Subgroups — C₃×#10614301 #14412708

Order 1920.

1452 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	C₂×C₃×#4150	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4094	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65293	C₂	1	3	yes	maximal, complemented
5	C₃×#65291	C₂	1	3	yes	maximal, complemented
6	C₂×C₃×#3942	C₂	1	3	yes	maximal, complemented
7	C₃×#65255	C₂	1	3	yes	maximal, complemented
8	#10614301	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₃×#4150	—	2	4	no	—
11	C₃×#4150	C₄	1	8	yes	complemented
12	C₂×C₃×Q₈×D₅	—	2	1	no	—
13	C₂×C₃×#711	—	2	3	no	—
14	C₂×C₃×#709	C₂²	1	3	yes	—
15	C₂²×C₃×Dic₁₀	C₂²	1	3	yes	—
16	C₃×C₄×C₅×Q₈	—	2	1	no	—
17	C₃×C₄×C₅×D₄	—	2	3	no	—
18	C₃×C₅×#117	C₂²	1	3	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	3	yes	—
20	C₃×#4094	—	2	4	no	—
21	C₂×C₃×#681	C₂²	1	3	yes	—
22	C₂²×C₃×#168	C₂²	1	3	yes	—
23	C₃×#3942	C₂²	1	3	yes	—
24	C₃×#3942	C₂²	1	3	yes	—
25	C₃×#3942	C₂²	1	6	yes	—
26	C₃×#3941	C₂²	1	1	yes	characteristic
27	C₃×#3941	C₂²	1	3	yes	—
28	C₃×#2898	—	5	1	no	maximal, Hall
29	C₂×#4150	C₂×C₃	1	1	yes	characteristic
30	C₅×#520	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×#4094	C₂×C₃	1	1	yes	characteristic, complemented
32	#65293	C₂×C₃	1	3	yes	complemented
33	#65291	C₂×C₃	1	3	yes	complemented
34	C₂×#3942	C₂×C₃	1	3	yes	complemented
35	#65255	C₂×C₃	1	3	yes	complemented
36	C₃×C₅×#41	C₂×C₄	1	4	yes	—
37	C₃×C₅×#41	D₄	1	4	yes	—
38	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
39	C₂×C₃×C₅×D₄	D₄	1	3	yes	—
40	C₂²×C₃×C₄×C₅	—	2	3	no	—
41	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
42	C₂×C₃×C₂²⋊D₅	—	2	3	no	—
43	C₂²×C₃×Dic₅	—	2	3	no	—
44	C₃×Q₈×D₅	—	2	8	no	—
45	C₃×#711	—	2	24	no	—
46	C₃×#709	—	2	6	no	—
47	C₃×#709	C₂×C₄	1	12	yes	complemented
48	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
49	C₂×C₃×C₄×D₅	—	2	3	no	—
50	C₂×C₃×Dic₁₀	—	2	3	no	—
51	C₂×C₃×Dic₁₀	—	2	6	no	—
52	C₂×C₃×Dic₁₀	C₂×C₄	1	12	yes	complemented
53	C₂×C₃×Dic₁₀	C₂³	1	3	yes	—
54	C₃×C₅×C₄⋊C₄	—	2	3	no	—
55	C₃×C₅×C₄⋊C₄	C₂³	1	3	yes	—
56	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
57	C₃×C₅×C₂²⋊C₄	—	2	3	no	—
58	C₃×C₄²×C₅	—	2	3	no	—
59	C₃×#681	—	2	6	no	—
60	C₂×C₃×#168	—	2	6	no	—
61	C₂×C₃×#168	C₂³	1	1	yes	characteristic
62	C₂×C₃×#168	C₂³	1	3	yes	—
63	C₂×C₃×2₋¹⁺⁴	—	5	1	no	—
64	C₂×C₃×#131	—	5	1	no	—
65	C₃×#520	D₅	1	1	yes	characteristic, complemented
66	C₃×#419	—	5	3	no	—
67	C₃×#417	—	5	3	no	—
68	C₃×#416	—	5	3	no	—
69	C₂×C₃×#103	—	5	3	no	—
70	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
71	#4150	—	2	4	no	—
72	#4150	C₃×C₄	1	8	yes	complemented
73	C₂×Q₈×D₅	—	2	1	no	—
74	C₂×#711	—	2	3	no	—
