Subgroups — C₃×C₅×#2666 #14275700

Order 1920.

736 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#398	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#398	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#398	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#398	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#395	C₂	1	1	yes	maximal, characteristic
8	C₃×C₅×#395	C₂	1	1	yes	maximal, characteristic
9	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic
10	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
11	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic
12	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic
13	C₃×C₅×#383	C₂	1	1	yes	maximal, characteristic
14	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic
15	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
16	C₅×#2666	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
34	C₃×C₅×#95	C₂²	1	1	yes	characteristic
35	C₃×C₅×#95	C₂²	1	1	yes	characteristic
36	C₃×C₅×#95	C₂²	1	1	yes	characteristic
37	C₃×C₅×#95	C₂²	1	1	yes	characteristic
38	C₃×C₅×#95	C₂²	1	1	yes	characteristic
39	C₃×C₅×#95	C₂²	1	1	yes	characteristic
40	C₃×C₅×#95	C₂²	1	1	yes	characteristic
41	C₃×C₅×#95	C₂²	1	1	yes	characteristic
42	C₃×C₅×#95	C₂²	1	1	yes	characteristic
43	C₃×C₅×#95	C₂²	1	1	yes	characteristic
44	C₃×C₅×#95	C₂²	1	1	yes	characteristic
45	C₃×C₅×#95	C₂²	1	1	yes	characteristic
46	C₃×C₅×#95	C₂²	1	1	yes	characteristic
47	C₃×C₅×#95	C₂²	1	1	yes	characteristic
48	C₃×C₅×#95	C₂²	1	1	yes	characteristic
49	C₃×C₅×#95	C₂²	1	1	yes	characteristic
50	C₃×C₅×#95	C₂²	1	1	yes	characteristic
51	C₃×C₅×#95	C₂²	1	1	yes	characteristic
52	C₃×#2666	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
53	C₅×#400	C₂×C₃	1	1	yes	characteristic
54	C₅×#400	C₂×C₃	1	1	yes	characteristic
55	C₅×#398	C₂×C₃	1	1	yes	characteristic
56	C₅×#398	C₂×C₃	1	1	yes	characteristic
57	C₅×#398	C₂×C₃	1	1	yes	characteristic
58	C₅×#398	C₂×C₃	1	1	yes	characteristic
59	C₅×#395	C₂×C₃	1	1	yes	characteristic
60	C₅×#395	C₂×C₃	1	1	yes	characteristic
61	C₅×#391	C₂×C₃	1	1	yes	characteristic
62	C₅×#389	C₂×C₃	1	1	yes	characteristic
63	C₅×#387	C₂×C₃	1	1	yes	characteristic
64	C₅×#387	C₂×C₃	1	1	yes	characteristic
65	C₅×#383	C₂×C₃	1	1	yes	characteristic
66	C₅×#382	C₂×C₃	1	1	yes	characteristic
67	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
68	C₂×C₃×C₅×Q₈	—	2	2	no	—
69	C₂×C₃×C₅×Q₈	—	4	1	no	—
70	C₂×C₃×C₅×Q₈	—	4	1	no	—
71	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
86	C₃×C₅×C₄⋊C₄	—	2	2	no	—
87	C₃×C₅×C₄⋊C₄	—	2	2	no	—
88	C₃×C₅×C₄⋊C₄	—	2	2	no	—
89	C₃×C₅×C₄⋊C₄	—	2	2	no	—
90	C₃×C₅×C₄⋊C₄	—	2	2	no	—
91	C₃×C₅×C₄⋊C₄	—	4	1	no	—
92	C₃×C₅×C₄⋊C₄	—	4	1	no	—
93	C₃×C₅×C₄⋊C₄	—	4	1	no	—
94	C₃×C₅×C₄⋊C₄	—	4	1	no	—
95	C₃×C₅×C₄⋊C₄	—	4	1	no	—
96	C₃×C₅×C₄⋊C₄	—	4	1	no	—
97	C₃×C₅×C₄⋊C₄	—	4	1	no	—
98	C₃×C₅×C₄⋊C₄	—	4	1	no	—
99	C₃×C₄²×C₅	—	4	1	no	—
100	C₃×C₄²×C₅	—	4	1	no	—
101	C₃×C₄²×C₅	Q₈	1	4	yes	complemented
102	C₃×#400	C₂×C₅	1	1	yes	characteristic
103	C₃×#400	C₂×C₅	1	1	yes	characteristic
