Subgroups — C₃×C₅×#2502 #14275536

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#398	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#391	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#385	C₂	1	4	yes	maximal
6	C₃×C₅×#384	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
8	C₅×#2502	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
12	C₃×C₅×C₂²⋊Q₈	—	2	4	no	—
13	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	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	8	yes	—
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
22	C₃×C₅×#95	C₂²	1	2	yes	—
23	C₃×C₅×#95	C₂²	1	8	yes	—
24	C₃×#2502	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
26	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
27	C₅×#398	C₂×C₃	1	4	yes	complemented
28	C₅×#391	C₂×C₃	1	2	yes	complemented
29	C₅×#385	C₂×C₃	1	4	yes	—
30	C₅×#384	C₂×C₃	1	2	yes	complemented
31	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
32	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
33	C₂×C₃×C₅×Q₈	—	2	2	no	—
34	C₂×C₃×C₅×Q₈	—	2	4	no	—
35	C₂²×C₃×C₄×C₅	—	2	4	no	—
36	C₂²×C₃×C₄×C₅	—	2	4	no	—
37	C₂²×C₃×C₄×C₅	—	4	4	no	—
38	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₃×C₅×C₄⋊C₄	—	2	4	no	—
46	C₃×C₅×C₄⋊C₄	—	2	4	no	—
47	C₃×C₅×C₄⋊C₄	—	2	2	no	—
48	C₃×C₅×C₄⋊C₄	—	2	4	no	—
49	C₃×C₅×C₄⋊C₄	—	4	8	no	—
50	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
51	C₃×C₅×C₂²⋊C₄	Q₈	1	8	yes	complemented
52	C₃×C₄²×C₅	—	2	4	no	—
53	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
54	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
55	C₃×#398	C₂×C₅	1	4	yes	complemented
56	C₃×#391	C₂×C₅	1	2	yes	complemented
57	C₃×#385	C₂×C₅	1	4	yes	—
58	C₃×#384	C₂×C₅	1	2	yes	complemented
59	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
60	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
61	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
62	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
63	C₅×C₂²⋊Q₈	—	2	4	no	—
64	C₂×C₅×C₄⋊C₄	—	2	4	no	—
65	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
68	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
69	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	8	yes	—
70	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
71	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
72	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
73	C₅×#95	C₂²×C₃	1	2	yes	—
74	C₅×#95	C₂²×C₃	1	8	yes	—
75	#2502	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
76	C₂³×C₃×C₅	—	2	2	no	—
77	C₂³×C₃×C₅	—	2	2	no	—
78	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
79	C₂³×C₃×C₅	C₂×Q₈	1	4	yes	—
80	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
81	C₃×C₅×Q₈	—	4	4	no	—
82	C₂×C₃×C₄×C₅	—	2	4	no	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	2	4	no	—
85	C₂×C₃×C₄×C₅	—	2	8	no	—
86	C₂×C₃×C₄×C₅	—	2	2	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	—	2	4	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	—	2	8	no	—
92	C₂×C₃×C₄×C₅	—	4	8	no	—
93	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂×Q₈	1	8	yes	—
96	C₂×C₃×C₄×C₅	#41	1	4	yes	—
97	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
98	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
99	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
100	C₃×C₂²⋊Q₈	—	2	4	no	—
101	C₂×C₃×C₄⋊C₄	—	2	4	no	—
102	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
103	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
104	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
105	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
106	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	8	yes	—
107	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
108	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
109	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
110	C₃×#95	C₂²×C₅	1	2	yes	—
111	C₃×#95	C₂²×C₅	1	8	yes	—
112	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
113	C₂×C₅×Q₈	—	2	2	no	—
114	C₂×C₅×Q₈	—	2	4	no	—
115	C₂²×C₄×C₅	—	2	4	no	—
116	C₂²×C₄×C₅	—	2	4	no	—
117	C₂²×C₄×C₅	—	4	4	no	—
118	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
119	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
120	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
121	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
122	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
