Subgroups — C₃×#10599178 #14285016

Order 1920.

504 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×#66050	C₂	1	1	yes	maximal, characteristic
2	C₃×#65124	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#331	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64764	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64701	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64701	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599178	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×#711	C₄	1	2	yes	—
10	C₃×C₅×#127	C₂²	1	1	yes	characteristic
11	C₃×#4084	—	2	1	no	—
12	C₃×#4084	—	2	1	no	—
13	C₃×#4082	C₄	1	2	yes	—
14	C₃×D₄×Dic₅	—	2	1	no	—
15	C₃×D₄×Dic₅	—	2	1	no	—
16	C₂×C₃×C₈×D₅	—	2	1	no	—
17	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
18	C₃×#4015	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₃×#3952	—	2	1	no	—
22	C₃×#3947	—	2	1	no	—
23	C₃×#3946	—	2	1	no	—
24	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
25	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
26	C₃×#1551	—	5	1	no	maximal, Hall
27	#66050	C₂×C₃	1	1	yes	characteristic
28	#65124	C₂×C₃	1	1	yes	characteristic, complemented
29	D₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
30	C₅×#331	C₂×C₃	1	1	yes	characteristic, complemented
31	#64764	C₂×C₃	1	1	yes	characteristic, complemented
32	#64701	C₂×C₃	1	1	yes	characteristic, complemented
33	#64701	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×C₃×C₅×D₄	—	2	1	no	—
35	C₂×C₃×C₅×D₄	—	2	1	no	—
36	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
37	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
38	C₂²×C₃×Dic₅	—	2	2	no	—
39	C₃×#711	—	4	4	no	—
40	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
42	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
43	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₅×C₈	—	2	1	no	—
45	C₂×C₃×C₅×C₈	—	2	1	no	—
46	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
47	C₃×C₂²⋊Dic₅	—	2	2	no	—
48	C₃×C₂²⋊Dic₅	—	2	2	no	—
49	C₃×C₄⋊Dic₅	—	2	1	no	—
50	C₃×C₄⋊Dic₅	—	2	1	no	—
51	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
52	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
53	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
54	C₂×C₃×#168	—	2	1	no	—
55	C₂×C₃×#168	—	2	1	no	—
56	C₃×C₈×D₅	—	4	2	no	—
57	C₃×#532	—	5	1	no	—
58	C₃×#432	—	5	1	no	—
59	C₂×C₃×C₄⋊C₈	—	5	1	no	—
60	C₃×#333	—	5	1	no	—
61	C₃×#333	—	5	1	no	—
62	C₃×#331	—	5	1	no	—
63	C₃×#331	D₅	1	1	yes	characteristic, complemented
64	C₂×#711	C₃×C₄	1	2	yes	—
65	C₅×#127	C₂²×C₃	1	1	yes	characteristic
66	#4084	—	2	1	no	—
67	#4084	—	2	1	no	—
68	#4082	C₃×C₄	1	2	yes	—
69	D₄×Dic₅	—	2	1	no	—
70	D₄×Dic₅	—	2	1	no	—
71	C₂×C₈×D₅	—	2	1	no	—
72	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
73	#4015	C₂²×C₃	1	1	yes	characteristic
74	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
75	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
76	#3952	—	2	1	no	—
77	#3947	—	2	1	no	—
78	#3946	—	2	1	no	—
79	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
80	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
81	#1551	—	5	1	no	Sylow
82	C₂³×C₃×C₅	—	2	2	no	—
83	C₂²×C₃×D₅	C₂²⋊C₄	1	1	yes	characteristic