104	C₃×#398	C₂×C₅	1	1	yes	characteristic
105	C₃×#398	C₂×C₅	1	1	yes	characteristic
106	C₃×#398	C₂×C₅	1	1	yes	characteristic
107	C₃×#398	C₂×C₅	1	1	yes	characteristic
108	C₃×#395	C₂×C₅	1	1	yes	characteristic
109	C₃×#395	C₂×C₅	1	1	yes	characteristic
110	C₃×#391	C₂×C₅	1	1	yes	characteristic
111	C₃×#389	C₂×C₅	1	1	yes	characteristic
112	C₃×#387	C₂×C₅	1	1	yes	characteristic
113	C₃×#387	C₂×C₅	1	1	yes	characteristic
114	C₃×#383	C₂×C₅	1	1	yes	characteristic
115	C₃×#382	C₂×C₅	1	1	yes	characteristic
116	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
117	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
126	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
130	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
133	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
134	C₅×#95	C₂²×C₃	1	1	yes	characteristic
135	C₅×#95	C₂²×C₃	1	1	yes	characteristic
136	C₅×#95	C₂²×C₃	1	1	yes	characteristic
137	C₅×#95	C₂²×C₃	1	1	yes	characteristic
138	C₅×#95	C₂²×C₃	1	1	yes	characteristic
139	C₅×#95	C₂²×C₃	1	1	yes	characteristic
140	C₅×#95	C₂²×C₃	1	1	yes	characteristic
141	C₅×#95	C₂²×C₃	1	1	yes	characteristic
142	C₅×#95	C₂²×C₃	1	1	yes	characteristic
143	C₅×#95	C₂²×C₃	1	1	yes	characteristic
144	C₅×#95	C₂²×C₃	1	1	yes	characteristic
145	C₅×#95	C₂²×C₃	1	1	yes	characteristic
146	C₅×#95	C₂²×C₃	1	1	yes	characteristic
147	C₅×#95	C₂²×C₃	1	1	yes	characteristic
148	C₅×#95	C₂²×C₃	1	1	yes	characteristic
149	C₅×#95	C₂²×C₃	1	1	yes	characteristic
150	C₅×#95	C₂²×C₃	1	1	yes	characteristic
151	C₅×#95	C₂²×C₃	1	1	yes	characteristic
152	#2666	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
153	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
154	C₃×C₅×Q₈	—	4	4	no	—
155	C₂×C₃×C₄×C₅	—	2	1	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	1	no	—
161	C₂×C₃×C₄×C₅	—	2	1	no	—
162	C₂×C₃×C₄×C₅	—	2	1	no	—
163	C₂×C₃×C₄×C₅	—	2	1	no	—
164	C₂×C₃×C₄×C₅	—	2	1	no	—
165	C₂×C₃×C₄×C₅	—	2	1	no	—
166	C₂×C₃×C₄×C₅	—	2	1	no	—
167	C₂×C₃×C₄×C₅	—	2	1	no	—
168	C₂×C₃×C₄×C₅	—	2	1	no	—
169	C₂×C₃×C₄×C₅	—	2	1	no	—
170	C₂×C₃×C₄×C₅	—	2	1	no	—
171	C₂×C₃×C₄×C₅	—	2	1	no	—
172	C₂×C₃×C₄×C₅	—	2	1	no	—
173	C₂×C₃×C₄×C₅	—	2	1	no	—
174	C₂×C₃×C₄×C₅	—	2	1	no	—
175	C₂×C₃×C₄×C₅	—	2	1	no	—
176	C₂×C₃×C₄×C₅	—	2	1	no	—
177	C₂×C₃×C₄×C₅	—	2	1	no	—
178	C₂×C₃×C₄×C₅	—	2	1	no	—
179	C₂×C₃×C₄×C₅	—	2	1	no	—
180	C₂×C₃×C₄×C₅	—	2	1	no	—
181	C₂×C₃×C₄×C₅	—	2	1	no	—
182	C₂×C₃×C₄×C₅	—	2	1	no	—
183	C₂×C₃×C₄×C₅	—	2	1	no	—
184	C₂×C₃×C₄×C₅	—	2	1	no	—
185	C₂×C₃×C₄×C₅	—	2	1	no	—
186	C₂×C₃×C₄×C₅	—	2	1	no	—
187	C₂×C₃×C₄×C₅	—	2	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	C₂×Q₈	1	2	yes	—
196	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
197	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
198	C₂×C₃×C₄×C₅	#41	1	2	yes	—
199	C₂×C₃×C₄×C₅	#41	1	2	yes	—
200	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
201	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
202	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
203	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
