Subgroups — C₂×C₃×C₅×#486 #14276162

Order 1920.

1056 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	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#486	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×C₅×#102	C₂	1	4	yes	maximal, complemented
5	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#486	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×Q₈	—	2	1	no	—
8	C₂²×C₃×C₅×D₄	—	2	1	no	—
9	C₂²×C₃×C₅×D₄	—	2	1	no	—
10	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
12	C₃×C₅×C₄⋊Q₈	—	2	2	no	—
13	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	complemented
14	C₃×C₅×#127	—	2	2	no	—
15	C₃×C₅×#127	C₂²	1	4	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₃×C₅×#102	C₂²	1	16	yes	complemented
20	C₃×C₄×C₅×C₈	C₂²	1	4	yes	complemented
21	C₂×C₃×#486	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
23	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic
24	C₅×#486	C₂×C₃	1	8	yes	direct product factor
25	C₂×C₅×#102	C₂×C₃	1	4	yes	complemented
26	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂⁴×C₃×C₅	—	2	2	no	—
28	C₂×C₃×C₅×Q₈	—	2	4	no	—
29	C₂×C₃×C₅×Q₈	—	4	4	no	—
30	C₂×C₃×C₅×D₄	—	2	4	no	—
31	C₂×C₃×C₅×D₄	—	2	4	no	—
32	C₂×C₃×C₅×D₄	—	2	2	no	—
33	C₂×C₃×C₅×D₄	—	2	8	no	—
34	C₂×C₃×C₅×D₄	—	4	4	no	—
35	C₂×C₃×C₅×D₄	—	4	4	no	—
36	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
37	C₂²×C₃×C₄×C₅	—	2	2	no	—
38	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂×C₃×C₅×C₈	—	2	4	no	—
42	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
43	C₃×C₅×C₄⋊C₄	—	2	4	no	—
44	C₃×C₅×C₄⋊C₄	—	2	2	no	—
45	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
46	C₃×C₄²×C₅	D₄	1	2	yes	—
47	C₃×C₄²×C₅	C₂³	1	2	yes	—
48	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
49	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic
50	C₃×#486	C₂×C₅	1	8	yes	direct product factor
51	C₂×C₃×#102	C₂×C₅	1	4	yes	complemented
52	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic, complemented
53	C₂²×C₅×Q₈	—	2	1	no	—
54	C₂²×C₅×D₄	—	2	1	no	—
55	C₂²×C₅×D₄	—	2	1	no	—
56	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
57	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
58	C₅×C₄⋊Q₈	—	2	2	no	—
59	C₅×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
60	C₅×#127	—	2	2	no	—
61	C₅×#127	C₂²×C₃	1	4	yes	—
62	C₂×C₅×C₄⋊C₄	—	2	1	no	—
63	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
64	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
65	C₅×#102	C₂²×C₃	1	16	yes	complemented
66	C₄×C₅×C₈	C₂²×C₃	1	4	yes	complemented
67	C₂×#486	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
68	C₂³×C₃×C₅	—	2	4	no	—
69	C₂³×C₃×C₅	—	4	4	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	—	4	8	no	—
74	C₃×C₅×D₄	—	2	8	no	—
75	C₃×C₅×D₄	—	4	4	no	—
76	C₃×C₅×D₄	—	4	8	no	—
77	C₃×C₅×D₄	—	4	8	no	—
78	C₂×C₃×C₄×C₅	—	2	4	no	—
79	C₂×C₃×C₄×C₅	—	4	4	no	—
80	C₂×C₃×C₄×C₅	D₈	1	4	yes	—
81	C₂×C₃×C₄×C₅	SD₁₆	1	4	yes	—
82	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
83	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
84	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
85	C₂×C₃×C₄×C₅	#41	1	4	yes	—
86	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
87	C₃×C₅×C₈	—	2	4	no	—
