C₃	semidirect
64. C₅×#498	C₂×C₃	semidirect
65. C₅×#489	C₂×C₃	semidirect
66. C₅×#488	C₂×C₃	semidirect
67. C₅×#485	C₂×C₃	semidirect
68. C₅×#483	C₂×C₃	semidirect
71. C₅×#479	C₂×C₃	semidirect
72. C₅×#478	C₂×C₃	semidirect
73. C₅×#476	C₂×C₃	semidirect
74. C₅×#475	C₂×C₃	semidirect
75. C₅×#433	C₂×C₃	semidirect
119. C₃×#544	C₂×C₅	semidirect
121. C₃×#501	C₂×C₅	semidirect
122. C₃×#498	C₂×C₅	semidirect
123. C₃×#489	C₂×C₅	semidirect
124. C₃×#488	C₂×C₅	semidirect
125. C₃×#485	C₂×C₅	semidirect
126. C₃×#483	C₂×C₅	semidirect
129. C₃×#479	C₂×C₅	semidirect
130. C₃×#478	C₂×C₅	semidirect
131. C₃×#476	C₂×C₅	semidirect
132. C₃×#475	C₂×C₅	semidirect
133. C₃×#433	C₂×C₅	semidirect
177. #3244	C₃×C₅	direct (N × H)
295. #544	C₂×C₃×C₅	semidirect
297. #501	C₂×C₃×C₅	semidirect
298. #498	C₂×C₃×C₅	semidirect
299. #489	C₂×C₃×C₅	semidirect
300. #488	C₂×C₃×C₅	semidirect
301. #485	C₂×C₃×C₅	semidirect
302. #483	C₂×C₃×C₅	semidirect
305. #479	C₂×C₃×C₅	semidirect
306. #478	C₂×C₃×C₅	semidirect
307. #476	C₂×C₃×C₅	semidirect
308. #475	C₂×C₃×C₅	semidirect
309. #433	C₂×C₃×C₅	semidirect
548. C₃×C₅	#3244	direct (N × H)
611. C₅	C₃×#3244	direct (N × H)
633. C₃	C₅×#3244	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×#542	2
C₃×C₅×#501	2
C₃×C₅×#498	2
C₃×C₅×#489	2
C₃×C₅×#488	2
C₃×C₅×#485	2
C₃×C₅×#483	2
C₃×C₅×#482	2
C₃×C₅×#481	2
C₃×C₅×#479	2
C₃×C₅×#478	2
C₃×C₅×#476	2
C₃×C₅×#475	2
C₃×C₅×#433	2
C₅×#3244	3
C₃×#3244	5

Subgroups — C3×C5×#3244 #14276278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3244 #14276278