204	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
205	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
206	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
207	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
208	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
209	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
210	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
211	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
212	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
213	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
214	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
215	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
216	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
217	C₃×#95	C₂²×C₅	1	1	yes	characteristic
218	C₃×#95	C₂²×C₅	1	1	yes	characteristic
219	C₃×#95	C₂²×C₅	1	1	yes	characteristic
220	C₃×#95	C₂²×C₅	1	1	yes	characteristic
221	C₃×#95	C₂²×C₅	1	1	yes	characteristic
222	C₃×#95	C₂²×C₅	1	1	yes	characteristic
223	C₃×#95	C₂²×C₅	1	1	yes	characteristic
224	C₃×#95	C₂²×C₅	1	1	yes	characteristic
225	C₃×#95	C₂²×C₅	1	1	yes	characteristic
226	C₃×#95	C₂²×C₅	1	1	yes	characteristic
227	C₃×#95	C₂²×C₅	1	1	yes	characteristic
228	C₃×#95	C₂²×C₅	1	1	yes	characteristic
229	C₃×#95	C₂²×C₅	1	1	yes	characteristic
230	C₃×#95	C₂²×C₅	1	1	yes	characteristic
231	C₃×#95	C₂²×C₅	1	1	yes	characteristic
232	C₃×#95	C₂²×C₅	1	1	yes	characteristic
233	C₃×#95	C₂²×C₅	1	1	yes	characteristic
234	C₃×#95	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₅×Q₈	—	2	2	no	—
236	C₂×C₅×Q₈	—	4	1	no	—
237	C₂×C₅×Q₈	—	4	1	no	—
238	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
239	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
240	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
241	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
242	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
243	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
244	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
245	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
246	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
247	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
248	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
249	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
250	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
251	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
252	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
253	C₅×C₄⋊C₄	—	2	2	no	—
254	C₅×C₄⋊C₄	—	2	2	no	—
255	C₅×C₄⋊C₄	—	2	2	no	—
256	C₅×C₄⋊C₄	—	2	2	no	—
257	C₅×C₄⋊C₄	—	2	2	no	—
258	C₅×C₄⋊C₄	—	4	1	no	—
259	C₅×C₄⋊C₄	—	4	1	no	—
260	C₅×C₄⋊C₄	—	4	1	no	—
261	C₅×C₄⋊C₄	—	4	1	no	—
262	C₅×C₄⋊C₄	—	4	1	no	—
263	C₅×C₄⋊C₄	—	4	1	no	—
264	C₅×C₄⋊C₄	—	4	1	no	—
265	C₅×C₄⋊C₄	—	4	1	no	—
266	C₄²×C₅	—	4	1	no	—
267	C₄²×C₅	—	4	1	no	—
268	C₄²×C₅	C₃×Q₈	1	4	yes	complemented
269	#400	C₂×C₃×C₅	1	1	yes	characteristic
270	#400	C₂×C₃×C₅	1	1	yes	characteristic
