Subgroups — C₃×C₅×#2283 #14275317

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#383	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#382	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#381	C₂	1	2	yes	maximal
5	C₃×C₅×#380	C₂	1	2	yes	maximal
6	C₃×C₄×C₅×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal
8	C₃×C₅×#376	C₂	1	2	yes	maximal, complemented
9	C₅×#2283	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
14	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
15	C₂×C₃×C₄²×C₅	C₄	1	8	yes	complemented
16	C₂×C₃×C₄²×C₅	C₂²	1	4	yes	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₃×C₅×#95	C₂²	1	4	yes	—
22	C₃×C₅×#95	C₂²	1	4	yes	—
23	C₃×C₅×#95	C₂²	1	4	yes	—
24	C₃×C₅×#95	C₂²	1	4	yes	—
25	C₃×#2283	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂²×C₄²×C₅	C₂×C₃	1	1	yes	characteristic
27	C₅×#383	C₂×C₃	1	2	yes	complemented
28	C₅×#382	C₂×C₃	1	2	yes	complemented
29	C₅×#381	C₂×C₃	1	2	yes	—
30	C₅×#380	C₂×C₃	1	2	yes	—
31	C₄×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
32	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	—
33	C₅×#376	C₂×C₃	1	2	yes	complemented
34	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	—	2	4	no	—
36	C₂²×C₃×C₄×C₅	—	2	4	no	—
37	C₂²×C₃×C₄×C₅	—	2	4	no	—
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
39	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
40	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₃×C₅×C₄⋊C₄	—	2	8	no	—
49	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
50	C₃×C₄²×C₅	—	2	8	no	—
51	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
52	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
53	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
54	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
55	C₂²×C₃×C₄²	C₂×C₅	1	1	yes	characteristic
56	C₃×#383	C₂×C₅	1	2	yes	complemented
57	C₃×#382	C₂×C₅	1	2	yes	complemented
58	C₃×#381	C₂×C₅	1	2	yes	—
59	C₃×#380	C₂×C₅	1	2	yes	—
60	C₃×C₄×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
61	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	2	yes	—
62	C₃×#376	C₂×C₅	1	2	yes	complemented
63	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
64	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
65	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
67	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
68	C₂×C₄²×C₅	C₃×C₄	1	8	yes	complemented
69	C₂×C₄²×C₅	C₂²×C₃	1	4	yes	—
70	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
74	C₅×#95	C₂²×C₃	1	4	yes	—
75	C₅×#95	C₂²×C₃	1	4	yes	—
76	C₅×#95	C₂²×C₃	1	4	yes	—
77	C₅×#95	C₂²×C₃	1	4	yes	—
78	#2283	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
79	C₂³×C₃×C₅	—	2	2	no	—
80	C₂³×C₃×C₅	—	2	2	no	—
81	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
82	C₂³×C₃×C₅	#41	1	4	yes	—
83	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
84	C₂×C₃×C₄×C₅	—	2	8	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	2	2	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	—	2	8	no	—
90	C₂×C₃×C₄×C₅	—	2	8	no	—
91	C₂×C₃×C₄×C₅	—	2	8	no	—
92	C₂×C₃×C₄×C₅	—	2	8	no	—
93	C₂×C₃×C₄×C₅	—	2	8	no	—
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	#41	1	4	yes	—
101	C₂×C₃×C₄×C₅	#41	1	4	yes	—
102	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
103	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
104	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
105	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
106	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
107	C₂×C₃×C₄²	C₄×C₅	1	8	yes	complemented
108	C₂×C₃×C₄²	C₂²×C₅	1	4	yes	—
109	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
110	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
111	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
112	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
113	C₃×#95	C₂²×C₅	1	4	yes	—
114	C₃×#95	C₂²×C₅	1	4	yes	—
115	C₃×#95	C₂²×C₅	1	4	yes	—
116	C₃×#95	C₂²×C₅	1	4	yes	—
117	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
118	C₂²×C₄×C₅	—	2	4	no	—
119	C₂²×C₄×C₅	—	2	4	no	—
120	C₂²×C₄×C₅	—	2	4	no	—
121	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
122	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
123	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
124	C₂²×C₄×C₅	C₂³×C₃	1	8	yes	—
125	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
131	C₅×C₄⋊C₄	—	2	8	no	—
132	C₅×C₂²⋊C₄	—	2	8	no	—
133	C₄²×C₅	—	2	8	no	—
134	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
135	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
136	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
137	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
