Subgroups — C₃×C₅×#2683 #14275717

Order 1920.

1184 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	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
2	C₃×C₅×#396	C₂	1	4	yes	maximal, complemented
3	C₃×C₅×#395	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#389	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#386	C₂	1	2	yes	maximal
7	C₅×#2683	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
11	C₃×C₅×C₂²⋊Q₈	—	2	16	no	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₃×C₅×#95	C₂²	1	4	yes	—
22	C₃×C₅×#95	C₂²	1	2	yes	—
23	C₃×#2683	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	4	yes	complemented
25	C₅×#396	C₂×C₃	1	4	yes	complemented
26	C₅×#395	C₂×C₃	1	2	yes	complemented
27	C₅×#390	C₂×C₃	1	1	yes	characteristic
28	C₅×#389	C₂×C₃	1	2	yes	complemented
29	C₅×#386	C₂×C₃	1	2	yes	—
30	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
31	C₂×C₃×C₅×Q₈	—	2	8	no	—
32	C₂×C₃×C₅×Q₈	—	4	2	no	—
33	C₂×C₃×C₅×D₄	—	4	1	no	—
34	C₂×C₃×C₅×D₄	—	4	1	no	—
35	C₂×C₃×C₅×D₄	Q₈	1	4	yes	complemented
36	C₂²×C₃×C₄×C₅	—	2	8	no	—
37	C₂²×C₃×C₄×C₅	—	4	2	no	—
38	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	4	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	C₃×C₅×C₄⋊C₄	—	2	8	no	—
44	C₃×C₅×C₄⋊C₄	—	2	8	no	—
45	C₃×C₅×C₄⋊C₄	—	4	2	no	—
46	C₃×C₅×C₄⋊C₄	—	4	1	no	—
47	C₃×C₅×C₄⋊C₄	D₄	1	8	yes	complemented
48	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
49	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
50	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
51	C₃×C₄²×C₅	—	4	1	no	—
52	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	4	yes	complemented
53	C₃×#396	C₂×C₅	1	4	yes	complemented
54	C₃×#395	C₂×C₅	1	2	yes	complemented
55	C₃×#390	C₂×C₅	1	1	yes	characteristic
56	C₃×#389	C₂×C₅	1	2	yes	complemented
57	C₃×#386	C₂×C₅	1	2	yes	—
58	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
59	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
60	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
61	C₅×C₂²⋊Q₈	—	2	16	no	—
62	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
63	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
64	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
65	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
67	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
68	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
69	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
70	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
71	C₅×#95	C₂²×C₃	1	4	yes	—
72	C₅×#95	C₂²×C₃	1	2	yes	—
73	#2683	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
74	C₂³×C₃×C₅	—	2	4	no	—
75	C₂³×C₃×C₅	—	2	2	no	—
76	C₂³×C₃×C₅	—	2	2	no	—
77	C₂³×C₃×C₅	—	2	4	no	—
78	C₂³×C₃×C₅	C₂×Q₈	1	4	yes	—
79	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
80	C₃×C₅×Q₈	—	4	8	no	—
81	C₃×C₅×D₄	—	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	1	no	—
85	C₂×C₃×C₄×C₅	—	2	1	no	—
86	C₂×C₃×C₄×C₅	—	2	4	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	2	no	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	4	8	no	—
94	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	8	yes	—
96	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
97	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
98	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
99	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
