Subgroups — C₃×C₅×#3152 #14276186

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#137	C₂	1	4	yes	maximal, complemented
2	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#497	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#494	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#492	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#3152	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
10	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
11	C₃×C₅×#137	—	2	16	no	—
12	C₂×C₃×C₅×Q₁₆	C₂²	1	8	yes	—
13	C₂×C₃×C₅×SD₁₆	C₂²	1	8	yes	—
14	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
15	C₃×C₅×C₄⋊Q₈	—	2	2	no	—
16	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₃×C₅×#127	C₂²	1	1	yes	characteristic
20	C₃×C₅×#124	C₂²	1	2	yes	—
21	C₃×C₅×#121	—	2	2	no	—
22	C₃×C₄×C₅×D₄	—	2	2	no	—
23	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
24	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₃×C₅×#97	C₂²	1	2	yes	—
26	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
27	C₃×#3152	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂×C₅×#137	C₂×C₃	1	4	yes	complemented
29	C₅×#532	C₂×C₃	1	1	yes	characteristic
30	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
31	C₅×#497	C₂×C₃	1	4	yes	complemented
32	C₅×#494	C₂×C₃	1	2	yes	complemented
33	C₅×#492	C₂×C₃	1	2	yes	complemented
34	C₄×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
35	C₃×C₅×#41	—	2	8	no	—
36	C₂×C₃×C₅×Q₈	—	2	2	no	—
37	C₂×C₃×C₅×Q₈	—	2	8	no	—
38	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
39	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
40	C₂×C₃×C₅×D₄	—	2	2	no	—
41	C₂×C₃×C₅×D₄	—	2	2	no	—
42	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
43	C₂²×C₃×C₄×C₅	—	2	2	no	—
44	C₂²×C₃×C₄×C₅	—	2	2	no	—
45	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₃×C₅×Q₁₆	—	2	16	no	—
48	C₃×C₅×SD₁₆	—	2	16	no	—
49	C₃×C₅×M₁₆	D₄	1	8	yes	complemented
50	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
51	C₃×C₅×C₄⋊C₄	—	2	4	no	—
52	C₃×C₅×C₄⋊C₄	—	2	4	no	—
53	C₃×C₅×C₄⋊C₄	—	2	2	no	—
54	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
55	C₃×C₄²×C₅	D₄	1	2	yes	—
56	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
57	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₃×#137	C₂×C₅	1	4	yes	complemented
59	C₃×#532	C₂×C₅	1	1	yes	characteristic
60	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
61	C₃×#497	C₂×C₅	1	4	yes	complemented
62	C₃×#494	C₂×C₅	1	2	yes	complemented
63	C₃×#492	C₂×C₅	1	2	yes	complemented
64	C₃×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
66	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
67	C₅×#137	—	2	16	no	—
68	C₂×C₅×Q₁₆	C₂²×C₃	1	8	yes	—
69	C₂×C₅×SD₁₆	C₂²×C₃	1	8	yes	—
70	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
71	C₅×C₄⋊Q₈	—	2	2	no	—
72	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
73	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
74	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
75	C₅×#127	C₂²×C₃	1	1	yes	characteristic
76	C₅×#124	C₂²×C₃	1	2	yes	—
77	C₅×#121	—	2	2	no	—
78	C₄×C₅×D₄	—	2	2	no	—
79	C₂×C₅×C₄⋊C₄	—	2	2	no	—
80	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
81	C₅×#97	C₂²×C₃	1	2	yes	—
82	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
83	#3152	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
84	C₂³×C₃×C₅	—	2	2	no	—
85	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
