Subgroups — C₃×C₅×#2527 #14275561

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 704 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, complemented
2	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#397	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#393	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic
8	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic
9	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic
13	C₃×C₅×#381	C₂	1	1	yes	maximal, characteristic
14	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
15	C₃×C₅×#376	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2527	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₂³×C₃×C₄×C₅	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×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₂²⋊C₄	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	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×#2527	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
53	C₅×#401	C₂×C₃	1	1	yes	characteristic, complemented
54	C₅×#400	C₂×C₃	1	1	yes	characteristic, complemented
55	C₅×#397	C₂×C₃	1	1	yes	characteristic
56	C₅×#393	C₂×C₃	1	1	yes	characteristic
57	C₅×#391	C₂×C₃	1	1	yes	characteristic, complemented
58	C₅×#391	C₂×C₃	1	1	yes	characteristic, complemented
59	C₅×#388	C₂×C₃	1	1	yes	characteristic
60	C₅×#388	C₂×C₃	1	1	yes	characteristic
61	C₅×#387	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#387	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#387	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#385	C₂×C₃	1	1	yes	characteristic
65	C₅×#381	C₂×C₃	1	1	yes	characteristic
66	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
67	C₅×#376	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₅×Q₈	—	2	2	no	—
70	C₂×C₃×C₅×Q₈	—	2	2	no	—
71	C₂×C₃×C₅×Q₈	—	4	1	no	—
72	C₂²×C₃×C₄×C₅	—	2	2	no	—
73	C₂²×C₃×C₄×C₅	—	2	2	no	—
74	C₂²×C₃×C₄×C₅	—	4	1	no	—
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	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
87	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
89	C₃×C₅×C₄⋊C₄	—	2	2	no	—
90	C₃×C₅×C₄⋊C₄	—	2	2	no	—
91	C₃×C₅×C₄⋊C₄	—	2	2	no	—
92	C₃×C₅×C₄⋊C₄	—	4	1	no	—
93	C₃×C₅×C₄⋊C₄	—	4	1	no	—
94	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
95	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
96	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
97	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
98	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
99	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
100	C₃×C₄²×C₅	—	2	2	no	—
101	C₃×C₄²×C₅	—	2	2	no	—
102	C₃×C₄²×C₅	—	2	2	no	—
103	C₃×C₄²×C₅	—	4	1	no	—
104	C₃×#401	C₂×C₅	1	1	yes	characteristic, complemented
105	C₃×#400	C₂×C₅	1	1	yes	characteristic, complemented
106	C₃×#397	C₂×C₅	1	1	yes	characteristic
107	C₃×#393	C₂×C₅	1	1	yes	characteristic
108	C₃×#391	C₂×C₅	1	1	yes	characteristic, complemented
109	C₃×#391	C₂×C₅	1	1	yes	characteristic, complemented
110	C₃×#388	C₂×C₅	1	1	yes	characteristic
111	C₃×#388	C₂×C₅	1	1	yes	characteristic
112	C₃×#387	C₂×C₅	1	1	yes	characteristic, complemented
113	C₃×#387	C₂×C₅	1	1	yes	characteristic, complemented
114	C₃×#387	C₂×C₅	1	1	yes	characteristic, complemented
115	C₃×#385	C₂×C₅	1	1	yes	characteristic
116	C₃×#381	C₂×C₅	1	1	yes	characteristic
117	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
118	C₃×#376	C₂×C₅	1	1	yes	characteristic, complemented
