Subgroups — C₃×#10613738 #14478161

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4047	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3944	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65196	C₂	1	4	yes	maximal, complemented
5	C₃×D₅×M₃₂	C₂	1	4	yes	maximal, complemented
6	C₃×#65190	C₂	1	4	yes	maximal, complemented
7	#10613738	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×#709	C₄	1	1	yes	characteristic
9	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₂×C₃×#681	C₄	1	1	yes	characteristic
11	C₃×#4047	C₄	1	2	yes	—
12	C₃×#4047	C₄	1	2	yes	—
13	C₃×#4047	C₂²	1	2	yes	—
14	C₃×#4047	C₂²	1	2	yes	—
15	C₂×C₃×#676	C₄	1	2	yes	—
16	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
17	C₃×C₅×M₃₂	C₂²	1	2	yes	—
18	C₃×C₅×M₃₂	C₂²	1	2	yes	complemented
19	C₂×C₃×C₅×C₁₆	C₂²	1	2	yes	complemented
20	C₃×#3944	C₂²	1	2	yes	—
21	C₃×#3944	C₂²	1	2	yes	complemented
22	C₂×C₃×#672	C₂²	1	2	yes	complemented
23	C₃×#3930	C₂²	1	8	yes	complemented
24	C₃×D₅×C₁₆	C₂²	1	8	yes	complemented
25	C₃×#3407	—	5	1	no	maximal, Hall
26	C₂×#4047	C₂×C₃	1	1	yes	characteristic
27	C₂×C₅×M₃₂	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×#3944	C₂×C₃	1	1	yes	characteristic, complemented
29	#65196	C₂×C₃	1	4	yes	complemented
30	D₅×M₃₂	C₂×C₃	1	4	yes	complemented
31	#65190	C₂×C₃	1	4	yes	complemented
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂×C₃×C₂²⋊D₅	C₈	1	2	yes	—
34	C₃×#709	C₈	1	2	yes	—
35	C₃×#709	C₈	1	2	yes	—
36	C₃×#709	C₂×C₄	1	2	yes	—
37	C₃×#709	C₂×C₄	1	2	yes	—
38	C₂×C₃×D₂₀	C₈	1	1	yes	characteristic
39	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
40	C₂×C₃×Dic₁₀	C₈	1	1	yes	characteristic
41	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
45	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
46	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
47	C₃×#681	C₂×C₄	1	2	yes	—
48	C₃×#681	C₂×C₄	1	2	yes	—
49	C₂×C₃×#168	C₂×C₄	1	2	yes	—
50	C₃×#676	C₂×C₄	1	4	yes	—
51	C₃×#676	C₂×C₄	1	4	yes	—
52	C₃×C₈×D₅	C₂×C₄	1	4	yes	—
53	C₃×C₈×D₅	C₂³	1	4	yes	—
54	C₃×C₅×C₁₆	C₂³	1	4	yes	—
55	C₃×#672	C₂³	1	4	yes	—
56	C₂×C₃×#131	—	5	1	no	—
57	C₃×#504	—	5	4	no	—
58	C₃×#504	—	5	4	no	—
59	C₂×C₃×M₃₂	—	5	1	no	—
60	C₂×C₃×M₃₂	—	5	4	no	—
61	C₂×C₃×M₃₂	D₅	1	1	yes	characteristic, complemented
62	C₂×#709	C₃×C₄	1	1	yes	characteristic
63	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
64	C₂×#681	C₃×C₄	1	1	yes	characteristic
65	#4047	C₃×C₄	1	2	yes	—
66	#4047	C₃×C₄	1	2	yes	—
67	#4047	C₂²×C₃	1	2	yes	—
68	#4047	C₂²×C₃	1	2	yes	—
69	C₂×#676	C₃×C₄	1	2	yes	—
70	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
71	C₅×M₃₂	C₂²×C₃	1	2	yes	—
72	C₅×M₃₂	C₂²×C₃	1	2	yes	complemented
73	C₂×C₅×C₁₆	C₂²×C₃	1	2	yes	complemented
74	#3944	C₂²×C₃	1	2	yes	—