271	#398	C₂×C₃×C₅	1	1	yes	characteristic
272	#398	C₂×C₃×C₅	1	1	yes	characteristic
273	#398	C₂×C₃×C₅	1	1	yes	characteristic
274	#398	C₂×C₃×C₅	1	1	yes	characteristic
275	#395	C₂×C₃×C₅	1	1	yes	characteristic
276	#395	C₂×C₃×C₅	1	1	yes	characteristic
277	#391	C₂×C₃×C₅	1	1	yes	characteristic
278	#389	C₂×C₃×C₅	1	1	yes	characteristic
279	#387	C₂×C₃×C₅	1	1	yes	characteristic
280	#387	C₂×C₃×C₅	1	1	yes	characteristic
281	#383	C₂×C₃×C₅	1	1	yes	characteristic
282	#382	C₂×C₃×C₅	1	1	yes	characteristic
283	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
284	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
285	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
286	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
287	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
288	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
289	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
290	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
291	C₃×C₄×C₅	—	2	2	no	—
292	C₃×C₄×C₅	—	2	2	no	—
293	C₃×C₄×C₅	—	2	2	no	—
294	C₃×C₄×C₅	—	2	2	no	—
295	C₃×C₄×C₅	—	2	2	no	—
296	C₃×C₄×C₅	—	4	1	no	—
297	C₃×C₄×C₅	—	4	1	no	—
298	C₃×C₄×C₅	—	4	1	no	—
299	C₃×C₄×C₅	—	4	1	no	—
300	C₃×C₄×C₅	—	4	1	no	—
301	C₃×C₄×C₅	—	4	1	no	—
302	C₃×C₄×C₅	—	4	1	no	—
303	C₃×C₄×C₅	—	4	1	no	—
304	C₃×C₄×C₅	—	4	1	no	—
305	C₃×C₄×C₅	—	4	1	no	—
306	C₂×C₃×Q₈	—	2	2	no	—
307	C₂×C₃×Q₈	—	4	1	no	—
308	C₂×C₃×Q₈	—	4	1	no	—
309	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
310	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
311	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
312	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
313	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
314	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
315	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
316	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
317	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
318	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
319	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
320	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
321	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
322	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
323	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
324	C₃×C₄⋊C₄	—	2	2	no	—
325	C₃×C₄⋊C₄	—	2	2	no	—
326	C₃×C₄⋊C₄	—	2	2	no	—
327	C₃×C₄⋊C₄	—	2	2	no	—
328	C₃×C₄⋊C₄	—	2	2	no	—
329	C₃×C₄⋊C₄	—	4	1	no	—
330	C₃×C₄⋊C₄	—	4	1	no	—
331	C₃×C₄⋊C₄	—	4	1	no	—
332	C₃×C₄⋊C₄	—	4	1	no	—
333	C₃×C₄⋊C₄	—	4	1	no	—
334	C₃×C₄⋊C₄	—	4	1	no	—
335	C₃×C₄⋊C₄	—	4	1	no	—
336	C₃×C₄⋊C₄	—	4	1	no	—
337	C₃×C₄²	—	4	1	no	—
338	C₃×C₄²	—	4	1	no	—
339	C₃×C₄²	C₅×Q₈	1	4	yes	complemented
340	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
341	C₅×Q₈	—	4	4	no	—
342	C₂×C₄×C₅	—	2	1	no	—
343	C₂×C₄×C₅	—	2	1	no	—
344	C₂×C₄×C₅	—	2	1	no	—
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	2	1	no	—
347	C₂×C₄×C₅	—	2	1	no	—
348	C₂×C₄×C₅	—	2	1	no	—
349	C₂×C₄×C₅	—	2	1	no	—
