Subgroups — C₃×#10615017 #14439079

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4096	C₂	1	4	yes	maximal, complemented
3	C₃×#65811	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65375	C₂	1	2	yes	maximal, complemented
5	C₃×#65363	C₂	1	2	yes	maximal, complemented
6	C₃×#65349	C₂	1	2	yes	maximal, complemented
7	C₃×#65347	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#3935	C₂	1	1	yes	maximal, characteristic, complemented
9	#10615017	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
11	C₂×C₃×#709	C₂²	1	2	yes	—
12	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₃×C₅×#127	C₂²	1	1	yes	characteristic
14	C₃×C₅×#124	C₂²	1	2	yes	—
15	C₃×C₅×#121	—	2	2	no	—
16	C₃×C₄×C₅×D₄	—	2	2	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₃×#4096	—	2	16	no	—
19	C₂×C₃×#689	C₂²	1	4	yes	—
20	C₂×C₃×#688	C₂²	1	4	yes	—
21	C₂×C₃×#687	C₂²	1	4	yes	—
22	C₂×C₃×#686	C₂²	1	4	yes	—
23	C₃×#4076	—	2	2	no	—
24	C₂²×C₃×#168	C₂²	1	2	yes	—
25	C₃×#4021	C₂²	1	2	yes	—
26	C₃×#4020	C₂²	1	1	yes	characteristic
27	C₃×C₄×D₂₀	—	2	2	no	—
28	C₃×#4015	C₂²	1	1	yes	characteristic
29	C₃×#3935	C₂²	1	2	yes	—
30	C₃×#3935	C₂²	1	2	yes	—
31	C₃×#3150	—	5	1	no	maximal, Hall
32	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×#4096	C₂×C₃	1	4	yes	complemented
34	#65811	C₂×C₃	1	1	yes	characteristic, complemented
35	#65375	C₂×C₃	1	2	yes	complemented
36	#65363	C₂×C₃	1	2	yes	complemented
37	#65349	C₂×C₃	1	2	yes	complemented
38	#65347	C₂×C₃	1	2	yes	complemented
39	C₂×#3935	C₂×C₃	1	1	yes	characteristic, complemented
40	C₃×C₅×#41	—	2	8	no	—
41	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
42	C₂×C₃×C₅×D₄	—	2	2	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	—	2	2	no	—
46	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
49	C₃×#709	—	2	8	no	—
50	C₂×C₃×D₂₀	—	2	2	no	—
51	C₂×C₃×D₂₀	C₂³	1	2	yes	—
52	C₂×C₃×C₄×D₅	—	2	2	no	—
53	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
54	C₃×C₅×C₄⋊C₄	—	2	2	no	—
55	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
56	C₃×C₄²×C₅	D₄	1	2	yes	—
57	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
58	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
59	C₃×#689	—	2	8	no	—
60	C₃×#688	—	2	8	no	—
61	C₃×#687	—	2	8	no	—
62	C₃×#686	—	2	8	no	—
63	C₃×#685	—	2	4	no	—
64	C₃×C₄⋊Dic₅	—	2	2	no	—
65	C₂×C₃×#168	D₄	1	8	yes	complemented
66	C₂×C₃×#168	C₂³	1	4	yes	—
67	C₂×C₃×#135	—	5	4	no	—
68	C₃×#532	—	5	1	no	—
69	C₃×#532	D₅	1	1	yes	characteristic, complemented
70	C₃×#497	—	5	2	no	—
71	C₃×#497	—	5	2	no	—
72	C₃×#496	—	5	2	no	—
73	C₃×#496	—	5	2	no	—
74	C₂×C₃×#97	—	5	1	no	—
75	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
76	C₂×#709	C₂²×C₃	1	2	yes	—
77	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
78	C₅×#127	C₂²×C₃	1	1	yes	characteristic
79	C₅×#124	C₂²×C₃	1	2	yes	—
80	C₅×#121	—	2	2	no	—
81	C₄×C₅×D₄	—	2	2	no	—
82	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
83	#4096	—	2	16	no	—
84	C₂×#689	C₂²×C₃	1	4	yes	—
85	C₂×#688	C₂²×C₃	1	4	yes	—
86	C₂×#687	C₂²×C₃	1	4	yes	—
87	C₂×#686	C₂²×C₃	1	4	yes	—
88	#4076	—	2	2	no	—
89	C₂²×#168	C₂²×C₃	1	2	yes	—
90	#4021	C₂²×C₃	1	2	yes	—
91	#4020	C₂²×C₃	1	1	yes	characteristic
92	C₄×D₂₀	—	2	2	no	—
93	#4015	C₂²×C₃	1	1	yes	characteristic
94	#3935	C₂²×C₃	1	2	yes	—
95	#3935	C₂²×C₃	1	2	yes	—
96	#3150	—	5	1	no	Sylow
97	C₂³×C₃×C₅	—	2	2	no	—
