Subgroups — C₃×#10610296 #14439550

Order 1920.

1192 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4054	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×#4050	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65859	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65001	C₂	1	4	yes	maximal, complemented
7	C₃×#64985	C₂	1	2	yes	maximal, complemented
8	C₃×#64984	C₂	1	2	yes	maximal, complemented
9	#10610296	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×#709	C₂²	1	2	yes	—
11	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×#117	C₂²	1	1	yes	characteristic
15	C₃×#4054	—	2	8	no	—
16	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic, complemented
17	C₃×#4050	—	2	4	no	—
18	C₂×C₃×D₄₀	—	2	4	no	—
19	C₂×C₃×D₄₀	C₂²	1	2	yes	—
20	C₂×C₃×D₄₀	C₂²	1	2	yes	—
21	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×D₄₀	C₂²	1	4	yes	complemented
23	C₂×C₃×#677	C₂²	1	4	yes	complemented
24	C₂×C₃×#677	C₂²	1	2	yes	complemented
25	C₃×#4041	—	2	4	no	—
26	C₃×#4028	—	2	4	no	—
27	C₃×#4021	C₂²	1	4	yes	complemented
28	C₃×#4020	C₂²	1	4	yes	complemented
29	C₃×C₅×#97	C₂²	1	2	yes	complemented
30	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
31	C₃×#3155	—	5	1	no	maximal, Hall
32	C₂×#4054	C₂×C₃	1	2	yes	complemented
33	C₂×#4050	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂²×D₄₀	C₂×C₃	1	1	yes	characteristic, complemented
35	#65859	C₂×C₃	1	2	yes	complemented
36	C₅×#405	C₂×C₃	1	1	yes	characteristic, complemented
37	#65001	C₂×C₃	1	4	yes	complemented
38	#64985	C₂×C₃	1	2	yes	complemented
39	#64984	C₂×C₃	1	2	yes	complemented
40	C₂³×C₃×D₅	—	2	2	no	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
43	C₃×#709	—	2	4	no	—
44	C₃×#709	—	2	4	no	—
45	C₂×C₃×D₂₀	—	2	4	no	—
46	C₂×C₃×D₂₀	—	2	4	no	—
47	C₂×C₃×D₂₀	—	2	2	no	—
48	C₂×C₃×D₂₀	—	2	8	no	—
49	C₂×C₃×D₂₀	C₂³	1	4	yes	—
50	C₂×C₃×D₂₀	C₂³	1	2	yes	—
51	C₂×C₃×C₄×D₅	—	2	2	no	—
52	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
53	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
54	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
55	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
58	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
59	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
60	C₃×C₄²×C₅	C₂³	1	2	yes	—
61	C₃×#685	—	2	8	no	—
62	C₃×Dic₂₀	—	2	2	no	—
63	C₃×D₄₀	—	2	4	no	—
64	C₃×D₄₀	—	2	4	no	—
65	C₃×D₄₀	—	2	2	no	—
66	C₃×D₄₀	—	2	8	no	—
67	C₃×#677	—	2	4	no	—
68	C₃×#677	—	2	8	no	—
69	C₂×C₃×AGL(1,ℤ/8)	—	5	2	no	—
70	C₂×C₃×#135	—	5	1	no	—
71	C₂²×C₃×D₈	—	5	1	no	—
72	C₃×#535	—	5	2	no	—
73	C₃×#496	—	5	4	no	—
74	C₃×#495	—	5	2	no	—
75	C₃×#493	—	5	2	no	—
76	C₃×#405	D₅	1	1	yes	characteristic, complemented
77	C₂×#709	C₂²×C₃	1	2	yes	—
78	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
79	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
80	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
81	C₅×#117	C₂²×C₃	1	1	yes	characteristic
82	#4054	—	2	8	no	—
83	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