88	C₂²×C₃×Q₈	—	2	1	no	—
89	C₂²×C₃×D₄	—	2	1	no	—
90	C₂²×C₃×D₄	—	2	1	no	—
91	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
92	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
93	C₃×C₄⋊Q₈	—	2	2	no	—
94	C₃×C₄⋊Q₈	C₂²×C₅	1	4	yes	complemented
95	C₃×#127	—	2	2	no	—
96	C₃×#127	C₂²×C₅	1	4	yes	—
97	C₂×C₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
99	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
100	C₃×#102	C₂²×C₅	1	16	yes	complemented
101	C₃×C₄×C₈	C₂²×C₅	1	4	yes	complemented
102	C₂⁴×C₅	—	2	2	no	—
103	C₂×C₅×Q₈	—	2	4	no	—
104	C₂×C₅×Q₈	—	4	4	no	—
105	C₂×C₅×D₄	—	2	2	no	—
106	C₂×C₅×D₄	—	2	4	no	—
107	C₂×C₅×D₄	—	2	4	no	—
108	C₂×C₅×D₄	—	2	8	no	—
109	C₂×C₅×D₄	—	4	4	no	—
110	C₂×C₅×D₄	—	4	4	no	—
111	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
116	C₂×C₅×C₈	—	2	4	no	—
117	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
118	C₅×C₄⋊C₄	—	2	4	no	—
119	C₅×C₄⋊C₄	—	2	2	no	—
120	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
121	C₄²×C₅	C₃×D₄	1	2	yes	—
122	C₄²×C₅	C₂³×C₃	1	2	yes	—
123	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
124	C₂×#127	C₂×C₃×C₅	1	1	yes	characteristic
125	#486	C₂×C₃×C₅	1	8	yes	direct product factor
126	C₂×#102	C₂×C₃×C₅	1	4	yes	complemented
127	C₂×C₄×C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
128	C₂²×C₃×C₅	—	4	4	no	—
129	C₂²×C₃×C₅	—	4	4	no	—
130	C₂²×C₃×C₅	—	4	4	no	—
131	C₂²×C₃×C₅	—	8	8	no	—
132	C₂²×C₃×C₅	#124	1	2	yes	—
133	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
134	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
135	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
136	C₃×C₄×C₅	—	4	4	no	—
137	C₃×C₄×C₅	#124	1	2	yes	—
138	C₃×C₄×C₅	C₂×D₈	1	4	yes	—
139	C₃×C₄×C₅	C₂×SD₁₆	1	4	yes	—
140	C₃×C₄×C₅	C₂×#41	1	2	yes	—
141	C₂⁴×C₃	—	2	2	no	—
142	C₂×C₃×Q₈	—	2	4	no	—
143	C₂×C₃×Q₈	—	4	4	no	—
144	C₂×C₃×D₄	—	2	2	no	—
145	C₂×C₃×D₄	—	2	4	no	—
146	C₂×C₃×D₄	—	2	4	no	—
147	C₂×C₃×D₄	—	2	8	no	—
148	C₂×C₃×D₄	—	4	4	no	—
149	C₂×C₃×D₄	—	4	4	no	—
150	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
151	C₂²×C₃×C₄	—	2	2	no	—
152	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
155	C₂×C₃×C₈	—	2	4	no	—
156	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
157	C₃×C₄⋊C₄	—	2	4	no	—
158	C₃×C₄⋊C₄	—	2	2	no	—
159	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
160	C₃×C₄²	C₅×D₄	1	2	yes	—
161	C₃×C₄²	C₂³×C₅	1	2	yes	—
162	C₂³×C₅	—	2	4	no	—
163	C₂³×C₅	—	4	4	no	—
164	C₂³×C₅	—	4	4	no	—
165	C₂³×C₅	—	4	4	no	—
166	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
167	C₅×Q₈	—	4	8	no	—
168	C₅×D₄	—	2	8	no	—
169	C₅×D₄	—	4	4	no	—
170	C₅×D₄	—	4	8	no	—
171	C₅×D₄	—	4	8	no	—
172	C₂×C₄×C₅	—	2	4	no	—
173	C₂×C₄×C₅	—	4	4	no	—
174	C₂×C₄×C₅	C₃×D₈	1	4	yes	—
175	C₂×C₄×C₅	C₃×SD₁₆	1	4	yes	—
176	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
177	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
178	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
179	C₂×C₄×C₅	C₃×#41	1	4	yes	—
180	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
181	C₅×C₈	—	2	4	no	—
182	C₂²×Q₈	—	2	1	no	—
183	C₂²×D₄	—	2	1	no	—
184	C₂²×D₄	—	2	1	no	—
185	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
186	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
