Subgroups — C₃×C₅×#2014 #14275048

Order 1920.

948 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×SD₁₆	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×#102	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#336	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2014	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₅×D₄	—	2	2	no	—
9	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
10	C₂×C₃×C₅×SD₁₆	—	2	4	no	—
11	C₂×C₃×C₅×SD₁₆	—	2	4	no	—
12	C₂×C₃×C₅×SD₁₆	—	2	4	no	—
13	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
14	C₃×C₅×#127	—	2	4	no	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₃×C₅×#102	—	2	4	no	—
18	C₃×C₅×#95	—	2	2	no	—
19	C₃×#2014	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₅×SD₁₆	C₂×C₃	1	2	yes	complemented
21	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic
22	C₂×C₅×#102	C₂×C₃	1	2	yes	complemented
23	C₅×#391	C₂×C₃	1	1	yes	characteristic, complemented
24	C₅×#336	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂⁴×C₃×C₅	—	2	2	no	—
26	C₂×C₃×C₅×Q₈	—	2	1	no	—
27	C₂×C₃×C₅×Q₈	—	2	2	no	—
28	C₂×C₃×C₅×Q₈	—	2	2	no	—
29	C₂×C₃×C₅×Q₈	D₄	1	2	yes	complemented
30	C₂×C₃×C₅×D₄	—	2	8	no	—
31	C₂×C₃×C₅×D₄	—	2	2	no	—
32	C₂×C₃×C₅×D₄	—	2	2	no	—
33	C₂×C₃×C₅×D₄	—	2	2	no	—
34	C₂×C₃×C₅×D₄	—	2	2	no	—
35	C₂×C₃×C₅×D₄	—	2	2	no	—
36	C₂×C₃×C₅×D₄	—	4	4	no	—
37	C₂×C₃×C₅×D₄	—	4	4	no	—
38	C₂×C₃×C₅×D₄	D₄	1	4	yes	—
39	C₂²×C₃×C₄×C₅	—	2	1	no	—
40	C₂²×C₃×C₄×C₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₃×C₅×SD₁₆	—	2	16	no	—
44	C₂×C₃×C₅×C₈	—	2	2	no	—
45	C₂×C₃×C₅×C₈	—	2	2	no	—
46	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
47	C₃×C₅×C₄⋊C₄	—	2	2	no	—
48	C₃×C₄²×C₅	—	2	2	no	—
49	C₂²×C₃×SD₁₆	C₂×C₅	1	2	yes	complemented
50	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic
51	C₂×C₃×#102	C₂×C₅	1	2	yes	complemented
52	C₃×#391	C₂×C₅	1	1	yes	characteristic, complemented
53	C₃×#336	C₂×C₅	1	1	yes	characteristic, complemented
54	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
55	C₂²×C₅×D₄	—	2	2	no	—
56	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
57	C₂×C₅×SD₁₆	—	2	4	no	—
58	C₂×C₅×SD₁₆	—	2	4	no	—
59	C₂×C₅×SD₁₆	—	2	4	no	—
60	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
61	C₅×#127	—	2	4	no	—
62	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
64	C₅×#102	—	2	4	no	—
65	C₅×#95	—	2	2	no	—
66	#2014	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
67	C₂³×C₃×C₅	—	2	4	no	—
68	C₂³×C₃×C₅	—	4	2	no	—
69	C₂³×C₃×C₅	—	4	2	no	—
70	C₂³×C₃×C₅	—	4	4	no	—
71	C₂³×C₃×C₅	—	4	4	no	—
72	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
73	C₃×C₅×Q₈	—	2	4	no	—
74	C₃×C₅×Q₈	—	4	2	no	—
75	C₃×C₅×D₄	—	2	4	no	—
76	C₃×C₅×D₄	—	2	4	no	—
77	C₃×C₅×D₄	—	4	16	no	—
78	C₃×C₅×D₄	—	4	2	no	—
79	C₃×C₅×D₄	—	4	2	no	—
80	C₂×C₃×C₄×C₅	—	2	2	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	2	2	no	—
83	C₂×C₃×C₄×C₅	—	4	1	no	—
84	C₂×C₃×C₄×C₅	—	4	1	no	—
85	C₂×C₃×C₄×C₅	—	4	1	no	—
86	C₂×C₃×C₄×C₅	—	4	2	no	—
87	C₂×C₃×C₄×C₅	SD₁₆	1	4	yes	complemented
88	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
92	C₃×C₅×C₈	—	2	4	no	—
93	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
