Subgroups — C₂×C₃×#65740 #14417849

Order 1920.

944 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4133	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×#4065	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#4010	C₂	1	2	yes	maximal, complemented
4	C₃×#65740	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3996	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₈×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#65740	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×#713	C₂²	1	2	yes	—
9	C₃×#4133	—	2	4	no	—
10	C₃×#4133	C₂²	1	8	yes	complemented
11	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
12	C₂×C₃×#700	—	2	2	no	—
13	C₂×C₃×#700	C₂²	1	2	yes	—
14	C₂×C₃×D₅⋊C₈	—	2	2	no	—
15	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×Q₁₆	C₄	1	1	yes	characteristic, complemented
17	C₂×C₃×#688	C₄	1	2	yes	complemented
18	C₃×#4065	C₄	1	4	yes	complemented
19	C₃×#4065	C₂²	1	4	yes	—
20	C₂×C₃×D₄₀	C₄	1	1	yes	characteristic, complemented
21	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
22	C₃×#4010	C₂²	1	8	yes	complemented
23	C₃×#3996	C₂²	1	4	yes	complemented
24	C₃×C₈×AGL(1,𝔽₅)	C₂²	1	4	yes	complemented
25	C₂×C₃×#443	—	5	1	no	maximal, Hall
26	C₂×#4133	C₂×C₃	1	2	yes	complemented
27	C₂×#4065	C₂×C₃	1	1	yes	characteristic
28	C₂×#4010	C₂×C₃	1	2	yes	complemented
29	#65740	C₂×C₃	1	8	yes	direct product factor
30	C₂×#3996	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×C₈×AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂²×C₃×AGL(1,𝔽₅)	—	2	1	no	—
33	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
34	C₃×#713	—	2	2	no	—
35	C₃×#713	—	2	2	no	—
36	C₃×#713	C₂×C₄	1	4	yes	—
37	C₃×#713	C₂³	1	4	yes	—
38	C₂×C₃×D₂₀	—	2	2	no	—
39	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
40	C₂×C₃×C₄×D₅	—	2	2	no	—
41	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
42	C₂×C₃×#170	—	2	2	no	—
43	C₂×C₃×#170	D₄	1	1	yes	characteristic
44	C₂×C₃×#170	D₄	1	1	yes	characteristic
45	C₃×C₄×AGL(1,𝔽₅)	—	2	1	no	—
46	C₃×C₄×AGL(1,𝔽₅)	C₂³	1	2	yes	—
47	C₃×#700	—	2	2	no	—
48	C₃×#700	—	2	8	no	—
49	C₃×#700	C₂³	1	4	yes	—
50	C₃×D₅⋊C₈	—	2	8	no	—
51	C₃×D₅⋊C₈	D₄	1	2	yes	—
52	C₃×D₅⋊C₈	C₂³	1	2	yes	—
53	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
54	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
55	C₃×#688	C₂×C₄	1	8	yes	complemented
56	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
57	C₃×D₄₀	C₂×C₄	1	4	yes	complemented
58	C₃×C₈×D₅	C₂×C₄	1	2	yes	—
59	C₃×C₈×D₅	C₂³	1	2	yes	—
60	C₂×C₃×#135	—	5	1	no	—
61	C₂×C₃×#131	—	5	2	no	—
62	C₃×#443	—	5	8	no	—
63	C₂×C₃×#108	—	5	1	no	—
64	C₂×C₃×#104	—	5	2	no	—
65	C₂×C₃×C₄×C₈	—	5	1	no	—
66	C₂×#713	C₂²×C₃	1	2	yes	—
67	#4133	—	2	4	no	—
68	#4133	C₂²×C₃	1	8	yes	complemented
69	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
70	C₂×#700	—	2	2	no	—
