Subgroups — C₃×C₅×#2534 #14275568

Order 1920.

1600 conjugacy classes of subgroups.

The subgroup lattice has 680 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	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#396	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#394	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#386	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#381	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#379	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2534	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	2	yes	—
15	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
18	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₅×#123	—	2	4	no	—
20	C₃×C₅×#120	—	2	4	no	—
21	C₃×C₄×C₅×D₄	—	2	4	no	—
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
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	2	yes	—
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×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic, complemented
35	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
36	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, 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×#2534	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	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#396	C₂×C₃	1	2	yes	complemented
46	C₅×#394	C₂×C₃	1	2	yes	complemented
47	C₅×#388	C₂×C₃	1	2	yes	complemented
48	C₅×#386	C₂×C₃	1	2	yes	complemented
49	C₅×#381	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#380	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#379	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂⁴×C₃×C₅	—	2	2	no	—
53	C₂⁴×C₃×C₅	—	2	4	no	—
54	C₂⁴×C₃×C₅	—	2	2	no	—
55	C₂⁴×C₃×C₅	—	2	2	no	—
56	C₂⁴×C₃×C₅	—	4	2	no	—
57	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
58	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
59	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₅×D₄	—	2	2	no	—
61	C₂×C₃×C₅×D₄	—	2	2	no	—
62	C₂×C₃×C₅×D₄	—	2	4	no	—
63	C₂×C₃×C₅×D₄	—	2	4	no	—
64	C₂×C₃×C₅×D₄	—	4	2	no	—
65	C₂×C₃×C₅×D₄	D₄	1	4	yes	—
66	C₂²×C₃×C₄×C₅	—	2	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	—	4	2	no	—
71	C₂²×C₃×C₄×C₅	—	4	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	2	yes	—
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	C₃×C₅×C₄⋊C₄	—	2	2	no	—
82	C₃×C₅×C₄⋊C₄	—	2	4	no	—
83	C₃×C₅×C₄⋊C₄	—	4	2	no	—
84	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
85	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
86	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
87	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
88	C₃×C₅×C₂²⋊C₄	—	2	4	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	—	2	2	no	—
93	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
94	C₃×C₄²×C₅	—	2	2	no	—
95	C₂×C₃×#123	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂×C₃×#120	C₂×C₅	1	1	yes	characteristic
97	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
98	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#396	C₂×C₅	1	2	yes	complemented
100	C₃×#394	C₂×C₅	1	2	yes	complemented
101	C₃×#388	C₂×C₅	1	2	yes	complemented
102	C₃×#386	C₂×C₅	1	2	yes	complemented
103	C₃×#381	C₂×C₅	1	1	yes	characteristic, complemented
104	C₃×#380	C₂×C₅	1	1	yes	characteristic, complemented
105	C₃×#379	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
107	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
108	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
109	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