75	C₂×#709	C₂²×C₃	1	3	yes	—
76	C₂²×Dic₁₀	C₂²×C₃	1	3	yes	—
77	C₄×C₅×Q₈	—	2	1	no	—
78	C₄×C₅×D₄	—	2	3	no	—
79	C₅×#117	C₂²×C₃	1	3	yes	—
80	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	3	yes	—
81	#4094	—	2	4	no	—
82	C₂×#681	C₂²×C₃	1	3	yes	—
83	C₂²×#168	C₂²×C₃	1	3	yes	—
84	#3942	C₂²×C₃	1	3	yes	—
85	#3942	C₂²×C₃	1	3	yes	—
86	#3942	C₂²×C₃	1	6	yes	—
87	#3941	C₂²×C₃	1	1	yes	characteristic
88	#3941	C₂²×C₃	1	3	yes	—
89	#2898	—	5	1	no	Sylow
90	C₂³×C₃×C₅	C₂×D₄	1	3	yes	—
91	C₂²×C₃×D₅	—	2	1	no	—
92	C₃×C₅×Q₈	C₂²⋊C₄	1	4	yes	—
93	C₃×C₅×D₄	C₂²⋊C₄	1	12	yes	—
94	C₂×C₃×C₄×C₅	—	2	1	no	—
95	C₂×C₃×C₄×C₅	—	2	3	no	—
96	C₂×C₃×C₄×C₅	—	8	3	no	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	6	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	6	yes	—
100	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
101	C₃×C₂²⋊D₅	—	2	12	no	—
102	C₂×C₃×Dic₅	—	2	12	no	—
103	C₂×C₃×Dic₅	—	2	3	no	—
104	C₃×D₂₀	—	2	1	no	—
105	C₃×D₂₀	C₂²×C₄	1	2	yes	—
106	C₃×C₄×D₅	—	2	12	no	—
107	C₃×Dic₁₀	—	2	12	no	—
108	C₃×Dic₁₀	—	2	3	no	—
109	C₃×Dic₁₀	C₂²×C₄	1	6	yes	—
110	C₃×#168	—	2	1	no	—
111	C₃×#168	—	2	3	no	—
112	C₃×2₋¹⁺⁴	—	5	8	no	—
113	C₃×2₋¹⁺⁴	—	10	4	no	—
114	C₂×C₃×#41	—	5	3	no	—
115	C₂×C₃×#41	—	10	3	no	—
116	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
117	C₂²×C₃×Q₈	—	5	3	no	—
118	C₂²×C₃×Q₈	—	10	1	no	—
119	C₃×#131	—	10	4	no	—
120	C₂×C₃×M₁₆	—	5	3	no	—
121	C₂²×C₃×C₈	—	5	3	no	—
122	C₃×C₄×Q₈	—	2	1	no	—
123	C₃×C₄×D₄	—	2	3	no	—
124	C₃×#117	C₂×D₅	1	3	yes	—
125	C₂×C₃×C₄⋊C₄	C₂×D₅	1	3	yes	—
126	C₃×#103	—	5	3	no	—
127	C₃×#103	—	5	6	no	—
128	C₃×#103	—	5	3	no	—
129	C₃×#102	—	5	1	no	—
130	C₃×#102	—	5	3	no	—
131	C₅×#41	C₂×C₃×C₄	1	4	yes	—
132	C₅×#41	C₃×D₄	1	4	yes	—
133	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
134	C₂×C₅×D₄	C₃×D₄	1	3	yes	—
135	C₂²×C₄×C₅	—	2	3	no	—
136	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
137	C₂×C₂²⋊D₅	—	2	3	no	—
138	C₂²×Dic₅	—	2	3	no	—
139	Q₈×D₅	—	2	8	no	—
140	#711	—	2	24	no	—
141	#709	—	2	6	no	—
142	#709	C₂×C₃×C₄	1	12	yes	complemented
143	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
144	C₂×C₄×D₅	—	2	3	no	—
145	C₂×Dic₁₀	—	2	3	no	—
146	C₂×Dic₁₀	—	2	6	no	—
147	C₂×Dic₁₀	C₂×C₃×C₄	1	12	yes	complemented
148	C₂×Dic₁₀	C₂³×C₃	1	3	yes	—
149	C₅×C₄⋊C₄	—	2	3	no	—
150	C₅×C₄⋊C₄	C₂³×C₃	1	3	yes	—
151	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
152	C₅×C₂²⋊C₄	—	2	3	no	—
153	C₄²×C₅	—	2	3	no	—
154	#681	—	2	6	no	—
155	C₂×#168	—	2	6	no	—
156	C₂×#168	C₂³×C₃	1	1	yes	characteristic
157	C₂×#168	C₂³×C₃	1	3	yes	—
158	C₂×2₋¹⁺⁴	—	5	1	no	—
159	C₂×#131	—	5	1	no	—
160	#520	C₃×D₅	1	1	yes	characteristic, complemented
161	#419	—	5	3	no	—
162	#417	—	5	3	no	—
