Subgroups — C₃×C₅×#2412 #14275446

Order 1920.

1628 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	C₂×C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#397	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#394	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#386	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#381	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#380	C₂	1	2	yes	maximal, complemented
12	C₅×#2412	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
18	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
19	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
20	C₃×C₅×#123	—	2	4	no	—
21	C₃×C₅×#120	—	2	4	no	—
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
24	C₂×C₃×C₅×C₂²⋊C₄	—	2	4	no	—
25	C₂×C₃×C₅×C₂²⋊C₄	—	2	4	no	—
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
35	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
36	C₃×C₅×#95	C₂²	1	2	yes	complemented
37	C₃×C₅×#95	C₂²	1	2	yes	complemented
38	C₃×C₅×#95	C₂²	1	2	yes	complemented
39	C₃×C₅×#95	C₂²	1	2	yes	complemented
40	C₃×#2412	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₂×C₅×#123	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×C₅×#120	C₂×C₃	1	1	yes	characteristic
43	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#397	C₂×C₃	1	2	yes	complemented
46	C₅×#394	C₂×C₃	1	2	yes	complemented
47	C₅×#386	C₂×C₃	1	2	yes	complemented
48	C₅×#386	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#385	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#381	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#380	C₂×C₃	1	2	yes	complemented
52	C₂⁴×C₃×C₅	—	2	2	no	—
53	C₂⁴×C₃×C₅	—	2	2	no	—
54	C₂⁴×C₃×C₅	—	2	4	no	—
55	C₂⁴×C₃×C₅	—	4	2	no	—
56	C₂⁴×C₃×C₅	D₄	1	4	yes	—
57	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
58	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
59	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
60	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
65	C₂×C₃×C₅×D₄	—	2	2	no	—
66	C₂×C₃×C₅×D₄	—	2	4	no	—
67	C₂×C₃×C₅×D₄	—	4	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	4	no	—
72	C₂²×C₃×C₄×C₅	—	2	2	no	—
73	C₂²×C₃×C₄×C₅	—	2	4	no	—
74	C₂²×C₃×C₄×C₅	—	4	2	no	—
75	C₂²×C₃×C₄×C₅	—	4	2	no	—
76	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
77	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
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	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
83	C₃×C₅×C₄⋊C₄	—	2	4	no	—
84	C₃×C₅×C₄⋊C₄	—	4	2	no	—
85	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
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	2	no	—
90	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
91	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
92	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
93	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
94	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	complemented
95	C₂×C₃×#123	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂×C₃×#120	C₂×C₅	1	1	yes	characteristic
97	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
98	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#397	C₂×C₅	1	2	yes	complemented
100	C₃×#394	C₂×C₅	1	2	yes	complemented
101	C₃×#386	C₂×C₅	1	1	yes	characteristic, complemented
102	C₃×#386	C₂×C₅	1	2	yes	complemented
103	C₃×#385	C₂×C₅	1	1	yes	characteristic, complemented
104	C₃×#381	C₂×C₅	1	1	yes	characteristic, complemented
105	C₃×#380	C₂×C₅	1	2	yes	complemented
106	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
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	1	yes	characteristic