110	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
111	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
112	C₅×#123	—	2	4	no	—
113	C₅×#120	—	2	4	no	—
114	C₄×C₅×D₄	—	2	4	no	—
115	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
116	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
117	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
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	1	yes	characteristic
121	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
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	2	yes	—
126	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
127	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
128	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
129	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, 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	#2534	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
134	C₂³×C₃×C₅	—	2	2	no	—
135	C₂³×C₃×C₅	—	2	2	no	—
136	C₂³×C₃×C₅	—	2	8	no	—
137	C₂³×C₃×C₅	—	2	2	no	—
138	C₂³×C₃×C₅	—	2	1	no	—
139	C₂³×C₃×C₅	—	2	2	no	—
140	C₂³×C₃×C₅	—	2	1	no	—
141	C₂³×C₃×C₅	—	2	2	no	—
142	C₂³×C₃×C₅	—	2	2	no	—
143	C₂³×C₃×C₅	—	2	2	no	—
144	C₂³×C₃×C₅	—	2	2	no	—
145	C₂³×C₃×C₅	—	2	2	no	—
146	C₂³×C₃×C₅	—	2	2	no	—
147	C₂³×C₃×C₅	—	4	8	no	—
148	C₂³×C₃×C₅	—	4	8	no	—
149	C₂³×C₃×C₅	—	4	4	no	—
150	C₂³×C₃×C₅	—	4	4	no	—
151	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
152	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
153	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
154	C₂³×C₃×C₅	#41	1	4	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	C₂×C₃×C₄×C₅	—	2	1	no	—
160	C₂×C₃×C₄×C₅	—	2	1	no	—
161	C₂×C₃×C₄×C₅	—	2	2	no	—
162	C₂×C₃×C₄×C₅	—	2	2	no	—
163	C₂×C₃×C₄×C₅	—	2	1	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	2	no	—
170	C₂×C₃×C₄×C₅	—	2	2	no	—
171	C₂×C₃×C₄×C₅	—	2	2	no	—
172	C₂×C₃×C₄×C₅	—	2	2	no	—
173	C₂×C₃×C₄×C₅	—	2	2	no	—
174	C₂×C₃×C₄×C₅	—	2	2	no	—
175	C₂×C₃×C₄×C₅	—	2	2	no	—
176	C₂×C₃×C₄×C₅	—	4	4	no	—
177	C₂×C₃×C₄×C₅	—	4	4	no	—
178	C₂×C₃×C₄×C₅	—	4	4	no	—
179	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
180	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
181	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
182	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
183	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
184	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
185	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
186	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
187	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
188	C₃×#123	—	2	4	no	—
189	C₃×#120	—	2	4	no	—
190	C₃×C₄×D₄	—	2	4	no	—
191	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
192	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
193	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
194	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
195	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
196	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
197	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
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	2	yes	—
201	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
202	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
203	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
204	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
205	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
206	C₃×#95	C₂²×C₅	1	2	yes	complemented
207	C₃×#95	C₂²×C₅	1	2	yes	complemented
208	C₃×#95	C₂²×C₅	1	2	yes	complemented