100	C₃×C₂²⋊Q₈	—	2	16	no	—
101	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
102	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
103	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
104	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
105	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
106	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
107	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
108	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
109	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
110	C₃×#95	C₂²×C₅	1	4	yes	—
111	C₃×#95	C₂²×C₅	1	2	yes	—
112	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
113	C₂×C₅×Q₈	—	2	8	no	—
114	C₂×C₅×Q₈	—	4	2	no	—
115	C₂×C₅×D₄	—	4	1	no	—
116	C₂×C₅×D₄	—	4	1	no	—
117	C₂×C₅×D₄	C₃×Q₈	1	4	yes	complemented
118	C₂²×C₄×C₅	—	2	8	no	—
119	C₂²×C₄×C₅	—	4	2	no	—
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	2	yes	—
123	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
124	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
125	C₅×C₄⋊C₄	—	2	8	no	—
126	C₅×C₄⋊C₄	—	2	8	no	—
127	C₅×C₄⋊C₄	—	4	2	no	—
128	C₅×C₄⋊C₄	—	4	1	no	—
129	C₅×C₄⋊C₄	C₃×D₄	1	8	yes	complemented
130	C₅×C₂²⋊C₄	—	2	8	no	—
131	C₅×C₂²⋊C₄	—	2	8	no	—
132	C₅×C₂²⋊C₄	—	4	2	no	—
133	C₄²×C₅	—	4	1	no	—
134	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	4	yes	complemented
135	#396	C₂×C₃×C₅	1	4	yes	complemented
136	#395	C₂×C₃×C₅	1	2	yes	complemented
137	#390	C₂×C₃×C₅	1	1	yes	characteristic
138	#389	C₂×C₃×C₅	1	2	yes	complemented
139	#386	C₂×C₃×C₅	1	2	yes	—
140	C₂²×C₃×C₅	—	2	4	no	—
141	C₂²×C₃×C₅	—	2	8	no	—
142	C₂²×C₃×C₅	—	4	4	no	—
143	C₂²×C₃×C₅	—	4	2	no	—
144	C₂²×C₃×C₅	—	4	2	no	—
145	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
146	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
147	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
148	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
149	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
150	C₃×C₄×C₅	—	2	4	no	—
151	C₃×C₄×C₅	—	2	2	no	—
152	C₃×C₄×C₅	—	2	8	no	—
153	C₃×C₄×C₅	—	4	4	no	—
154	C₃×C₄×C₅	—	4	2	no	—
155	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
156	C₂×C₃×Q₈	—	2	8	no	—
157	C₂×C₃×Q₈	—	4	2	no	—
158	C₂×C₃×D₄	—	4	1	no	—
159	C₂×C₃×D₄	—	4	1	no	—
160	C₂×C₃×D₄	C₅×Q₈	1	4	yes	complemented
161	C₂²×C₃×C₄	—	2	8	no	—
162	C₂²×C₃×C₄	—	4	2	no	—
163	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
164	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
165	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
166	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
167	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
168	C₃×C₄⋊C₄	—	2	8	no	—
169	C₃×C₄⋊C₄	—	2	8	no	—
170	C₃×C₄⋊C₄	—	4	2	no	—
171	C₃×C₄⋊C₄	—	4	1	no	—
172	C₃×C₄⋊C₄	C₅×D₄	1	8	yes	complemented
173	C₃×C₂²⋊C₄	—	2	8	no	—
174	C₃×C₂²⋊C₄	—	2	8	no	—
175	C₃×C₂²⋊C₄	—	4	2	no	—
176	C₃×C₄²	—	4	1	no	—
177	C₂³×C₅	—	2	4	no	—
178	C₂³×C₅	—	2	2	no	—
179	C₂³×C₅	—	2	2	no	—
180	C₂³×C₅	—	2	4	no	—
181	C₂³×C₅	C₂×C₃×Q₈	1	4	yes	—
182	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
183	C₅×Q₈	—	4	8	no	—
184	C₅×D₄	—	4	4	no	—
185	C₂×C₄×C₅	—	2	4	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	1	no	—
188	C₂×C₄×C₅	—	2	1	no	—
189	C₂×C₄×C₅	—	2	4	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	4	no	—
192	C₂×C₄×C₅	—	2	4	no	—
193	C₂×C₄×C₅	—	2	4	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	4	no	—
