Subgroups — C₂×C₃×#65132 #14425819

Order 1920.

1296 conjugacy classes of subgroups.

The subgroup lattice has 424 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	C₂×C₃×#4020	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3953	C₂	1	2	yes	maximal, complemented
6	C₃×#65132	C₂	1	8	yes	maximal, direct product factor
7	C₂×#65132	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×D₂₀	—	2	1	no	—
9	C₂²×C₃×D₂₀	—	2	1	no	—
10	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
11	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×D₅	—	2	1	no	—
13	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×#685	—	2	1	no	—
16	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×D₄₀	—	2	8	no	—
18	C₂×C₃×D₄₀	C₂²	1	8	yes	complemented
19	C₃×#4020	—	2	2	no	—
20	C₃×#4020	C₂²	1	4	yes	complemented
21	C₃×C₄×D₂₀	—	2	2	no	—
22	C₃×C₄×D₂₀	C₂²	1	4	yes	complemented
23	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
24	C₃×#3953	C₂²	1	8	yes	complemented
25	C₂×C₃×#459	—	5	1	no	maximal, Hall
26	C₂²×D₄₀	C₂×C₃	1	2	yes	complemented
27	C₂×#4020	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×C₄×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×#3953	C₂×C₃	1	2	yes	complemented
31	#65132	C₂×C₃	1	8	yes	direct product factor
32	C₂³×C₃×D₅	—	2	1	no	—
33	C₂³×C₃×D₅	—	2	2	no	—
34	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂²×C₃×Dic₅	—	2	1	no	—
38	C₂×C₃×D₂₀	—	2	1	no	—
39	C₂×C₃×D₂₀	—	2	2	no	—
40	C₂×C₃×D₂₀	—	2	4	no	—
41	C₂×C₃×D₂₀	—	2	4	no	—
42	C₂×C₃×D₂₀	—	2	4	no	—
43	C₂×C₃×D₂₀	—	2	4	no	—
44	C₂×C₃×D₂₀	—	2	2	no	—
45	C₂×C₃×D₂₀	—	4	4	no	—
46	C₂×C₃×D₂₀	—	4	4	no	—
47	C₂×C₃×D₂₀	D₄	1	4	yes	complemented
48	C₂×C₃×D₂₀	C₂³	1	4	yes	—
49	C₂×C₃×D₂₀	C₂³	1	2	yes	—
50	C₂×C₃×C₄×D₅	—	2	4	no	—
51	C₂×C₃×C₄×D₅	—	4	4	no	—
52	C₂×C₃×C₅×C₈	—	2	4	no	—
53	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
54	C₃×C₄²×C₅	D₄	1	2	yes	—
55	C₃×C₄²×C₅	C₂³	1	2	yes	—
56	C₃×#685	—	2	4	no	—
57	C₃×C₄⋊Dic₅	—	2	1	no	—
58	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
59	C₃×D₄₀	—	2	16	no	—
60	C₂²×C₃×D₈	—	5	2	no	—
61	C₂×C₃×#127	—	5	1	no	—
62	C₂×C₃×C₄×D₄	—	5	1	no	—
63	C₃×#459	—	5	8	no	—
64	C₂×C₃×C₄⋊C₈	D₅	1	1	yes	characteristic, complemented
65	C₂×C₃×#102	—	5	2	no	—
66	C₂²×D₂₀	—	2	1	no	—
67	C₂²×D₂₀	—	2	1	no	—
68	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
69	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
70	C₂²×C₄×D₅	—	2	1	no	—
71	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
72	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
