Subgroups — C₂×C₃×#66086 #14509964

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4149	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66086	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×#4054	C₂	1	6	yes	maximal, complemented
5	C₂×C₃×#4050	C₂	1	3	yes	maximal, complemented
6	C₂²×C₃×D₄₀	C₂	1	3	yes	maximal, complemented
7	C₂×#66086	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
9	C₃×#4149	—	2	8	no	—
10	C₃×#4149	C₂²	1	16	yes	complemented
11	C₂×C₃×#713	—	2	2	no	—
12	C₂×C₃×D₄×D₅	—	2	6	no	—
13	C₂×C₃×#709	C₂²	1	6	yes	complemented
14	C₂²×C₃×D₂₀	C₂²	1	6	yes	complemented
15	C₃×C₅×#131	C₂²	1	8	yes	complemented
16	C₂×C₃×C₅×M₁₆	C₂²	1	3	yes	complemented
17	C₂²×C₃×C₅×C₈	C₂²	1	3	yes	complemented
18	C₃×#4054	C₂²	1	48	yes	complemented
19	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic, complemented
20	C₃×#4050	C₂²	1	24	yes	complemented
21	C₂×C₃×D₄₀	C₂²	1	3	yes	complemented
22	C₂×C₃×D₄₀	C₂²	1	6	yes	complemented
23	C₂×C₃×D₄₀	C₂²	1	24	yes	complemented
24	C₂×C₃×#677	C₂²	1	6	yes	complemented
25	C₂×C₃×#576	—	5	1	no	maximal, Hall
26	C₂×#4149	C₂×C₃	1	2	yes	complemented
27	C₂×C₅×#131	C₂×C₃	1	1	yes	characteristic, complemented
28	#66086	C₂×C₃	1	16	yes	direct product factor
29	C₂×#4054	C₂×C₃	1	6	yes	complemented
30	C₂×#4050	C₂×C₃	1	3	yes	complemented
31	C₂²×D₄₀	C₂×C₃	1	3	yes	complemented
32	C₂³×C₃×D₅	—	2	6	no	—
33	C₃×C₅×#41	D₄	1	4	yes	—
34	C₃×C₅×#41	C₂³	1	4	yes	—
35	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
36	C₂×C₃×C₅×D₄	D₄	1	3	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
38	C₂×C₃×C₂²⋊D₅	—	2	6	no	—
39	C₃×#713	—	2	16	no	—
40	C₃×D₄×D₅	—	2	48	no	—
41	C₃×#709	—	2	12	no	—
42	C₃×#709	C₂³	1	24	yes	complemented
43	C₂×C₃×D₂₀	—	2	6	no	—
44	C₂×C₃×D₂₀	—	2	12	no	—
45	C₂×C₃×D₂₀	C₂³	1	6	yes	—
46	C₂×C₃×D₂₀	C₂³	1	24	yes	complemented
47	C₂×C₃×C₄×D₅	—	2	6	no	—
48	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
49	C₃×C₅×M₁₆	C₂³	1	12	yes	complemented
50	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₅×C₈	C₂³	1	3	yes	—
52	C₂×C₃×C₅×C₈	C₂³	1	12	yes	complemented
53	C₃×Dic₂₀	C₂³	1	4	yes	complemented
54	C₃×D₄₀	C₂³	1	12	yes	complemented
55	C₃×D₄₀	C₂³	1	24	yes	complemented
56	C₃×#677	C₂³	1	24	yes	complemented
57	C₂×C₃×H(5,𝔽₂)	—	5	2	no	—
58	C₃×#576	—	5	16	no	—
59	C₂×C₃×AGL(1,ℤ/8)	—	5	6	no	—
