Subgroups — C₃×C₅×#2414 #14275448

Order 1920.

1408 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#394	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#392	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#390	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2414	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
16	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
17	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
18	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₃×C₅×#121	—	2	4	no	—
20	C₃×C₅×#121	—	2	4	no	—
21	C₃×C₄×C₅×D₄	—	2	4	no	—
22	C₃×C₅×#117	—	2	4	no	—
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	2	yes	—
27	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
35	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
37	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
38	C₃×C₅×#95	C₂²	1	2	yes	—
39	C₃×C₅×#95	C₂²	1	2	yes	—
40	C₃×#2414	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#394	C₂×C₃	1	2	yes	complemented
46	C₅×#392	C₂×C₃	1	2	yes	complemented
47	C₅×#390	C₂×C₃	1	2	yes	complemented
48	C₅×#390	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#388	C₂×C₃	1	2	yes	complemented
51	C₅×#380	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
53	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
54	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
55	C₂×C₃×C₅×D₄	—	2	2	no	—
56	C₂×C₃×C₅×D₄	—	2	2	no	—
57	C₂×C₃×C₅×D₄	—	2	4	no	—
58	C₂×C₃×C₅×D₄	—	2	4	no	—
59	C₂×C₃×C₅×D₄	—	2	4	no	—
60	C₂×C₃×C₅×D₄	—	2	2	no	—
61	C₂×C₃×C₅×D₄	—	2	2	no	—
62	C₂×C₃×C₅×D₄	—	2	2	no	—
63	C₂×C₃×C₅×D₄	—	2	2	no	—
64	C₂×C₃×C₅×D₄	—	4	2	no	—
65	C₂×C₃×C₅×D₄	—	4	2	no	—
66	C₂×C₃×C₅×D₄	—	4	2	no	—
67	C₂²×C₃×C₄×C₅	—	2	2	no	—
68	C₂²×C₃×C₄×C₅	—	2	2	no	—
69	C₂²×C₃×C₄×C₅	—	2	2	no	—
70	C₂²×C₃×C₄×C₅	—	2	2	no	—
71	C₂²×C₃×C₄×C₅	—	2	2	no	—
72	C₂²×C₃×C₄×C₅	D₄	1	4	yes	complemented
73	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
75	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
77	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₃×C₅×C₄⋊C₄	—	2	2	no	—
82	C₃×C₅×C₄⋊C₄	—	2	2	no	—
83	C₃×C₅×C₄⋊C₄	—	2	2	no	—
84	C₃×C₅×C₄⋊C₄	—	4	2	no	—
85	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	complemented
86	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
87	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
88	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
89	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
90	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
91	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
92	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
93	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
94	C₃×C₄²×C₅	—	2	4	no	—
95	C₃×C₄²×C₅	—	2	2	no	—
96	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
97	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
98	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
99	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
100	C₃×#394	C₂×C₅	1	2	yes	complemented
101	C₃×#392	C₂×C₅	1	2	yes	complemented
102	C₃×#390	C₂×C₅	1	2	yes	complemented
103	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
104	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
105	C₃×#388	C₂×C₅	1	2	yes	complemented
106	C₃×#380	C₂×C₅	1	1	yes	characteristic, complemented
107	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
108	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
109	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