75	#3944	C₂²×C₃	1	2	yes	complemented
76	C₂×#672	C₂²×C₃	1	2	yes	complemented
77	#3930	C₂²×C₃	1	8	yes	complemented
78	D₅×C₁₆	C₂²×C₃	1	8	yes	complemented
79	#3407	—	5	1	no	Sylow
80	C₂³×C₃×C₅	C₂×C₈	1	1	yes	characteristic
81	C₂²×C₃×D₅	C₂×C₈	1	2	yes	—
82	C₂×C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
83	C₂×C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
84	C₂×C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
85	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₃×C₂²⋊D₅	C₂×C₈	1	4	yes	—
89	C₃×C₂²⋊D₅	C₂×C₈	1	4	yes	—
90	C₂×C₃×Dic₅	C₂×C₈	1	2	yes	—
91	C₃×D₂₀	C₂×C₈	1	2	yes	—
92	C₃×D₂₀	C₂×C₈	1	2	yes	—
93	C₃×C₄×D₅	C₂×C₈	1	4	yes	—
94	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
95	C₃×Dic₁₀	C₂×C₈	1	2	yes	—
96	C₃×Dic₁₀	C₂×C₈	1	2	yes	—
97	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
98	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
99	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
100	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
101	C₃×#168	C₂²×C₄	1	4	yes	—
102	C₂×C₃×#41	—	5	1	no	—
103	C₃×#131	—	5	2	no	—
104	C₃×#131	—	5	2	no	—
105	C₃×#131	—	5	2	no	—
106	C₃×#131	—	5	2	no	—
107	C₂×C₃×M₁₆	—	5	1	no	—
108	C₂×C₃×M₁₆	—	5	2	no	—
109	C₂²×C₃×C₈	—	5	2	no	—
110	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
111	C₃×M₃₂	—	5	2	no	—
112	C₃×M₃₂	—	5	2	no	—
113	C₃×M₃₂	—	5	8	no	—
114	C₃×M₃₂	C₂×D₅	1	2	yes	—
115	C₃×M₃₂	C₂×D₅	1	2	yes	complemented
116	C₂×C₃×C₁₆	—	5	2	no	—
117	C₂×C₃×C₁₆	—	5	8	no	—
118	C₂×C₃×C₁₆	C₂×D₅	1	2	yes	complemented
119	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
120	C₂×C₂²⋊D₅	C₃×C₈	1	2	yes	—
121	#709	C₃×C₈	1	2	yes	—
122	#709	C₃×C₈	1	2	yes	—
123	#709	C₂×C₃×C₄	1	2	yes	—
124	#709	C₂×C₃×C₄	1	2	yes	—
125	C₂×D₂₀	C₃×C₈	1	1	yes	characteristic
126	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
127	C₂×Dic₁₀	C₃×C₈	1	1	yes	characteristic
128	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
129	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
130	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
131	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
132	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
133	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
134	#681	C₂×C₃×C₄	1	2	yes	—
135	#681	C₂×C₃×C₄	1	2	yes	—
136	C₂×#168	C₂×C₃×C₄	1	2	yes	—
137	#676	C₂×C₃×C₄	1	4	yes	—
138	#676	C₂×C₃×C₄	1	4	yes	—
139	C₈×D₅	C₂×C₃×C₄	1	4	yes	—
140	C₈×D₅	C₂³×C₃	1	4	yes	—
141	C₅×C₁₆	C₂³×C₃	1	4	yes	—
142	#672	C₂³×C₃	1	4	yes	—
143	C₂×#131	—	5	1	no	—
144	#504	—	5	4	no	—
145	#504	—	5	4	no	—
146	C₂×M₃₂	—	5	1	no	—
147	C₂×M₃₂	—	5	4	no	—
148	C₂×M₃₂	C₃×D₅	1	1	yes	characteristic, complemented
149	C₂²×C₃×C₅	—	4	1	no	—
150	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