209	C₂⁴×C₅	—	2	2	no	—
210	C₂⁴×C₅	—	2	4	no	—
211	C₂⁴×C₅	—	2	2	no	—
212	C₂⁴×C₅	—	2	2	no	—
213	C₂⁴×C₅	—	4	2	no	—
214	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
215	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
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	—	4	2	no	—
222	C₂×C₅×D₄	C₃×D₄	1	4	yes	—
223	C₂²×C₄×C₅	—	2	2	no	—
224	C₂²×C₄×C₅	—	2	2	no	—
225	C₂²×C₄×C₅	—	2	2	no	—
226	C₂²×C₄×C₅	—	2	2	no	—
227	C₂²×C₄×C₅	—	4	2	no	—
228	C₂²×C₄×C₅	—	4	2	no	—
229	C₂²×C₄×C₅	C₃×D₄	1	4	yes	complemented
230	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
231	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
232	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
233	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
234	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
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	C₅×C₄⋊C₄	—	2	2	no	—
239	C₅×C₄⋊C₄	—	2	4	no	—
240	C₅×C₄⋊C₄	—	4	2	no	—
241	C₅×C₂²⋊C₄	—	2	2	no	—
242	C₅×C₂²⋊C₄	—	2	2	no	—
243	C₅×C₂²⋊C₄	—	2	2	no	—
244	C₅×C₂²⋊C₄	—	2	4	no	—
245	C₅×C₂²⋊C₄	—	2	4	no	—
246	C₅×C₂²⋊C₄	—	2	4	no	—
247	C₅×C₂²⋊C₄	—	2	4	no	—
248	C₅×C₂²⋊C₄	—	2	4	no	—
249	C₅×C₂²⋊C₄	—	2	2	no	—
250	C₅×C₂²⋊C₄	—	4	2	no	—
251	C₄²×C₅	—	2	2	no	—
252	C₂×#123	C₂×C₃×C₅	1	1	yes	characteristic, complemented
253	C₂×#120	C₂×C₃×C₅	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
255	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
256	#396	C₂×C₃×C₅	1	2	yes	complemented
257	#394	C₂×C₃×C₅	1	2	yes	complemented
258	#388	C₂×C₃×C₅	1	2	yes	complemented
259	#386	C₂×C₃×C₅	1	2	yes	complemented
260	#381	C₂×C₃×C₅	1	1	yes	characteristic, complemented
261	#380	C₂×C₃×C₅	1	1	yes	characteristic, complemented
262	#379	C₂×C₃×C₅	1	1	yes	characteristic, complemented
263	C₂²×C₃×C₅	—	2	2	no	—
264	C₂²×C₃×C₅	—	2	2	no	—
265	C₂²×C₃×C₅	—	2	4	no	—
266	C₂²×C₃×C₅	—	2	4	no	—
267	C₂²×C₃×C₅	—	2	2	no	—
268	C₂²×C₃×C₅	—	2	4	no	—
269	C₂²×C₃×C₅	—	2	4	no	—
270	C₂²×C₃×C₅	—	2	4	no	—
271	C₂²×C₃×C₅	—	2	4	no	—
272	C₂²×C₃×C₅	—	4	16	no	—
273	C₂²×C₃×C₅	—	4	2	no	—
274	C₂²×C₃×C₅	—	4	1	no	—
275	C₂²×C₃×C₅	—	4	1	no	—
276	C₂²×C₃×C₅	—	4	2	no	—
277	C₂²×C₃×C₅	—	4	2	no	—
278	C₂²×C₃×C₅	—	4	2	no	—
279	C₂²×C₃×C₅	—	4	2	no	—
280	C₂²×C₃×C₅	#121	1	4	yes	—
281	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
282	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
283	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
284	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
285	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
286	C₃×C₄×C₅	—	2	2	no	—
287	C₃×C₄×C₅	—	2	2	no	—
288	C₃×C₄×C₅	—	2	2	no	—
289	C₃×C₄×C₅	—	4	2	no	—
290	C₃×C₄×C₅	—	4	1	no	—
291	C₃×C₄×C₅	—	4	1	no	—
292	C₃×C₄×C₅	—	4	2	no	—
293	C₃×C₄×C₅	—	4	2	no	—
294	C₂⁴×C₃	—	2	2	no	—
295	C₂⁴×C₃	—	2	4	no	—
296	C₂⁴×C₃	—	2	2	no	—
297	C₂⁴×C₃	—	2	2	no	—
298	C₂⁴×C₃	—	4	2	no	—
299	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
300	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
301	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
302	C₂×C₃×D₄	—	2	2	no	—
303	C₂×C₃×D₄	—	2	2	no	—
304	C₂×C₃×D₄	—	2	4	no	—
305	C₂×C₃×D₄	—	2	4	no	—
306	C₂×C₃×D₄	—	4	2	no	—
307	C₂×C₃×D₄	C₅×D₄	1	4	yes	—
308	C₂²×C₃×C₄	—	2	2	no	—
309	C₂²×C₃×C₄	—	2	2	no	—
310	C₂²×C₃×C₄	—	2	2	no	—
311	C₂²×C₃×C₄	—	2	2	no	—
312	C₂²×C₃×C₄	—	4	2	no	—
313	C₂²×C₃×C₄	—	4	2	no	—
314	C₂²×C₃×C₄	C₅×D₄	1	4	yes	complemented
315	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
316	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
317	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