73	C₂×#685	—	2	1	no	—
74	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
75	C₂×D₄₀	—	2	8	no	—
76	C₂×D₄₀	C₂²×C₃	1	8	yes	complemented
77	#4020	—	2	2	no	—
78	#4020	C₂²×C₃	1	4	yes	complemented
79	C₄×D₂₀	—	2	2	no	—
80	C₄×D₂₀	C₂²×C₃	1	4	yes	complemented
81	C₅×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
82	#3953	C₂²×C₃	1	8	yes	complemented
83	C₂×#459	—	5	1	no	Sylow
84	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₃×D₅	—	2	4	no	—
86	C₂²×C₃×D₅	—	2	2	no	—
87	C₂²×C₃×D₅	—	2	4	no	—
88	C₂²×C₃×D₅	—	4	2	no	—
89	C₂²×C₃×D₅	—	4	2	no	—
90	C₂²×C₃×D₅	—	4	4	no	—
91	C₂²×C₃×D₅	—	4	4	no	—
92	C₂²×C₃×D₅	—	4	4	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	D₈	1	4	yes	complemented
95	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	#41	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
101	C₂×C₃×Dic₅	—	2	2	no	—
102	C₂×C₃×Dic₅	—	4	2	no	—
103	C₃×D₂₀	—	2	4	no	—
104	C₃×D₂₀	—	2	4	no	—
105	C₃×D₂₀	—	2	2	no	—
106	C₃×D₂₀	—	2	4	no	—
107	C₃×D₂₀	—	4	8	no	—
108	C₃×D₂₀	—	4	4	no	—
109	C₃×D₂₀	—	4	8	no	—
110	C₃×D₂₀	C₂×D₄	1	4	yes	complemented
111	C₃×C₄×D₅	—	4	8	no	—
112	C₃×C₅×C₈	—	2	4	no	—
113	C₂²×C₃×D₄	—	5	1	no	—
114	C₂²×C₃×D₄	—	5	2	no	—
115	C₂²×C₃×D₄	—	10	1	no	—
116	C₂²×C₃×D₄	—	10	1	no	—
117	C₂³×C₃×C₄	—	10	1	no	—
118	C₂×C₃×D₈	—	5	8	no	—
119	C₂×C₃×D₈	—	10	8	no	—
120	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
121	C₃×#127	—	5	4	no	—
122	C₃×#127	—	10	2	no	—
123	C₃×C₄×D₄	—	5	4	no	—
124	C₃×C₄×D₄	—	10	2	no	—
125	C₂×C₃×C₄⋊C₄	—	5	1	no	—
126	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
127	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
128	C₃×C₄⋊C₈	C₂×D₅	1	4	yes	complemented
129	C₃×#102	—	5	8	no	—
130	C₂³×D₅	—	2	1	no	—
131	C₂³×D₅	—	2	2	no	—
132	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
135	C₂²×Dic₅	—	2	1	no	—
136	C₂×D₂₀	—	2	1	no	—
137	C₂×D₂₀	—	2	2	no	—
138	C₂×D₂₀	—	2	4	no	—
139	C₂×D₂₀	—	2	4	no	—
140	C₂×D₂₀	—	2	4	no	—
141	C₂×D₂₀	—	2	4	no	—
142	C₂×D₂₀	—	2	2	no	—
143	C₂×D₂₀	—	4	4	no	—
144	C₂×D₂₀	—	4	4	no	—
145	C₂×D₂₀	C₃×D₄	1	4	yes	complemented
146	C₂×D₂₀	C₂³×C₃	1	4	yes	—
147	C₂×D₂₀	C₂³×C₃	1	2	yes	—
148	C₂×C₄×D₅	—	2	4	no	—
149	C₂×C₄×D₅	—	4	4	no	—
150	C₂×C₅×C₈	—	2	4	no	—
151	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
152	C₄²×C₅	C₃×D₄	1	2	yes	—
153	C₄²×C₅	C₂³×C₃	1	2	yes	—
154	#685	—	2	4	no	—
155	C₄⋊Dic₅	—	2	1	no	—
156	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
157	D₄₀	—	2	16	no	—
158	C₂²×D₈	—	5	2	no	—
159	C₂×#127	—	5	1	no	—
160	C₂×C₄×D₄	—	5	1	no	—
