Finite Group Databasebeta

← C5×D8×S4 #14511194

Subgroups — C5×D8×S4 #14511194

Order 1920.

674 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 674 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C5×D4×S4C212yesmaximal, complemented
2C5×A4×D8C211yesmaximal, characteristic, complemented
3C5×#5415C212yesmaximal, complemented
4C5×#5402C211yesmaximal, characteristic, complemented
5C5×C8×S4C211yesmaximal, characteristic, complemented
6C5×D4×D8—31nomaximal, Hall
7C22×C5×S4—22no—
8C5×D4×A4C2212yescomplemented
9C5×GL(2,ℤ/4)—22no—
10C5×C4⋊S4C2212yescomplemented
11C4×C5×S4C2211yescharacteristic
12C5×D3×D8—41nomaximal
13C5×C8×A4C2211yescharacteristic, complemented
14C5×A4⋊C8C2211yescharacteristic, complemented
15D8×S4C511yesmaximal, characteristic, direct product factor, Hall
16C22×C5×D8—31no—
17C22×C5×D8D311yescharacteristic, complemented
18C5×D42—32no—
19C5×#493—31no—
20C5×#466—31no—
21C5×#466—31no—
22C5×#459—32no—
23C5×#447—32no—
24C5×#447—32no—
25C4×C5×D8—31no—
26C5×C8×D4—31no—
27C22×C5×A4—22no—
28C2×C5×S4—22no—
29C2×C5×S4—44no—
30C2×C5×S4D411yescharacteristic
31C5×D3×D4—42no—
32C4×C5×A4C2311yescharacteristic
33C5×SL(2,ℤ/4)D411yescharacteristic
34C3×C5×D8—41no—
35C5×#213—42no—
36C5×D24—41no—
37C5×D3×C8—41no—
38D4×S4C2×C512yescomplemented
39A4×D8C2×C511yescharacteristic, complemented
40#5415C2×C512yescomplemented
41#5402C2×C511yescharacteristic, complemented
42C8×S4C2×C511yescharacteristic, complemented
43C22×C5×D4—32no—
44C22×C5×D4—62no—
45C22×C5×D4C2×D312yescomplemented
46C2×C5×D8—31no—
47C2×C5×D8—32no—
48C2×C5×D8—31no—
49C2×C5×D8—32no—
50C2×C5×D8—31no—
51C2×C5×D8—32no—
52C2×C5×D8—62no—
53C2×C5×D8—61no—
54C2×C5×D8—61no—
55C22×C5×C8—31no—
56C22×C5×C8C2×D311yescharacteristic, complemented
57C5×#127—32no—
58C5×#121—32no—
59C5×#121—32no—
60C5×#121—62no—
61C5×#120—62no—
62C5×#120—62no—
63C4×C5×D4—31no—
64C4×C5×D4—32no—
65C5×#107—31no—
66C5×C4⋊C8—31no—
67C5×#102—32no—
68C5×#102—32no—
69C5×#102—32no—
70C5×C22⋊C8—31no—
71C5×C22⋊C8—31no—
72C4×C5×C8—31no—
73D4×D8—31noSylow
74C22×C5×D3—82no—
75C2×C5×A4—42no—
76C2×C5×A4C2×D411yescharacteristic
77C5×S4—42no—
78C5×S4D812yesdirect product factor
79C3×C5×D4—42no—
80C5×#67—82no—
81C5×D12—42no—
82C4×C5×D3—41no—
83C3×C5×C8—41no—
84C5×C3⋊C8—41no—
85C22×S4—22no—
86D4×A4C22×C512yescomplemented
87GL(2,ℤ/4)—22no—
88C4⋊S4C22×C512yescomplemented
89C4×S4C22×C511yescharacteristic
90D3×D8—41no—
91C8×A4C22×C511yescharacteristic, complemented
92A4⋊C8C22×C511yescharacteristic, complemented
93C24×C5—22no—
94C24×C5—62no—
95C2×C5×D4—31no—
96C2×C5×D4—32no—
97C2×C5×D4—32no—
98C2×C5×D4—32no—
99C2×C5×D4—62no—
100C2×C5×D4—62no—
101C2×C5×D4—62no—
102C2×C5×D4—62no—
103C2×C5×D4—62no—
104C2×C5×D4—62no—
105C2×C5×D4—62no—
106C2×C5×D4—62no—
107C2×C5×D4—122no—
108C2×C5×D4—124no—
109C2×C5×D4—124no—
110C22×C4×C5—31no—
111C22×C4×C5—62no—
112C22×C4×C5C22×D311yescharacteristic
113C5×D8—32no—
114C5×D8—31no—
115C5×D8—61no—
116C5×D8—61no—
117C5×D8—62no—
118C5×D8—62no—
119C5×D8—61no—
120C5×D8—122no—
121C5×D8S411yescharacteristic, direct product factor
122C2×C5×C8—31no—
123C2×C5×C8—31no—
124C2×C5×C8—31no—
125C2×C5×C8—31no—
126C2×C5×C8—61no—
127C2×C5×C8—61no—
128C5×C4⋊C4—31no—
129C5×C4⋊C4—32no—
130C5×C22⋊C4—31no—
131C5×C22⋊C4—31no—
132C5×C22⋊C4—62no—
133C5×C22⋊C4—62no—
134C5×C22⋊C4—62no—
135C42×C5—31no—
136C22×D8—31no—
137C22×D8C5×D311yescharacteristic, complemented
138D42—32no—
139#493—31no—
140#466—31no—
141#466—31no—
142#459—32no—
143#447—32no—
144#447—32no—
145C4×D8—31no—
146C8×D4—31no—
147C22×C3×C5—82no—
148C2×C5×D3—41no—
149C2×C5×D3—82no—
150C2×C5×D3—164no—
151C5×A4C2×D811yescharacteristic, complemented
152C3×C4×C5—41no—
153C5×Dic3—41no—
154C22×A4—22no—
155C2×S4—22no—
156C2×S4—44no—
157C2×S4C5×D411yescharacteristic
158D3×D4—42no—
159C4×A4C23×C511yescharacteristic
160SL(2,ℤ/4)C5×D411yescharacteristic
161C3×D8—41no—
162#213—42no—
163D24—41no—
164D3×C8—41no—
165C23×C5—31no—
166C23×C5—42no—
167C23×C5—62no—
168C23×C5—62no—
169C23×C5—62no—
170C23×C5—122no—
171C23×C5—122no—
172C23×C5—124no—
173C23×C5—122no—
174C23×C5—242no—
175C23×C5D3×D411yescharacteristic
176C5×D4—32no—
177C5×D4—32no—
