Subgroups — C₃×C₅×#3169 #14276203

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#532	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#493	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#486	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#466	C₂	1	4	yes	maximal, complemented
6	C₃×C₄×C₅×D₈	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#3169	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	—	2	2	no	—
10	C₂×C₃×C₅×D₈	C₂²	1	4	yes	—
11	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
12	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
13	C₃×C₅×#127	C₂²	1	2	yes	—
14	C₃×C₅×#124	—	2	2	no	—
15	C₃×C₅×#121	—	2	2	no	—
16	C₃×C₅×#121	C₂²	1	4	yes	—
17	C₃×C₄×C₅×D₄	—	2	2	no	—
18	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
19	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
20	C₃×C₅×#107	C₂²	1	4	yes	—
21	C₃×C₅×#102	C₂²	1	8	yes	—
22	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
25	C₃×#3169	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₅×#532	C₂×C₃	1	2	yes	complemented
27	C₅×#500	C₂×C₃	1	1	yes	characteristic, complemented
28	C₅×#493	C₂×C₃	1	1	yes	characteristic, complemented
29	C₅×#486	C₂×C₃	1	2	yes	complemented
30	C₅×#466	C₂×C₃	1	4	yes	complemented
31	C₄×C₅×D₈	C₂×C₃	1	4	yes	complemented
32	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic, complemented
33	C₃×C₅×#41	—	4	8	no	—
34	C₂×C₃×C₅×Q₈	—	2	2	no	—
35	C₂×C₃×C₅×D₄	—	2	4	no	—
36	C₂×C₃×C₅×D₄	—	2	2	no	—
37	C₂×C₃×C₅×D₄	—	2	2	no	—
38	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
39	C₂²×C₃×C₄×C₅	—	2	4	no	—
40	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₃×C₅×D₈	—	2	8	no	—
44	C₂×C₃×C₅×C₈	—	2	4	no	—
45	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
46	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
47	C₃×C₅×C₄⋊C₄	—	2	2	no	—
48	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
49	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
50	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
51	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
52	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
53	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
54	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₃×#532	C₂×C₅	1	2	yes	complemented
56	C₃×#500	C₂×C₅	1	1	yes	characteristic, complemented
57	C₃×#493	C₂×C₅	1	1	yes	characteristic, complemented
58	C₃×#486	C₂×C₅	1	2	yes	complemented
59	C₃×#466	C₂×C₅	1	4	yes	complemented
60	C₃×C₄×D₈	C₂×C₅	1	4	yes	complemented
61	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic, complemented
62	C₂×C₅×#41	—	2	2	no	—
63	C₂×C₅×D₈	C₂²×C₃	1	4	yes	—
64	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
65	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
66	C₅×#127	C₂²×C₃	1	2	yes	—
67	C₅×#124	—	2	2	no	—
68	C₅×#121	—	2	2	no	—
69	C₅×#121	C₂²×C₃	1	4	yes	—
70	C₄×C₅×D₄	—	2	2	no	—
71	C₄×C₅×D₄	C₂²×C₃	1	4	yes	—
72	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
73	C₅×#107	C₂²×C₃	1	4	yes	—
74	C₅×#102	C₂²×C₃	1	8	yes	—
75	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
76	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
77	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
78	#3169	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
79	C₂³×C₃×C₅	—	2	4	no	—
80	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
81	C₃×C₅×Q₈	—	4	4	no	—
82	C₃×C₅×D₄	—	2	8	no	—
83	C₃×C₅×D₄	—	4	8	no	—
84	C₃×C₅×D₄	—	4	4	no	—
