Subgroups — C₃×C₅×#2655 #14275689

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#401	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#398	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#398	C₂	1	1	yes	maximal, characteristic
8	C₃×C₅×#398	C₂	1	1	yes	maximal, characteristic
9	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
10	C₃×C₅×#387	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×#387	C₂	1	1	yes	maximal, characteristic
14	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic
15	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
16	C₅×#2655	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×C₄⋊C₄	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×C₄²×C₅	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
32	C₃×C₅×#95	C₂²	1	1	yes	characteristic
33	C₃×C₅×#95	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×#2655	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
53	C₅×#401	C₂×C₃	1	1	yes	characteristic
54	C₅×#400	C₂×C₃	1	1	yes	characteristic
55	C₅×#400	C₂×C₃	1	1	yes	characteristic
56	C₅×#400	C₂×C₃	1	1	yes	characteristic
57	C₅×#400	C₂×C₃	1	1	yes	characteristic
58	C₅×#398	C₂×C₃	1	1	yes	characteristic
59	C₅×#398	C₂×C₃	1	1	yes	characteristic
60	C₅×#398	C₂×C₃	1	1	yes	characteristic
61	C₅×#389	C₂×C₃	1	1	yes	characteristic
62	C₅×#387	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×#387	C₂×C₃	1	1	yes	characteristic
66	C₅×#387	C₂×C₃	1	1	yes	characteristic
67	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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	C₃×C₅×C₄⋊C₄	—	2	2	no	—
84	C₃×C₅×C₄⋊C₄	—	2	2	no	—
85	C₃×C₅×C₄⋊C₄	—	2	2	no	—
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×C₄²×C₅	—	2	2	no	—
96	C₃×C₄²×C₅	—	4	1	no	—
97	C₃×C₄²×C₅	—	4	1	no	—
98	C₃×#401	C₂×C₅	1	1	yes	characteristic
99	C₃×#400	C₂×C₅	1	1	yes	characteristic
100	C₃×#400	C₂×C₅	1	1	yes	characteristic
101	C₃×#400	C₂×C₅	1	1	yes	characteristic
102	C₃×#400	C₂×C₅	1	1	yes	characteristic
103	C₃×#398	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×#389	C₂×C₅	1	1	yes	characteristic
107	C₃×#387	C₂×C₅	1	1	yes	characteristic
108	C₃×#387	C₂×C₅	1	1	yes	characteristic
109	C₃×#387	C₂×C₅	1	1	yes	characteristic
110	C₃×#387	C₂×C₅	1	1	yes	characteristic
111	C₃×#387	C₂×C₅	1	1	yes	characteristic
112	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
113	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₅×C₄⋊C₄	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×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
126	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
128	C₅×#95	C₂²×C₃	1	1	yes	characteristic
129	C₅×#95	C₂²×C₃	1	1	yes	characteristic
130	C₅×#95	C₂²×C₃	1	1	yes	characteristic
131	C₅×#95	C₂²×C₃	1	1	yes	characteristic
132	C₅×#95	C₂²×C₃	1	1	yes	characteristic
133	C₅×#95	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	#2655	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
149	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	1	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	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	#41	1	2	yes	—
193	C₂×C₃×C₄×C₅	#41	1	2	yes	—
194	C₂×C₃×C₄×C₅	#41	1	2	yes	—
195	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
196	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
197	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
198	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
199	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
200	C₂×C₃×C₄⋊C₄	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×C₄²	C₂²×C₅	1	1	yes	characteristic
208	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
