Subgroups — C₃×C₅×#2296 #14275330

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 324 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	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#389	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#385	C₂	1	4	yes	maximal
6	C₃×C₄×C₅×C₄⋊C₄	C₂	1	4	yes	maximal, complemented
7	C₅×#2296	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₃×C₅×#117	—	2	4	no	—
11	C₃×C₅×#117	C₄	1	8	yes	complemented
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	8	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₄²×C₅	—	2	4	no	—
18	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
19	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
21	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
22	C₃×C₅×#95	C₂²	1	8	yes	—
23	C₃×#2296	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic
25	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic
26	C₂²×C₄²×C₅	C₂×C₃	1	1	yes	characteristic
27	C₅×#389	C₂×C₃	1	4	yes	complemented
28	C₅×#385	C₂×C₃	1	4	yes	—
29	C₄×C₅×C₄⋊C₄	C₂×C₃	1	4	yes	complemented
30	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	—	2	4	no	—
32	C₂²×C₃×C₄×C₅	—	2	8	no	—
33	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
34	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
35	C₂²×C₃×C₄×C₅	Q₈	1	4	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₃×C₅×C₄⋊C₄	—	2	4	no	—
42	C₃×C₅×C₄⋊C₄	—	2	16	no	—
43	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
44	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
45	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
46	C₃×C₄²×C₅	—	2	4	no	—
47	C₃×C₄²×C₅	—	2	4	no	—
48	C₃×C₄²×C₅	—	2	4	no	—
49	C₃×C₄²×C₅	C₂×C₄	1	8	yes	complemented
50	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic
51	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic
52	C₂²×C₃×C₄²	C₂×C₅	1	1	yes	characteristic
53	C₃×#389	C₂×C₅	1	4	yes	complemented
54	C₃×#385	C₂×C₅	1	4	yes	—
55	C₃×C₄×C₄⋊C₄	C₂×C₅	1	4	yes	complemented
56	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
57	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
58	C₅×#117	—	2	4	no	—
59	C₅×#117	C₃×C₄	1	8	yes	complemented
60	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	8	yes	—
61	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
62	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
63	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
64	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
65	C₂×C₄²×C₅	—	2	4	no	—
66	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
67	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
68	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
69	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
70	C₅×#95	C₂²×C₃	1	8	yes	—
71	#2296	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
72	C₂³×C₃×C₅	—	2	4	no	—
73	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
74	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
75	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
76	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
77	C₂×C₃×C₄×C₅	—	2	16	no	—
78	C₂×C₃×C₄×C₅	—	2	4	no	—
79	C₂×C₃×C₄×C₅	—	2	8	no	—
80	C₂×C₃×C₄×C₅	—	2	4	no	—
81	C₂×C₃×C₄×C₅	—	2	4	no	—
82	C₂×C₃×C₄×C₅	—	2	8	no	—
83	C₂×C₃×C₄×C₅	C₄⋊C₄	1	16	yes	complemented
84	C₂×C₃×C₄×C₅	C₂²×C₄	1	8	yes	—
85	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
86	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
87	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
88	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
91	C₂×C₃×C₄×C₅	#41	1	8	yes	—
92	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
93	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
94	C₃×#117	—	2	4	no	—
95	C₃×#117	C₄×C₅	1	8	yes	complemented
96	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	8	yes	—
97	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
98	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
99	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
100	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
101	C₂×C₃×C₄²	—	2	4	no	—
102	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
103	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
104	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
105	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
106	C₃×#95	C₂²×C₅	1	8	yes	—
107	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
108	C₂²×C₄×C₅	—	2	4	no	—
109	C₂²×C₄×C₅	—	2	8	no	—
110	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
111	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
112	C₂²×C₄×C₅	C₃×Q₈	1	4	yes	—
113	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
114	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
115	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
116	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
118	C₅×C₄⋊C₄	—	2	4	no	—
119	C₅×C₄⋊C₄	—	2	16	no	—
120	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	complemented
