Subgroups — C₃×#10602507 #14301712

Order 1920.

684 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#525	C₂	1	1	yes	maximal, characteristic
2	C₃×#66153	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65526	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65496	C₂	1	2	yes	maximal, complemented
5	C₃×#64753	C₂	1	2	yes	maximal, complemented
6	#10602507	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₃×C₅×#123	C₄	1	2	yes	—
10	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
11	C₃×C₅×#121	—	2	1	no	—
12	C₃×C₅×#120	C₄	1	2	yes	—
13	C₃×C₄×C₅×D₄	—	2	2	no	—
14	C₃×C₅×#117	C₂²	1	1	yes	characteristic
15	C₃×#4094	—	2	4	no	—
16	C₂×C₃×#681	—	2	2	no	—
17	C₂×C₃×#681	C₂²	1	2	yes	—
18	C₂×C₃×#681	C₂²	1	2	yes	—
19	C₃×#3968	—	2	1	no	—
20	C₃×#3965	—	2	1	no	—
21	C₃×C₂²⋊#168	—	2	4	no	—
22	C₃×#1891	—	5	1	no	maximal, Hall
23	C₅×#525	C₂×C₃	1	1	yes	characteristic
24	#66153	C₂×C₃	1	1	yes	characteristic, complemented
25	#65526	C₂×C₃	1	1	yes	characteristic, complemented
26	#65496	C₂×C₃	1	2	yes	complemented
27	#64753	C₂×C₃	1	2	yes	complemented
28	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
29	C₃×C₅×#41	—	2	2	no	—
30	C₃×C₅×#41	—	2	2	no	—
31	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
32	C₂×C₃×C₅×D₄	—	2	2	no	—
33	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
34	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	—	2	2	no	—
36	C₂²×C₃×C₄×C₅	—	2	1	no	—
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	—	2	2	no	—
39	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₃×C₅×C₄⋊C₄	—	2	2	no	—
43	C₃×C₅×C₄⋊C₄	—	2	1	no	—
44	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
45	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
46	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
47	C₃×C₄²×C₅	—	2	1	no	—
48	C₃×#681	—	2	4	no	—
49	C₃×#681	—	2	2	no	—
50	C₃×#681	—	2	2	no	—
51	C₃×#681	—	2	2	no	—
52	C₃×#681	—	2	2	no	—
53	C₂×C₃×#168	—	2	4	no	—
54	C₂×C₃×#168	—	2	2	no	—
55	C₂×C₃×#168	D₄	1	4	yes	complemented
56	C₃×#568	—	5	1	no	—
57	C₃×#525	D₅	1	1	yes	characteristic
58	C₃×#413	—	5	1	no	—
59	C₃×#407	—	5	2	no	—
60	C₃×#344	—	5	2	no	—
61	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
62	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
63	C₅×#123	C₃×C₄	1	2	yes	—
64	C₅×C₂²⋊Q₈	—	2	1	no	—
65	C₅×#121	—	2	1	no	—
66	C₅×#120	C₃×C₄	1	2	yes	—
67	C₄×C₅×D₄	—	2	2	no	—
68	C₅×#117	C₂²×C₃	1	1	yes	characteristic
69	#4094	—	2	4	no	—
70	C₂×#681	—	2	2	no	—
71	C₂×#681	C₂²×C₃	1	2	yes	—
72	C₂×#681	C₂²×C₃	1	2	yes	—
73	#3968	—	2	1	no	—
74	#3965	—	2	1	no	—
75	C₂²⋊#168	—	2	4	no	—
76	#1891	—	5	1	no	Sylow
77	C₂³×C₃×C₅	—	2	1	no	—
78	C₂³×C₃×C₅	—	2	2	no	—
79	C₂³×C₃×C₅	—	4	2	no	—
80	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
81	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
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	—	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	2	no	—