84	#4050	—	2	4	no	—
85	C₂×D₄₀	—	2	4	no	—
86	C₂×D₄₀	C₂²×C₃	1	2	yes	—
87	C₂×D₄₀	C₂²×C₃	1	2	yes	—
88	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic, complemented
89	C₂×D₄₀	C₂²×C₃	1	4	yes	complemented
90	C₂×#677	C₂²×C₃	1	2	yes	complemented
91	C₂×#677	C₂²×C₃	1	4	yes	complemented
92	#4041	—	2	4	no	—
93	#4028	—	2	4	no	—
94	#4021	C₂²×C₃	1	4	yes	complemented
95	#4020	C₂²×C₃	1	4	yes	complemented
96	C₅×#97	C₂²×C₃	1	2	yes	complemented
97	C₄×C₅×C₈	C₂²×C₃	1	2	yes	complemented
98	#3155	—	5	1	no	Sylow
99	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₃×D₅	—	2	4	no	—
101	C₂²×C₃×D₅	—	2	2	no	—
102	C₂²×C₃×D₅	—	4	4	no	—
103	C₂²×C₃×D₅	—	8	4	no	—
104	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
109	C₃×C₂²⋊D₅	—	4	4	no	—
110	C₂×C₃×Dic₅	—	2	2	no	—
111	C₃×D₂₀	—	2	4	no	—
112	C₃×D₂₀	—	2	2	no	—
113	C₃×D₂₀	—	2	4	no	—
114	C₃×D₂₀	—	2	2	no	—
115	C₃×D₂₀	—	4	4	no	—
116	C₃×D₂₀	—	8	8	no	—
117	C₃×C₄×D₅	—	4	4	no	—
118	C₃×Dic₁₀	—	2	2	no	—
119	C₃×Dic₁₀	—	2	2	no	—
120	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
121	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
122	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
123	C₂×C₃×#41	—	5	2	no	—
124	C₂²×C₃×D₄	—	5	2	no	—
125	C₃×AGL(1,ℤ/8)	—	10	8	no	—
126	C₃×#135	—	10	4	no	—
127	C₂×C₃×Q₁₆	—	5	1	no	—
128	C₂×C₃×SD₁₆	—	5	2	no	—
129	C₂×C₃×SD₁₆	—	5	4	no	—
130	C₂×C₃×D₈	—	5	2	no	—
131	C₂×C₃×D₈	—	5	2	no	—
132	C₂×C₃×D₈	—	5	1	no	—
133	C₂×C₃×D₈	—	5	4	no	—
134	C₂×C₃×D₈	—	10	4	no	—
135	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
136	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
137	C₃×#127	—	5	4	no	—
138	C₃×#124	—	5	4	no	—
139	C₃×#121	—	10	4	no	—
140	C₃×#120	—	10	4	no	—
141	C₃×#117	C₂×D₅	1	1	yes	characteristic
142	C₃×#97	C₂×D₅	1	2	yes	complemented
143	C₃×C₄×C₈	C₂×D₅	1	2	yes	complemented
144	C₂³×D₅	—	2	2	no	—
145	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
146	C₂×C₂²⋊D₅	—	2	2	no	—
147	#709	—	2	4	no	—
148	#709	—	2	4	no	—
149	C₂×D₂₀	—	2	4	no	—
150	C₂×D₂₀	—	2	4	no	—
151	C₂×D₂₀	—	2	2	no	—
152	C₂×D₂₀	—	2	8	no	—
153	C₂×D₂₀	C₂³×C₃	1	4	yes	—
154	C₂×D₂₀	C₂³×C₃	1	2	yes	—
155	C₂×C₄×D₅	—	2	2	no	—
156	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
157	C₅×M₁₆	C₃×D₄	1	4	yes	complemented
158	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
159	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
160	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
161	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
162	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
163	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
164	C₄²×C₅	C₂³×C₃	1	2	yes	—
165	#685	—	2	8	no	—
166	Dic₂₀	—	2	2	no	—
167	D₄₀	—	2	4	no	—
168	D₄₀	—	2	4	no	—
169	D₄₀	—	2	2	no	—
170	D₄₀	—	2	8	no	—
171	#677	—	2	4	no	—
172	#677	—	2	8	no	—
173	C₂×AGL(1,ℤ/8)	—	5	2	no	—
174	C₂×#135	—	5	1	no	—
175	C₂²×D₈	—	5	1	no	—
176	#535	—	5	2	no	—
177	#496	—	5	4	no	—
178	#495	—	5	2	no	—
179	#493	—	5	2	no	—
180	#405	C₃×D₅	1	1	yes	characteristic, complemented
181	C₂²×C₃×C₅	—	2	2	no	—
