Subgroups — C₃×#10613962 #14322714

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic
2	C₃×#65501	C₂	1	2	yes	maximal
3	C₃×#65270	C₂	1	4	yes	maximal, complemented
4	C₃×#65240	C₂	1	4	yes	maximal
5	C₃×#65225	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65224	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄×C₄⋊Dic₅	C₂	1	2	yes	maximal, complemented
8	#10613962	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₃×C₅×#117	C₄	1	8	yes	complemented
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₂²⋊Dic₅	C₂²	1	4	yes	—
16	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
17	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	4	yes	—
19	C₂×C₃×C₄×Dic₅	C₂²	1	4	yes	—
20	C₃×#3963	C₂²	1	4	yes	—
21	C₃×#3963	C₂²	1	4	yes	—
22	C₃×#3963	C₂²	1	4	yes	—
23	C₃×#2314	—	5	1	no	maximal, Hall
24	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic
25	#65501	C₂×C₃	1	2	yes	—
26	#65270	C₂×C₃	1	4	yes	complemented
27	#65240	C₂×C₃	1	4	yes	—
28	#65225	C₂×C₃	1	1	yes	characteristic, complemented
29	#65224	C₂×C₃	1	1	yes	characteristic, complemented
30	C₄×C₄⋊Dic₅	C₂×C₃	1	2	yes	complemented
31	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	—	2	2	no	—
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
40	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
41	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	—
42	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
43	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
44	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
45	C₃×C₂²⋊Dic₅	—	4	4	no	—
46	C₃×C₄⋊Dic₅	—	2	4	no	—
47	C₃×C₄⋊Dic₅	—	2	4	no	—
48	C₃×C₄⋊Dic₅	—	4	4	no	—
49	C₃×C₄×Dic₅	—	4	4	no	—
50	C₂×C₃×#117	D₅	1	1	yes	characteristic
51	C₃×#388	—	5	4	no	—
52	C₃×#387	—	5	4	no	—
53	C₃×#384	—	5	1	no	—
54	C₃×#382	—	5	1	no	—
55	C₃×#380	—	5	2	no	—
56	C₃×C₄×C₄⋊C₄	—	5	2	no	—
57	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
58	C₅×#117	C₃×C₄	1	8	yes	complemented
59	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
60	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
61	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
62	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₂²⋊Dic₅	C₂²×C₃	1	4	yes	—
64	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
65	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
66	C₂×C₄⋊Dic₅	C₂²×C₃	1	4	yes	—
67	C₂×C₄×Dic₅	C₂²×C₃	1	4	yes	—
68	#3963	C₂²×C₃	1	4	yes	—
69	#3963	C₂²×C₃	1	4	yes	—
70	#3963	C₂²×C₃	1	4	yes	—
71	#2314	—	5	1	no	Sylow
72	C₂³×C₃×C₅	—	2	1	no	—
73	C₂³×C₃×C₅	—	2	1	no	—
74	C₂³×C₃×C₅	—	2	2	no	—
75	C₂³×C₃×C₅	—	2	2	no	—
76	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
77	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
78	C₂×C₃×C₄×C₅	—	2	1	no	—
79	C₂×C₃×C₄×C₅	—	2	1	no	—
80	C₂×C₃×C₄×C₅	—	2	2	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	2	2	no	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	2	8	no	—
85	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
86	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
87	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	#41	1	2	yes	—
90	C₂×C₃×C₄×C₅	#41	1	2	yes	—