84	C₃×C₅×D₄	—	4	2	no	—
85	C₃×C₅×D₄	—	4	1	no	—
86	C₃×C₅×D₄	—	4	1	no	—
87	C₃×C₅×D₄	—	4	1	no	—
88	C₃×C₅×D₄	—	4	1	no	—
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₃×C₂²⋊D₅	—	4	4	no	—
93	C₂×C₃×Dic₅	—	2	2	no	—
94	C₂×C₃×Dic₅	—	4	4	no	—
95	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
98	C₃×C₄×D₅	—	2	2	no	—
99	C₃×C₄×D₅	—	2	1	no	—
100	C₃×C₄×D₅	—	2	1	no	—
101	C₃×C₄×D₅	—	2	1	no	—
102	C₃×C₄×D₅	—	2	1	no	—
103	C₃×Dic₁₀	—	4	2	no	—
104	C₃×C₅×C₈	—	4	1	no	—
105	C₃×C₅×C₈	—	4	1	no	—
106	C₃×#168	—	4	1	no	—
107	C₃×#168	—	4	1	no	—
108	C₂×C₃×#41	—	5	2	no	—
109	C₂²×C₃×C₈	—	10	1	no	—
110	C₃×C₄⋊Q₈	—	5	1	no	—
111	C₃×#127	C₂×D₅	1	1	yes	characteristic
112	C₃×#124	—	5	2	no	—
113	C₃×#121	—	10	1	no	—
114	C₃×#121	—	10	1	no	—
115	C₃×C₄×D₄	—	10	1	no	—
116	C₃×C₄×D₄	—	10	1	no	—
117	C₂×C₃×C₄²	—	5	1	no	—
118	C₃×C₄⋊C₈	—	5	1	no	—
119	C₃×C₄⋊C₈	—	5	1	no	—
120	C₃×C₄⋊C₈	—	10	1	no	—
121	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
122	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
123	C₃×C₂²⋊C₈	—	10	1	no	—
124	C₃×#97	—	10	1	no	—
125	C₂×C₅×D₄	—	2	1	no	—
126	C₂×C₅×D₄	—	2	1	no	—
127	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
128	C₂×C₂²⋊D₅	—	2	2	no	—
129	C₂²×Dic₅	—	2	2	no	—
130	#711	—	4	4	no	—
131	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
132	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
133	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
134	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	—	2	1	no	—
137	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
138	C₂²⋊Dic₅	—	2	2	no	—
139	C₂²⋊Dic₅	—	2	2	no	—
140	C₄⋊Dic₅	—	2	1	no	—
141	C₄⋊Dic₅	—	2	1	no	—
142	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
143	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
144	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
145	C₂×#168	—	2	1	no	—
146	C₂×#168	—	2	1	no	—
147	C₈×D₅	—	4	2	no	—
148	#532	—	5	1	no	—
149	#432	—	5	1	no	—
150	C₂×C₄⋊C₈	—	5	1	no	—
151	#333	—	5	1	no	—
152	#333	—	5	1	no	—
153	#331	—	5	1	no	—
154	#331	C₃×D₅	1	1	yes	characteristic, complemented
155	C₂²×C₃×C₅	—	4	2	no	—
156	C₂²×C₃×C₅	—	4	2	no	—
157	C₂²×C₃×C₅	—	4	2	no	—
158	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₃×D₅	—	2	1	no	—
160	C₂×C₃×D₅	—	2	1	no	—
161	C₂×C₃×D₅	#100	1	2	yes	—
162	C₃×C₄×C₅	—	2	1	no	—
163	C₃×C₄×C₅	#135	1	1	yes	characteristic
164	C₃×C₄×C₅	#135	1	1	yes	characteristic
165	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
166	C₃×C₄×C₅	#137	1	1	yes	characteristic
167	C₃×Dic₅	—	2	1	no	—
168	C₃×Dic₅	—	2	1	no	—
169	C₃×Dic₅	—	2	1	no	—
170	C₃×Dic₅	—	4	2	no	—
171	C₃×#41	—	20	4	no	—
172	C₂×C₃×Q₈	—	5	2	no	—
173	C₂×C₃×D₄	—	2	1	no	—
174	C₂×C₃×D₄	—	2	1	no	—
175	C₂×C₃×D₄	—	10	2	no	—
176	C₂×C₃×D₄	C₄×D₅	1	2	yes	—
177	C₂²×C₃×C₄	—	5	1	no	—
178	C₂²×C₃×C₄	—	5	1	no	—
179	C₂²×C₃×C₄	—	5	1	no	—
180	C₂²×C₃×C₄	—	10	2	no	—
181	C₂×C₃×C₈	—	2	1	no	—
182	C₂×C₃×C₈	—	2	1	no	—
183	C₂×C₃×C₈	—	10	1	no	—
184	C₂×C₃×C₈	—	10	1	no	—
185	C₂×C₃×C₈	—	20	2	no	—
186	C₃×C₄⋊C₄	—	10	1	no	—
187	C₃×C₄⋊C₄	—	10	1	no	—
188	C₃×C₂²⋊C₄	—	10	2	no	—
189	C₃×C₂²⋊C₄	—	10	2	no	—
190	C₃×C₄²	—	5	1	no	—
191	C₃×C₄²	—	5	1	no	—
192	C₃×C₄²	—	5	1	no	—
193	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
194	C₂³×C₅	—	2	2	no	—