350	C₂×C₄×C₅	—	2	1	no	—
351	C₂×C₄×C₅	—	2	1	no	—
352	C₂×C₄×C₅	—	2	1	no	—
353	C₂×C₄×C₅	—	2	1	no	—
354	C₂×C₄×C₅	—	2	1	no	—
355	C₂×C₄×C₅	—	2	1	no	—
356	C₂×C₄×C₅	—	2	1	no	—
357	C₂×C₄×C₅	—	2	1	no	—
358	C₂×C₄×C₅	—	2	1	no	—
359	C₂×C₄×C₅	—	2	1	no	—
360	C₂×C₄×C₅	—	2	1	no	—
361	C₂×C₄×C₅	—	2	1	no	—
362	C₂×C₄×C₅	—	2	1	no	—
363	C₂×C₄×C₅	—	2	1	no	—
364	C₂×C₄×C₅	—	2	1	no	—
365	C₂×C₄×C₅	—	2	1	no	—
366	C₂×C₄×C₅	—	2	1	no	—
367	C₂×C₄×C₅	—	2	1	no	—
368	C₂×C₄×C₅	—	2	1	no	—
369	C₂×C₄×C₅	—	2	1	no	—
370	C₂×C₄×C₅	—	2	1	no	—
371	C₂×C₄×C₅	—	2	1	no	—
372	C₂×C₄×C₅	—	2	1	no	—
373	C₂×C₄×C₅	—	2	1	no	—
374	C₂×C₄×C₅	—	2	1	no	—
375	C₂×C₄×C₅	—	2	1	no	—
376	C₂×C₄×C₅	—	2	1	no	—
377	C₂×C₄×C₅	—	2	1	no	—
378	C₂×C₄×C₅	—	2	1	no	—
379	C₂×C₄×C₅	—	2	1	no	—
380	C₂×C₄×C₅	—	2	1	no	—
381	C₂×C₄×C₅	—	2	1	no	—
382	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
383	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
384	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
385	C₂×C₄×C₅	C₃×#41	1	2	yes	—
386	C₂×C₄×C₅	C₃×#41	1	2	yes	—
387	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
401	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
402	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
403	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
404	#95	C₂²×C₃×C₅	1	1	yes	characteristic
405	#95	C₂²×C₃×C₅	1	1	yes	characteristic
406	#95	C₂²×C₃×C₅	1	1	yes	characteristic
407	#95	C₂²×C₃×C₅	1	1	yes	characteristic
408	#95	C₂²×C₃×C₅	1	1	yes	characteristic
409	#95	C₂²×C₃×C₅	1	1	yes	characteristic
410	#95	C₂²×C₃×C₅	1	1	yes	characteristic
411	#95	C₂²×C₃×C₅	1	1	yes	characteristic
412	#95	C₂²×C₃×C₅	1	1	yes	characteristic
413	#95	C₂²×C₃×C₅	1	1	yes	characteristic
414	#95	C₂²×C₃×C₅	1	1	yes	characteristic
415	#95	C₂²×C₃×C₅	1	1	yes	characteristic
416	#95	C₂²×C₃×C₅	1	1	yes	characteristic
417	#95	C₂²×C₃×C₅	1	1	yes	characteristic
418	#95	C₂²×C₃×C₅	1	1	yes	characteristic
419	#95	C₂²×C₃×C₅	1	1	yes	characteristic
420	#95	C₂²×C₃×C₅	1	1	yes	characteristic
421	#95	C₂²×C₃×C₅	1	1	yes	characteristic
422	C₂×C₃×C₅	#533	1	1	yes	characteristic
423	C₂×C₃×C₅	#538	1	1	yes	characteristic
424	C₂×C₃×C₅	#539	1	1	yes	characteristic
425	C₂×C₃×C₅	#541	1	1	yes	characteristic
426	C₂×C₃×C₅	#542	1	1	yes	characteristic
427	C₂×C₃×C₅	#544	1	1	yes	characteristic
428	C₂×C₃×C₅	#544	1	1	yes	characteristic
429	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
430	C₃×Q₈	—	4	4	no	—
431	C₂×C₃×C₄	—	2	1	no	—
432	C₂×C₃×C₄	—	2	1	no	—
433	C₂×C₃×C₄	—	2	1	no	—
434	C₂×C₃×C₄	—	2	1	no	—
435	C₂×C₃×C₄	—	2	1	no	—
436	C₂×C₃×C₄	—	2	1	no	—
437	C₂×C₃×C₄	—	2	1	no	—
438	C₂×C₃×C₄	—	2	1	no	—
439	C₂×C₃×C₄	—	2	1	no	—
440	C₂×C₃×C₄	—	2	1	no	—
441	C₂×C₃×C₄	—	2	1	no	—
442	C₂×C₃×C₄	—	2	1	no	—
443	C₂×C₃×C₄	—	2	1	no	—
444	C₂×C₃×C₄	—	2	1	no	—
445	C₂×C₃×C₄	—	2	1	no	—
446	C₂×C₃×C₄	—	2	1	no	—
447	C₂×C₃×C₄	—	2	1	no	—
448	C₂×C₃×C₄	—	2	1	no	—
449	C₂×C₃×C₄	—	2	1	no	—
450	C₂×C₃×C₄	—	2	1	no	—
451	C₂×C₃×C₄	—	2	1	no	—
452	C₂×C₃×C₄	—	2	1	no	—
453	C₂×C₃×C₄	—	2	1	no	—
454	C₂×C₃×C₄	—	2	1	no	—
455	C₂×C₃×C₄	—	2	1	no	—