138	C₂²×C₄²	C₂×C₃×C₅	1	1	yes	characteristic
139	#383	C₂×C₃×C₅	1	2	yes	complemented
140	#382	C₂×C₃×C₅	1	2	yes	complemented
141	#381	C₂×C₃×C₅	1	2	yes	—
142	#380	C₂×C₃×C₅	1	2	yes	—
143	C₄×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
144	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	—
145	#376	C₂×C₃×C₅	1	2	yes	complemented
146	C₂²×C₃×C₅	—	2	2	no	—
147	C₂²×C₃×C₅	—	2	2	no	—
148	C₂²×C₃×C₅	—	2	8	no	—
149	C₂²×C₃×C₅	#117	1	4	yes	—
150	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
151	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
152	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
153	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
154	C₃×C₄×C₅	—	2	2	no	—
155	C₃×C₄×C₅	—	2	2	no	—
156	C₃×C₄×C₅	—	2	2	no	—
157	C₃×C₄×C₅	—	2	2	no	—
158	C₃×C₄×C₅	—	4	8	no	—
159	C₃×C₄×C₅	#117	1	4	yes	—
160	C₃×C₄×C₅	#117	1	4	yes	—
161	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
162	C₂²×C₃×C₄	—	2	4	no	—
163	C₂²×C₃×C₄	—	2	4	no	—
164	C₂²×C₃×C₄	—	2	4	no	—
165	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
166	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
167	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
168	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	—
169	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
172	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
175	C₃×C₄⋊C₄	—	2	8	no	—
176	C₃×C₂²⋊C₄	—	2	8	no	—
177	C₃×C₄²	—	2	8	no	—
178	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
179	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
180	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
181	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
182	C₂³×C₅	—	2	2	no	—
183	C₂³×C₅	—	2	2	no	—
184	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
185	C₂³×C₅	C₃×#41	1	4	yes	—
186	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
187	C₂×C₄×C₅	—	2	8	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	8	no	—
193	C₂×C₄×C₅	—	2	8	no	—
194	C₂×C₄×C₅	—	2	8	no	—
195	C₂×C₄×C₅	—	2	8	no	—
196	C₂×C₄×C₅	—	2	8	no	—
197	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
198	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
199	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
200	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
201	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
202	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
203	C₂×C₄×C₅	C₃×#41	1	4	yes	—
204	C₂×C₄×C₅	C₃×#41	1	4	yes	—
205	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
206	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
207	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
208	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
209	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
210	C₂×C₄²	C₃×C₄×C₅	1	8	yes	complemented
211	C₂×C₄²	C₂²×C₃×C₅	1	4	yes	—
212	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
213	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
214	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
215	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
216	#95	C₂²×C₃×C₅	1	4	yes	—
217	#95	C₂²×C₃×C₅	1	4	yes	—
218	#95	C₂²×C₃×C₅	1	4	yes	—
219	#95	C₂²×C₃×C₅	1	4	yes	—
220	C₂×C₃×C₅	—	2	4	no	—
221	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
222	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
223	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
224	C₂×C₃×C₅	#529	1	4	yes	—
225	C₂³×C₃	—	2	2	no	—
226	C₂³×C₃	—	2	2	no	—
227	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
228	C₂³×C₃	C₅×#41	1	4	yes	—
229	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
230	C₂×C₃×C₄	—	2	8	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	8	no	—
236	C₂×C₃×C₄	—	2	8	no	—
237	C₂×C₃×C₄	—	2	8	no	—
238	C₂×C₃×C₄	—	2	8	no	—
239	C₂×C₃×C₄	—	2	8	no	—
240	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
241	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
242	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
243	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
244	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
245	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
246	C₂×C₃×C₄	C₅×#41	1	4	yes	—
247	C₂×C₃×C₄	C₅×#41	1	4	yes	—
248	C₂²×C₅	—	2	2	no	—
249	C₂²×C₅	—	2	2	no	—
250	C₂²×C₅	—	2	8	no	—
251	C₂²×C₅	C₃×#117	1	4	yes	—
252	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
253	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
254	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
255	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
256	C₄×C₅	—	2	2	no	—
257	C₄×C₅	—	2	2	no	—
258	C₄×C₅	—	2	2	no	—
259	C₄×C₅	—	2	2	no	—
260	C₄×C₅	—	4	8	no	—