110	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
111	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
112	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
113	C₅×#123	—	2	4	no	—
114	C₅×#120	—	2	4	no	—
115	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
116	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
117	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
118	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
119	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
121	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	1	yes	characteristic
127	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
128	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
129	C₅×#95	C₂²×C₃	1	2	yes	complemented
130	C₅×#95	C₂²×C₃	1	2	yes	complemented
131	C₅×#95	C₂²×C₃	1	2	yes	complemented
132	C₅×#95	C₂²×C₃	1	2	yes	complemented
133	#2412	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
134	C₂³×C₃×C₅	—	2	1	no	—
135	C₂³×C₃×C₅	—	2	1	no	—
136	C₂³×C₃×C₅	—	2	2	no	—
137	C₂³×C₃×C₅	—	2	2	no	—
138	C₂³×C₃×C₅	—	2	2	no	—
139	C₂³×C₃×C₅	—	2	8	no	—
140	C₂³×C₃×C₅	—	2	8	no	—
141	C₂³×C₃×C₅	—	2	1	no	—
142	C₂³×C₃×C₅	—	2	1	no	—
143	C₂³×C₃×C₅	—	2	2	no	—
144	C₂³×C₃×C₅	—	2	2	no	—
145	C₂³×C₃×C₅	—	2	1	no	—
146	C₂³×C₃×C₅	—	2	1	no	—
147	C₂³×C₃×C₅	—	2	1	no	—
148	C₂³×C₃×C₅	—	2	2	no	—
149	C₂³×C₃×C₅	—	2	2	no	—
150	C₂³×C₃×C₅	—	4	4	no	—
151	C₂³×C₃×C₅	—	4	8	no	—
152	C₂³×C₃×C₅	—	4	8	no	—
153	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
154	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
155	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
156	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
157	C₂³×C₃×C₅	#41	1	2	yes	—
158	C₂³×C₃×C₅	#41	1	4	yes	—
159	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
160	C₃×C₅×D₄	—	4	4	no	—
161	C₃×C₅×D₄	—	4	4	no	—
162	C₃×C₅×D₄	—	4	4	no	—
163	C₂×C₃×C₄×C₅	—	2	2	no	—
164	C₂×C₃×C₄×C₅	—	2	2	no	—
165	C₂×C₃×C₄×C₅	—	2	2	no	—
166	C₂×C₃×C₄×C₅	—	2	2	no	—
167	C₂×C₃×C₄×C₅	—	2	2	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	2	no	—
172	C₂×C₃×C₄×C₅	—	2	1	no	—
173	C₂×C₃×C₄×C₅	—	2	2	no	—
174	C₂×C₃×C₄×C₅	—	2	2	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	2	no	—
179	C₂×C₃×C₄×C₅	—	2	2	no	—
180	C₂×C₃×C₄×C₅	—	2	2	no	—
181	C₂×C₃×C₄×C₅	—	4	8	no	—
182	C₂×C₃×C₄×C₅	—	4	4	no	—
183	C₂×C₃×C₄×C₅	—	4	4	no	—
184	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
185	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
186	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
187	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
188	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
189	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
190	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
191	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
192	C₃×#123	—	2	4	no	—
193	C₃×#120	—	2	4	no	—
194	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
195	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
196	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
197	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
198	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
199	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
200	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
201	C₂×C₃×C₂²⋊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	1	yes	characteristic
205	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
206	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
207	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
208	C₃×#95	C₂²×C₅	1	2	yes	complemented
