Subgroups — C₃×#10602610 #14301379

Order 1920.

664 conjugacy classes of subgroups.

The subgroup lattice has 384 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	1	yes	maximal, characteristic
2	C₃×#66153	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65529	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65525	C₂	1	2	yes	maximal, complemented
5	C₃×#64743	C₂	1	2	yes	maximal, complemented
6	#10602610	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
9	C₃×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
10	C₃×C₅×#127	C₄	1	1	yes	characteristic, complemented
11	C₃×C₅×#124	C₄	1	1	yes	characteristic, complemented
12	C₃×C₅×#124	C₄	1	1	yes	characteristic, complemented
13	C₃×C₅×#121	—	2	2	no	—
14	C₃×C₄×C₅×D₄	—	2	2	no	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₃×#4094	—	2	4	no	—
17	C₃×#4072	C₂²	1	2	yes	—
18	C₂×C₃×#681	—	2	2	no	—
19	C₂×C₃×#681	C₂²	1	2	yes	—
20	C₃×#3969	—	2	4	no	—
21	C₃×#3966	—	2	2	no	—
22	C₃×#1884	—	5	1	no	maximal, Hall
23	C₅×#532	C₂×C₃	1	1	yes	characteristic
24	#66153	C₂×C₃	1	1	yes	characteristic, complemented
25	#65529	C₂×C₃	1	1	yes	characteristic, complemented
26	#65525	C₂×C₃	1	2	yes	complemented
27	#64743	C₂×C₃	1	2	yes	complemented
28	C₃×C₅×#41	—	2	2	no	—
29	C₃×C₅×#41	—	2	2	no	—
30	C₃×C₅×#41	—	2	2	no	—
31	C₃×C₅×#41	—	2	2	no	—
32	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
33	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
34	C₂×C₃×C₅×D₄	—	2	2	no	—
35	C₂×C₃×C₅×D₄	—	2	1	no	—
36	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
39	C₂²×C₃×C₄×C₅	—	2	1	no	—
40	C₂²×C₃×C₄×C₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₃×C₅×C₄⋊C₄	—	2	2	no	—
44	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
45	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
46	C₃×C₄²×C₅	—	2	1	no	—
47	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
48	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
49	C₃×C₂²⋊Dic₅	—	2	2	no	—
50	C₃×C₄⋊Dic₅	—	2	2	no	—
51	C₃×C₄×Dic₅	—	2	2	no	—
52	C₃×#681	—	2	4	no	—
53	C₃×#681	—	2	2	no	—
54	C₃×#681	D₄	1	4	yes	complemented
55	C₂×C₃×#168	—	2	4	no	—
56	C₂×C₃×#168	—	2	2	no	—
57	C₃×#568	—	5	1	no	—
58	C₃×#532	D₅	1	1	yes	characteristic
59	C₃×#421	—	5	2	no	—
60	C₃×#410	—	5	1	no	—
61	C₃×#339	—	5	2	no	—
62	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
64	C₅×C₄⋊Q₈	C₃×C₄	1	1	yes	characteristic, complemented
65	C₅×#127	C₃×C₄	1	1	yes	characteristic, complemented
66	C₅×#124	C₃×C₄	1	1	yes	characteristic, complemented
67	C₅×#124	C₃×C₄	1	1	yes	characteristic, complemented
68	C₅×#121	—	2	2	no	—
69	C₄×C₅×D₄	—	2	2	no	—
70	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
71	#4094	—	2	4	no	—
72	#4072	C₂²×C₃	1	2	yes	—
73	C₂×#681	—	2	2	no	—
74	C₂×#681	C₂²×C₃	1	2	yes	—
75	#3969	—	2	4	no	—
76	#3966	—	2	2	no	—
77	#1884	—	5	1	no	Sylow
78	C₂³×C₃×C₅	—	2	1	no	—
79	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
80	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
81	C₃×C₅×Q₈	—	2	2	no	—
82	C₃×C₅×Q₈	—	2	2	no	—
83	C₃×C₅×D₄	—	2	4	no	—
84	C₃×C₅×D₄	—	2	2	no	—
85	C₃×C₅×D₄	—	2	2	no	—
86	C₃×C₅×D₄	—	4	4	no	—
87	C₃×C₅×D₄	—	4	2	no	—
88	C₂×C₃×C₄×C₅	—	2	1	no	—
89	C₂×C₃×C₄×C₅	—	2	2	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	1	no	—
92	C₂×C₃×C₄×C₅	—	2	1	no	—
93	C₂×C₃×C₄×C₅	—	4	2	no	—
94	C₂×C₃×C₄×C₅	—	4	1	no	—
95	C₂×C₃×C₄×C₅	—	4	1	no	—
96	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	#41	1	2	yes	—
101	C₂×C₃×Dic₅	—	4	2	no	—
102	C₃×#168	—	2	4	no	—
103	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
104	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
105	C₃×#131	—	10	4	no	—
106	C₂×C₃×M₁₆	—	5	2	no	—
107	C₂×C₃×M₁₆	—	10	2	no	—
108	C₃×C₄⋊Q₈	Dic₅	1	1	yes	characteristic, complemented
109	C₃×#127	Dic₅	1	1	yes	characteristic, complemented
110	C₃×#124	Dic₅	1	1	yes	characteristic, complemented
111	C₃×#124	Dic₅	1	1	yes	characteristic, complemented
112	C₃×#121	—	2	2	no	—
113	C₃×C₄×D₄	—	2	2	no	—
114	C₃×#117	—	5	2	no	—
115	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
116	C₃×#104	—	10	4	no	—