119	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
120	C₂³×C₄×C₅	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×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
130	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₅×C₂²⋊C₄	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	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₄²×C₅	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	C₅×#95	C₂²×C₃	1	1	yes	characteristic
153	C₅×#95	C₂²×C₃	1	1	yes	characteristic
154	#2527	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
155	C₂³×C₃×C₅	—	2	1	no	—
156	C₂³×C₃×C₅	—	2	1	no	—
157	C₂³×C₃×C₅	—	2	1	no	—
158	C₂³×C₃×C₅	—	2	1	no	—
159	C₂³×C₃×C₅	—	2	1	no	—
160	C₂³×C₃×C₅	—	2	1	no	—
161	C₂³×C₃×C₅	#41	1	2	yes	—
162	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
163	C₃×C₅×Q₈	—	4	4	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	—	2	1	no	—
196	C₂×C₃×C₄×C₅	—	2	1	no	—
197	C₂×C₃×C₄×C₅	—	2	1	no	—
198	C₂×C₃×C₄×C₅	—	2	1	no	—
199	C₂×C₃×C₄×C₅	—	2	1	no	—
200	C₂×C₃×C₄×C₅	—	2	1	no	—
201	C₂×C₃×C₄×C₅	—	2	1	no	—
202	C₂×C₃×C₄×C₅	—	4	4	no	—
203	C₂×C₃×C₄×C₅	#41	1	2	yes	—
204	C₂×C₃×C₄×C₅	#41	1	2	yes	—
205	C₂×C₃×C₄×C₅	#41	1	2	yes	—
206	C₂×C₃×C₄×C₅	#41	1	2	yes	—
207	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
208	C₂³×C₃×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×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
215	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
216	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
217	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
218	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
219	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
220	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
221	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
222	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
223	C₂×C₃×C₄²	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	C₃×#95	C₂²×C₅	1	1	yes	characteristic
236	C₃×#95	C₂²×C₅	1	1	yes	characteristic
237	C₃×#95	C₂²×C₅	1	1	yes	characteristic
238	C₃×#95	C₂²×C₅	1	1	yes	characteristic
239	C₃×#95	C₂²×C₅	1	1	yes	characteristic
240	C₃×#95	C₂²×C₅	1	1	yes	characteristic
241	C₃×#95	C₂²×C₅	1	1	yes	characteristic
242	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
243	C₂×C₅×Q₈	—	2	2	no	—
244	C₂×C₅×Q₈	—	2	2	no	—
245	C₂×C₅×Q₈	—	4	1	no	—
246	C₂²×C₄×C₅	—	2	2	no	—
247	C₂²×C₄×C₅	—	2	2	no	—
248	C₂²×C₄×C₅	—	4	1	no	—
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	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
254	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
255	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
256	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
257	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
258	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
259	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
260	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
261	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
262	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
263	C₅×C₄⋊C₄	—	2	2	no	—
264	C₅×C₄⋊C₄	—	2	2	no	—
265	C₅×C₄⋊C₄	—	2	2	no	—
266	C₅×C₄⋊C₄	—	4	1	no	—
267	C₅×C₄⋊C₄	—	4	1	no	—
268	C₅×C₂²⋊C₄	—	2	2	no	—
269	C₅×C₂²⋊C₄	—	2	2	no	—
270	C₅×C₂²⋊C₄	—	2	2	no	—
271	C₅×C₂²⋊C₄	—	2	2	no	—
272	C₅×C₂²⋊C₄	—	2	2	no	—
273	C₅×C₂²⋊C₄	—	4	1	no	—
274	C₄²×C₅	—	2	2	no	—