71	C₂×#700	C₂²×C₃	1	2	yes	—
72	C₂×D₅⋊C₈	—	2	2	no	—
73	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₅×Q₁₆	C₃×C₄	1	1	yes	characteristic, complemented
75	C₂×#688	C₃×C₄	1	2	yes	complemented
76	#4065	C₃×C₄	1	4	yes	complemented
77	#4065	C₂²×C₃	1	4	yes	—
78	C₂×D₄₀	C₃×C₄	1	1	yes	characteristic, complemented
79	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
80	#4010	C₂²×C₃	1	8	yes	complemented
81	#3996	C₂²×C₃	1	4	yes	complemented
82	C₈×AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	complemented
83	C₂×#443	—	5	1	no	Sylow
84	C₂²×C₃×D₅	—	2	2	no	—
85	C₂²×C₃×D₅	#41	1	1	yes	characteristic
86	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
87	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
88	C₃×C₅×Q₈	—	2	2	no	—
89	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
93	C₃×D₂₀	—	2	4	no	—
94	C₃×D₂₀	—	2	4	no	—
95	C₃×D₂₀	—	2	2	no	—
96	C₃×D₂₀	C₂²×C₄	1	4	yes	—
97	C₃×C₄×D₅	—	2	4	no	—
98	C₃×C₄×D₅	—	2	4	no	—
99	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
100	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
101	C₃×C₄×D₅	#41	1	1	yes	characteristic
102	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
103	C₃×#170	—	2	4	no	—
104	C₃×#170	C₂×D₄	1	2	yes	—
105	C₃×#170	C₂×D₄	1	2	yes	—
106	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
107	C₃×#168	C₂²×C₄	1	2	yes	—
108	C₂×C₃×#41	—	5	2	no	—
109	C₃×#135	—	5	4	no	—
110	C₃×#135	—	5	4	no	—
111	C₂×C₃×Q₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
112	C₂×C₃×SD₁₆	—	5	2	no	—
113	C₂×C₃×D₈	—	5	1	no	—
114	C₃×#131	—	5	8	no	—
115	C₃×#131	—	10	4	no	—
116	C₂×C₃×M₁₆	—	5	2	no	—
117	C₂×C₃×M₁₆	—	10	2	no	—
118	C₂²×C₃×C₈	—	5	1	no	—
119	C₂²×C₃×C₈	—	5	1	no	—
120	C₂²×C₃×C₈	—	10	2	no	—
121	C₂×C₃×C₄²	—	5	1	no	—
122	C₃×#108	—	5	4	no	—
123	C₃×#104	—	5	8	no	—
124	C₃×C₄×C₈	—	5	4	no	—
125	C₂²×AGL(1,𝔽₅)	—	2	1	no	—
126	C₂×C₅×Q₈	C₂×C₃×C₄	1	2	yes	—
127	#713	—	2	2	no	—
128	#713	—	2	2	no	—
129	#713	C₂×C₃×C₄	1	4	yes	—
130	#713	C₂³×C₃	1	4	yes	—
131	C₂×D₂₀	—	2	2	no	—
132	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
133	C₂×C₄×D₅	—	2	2	no	—
134	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
135	C₂×#170	—	2	2	no	—
136	C₂×#170	C₃×D₄	1	1	yes	characteristic
137	C₂×#170	C₃×D₄	1	1	yes	characteristic
138	C₄×AGL(1,𝔽₅)	—	2	1	no	—
139	C₄×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
140	#700	—	2	2	no	—
141	#700	—	2	8	no	—
142	#700	C₂³×C₃	1	4	yes	—
143	D₅⋊C₈	—	2	8	no	—
144	D₅⋊C₈	C₃×D₄	1	2	yes	—
145	D₅⋊C₈	C₂³×C₃	1	2	yes	—
146	C₅×Q₁₆	C₂×C₃×C₄	1	4	yes	complemented
147	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
148	#688	C₂×C₃×C₄	1	8	yes	complemented
149	C₂×#168	C₂×C₃×C₄	1	1	yes	characteristic
150	D₄₀	C₂×C₃×C₄	1	4	yes	complemented
151	C₈×D₅	C₂×C₃×C₄	1	2	yes	—
152	C₈×D₅	C₂³×C₃	1	2	yes	—
153	C₂×#135	—	5	1	no	—
154	C₂×#131	—	5	2	no	—
155	#443	—	5	8	no	—
