Subgroups — C₃×#10610310 #14418024

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66082	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4047	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65414	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65294	C₂	1	2	yes	maximal, complemented
6	C₃×#65006	C₂	1	4	yes	maximal, complemented
7	C₃×#64989	C₂	1	4	yes	maximal, complemented
8	#10610310	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×#709	C₂²	1	2	yes	—
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₅×#117	C₂²	1	1	yes	characteristic
13	C₂×C₃×#681	C₂²	1	2	yes	—
14	C₃×#4055	C₄	1	4	yes	complemented
15	C₃×#4054	C₄	1	4	yes	complemented
16	C₃×#4050	C₂²	1	4	yes	—
17	C₃×#4047	—	2	2	no	—
18	C₃×#4047	—	2	2	no	—
19	C₃×#4047	C₂²	1	4	yes	complemented
20	C₃×#4047	C₂²	1	4	yes	complemented
21	C₂×C₃×#676	—	2	2	no	—
22	C₂×C₃×C₈×D₅	—	2	2	no	—
23	C₃×C₅×#97	C₂²	1	2	yes	complemented
24	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
25	C₃×#3951	C₂²	1	4	yes	complemented
26	C₃×#3937	C₂²	1	8	yes	complemented
27	C₃×#2955	—	5	1	no	maximal, Hall
28	#66082	C₂×C₃	1	1	yes	characteristic
29	C₂×#4047	C₂×C₃	1	2	yes	complemented
30	C₅×#405	C₂×C₃	1	1	yes	characteristic, complemented
31	#65414	C₂×C₃	1	1	yes	characteristic, complemented
32	#65294	C₂×C₃	1	2	yes	complemented
33	#65006	C₂×C₃	1	4	yes	complemented
34	#64989	C₂×C₃	1	4	yes	complemented
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
37	C₃×#709	—	2	2	no	—
38	C₃×#709	—	2	2	no	—
39	C₃×#709	C₂×C₄	1	4	yes	—
40	C₃×#709	C₂³	1	4	yes	—
41	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
42	C₂×C₃×C₄×D₅	—	2	2	no	—
43	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
44	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	—
45	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
46	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
47	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
48	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
49	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₃×C₅×C₄⋊C₄	—	2	1	no	—
51	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
52	C₃×C₄²×C₅	C₂³	1	2	yes	—
53	C₃×#681	—	2	2	no	—
54	C₃×#681	C₂³	1	4	yes	—
55	C₂×C₃×#168	—	2	2	no	—
56	C₃×Dic₂₀	C₂×C₄	1	4	yes	—
57	C₃×D₄₀	C₂×C₄	1	4	yes	—
58	C₃×#677	C₂×C₄	1	8	yes	—
59	C₃×#676	—	2	4	no	—
60	C₃×#676	—	2	4	no	—
61	C₃×C₈×D₅	—	2	4	no	—
62	C₃×C₈×D₅	—	2	4	no	—
63	C₃×#575	—	5	1	no	—
64	C₂×C₃×#131	—	5	2	no	—
65	C₃×#444	—	5	4	no	—
66	C₃×#443	—	5	4	no	—
67	C₃×#430	—	5	1	no	—
68	C₃×#421	—	5	2	no	—
69	C₃×#405	D₅	1	1	yes	characteristic, complemented
70	C₂×#709	C₂²×C₃	1	2	yes	—
71	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
73	C₅×#117	C₂²×C₃	1	1	yes	characteristic
74	C₂×#681	C₂²×C₃	1	2	yes	—
75	#4055	C₃×C₄	1	4	yes	complemented
76	#4054	C₃×C₄	1	4	yes	complemented
77	#4050	C₂²×C₃	1	4	yes	—
78	#4047	—	2	2	no	—
79	#4047	—	2	2	no	—
80	#4047	C₂²×C₃	1	4	yes	complemented
81	#4047	C₂²×C₃	1	4	yes	complemented
82	C₂×#676	—	2	2	no	—
83	C₂×C₈×D₅	—	2	2	no	—
84	C₅×#97	C₂²×C₃	1	2	yes	complemented
85	C₄×C₅×C₈	C₂²×C₃	1	2	yes	complemented
86	#3951	C₂²×C₃	1	4	yes	complemented
87	#3937	C₂²×C₃	1	8	yes	complemented
88	#2955	—	5	1	no	Sylow
89	C₂³×C₃×C₅	#41	1	1	yes	characteristic
90	C₂²×C₃×D₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
96	C₃×C₂²⋊D₅	—	2	4	no	—
97	C₃×C₂²⋊D₅	—	2	4	no	—
98	C₂×C₃×Dic₅	—	2	2	no	—