60	C₂×C₃×#135	—	5	3	no	—
61	C₂²×C₃×D₈	—	5	3	no	—
62	C₂×C₃×#131	D₅	1	1	yes	characteristic, complemented
63	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
64	#4149	—	2	8	no	—
65	#4149	C₂²×C₃	1	16	yes	complemented
66	C₂×#713	—	2	2	no	—
67	C₂×D₄×D₅	—	2	6	no	—
68	C₂×#709	C₂²×C₃	1	6	yes	complemented
69	C₂²×D₂₀	C₂²×C₃	1	6	yes	complemented
70	C₅×#131	C₂²×C₃	1	8	yes	complemented
71	C₂×C₅×M₁₆	C₂²×C₃	1	3	yes	complemented
72	C₂²×C₅×C₈	C₂²×C₃	1	3	yes	complemented
73	#4054	C₂²×C₃	1	48	yes	complemented
74	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
75	#4050	C₂²×C₃	1	24	yes	complemented
76	C₂×D₄₀	C₂²×C₃	1	3	yes	complemented
77	C₂×D₄₀	C₂²×C₃	1	6	yes	complemented
78	C₂×D₄₀	C₂²×C₃	1	24	yes	complemented
79	C₂×#677	C₂²×C₃	1	6	yes	complemented
80	C₂×#576	—	5	1	no	Sylow
81	C₂³×C₃×C₅	C₂×D₄	1	3	yes	—
82	C₂²×C₃×D₅	—	2	6	no	—
83	C₂²×C₃×D₅	—	2	24	no	—
84	C₂²×C₃×D₅	—	8	12	no	—
85	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
86	C₃×C₅×D₄	C₂×D₄	1	12	yes	—
87	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
88	C₂×C₃×C₄×C₅	C₂×D₄	1	6	yes	—
89	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
91	C₃×C₂²⋊D₅	—	2	24	no	—
92	C₂×C₃×Dic₅	—	2	2	no	—
93	C₃×D₂₀	—	2	6	no	—
94	C₃×D₂₀	—	2	24	no	—
95	C₃×D₂₀	C₂⁴	1	12	yes	—
96	C₃×C₄×D₅	—	2	24	no	—
97	C₃×Dic₁₀	—	2	2	no	—
98	C₃×Dic₁₀	C₂⁴	1	4	yes	—
99	C₃×C₅×C₈	C₂⁴	1	6	yes	—
100	C₃×C₅×C₈	C₂⁴	1	2	yes	—
101	C₃×H(5,𝔽₂)	—	5	16	no	—
102	C₃×H(5,𝔽₂)	—	10	8	no	—
103	C₂×C₃×#41	—	5	6	no	—
104	C₂×C₃×#41	—	10	2	no	—
105	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
106	C₂²×C₃×D₄	—	5	6	no	—
107	C₂²×C₃×D₄	—	10	6	no	—
108	C₃×AGL(1,ℤ/8)	—	5	48	no	—
109	C₃×#135	—	5	24	no	—
110	C₂×C₃×Q₁₆	—	5	1	no	—
111	C₂×C₃×SD₁₆	—	5	6	no	—
112	C₂×C₃×D₈	—	5	3	no	—
113	C₂×C₃×D₈	—	5	6	no	—
114	C₂×C₃×D₈	—	5	24	no	—
115	C₃×#131	C₂×D₅	1	8	yes	complemented
116	C₂×C₃×M₁₆	C₂×D₅	1	3	yes	complemented
117	C₂²×C₃×C₈	C₂×D₅	1	3	yes	complemented
118	C₂³×D₅	—	2	6	no	—
119	C₅×#41	C₃×D₄	1	4	yes	—
120	C₅×#41	C₂³×C₃	1	4	yes	—
121	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
122	C₂×C₅×D₄	C₃×D₄	1	3	yes	—
123	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
124	C₂×C₂²⋊D₅	—	2	6	no	—
125	#713	—	2	16	no	—
126	D₄×D₅	—	2	48	no	—
127	#709	—	2	12	no	—
128	#709	C₂³×C₃	1	24	yes	complemented
129	C₂×D₂₀	—	2	6	no	—
