Subgroups — C₃×#10603920 #14295518

Order 1920.

568 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	C₂×C₃×#4131	C₂	1	1	yes	maximal, characteristic
2	C₃×#65777	C₂	1	1	yes	maximal, characteristic
3	C₃×#65691	C₂	1	2	yes	maximal, complemented
4	C₃×#65029	C₂	1	1	yes	maximal, characteristic
5	C₃×#64867	C₂	1	2	yes	maximal, complemented
6	#10603920	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×#711	C₂²	1	1	yes	characteristic
8	C₂×C₃×#704	C₄	1	1	yes	characteristic, complemented
9	C₂×C₃×#704	C₂²	1	2	yes	—
10	C₂×C₃×#704	C₂²	1	1	yes	characteristic
11	C₂²×C₃×#170	C₄	1	1	yes	characteristic, complemented
12	C₂²×C₃×#170	C₂²	1	1	yes	characteristic
13	C₃×#4131	—	2	2	no	—
14	C₃×#4131	—	2	2	no	—
15	C₂×C₃×#700	C₄	1	1	yes	characteristic, complemented
16	C₂×C₃×D₅⋊C₈	C₄	1	1	yes	characteristic, complemented
17	C₃×#4023	C₂²	1	2	yes	—
18	C₃×#4013	C₄	1	2	yes	complemented
19	C₃×#4005	C₄	1	2	yes	complemented
20	C₃×#4002	—	2	2	no	—
21	C₃×C₄×#170	—	2	2	no	—
22	C₃×C₅×#99	C₄	1	1	yes	characteristic
23	C₃×#3966	C₄	1	1	yes	characteristic
24	C₃×#3938	C₄	1	2	yes	—
25	C₃×#1757	—	5	1	no	maximal, Hall
26	C₂×#4131	C₂×C₃	1	1	yes	characteristic
27	#65777	C₂×C₃	1	1	yes	characteristic
28	#65691	C₂×C₃	1	2	yes	complemented
29	#65029	C₂×C₃	1	1	yes	characteristic
30	#64867	C₂×C₃	1	2	yes	complemented
31	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
32	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
33	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
36	C₃×#711	—	2	2	no	—
37	C₃×#711	—	2	2	no	—
38	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
40	C₃×#704	—	2	2	no	—
41	C₃×#704	—	2	2	no	—
42	C₃×#704	—	2	2	no	—
43	C₃×#704	C₂×C₄	1	4	yes	—
44	C₂×C₃×#170	—	2	2	no	—
45	C₂×C₃×#170	—	2	1	no	—
46	C₂×C₃×#170	—	2	1	no	—
47	C₂×C₃×#170	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃×#170	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×#170	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×#170	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×#170	D₄	1	2	yes	—
52	C₂×C₃×#170	D₄	1	2	yes	—
53	C₃×#700	—	2	2	no	—
54	C₃×D₅⋊C₈	—	2	1	no	—
55	C₃×D₅⋊C₈	—	2	1	no	—
56	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
57	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
58	C₃×#683	—	2	2	no	—
59	C₃×C₄×Dic₅	—	2	2	no	—
60	C₂×C₃×#131	—	5	1	no	—
61	C₃×#413	—	5	1	no	—
62	C₃×#410	—	5	1	no	—
63	C₃×#405	—	5	2	no	—
64	C₃×#344	—	5	2	no	—
65	C₂×#711	C₂²×C₃	1	1	yes	characteristic
66	C₂×#704	C₃×C₄	1	1	yes	characteristic, complemented
67	C₂×#704	C₂²×C₃	1	2	yes	—
68	C₂×#704	C₂²×C₃	1	1	yes	characteristic
69	C₂²×#170	C₃×C₄	1	1	yes	characteristic, complemented
70	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
