Subgroups — C₂×C₃×C₅×#495 #14276180

Order 1920.

1184 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₅×SD₁₆	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₅×#124	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#495	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#495	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	2	yes	—
10	C₂×C₃×C₅×Q₁₆	—	2	4	no	—
11	C₂×C₃×C₅×Q₁₆	C₂²	1	4	yes	complemented
12	C₂×C₃×C₅×SD₁₆	—	2	8	no	—
13	C₂×C₃×C₅×SD₁₆	C₂²	1	8	yes	complemented
14	C₂×C₃×C₅×D₈	—	2	4	no	—
15	C₂×C₃×C₅×D₈	C₂²	1	4	yes	—
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×#124	—	2	4	no	—
19	C₃×C₅×#124	C₂²	1	8	yes	complemented
20	C₂×C₃×C₅×C₂²⋊C₄	—	2	4	no	—
21	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₃×C₄×C₅×C₈	C₂²	1	4	yes	complemented
23	C₂×C₃×#495	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂²×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂²×C₅×SD₁₆	C₂×C₃	1	2	yes	complemented
26	C₂²×C₅×D₈	C₂×C₃	1	1	yes	characteristic
27	C₂×C₅×#124	C₂×C₃	1	2	yes	complemented
28	C₅×#495	C₂×C₃	1	8	yes	direct product factor
29	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂⁴×C₃×C₅	—	2	2	no	—
31	C₂×C₃×C₅×Q₈	—	2	2	no	—
32	C₂×C₃×C₅×Q₈	—	2	4	no	—
33	C₂×C₃×C₅×Q₈	—	2	4	no	—
34	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
35	C₂×C₃×C₅×D₄	—	2	4	no	—
36	C₂×C₃×C₅×D₄	—	2	4	no	—
37	C₂×C₃×C₅×D₄	—	2	2	no	—
38	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
39	C₂²×C₃×C₄×C₅	—	2	2	no	—
40	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₃×C₅×Q₁₆	—	2	8	no	—
43	C₃×C₅×SD₁₆	—	2	16	no	—
44	C₃×C₅×D₈	—	2	8	no	—
45	C₂×C₃×C₅×C₈	D₄	1	4	yes	—
46	C₂×C₃×C₅×C₈	D₄	1	4	yes	—
47	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
48	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
49	C₃×C₅×C₂²⋊C₄	—	2	16	no	—
50	C₃×C₄²×C₅	D₄	1	2	yes	—
51	C₃×C₄²×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
53	C₂²×C₃×SD₁₆	C₂×C₅	1	2	yes	complemented
54	C₂²×C₃×D₈	C₂×C₅	1	1	yes	characteristic
55	C₂×C₃×#124	C₂×C₅	1	2	yes	complemented
56	C₃×#495	C₂×C₅	1	8	yes	direct product factor
57	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic, complemented
58	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
59	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
60	C₂×C₅×Q₁₆	—	2	4	no	—
61	C₂×C₅×Q₁₆	C₂²×C₃	1	4	yes	complemented
62	C₂×C₅×SD₁₆	—	2	8	no	—
63	C₂×C₅×SD₁₆	C₂²×C₃	1	8	yes	complemented
64	C₂×C₅×D₈	—	2	4	no	—
65	C₂×C₅×D₈	C₂²×C₃	1	4	yes	—
66	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
67	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
68	C₅×#124	—	2	4	no	—
69	C₅×#124	C₂²×C₃	1	8	yes	complemented
70	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
71	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
72	C₄×C₅×C₈	C₂²×C₃	1	4	yes	complemented
73	C₂×#495	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
74	C₂³×C₃×C₅	—	2	4	no	—
75	C₂³×C₃×C₅	—	4	4	no	—
76	C₂³×C₃×C₅	—	4	8	no	—
77	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
78	C₃×C₅×Q₈	—	2	4	no	—
79	C₃×C₅×Q₈	—	2	4	no	—
80	C₃×C₅×Q₈	—	4	4	no	—
81	C₃×C₅×D₄	—	2	4	no	—
82	C₃×C₅×D₄	—	2	4	no	—
83	C₃×C₅×D₄	—	4	4	no	—
84	C₂×C₃×C₄×C₅	—	2	4	no	—
85	C₂×C₃×C₄×C₅	—	2	4	no	—
86	C₂×C₃×C₄×C₅	—	4	4	no	—
87	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
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	C₂⁴	1	1	yes	characteristic
92	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