117	C₃×#99	—	10	2	no	—
118	C₅×#41	—	2	2	no	—
119	C₅×#41	—	2	2	no	—
120	C₅×#41	—	2	2	no	—
121	C₅×#41	—	2	2	no	—
122	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
123	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
124	C₂×C₅×D₄	—	2	2	no	—
125	C₂×C₅×D₄	—	2	1	no	—
126	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
127	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
128	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
129	C₂²×C₄×C₅	—	2	1	no	—
130	C₂²×C₄×C₅	—	2	1	no	—
131	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
132	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
133	C₅×C₄⋊C₄	—	2	2	no	—
134	C₅×C₂²⋊C₄	—	2	2	no	—
135	C₅×C₂²⋊C₄	—	2	2	no	—
136	C₄²×C₅	—	2	1	no	—
137	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
138	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
139	C₂²⋊Dic₅	—	2	2	no	—
140	C₄⋊Dic₅	—	2	2	no	—
141	C₄×Dic₅	—	2	2	no	—
142	#681	—	2	4	no	—
143	#681	—	2	2	no	—
144	#681	C₃×D₄	1	4	yes	complemented
145	C₂×#168	—	2	4	no	—
146	C₂×#168	—	2	2	no	—
147	#568	—	5	1	no	—
148	#532	C₃×D₅	1	1	yes	characteristic
149	#421	—	5	2	no	—
150	#410	—	5	1	no	—
151	#339	—	5	2	no	—
152	C₂²×C₃×C₅	—	2	2	no	—
153	C₂²×C₃×C₅	—	4	1	no	—
154	C₂²×C₃×C₅	—	4	2	no	—
155	C₂²×C₃×C₅	—	4	2	no	—
156	C₂²×C₃×C₅	—	4	1	no	—
157	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₃×C₅	#121	1	2	yes	—
159	C₃×C₄×C₅	—	2	2	no	—
160	C₃×C₄×C₅	—	2	2	no	—
161	C₃×C₄×C₅	—	4	1	no	—
162	C₃×C₄×C₅	—	4	1	no	—
163	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
164	C₃×C₄×C₅	#120	1	1	yes	characteristic
165	C₃×C₄×C₅	#123	1	1	yes	characteristic
166	C₃×Dic₅	—	8	2	no	—
167	C₃×#41	—	2	2	no	—
168	C₃×#41	—	2	2	no	—
169	C₃×#41	—	2	2	no	—
170	C₃×#41	—	2	2	no	—
171	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
172	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
173	C₂×C₃×D₄	—	2	2	no	—
174	C₂×C₃×D₄	—	2	1	no	—
175	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
176	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
177	C₂×C₃×D₄	C₂²⋊D₅	1	2	yes	—
178	C₂²×C₃×C₄	—	2	1	no	—
179	C₂²×C₃×C₄	—	2	1	no	—
180	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
181	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
182	C₃×M₁₆	—	5	4	no	—
183	C₃×M₁₆	—	10	4	no	—
184	C₃×M₁₆	—	10	2	no	—
185	C₂×C₃×C₈	—	10	4	no	—
186	C₂×C₃×C₈	—	10	2	no	—
187	C₃×C₄⋊C₄	—	2	2	no	—
188	C₃×C₄⋊C₄	—	10	2	no	—
189	C₃×C₂²⋊C₄	—	2	2	no	—
190	C₃×C₂²⋊C₄	—	2	2	no	—
191	C₃×C₂²⋊C₄	—	10	2	no	—
192	C₃×C₄²	—	2	1	no	—
193	C₃×C₄²	—	10	2	no	—
194	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
195	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
196	C₂³×C₅	—	2	1	no	—
197	C₂³×C₅	C₃×C₂²⋊C₄	1	2	yes	—
198	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
199	C₅×Q₈	—	2	2	no	—
200	C₅×Q₈	—	2	2	no	—
201	C₅×D₄	—	2	4	no	—
202	C₅×D₄	—	2	2	no	—
203	C₅×D₄	—	2	2	no	—
204	C₅×D₄	—	4	4	no	—
205	C₅×D₄	—	4	2	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	4	2	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	4	1	no	—
214	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
215	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
217	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₃×#41	1	2	yes	—
219	C₂×Dic₅	—	4	2	no	—
220	#168	—	2	4	no	—
221	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
222	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
223	#131	—	10	4	no	—
224	C₂×M₁₆	—	5	2	no	—
225	C₂×M₁₆	—	10	2	no	—
226	C₄⋊Q₈	C₃×Dic₅	1	1	yes	characteristic, complemented
227	#127	C₃×Dic₅	1	1	yes	characteristic, complemented
228	#124	C₃×Dic₅	1	1	yes	characteristic, complemented
229	#124	C₃×Dic₅	1	1	yes	characteristic, complemented
230	#121	—	2	2	no	—
231	C₄×D₄	—	2	2	no	—
232	#117	—	5	2	no	—
233	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
234	#104	—	10	4	no	—
235	#99	—	10	2	no	—
236	C₂×C₃×C₅	—	2	2	no	—
237	C₂×C₃×C₅	—	2	1	no	—
238	C₂×C₃×C₅	—	4	2	no	—
239	C₂×C₃×C₅	—	8	1	no	—
240	C₂×C₃×C₅	#386	1	1	yes	characteristic
241	C₂³×C₃	—	2	1	no	—
242	C₂³×C₃	C₂²⋊Dic₅	1	2	yes	—
