Subgroups — C₂×C₃×C₅×#496 #14276182

Order 1920.

1336 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	C₂²×C₃×C₅×SD₁₆	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃×C₅×D₈	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#496	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#496	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₅×D₄	—	2	2	no	—
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
12	C₂×C₃×C₅×SD₁₆	—	2	8	no	—
13	C₂×C₃×C₅×SD₁₆	C₂²	1	8	yes	complemented
14	C₂×C₃×C₅×D₈	—	2	8	no	—
15	C₂×C₃×C₅×D₈	C₂²	1	8	yes	complemented
16	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
17	C₃×C₅×#127	—	2	2	no	—
18	C₃×C₅×#127	C₂²	1	4	yes	complemented
19	C₃×C₅×#124	—	2	2	no	—
20	C₃×C₅×#124	C₂²	1	4	yes	complemented
21	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₃×C₅×#97	C₂²	1	4	yes	complemented
24	C₂×C₃×#496	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂²×C₅×SD₁₆	C₂×C₃	1	2	yes	complemented
26	C₂²×C₅×D₈	C₂×C₃	1	2	yes	complemented
27	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic, complemented
29	C₅×#496	C₂×C₃	1	8	yes	direct product factor
30	C₂×C₅×#97	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂⁴×C₃×C₅	—	2	1	no	—
32	C₂⁴×C₃×C₅	—	2	2	no	—
33	C₂×C₃×C₅×Q₈	—	2	1	no	—
34	C₂×C₃×C₅×Q₈	—	2	4	no	—
35	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
36	C₂×C₃×C₅×D₄	—	2	4	no	—
37	C₂×C₃×C₅×D₄	—	2	4	no	—
38	C₂×C₃×C₅×D₄	—	2	4	no	—
39	C₂×C₃×C₅×D₄	—	2	8	no	—
40	C₂×C₃×C₅×D₄	—	2	1	no	—
41	C₂×C₃×C₅×D₄	—	2	2	no	—
42	C₂×C₃×C₅×D₄	—	4	8	no	—
43	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
44	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
45	C₂²×C₃×C₄×C₅	—	2	1	no	—
46	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₃×C₅×SD₁₆	—	2	16	no	—
49	C₃×C₅×D₈	—	2	16	no	—
50	C₂×C₃×C₅×C₈	D₄	1	8	yes	complemented
51	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
52	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
53	C₃×C₄²×C₅	D₄	1	2	yes	—
54	C₃×C₄²×C₅	C₂³	1	2	yes	—
55	C₂²×C₃×SD₁₆	C₂×C₅	1	2	yes	complemented
56	C₂²×C₃×D₈	C₂×C₅	1	2	yes	complemented
57	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic, complemented
58	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
59	C₃×#496	C₂×C₅	1	8	yes	direct product factor
60	C₂×C₃×#97	C₂×C₅	1	1	yes	characteristic, complemented
61	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
62	C₂²×C₅×D₄	—	2	2	no	—
63	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
64	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
65	C₂×C₅×SD₁₆	—	2	8	no	—
66	C₂×C₅×SD₁₆	C₂²×C₃	1	8	yes	complemented
67	C₂×C₅×D₈	—	2	8	no	—
68	C₂×C₅×D₈	C₂²×C₃	1	8	yes	complemented
69	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
70	C₅×#127	—	2	2	no	—
71	C₅×#127	C₂²×C₃	1	4	yes	complemented
72	C₅×#124	—	2	2	no	—
73	C₅×#124	C₂²×C₃	1	4	yes	complemented
74	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
76	C₅×#97	C₂²×C₃	1	4	yes	complemented