110	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
111	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
112	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
113	C₅×#121	—	2	4	no	—
114	C₅×#121	—	2	4	no	—
115	C₄×C₅×D₄	—	2	4	no	—
116	C₅×#117	—	2	4	no	—
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	2	yes	—
121	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
123	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
124	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
125	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
126	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
127	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
129	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
130	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
131	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
132	C₅×#95	C₂²×C₃	1	2	yes	—
133	C₅×#95	C₂²×C₃	1	2	yes	—
134	#2414	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
135	C₂³×C₃×C₅	—	2	1	no	—
136	C₂³×C₃×C₅	—	2	1	no	—
137	C₂³×C₃×C₅	—	2	1	no	—
138	C₂³×C₃×C₅	—	2	1	no	—
139	C₂³×C₃×C₅	—	2	1	no	—
140	C₂³×C₃×C₅	—	2	1	no	—
141	C₂³×C₃×C₅	—	2	1	no	—
142	C₂³×C₃×C₅	—	2	1	no	—
143	C₂³×C₃×C₅	—	2	1	no	—
144	C₂³×C₃×C₅	—	2	1	no	—
145	C₂³×C₃×C₅	—	2	1	no	—
146	C₂³×C₃×C₅	—	2	1	no	—
147	C₂³×C₃×C₅	—	2	2	no	—
148	C₂³×C₃×C₅	—	2	2	no	—
149	C₂³×C₃×C₅	—	2	2	no	—
150	C₂³×C₃×C₅	—	2	2	no	—
151	C₂³×C₃×C₅	—	2	2	no	—
152	C₂³×C₃×C₅	—	2	2	no	—
153	C₂³×C₃×C₅	—	2	2	no	—
154	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
155	C₂³×C₃×C₅	#41	1	2	yes	—
156	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
157	C₃×C₅×D₄	—	2	8	no	—
158	C₃×C₅×D₄	—	4	8	no	—
159	C₃×C₅×D₄	—	4	8	no	—
160	C₃×C₅×D₄	—	4	4	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	2	no	—
166	C₂×C₃×C₄×C₅	—	2	2	no	—
167	C₂×C₃×C₄×C₅	—	2	8	no	—
168	C₂×C₃×C₄×C₅	—	2	1	no	—
169	C₂×C₃×C₄×C₅	—	2	2	no	—
170	C₂×C₃×C₄×C₅	—	2	1	no	—
171	C₂×C₃×C₄×C₅	—	2	1	no	—
172	C₂×C₃×C₄×C₅	—	2	2	no	—
173	C₂×C₃×C₄×C₅	—	2	2	no	—
174	C₂×C₃×C₄×C₅	—	2	1	no	—
175	C₂×C₃×C₄×C₅	—	2	1	no	—
176	C₂×C₃×C₄×C₅	—	2	2	no	—
177	C₂×C₃×C₄×C₅	—	2	2	no	—
178	C₂×C₃×C₄×C₅	—	2	1	no	—
179	C₂×C₃×C₄×C₅	—	2	2	no	—
180	C₂×C₃×C₄×C₅	—	4	4	no	—
181	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
182	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
183	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
184	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
185	C₂×C₃×C₄×C₅	#41	1	2	yes	—
186	C₂×C₃×C₄×C₅	#41	1	2	yes	—
187	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
188	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
189	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
190	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
191	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
192	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
193	C₃×#121	—	2	4	no	—
194	C₃×#121	—	2	4	no	—
195	C₃×C₄×D₄	—	2	4	no	—
196	C₃×#117	—	2	4	no	—
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	2	yes	—
201	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
202	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
203	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
204	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
205	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
206	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
207	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