243	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
244	C₃×Q₈	—	2	2	no	—
245	C₃×Q₈	—	2	2	no	—
246	C₃×D₄	—	2	4	no	—
247	C₃×D₄	—	2	2	no	—
248	C₃×D₄	—	2	2	no	—
249	C₃×D₄	—	4	4	no	—
250	C₃×D₄	—	4	2	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	4	2	no	—
257	C₂×C₃×C₄	—	4	1	no	—
258	C₂×C₃×C₄	—	4	1	no	—
259	C₂×C₃×C₄	—	20	2	no	—
260	C₂×C₃×C₄	C₂²⋊Dic₅	1	2	yes	—
261	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
262	C₂×C₃×C₄	#711	1	2	yes	—
263	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
265	C₃×C₈	—	10	4	no	—
266	C₂²×C₅	—	2	2	no	—
267	C₂²×C₅	—	4	1	no	—
268	C₂²×C₅	—	4	2	no	—
269	C₂²×C₅	—	4	2	no	—
270	C₂²×C₅	—	4	1	no	—
271	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
272	C₂²×C₅	C₃×#121	1	2	yes	—
273	C₄×C₅	—	2	2	no	—
274	C₄×C₅	—	2	2	no	—
275	C₄×C₅	—	4	1	no	—
276	C₄×C₅	—	4	1	no	—
277	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
278	C₄×C₅	C₃×#120	1	1	yes	characteristic
279	C₄×C₅	C₃×#123	1	1	yes	characteristic
280	Dic₅	—	8	2	no	—
281	#41	—	2	2	no	—
282	#41	—	2	2	no	—
283	#41	—	2	2	no	—
284	#41	—	2	2	no	—
285	C₂×Q₈	C₂×C₃×Dic₅	1	1	yes	characteristic
286	C₂×Q₈	C₂×C₃×Dic₅	1	1	yes	characteristic
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	C₂×C₃×Dic₅	1	1	yes	characteristic
290	C₂×D₄	C₂×C₃×Dic₅	1	1	yes	characteristic
291	C₂×D₄	C₃×C₂²⋊D₅	1	2	yes	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
295	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
296	M₁₆	—	5	4	no	—
297	M₁₆	—	10	4	no	—
298	M₁₆	—	10	2	no	—
299	C₂×C₈	—	10	4	no	—
300	C₂×C₈	—	10	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	10	2	no	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	10	2	no	—
306	C₄²	—	2	1	no	—
307	C₄²	—	10	2	no	—
308	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
309	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
310	C₃×C₅	#1884	1	1	yes	characteristic, complemented, Hall
311	C₂²×C₃	—	2	2	no	—
312	C₂²×C₃	—	4	1	no	—
313	C₂²×C₃	—	4	2	no	—
314	C₂²×C₃	—	4	2	no	—
315	C₂²×C₃	—	4	1	no	—
316	C₂²×C₃	#4085	1	2	yes	—
317	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
318	C₃×C₄	—	2	2	no	—
319	C₃×C₄	—	2	2	no	—
320	C₃×C₄	—	4	1	no	—
321	C₃×C₄	—	4	1	no	—
322	C₃×C₄	—	40	2	no	—
323	C₃×C₄	D₄×Dic₅	1	2	yes	—
324	C₃×C₄	#4081	1	1	yes	characteristic
325	C₃×C₄	#4083	1	1	yes	characteristic
326	C₂×C₅	—	2	2	no	—
327	C₂×C₅	—	2	1	no	—
328	C₂×C₅	—	4	2	no	—
329	C₂×C₅	—	8	1	no	—
330	C₂×C₅	C₃×#386	1	1	yes	characteristic
331	C₂³	—	2	1	no	—
332	C₂³	C₃×C₂²⋊Dic₅	1	2	yes	—
333	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
334	Q₈	—	2	2	no	—
335	Q₈	—	2	2	no	—
336	D₄	—	2	4	no	—
337	D₄	—	2	2	no	—
338	D₄	—	2	2	no	—
339	D₄	—	4	4	no	—
340	D₄	—	4	2	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	20	2	no	—
350	C₂×C₄	C₃×C₂²⋊Dic₅	1	2	yes	—
351	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
352	C₂×C₄	C₃×#711	1	2	yes	—
353	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
354	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
355	C₈	—	10	4	no	—
356	C₂×C₃	—	2	1	no	—
357	C₂×C₃	—	2	2	no	—
358	C₂×C₃	—	4	2	no	—
359	C₂×C₃	—	8	1	no	—
360	C₂×C₃	#65509	1	1	yes	characteristic
361	C₅	C₃×#1884	1	1	yes	characteristic, complemented, Sylow
362	C₂²	—	2	2	no	—
363	C₂²	—	4	1	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	1	no	—
367	C₂²	C₃×#4085	1	2	yes	—
368	C₂²	C₂×C₃×C₂²⋊Dic₅	1	1	yes	characteristic
369	C₄	—	2	2	no	—
370	C₄	—	2	2	no	—
371	C₄	—	4	1	no	—
372	C₄	—	4	1	no	—
373	C₄	—	40	2	no	—
374	C₄	C₃×D₄×Dic₅	1	2	yes	—
375	C₄	C₃×#4081	1	1	yes	characteristic
376	C₄	C₃×#4083	1	1	yes	characteristic
377	C₃	#10602610	1	1	yes	characteristic, direct product factor, Sylow
378	C₂	—	2	1	no	—
379	C₂	—	2	2	no	—
380	C₂	—	4	2	no	—
381	C₂	—	8	1	no	—
382	C₂	C₃×#65509	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	#4083
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting, prime radical	C₃×C₅×#532	C₂
socle	C₂×C₃×C₅	#386
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₃×#532	D₅
hypocenter	C₅	C₃×#1884
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₃×#532