209	C₃×#95	C₂²×C₅	1	2	yes	complemented
210	C₃×#95	C₂²×C₅	1	2	yes	complemented
211	C₃×#95	C₂²×C₅	1	2	yes	complemented
212	C₂⁴×C₅	—	2	2	no	—
213	C₂⁴×C₅	—	2	2	no	—
214	C₂⁴×C₅	—	2	4	no	—
215	C₂⁴×C₅	—	4	2	no	—
216	C₂⁴×C₅	C₃×D₄	1	4	yes	—
217	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
218	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
219	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
220	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
221	C₂×C₅×D₄	—	2	2	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	—	2	4	no	—
227	C₂×C₅×D₄	—	4	2	no	—
228	C₂²×C₄×C₅	—	2	2	no	—
229	C₂²×C₄×C₅	—	2	2	no	—
230	C₂²×C₄×C₅	—	2	2	no	—
231	C₂²×C₄×C₅	—	2	4	no	—
232	C₂²×C₄×C₅	—	2	2	no	—
233	C₂²×C₄×C₅	—	2	4	no	—
234	C₂²×C₄×C₅	—	4	2	no	—
235	C₂²×C₄×C₅	—	4	2	no	—
236	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
237	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
241	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
242	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
243	C₅×C₄⋊C₄	—	2	4	no	—
244	C₅×C₄⋊C₄	—	4	2	no	—
245	C₅×C₂²⋊C₄	—	2	4	no	—
246	C₅×C₂²⋊C₄	—	2	2	no	—
247	C₅×C₂²⋊C₄	—	2	4	no	—
248	C₅×C₂²⋊C₄	—	2	2	no	—
249	C₅×C₂²⋊C₄	—	2	2	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	—	4	2	no	—
254	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	complemented
255	C₂×#123	C₂×C₃×C₅	1	1	yes	characteristic, complemented
256	C₂×#120	C₂×C₃×C₅	1	1	yes	characteristic
257	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
258	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
259	#397	C₂×C₃×C₅	1	2	yes	complemented
260	#394	C₂×C₃×C₅	1	2	yes	complemented
261	#386	C₂×C₃×C₅	1	1	yes	characteristic, complemented
262	#386	C₂×C₃×C₅	1	2	yes	complemented
263	#385	C₂×C₃×C₅	1	1	yes	characteristic, complemented
264	#381	C₂×C₃×C₅	1	1	yes	characteristic, complemented
265	#380	C₂×C₃×C₅	1	2	yes	complemented
266	C₂²×C₃×C₅	—	2	2	no	—
267	C₂²×C₃×C₅	—	2	2	no	—
268	C₂²×C₃×C₅	—	2	2	no	—
269	C₂²×C₃×C₅	—	2	2	no	—
270	C₂²×C₃×C₅	—	2	4	no	—
271	C₂²×C₃×C₅	—	2	4	no	—
272	C₂²×C₃×C₅	—	2	4	no	—
273	C₂²×C₃×C₅	—	2	4	no	—
274	C₂²×C₃×C₅	—	2	2	no	—
275	C₂²×C₃×C₅	—	2	2	no	—
276	C₂²×C₃×C₅	—	2	2	no	—
277	C₂²×C₃×C₅	—	4	16	no	—
278	C₂²×C₃×C₅	—	4	2	no	—
279	C₂²×C₃×C₅	—	4	2	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	#121	1	4	yes	—
286	C₂²×C₃×C₅	#123	1	4	yes	complemented
287	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
288	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
289	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
290	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
291	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
292	C₃×C₄×C₅	—	2	4	no	—
293	C₃×C₄×C₅	—	4	2	no	—
294	C₃×C₄×C₅	—	4	1	no	—
295	C₃×C₄×C₅	—	4	1	no	—
296	C₃×C₄×C₅	—	4	2	no	—
297	C₃×C₄×C₅	—	4	1	no	—
298	C₃×C₄×C₅	—	4	2	no	—
299	C₂⁴×C₃	—	2	2	no	—
300	C₂⁴×C₃	—	2	2	no	—
301	C₂⁴×C₃	—	2	4	no	—
302	C₂⁴×C₃	—	4	2	no	—
303	C₂⁴×C₃	C₅×D₄	1	4	yes	—
304	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
305	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
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	2	no	—
311	C₂×C₃×D₄	—	2	2	no	—
312	C₂×C₃×D₄	—	2	2	no	—
313	C₂×C₃×D₄	—	2	4	no	—
314	C₂×C₃×D₄	—	4	2	no	—
315	C₂²×C₃×C₄	—	2	2	no	—
316	C₂²×C₃×C₄	—	2	2	no	—
317	C₂²×C₃×C₄	—	2	2	no	—
318	C₂²×C₃×C₄	—	2	4	no	—
319	C₂²×C₃×C₄	—	2	2	no	—
320	C₂²×C₃×C₄	—	2	4	no	—
321	C₂²×C₃×C₄	—	4	2	no	—
322	C₂²×C₃×C₄	—	4	2	no	—
323	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
324	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
325	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