99	C₃×D₂₀	—	2	2	no	—
100	C₃×D₂₀	C₂²×C₄	1	4	yes	—
101	C₃×C₄×D₅	—	2	4	no	—
102	C₃×C₄×D₅	—	2	4	no	—
103	C₃×Dic₁₀	—	2	2	no	—
104	C₃×Dic₁₀	C₂²×C₄	1	4	yes	—
105	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
106	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
107	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
108	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
109	C₃×#168	—	2	4	no	—
110	C₂×C₃×#41	—	5	2	no	—
111	C₃×#137	—	5	4	no	—
112	C₃×AGL(1,ℤ/8)	—	5	4	no	—
113	C₃×#135	—	5	4	no	—
114	C₃×#131	—	5	4	no	—
115	C₃×#131	—	5	4	no	—
116	C₃×#131	—	10	2	no	—
117	C₃×#131	—	10	2	no	—
118	C₂×C₃×M₁₆	—	5	2	no	—
119	C₂×C₃×M₁₆	—	10	2	no	—
120	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
121	C₂²×C₃×C₈	—	10	2	no	—
122	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
123	C₃×#117	C₂×D₅	1	1	yes	characteristic
124	C₃×#108	—	5	4	no	—
125	C₃×#104	—	5	8	no	—
126	C₃×#97	C₂×D₅	1	2	yes	complemented
127	C₃×C₄×C₈	C₂×D₅	1	2	yes	complemented
128	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
129	C₂×C₂²⋊D₅	—	2	2	no	—
130	#709	—	2	2	no	—
131	#709	—	2	2	no	—
132	#709	C₂×C₃×C₄	1	4	yes	—
133	#709	C₂³×C₃	1	4	yes	—
134	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
135	C₂×C₄×D₅	—	2	2	no	—
136	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
137	C₅×M₁₆	C₂×C₃×C₄	1	4	yes	—
138	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
139	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
140	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
141	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
142	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
143	C₅×C₄⋊C₄	—	2	1	no	—
144	C₅×C₂²⋊C₄	—	2	1	no	—
145	C₄²×C₅	C₂³×C₃	1	2	yes	—
146	#681	—	2	2	no	—
147	#681	C₂³×C₃	1	4	yes	—
148	C₂×#168	—	2	2	no	—
149	Dic₂₀	C₂×C₃×C₄	1	4	yes	—
150	D₄₀	C₂×C₃×C₄	1	4	yes	—
151	#677	C₂×C₃×C₄	1	8	yes	—
152	#676	—	2	4	no	—
153	#676	—	2	4	no	—
154	C₈×D₅	—	2	4	no	—
155	C₈×D₅	—	2	4	no	—
156	#575	—	5	1	no	—
157	C₂×#131	—	5	2	no	—
158	#444	—	5	4	no	—
159	#443	—	5	4	no	—
160	#430	—	5	1	no	—
161	#421	—	5	2	no	—
162	#405	C₃×D₅	1	1	yes	characteristic, complemented
163	C₂²×C₃×C₅	—	4	1	no	—
164	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
165	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
166	C₂×C₃×D₅	—	2	4	no	—
167	C₂×C₃×D₅	—	4	4	no	—
168	C₃×C₄×C₅	—	4	2	no	—
169	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
170	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
171	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
172	C₃×Dic₅	—	2	4	no	—
173	C₃×#41	—	5	4	no	—
174	C₃×#41	—	5	4	no	—
175	C₃×#41	—	10	2	no	—
176	C₃×#41	—	10	2	no	—
177	C₂×C₃×Q₈	—	5	2	no	—
178	C₂×C₃×D₄	—	5	2	no	—
179	C₂×C₃×D₄	—	10	2	no	—
180	C₂²×C₃×C₄	—	10	2	no	—
181	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
182	C₃×Q₁₆	—	5	4	no	—
183	C₃×SD₁₆	—	5	8	no	—
184	C₃×D₈	—	5	4	no	—
185	C₃×M₁₆	—	5	4	no	—
186	C₃×M₁₆	—	10	2	no	—
187	C₃×M₁₆	—	10	4	no	—
188	C₃×M₁₆	—	10	4	no	—
189	C₃×M₁₆	C₄×D₅	1	4	yes	—
190	C₂×C₃×C₈	—	10	2	no	—
191	C₂×C₃×C₈	—	10	4	no	—
192	C₂×C₃×C₈	—	10	4	no	—
193	C₂×C₃×C₈	D₂₀	1	2	yes	—
194	C₂×C₃×C₈	D₂₀	1	2	yes	—
195	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
196	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
197	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
198	C₃×C₄⋊C₄	—	2	1	no	—
199	C₃×C₂²⋊C₄	—	2	1	no	—
200	C₃×C₄²	C₂²×D₅	1	2	yes	—