94	C₂²×C₃×D₄	—	2	2	no	—
95	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
96	C₂×C₃×SD₁₆	—	2	4	no	—
97	C₂×C₃×SD₁₆	—	2	4	no	—
98	C₂×C₃×SD₁₆	—	2	4	no	—
99	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
100	C₃×#127	—	2	4	no	—
101	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
102	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
103	C₃×#102	—	2	4	no	—
104	C₃×#95	—	2	2	no	—
105	C₂⁴×C₅	—	2	2	no	—
106	C₂×C₅×Q₈	—	2	1	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	C₃×D₄	1	2	yes	complemented
110	C₂×C₅×D₄	—	2	8	no	—
111	C₂×C₅×D₄	—	2	2	no	—
112	C₂×C₅×D₄	—	2	2	no	—
113	C₂×C₅×D₄	—	2	2	no	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	—	2	2	no	—
116	C₂×C₅×D₄	—	4	4	no	—
117	C₂×C₅×D₄	—	4	4	no	—
118	C₂×C₅×D₄	C₃×D₄	1	4	yes	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
122	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
123	C₅×SD₁₆	—	2	16	no	—
124	C₂×C₅×C₈	—	2	2	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
127	C₅×C₄⋊C₄	—	2	2	no	—
128	C₄²×C₅	—	2	2	no	—
129	C₂²×SD₁₆	C₂×C₃×C₅	1	2	yes	complemented
130	C₂×#127	C₂×C₃×C₅	1	1	yes	characteristic
131	C₂×#102	C₂×C₃×C₅	1	2	yes	complemented
132	#391	C₂×C₃×C₅	1	1	yes	characteristic, complemented
133	#336	C₂×C₃×C₅	1	1	yes	characteristic, complemented
134	C₂²×C₃×C₅	—	4	4	no	—
135	C₂²×C₃×C₅	—	4	8	no	—
136	C₂²×C₃×C₅	—	8	4	no	—
137	C₂²×C₃×C₅	—	8	2	no	—
138	C₂²×C₃×C₅	—	8	2	no	—
139	C₂²×C₃×C₅	#120	1	1	yes	characteristic
140	C₂²×C₃×C₅	#121	1	1	yes	characteristic
141	C₂²×C₃×C₅	#127	1	1	yes	characteristic
142	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
143	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
144	C₃×C₄×C₅	—	2	4	no	—
145	C₃×C₄×C₅	—	4	2	no	—
146	C₃×C₄×C₅	—	8	1	no	—
147	C₃×C₄×C₅	#120	1	2	yes	—
148	C₃×C₄×C₅	#121	1	2	yes	—
149	C₂⁴×C₃	—	2	2	no	—
150	C₂×C₃×Q₈	—	2	1	no	—
151	C₂×C₃×Q₈	—	2	2	no	—
152	C₂×C₃×Q₈	—	2	2	no	—
153	C₂×C₃×Q₈	C₅×D₄	1	2	yes	complemented
154	C₂×C₃×D₄	—	2	8	no	—
155	C₂×C₃×D₄	—	2	2	no	—
156	C₂×C₃×D₄	—	2	2	no	—
157	C₂×C₃×D₄	—	2	2	no	—
158	C₂×C₃×D₄	—	2	2	no	—
159	C₂×C₃×D₄	—	2	2	no	—
160	C₂×C₃×D₄	—	4	4	no	—
161	C₂×C₃×D₄	—	4	4	no	—
162	C₂×C₃×D₄	C₅×D₄	1	4	yes	—
163	C₂²×C₃×C₄	—	2	1	no	—
164	C₂²×C₃×C₄	—	2	1	no	—
165	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
166	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
167	C₃×SD₁₆	—	2	16	no	—
168	C₂×C₃×C₈	—	2	2	no	—
169	C₂×C₃×C₈	—	2	2	no	—
170	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
171	C₃×C₄⋊C₄	—	2	2	no	—
172	C₃×C₄²	—	2	2	no	—
173	C₂³×C₅	—	2	4	no	—
174	C₂³×C₅	—	4	2	no	—
175	C₂³×C₅	—	4	2	no	—
176	C₂³×C₅	—	4	4	no	—
177	C₂³×C₅	—	4	4	no	—
178	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
179	C₅×Q₈	—	2	4	no	—
180	C₅×Q₈	—	4	2	no	—
181	C₅×D₄	—	2	4	no	—
182	C₅×D₄	—	2	4	no	—
183	C₅×D₄	—	4	16	no	—
184	C₅×D₄	—	4	2	no	—
185	C₅×D₄	—	4	2	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	4	1	no	—
190	C₂×C₄×C₅	—	4	1	no	—
191	C₂×C₄×C₅	—	4	1	no	—
192	C₂×C₄×C₅	—	4	2	no	—
193	C₂×C₄×C₅	C₃×SD₁₆	1	4	yes	complemented
194	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
196	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