326	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
327	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
328	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
329	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
330	C₃×C₄⋊C₄	—	2	4	no	—
331	C₃×C₄⋊C₄	—	4	2	no	—
332	C₃×C₂²⋊C₄	—	2	4	no	—
333	C₃×C₂²⋊C₄	—	2	2	no	—
334	C₃×C₂²⋊C₄	—	2	4	no	—
335	C₃×C₂²⋊C₄	—	2	2	no	—
336	C₃×C₂²⋊C₄	—	2	2	no	—
337	C₃×C₂²⋊C₄	—	2	2	no	—
338	C₃×C₂²⋊C₄	—	2	4	no	—
339	C₃×C₂²⋊C₄	—	2	4	no	—
340	C₃×C₂²⋊C₄	—	4	2	no	—
341	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	complemented
342	C₂³×C₅	—	2	1	no	—
343	C₂³×C₅	—	2	1	no	—
344	C₂³×C₅	—	2	2	no	—
345	C₂³×C₅	—	2	2	no	—
346	C₂³×C₅	—	2	2	no	—
347	C₂³×C₅	—	2	8	no	—
348	C₂³×C₅	—	2	8	no	—
349	C₂³×C₅	—	2	1	no	—
350	C₂³×C₅	—	2	1	no	—
351	C₂³×C₅	—	2	2	no	—
352	C₂³×C₅	—	2	2	no	—
353	C₂³×C₅	—	2	1	no	—
354	C₂³×C₅	—	2	1	no	—
355	C₂³×C₅	—	2	1	no	—
356	C₂³×C₅	—	2	2	no	—
357	C₂³×C₅	—	2	2	no	—
358	C₂³×C₅	—	4	4	no	—
359	C₂³×C₅	—	4	8	no	—
360	C₂³×C₅	—	4	8	no	—
361	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
362	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
363	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
364	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
365	C₂³×C₅	C₃×#41	1	2	yes	—
366	C₂³×C₅	C₃×#41	1	4	yes	—
367	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
368	C₅×D₄	—	4	4	no	—
369	C₅×D₄	—	4	4	no	—
370	C₅×D₄	—	4	4	no	—
371	C₂×C₄×C₅	—	2	2	no	—
372	C₂×C₄×C₅	—	2	2	no	—
373	C₂×C₄×C₅	—	2	2	no	—
374	C₂×C₄×C₅	—	2	2	no	—
375	C₂×C₄×C₅	—	2	2	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	1	no	—
381	C₂×C₄×C₅	—	2	2	no	—
382	C₂×C₄×C₅	—	2	2	no	—
383	C₂×C₄×C₅	—	2	1	no	—
384	C₂×C₄×C₅	—	2	2	no	—
385	C₂×C₄×C₅	—	2	2	no	—
386	C₂×C₄×C₅	—	2	2	no	—
387	C₂×C₄×C₅	—	2	2	no	—
388	C₂×C₄×C₅	—	2	2	no	—
389	C₂×C₄×C₅	—	4	8	no	—
390	C₂×C₄×C₅	—	4	4	no	—
391	C₂×C₄×C₅	—	4	4	no	—
392	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
393	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
394	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
395	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
396	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
397	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
398	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
399	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
400	#123	—	2	4	no	—
401	#120	—	2	4	no	—
402	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
403	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
404	C₂×C₂²⋊C₄	—	2	4	no	—
405	C₂×C₂²⋊C₄	—	2	4	no	—
406	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
407	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
408	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
409	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
410	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
411	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
412	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
413	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
414	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
415	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
416	#95	C₂²×C₃×C₅	1	2	yes	complemented
417	#95	C₂²×C₃×C₅	1	2	yes	complemented
418	#95	C₂²×C₃×C₅	1	2	yes	complemented
419	#95	C₂²×C₃×C₅	1	2	yes	complemented
420	C₂×C₃×C₅	—	2	4	no	—
421	C₂×C₃×C₅	—	2	4	no	—
422	C₂×C₃×C₅	—	4	2	no	—
423	C₂×C₃×C₅	—	8	1	no	—
424	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
425	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
426	C₂×C₃×C₅	#534	1	1	yes	characteristic
427	C₂×C₃×C₅	#546	1	2	yes	—