77	C₂×#496	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
78	C₂³×C₃×C₅	—	2	2	no	—
79	C₂³×C₃×C₅	—	2	4	no	—
80	C₂³×C₃×C₅	—	4	2	no	—
81	C₂³×C₃×C₅	—	4	4	no	—
82	C₂³×C₃×C₅	—	4	8	no	—
83	C₂³×C₃×C₅	—	4	4	no	—
84	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
85	C₃×C₅×Q₈	—	2	4	no	—
86	C₃×C₅×Q₈	—	4	2	no	—
87	C₃×C₅×D₄	—	2	4	no	—
88	C₃×C₅×D₄	—	2	4	no	—
89	C₃×C₅×D₄	—	2	4	no	—
90	C₃×C₅×D₄	—	4	16	no	—
91	C₃×C₅×D₄	—	4	2	no	—
92	C₃×C₅×D₄	—	4	4	no	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	4	2	no	—
96	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
97	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
99	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
100	C₃×C₅×C₈	C₂×D₄	1	8	yes	complemented
101	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
102	C₂²×C₃×D₄	—	2	2	no	—
103	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
104	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
105	C₂×C₃×SD₁₆	—	2	8	no	—
106	C₂×C₃×SD₁₆	C₂²×C₅	1	8	yes	complemented
107	C₂×C₃×D₈	—	2	8	no	—
108	C₂×C₃×D₈	C₂²×C₅	1	8	yes	complemented
109	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
110	C₃×#127	—	2	2	no	—
111	C₃×#127	C₂²×C₅	1	4	yes	complemented
112	C₃×#124	—	2	2	no	—
113	C₃×#124	C₂²×C₅	1	4	yes	complemented
114	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
115	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
116	C₃×#97	C₂²×C₅	1	4	yes	complemented
117	C₂⁴×C₅	—	2	1	no	—
118	C₂⁴×C₅	—	2	2	no	—
119	C₂×C₅×Q₈	—	2	1	no	—
120	C₂×C₅×Q₈	—	2	4	no	—
121	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
122	C₂×C₅×D₄	—	2	4	no	—
123	C₂×C₅×D₄	—	2	4	no	—
124	C₂×C₅×D₄	—	2	4	no	—
125	C₂×C₅×D₄	—	2	1	no	—
126	C₂×C₅×D₄	—	2	2	no	—
127	C₂×C₅×D₄	—	2	8	no	—
128	C₂×C₅×D₄	—	4	8	no	—
129	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
130	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
131	C₂²×C₄×C₅	—	2	1	no	—
132	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
133	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
134	C₅×SD₁₆	—	2	16	no	—
135	C₅×D₈	—	2	16	no	—
136	C₂×C₅×C₈	C₃×D₄	1	8	yes	complemented
137	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
138	C₅×C₂²⋊C₄	—	2	8	no	—
139	C₄²×C₅	C₃×D₄	1	2	yes	—
140	C₄²×C₅	C₂³×C₃	1	2	yes	—
141	C₂²×SD₁₆	C₂×C₃×C₅	1	2	yes	complemented
142	C₂²×D₈	C₂×C₃×C₅	1	2	yes	complemented
143	C₂×#127	C₂×C₃×C₅	1	1	yes	characteristic, complemented
144	C₂×#124	C₂×C₃×C₅	1	1	yes	characteristic, complemented
145	#496	C₂×C₃×C₅	1	8	yes	direct product factor
146	C₂×#97	C₂×C₃×C₅	1	1	yes	characteristic, complemented
147	C₂²×C₃×C₅	—	4	2	no	—
148	C₂²×C₃×C₅	—	4	4	no	—
149	C₂²×C₃×C₅	—	4	8	no	—
150	C₂²×C₃×C₅	—	4	4	no	—
151	C₂²×C₃×C₅	—	8	8	no	—
152	C₂²×C₃×C₅	—	8	4	no	—
153	C₂²×C₃×C₅	#127	1	2	yes	—
154	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	4	yes	—
155	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
156	C₃×C₄×C₅	—	2	4	no	—
157	C₃×C₄×C₅	—	4	2	no	—