182	C₂²×C₃×C₅	#127	1	2	yes	—
183	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₃×D₅	—	4	2	no	—
185	C₂×C₃×D₅	—	4	4	no	—
186	C₂×C₃×D₅	—	4	4	no	—
187	C₂×C₃×D₅	—	4	8	no	—
188	C₂×C₃×D₅	—	8	8	no	—
189	C₃×C₄×C₅	—	2	4	no	—
190	C₃×C₄×C₅	#127	1	2	yes	—
191	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
192	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₃×Dic₅	—	4	2	no	—
194	C₂⁴×C₃	—	10	2	no	—
195	C₃×#41	—	10	4	no	—
196	C₃×#41	—	10	4	no	—
197	C₂×C₃×Q₈	—	5	2	no	—
198	C₂×C₃×D₄	—	5	4	no	—
199	C₂×C₃×D₄	—	5	2	no	—
200	C₂×C₃×D₄	—	10	2	no	—
201	C₂×C₃×D₄	—	10	4	no	—
202	C₂×C₃×D₄	—	10	4	no	—
203	C₂×C₃×D₄	—	10	2	no	—
204	C₂×C₃×D₄	—	10	8	no	—
205	C₂²×C₃×C₄	—	10	2	no	—
206	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
207	C₃×Q₁₆	—	10	2	no	—
208	C₃×SD₁₆	—	10	4	no	—
209	C₃×SD₁₆	—	10	8	no	—
210	C₃×D₈	—	10	4	no	—
211	C₃×D₈	—	10	4	no	—
212	C₃×D₈	—	10	2	no	—
213	C₃×D₈	—	10	8	no	—
214	C₃×M₁₆	D₂₀	1	4	yes	complemented
215	C₂×C₃×C₈	D₂₀	1	4	yes	complemented
216	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
217	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
218	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
219	C₃×C₄⋊C₄	D₂₀	1	2	yes	—
220	C₃×C₂²⋊C₄	—	10	8	no	—
221	C₃×C₂²⋊C₄	D₂₀	1	2	yes	—
222	C₃×C₄²	C₂²×D₅	1	2	yes	—
223	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
224	C₂²×D₅	—	2	4	no	—
225	C₂²×D₅	—	2	2	no	—
226	C₂²×D₅	—	4	4	no	—
227	C₂²×D₅	—	8	4	no	—
228	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
229	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
231	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
232	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
233	C₂²⋊D₅	—	4	4	no	—
234	C₂×Dic₅	—	2	2	no	—
235	D₂₀	—	2	4	no	—
236	D₂₀	—	2	2	no	—
237	D₂₀	—	2	4	no	—
238	D₂₀	—	2	2	no	—
239	D₂₀	—	4	4	no	—
240	D₂₀	—	8	8	no	—
241	C₄×D₅	—	4	4	no	—
242	Dic₁₀	—	2	2	no	—
243	Dic₁₀	—	2	2	no	—
244	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
245	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
246	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
247	C₂×#41	—	5	2	no	—
248	C₂²×D₄	—	5	2	no	—
249	AGL(1,ℤ/8)	—	10	8	no	—
250	#135	—	10	4	no	—
251	C₂×Q₁₆	—	5	1	no	—
252	C₂×SD₁₆	—	5	2	no	—
253	C₂×SD₁₆	—	5	4	no	—
254	C₂×D₈	—	5	2	no	—
255	C₂×D₈	—	5	2	no	—
256	C₂×D₈	—	5	1	no	—
257	C₂×D₈	—	5	4	no	—
258	C₂×D₈	—	10	4	no	—
259	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
260	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
261	#127	—	5	4	no	—
262	#124	—	5	4	no	—
263	#121	—	10	4	no	—
264	#120	—	10	4	no	—
265	#117	C₂×C₃×D₅	1	1	yes	characteristic
266	#97	C₂×C₃×D₅	1	2	yes	complemented
267	C₄×C₈	C₂×C₃×D₅	1	2	yes	complemented
268	C₂×C₃×C₅	—	2	2	no	—
269	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
270	C₂×C₃×C₅	#576	1	2	yes	—
271	C₃×D₅	—	8	2	no	—
272	C₃×D₅	—	8	4	no	—
273	C₂³×C₃	—	10	4	no	—
274	C₂³×C₃	—	10	2	no	—
275	C₂³×C₃	—	20	4	no	—
276	C₂³×C₃	—	40	4	no	—
277	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
278	C₃×Q₈	—	10	2	no	—