275	C₄²×C₅	—	2	2	no	—
276	C₄²×C₅	—	2	2	no	—
277	C₄²×C₅	—	4	1	no	—
278	#401	C₂×C₃×C₅	1	1	yes	characteristic, complemented
279	#400	C₂×C₃×C₅	1	1	yes	characteristic, complemented
280	#397	C₂×C₃×C₅	1	1	yes	characteristic
281	#393	C₂×C₃×C₅	1	1	yes	characteristic
282	#391	C₂×C₃×C₅	1	1	yes	characteristic, complemented
283	#391	C₂×C₃×C₅	1	1	yes	characteristic, complemented
284	#388	C₂×C₃×C₅	1	1	yes	characteristic
285	#388	C₂×C₃×C₅	1	1	yes	characteristic
286	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
287	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
288	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
289	#385	C₂×C₃×C₅	1	1	yes	characteristic
290	#381	C₂×C₃×C₅	1	1	yes	characteristic
291	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
292	#376	C₂×C₃×C₅	1	1	yes	characteristic, complemented
293	C₂²×C₃×C₅	—	2	2	no	—
294	C₂²×C₃×C₅	—	2	2	no	—
295	C₂²×C₃×C₅	—	2	2	no	—
296	C₂²×C₃×C₅	—	4	1	no	—
297	C₂²×C₃×C₅	—	4	1	no	—
298	C₂²×C₃×C₅	—	4	1	no	—
299	C₂²×C₃×C₅	—	4	1	no	—
300	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
301	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
302	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
303	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
304	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
305	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
306	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
307	C₃×C₄×C₅	—	2	2	no	—
308	C₃×C₄×C₅	—	2	2	no	—
309	C₃×C₄×C₅	—	2	2	no	—
310	C₃×C₄×C₅	—	2	2	no	—
311	C₃×C₄×C₅	—	4	1	no	—
312	C₃×C₄×C₅	—	4	1	no	—
313	C₃×C₄×C₅	—	4	1	no	—
314	C₃×C₄×C₅	—	4	1	no	—
315	C₃×C₄×C₅	—	4	1	no	—
316	C₃×C₄×C₅	—	4	1	no	—
317	C₃×C₄×C₅	—	4	1	no	—
318	C₃×C₄×C₅	—	4	1	no	—
319	C₃×C₄×C₅	—	4	1	no	—
320	C₃×C₄×C₅	—	4	1	no	—
321	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
322	C₂×C₃×Q₈	—	2	2	no	—
323	C₂×C₃×Q₈	—	2	2	no	—
324	C₂×C₃×Q₈	—	4	1	no	—
325	C₂²×C₃×C₄	—	2	2	no	—
326	C₂²×C₃×C₄	—	2	2	no	—
327	C₂²×C₃×C₄	—	4	1	no	—
328	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
329	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
330	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
331	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
332	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
333	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
334	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
335	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
336	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
337	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
338	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
339	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
340	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
341	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
342	C₃×C₄⋊C₄	—	2	2	no	—
343	C₃×C₄⋊C₄	—	2	2	no	—
344	C₃×C₄⋊C₄	—	2	2	no	—
345	C₃×C₄⋊C₄	—	4	1	no	—
346	C₃×C₄⋊C₄	—	4	1	no	—
347	C₃×C₂²⋊C₄	—	2	2	no	—
348	C₃×C₂²⋊C₄	—	2	2	no	—
349	C₃×C₂²⋊C₄	—	2	2	no	—
350	C₃×C₂²⋊C₄	—	2	2	no	—
351	C₃×C₂²⋊C₄	—	2	2	no	—
352	C₃×C₂²⋊C₄	—	4	1	no	—
353	C₃×C₄²	—	2	2	no	—
354	C₃×C₄²	—	2	2	no	—
355	C₃×C₄²	—	2	2	no	—
356	C₃×C₄²	—	4	1	no	—
357	C₂³×C₅	—	2	1	no	—
358	C₂³×C₅	—	2	1	no	—
359	C₂³×C₅	—	2	1	no	—
360	C₂³×C₅	—	2	1	no	—
361	C₂³×C₅	—	2	1	no	—
362	C₂³×C₅	—	2	1	no	—
363	C₂³×C₅	C₃×#41	1	2	yes	—
364	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