208	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
209	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
210	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
211	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
212	C₃×#95	C₂²×C₅	1	2	yes	—
213	C₃×#95	C₂²×C₅	1	2	yes	—
214	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
215	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
216	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
217	C₂×C₅×D₄	—	2	2	no	—
218	C₂×C₅×D₄	—	2	2	no	—
219	C₂×C₅×D₄	—	2	4	no	—
220	C₂×C₅×D₄	—	2	4	no	—
221	C₂×C₅×D₄	—	2	4	no	—
222	C₂×C₅×D₄	—	2	2	no	—
223	C₂×C₅×D₄	—	2	2	no	—
224	C₂×C₅×D₄	—	2	2	no	—
225	C₂×C₅×D₄	—	2	2	no	—
226	C₂×C₅×D₄	—	4	2	no	—
227	C₂×C₅×D₄	—	4	2	no	—
228	C₂×C₅×D₄	—	4	2	no	—
229	C₂²×C₄×C₅	—	2	2	no	—
230	C₂²×C₄×C₅	—	2	2	no	—
231	C₂²×C₄×C₅	—	2	2	no	—
232	C₂²×C₄×C₅	—	2	2	no	—
233	C₂²×C₄×C₅	—	2	2	no	—
234	C₂²×C₄×C₅	C₃×D₄	1	4	yes	complemented
235	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
236	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
237	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
238	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
239	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
240	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
241	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
242	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
243	C₅×C₄⋊C₄	—	2	2	no	—
244	C₅×C₄⋊C₄	—	2	2	no	—
245	C₅×C₄⋊C₄	—	2	2	no	—
246	C₅×C₄⋊C₄	—	4	2	no	—
247	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	complemented
248	C₅×C₂²⋊C₄	—	2	2	no	—
249	C₅×C₂²⋊C₄	—	2	4	no	—
250	C₅×C₂²⋊C₄	—	2	2	no	—
251	C₅×C₂²⋊C₄	—	2	4	no	—
252	C₅×C₂²⋊C₄	—	2	4	no	—
253	C₅×C₂²⋊C₄	—	2	4	no	—
254	C₅×C₂²⋊C₄	—	4	2	no	—
255	C₅×C₂²⋊C₄	—	4	2	no	—
256	C₄²×C₅	—	2	4	no	—
257	C₄²×C₅	—	2	2	no	—
258	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic, complemented
259	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic, complemented
260	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
261	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic, complemented
262	#394	C₂×C₃×C₅	1	2	yes	complemented
263	#392	C₂×C₃×C₅	1	2	yes	complemented
264	#390	C₂×C₃×C₅	1	2	yes	complemented
265	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
266	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
267	#388	C₂×C₃×C₅	1	2	yes	complemented
268	#380	C₂×C₃×C₅	1	1	yes	characteristic, complemented
269	C₂²×C₃×C₅	—	2	2	no	—
270	C₂²×C₃×C₅	—	2	2	no	—
271	C₂²×C₃×C₅	—	2	2	no	—
272	C₂²×C₃×C₅	—	2	2	no	—
273	C₂²×C₃×C₅	—	2	2	no	—
274	C₂²×C₃×C₅	—	2	2	no	—
275	C₂²×C₃×C₅	—	4	1	no	—
276	C₂²×C₃×C₅	—	4	1	no	—
277	C₂²×C₃×C₅	—	4	1	no	—
278	C₂²×C₃×C₅	—	4	1	no	—
279	C₂²×C₃×C₅	—	4	1	no	—
280	C₂²×C₃×C₅	—	4	1	no	—
281	C₂²×C₃×C₅	—	4	1	no	—
282	C₂²×C₃×C₅	—	4	1	no	—
283	C₂²×C₃×C₅	—	4	2	no	—
284	C₂²×C₃×C₅	—	4	2	no	—
285	C₂²×C₃×C₅	—	4	2	no	—
286	C₂²×C₃×C₅	—	4	2	no	—
287	C₂²×C₃×C₅	—	4	2	no	—
288	C₂²×C₃×C₅	—	4	2	no	—
289	C₂²×C₃×C₅	—	4	2	no	—
290	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
291	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
292	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
293	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
294	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
295	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
296	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
297	C₃×C₄×C₅	—	2	2	no	—
298	C₃×C₄×C₅	—	2	2	no	—