161	#459	—	5	8	no	—
162	C₂×C₄⋊C₈	C₃×D₅	1	1	yes	characteristic, complemented
163	C₂×#102	—	5	2	no	—
164	C₂²×C₃×C₅	#121	1	2	yes	—
165	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
166	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
167	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₃×D₅	—	2	4	no	—
169	C₂×C₃×D₅	—	4	2	no	—
170	C₂×C₃×D₅	—	4	2	no	—
171	C₂×C₃×D₅	—	4	8	no	—
172	C₂×C₃×D₅	—	4	4	no	—
173	C₂×C₃×D₅	—	4	4	no	—
174	C₂×C₃×D₅	—	4	4	no	—
175	C₂×C₃×D₅	—	8	8	no	—
176	C₃×C₄×C₅	—	2	2	no	—
177	C₃×C₄×C₅	#121	1	2	yes	—
178	C₃×C₄×C₅	C₂×D₈	1	4	yes	complemented
179	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
180	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
181	C₃×Dic₅	—	4	2	no	—
182	C₂⁴×C₃	—	10	1	no	—
183	C₂⁴×C₃	—	10	2	no	—
184	C₂×C₃×D₄	—	5	4	no	—
185	C₂×C₃×D₄	—	5	2	no	—
186	C₂×C₃×D₄	—	5	4	no	—
187	C₂×C₃×D₄	—	10	1	no	—
188	C₂×C₃×D₄	—	10	4	no	—
189	C₂×C₃×D₄	—	10	4	no	—
190	C₂×C₃×D₄	—	10	2	no	—
191	C₂×C₃×D₄	—	10	4	no	—
192	C₂×C₃×D₄	—	10	2	no	—
193	C₂×C₃×D₄	—	10	4	no	—
194	C₂×C₃×D₄	—	20	4	no	—
195	C₂×C₃×D₄	—	20	4	no	—
196	C₂²×C₃×C₄	—	10	1	no	—
197	C₂²×C₃×C₄	—	10	4	no	—
198	C₂²×C₃×C₄	—	20	4	no	—
199	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
200	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
201	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
202	C₃×D₈	—	10	16	no	—
203	C₂×C₃×C₈	—	2	4	no	—
204	C₂×C₃×C₈	C₂²×D₅	1	4	yes	—
205	C₃×C₄⋊C₄	—	5	2	no	—
206	C₃×C₄⋊C₄	—	10	1	no	—
207	C₃×C₂²⋊C₄	—	10	4	no	—
208	C₃×C₄²	D₂₀	1	2	yes	—
209	C₃×C₄²	C₂²×D₅	1	2	yes	—
210	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
211	C₂²×D₅	—	2	4	no	—
212	C₂²×D₅	—	2	2	no	—
213	C₂²×D₅	—	2	4	no	—
214	C₂²×D₅	—	4	2	no	—
215	C₂²×D₅	—	4	2	no	—
216	C₂²×D₅	—	4	4	no	—
217	C₂²×D₅	—	4	4	no	—
218	C₂²×D₅	—	4	4	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	C₃×D₈	1	4	yes	complemented
221	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
222	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
224	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
225	C₂×C₄×C₅	C₃×#41	1	2	yes	—
226	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
227	C₂×Dic₅	—	2	2	no	—
228	C₂×Dic₅	—	4	2	no	—
229	D₂₀	—	2	4	no	—
230	D₂₀	—	2	4	no	—
231	D₂₀	—	2	2	no	—
232	D₂₀	—	2	4	no	—
233	D₂₀	—	4	8	no	—
234	D₂₀	—	4	4	no	—
235	D₂₀	—	4	8	no	—
236	D₂₀	C₂×C₃×D₄	1	4	yes	complemented
237	C₄×D₅	—	4	8	no	—
238	C₅×C₈	—	2	4	no	—
239	C₂²×D₄	—	5	1	no	—
240	C₂²×D₄	—	5	2	no	—
241	C₂²×D₄	—	10	1	no	—
242	C₂²×D₄	—	10	1	no	—
243	C₂³×C₄	—	10	1	no	—
