Finite Group Databasebeta

← C2×C5×C8×S4 #14511173

Subgroups — C2×C5×C8×S4 #14511173

Order 1920.

670 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×S4C211yesmaximal, characteristic
2C2×C5×C8×A4C211yesmaximal, characteristic, complemented
3C2×C5×A4⋊C8C211yesmaximal, characteristic, complemented
4C5×C8×S4C214yesmaximal, direct product factor
5C2×C5×C8×D4—31nomaximal, Hall
6C22×C5×S4C411yescharacteristic
7C2×C4×C5×A4C2211yescharacteristic
8C2×C5×SL(2,ℤ/4)C411yescharacteristic
9C4×C5×S4C412yes—
10C4×C5×S4C2212yes—
11C2×C5×D3×C8—41nomaximal
12C5×C8×A4C2212yescomplemented
13C5×A4⋊C8C2212yescomplemented
14C2×C8×S4C511yesmaximal, characteristic, direct product factor, Hall
15C23×C5×C8—31no—
16C23×C5×C8D311yescharacteristic, complemented
17C2×C4×C5×D4—31no—
18C5×C8×D4—34no—
19C5×C8×D4—34no—
20C2×C5×C4⋊C8—31no—
21C2×C5×C22⋊C8—31no—
22C2×C5×C22⋊C8—31no—
23C2×C4×C5×C8—31no—
24C22×C5×A4C2×C411yescharacteristic
25C2×C5×S4C814yesdirect product factor
26C2×C5×S4C2×C412yes—
27C2×C4×C5×D3—41no—
28C4×C5×A4C2×C411yescharacteristic
29C4×C5×A4C2311yescharacteristic
30C5×SL(2,ℤ/4)C2×C412yes—
31C2×C3×C5×C8—41no—
32C2×C5×C3⋊C8—41no—
33C5×D3×C8—44no—
34C2×C4×S4C2×C511yescharacteristic
35C2×C8×A4C2×C511yescharacteristic, complemented
36C2×A4⋊C8C2×C511yescharacteristic, complemented
37C8×S4C2×C514yesdirect product factor
38C22×C5×D4—31no—
39C23×C4×C5—31no—
40C23×C4×C5C2×D311yescharacteristic
41C22×C5×C8—31no—
42C22×C5×C8—31no—
43C22×C5×C8—32no—
44C22×C5×C8—31no—
45C22×C5×C8—31no—
46C22×C5×C8—34no—
47C22×C5×C8—61no—
48C22×C5×C8—62no—
49C22×C5×C8—61no—
50C22×C5×C8C2×D312yescomplemented
51C4×C5×D4—32no—
52C4×C5×D4—32no—
53C4×C5×D4—32no—
54C4×C5×D4—32no—
55C2×C5×C4⋊C4—31no—
56C2×C5×C22⋊C4—31no—
57C2×C5×C22⋊C4—31no—
58C2×C42×C5—31no—
59C5×C4⋊C8—34no—
60C5×C22⋊C8—34no—
61C5×C22⋊C8—32no—
62C5×C22⋊C8—32no—
63C4×C5×C8—34no—
64C2×C8×D4—31noSylow
65C22×C5×D3—41no—
66C2×C5×A4C2×C812yescomplemented
67C2×C5×A4C22×C411yescharacteristic
68C5×S4C2×C814yesdirect product factor
69C2×C3×C4×C5—41no—
70C2×C5×Dic3—41no—
71C4×C5×D3—42no—
72C4×C5×D3—42no—
73C3×C5×C8—42no—
74C5×C3⋊C8—42no—
75C22×S4C4×C511yescharacteristic
76C2×C4×A4C22×C511yescharacteristic
77C2×SL(2,ℤ/4)C4×C511yescharacteristic
78C4×S4C4×C512yes—
79C4×S4C22×C512yes—
80C2×D3×C8—41no—
81C8×A4C22×C512yescomplemented
82A4⋊C8C22×C512yescomplemented
83C24×C5—31no—
84C24×C5C4×D311yescharacteristic
85C2×C5×D4—32no—
86C2×C5×D4—34no—
87C2×C5×D4—34no—
88C2×C5×D4—32no—
89C22×C4×C5—31no—
90C22×C4×C5—31no—
91C22×C4×C5—31no—
92C22×C4×C5—31no—
93C22×C4×C5—31no—
94C22×C4×C5—31no—
95C22×C4×C5—31no—
96C22×C4×C5—32no—
97C22×C4×C5—32no—
98C22×C4×C5—61no—
99C22×C4×C5—61no—
100C22×C4×C5—61no—
101C22×C4×C5—61no—
102C22×C4×C5C4×D311yescharacteristic
