Subgroups — C₃×#10615730 #14418021

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#575	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4094	C₂	1	2	yes	maximal, complemented
3	C₃×#65525	C₂	1	2	yes	maximal, complemented
4	C₃×#65486	C₂	1	4	yes	maximal, complemented
5	C₃×#65485	C₂	1	4	yes	maximal, complemented
6	C₃×#65414	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65411	C₂	1	1	yes	maximal, characteristic, complemented
8	#10615730	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
10	C₃×C₅×#137	C₄	1	4	yes	complemented
11	C₃×C₅×AGL(1,ℤ/8)	C₄	1	4	yes	complemented
12	C₃×C₅×#135	C₂²	1	4	yes	—
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₃×#4094	—	2	2	no	—
15	C₃×#4094	—	2	2	no	—
16	C₃×#4094	C₂²	1	4	yes	complemented
17	C₃×#4094	C₂²	1	4	yes	complemented
18	C₃×#4072	C₂²	1	1	yes	characteristic
19	C₂×C₃×#681	—	2	2	no	—
20	C₂×C₃×#681	C₂²	1	2	yes	—
21	C₂²×C₃×#168	—	2	2	no	—
22	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
23	C₃×#3969	C₂²	1	8	yes	complemented
24	C₃×#3951	C₂²	1	4	yes	complemented
25	C₃×#3947	C₂²	1	2	yes	complemented
26	C₃×C₈×Dic₅	C₂²	1	2	yes	complemented
27	C₃×#2955	—	5	1	no	maximal, Hall
28	C₅×#575	C₂×C₃	1	1	yes	characteristic
29	C₂×#4094	C₂×C₃	1	2	yes	complemented
30	#65525	C₂×C₃	1	2	yes	complemented
31	#65486	C₂×C₃	1	4	yes	complemented
32	#65485	C₂×C₃	1	4	yes	complemented
33	#65414	C₂×C₃	1	1	yes	characteristic, complemented
34	#65411	C₂×C₃	1	1	yes	characteristic, complemented
35	C₃×C₅×#41	—	2	2	no	—
36	C₃×C₅×#41	—	2	2	no	—
37	C₃×C₅×#41	C₂×C₄	1	4	yes	—
38	C₃×C₅×#41	C₂³	1	4	yes	—
39	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
40	C₂×C₃×C₅×D₄	—	2	2	no	—
41	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
42	C₂²×C₃×C₄×C₅	—	2	2	no	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	—
45	C₃×C₅×SD₁₆	C₂×C₄	1	8	yes	—
46	C₃×C₅×D₈	C₂×C₄	1	4	yes	—
47	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	—
48	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
49	C₃×C₂²⋊Dic₅	—	2	1	no	—
50	C₃×C₄⋊Dic₅	—	2	1	no	—
51	C₃×C₄×Dic₅	C₂³	1	2	yes	—
52	C₃×#681	—	2	2	no	—
53	C₃×#681	—	2	4	no	—
54	C₃×#681	—	2	4	no	—
55	C₃×#681	C₂³	1	4	yes	—
56	C₂×C₃×#168	—	2	2	no	—
57	C₂×C₃×#168	—	2	4	no	—
58	C₂×C₃×#168	—	2	4	no	—
59	C₂×C₃×#168	D₄	1	2	yes	—
60	C₂×C₃×#168	D₄	1	2	yes	—
61	C₂×C₃×#168	C₂³	1	1	yes	characteristic
62	C₂×C₃×#168	C₂³	1	1	yes	characteristic
63	C₃×#575	D₅	1	1	yes	characteristic
64	C₂×C₃×#131	—	5	2	no	—
65	C₃×#444	—	5	4	no	—
66	C₃×#443	—	5	4	no	—
67	C₃×#430	—	5	1	no	—
68	C₃×#421	—	5	2	no	—
69	C₃×#405	—	5	1	no	—
70	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