151	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
152	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
153	C₂×C₃×D₅	—	4	2	no	—
154	C₂×C₃×D₅	C₂²×C₈	1	4	yes	—
155	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
156	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
157	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
158	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
159	C₃×Dic₅	C₂²×C₈	1	4	yes	—
160	C₃×#41	—	5	2	no	—
161	C₃×#41	—	5	2	no	—
162	C₃×#41	—	5	2	no	—
163	C₃×#41	—	5	2	no	—
164	C₂×C₃×Q₈	—	5	1	no	—
165	C₂×C₃×D₄	—	5	2	no	—
166	C₂×C₃×D₄	—	5	1	no	—
167	C₂²×C₃×C₄	—	5	2	no	—
168	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
169	C₃×M₁₆	—	5	2	no	—
170	C₃×M₁₆	—	5	2	no	—
171	C₃×M₁₆	—	5	4	no	—
172	C₃×M₁₆	—	5	4	no	—
173	C₂×C₃×C₈	—	5	2	no	—
174	C₂×C₃×C₈	—	5	4	no	—
175	C₂×C₃×C₈	—	5	4	no	—
176	C₂×C₃×C₈	C₄×D₅	1	1	yes	characteristic
177	C₂×C₃×C₈	C₄×D₅	1	1	yes	characteristic
178	C₂×C₃×C₈	C₄×D₅	1	1	yes	characteristic
179	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
180	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
181	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
182	C₃×C₁₆	—	5	4	no	—
183	C₃×C₁₆	C₂²×D₅	1	4	yes	—
184	C₂³×C₅	C₂×C₃×C₈	1	1	yes	characteristic
185	C₂²×D₅	C₂×C₃×C₈	1	2	yes	—
186	C₂×C₄×C₅	C₂×C₃×C₈	1	1	yes	characteristic
187	C₂×C₄×C₅	C₂×C₃×C₈	1	1	yes	characteristic
188	C₂×C₄×C₅	C₂×C₃×C₈	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
192	C₂²⋊D₅	C₂×C₃×C₈	1	4	yes	—
193	C₂²⋊D₅	C₂×C₃×C₈	1	4	yes	—
194	C₂×Dic₅	C₂×C₃×C₈	1	2	yes	—
195	D₂₀	C₂×C₃×C₈	1	2	yes	—
196	D₂₀	C₂×C₃×C₈	1	2	yes	—
197	C₄×D₅	C₂×C₃×C₈	1	4	yes	—
198	C₄×D₅	C₂²×C₃×C₄	1	4	yes	—
199	Dic₁₀	C₂×C₃×C₈	1	2	yes	—
200	Dic₁₀	C₂×C₃×C₈	1	2	yes	—
201	C₅×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
202	C₅×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
203	C₅×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
204	C₅×C₈	C₂⁴×C₃	1	1	yes	characteristic
205	#168	C₂²×C₃×C₄	1	4	yes	—
206	C₂×#41	—	5	1	no	—
207	#131	—	5	2	no	—
208	#131	—	5	2	no	—
209	#131	—	5	2	no	—
210	#131	—	5	2	no	—
211	C₂×M₁₆	—	5	1	no	—
212	C₂×M₁₆	—	5	2	no	—
213	C₂²×C₈	—	5	2	no	—
214	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
215	M₃₂	—	5	2	no	—
216	M₃₂	—	5	2	no	—
217	M₃₂	—	5	8	no	—
218	M₃₂	C₂×C₃×D₅	1	2	yes	—
219	M₃₂	C₂×C₃×D₅	1	2	yes	complemented
220	C₂×C₁₆	—	5	2	no	—
221	C₂×C₁₆	—	5	8	no	—
222	C₂×C₁₆	C₂×C₃×D₅	1	2	yes	complemented
223	C₂×C₃×C₅	—	2	1	no	—
224	C₂×C₃×C₅	—	2	1	no	—
225	C₂×C₃×C₅	—	2	1	no	—
226	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
227	C₃×D₅	—	2	4	no	—
228	C₂³×C₃	—	5	2	no	—
229	C₂³×C₃	C₈×D₅	1	1	yes	characteristic
230	C₃×Q₈	—	5	2	no	—
231	C₃×Q₈	—	5	2	no	—
232	C₃×D₄	—	5	4	no	—
