Subgroups — C₂×C₃×#65001 #14438968

Order 1920.

1336 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₄₀	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃×#677	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#4021	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4020	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65001	C₂	1	8	yes	maximal, direct product factor
7	C₂×#65001	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×D₂₀	—	2	2	no	—
9	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
10	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
11	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×#685	—	2	2	no	—
15	C₂×C₃×D₄₀	—	2	8	no	—
16	C₂×C₃×D₄₀	C₂²	1	8	yes	complemented
17	C₂×C₃×#677	—	2	8	no	—
18	C₂×C₃×#677	C₂²	1	8	yes	complemented
19	C₃×#4021	—	2	2	no	—
20	C₃×#4021	C₂²	1	4	yes	complemented
21	C₃×#4020	—	2	2	no	—
22	C₃×#4020	C₂²	1	4	yes	complemented
23	C₃×C₅×#97	C₂²	1	4	yes	complemented
24	C₂×C₃×#496	—	5	1	no	maximal, Hall
25	C₂²×D₄₀	C₂×C₃	1	2	yes	complemented
26	C₂²×#677	C₂×C₃	1	2	yes	complemented
27	C₂×#4021	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×#4020	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×C₅×#97	C₂×C₃	1	1	yes	characteristic, complemented
30	#65001	C₂×C₃	1	8	yes	direct product factor
31	C₂³×C₃×D₅	—	2	2	no	—
32	C₂³×C₃×D₅	—	2	1	no	—
33	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂²×C₃×Dic₅	—	2	1	no	—
36	C₂×C₃×D₂₀	—	2	4	no	—
37	C₂×C₃×D₂₀	—	2	4	no	—
38	C₂×C₃×D₂₀	—	2	4	no	—
39	C₂×C₃×D₂₀	—	2	8	no	—
40	C₂×C₃×D₂₀	—	2	2	no	—
41	C₂×C₃×D₂₀	—	2	1	no	—
42	C₂×C₃×D₂₀	—	4	8	no	—
43	C₂×C₃×D₂₀	C₂³	1	4	yes	—
44	C₂×C₃×D₂₀	C₂³	1	2	yes	—
45	C₂×C₃×Dic₁₀	—	2	4	no	—
46	C₂×C₃×Dic₁₀	—	2	1	no	—
47	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
48	C₂×C₃×C₅×C₈	D₄	1	8	yes	complemented
49	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
50	C₃×C₄²×C₅	D₄	1	2	yes	—
51	C₃×C₄²×C₅	C₂³	1	2	yes	—
52	C₃×#685	—	2	8	no	—
53	C₃×D₄₀	—	2	16	no	—
54	C₃×#677	—	2	16	no	—
55	C₂²×C₃×SD₁₆	—	5	2	no	—
56	C₂²×C₃×D₈	—	5	2	no	—
57	C₂×C₃×#127	—	5	1	no	—
58	C₂×C₃×#124	—	5	1	no	—
59	C₃×#496	—	5	8	no	—
60	C₂×C₃×#97	D₅	1	1	yes	characteristic, complemented
61	C₂²×D₂₀	—	2	2	no	—
62	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
63	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
64	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
66	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
67	C₂×#685	—	2	2	no	—
68	C₂×D₄₀	—	2	8	no	—
69	C₂×D₄₀	C₂²×C₃	1	8	yes	complemented
70	C₂×#677	—	2	8	no	—