91	C₂×C₃×Dic₅	—	2	4	no	—
92	C₂×C₃×Dic₅	—	2	4	no	—
93	C₂×C₃×Dic₅	—	2	4	no	—
94	C₂×C₃×Dic₅	—	2	4	no	—
95	C₂×C₃×Dic₅	—	2	4	no	—
96	C₂×C₃×Dic₅	—	2	4	no	—
97	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
98	C₃×#117	Dic₅	1	8	yes	complemented
99	C₂×C₃×C₄⋊C₄	—	5	2	no	—
100	C₂×C₃×C₄⋊C₄	—	5	2	no	—
101	C₂×C₃×C₄⋊C₄	—	5	4	no	—
102	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
103	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
104	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
105	C₂×C₃×C₄²	—	5	4	no	—
106	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
107	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
108	C₃×#95	—	5	4	no	—
109	C₃×#95	—	5	4	no	—
110	C₃×#95	—	5	4	no	—
111	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
115	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
116	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
117	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
119	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
120	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
121	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
122	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
123	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
124	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
125	C₂²⋊Dic₅	—	4	4	no	—
126	C₄⋊Dic₅	—	2	4	no	—
127	C₄⋊Dic₅	—	2	4	no	—
128	C₄⋊Dic₅	—	4	4	no	—
129	C₄×Dic₅	—	4	4	no	—
130	C₂×#117	C₃×D₅	1	1	yes	characteristic
131	#388	—	5	4	no	—
132	#387	—	5	4	no	—
133	#384	—	5	1	no	—
134	#382	—	5	1	no	—
135	#380	—	5	2	no	—
136	C₄×C₄⋊C₄	—	5	2	no	—
137	C₂²×C₃×C₅	—	2	2	no	—
138	C₂²×C₃×C₅	—	2	4	no	—
139	C₂²×C₃×C₅	—	4	1	no	—
140	C₂²×C₃×C₅	—	4	1	no	—
141	C₂²×C₃×C₅	—	4	2	no	—
142	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
143	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
144	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
145	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
146	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
147	C₃×C₄×C₅	—	2	2	no	—
148	C₃×C₄×C₅	—	2	4	no	—
149	C₃×C₄×C₅	—	2	4	no	—
150	C₃×C₄×C₅	#117	1	4	yes	—
151	C₃×Dic₅	—	4	4	no	—
152	C₃×Dic₅	—	4	4	no	—
153	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
154	C₂²×C₃×C₄	—	2	2	no	—
155	C₂²×C₃×C₄	—	2	2	no	—
156	C₂²×C₃×C₄	—	5	4	no	—
157	C₂²×C₃×C₄	—	5	4	no	—
158	C₂²×C₃×C₄	C₂×Dic₅	1	4	yes	—
159	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
161	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
162	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
163	C₃×C₄⋊C₄	—	10	4	no	—
164	C₃×C₄⋊C₄	—	10	4	no	—
165	C₃×C₄⋊C₄	—	20	4	no	—
166	C₃×C₄⋊C₄	C₂×Dic₅	1	8	yes	—
167	C₃×C₂²⋊C₄	—	20	4	no	—
168	C₃×C₂²⋊C₄	C₂×Dic₅	1	8	yes	—
169	C₃×C₄²	—	20	4	no	—
170	C₃×C₄²	C₂×Dic₅	1	4	yes	—
171	C₃×C₄²	C₂×Dic₅	1	4	yes	—
172	C₂³×C₅	—	2	1	no	—
173	C₂³×C₅	—	2	1	no	—
174	C₂³×C₅	—	2	2	no	—
175	C₂³×C₅	—	2	2	no	—
176	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
177	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
178	C₂×C₄×C₅	—	2	1	no	—
179	C₂×C₄×C₅	—	2	1	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	8	no	—
185	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