163	#416	—	5	3	no	—
164	C₂×#103	—	5	3	no	—
165	C₂²×C₃×C₅	—	2	3	no	—
166	C₂²×C₃×C₅	—	2	3	no	—
167	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	6	yes	—
168	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₃×D₅	—	2	2	no	—
170	C₂×C₃×D₅	—	4	1	no	—
171	C₂×C₃×D₅	—	4	1	no	—
172	C₃×C₄×C₅	—	4	3	no	—
173	C₃×C₄×C₅	—	4	1	no	—
174	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	6	yes	—
175	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
176	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
177	C₃×Dic₅	—	2	6	no	—
178	C₃×#41	—	5	12	no	—
179	C₃×#41	—	10	24	no	—
180	C₃×#41	—	10	6	no	—
181	C₃×#41	C₄×D₅	1	4	yes	—
182	C₃×#41	D₂₀	1	4	yes	—
183	C₂×C₃×Q₈	—	5	12	no	—
184	C₂×C₃×Q₈	—	5	3	no	—
185	C₂×C₃×Q₈	—	10	8	no	—
186	C₂×C₃×Q₈	—	10	6	no	—
187	C₂×C₃×Q₈	—	10	3	no	—
188	C₂×C₃×Q₈	C₂²⋊D₅	1	1	yes	characteristic
189	C₂×C₃×D₄	—	5	1	no	—
190	C₂×C₃×D₄	—	10	3	no	—
191	C₂×C₃×D₄	C₂²⋊D₅	1	3	yes	—
192	C₂²×C₃×C₄	—	2	3	no	—
193	C₂²×C₃×C₄	—	10	3	no	—
194	C₂²×C₃×C₄	—	10	3	no	—
195	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
196	C₃×M₁₆	—	10	6	no	—
197	C₂×C₃×C₈	—	5	1	no	—
198	C₂×C₃×C₈	—	5	3	no	—
199	C₂×C₃×C₈	—	10	6	no	—
200	C₃×C₄⋊C₄	—	2	3	no	—
201	C₃×C₄⋊C₄	C₂²×D₅	1	3	yes	—
202	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
203	C₃×C₂²⋊C₄	—	2	3	no	—
204	C₃×C₄²	—	2	3	no	—
205	C₂³×C₅	C₂×C₃×D₄	1	3	yes	—
206	C₂²×D₅	—	2	1	no	—
207	C₅×Q₈	C₃×C₂²⋊C₄	1	4	yes	—
208	C₅×D₄	C₃×C₂²⋊C₄	1	12	yes	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	2	3	no	—
211	C₂×C₄×C₅	—	8	3	no	—
212	C₂×C₄×C₅	C₂²×C₃×C₄	1	6	yes	—
213	C₂×C₄×C₅	C₂×C₃×D₄	1	6	yes	—
214	C₂×C₄×C₅	C₂×C₃×D₄	1	3	yes	—
215	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
216	C₂²⋊D₅	—	2	12	no	—
217	C₂×Dic₅	—	2	12	no	—
218	C₂×Dic₅	—	2	3	no	—
219	D₂₀	—	2	1	no	—
220	D₂₀	C₂²×C₃×C₄	1	2	yes	—
221	C₄×D₅	—	2	12	no	—
222	Dic₁₀	—	2	12	no	—
223	Dic₁₀	—	2	3	no	—
224	Dic₁₀	C₂²×C₃×C₄	1	6	yes	—
225	#168	—	2	1	no	—
226	#168	—	2	3	no	—
227	2₋¹⁺⁴	—	5	8	no	—
228	2₋¹⁺⁴	—	10	4	no	—
229	C₂×#41	—	5	3	no	—
230	C₂×#41	—	10	3	no	—
231	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
232	C₂²×Q₈	—	5	3	no	—
233	C₂²×Q₈	—	10	1	no	—
234	#131	—	10	4	no	—
235	C₂×M₁₆	—	5	3	no	—
236	C₂²×C₈	—	5	3	no	—
237	C₄×Q₈	—	2	1	no	—
238	C₄×D₄	—	2	3	no	—
239	#117	C₂×C₃×D₅	1	3	yes	—
240	C₂×C₄⋊C₄	C₂×C₃×D₅	1	3	yes	—
241	#103	—	5	3	no	—
242	#103	—	5	6	no	—
243	#103	—	5	3	no	—
244	#102	—	5	1	no	—
245	#102	—	5	3	no	—
246	C₂×C₃×C₅	—	2	6	no	—
247	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₃×C₅	#577	1	1	yes	characteristic
249	C₂×C₃×C₅	#578	1	1	yes	characteristic
250	C₃×D₅	—	4	2	no	—
251	C₂³×C₃	—	10	1	no	—