209	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
210	C₃×#95	C₂²×C₅	1	1	yes	characteristic
211	C₃×#95	C₂²×C₅	1	1	yes	characteristic
212	C₃×#95	C₂²×C₅	1	1	yes	characteristic
213	C₃×#95	C₂²×C₅	1	1	yes	characteristic
214	C₃×#95	C₂²×C₅	1	1	yes	characteristic
215	C₃×#95	C₂²×C₅	1	1	yes	characteristic
216	C₃×#95	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	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
231	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
232	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
233	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
234	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
235	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
236	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
237	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
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	C₅×C₄⋊C₄	—	2	2	no	—
246	C₅×C₄⋊C₄	—	2	2	no	—
247	C₅×C₄⋊C₄	—	2	2	no	—
248	C₅×C₄⋊C₄	—	2	2	no	—
249	C₅×C₄⋊C₄	—	2	2	no	—
250	C₅×C₄⋊C₄	—	2	2	no	—
251	C₅×C₄⋊C₄	—	2	2	no	—
252	C₅×C₄⋊C₄	—	2	2	no	—
253	C₅×C₄⋊C₄	—	4	1	no	—
254	C₅×C₄⋊C₄	—	4	1	no	—
255	C₅×C₄⋊C₄	—	4	1	no	—
256	C₅×C₄⋊C₄	—	4	1	no	—
257	C₄²×C₅	—	2	2	no	—
258	C₄²×C₅	—	4	1	no	—
259	C₄²×C₅	—	4	1	no	—
260	#401	C₂×C₃×C₅	1	1	yes	characteristic
261	#400	C₂×C₃×C₅	1	1	yes	characteristic
262	#400	C₂×C₃×C₅	1	1	yes	characteristic
263	#400	C₂×C₃×C₅	1	1	yes	characteristic
264	#400	C₂×C₃×C₅	1	1	yes	characteristic
265	#398	C₂×C₃×C₅	1	1	yes	characteristic
266	#398	C₂×C₃×C₅	1	1	yes	characteristic
267	#398	C₂×C₃×C₅	1	1	yes	characteristic
268	#389	C₂×C₃×C₅	1	1	yes	characteristic
269	#387	C₂×C₃×C₅	1	1	yes	characteristic
270	#387	C₂×C₃×C₅	1	1	yes	characteristic
271	#387	C₂×C₃×C₅	1	1	yes	characteristic
272	#387	C₂×C₃×C₅	1	1	yes	characteristic
273	#387	C₂×C₃×C₅	1	1	yes	characteristic
274	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
275	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
276	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
277	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
278	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
279	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
280	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
281	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
282	C₃×C₄×C₅	—	2	2	no	—
283	C₃×C₄×C₅	—	2	2	no	—
284	C₃×C₄×C₅	—	2	2	no	—
285	C₃×C₄×C₅	—	4	1	no	—
286	C₃×C₄×C₅	—	4	1	no	—
287	C₃×C₄×C₅	—	4	1	no	—
288	C₃×C₄×C₅	—	4	1	no	—
289	C₃×C₄×C₅	—	4	1	no	—
290	C₃×C₄×C₅	—	4	1	no	—
291	C₃×C₄×C₅	—	4	1	no	—
292	C₃×C₄×C₅	—	4	1	no	—
293	C₃×C₄×C₅	—	4	1	no	—
294	C₃×C₄×C₅	—	4	1	no	—
295	C₃×C₄×C₅	—	4	1	no	—
296	C₃×C₄×C₅	—	4	1	no	—
297	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
298	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
299	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
300	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
301	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
302	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
303	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
304	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
305	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
306	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
307	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
308	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
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	C₃×C₄⋊C₄	—	2	2	no	—
313	C₃×C₄⋊C₄	—	2	2	no	—
314	C₃×C₄⋊C₄	—	2	2	no	—
315	C₃×C₄⋊C₄	—	2	2	no	—
316	C₃×C₄⋊C₄	—	2	2	no	—