156	C₂×#108	—	5	1	no	—
157	C₂×#104	—	5	2	no	—
158	C₂×C₄×C₈	—	5	1	no	—
159	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
160	C₂×C₃×D₅	—	2	2	no	—
161	C₂×C₃×D₅	—	2	4	no	—
162	C₂×C₃×D₅	—	4	4	no	—
163	C₂×C₃×D₅	C₄×D₄	1	1	yes	characteristic
164	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
165	C₃×AGL(1,𝔽₅)	—	2	4	no	—
166	C₃×C₄×C₅	—	2	4	no	—
167	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
168	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
169	C₃×Dic₅	C₄×D₄	1	1	yes	characteristic
170	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
171	C₃×#41	—	5	4	no	—
172	C₃×#41	—	5	4	no	—
173	C₃×#41	—	10	2	no	—
174	C₃×#41	—	10	2	no	—
175	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	2	yes	—
176	C₂×C₃×D₄	—	5	2	no	—
177	C₂×C₃×D₄	—	10	2	no	—
178	C₂²×C₃×C₄	—	5	1	no	—
179	C₂²×C₃×C₄	—	10	2	no	—
180	C₂²×C₃×C₄	—	10	1	no	—
181	C₃×Q₁₆	C₂×AGL(1,𝔽₅)	1	4	yes	complemented
182	C₃×SD₁₆	—	5	8	no	—
183	C₃×D₈	—	5	4	no	—
184	C₃×M₁₆	—	5	4	no	—
185	C₃×M₁₆	—	10	8	no	—
186	C₃×M₁₆	—	10	2	no	—
187	C₂×C₃×C₈	—	5	2	no	—
188	C₂×C₃×C₈	—	5	2	no	—
189	C₂×C₃×C₈	—	5	1	no	—
190	C₂×C₃×C₈	—	5	1	no	—
191	C₂×C₃×C₈	—	5	1	no	—
192	C₂×C₃×C₈	—	5	2	no	—
193	C₂×C₃×C₈	—	5	2	no	—
194	C₂×C₃×C₈	—	10	8	no	—
195	C₂×C₃×C₈	—	10	2	no	—
196	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
197	C₃×C₄²	—	5	2	no	—
198	C₃×C₄²	—	10	1	no	—
199	C₂²×D₅	—	2	2	no	—
200	C₂²×D₅	C₃×#41	1	1	yes	characteristic
201	C₂×AGL(1,𝔽₅)	—	2	4	no	—
202	C₂×AGL(1,𝔽₅)	—	2	2	no	—
203	C₅×Q₈	—	2	2	no	—
204	C₅×Q₈	C₂²×C₃×C₄	1	4	yes	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
207	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
208	D₂₀	—	2	4	no	—
209	D₂₀	—	2	4	no	—
210	D₂₀	—	2	2	no	—
211	D₂₀	C₂²×C₃×C₄	1	4	yes	—
212	C₄×D₅	—	2	4	no	—
213	C₄×D₅	—	2	4	no	—
214	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
215	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
216	C₄×D₅	C₃×#41	1	1	yes	characteristic
217	C₄×D₅	C₂⁴×C₃	1	1	yes	characteristic
218	#170	—	2	4	no	—
219	#170	C₂×C₃×D₄	1	2	yes	—
220	#170	C₂×C₃×D₄	1	2	yes	—
221	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
222	#168	C₂²×C₃×C₄	1	2	yes	—
223	C₂×#41	—	5	2	no	—
224	#135	—	5	4	no	—
225	#135	—	5	4	no	—
226	C₂×Q₁₆	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
227	C₂×SD₁₆	—	5	2	no	—
228	C₂×D₈	—	5	1	no	—
229	#131	—	5	8	no	—
230	#131	—	10	4	no	—
231	C₂×M₁₆	—	5	2	no	—
232	C₂×M₁₆	—	10	2	no	—
233	C₂²×C₈	—	5	1	no	—
234	C₂²×C₈	—	5	1	no	—
235	C₂²×C₈	—	10	2	no	—
236	C₂×C₄²	—	5	1	no	—
237	#108	—	5	4	no	—
238	#104	—	5	8	no	—
239	C₄×C₈	—	5	4	no	—
240	C₂×C₃×C₅	#443	1	2	yes	complemented
241	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
242	C₃×D₅	—	2	1	no	—
243	C₃×D₅	—	2	1	no	—
244	C₃×D₅	—	4	4	no	—
245	C₂³×C₃	—	5	1	no	—
246	C₂³×C₃	—	10	2	no	—
247	C₃×Q₈	—	2	2	no	—