318	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
319	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
320	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
321	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
322	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
323	C₃×C₄⋊C₄	—	2	2	no	—
324	C₃×C₄⋊C₄	—	2	4	no	—
325	C₃×C₄⋊C₄	—	4	2	no	—
326	C₃×C₂²⋊C₄	—	2	2	no	—
327	C₃×C₂²⋊C₄	—	2	2	no	—
328	C₃×C₂²⋊C₄	—	2	2	no	—
329	C₃×C₂²⋊C₄	—	2	4	no	—
330	C₃×C₂²⋊C₄	—	2	4	no	—
331	C₃×C₂²⋊C₄	—	2	4	no	—
332	C₃×C₂²⋊C₄	—	2	4	no	—
333	C₃×C₂²⋊C₄	—	2	4	no	—
334	C₃×C₂²⋊C₄	—	2	2	no	—
335	C₃×C₂²⋊C₄	—	4	2	no	—
336	C₃×C₄²	—	2	2	no	—
337	C₂³×C₅	—	2	2	no	—
338	C₂³×C₅	—	2	2	no	—
339	C₂³×C₅	—	2	8	no	—
340	C₂³×C₅	—	2	2	no	—
341	C₂³×C₅	—	2	1	no	—
342	C₂³×C₅	—	2	2	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	2	no	—
348	C₂³×C₅	—	2	2	no	—
349	C₂³×C₅	—	2	2	no	—
350	C₂³×C₅	—	4	8	no	—
351	C₂³×C₅	—	4	8	no	—
352	C₂³×C₅	—	4	4	no	—
353	C₂³×C₅	—	4	4	no	—
354	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
355	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
356	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
357	C₂³×C₅	C₃×#41	1	4	yes	—
358	C₂³×C₅	C₃×#41	1	2	yes	—
359	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
360	C₅×D₄	—	2	8	no	—
361	C₅×D₄	—	4	8	no	—
362	C₂×C₄×C₅	—	2	1	no	—
363	C₂×C₄×C₅	—	2	1	no	—
364	C₂×C₄×C₅	—	2	2	no	—
365	C₂×C₄×C₅	—	2	2	no	—
366	C₂×C₄×C₅	—	2	1	no	—
367	C₂×C₄×C₅	—	2	2	no	—
368	C₂×C₄×C₅	—	2	2	no	—
369	C₂×C₄×C₅	—	2	2	no	—
370	C₂×C₄×C₅	—	2	2	no	—
371	C₂×C₄×C₅	—	2	1	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	2	no	—
377	C₂×C₄×C₅	—	2	2	no	—
378	C₂×C₄×C₅	—	2	2	no	—
379	C₂×C₄×C₅	—	4	4	no	—
380	C₂×C₄×C₅	—	4	4	no	—
381	C₂×C₄×C₅	—	4	4	no	—
382	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
383	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
384	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
385	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
386	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
387	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
388	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
389	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
390	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
391	#123	—	2	4	no	—
392	#120	—	2	4	no	—
393	C₄×D₄	—	2	4	no	—
394	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
395	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
396	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
397	C₂×C₂²⋊C₄	—	2	4	no	—
398	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
399	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
400	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
403	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
404	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
405	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
406	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
407	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
408	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
409	#95	C₂²×C₃×C₅	1	2	yes	complemented
410	#95	C₂²×C₃×C₅	1	2	yes	complemented
411	#95	C₂²×C₃×C₅	1	2	yes	complemented
412	C₂×C₃×C₅	—	2	4	no	—
413	C₂×C₃×C₅	—	4	2	no	—
414	C₂×C₃×C₅	—	4	4	no	—
415	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
416	C₂×C₃×C₅	#525	1	1	yes	characteristic
417	C₂×C₃×C₅	#534	1	1	yes	characteristic
418	C₂×C₃×C₅	#546	1	2	yes	—
419	C₂×C₃×C₅	#551	1	2	yes	—
420	C₂³×C₃	—	2	2	no	—
421	C₂³×C₃	—	2	2	no	—
422	C₂³×C₃	—	2	8	no	—
423	C₂³×C₃	—	2	2	no	—