428	C₂×C₃×C₅	#551	1	2	yes	—
429	C₂³×C₃	—	2	1	no	—
430	C₂³×C₃	—	2	1	no	—
431	C₂³×C₃	—	2	2	no	—
432	C₂³×C₃	—	2	2	no	—
433	C₂³×C₃	—	2	2	no	—
434	C₂³×C₃	—	2	8	no	—
435	C₂³×C₃	—	2	8	no	—
436	C₂³×C₃	—	2	1	no	—
437	C₂³×C₃	—	2	1	no	—
438	C₂³×C₃	—	2	2	no	—
439	C₂³×C₃	—	2	2	no	—
440	C₂³×C₃	—	2	1	no	—
441	C₂³×C₃	—	2	1	no	—
442	C₂³×C₃	—	2	1	no	—
443	C₂³×C₃	—	2	2	no	—
444	C₂³×C₃	—	2	2	no	—
445	C₂³×C₃	—	4	4	no	—
446	C₂³×C₃	—	4	8	no	—
447	C₂³×C₃	—	4	8	no	—
448	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
449	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
450	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
451	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
452	C₂³×C₃	C₅×#41	1	2	yes	—
453	C₂³×C₃	C₅×#41	1	4	yes	—
454	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
455	C₃×D₄	—	4	4	no	—
456	C₃×D₄	—	4	4	no	—
457	C₃×D₄	—	4	4	no	—
458	C₂×C₃×C₄	—	2	2	no	—
459	C₂×C₃×C₄	—	2	2	no	—
460	C₂×C₃×C₄	—	2	2	no	—
461	C₂×C₃×C₄	—	2	2	no	—
462	C₂×C₃×C₄	—	2	2	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	2	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	1	no	—
471	C₂×C₃×C₄	—	2	2	no	—
472	C₂×C₃×C₄	—	2	2	no	—
473	C₂×C₃×C₄	—	2	2	no	—
474	C₂×C₃×C₄	—	2	2	no	—
475	C₂×C₃×C₄	—	2	2	no	—
476	C₂×C₃×C₄	—	4	8	no	—
477	C₂×C₃×C₄	—	4	4	no	—
478	C₂×C₃×C₄	—	4	4	no	—
479	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
480	C₂²×C₅	—	2	2	no	—
481	C₂²×C₅	—	2	2	no	—
482	C₂²×C₅	—	2	2	no	—
483	C₂²×C₅	—	2	2	no	—
484	C₂²×C₅	—	2	4	no	—
485	C₂²×C₅	—	2	4	no	—
486	C₂²×C₅	—	2	4	no	—
487	C₂²×C₅	—	2	4	no	—
488	C₂²×C₅	—	2	2	no	—
489	C₂²×C₅	—	2	2	no	—
490	C₂²×C₅	—	2	2	no	—
491	C₂²×C₅	—	4	16	no	—
492	C₂²×C₅	—	4	2	no	—
493	C₂²×C₅	—	4	2	no	—
494	C₂²×C₅	—	4	1	no	—
495	C₂²×C₅	—	4	1	no	—
496	C₂²×C₅	—	4	1	no	—
497	C₂²×C₅	—	4	2	no	—
498	C₂²×C₅	—	4	2	no	—
499	C₂²×C₅	C₃×#121	1	4	yes	—
500	C₂²×C₅	C₃×#123	1	4	yes	complemented
501	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
502	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
503	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
504	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
505	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
506	C₄×C₅	—	2	4	no	—
507	C₄×C₅	—	4	2	no	—
508	C₄×C₅	—	4	1	no	—
509	C₄×C₅	—	4	1	no	—
510	C₄×C₅	—	4	2	no	—
511	C₄×C₅	—	4	1	no	—
512	C₄×C₅	—	4	2	no	—
513	C₂⁴	—	2	2	no	—
514	C₂⁴	—	2	2	no	—
515	C₂⁴	—	2	4	no	—
516	C₂⁴	—	4	2	no	—
517	C₂⁴	C₃×C₅×D₄	1	4	yes	—
518	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
519	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
520	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
521	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
522	C₂×D₄	—	2	2	no	—
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	—	2	2	no	—
525	C₂×D₄	—	2	2	no	—
526	C₂×D₄	—	2	2	no	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	—	4	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	4	2	no	—
536	C₂²×C₄	—	4	2	no	—
537	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
538	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
539	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
540	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
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	2	yes	—
544	C₄⋊C₄	—	2	4	no	—
545	C₄⋊C₄	—	4	2	no	—
546	C₂²⋊C₄	—	2	4	no	—
547	C₂²⋊C₄	—	2	2	no	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	2	2	no	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	2	4	no	—
553	C₂²⋊C₄	—	2	4	no	—
554	C₂²⋊C₄	—	4	2	no	—
555	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
556	C₃×C₅	#2412	1	1	yes	characteristic, direct product factor, Hall