103C22×C4×C5C22×D311yescharacteristic
104C2×C5×C8—31no—
105C2×C5×C8—32no—
106C2×C5×C8—32no—
107C2×C5×C8—32no—
108C2×C5×C8—32no—
109C2×C5×C8—32no—
110C2×C5×C8—61no—
111C2×C5×C8—64no—
112C2×C5×C8—61no—
113C2×C5×C8—61no—
114C2×C5×C8—61no—
115C2×C5×C8—61no—
116C2×C5×C8—64no—
117C2×C5×C8S411yescharacteristic, direct product factor
118C5×C4⋊C4—32no—
119C5×C4⋊C4—32no—
120C5×C22⋊C4—32no—
121C5×C22⋊C4—32no—
122C5×C22⋊C4—32no—
123C5×C22⋊C4—32no—
124C42×C5—32no—
125C42×C5—32no—
126C23×C8—31no—
127C23×C8C5×D311yescharacteristic, complemented
128C2×C4×D4—31no—
129C8×D4—34no—
130C8×D4—34no—
131C2×C4⋊C8—31no—
132C2×C22⋊C8—31no—
133C2×C22⋊C8—31no—
134C2×C4×C8—31no—
135C22×C3×C5—41no—
136C2×C5×D3—44no—
137C2×C5×D3—42no—
138C5×A4C22×C811yescharacteristic, complemented
139C3×C4×C5—41no—
140C3×C4×C5—41no—
141C5×Dic3—42no—
142C22×A4C2×C4×C511yescharacteristic
143C2×S4C5×C814yesdirect product factor
144C2×S4C2×C4×C512yes—
145C2×C4×D3—41no—
146C4×A4C2×C4×C511yescharacteristic
147C4×A4C23×C511yescharacteristic
148SL(2,ℤ/4)C2×C4×C512yes—
149C2×C3×C8—41no—
150C2×C3⋊C8—41no—
151D3×C8—44no—
152C23×C5—31no—
153C23×C5—31no—
154C23×C5—32no—
155C23×C5—32no—
156C23×C5—34no—
157C23×C5—61no—
158C23×C5—62no—
159C23×C5—61no—
160C23×C5D3×C812yescomplemented
161C23×C5C2×C4×D311yescharacteristic
162C5×D4—38no—
163C5×D4—34no—
164C5×D4—34no—
165C2×C4×C5—32no—
166C2×C4×C5—34no—
167C2×C4×C5—31no—
168C2×C4×C5—31no—
169C2×C4×C5—31no—
170C2×C4×C5—31no—
171C2×C4×C5—31no—
172C2×C4×C5—31no—
173C2×C4×C5—31no—
174C2×C4×C5—32no—
175C2×C4×C5—32no—
176C2×C4×C5—61no—
177C2×C4×C5—62no—
178C2×C4×C5—62no—
179C2×C4×C5—62no—
180C2×C4×C5—61no—
181C2×C4×C5—61no—
182C2×C4×C5—62no—
183C2×C4×C5—62no—
184C2×C4×C5C2×S411yescharacteristic
185C5×C8—32no—
186C5×C8—62no—
187C5×C8—62no—
188C5×C8C2×S412yesdirect product factor
189C22×D4—31no—
190C23×C4—31no—
191C23×C4C2×C5×D311yescharacteristic
192C22×C8—31no—
193C22×C8—31no—
194C22×C8—32no—
195C22×C8—31no—
196C22×C8—34no—
197C22×C8—31no—
198C22×C8—61no—
199C22×C8—62no—
200C22×C8—61no—
201C22×C8C2×C5×D312yescomplemented
202C4×D4—32no—
203C4×D4—32no—
204C4×D4—32no—
205C4×D4—32no—
206C2×C4⋊C4—31no—
207C2×C22⋊C4—31no—
208C2×C22⋊C4—31no—
209C2×C42—31no—
210C4⋊C8—34no—
211C22⋊C8—34no—
212C22⋊C8—32no—
213C22⋊C8—32no—
214C4×C8—34no—
215C2×C3×C5—41no—
216C2×C3×C5—42no—
217C5×D3—44no—
218C22×D3—41no—
219C2×A4C2×C5×C812yescomplemented
220C2×A4C22×C4×C511yescharacteristic
221S4C2×C5×C814yesdirect product factor
222C2×C3×C4—41no—
223C2×Dic3—41no—
224C4×D3—42no—
225C4×D3—42no—
226C3×C8—42no—
227C3⋊C8—42no—
228C22×C5—32no—
229C22×C5—31no—
230C22×C5—31no—
231C22×C5—31no—
232C22×C5—32no—
233C22×C5—32no—
234C22×C5—34no—
235C22×C5—61no—
236C22×C5—62no—
237C22×C5—64no—
238C22×C5—62no—
239C22×C5—64no—