279	C₃×Q₈	—	10	2	no	—
280	C₃×D₄	—	10	4	no	—
281	C₃×D₄	—	10	2	no	—
282	C₃×D₄	—	10	4	no	—
283	C₃×D₄	—	10	2	no	—
284	C₃×D₄	—	20	4	no	—
285	C₃×D₄	—	20	4	no	—
286	C₃×D₄	—	40	8	no	—
287	C₂×C₃×C₄	—	10	2	no	—
288	C₂×C₃×C₄	—	20	4	no	—
289	C₂×C₃×C₄	C₂×D₂₀	1	4	yes	—
290	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
291	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
292	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
294	C₃×C₈	C₂×D₂₀	1	2	yes	—
295	C₃×C₈	C₂×D₂₀	1	2	yes	—
296	C₃×C₈	C₂×D₂₀	1	4	yes	—
297	C₂²×C₅	—	2	2	no	—
298	C₂²×C₅	C₃×#127	1	2	yes	—
299	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
300	C₂×D₅	—	4	4	no	—
301	C₂×D₅	—	4	8	no	—
302	C₂×D₅	—	4	2	no	—
303	C₂×D₅	—	4	4	no	—
304	C₂×D₅	—	8	8	no	—
305	C₄×C₅	—	2	4	no	—
306	C₄×C₅	C₃×#127	1	2	yes	—
307	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
308	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
309	Dic₅	—	4	2	no	—
310	C₂⁴	—	10	2	no	—
311	#41	—	10	4	no	—
312	#41	—	10	4	no	—
313	C₂×Q₈	—	5	2	no	—
314	C₂×D₄	—	5	4	no	—
315	C₂×D₄	—	5	2	no	—
316	C₂×D₄	—	10	2	no	—
317	C₂×D₄	—	10	4	no	—
318	C₂×D₄	—	10	4	no	—
319	C₂×D₄	—	10	2	no	—
320	C₂×D₄	—	10	8	no	—
321	C₂²×C₄	—	10	2	no	—
322	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
323	Q₁₆	—	10	2	no	—
324	SD₁₆	—	10	4	no	—
325	SD₁₆	—	10	8	no	—
326	D₈	—	10	4	no	—
327	D₈	—	10	4	no	—
328	D₈	—	10	2	no	—
329	D₈	—	10	8	no	—
330	M₁₆	C₃×D₂₀	1	4	yes	complemented
331	C₂×C₈	C₃×D₂₀	1	4	yes	complemented
332	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
333	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
334	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
335	C₄⋊C₄	C₃×D₂₀	1	2	yes	—
336	C₂²⋊C₄	—	10	8	no	—
337	C₂²⋊C₄	C₃×D₂₀	1	2	yes	—
338	C₄²	C₂²×C₃×D₅	1	2	yes	—
339	C₃×C₅	#3155	1	1	yes	characteristic, complemented, Hall
340	C₂²×C₃	—	2	2	no	—
341	C₂²×C₃	—	20	2	no	—
342	C₂²×C₃	—	20	4	no	—
343	C₂²×C₃	—	20	4	no	—
344	C₂²×C₃	—	20	8	no	—
345	C₂²×C₃	—	40	8	no	—
346	C₂²×C₃	#4020	1	2	yes	—
347	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
348	C₃×C₄	—	2	4	no	—
349	C₃×C₄	—	20	2	no	—
350	C₃×C₄	#4020	1	2	yes	—
351	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
352	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
353	C₂×C₅	—	2	2	no	—
354	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
355	C₂×C₅	C₃×#576	1	2	yes	—
356	D₅	—	8	4	no	—
357	D₅	—	8	2	no	—
358	C₂³	—	10	4	no	—
359	C₂³	—	10	2	no	—
360	C₂³	—	20	4	no	—
361	C₂³	—	40	4	no	—
362	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
363	Q₈	—	10	2	no	—
364	Q₈	—	10	2	no	—
365	D₄	—	10	4	no	—
366	D₄	—	10	2	no	—
367	D₄	—	10	4	no	—
368	D₄	—	10	2	no	—
369	D₄	—	20	4	no	—
370	D₄	—	20	4	no	—
371	D₄	—	40	8	no	—
372	C₂×C₄	—	10	2	no	—
373	C₂×C₄	—	20	4	no	—
374	C₂×C₄	C₂×C₃×D₂₀	1	4	yes	—
375	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
376	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
377	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
378	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