195	C₂²×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
196	C₅×D₄	—	4	2	no	—
197	C₅×D₄	—	4	1	no	—
198	C₅×D₄	—	4	1	no	—
199	C₅×D₄	—	4	1	no	—
200	C₅×D₄	—	4	1	no	—
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	C₂²⋊D₅	—	4	4	no	—
205	C₂×Dic₅	—	2	2	no	—
206	C₂×Dic₅	—	4	4	no	—
207	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
210	C₄×D₅	—	2	2	no	—
211	C₄×D₅	—	2	1	no	—
212	C₄×D₅	—	2	1	no	—
213	C₄×D₅	—	2	1	no	—
214	C₄×D₅	—	2	1	no	—
215	Dic₁₀	—	4	2	no	—
216	C₅×C₈	—	4	1	no	—
217	C₅×C₈	—	4	1	no	—
218	#168	—	4	1	no	—
219	#168	—	4	1	no	—
220	C₂×#41	—	5	2	no	—
221	C₂²×C₈	—	10	1	no	—
222	C₄⋊Q₈	—	5	1	no	—
223	#127	C₂×C₃×D₅	1	1	yes	characteristic
224	#124	—	5	2	no	—
225	#121	—	10	1	no	—
226	#121	—	10	1	no	—
227	C₄×D₄	—	10	1	no	—
228	C₄×D₄	—	10	1	no	—
229	C₂×C₄²	—	5	1	no	—
230	C₄⋊C₈	—	5	1	no	—
231	C₄⋊C₈	—	5	1	no	—
232	C₄⋊C₈	—	10	1	no	—
233	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
234	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
235	C₂²⋊C₈	—	10	1	no	—
236	#97	—	10	1	no	—
237	C₂×C₃×C₅	—	8	2	no	—
238	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
239	C₂×C₃×C₅	#416	1	1	yes	characteristic
240	C₂×C₃×C₅	#417	1	1	yes	characteristic
241	C₃×D₅	—	2	2	no	—
242	C₂³×C₃	—	2	2	no	—
243	C₂³×C₃	—	5	1	no	—
244	C₃×Q₈	—	20	2	no	—
245	C₃×D₄	—	4	2	no	—
246	C₃×D₄	—	4	1	no	—
247	C₃×D₄	—	4	1	no	—
248	C₃×D₄	—	4	1	no	—
249	C₃×D₄	—	4	1	no	—
250	C₃×D₄	—	20	4	no	—
251	C₂×C₃×C₄	—	5	1	no	—
252	C₂×C₃×C₄	—	5	1	no	—
253	C₂×C₃×C₄	—	5	1	no	—
254	C₂×C₃×C₄	—	10	2	no	—
255	C₂×C₃×C₄	—	10	1	no	—
256	C₂×C₃×C₄	—	10	1	no	—
257	C₂×C₃×C₄	—	10	1	no	—
258	C₂×C₃×C₄	—	10	1	no	—
259	C₂×C₃×C₄	—	10	2	no	—
260	C₂×C₃×C₄	—	20	4	no	—
261	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
262	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
263	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
264	C₃×C₈	—	4	1	no	—
265	C₃×C₈	—	4	1	no	—
266	C₃×C₈	—	20	1	no	—
267	C₃×C₈	—	20	1	no	—
268	C₂²×C₅	—	4	2	no	—
269	C₂²×C₅	—	4	2	no	—
270	C₂²×C₅	—	4	2	no	—
271	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×D₅	—	2	1	no	—
273	C₂×D₅	—	2	1	no	—
274	C₂×D₅	C₃×#100	1	2	yes	—
275	C₄×C₅	—	2	1	no	—
276	C₄×C₅	C₃×#135	1	1	yes	characteristic
277	C₄×C₅	C₃×#135	1	1	yes	characteristic
278	C₄×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
279	C₄×C₅	C₃×#137	1	1	yes	characteristic
280	Dic₅	—	2	1	no	—
281	Dic₅	—	2	1	no	—
282	Dic₅	—	2	1	no	—
283	Dic₅	—	4	2	no	—
284	#41	—	20	4	no	—
285	C₂×Q₈	—	5	2	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	1	no	—
288	C₂×D₄	—	10	2	no	—
289	C₂×D₄	C₃×C₄×D₅	1	2	yes	—
290	C₂²×C₄	—	5	1	no	—
291	C₂²×C₄	—	5	1	no	—
292	C₂²×C₄	—	5	1	no	—
293	C₂²×C₄	—	10	2	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	10	1	no	—
297	C₂×C₈	—	10	1	no	—
298	C₂×C₈	—	20	2	no	—
299	C₄⋊C₄	—	10	1	no	—
300	C₄⋊C₄	—	10	1	no	—
301	C₂²⋊C₄	—	10	2	no	—
302	C₂²⋊C₄	—	10	2	no	—
303	C₄²	—	5	1	no	—
304	C₄²	—	5	1	no	—
305	C₄²	—	5	1	no	—
306	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
307	C₃×C₅	#1551	1	1	yes	characteristic, complemented, Hall
308	C₂²×C₃	—	4	2	no	—
309	C₂²×C₃	—	4	2	no	—
310	C₂²×C₃	—	4	2	no	—
311	C₂²×C₃	—	5	2	no	—
312	C₂²×C₃	—	10	1	no	—
313	C₂²×C₃	—	10	1	no	—