71	C₂×#677	C₂²×C₃	1	8	yes	complemented
72	#4021	—	2	2	no	—
73	#4021	C₂²×C₃	1	4	yes	complemented
74	#4020	—	2	2	no	—
75	#4020	C₂²×C₃	1	4	yes	complemented
76	C₅×#97	C₂²×C₃	1	4	yes	complemented
77	C₂×#496	—	5	1	no	Sylow
78	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₃×D₅	—	2	2	no	—
80	C₂²×C₃×D₅	—	2	4	no	—
81	C₂²×C₃×D₅	—	4	4	no	—
82	C₂²×C₃×D₅	—	4	2	no	—
83	C₂²×C₃×D₅	—	4	8	no	—
84	C₂²×C₃×D₅	—	4	4	no	—
85	C₂×C₃×C₄×C₅	—	2	4	no	—
86	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
87	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
89	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
90	C₂×C₃×Dic₅	—	2	2	no	—
91	C₂×C₃×Dic₅	—	4	2	no	—
92	C₃×D₂₀	—	2	4	no	—
93	C₃×D₂₀	—	2	4	no	—
94	C₃×D₂₀	—	2	4	no	—
95	C₃×D₂₀	—	4	16	no	—
96	C₃×D₂₀	—	4	4	no	—
97	C₃×D₂₀	—	4	2	no	—
98	C₃×Dic₁₀	—	2	4	no	—
99	C₃×Dic₁₀	—	4	2	no	—
100	C₃×C₅×C₈	C₂×D₄	1	8	yes	complemented
101	C₂²×C₃×Q₈	—	5	1	no	—
102	C₂²×C₃×D₄	—	5	1	no	—
103	C₂²×C₃×D₄	—	5	2	no	—
104	C₂²×C₃×D₄	—	10	2	no	—
105	C₂×C₃×SD₁₆	—	5	8	no	—
106	C₂×C₃×SD₁₆	—	10	8	no	—
107	C₂×C₃×D₈	—	5	8	no	—
108	C₂×C₃×D₈	—	10	8	no	—
109	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
110	C₃×#127	—	5	4	no	—
111	C₃×#127	—	10	2	no	—
112	C₃×#124	—	5	4	no	—
113	C₃×#124	—	10	2	no	—
114	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
115	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
116	C₃×#97	C₂×D₅	1	4	yes	complemented
117	C₂³×D₅	—	2	2	no	—
118	C₂³×D₅	—	2	1	no	—
119	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
120	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
121	C₂²×Dic₅	—	2	1	no	—
122	C₂×D₂₀	—	2	4	no	—
123	C₂×D₂₀	—	2	4	no	—
124	C₂×D₂₀	—	2	4	no	—
125	C₂×D₂₀	—	2	8	no	—
126	C₂×D₂₀	—	2	2	no	—
127	C₂×D₂₀	—	2	1	no	—
128	C₂×D₂₀	—	4	8	no	—
129	C₂×D₂₀	C₂³×C₃	1	4	yes	—
130	C₂×D₂₀	C₂³×C₃	1	2	yes	—
131	C₂×Dic₁₀	—	2	4	no	—
132	C₂×Dic₁₀	—	2	1	no	—
133	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
134	C₂×C₅×C₈	C₃×D₄	1	8	yes	complemented
135	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
136	C₄²×C₅	C₃×D₄	1	2	yes	—
137	C₄²×C₅	C₂³×C₃	1	2	yes	—
138	#685	—	2	8	no	—
139	D₄₀	—	2	16	no	—
140	#677	—	2	16	no	—
141	C₂²×SD₁₆	—	5	2	no	—
142	C₂²×D₈	—	5	2	no	—
143	C₂×#127	—	5	1	no	—
144	C₂×#124	—	5	1	no	—
145	#496	—	5	8	no	—
146	C₂×#97	C₃×D₅	1	1	yes	characteristic, complemented
147	C₂²×C₃×C₅	#127	1	2	yes	—
148	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	4	yes	—
149	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₃×D₅	—	4	4	no	—
151	C₂×C₃×D₅	—	4	2	no	—
152	C₂×C₃×D₅	—	4	8	no	—
153	C₂×C₃×D₅	—	4	4	no	—