299	C₃×C₄×C₅	—	2	4	no	—
300	C₃×C₄×C₅	—	4	1	no	—
301	C₃×C₄×C₅	—	4	1	no	—
302	C₃×C₄×C₅	—	4	2	no	—
303	C₃×C₄×C₅	—	4	2	no	—
304	C₃×C₄×C₅	#121	1	4	yes	—
305	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
306	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
307	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
308	C₂×C₃×D₄	—	2	2	no	—
309	C₂×C₃×D₄	—	2	2	no	—
310	C₂×C₃×D₄	—	2	4	no	—
311	C₂×C₃×D₄	—	2	4	no	—
312	C₂×C₃×D₄	—	2	4	no	—
313	C₂×C₃×D₄	—	2	2	no	—
314	C₂×C₃×D₄	—	2	2	no	—
315	C₂×C₃×D₄	—	2	2	no	—
316	C₂×C₃×D₄	—	2	2	no	—
317	C₂×C₃×D₄	—	4	2	no	—
318	C₂×C₃×D₄	—	4	2	no	—
319	C₂×C₃×D₄	—	4	2	no	—
320	C₂²×C₃×C₄	—	2	2	no	—
321	C₂²×C₃×C₄	—	2	2	no	—
322	C₂²×C₃×C₄	—	2	2	no	—
323	C₂²×C₃×C₄	—	2	2	no	—
324	C₂²×C₃×C₄	—	2	2	no	—
325	C₂²×C₃×C₄	C₅×D₄	1	4	yes	complemented
326	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
327	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
328	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
329	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
330	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
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	C₃×C₄⋊C₄	—	2	2	no	—
335	C₃×C₄⋊C₄	—	2	2	no	—
336	C₃×C₄⋊C₄	—	2	2	no	—
337	C₃×C₄⋊C₄	—	4	2	no	—
338	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	complemented
339	C₃×C₂²⋊C₄	—	2	2	no	—
340	C₃×C₂²⋊C₄	—	2	4	no	—
341	C₃×C₂²⋊C₄	—	2	2	no	—
342	C₃×C₂²⋊C₄	—	2	4	no	—
343	C₃×C₂²⋊C₄	—	2	4	no	—
344	C₃×C₂²⋊C₄	—	2	4	no	—
345	C₃×C₂²⋊C₄	—	4	2	no	—
346	C₃×C₂²⋊C₄	—	4	2	no	—
347	C₃×C₄²	—	2	4	no	—
348	C₃×C₄²	—	2	2	no	—
349	C₂³×C₅	—	2	1	no	—
350	C₂³×C₅	—	2	1	no	—
351	C₂³×C₅	—	2	1	no	—
352	C₂³×C₅	—	2	1	no	—
353	C₂³×C₅	—	2	1	no	—
354	C₂³×C₅	—	2	1	no	—
355	C₂³×C₅	—	2	1	no	—
356	C₂³×C₅	—	2	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	2	no	—
362	C₂³×C₅	—	2	2	no	—
363	C₂³×C₅	—	2	2	no	—
364	C₂³×C₅	—	2	2	no	—
365	C₂³×C₅	—	2	2	no	—
366	C₂³×C₅	—	2	2	no	—
367	C₂³×C₅	—	2	2	no	—
368	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
369	C₂³×C₅	C₃×#41	1	2	yes	—
370	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
371	C₅×D₄	—	2	8	no	—
372	C₅×D₄	—	4	8	no	—
373	C₅×D₄	—	4	8	no	—
374	C₅×D₄	—	4	4	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	2	no	—
380	C₂×C₄×C₅	—	2	2	no	—
381	C₂×C₄×C₅	—	2	8	no	—
382	C₂×C₄×C₅	—	2	1	no	—
383	C₂×C₄×C₅	—	2	2	no	—
384	C₂×C₄×C₅	—	2	1	no	—
385	C₂×C₄×C₅	—	2	1	no	—
386	C₂×C₄×C₅	—	2	2	no	—
387	C₂×C₄×C₅	—	2	2	no	—
388	C₂×C₄×C₅	—	2	1	no	—
389	C₂×C₄×C₅	—	2	1	no	—
390	C₂×C₄×C₅	—	2	2	no	—
391	C₂×C₄×C₅	—	2	2	no	—
392	C₂×C₄×C₅	—	2	1	no	—
393	C₂×C₄×C₅	—	2	2	no	—
394	C₂×C₄×C₅	—	4	4	no	—
395	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
396	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
397	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
398	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
399	C₂×C₄×C₅	C₃×#41	1	2	yes	—
400	C₂×C₄×C₅	C₃×#41	1	2	yes	—
401	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
402	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
403	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
404	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
405	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
406	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
407	#121	—	2	4	no	—
408	#121	—	2	4	no	—
409	C₄×D₄	—	2	4	no	—
410	#117	—	2	4	no	—
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	2	yes	—
415	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