201	C₂³×C₅	C₃×#41	1	1	yes	characteristic
202	C₂²×D₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
205	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
206	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
208	C₂²⋊D₅	—	2	4	no	—
209	C₂²⋊D₅	—	2	4	no	—
210	C₂×Dic₅	—	2	2	no	—
211	D₂₀	—	2	2	no	—
212	D₂₀	C₂²×C₃×C₄	1	4	yes	—
213	C₄×D₅	—	2	4	no	—
214	C₄×D₅	—	2	4	no	—
215	Dic₁₀	—	2	2	no	—
216	Dic₁₀	C₂²×C₃×C₄	1	4	yes	—
217	C₅×C₈	C₂²×C₃×C₄	1	4	yes	—
218	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
219	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
220	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
221	#168	—	2	4	no	—
222	C₂×#41	—	5	2	no	—
223	#137	—	5	4	no	—
224	AGL(1,ℤ/8)	—	5	4	no	—
225	#135	—	5	4	no	—
226	#131	—	5	4	no	—
227	#131	—	5	4	no	—
228	#131	—	10	2	no	—
229	#131	—	10	2	no	—
230	C₂×M₁₆	—	5	2	no	—
231	C₂×M₁₆	—	10	2	no	—
232	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
233	C₂²×C₈	—	10	2	no	—
234	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
235	#117	C₂×C₃×D₅	1	1	yes	characteristic
236	#108	—	5	4	no	—
237	#104	—	5	8	no	—
238	#97	C₂×C₃×D₅	1	2	yes	complemented
239	C₄×C₈	C₂×C₃×D₅	1	2	yes	complemented
240	C₂×C₃×C₅	—	2	1	no	—
241	C₂×C₃×C₅	—	2	2	no	—
242	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
243	C₃×D₅	—	4	4	no	—
244	C₂³×C₃	—	10	2	no	—
245	C₂³×C₃	#709	1	1	yes	characteristic
246	C₃×Q₈	—	5	4	no	—
247	C₃×Q₈	—	10	2	no	—
248	C₃×D₄	—	5	4	no	—
249	C₃×D₄	—	10	4	no	—
250	C₃×D₄	—	10	4	no	—
251	C₃×D₄	—	10	2	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	10	2	no	—
254	C₂×C₃×C₄	—	10	4	no	—
255	C₂×C₃×C₄	—	10	4	no	—
256	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
257	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
258	C₂×C₃×C₄	#709	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
260	C₃×C₈	—	10	4	no	—
261	C₃×C₈	C₂×C₄×D₅	1	4	yes	—
262	C₃×C₈	C₂×D₂₀	1	2	yes	—
263	C₃×C₈	C₂×D₂₀	1	1	yes	characteristic
264	C₃×C₈	C₂×D₂₀	1	1	yes	characteristic
265	C₂²×C₅	—	4	1	no	—
266	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
267	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
268	C₂×D₅	—	2	4	no	—
269	C₂×D₅	—	4	4	no	—
270	C₄×C₅	—	4	2	no	—
271	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
272	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
273	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
274	Dic₅	—	2	4	no	—
275	#41	—	5	4	no	—
276	#41	—	5	4	no	—
277	#41	—	10	2	no	—
278	#41	—	10	2	no	—
279	C₂×Q₈	—	5	2	no	—
280	C₂×D₄	—	5	2	no	—
281	C₂×D₄	—	10	2	no	—
282	C₂²×C₄	—	10	2	no	—
283	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
284	Q₁₆	—	5	4	no	—
285	SD₁₆	—	5	8	no	—
286	D₈	—	5	4	no	—
287	M₁₆	—	5	4	no	—
288	M₁₆	—	10	2	no	—
289	M₁₆	—	10	4	no	—
290	M₁₆	—	10	4	no	—
291	M₁₆	C₃×C₄×D₅	1	4	yes	—
292	C₂×C₈	—	10	2	no	—
293	C₂×C₈	—	10	4	no	—
294	C₂×C₈	—	10	4	no	—
295	C₂×C₈	C₃×D₂₀	1	2	yes	—
296	C₂×C₈	C₃×D₂₀	1	2	yes	—
297	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
298	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
299	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
300	C₄⋊C₄	—	2	1	no	—
301	C₂²⋊C₄	—	2	1	no	—
302	C₄²	C₂²×C₃×D₅	1	2	yes	—
303	C₃×C₅	#2955	1	1	yes	characteristic, complemented, Hall
304	C₂²×C₃	—	4	1	no	—
305	C₂²×C₃	—	10	4	no	—
306	C₂²×C₃	—	20	4	no	—
307	C₂²×C₃	C₄×D₂₀	1	2	yes	—
308	C₂²×C₃	C₂×#709	1	1	yes	characteristic