71	#4131	—	2	2	no	—
72	#4131	—	2	2	no	—
73	C₂×#700	C₃×C₄	1	1	yes	characteristic, complemented
74	C₂×D₅⋊C₈	C₃×C₄	1	1	yes	characteristic, complemented
75	#4023	C₂²×C₃	1	2	yes	—
76	#4013	C₃×C₄	1	2	yes	complemented
77	#4005	C₃×C₄	1	2	yes	complemented
78	#4002	—	2	2	no	—
79	C₄×#170	—	2	2	no	—
80	C₅×#99	C₃×C₄	1	1	yes	characteristic
81	#3966	C₃×C₄	1	1	yes	characteristic
82	#3938	C₃×C₄	1	2	yes	—
83	#1757	—	5	1	no	Sylow
84	C₂³×C₃×C₅	C₄²	1	1	yes	characteristic
85	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₃×D₅	C₄²	1	1	yes	characteristic
87	C₃×C₅×D₄	—	2	2	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
90	C₃×C₂²⋊D₅	—	2	2	no	—
91	C₃×C₂²⋊D₅	—	2	2	no	—
92	C₂×C₃×Dic₅	—	2	1	no	—
93	C₂×C₃×Dic₅	—	2	1	no	—
94	C₂×C₃×Dic₅	—	2	2	no	—
95	C₂×C₃×Dic₅	C₄²	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	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
99	C₂×C₃×Dic₅	#41	1	2	yes	—
100	C₃×C₄×D₅	—	2	1	no	—
101	C₃×C₄×D₅	—	2	1	no	—
102	C₃×Dic₁₀	—	2	2	no	—
103	C₃×#170	—	2	1	no	—
104	C₃×#170	—	2	1	no	—
105	C₃×#170	—	2	4	no	—
106	C₃×#170	C₂²⋊C₄	1	1	yes	characteristic
107	C₃×#170	C₂²⋊C₄	1	1	yes	characteristic
108	C₃×#170	C₂²⋊C₄	1	2	yes	—
109	C₂×C₃×#41	—	5	1	no	—
110	C₃×#131	—	10	2	no	—
111	C₃×#131	—	10	2	no	—
112	C₂×C₃×M₁₆	—	5	1	no	—
113	C₂×C₃×M₁₆	—	5	1	no	—
114	C₂×C₃×M₁₆	—	5	1	no	—
115	C₂×C₃×M₁₆	—	5	2	no	—
116	C₂²×C₃×C₈	—	5	1	no	—
117	C₂²×C₃×C₈	—	5	1	no	—
118	C₂²×C₃×C₈	—	5	1	no	—
119	C₃×#117	—	5	2	no	—
120	C₃×#101	—	5	2	no	—
121	C₃×#100	—	5	2	no	—
122	C₃×#99	—	5	1	no	—
123	C₃×#99	—	5	2	no	—
124	C₃×#99	AGL(1,𝔽₅)	1	1	yes	characteristic
125	C₃×#97	—	10	2	no	—
126	C₃×C₄×C₈	—	10	2	no	—
127	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
128	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
129	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
130	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
131	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
132	#711	—	2	2	no	—
133	#711	—	2	2	no	—
134	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
135	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
136	#704	—	2	2	no	—
137	#704	—	2	2	no	—
138	#704	—	2	2	no	—
139	#704	C₂×C₃×C₄	1	4	yes	—
140	C₂×#170	—	2	2	no	—
141	C₂×#170	—	2	1	no	—
142	C₂×#170	—	2	1	no	—
143	C₂×#170	C₂×C₃×C₄	1	1	yes	characteristic
144	C₂×#170	C₂×C₃×C₄	1	1	yes	characteristic
145	C₂×#170	C₂×C₃×C₄	1	1	yes	characteristic
146	C₂×#170	C₂×C₃×C₄	1	1	yes	characteristic
147	C₂×#170	C₃×D₄	1	2	yes	—
148	C₂×#170	C₃×D₄	1	2	yes	—
149	#700	—	2	2	no	—
150	D₅⋊C₈	—	2	1	no	—
151	D₅⋊C₈	—	2	1	no	—
152	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