Complements

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

N	H ≅ G/N	type
2. C₃×#66153	C₂	semidirect
3. C₃×#65529	C₂	semidirect
4. C₃×#65525	C₂	semidirect
5. C₃×#64743	C₂	semidirect
6. #10602610	C₃	direct (N × H)
9. C₃×C₅×C₄⋊Q₈	C₄	semidirect
10. C₃×C₅×#127	C₄	semidirect
11. C₃×C₅×#124	C₄	semidirect
12. C₃×C₅×#124	C₄	semidirect
24. #66153	C₂×C₃	semidirect
25. #65529	C₂×C₃	semidirect
26. #65525	C₂×C₃	semidirect
27. #64743	C₂×C₃	semidirect
54. C₃×#681	D₄	semidirect
64. C₅×C₄⋊Q₈	C₃×C₄	semidirect
65. C₅×#127	C₃×C₄	semidirect
66. C₅×#124	C₃×C₄	semidirect
67. C₅×#124	C₃×C₄	semidirect
108. C₃×C₄⋊Q₈	Dic₅	semidirect
109. C₃×#127	Dic₅	semidirect
110. C₃×#124	Dic₅	semidirect
111. C₃×#124	Dic₅	semidirect
144. #681	C₃×D₄	semidirect
226. C₄⋊Q₈	C₃×Dic₅	semidirect
227. #127	C₃×Dic₅	semidirect
228. #124	C₃×Dic₅	semidirect
229. #124	C₃×Dic₅	semidirect
310. C₃×C₅	#1884	semidirect
361. C₅	C₃×#1884	semidirect
377. C₃	#10602610	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×#66153	2
C₃×#65529	2
C₃×#65525	2
C₃×#64743	2
#10602610	3
C₃×#1884	5

Subgroups — C3×#10602610 #14301379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10602610 #14301379