158	C₃×C₄×C₅	#127	1	2	yes	—
159	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
160	C₂⁴×C₃	—	2	1	no	—
161	C₂⁴×C₃	—	2	2	no	—
162	C₂×C₃×Q₈	—	2	1	no	—
163	C₂×C₃×Q₈	—	2	4	no	—
164	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
165	C₂×C₃×D₄	—	2	4	no	—
166	C₂×C₃×D₄	—	2	4	no	—
167	C₂×C₃×D₄	—	2	4	no	—
168	C₂×C₃×D₄	—	2	1	no	—
169	C₂×C₃×D₄	—	2	2	no	—
170	C₂×C₃×D₄	—	2	8	no	—
171	C₂×C₃×D₄	—	4	8	no	—
172	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
173	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
174	C₂²×C₃×C₄	—	2	1	no	—
175	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
176	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
177	C₃×SD₁₆	—	2	16	no	—
178	C₃×D₈	—	2	16	no	—
179	C₂×C₃×C₈	C₅×D₄	1	8	yes	complemented
180	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
181	C₃×C₂²⋊C₄	—	2	8	no	—
182	C₃×C₄²	C₅×D₄	1	2	yes	—
183	C₃×C₄²	C₂³×C₅	1	2	yes	—
184	C₂³×C₅	—	2	2	no	—
185	C₂³×C₅	—	2	4	no	—
186	C₂³×C₅	—	4	2	no	—
187	C₂³×C₅	—	4	4	no	—
188	C₂³×C₅	—	4	8	no	—
189	C₂³×C₅	—	4	4	no	—
190	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
191	C₅×Q₈	—	2	4	no	—
192	C₅×Q₈	—	4	2	no	—
193	C₅×D₄	—	2	4	no	—
194	C₅×D₄	—	2	4	no	—
195	C₅×D₄	—	2	4	no	—
196	C₅×D₄	—	4	16	no	—
197	C₅×D₄	—	4	2	no	—
198	C₅×D₄	—	4	4	no	—
199	C₂×C₄×C₅	—	2	4	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	4	2	no	—
202	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
203	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
205	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
206	C₅×C₈	C₂×C₃×D₄	1	8	yes	complemented
207	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
208	C₂²×D₄	—	2	2	no	—
209	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
210	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
211	C₂×SD₁₆	—	2	8	no	—
212	C₂×SD₁₆	C₂²×C₃×C₅	1	8	yes	complemented
213	C₂×D₈	—	2	8	no	—
214	C₂×D₈	C₂²×C₃×C₅	1	8	yes	complemented
215	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
216	#127	—	2	2	no	—
217	#127	C₂²×C₃×C₅	1	4	yes	complemented
218	#124	—	2	2	no	—
219	#124	C₂²×C₃×C₅	1	4	yes	complemented
220	C₂×C₂²⋊C₄	—	2	2	no	—
221	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
222	#97	C₂²×C₃×C₅	1	4	yes	complemented
223	C₂×C₃×C₅	—	8	4	no	—
224	C₂×C₃×C₅	—	8	2	no	—
225	C₂×C₃×C₅	#496	1	4	yes	direct product factor
226	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
227	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
228	C₂³×C₃	—	2	2	no	—
229	C₂³×C₃	—	2	4	no	—
230	C₂³×C₃	—	4	2	no	—
231	C₂³×C₃	—	4	4	no	—
232	C₂³×C₃	—	4	8	no	—
233	C₂³×C₃	—	4	4	no	—
234	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
235	C₃×Q₈	—	2	4	no	—
236	C₃×Q₈	—	4	2	no	—
237	C₃×D₄	—	2	4	no	—
238	C₃×D₄	—	2	4	no	—
239	C₃×D₄	—	2	4	no	—
240	C₃×D₄	—	4	16	no	—
241	C₃×D₄	—	4	2	no	—
242	C₃×D₄	—	4	4	no	—
243	C₂×C₃×C₄	—	2	4	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	4	2	no	—
246	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
