Subgroups — C₃×C₅×#2344 #14275378

Order 1920.

1208 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#117	C₂	1	2	yes	maximal
2	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#389	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#387	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#381	C₂	1	2	yes	maximal
6	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic
7	C₃×C₄×C₅×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₅×#2344	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₃×C₅×#117	—	2	8	no	—
13	C₂×C₃×C₅×C₄⋊C₄	C₄	1	8	yes	complemented
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄²×C₅	C₂²	1	4	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₃×C₅×#95	C₂²	1	4	yes	—
26	C₃×C₅×#95	C₂²	1	2	yes	—
27	C₃×C₅×#95	C₂²	1	4	yes	—
28	C₃×#2344	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×#117	C₂×C₃	1	2	yes	—
30	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
31	C₅×#389	C₂×C₃	1	2	yes	complemented
32	C₅×#387	C₂×C₃	1	4	yes	complemented
33	C₅×#381	C₂×C₃	1	2	yes	—
34	C₅×#380	C₂×C₃	1	1	yes	characteristic
35	C₄×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
36	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
37	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	—	2	4	no	—
39	C₂²×C₃×C₄×C₅	—	2	4	no	—
40	C₂²×C₃×C₄×C₅	—	2	4	no	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	8	yes	—
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₃×C₅×C₄⋊C₄	—	2	8	no	—
51	C₃×C₅×C₄⋊C₄	—	2	4	no	—
52	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	—
53	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
54	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
55	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
56	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
57	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	—
58	C₃×C₄²×C₅	—	2	8	no	—
59	C₃×C₄²×C₅	—	2	4	no	—
60	C₂×C₃×#117	C₂×C₅	1	2	yes	—
61	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
62	C₃×#389	C₂×C₅	1	2	yes	complemented
63	C₃×#387	C₂×C₅	1	4	yes	complemented
64	C₃×#381	C₂×C₅	1	2	yes	—
65	C₃×#380	C₂×C₅	1	1	yes	characteristic
66	C₃×C₄×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
67	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
68	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
69	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
70	C₅×#117	—	2	8	no	—
71	C₂×C₅×C₄⋊C₄	C₃×C₄	1	8	yes	complemented
72	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
73	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
74	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
76	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
81	C₂×C₄²×C₅	C₂²×C₃	1	4	yes	—
82	C₅×#95	C₂²×C₃	1	2	yes	—
83	C₅×#95	C₂²×C₃	1	4	yes	—
84	C₅×#95	C₂²×C₃	1	2	yes	—
85	C₅×#95	C₂²×C₃	1	4	yes	—
86	#2344	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
87	C₂³×C₃×C₅	—	2	2	no	—
88	C₂³×C₃×C₅	—	2	2	no	—
89	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
90	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
91	C₂³×C₃×C₅	#41	1	2	yes	—
92	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	—	2	16	no	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	8	no	—
102	C₂×C₃×C₄×C₅	—	2	4	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	4	no	—
106	C₂×C₃×C₄×C₅	—	2	4	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
109	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
113	C₂×C₃×C₄×C₅	#41	1	4	yes	—
114	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
115	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
116	C₃×#117	—	2	8	no	—
117	C₂×C₃×C₄⋊C₄	C₄×C₅	1	8	yes	complemented
118	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
119	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
120	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
121	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
122	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
123	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
124	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
125	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
126	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
127	C₂×C₃×C₄²	C₂²×C₅	1	4	yes	—
128	C₃×#95	C₂²×C₅	1	2	yes	—
129	C₃×#95	C₂²×C₅	1	4	yes	—
130	C₃×#95	C₂²×C₅	1	2	yes	—
131	C₃×#95	C₂²×C₅	1	4	yes	—
132	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
133	C₂²×C₄×C₅	—	2	4	no	—
134	C₂²×C₄×C₅	—	2	4	no	—
135	C₂²×C₄×C₅	—	2	4	no	—
136	C₂²×C₄×C₅	C₂×C₃×C₄	1	8	yes	—
137	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
138	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
139	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
140	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
141	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
142	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
144	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
145	C₅×C₄⋊C₄	—	2	8	no	—
146	C₅×C₄⋊C₄	—	2	4	no	—
147	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
148	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