93	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
94	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
95	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
96	C₂×C₃×Q₁₆	—	2	4	no	—
97	C₂×C₃×Q₁₆	C₂²×C₅	1	4	yes	complemented
98	C₂×C₃×SD₁₆	—	2	8	no	—
99	C₂×C₃×SD₁₆	C₂²×C₅	1	8	yes	complemented
100	C₂×C₃×D₈	—	2	4	no	—
101	C₂×C₃×D₈	C₂²×C₅	1	4	yes	—
102	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
103	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
104	C₃×#124	—	2	4	no	—
105	C₃×#124	C₂²×C₅	1	8	yes	complemented
106	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
107	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
108	C₃×C₄×C₈	C₂²×C₅	1	4	yes	complemented
109	C₂⁴×C₅	—	2	2	no	—
110	C₂×C₅×Q₈	—	2	2	no	—
111	C₂×C₅×Q₈	—	2	4	no	—
112	C₂×C₅×Q₈	—	2	4	no	—
113	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
114	C₂×C₅×D₄	—	2	4	no	—
115	C₂×C₅×D₄	—	2	4	no	—
116	C₂×C₅×D₄	—	2	2	no	—
117	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
120	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
121	C₅×Q₁₆	—	2	8	no	—
122	C₅×SD₁₆	—	2	16	no	—
123	C₅×D₈	—	2	8	no	—
124	C₂×C₅×C₈	C₃×D₄	1	4	yes	—
125	C₂×C₅×C₈	C₃×D₄	1	4	yes	—
126	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
127	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
128	C₅×C₂²⋊C₄	—	2	16	no	—
129	C₄²×C₅	C₃×D₄	1	2	yes	—
130	C₄²×C₅	C₂³×C₃	1	2	yes	—
131	C₂²×Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
132	C₂²×SD₁₆	C₂×C₃×C₅	1	2	yes	complemented
133	C₂²×D₈	C₂×C₃×C₅	1	1	yes	characteristic
134	C₂×#124	C₂×C₃×C₅	1	2	yes	complemented
135	#495	C₂×C₃×C₅	1	8	yes	direct product factor
136	C₂×C₄×C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
137	C₂²×C₃×C₅	—	4	4	no	—
138	C₂²×C₃×C₅	—	4	8	no	—
139	C₂²×C₃×C₅	—	8	8	no	—
140	C₂²×C₃×C₅	#127	1	2	yes	—
141	C₂²×C₃×C₅	#135	1	4	yes	—
142	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
143	C₃×C₄×C₅	—	2	4	no	—
144	C₃×C₄×C₅	—	4	4	no	—
145	C₃×C₄×C₅	#127	1	2	yes	—
146	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
147	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
148	C₂⁴×C₃	—	2	2	no	—
149	C₂×C₃×Q₈	—	2	2	no	—
150	C₂×C₃×Q₈	—	2	4	no	—
151	C₂×C₃×Q₈	—	2	4	no	—
152	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
153	C₂×C₃×D₄	—	2	4	no	—
154	C₂×C₃×D₄	—	2	4	no	—
155	C₂×C₃×D₄	—	2	2	no	—
156	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
157	C₂²×C₃×C₄	—	2	2	no	—
158	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
159	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
160	C₃×Q₁₆	—	2	8	no	—
161	C₃×SD₁₆	—	2	16	no	—
162	C₃×D₈	—	2	8	no	—
163	C₂×C₃×C₈	C₅×D₄	1	4	yes	—
164	C₂×C₃×C₈	C₅×D₄	1	4	yes	—
165	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
166	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
167	C₃×C₂²⋊C₄	—	2	16	no	—
168	C₃×C₄²	C₅×D₄	1	2	yes	—
169	C₃×C₄²	C₂³×C₅	1	2	yes	—
170	C₂³×C₅	—	2	4	no	—
171	C₂³×C₅	—	4	4	no	—
172	C₂³×C₅	—	4	8	no	—
173	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
174	C₅×Q₈	—	2	4	no	—
175	C₅×Q₈	—	2	4	no	—
176	C₅×Q₈	—	4	4	no	—
177	C₅×D₄	—	2	4	no	—
178	C₅×D₄	—	2	4	no	—
179	C₅×D₄	—	4	4	no	—
180	C₂×C₄×C₅	—	2	4	no	—
181	C₂×C₄×C₅	—	2	4	no	—
182	C₂×C₄×C₅	—	4	4	no	—
183	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
184	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
186	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
187	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