187	C₄⋊Q₈	—	2	2	no	—
188	C₄⋊Q₈	C₂²×C₃×C₅	1	4	yes	complemented
189	#127	—	2	2	no	—
190	#127	C₂²×C₃×C₅	1	4	yes	—
191	C₂×C₄⋊C₄	—	2	1	no	—
192	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
193	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
194	#102	C₂²×C₃×C₅	1	16	yes	complemented
195	C₄×C₈	C₂²×C₃×C₅	1	4	yes	complemented
196	C₂×C₃×C₅	—	8	4	no	—
197	C₂×C₃×C₅	#486	1	4	yes	direct product factor
198	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
199	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
200	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
201	C₂³×C₃	—	2	4	no	—
202	C₂³×C₃	—	4	4	no	—
203	C₂³×C₃	—	4	4	no	—
204	C₂³×C₃	—	4	4	no	—
205	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
206	C₃×Q₈	—	4	8	no	—
207	C₃×D₄	—	2	8	no	—
208	C₃×D₄	—	4	4	no	—
209	C₃×D₄	—	4	8	no	—
210	C₃×D₄	—	4	8	no	—
211	C₂×C₃×C₄	—	2	4	no	—
212	C₂×C₃×C₄	—	4	4	no	—
213	C₂×C₃×C₄	C₅×D₈	1	4	yes	—
214	C₂×C₃×C₄	C₅×SD₁₆	1	4	yes	—
215	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
216	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
217	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
218	C₂×C₃×C₄	C₅×#41	1	4	yes	—
219	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
220	C₃×C₈	—	2	4	no	—
221	C₂²×C₅	—	4	4	no	—
222	C₂²×C₅	—	4	4	no	—
223	C₂²×C₅	—	4	4	no	—
224	C₂²×C₅	—	8	8	no	—
225	C₂²×C₅	C₃×#124	1	2	yes	—
226	C₂²×C₅	C₂×C₃×D₈	1	2	yes	—
227	C₂²×C₅	C₂×C₃×SD₁₆	1	2	yes	—
228	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
229	C₄×C₅	—	4	4	no	—
230	C₄×C₅	C₃×#124	1	2	yes	—
231	C₄×C₅	C₂×C₃×D₈	1	4	yes	—
232	C₄×C₅	C₂×C₃×SD₁₆	1	4	yes	—
233	C₄×C₅	C₂×C₃×#41	1	2	yes	—
234	C₂⁴	—	2	2	no	—
235	C₂×Q₈	—	2	4	no	—
236	C₂×Q₈	—	4	4	no	—
237	C₂×D₄	—	2	2	no	—
238	C₂×D₄	—	2	4	no	—
239	C₂×D₄	—	2	4	no	—
240	C₂×D₄	—	2	8	no	—
241	C₂×D₄	—	4	4	no	—
242	C₂×D₄	—	4	4	no	—
243	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
246	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
247	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
248	C₂×C₈	—	2	4	no	—
249	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
250	C₄⋊C₄	—	2	4	no	—
251	C₄⋊C₄	—	2	2	no	—
252	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
253	C₄²	C₃×C₅×D₄	1	2	yes	—
254	C₄²	C₂³×C₃×C₅	1	2	yes	—
255	C₃×C₅	C₂×#486	1	1	yes	characteristic, direct product factor, Hall
256	C₂²×C₃	—	4	4	no	—
257	C₂²×C₃	—	4	4	no	—
258	C₂²×C₃	—	4	4	no	—
259	C₂²×C₃	—	8	8	no	—
260	C₂²×C₃	C₅×#124	1	2	yes	—
261	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
262	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
263	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
264	C₃×C₄	—	4	4	no	—
265	C₃×C₄	C₅×#124	1	2	yes	—
266	C₃×C₄	C₂×C₅×D₈	1	4	yes	—
267	C₃×C₄	C₂×C₅×SD₁₆	1	4	yes	—
268	C₃×C₄	C₂×C₅×#41	1	2	yes	—
269	C₂×C₅	—	8	4	no	—
270	C₂×C₅	C₃×#486	1	4	yes	direct product factor
271	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
272	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
273	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
274	C₂³	—	2	4	no	—
275	C₂³	—	4	4	no	—
276	C₂³	—	4	4	no	—
277	C₂³	—	4	4	no	—
278	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
279	Q₈	—	4	8	no	—
280	D₄	—	2	8	no	—