317	C₃×C₄⋊C₄	—	2	2	no	—
318	C₃×C₄⋊C₄	—	2	2	no	—
319	C₃×C₄⋊C₄	—	2	2	no	—
320	C₃×C₄⋊C₄	—	4	1	no	—
321	C₃×C₄⋊C₄	—	4	1	no	—
322	C₃×C₄⋊C₄	—	4	1	no	—
323	C₃×C₄⋊C₄	—	4	1	no	—
324	C₃×C₄²	—	2	2	no	—
325	C₃×C₄²	—	4	1	no	—
326	C₃×C₄²	—	4	1	no	—
327	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
328	C₂×C₄×C₅	—	2	1	no	—
329	C₂×C₄×C₅	—	2	1	no	—
330	C₂×C₄×C₅	—	2	1	no	—
331	C₂×C₄×C₅	—	2	1	no	—
332	C₂×C₄×C₅	—	2	1	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	1	no	—
338	C₂×C₄×C₅	—	2	1	no	—
339	C₂×C₄×C₅	—	2	1	no	—
340	C₂×C₄×C₅	—	2	1	no	—
341	C₂×C₄×C₅	—	2	1	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	C₃×#41	1	2	yes	—
371	C₂×C₄×C₅	C₃×#41	1	2	yes	—
372	C₂×C₄×C₅	C₃×#41	1	2	yes	—
373	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
385	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
386	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
387	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
388	#95	C₂²×C₃×C₅	1	1	yes	characteristic
389	#95	C₂²×C₃×C₅	1	1	yes	characteristic
390	#95	C₂²×C₃×C₅	1	1	yes	characteristic
391	#95	C₂²×C₃×C₅	1	1	yes	characteristic
392	#95	C₂²×C₃×C₅	1	1	yes	characteristic
393	#95	C₂²×C₃×C₅	1	1	yes	characteristic
394	#95	C₂²×C₃×C₅	1	1	yes	characteristic
395	#95	C₂²×C₃×C₅	1	1	yes	characteristic
396	#95	C₂²×C₃×C₅	1	1	yes	characteristic
397	#95	C₂²×C₃×C₅	1	1	yes	characteristic
398	#95	C₂²×C₃×C₅	1	1	yes	characteristic
399	#95	C₂²×C₃×C₅	1	1	yes	characteristic
400	#95	C₂²×C₃×C₅	1	1	yes	characteristic
401	#95	C₂²×C₃×C₅	1	1	yes	characteristic
402	#95	C₂²×C₃×C₅	1	1	yes	characteristic
403	#95	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	C₂×C₃×C₅	#529	1	1	yes	characteristic
409	C₂×C₃×C₅	#539	1	1	yes	characteristic
410	C₂×C₃×C₅	#539	1	1	yes	characteristic
411	C₂×C₃×C₅	#541	1	1	yes	characteristic
412	C₂×C₃×C₅	#541	1	1	yes	characteristic
413	C₂×C₃×C₅	#541	1	1	yes	characteristic
414	C₂×C₃×C₅	#542	1	1	yes	characteristic
415	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
416	C₂×C₃×C₄	—	2	1	no	—
417	C₂×C₃×C₄	—	2	1	no	—
418	C₂×C₃×C₄	—	2	1	no	—
419	C₂×C₃×C₄	—	2	1	no	—
420	C₂×C₃×C₄	—	2	1	no	—
421	C₂×C₃×C₄	—	2	1	no	—
422	C₂×C₃×C₄	—	2	1	no	—
423	C₂×C₃×C₄	—	2	1	no	—
424	C₂×C₃×C₄	—	2	1	no	—
425	C₂×C₃×C₄	—	2	1	no	—
426	C₂×C₃×C₄	—	2	1	no	—
427	C₂×C₃×C₄	—	2	1	no	—
428	C₂×C₃×C₄	—	2	1	no	—
429	C₂×C₃×C₄	—	2	1	no	—
430	C₂×C₃×C₄	—	2	1	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	C₅×#41	1	2	yes	—
459	C₂×C₃×C₄	C₅×#41	1	2	yes	—
460	C₂×C₃×C₄	C₅×#41	1	2	yes	—
461	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
462	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
463	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
464	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
465	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
466	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
467	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
468	C₄×C₅	—	2	2	no	—
469	C₄×C₅	—	2	2	no	—
470	C₄×C₅	—	2	2	no	—
471	C₄×C₅	—	4	1	no	—
472	C₄×C₅	—	4	1	no	—
473	C₄×C₅	—	4	1	no	—
474	C₄×C₅	—	4	1	no	—
475	C₄×C₅	—	4	1	no	—
476	C₄×C₅	—	4	1	no	—
477	C₄×C₅	—	4	1	no	—
478	C₄×C₅	—	4	1	no	—
479	C₄×C₅	—	4	1	no	—
480	C₄×C₅	—	4	1	no	—
481	C₄×C₅	—	4	1	no	—
482	C₄×C₅	—	4	1	no	—
483	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
484	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
485	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
486	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
487	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
488	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