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	2	yes	—
420	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
421	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
422	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
423	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
424	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
425	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
426	#95	C₂²×C₃×C₅	1	2	yes	—
427	#95	C₂²×C₃×C₅	1	2	yes	—
428	C₂×C₃×C₅	—	4	2	no	—
429	C₂×C₃×C₅	—	4	2	no	—
430	C₂×C₃×C₅	—	8	2	no	—
431	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
432	C₂×C₃×C₅	#525	1	1	yes	characteristic
433	C₂×C₃×C₅	#535	1	1	yes	characteristic
434	C₂×C₃×C₅	#546	1	1	yes	characteristic
435	C₂×C₃×C₅	#550	1	1	yes	characteristic
436	C₂×C₃×C₅	#553	1	1	yes	characteristic
437	C₂×C₃×C₅	#555	1	1	yes	characteristic
438	C₂³×C₃	—	2	1	no	—
439	C₂³×C₃	—	2	1	no	—
440	C₂³×C₃	—	2	1	no	—
441	C₂³×C₃	—	2	1	no	—
442	C₂³×C₃	—	2	1	no	—
443	C₂³×C₃	—	2	1	no	—
444	C₂³×C₃	—	2	1	no	—
445	C₂³×C₃	—	2	1	no	—
446	C₂³×C₃	—	2	1	no	—
447	C₂³×C₃	—	2	1	no	—
448	C₂³×C₃	—	2	1	no	—
449	C₂³×C₃	—	2	1	no	—
450	C₂³×C₃	—	2	2	no	—
451	C₂³×C₃	—	2	2	no	—
452	C₂³×C₃	—	2	2	no	—
453	C₂³×C₃	—	2	2	no	—
454	C₂³×C₃	—	2	2	no	—
455	C₂³×C₃	—	2	2	no	—
456	C₂³×C₃	—	2	2	no	—
457	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
458	C₂³×C₃	C₅×#41	1	2	yes	—
459	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
460	C₃×D₄	—	2	8	no	—
461	C₃×D₄	—	4	8	no	—
462	C₃×D₄	—	4	8	no	—
463	C₃×D₄	—	4	4	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	2	no	—
469	C₂×C₃×C₄	—	2	2	no	—
470	C₂×C₃×C₄	—	2	8	no	—
471	C₂×C₃×C₄	—	2	1	no	—
472	C₂×C₃×C₄	—	2	2	no	—
473	C₂×C₃×C₄	—	2	1	no	—
474	C₂×C₃×C₄	—	2	1	no	—
475	C₂×C₃×C₄	—	2	2	no	—
476	C₂×C₃×C₄	—	2	2	no	—
477	C₂×C₃×C₄	—	2	1	no	—
478	C₂×C₃×C₄	—	2	1	no	—
479	C₂×C₃×C₄	—	2	2	no	—
480	C₂×C₃×C₄	—	2	2	no	—
481	C₂×C₃×C₄	—	2	1	no	—
482	C₂×C₃×C₄	—	2	2	no	—
483	C₂×C₃×C₄	—	4	4	no	—
484	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
485	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
486	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
487	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
488	C₂×C₃×C₄	C₅×#41	1	2	yes	—
489	C₂×C₃×C₄	C₅×#41	1	2	yes	—
490	C₂²×C₅	—	2	2	no	—
491	C₂²×C₅	—	2	2	no	—
492	C₂²×C₅	—	2	2	no	—
493	C₂²×C₅	—	2	2	no	—
494	C₂²×C₅	—	2	2	no	—
495	C₂²×C₅	—	2	2	no	—
496	C₂²×C₅	—	4	1	no	—
497	C₂²×C₅	—	4	1	no	—
498	C₂²×C₅	—	4	1	no	—
499	C₂²×C₅	—	4	1	no	—
500	C₂²×C₅	—	4	1	no	—
501	C₂²×C₅	—	4	1	no	—
502	C₂²×C₅	—	4	1	no	—
503	C₂²×C₅	—	4	1	no	—
504	C₂²×C₅	—	4	2	no	—
505	C₂²×C₅	—	4	2	no	—
506	C₂²×C₅	—	4	2	no	—
507	C₂²×C₅	—	4	2	no	—
508	C₂²×C₅	—	4	2	no	—
509	C₂²×C₅	—	4	2	no	—
510	C₂²×C₅	—	4	2	no	—
511	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
512	C₂²×C₅	C₂²×C₃×D₄	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×H(5,𝔽₂)	1	1	yes	characteristic
518	C₄×C₅	—	2	2	no	—
519	C₄×C₅	—	2	2	no	—
520	C₄×C₅	—	2	4	no	—
521	C₄×C₅	—	4	1	no	—
522	C₄×C₅	—	4	1	no	—
523	C₄×C₅	—	4	2	no	—
524	C₄×C₅	—	4	2	no	—
525	C₄×C₅	C₃×#121	1	4	yes	—
526	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
527	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
528	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
529	C₂×D₄	—	2	2	no	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	2	4	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	2	2	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	4	2	no	—
539	C₂×D₄	—	4	2	no	—