71	C₅×#137	C₃×C₄	1	4	yes	complemented
72	C₅×AGL(1,ℤ/8)	C₃×C₄	1	4	yes	complemented
73	C₅×#135	C₂²×C₃	1	4	yes	—
74	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
75	#4094	—	2	2	no	—
76	#4094	—	2	2	no	—
77	#4094	C₂²×C₃	1	4	yes	complemented
78	#4094	C₂²×C₃	1	4	yes	complemented
79	#4072	C₂²×C₃	1	1	yes	characteristic
80	C₂×#681	—	2	2	no	—
81	C₂×#681	C₂²×C₃	1	2	yes	—
82	C₂²×#168	—	2	2	no	—
83	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
84	#3969	C₂²×C₃	1	8	yes	complemented
85	#3951	C₂²×C₃	1	4	yes	complemented
86	#3947	C₂²×C₃	1	2	yes	complemented
87	C₈×Dic₅	C₂²×C₃	1	2	yes	complemented
88	#2955	—	5	1	no	Sylow
89	C₂³×C₃×C₅	—	2	2	no	—
90	C₂³×C₃×C₅	#41	1	1	yes	characteristic
91	C₃×C₅×Q₈	—	2	2	no	—
92	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
93	C₃×C₅×D₄	—	2	4	no	—
94	C₃×C₅×D₄	—	2	4	no	—
95	C₃×C₅×D₄	—	2	2	no	—
96	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	—	2	4	no	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
104	C₂×C₃×Dic₅	—	2	2	no	—
105	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
106	C₃×#168	—	2	4	no	—
107	C₃×#168	C₂×D₄	1	1	yes	characteristic
108	C₃×#168	C₂×D₄	1	2	yes	—
109	C₃×#168	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×#41	C₂×D₅	1	2	yes	—
111	C₃×#137	Dic₅	1	4	yes	complemented
112	C₃×AGL(1,ℤ/8)	Dic₅	1	4	yes	complemented
113	C₃×#135	C₂×D₅	1	4	yes	—
114	C₃×#131	—	5	4	no	—
115	C₃×#131	—	5	4	no	—
116	C₃×#131	—	10	2	no	—
117	C₃×#131	—	10	2	no	—
118	C₂×C₃×M₁₆	—	5	2	no	—
119	C₂×C₃×M₁₆	—	10	2	no	—
120	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
121	C₂²×C₃×C₈	—	5	1	no	—
122	C₂²×C₃×C₈	—	10	2	no	—
123	C₃×#117	—	5	1	no	—
124	C₃×#108	—	5	4	no	—
125	C₃×#104	—	5	8	no	—
126	C₃×#97	—	5	2	no	—
127	C₃×C₄×C₈	—	5	2	no	—
128	C₅×#41	—	2	2	no	—
129	C₅×#41	—	2	2	no	—
130	C₅×#41	C₂×C₃×C₄	1	4	yes	—
131	C₅×#41	C₂³×C₃	1	4	yes	—
132	C₂×C₅×Q₈	C₂×C₃×C₄	1	2	yes	—
133	C₂×C₅×D₄	—	2	2	no	—
134	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
135	C₂²×C₄×C₅	—	2	2	no	—
136	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
137	C₅×Q₁₆	C₂×C₃×C₄	1	4	yes	—
138	C₅×SD₁₆	C₂×C₃×C₄	1	8	yes	—
139	C₅×D₈	C₂×C₃×C₄	1	4	yes	—
140	C₅×M₁₆	C₂×C₃×C₄	1	4	yes	—
141	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
142	C₂²⋊Dic₅	—	2	1	no	—
143	C₄⋊Dic₅	—	2	1	no	—
144	C₄×Dic₅	C₂³×C₃	1	2	yes	—
145	#681	—	2	2	no	—
146	#681	—	2	4	no	—
147	#681	—	2	4	no	—
148	#681	C₂³×C₃	1	4	yes	—
149	C₂×#168	—	2	2	no	—
150	C₂×#168	—	2	4	no	—
151	C₂×#168	—	2	4	no	—
152	C₂×#168	C₃×D₄	1	2	yes	—
153	C₂×#168	C₃×D₄	1	2	yes	—
154	C₂×#168	C₂³×C₃	1	1	yes	characteristic