247	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
249	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
250	C₃×C₈	C₂×C₅×D₄	1	8	yes	complemented
251	C₂²×C₅	—	4	8	no	—
252	C₂²×C₅	—	4	4	no	—
253	C₂²×C₅	—	4	2	no	—
254	C₂²×C₅	—	4	4	no	—
255	C₂²×C₅	—	8	8	no	—
256	C₂²×C₅	—	8	4	no	—
257	C₂²×C₅	C₃×#127	1	2	yes	—
258	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	4	yes	—
259	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
260	C₄×C₅	—	2	4	no	—
261	C₄×C₅	—	4	2	no	—
262	C₄×C₅	C₃×#127	1	2	yes	—
263	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
264	C₂⁴	—	2	1	no	—
265	C₂⁴	—	2	2	no	—
266	C₂×Q₈	—	2	1	no	—
267	C₂×Q₈	—	2	4	no	—
268	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
269	C₂×D₄	—	2	4	no	—
270	C₂×D₄	—	2	4	no	—
271	C₂×D₄	—	2	4	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	8	no	—
275	C₂×D₄	—	4	8	no	—
276	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
277	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
280	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
281	SD₁₆	—	2	16	no	—
282	D₈	—	2	16	no	—
283	C₂×C₈	C₃×C₅×D₄	1	8	yes	complemented
284	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
285	C₂²⋊C₄	—	2	8	no	—
286	C₄²	C₃×C₅×D₄	1	2	yes	—
287	C₄²	C₂³×C₃×C₅	1	2	yes	—
288	C₃×C₅	C₂×#496	1	1	yes	characteristic, direct product factor, Hall
289	C₂²×C₃	—	4	2	no	—
290	C₂²×C₃	—	4	4	no	—
291	C₂²×C₃	—	4	8	no	—
292	C₂²×C₃	—	4	4	no	—
293	C₂²×C₃	—	8	8	no	—
294	C₂²×C₃	—	8	4	no	—
295	C₂²×C₃	C₅×#127	1	2	yes	—
296	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	4	yes	—
297	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
298	C₃×C₄	—	2	4	no	—
299	C₃×C₄	—	4	2	no	—
300	C₃×C₄	C₅×#127	1	2	yes	—
301	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
302	C₂×C₅	—	8	4	no	—
303	C₂×C₅	—	8	2	no	—
304	C₂×C₅	C₃×#496	1	4	yes	direct product factor
305	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
306	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	4	no	—
309	C₂³	—	4	2	no	—
310	C₂³	—	4	4	no	—
311	C₂³	—	4	8	no	—
312	C₂³	—	4	4	no	—
313	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
314	Q₈	—	2	4	no	—
315	Q₈	—	4	2	no	—
316	D₄	—	2	4	no	—
317	D₄	—	2	4	no	—
318	D₄	—	2	4	no	—
319	D₄	—	4	16	no	—
320	D₄	—	4	2	no	—
321	D₄	—	4	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
326	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
327	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
328	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
329	C₈	C₂×C₃×C₅×D₄	1	8	yes	complemented
330	C₂×C₃	—	8	4	no	—
331	C₂×C₃	—	8	2	no	—
332	C₂×C₃	C₅×#496	1	4	yes	direct product factor
333	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
334	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
335	C₅	C₂×C₃×#496	1	1	yes	characteristic, direct product factor, Sylow
336	C₂²	—	4	2	no	—
337	C₂²	—	4	4	no	—
338	C₂²	—	4	8	no	—
339	C₂²	—	4	4	no	—
340	C₂²	—	8	8	no	—