130	C₂×D₂₀	—	2	12	no	—
131	C₂×D₂₀	C₂³×C₃	1	6	yes	—
132	C₂×D₂₀	C₂³×C₃	1	24	yes	complemented
133	C₂×C₄×D₅	—	2	6	no	—
134	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
135	C₅×M₁₆	C₂³×C₃	1	12	yes	complemented
136	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
137	C₂×C₅×C₈	C₂³×C₃	1	3	yes	—
138	C₂×C₅×C₈	C₂³×C₃	1	12	yes	complemented
139	Dic₂₀	C₂³×C₃	1	4	yes	complemented
140	D₄₀	C₂³×C₃	1	12	yes	complemented
141	D₄₀	C₂³×C₃	1	24	yes	complemented
142	#677	C₂³×C₃	1	24	yes	complemented
143	C₂×H(5,𝔽₂)	—	5	2	no	—
144	#576	—	5	16	no	—
145	C₂×AGL(1,ℤ/8)	—	5	6	no	—
146	C₂×#135	—	5	3	no	—
147	C₂²×D₈	—	5	3	no	—
148	C₂×#131	C₃×D₅	1	1	yes	characteristic, complemented
149	C₂²×C₃×C₅	—	2	6	no	—
150	C₂²×C₃×C₅	C₂²×D₄	1	6	yes	—
151	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₃×D₅	—	2	12	no	—
153	C₂×C₃×D₅	—	4	12	no	—
154	C₂×C₃×D₅	—	8	24	no	—
155	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
156	C₃×C₄×C₅	C₂²×D₄	1	6	yes	—
157	C₃×C₄×C₅	C₂⁵	1	1	yes	characteristic
158	C₃×Dic₅	—	2	4	no	—
159	C₂⁴×C₃	—	10	6	no	—
160	C₃×#41	—	5	24	no	—
161	C₃×#41	—	10	16	no	—
162	C₃×#41	—	10	12	no	—
163	C₃×#41	D₂₀	1	4	yes	—
164	C₃×#41	C₂²×D₅	1	4	yes	—
165	C₂×C₃×Q₈	—	5	2	no	—
166	C₂×C₃×Q₈	D₂₀	1	1	yes	characteristic
167	C₂×C₃×D₄	—	5	6	no	—
168	C₂×C₃×D₄	—	5	24	no	—
169	C₂×C₃×D₄	—	10	6	no	—
170	C₂×C₃×D₄	—	10	48	no	—
171	C₂×C₃×D₄	—	10	6	no	—
172	C₂×C₃×D₄	—	10	12	no	—
173	C₂×C₃×D₄	D₂₀	1	3	yes	—
174	C₂²×C₃×C₄	—	10	6	no	—
175	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
176	C₃×Q₁₆	—	5	4	no	—
177	C₃×SD₁₆	—	5	24	no	—
178	C₃×D₈	—	5	12	no	—
179	C₃×D₈	—	5	24	no	—
180	C₃×M₁₆	C₂²×D₅	1	12	yes	complemented
181	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
182	C₂×C₃×C₈	C₂²×D₅	1	3	yes	—
183	C₂×C₃×C₈	C₂²×D₅	1	12	yes	complemented
184	C₂³×C₅	C₂×C₃×D₄	1	3	yes	—
185	C₂²×D₅	—	2	6	no	—
186	C₂²×D₅	—	2	24	no	—
187	C₂²×D₅	—	8	12	no	—
188	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
189	C₅×D₄	C₂×C₃×D₄	1	12	yes	—
190	C₂×C₄×C₅	C₂×C₃×D₄	1	3	yes	—
191	C₂×C₄×C₅	C₂×C₃×D₄	1	6	yes	—
192	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂⁴×C₃	1	6	yes	—
194	C₂²⋊D₅	—	2	24	no	—
195	C₂×Dic₅	—	2	2	no	—
196	D₂₀	—	2	6	no	—
197	D₂₀	—	2	24	no	—
198	D₂₀	C₂⁴×C₃	1	12	yes	—
199	C₄×D₅	—	2	24	no	—
200	Dic₁₀	—	2	2	no	—
201	Dic₁₀	C₂⁴×C₃	1	4	yes	—