154	C₂×C₃×D₅	—	8	8	no	—
155	C₂×C₃×D₅	—	8	4	no	—
156	C₃×C₄×C₅	—	2	4	no	—
157	C₃×C₄×C₅	#127	1	2	yes	—
158	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
159	C₃×Dic₅	—	4	2	no	—
160	C₂⁴×C₃	—	10	1	no	—
161	C₂⁴×C₃	—	10	2	no	—
162	C₂×C₃×Q₈	—	5	2	no	—
163	C₂×C₃×Q₈	—	10	1	no	—
164	C₂×C₃×Q₈	—	10	4	no	—
165	C₂×C₃×D₄	—	5	2	no	—
166	C₂×C₃×D₄	—	5	4	no	—
167	C₂×C₃×D₄	—	10	4	no	—
168	C₂×C₃×D₄	—	10	4	no	—
169	C₂×C₃×D₄	—	10	4	no	—
170	C₂×C₃×D₄	—	10	1	no	—
171	C₂×C₃×D₄	—	10	8	no	—
172	C₂×C₃×D₄	—	10	2	no	—
173	C₂×C₃×D₄	—	20	8	no	—
174	C₂²×C₃×C₄	—	10	1	no	—
175	C₂²×C₃×C₄	D₂₀	1	2	yes	—
176	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
177	C₃×SD₁₆	—	10	16	no	—
178	C₃×D₈	—	10	16	no	—
179	C₂×C₃×C₈	D₂₀	1	8	yes	complemented
180	C₂×C₃×C₈	C₂²×D₅	1	4	yes	—
181	C₃×C₂²⋊C₄	—	10	8	no	—
182	C₃×C₄²	D₂₀	1	2	yes	—
183	C₃×C₄²	C₂²×D₅	1	2	yes	—
184	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
185	C₂²×D₅	—	2	2	no	—
186	C₂²×D₅	—	2	4	no	—
187	C₂²×D₅	—	4	4	no	—
188	C₂²×D₅	—	4	2	no	—
189	C₂²×D₅	—	4	8	no	—
190	C₂²×D₅	—	4	4	no	—
191	C₂×C₄×C₅	—	2	4	no	—
192	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
193	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
195	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
196	C₂×Dic₅	—	2	2	no	—
197	C₂×Dic₅	—	4	2	no	—
198	D₂₀	—	2	4	no	—
199	D₂₀	—	2	4	no	—
200	D₂₀	—	2	4	no	—
201	D₂₀	—	4	16	no	—
202	D₂₀	—	4	4	no	—
203	D₂₀	—	4	2	no	—
204	Dic₁₀	—	2	4	no	—
205	Dic₁₀	—	4	2	no	—
206	C₅×C₈	C₂×C₃×D₄	1	8	yes	complemented
207	C₂²×Q₈	—	5	1	no	—
208	C₂²×D₄	—	5	1	no	—
209	C₂²×D₄	—	5	2	no	—
210	C₂²×D₄	—	10	2	no	—
211	C₂×SD₁₆	—	5	8	no	—
212	C₂×SD₁₆	—	10	8	no	—
213	C₂×D₈	—	5	8	no	—
214	C₂×D₈	—	10	8	no	—
215	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
216	#127	—	5	4	no	—
217	#127	—	10	2	no	—
218	#124	—	5	4	no	—
219	#124	—	10	2	no	—
220	C₂×C₂²⋊C₄	—	10	2	no	—
221	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
222	#97	C₂×C₃×D₅	1	4	yes	complemented
223	C₂×C₃×C₅	#496	1	4	yes	complemented
224	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
225	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
226	C₃×D₅	—	8	4	no	—
227	C₃×D₅	—	8	2	no	—
228	C₂³×C₃	—	10	2	no	—
229	C₂³×C₃	—	10	4	no	—
230	C₂³×C₃	—	20	2	no	—
231	C₂³×C₃	—	20	4	no	—
232	C₂³×C₃	—	20	8	no	—
233	C₂³×C₃	—	20	4	no	—
234	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
235	C₃×Q₈	—	10	4	no	—
236	C₃×Q₈	—	20	2	no	—
237	C₃×D₄	—	10	4	no	—
238	C₃×D₄	—	10	4	no	—
239	C₃×D₄	—	10	4	no	—
240	C₃×D₄	—	20	16	no	—
241	C₃×D₄	—	20	2	no	—
242	C₃×D₄	—	20	4	no	—
243	C₂×C₃×C₄	—	2	4	no	—