252	C₂³×C₃	C₂×C₂²⋊D₅	1	3	yes	—
253	C₃×Q₈	—	5	6	no	—
254	C₃×Q₈	—	10	3	no	—
255	C₃×Q₈	—	10	12	no	—
256	C₃×Q₈	#685	1	4	yes	—
257	C₃×D₄	—	5	2	no	—
258	C₃×D₄	—	10	12	no	—
259	C₃×D₄	—	10	1	no	—
260	C₃×D₄	#685	1	12	yes	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	3	no	—
263	C₂×C₃×C₄	—	8	3	no	—
264	C₂×C₃×C₄	—	10	3	no	—
265	C₂×C₃×C₄	—	10	12	no	—
266	C₂×C₃×C₄	—	10	12	no	—
267	C₂×C₃×C₄	C₂×C₄×D₅	1	6	yes	—
268	C₂×C₃×C₄	C₂×D₂₀	1	6	yes	—
269	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	3	yes	—
270	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
271	C₃×C₈	—	10	1	no	—
272	C₃×C₈	—	10	3	no	—
273	C₂²×C₅	—	2	3	no	—
274	C₂²×C₅	—	2	3	no	—
275	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	6	yes	—
276	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
277	C₂×D₅	—	2	2	no	—
278	C₂×D₅	—	4	1	no	—
279	C₂×D₅	—	4	1	no	—
280	C₄×C₅	—	4	3	no	—
281	C₄×C₅	—	4	1	no	—
282	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	6	yes	—
283	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
284	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
285	Dic₅	—	2	6	no	—
286	#41	—	5	12	no	—
287	#41	—	10	24	no	—
288	#41	—	10	6	no	—
289	#41	C₃×C₄×D₅	1	4	yes	—
290	#41	C₃×D₂₀	1	4	yes	—
291	C₂×Q₈	—	5	12	no	—
292	C₂×Q₈	—	5	3	no	—
293	C₂×Q₈	—	10	8	no	—
294	C₂×Q₈	—	10	6	no	—
295	C₂×Q₈	—	10	3	no	—
296	C₂×Q₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
297	C₂×D₄	—	5	1	no	—
298	C₂×D₄	—	10	3	no	—
299	C₂×D₄	C₃×C₂²⋊D₅	1	3	yes	—
300	C₂²×C₄	—	2	3	no	—
301	C₂²×C₄	—	10	3	no	—
302	C₂²×C₄	—	10	3	no	—
303	C₂²×C₄	C₂²×C₃×D₅	1	3	yes	—
304	M₁₆	—	10	6	no	—
305	C₂×C₈	—	5	1	no	—
306	C₂×C₈	—	5	3	no	—
307	C₂×C₈	—	10	6	no	—
308	C₄⋊C₄	—	2	3	no	—
309	C₄⋊C₄	C₂²×C₃×D₅	1	3	yes	—
310	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
311	C₂²⋊C₄	—	2	3	no	—
312	C₄²	—	2	3	no	—
313	C₃×C₅	#2898	1	1	yes	characteristic, complemented, Hall
314	C₂²×C₃	—	2	3	no	—
315	C₂²×C₃	—	2	3	no	—
316	C₂²×C₃	—	10	2	no	—
317	C₂²×C₃	—	20	1	no	—
318	C₂²×C₃	—	20	1	no	—
319	C₂²×C₃	C₂×#685	1	6	yes	—
320	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
321	C₃×C₄	—	4	3	no	—
322	C₃×C₄	—	4	1	no	—
323	C₃×C₄	—	10	6	no	—
324	C₃×C₄	C₂×#685	1	6	yes	—
325	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
326	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
327	C₂×C₅	—	2	6	no	—
328	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
329	C₂×C₅	C₃×#577	1	1	yes	characteristic
330	C₂×C₅	C₃×#578	1	1	yes	characteristic
331	D₅	—	4	2	no	—
332	C₂³	—	10	1	no	—
333	C₂³	C₂×C₃×C₂²⋊D₅	1	3	yes	—
334	Q₈	—	5	6	no	—
335	Q₈	—	10	3	no	—
336	Q₈	—	10	12	no	—
337	Q₈	C₃×#685	1	4	yes	—
338	D₄	—	5	2	no	—