261	C₄×C₅	C₃×#117	1	4	yes	—
262	C₄×C₅	C₃×#117	1	4	yes	—
263	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
268	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
269	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
270	C₂²×C₄	C₂³×C₃×C₅	1	8	yes	—
271	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
272	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
273	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
274	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
275	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
276	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
277	C₄⋊C₄	—	2	8	no	—
278	C₂²⋊C₄	—	2	8	no	—
279	C₄²	—	2	8	no	—
280	C₄²	C₂×C₃×C₄×C₅	1	4	yes	—
281	C₄²	C₂×C₃×C₄×C₅	1	4	yes	—
282	C₄²	C₂×C₃×C₄×C₅	1	4	yes	—
283	C₄²	C₂×C₃×C₄×C₅	1	4	yes	—
284	C₃×C₅	#2283	1	1	yes	characteristic, direct product factor, Hall
285	C₂²×C₃	—	2	2	no	—
286	C₂²×C₃	—	2	2	no	—
287	C₂²×C₃	—	2	8	no	—
288	C₂²×C₃	C₅×#117	1	4	yes	—
289	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
290	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
291	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
292	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
293	C₃×C₄	—	2	2	no	—
294	C₃×C₄	—	2	2	no	—
295	C₃×C₄	—	2	2	no	—
296	C₃×C₄	—	2	2	no	—
297	C₃×C₄	—	4	8	no	—
298	C₃×C₄	C₅×#117	1	4	yes	—
299	C₃×C₄	C₅×#117	1	4	yes	—
300	C₂×C₅	—	2	4	no	—
301	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
302	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
303	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
304	C₂×C₅	C₃×#529	1	4	yes	—
305	C₂³	—	2	2	no	—
306	C₂³	—	2	2	no	—
307	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
308	C₂³	C₃×C₅×#41	1	4	yes	—
309	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
310	C₂×C₄	—	2	8	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
321	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
322	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
323	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
324	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
325	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
326	C₂×C₄	C₃×C₅×#41	1	4	yes	—
327	C₂×C₄	C₃×C₅×#41	1	4	yes	—
328	C₂×C₃	—	2	4	no	—
329	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
330	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
331	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
332	C₂×C₃	C₅×#529	1	4	yes	—
333	C₅	C₃×#2283	1	1	yes	characteristic, direct product factor, Sylow
334	C₂²	—	2	2	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	2	8	no	—
337	C₂²	C₃×C₅×#117	1	4	yes	—
338	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
339	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
340	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
341	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
342	C₄	—	2	2	no	—
343	C₄	—	2	2	no	—
344	C₄	—	2	2	no	—
345	C₄	—	2	2	no	—
346	C₄	—	4	8	no	—
347	C₄	C₃×C₅×#117	1	4	yes	—
348	C₄	C₃×C₅×#117	1	4	yes	—
349	C₃	C₅×#2283	1	1	yes	characteristic, direct product factor, Sylow
350	C₂	—	2	4	no	—
351	C₂	C₂×C₃×C₅×#117	1	1	yes	characteristic
352	C₂	C₂×C₃×C₅×#117	1	1	yes	characteristic
353	C₂	C₂×C₃×C₅×#117	1	1	yes	characteristic
354	C₂	C₃×C₅×#529	1	4	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄×C₅	C₂³
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×C₅	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₃×C₅×#383	C₂	semidirect
3. C₃×C₅×#382	C₂	semidirect
6. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
8. C₃×C₅×#376	C₂	semidirect
9. C₅×#2283	C₃	direct (N × H)
15. C₂×C₃×C₄²×C₅	C₄	semidirect
25. C₃×#2283	C₅	direct (N × H)
27. C₅×#383	C₂×C₃	semidirect
28. C₅×#382	C₂×C₃	semidirect
31. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
33. C₅×#376	C₂×C₃	semidirect
56. C₃×#383	C₂×C₅	semidirect
57. C₃×#382	C₂×C₅	semidirect
60. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
62. C₃×#376	C₂×C₅	semidirect
68. C₂×C₄²×C₅	C₃×C₄	semidirect
78. #2283	C₃×C₅	direct (N × H)
107. C₂×C₃×C₄²	C₄×C₅	semidirect
139. #383	C₂×C₃×C₅	semidirect
140. #382	C₂×C₃×C₅	semidirect
143. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
145. #376	C₂×C₃×C₅	semidirect
210. C₂×C₄²	C₃×C₄×C₅	semidirect
284. C₃×C₅	#2283	direct (N × H)
333. C₅	C₃×#2283	direct (N × H)
349. C₃	C₅×#2283	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄²×C₅	2
C₃×C₅×#383	2
C₃×C₅×#382	2
C₃×C₅×#381	2
C₃×C₅×#380	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₃×C₅×#376	2
C₅×#2283	3
C₃×#2283	5

Subgroups — C3×C5×#2283 #14275317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2283 #14275317