89	C₂×C₃×C₄×C₅	—	2	1	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	4	1	no	—
92	C₂×C₃×C₄×C₅	—	4	2	no	—
93	C₂×C₃×C₄×C₅	—	4	1	no	—
94	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	#41	1	2	yes	—
99	C₃×#168	—	2	4	no	—
100	C₃×#168	—	4	2	no	—
101	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
102	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
103	C₃×#131	—	10	4	no	—
104	C₂×C₃×M₁₆	—	5	2	no	—
105	C₂×C₃×M₁₆	—	5	2	no	—
106	C₂×C₃×M₁₆	—	10	2	no	—
107	C₃×#123	Dic₅	1	2	yes	—
108	C₃×C₂²⋊Q₈	—	2	1	no	—
109	C₃×#121	—	2	1	no	—
110	C₃×#120	Dic₅	1	2	yes	—
111	C₃×C₄×D₄	—	2	2	no	—
112	C₃×#117	C₂×D₅	1	1	yes	characteristic
113	C₃×#101	—	10	1	no	—
114	C₃×#100	—	10	1	no	—
115	C₃×C₂²⋊C₈	—	10	4	no	—
116	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
117	C₅×#41	—	2	2	no	—
118	C₅×#41	—	2	2	no	—
119	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
120	C₂×C₅×D₄	—	2	2	no	—
121	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
122	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	—	2	1	no	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	2	2	no	—
127	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
129	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
130	C₅×C₄⋊C₄	—	2	2	no	—
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₂²⋊C₄	—	2	2	no	—
133	C₅×C₂²⋊C₄	—	2	2	no	—
134	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
135	C₄²×C₅	—	2	1	no	—
136	#681	—	2	4	no	—
137	#681	—	2	2	no	—
138	#681	—	2	2	no	—
139	#681	—	2	2	no	—
140	#681	—	2	2	no	—
141	C₂×#168	—	2	4	no	—
142	C₂×#168	—	2	2	no	—
143	C₂×#168	C₃×D₄	1	4	yes	complemented
144	#568	—	5	1	no	—
145	#525	C₃×D₅	1	1	yes	characteristic
146	#413	—	5	1	no	—
147	#407	—	5	2	no	—
148	#344	—	5	2	no	—
149	C₂²×C₃×C₅	—	2	2	no	—
150	C₂²×C₃×C₅	—	2	4	no	—
151	C₂²×C₃×C₅	—	2	2	no	—
152	C₂²×C₃×C₅	—	4	1	no	—
153	C₂²×C₃×C₅	—	4	2	no	—
154	C₂²×C₃×C₅	—	4	1	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	C₄×D₄	1	2	yes	—
159	C₃×C₄×C₅	—	2	2	no	—
160	C₃×C₄×C₅	—	4	2	no	—
161	C₃×C₄×C₅	—	4	1	no	—
162	C₃×C₄×C₅	#120	1	1	yes	characteristic
163	C₃×C₄×C₅	#121	1	2	yes	—
164	C₃×C₄×C₅	#123	1	1	yes	characteristic
165	C₂⁴×C₃	C₂×Dic₅	1	1	yes	characteristic
166	C₃×#41	—	2	2	no	—
167	C₃×#41	—	2	2	no	—
168	C₂×C₃×Q₈	C₂²⋊D₅	1	1	yes	characteristic
169	C₂×C₃×D₄	—	2	2	no	—
170	C₂×C₃×D₄	C₂×Dic₅	1	2	yes	—
171	C₂×C₃×D₄	C₂²⋊D₅	1	1	yes	characteristic
172	C₂²×C₃×C₄	—	2	2	no	—
173	C₂²×C₃×C₄	—	2	2	no	—
174	C₂²×C₃×C₄	—	2	1	no	—
175	C₂²×C₃×C₄	—	2	1	no	—
176	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
178	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
179	C₃×M₁₆	—	10	4	no	—
180	C₃×M₁₆	—	10	2	no	—
181	C₃×M₁₆	—	10	2	no	—
182	C₃×M₁₆	—	10	2	no	—
183	C₃×M₁₆	—	10	2	no	—
184	C₂×C₃×C₈	—	5	4	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	—	2	1	no	—
189	C₃×C₂²⋊C₄	—	2	2	no	—
190	C₃×C₂²⋊C₄	—	2	2	no	—
191	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
192	C₃×C₄²	—	2	1	no	—
193	C₂³×C₅	—	2	1	no	—