86	C₃×C₅×Q₈	—	2	8	no	—
87	C₃×C₅×Q₈	—	2	4	no	—
88	C₃×C₅×Q₈	—	4	4	no	—
89	C₃×C₅×D₄	—	2	4	no	—
90	C₃×C₅×D₄	—	4	4	no	—
91	C₃×C₅×D₄	—	4	4	no	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	—	2	4	no	—
95	C₂×C₃×C₄×C₅	—	4	4	no	—
96	C₂×C₃×C₄×C₅	—	4	4	no	—
97	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
100	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
102	C₃×C₅×C₈	C₂×D₄	1	8	yes	—
103	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
104	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
105	C₃×#137	—	2	16	no	—
106	C₂×C₃×Q₁₆	C₂²×C₅	1	8	yes	—
107	C₂×C₃×SD₁₆	C₂²×C₅	1	8	yes	—
108	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
109	C₃×C₄⋊Q₈	—	2	2	no	—
110	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
111	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
112	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
113	C₃×#127	C₂²×C₅	1	1	yes	characteristic
114	C₃×#124	C₂²×C₅	1	2	yes	—
115	C₃×#121	—	2	2	no	—
116	C₃×C₄×D₄	—	2	2	no	—
117	C₂×C₃×C₄⋊C₄	—	2	2	no	—
118	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
119	C₃×#97	C₂²×C₅	1	2	yes	—
120	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
121	C₅×#41	—	2	8	no	—
122	C₂×C₅×Q₈	—	2	2	no	—
123	C₂×C₅×Q₈	—	2	8	no	—
124	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
125	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
126	C₂×C₅×D₄	—	2	2	no	—
127	C₂×C₅×D₄	—	2	2	no	—
128	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	—	2	2	no	—
131	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
132	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
133	C₅×Q₁₆	—	2	16	no	—
134	C₅×SD₁₆	—	2	16	no	—
135	C₅×M₁₆	C₃×D₄	1	8	yes	complemented
136	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
137	C₅×C₄⋊C₄	—	2	4	no	—
138	C₅×C₄⋊C₄	—	2	4	no	—
139	C₅×C₄⋊C₄	—	2	2	no	—
140	C₅×C₂²⋊C₄	—	2	4	no	—
141	C₄²×C₅	C₃×D₄	1	2	yes	—
142	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
143	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
144	C₂×#137	C₂×C₃×C₅	1	4	yes	complemented
145	#532	C₂×C₃×C₅	1	1	yes	characteristic
146	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
147	#497	C₂×C₃×C₅	1	4	yes	complemented
148	#494	C₂×C₃×C₅	1	2	yes	complemented
149	#492	C₂×C₃×C₅	1	2	yes	complemented
150	C₄×M₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
151	C₂²×C₃×C₅	—	2	2	no	—
152	C₂²×C₃×C₅	—	4	2	no	—
153	C₂²×C₃×C₅	—	4	4	no	—
154	C₂²×C₃×C₅	#127	1	2	yes	—
155	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
156	C₃×C₄×C₅	—	2	2	no	—
157	C₃×C₄×C₅	—	4	2	no	—
158	C₃×C₄×C₅	—	4	4	no	—
159	C₃×C₄×C₅	#127	1	2	yes	—
160	C₃×C₄×C₅	#137	1	4	yes	complemented
161	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
162	C₃×#41	—	2	8	no	—
163	C₂×C₃×Q₈	—	2	2	no	—
164	C₂×C₃×Q₈	—	2	8	no	—
165	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
166	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
167	C₂×C₃×D₄	—	2	2	no	—
168	C₂×C₃×D₄	—	2	2	no	—
169	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
170	C₂²×C₃×C₄	—	2	2	no	—
171	C₂²×C₃×C₄	—	2	2	no	—
172	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
173	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
174	C₃×Q₁₆	—	2	16	no	—
175	C₃×SD₁₆	—	2	16	no	—
176	C₃×M₁₆	C₅×D₄	1	8	yes	complemented
177	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
178	C₃×C₄⋊C₄	—	2	4	no	—
179	C₃×C₄⋊C₄	—	2	4	no	—
180	C₃×C₄⋊C₄	—	2	2	no	—