149	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
150	C₅×C₂²⋊C₄	—	2	4	no	—
151	C₅×C₂²⋊C₄	—	2	2	no	—
152	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	—
153	C₄²×C₅	—	2	8	no	—
154	C₄²×C₅	—	2	4	no	—
155	C₂×#117	C₂×C₃×C₅	1	2	yes	—
156	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
157	#389	C₂×C₃×C₅	1	2	yes	complemented
158	#387	C₂×C₃×C₅	1	4	yes	complemented
159	#381	C₂×C₃×C₅	1	2	yes	—
160	#380	C₂×C₃×C₅	1	1	yes	characteristic
161	C₄×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
162	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
163	C₂²×C₃×C₅	—	2	2	no	—
164	C₂²×C₃×C₅	—	2	2	no	—
165	C₂²×C₃×C₅	—	2	4	no	—
166	C₂²×C₃×C₅	—	2	4	no	—
167	C₂²×C₃×C₅	C₄×D₄	1	4	yes	—
168	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
169	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
170	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
171	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
172	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
173	C₃×C₄×C₅	—	2	2	no	—
174	C₃×C₄×C₅	—	2	4	no	—
175	C₃×C₄×C₅	—	2	4	no	—
176	C₃×C₄×C₅	—	2	4	no	—
177	C₃×C₄×C₅	—	4	4	no	—
178	C₃×C₄×C₅	—	4	2	no	—
179	C₃×C₄×C₅	#117	1	4	yes	complemented
180	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
181	C₂²×C₃×C₄	—	2	4	no	—
182	C₂²×C₃×C₄	—	2	4	no	—
183	C₂²×C₃×C₄	—	2	4	no	—
184	C₂²×C₃×C₄	C₂×C₄×C₅	1	8	yes	—
185	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
186	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
187	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
188	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
189	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
190	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
191	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
192	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
193	C₃×C₄⋊C₄	—	2	8	no	—
194	C₃×C₄⋊C₄	—	2	4	no	—
195	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	—
196	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
197	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
198	C₃×C₂²⋊C₄	—	2	4	no	—
199	C₃×C₂²⋊C₄	—	2	2	no	—
200	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	—
201	C₃×C₄²	—	2	8	no	—
202	C₃×C₄²	—	2	4	no	—
203	C₂³×C₅	—	2	2	no	—
204	C₂³×C₅	—	2	2	no	—
205	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
206	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
207	C₂³×C₅	C₃×#41	1	2	yes	—
208	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
209	C₂×C₄×C₅	—	2	16	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	8	no	—
218	C₂×C₄×C₅	—	2	4	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	4	no	—
222	C₂×C₄×C₅	—	2	4	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
225	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
226	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
227	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
228	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
229	C₂×C₄×C₅	C₃×#41	1	4	yes	—
230	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
231	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
232	#117	—	2	8	no	—
233	C₂×C₄⋊C₄	C₃×C₄×C₅	1	8	yes	complemented
234	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
235	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
236	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
238	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
239	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
240	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
241	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
242	C₂×C₄²	C₂²×C₃×C₅	1	4	yes	—
243	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
244	#95	C₂²×C₃×C₅	1	2	yes	—
245	#95	C₂²×C₃×C₅	1	4	yes	—
246	#95	C₂²×C₃×C₅	1	2	yes	—
247	#95	C₂²×C₃×C₅	1	4	yes	—
248	C₂×C₃×C₅	—	2	4	no	—
249	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
250	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
251	C₂×C₃×C₅	#519	1	1	yes	characteristic
252	C₂×C₃×C₅	#547	1	2	yes	—
253	C₂×C₃×C₅	#552	1	2	yes	—
254	C₂³×C₃	—	2	2	no	—
255	C₂³×C₃	—	2	2	no	—
256	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
257	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
258	C₂³×C₃	C₅×#41	1	2	yes	—
259	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
260	C₂×C₃×C₄	—	2	16	no	—
261	C₂×C₃×C₄	—	2	2	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	8	no	—
269	C₂×C₃×C₄	—	2	4	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	4	no	—
273	C₂×C₃×C₄	—	2	4	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
276	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
277	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
278	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
279	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
280	C₂×C₃×C₄	C₅×#41	1	4	yes	—
281	C₂²×C₅	—	2	2	no	—
282	C₂²×C₅	—	2	2	no	—
283	C₂²×C₅	—	2	4	no	—
284	C₂²×C₅	—	2	4	no	—
285	C₂²×C₅	C₃×C₄×D₄	1	4	yes	—
286	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
287	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