202	C₅×C₈	C₂⁴×C₃	1	6	yes	—
203	C₅×C₈	C₂⁴×C₃	1	2	yes	—
204	H(5,𝔽₂)	—	5	16	no	—
205	H(5,𝔽₂)	—	10	8	no	—
206	C₂×#41	—	5	6	no	—
207	C₂×#41	—	10	2	no	—
208	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
209	C₂²×D₄	—	5	6	no	—
210	C₂²×D₄	—	10	6	no	—
211	AGL(1,ℤ/8)	—	5	48	no	—
212	#135	—	5	24	no	—
213	C₂×Q₁₆	—	5	1	no	—
214	C₂×SD₁₆	—	5	6	no	—
215	C₂×D₈	—	5	3	no	—
216	C₂×D₈	—	5	6	no	—
217	C₂×D₈	—	5	24	no	—
218	#131	C₂×C₃×D₅	1	8	yes	complemented
219	C₂×M₁₆	C₂×C₃×D₅	1	3	yes	complemented
220	C₂²×C₈	C₂×C₃×D₅	1	3	yes	complemented
221	C₂×C₃×C₅	—	2	6	no	—
222	C₂×C₃×C₅	#576	1	2	yes	complemented
223	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
224	C₃×D₅	—	4	12	no	—
225	C₂³×C₃	—	10	6	no	—
226	C₂³×C₃	—	10	24	no	—
227	C₂³×C₃	—	40	12	no	—
228	C₂³×C₃	C₂×D₂₀	1	3	yes	—
229	C₃×Q₈	—	5	4	no	—
230	C₃×Q₈	—	10	2	no	—
231	C₃×Q₈	C₂×D₂₀	1	4	yes	—
232	C₃×D₄	—	5	12	no	—
233	C₃×D₄	—	10	24	no	—
234	C₃×D₄	—	10	24	no	—
235	C₃×D₄	—	10	6	no	—
236	C₃×D₄	C₂×D₂₀	1	12	yes	—
237	C₂×C₃×C₄	—	10	2	no	—
238	C₂×C₃×C₄	—	10	24	no	—
239	C₂×C₃×C₄	C₂×D₂₀	1	6	yes	—
240	C₂×C₃×C₄	C₂×D₂₀	1	3	yes	—
241	C₂×C₃×C₄	C₂³×D₅	1	6	yes	—
242	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
243	C₃×C₈	C₂³×D₅	1	2	yes	—
244	C₃×C₈	C₂³×D₅	1	6	yes	—
245	C₂²×C₅	—	2	6	no	—
246	C₂²×C₅	C₂²×C₃×D₄	1	6	yes	—
247	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
248	C₂×D₅	—	2	12	no	—
249	C₂×D₅	—	4	12	no	—
250	C₂×D₅	—	8	24	no	—
251	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
252	C₄×C₅	C₂²×C₃×D₄	1	6	yes	—
253	C₄×C₅	C₂⁵×C₃	1	1	yes	characteristic
254	Dic₅	—	2	4	no	—
255	C₂⁴	—	10	6	no	—
256	#41	—	5	24	no	—
257	#41	—	10	16	no	—
258	#41	—	10	12	no	—
259	#41	C₃×D₂₀	1	4	yes	—
260	#41	C₂²×C₃×D₅	1	4	yes	—
261	C₂×Q₈	—	5	2	no	—
262	C₂×Q₈	C₃×D₂₀	1	1	yes	characteristic
263	C₂×D₄	—	5	6	no	—
264	C₂×D₄	—	5	24	no	—
265	C₂×D₄	—	10	6	no	—
266	C₂×D₄	—	10	48	no	—
267	C₂×D₄	—	10	6	no	—
268	C₂×D₄	—	10	12	no	—
269	C₂×D₄	C₃×D₂₀	1	3	yes	—
270	C₂²×C₄	—	10	6	no	—
271	C₂²×C₄	C₂²×C₃×D₅	1	3	yes	—
272	Q₁₆	—	5	4	no	—
273	SD₁₆	—	5	24	no	—
274	D₈	—	5	12	no	—
275	D₈	—	5	24	no	—
276	M₁₆	C₂²×C₃×D₅	1	12	yes	complemented
277	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
278	C₂×C₈	C₂²×C₃×D₅	1	3	yes	—
279	C₂×C₈	C₂²×C₃×D₅	1	12	yes	complemented
280	C₃×C₅	C₂×#576	1	1	yes	characteristic, complemented, Hall