181	C₃×C₂²⋊C₄	—	2	4	no	—
182	C₃×C₄²	C₅×D₄	1	2	yes	—
183	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
184	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
185	C₂³×C₅	—	2	2	no	—
186	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
187	C₅×Q₈	—	2	8	no	—
188	C₅×Q₈	—	2	4	no	—
189	C₅×Q₈	—	4	4	no	—
190	C₅×D₄	—	2	4	no	—
191	C₅×D₄	—	4	4	no	—
192	C₅×D₄	—	4	4	no	—
193	C₂×C₄×C₅	—	2	4	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	4	no	—
196	C₂×C₄×C₅	—	4	4	no	—
197	C₂×C₄×C₅	—	4	4	no	—
198	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
199	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
200	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
201	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
202	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
203	C₅×C₈	C₂×C₃×D₄	1	8	yes	—
204	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
205	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
206	#137	—	2	16	no	—
207	C₂×Q₁₆	C₂²×C₃×C₅	1	8	yes	—
208	C₂×SD₁₆	C₂²×C₃×C₅	1	8	yes	—
209	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
210	C₄⋊Q₈	—	2	2	no	—
211	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
212	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
213	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
214	#127	C₂²×C₃×C₅	1	1	yes	characteristic
215	#124	C₂²×C₃×C₅	1	2	yes	—
216	#121	—	2	2	no	—
217	C₄×D₄	—	2	2	no	—
218	C₂×C₄⋊C₄	—	2	2	no	—
219	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
220	#97	C₂²×C₃×C₅	1	2	yes	—
221	C₄×C₈	C₂²×C₃×C₅	1	2	yes	—
222	C₂×C₃×C₅	—	2	2	no	—
223	C₂×C₃×C₅	—	8	2	no	—
224	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
225	C₂×C₃×C₅	C₂×#137	1	2	yes	—
226	C₂³×C₃	—	2	2	no	—
227	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
228	C₃×Q₈	—	2	8	no	—
229	C₃×Q₈	—	2	4	no	—
230	C₃×Q₈	—	4	4	no	—
231	C₃×D₄	—	2	4	no	—
232	C₃×D₄	—	4	4	no	—
233	C₃×D₄	—	4	4	no	—
234	C₂×C₃×C₄	—	2	4	no	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	2	4	no	—
237	C₂×C₃×C₄	—	4	4	no	—
238	C₂×C₃×C₄	—	4	4	no	—
239	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
240	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
242	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
243	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
244	C₃×C₈	C₂×C₅×D₄	1	8	yes	—
245	C₂²×C₅	—	2	2	no	—
246	C₂²×C₅	—	4	4	no	—
247	C₂²×C₅	—	4	2	no	—
248	C₂²×C₅	C₃×#127	1	2	yes	—
249	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
250	C₄×C₅	—	2	2	no	—
251	C₄×C₅	—	4	2	no	—
252	C₄×C₅	—	4	4	no	—
253	C₄×C₅	C₃×#127	1	2	yes	—
254	C₄×C₅	C₃×#137	1	4	yes	complemented
255	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
256	#41	—	2	8	no	—
257	C₂×Q₈	—	2	2	no	—
258	C₂×Q₈	—	2	8	no	—
259	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
260	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
267	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
268	Q₁₆	—	2	16	no	—
269	SD₁₆	—	2	16	no	—
270	M₁₆	C₃×C₅×D₄	1	8	yes	complemented
271	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
272	C₄⋊C₄	—	2	4	no	—
273	C₄⋊C₄	—	2	4	no	—
274	C₄⋊C₄	—	2	2	no	—
275	C₂²⋊C₄	—	2	4	no	—
276	C₄²	C₃×C₅×D₄	1	2	yes	—
277	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
278	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
279	C₃×C₅	#3152	1	1	yes	characteristic, direct product factor, Hall
280	C₂²×C₃	—	2	2	no	—
281	C₂²×C₃	—	4	2	no	—
282	C₂²×C₃	—	4	4	no	—