424	C₂³×C₃	—	2	1	no	—
425	C₂³×C₃	—	2	2	no	—
426	C₂³×C₃	—	2	1	no	—
427	C₂³×C₃	—	2	2	no	—
428	C₂³×C₃	—	2	2	no	—
429	C₂³×C₃	—	2	2	no	—
430	C₂³×C₃	—	2	2	no	—
431	C₂³×C₃	—	2	2	no	—
432	C₂³×C₃	—	2	2	no	—
433	C₂³×C₃	—	4	8	no	—
434	C₂³×C₃	—	4	8	no	—
435	C₂³×C₃	—	4	4	no	—
436	C₂³×C₃	—	4	4	no	—
437	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
438	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
439	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
440	C₂³×C₃	C₅×#41	1	4	yes	—
441	C₂³×C₃	C₅×#41	1	2	yes	—
442	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
443	C₃×D₄	—	2	8	no	—
444	C₃×D₄	—	4	8	no	—
445	C₂×C₃×C₄	—	2	1	no	—
446	C₂×C₃×C₄	—	2	1	no	—
447	C₂×C₃×C₄	—	2	2	no	—
448	C₂×C₃×C₄	—	2	2	no	—
449	C₂×C₃×C₄	—	2	1	no	—
450	C₂×C₃×C₄	—	2	2	no	—
451	C₂×C₃×C₄	—	2	2	no	—
452	C₂×C₃×C₄	—	2	2	no	—
453	C₂×C₃×C₄	—	2	2	no	—
454	C₂×C₃×C₄	—	2	1	no	—
455	C₂×C₃×C₄	—	2	2	no	—
456	C₂×C₃×C₄	—	2	2	no	—
457	C₂×C₃×C₄	—	2	2	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	—	4	4	no	—
463	C₂×C₃×C₄	—	4	4	no	—
464	C₂×C₃×C₄	—	4	4	no	—
465	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
466	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
467	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
468	C₂²×C₅	—	2	2	no	—
469	C₂²×C₅	—	2	2	no	—
470	C₂²×C₅	—	2	4	no	—
471	C₂²×C₅	—	2	4	no	—
472	C₂²×C₅	—	2	2	no	—
473	C₂²×C₅	—	2	4	no	—
474	C₂²×C₅	—	2	4	no	—
475	C₂²×C₅	—	2	4	no	—
476	C₂²×C₅	—	2	4	no	—
477	C₂²×C₅	—	4	16	no	—
478	C₂²×C₅	—	4	2	no	—
479	C₂²×C₅	—	4	1	no	—
480	C₂²×C₅	—	4	1	no	—
481	C₂²×C₅	—	4	2	no	—
482	C₂²×C₅	—	4	2	no	—
483	C₂²×C₅	—	4	2	no	—
484	C₂²×C₅	—	4	2	no	—
485	C₂²×C₅	C₃×#121	1	4	yes	—
486	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
487	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
488	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
489	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
490	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
491	C₄×C₅	—	2	2	no	—
492	C₄×C₅	—	2	2	no	—
493	C₄×C₅	—	2	2	no	—
494	C₄×C₅	—	4	2	no	—
495	C₄×C₅	—	4	1	no	—
496	C₄×C₅	—	4	1	no	—
497	C₄×C₅	—	4	2	no	—
498	C₄×C₅	—	4	2	no	—
499	C₂⁴	—	2	2	no	—
500	C₂⁴	—	2	4	no	—
501	C₂⁴	—	2	2	no	—
502	C₂⁴	—	2	2	no	—
503	C₂⁴	—	4	2	no	—
504	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
505	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
506	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
507	C₂×D₄	—	2	2	no	—
508	C₂×D₄	—	2	2	no	—
509	C₂×D₄	—	2	4	no	—
510	C₂×D₄	—	2	4	no	—
511	C₂×D₄	—	4	2	no	—
512	C₂×D₄	C₃×C₅×D₄	1	4	yes	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	—	4	2	no	—
519	C₂²×C₄	C₃×C₅×D₄	1	4	yes	complemented
520	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
521	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
522	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
523	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
524	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
525	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
526	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
527	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	4	no	—
530	C₄⋊C₄	—	4	2	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	4	no	—
536	C₂²⋊C₄	—	2	4	no	—
537	C₂²⋊C₄	—	2	4	no	—
538	C₂²⋊C₄	—	2	4	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	4	2	no	—
541	C₄²	—	2	2	no	—
542	C₃×C₅	#2534	1	1	yes	characteristic, direct product factor, Hall
543	C₂²×C₃	—	2	2	no	—
544	C₂²×C₃	—	2	2	no	—
545	C₂²×C₃	—	2	4	no	—
546	C₂²×C₃	—	2	4	no	—
547	C₂²×C₃	—	2	2	no	—
