Subgroups — C₂×C₃×#65006 #14417932

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₂₀
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#97	C₂
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×C₃×#4050	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×#97	D₅
hypocenter	C₅	C₂×C₃×#444
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₈ ◁ C₂×C₃×#97

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4047	C₂	semidirect
3. C₂×C₃×C₅×#97	C₂	semidirect
4. C₂×C₃×#3951	C₂	semidirect
5. C₂×C₃×#3937	C₂	semidirect
6. C₃×#65006	C₂	direct (N × H)
7. C₂×#65006	C₃	direct (N × H)
13. C₂×C₃×Dic₂₀	C₄	semidirect
14. C₃×#4050	C₄	semidirect
16. C₂×C₃×D₄₀	C₄	semidirect
17. C₂×C₃×#677	C₄	semidirect
19. C₃×#4047	C₂²	semidirect
22. C₃×C₅×#97	C₂²	semidirect
23. C₃×#3951	C₂²	semidirect
24. C₃×#3937	C₂²	semidirect
27. C₂×#4047	C₂×C₃	semidirect
28. C₂×C₅×#97	C₂×C₃	semidirect
29. C₂×#3951	C₂×C₃	semidirect
30. C₂×#3937	C₂×C₃	semidirect
31. #65006	C₂×C₃	direct (N × H)
54. C₃×Dic₂₀	C₂×C₄	semidirect
55. C₃×D₄₀	C₂×C₄	semidirect
56. C₃×#677	C₂×C₄	semidirect
64. C₂×C₃×#97	D₅	semidirect
70. C₂×Dic₂₀	C₃×C₄	semidirect
71. #4050	C₃×C₄	semidirect
73. C₂×D₄₀	C₃×C₄	semidirect
74. C₂×#677	C₃×C₄	semidirect
76. #4047	C₂²×C₃	semidirect
79. C₅×#97	C₂²×C₃	semidirect
80. #3951	C₂²×C₃	semidirect
81. #3937	C₂²×C₃	semidirect
122. C₃×#97	C₂×D₅	semidirect
145. Dic₂₀	C₂×C₃×C₄	semidirect
146. D₄₀	C₂×C₃×C₄	semidirect
147. #677	C₂×C₃×C₄	semidirect
155. C₂×#97	C₃×D₅	semidirect
234. #97	C₂×C₃×D₅	semidirect
237. C₂×C₃×C₅	#444	semidirect
302. C₃×C₅	C₂×#444	semidirect
317. C₂×C₅	C₃×#444	semidirect
346. C₂×C₃	#65006	direct (N × H)
348. C₅	C₂×C₃×#444	semidirect
361. C₃	C₂×#65006	direct (N × H)
365. C₂	C₃×#65006	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×#4050	2
C₂×C₃×#4047	2
C₂×C₃×C₅×#97	2
C₂×C₃×#3951	2
C₂×C₃×#3937	2
C₃×#65006	2
C₂×#65006	3
C₂×C₃×#444	5

Subgroups — C2×C3×#65006 #14417932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65006 #14417932