248	C₃×Q₈	C₂²×AGL(1,𝔽₅)	1	4	yes	—
249	C₃×D₄	—	5	4	no	—
250	C₃×D₄	—	10	4	no	—
251	C₃×D₄	—	10	4	no	—
252	C₃×D₄	—	10	2	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	5	1	no	—
255	C₂×C₃×C₄	—	5	1	no	—
256	C₂×C₃×C₄	—	5	1	no	—
257	C₂×C₃×C₄	—	5	1	no	—
258	C₂×C₃×C₄	—	5	1	no	—
259	C₂×C₃×C₄	—	10	4	no	—
260	C₂×C₃×C₄	—	10	4	no	—
261	C₂×C₃×C₄	—	10	2	no	—
262	C₂×C₃×C₄	—	10	4	no	—
263	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
264	C₃×C₈	—	5	2	no	—
265	C₃×C₈	—	5	2	no	—
266	C₃×C₈	—	5	2	no	—
267	C₃×C₈	—	10	4	no	—
268	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
269	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
270	C₂×D₅	—	2	2	no	—
271	C₂×D₅	—	2	4	no	—
272	C₂×D₅	—	4	4	no	—
273	C₂×D₅	C₃×C₄×D₄	1	1	yes	characteristic
274	C₂×D₅	C₂×C₃×#41	1	1	yes	characteristic
275	AGL(1,𝔽₅)	—	2	4	no	—
276	C₄×C₅	—	2	4	no	—
277	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
278	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
279	Dic₅	C₃×C₄×D₄	1	1	yes	characteristic
280	Dic₅	C₂²×C₃×D₄	1	1	yes	characteristic
281	#41	—	5	4	no	—
282	#41	—	5	4	no	—
283	#41	—	10	2	no	—
284	#41	—	10	2	no	—
285	C₂×Q₈	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
286	C₂×D₄	—	5	2	no	—
287	C₂×D₄	—	10	2	no	—
288	C₂²×C₄	—	5	1	no	—
289	C₂²×C₄	—	10	2	no	—
290	C₂²×C₄	—	10	1	no	—
291	Q₁₆	C₂×C₃×AGL(1,𝔽₅)	1	4	yes	complemented
292	SD₁₆	—	5	8	no	—
293	D₈	—	5	4	no	—
294	M₁₆	—	5	4	no	—
295	M₁₆	—	10	8	no	—
296	M₁₆	—	10	2	no	—
297	C₂×C₈	—	5	2	no	—
298	C₂×C₈	—	5	1	no	—
299	C₂×C₈	—	5	1	no	—
300	C₂×C₈	—	5	2	no	—
301	C₂×C₈	—	5	1	no	—
302	C₂×C₈	—	5	2	no	—
303	C₂×C₈	—	5	2	no	—
304	C₂×C₈	—	10	8	no	—
305	C₂×C₈	—	10	2	no	—
306	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
307	C₄²	—	5	2	no	—
308	C₄²	—	10	1	no	—
309	C₃×C₅	C₂×#443	1	1	yes	characteristic, complemented, Hall
310	C₂²×C₃	—	5	1	no	—
311	C₂²×C₃	—	5	1	no	—
312	C₂²×C₃	—	10	2	no	—
313	C₂²×C₃	—	10	4	no	—
314	C₂²×C₃	—	20	4	no	—
315	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
316	C₃×C₄	—	2	4	no	—
317	C₃×C₄	—	5	1	no	—
318	C₃×C₄	—	5	1	no	—
319	C₃×C₄	—	10	4	no	—
320	C₃×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
321	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
322	C₂×C₅	C₃×#443	1	2	yes	complemented
323	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
324	D₅	—	2	1	no	—
325	D₅	—	2	1	no	—
326	D₅	—	4	4	no	—
327	C₂³	—	5	1	no	—
328	C₂³	—	10	2	no	—
329	Q₈	—	2	2	no	—
330	Q₈	C₂²×C₃×AGL(1,𝔽₅)	1	4	yes	—
331	D₄	—	5	4	no	—
332	D₄	—	10	4	no	—
333	D₄	—	10	4	no	—
334	D₄	—	10	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	5	1	no	—
337	C₂×C₄	—	5	1	no	—
338	C₂×C₄	—	5	1	no	—
339	C₂×C₄	—	5	1	no	—
340	C₂×C₄	—	5	1	no	—
341	C₂×C₄	—	10	4	no	—
342	C₂×C₄	—	10	4	no	—
343	C₂×C₄	—	10	2	no	—
344	C₂×C₄	—	10	4	no	—
345	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