456	C₂×C₃×C₄	—	2	1	no	—
457	C₂×C₃×C₄	—	2	1	no	—
458	C₂×C₃×C₄	—	2	1	no	—
459	C₂×C₃×C₄	—	2	1	no	—
460	C₂×C₃×C₄	—	2	1	no	—
461	C₂×C₃×C₄	—	2	1	no	—
462	C₂×C₃×C₄	—	2	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	C₂×C₅×Q₈	1	2	yes	—
472	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
473	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
474	C₂×C₃×C₄	C₅×#41	1	2	yes	—
475	C₂×C₃×C₄	C₅×#41	1	2	yes	—
476	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
477	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
478	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
479	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
480	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
481	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
482	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
483	C₄×C₅	—	2	2	no	—
484	C₄×C₅	—	2	2	no	—
485	C₄×C₅	—	2	2	no	—
486	C₄×C₅	—	2	2	no	—
487	C₄×C₅	—	2	2	no	—
488	C₄×C₅	—	4	1	no	—
489	C₄×C₅	—	4	1	no	—
490	C₄×C₅	—	4	1	no	—
491	C₄×C₅	—	4	1	no	—
492	C₄×C₅	—	4	1	no	—
493	C₄×C₅	—	4	1	no	—
494	C₄×C₅	—	4	1	no	—
495	C₄×C₅	—	4	1	no	—
496	C₄×C₅	—	4	1	no	—
497	C₄×C₅	—	4	1	no	—
498	C₂×Q₈	—	2	2	no	—
499	C₂×Q₈	—	4	1	no	—
500	C₂×Q₈	—	4	1	no	—
501	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
502	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
503	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
504	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
505	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
506	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
507	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
508	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
509	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
510	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
511	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
512	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
513	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
514	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
515	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	4	1	no	—
522	C₄⋊C₄	—	4	1	no	—
523	C₄⋊C₄	—	4	1	no	—
524	C₄⋊C₄	—	4	1	no	—
525	C₄⋊C₄	—	4	1	no	—
526	C₄⋊C₄	—	4	1	no	—
527	C₄⋊C₄	—	4	1	no	—
528	C₄⋊C₄	—	4	1	no	—
529	C₄²	—	4	1	no	—
530	C₄²	—	4	1	no	—
531	C₄²	C₃×C₅×Q₈	1	4	yes	complemented
532	C₃×C₅	#2666	1	1	yes	characteristic, direct product factor, Hall
533	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
534	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
535	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
536	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
537	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
538	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
539	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
540	C₃×C₄	—	2	2	no	—
541	C₃×C₄	—	2	2	no	—
542	C₃×C₄	—	2	2	no	—
543	C₃×C₄	—	2	2	no	—
544	C₃×C₄	—	2	2	no	—
545	C₃×C₄	—	4	1	no	—
546	C₃×C₄	—	4	1	no	—
547	C₃×C₄	—	4	1	no	—