244	C₂×D₈	—	5	8	no	—
245	C₂×D₈	—	10	8	no	—
246	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
247	#127	—	5	4	no	—
248	#127	—	10	2	no	—
249	C₄×D₄	—	5	4	no	—
250	C₄×D₄	—	10	2	no	—
251	C₂×C₄⋊C₄	—	5	1	no	—
252	C₂×C₂²⋊C₄	—	10	1	no	—
253	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
254	C₄⋊C₈	C₂×C₃×D₅	1	4	yes	complemented
255	#102	—	5	8	no	—
256	C₂×C₃×C₅	#459	1	4	yes	complemented
257	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
258	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
259	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
260	C₃×D₅	—	4	4	no	—
261	C₃×D₅	—	8	4	no	—
262	C₂³×C₃	—	10	2	no	—
263	C₂³×C₃	—	10	4	no	—
264	C₂³×C₃	—	10	4	no	—
265	C₂³×C₃	—	20	2	no	—
266	C₂³×C₃	—	20	2	no	—
267	C₂³×C₃	—	20	4	no	—
268	C₂³×C₃	—	20	4	no	—
269	C₂³×C₃	—	20	4	no	—
270	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
271	C₃×D₄	—	5	4	no	—
272	C₃×D₄	—	10	4	no	—
273	C₃×D₄	—	10	2	no	—
274	C₃×D₄	—	10	4	no	—
275	C₃×D₄	—	10	4	no	—
276	C₃×D₄	—	20	8	no	—
277	C₃×D₄	—	20	4	no	—
278	C₃×D₄	—	20	8	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	10	2	no	—
281	C₂×C₃×C₄	—	20	2	no	—
282	C₂×C₃×C₄	—	20	8	no	—
283	C₂×C₃×C₄	D₄₀	1	4	yes	complemented
284	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
285	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
287	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
288	C₂×C₃×C₄	#713	1	2	yes	—
289	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
290	C₃×C₈	—	2	4	no	—
291	C₂²×C₅	C₃×#121	1	2	yes	—
292	C₂²×C₅	C₂×C₃×D₈	1	2	yes	—
293	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
294	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
295	C₂×D₅	—	2	4	no	—
296	C₂×D₅	—	4	2	no	—
297	C₂×D₅	—	4	2	no	—
298	C₂×D₅	—	4	8	no	—
299	C₂×D₅	—	4	4	no	—
300	C₂×D₅	—	4	4	no	—
301	C₂×D₅	—	4	4	no	—
302	C₂×D₅	—	8	8	no	—
303	C₄×C₅	—	2	2	no	—
304	C₄×C₅	C₃×#121	1	2	yes	—
305	C₄×C₅	C₂×C₃×D₈	1	4	yes	complemented
306	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
307	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
308	Dic₅	—	4	2	no	—
309	C₂⁴	—	10	1	no	—
310	C₂⁴	—	10	2	no	—
311	C₂×D₄	—	5	4	no	—
312	C₂×D₄	—	5	2	no	—
313	C₂×D₄	—	5	4	no	—
314	C₂×D₄	—	10	1	no	—
315	C₂×D₄	—	10	4	no	—
316	C₂×D₄	—	10	4	no	—
317	C₂×D₄	—	10	2	no	—
318	C₂×D₄	—	10	4	no	—
319	C₂×D₄	—	10	2	no	—
320	C₂×D₄	—	10	4	no	—
321	C₂×D₄	—	20	4	no	—
322	C₂×D₄	—	20	4	no	—
323	C₂²×C₄	—	10	1	no	—
324	C₂²×C₄	—	10	4	no	—
325	C₂²×C₄	—	20	4	no	—
326	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