233	C₃×D₄	—	5	4	no	—
234	C₃×D₄	—	5	2	no	—
235	C₃×D₄	—	5	2	no	—
236	C₂×C₃×C₄	—	5	2	no	—
237	C₂×C₃×C₄	—	5	4	no	—
238	C₂×C₃×C₄	—	5	4	no	—
239	C₂×C₃×C₄	C₈×D₅	1	1	yes	characteristic
240	C₂×C₃×C₄	C₈×D₅	1	1	yes	characteristic
241	C₂×C₃×C₄	C₈×D₅	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
245	C₃×C₈	—	5	4	no	—
246	C₃×C₈	C₂×C₄×D₅	1	1	yes	characteristic
247	C₃×C₈	C₂×C₄×D₅	1	1	yes	characteristic
248	C₃×C₈	C₂×C₄×D₅	1	1	yes	characteristic
249	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
250	C₂²×C₅	—	4	1	no	—
251	C₂²×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
252	C₂²×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
253	C₂²×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
254	C₂×D₅	—	4	2	no	—
255	C₂×D₅	C₂²×C₃×C₈	1	4	yes	—
256	C₄×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
257	C₄×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
258	C₄×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
259	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
260	Dic₅	C₂²×C₃×C₈	1	4	yes	—
261	#41	—	5	2	no	—
262	#41	—	5	2	no	—
263	#41	—	5	2	no	—
264	#41	—	5	2	no	—
265	C₂×Q₈	—	5	1	no	—
266	C₂×D₄	—	5	2	no	—
267	C₂×D₄	—	5	1	no	—
268	C₂²×C₄	—	5	2	no	—
269	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
270	M₁₆	—	5	2	no	—
271	M₁₆	—	5	2	no	—
272	M₁₆	—	5	4	no	—
273	M₁₆	—	5	4	no	—
274	C₂×C₈	—	5	2	no	—
275	C₂×C₈	—	5	4	no	—
276	C₂×C₈	—	5	4	no	—
277	C₂×C₈	C₃×C₄×D₅	1	1	yes	characteristic
278	C₂×C₈	C₃×C₄×D₅	1	1	yes	characteristic
279	C₂×C₈	C₃×C₄×D₅	1	1	yes	characteristic
280	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
281	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
282	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
283	C₁₆	—	5	4	no	—
284	C₁₆	C₂²×C₃×D₅	1	4	yes	—
285	C₃×C₅	#3407	1	1	yes	characteristic, complemented, Hall
286	C₂²×C₃	—	4	1	no	—
287	C₂²×C₃	—	5	4	no	—
288	C₂²×C₃	—	20	2	no	—
289	C₂²×C₃	C₂×C₈×D₅	1	1	yes	characteristic
290	C₂²×C₃	C₂×C₈×D₅	1	1	yes	characteristic
291	C₂²×C₃	C₂×C₈×D₅	1	1	yes	characteristic
292	C₃×C₄	—	5	4	no	—
293	C₃×C₄	C₂×C₈×D₅	1	1	yes	characteristic
294	C₃×C₄	C₂×C₈×D₅	1	1	yes	characteristic
295	C₃×C₄	C₂×C₈×D₅	1	1	yes	characteristic
296	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
297	C₂×C₅	—	2	1	no	—
298	C₂×C₅	—	2	1	no	—
299	C₂×C₅	—	2	1	no	—
300	C₂×C₅	C₂³×C₃×C₈	1	1	yes	characteristic
301	D₅	—	2	4	no	—
302	C₂³	—	5	2	no	—
303	C₂³	C₃×C₈×D₅	1	1	yes	characteristic
304	Q₈	—	5	2	no	—
305	Q₈	—	5	2	no	—
306	D₄	—	5	4	no	—
307	D₄	—	5	4	no	—
308	D₄	—	5	2	no	—
309	D₄	—	5	2	no	—
310	C₂×C₄	—	5	2	no	—
311	C₂×C₄	—	5	4	no	—
312	C₂×C₄	—	5	4	no	—
313	C₂×C₄	C₃×C₈×D₅	1	1	yes	characteristic
314	C₂×C₄	C₃×C₈×D₅	1	1	yes	characteristic
315	C₂×C₄	C₃×C₈×D₅	1	1	yes	characteristic