155	C₂×#168	C₂³×C₃	1	1	yes	characteristic
156	#575	C₃×D₅	1	1	yes	characteristic
157	C₂×#131	—	5	2	no	—
158	#444	—	5	4	no	—
159	#443	—	5	4	no	—
160	#430	—	5	1	no	—
161	#421	—	5	2	no	—
162	#405	—	5	1	no	—
163	C₂²×C₃×C₅	—	2	4	no	—
164	C₂²×C₃×C₅	—	4	1	no	—
165	C₂²×C₃×C₅	—	4	4	no	—
166	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
167	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
168	C₃×C₄×C₅	—	2	4	no	—
169	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
170	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
171	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
172	C₃×Dic₅	—	4	2	no	—
173	C₃×#41	—	2	2	no	—
174	C₃×#41	—	2	2	no	—
175	C₃×#41	C₂×Dic₅	1	4	yes	—
176	C₃×#41	C₂²×D₅	1	4	yes	—
177	C₂×C₃×Q₈	C₂×Dic₅	1	2	yes	—
178	C₂×C₃×D₄	—	2	2	no	—
179	C₂×C₃×D₄	C₂×Dic₅	1	2	yes	—
180	C₂²×C₃×C₄	—	2	2	no	—
181	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
182	C₃×Q₁₆	C₂×Dic₅	1	4	yes	—
183	C₃×SD₁₆	C₂×Dic₅	1	8	yes	—
184	C₃×D₈	C₂×Dic₅	1	4	yes	—
185	C₃×M₁₆	—	5	4	no	—
186	C₃×M₁₆	—	10	4	no	—
187	C₃×M₁₆	—	10	4	no	—
188	C₃×M₁₆	—	10	2	no	—
189	C₃×M₁₆	C₂×Dic₅	1	4	yes	—
190	C₂×C₃×C₈	—	5	2	no	—
191	C₂×C₃×C₈	—	5	2	no	—
192	C₂×C₃×C₈	—	5	1	no	—
193	C₂×C₃×C₈	—	5	1	no	—
194	C₂×C₃×C₈	—	10	4	no	—
195	C₂×C₃×C₈	—	10	4	no	—
196	C₂×C₃×C₈	—	10	2	no	—
197	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
198	C₃×C₄⋊C₄	—	10	1	no	—
199	C₃×C₂²⋊C₄	—	10	1	no	—
200	C₃×C₄²	—	5	2	no	—
201	C₂³×C₅	—	2	2	no	—
202	C₂³×C₅	C₃×#41	1	1	yes	characteristic
203	C₅×Q₈	—	2	2	no	—
204	C₅×Q₈	C₂²×C₃×C₄	1	4	yes	—
205	C₅×D₄	—	2	4	no	—
206	C₅×D₄	—	2	4	no	—
207	C₅×D₄	—	2	2	no	—
208	C₅×D₄	C₂²×C₃×C₄	1	4	yes	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	4	no	—
211	C₂×C₄×C₅	—	2	4	no	—
212	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
213	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
214	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
216	C₂×Dic₅	—	2	2	no	—
217	C₅×C₈	C₂²×C₃×C₄	1	4	yes	—
218	#168	—	2	4	no	—
219	#168	C₂×C₃×D₄	1	1	yes	characteristic
220	#168	C₂×C₃×D₄	1	2	yes	—
221	#168	C₂×C₃×D₄	1	1	yes	characteristic
222	C₂×#41	C₂×C₃×D₅	1	2	yes	—
223	#137	C₃×Dic₅	1	4	yes	complemented
224	AGL(1,ℤ/8)	C₃×Dic₅	1	4	yes	complemented
225	#135	C₂×C₃×D₅	1	4	yes	—
226	#131	—	5	4	no	—
227	#131	—	5	4	no	—
228	#131	—	10	2	no	—
229	#131	—	10	2	no	—
230	C₂×M₁₆	—	5	2	no	—
231	C₂×M₁₆	—	10	2	no	—
232	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
233	C₂²×C₈	—	5	1	no	—
234	C₂²×C₈	—	10	2	no	—
235	#117	—	5	1	no	—
236	#108	—	5	4	no	—
237	#104	—	5	8	no	—
238	#97	—	5	2	no	—
239	C₄×C₈	—	5	2	no	—
240	C₂×C₃×C₅	—	2	1	no	—