548	C₂²×C₃	—	2	4	no	—
549	C₂²×C₃	—	2	4	no	—
550	C₂²×C₃	—	2	4	no	—
551	C₂²×C₃	—	2	4	no	—
552	C₂²×C₃	—	4	16	no	—
553	C₂²×C₃	—	4	2	no	—
554	C₂²×C₃	—	4	1	no	—
555	C₂²×C₃	—	4	1	no	—
556	C₂²×C₃	—	4	2	no	—
557	C₂²×C₃	—	4	2	no	—
558	C₂²×C₃	—	4	2	no	—
559	C₂²×C₃	—	4	2	no	—
560	C₂²×C₃	C₅×#121	1	4	yes	—
561	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
562	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
563	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
564	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
565	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
566	C₃×C₄	—	2	2	no	—
567	C₃×C₄	—	2	2	no	—
568	C₃×C₄	—	2	2	no	—
569	C₃×C₄	—	4	2	no	—
570	C₃×C₄	—	4	1	no	—
571	C₃×C₄	—	4	1	no	—
572	C₃×C₄	—	4	2	no	—
573	C₃×C₄	—	4	2	no	—
574	C₂×C₅	—	2	4	no	—
575	C₂×C₅	—	4	4	no	—
576	C₂×C₅	—	4	2	no	—
577	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
578	C₂×C₅	C₃×#525	1	1	yes	characteristic
579	C₂×C₅	C₃×#534	1	1	yes	characteristic
580	C₂×C₅	C₃×#546	1	2	yes	—
581	C₂×C₅	C₃×#551	1	2	yes	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	8	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	1	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	4	8	no	—
596	C₂³	—	4	8	no	—
597	C₂³	—	4	4	no	—
598	C₂³	—	4	4	no	—
599	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
600	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
601	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
602	C₂³	C₃×C₅×#41	1	4	yes	—
603	C₂³	C₃×C₅×#41	1	2	yes	—
604	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
605	D₄	—	2	8	no	—
606	D₄	—	4	8	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	4	4	no	—
625	C₂×C₄	—	4	4	no	—
626	C₂×C₄	—	4	4	no	—
627	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
628	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
629	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
630	C₂×C₃	—	2	4	no	—
631	C₂×C₃	—	4	4	no	—
632	C₂×C₃	—	4	2	no	—
633	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
634	C₂×C₃	C₅×#525	1	1	yes	characteristic
635	C₂×C₃	C₅×#534	1	1	yes	characteristic
636	C₂×C₃	C₅×#546	1	2	yes	—
637	C₂×C₃	C₅×#551	1	2	yes	—
638	C₅	C₃×#2534	1	1	yes	characteristic, direct product factor, Sylow
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	4	no	—
642	C₂²	—	2	4	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	4	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	2	4	no	—
647	C₂²	—	2	4	no	—
648	C₂²	—	4	16	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	2	no	—
656	C₂²	C₃×C₅×#121	1	4	yes	—
657	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
658	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
659	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
660	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
661	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
662	C₄	—	2	2	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	4	2	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	2	no	—
670	C₃	C₅×#2534	1	1	yes	characteristic, direct product factor, Sylow
671	C₂	—	2	4	no	—
672	C₂	—	4	4	no	—
673	C₂	—	4	2	no	—
674	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
675	C₂	C₃×C₅×#525	1	1	yes	characteristic
676	C₂	C₃×C₅×#534	1	1	yes	characteristic
677	C₂	C₃×C₅×#546	1	2	yes	—
678	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. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
4. C₂²×C₃×C₅×C₂²⋊C₄	C₂	semidirect
5. C₃×C₅×#396	C₂	semidirect
6. C₃×C₅×#394	C₂	semidirect
7. C₃×C₅×#388	C₂	semidirect
8. C₃×C₅×#386	C₂	semidirect