327	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
328	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
329	D₈	—	10	16	no	—
330	C₂×C₈	—	2	4	no	—
331	C₂×C₈	C₂²×C₃×D₅	1	4	yes	—
332	C₄⋊C₄	—	5	2	no	—
333	C₄⋊C₄	—	10	1	no	—
334	C₂²⋊C₄	—	10	4	no	—
335	C₄²	C₃×D₂₀	1	2	yes	—
336	C₄²	C₂²×C₃×D₅	1	2	yes	—
337	C₃×C₅	C₂×#459	1	1	yes	characteristic, complemented, Hall
338	C₂²×C₃	—	10	4	no	—
339	C₂²×C₃	—	20	2	no	—
340	C₂²×C₃	—	20	2	no	—
341	C₂²×C₃	—	20	8	no	—
342	C₂²×C₃	—	20	4	no	—
343	C₂²×C₃	—	20	4	no	—
344	C₂²×C₃	—	20	4	no	—
345	C₂²×C₃	—	40	8	no	—
346	C₂²×C₃	#4041	1	2	yes	—
347	C₂²×C₃	C₂×D₄₀	1	2	yes	—
348	C₂²×C₃	#4054	1	2	yes	—
349	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
350	C₃×C₄	—	2	2	no	—
351	C₃×C₄	—	20	2	no	—
352	C₃×C₄	#4041	1	2	yes	—
353	C₃×C₄	C₂×D₄₀	1	4	yes	complemented
354	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
355	C₃×C₄	C₂×#713	1	1	yes	characteristic
356	C₂×C₅	C₃×#459	1	4	yes	complemented
357	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
358	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
359	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
360	D₅	—	4	4	no	—
361	D₅	—	8	4	no	—
362	C₂³	—	10	2	no	—
363	C₂³	—	10	4	no	—
364	C₂³	—	10	4	no	—
365	C₂³	—	20	2	no	—
366	C₂³	—	20	2	no	—
367	C₂³	—	20	4	no	—
368	C₂³	—	20	4	no	—
369	C₂³	—	20	4	no	—
370	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
371	D₄	—	5	4	no	—
372	D₄	—	10	4	no	—
373	D₄	—	10	2	no	—
374	D₄	—	10	4	no	—
375	D₄	—	10	4	no	—
376	D₄	—	20	8	no	—
377	D₄	—	20	4	no	—
378	D₄	—	20	8	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	10	2	no	—
381	C₂×C₄	—	20	2	no	—
382	C₂×C₄	—	20	8	no	—
383	C₂×C₄	C₃×D₄₀	1	4	yes	complemented
384	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
385	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
386	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
387	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
388	C₂×C₄	C₃×#713	1	2	yes	—
389	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
390	C₈	—	2	4	no	—
391	C₂×C₃	—	20	4	no	—
392	C₂×C₃	—	40	4	no	—
393	C₂×C₃	#65132	1	4	yes	direct product factor
394	C₂×C₃	C₂×#4041	1	1	yes	characteristic
395	C₂×C₃	C₂²×D₄₀	1	1	yes	characteristic
396	C₂×C₃	C₂×#4054	1	1	yes	characteristic
397	C₅	C₂×C₃×#459	1	1	yes	characteristic, complemented, Sylow
398	C₂²	—	10	4	no	—
399	C₂²	—	20	8	no	—
400	C₂²	—	20	2	no	—
401	C₂²	—	20	2	no	—
402	C₂²	—	20	4	no	—
403	C₂²	—	20	4	no	—
404	C₂²	—	20	4	no	—
405	C₂²	—	40	8	no	—