241	C₂×C₃×C₅	—	2	2	no	—
242	C₂×C₃×C₅	—	4	4	no	—
243	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
244	C₂³×C₃	—	2	2	no	—
245	C₂³×C₃	#711	1	1	yes	characteristic
246	C₃×Q₈	—	2	2	no	—
247	C₃×Q₈	C₂²×Dic₅	1	4	yes	—
248	C₃×D₄	—	2	4	no	—
249	C₃×D₄	—	2	4	no	—
250	C₃×D₄	—	2	2	no	—
251	C₃×D₄	C₂²×Dic₅	1	4	yes	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	—	10	2	no	—
256	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
257	C₂×C₃×C₄	#711	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
259	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
260	C₃×C₈	—	5	1	no	—
261	C₃×C₈	—	5	2	no	—
262	C₃×C₈	—	5	1	no	—
263	C₃×C₈	—	10	4	no	—
264	C₃×C₈	C₂²×Dic₅	1	4	yes	—
265	C₂²×C₅	—	2	4	no	—
266	C₂²×C₅	—	4	1	no	—
267	C₂²×C₅	—	4	4	no	—
268	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
269	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
270	C₄×C₅	—	2	4	no	—
271	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
272	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
273	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
274	Dic₅	—	4	2	no	—
275	#41	—	2	2	no	—
276	#41	—	2	2	no	—
277	#41	C₂×C₃×Dic₅	1	4	yes	—
278	#41	C₂²×C₃×D₅	1	4	yes	—
279	C₂×Q₈	C₂×C₃×Dic₅	1	2	yes	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	C₂×C₃×Dic₅	1	2	yes	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
284	Q₁₆	C₂×C₃×Dic₅	1	4	yes	—
285	SD₁₆	C₂×C₃×Dic₅	1	8	yes	—
286	D₈	C₂×C₃×Dic₅	1	4	yes	—
287	M₁₆	—	5	4	no	—
288	M₁₆	—	10	4	no	—
289	M₁₆	—	10	4	no	—
290	M₁₆	—	10	2	no	—
291	M₁₆	C₂×C₃×Dic₅	1	4	yes	—
292	C₂×C₈	—	5	2	no	—
293	C₂×C₈	—	5	2	no	—
294	C₂×C₈	—	5	1	no	—
295	C₂×C₈	—	5	1	no	—
296	C₂×C₈	—	10	4	no	—
297	C₂×C₈	—	10	4	no	—
298	C₂×C₈	—	10	2	no	—
299	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
300	C₄⋊C₄	—	10	1	no	—
301	C₂²⋊C₄	—	10	1	no	—
302	C₄²	—	5	2	no	—
303	C₃×C₅	#2955	1	1	yes	characteristic, complemented, Hall
304	C₂²×C₃	—	2	4	no	—
305	C₂²×C₃	—	4	1	no	—
306	C₂²×C₃	—	4	4	no	—
307	C₂²×C₃	D₄×Dic₅	1	2	yes	—
308	C₂²×C₃	C₂×#711	1	1	yes	characteristic
309	C₃×C₄	—	2	4	no	—
310	C₃×C₄	—	20	2	no	—
311	C₃×C₄	D₄×Dic₅	1	2	yes	—
312	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
313	C₃×C₄	C₂³×Dic₅	1	1	yes	characteristic
314	C₂×C₅	—	2	1	no	—
315	C₂×C₅	—	2	2	no	—
316	C₂×C₅	—	4	4	no	—
317	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
318	C₂³	—	2	2	no	—
319	C₂³	C₃×#711	1	1	yes	characteristic
320	Q₈	—	2	2	no	—
321	Q₈	C₂²×C₃×Dic₅	1	4	yes	—
322	D₄	—	2	4	no	—
323	D₄	—	2	4	no	—
324	D₄	—	2	2	no	—
325	D₄	C₂²×C₃×Dic₅	1	4	yes	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	10	2	no	—
