Subgroups — C₂×C₃×#65733 #14417934

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×#4131	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×#4058	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#4008	C₂	1	2	yes	maximal, complemented
4	C₃×#65733	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3995	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#3992	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#65733	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×#711	C₂²	1	2	yes	—
9	C₂×C₃×#704	—	2	2	no	—
10	C₂²×C₃×#170	—	2	2	no	—
11	C₃×#4131	—	2	4	no	—
12	C₃×#4131	C₂²	1	8	yes	complemented
13	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
14	C₂×C₃×#700	C₂²	1	2	yes	—
15	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×D₈	C₄	1	1	yes	characteristic, complemented
17	C₂×C₃×#687	C₄	1	2	yes	complemented
18	C₃×#4058	C₄	1	4	yes	complemented
19	C₃×#4058	C₂²	1	4	yes	—
20	C₂×C₃×Dic₂₀	C₄	1	1	yes	characteristic, complemented
21	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
22	C₃×#4008	C₂²	1	8	yes	complemented
23	C₃×#3995	C₂²	1	4	yes	complemented
24	C₃×#3992	C₂²	1	4	yes	complemented
25	C₂×C₃×#444	—	5	1	no	maximal, Hall
26	C₂×#4131	C₂×C₃	1	2	yes	complemented
27	C₂×#4058	C₂×C₃	1	1	yes	characteristic
28	C₂×#4008	C₂×C₃	1	2	yes	complemented
29	#65733	C₂×C₃	1	8	yes	direct product factor
30	C₂×#3995	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×#3992	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂²×C₃×AGL(1,𝔽₅)	—	2	1	no	—
33	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
34	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
35	C₂²×C₃×Dic₅	—	2	2	no	—
36	C₃×#711	—	2	2	no	—
37	C₃×#711	—	2	2	no	—
38	C₃×#711	C₂×C₄	1	4	yes	—
39	C₃×#711	C₂³	1	4	yes	—
40	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
41	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
42	C₃×#704	—	2	8	no	—
43	C₂×C₃×#170	—	2	2	no	—
44	C₂×C₃×#170	—	2	8	no	—
45	C₂×C₃×#170	D₄	1	2	yes	—
46	C₃×C₄×AGL(1,𝔽₅)	—	2	1	no	—
47	C₃×C₄×AGL(1,𝔽₅)	C₂³	1	2	yes	—
48	C₃×#700	—	2	2	no	—
49	C₃×#700	C₂³	1	4	yes	—
50	C₃×D₅⋊C₈	D₄	1	2	yes	—
51	C₃×D₅⋊C₈	C₂³	1	2	yes	—
52	C₃×C₅×D₈	C₂×C₄	1	4	yes	complemented
53	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
54	C₃×#687	C₂×C₄	1	8	yes	complemented
55	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
56	C₃×Dic₂₀	C₂×C₄	1	4	yes	complemented
57	C₃×C₈×D₅	C₂×C₄	1	2	yes	—
58	C₃×C₈×D₅	C₂³	1	2	yes	—
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	—	5	1	no	—
65	C₂×#711	C₂²×C₃	1	2	yes	—
66	C₂×#704	—	2	2	no	—
67	C₂²×#170	—	2	2	no	—
68	#4131	—	2	4	no	—
69	#4131	C₂²×C₃	1	8	yes	complemented
70	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
71	C₂×#700	C₂²×C₃	1	2	yes	—
72	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₅×D₈	C₃×C₄	1	1	yes	characteristic, complemented
74	C₂×#687	C₃×C₄	1	2	yes	complemented
75	#4058	C₃×C₄	1	4	yes	complemented
76	#4058	C₂²×C₃	1	4	yes	—
77	C₂×Dic₂₀	C₃×C₄	1	1	yes	characteristic, complemented
78	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
79	#4008	C₂²×C₃	1	8	yes	complemented
80	#3995	C₂²×C₃	1	4	yes	complemented
81	#3992	C₂²×C₃	1	4	yes	complemented
82	C₂×#444	—	5	1	no	Sylow
83	C₂³×C₃×C₅	—	2	2	no	—
84	C₂²×C₃×D₅	#41	1	1	yes	characteristic
85	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
86	C₂×C₃×AGL(1,𝔽₅)	—	4	2	no	—
87	C₃×C₅×D₄	—	2	2	no	—