153	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
154	#683	—	2	2	no	—
155	C₄×Dic₅	—	2	2	no	—
156	C₂×#131	—	5	1	no	—
157	#413	—	5	1	no	—
158	#410	—	5	1	no	—
159	#405	—	5	2	no	—
160	#344	—	5	2	no	—
161	C₂²×C₃×C₅	—	2	1	no	—
162	C₂²×C₃×C₅	—	4	1	no	—
163	C₂²×C₃×C₅	—	4	1	no	—
164	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
165	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
166	C₂×C₃×D₅	—	2	1	no	—
167	C₂×C₃×D₅	—	4	1	no	—
168	C₃×C₄×C₅	—	2	1	no	—
169	C₃×C₄×C₅	—	4	2	no	—
170	C₃×Dic₅	—	2	1	no	—
171	C₃×Dic₅	—	4	2	no	—
172	C₃×Dic₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₃×Dic₅	#117	1	1	yes	characteristic
174	C₃×Dic₅	C₄×D₄	1	2	yes	—
175	C₃×#41	—	10	2	no	—
176	C₃×#41	—	10	2	no	—
177	C₂×C₃×Q₈	—	5	1	no	—
178	C₂×C₃×D₄	—	5	1	no	—
179	C₂×C₃×D₄	—	5	1	no	—
180	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
181	C₂²×C₃×C₄	—	5	1	no	—
182	C₂²×C₃×C₄	—	5	1	no	—
183	C₂²×C₃×C₄	—	5	1	no	—
184	C₃×M₁₆	—	5	4	no	—
185	C₃×M₁₆	—	10	2	no	—
186	C₃×M₁₆	—	10	2	no	—
187	C₃×M₁₆	—	10	2	no	—
188	C₃×M₁₆	—	10	2	no	—
189	C₂×C₃×C₈	—	5	2	no	—
190	C₂×C₃×C₈	—	5	2	no	—
191	C₂×C₃×C₈	—	5	1	no	—
192	C₂×C₃×C₈	—	5	1	no	—
193	C₂×C₃×C₈	—	5	1	no	—
194	C₂×C₃×C₈	—	5	1	no	—
195	C₂×C₃×C₈	—	10	1	no	—
196	C₂×C₃×C₈	—	10	1	no	—
197	C₂×C₃×C₈	—	10	1	no	—
198	C₂×C₃×C₈	—	10	1	no	—
199	C₂×C₃×C₈	—	10	2	no	—
200	C₃×C₄⋊C₄	—	10	2	no	—
201	C₃×C₂²⋊C₄	—	5	2	no	—
202	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
203	C₃×C₄²	—	10	2	no	—
204	C₂³×C₅	C₃×C₄²	1	1	yes	characteristic
205	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
206	C₂²×D₅	C₃×C₄²	1	1	yes	characteristic
207	C₅×D₄	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
210	C₂²⋊D₅	—	2	2	no	—
211	C₂²⋊D₅	—	2	2	no	—
212	C₂×Dic₅	—	2	1	no	—
213	C₂×Dic₅	—	2	1	no	—
214	C₂×Dic₅	—	2	2	no	—
215	C₂×Dic₅	C₃×C₄²	1	1	yes	characteristic
216	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
217	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
218	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
219	C₂×Dic₅	C₃×#41	1	2	yes	—
220	C₄×D₅	—	2	1	no	—
221	C₄×D₅	—	2	1	no	—
222	Dic₁₀	—	2	2	no	—
223	#170	—	2	1	no	—
224	#170	—	2	1	no	—
225	#170	—	2	4	no	—
226	#170	C₃×C₂²⋊C₄	1	1	yes	characteristic
227	#170	C₃×C₂²⋊C₄	1	1	yes	characteristic
228	#170	C₃×C₂²⋊C₄	1	2	yes	—
229	C₂×#41	—	5	1	no	—
230	#131	—	10	2	no	—
231	#131	—	10	2	no	—
232	C₂×M₁₆	—	5	1	no	—
233	C₂×M₁₆	—	5	1	no	—
234	C₂×M₁₆	—	5	1	no	—
235	C₂×M₁₆	—	5	2	no	—
236	C₂²×C₈	—	5	1	no	—
237	C₂²×C₈	—	5	1	no	—
238	C₂²×C₈	—	5	1	no	—
239	#117	—	5	2	no	—
240	#101	—	5	2	no	—
241	#100	—	5	2	no	—
242	#99	—	5	1	no	—
243	#99	—	5	2	no	—
244	#99	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
245	#97	—	10	2	no	—