365	C₅×Q₈	—	4	4	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	—	2	1	no	—
383	C₂×C₄×C₅	—	2	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	—	2	1	no	—
394	C₂×C₄×C₅	—	2	1	no	—
395	C₂×C₄×C₅	—	2	1	no	—
396	C₂×C₄×C₅	—	2	1	no	—
397	C₂×C₄×C₅	—	2	1	no	—
398	C₂×C₄×C₅	—	2	1	no	—
399	C₂×C₄×C₅	—	2	1	no	—
400	C₂×C₄×C₅	—	2	1	no	—
401	C₂×C₄×C₅	—	2	1	no	—
402	C₂×C₄×C₅	—	2	1	no	—
403	C₂×C₄×C₅	—	2	1	no	—
404	C₂×C₄×C₅	—	4	4	no	—
405	C₂×C₄×C₅	C₃×#41	1	2	yes	—
406	C₂×C₄×C₅	C₃×#41	1	2	yes	—
407	C₂×C₄×C₅	C₃×#41	1	2	yes	—
408	C₂×C₄×C₅	C₃×#41	1	2	yes	—
409	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
410	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
417	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
418	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
419	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
421	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
422	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
423	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
424	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
425	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
426	#95	C₂²×C₃×C₅	1	1	yes	characteristic
427	#95	C₂²×C₃×C₅	1	1	yes	characteristic
428	#95	C₂²×C₃×C₅	1	1	yes	characteristic
429	#95	C₂²×C₃×C₅	1	1	yes	characteristic
430	#95	C₂²×C₃×C₅	1	1	yes	characteristic
431	#95	C₂²×C₃×C₅	1	1	yes	characteristic
432	#95	C₂²×C₃×C₅	1	1	yes	characteristic
433	#95	C₂²×C₃×C₅	1	1	yes	characteristic
434	#95	C₂²×C₃×C₅	1	1	yes	characteristic
435	#95	C₂²×C₃×C₅	1	1	yes	characteristic
436	#95	C₂²×C₃×C₅	1	1	yes	characteristic
437	#95	C₂²×C₃×C₅	1	1	yes	characteristic
438	#95	C₂²×C₃×C₅	1	1	yes	characteristic
439	#95	C₂²×C₃×C₅	1	1	yes	characteristic
440	#95	C₂²×C₃×C₅	1	1	yes	characteristic
441	#95	C₂²×C₃×C₅	1	1	yes	characteristic
442	#95	C₂²×C₃×C₅	1	1	yes	characteristic
443	#95	C₂²×C₃×C₅	1	1	yes	characteristic
444	C₂×C₃×C₅	—	4	2	no	—
445	C₂×C₃×C₅	#529	1	1	yes	characteristic
446	C₂×C₃×C₅	#529	1	1	yes	characteristic
447	C₂×C₃×C₅	#542	1	1	yes	characteristic
448	C₂×C₃×C₅	#551	1	1	yes	characteristic
449	C₂×C₃×C₅	#551	1	1	yes	characteristic
450	C₂×C₃×C₅	#552	1	1	yes	characteristic
451	C₂×C₃×C₅	#556	1	1	yes	characteristic
452	C₂³×C₃	—	2	1	no	—
453	C₂³×C₃	—	2	1	no	—
454	C₂³×C₃	—	2	1	no	—
455	C₂³×C₃	—	2	1	no	—
456	C₂³×C₃	—	2	1	no	—
457	C₂³×C₃	—	2	1	no	—
458	C₂³×C₃	C₅×#41	1	2	yes	—
459	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
460	C₃×Q₈	—	4	4	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	—	2	1	no	—
472	C₂×C₃×C₄	—	2	1	no	—
473	C₂×C₃×C₄	—	2	1	no	—
474	C₂×C₃×C₄	—	2	1	no	—
475	C₂×C₃×C₄	—	2	1	no	—
476	C₂×C₃×C₄	—	2	1	no	—
477	C₂×C₃×C₄	—	2	1	no	—
478	C₂×C₃×C₄	—	2	1	no	—
479	C₂×C₃×C₄	—	2	1	no	—
480	C₂×C₃×C₄	—	2	1	no	—
481	C₂×C₃×C₄	—	2	1	no	—
482	C₂×C₃×C₄	—	2	1	no	—
483	C₂×C₃×C₄	—	2	1	no	—
484	C₂×C₃×C₄	—	2	1	no	—
485	C₂×C₃×C₄	—	2	1	no	—
486	C₂×C₃×C₄	—	2	1	no	—
487	C₂×C₃×C₄	—	2	1	no	—
488	C₂×C₃×C₄	—	2	1	no	—
489	C₂×C₃×C₄	—	2	1	no	—
490	C₂×C₃×C₄	—	2	1	no	—
491	C₂×C₃×C₄	—	2	1	no	—
492	C₂×C₃×C₄	—	2	1	no	—
493	C₂×C₃×C₄	—	2	1	no	—
494	C₂×C₃×C₄	—	2	1	no	—
495	C₂×C₃×C₄	—	2	1	no	—
496	C₂×C₃×C₄	—	2	1	no	—
497	C₂×C₃×C₄	—	2	1	no	—
498	C₂×C₃×C₄	—	2	1	no	—
499	C₂×C₃×C₄	—	4	4	no	—
500	C₂×C₃×C₄	C₅×#41	1	2	yes	—
501	C₂×C₃×C₄	C₅×#41	1	2	yes	—
502	C₂×C₃×C₄	C₅×#41	1	2	yes	—
503	C₂×C₃×C₄	C₅×#41	1	2	yes	—
504	C₂²×C₅	—	2	2	no	—
505	C₂²×C₅	—	2	2	no	—
506	C₂²×C₅	—	2	2	no	—
507	C₂²×C₅	—	4	1	no	—