88	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₃×C₂²⋊D₅	—	2	4	no	—
91	C₃×C₂²⋊D₅	—	2	4	no	—
92	C₂×C₃×Dic₅	—	2	2	no	—
93	C₂×C₃×Dic₅	—	2	4	no	—
94	C₂×C₃×Dic₅	—	2	4	no	—
95	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
96	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
97	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
98	C₃×C₄×D₅	#41	1	1	yes	characteristic
99	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
100	C₃×Dic₁₀	—	2	2	no	—
101	C₃×Dic₁₀	C₂²×C₄	1	4	yes	—
102	C₃×#170	—	2	4	no	—
103	C₃×#170	C₂×D₄	1	4	yes	—
104	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
105	C₃×#168	C₂²×C₄	1	2	yes	—
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	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
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	—	5	1	no	—
117	C₂²×C₃×C₈	—	5	1	no	—
118	C₂²×C₃×C₈	—	10	2	no	—
119	C₂×C₃×C₄²	—	5	1	no	—
120	C₃×#108	—	5	4	no	—
121	C₃×#104	—	5	8	no	—
122	C₃×#97	—	5	4	no	—
123	C₂²×AGL(1,𝔽₅)	—	2	1	no	—
124	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
125	C₂×C₂²⋊D₅	—	2	2	no	—
126	C₂²×Dic₅	—	2	2	no	—
127	#711	—	2	2	no	—
128	#711	—	2	2	no	—
129	#711	C₂×C₃×C₄	1	4	yes	—
130	#711	C₂³×C₃	1	4	yes	—
131	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
132	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
133	#704	—	2	8	no	—
134	C₂×#170	—	2	2	no	—
135	C₂×#170	—	2	8	no	—
136	C₂×#170	C₃×D₄	1	2	yes	—
137	C₄×AGL(1,𝔽₅)	—	2	1	no	—
138	C₄×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
139	#700	—	2	2	no	—
140	#700	C₂³×C₃	1	4	yes	—
141	D₅⋊C₈	C₃×D₄	1	2	yes	—
142	D₅⋊C₈	C₂³×C₃	1	2	yes	—
143	C₅×D₈	C₂×C₃×C₄	1	4	yes	complemented
144	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
145	#687	C₂×C₃×C₄	1	8	yes	complemented
146	C₂×#168	C₂×C₃×C₄	1	1	yes	characteristic
147	Dic₂₀	C₂×C₃×C₄	1	4	yes	complemented
148	C₈×D₅	C₂×C₃×C₄	1	2	yes	—
149	C₈×D₅	C₂³×C₃	1	2	yes	—
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	—	5	1	no	—
156	C₂²×C₃×C₅	—	2	4	no	—
157	C₂²×C₃×C₅	—	4	4	no	—
158	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
159	C₂×C₃×D₅	—	2	2	no	—
160	C₂×C₃×D₅	C₄×D₄	1	1	yes	characteristic
161	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
162	C₃×AGL(1,𝔽₅)	—	4	2	no	—
163	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
164	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
165	C₃×Dic₅	—	2	4	no	—
166	C₃×Dic₅	C₄×D₄	1	1	yes	characteristic
167	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
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	—	10	2	no	—
174	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
175	C₂²×C₃×C₄	—	5	1	no	—
176	C₂²×C₃×C₄	—	10	2	no	—
177	C₂²×C₃×C₄	—	10	1	no	—
178	C₃×Q₁₆	—	5	4	no	—
179	C₃×SD₁₆	—	5	8	no	—
180	C₃×D₈	C₂×AGL(1,𝔽₅)	1	4	yes	complemented
181	C₃×M₁₆	—	5	4	no	—
182	C₃×M₁₆	—	10	8	no	—
183	C₃×M₁₆	—	10	2	no	—
184	C₂×C₃×C₈	—	5	2	no	—
185	C₂×C₃×C₈	—	5	2	no	—
186	C₂×C₃×C₈	—	5	2	no	—
187	C₂×C₃×C₈	—	5	1	no	—
188	C₂×C₃×C₈	—	5	2	no	—
189	C₂×C₃×C₈	—	5	2	no	—
190	C₂×C₃×C₈	—	10	8	no	—
191	C₂×C₃×C₈	—	10	2	no	—
192	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
193	C₃×C₄²	—	5	2	no	—
194	C₃×C₄²	—	10	1	no	—
195	C₂³×C₅	—	2	2	no	—
196	C₂²×D₅	C₃×#41	1	1	yes	characteristic
197	C₂×AGL(1,𝔽₅)	—	2	2	no	—
198	C₂×AGL(1,𝔽₅)	—	4	2	no	—
199	C₅×D₄	—	2	2	no	—
200	C₅×D₄	C₂²×C₃×C₄	1	4	yes	—
201	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
