Subgroups — C₃×C₅×#2546 #14275580

Order 1920.

1080 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×C₄⋊Q₈	C₂	1	2	yes	maximal
2	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#398	C₂	1	4	yes	maximal
5	C₃×C₅×#391	C₂	1	2	yes	maximal
6	C₃×C₅×#389	C₂	1	4	yes	maximal
7	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
8	C₅×#2546	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₃×C₅×C₄⋊Q₈	—	2	8	no	—
12	C₃×C₅×C₄⋊Q₈	—	2	4	no	—
13	C₃×C₄×C₅×Q₈	—	2	4	no	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	8	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
21	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₃×C₅×#95	C₂²	1	2	yes	—
24	C₃×C₅×#95	C₂²	1	8	yes	—
25	C₃×#2546	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	2	yes	—
27	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
28	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic
29	C₅×#398	C₂×C₃	1	4	yes	—
30	C₅×#391	C₂×C₃	1	2	yes	—
31	C₅×#389	C₂×C₃	1	4	yes	—
32	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
33	C₂×C₃×C₅×Q₈	—	2	2	no	—
34	C₂×C₃×C₅×Q₈	—	2	4	no	—
35	C₂×C₃×C₅×Q₈	—	2	4	no	—
36	C₂×C₃×C₅×Q₈	—	2	2	no	—
37	C₂×C₃×C₅×Q₈	—	2	4	no	—
38	C₂×C₃×C₅×Q₈	D₄	1	4	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	2	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	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₃×C₅×C₄⋊C₄	—	2	4	no	—
47	C₃×C₅×C₄⋊C₄	—	2	2	no	—
48	C₃×C₅×C₄⋊C₄	—	2	16	no	—
49	C₃×C₅×C₄⋊C₄	—	2	4	no	—
50	C₃×C₅×C₄⋊C₄	—	2	4	no	—
51	C₃×C₅×C₄⋊C₄	Q₈	1	8	yes	complemented
52	C₃×C₄²×C₅	—	2	4	no	—
53	C₃×C₄²×C₅	—	2	4	no	—
54	C₃×C₄²×C₅	D₄	1	4	yes	—
55	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	2	yes	—
56	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
57	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic
58	C₃×#398	C₂×C₅	1	4	yes	—
59	C₃×#391	C₂×C₅	1	2	yes	—
60	C₃×#389	C₂×C₅	1	4	yes	—
61	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
62	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
63	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
64	C₅×C₄⋊Q₈	—	2	8	no	—
65	C₅×C₄⋊Q₈	—	2	4	no	—
66	C₄×C₅×Q₈	—	2	4	no	—
67	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
68	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	8	yes	—
69	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
71	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
72	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
73	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
74	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
75	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
76	C₅×#95	C₂²×C₃	1	2	yes	—
77	C₅×#95	C₂²×C₃	1	8	yes	—
78	#2546	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
79	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
80	C₃×C₅×Q₈	—	2	8	no	—
81	C₃×C₅×Q₈	—	4	8	no	—
82	C₂×C₃×C₄×C₅	—	2	4	no	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	2	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	4	no	—
92	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
94	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂×Q₈	1	8	yes	—
98	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
99	C₂×C₃×C₄×C₅	#41	1	2	yes	—
100	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
101	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
102	C₃×C₄⋊Q₈	—	2	8	no	—
103	C₃×C₄⋊Q₈	—	2	4	no	—
104	C₃×C₄×Q₈	—	2	4	no	—
105	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
106	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	8	yes	—
107	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
108	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
109	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
110	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
111	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
112	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
113	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
114	C₃×#95	C₂²×C₅	1	2	yes	—
115	C₃×#95	C₂²×C₅	1	8	yes	—
116	C₂×C₅×Q₈	—	2	2	no	—
117	C₂×C₅×Q₈	—	2	4	no	—
118	C₂×C₅×Q₈	—	2	4	no	—
119	C₂×C₅×Q₈	—	2	2	no	—
120	C₂×C₅×Q₈	—	2	4	no	—
121	C₂×C₅×Q₈	C₃×D₄	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	2	yes	—