194	C₂³×C₅	—	2	2	no	—
195	C₂³×C₅	—	4	2	no	—
196	C₂³×C₅	C₃×C₂²⋊C₄	1	2	yes	—
197	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
198	C₅×Q₈	—	2	2	no	—
199	C₅×D₄	—	2	4	no	—
200	C₅×D₄	—	2	2	no	—
201	C₅×D₄	—	4	4	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	4	1	no	—
208	C₂×C₄×C₅	—	4	2	no	—
209	C₂×C₄×C₅	—	4	1	no	—
210	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
211	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
212	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
214	C₂×C₄×C₅	C₃×#41	1	2	yes	—
215	#168	—	2	4	no	—
216	#168	—	4	2	no	—
217	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
218	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
219	#131	—	10	4	no	—
220	C₂×M₁₆	—	5	2	no	—
221	C₂×M₁₆	—	5	2	no	—
222	C₂×M₁₆	—	10	2	no	—
223	#123	C₃×Dic₅	1	2	yes	—
224	C₂²⋊Q₈	—	2	1	no	—
225	#121	—	2	1	no	—
226	#120	C₃×Dic₅	1	2	yes	—
227	C₄×D₄	—	2	2	no	—
228	#117	C₂×C₃×D₅	1	1	yes	characteristic
229	#101	—	10	1	no	—
230	#100	—	10	1	no	—
231	C₂²⋊C₈	—	10	4	no	—
232	C₂×C₃×C₅	—	2	1	no	—
233	C₂×C₃×C₅	—	2	2	no	—
234	C₂×C₃×C₅	—	4	2	no	—
235	C₂×C₃×C₅	—	4	2	no	—
236	C₂×C₃×C₅	#386	1	1	yes	characteristic
237	C₂³×C₃	—	2	1	no	—
238	C₂³×C₃	—	2	2	no	—
239	C₂³×C₃	—	4	2	no	—
240	C₂³×C₃	C₂²⋊Dic₅	1	2	yes	—
241	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
242	C₃×Q₈	—	2	2	no	—
243	C₃×D₄	—	2	4	no	—
244	C₃×D₄	—	2	2	no	—
245	C₃×D₄	—	4	4	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	4	1	no	—
252	C₂×C₃×C₄	—	4	1	no	—
253	C₂×C₃×C₄	—	4	2	no	—
254	C₂×C₃×C₄	C₂²⋊Dic₅	1	2	yes	—
255	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
256	C₂×C₃×C₄	#711	1	2	yes	—
257	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
259	C₃×C₈	—	10	4	no	—
260	C₃×C₈	—	20	2	no	—
261	C₂²×C₅	—	2	2	no	—
262	C₂²×C₅	—	2	4	no	—
263	C₂²×C₅	—	2	2	no	—
264	C₂²×C₅	—	4	1	no	—
265	C₂²×C₅	—	4	2	no	—
266	C₂²×C₅	—	4	1	no	—
267	C₂²×C₅	—	4	2	no	—
268	C₂²×C₅	—	4	1	no	—
269	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
270	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
271	C₄×C₅	—	2	2	no	—
272	C₄×C₅	—	4	2	no	—
273	C₄×C₅	—	4	1	no	—
274	C₄×C₅	C₃×#120	1	1	yes	characteristic
275	C₄×C₅	C₃×#121	1	2	yes	—
276	C₄×C₅	C₃×#123	1	1	yes	characteristic
277	C₂⁴	C₂×C₃×Dic₅	1	1	yes	characteristic
278	#41	—	2	2	no	—
279	#41	—	2	2	no	—
280	C₂×Q₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	C₂×C₃×Dic₅	1	2	yes	—
283	C₂×D₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
289	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
290	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
291	M₁₆	—	10	4	no	—
292	M₁₆	—	10	2	no	—
293	M₁₆	—	10	2	no	—
294	M₁₆	—	10	2	no	—
295	M₁₆	—	10	2	no	—
296	C₂×C₈	—	5	4	no	—
297	C₂×C₈	—	10	4	no	—
298	C₂×C₈	—	10	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₂²⋊C₄	—	2	2	no	—
302	C₂²⋊C₄	—	2	2	no	—
303	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
304	C₄²	—	2	1	no	—