124	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
125	C₅×C₄⋊C₄	—	2	4	no	—
126	C₅×C₄⋊C₄	—	2	4	no	—
127	C₅×C₄⋊C₄	—	2	2	no	—
128	C₅×C₄⋊C₄	—	2	4	no	—
129	C₅×C₄⋊C₄	—	4	8	no	—
130	C₅×C₂²⋊C₄	—	2	4	no	—
131	C₅×C₂²⋊C₄	C₃×Q₈	1	8	yes	complemented
132	C₄²×C₅	—	2	4	no	—
133	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
134	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
135	#398	C₂×C₃×C₅	1	4	yes	complemented
136	#391	C₂×C₃×C₅	1	2	yes	complemented
137	#385	C₂×C₃×C₅	1	4	yes	—
138	#384	C₂×C₃×C₅	1	2	yes	complemented
139	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
140	C₂²×C₃×C₅	—	2	2	no	—
141	C₂²×C₃×C₅	—	2	2	no	—
142	C₂²×C₃×C₅	—	2	8	no	—
143	C₂²×C₃×C₅	C₄⋊Q₈	1	4	yes	—
144	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
145	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
146	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
147	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
148	C₃×C₄×C₅	—	2	2	no	—
149	C₃×C₄×C₅	—	2	8	no	—
150	C₃×C₄×C₅	—	4	2	no	—
151	C₃×C₄×C₅	—	4	2	no	—
152	C₃×C₄×C₅	—	4	4	no	—
153	C₃×C₄×C₅	#123	1	4	yes	—
154	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
155	C₂×C₃×Q₈	—	2	2	no	—
156	C₂×C₃×Q₈	—	2	4	no	—
157	C₂²×C₃×C₄	—	2	4	no	—
158	C₂²×C₃×C₄	—	2	4	no	—
159	C₂²×C₃×C₄	—	4	4	no	—
160	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
161	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
162	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
163	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
164	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
165	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
166	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
167	C₃×C₄⋊C₄	—	2	4	no	—
168	C₃×C₄⋊C₄	—	2	4	no	—
169	C₃×C₄⋊C₄	—	2	2	no	—
170	C₃×C₄⋊C₄	—	2	4	no	—
171	C₃×C₄⋊C₄	—	4	8	no	—
172	C₃×C₂²⋊C₄	—	2	4	no	—
173	C₃×C₂²⋊C₄	C₅×Q₈	1	8	yes	complemented
174	C₃×C₄²	—	2	4	no	—
175	C₂³×C₅	—	2	2	no	—
176	C₂³×C₅	—	2	2	no	—
177	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
178	C₂³×C₅	C₂×C₃×Q₈	1	4	yes	—
179	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
180	C₅×Q₈	—	4	4	no	—
181	C₂×C₄×C₅	—	2	4	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	4	no	—
184	C₂×C₄×C₅	—	2	8	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	4	no	—
188	C₂×C₄×C₅	—	2	4	no	—
189	C₂×C₄×C₅	—	2	4	no	—
190	C₂×C₄×C₅	—	2	8	no	—
191	C₂×C₄×C₅	—	4	8	no	—
192	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
193	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
194	C₂×C₄×C₅	C₂×C₃×Q₈	1	8	yes	—
195	C₂×C₄×C₅	C₃×#41	1	4	yes	—
196	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
197	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
198	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
199	C₂²⋊Q₈	—	2	4	no	—
200	C₂×C₄⋊C₄	—	2	4	no	—
201	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
202	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
203	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
204	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
205	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	8	yes	—
206	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
207	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
208	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
209	#95	C₂²×C₃×C₅	1	2	yes	—
210	#95	C₂²×C₃×C₅	1	8	yes	—
211	C₂×C₃×C₅	—	2	4	no	—
212	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
213	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
214	C₂×C₃×C₅	#535	1	1	yes	characteristic
215	C₂×C₃×C₅	#554	1	4	yes	—
216	C₂³×C₃	—	2	2	no	—
217	C₂³×C₃	—	2	2	no	—
218	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
219	C₂³×C₃	C₂×C₅×Q₈	1	4	yes	—
220	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
221	C₃×Q₈	—	4	4	no	—
222	C₂×C₃×C₄	—	2	4	no	—
223	C₂×C₃×C₄	—	2	2	no	—
224	C₂×C₃×C₄	—	2	4	no	—
225	C₂×C₃×C₄	—	2	8	no	—
226	C₂×C₃×C₄	—	2	2	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	2	4	no	—
229	C₂×C₃×C₄	—	2	4	no	—
230	C₂×C₃×C₄	—	2	4	no	—
231	C₂×C₃×C₄	—	2	8	no	—
232	C₂×C₃×C₄	—	4	8	no	—
233	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
234	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
235	C₂×C₃×C₄	C₂×C₅×Q₈	1	8	yes	—
236	C₂×C₃×C₄	C₅×#41	1	4	yes	—
237	C₂²×C₅	—	2	2	no	—
238	C₂²×C₅	—	2	2	no	—
239	C₂²×C₅	—	2	8	no	—
240	C₂²×C₅	C₃×C₄⋊Q₈	1	4	yes	—