240C22×C5C2×D3×C811yescharacteristic, complemented
241C22×C5C4×S411yescharacteristic
242C4×C5—34no—
243C4×C5—31no—
244C4×C5—31no—
245C4×C5—62no—
246C4×C5—62no—
247C4×C5C4×S411yescharacteristic
248C4×C5C22×S411yescharacteristic
249C24—31no—
250C24C4×C5×D311yescharacteristic
251C2×D4—32no—
252C2×D4—34no—
253C2×D4—34no—
254C2×D4—32no—
255C22×C4—31no—
256C22×C4—31no—
257C22×C4—31no—
258C22×C4—31no—
259C22×C4—31no—
260C22×C4—32no—
261C22×C4—31no—
262C22×C4—31no—
263C22×C4—32no—
264C22×C4—61no—
265C22×C4—61no—
266C22×C4—61no—
267C22×C4—61no—
268C22×C4C4×C5×D311yescharacteristic
269C22×C4C22×C5×D311yescharacteristic
270C2×C8—31no—
271C2×C8—32no—
272C2×C8—32no—
273C2×C8—32no—
274C2×C8—32no—
275C2×C8—32no—
276C2×C8—61no—
277C2×C8—64no—
278C2×C8—61no—
279C2×C8—61no—
280C2×C8—61no—
281C2×C8—61no—
282C2×C8—64no—
283C2×C8C5×S411yescharacteristic, direct product factor
284C4⋊C4—32no—
285C4⋊C4—32no—
286C22⋊C4—32no—
287C22⋊C4—32no—
288C22⋊C4—32no—
289C22⋊C4—32no—
290C42—32no—
291C42—32no—
292C3×C5—41noHall
293C22×C3—41no—
294C2×D3—42no—
295C2×D3—44no—
296A4C22×C5×C811yescharacteristic, complemented
297C3×C4—41no—
298C3×C4—41no—
299Dic3—42no—
300C2×C5—31no—
301C2×C5—31no—
302C2×C5—32no—
303C2×C5—64no—
304C2×C5C8×S412yesdirect product factor
305C2×C5C2×C4×S411yescharacteristic
306C23—31no—
307C23—31no—
308C23—32no—
309C23—32no—
310C23—34no—
311C23—61no—
312C23—62no—
313C23—61no—
314C23C5×D3×C812yescomplemented
315C23C2×C4×C5×D311yescharacteristic
316D4—38no—
317D4—34no—
318D4—34no—
319C2×C4—32no—
320C2×C4—34no—
321C2×C4—31no—
322C2×C4—31no—
323C2×C4—31no—
324C2×C4—31no—
325C2×C4—31no—
326C2×C4—31no—
327C2×C4—31no—
328C2×C4—32no—
329C2×C4—32no—
330C2×C4—61no—
331C2×C4—62no—
332C2×C4—62no—
333C2×C4—61no—
334C2×C4—62no—
335C2×C4—61no—
336C2×C4—62no—
337C2×C4—62no—
338C2×C4C2×C5×S411yescharacteristic
339C8—32no—
340C8—62no—
341C8—62no—
342C8C2×C5×S412yesdirect product factor
343C2×C3—41no—
344C2×C3—42no—
345D3—44no—
346C5C2×C8×S411yescharacteristic, direct product factor, Sylow
347C22—32no—
348C22—31no—
349C22—31no—
350C22—31no—
351C22—32no—
352C22—32no—
353C22—34no—
354C22—61no—
355C22—62no—
356C22—64no—
357C22—62no—
358C22—64no—
359C22C2×C5×D3×C811yescharacteristic, complemented
360C22C4×C5×S411yescharacteristic
361C4—34no—
362C4—31no—
363C4—31no—
364C4—62no—
365C4—62no—
366C4C4×C5×S411yescharacteristic
367C4C22×C5×S411yescharacteristic
368C3—41noSylow
369C2—31no—
370C2—31no—
371C2—32no—
372C2—64no—
373C2C5×C8×S412yesdirect product factor
374C2C2×C4×C5×S411yescharacteristic
subgroupG/H
center, hypercenterC2×C5×C8S4
commutator, hypocenterA4C22×C5×C8
FrattiniC4C22×C5×S4
FittingC23×C5×C8D3
socleC24×C5C4×D3
prime radicalC22×C5×S4C4
cosocleC4×A4C23×C5
LCSG ▷ A4
UCSC1 ◁ C2×C5×C8