557	C₂²×C₃	—	2	2	no	—
558	C₂²×C₃	—	2	2	no	—
559	C₂²×C₃	—	2	2	no	—
560	C₂²×C₃	—	2	2	no	—
561	C₂²×C₃	—	2	4	no	—
562	C₂²×C₃	—	2	4	no	—
563	C₂²×C₃	—	2	4	no	—
564	C₂²×C₃	—	2	4	no	—
565	C₂²×C₃	—	2	2	no	—
566	C₂²×C₃	—	2	2	no	—
567	C₂²×C₃	—	2	2	no	—
568	C₂²×C₃	—	4	16	no	—
569	C₂²×C₃	—	4	2	no	—
570	C₂²×C₃	—	4	2	no	—
571	C₂²×C₃	—	4	1	no	—
572	C₂²×C₃	—	4	1	no	—
573	C₂²×C₃	—	4	1	no	—
574	C₂²×C₃	—	4	2	no	—
575	C₂²×C₃	—	4	2	no	—
576	C₂²×C₃	C₅×#121	1	4	yes	—
577	C₂²×C₃	C₅×#123	1	4	yes	complemented
578	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
579	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
580	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
581	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
582	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
583	C₃×C₄	—	2	4	no	—
584	C₃×C₄	—	4	2	no	—
585	C₃×C₄	—	4	1	no	—
586	C₃×C₄	—	4	1	no	—
587	C₃×C₄	—	4	2	no	—
588	C₃×C₄	—	4	1	no	—
589	C₃×C₄	—	4	2	no	—
590	C₂×C₅	—	2	4	no	—
591	C₂×C₅	—	2	4	no	—
592	C₂×C₅	—	4	2	no	—
593	C₂×C₅	—	8	1	no	—
594	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
595	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
596	C₂×C₅	C₃×#534	1	1	yes	characteristic
597	C₂×C₅	C₃×#546	1	2	yes	—
598	C₂×C₅	C₃×#551	1	2	yes	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	8	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	8	no	—
609	C₂³	—	2	2	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	4	4	no	—
616	C₂³	—	4	8	no	—
617	C₂³	—	4	8	no	—
618	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
619	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
620	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
621	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
622	C₂³	C₃×C₅×#41	1	2	yes	—
623	C₂³	C₃×C₅×#41	1	4	yes	—
624	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
625	D₄	—	4	4	no	—
626	D₄	—	4	4	no	—
627	D₄	—	4	4	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	4	8	no	—
647	C₂×C₄	—	4	4	no	—
648	C₂×C₄	—	4	4	no	—
649	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
650	C₂×C₃	—	2	4	no	—
651	C₂×C₃	—	2	4	no	—
652	C₂×C₃	—	4	2	no	—
653	C₂×C₃	—	8	1	no	—
654	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
655	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
656	C₂×C₃	C₅×#534	1	1	yes	characteristic
657	C₂×C₃	C₅×#546	1	2	yes	—
658	C₂×C₃	C₅×#551	1	2	yes	—
659	C₅	C₃×#2412	1	1	yes	characteristic, direct product factor, Sylow
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	4	no	—
665	C₂²	—	2	4	no	—
666	C₂²	—	2	4	no	—
667	C₂²	—	2	4	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	4	16	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	4	2	no	—
674	C₂²	—	4	1	no	—
675	C₂²	—	4	1	no	—
676	C₂²	—	4	1	no	—
677	C₂²	—	4	2	no	—
678	C₂²	—	4	2	no	—
679	C₂²	C₃×C₅×#121	1	4	yes	—
680	C₂²	C₃×C₅×#123	1	4	yes	complemented
681	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
682	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
683	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
684	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
685	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
686	C₄	—	2	4	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	1	no	—
689	C₄	—	4	1	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	1	no	—
692	C₄	—	4	2	no	—
693	C₃	C₅×#2412	1	1	yes	characteristic, direct product factor, Sylow
694	C₂	—	2	4	no	—
695	C₂	—	2	4	no	—
696	C₂	—	4	2	no	—
697	C₂	—	8	1	no	—
698	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
699	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