125	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
127	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
129	C₅×C₄⋊C₄	—	2	4	no	—
130	C₅×C₄⋊C₄	—	2	2	no	—
131	C₅×C₄⋊C₄	—	2	16	no	—
132	C₅×C₄⋊C₄	—	2	4	no	—
133	C₅×C₄⋊C₄	—	2	4	no	—
134	C₅×C₄⋊C₄	C₃×Q₈	1	8	yes	complemented
135	C₄²×C₅	—	2	4	no	—
136	C₄²×C₅	—	2	4	no	—
137	C₄²×C₅	C₃×D₄	1	4	yes	—
138	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	2	yes	—
139	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
140	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
141	#398	C₂×C₃×C₅	1	4	yes	—
142	#391	C₂×C₃×C₅	1	2	yes	—
143	#389	C₂×C₃×C₅	1	4	yes	—
144	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
145	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
146	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
147	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
148	C₂²×C₃×C₅	C₂×#41	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	C₃×C₄×C₅	#121	1	4	yes	—
156	C₃×C₄×C₅	C₄⋊Q₈	1	4	yes	complemented
157	C₂×C₃×Q₈	—	2	2	no	—
158	C₂×C₃×Q₈	—	2	4	no	—
159	C₂×C₃×Q₈	—	2	4	no	—
160	C₂×C₃×Q₈	—	2	2	no	—
161	C₂×C₃×Q₈	—	2	4	no	—
162	C₂×C₃×Q₈	C₅×D₄	1	4	yes	—
163	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
164	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
165	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
166	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
167	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
168	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
169	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
170	C₃×C₄⋊C₄	—	2	4	no	—
171	C₃×C₄⋊C₄	—	2	2	no	—
172	C₃×C₄⋊C₄	—	2	16	no	—
173	C₃×C₄⋊C₄	—	2	4	no	—
174	C₃×C₄⋊C₄	—	2	4	no	—
175	C₃×C₄⋊C₄	C₅×Q₈	1	8	yes	complemented
176	C₃×C₄²	—	2	4	no	—
177	C₃×C₄²	—	2	4	no	—
178	C₃×C₄²	C₅×D₄	1	4	yes	—
179	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
180	C₅×Q₈	—	2	8	no	—
181	C₅×Q₈	—	4	8	no	—
182	C₂×C₄×C₅	—	2	4	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	2	4	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	2	4	no	—
189	C₂×C₄×C₅	—	2	4	no	—
190	C₂×C₄×C₅	—	2	4	no	—
191	C₂×C₄×C₅	—	2	4	no	—
192	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
193	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
194	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
195	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
196	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
197	C₂×C₄×C₅	C₂×C₃×Q₈	1	8	yes	—
198	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
199	C₂×C₄×C₅	C₃×#41	1	2	yes	—
200	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
201	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
202	C₄⋊Q₈	—	2	8	no	—
203	C₄⋊Q₈	—	2	4	no	—
204	C₄×Q₈	—	2	4	no	—
205	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
207	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
208	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	8	yes	—
209	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
210	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
211	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
212	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
213	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
214	#95	C₂²×C₃×C₅	1	2	yes	—
215	#95	C₂²×C₃×C₅	1	8	yes	—
216	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
217	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
218	C₂×C₃×C₅	#536	1	1	yes	characteristic
219	C₂×C₃×C₅	D₄×Q₈	1	2	yes	—
220	C₂×C₃×C₅	#557	1	2	yes	—
221	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
222	C₃×Q₈	—	2	8	no	—
223	C₃×Q₈	—	4	8	no	—
224	C₂×C₃×C₄	—	2	4	no	—
225	C₂×C₃×C₄	—	2	2	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	2	no	—
230	C₂×C₃×C₄	—	2	4	no	—
231	C₂×C₃×C₄	—	2	4	no	—
232	C₂×C₃×C₄	—	2	4	no	—
233	C₂×C₃×C₄	—	2	4	no	—
234	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
235	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
236	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
237	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
238	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
239	C₂×C₃×C₄	C₂×C₅×Q₈	1	8	yes	—
240	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
241	C₂×C₃×C₄	C₅×#41	1	2	yes	—