314	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	10	1	no	—
317	C₃×C₄	—	10	1	no	—
318	C₃×C₄	—	10	1	no	—
319	C₃×C₄	—	20	2	no	—
320	C₃×C₄	#4057	1	1	yes	characteristic
321	C₃×C₄	#4058	1	1	yes	characteristic
322	C₃×C₄	#4061	1	1	yes	characteristic
323	C₃×C₄	#4062	1	1	yes	characteristic
324	C₂×C₅	—	8	2	no	—
325	C₂×C₅	C₂×C₃×#100	1	1	yes	characteristic
326	C₂×C₅	C₃×#416	1	1	yes	characteristic
327	C₂×C₅	C₃×#417	1	1	yes	characteristic
328	D₅	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	5	1	no	—
331	Q₈	—	20	2	no	—
332	D₄	—	4	2	no	—
333	D₄	—	4	1	no	—
334	D₄	—	4	1	no	—
335	D₄	—	4	1	no	—
336	D₄	—	4	1	no	—
337	D₄	—	20	4	no	—
338	C₂×C₄	—	5	1	no	—
339	C₂×C₄	—	5	1	no	—
340	C₂×C₄	—	5	1	no	—
341	C₂×C₄	—	10	2	no	—
342	C₂×C₄	—	10	1	no	—
343	C₂×C₄	—	10	1	no	—
344	C₂×C₄	—	10	1	no	—
345	C₂×C₄	—	10	1	no	—
346	C₂×C₄	—	10	2	no	—
347	C₂×C₄	—	20	4	no	—
348	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
349	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
350	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
351	C₈	—	4	1	no	—
352	C₈	—	4	1	no	—
353	C₈	—	20	1	no	—
354	C₈	—	20	1	no	—
355	C₂×C₃	—	8	2	no	—
356	C₂×C₃	—	10	2	no	—
357	C₂×C₃	D₅×#100	1	1	yes	characteristic
358	C₂×C₃	#65060	1	1	yes	characteristic
359	C₂×C₃	#65061	1	1	yes	characteristic
360	C₅	C₃×#1551	1	1	yes	characteristic, complemented, Sylow
361	C₂²	—	4	2	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	5	2	no	—
365	C₂²	—	10	1	no	—
366	C₂²	—	10	1	no	—
367	C₂²	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
368	C₄	—	2	1	no	—
369	C₄	—	10	1	no	—
370	C₄	—	10	1	no	—
371	C₄	—	10	1	no	—
372	C₄	—	20	2	no	—
373	C₄	C₃×#4057	1	1	yes	characteristic
374	C₄	C₃×#4058	1	1	yes	characteristic
375	C₄	C₃×#4061	1	1	yes	characteristic
376	C₄	C₃×#4062	1	1	yes	characteristic
377	C₃	#10599178	1	1	yes	characteristic, direct product factor, Sylow
378	C₂	—	8	2	no	—
379	C₂	—	10	2	no	—
380	C₂	C₃×D₅×#100	1	1	yes	characteristic
381	C₂	C₃×#65060	1	1	yes	characteristic
382	C₂	C₃×#65061	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₅×C₂²⋊C₄
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₄²	C₂²×C₃×D₅
Fitting	C₃×C₅×#331	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₃×#66050	C₂
cosocle	C₄²×C₅	C₂³×C₃
hypercenter	C₃×#331	D₅
hypocenter	C₅	C₃×#1551
LCS	G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#331

Complements

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

N	H ≅ G/N	type
2. C₃×#65124	C₂	semidirect
3. C₃×D₅×C₄⋊C₈	C₂	semidirect
4. C₃×C₅×#331	C₂	semidirect
5. C₃×#64764	C₂	semidirect
6. C₃×#64701	C₂	semidirect
7. C₃×#64701	C₂	semidirect
8. #10599178	C₃	direct (N × H)
28. #65124	C₂×C₃	semidirect
29. D₅×C₄⋊C₈	C₂×C₃	semidirect
30. C₅×#331	C₂×C₃	semidirect
31. #64764	C₂×C₃	semidirect
32. #64701	C₂×C₃	semidirect
33. #64701	C₂×C₃	semidirect
63. C₃×#331	D₅	semidirect
154. #331	C₃×D₅	semidirect
307. C₃×C₅	#1551	semidirect
360. C₅	C₃×#1551	semidirect
377. C₃	#10599178	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×#66050	2
C₃×#65124	2
C₃×D₅×C₄⋊C₈	2
C₃×C₅×#331	2
C₃×#64764	2
C₃×#64701	2
#10599178	3
C₃×#1551	5

Subgroups — C3×#10599178 #14285016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10599178 #14285016