244	C₂×C₃×C₄	—	10	2	no	—
245	C₂×C₃×C₄	—	20	2	no	—
246	C₂×C₃×C₄	C₂×D₂₀	1	4	yes	—
247	C₂×C₃×C₄	C₂×D₂₀	1	4	yes	—
248	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
250	C₃×C₈	C₂×D₂₀	1	8	yes	complemented
251	C₂²×C₅	C₃×#127	1	2	yes	—
252	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	4	yes	—
253	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
254	C₂×D₅	—	4	8	no	—
255	C₂×D₅	—	4	4	no	—
256	C₂×D₅	—	4	4	no	—
257	C₂×D₅	—	4	2	no	—
258	C₂×D₅	—	8	8	no	—
259	C₂×D₅	—	8	4	no	—
260	C₄×C₅	—	2	4	no	—
261	C₄×C₅	C₃×#127	1	2	yes	—
262	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
263	Dic₅	—	4	2	no	—
264	C₂⁴	—	10	1	no	—
265	C₂⁴	—	10	2	no	—
266	C₂×Q₈	—	5	2	no	—
267	C₂×Q₈	—	10	1	no	—
268	C₂×Q₈	—	10	4	no	—
269	C₂×D₄	—	5	2	no	—
270	C₂×D₄	—	5	4	no	—
271	C₂×D₄	—	10	4	no	—
272	C₂×D₄	—	10	4	no	—
273	C₂×D₄	—	10	4	no	—
274	C₂×D₄	—	10	1	no	—
275	C₂×D₄	—	10	8	no	—
276	C₂×D₄	—	10	2	no	—
277	C₂×D₄	—	20	8	no	—
278	C₂²×C₄	—	10	1	no	—
279	C₂²×C₄	C₃×D₂₀	1	2	yes	—
280	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
281	SD₁₆	—	10	16	no	—
282	D₈	—	10	16	no	—
283	C₂×C₈	C₃×D₂₀	1	8	yes	complemented
284	C₂×C₈	C₂²×C₃×D₅	1	4	yes	—
285	C₂²⋊C₄	—	10	8	no	—
286	C₄²	C₃×D₂₀	1	2	yes	—
287	C₄²	C₂²×C₃×D₅	1	2	yes	—
288	C₃×C₅	C₂×#496	1	1	yes	characteristic, complemented, Hall
289	C₂²×C₃	—	20	2	no	—
290	C₂²×C₃	—	20	4	no	—
291	C₂²×C₃	—	20	8	no	—
292	C₂²×C₃	—	20	4	no	—
293	C₂²×C₃	—	40	8	no	—
294	C₂²×C₃	—	40	4	no	—
295	C₂²×C₃	#4020	1	2	yes	—
296	C₂²×C₃	#4054	1	4	yes	—
297	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
298	C₃×C₄	—	2	4	no	—
299	C₃×C₄	—	20	2	no	—
300	C₃×C₄	#4020	1	2	yes	—
301	C₃×C₄	C₂²×D₂₀	1	2	yes	—
302	C₂×C₅	C₃×#496	1	4	yes	complemented
303	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
304	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
305	D₅	—	8	4	no	—
306	D₅	—	8	2	no	—
307	C₂³	—	10	2	no	—
308	C₂³	—	10	4	no	—
309	C₂³	—	20	2	no	—
310	C₂³	—	20	4	no	—
311	C₂³	—	20	8	no	—
312	C₂³	—	20	4	no	—
313	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
314	Q₈	—	10	4	no	—
315	Q₈	—	20	2	no	—
316	D₄	—	10	4	no	—
317	D₄	—	10	4	no	—
318	D₄	—	10	4	no	—
319	D₄	—	20	16	no	—
320	D₄	—	20	2	no	—
321	D₄	—	20	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	10	2	no	—
324	C₂×C₄	—	20	2	no	—
325	C₂×C₄	C₂×C₃×D₂₀	1	4	yes	—
326	C₂×C₄	C₂×C₃×D₂₀	1	4	yes	—
327	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
328	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
329	C₈	C₂×C₃×D₂₀	1	8	yes	complemented
330	C₂×C₃	—	40	4	no	—
331	C₂×C₃	—	40	2	no	—