241	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
242	C₂²×C₅	C₂²×C₃×Q₈	1	2	yes	—
243	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
244	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
245	C₄×C₅	—	2	2	no	—
246	C₄×C₅	—	2	8	no	—
247	C₄×C₅	—	4	2	no	—
248	C₄×C₅	—	4	2	no	—
249	C₄×C₅	—	4	4	no	—
250	C₄×C₅	C₃×#123	1	4	yes	—
251	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
252	C₂×Q₈	—	2	2	no	—
253	C₂×Q₈	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	4	4	no	—
257	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
258	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
259	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
260	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
261	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
262	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
263	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
264	C₄⋊C₄	—	2	4	no	—
265	C₄⋊C₄	—	2	4	no	—
266	C₄⋊C₄	—	2	2	no	—
267	C₄⋊C₄	—	2	4	no	—
268	C₄⋊C₄	—	4	8	no	—
269	C₂²⋊C₄	—	2	4	no	—
270	C₂²⋊C₄	C₃×C₅×Q₈	1	8	yes	complemented
271	C₄²	—	2	4	no	—
272	C₃×C₅	#2502	1	1	yes	characteristic, direct product factor, Hall
273	C₂²×C₃	—	2	2	no	—
274	C₂²×C₃	—	2	2	no	—
275	C₂²×C₃	—	2	8	no	—
276	C₂²×C₃	C₅×C₄⋊Q₈	1	4	yes	—
277	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
278	C₂²×C₃	C₂²×C₅×Q₈	1	2	yes	—
279	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
280	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
281	C₃×C₄	—	2	2	no	—
282	C₃×C₄	—	2	8	no	—
283	C₃×C₄	—	4	2	no	—
284	C₃×C₄	—	4	2	no	—
285	C₃×C₄	—	4	4	no	—
286	C₃×C₄	C₅×#123	1	4	yes	—
287	C₂×C₅	—	2	4	no	—
288	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
289	C₂×C₅	C₂×C₃×C₄⋊Q₈	1	1	yes	characteristic
290	C₂×C₅	C₃×#535	1	1	yes	characteristic
291	C₂×C₅	C₃×#554	1	4	yes	—
292	C₂³	—	2	2	no	—
293	C₂³	—	2	2	no	—
294	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
295	C₂³	C₂×C₃×C₅×Q₈	1	4	yes	—
296	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
297	Q₈	—	4	4	no	—
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	4	8	no	—
309	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
310	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
311	C₂×C₄	C₂×C₃×C₅×Q₈	1	8	yes	—
312	C₂×C₄	C₃×C₅×#41	1	4	yes	—
313	C₂×C₃	—	2	4	no	—
314	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
315	C₂×C₃	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
316	C₂×C₃	C₅×#535	1	1	yes	characteristic
317	C₂×C₃	C₅×#554	1	4	yes	—
318	C₅	C₃×#2502	1	1	yes	characteristic, direct product factor, Sylow
319	C₂²	—	2	2	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	8	no	—
322	C₂²	C₃×C₅×C₄⋊Q₈	1	4	yes	—
323	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
324	C₂²	C₂²×C₃×C₅×Q₈	1	2	yes	—
325	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
326	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
327	C₄	—	2	2	no	—
328	C₄	—	2	8	no	—
329	C₄	—	4	2	no	—
330	C₄	—	4	4	no	—
331	C₄	—	4	2	no	—
332	C₄	C₃×C₅×#123	1	4	yes	—
333	C₃	C₅×#2502	1	1	yes	characteristic, direct product factor, Sylow
334	C₂	—	2	4	no	—
335	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
336	C₂	C₂×C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
337	C₂	C₃×C₅×#535	1	1	yes	characteristic
338	C₂	C₃×C₅×#554	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
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
3. C₃×C₅×#398	C₂	semidirect
4. C₃×C₅×#391	C₂	semidirect
6. C₃×C₅×#384	C₂	semidirect
8. C₅×#2502	C₃	direct (N × H)
24. C₃×#2502	C₅	direct (N × H)
27. C₅×#398	C₂×C₃	semidirect
28. C₅×#391	C₂×C₃	semidirect
30. C₅×#384	C₂×C₃	semidirect
51. C₃×C₅×C₂²⋊C₄	Q₈	semidirect
55. C₃×#398	C₂×C₅	semidirect
56. C₃×#391	C₂×C₅	semidirect
58. C₃×#384	C₂×C₅	semidirect
75. #2502	C₃×C₅	direct (N × H)
131. C₅×C₂²⋊C₄	C₃×Q₈	semidirect
135. #398	C₂×C₃×C₅	semidirect
136. #391	C₂×C₃×C₅	semidirect
138. #384	C₂×C₃×C₅	semidirect
173. C₃×C₂²⋊C₄	C₅×Q₈	semidirect
270. C₂²⋊C₄	C₃×C₅×Q₈	semidirect
272. C₃×C₅	#2502	direct (N × H)
318. C₅	C₃×#2502	direct (N × H)
333. C₃	C₅×#2502	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×C₂²⋊Q₈	2
C₂²×C₃×C₅×C₄⋊C₄	2
C₃×C₅×#398	2
C₃×C₅×#391	2
C₃×C₅×#385	2
C₃×C₅×#384	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2502	3
C₃×#2502	5

Subgroups — C3×C5×#2502 #14275536

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2502 #14275536