98	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₃×D₅	—	2	2	no	—
100	C₃×C₅×Q₈	—	2	4	no	—
101	C₃×C₅×D₄	—	2	4	no	—
102	C₃×C₅×D₄	—	4	4	no	—
103	C₃×C₅×D₄	—	4	4	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	4	2	no	—
106	C₂×C₃×C₄×C₅	—	4	4	no	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
109	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	C₃×C₂²⋊D₅	—	4	4	no	—
113	C₂×C₃×Dic₅	—	2	2	no	—
114	C₃×D₂₀	—	2	4	no	—
115	C₃×D₂₀	—	4	4	no	—
116	C₃×C₄×D₅	—	4	4	no	—
117	C₃×Dic₁₀	—	2	4	no	—
118	C₃×#168	C₂×D₄	1	8	yes	—
119	C₂×C₃×#41	—	5	2	no	—
120	C₂×C₃×#41	C₂×D₅	1	2	yes	—
121	C₃×#135	—	10	16	no	—
122	C₂×C₃×Q₁₆	—	5	4	no	—
123	C₂×C₃×SD₁₆	—	5	4	no	—
124	C₂×C₃×SD₁₆	—	5	4	no	—
125	C₂×C₃×D₈	—	5	4	no	—
126	C₂²×C₃×C₈	—	5	2	no	—
127	C₃×C₄⋊Q₈	—	5	1	no	—
128	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
129	C₃×#127	—	5	1	no	—
130	C₃×#127	C₂×D₅	1	1	yes	characteristic
131	C₃×#124	—	5	2	no	—
132	C₃×#124	C₂×D₅	1	2	yes	—
133	C₃×#121	—	2	2	no	—
134	C₃×#121	—	10	2	no	—
135	C₃×C₄×D₄	—	2	2	no	—
136	C₃×C₄×D₄	—	10	2	no	—
137	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
138	C₃×#97	—	5	2	no	—
139	C₃×#97	—	5	2	no	—
140	C₅×#41	—	2	8	no	—
141	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
142	C₂×C₅×D₄	—	2	2	no	—
143	C₂×C₅×D₄	—	2	2	no	—
144	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
145	C₂²×C₄×C₅	—	2	2	no	—
146	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
147	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
148	C₂×C₂²⋊D₅	—	2	2	no	—
149	#709	—	2	8	no	—
150	C₂×D₂₀	—	2	2	no	—
151	C₂×D₂₀	C₂³×C₃	1	2	yes	—
152	C₂×C₄×D₅	—	2	2	no	—
153	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
154	C₅×C₄⋊C₄	—	2	2	no	—
155	C₅×C₂²⋊C₄	—	2	4	no	—
156	C₄²×C₅	C₃×D₄	1	2	yes	—
157	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
158	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
159	#689	—	2	8	no	—
160	#688	—	2	8	no	—
161	#687	—	2	8	no	—
162	#686	—	2	8	no	—
163	#685	—	2	4	no	—
164	C₄⋊Dic₅	—	2	2	no	—
165	C₂×#168	C₃×D₄	1	8	yes	complemented
166	C₂×#168	C₂³×C₃	1	4	yes	—
167	C₂×#135	—	5	4	no	—
168	#532	—	5	1	no	—
169	#532	C₃×D₅	1	1	yes	characteristic, complemented
170	#497	—	5	2	no	—
171	#497	—	5	2	no	—
172	#496	—	5	2	no	—
173	#496	—	5	2	no	—
174	C₂×#97	—	5	1	no	—
175	C₂²×C₃×C₅	—	2	2	no	—
176	C₂²×C₃×C₅	—	4	2	no	—
177	C₂²×C₃×C₅	—	4	4	no	—
178	C₂²×C₃×C₅	#127	1	2	yes	—
179	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₃×D₅	—	4	2	no	—
181	C₂×C₃×D₅	—	4	4	no	—
182	C₃×C₄×C₅	—	2	2	no	—
183	C₃×C₄×C₅	—	2	2	no	—
184	C₃×C₄×C₅	—	4	2	no	—
185	C₃×C₄×C₅	#127	1	2	yes	—
186	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
187	C₃×Dic₅	—	4	2	no	—
188	C₃×#41	—	2	8	no	—
189	C₃×#41	—	10	8	no	—
190	C₂×C₃×Q₈	—	5	2	no	—
191	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
192	C₂×C₃×D₄	—	2	2	no	—
193	C₂×C₃×D₄	—	2	2	no	—
194	C₂×C₃×D₄	—	5	2	no	—
195	C₂×C₃×D₄	—	10	2	no	—
196	C₂×C₃×D₄	—	10	2	no	—
197	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
198	C₂²×C₃×C₄	—	2	2	no	—
199	C₂²×C₃×C₄	—	10	2	no	—
200	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
201	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
202	C₃×Q₁₆	—	10	8	no	—
203	C₃×SD₁₆	—	10	8	no	—
204	C₃×SD₁₆	—	10	8	no	—
205	C₃×D₈	—	10	8	no	—
206	C₂×C₃×C₈	—	5	8	no	—
207	C₂×C₃×C₈	—	5	4	no	—
208	C₃×C₄⋊C₄	—	2	2	no	—
