Subgroups — C₃×#10602543 #14281862

Order 1920.

424 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×#529	C₂	1	1	yes	maximal, characteristic
2	C₃×#65214	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65214	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×Q₈⋊#168	C₂	1	2	yes	maximal, complemented
5	C₃×D₄⋊#168	C₂	1	2	yes	maximal, complemented
6	#10602543	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₅×#126	—	2	1	no	—
8	C₃×C₅×#125	C₄	1	1	yes	characteristic
9	C₃×C₅×#124	C₄	1	1	yes	characteristic
10	C₃×C₅×#123	—	2	1	no	—
11	C₃×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
12	C₃×C₅×#121	C₄	1	1	yes	characteristic
13	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₄×C₅×D₄	—	2	1	no	—
15	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₃×C₅×#117	—	2	1	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₃×C₂²⋊#168	—	2	1	no	—
19	C₃×C₂²⋊#168	—	2	1	no	—
20	C₃×C₄⋊#168	—	2	1	no	—
21	C₃×C₄⋊#168	C₂²	1	2	yes	—
22	C₃×C₄×#168	—	2	1	no	—
23	C₃×C₄×#168	C₂²	1	2	yes	—
24	C₃×#1482	—	5	1	no	maximal, Hall
25	C₅×#529	C₂×C₃	1	1	yes	characteristic
26	#65214	C₂×C₃	1	1	yes	characteristic, complemented
27	#65214	C₂×C₃	1	1	yes	characteristic, complemented
28	Q₈⋊#168	C₂×C₃	1	2	yes	complemented
29	D₄⋊#168	C₂×C₃	1	2	yes	complemented
30	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
31	C₂×C₃×C₅×D₄	—	2	1	no	—
32	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
37	C₃×C₅×C₄⋊C₄	—	2	1	no	—
38	C₃×C₅×C₄⋊C₄	—	2	1	no	—
39	C₃×C₅×C₄⋊C₄	—	2	1	no	—
40	C₃×C₅×C₄⋊C₄	—	2	1	no	—
41	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
42	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
43	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
44	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
45	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
46	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
48	C₃×C₄²×C₅	—	2	1	no	—
49	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
50	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
52	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₂×C₃×#168	—	2	2	no	—
54	C₂×C₃×#168	—	2	2	no	—
55	C₃×#529	D₅	1	1	yes	characteristic
56	C₃×#431	—	5	1	no	—
57	C₃×#431	—	5	1	no	—
58	C₃×Q₈⋊C₈	—	5	2	no	—
59	C₃×D₄⋊C₈	—	5	2	no	—
60	C₅×#126	—	2	1	no	—
61	C₅×#125	C₃×C₄	1	1	yes	characteristic
62	C₅×#124	C₃×C₄	1	1	yes	characteristic
63	C₅×#123	—	2	1	no	—
64	C₅×C₂²⋊Q₈	C₃×C₄	1	1	yes	characteristic
65	C₅×#121	C₃×C₄	1	1	yes	characteristic
66	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
67	C₄×C₅×D₄	—	2	1	no	—
68	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
69	C₅×#117	—	2	1	no	—
70	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
71	C₂²⋊#168	—	2	1	no	—
72	C₂²⋊#168	—	2	1	no	—
73	C₄⋊#168	—	2	1	no	—
74	C₄⋊#168	C₂²×C₃	1	2	yes	—
75	C₄×#168	—	2	1	no	—
76	C₄×#168	C₂²×C₃	1	2	yes	—
77	#1482	—	5	1	no	Sylow
78	C₂³×C₃×C₅	—	2	1	no	—
79	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
80	C₃×C₅×Q₈	—	2	2	no	—
81	C₃×C₅×D₄	—	2	2	no	—