85	C₃×C₅×D₄	—	4	4	no	—
86	C₂×C₃×C₄×C₅	—	2	2	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	—	2	4	no	—
89	C₂×C₃×C₄×C₅	—	4	8	no	—
90	C₂×C₃×C₄×C₅	D₈	1	4	yes	complemented
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
97	C₃×C₅×C₈	—	2	2	no	—
98	C₃×C₅×C₈	#41	1	4	yes	complemented
99	C₂×C₃×#41	—	2	2	no	—
100	C₂×C₃×D₈	C₂²×C₅	1	4	yes	—
101	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
102	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
103	C₃×#127	C₂²×C₅	1	2	yes	—
104	C₃×#124	—	2	2	no	—
105	C₃×#121	—	2	2	no	—
106	C₃×#121	C₂²×C₅	1	4	yes	—
107	C₃×C₄×D₄	—	2	2	no	—
108	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
109	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
110	C₃×#107	C₂²×C₅	1	4	yes	—
111	C₃×#102	C₂²×C₅	1	8	yes	—
112	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
113	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
114	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
115	C₅×#41	—	4	8	no	—
116	C₂×C₅×Q₈	—	2	2	no	—
117	C₂×C₅×D₄	—	2	4	no	—
118	C₂×C₅×D₄	—	2	2	no	—
119	C₂×C₅×D₄	—	2	2	no	—
120	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
121	C₂²×C₄×C₅	—	2	4	no	—
122	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
125	C₅×D₈	—	2	8	no	—
126	C₂×C₅×C₈	—	2	4	no	—
127	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
128	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
129	C₅×C₄⋊C₄	—	2	2	no	—
130	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
131	C₅×C₂²⋊C₄	—	2	4	no	—
132	C₅×C₂²⋊C₄	—	2	4	no	—
133	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
134	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
135	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
136	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
137	#532	C₂×C₃×C₅	1	2	yes	complemented
138	#500	C₂×C₃×C₅	1	1	yes	characteristic, complemented
139	#493	C₂×C₃×C₅	1	1	yes	characteristic, complemented
140	#486	C₂×C₃×C₅	1	2	yes	complemented
141	#466	C₂×C₃×C₅	1	4	yes	complemented
142	C₄×D₈	C₂×C₃×C₅	1	4	yes	complemented
143	C₂×C₄×C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
144	C₂²×C₃×C₅	—	2	1	no	—
145	C₂²×C₃×C₅	—	2	1	no	—
146	C₂²×C₃×C₅	—	4	4	no	—
147	C₂²×C₃×C₅	—	4	4	no	—
148	C₂²×C₃×C₅	—	4	4	no	—
149	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
150	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
151	C₃×C₄×C₅	—	2	1	no	—
152	C₃×C₄×C₅	—	2	1	no	—
153	C₃×C₄×C₅	—	4	4	no	—
154	C₃×C₄×C₅	C₂×D₈	1	2	yes	—
155	C₃×C₄×C₅	C₂×D₈	1	2	yes	—
156	C₃×C₄×C₅	#135	1	2	yes	—
157	C₃×C₄×C₅	C₂×#41	1	2	yes	—
158	C₃×#41	—	4	8	no	—
159	C₂×C₃×Q₈	—	2	2	no	—
160	C₂×C₃×D₄	—	2	4	no	—
161	C₂×C₃×D₄	—	2	2	no	—
162	C₂×C₃×D₄	—	2	2	no	—
163	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
164	C₂²×C₃×C₄	—	2	4	no	—
165	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
166	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
168	C₃×D₈	—	2	8	no	—
169	C₂×C₃×C₈	—	2	4	no	—
170	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
171	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
172	C₃×C₄⋊C₄	—	2	2	no	—
173	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
174	C₃×C₂²⋊C₄	—	2	4	no	—
175	C₃×C₂²⋊C₄	—	2	4	no	—
176	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
177	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
178	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
179	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
180	C₂³×C₅	—	2	4	no	—
181	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