121	C₅×C₂²⋊C₄	—	2	4	no	—
122	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
123	C₄²×C₅	—	2	4	no	—
124	C₄²×C₅	—	2	4	no	—
125	C₄²×C₅	—	2	4	no	—
126	C₄²×C₅	C₂×C₃×C₄	1	8	yes	complemented
127	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic
128	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic
129	C₂²×C₄²	C₂×C₃×C₅	1	1	yes	characteristic
130	#389	C₂×C₃×C₅	1	4	yes	complemented
131	#385	C₂×C₃×C₅	1	4	yes	—
132	C₄×C₄⋊C₄	C₂×C₃×C₅	1	4	yes	complemented
133	C₂²×C₃×C₅	—	2	4	no	—
134	C₂²×C₃×C₅	—	2	4	no	—
135	C₂²×C₃×C₅	—	2	4	no	—
136	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	4	yes	—
137	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
138	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
139	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
140	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
141	C₃×C₄×C₅	—	2	8	no	—
142	C₃×C₄×C₅	—	2	8	no	—
143	C₃×C₄×C₅	—	4	4	no	—
144	C₃×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
145	C₃×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
146	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
147	C₂²×C₃×C₄	—	2	4	no	—
148	C₂²×C₃×C₄	—	2	8	no	—
149	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
150	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
151	C₂²×C₃×C₄	C₅×Q₈	1	4	yes	—
152	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
153	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
154	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
155	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
157	C₃×C₄⋊C₄	—	2	4	no	—
158	C₃×C₄⋊C₄	—	2	16	no	—
159	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
160	C₃×C₂²⋊C₄	—	2	4	no	—
161	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	—
162	C₃×C₄²	—	2	4	no	—
163	C₃×C₄²	—	2	4	no	—
164	C₃×C₄²	—	2	4	no	—
165	C₃×C₄²	C₂×C₄×C₅	1	8	yes	complemented
166	C₂³×C₅	—	2	4	no	—
167	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
168	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
169	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
170	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
171	C₂×C₄×C₅	—	2	16	no	—
172	C₂×C₄×C₅	—	2	4	no	—
173	C₂×C₄×C₅	—	2	8	no	—
174	C₂×C₄×C₅	—	2	4	no	—
175	C₂×C₄×C₅	—	2	4	no	—
176	C₂×C₄×C₅	—	2	8	no	—
177	C₂×C₄×C₅	C₃×C₄⋊C₄	1	16	yes	complemented
178	C₂×C₄×C₅	C₂²×C₃×C₄	1	8	yes	—
179	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
180	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
181	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
182	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
183	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
184	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
185	C₂×C₄×C₅	C₃×#41	1	8	yes	—
186	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
187	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
188	#117	—	2	4	no	—
189	#117	C₃×C₄×C₅	1	8	yes	complemented
190	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
191	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	8	yes	—
192	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
193	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
194	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
195	C₂×C₄²	—	2	4	no	—
196	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
197	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
198	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
199	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
200	#95	C₂²×C₃×C₅	1	8	yes	—
201	C₂×C₃×C₅	—	2	4	no	—
202	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
203	C₂×C₃×C₅	C₄×#41	1	2	yes	—
204	C₂×C₃×C₅	#525	1	2	yes	—
205	C₂×C₃×C₅	#533	1	2	yes	—
206	C₂³×C₃	—	2	4	no	—
207	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
208	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
209	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
210	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
211	C₂×C₃×C₄	—	2	16	no	—
212	C₂×C₃×C₄	—	2	4	no	—
213	C₂×C₃×C₄	—	2	8	no	—
214	C₂×C₃×C₄	—	2	4	no	—
215	C₂×C₃×C₄	—	2	4	no	—
216	C₂×C₃×C₄	—	2	8	no	—
217	C₂×C₃×C₄	C₅×C₄⋊C₄	1	16	yes	complemented
218	C₂×C₃×C₄	C₂²×C₄×C₅	1	8	yes	—
219	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
220	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
221	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
222	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
223	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
224	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
225	C₂×C₃×C₄	C₅×#41	1	8	yes	—
226	C₂²×C₅	—	2	4	no	—
227	C₂²×C₅	—	2	4	no	—
228	C₂²×C₅	—	2	4	no	—
229	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
230	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
231	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
232	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
233	C₂²×C₅	C₂×C₃×#41	1	4	yes	—
234	C₄×C₅	—	2	8	no	—
235	C₄×C₅	—	2	8	no	—
236	C₄×C₅	—	4	4	no	—