186	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
187	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
188	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
189	C₂×C₄×C₅	C₃×#41	1	2	yes	—
190	C₂×C₄×C₅	C₃×#41	1	2	yes	—
191	C₂×Dic₅	—	2	4	no	—
192	C₂×Dic₅	—	2	4	no	—
193	C₂×Dic₅	—	2	4	no	—
194	C₂×Dic₅	—	2	4	no	—
195	C₂×Dic₅	—	2	4	no	—
196	C₂×Dic₅	—	2	4	no	—
197	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
198	#117	C₃×Dic₅	1	8	yes	complemented
199	C₂×C₄⋊C₄	—	5	2	no	—
200	C₂×C₄⋊C₄	—	5	2	no	—
201	C₂×C₄⋊C₄	—	5	4	no	—
202	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
203	C₂×C₂²⋊C₄	—	5	4	no	—
204	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
205	C₂×C₄²	—	5	4	no	—
206	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
207	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
208	#95	—	5	4	no	—
209	#95	—	5	4	no	—
210	#95	—	5	4	no	—
211	C₂×C₃×C₅	—	4	2	no	—
212	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
213	C₂×C₃×C₅	#520	1	2	yes	—
214	C₂×C₃×C₅	#540	1	1	yes	characteristic
215	C₂×C₃×C₅	#541	1	1	yes	characteristic
216	C₂×C₃×C₅	#542	1	2	yes	—
217	C₂³×C₃	—	2	1	no	—
218	C₂³×C₃	—	2	1	no	—
219	C₂³×C₃	—	2	2	no	—
220	C₂³×C₃	—	2	2	no	—
221	C₂³×C₃	C₂²×Dic₅	1	2	yes	—
222	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
223	C₂×C₃×C₄	—	2	1	no	—
224	C₂×C₃×C₄	—	2	1	no	—
225	C₂×C₃×C₄	—	2	2	no	—
226	C₂×C₃×C₄	—	2	2	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	2	8	no	—
230	C₂×C₃×C₄	—	10	4	no	—
231	C₂×C₃×C₄	—	10	4	no	—
232	C₂×C₃×C₄	—	10	4	no	—
233	C₂×C₃×C₄	—	10	4	no	—
234	C₂×C₃×C₄	—	10	4	no	—
235	C₂×C₃×C₄	—	10	4	no	—
236	C₂×C₃×C₄	#709	1	2	yes	—
237	C₂×C₃×C₄	#709	1	2	yes	—
238	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
239	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
240	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
241	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
242	C₂²×C₅	—	2	2	no	—
243	C₂²×C₅	—	2	4	no	—
244	C₂²×C₅	—	4	1	no	—
245	C₂²×C₅	—	4	1	no	—
246	C₂²×C₅	—	4	2	no	—
247	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
248	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
249	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
250	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
251	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
252	C₄×C₅	—	2	2	no	—
253	C₄×C₅	—	2	4	no	—
254	C₄×C₅	—	2	4	no	—
255	C₄×C₅	C₃×#117	1	4	yes	—
256	Dic₅	—	4	4	no	—
257	Dic₅	—	4	4	no	—
258	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	5	4	no	—
262	C₂²×C₄	—	5	4	no	—
263	C₂²×C₄	C₂×C₃×Dic₅	1	4	yes	—
264	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
265	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
266	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
267	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
268	C₄⋊C₄	—	10	4	no	—
269	C₄⋊C₄	—	10	4	no	—
270	C₄⋊C₄	—	20	4	no	—
271	C₄⋊C₄	C₂×C₃×Dic₅	1	8	yes	—
272	C₂²⋊C₄	—	20	4	no	—
273	C₂²⋊C₄	C₂×C₃×Dic₅	1	8	yes	—
274	C₄²	—	20	4	no	—
275	C₄²	C₂×C₃×Dic₅	1	4	yes	—
276	C₄²	C₂×C₃×Dic₅	1	4	yes	—
277	C₃×C₅	#2314	1	1	yes	characteristic, complemented, Hall
278	C₂²×C₃	—	2	2	no	—