700	C₂	C₃×C₅×#534	1	1	yes	characteristic
701	C₂	C₃×C₅×#546	1	2	yes	—
702	C₂	C₃×C₅×#551	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#120	C₂
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×#123	C₂	semidirect
3. C₂²×C₃×C₅×C₂²⋊C₄	C₂	semidirect
4. C₂²×C₃×C₅×C₂²⋊C₄	C₂	semidirect
5. C₃×C₅×#397	C₂	semidirect
6. C₃×C₅×#394	C₂	semidirect
7. C₃×C₅×#386	C₂	semidirect
8. C₃×C₅×#386	C₂	semidirect
9. C₃×C₅×#385	C₂	semidirect
10. C₃×C₅×#381	C₂	semidirect
11. C₃×C₅×#380	C₂	semidirect
12. C₅×#2412	C₃	direct (N × H)
22. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
23. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
34. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
35. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
36. C₃×C₅×#95	C₂²	semidirect
37. C₃×C₅×#95	C₂²	semidirect
38. C₃×C₅×#95	C₂²	semidirect
39. C₃×C₅×#95	C₂²	semidirect
40. C₃×#2412	C₅	direct (N × H)
41. C₂×C₅×#123	C₂×C₃	semidirect
43. C₂²×C₅×C₂²⋊C₄	C₂×C₃	semidirect
44. C₂²×C₅×C₂²⋊C₄	C₂×C₃	semidirect
45. C₅×#397	C₂×C₃	semidirect
46. C₅×#394	C₂×C₃	semidirect
47. C₅×#386	C₂×C₃	semidirect
48. C₅×#386	C₂×C₃	semidirect
49. C₅×#385	C₂×C₃	semidirect
50. C₅×#381	C₂×C₃	semidirect
51. C₅×#380	C₂×C₃	semidirect
94. C₃×C₅×C₂²⋊C₄	D₄	semidirect
95. C₂×C₃×#123	C₂×C₅	semidirect
97. C₂²×C₃×C₂²⋊C₄	C₂×C₅	semidirect
98. C₂²×C₃×C₂²⋊C₄	C₂×C₅	semidirect
99. C₃×#397	C₂×C₅	semidirect
100. C₃×#394	C₂×C₅	semidirect
101. C₃×#386	C₂×C₅	semidirect
102. C₃×#386	C₂×C₅	semidirect
103. C₃×#385	C₂×C₅	semidirect
104. C₃×#381	C₂×C₅	semidirect
105. C₃×#380	C₂×C₅	semidirect
115. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
116. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
127. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
128. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
129. C₅×#95	C₂²×C₃	semidirect
130. C₅×#95	C₂²×C₃	semidirect
131. C₅×#95	C₂²×C₃	semidirect
132. C₅×#95	C₂²×C₃	semidirect
133. #2412	C₃×C₅	direct (N × H)
194. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
195. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
206. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
207. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
208. C₃×#95	C₂²×C₅	semidirect
209. C₃×#95	C₂²×C₅	semidirect
210. C₃×#95	C₂²×C₅	semidirect
211. C₃×#95	C₂²×C₅	semidirect
254. C₅×C₂²⋊C₄	C₃×D₄	semidirect
255. C₂×#123	C₂×C₃×C₅	semidirect
257. C₂²×C₂²⋊C₄	C₂×C₃×C₅	semidirect
258. C₂²×C₂²⋊C₄	C₂×C₃×C₅	semidirect
259. #397	C₂×C₃×C₅	semidirect
260. #394	C₂×C₃×C₅	semidirect
261. #386	C₂×C₃×C₅	semidirect
262. #386	C₂×C₃×C₅	semidirect
263. #385	C₂×C₃×C₅	semidirect
264. #381	C₂×C₃×C₅	semidirect
265. #380	C₂×C₃×C₅	semidirect
286. C₂²×C₃×C₅	#123	semidirect
341. C₃×C₂²⋊C₄	C₅×D₄	semidirect
402. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
403. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
414. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
415. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
416. #95	C₂²×C₃×C₅	semidirect
417. #95	C₂²×C₃×C₅	semidirect
418. #95	C₂²×C₃×C₅	semidirect
419. #95	C₂²×C₃×C₅	semidirect
500. C₂²×C₅	C₃×#123	semidirect
555. C₂²⋊C₄	C₃×C₅×D₄	semidirect
556. C₃×C₅	#2412	direct (N × H)
577. C₂²×C₃	C₅×#123	semidirect
659. C₅	C₃×#2412	direct (N × H)
680. C₂²	C₃×C₅×#123	semidirect
693. C₃	C₅×#2412	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×#123	2
C₂×C₃×C₅×#120	2
C₂²×C₃×C₅×C₂²⋊C₄	2
C₃×C₅×#397	2
C₃×C₅×#394	2
C₃×C₅×#386	2
C₃×C₅×#385	2
C₃×C₅×#381	2
C₃×C₅×#380	2
C₅×#2412	3
C₃×#2412	5

Subgroups — C3×C5×#2412 #14275446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2412 #14275446