237	C₄×C₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
238	C₄×C₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
239	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
240	C₂²×C₄	—	2	4	no	—
241	C₂²×C₄	—	2	8	no	—
242	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
243	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
244	C₂²×C₄	C₃×C₅×Q₈	1	4	yes	—
245	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
246	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
247	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
248	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
249	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
250	C₄⋊C₄	—	2	4	no	—
251	C₄⋊C₄	—	2	16	no	—
252	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	complemented
253	C₂²⋊C₄	—	2	4	no	—
254	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
255	C₄²	—	2	4	no	—
256	C₄²	—	2	4	no	—
257	C₄²	—	2	4	no	—
258	C₄²	C₂×C₃×C₄×C₅	1	8	yes	complemented
259	C₃×C₅	#2296	1	1	yes	characteristic, direct product factor, Hall
260	C₂²×C₃	—	2	4	no	—
261	C₂²×C₃	—	2	4	no	—
262	C₂²×C₃	—	2	4	no	—
263	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
264	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
265	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
266	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
267	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
268	C₃×C₄	—	2	8	no	—
269	C₃×C₄	—	2	8	no	—
270	C₃×C₄	—	4	4	no	—
271	C₃×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
272	C₃×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
273	C₂×C₅	—	2	4	no	—
274	C₂×C₅	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
275	C₂×C₅	C₃×C₄×#41	1	2	yes	—
276	C₂×C₅	C₃×#525	1	2	yes	—
277	C₂×C₅	C₃×#533	1	2	yes	—
278	C₂³	—	2	4	no	—
279	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
280	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
281	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
282	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
283	C₂×C₄	—	2	16	no	—
284	C₂×C₄	—	2	4	no	—
285	C₂×C₄	—	2	8	no	—
286	C₂×C₄	—	2	4	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	8	no	—
289	C₂×C₄	C₃×C₅×C₄⋊C₄	1	16	yes	complemented
290	C₂×C₄	C₂²×C₃×C₄×C₅	1	8	yes	—
291	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
292	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
293	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
294	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
295	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
296	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
297	C₂×C₄	C₃×C₅×#41	1	8	yes	—
298	C₂×C₃	—	2	4	no	—
299	C₂×C₃	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
300	C₂×C₃	C₄×C₅×#41	1	2	yes	—
301	C₂×C₃	C₅×#525	1	2	yes	—
302	C₂×C₃	C₅×#533	1	2	yes	—
303	C₅	C₃×#2296	1	1	yes	characteristic, direct product factor, Sylow
304	C₂²	—	2	4	no	—
305	C₂²	—	2	4	no	—
306	C₂²	—	2	4	no	—
307	C₂²	C₂×C₃×C₅×C₄⋊C₄	1	4	yes	—
308	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
309	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
310	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
311	C₂²	C₂×C₃×C₅×#41	1	4	yes	—
312	C₄	—	2	8	no	—
313	C₄	—	2	8	no	—
314	C₄	—	4	4	no	—
315	C₄	C₂×C₃×C₅×C₄⋊C₄	1	4	yes	—
316	C₄	C₂×C₃×C₅×C₄⋊C₄	1	4	yes	—
317	C₃	C₅×#2296	1	1	yes	characteristic, direct product factor, Sylow
318	C₂	—	2	4	no	—
319	C₂	C₂²×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
320	C₂	C₃×C₄×C₅×#41	1	2	yes	—
321	C₂	C₃×C₅×#525	1	2	yes	—
322	C₂	C₃×C₅×#533	1	2	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
4. C₃×C₅×#389	C₂	semidirect
6. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
7. C₅×#2296	C₃	direct (N × H)
11. C₃×C₅×#117	C₄	semidirect
23. C₃×#2296	C₅	direct (N × H)
27. C₅×#389	C₂×C₃	semidirect
29. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
43. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
49. C₃×C₄²×C₅	C₂×C₄	semidirect
53. C₃×#389	C₂×C₅	semidirect
55. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
59. C₅×#117	C₃×C₄	semidirect
71. #2296	C₃×C₅	direct (N × H)
83. C₂×C₃×C₄×C₅	C₄⋊C₄	semidirect
95. C₃×#117	C₄×C₅	semidirect
120. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
126. C₄²×C₅	C₂×C₃×C₄	semidirect
130. #389	C₂×C₃×C₅	semidirect
132. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
159. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
165. C₃×C₄²	C₂×C₄×C₅	semidirect
177. C₂×C₄×C₅	C₃×C₄⋊C₄	semidirect
189. #117	C₃×C₄×C₅	semidirect
217. C₂×C₃×C₄	C₅×C₄⋊C₄	semidirect
252. C₄⋊C₄	C₂×C₃×C₄×C₅	semidirect
258. C₄²	C₂×C₃×C₄×C₅	semidirect
259. C₃×C₅	#2296	direct (N × H)
289. C₂×C₄	C₃×C₅×C₄⋊C₄	semidirect
303. C₅	C₃×#2296	direct (N × H)
317. C₃	C₅×#2296	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×C₄²×C₅	2
C₃×C₅×#389	2
C₃×C₅×#385	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2296	3
C₃×#2296	5

Subgroups — C3×C5×#2296 #14275330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2296 #14275330