197	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
198	C₅×C₈	—	2	4	no	—
199	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
200	C₂²×D₄	—	2	2	no	—
201	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
202	C₂×SD₁₆	—	2	4	no	—
203	C₂×SD₁₆	—	2	4	no	—
204	C₂×SD₁₆	—	2	4	no	—
205	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
206	#127	—	2	4	no	—
207	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
208	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
209	#102	—	2	4	no	—
210	#95	—	2	2	no	—
211	C₂×C₃×C₅	—	8	4	no	—
212	C₂×C₃×C₅	#392	1	1	yes	characteristic
213	C₂×C₃×C₅	#450	1	2	yes	—
214	C₂×C₃×C₅	#460	1	2	yes	—
215	C₂×C₃×C₅	#492	1	1	yes	characteristic
216	C₂×C₃×C₅	#496	1	1	yes	characteristic
217	C₂³×C₃	—	2	4	no	—
218	C₂³×C₃	—	4	2	no	—
219	C₂³×C₃	—	4	2	no	—
220	C₂³×C₃	—	4	4	no	—
221	C₂³×C₃	—	4	4	no	—
222	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
223	C₃×Q₈	—	2	4	no	—
224	C₃×Q₈	—	4	2	no	—
225	C₃×D₄	—	2	4	no	—
226	C₃×D₄	—	2	4	no	—
227	C₃×D₄	—	4	16	no	—
228	C₃×D₄	—	4	2	no	—
229	C₃×D₄	—	4	2	no	—
230	C₂×C₃×C₄	—	2	2	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	4	1	no	—
234	C₂×C₃×C₄	—	4	1	no	—
235	C₂×C₃×C₄	—	4	1	no	—
236	C₂×C₃×C₄	—	4	2	no	—
237	C₂×C₃×C₄	C₅×SD₁₆	1	4	yes	complemented
238	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
240	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
241	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
242	C₃×C₈	—	2	4	no	—
243	C₂²×C₅	—	4	4	no	—
244	C₂²×C₅	—	4	8	no	—
245	C₂²×C₅	—	8	4	no	—
246	C₂²×C₅	—	8	2	no	—
247	C₂²×C₅	—	8	2	no	—
248	C₂²×C₅	C₃×#120	1	1	yes	characteristic
249	C₂²×C₅	C₃×#121	1	1	yes	characteristic
250	C₂²×C₅	C₃×#127	1	1	yes	characteristic
251	C₂²×C₅	C₂×C₃×SD₁₆	1	2	yes	—
252	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
253	C₄×C₅	—	2	4	no	—
254	C₄×C₅	—	4	2	no	—
255	C₄×C₅	—	8	1	no	—
256	C₄×C₅	C₃×#120	1	2	yes	—
257	C₄×C₅	C₃×#121	1	2	yes	—
258	C₂⁴	—	2	2	no	—
259	C₂×Q₈	—	2	1	no	—
260	C₂×Q₈	—	2	2	no	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	C₃×C₅×D₄	1	2	yes	complemented
263	C₂×D₄	—	2	8	no	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	4	4	no	—
270	C₂×D₄	—	4	4	no	—
271	C₂×D₄	C₃×C₅×D₄	1	4	yes	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
275	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
276	SD₁₆	—	2	16	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	C₃×C₅×D₄	1	4	yes	complemented
280	C₄⋊C₄	—	2	2	no	—
281	C₄²	—	2	2	no	—
282	C₃×C₅	#2014	1	1	yes	characteristic, direct product factor, Hall
283	C₂²×C₃	—	4	4	no	—
284	C₂²×C₃	—	4	8	no	—
285	C₂²×C₃	—	8	4	no	—
286	C₂²×C₃	—	8	2	no	—
287	C₂²×C₃	—	8	2	no	—
288	C₂²×C₃	C₅×#120	1	1	yes	characteristic
289	C₂²×C₃	C₅×#121	1	1	yes	characteristic
290	C₂²×C₃	C₅×#127	1	1	yes	characteristic
291	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
292	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
293	C₃×C₄	—	2	4	no	—
294	C₃×C₄	—	4	2	no	—
295	C₃×C₄	—	8	1	no	—
296	C₃×C₄	C₅×#120	1	2	yes	—
297	C₃×C₄	C₅×#121	1	2	yes	—
298	C₂×C₅	—	8	4	no	—
299	C₂×C₅	C₃×#392	1	1	yes	characteristic
300	C₂×C₅	C₃×#450	1	2	yes	—
301	C₂×C₅	C₃×#460	1	2	yes	—