82	C₃×C₅×D₄	—	4	2	no	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	1	no	—
86	C₂×C₃×C₄×C₅	—	2	1	no	—
87	C₂×C₃×C₄×C₅	—	2	1	no	—
88	C₂×C₃×C₄×C₅	—	4	1	no	—
89	C₂×C₃×C₄×C₅	—	4	2	no	—
90	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂²×C₄	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	C₃×#168	—	4	2	no	—
97	C₃×#168	—	4	2	no	—
98	C₃×#126	—	2	1	no	—
99	C₃×#125	Dic₅	1	1	yes	characteristic
100	C₃×#124	Dic₅	1	1	yes	characteristic
101	C₃×#123	—	2	1	no	—
102	C₃×C₂²⋊Q₈	Dic₅	1	1	yes	characteristic
103	C₃×#121	Dic₅	1	1	yes	characteristic
104	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
105	C₃×C₄×D₄	—	2	1	no	—
106	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
107	C₃×#117	—	2	1	no	—
108	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
109	C₃×C₄⋊C₈	—	5	2	no	—
110	C₃×C₄⋊C₈	—	10	1	no	—
111	C₃×C₂²⋊C₈	—	10	1	no	—
112	C₃×C₂²⋊C₈	—	10	1	no	—
113	C₃×C₄×C₈	—	5	2	no	—
114	C₃×C₄×C₈	—	10	1	no	—
115	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
116	C₂×C₅×D₄	—	2	1	no	—
117	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	—	2	1	no	—
119	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
122	C₅×C₄⋊C₄	—	2	1	no	—
123	C₅×C₄⋊C₄	—	2	1	no	—
124	C₅×C₄⋊C₄	—	2	1	no	—
125	C₅×C₄⋊C₄	—	2	1	no	—
126	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
127	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
128	C₅×C₂²⋊C₄	—	2	1	no	—
129	C₅×C₂²⋊C₄	—	2	1	no	—
130	C₅×C₂²⋊C₄	—	2	1	no	—
131	C₅×C₂²⋊C₄	—	2	1	no	—
132	C₅×C₂²⋊C₄	—	2	1	no	—
133	C₄²×C₅	—	2	1	no	—
134	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
135	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
136	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
137	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
138	C₂×#168	—	2	2	no	—
139	C₂×#168	—	2	2	no	—
140	#529	C₃×D₅	1	1	yes	characteristic
141	#431	—	5	1	no	—
142	#431	—	5	1	no	—
143	Q₈⋊C₈	—	5	2	no	—
144	D₄⋊C₈	—	5	2	no	—
145	C₂²×C₃×C₅	—	2	1	no	—
146	C₂²×C₃×C₅	—	2	1	no	—
147	C₂²×C₃×C₅	—	2	1	no	—
148	C₂²×C₃×C₅	—	4	1	no	—
149	C₂²×C₃×C₅	—	4	1	no	—
150	C₂²×C₃×C₅	—	4	1	no	—
151	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₃×C₄×C₅	—	2	1	no	—
153	C₃×C₄×C₅	—	2	1	no	—
154	C₃×C₄×C₅	—	2	1	no	—
155	C₃×C₄×C₅	—	2	1	no	—
156	C₃×C₄×C₅	—	4	1	no	—
157	C₃×C₄×C₅	—	4	1	no	—
158	C₃×C₄×C₅	—	4	1	no	—
159	C₃×C₄×C₅	#131	1	2	yes	—
160	C₃×C₄×C₅	#135	1	2	yes	—
161	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
162	C₂×C₃×D₄	—	2	1	no	—
163	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
164	C₂²×C₃×C₄	—	2	1	no	—
165	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
166	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
168	C₂×C₃×C₈	—	10	2	no	—
169	C₂×C₃×C₈	—	10	2	no	—
170	C₃×C₄⋊C₄	—	2	1	no	—
171	C₃×C₄⋊C₄	—	2	1	no	—
172	C₃×C₄⋊C₄	—	2	1	no	—
173	C₃×C₄⋊C₄	—	2	1	no	—
174	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
175	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
176	C₃×C₂²⋊C₄	—	2	1	no	—
177	C₃×C₂²⋊C₄	—	2	1	no	—
178	C₃×C₂²⋊C₄	—	2	1	no	—
179	C₃×C₂²⋊C₄	—	2	1	no	—