540	C₂×D₄	—	4	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	C₃×C₅×D₄	1	4	yes	complemented
547	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
548	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
549	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
550	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
551	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
552	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
553	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
554	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	2	no	—
557	C₄⋊C₄	—	2	2	no	—
558	C₄⋊C₄	—	4	2	no	—
559	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	2	4	no	—
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	2	4	no	—
564	C₂²⋊C₄	—	2	4	no	—
565	C₂²⋊C₄	—	2	4	no	—
566	C₂²⋊C₄	—	4	2	no	—
567	C₂²⋊C₄	—	4	2	no	—
568	C₄²	—	2	4	no	—
569	C₄²	—	2	2	no	—
570	C₃×C₅	#2414	1	1	yes	characteristic, direct product factor, Hall
571	C₂²×C₃	—	2	2	no	—
572	C₂²×C₃	—	2	2	no	—
573	C₂²×C₃	—	2	2	no	—
574	C₂²×C₃	—	2	2	no	—
575	C₂²×C₃	—	2	2	no	—
576	C₂²×C₃	—	2	2	no	—
577	C₂²×C₃	—	4	1	no	—
578	C₂²×C₃	—	4	1	no	—
579	C₂²×C₃	—	4	1	no	—
580	C₂²×C₃	—	4	1	no	—
581	C₂²×C₃	—	4	1	no	—
582	C₂²×C₃	—	4	1	no	—
583	C₂²×C₃	—	4	1	no	—
584	C₂²×C₃	—	4	1	no	—
585	C₂²×C₃	—	4	2	no	—
586	C₂²×C₃	—	4	2	no	—
587	C₂²×C₃	—	4	2	no	—
588	C₂²×C₃	—	4	2	no	—
589	C₂²×C₃	—	4	2	no	—
590	C₂²×C₃	—	4	2	no	—
591	C₂²×C₃	—	4	2	no	—
592	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
593	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
594	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
595	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
596	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
597	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
598	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
599	C₃×C₄	—	2	2	no	—
600	C₃×C₄	—	2	2	no	—
601	C₃×C₄	—	2	4	no	—
602	C₃×C₄	—	4	1	no	—
603	C₃×C₄	—	4	1	no	—
604	C₃×C₄	—	4	2	no	—
605	C₃×C₄	—	4	2	no	—
606	C₃×C₄	C₅×#121	1	4	yes	—
607	C₂×C₅	—	4	2	no	—
608	C₂×C₅	—	4	2	no	—
609	C₂×C₅	—	8	2	no	—
610	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
611	C₂×C₅	C₃×#525	1	1	yes	characteristic
612	C₂×C₅	C₃×#535	1	1	yes	characteristic
613	C₂×C₅	C₃×#546	1	1	yes	characteristic
614	C₂×C₅	C₃×#550	1	1	yes	characteristic
615	C₂×C₅	C₃×#553	1	1	yes	characteristic
616	C₂×C₅	C₃×#555	1	1	yes	characteristic
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
637	C₂³	C₃×C₅×#41	1	2	yes	—
638	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
639	D₄	—	2	8	no	—
640	D₄	—	4	8	no	—
641	D₄	—	4	8	no	—
642	D₄	—	4	4	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	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	8	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
664	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
665	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
666	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
667	C₂×C₄	C₃×C₅×#41	1	2	yes	—
668	C₂×C₄	C₃×C₅×#41	1	2	yes	—
669	C₂×C₃	—	4	2	no	—
670	C₂×C₃	—	4	2	no	—
671	C₂×C₃	—	8	2	no	—
672	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
673	C₂×C₃	C₅×#525	1	1	yes	characteristic
674	C₂×C₃	C₅×#535	1	1	yes	characteristic
675	C₂×C₃	C₅×#546	1	1	yes	characteristic
676	C₂×C₃	C₅×#550	1	1	yes	characteristic
677	C₂×C₃	C₅×#553	1	1	yes	characteristic
678	C₂×C₃	C₅×#555	1	1	yes	characteristic
679	C₅	C₃×#2414	1	1	yes	characteristic, direct product factor, Sylow