246	C₄×C₈	—	10	2	no	—
247	C₂×C₃×C₅	—	2	2	no	—
248	C₂×C₃×C₅	—	2	1	no	—
249	C₂×C₃×C₅	—	4	1	no	—
250	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
251	C₃×D₅	—	4	1	no	—
252	C₂³×C₃	—	5	1	no	—
253	C₂³×C₃	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
254	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
255	C₃×Q₈	—	10	2	no	—
256	C₃×D₄	—	2	2	no	—
257	C₃×D₄	—	10	2	no	—
258	C₃×D₄	—	10	2	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	5	1	no	—
261	C₂×C₃×C₄	—	5	1	no	—
262	C₂×C₃×C₄	—	5	2	no	—
263	C₂×C₃×C₄	—	5	2	no	—
264	C₂×C₃×C₄	—	5	1	no	—
265	C₂×C₃×C₄	—	10	1	no	—
266	C₂×C₃×C₄	—	10	1	no	—
267	C₂×C₃×C₄	—	10	1	no	—
268	C₂×C₃×C₄	—	10	1	no	—
269	C₂×C₃×C₄	—	10	2	no	—
270	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
271	C₃×C₈	—	5	1	no	—
272	C₃×C₈	—	5	1	no	—
273	C₃×C₈	—	5	2	no	—
274	C₃×C₈	—	10	1	no	—
275	C₃×C₈	—	10	1	no	—
276	C₃×C₈	—	10	4	no	—
277	C₂²×C₅	—	2	1	no	—
278	C₂²×C₅	—	4	1	no	—
279	C₂²×C₅	—	4	1	no	—
280	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
281	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
282	C₂×D₅	—	2	1	no	—
283	C₂×D₅	—	4	1	no	—
284	C₄×C₅	—	2	1	no	—
285	C₄×C₅	—	4	2	no	—
286	Dic₅	—	2	1	no	—
287	Dic₅	—	4	2	no	—
288	Dic₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
289	Dic₅	C₃×#117	1	1	yes	characteristic
290	Dic₅	C₃×C₄×D₄	1	2	yes	—
291	#41	—	10	2	no	—
292	#41	—	10	2	no	—
293	C₂×Q₈	—	5	1	no	—
294	C₂×D₄	—	5	1	no	—
295	C₂×D₄	—	5	1	no	—
296	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
297	C₂²×C₄	—	5	1	no	—
298	C₂²×C₄	—	5	1	no	—
299	C₂²×C₄	—	5	1	no	—
300	M₁₆	—	5	4	no	—
301	M₁₆	—	10	2	no	—
302	M₁₆	—	10	2	no	—
303	M₁₆	—	10	2	no	—
304	M₁₆	—	10	2	no	—
305	C₂×C₈	—	5	2	no	—
306	C₂×C₈	—	5	2	no	—
307	C₂×C₈	—	5	1	no	—
308	C₂×C₈	—	5	1	no	—
309	C₂×C₈	—	5	1	no	—
310	C₂×C₈	—	5	1	no	—
311	C₂×C₈	—	10	1	no	—
312	C₂×C₈	—	10	1	no	—
313	C₂×C₈	—	10	1	no	—
314	C₂×C₈	—	10	1	no	—
315	C₂×C₈	—	10	2	no	—
316	C₄⋊C₄	—	10	2	no	—
317	C₂²⋊C₄	—	5	2	no	—
318	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
319	C₄²	—	10	2	no	—
320	C₃×C₅	#1757	1	1	yes	characteristic, complemented, Hall
321	C₂²×C₃	—	2	1	no	—
322	C₂²×C₃	—	4	1	no	—
323	C₂²×C₃	—	4	1	no	—
324	C₂²×C₃	—	10	1	no	—
325	C₂²×C₃	—	20	1	no	—
326	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
327	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	2	yes	—
328	C₃×C₄	—	2	1	no	—
329	C₃×C₄	—	4	2	no	—
330	C₃×C₄	—	5	1	no	—
331	C₃×C₄	—	5	1	no	—
332	C₃×C₄	—	5	2	no	—
333	C₃×C₄	—	10	1	no	—
334	C₃×C₄	—	20	2	no	—
335	C₂×C₅	—	2	2	no	—
336	C₂×C₅	—	2	1	no	—
337	C₂×C₅	—	4	1	no	—
338	C₂×C₅	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic
339	D₅	—	4	1	no	—
340	C₂³	—	5	1	no	—