309	C₃×C₄	—	4	2	no	—
310	C₃×C₄	—	10	4	no	—
311	C₃×C₄	C₄×D₂₀	1	2	yes	—
312	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
313	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
314	C₂×C₅	—	2	1	no	—
315	C₂×C₅	—	2	2	no	—
316	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
317	D₅	—	4	4	no	—
318	C₂³	—	10	2	no	—
319	C₂³	C₃×#709	1	1	yes	characteristic
320	Q₈	—	5	4	no	—
321	Q₈	—	10	2	no	—
322	D₄	—	5	4	no	—
323	D₄	—	10	4	no	—
324	D₄	—	10	4	no	—
325	D₄	—	10	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	10	2	no	—
328	C₂×C₄	—	10	4	no	—
329	C₂×C₄	—	10	4	no	—
330	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
331	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
332	C₂×C₄	C₃×#709	1	1	yes	characteristic
333	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
334	C₈	—	10	4	no	—
335	C₈	C₂×C₃×C₄×D₅	1	4	yes	—
336	C₈	C₂×C₃×D₂₀	1	1	yes	characteristic
337	C₈	C₂×C₃×D₂₀	1	2	yes	—
338	C₈	C₂×C₃×D₂₀	1	1	yes	characteristic
339	C₂×C₃	—	2	1	no	—
340	C₂×C₃	—	2	2	no	—
341	C₂×C₃	—	20	4	no	—
342	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
343	C₅	C₃×#2955	1	1	yes	characteristic, complemented, Sylow
344	C₂²	—	4	1	no	—
345	C₂²	—	10	4	no	—
346	C₂²	—	20	4	no	—
347	C₂²	C₃×C₄×D₂₀	1	2	yes	—
348	C₂²	C₂×C₃×#709	1	1	yes	characteristic
349	C₄	—	4	2	no	—
350	C₄	—	10	4	no	—
351	C₄	C₃×C₄×D₂₀	1	2	yes	—
352	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
353	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
354	C₃	#10610310	1	1	yes	characteristic, direct product factor, Sylow
355	C₂	—	2	1	no	—
356	C₂	—	2	2	no	—
357	C₂	—	20	4	no	—
358	C₂	C₂×C₃×C₄×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₈	C₂×D₂₀
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#405	C₂
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	C₃×#66082	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#405	D₅
hypocenter	C₅	C₃×#2955
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₈ ◁ C₂²×C₃×C₈ ◁ C₃×#405

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4047	C₂	semidirect
3. C₃×C₅×#405	C₂	semidirect
4. C₃×#65414	C₂	semidirect
5. C₃×#65294	C₂	semidirect
6. C₃×#65006	C₂	semidirect
7. C₃×#64989	C₂	semidirect
8. #10610310	C₃	direct (N × H)
14. C₃×#4055	C₄	semidirect
15. C₃×#4054	C₄	semidirect
19. C₃×#4047	C₂²	semidirect
20. C₃×#4047	C₂²	semidirect
23. C₃×C₅×#97	C₂²	semidirect
24. C₃×C₄×C₅×C₈	C₂²	semidirect
25. C₃×#3951	C₂²	semidirect
26. C₃×#3937	C₂²	semidirect
29. C₂×#4047	C₂×C₃	semidirect
30. C₅×#405	C₂×C₃	semidirect
31. #65414	C₂×C₃	semidirect
32. #65294	C₂×C₃	semidirect
33. #65006	C₂×C₃	semidirect
34. #64989	C₂×C₃	semidirect
69. C₃×#405	D₅	semidirect
75. #4055	C₃×C₄	semidirect
76. #4054	C₃×C₄	semidirect
80. #4047	C₂²×C₃	semidirect
81. #4047	C₂²×C₃	semidirect
84. C₅×#97	C₂²×C₃	semidirect
85. C₄×C₅×C₈	C₂²×C₃	semidirect
86. #3951	C₂²×C₃	semidirect
87. #3937	C₂²×C₃	semidirect
126. C₃×#97	C₂×D₅	semidirect
127. C₃×C₄×C₈	C₂×D₅	semidirect
162. #405	C₃×D₅	semidirect
238. #97	C₂×C₃×D₅	semidirect
239. C₄×C₈	C₂×C₃×D₅	semidirect
303. C₃×C₅	#2955	semidirect
343. C₅	C₃×#2955	semidirect
354. C₃	#10610310	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×#66082	2
C₂×C₃×#4047	2
C₃×C₅×#405	2
C₃×#65414	2
C₃×#65294	2
C₃×#65006	2
C₃×#64989	2
#10610310	3
C₃×#2955	5

Subgroups — C3×#10610310 #14418024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610310 #14418024