406	C₂²	C₃×#4041	1	2	yes	—
407	C₂²	C₂×C₃×D₄₀	1	2	yes	—
408	C₂²	C₃×#4054	1	2	yes	—
409	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	20	2	no	—
412	C₄	C₃×#4041	1	2	yes	—
413	C₄	C₂×C₃×D₄₀	1	4	yes	complemented
414	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
415	C₄	C₂×C₃×#713	1	1	yes	characteristic
416	C₃	C₂×#65132	1	1	yes	characteristic, direct product factor, Sylow
417	C₂	—	20	4	no	—
418	C₂	—	40	4	no	—
419	C₂	C₃×#65132	1	4	yes	direct product factor
420	C₂	C₂×C₃×#4041	1	1	yes	characteristic
421	C₂	C₂²×C₃×D₄₀	1	1	yes	characteristic
422	C₂	C₂×C₃×#4054	1	1	yes	characteristic

	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×C₄⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₃×C₄⋊C₈	D₅
hypocenter	C₅	C₂×C₃×#459
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₄₀	C₂	semidirect
2. C₂×C₃×#4020	C₂	semidirect
3. C₂×C₃×C₄×D₂₀	C₂	semidirect
4. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
5. C₂×C₃×#3953	C₂	semidirect
6. C₃×#65132	C₂	direct (N × H)
7. C₂×#65132	C₃	direct (N × H)
18. C₂×C₃×D₄₀	C₂²	semidirect
20. C₃×#4020	C₂²	semidirect
22. C₃×C₄×D₂₀	C₂²	semidirect
23. C₃×C₅×C₄⋊C₈	C₂²	semidirect
24. C₃×#3953	C₂²	semidirect
26. C₂²×D₄₀	C₂×C₃	semidirect
27. C₂×#4020	C₂×C₃	semidirect
28. C₂×C₄×D₂₀	C₂×C₃	semidirect
29. C₂×C₅×C₄⋊C₈	C₂×C₃	semidirect
30. C₂×#3953	C₂×C₃	semidirect
31. #65132	C₂×C₃	direct (N × H)
47. C₂×C₃×D₂₀	D₄	semidirect
64. C₂×C₃×C₄⋊C₈	D₅	semidirect
76. C₂×D₄₀	C₂²×C₃	semidirect
78. #4020	C₂²×C₃	semidirect
80. C₄×D₂₀	C₂²×C₃	semidirect
81. C₅×C₄⋊C₈	C₂²×C₃	semidirect
82. #3953	C₂²×C₃	semidirect
94. C₂×C₃×C₄×C₅	D₈	semidirect
110. C₃×D₂₀	C₂×D₄	semidirect
128. C₃×C₄⋊C₈	C₂×D₅	semidirect
145. C₂×D₂₀	C₃×D₄	semidirect
162. C₂×C₄⋊C₈	C₃×D₅	semidirect
178. C₃×C₄×C₅	C₂×D₈	semidirect
220. C₂×C₄×C₅	C₃×D₈	semidirect
236. D₂₀	C₂×C₃×D₄	semidirect
254. C₄⋊C₈	C₂×C₃×D₅	semidirect
256. C₂×C₃×C₅	#459	semidirect
283. C₂×C₃×C₄	D₄₀	semidirect
305. C₄×C₅	C₂×C₃×D₈	semidirect
337. C₃×C₅	C₂×#459	semidirect
353. C₃×C₄	C₂×D₄₀	semidirect
356. C₂×C₅	C₃×#459	semidirect
383. C₂×C₄	C₃×D₄₀	semidirect
393. C₂×C₃	#65132	direct (N × H)
397. C₅	C₂×C₃×#459	semidirect
413. C₄	C₂×C₃×D₄₀	semidirect
416. C₃	C₂×#65132	direct (N × H)
419. C₂	C₃×#65132	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
C₂×C₃×#4020	2
C₂×C₃×C₄×D₂₀	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₃×#3953	2
C₃×#65132	2
C₂×#65132	3
C₂×C₃×#459	5

Subgroups — C2×C3×#65132 #14425819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65132 #14425819