182	C₅×Q₈	—	4	4	no	—
183	C₅×D₄	—	2	8	no	—
184	C₅×D₄	—	4	8	no	—
185	C₅×D₄	—	4	4	no	—
186	C₅×D₄	—	4	4	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	4	no	—
190	C₂×C₄×C₅	—	4	8	no	—
191	C₂×C₄×C₅	C₃×D₈	1	4	yes	complemented
192	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
198	C₅×C₈	—	2	2	no	—
199	C₅×C₈	C₃×#41	1	4	yes	complemented
200	C₂×#41	—	2	2	no	—
201	C₂×D₈	C₂²×C₃×C₅	1	4	yes	—
202	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
203	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
204	#127	C₂²×C₃×C₅	1	2	yes	—
205	#124	—	2	2	no	—
206	#121	—	2	2	no	—
207	#121	C₂²×C₃×C₅	1	4	yes	—
208	C₄×D₄	—	2	2	no	—
209	C₄×D₄	C₂²×C₃×C₅	1	4	yes	—
210	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
211	#107	C₂²×C₃×C₅	1	4	yes	—
212	#102	C₂²×C₃×C₅	1	8	yes	—
213	C₄×C₈	C₂²×C₃×C₅	1	2	yes	—
214	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
215	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
216	C₂×C₃×C₅	—	2	2	no	—
217	C₂×C₃×C₅	—	8	4	no	—
218	C₂×C₃×C₅	#532	1	1	yes	characteristic
219	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
220	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
221	C₂³×C₃	—	2	4	no	—
222	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
223	C₃×Q₈	—	4	4	no	—
224	C₃×D₄	—	2	8	no	—
225	C₃×D₄	—	4	8	no	—
226	C₃×D₄	—	4	4	no	—
227	C₃×D₄	—	4	4	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	2	2	no	—
230	C₂×C₃×C₄	—	2	4	no	—
231	C₂×C₃×C₄	—	4	8	no	—
232	C₂×C₃×C₄	C₅×D₈	1	4	yes	complemented
233	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
234	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
235	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
236	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
237	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
238	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
239	C₃×C₈	—	2	2	no	—
240	C₃×C₈	C₅×#41	1	4	yes	complemented
241	C₂²×C₅	—	2	1	no	—
242	C₂²×C₅	—	2	1	no	—
243	C₂²×C₅	—	4	4	no	—
244	C₂²×C₅	—	4	4	no	—
245	C₂²×C₅	—	4	4	no	—
246	C₂²×C₅	C₂×C₃×D₈	1	2	yes	—
247	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
248	C₄×C₅	—	2	1	no	—
249	C₄×C₅	—	2	1	no	—
250	C₄×C₅	—	4	4	no	—
251	C₄×C₅	C₂×C₃×D₈	1	2	yes	—
252	C₄×C₅	C₂×C₃×D₈	1	2	yes	—
253	C₄×C₅	C₃×#135	1	2	yes	—
254	C₄×C₅	C₂×C₃×#41	1	2	yes	—
255	#41	—	4	8	no	—
256	C₂×Q₈	—	2	2	no	—
257	C₂×D₄	—	2	4	no	—
258	C₂×D₄	—	2	2	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
263	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
264	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
265	D₈	—	2	8	no	—
266	C₂×C₈	—	2	4	no	—
267	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
268	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
271	C₂²⋊C₄	—	2	4	no	—
272	C₂²⋊C₄	—	2	4	no	—
273	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
274	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
275	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
276	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
277	C₃×C₅	#3169	1	1	yes	characteristic, direct product factor, Hall
278	C₂²×C₃	—	2	1	no	—
279	C₂²×C₃	—	2	1	no	—
280	C₂²×C₃	—	4	4	no	—
281	C₂²×C₃	—	4	4	no	—
282	C₂²×C₃	—	4	4	no	—
283	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
284	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
285	C₃×C₄	—	2	1	no	—
286	C₃×C₄	—	2	1	no	—
287	C₃×C₄	—	4	4	no	—
288	C₃×C₄	C₂×C₅×D₈	1	2	yes	—
289	C₃×C₄	C₂×C₅×D₈	1	2	yes	—