332	C₂×C₃	#65001	1	4	yes	direct product factor
333	C₂×C₃	C₂×#4020	1	1	yes	characteristic
334	C₂×C₃	C₂×#4054	1	2	yes	—
335	C₅	C₂×C₃×#496	1	1	yes	characteristic, complemented, Sylow
336	C₂²	—	20	2	no	—
337	C₂²	—	20	4	no	—
338	C₂²	—	20	8	no	—
339	C₂²	—	20	4	no	—
340	C₂²	—	40	8	no	—
341	C₂²	—	40	4	no	—
342	C₂²	C₃×#4020	1	2	yes	—
343	C₂²	C₃×#4054	1	4	yes	—
344	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
345	C₄	—	2	4	no	—
346	C₄	—	20	2	no	—
347	C₄	C₃×#4020	1	2	yes	—
348	C₄	C₂²×C₃×D₂₀	1	2	yes	—
349	C₃	C₂×#65001	1	1	yes	characteristic, direct product factor, Sylow
350	C₂	—	40	4	no	—
351	C₂	—	40	2	no	—
352	C₂	C₃×#65001	1	4	yes	direct product factor
353	C₂	C₂×C₃×#4020	1	1	yes	characteristic
354	C₂	C₂×C₃×#4054	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂×D₂₀
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#97	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₃×#97	D₅
hypocenter	C₅	C₂×C₃×#496
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×#97

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₄₀	C₂	semidirect
2. C₂²×C₃×#677	C₂	semidirect
3. C₂×C₃×#4021	C₂	semidirect
4. C₂×C₃×#4020	C₂	semidirect
5. C₂×C₃×C₅×#97	C₂	semidirect
6. C₃×#65001	C₂	direct (N × H)
7. C₂×#65001	C₃	direct (N × H)
16. C₂×C₃×D₄₀	C₂²	semidirect
18. C₂×C₃×#677	C₂²	semidirect
20. C₃×#4021	C₂²	semidirect
22. C₃×#4020	C₂²	semidirect
23. C₃×C₅×#97	C₂²	semidirect
25. C₂²×D₄₀	C₂×C₃	semidirect
26. C₂²×#677	C₂×C₃	semidirect
27. C₂×#4021	C₂×C₃	semidirect
28. C₂×#4020	C₂×C₃	semidirect
29. C₂×C₅×#97	C₂×C₃	semidirect
30. #65001	C₂×C₃	direct (N × H)
48. C₂×C₃×C₅×C₈	D₄	semidirect
60. C₂×C₃×#97	D₅	semidirect
69. C₂×D₄₀	C₂²×C₃	semidirect
71. C₂×#677	C₂²×C₃	semidirect
73. #4021	C₂²×C₃	semidirect
75. #4020	C₂²×C₃	semidirect
76. C₅×#97	C₂²×C₃	semidirect
100. C₃×C₅×C₈	C₂×D₄	semidirect
116. C₃×#97	C₂×D₅	semidirect
134. C₂×C₅×C₈	C₃×D₄	semidirect
146. C₂×#97	C₃×D₅	semidirect
179. C₂×C₃×C₈	D₂₀	semidirect
206. C₅×C₈	C₂×C₃×D₄	semidirect
222. #97	C₂×C₃×D₅	semidirect
223. C₂×C₃×C₅	#496	semidirect
250. C₃×C₈	C₂×D₂₀	semidirect
283. C₂×C₈	C₃×D₂₀	semidirect
288. C₃×C₅	C₂×#496	semidirect
302. C₂×C₅	C₃×#496	semidirect
329. C₈	C₂×C₃×D₂₀	semidirect
332. C₂×C₃	#65001	direct (N × H)
335. C₅	C₂×C₃×#496	semidirect
349. C₃	C₂×#65001	direct (N × H)
352. C₂	C₃×#65001	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×D₄₀	2
C₂²×C₃×#677	2
C₂×C₃×#4021	2
C₂×C₃×#4020	2
C₂×C₃×C₅×#97	2
C₃×#65001	2
C₂×#65001	3
C₂×C₃×#496	5

Subgroups — C2×C3×#65001 #14438968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65001 #14438968