180	C₃×C₂²⋊C₄	—	2	1	no	—
181	C₃×C₄²	—	2	1	no	—
182	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
183	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
184	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
185	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
186	C₂³×C₅	—	2	1	no	—
187	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
188	C₅×Q₈	—	2	2	no	—
189	C₅×D₄	—	2	2	no	—
190	C₅×D₄	—	4	2	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	1	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	1	no	—
196	C₂×C₄×C₅	—	4	1	no	—
197	C₂×C₄×C₅	—	4	2	no	—
198	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
204	#168	—	4	2	no	—
205	#168	—	4	2	no	—
206	#126	—	2	1	no	—
207	#125	C₃×Dic₅	1	1	yes	characteristic
208	#124	C₃×Dic₅	1	1	yes	characteristic
209	#123	—	2	1	no	—
210	C₂²⋊Q₈	C₃×Dic₅	1	1	yes	characteristic
211	#121	C₃×Dic₅	1	1	yes	characteristic
212	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
213	C₄×D₄	—	2	1	no	—
214	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
215	#117	—	2	1	no	—
216	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
217	C₄⋊C₈	—	5	2	no	—
218	C₄⋊C₈	—	10	1	no	—
219	C₂²⋊C₈	—	10	1	no	—
220	C₂²⋊C₈	—	10	1	no	—
221	C₄×C₈	—	5	2	no	—
222	C₄×C₈	—	10	1	no	—
223	C₂×C₃×C₅	—	4	1	no	—
224	C₂×C₃×C₅	—	8	1	no	—
225	C₂×C₃×C₅	#408	1	1	yes	characteristic
226	C₂×C₃×C₅	#416	1	1	yes	characteristic
227	C₂×C₃×C₅	#421	1	1	yes	characteristic
228	C₂³×C₃	—	2	1	no	—
229	C₂³×C₃	C₂²⋊Dic₅	1	1	yes	characteristic
230	C₃×Q₈	—	2	2	no	—
231	C₃×D₄	—	2	2	no	—
232	C₃×D₄	—	4	2	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	4	1	no	—
239	C₂×C₃×C₄	—	4	2	no	—
240	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
246	C₃×C₈	—	20	2	no	—
247	C₃×C₈	—	20	2	no	—
248	C₂²×C₅	—	2	1	no	—
249	C₂²×C₅	—	2	1	no	—
250	C₂²×C₅	—	2	1	no	—
251	C₂²×C₅	—	4	1	no	—
252	C₂²×C₅	—	4	1	no	—
253	C₂²×C₅	—	4	1	no	—
254	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
255	C₄×C₅	—	2	1	no	—
256	C₄×C₅	—	2	1	no	—
257	C₄×C₅	—	2	1	no	—
258	C₄×C₅	—	2	1	no	—
259	C₄×C₅	—	4	1	no	—
260	C₄×C₅	—	4	1	no	—
261	C₄×C₅	—	4	1	no	—
262	C₄×C₅	C₃×#131	1	2	yes	—
263	C₄×C₅	C₃×#135	1	2	yes	—
264	C₂×Q₈	C₂×C₃×Dic₅	1	1	yes	characteristic
265	C₂×D₄	—	2	1	no	—
266	C₂×D₄	C₂×C₃×Dic₅	1	1	yes	characteristic
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
269	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
270	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
271	C₂×C₈	—	10	2	no	—
272	C₂×C₈	—	10	2	no	—
273	C₄⋊C₄	—	2	1	no	—
274	C₄⋊C₄	—	2	1	no	—
275	C₄⋊C₄	—	2	1	no	—
276	C₄⋊C₄	—	2	1	no	—
277	C₄⋊C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
278	C₄⋊C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
279	C₂²⋊C₄	—	2	1	no	—
280	C₂²⋊C₄	—	2	1	no	—
281	C₂²⋊C₄	—	2	1	no	—
282	C₂²⋊C₄	—	2	1	no	—
283	C₂²⋊C₄	—	2	1	no	—
284	C₄²	—	2	1	no	—
285	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
286	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
287	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