288	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
289	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
290	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
291	C₄×C₅	—	2	2	no	—
292	C₄×C₅	—	2	4	no	—
293	C₄×C₅	—	2	4	no	—
294	C₄×C₅	—	2	4	no	—
295	C₄×C₅	—	4	4	no	—
296	C₄×C₅	—	4	2	no	—
297	C₄×C₅	C₃×#117	1	4	yes	complemented
298	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	C₂×C₃×C₄×C₅	1	8	yes	—
303	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
304	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
305	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
306	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
307	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
308	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
309	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
310	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
311	C₄⋊C₄	—	2	8	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
314	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
315	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
316	C₂²⋊C₄	—	2	4	no	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	—
319	C₄²	—	2	8	no	—
320	C₄²	—	2	4	no	—
321	C₃×C₅	#2344	1	1	yes	characteristic, direct product factor, Hall
322	C₂²×C₃	—	2	2	no	—
323	C₂²×C₃	—	2	2	no	—
324	C₂²×C₃	—	2	4	no	—
325	C₂²×C₃	—	2	4	no	—
326	C₂²×C₃	C₄×C₅×D₄	1	4	yes	—
327	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
328	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
329	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
330	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
331	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
332	C₃×C₄	—	2	2	no	—
333	C₃×C₄	—	2	4	no	—
334	C₃×C₄	—	2	4	no	—
335	C₃×C₄	—	2	4	no	—
336	C₃×C₄	—	4	4	no	—
337	C₃×C₄	—	4	2	no	—
338	C₃×C₄	C₅×#117	1	4	yes	complemented
339	C₂×C₅	—	2	4	no	—
340	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
341	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
342	C₂×C₅	C₃×#519	1	1	yes	characteristic
343	C₂×C₅	C₃×#547	1	2	yes	—
344	C₂×C₅	C₃×#552	1	2	yes	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
348	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
349	C₂³	C₃×C₅×#41	1	2	yes	—
350	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
351	C₂×C₄	—	2	16	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
367	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
368	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
369	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
370	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
371	C₂×C₄	C₃×C₅×#41	1	4	yes	—
372	C₂×C₃	—	2	4	no	—
373	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
374	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
375	C₂×C₃	C₅×#519	1	1	yes	characteristic
376	C₂×C₃	C₅×#547	1	2	yes	—
377	C₂×C₃	C₅×#552	1	2	yes	—
378	C₅	C₃×#2344	1	1	yes	characteristic, direct product factor, Sylow
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	4	no	—
383	C₂²	C₃×C₄×C₅×D₄	1	4	yes	—
384	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
385	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
386	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
387	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
388	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
389	C₄	—	2	2	no	—
390	C₄	—	2	4	no	—
391	C₄	—	2	4	no	—
392	C₄	—	2	4	no	—
393	C₄	—	4	4	no	—
394	C₄	—	4	2	no	—
395	C₄	C₃×C₅×#117	1	4	yes	complemented
396	C₃	C₅×#2344	1	1	yes	characteristic, direct product factor, Sylow
397	C₂	—	2	4	no	—
398	C₂	C₂×C₃×C₅×#117	1	1	yes	characteristic
399	C₂	C₂×C₃×C₄×C₅×D₄	1	1	yes	characteristic
400	C₂	C₃×C₅×#519	1	1	yes	characteristic
401	C₂	C₃×C₅×#547	1	2	yes	—
402	C₂	C₃×C₅×#552	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#389	C₂	semidirect
4. C₃×C₅×#387	C₂	semidirect
7. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
9. C₅×#2344	C₃	direct (N × H)
13. C₂×C₃×C₅×C₄⋊C₄	C₄	semidirect
28. C₃×#2344	C₅	direct (N × H)
31. C₅×#389	C₂×C₃	semidirect
32. C₅×#387	C₂×C₃	semidirect
35. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
62. C₃×#389	C₂×C₅	semidirect
63. C₃×#387	C₂×C₅	semidirect
66. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
71. C₂×C₅×C₄⋊C₄	C₃×C₄	semidirect
86. #2344	C₃×C₅	direct (N × H)
117. C₂×C₃×C₄⋊C₄	C₄×C₅	semidirect
157. #389	C₂×C₃×C₅	semidirect
158. #387	C₂×C₃×C₅	semidirect
161. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
179. C₃×C₄×C₅	#117	semidirect
233. C₂×C₄⋊C₄	C₃×C₄×C₅	semidirect
297. C₄×C₅	C₃×#117	semidirect
321. C₃×C₅	#2344	direct (N × H)
338. C₃×C₄	C₅×#117	semidirect
378. C₅	C₃×#2344	direct (N × H)
395. C₄	C₃×C₅×#117	semidirect
396. C₃	C₅×#2344	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×#117	2
C₂²×C₃×C₅×C₄⋊C₄	2
C₃×C₅×#389	2
C₃×C₅×#387	2
C₃×C₅×#381	2
C₃×C₅×#380	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2344	3
C₃×#2344	5

Subgroups — C3×C5×#2344 #14275378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2344 #14275378