281	D₄	—	4	4	no	—
282	D₄	—	4	8	no	—
283	D₄	—	4	8	no	—
284	C₂×C₄	—	2	4	no	—
285	C₂×C₄	—	4	4	no	—
286	C₂×C₄	C₃×C₅×D₈	1	4	yes	—
287	C₂×C₄	C₃×C₅×SD₁₆	1	4	yes	—
288	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
289	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
290	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
291	C₂×C₄	C₃×C₅×#41	1	4	yes	—
292	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
293	C₈	—	2	4	no	—
294	C₂×C₃	—	8	4	no	—
295	C₂×C₃	C₅×#486	1	4	yes	direct product factor
296	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
297	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
298	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
299	C₅	C₂×C₃×#486	1	1	yes	characteristic, direct product factor, Sylow
300	C₂²	—	4	4	no	—
301	C₂²	—	4	4	no	—
302	C₂²	—	4	4	no	—
303	C₂²	—	8	8	no	—
304	C₂²	C₃×C₅×#124	1	2	yes	—
305	C₂²	C₂×C₃×C₅×D₈	1	2	yes	—
306	C₂²	C₂×C₃×C₅×SD₁₆	1	2	yes	—
307	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
308	C₄	—	4	4	no	—
309	C₄	C₃×C₅×#124	1	2	yes	—
310	C₄	C₂×C₃×C₅×D₈	1	4	yes	—
311	C₄	C₂×C₃×C₅×SD₁₆	1	4	yes	—
312	C₄	C₂×C₃×C₅×#41	1	2	yes	—
313	C₃	C₂×C₅×#486	1	1	yes	characteristic, direct product factor, Sylow
314	C₂	—	8	4	no	—
315	C₂	C₃×C₅×#486	1	4	yes	direct product factor
316	C₂	C₂×C₃×C₅×#124	1	1	yes	characteristic
317	C₂	C₂²×C₃×C₅×D₈	1	1	yes	characteristic
318	C₂	C₂²×C₃×C₅×SD₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#127	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. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
3. C₃×C₅×#486	C₂	direct (N × H)
4. C₂×C₃×C₅×#102	C₂	semidirect
5. C₂×C₃×C₄×C₅×C₈	C₂	semidirect
6. C₂×C₅×#486	C₃	direct (N × H)
13. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
19. C₃×C₅×#102	C₂²	semidirect
20. C₃×C₄×C₅×C₈	C₂²	semidirect
21. C₂×C₃×#486	C₅	direct (N × H)
22. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
24. C₅×#486	C₂×C₃	direct (N × H)
25. C₂×C₅×#102	C₂×C₃	semidirect
26. C₂×C₄×C₅×C₈	C₂×C₃	semidirect
48. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
50. C₃×#486	C₂×C₅	direct (N × H)
51. C₂×C₃×#102	C₂×C₅	semidirect
52. C₂×C₃×C₄×C₈	C₂×C₅	semidirect
59. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
65. C₅×#102	C₂²×C₃	semidirect
66. C₄×C₅×C₈	C₂²×C₃	semidirect
67. C₂×#486	C₃×C₅	direct (N × H)
94. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
100. C₃×#102	C₂²×C₅	semidirect
101. C₃×C₄×C₈	C₂²×C₅	semidirect
123. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
125. #486	C₂×C₃×C₅	direct (N × H)
126. C₂×#102	C₂×C₃×C₅	semidirect
127. C₂×C₄×C₈	C₂×C₃×C₅	semidirect
188. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
194. #102	C₂²×C₃×C₅	semidirect
195. C₄×C₈	C₂²×C₃×C₅	semidirect
197. C₂×C₃×C₅	#486	direct (N × H)
255. C₃×C₅	C₂×#486	direct (N × H)
270. C₂×C₅	C₃×#486	direct (N × H)
295. C₂×C₃	C₅×#486	direct (N × H)
299. C₅	C₂×C₃×#486	direct (N × H)
313. C₃	C₂×C₅×#486	direct (N × H)
315. C₂	C₃×C₅×#486	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×C₅×#127	2
C₃×C₅×#486	2
C₂×C₃×C₅×#102	2
C₂×C₃×C₄×C₅×C₈	2
C₂×C₅×#486	3
C₂×C₃×#486	5

Subgroups — C2×C3×C5×#486 #14276162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#486 #14276162