281	C₂²×C₃	—	2	6	no	—
282	C₂²×C₃	—	10	12	no	—
283	C₂²×C₃	—	20	12	no	—
284	C₂²×C₃	—	40	24	no	—
285	C₂²×C₃	C₂²×D₂₀	1	6	yes	—
286	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
287	C₃×C₄	—	10	4	no	—
288	C₃×C₄	C₂²×D₂₀	1	6	yes	—
289	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
290	C₃×C₄	C₂⁴×D₅	1	1	yes	characteristic
291	C₂×C₅	—	2	6	no	—
292	C₂×C₅	C₃×#576	1	2	yes	complemented
293	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
294	D₅	—	4	12	no	—
295	C₂³	—	10	6	no	—
296	C₂³	—	10	24	no	—
297	C₂³	—	40	12	no	—
298	C₂³	C₂×C₃×D₂₀	1	3	yes	—
299	Q₈	—	5	4	no	—
300	Q₈	—	10	2	no	—
301	Q₈	C₂×C₃×D₂₀	1	4	yes	—
302	D₄	—	5	12	no	—
303	D₄	—	10	24	no	—
304	D₄	—	10	24	no	—
305	D₄	—	10	6	no	—
306	D₄	C₂×C₃×D₂₀	1	12	yes	—
307	C₂×C₄	—	10	2	no	—
308	C₂×C₄	—	10	24	no	—
309	C₂×C₄	C₂×C₃×D₂₀	1	3	yes	—
310	C₂×C₄	C₂×C₃×D₂₀	1	6	yes	—
311	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
312	C₂×C₄	C₂³×C₃×D₅	1	6	yes	—
313	C₈	C₂³×C₃×D₅	1	2	yes	—
314	C₈	C₂³×C₃×D₅	1	6	yes	—
315	C₂×C₃	—	2	6	no	—
316	C₂×C₃	—	20	12	no	—
317	C₂×C₃	#66086	1	2	yes	direct product factor
318	C₂×C₃	C₂³×D₂₀	1	1	yes	characteristic
319	C₅	C₂×C₃×#576	1	1	yes	characteristic, complemented, Sylow
320	C₂²	—	2	6	no	—
321	C₂²	—	10	12	no	—
322	C₂²	—	20	12	no	—
323	C₂²	—	40	24	no	—
324	C₂²	C₂²×C₃×D₂₀	1	6	yes	—
325	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
326	C₄	—	10	4	no	—
327	C₄	C₂²×C₃×D₂₀	1	6	yes	—
328	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
329	C₄	C₂⁴×C₃×D₅	1	1	yes	characteristic
330	C₃	C₂×#66086	1	1	yes	characteristic, direct product factor, Sylow
331	C₂	—	2	6	no	—
332	C₂	—	20	12	no	—
333	C₂	C₃×#66086	1	2	yes	direct product factor
334	C₂	C₂³×C₃×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₂₀
commutator, cosocle	C₄×C₅	C₂⁵×C₃
Frattini	C₄	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×#131	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₃×#131	D₅
hypocenter	C₅	C₂×C₃×#576
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×#41 ◁ C₂×C₃×#131

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4149	C₂	semidirect
2. C₂×C₃×C₅×#131	C₂	semidirect
3. C₃×#66086	C₂	direct (N × H)
4. C₂×C₃×#4054	C₂	semidirect
5. C₂×C₃×#4050	C₂	semidirect
6. C₂²×C₃×D₄₀	C₂	semidirect
7. C₂×#66086	C₃	direct (N × H)