202	C₂²⋊D₅	—	2	4	no	—
203	C₂²⋊D₅	—	2	4	no	—
204	C₂×Dic₅	—	2	2	no	—
205	C₂×Dic₅	—	2	4	no	—
206	C₂×Dic₅	—	2	4	no	—
207	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
208	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
209	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
210	C₄×D₅	C₃×#41	1	1	yes	characteristic
211	C₄×D₅	C₂⁴×C₃	1	1	yes	characteristic
212	Dic₁₀	—	2	2	no	—
213	Dic₁₀	C₂²×C₃×C₄	1	4	yes	—
214	#170	—	2	4	no	—
215	#170	C₂×C₃×D₄	1	4	yes	—
216	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
217	#168	C₂²×C₃×C₄	1	2	yes	—
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	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
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	—	5	1	no	—
229	C₂²×C₈	—	5	1	no	—
230	C₂²×C₈	—	10	2	no	—
231	C₂×C₄²	—	5	1	no	—
232	#108	—	5	4	no	—
233	#104	—	5	8	no	—
234	#97	—	5	4	no	—
235	C₂×C₃×C₅	—	4	4	no	—
236	C₂×C₃×C₅	#444	1	2	yes	complemented
237	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
238	C₃×D₅	—	2	1	no	—
239	C₃×D₅	—	2	1	no	—
240	C₂³×C₃	—	2	2	no	—
241	C₂³×C₃	—	5	1	no	—
242	C₃×Q₈	—	5	4	no	—
243	C₃×Q₈	—	10	2	no	—
244	C₃×D₄	—	2	2	no	—
245	C₃×D₄	—	10	4	no	—
246	C₃×D₄	—	10	4	no	—
247	C₃×D₄	C₂²×AGL(1,𝔽₅)	1	4	yes	—
248	C₂×C₃×C₄	—	5	1	no	—
249	C₂×C₃×C₄	—	5	1	no	—
250	C₂×C₃×C₄	—	5	1	no	—
251	C₂×C₃×C₄	—	5	1	no	—
252	C₂×C₃×C₄	—	5	1	no	—
253	C₂×C₃×C₄	—	10	4	no	—
254	C₂×C₃×C₄	—	10	4	no	—
255	C₂×C₃×C₄	—	10	2	no	—
256	C₂×C₃×C₄	—	10	2	no	—
257	C₂×C₃×C₄	—	20	2	no	—
258	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
259	C₃×C₈	—	5	4	no	—
260	C₃×C₈	—	5	2	no	—
261	C₃×C₈	—	10	4	no	—
262	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
263	C₂²×C₅	—	2	4	no	—
264	C₂²×C₅	—	4	4	no	—
265	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
266	C₂×D₅	—	2	2	no	—
267	C₂×D₅	C₃×C₄×D₄	1	1	yes	characteristic
268	C₂×D₅	C₂×C₃×#41	1	1	yes	characteristic
269	AGL(1,𝔽₅)	—	4	2	no	—
270	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
271	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
272	Dic₅	—	2	4	no	—
273	Dic₅	C₃×C₄×D₄	1	1	yes	characteristic
274	Dic₅	C₂²×C₃×D₄	1	1	yes	characteristic
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	—	10	2	no	—
281	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
282	C₂²×C₄	—	5	1	no	—
283	C₂²×C₄	—	10	2	no	—
284	C₂²×C₄	—	10	1	no	—
285	Q₁₆	—	5	4	no	—
286	SD₁₆	—	5	8	no	—
287	D₈	C₂×C₃×AGL(1,𝔽₅)	1	4	yes	complemented
288	M₁₆	—	5	4	no	—
289	M₁₆	—	10	8	no	—
290	M₁₆	—	10	2	no	—
291	C₂×C₈	—	5	2	no	—
292	C₂×C₈	—	5	2	no	—
293	C₂×C₈	—	5	2	no	—
294	C₂×C₈	—	5	1	no	—
295	C₂×C₈	—	5	2	no	—
296	C₂×C₈	—	5	2	no	—
297	C₂×C₈	—	10	8	no	—
298	C₂×C₈	—	10	2	no	—
299	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
300	C₄²	—	5	2	no	—
301	C₄²	—	10	1	no	—
302	C₃×C₅	C₂×#444	1	1	yes	characteristic, complemented, Hall
303	C₂²×C₃	—	2	4	no	—
304	C₂²×C₃	—	4	4	no	—
305	C₂²×C₃	—	5	1	no	—
306	C₂²×C₃	—	5	1	no	—
307	C₂²×C₃	—	10	2	no	—
308	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
309	C₃×C₄	—	5	1	no	—
310	C₃×C₄	—	5	1	no	—
311	C₃×C₄	—	10	4	no	—
312	C₃×C₄	—	20	2	no	—
313	C₃×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
314	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
315	C₂×C₅	—	4	4	no	—
316	C₂×C₅	C₃×#444	1	2	yes	complemented
317	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
318	D₅	—	2	1	no	—