242	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
243	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
244	C₂²×C₅	C₂²×C₃×Q₈	1	2	yes	—
245	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
246	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
247	C₄×C₅	—	2	4	no	—
248	C₄×C₅	—	2	2	no	—
249	C₄×C₅	—	2	8	no	—
250	C₄×C₅	—	4	4	no	—
251	C₄×C₅	—	4	2	no	—
252	C₄×C₅	C₃×#121	1	4	yes	—
253	C₄×C₅	C₃×C₄⋊Q₈	1	4	yes	complemented
254	C₂×Q₈	—	2	2	no	—
255	C₂×Q₈	—	2	4	no	—
256	C₂×Q₈	—	2	4	no	—
257	C₂×Q₈	—	2	2	no	—
258	C₂×Q₈	—	2	4	no	—
259	C₂×Q₈	C₃×C₅×D₄	1	4	yes	—
260	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
261	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
262	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
263	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
264	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
265	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
266	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
267	C₄⋊C₄	—	2	4	no	—
268	C₄⋊C₄	—	2	2	no	—
269	C₄⋊C₄	—	2	16	no	—
270	C₄⋊C₄	—	2	4	no	—
271	C₄⋊C₄	—	2	4	no	—
272	C₄⋊C₄	C₃×C₅×Q₈	1	8	yes	complemented
273	C₄²	—	2	4	no	—
274	C₄²	—	2	4	no	—
275	C₄²	C₃×C₅×D₄	1	4	yes	—
276	C₃×C₅	#2546	1	1	yes	characteristic, direct product factor, Hall
277	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
278	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
279	C₂²×C₃	C₂²×C₅×Q₈	1	2	yes	—
280	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
281	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
282	C₃×C₄	—	2	4	no	—
283	C₃×C₄	—	2	2	no	—
284	C₃×C₄	—	2	8	no	—
285	C₃×C₄	—	4	4	no	—
286	C₃×C₄	—	4	2	no	—
287	C₃×C₄	C₅×#121	1	4	yes	—
288	C₃×C₄	C₅×C₄⋊Q₈	1	4	yes	complemented
289	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
290	C₂×C₅	C₂×C₃×C₄⋊Q₈	1	1	yes	characteristic
291	C₂×C₅	C₃×#536	1	1	yes	characteristic
292	C₂×C₅	C₃×D₄×Q₈	1	2	yes	—
293	C₂×C₅	C₃×#557	1	2	yes	—
294	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
295	Q₈	—	2	8	no	—
296	Q₈	—	4	8	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
308	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
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×D₄	1	2	yes	—
312	C₂×C₄	C₂×C₃×C₅×Q₈	1	8	yes	—
313	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
314	C₂×C₄	C₃×C₅×#41	1	2	yes	—
315	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
316	C₂×C₃	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
317	C₂×C₃	C₅×#536	1	1	yes	characteristic
318	C₂×C₃	C₅×D₄×Q₈	1	2	yes	—
319	C₂×C₃	C₅×#557	1	2	yes	—
320	C₅	C₃×#2546	1	1	yes	characteristic, direct product factor, Sylow
321	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
322	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
323	C₂²	C₂²×C₃×C₅×Q₈	1	2	yes	—
324	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
325	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
326	C₄	—	2	4	no	—
327	C₄	—	2	2	no	—
328	C₄	—	2	8	no	—
329	C₄	—	4	4	no	—
330	C₄	—	4	2	no	—
331	C₄	C₃×C₅×#121	1	4	yes	—
332	C₄	C₃×C₅×C₄⋊Q₈	1	4	yes	complemented
333	C₃	C₅×#2546	1	1	yes	characteristic, direct product factor, Sylow
334	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
335	C₂	C₂×C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
336	C₂	C₃×C₅×#536	1	1	yes	characteristic
337	C₂	C₃×C₅×D₄×Q₈	1	2	yes	—
338	C₂	C₃×C₅×#557	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
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
8. C₅×#2546	C₃	direct (N × H)
25. C₃×#2546	C₅	direct (N × H)
51. C₃×C₅×C₄⋊C₄	Q₈	semidirect
78. #2546	C₃×C₅	direct (N × H)
134. C₅×C₄⋊C₄	C₃×Q₈	semidirect
156. C₃×C₄×C₅	C₄⋊Q₈	semidirect
175. C₃×C₄⋊C₄	C₅×Q₈	semidirect
253. C₄×C₅	C₃×C₄⋊Q₈	semidirect
272. C₄⋊C₄	C₃×C₅×Q₈	semidirect
276. C₃×C₅	#2546	direct (N × H)
288. C₃×C₄	C₅×C₄⋊Q₈	semidirect
320. C₅	C₃×#2546	direct (N × H)
332. C₄	C₃×C₅×C₄⋊Q₈	semidirect
333. C₃	C₅×#2546	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×C₄⋊Q₈	2
C₂×C₃×C₄×C₅×Q₈	2
C₃×C₅×#398	2
C₃×C₅×#391	2
C₃×C₅×#389	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2546	3
C₃×#2546	5

Subgroups — C3×C5×#2546 #14275580

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2546 #14275580