339	D₄	—	10	12	no	—
340	D₄	—	10	1	no	—
341	D₄	C₃×#685	1	12	yes	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	3	no	—
344	C₂×C₄	—	8	3	no	—
345	C₂×C₄	—	10	3	no	—
346	C₂×C₄	—	10	12	no	—
347	C₂×C₄	—	10	12	no	—
348	C₂×C₄	C₂×C₃×C₄×D₅	1	6	yes	—
349	C₂×C₄	C₂×C₃×D₂₀	1	6	yes	—
350	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	3	yes	—
351	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
352	C₈	—	10	1	no	—
353	C₈	—	10	3	no	—
354	C₂×C₃	—	2	6	no	—
355	C₂×C₃	—	20	2	no	—
356	C₂×C₃	C₂²×#685	1	1	yes	characteristic
357	C₂×C₃	#66170	1	1	yes	characteristic
358	C₂×C₃	#66172	1	1	yes	characteristic
359	C₅	C₃×#2898	1	1	yes	characteristic, complemented, Sylow
360	C₂²	—	2	3	no	—
361	C₂²	—	2	3	no	—
362	C₂²	—	10	2	no	—
363	C₂²	—	20	1	no	—
364	C₂²	—	20	1	no	—
365	C₂²	C₂×C₃×#685	1	6	yes	—
366	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
367	C₄	—	4	3	no	—
368	C₄	—	4	1	no	—
369	C₄	—	10	6	no	—
370	C₄	C₂×C₃×#685	1	6	yes	—
371	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
372	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
373	C₃	#10614301	1	1	yes	characteristic, direct product factor, Sylow
374	C₂	—	2	6	no	—
375	C₂	—	20	2	no	—
376	C₂	C₂²×C₃×#685	1	1	yes	characteristic
377	C₂	C₃×#66170	1	1	yes	characteristic
378	C₂	C₃×#66172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×C₂²⋊D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#520	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4150	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#520	D₅
hypocenter	C₅	C₃×#2898
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#41 ◁ C₃×#520

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#520	C₂	semidirect
3. C₂×C₃×#4094	C₂	semidirect
4. C₃×#65293	C₂	semidirect
5. C₃×#65291	C₂	semidirect
6. C₂×C₃×#3942	C₂	semidirect
7. C₃×#65255	C₂	semidirect
8. #10614301	C₃	direct (N × H)
11. C₃×#4150	C₄	semidirect
30. C₅×#520	C₂×C₃	semidirect
31. C₂×#4094	C₂×C₃	semidirect
32. #65293	C₂×C₃	semidirect
33. #65291	C₂×C₃	semidirect
34. C₂×#3942	C₂×C₃	semidirect
35. #65255	C₂×C₃	semidirect
47. C₃×#709	C₂×C₄	semidirect
52. C₂×C₃×Dic₁₀	C₂×C₄	semidirect
65. C₃×#520	D₅	semidirect
72. #4150	C₃×C₄	semidirect
142. #709	C₂×C₃×C₄	semidirect
147. C₂×Dic₁₀	C₂×C₃×C₄	semidirect
160. #520	C₃×D₅	semidirect
313. C₃×C₅	#2898	semidirect
359. C₅	C₃×#2898	semidirect
373. C₃	#10614301	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×#4150	2
C₃×C₅×#520	2
C₂×C₃×#4094	2
C₃×#65293	2
C₃×#65291	2
C₂×C₃×#3942	2
C₃×#65255	2
#10614301	3
C₃×#2898	5

Subgroups — C3×#10614301 #14412708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10614301 #14412708