319	D₅	—	2	1	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	5	1	no	—
322	Q₈	—	5	4	no	—
323	Q₈	—	10	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	10	4	no	—
326	D₄	—	10	4	no	—
327	D₄	C₂²×C₃×AGL(1,𝔽₅)	1	4	yes	—
328	C₂×C₄	—	5	1	no	—
329	C₂×C₄	—	5	1	no	—
330	C₂×C₄	—	5	1	no	—
331	C₂×C₄	—	5	1	no	—
332	C₂×C₄	—	5	1	no	—
333	C₂×C₄	—	10	4	no	—
334	C₂×C₄	—	10	4	no	—
335	C₂×C₄	—	10	2	no	—
336	C₂×C₄	—	10	2	no	—
337	C₂×C₄	—	20	2	no	—
338	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
339	C₈	—	5	4	no	—
340	C₈	—	5	2	no	—
341	C₈	—	10	4	no	—
342	C₈	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
343	C₂×C₃	—	4	4	no	—
344	C₂×C₃	—	10	1	no	—
345	C₂×C₃	—	10	1	no	—
346	C₂×C₃	#65733	1	2	yes	direct product factor
347	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
348	C₅	C₂×C₃×#444	1	1	yes	characteristic, complemented, Sylow
349	C₂²	—	2	4	no	—
350	C₂²	—	4	4	no	—
351	C₂²	—	5	1	no	—
352	C₂²	—	5	1	no	—
353	C₂²	—	10	2	no	—
354	C₂²	C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
355	C₄	—	5	1	no	—
356	C₄	—	5	1	no	—
357	C₄	—	10	4	no	—
358	C₄	—	20	2	no	—
359	C₄	C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
360	C₄	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
361	C₃	C₂×#65733	1	1	yes	characteristic, direct product factor, Sylow
362	C₂	—	4	4	no	—
363	C₂	—	10	1	no	—
364	C₂	—	10	1	no	—
365	C₂	C₃×#65733	1	2	yes	direct product factor
366	C₂	C₂×C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₄×AGL(1,𝔽₅)
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₄	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×D₈	C₄
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×C₃×#4058	C₂
cosocle	C₄×D₅	C₂⁴×C₃
hypercenter	C₂×C₃×D₈	AGL(1,𝔽₅)
hypocenter	C₅	C₂×C₃×#444
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4131	C₂	semidirect
3. C₂×C₃×#4008	C₂	semidirect
4. C₃×#65733	C₂	direct (N × H)
5. C₂×C₃×#3995	C₂	semidirect
6. C₂×C₃×#3992	C₂	semidirect
7. C₂×#65733	C₃	direct (N × H)
12. C₃×#4131	C₂²	semidirect
16. C₂×C₃×C₅×D₈	C₄	semidirect
17. C₂×C₃×#687	C₄	semidirect
18. C₃×#4058	C₄	semidirect
20. C₂×C₃×Dic₂₀	C₄	semidirect
22. C₃×#4008	C₂²	semidirect
23. C₃×#3995	C₂²	semidirect
24. C₃×#3992	C₂²	semidirect
26. C₂×#4131	C₂×C₃	semidirect
28. C₂×#4008	C₂×C₃	semidirect
29. #65733	C₂×C₃	direct (N × H)
30. C₂×#3995	C₂×C₃	semidirect
31. C₂×#3992	C₂×C₃	semidirect
52. C₃×C₅×D₈	C₂×C₄	semidirect
54. C₃×#687	C₂×C₄	semidirect
56. C₃×Dic₂₀	C₂×C₄	semidirect
69. #4131	C₂²×C₃	semidirect
73. C₂×C₅×D₈	C₃×C₄	semidirect
74. C₂×#687	C₃×C₄	semidirect
75. #4058	C₃×C₄	semidirect
77. C₂×Dic₂₀	C₃×C₄	semidirect
79. #4008	C₂²×C₃	semidirect
80. #3995	C₂²×C₃	semidirect
81. #3992	C₂²×C₃	semidirect
111. C₂×C₃×D₈	AGL(1,𝔽₅)	semidirect
143. C₅×D₈	C₂×C₃×C₄	semidirect
145. #687	C₂×C₃×C₄	semidirect
147. Dic₂₀	C₂×C₃×C₄	semidirect
180. C₃×D₈	C₂×AGL(1,𝔽₅)	semidirect
223. C₂×D₈	C₃×AGL(1,𝔽₅)	semidirect
236. C₂×C₃×C₅	#444	semidirect
287. D₈	C₂×C₃×AGL(1,𝔽₅)	semidirect
302. C₃×C₅	C₂×#444	semidirect
316. C₂×C₅	C₃×#444	semidirect
346. C₂×C₃	#65733	direct (N × H)
348. C₅	C₂×C₃×#444	semidirect
361. C₃	C₂×#65733	direct (N × H)
365. C₂	C₃×#65733	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
C₂×C₃×#4058	2
C₂×C₃×#4008	2
C₃×#65733	2
C₂×C₃×#3995	2
C₂×C₃×#3992	2
C₂×#65733	3
C₂×C₃×#444	5

Subgroups — C2×C3×#65733 #14417934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65733 #14417934