346	C₈	—	5	2	no	—
347	C₈	—	5	2	no	—
348	C₈	—	5	2	no	—
349	C₈	—	10	4	no	—
350	C₈	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
351	C₂×C₃	—	10	1	no	—
352	C₂×C₃	—	10	1	no	—
353	C₂×C₃	—	20	4	no	—
354	C₂×C₃	#65740	1	2	yes	direct product factor
355	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
356	C₅	C₂×C₃×#443	1	1	yes	characteristic, complemented, Sylow
357	C₂²	—	5	1	no	—
358	C₂²	—	5	1	no	—
359	C₂²	—	10	2	no	—
360	C₂²	—	10	4	no	—
361	C₂²	—	20	4	no	—
362	C₂²	C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
363	C₄	—	2	4	no	—
364	C₄	—	5	1	no	—
365	C₄	—	5	1	no	—
366	C₄	—	10	4	no	—
367	C₄	C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
368	C₄	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
369	C₃	C₂×#65740	1	1	yes	characteristic, direct product factor, Sylow
370	C₂	—	10	1	no	—
371	C₂	—	10	1	no	—
372	C₂	—	20	4	no	—
373	C₂	C₃×#65740	1	2	yes	direct product factor
374	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×Q₁₆	C₄
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×C₃×#4065	C₂
cosocle	C₄×D₅	C₂⁴×C₃
hypercenter	C₂×C₃×Q₁₆	AGL(1,𝔽₅)
hypocenter	C₅	C₂×C₃×#443
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4133	C₂	semidirect
3. C₂×C₃×#4010	C₂	semidirect
4. C₃×#65740	C₂	direct (N × H)
5. C₂×C₃×#3996	C₂	semidirect
6. C₂×C₃×C₈×AGL(1,𝔽₅)	C₂	semidirect
7. C₂×#65740	C₃	direct (N × H)
10. C₃×#4133	C₂²	semidirect
16. C₂×C₃×C₅×Q₁₆	C₄	semidirect
17. C₂×C₃×#688	C₄	semidirect
18. C₃×#4065	C₄	semidirect
20. C₂×C₃×D₄₀	C₄	semidirect
22. C₃×#4010	C₂²	semidirect
23. C₃×#3996	C₂²	semidirect
24. C₃×C₈×AGL(1,𝔽₅)	C₂²	semidirect
26. C₂×#4133	C₂×C₃	semidirect
28. C₂×#4010	C₂×C₃	semidirect
29. #65740	C₂×C₃	direct (N × H)
30. C₂×#3996	C₂×C₃	semidirect
31. C₂×C₈×AGL(1,𝔽₅)	C₂×C₃	semidirect
53. C₃×C₅×Q₁₆	C₂×C₄	semidirect
55. C₃×#688	C₂×C₄	semidirect
57. C₃×D₄₀	C₂×C₄	semidirect
68. #4133	C₂²×C₃	semidirect
74. C₂×C₅×Q₁₆	C₃×C₄	semidirect
75. C₂×#688	C₃×C₄	semidirect
76. #4065	C₃×C₄	semidirect
78. C₂×D₄₀	C₃×C₄	semidirect
80. #4010	C₂²×C₃	semidirect
81. #3996	C₂²×C₃	semidirect
82. C₈×AGL(1,𝔽₅)	C₂²×C₃	semidirect
111. C₂×C₃×Q₁₆	AGL(1,𝔽₅)	semidirect
146. C₅×Q₁₆	C₂×C₃×C₄	semidirect
148. #688	C₂×C₃×C₄	semidirect
150. D₄₀	C₂×C₃×C₄	semidirect
181. C₃×Q₁₆	C₂×AGL(1,𝔽₅)	semidirect
226. C₂×Q₁₆	C₃×AGL(1,𝔽₅)	semidirect
240. C₂×C₃×C₅	#443	semidirect
291. Q₁₆	C₂×C₃×AGL(1,𝔽₅)	semidirect
309. C₃×C₅	C₂×#443	semidirect
322. C₂×C₅	C₃×#443	semidirect
354. C₂×C₃	#65740	direct (N × H)
356. C₅	C₂×C₃×#443	semidirect
369. C₃	C₂×#65740	direct (N × H)
373. C₂	C₃×#65740	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×#4133	2
C₂×C₃×#4065	2
C₂×C₃×#4010	2
C₃×#65740	2
C₂×C₃×#3996	2
C₂×C₃×C₈×AGL(1,𝔽₅)	2
C₂×#65740	3
C₂×C₃×#443	5

Subgroups — C2×C3×#65740 #14417849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65740 #14417849