379	C₈	C₂×C₃×D₂₀	1	2	yes	—
380	C₈	C₂×C₃×D₂₀	1	2	yes	—
381	C₈	C₂×C₃×D₂₀	1	4	yes	—
382	C₂×C₃	—	2	2	no	—
383	C₂×C₃	—	40	4	no	—
384	C₂×C₃	—	40	2	no	—
385	C₂×C₃	C₂×#4020	1	1	yes	characteristic
386	C₂×C₃	#66086	1	2	yes	—
387	C₅	C₃×#3155	1	1	yes	characteristic, complemented, Sylow
388	C₂²	—	2	2	no	—
389	C₂²	—	20	2	no	—
390	C₂²	—	20	4	no	—
391	C₂²	—	20	4	no	—
392	C₂²	—	20	8	no	—
393	C₂²	—	40	8	no	—
394	C₂²	C₃×#4020	1	2	yes	—
395	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
396	C₄	—	2	4	no	—
397	C₄	—	20	2	no	—
398	C₄	C₃×#4020	1	2	yes	—
399	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
400	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
401	C₃	#10610296	1	1	yes	characteristic, direct product factor, Sylow
402	C₂	—	2	2	no	—
403	C₂	—	40	4	no	—
404	C₂	—	40	2	no	—
405	C₂	C₂×C₃×#4020	1	1	yes	characteristic
406	C₂	C₃×#66086	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂²×D₂₀
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#405	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#405	D₅
hypocenter	C₅	C₃×#3155
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117 ◁ C₃×#405

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4054	C₂	semidirect
2. C₂×C₃×#4050	C₂	semidirect
3. C₂²×C₃×D₄₀	C₂	semidirect
4. C₃×#65859	C₂	semidirect
5. C₃×C₅×#405	C₂	semidirect
6. C₃×#65001	C₂	semidirect
7. C₃×#64985	C₂	semidirect
8. C₃×#64984	C₂	semidirect
9. #10610296	C₃	direct (N × H)
16. C₂×C₃×Dic₂₀	C₂²	semidirect
21. C₂×C₃×D₄₀	C₂²	semidirect
22. C₂×C₃×D₄₀	C₂²	semidirect
23. C₂×C₃×#677	C₂²	semidirect
24. C₂×C₃×#677	C₂²	semidirect
27. C₃×#4021	C₂²	semidirect
28. C₃×#4020	C₂²	semidirect
29. C₃×C₅×#97	C₂²	semidirect
30. C₃×C₄×C₅×C₈	C₂²	semidirect
32. C₂×#4054	C₂×C₃	semidirect
33. C₂×#4050	C₂×C₃	semidirect
34. C₂²×D₄₀	C₂×C₃	semidirect
35. #65859	C₂×C₃	semidirect
36. C₅×#405	C₂×C₃	semidirect
37. #65001	C₂×C₃	semidirect
38. #64985	C₂×C₃	semidirect
39. #64984	C₂×C₃	semidirect
53. C₃×C₅×M₁₆	D₄	semidirect
54. C₂×C₃×C₅×C₈	D₄	semidirect
76. C₃×#405	D₅	semidirect
83. C₂×Dic₂₀	C₂²×C₃	semidirect
88. C₂×D₄₀	C₂²×C₃	semidirect
89. C₂×D₄₀	C₂²×C₃	semidirect
90. C₂×#677	C₂²×C₃	semidirect
91. C₂×#677	C₂²×C₃	semidirect
94. #4021	C₂²×C₃	semidirect
95. #4020	C₂²×C₃	semidirect
96. C₅×#97	C₂²×C₃	semidirect
97. C₄×C₅×C₈	C₂²×C₃	semidirect
142. C₃×#97	C₂×D₅	semidirect
143. C₃×C₄×C₈	C₂×D₅	semidirect
157. C₅×M₁₆	C₃×D₄	semidirect
158. C₂×C₅×C₈	C₃×D₄	semidirect
180. #405	C₃×D₅	semidirect
214. C₃×M₁₆	D₂₀	semidirect
215. C₂×C₃×C₈	D₂₀	semidirect
266. #97	C₂×C₃×D₅	semidirect
267. C₄×C₈	C₂×C₃×D₅	semidirect
330. M₁₆	C₃×D₂₀	semidirect
331. C₂×C₈	C₃×D₂₀	semidirect
339. C₃×C₅	#3155	semidirect
387. C₅	C₃×#3155	semidirect
401. C₃	#10610296	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×#4054	2
C₂×C₃×#4050	2
C₂²×C₃×D₄₀	2
C₃×#65859	2
C₃×C₅×#405	2
C₃×#65001	2
C₃×#64985	2
C₃×#64984	2
#10610296	3
C₃×#3155	5

Subgroups — C3×#10610296 #14439550

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610296 #14439550