Complements

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

NH ≅ G/Ntype
2. C2×C5×C8×A4C2semidirect
3. C2×C5×A4⋊C8C2semidirect
4. C5×C8×S4C2direct (N × H)
12. C5×C8×A4C22semidirect
13. C5×A4⋊C8C22semidirect
14. C2×C8×S4C5direct (N × H)
16. C23×C5×C8D3semidirect
25. C2×C5×S4C8direct (N × H)
35. C2×C8×A4C2×C5semidirect
36. C2×A4⋊C8C2×C5semidirect
37. C8×S4C2×C5direct (N × H)
50. C22×C5×C8C2×D3semidirect
66. C2×C5×A4C2×C8semidirect
68. C5×S4C2×C8direct (N × H)
81. C8×A4C22×C5semidirect
82. A4⋊C8C22×C5semidirect
117. C2×C5×C8S4direct (N × H)
127. C23×C8C5×D3semidirect
138. C5×A4C22×C8semidirect
143. C2×S4C5×C8direct (N × H)
160. C23×C5D3×C8semidirect
188. C5×C8C2×S4direct (N × H)
201. C22×C8C2×C5×D3semidirect
219. C2×A4C2×C5×C8semidirect
221. S4C2×C5×C8direct (N × H)
240. C22×C5C2×D3×C8semidirect
283. C2×C8C5×S4direct (N × H)
296. A4C22×C5×C8semidirect
304. C2×C5C8×S4direct (N × H)
314. C23C5×D3×C8semidirect
342. C8C2×C5×S4direct (N × H)
346. C5C2×C8×S4direct (N × H)
359. C22C2×C5×D3×C8semidirect
373. C2C5×C8×S4direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C5×S42
C2×C5×C8×A42
C2×C5×A4⋊C82
C5×C8×S42
C2×C5×C8×D43
C2×C5×D3×C84
C2×C8×S45