10. C₃×#4149	C₂²	semidirect
13. C₂×C₃×#709	C₂²	semidirect
14. C₂²×C₃×D₂₀	C₂²	semidirect
15. C₃×C₅×#131	C₂²	semidirect
16. C₂×C₃×C₅×M₁₆	C₂²	semidirect
17. C₂²×C₃×C₅×C₈	C₂²	semidirect
18. C₃×#4054	C₂²	semidirect
19. C₂×C₃×Dic₂₀	C₂²	semidirect
20. C₃×#4050	C₂²	semidirect
21. C₂×C₃×D₄₀	C₂²	semidirect
22. C₂×C₃×D₄₀	C₂²	semidirect
23. C₂×C₃×D₄₀	C₂²	semidirect
24. C₂×C₃×#677	C₂²	semidirect
26. C₂×#4149	C₂×C₃	semidirect
27. C₂×C₅×#131	C₂×C₃	semidirect
28. #66086	C₂×C₃	direct (N × H)
29. C₂×#4054	C₂×C₃	semidirect
30. C₂×#4050	C₂×C₃	semidirect
31. C₂²×D₄₀	C₂×C₃	semidirect
42. C₃×#709	C₂³	semidirect
46. C₂×C₃×D₂₀	C₂³	semidirect
49. C₃×C₅×M₁₆	C₂³	semidirect
52. C₂×C₃×C₅×C₈	C₂³	semidirect
53. C₃×Dic₂₀	C₂³	semidirect
54. C₃×D₄₀	C₂³	semidirect
55. C₃×D₄₀	C₂³	semidirect
56. C₃×#677	C₂³	semidirect
62. C₂×C₃×#131	D₅	semidirect
65. #4149	C₂²×C₃	semidirect
68. C₂×#709	C₂²×C₃	semidirect
69. C₂²×D₂₀	C₂²×C₃	semidirect
70. C₅×#131	C₂²×C₃	semidirect
71. C₂×C₅×M₁₆	C₂²×C₃	semidirect
72. C₂²×C₅×C₈	C₂²×C₃	semidirect
73. #4054	C₂²×C₃	semidirect
74. C₂×Dic₂₀	C₂²×C₃	semidirect
75. #4050	C₂²×C₃	semidirect
76. C₂×D₄₀	C₂²×C₃	semidirect
77. C₂×D₄₀	C₂²×C₃	semidirect
78. C₂×D₄₀	C₂²×C₃	semidirect
79. C₂×#677	C₂²×C₃	semidirect
115. C₃×#131	C₂×D₅	semidirect
116. C₂×C₃×M₁₆	C₂×D₅	semidirect
117. C₂²×C₃×C₈	C₂×D₅	semidirect
128. #709	C₂³×C₃	semidirect
132. C₂×D₂₀	C₂³×C₃	semidirect
135. C₅×M₁₆	C₂³×C₃	semidirect
138. C₂×C₅×C₈	C₂³×C₃	semidirect
139. Dic₂₀	C₂³×C₃	semidirect
140. D₄₀	C₂³×C₃	semidirect
141. D₄₀	C₂³×C₃	semidirect
142. #677	C₂³×C₃	semidirect
148. C₂×#131	C₃×D₅	semidirect
180. C₃×M₁₆	C₂²×D₅	semidirect
183. C₂×C₃×C₈	C₂²×D₅	semidirect
218. #131	C₂×C₃×D₅	semidirect
219. C₂×M₁₆	C₂×C₃×D₅	semidirect
220. C₂²×C₈	C₂×C₃×D₅	semidirect
222. C₂×C₃×C₅	#576	semidirect
276. M₁₆	C₂²×C₃×D₅	semidirect
279. C₂×C₈	C₂²×C₃×D₅	semidirect
280. C₃×C₅	C₂×#576	semidirect
292. C₂×C₅	C₃×#576	semidirect
317. C₂×C₃	#66086	direct (N × H)
319. C₅	C₂×C₃×#576	semidirect
330. C₃	C₂×#66086	direct (N × H)
333. C₂	C₃×#66086	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×#4149	2
C₂×C₃×C₅×#131	2
C₃×#66086	2
C₂×C₃×#4054	2
C₂×C₃×#4050	2
C₂²×C₃×D₄₀	2
C₂×#66086	3
C₂×C₃×#576	5

Subgroups — C2×C3×#66086 #14509964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66086 #14509964