680	C₂²	—	2	2	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	4	1	no	—
690	C₂²	—	4	1	no	—
691	C₂²	—	4	1	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
702	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
703	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
704	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
705	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
706	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
707	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
708	C₄	—	2	2	no	—
709	C₄	—	2	2	no	—
710	C₄	—	2	4	no	—
711	C₄	—	4	1	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	1	no	—
714	C₄	—	4	2	no	—
715	C₄	C₃×C₅×#121	1	4	yes	—
716	C₃	C₅×#2414	1	1	yes	characteristic, direct product factor, Sylow
717	C₂	—	4	2	no	—
718	C₂	—	4	2	no	—
719	C₂	—	8	2	no	—
720	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
721	C₂	C₃×C₅×#525	1	1	yes	characteristic
722	C₂	C₃×C₅×#535	1	1	yes	characteristic
723	C₂	C₃×C₅×#546	1	1	yes	characteristic
724	C₂	C₃×C₅×#550	1	1	yes	characteristic
725	C₂	C₃×C₅×#553	1	1	yes	characteristic
726	C₂	C₃×C₅×#555	1	1	yes	characteristic

	subgroup	G/H
center, socle	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
1. C₂×C₃×C₅×#121	C₂	semidirect
2. C₂×C₃×C₅×#121	C₂	semidirect
3. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
4. C₂×C₃×C₅×#117	C₂	semidirect
5. C₃×C₅×#394	C₂	semidirect
6. C₃×C₅×#392	C₂	semidirect
7. C₃×C₅×#390	C₂	semidirect
8. C₃×C₅×#390	C₂	semidirect
9. C₃×C₅×#389	C₂	semidirect
10. C₃×C₅×#388	C₂	semidirect
11. C₃×C₅×#380	C₂	semidirect
12. C₅×#2414	C₃	direct (N × H)
40. C₃×#2414	C₅	direct (N × H)
41. C₂×C₅×#121	C₂×C₃	semidirect
42. C₂×C₅×#121	C₂×C₃	semidirect
43. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
44. C₂×C₅×#117	C₂×C₃	semidirect
45. C₅×#394	C₂×C₃	semidirect
46. C₅×#392	C₂×C₃	semidirect
47. C₅×#390	C₂×C₃	semidirect
48. C₅×#390	C₂×C₃	semidirect
49. C₅×#389	C₂×C₃	semidirect
50. C₅×#388	C₂×C₃	semidirect
51. C₅×#380	C₂×C₃	semidirect
72. C₂²×C₃×C₄×C₅	D₄	semidirect
85. C₃×C₅×C₄⋊C₄	D₄	semidirect
96. C₂×C₃×#121	C₂×C₅	semidirect
97. C₂×C₃×#121	C₂×C₅	semidirect
98. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
99. C₂×C₃×#117	C₂×C₅	semidirect
100. C₃×#394	C₂×C₅	semidirect
101. C₃×#392	C₂×C₅	semidirect
102. C₃×#390	C₂×C₅	semidirect
103. C₃×#390	C₂×C₅	semidirect
104. C₃×#389	C₂×C₅	semidirect
105. C₃×#388	C₂×C₅	semidirect
106. C₃×#380	C₂×C₅	semidirect
134. #2414	C₃×C₅	direct (N × H)
234. C₂²×C₄×C₅	C₃×D₄	semidirect
247. C₅×C₄⋊C₄	C₃×D₄	semidirect
258. C₂×#121	C₂×C₃×C₅	semidirect
259. C₂×#121	C₂×C₃×C₅	semidirect
260. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
261. C₂×#117	C₂×C₃×C₅	semidirect
262. #394	C₂×C₃×C₅	semidirect
263. #392	C₂×C₃×C₅	semidirect
264. #390	C₂×C₃×C₅	semidirect
265. #390	C₂×C₃×C₅	semidirect
266. #389	C₂×C₃×C₅	semidirect
267. #388	C₂×C₃×C₅	semidirect
268. #380	C₂×C₃×C₅	semidirect
325. C₂²×C₃×C₄	C₅×D₄	semidirect
338. C₃×C₄⋊C₄	C₅×D₄	semidirect
546. C₂²×C₄	C₃×C₅×D₄	semidirect
559. C₄⋊C₄	C₃×C₅×D₄	semidirect
570. C₃×C₅	#2414	direct (N × H)
679. C₅	C₃×#2414	direct (N × H)
716. C₃	C₅×#2414	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×#121	2
C₂×C₃×C₄×C₅×D₄	2
C₂×C₃×C₅×#117	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₅×#390	2
C₃×C₅×#389	2
C₃×C₅×#388	2
C₃×C₅×#380	2
C₅×#2414	3
C₃×#2414	5

Subgroups — C3×C5×#2414 #14275448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2414 #14275448