548	C₃×C₄	—	4	1	no	—
549	C₃×C₄	—	4	1	no	—
550	C₃×C₄	—	4	1	no	—
551	C₃×C₄	—	4	1	no	—
552	C₃×C₄	—	4	1	no	—
553	C₃×C₄	—	4	1	no	—
554	C₃×C₄	—	4	1	no	—
555	C₂×C₅	C₃×#533	1	1	yes	characteristic
556	C₂×C₅	C₃×#538	1	1	yes	characteristic
557	C₂×C₅	C₃×#539	1	1	yes	characteristic
558	C₂×C₅	C₃×#541	1	1	yes	characteristic
559	C₂×C₅	C₃×#542	1	1	yes	characteristic
560	C₂×C₅	C₃×#544	1	1	yes	characteristic
561	C₂×C₅	C₃×#544	1	1	yes	characteristic
562	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
563	Q₈	—	4	4	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	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	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
605	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
606	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
607	C₂×C₄	C₃×C₅×#41	1	2	yes	—
608	C₂×C₄	C₃×C₅×#41	1	2	yes	—
609	C₂×C₃	C₅×#533	1	1	yes	characteristic
610	C₂×C₃	C₅×#538	1	1	yes	characteristic
611	C₂×C₃	C₅×#539	1	1	yes	characteristic
612	C₂×C₃	C₅×#541	1	1	yes	characteristic
613	C₂×C₃	C₅×#542	1	1	yes	characteristic
614	C₂×C₃	C₅×#544	1	1	yes	characteristic
615	C₂×C₃	C₅×#544	1	1	yes	characteristic
616	C₅	C₃×#2666	1	1	yes	characteristic, direct product factor, Sylow
617	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
618	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
619	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
620	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
621	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
622	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
623	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
624	C₄	—	2	2	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	2	no	—
627	C₄	—	2	2	no	—
628	C₄	—	2	2	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	1	no	—
632	C₄	—	4	1	no	—
633	C₄	—	4	1	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	1	no	—
636	C₄	—	4	1	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	1	no	—
639	C₃	C₅×#2666	1	1	yes	characteristic, direct product factor, Sylow
640	C₂	C₃×C₅×#533	1	1	yes	characteristic
641	C₂	C₃×C₅×#538	1	1	yes	characteristic
642	C₂	C₃×C₅×#539	1	1	yes	characteristic
643	C₂	C₃×C₅×#541	1	1	yes	characteristic
644	C₂	C₃×C₅×#542	1	1	yes	characteristic
645	C₂	C₃×C₅×#544	1	1	yes	characteristic
646	C₂	C₃×C₅×#544	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
16. C₅×#2666	C₃	direct (N × H)
52. C₃×#2666	C₅	direct (N × H)
101. C₃×C₄²×C₅	Q₈	semidirect
152. #2666	C₃×C₅	direct (N × H)
268. C₄²×C₅	C₃×Q₈	semidirect
339. C₃×C₄²	C₅×Q₈	semidirect
531. C₄²	C₃×C₅×Q₈	semidirect
532. C₃×C₅	#2666	direct (N × H)
616. C₅	C₃×#2666	direct (N × H)
639. C₃	C₅×#2666	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×#400	2
C₃×C₅×#398	2
C₃×C₅×#395	2
C₃×C₅×#391	2
C₃×C₅×#389	2
C₃×C₅×#387	2
C₃×C₅×#383	2
C₃×C₅×#382	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2666	3
C₃×#2666	5

Subgroups — C3×C5×#2666 #14275700

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2666 #14275700