341	C₂²	—	8	4	no	—
342	C₂²	C₃×C₅×#127	1	2	yes	—
343	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	4	yes	—
344	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
345	C₄	—	2	4	no	—
346	C₄	—	4	2	no	—
347	C₄	C₃×C₅×#127	1	2	yes	—
348	C₄	C₂²×C₃×C₅×D₄	1	2	yes	—
349	C₃	C₂×C₅×#496	1	1	yes	characteristic, direct product factor, Sylow
350	C₂	—	8	4	no	—
351	C₂	—	8	2	no	—
352	C₂	C₃×C₅×#496	1	4	yes	direct product factor
353	C₂	C₂×C₃×C₅×#127	1	1	yes	characteristic
354	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×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
2. C₂²×C₃×C₅×D₈	C₂	semidirect
3. C₂×C₃×C₅×#127	C₂	semidirect
4. C₂×C₃×C₅×#124	C₂	semidirect
5. C₃×C₅×#496	C₂	direct (N × H)
6. C₂×C₃×C₅×#97	C₂	semidirect
7. C₂×C₅×#496	C₃	direct (N × H)
13. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
15. C₂×C₃×C₅×D₈	C₂²	semidirect
18. C₃×C₅×#127	C₂²	semidirect
20. C₃×C₅×#124	C₂²	semidirect
23. C₃×C₅×#97	C₂²	semidirect
24. C₂×C₃×#496	C₅	direct (N × H)
25. C₂²×C₅×SD₁₆	C₂×C₃	semidirect
26. C₂²×C₅×D₈	C₂×C₃	semidirect
27. C₂×C₅×#127	C₂×C₃	semidirect
28. C₂×C₅×#124	C₂×C₃	semidirect
29. C₅×#496	C₂×C₃	direct (N × H)
30. C₂×C₅×#97	C₂×C₃	semidirect
50. C₂×C₃×C₅×C₈	D₄	semidirect
55. C₂²×C₃×SD₁₆	C₂×C₅	semidirect
56. C₂²×C₃×D₈	C₂×C₅	semidirect
57. C₂×C₃×#127	C₂×C₅	semidirect
58. C₂×C₃×#124	C₂×C₅	semidirect
59. C₃×#496	C₂×C₅	direct (N × H)
60. C₂×C₃×#97	C₂×C₅	semidirect
66. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
68. C₂×C₅×D₈	C₂²×C₃	semidirect
71. C₅×#127	C₂²×C₃	semidirect
73. C₅×#124	C₂²×C₃	semidirect
76. C₅×#97	C₂²×C₃	semidirect
77. C₂×#496	C₃×C₅	direct (N × H)
100. C₃×C₅×C₈	C₂×D₄	semidirect
106. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
108. C₂×C₃×D₈	C₂²×C₅	semidirect
111. C₃×#127	C₂²×C₅	semidirect
113. C₃×#124	C₂²×C₅	semidirect
116. C₃×#97	C₂²×C₅	semidirect
136. C₂×C₅×C₈	C₃×D₄	semidirect
141. C₂²×SD₁₆	C₂×C₃×C₅	semidirect
142. C₂²×D₈	C₂×C₃×C₅	semidirect
143. C₂×#127	C₂×C₃×C₅	semidirect
144. C₂×#124	C₂×C₃×C₅	semidirect
145. #496	C₂×C₃×C₅	direct (N × H)
146. C₂×#97	C₂×C₃×C₅	semidirect
179. C₂×C₃×C₈	C₅×D₄	semidirect
206. C₅×C₈	C₂×C₃×D₄	semidirect
212. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
214. C₂×D₈	C₂²×C₃×C₅	semidirect
217. #127	C₂²×C₃×C₅	semidirect
219. #124	C₂²×C₃×C₅	semidirect
222. #97	C₂²×C₃×C₅	semidirect
225. C₂×C₃×C₅	#496	direct (N × H)
250. C₃×C₈	C₂×C₅×D₄	semidirect
283. C₂×C₈	C₃×C₅×D₄	semidirect
288. C₃×C₅	C₂×#496	direct (N × H)
304. C₂×C₅	C₃×#496	direct (N × H)
329. C₈	C₂×C₃×C₅×D₄	semidirect
332. C₂×C₃	C₅×#496	direct (N × H)
335. C₅	C₂×C₃×#496	direct (N × H)
349. C₃	C₂×C₅×#496	direct (N × H)
352. C₂	C₃×C₅×#496	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
C₂²×C₃×C₅×D₈	2
C₂×C₃×C₅×#127	2
C₂×C₃×C₅×#124	2
C₃×C₅×#496	2
C₂×C₃×C₅×#97	2
C₂×C₅×#496	3
C₂×C₃×#496	5

Subgroups — C2×C3×C5×#496 #14276182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#496 #14276182