178C5×D4—32no—
179C5×D4—62no—
180C5×D4—62no—
181C5×D4—62no—
182C5×D4—62no—
183C5×D4—124no—
184C5×D4—122no—
185C5×D4—122no—
186C5×D4—122no—
187C5×D4—124no—
188C5×D4—122no—
189C5×D4—242no—
190C5×D4C2×S412yescomplemented
191C2×C4×C5—31no—
192C2×C4×C5—31no—
193C2×C4×C5—31no—
194C2×C4×C5—31no—
195C2×C4×C5—31no—
196C2×C4×C5—61no—
197C2×C4×C5—61no—
198C2×C4×C5—62no—
199C2×C4×C5—124no—
200C5×C8—31no—
201C5×C8—61no—
202C5×C8—61no—
203C5×C8C2×S411yescharacteristic, complemented
204C22×D4—32no—
205C22×D4—62no—
206C22×D4C2×C5×D312yescomplemented
207C2×D8—31no—
208C2×D8—32no—
209C2×D8—31no—
210C2×D8—32no—
211C2×D8—31no—
212C2×D8—32no—
213C2×D8—62no—
214C2×D8—61no—
215C2×D8—61no—
216C22×C8—31no—
217C22×C8C2×C5×D311yescharacteristic, complemented
218#127—32no—
219#121—32no—
220#121—32no—
221#121—62no—
222#120—62no—
223#120—62no—
224C4×D4—31no—
225C4×D4—32no—
226#107—31no—
227C4⋊C8—31no—
228#102—32no—
229#102—32no—
230#102—32no—
231C22⋊C8—31no—
232C22⋊C8—31no—
233C4×C8—31no—
234C2×C3×C5—41no—
235C2×C3×C5—162no—
236C5×D3—42no—
237C5×D3—162no—
238C22×D3—82no—
239C2×A4—42no—
240C2×A4C2×C5×D411yescharacteristic
241S4—42no—
242S4C5×D812yesdirect product factor
243C3×D4—42no—
244#67—82no—
245D12—42no—
246C4×D3—41no—
247C3×C8—41no—
248C3⋊C8—41no—
249C22×C5—22no—
250C22×C5—31no—
251C22×C5—31no—
252C22×C5—32no—
253C22×C5—61no—
254C22×C5—61no—
255C22×C5—62no—
256C22×C5—122no—
257C22×C5—122no—
258C22×C5—122no—
259C22×C5—122no—
260C22×C5—122no—
261C22×C5—122no—
262C22×C5—122no—
263C22×C5—244no—
264C22×C5—244no—
265C22×C5D3×D811yescharacteristic, complemented
266C4×C5—32no—
267C4×C5—31no—
268C4×C5—61no—
269C4×C5—61no—
270C4×C5—122no—
271C4×C5C22×S411yescharacteristic
272C24—22no—
273C24—62no—
274C2×D4—31no—
275C2×D4—32no—
276C2×D4—32no—
277C2×D4—32no—
278C2×D4—62no—
279C2×D4—62no—
280C2×D4—62no—
281C2×D4—62no—
282C2×D4—62no—
283C2×D4—62no—
284C2×D4—62no—
285C2×D4—62no—
286C2×D4—122no—
287C2×D4—124no—
288C2×D4—124no—
289C22×C4—31no—
290C22×C4—62no—
291C22×C4C22×C5×D311yescharacteristic
292D8—32no—
293D8—31no—
294D8—61no—
295D8—61no—
296D8—62no—
297D8—62no—
298D8—61no—
299D8—122no—
300D8C5×S411yescharacteristic, direct product factor
301C2×C8—31no—
302C2×C8—31no—
303C2×C8—31no—
304C2×C8—31no—
305C2×C8—61no—
306C2×C8—61no—
307C4⋊C4—31no—
308C4⋊C4—32no—
309C22⋊C4—31no—
310C22⋊C4—31no—
311C22⋊C4—62no—
312C22⋊C4—62no—
313C22⋊C4—62no—
314C42—31no—
315C3×C5—41noHall
316C22×C3—82no—
317C2×D3—41no—
318C2×D3—82no—
319C2×D3—164no—
320A4C2×C5×D811yescharacteristic, complemented
321C3×C4—41no—
322Dic3—41no—
323C2×C5—31no—
324C2×C5—31no—
325C2×C5—42no—
326C2×C5—62no—
327C2×C5—122no—
328C2×C5—242no—
329C2×C5D4×S411yescharacteristic
330C23—31no—
331C23—42no—
332C23—62no—
333C23—62no—
334C23—62no—
335C23—122no—
336C23—122no—
337C23—124no—
338C23—122no—
339C23—242no—
340C23C5×D3×D411yescharacteristic
341D4—32no—
342D4—32no—
343D4—32no—
344D4—62no—
345D4—62no—
346D4—62no—
347D4—62no—
348D4—124no—
349D4—122no—
350D4—122no—
351D4—122no—
352D4—124no—
353D4—122no—
354D4—242no—
355D4C2×C5×S412yescomplemented
356C2×C4—31no—
357C2×C4—31no—
358C2×C4—31no—
359C2×C4—31no—
360C2×C4—31no—
361C2×C4—61no—
362C2×C4—61no—
363C2×C4—62no—
364C2×C4—124no—
365C8—31no—
366C8—61no—
367C8—61no—
368C8C2×C5×S411yescharacteristic, complemented
369C2×C3—41no—
370C2×C3—162no—
371D3—42no—
372D3—162no—
373C5D8×S411yescharacteristic, direct product factor, Sylow
374C22—22no—
375C22—31no—
376C22—31no—
377C22—32no—
378C22—61no—
379C22—61no—
380C22—62no—
381C22—122no—
382C22—122no—
383C22—122no—
384C22—122no—
385C22—122no—
386C22—122no—
387C22—122no—
388C22—244no—
389C22—244no—
390C22C5×D3×D811yescharacteristic, complemented
391C4—32no—
392C4—31no—
393C4—61no—
394C4—61no—
395C4—122no—
396C4C22×C5×S411yescharacteristic
397C3—41noSylow
398C2—31no—
399C2—31no—
400C2—42no—
401C2—62no—
402C2—122no—
403C2—242no—
404C2C5×D4×S411yescharacteristic
subgroupG/H
centerC2×C5D4×S4
commutator, cosocleC4×A4C23×C5
FrattiniC4C22×C5×S4
FittingC22×C5×D8D3
socleC23×C5D3×D4
hypercenterC5×D8S4
hypocenterA4C2×C5×D8
LCSG ▷ C4×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×D8