288	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
289	C₃×C₅	#1482	1	1	yes	characteristic, complemented, Hall
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	2	1	no	—
292	C₂²×C₃	—	2	1	no	—
293	C₂²×C₃	—	4	1	no	—
294	C₂²×C₃	—	4	1	no	—
295	C₂²×C₃	—	4	1	no	—
296	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
297	C₃×C₄	—	2	1	no	—
298	C₃×C₄	—	2	1	no	—
299	C₃×C₄	—	2	1	no	—
300	C₃×C₄	—	2	1	no	—
301	C₃×C₄	—	4	1	no	—
302	C₃×C₄	—	4	1	no	—
303	C₃×C₄	—	4	1	no	—
304	C₃×C₄	#4094	1	2	yes	—
305	C₃×C₄	#4096	1	2	yes	—
306	C₂×C₅	—	4	1	no	—
307	C₂×C₅	—	8	1	no	—
308	C₂×C₅	C₃×#408	1	1	yes	characteristic
309	C₂×C₅	C₃×#416	1	1	yes	characteristic
310	C₂×C₅	C₃×#421	1	1	yes	characteristic
311	C₂³	—	2	1	no	—
312	C₂³	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
313	Q₈	—	2	2	no	—
314	D₄	—	2	2	no	—
315	D₄	—	4	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
324	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
325	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
326	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
327	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
328	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
329	C₈	—	20	2	no	—
330	C₈	—	20	2	no	—
331	C₂×C₃	—	4	1	no	—
332	C₂×C₃	—	8	1	no	—
333	C₂×C₃	#65522	1	1	yes	characteristic
334	C₂×C₃	#65523	1	1	yes	characteristic
335	C₂×C₃	#65525	1	1	yes	characteristic
336	C₅	C₃×#1482	1	1	yes	characteristic, complemented, Sylow
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	4	1	no	—
341	C₂²	—	4	1	no	—
342	C₂²	—	4	1	no	—
343	C₂²	C₂×C₃×C₂²⋊Dic₅	1	1	yes	characteristic
344	C₄	—	2	1	no	—
345	C₄	—	2	1	no	—
346	C₄	—	2	1	no	—
347	C₄	—	2	1	no	—
348	C₄	—	4	1	no	—
349	C₄	—	4	1	no	—
350	C₄	—	4	1	no	—
351	C₄	C₃×#4094	1	2	yes	—
352	C₄	C₃×#4096	1	2	yes	—
353	C₃	#10602543	1	1	yes	characteristic, direct product factor, Sylow
354	C₂	—	4	1	no	—
355	C₂	—	8	1	no	—
356	C₂	C₃×#65522	1	1	yes	characteristic
357	C₂	C₃×#65523	1	1	yes	characteristic
358	C₂	C₃×#65525	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×C₂²⋊D₅
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₄²	C₂²×C₃×D₅
Fitting	C₃×C₅×#529	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₃×C₅×#121	C₄
cosocle	C₄²×C₅	C₂³×C₃
hypercenter	C₃×#529	D₅
hypocenter	C₅	C₃×#1482
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×#529

Complements

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

N	H ≅ G/N	type
2. C₃×#65214	C₂	semidirect
3. C₃×#65214	C₂	semidirect
4. C₃×Q₈⋊#168	C₂	semidirect
5. C₃×D₄⋊#168	C₂	semidirect
6. #10602543	C₃	direct (N × H)
26. #65214	C₂×C₃	semidirect
27. #65214	C₂×C₃	semidirect
28. Q₈⋊#168	C₂×C₃	semidirect
29. D₄⋊#168	C₂×C₃	semidirect
289. C₃×C₅	#1482	semidirect
336. C₅	C₃×#1482	semidirect
353. C₃	#10602543	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×#529	2
C₃×#65214	2
C₃×Q₈⋊#168	2
C₃×D₄⋊#168	2
#10602543	3
C₃×#1482	5

Subgroups — C3×#10602543 #14281862

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10602543 #14281862