302	C₂×C₅	C₃×#492	1	1	yes	characteristic
303	C₂×C₅	C₃×#496	1	1	yes	characteristic
304	C₂³	—	2	4	no	—
305	C₂³	—	4	2	no	—
306	C₂³	—	4	2	no	—
307	C₂³	—	4	4	no	—
308	C₂³	—	4	4	no	—
309	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
310	Q₈	—	2	4	no	—
311	Q₈	—	4	2	no	—
312	D₄	—	2	4	no	—
313	D₄	—	2	4	no	—
314	D₄	—	4	16	no	—
315	D₄	—	4	2	no	—
316	D₄	—	4	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	C₃×C₅×SD₁₆	1	4	yes	complemented
325	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
326	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
327	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
328	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
329	C₈	—	2	4	no	—
330	C₂×C₃	—	8	4	no	—
331	C₂×C₃	C₅×#392	1	1	yes	characteristic
332	C₂×C₃	C₅×#450	1	2	yes	—
333	C₂×C₃	C₅×#460	1	2	yes	—
334	C₂×C₃	C₅×#492	1	1	yes	characteristic
335	C₂×C₃	C₅×#496	1	1	yes	characteristic
336	C₅	C₃×#2014	1	1	yes	characteristic, direct product factor, Sylow
337	C₂²	—	4	8	no	—
338	C₂²	—	4	4	no	—
339	C₂²	—	8	4	no	—
340	C₂²	—	8	2	no	—
341	C₂²	—	8	2	no	—
342	C₂²	C₃×C₅×#120	1	1	yes	characteristic
343	C₂²	C₃×C₅×#121	1	1	yes	characteristic
344	C₂²	C₃×C₅×#127	1	1	yes	characteristic
345	C₂²	C₂×C₃×C₅×SD₁₆	1	2	yes	—
346	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
347	C₄	—	2	4	no	—
348	C₄	—	4	2	no	—
349	C₄	—	8	1	no	—
350	C₄	C₃×C₅×#120	1	2	yes	—
351	C₄	C₃×C₅×#121	1	2	yes	—
352	C₃	C₅×#2014	1	1	yes	characteristic, direct product factor, Sylow
353	C₂	—	8	4	no	—
354	C₂	C₃×C₅×#392	1	1	yes	characteristic
355	C₂	C₃×C₅×#450	1	2	yes	—
356	C₂	C₃×C₅×#460	1	2	yes	—
357	C₂	C₃×C₅×#492	1	1	yes	characteristic
358	C₂	C₃×C₅×#496	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
prime radical	C₂×C₃×C₅×#127	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×SD₁₆	C₂	semidirect
3. C₂×C₃×C₅×#102	C₂	semidirect
4. C₃×C₅×#391	C₂	semidirect
5. C₃×C₅×#336	C₂	semidirect
6. C₅×#2014	C₃	direct (N × H)
19. C₃×#2014	C₅	direct (N × H)
20. C₂²×C₅×SD₁₆	C₂×C₃	semidirect
22. C₂×C₅×#102	C₂×C₃	semidirect
23. C₅×#391	C₂×C₃	semidirect
24. C₅×#336	C₂×C₃	semidirect
29. C₂×C₃×C₅×Q₈	D₄	semidirect
46. C₂×C₃×C₅×C₈	D₄	semidirect
49. C₂²×C₃×SD₁₆	C₂×C₅	semidirect
51. C₂×C₃×#102	C₂×C₅	semidirect
52. C₃×#391	C₂×C₅	semidirect
53. C₃×#336	C₂×C₅	semidirect
66. #2014	C₃×C₅	direct (N × H)
87. C₂×C₃×C₄×C₅	SD₁₆	semidirect
109. C₂×C₅×Q₈	C₃×D₄	semidirect
126. C₂×C₅×C₈	C₃×D₄	semidirect
129. C₂²×SD₁₆	C₂×C₃×C₅	semidirect
131. C₂×#102	C₂×C₃×C₅	semidirect
132. #391	C₂×C₃×C₅	semidirect
133. #336	C₂×C₃×C₅	semidirect
153. C₂×C₃×Q₈	C₅×D₄	semidirect
170. C₂×C₃×C₈	C₅×D₄	semidirect
193. C₂×C₄×C₅	C₃×SD₁₆	semidirect
237. C₂×C₃×C₄	C₅×SD₁₆	semidirect
262. C₂×Q₈	C₃×C₅×D₄	semidirect
279. C₂×C₈	C₃×C₅×D₄	semidirect
282. C₃×C₅	#2014	direct (N × H)
324. C₂×C₄	C₃×C₅×SD₁₆	semidirect
336. C₅	C₃×#2014	direct (N × H)
352. C₃	C₅×#2014	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₅×SD₁₆	2
C₂×C₃×C₅×#127	2
C₂×C₃×C₅×#102	2
C₃×C₅×#391	2
C₃×C₅×#336	2
C₅×#2014	3
C₃×#2014	5

Subgroups — C3×C5×#2014 #14275048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2014 #14275048