209	C₃×C₄⋊C₄	—	10	2	no	—
210	C₃×C₂²⋊C₄	—	2	4	no	—
211	C₃×C₂²⋊C₄	—	10	4	no	—
212	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
213	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
214	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
215	C₂³×C₅	—	2	2	no	—
216	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
217	C₂²×D₅	—	2	2	no	—
218	C₅×Q₈	—	2	4	no	—
219	C₅×D₄	—	2	4	no	—
220	C₅×D₄	—	4	4	no	—
221	C₅×D₄	—	4	4	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	4	2	no	—
224	C₂×C₄×C₅	—	4	4	no	—
225	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
226	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
227	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
228	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
230	C₂²⋊D₅	—	4	4	no	—
231	C₂×Dic₅	—	2	2	no	—
232	D₂₀	—	2	4	no	—
233	D₂₀	—	4	4	no	—
234	C₄×D₅	—	4	4	no	—
235	Dic₁₀	—	2	4	no	—
236	#168	C₂×C₃×D₄	1	8	yes	—
237	C₂×#41	—	5	2	no	—
238	C₂×#41	C₂×C₃×D₅	1	2	yes	—
239	#135	—	10	16	no	—
240	C₂×Q₁₆	—	5	4	no	—
241	C₂×SD₁₆	—	5	4	no	—
242	C₂×SD₁₆	—	5	4	no	—
243	C₂×D₈	—	5	4	no	—
244	C₂²×C₈	—	5	2	no	—
245	C₄⋊Q₈	—	5	1	no	—
246	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
247	#127	—	5	1	no	—
248	#127	C₂×C₃×D₅	1	1	yes	characteristic
249	#124	—	5	2	no	—
250	#124	C₂×C₃×D₅	1	2	yes	—
251	#121	—	2	2	no	—
252	#121	—	10	2	no	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	—	10	2	no	—
255	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
256	#97	—	5	2	no	—
257	#97	—	5	2	no	—
258	C₂×C₃×C₅	—	2	2	no	—
259	C₂×C₃×C₅	—	8	2	no	—
260	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
261	C₂×C₃×C₅	#575	1	2	yes	—
262	C₃×D₅	—	8	2	no	—
263	C₂³×C₃	—	2	2	no	—
264	C₂³×C₃	—	10	2	no	—
265	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
266	C₃×Q₈	—	2	4	no	—
267	C₃×Q₈	—	10	4	no	—
268	C₃×D₄	—	2	4	no	—
269	C₃×D₄	—	4	4	no	—
270	C₃×D₄	—	4	4	no	—
271	C₃×D₄	—	10	4	no	—
272	C₃×D₄	—	20	4	no	—
273	C₃×D₄	—	20	4	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	4	2	no	—
276	C₂×C₃×C₄	—	4	4	no	—
277	C₂×C₃×C₄	—	10	2	no	—
278	C₂×C₃×C₄	—	20	4	no	—
279	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
280	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
281	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
282	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
284	C₃×C₈	—	5	8	no	—
285	C₂²×C₅	—	2	2	no	—
286	C₂²×C₅	—	4	4	no	—
287	C₂²×C₅	—	4	2	no	—
288	C₂²×C₅	C₃×#127	1	2	yes	—
289	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
290	C₂×D₅	—	4	4	no	—
291	C₂×D₅	—	4	2	no	—
292	C₄×C₅	—	2	2	no	—
293	C₄×C₅	—	2	2	no	—
294	C₄×C₅	—	4	2	no	—
295	C₄×C₅	C₃×#127	1	2	yes	—
296	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
297	Dic₅	—	4	2	no	—
298	#41	—	2	8	no	—
299	#41	—	10	8	no	—
300	C₂×Q₈	—	5	2	no	—
301	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	5	2	no	—
305	C₂×D₄	—	10	2	no	—
306	C₂×D₄	—	10	2	no	—
307	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	10	2	no	—
310	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
311	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
312	Q₁₆	—	10	8	no	—
313	SD₁₆	—	10	8	no	—
314	SD₁₆	—	10	8	no	—
315	D₈	—	10	8	no	—
316	C₂×C₈	—	5	8	no	—
317	C₂×C₈	—	5	4	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	10	2	no	—
320	C₂²⋊C₄	—	2	4	no	—
321	C₂²⋊C₄	—	10	4	no	—