188	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
189	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
190	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
191	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
192	C₂×Q₁₆	—	2	4	no	—
193	C₂×Q₁₆	C₂²×C₃×C₅	1	4	yes	complemented
194	C₂×SD₁₆	—	2	8	no	—
195	C₂×SD₁₆	C₂²×C₃×C₅	1	8	yes	complemented
196	C₂×D₈	—	2	4	no	—
197	C₂×D₈	C₂²×C₃×C₅	1	4	yes	—
198	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
199	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
200	#124	—	2	4	no	—
201	#124	C₂²×C₃×C₅	1	8	yes	complemented
202	C₂×C₂²⋊C₄	—	2	4	no	—
203	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
204	C₄×C₈	C₂²×C₃×C₅	1	4	yes	complemented
205	C₂×C₃×C₅	—	8	4	no	—
206	C₂×C₃×C₅	#495	1	4	yes	direct product factor
207	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
208	C₂×C₃×C₅	C₂×#135	1	2	yes	—
209	C₂³×C₃	—	2	4	no	—
210	C₂³×C₃	—	4	4	no	—
211	C₂³×C₃	—	4	8	no	—
212	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
213	C₃×Q₈	—	2	4	no	—
214	C₃×Q₈	—	2	4	no	—
215	C₃×Q₈	—	4	4	no	—
216	C₃×D₄	—	2	4	no	—
217	C₃×D₄	—	2	4	no	—
218	C₃×D₄	—	4	4	no	—
219	C₂×C₃×C₄	—	2	4	no	—
220	C₂×C₃×C₄	—	2	4	no	—
221	C₂×C₃×C₄	—	4	4	no	—
222	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
223	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
224	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
225	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
226	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
227	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
228	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
229	C₂²×C₅	—	4	8	no	—
230	C₂²×C₅	—	4	4	no	—
231	C₂²×C₅	—	8	8	no	—
232	C₂²×C₅	C₃×#127	1	2	yes	—
233	C₂²×C₅	C₃×#135	1	4	yes	—
234	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
235	C₄×C₅	—	2	4	no	—
236	C₄×C₅	—	4	4	no	—
237	C₄×C₅	C₃×#127	1	2	yes	—
238	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
239	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
240	C₂⁴	—	2	2	no	—
241	C₂×Q₈	—	2	2	no	—
242	C₂×Q₈	—	2	4	no	—
243	C₂×Q₈	—	2	4	no	—
244	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
245	C₂×D₄	—	2	4	no	—
246	C₂×D₄	—	2	4	no	—
247	C₂×D₄	—	2	2	no	—
248	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
251	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
252	Q₁₆	—	2	8	no	—
253	SD₁₆	—	2	16	no	—
254	D₈	—	2	8	no	—
255	C₂×C₈	C₃×C₅×D₄	1	4	yes	—
256	C₂×C₈	C₃×C₅×D₄	1	4	yes	—
257	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
258	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
259	C₂²⋊C₄	—	2	16	no	—
260	C₄²	C₃×C₅×D₄	1	2	yes	—
261	C₄²	C₂³×C₃×C₅	1	2	yes	—
262	C₃×C₅	C₂×#495	1	1	yes	characteristic, direct product factor, Hall
263	C₂²×C₃	—	4	4	no	—
264	C₂²×C₃	—	4	8	no	—
265	C₂²×C₃	—	8	8	no	—
266	C₂²×C₃	C₅×#127	1	2	yes	—
267	C₂²×C₃	C₅×#135	1	4	yes	—
268	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
269	C₃×C₄	—	2	4	no	—
270	C₃×C₄	—	4	4	no	—
271	C₃×C₄	C₅×#127	1	2	yes	—
272	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
273	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
274	C₂×C₅	—	8	4	no	—
275	C₂×C₅	C₃×#495	1	4	yes	direct product factor
276	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
277	C₂×C₅	C₂×C₃×#135	1	2	yes	—
278	C₂³	—	2	4	no	—
279	C₂³	—	4	4	no	—
280	C₂³	—	4	8	no	—
281	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
282	Q₈	—	2	4	no	—