196	C₂×C₄×C₅	—	4	8	no	—
197	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
198	C₂×C₄×C₅	C₂×C₃×D₄	1	8	yes	—
199	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
200	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
201	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
202	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
203	C₂²⋊Q₈	—	2	16	no	—
204	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
205	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
206	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
207	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
208	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
209	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
210	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
211	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
212	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
213	#95	C₂²×C₃×C₅	1	4	yes	—
214	#95	C₂²×C₃×C₅	1	2	yes	—
215	C₂×C₃×C₅	—	4	4	no	—
216	C₂×C₃×C₅	#537	1	2	yes	—
217	C₂×C₃×C₅	#543	1	1	yes	characteristic
218	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
219	C₂×C₃×C₅	D₄×Q₈	1	2	yes	—
220	C₂×C₃×C₅	#563	1	1	yes	characteristic
221	C₂³×C₃	—	2	4	no	—
222	C₂³×C₃	—	2	2	no	—
223	C₂³×C₃	—	2	2	no	—
224	C₂³×C₃	—	2	4	no	—
225	C₂³×C₃	C₂×C₅×Q₈	1	4	yes	—
226	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
227	C₃×Q₈	—	4	8	no	—
228	C₃×D₄	—	4	4	no	—
229	C₂×C₃×C₄	—	2	4	no	—
230	C₂×C₃×C₄	—	2	2	no	—
231	C₂×C₃×C₄	—	2	1	no	—
232	C₂×C₃×C₄	—	2	1	no	—
233	C₂×C₃×C₄	—	2	4	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	4	no	—
236	C₂×C₃×C₄	—	2	4	no	—
237	C₂×C₃×C₄	—	2	4	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	—	4	8	no	—
241	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
242	C₂×C₃×C₄	C₂×C₅×D₄	1	8	yes	—
243	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
244	C₂²×C₅	—	2	4	no	—
245	C₂²×C₅	—	2	8	no	—
246	C₂²×C₅	—	4	2	no	—
247	C₂²×C₅	—	4	4	no	—
248	C₂²×C₅	—	4	2	no	—
249	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
250	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
251	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
252	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
253	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
254	C₄×C₅	—	2	4	no	—
255	C₄×C₅	—	2	2	no	—
256	C₄×C₅	—	2	8	no	—
257	C₄×C₅	—	4	4	no	—
258	C₄×C₅	—	4	2	no	—
259	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
260	C₂×Q₈	—	2	8	no	—
261	C₂×Q₈	—	4	2	no	—
262	C₂×D₄	—	4	1	no	—
263	C₂×D₄	—	4	1	no	—
264	C₂×D₄	C₃×C₅×Q₈	1	4	yes	complemented
265	C₂²×C₄	—	2	8	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
268	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
269	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
270	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
271	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
272	C₄⋊C₄	—	2	8	no	—
273	C₄⋊C₄	—	2	8	no	—
274	C₄⋊C₄	—	4	2	no	—
275	C₄⋊C₄	—	4	1	no	—
276	C₄⋊C₄	C₃×C₅×D₄	1	8	yes	complemented
277	C₂²⋊C₄	—	2	8	no	—
278	C₂²⋊C₄	—	2	8	no	—
279	C₂²⋊C₄	—	4	2	no	—
280	C₄²	—	4	1	no	—
281	C₃×C₅	#2683	1	1	yes	characteristic, direct product factor, Hall
282	C₂²×C₃	—	2	4	no	—
283	C₂²×C₃	—	2	8	no	—
284	C₂²×C₃	—	4	4	no	—
285	C₂²×C₃	—	4	2	no	—
286	C₂²×C₃	—	4	2	no	—
287	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