290	C₃×C₄	C₅×#135	1	2	yes	—
291	C₃×C₄	C₂×C₅×#41	1	2	yes	—
292	C₂×C₅	—	2	2	no	—
293	C₂×C₅	—	8	4	no	—
294	C₂×C₅	C₃×#532	1	1	yes	characteristic
295	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
296	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
297	C₂³	—	2	4	no	—
298	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
299	Q₈	—	4	4	no	—
300	D₄	—	2	8	no	—
301	D₄	—	4	8	no	—
302	D₄	—	4	4	no	—
303	D₄	—	4	4	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	4	8	no	—
308	C₂×C₄	C₃×C₅×D₈	1	4	yes	complemented
309	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
310	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
311	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
312	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
313	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
314	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
315	C₈	—	2	2	no	—
316	C₈	C₃×C₅×#41	1	4	yes	complemented
317	C₂×C₃	—	2	2	no	—
318	C₂×C₃	—	8	4	no	—
319	C₂×C₃	C₅×#532	1	1	yes	characteristic
320	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
321	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
322	C₅	C₃×#3169	1	1	yes	characteristic, direct product factor, Sylow
323	C₂²	—	2	1	no	—
324	C₂²	—	2	1	no	—
325	C₂²	—	4	4	no	—
326	C₂²	—	4	4	no	—
327	C₂²	—	4	4	no	—
328	C₂²	C₂×C₃×C₅×D₈	1	2	yes	—
329	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
330	C₄	—	2	1	no	—
331	C₄	—	2	1	no	—
332	C₄	—	4	4	no	—
333	C₄	C₂×C₃×C₅×D₈	1	2	yes	—
334	C₄	C₂×C₃×C₅×D₈	1	2	yes	—
335	C₄	C₃×C₅×#135	1	2	yes	—
336	C₄	C₂×C₃×C₅×#41	1	2	yes	—
337	C₃	C₅×#3169	1	1	yes	characteristic, direct product factor, Sylow
338	C₂	—	2	2	no	—
339	C₂	—	8	4	no	—
340	C₂	C₃×C₅×#532	1	1	yes	characteristic
341	C₂	C₂²×C₃×C₅×D₈	1	1	yes	characteristic
342	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
socle	C₂²×C₃×C₅	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#532	C₂	semidirect
2. C₃×C₅×#500	C₂	semidirect
3. C₃×C₅×#493	C₂	semidirect
4. C₃×C₅×#486	C₂	semidirect
5. C₃×C₅×#466	C₂	semidirect
6. C₃×C₄×C₅×D₈	C₂	semidirect
7. C₂×C₃×C₄×C₅×C₈	C₂	semidirect
8. C₅×#3169	C₃	direct (N × H)
25. C₃×#3169	C₅	direct (N × H)
26. C₅×#532	C₂×C₃	semidirect
27. C₅×#500	C₂×C₃	semidirect
28. C₅×#493	C₂×C₃	semidirect
29. C₅×#486	C₂×C₃	semidirect
30. C₅×#466	C₂×C₃	semidirect
31. C₄×C₅×D₈	C₂×C₃	semidirect
32. C₂×C₄×C₅×C₈	C₂×C₃	semidirect
55. C₃×#532	C₂×C₅	semidirect
56. C₃×#500	C₂×C₅	semidirect
57. C₃×#493	C₂×C₅	semidirect
58. C₃×#486	C₂×C₅	semidirect
59. C₃×#466	C₂×C₅	semidirect
60. C₃×C₄×D₈	C₂×C₅	semidirect
61. C₂×C₃×C₄×C₈	C₂×C₅	semidirect
78. #3169	C₃×C₅	direct (N × H)
90. C₂×C₃×C₄×C₅	D₈	semidirect
98. C₃×C₅×C₈	#41	semidirect
137. #532	C₂×C₃×C₅	semidirect
138. #500	C₂×C₃×C₅	semidirect
139. #493	C₂×C₃×C₅	semidirect
140. #486	C₂×C₃×C₅	semidirect
141. #466	C₂×C₃×C₅	semidirect
142. C₄×D₈	C₂×C₃×C₅	semidirect
143. C₂×C₄×C₈	C₂×C₃×C₅	semidirect
191. C₂×C₄×C₅	C₃×D₈	semidirect
199. C₅×C₈	C₃×#41	semidirect
232. C₂×C₃×C₄	C₅×D₈	semidirect
240. C₃×C₈	C₅×#41	semidirect
277. C₃×C₅	#3169	direct (N × H)
308. C₂×C₄	C₃×C₅×D₈	semidirect
316. C₈	C₃×C₅×#41	semidirect
322. C₅	C₃×#3169	direct (N × H)
337. C₃	C₅×#3169	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#532	2
C₃×C₅×#500	2
C₃×C₅×#493	2
C₃×C₅×#486	2
C₃×C₅×#466	2
C₃×C₄×C₅×D₈	2
C₂×C₃×C₄×C₅×C₈	2
C₅×#3169	3
C₃×#3169	5

Subgroups — C3×C5×#3169 #14276203

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3169 #14276203