9. C₃×C₅×#381	C₂	semidirect
10. C₃×C₅×#380	C₂	semidirect
11. C₃×C₅×#379	C₂	semidirect
12. C₅×#2534	C₃	direct (N × H)
18. C₂³×C₃×C₄×C₅	C₂²	semidirect
22. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
23. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
24. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
34. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
35. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
36. C₂×C₃×C₄²×C₅	C₂²	semidirect
37. C₃×C₅×#95	C₂²	semidirect
38. C₃×C₅×#95	C₂²	semidirect
39. C₃×C₅×#95	C₂²	semidirect
40. C₃×#2534	C₅	direct (N × H)
41. C₂×C₅×#123	C₂×C₃	semidirect
43. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
44. C₂²×C₅×C₂²⋊C₄	C₂×C₃	semidirect
45. C₅×#396	C₂×C₃	semidirect
46. C₅×#394	C₂×C₃	semidirect
47. C₅×#388	C₂×C₃	semidirect
48. C₅×#386	C₂×C₃	semidirect
49. C₅×#381	C₂×C₃	semidirect
50. C₅×#380	C₂×C₃	semidirect
51. C₅×#379	C₂×C₃	semidirect
72. C₂²×C₃×C₄×C₅	D₄	semidirect
95. C₂×C₃×#123	C₂×C₅	semidirect
97. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
98. C₂²×C₃×C₂²⋊C₄	C₂×C₅	semidirect
99. C₃×#396	C₂×C₅	semidirect
100. C₃×#394	C₂×C₅	semidirect
101. C₃×#388	C₂×C₅	semidirect
102. C₃×#386	C₂×C₅	semidirect
103. C₃×#381	C₂×C₅	semidirect
104. C₃×#380	C₂×C₅	semidirect
105. C₃×#379	C₂×C₅	semidirect
111. C₂³×C₄×C₅	C₂²×C₃	semidirect
115. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
116. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
117. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
127. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
128. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
129. C₂×C₄²×C₅	C₂²×C₃	semidirect
130. C₅×#95	C₂²×C₃	semidirect
131. C₅×#95	C₂²×C₃	semidirect
132. C₅×#95	C₂²×C₃	semidirect
133. #2534	C₃×C₅	direct (N × H)
187. C₂³×C₃×C₄	C₂²×C₅	semidirect
191. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
192. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
193. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
203. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
204. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
205. C₂×C₃×C₄²	C₂²×C₅	semidirect
206. C₃×#95	C₂²×C₅	semidirect
207. C₃×#95	C₂²×C₅	semidirect
208. C₃×#95	C₂²×C₅	semidirect
229. C₂²×C₄×C₅	C₃×D₄	semidirect
252. C₂×#123	C₂×C₃×C₅	semidirect
254. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
255. C₂²×C₂²⋊C₄	C₂×C₃×C₅	semidirect
256. #396	C₂×C₃×C₅	semidirect
257. #394	C₂×C₃×C₅	semidirect
258. #388	C₂×C₃×C₅	semidirect
259. #386	C₂×C₃×C₅	semidirect
260. #381	C₂×C₃×C₅	semidirect
261. #380	C₂×C₃×C₅	semidirect
262. #379	C₂×C₃×C₅	semidirect
314. C₂²×C₃×C₄	C₅×D₄	semidirect
390. C₂³×C₄	C₂²×C₃×C₅	semidirect
394. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
395. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
396. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
406. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
407. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
408. C₂×C₄²	C₂²×C₃×C₅	semidirect
409. #95	C₂²×C₃×C₅	semidirect
410. #95	C₂²×C₃×C₅	semidirect
411. #95	C₂²×C₃×C₅	semidirect
519. C₂²×C₄	C₃×C₅×D₄	semidirect
542. C₃×C₅	#2534	direct (N × H)
638. C₅	C₃×#2534	direct (N × H)
670. C₃	C₅×#2534	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
C₂×C₃×C₄×C₅×D₄	2
C₂²×C₃×C₅×C₂²⋊C₄	2
C₃×C₅×#396	2
C₃×C₅×#394	2
C₃×C₅×#388	2
C₃×C₅×#386	2
C₃×C₅×#381	2
C₃×C₅×#380	2
C₃×C₅×#379	2
C₅×#2534	3
C₃×#2534	5

Subgroups — C3×C5×#2534 #14275568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2534 #14275568