305	C₃×C₅	#1891	1	1	yes	characteristic, complemented, Hall
306	C₂²×C₃	—	2	2	no	—
307	C₂²×C₃	—	2	4	no	—
308	C₂²×C₃	—	2	2	no	—
309	C₂²×C₃	—	4	1	no	—
310	C₂²×C₃	—	4	2	no	—
311	C₂²×C₃	—	4	1	no	—
312	C₂²×C₃	—	4	2	no	—
313	C₂²×C₃	—	4	1	no	—
314	C₂²×C₃	D₄×Dic₅	1	2	yes	—
315	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
316	C₃×C₄	—	2	2	no	—
317	C₃×C₄	—	4	2	no	—
318	C₃×C₄	—	4	1	no	—
319	C₃×C₄	#4081	1	1	yes	characteristic
320	C₃×C₄	#4083	1	1	yes	characteristic
321	C₃×C₄	#4085	1	2	yes	—
322	C₂×C₅	—	2	1	no	—
323	C₂×C₅	—	2	2	no	—
324	C₂×C₅	—	4	2	no	—
325	C₂×C₅	—	4	2	no	—
326	C₂×C₅	C₃×#386	1	1	yes	characteristic
327	C₂³	—	2	2	no	—
328	C₂³	—	2	1	no	—
329	C₂³	—	4	2	no	—
330	C₂³	C₃×C₂²⋊Dic₅	1	2	yes	—
331	C₂³	C₂²×C₃×Dic₅	1	1	yes	characteristic
332	Q₈	—	2	2	no	—
333	D₄	—	2	4	no	—
334	D₄	—	2	2	no	—
335	D₄	—	4	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	C₃×C₂²⋊Dic₅	1	2	yes	—
345	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
346	C₂×C₄	C₃×#711	1	2	yes	—
347	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
348	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
349	C₈	—	10	4	no	—
350	C₈	—	20	2	no	—
351	C₂×C₃	—	2	1	no	—
352	C₂×C₃	—	2	2	no	—
353	C₂×C₃	—	4	2	no	—
354	C₂×C₃	—	4	2	no	—
355	C₂×C₃	#65509	1	1	yes	characteristic
356	C₅	C₃×#1891	1	1	yes	characteristic, complemented, Sylow
357	C₂²	—	2	2	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	4	1	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	1	no	—
365	C₂²	C₃×D₄×Dic₅	1	2	yes	—
366	C₂²	C₂×C₃×C₂²⋊Dic₅	1	1	yes	characteristic
367	C₄	—	2	2	no	—
368	C₄	—	4	2	no	—
369	C₄	—	4	1	no	—
370	C₄	C₃×#4081	1	1	yes	characteristic
371	C₄	C₃×#4083	1	1	yes	characteristic
372	C₄	C₃×#4085	1	2	yes	—
373	C₃	#10602507	1	1	yes	characteristic, direct product factor, Sylow
374	C₂	—	2	1	no	—
375	C₂	—	2	2	no	—
376	C₂	—	4	2	no	—
377	C₂	—	4	2	no	—
378	C₂	C₃×#65509	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	#4083
commutator	C₂³×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting, prime radical	C₃×C₅×#525	C₂
socle	C₂×C₃×C₅	#386
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₃×#525	D₅
hypocenter	C₅	C₃×#1891
LCS	G ▷ C₂³×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₃×#525

Complements

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

N	H ≅ G/N	type
2. C₃×#66153	C₂	semidirect
3. C₃×#65526	C₂	semidirect
4. C₃×#65496	C₂	semidirect
5. C₃×#64753	C₂	semidirect
6. #10602507	C₃	direct (N × H)
24. #66153	C₂×C₃	semidirect
25. #65526	C₂×C₃	semidirect
26. #65496	C₂×C₃	semidirect
27. #64753	C₂×C₃	semidirect
55. C₂×C₃×#168	D₄	semidirect
143. C₂×#168	C₃×D₄	semidirect
305. C₃×C₅	#1891	semidirect
356. C₅	C₃×#1891	semidirect
373. C₃	#10602507	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×#525	2
C₃×#66153	2
C₃×#65526	2
C₃×#65496	2
C₃×#64753	2
#10602507	3
C₃×#1891	5

Subgroups — C3×#10602507 #14301712

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10602507 #14301712