330	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
331	C₂×C₄	C₃×#711	1	1	yes	characteristic
332	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
333	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
334	C₈	—	5	1	no	—
335	C₈	—	5	2	no	—
336	C₈	—	5	1	no	—
337	C₈	—	10	4	no	—
338	C₈	C₂²×C₃×Dic₅	1	4	yes	—
339	C₂×C₃	—	2	1	no	—
340	C₂×C₃	—	2	2	no	—
341	C₂×C₃	—	4	4	no	—
342	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
343	C₅	C₃×#2955	1	1	yes	characteristic, complemented, Sylow
344	C₂²	—	2	4	no	—
345	C₂²	—	4	1	no	—
346	C₂²	—	4	4	no	—
347	C₂²	C₃×D₄×Dic₅	1	2	yes	—
348	C₂²	C₂×C₃×#711	1	1	yes	characteristic
349	C₄	—	2	4	no	—
350	C₄	—	20	2	no	—
351	C₄	C₃×D₄×Dic₅	1	2	yes	—
352	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
353	C₄	C₂³×C₃×Dic₅	1	1	yes	characteristic
354	C₃	#10615730	1	1	yes	characteristic, direct product factor, Sylow
355	C₂	—	2	1	no	—
356	C₂	—	2	2	no	—
357	C₂	—	4	4	no	—
358	C₂	C₂×C₃×D₄×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting, prime radical	C₃×C₅×#575	C₂
socle	C₂×C₃×C₅	C₂×C₄×D₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#575	D₅
hypocenter	C₅	C₃×#2955
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₃×#575

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4094	C₂	semidirect
3. C₃×#65525	C₂	semidirect
4. C₃×#65486	C₂	semidirect
5. C₃×#65485	C₂	semidirect
6. C₃×#65414	C₂	semidirect
7. C₃×#65411	C₂	semidirect
8. #10615730	C₃	direct (N × H)
10. C₃×C₅×#137	C₄	semidirect
11. C₃×C₅×AGL(1,ℤ/8)	C₄	semidirect
16. C₃×#4094	C₂²	semidirect
17. C₃×#4094	C₂²	semidirect
23. C₃×#3969	C₂²	semidirect
24. C₃×#3951	C₂²	semidirect
25. C₃×#3947	C₂²	semidirect
26. C₃×C₈×Dic₅	C₂²	semidirect
29. C₂×#4094	C₂×C₃	semidirect
30. #65525	C₂×C₃	semidirect
31. #65486	C₂×C₃	semidirect
32. #65485	C₂×C₃	semidirect
33. #65414	C₂×C₃	semidirect
34. #65411	C₂×C₃	semidirect
71. C₅×#137	C₃×C₄	semidirect
72. C₅×AGL(1,ℤ/8)	C₃×C₄	semidirect
77. #4094	C₂²×C₃	semidirect
78. #4094	C₂²×C₃	semidirect
84. #3969	C₂²×C₃	semidirect
85. #3951	C₂²×C₃	semidirect
86. #3947	C₂²×C₃	semidirect
87. C₈×Dic₅	C₂²×C₃	semidirect
111. C₃×#137	Dic₅	semidirect
112. C₃×AGL(1,ℤ/8)	Dic₅	semidirect
223. #137	C₃×Dic₅	semidirect
224. AGL(1,ℤ/8)	C₃×Dic₅	semidirect
303. C₃×C₅	#2955	semidirect
343. C₅	C₃×#2955	semidirect
354. C₃	#10615730	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×#575	2
C₂×C₃×#4094	2
C₃×#65525	2
C₃×#65486	2
C₃×#65485	2
C₃×#65414	2
C₃×#65411	2
#10615730	3
C₃×#2955	5

Subgroups — C3×#10615730 #14418021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615730 #14418021