279	C₂²×C₃	—	2	4	no	—
280	C₂²×C₃	—	4	1	no	—
281	C₂²×C₃	—	4	2	no	—
282	C₂²×C₃	—	4	1	no	—
283	C₂²×C₃	C₂×#709	1	1	yes	characteristic
284	C₂²×C₃	C₂×#709	1	1	yes	characteristic
285	C₂²×C₃	#4149	1	2	yes	—
286	C₂²×C₃	#4150	1	2	yes	—
287	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
288	C₃×C₄	—	2	2	no	—
289	C₃×C₄	—	2	4	no	—
290	C₃×C₄	—	2	4	no	—
291	C₃×C₄	—	20	4	no	—
292	C₃×C₄	—	20	4	no	—
293	C₃×C₄	#4072	1	4	yes	—
294	C₂×C₅	—	4	2	no	—
295	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
296	C₂×C₅	C₃×#520	1	2	yes	—
297	C₂×C₅	C₃×#540	1	1	yes	characteristic
298	C₂×C₅	C₃×#541	1	1	yes	characteristic
299	C₂×C₅	C₃×#542	1	2	yes	—
300	C₂³	—	2	1	no	—
301	C₂³	—	2	1	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	C₂²×C₃×Dic₅	1	2	yes	—
305	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	10	4	no	—
314	C₂×C₄	—	10	4	no	—
315	C₂×C₄	—	10	4	no	—
316	C₂×C₄	—	10	4	no	—
317	C₂×C₄	—	10	4	no	—
318	C₂×C₄	—	10	4	no	—
319	C₂×C₄	C₃×#709	1	2	yes	—
320	C₂×C₄	C₃×#709	1	2	yes	—
321	C₂×C₄	C₂²×C₃×Dic₅	1	4	yes	—
322	C₂×C₄	C₂²×C₃×Dic₅	1	4	yes	—
323	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
324	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
325	C₂×C₃	—	4	2	no	—
326	C₂×C₃	#65852	1	1	yes	characteristic
327	C₂×C₃	#65868	1	2	yes	—
328	C₂×C₃	#65869	1	1	yes	characteristic
329	C₂×C₃	C₂×#4072	1	1	yes	characteristic
330	C₂×C₃	#66161	1	2	yes	—
331	C₅	C₃×#2314	1	1	yes	characteristic, complemented, Sylow
332	C₂²	—	2	2	no	—
333	C₂²	—	2	4	no	—
334	C₂²	—	4	1	no	—
335	C₂²	—	4	2	no	—
336	C₂²	—	4	1	no	—
337	C₂²	C₂×C₃×#709	1	1	yes	characteristic
338	C₂²	C₂×C₃×#709	1	1	yes	characteristic
339	C₂²	C₃×#4149	1	2	yes	—
340	C₂²	C₃×#4150	1	2	yes	—
341	C₂²	C₂³×C₃×Dic₅	1	1	yes	characteristic
342	C₄	—	2	2	no	—
343	C₄	—	2	4	no	—
344	C₄	—	2	4	no	—
345	C₄	—	20	4	no	—
346	C₄	—	20	4	no	—
347	C₄	C₃×#4072	1	4	yes	—
348	C₃	#10613962	1	1	yes	characteristic, direct product factor, Sylow
349	C₂	—	4	2	no	—
350	C₂	C₃×#65852	1	1	yes	characteristic
351	C₂	C₃×#65868	1	2	yes	—
352	C₂	C₃×#65869	1	1	yes	characteristic
353	C₂	C₂×C₃×#4072	1	1	yes	characteristic
354	C₂	C₃×#66161	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×C₅	C₂³
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×#117	D₅
hypocenter	C₅	C₃×#2314
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#117

Complements

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

N	H ≅ G/N	type
3. C₃×#65270	C₂	semidirect
5. C₃×#65225	C₂	semidirect
6. C₃×#65224	C₂	semidirect
7. C₃×C₄×C₄⋊Dic₅	C₂	semidirect
8. #10613962	C₃	direct (N × H)
10. C₃×C₅×#117	C₄	semidirect
26. #65270	C₂×C₃	semidirect
28. #65225	C₂×C₃	semidirect
29. #65224	C₂×C₃	semidirect
30. C₄×C₄⋊Dic₅	C₂×C₃	semidirect
58. C₅×#117	C₃×C₄	semidirect
98. C₃×#117	Dic₅	semidirect
198. #117	C₃×Dic₅	semidirect
277. C₃×C₅	#2314	semidirect
331. C₅	C₃×#2314	semidirect
348. C₃	#10613962	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×#117	2
C₃×#65501	2
C₃×#65270	2
C₃×#65240	2
C₃×#65225	2
C₃×#65224	2
C₃×C₄×C₄⋊Dic₅	2
#10613962	3
C₃×#2314	5

Subgroups — C3×#10613962 #14322714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613962 #14322714