489	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
490	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
491	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
492	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
493	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
494	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
495	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
496	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
497	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	4	1	no	—
507	C₄⋊C₄	—	4	1	no	—
508	C₄⋊C₄	—	4	1	no	—
509	C₄⋊C₄	—	4	1	no	—
510	C₄²	—	2	2	no	—
511	C₄²	—	4	1	no	—
512	C₄²	—	4	1	no	—
513	C₃×C₅	#2655	1	1	yes	characteristic, direct product factor, Hall
514	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
515	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
516	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
517	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
518	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
519	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
520	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
521	C₃×C₄	—	2	2	no	—
522	C₃×C₄	—	2	2	no	—
523	C₃×C₄	—	2	2	no	—
524	C₃×C₄	—	4	1	no	—
525	C₃×C₄	—	4	1	no	—
526	C₃×C₄	—	4	1	no	—
527	C₃×C₄	—	4	1	no	—
528	C₃×C₄	—	4	1	no	—
529	C₃×C₄	—	4	1	no	—
530	C₃×C₄	—	4	1	no	—
531	C₃×C₄	—	4	1	no	—
532	C₃×C₄	—	4	1	no	—
533	C₃×C₄	—	4	1	no	—
534	C₃×C₄	—	4	1	no	—
535	C₃×C₄	—	4	1	no	—
536	C₂×C₅	C₃×#529	1	1	yes	characteristic
537	C₂×C₅	C₃×#539	1	1	yes	characteristic
538	C₂×C₅	C₃×#539	1	1	yes	characteristic
539	C₂×C₅	C₃×#541	1	1	yes	characteristic
540	C₂×C₅	C₃×#541	1	1	yes	characteristic
541	C₂×C₅	C₃×#541	1	1	yes	characteristic
542	C₂×C₅	C₃×#542	1	1	yes	characteristic
543	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	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	C₃×C₅×#41	1	2	yes	—
587	C₂×C₄	C₃×C₅×#41	1	2	yes	—
588	C₂×C₄	C₃×C₅×#41	1	2	yes	—
589	C₂×C₃	C₅×#529	1	1	yes	characteristic
590	C₂×C₃	C₅×#539	1	1	yes	characteristic
591	C₂×C₃	C₅×#539	1	1	yes	characteristic
592	C₂×C₃	C₅×#541	1	1	yes	characteristic
593	C₂×C₃	C₅×#541	1	1	yes	characteristic
594	C₂×C₃	C₅×#541	1	1	yes	characteristic
595	C₂×C₃	C₅×#542	1	1	yes	characteristic
596	C₅	C₃×#2655	1	1	yes	characteristic, direct product factor, Sylow
597	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
598	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
599	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
600	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
601	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
602	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
603	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	1	no	—
618	C₄	—	4	1	no	—
619	C₃	C₅×#2655	1	1	yes	characteristic, direct product factor, Sylow
620	C₂	C₃×C₅×#529	1	1	yes	characteristic
621	C₂	C₃×C₅×#539	1	1	yes	characteristic
622	C₂	C₃×C₅×#539	1	1	yes	characteristic
623	C₂	C₃×C₅×#541	1	1	yes	characteristic
624	C₂	C₃×C₅×#541	1	1	yes	characteristic
625	C₂	C₃×C₅×#541	1	1	yes	characteristic
626	C₂	C₃×C₅×#542	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×#2655	C₃	direct (N × H)
52. C₃×#2655	C₅	direct (N × H)
148. #2655	C₃×C₅	direct (N × H)
513. C₃×C₅	#2655	direct (N × H)
596. C₅	C₃×#2655	direct (N × H)
619. C₃	C₅×#2655	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×#401	2
C₃×C₅×#400	2
C₃×C₅×#398	2
C₃×C₅×#389	2
C₃×C₅×#387	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2655	3
C₃×#2655	5

Subgroups — C3×C5×#2655 #14275689

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2655 #14275689