322	C₄²	C₃×C₂²⋊D₅	1	2	yes	—
323	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
324	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
325	C₃×C₅	#3150	1	1	yes	characteristic, complemented, Hall
326	C₂²×C₃	—	2	2	no	—
327	C₂²×C₃	—	4	2	no	—
328	C₂²×C₃	—	4	4	no	—
329	C₂²×C₃	—	20	2	no	—
330	C₂²×C₃	—	20	4	no	—
331	C₂²×C₃	#4086	1	2	yes	—
332	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
333	C₃×C₄	—	2	2	no	—
334	C₃×C₄	—	2	2	no	—
335	C₃×C₄	—	4	2	no	—
336	C₃×C₄	—	20	2	no	—
337	C₃×C₄	#4086	1	2	yes	—
338	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
339	C₂×C₅	—	2	2	no	—
340	C₂×C₅	—	8	2	no	—
341	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
342	C₂×C₅	C₃×#575	1	2	yes	—
343	D₅	—	8	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	10	2	no	—
346	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
347	Q₈	—	2	4	no	—
348	Q₈	—	10	4	no	—
349	D₄	—	2	4	no	—
350	D₄	—	4	4	no	—
351	D₄	—	4	4	no	—
352	D₄	—	10	4	no	—
353	D₄	—	20	4	no	—
354	D₄	—	20	4	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	10	2	no	—
359	C₂×C₄	—	20	4	no	—
360	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
361	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
362	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
363	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
364	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
365	C₈	—	5	8	no	—
366	C₂×C₃	—	2	2	no	—
367	C₂×C₃	—	8	2	no	—
368	C₂×C₃	—	40	2	no	—
369	C₂×C₃	C₂×#4086	1	1	yes	characteristic
370	C₂×C₃	#66156	1	2	yes	—
371	C₅	C₃×#3150	1	1	yes	characteristic, complemented, Sylow
372	C₂²	—	2	2	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	20	2	no	—
376	C₂²	—	20	4	no	—
377	C₂²	C₃×#4086	1	2	yes	—
378	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	4	2	no	—
382	C₄	—	20	2	no	—
383	C₄	C₃×#4086	1	2	yes	—
384	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
385	C₃	#10615017	1	1	yes	characteristic, direct product factor, Sylow
386	C₂	—	2	2	no	—
387	C₂	—	8	2	no	—
388	C₂	—	40	2	no	—
389	C₂	C₂×C₃×#4086	1	1	yes	characteristic
390	C₂	C₃×#66156	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#532	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#532	D₅
hypocenter	C₅	C₃×#3150
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×#532

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#532	C₂	semidirect
2. C₂×C₃×#4096	C₂	semidirect
3. C₃×#65811	C₂	semidirect
4. C₃×#65375	C₂	semidirect
5. C₃×#65363	C₂	semidirect
6. C₃×#65349	C₂	semidirect
7. C₃×#65347	C₂	semidirect
8. C₂×C₃×#3935	C₂	semidirect
9. #10615017	C₃	direct (N × H)
32. C₅×#532	C₂×C₃	semidirect
33. C₂×#4096	C₂×C₃	semidirect
34. #65811	C₂×C₃	semidirect
35. #65375	C₂×C₃	semidirect
36. #65363	C₂×C₃	semidirect
37. #65349	C₂×C₃	semidirect
38. #65347	C₂×C₃	semidirect
39. C₂×#3935	C₂×C₃	semidirect
65. C₂×C₃×#168	D₄	semidirect
69. C₃×#532	D₅	semidirect
165. C₂×#168	C₃×D₄	semidirect
169. #532	C₃×D₅	semidirect
325. C₃×C₅	#3150	semidirect
371. C₅	C₃×#3150	semidirect
385. C₃	#10615017	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×#532	2
C₂×C₃×#4096	2
C₃×#65811	2
C₃×#65375	2
C₃×#65363	2
C₃×#65349	2
C₃×#65347	2
C₂×C₃×#3935	2
#10615017	3
C₃×#3150	5

Subgroups — C3×#10615017 #14439079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615017 #14439079