283	Q₈	—	2	4	no	—
284	Q₈	—	4	4	no	—
285	D₄	—	2	4	no	—
286	D₄	—	2	4	no	—
287	D₄	—	4	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	4	4	no	—
291	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
292	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
293	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
294	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
295	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
296	C₈	C₂×C₃×C₅×D₄	1	4	yes	—
297	C₈	C₂×C₃×C₅×D₄	1	4	yes	—
298	C₂×C₃	—	8	4	no	—
299	C₂×C₃	C₅×#495	1	4	yes	direct product factor
300	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
301	C₂×C₃	C₂×C₅×#135	1	2	yes	—
302	C₅	C₂×C₃×#495	1	1	yes	characteristic, direct product factor, Sylow
303	C₂²	—	4	4	no	—
304	C₂²	—	4	8	no	—
305	C₂²	—	8	8	no	—
306	C₂²	C₃×C₅×#127	1	2	yes	—
307	C₂²	C₃×C₅×#135	1	4	yes	—
308	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
309	C₄	—	2	4	no	—
310	C₄	—	4	4	no	—
311	C₄	C₃×C₅×#127	1	2	yes	—
312	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
313	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
314	C₃	C₂×C₅×#495	1	1	yes	characteristic, direct product factor, Sylow
315	C₂	—	8	4	no	—
316	C₂	C₃×C₅×#495	1	4	yes	direct product factor
317	C₂	C₂×C₃×C₅×#127	1	1	yes	characteristic
318	C₂	C₂×C₃×C₅×#135	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂²×C₃×C₅×D₈	C₂
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×Q₁₆	C₂	semidirect
2. C₂²×C₃×C₅×SD₁₆	C₂	semidirect
4. C₂×C₃×C₅×#124	C₂	semidirect
5. C₃×C₅×#495	C₂	direct (N × H)
6. C₂×C₃×C₄×C₅×C₈	C₂	semidirect
7. C₂×C₅×#495	C₃	direct (N × H)
11. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
13. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
19. C₃×C₅×#124	C₂²	semidirect
22. C₃×C₄×C₅×C₈	C₂²	semidirect
23. C₂×C₃×#495	C₅	direct (N × H)
24. C₂²×C₅×Q₁₆	C₂×C₃	semidirect
25. C₂²×C₅×SD₁₆	C₂×C₃	semidirect
27. C₂×C₅×#124	C₂×C₃	semidirect
28. C₅×#495	C₂×C₃	direct (N × H)
29. C₂×C₄×C₅×C₈	C₂×C₃	semidirect
52. C₂²×C₃×Q₁₆	C₂×C₅	semidirect
53. C₂²×C₃×SD₁₆	C₂×C₅	semidirect
55. C₂×C₃×#124	C₂×C₅	semidirect
56. C₃×#495	C₂×C₅	direct (N × H)
57. C₂×C₃×C₄×C₈	C₂×C₅	semidirect
61. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
63. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
69. C₅×#124	C₂²×C₃	semidirect
72. C₄×C₅×C₈	C₂²×C₃	semidirect
73. C₂×#495	C₃×C₅	direct (N × H)
97. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
99. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
105. C₃×#124	C₂²×C₅	semidirect
108. C₃×C₄×C₈	C₂²×C₅	semidirect
131. C₂²×Q₁₆	C₂×C₃×C₅	semidirect
132. C₂²×SD₁₆	C₂×C₃×C₅	semidirect
134. C₂×#124	C₂×C₃×C₅	semidirect
135. #495	C₂×C₃×C₅	direct (N × H)
136. C₂×C₄×C₈	C₂×C₃×C₅	semidirect
193. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
195. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
201. #124	C₂²×C₃×C₅	semidirect
204. C₄×C₈	C₂²×C₃×C₅	semidirect
206. C₂×C₃×C₅	#495	direct (N × H)
262. C₃×C₅	C₂×#495	direct (N × H)
275. C₂×C₅	C₃×#495	direct (N × H)
299. C₂×C₃	C₅×#495	direct (N × H)
302. C₅	C₂×C₃×#495	direct (N × H)
314. C₃	C₂×C₅×#495	direct (N × H)
316. C₂	C₃×C₅×#495	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×Q₁₆	2
C₂²×C₃×C₅×SD₁₆	2
C₂²×C₃×C₅×D₈	2
C₂×C₃×C₅×#124	2
C₃×C₅×#495	2
C₂×C₃×C₄×C₅×C₈	2
C₂×C₅×#495	3
C₂×C₃×#495	5

Subgroups — C2×C3×C5×#495 #14276180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#495 #14276180