508	C₂²×C₅	—	4	1	no	—
509	C₂²×C₅	—	4	1	no	—
510	C₂²×C₅	—	4	1	no	—
511	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
512	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
513	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
514	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
515	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
516	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
517	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
518	C₄×C₅	—	2	2	no	—
519	C₄×C₅	—	2	2	no	—
520	C₄×C₅	—	2	2	no	—
521	C₄×C₅	—	2	2	no	—
522	C₄×C₅	—	4	1	no	—
523	C₄×C₅	—	4	1	no	—
524	C₄×C₅	—	4	1	no	—
525	C₄×C₅	—	4	1	no	—
526	C₄×C₅	—	4	1	no	—
527	C₄×C₅	—	4	1	no	—
528	C₄×C₅	—	4	1	no	—
529	C₄×C₅	—	4	1	no	—
530	C₄×C₅	—	4	1	no	—
531	C₄×C₅	—	4	1	no	—
532	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
533	C₂×Q₈	—	2	2	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	4	1	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	4	1	no	—
539	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
540	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
541	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
542	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
543	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
544	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
545	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
546	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
547	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
548	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
549	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
550	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
551	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
552	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
553	C₄⋊C₄	—	2	2	no	—
554	C₄⋊C₄	—	2	2	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	4	1	no	—
557	C₄⋊C₄	—	4	1	no	—
558	C₂²⋊C₄	—	2	2	no	—
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	4	1	no	—
564	C₄²	—	2	2	no	—
565	C₄²	—	2	2	no	—
566	C₄²	—	2	2	no	—
567	C₄²	—	4	1	no	—
568	C₃×C₅	#2527	1	1	yes	characteristic, direct product factor, Hall
569	C₂²×C₃	—	2	2	no	—
570	C₂²×C₃	—	2	2	no	—
571	C₂²×C₃	—	2	2	no	—
572	C₂²×C₃	—	4	1	no	—
573	C₂²×C₃	—	4	1	no	—
574	C₂²×C₃	—	4	1	no	—
575	C₂²×C₃	—	4	1	no	—
576	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
577	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
578	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
579	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
580	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
581	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
582	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
583	C₃×C₄	—	2	2	no	—
584	C₃×C₄	—	2	2	no	—
585	C₃×C₄	—	2	2	no	—
586	C₃×C₄	—	2	2	no	—
587	C₃×C₄	—	4	1	no	—
588	C₃×C₄	—	4	1	no	—
589	C₃×C₄	—	4	1	no	—
590	C₃×C₄	—	4	1	no	—
591	C₃×C₄	—	4	1	no	—
592	C₃×C₄	—	4	1	no	—
593	C₃×C₄	—	4	1	no	—
594	C₃×C₄	—	4	1	no	—
595	C₃×C₄	—	4	1	no	—
596	C₃×C₄	—	4	1	no	—
597	C₂×C₅	—	4	2	no	—
598	C₂×C₅	C₃×#529	1	1	yes	characteristic
599	C₂×C₅	C₃×#529	1	1	yes	characteristic
600	C₂×C₅	C₃×#542	1	1	yes	characteristic
601	C₂×C₅	C₃×#551	1	1	yes	characteristic
602	C₂×C₅	C₃×#551	1	1	yes	characteristic
603	C₂×C₅	C₃×#552	1	1	yes	characteristic
604	C₂×C₅	C₃×#556	1	1	yes	characteristic
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	C₃×C₅×#41	1	2	yes	—