341	C₂³	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
342	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
343	Q₈	—	10	2	no	—
344	D₄	—	2	2	no	—
345	D₄	—	10	2	no	—
346	D₄	—	10	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	5	1	no	—
349	C₂×C₄	—	5	1	no	—
350	C₂×C₄	—	5	2	no	—
351	C₂×C₄	—	5	2	no	—
352	C₂×C₄	—	5	1	no	—
353	C₂×C₄	—	10	1	no	—
354	C₂×C₄	—	10	1	no	—
355	C₂×C₄	—	10	1	no	—
356	C₂×C₄	—	10	1	no	—
357	C₂×C₄	—	10	2	no	—
358	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
359	C₈	—	5	1	no	—
360	C₈	—	5	1	no	—
361	C₈	—	5	2	no	—
362	C₈	—	10	1	no	—
363	C₈	—	10	1	no	—
364	C₈	—	10	4	no	—
365	C₂×C₃	—	2	2	no	—
366	C₂×C₃	—	2	1	no	—
367	C₂×C₃	—	4	1	no	—
368	C₂×C₃	—	20	1	no	—
369	C₂×C₃	C₂²⋊C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
370	C₅	C₃×#1757	1	1	yes	characteristic, complemented, Sylow
371	C₂²	—	2	1	no	—
372	C₂²	—	4	1	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	10	1	no	—
375	C₂²	—	20	1	no	—
376	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
377	C₂²	C₃×D₄×AGL(1,𝔽₅)	1	2	yes	—
378	C₄	—	2	1	no	—
379	C₄	—	4	2	no	—
380	C₄	—	5	1	no	—
381	C₄	—	5	2	no	—
382	C₄	—	5	1	no	—
383	C₄	—	10	1	no	—
384	C₄	—	20	2	no	—
385	C₃	#10603920	1	1	yes	characteristic, direct product factor, Sylow
386	C₂	—	2	2	no	—
387	C₂	—	2	1	no	—
388	C₂	—	4	1	no	—
389	C₂	—	20	1	no	—
390	C₂	C₃×C₂²⋊C₄×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²⋊C₄×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂×C₃×C₄²
Frattini	C₂³	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×#99	C₄
socle	C₂×C₃×C₅	C₄×C₂²⋊C₄
prime radical	C₂×C₃×#711	C₂²
cosocle	C₂²×Dic₅	C₂³×C₃
hypercenter	C₃×#99	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#1757
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂³×C₃ ◁ C₃×#99

Complements

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

N	H ≅ G/N	type
3. C₃×#65691	C₂	semidirect
5. C₃×#64867	C₂	semidirect
6. #10603920	C₃	direct (N × H)
8. C₂×C₃×#704	C₄	semidirect
11. C₂²×C₃×#170	C₄	semidirect
15. C₂×C₃×#700	C₄	semidirect
16. C₂×C₃×D₅⋊C₈	C₄	semidirect
18. C₃×#4013	C₄	semidirect
19. C₃×#4005	C₄	semidirect
28. #65691	C₂×C₃	semidirect
30. #64867	C₂×C₃	semidirect
66. C₂×#704	C₃×C₄	semidirect
69. C₂²×#170	C₃×C₄	semidirect
73. C₂×#700	C₃×C₄	semidirect
74. C₂×D₅⋊C₈	C₃×C₄	semidirect
76. #4013	C₃×C₄	semidirect
77. #4005	C₃×C₄	semidirect
320. C₃×C₅	#1757	semidirect
370. C₅	C₃×#1757	semidirect
385. C₃	#10603920	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×#4131	2
C₃×#65777	2
C₃×#65691	2
C₃×#65029	2
C₃×#64867	2
#10603920	3
C₃×#1757	5

Subgroups — C3×#10603920 #14295518

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10603920 #14295518