283	C₂²×C₃	C₅×#127	1	2	yes	—
284	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
285	C₃×C₄	—	2	2	no	—
286	C₃×C₄	—	4	2	no	—
287	C₃×C₄	—	4	4	no	—
288	C₃×C₄	C₅×#127	1	2	yes	—
289	C₃×C₄	C₅×#137	1	4	yes	complemented
290	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
291	C₂×C₅	—	2	2	no	—
292	C₂×C₅	—	8	2	no	—
293	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
294	C₂×C₅	C₂×C₃×#137	1	2	yes	—
295	C₂³	—	2	2	no	—
296	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
297	Q₈	—	2	8	no	—
298	Q₈	—	2	4	no	—
299	Q₈	—	4	4	no	—
300	D₄	—	2	4	no	—
301	D₄	—	4	4	no	—
302	D₄	—	4	4	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	4	4	no	—
307	C₂×C₄	—	4	4	no	—
308	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
309	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
310	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
311	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
312	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
313	C₈	C₂×C₃×C₅×D₄	1	8	yes	—
314	C₂×C₃	—	2	2	no	—
315	C₂×C₃	—	8	2	no	—
316	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
317	C₂×C₃	C₂×C₅×#137	1	2	yes	—
318	C₅	C₃×#3152	1	1	yes	characteristic, direct product factor, Sylow
319	C₂²	—	2	2	no	—
320	C₂²	—	4	2	no	—
321	C₂²	—	4	4	no	—
322	C₂²	C₃×C₅×#127	1	2	yes	—
323	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
324	C₄	—	2	2	no	—
325	C₄	—	4	2	no	—
326	C₄	—	4	4	no	—
327	C₄	C₃×C₅×#127	1	2	yes	—
328	C₄	C₃×C₅×#137	1	4	yes	complemented
329	C₄	C₂²×C₃×C₅×D₄	1	2	yes	—
330	C₃	C₅×#3152	1	1	yes	characteristic, direct product factor, Sylow
331	C₂	—	2	2	no	—
332	C₂	—	8	2	no	—
333	C₂	C₂×C₃×C₅×#127	1	1	yes	characteristic
334	C₂	C₂×C₃×C₅×#137	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₃×C₅×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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×#137	C₂	semidirect
3. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
4. C₃×C₅×#497	C₂	semidirect
5. C₃×C₅×#494	C₂	semidirect
6. C₃×C₅×#492	C₂	semidirect
7. C₃×C₄×C₅×M₁₆	C₂	semidirect
8. C₅×#3152	C₃	direct (N × H)
27. C₃×#3152	C₅	direct (N × H)
28. C₂×C₅×#137	C₂×C₃	semidirect
30. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
31. C₅×#497	C₂×C₃	semidirect
32. C₅×#494	C₂×C₃	semidirect
33. C₅×#492	C₂×C₃	semidirect
34. C₄×C₅×M₁₆	C₂×C₃	semidirect
49. C₃×C₅×M₁₆	D₄	semidirect
58. C₂×C₃×#137	C₂×C₅	semidirect
60. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
61. C₃×#497	C₂×C₅	semidirect
62. C₃×#494	C₂×C₅	semidirect
63. C₃×#492	C₂×C₅	semidirect
64. C₃×C₄×M₁₆	C₂×C₅	semidirect
83. #3152	C₃×C₅	direct (N × H)
135. C₅×M₁₆	C₃×D₄	semidirect
144. C₂×#137	C₂×C₃×C₅	semidirect
146. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
147. #497	C₂×C₃×C₅	semidirect
148. #494	C₂×C₃×C₅	semidirect
149. #492	C₂×C₃×C₅	semidirect
150. C₄×M₁₆	C₂×C₃×C₅	semidirect
160. C₃×C₄×C₅	#137	semidirect
176. C₃×M₁₆	C₅×D₄	semidirect
254. C₄×C₅	C₃×#137	semidirect
270. M₁₆	C₃×C₅×D₄	semidirect
279. C₃×C₅	#3152	direct (N × H)
289. C₃×C₄	C₅×#137	semidirect
318. C₅	C₃×#3152	direct (N × H)
328. C₄	C₃×C₅×#137	semidirect
330. C₃	C₅×#3152	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×#137	2
C₃×C₅×#532	2
C₂×C₃×C₅×C₄⋊Q₈	2
C₃×C₅×#497	2
C₃×C₅×#494	2
C₃×C₅×#492	2
C₃×C₄×C₅×M₁₆	2
C₅×#3152	3
C₃×#3152	5

Subgroups — C3×C5×#3152 #14276186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3152 #14276186