288	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
289	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
290	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
291	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
292	C₃×C₄	—	2	4	no	—
293	C₃×C₄	—	2	2	no	—
294	C₃×C₄	—	2	8	no	—
295	C₃×C₄	—	4	4	no	—
296	C₃×C₄	—	4	2	no	—
297	C₂×C₅	—	4	4	no	—
298	C₂×C₅	C₃×#537	1	2	yes	—
299	C₂×C₅	C₃×#543	1	1	yes	characteristic
300	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
301	C₂×C₅	C₃×D₄×Q₈	1	2	yes	—
302	C₂×C₅	C₃×#563	1	1	yes	characteristic
303	C₂³	—	2	4	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	2	2	no	—
306	C₂³	—	2	4	no	—
307	C₂³	C₂×C₃×C₅×Q₈	1	4	yes	—
308	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
309	Q₈	—	4	8	no	—
310	D₄	—	4	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	4	8	no	—
323	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
324	C₂×C₄	C₂×C₃×C₅×D₄	1	8	yes	—
325	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
326	C₂×C₃	—	4	4	no	—
327	C₂×C₃	C₅×#537	1	2	yes	—
328	C₂×C₃	C₅×#543	1	1	yes	characteristic
329	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
330	C₂×C₃	C₅×D₄×Q₈	1	2	yes	—
331	C₂×C₃	C₅×#563	1	1	yes	characteristic
332	C₅	C₃×#2683	1	1	yes	characteristic, direct product factor, Sylow
333	C₂²	—	2	4	no	—
334	C₂²	—	2	8	no	—
335	C₂²	—	4	4	no	—
336	C₂²	—	4	2	no	—
337	C₂²	—	4	2	no	—
338	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
339	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
340	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
341	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
342	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
343	C₄	—	2	4	no	—
344	C₄	—	2	2	no	—
345	C₄	—	2	8	no	—
346	C₄	—	4	4	no	—
347	C₄	—	4	2	no	—
348	C₃	C₅×#2683	1	1	yes	characteristic, direct product factor, Sylow
349	C₂	—	4	4	no	—
350	C₂	C₃×C₅×#537	1	2	yes	—
351	C₂	C₃×C₅×#543	1	1	yes	characteristic
352	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
353	C₂	C₃×C₅×D₄×Q₈	1	2	yes	—
354	C₂	C₃×C₅×#563	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
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×C₂²⋊Q₈	C₂	semidirect
2. C₃×C₅×#396	C₂	semidirect
3. C₃×C₅×#395	C₂	semidirect
5. C₃×C₅×#389	C₂	semidirect
7. C₅×#2683	C₃	direct (N × H)
23. C₃×#2683	C₅	direct (N × H)
24. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
25. C₅×#396	C₂×C₃	semidirect
26. C₅×#395	C₂×C₃	semidirect
28. C₅×#389	C₂×C₃	semidirect
35. C₂×C₃×C₅×D₄	Q₈	semidirect
47. C₃×C₅×C₄⋊C₄	D₄	semidirect
52. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
53. C₃×#396	C₂×C₅	semidirect
54. C₃×#395	C₂×C₅	semidirect
56. C₃×#389	C₂×C₅	semidirect
73. #2683	C₃×C₅	direct (N × H)
117. C₂×C₅×D₄	C₃×Q₈	semidirect
129. C₅×C₄⋊C₄	C₃×D₄	semidirect
134. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
135. #396	C₂×C₃×C₅	semidirect
136. #395	C₂×C₃×C₅	semidirect
138. #389	C₂×C₃×C₅	semidirect
160. C₂×C₃×D₄	C₅×Q₈	semidirect
172. C₃×C₄⋊C₄	C₅×D₄	semidirect
264. C₂×D₄	C₃×C₅×Q₈	semidirect
276. C₄⋊C₄	C₃×C₅×D₄	semidirect
281. C₃×C₅	#2683	direct (N × H)
332. C₅	C₃×#2683	direct (N × H)
348. C₃	C₅×#2683	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
C₃×C₅×#396	2
C₃×C₅×#395	2
C₃×C₅×#390	2
C₃×C₅×#389	2
C₃×C₅×#386	2
C₅×#2683	3
C₃×#2683	5

Subgroups — C3×C5×#2683 #14275717

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2683 #14275717