316	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
317	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
318	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
319	C₈	—	5	4	no	—
320	C₈	C₂×C₃×C₄×D₅	1	1	yes	characteristic
321	C₈	C₂×C₃×C₄×D₅	1	1	yes	characteristic
322	C₈	C₂×C₃×C₄×D₅	1	1	yes	characteristic
323	C₈	C₂³×C₃×D₅	1	1	yes	characteristic
324	C₂×C₃	—	2	1	no	—
325	C₂×C₃	—	2	1	no	—
326	C₂×C₃	—	2	1	no	—
327	C₂×C₃	—	10	4	no	—
328	C₂×C₃	C₂²×C₈×D₅	1	1	yes	characteristic
329	C₅	C₃×#3407	1	1	yes	characteristic, complemented, Sylow
330	C₂²	—	4	1	no	—
331	C₂²	—	5	4	no	—
332	C₂²	—	20	2	no	—
333	C₂²	C₂×C₃×C₈×D₅	1	1	yes	characteristic
334	C₂²	C₂×C₃×C₈×D₅	1	1	yes	characteristic
335	C₂²	C₂×C₃×C₈×D₅	1	1	yes	characteristic
336	C₄	—	5	4	no	—
337	C₄	C₂×C₃×C₈×D₅	1	1	yes	characteristic
338	C₄	C₂×C₃×C₈×D₅	1	1	yes	characteristic
339	C₄	C₂×C₃×C₈×D₅	1	1	yes	characteristic
340	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
341	C₃	#10613738	1	1	yes	characteristic, direct product factor, Sylow
342	C₂	—	2	1	no	—
343	C₂	—	2	1	no	—
344	C₂	—	2	1	no	—
345	C₂	—	10	4	no	—
346	C₂	C₂²×C₃×C₈×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₈	C₂³×D₅
commutator	C₂×C₅	C₂³×C₃×C₈
Frattini	C₈	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×M₃₂	C₂
socle	C₂×C₃×C₅	C₂³×C₈
prime radical	C₂×C₃×#709	C₄
cosocle	C₅×C₈	C₂⁴×C₃
hypercenter	C₂×C₃×M₃₂	D₅
hypocenter	C₅	C₃×#3407
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₈ ◁ C₂×C₃×M₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×M₃₂	C₂	semidirect
3. C₂×C₃×#3944	C₂	semidirect
4. C₃×#65196	C₂	semidirect
5. C₃×D₅×M₃₂	C₂	semidirect
6. C₃×#65190	C₂	semidirect
7. #10613738	C₃	direct (N × H)
18. C₃×C₅×M₃₂	C₂²	semidirect
19. C₂×C₃×C₅×C₁₆	C₂²	semidirect
21. C₃×#3944	C₂²	semidirect
22. C₂×C₃×#672	C₂²	semidirect
23. C₃×#3930	C₂²	semidirect
24. C₃×D₅×C₁₆	C₂²	semidirect
27. C₂×C₅×M₃₂	C₂×C₃	semidirect
28. C₂×#3944	C₂×C₃	semidirect
29. #65196	C₂×C₃	semidirect
30. D₅×M₃₂	C₂×C₃	semidirect
31. #65190	C₂×C₃	semidirect
61. C₂×C₃×M₃₂	D₅	semidirect
72. C₅×M₃₂	C₂²×C₃	semidirect
73. C₂×C₅×C₁₆	C₂²×C₃	semidirect
75. #3944	C₂²×C₃	semidirect
76. C₂×#672	C₂²×C₃	semidirect
77. #3930	C₂²×C₃	semidirect
78. D₅×C₁₆	C₂²×C₃	semidirect
115. C₃×M₃₂	C₂×D₅	semidirect
118. C₂×C₃×C₁₆	C₂×D₅	semidirect
148. C₂×M₃₂	C₃×D₅	semidirect
219. M₃₂	C₂×C₃×D₅	semidirect
222. C₂×C₁₆	C₂×C₃×D₅	semidirect
285. C₃×C₅	#3407	semidirect
329. C₅	C₃×#3407	semidirect
341. C₃	#10613738	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×#4047	2
C₂×C₃×C₅×M₃₂	2
C₂×C₃×#3944	2
C₃×#65196	2
C₃×D₅×M₃₂	2
C₃×#65190	2
#10613738	3
C₃×#3407	5

Subgroups — C3×#10613738 #14478161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613738 #14478161