Complements

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

NH ≅ G/Ntype
1. C5×D4×S4C2semidirect
2. C5×A4×D8C2semidirect
3. C5×#5415C2semidirect
4. C5×#5402C2semidirect
5. C5×C8×S4C2semidirect
8. C5×D4×A4C22semidirect
10. C5×C4⋊S4C22semidirect
13. C5×C8×A4C22semidirect
14. C5×A4⋊C8C22semidirect
15. D8×S4C5direct (N × H)
17. C22×C5×D8D3semidirect
38. D4×S4C2×C5semidirect
39. A4×D8C2×C5semidirect
40. #5415C2×C5semidirect
41. #5402C2×C5semidirect
42. C8×S4C2×C5semidirect
45. C22×C5×D4C2×D3semidirect
56. C22×C5×C8C2×D3semidirect
78. C5×S4D8direct (N × H)
86. D4×A4C22×C5semidirect
88. C4⋊S4C22×C5semidirect
91. C8×A4C22×C5semidirect
92. A4⋊C8C22×C5semidirect
121. C5×D8S4direct (N × H)
137. C22×D8C5×D3semidirect
151. C5×A4C2×D8semidirect
190. C5×D4C2×S4semidirect
203. C5×C8C2×S4semidirect
206. C22×D4C2×C5×D3semidirect
217. C22×C8C2×C5×D3semidirect
242. S4C5×D8direct (N × H)
265. C22×C5D3×D8semidirect
300. D8C5×S4direct (N × H)
320. A4C2×C5×D8semidirect
355. D4C2×C5×S4semidirect
368. C8C2×C5×S4semidirect
373. C5D8×S4direct (N × H)
390. C22C5×D3×D8semidirect

Maximal subgroups

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

subgroupindex
C5×D4×S42
C5×A4×D82
C5×#54152
C5×#54022
C5×C8×S42
C5×D4×D83
C5×D3×D84
D8×S45