612	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
613	Q₈	—	4	4	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	4	4	no	—
653	C₂×C₄	C₃×C₅×#41	1	2	yes	—
654	C₂×C₄	C₃×C₅×#41	1	2	yes	—
655	C₂×C₄	C₃×C₅×#41	1	2	yes	—
656	C₂×C₄	C₃×C₅×#41	1	2	yes	—
657	C₂×C₃	—	4	2	no	—
658	C₂×C₃	C₅×#529	1	1	yes	characteristic
659	C₂×C₃	C₅×#529	1	1	yes	characteristic
660	C₂×C₃	C₅×#542	1	1	yes	characteristic
661	C₂×C₃	C₅×#551	1	1	yes	characteristic
662	C₂×C₃	C₅×#551	1	1	yes	characteristic
663	C₂×C₃	C₅×#552	1	1	yes	characteristic
664	C₂×C₃	C₅×#556	1	1	yes	characteristic
665	C₅	C₃×#2527	1	1	yes	characteristic, direct product factor, Sylow
666	C₂²	—	2	2	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	4	1	no	—
670	C₂²	—	4	1	no	—
671	C₂²	—	4	1	no	—
672	C₂²	—	4	1	no	—
673	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
674	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
675	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
676	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
677	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
678	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
679	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
680	C₄	—	2	2	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	4	1	no	—
685	C₄	—	4	1	no	—
686	C₄	—	4	1	no	—
687	C₄	—	4	1	no	—
688	C₄	—	4	1	no	—
689	C₄	—	4	1	no	—
690	C₄	—	4	1	no	—
691	C₄	—	4	1	no	—
692	C₄	—	4	1	no	—
693	C₄	—	4	1	no	—
694	C₃	C₅×#2527	1	1	yes	characteristic, direct product factor, Sylow
695	C₂	—	4	2	no	—
696	C₂	C₃×C₅×#529	1	1	yes	characteristic
697	C₂	C₃×C₅×#529	1	1	yes	characteristic
698	C₂	C₃×C₅×#542	1	1	yes	characteristic
699	C₂	C₃×C₅×#551	1	1	yes	characteristic
700	C₂	C₃×C₅×#551	1	1	yes	characteristic
701	C₂	C₃×C₅×#552	1	1	yes	characteristic
702	C₂	C₃×C₅×#556	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
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
1. C₃×C₅×#401	C₂	semidirect
2. C₃×C₅×#400	C₂	semidirect
5. C₃×C₅×#391	C₂	semidirect
6. C₃×C₅×#391	C₂	semidirect
9. C₃×C₅×#387	C₂	semidirect
10. C₃×C₅×#387	C₂	semidirect
11. C₃×C₅×#387	C₂	semidirect
15. C₃×C₅×#376	C₂	semidirect
16. C₅×#2527	C₃	direct (N × H)
52. C₃×#2527	C₅	direct (N × H)
53. C₅×#401	C₂×C₃	semidirect
54. C₅×#400	C₂×C₃	semidirect
57. C₅×#391	C₂×C₃	semidirect
58. C₅×#391	C₂×C₃	semidirect
61. C₅×#387	C₂×C₃	semidirect
62. C₅×#387	C₂×C₃	semidirect
63. C₅×#387	C₂×C₃	semidirect
67. C₅×#376	C₂×C₃	semidirect
104. C₃×#401	C₂×C₅	semidirect
105. C₃×#400	C₂×C₅	semidirect
108. C₃×#391	C₂×C₅	semidirect
109. C₃×#391	C₂×C₅	semidirect
112. C₃×#387	C₂×C₅	semidirect
113. C₃×#387	C₂×C₅	semidirect
114. C₃×#387	C₂×C₅	semidirect
118. C₃×#376	C₂×C₅	semidirect
154. #2527	C₃×C₅	direct (N × H)
278. #401	C₂×C₃×C₅	semidirect
279. #400	C₂×C₃×C₅	semidirect
282. #391	C₂×C₃×C₅	semidirect
283. #391	C₂×C₃×C₅	semidirect
286. #387	C₂×C₃×C₅	semidirect
287. #387	C₂×C₃×C₅	semidirect
288. #387	C₂×C₃×C₅	semidirect
292. #376	C₂×C₃×C₅	semidirect
568. C₃×C₅	#2527	direct (N × H)
665. C₅	C₃×#2527	direct (N × H)
694. C₃	C₅×#2527	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×#397	2
C₃×C₅×#393	2
C₃×C₅×#391	2
C₃×C₅×#388	2
C₃×C₅×#387	2
C₃×C₅×#385	2
C₃×C₅×#381	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₃×C₅×#376	2
C₅×#2527	3
C₃×#2527	5

Subgroups — C3×C5×#2527 #14275561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2527 #14275561