Finite Group Databasebeta

← D5×#5079 #14437710

Subgroups — D5×#5079 #14437710

Order 1920.

848 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×C4⋊Q8C211yesmaximal, characteristic
2D5×#869C211yesmaximal, characteristic
3#11751180C211yesmaximal, characteristic, complemented
4C5×#5079C211yesmaximal, characteristic, complemented
5#11749349C214yesmaximal, complemented
6D5×#835C214yesmaximal
7C4×D5×C3⋊C8C211yesmaximal, characteristic
8#11746924C211yesmaximal, characteristic, complemented
9#11746920C211yesmaximal, characteristic, complemented
10D5×#487—31nomaximal, Hall
11C2×C3×Q8×D5C2212yes—
12C2×D5×Dic6—21no—
13C3×C5×C4⋊Q8C2211yescharacteristic
14#91758C2211yescharacteristic
15C5×#869C2211yescharacteristic
16C3×#4090C2212yes—
17C3×D5×C4⋊C4—21no—
18C3×D5×C4⋊C4—21no—
19C3×#4034—21no—
20C3×#4034—21no—
21C3×C42×D5C2211yescharacteristic
22C3×#4015C2211yescharacteristic
23#91468—21no—
24#91468C2212yes—
25D5×C4⋊Dic3—21no—
26D5×C4⋊Dic3C2212yes—
27#91376—21no—
28C2×D5×C3⋊C8C2212yes—
29#91119C2214yes—
30C4×C3⋊#168C2211yescharacteristic
31C5×#835C2214yes—
32C4×C5×C3⋊C8C2211yescharacteristic
33#90971C2214yes—
34#90970C2214yes—
35Dic5×C3⋊C8C2212yes—
36C2×#5079—51nomaximal, Hall
37D5×C4⋊Q8—31no—
38D5×C4⋊Q8D311yescharacteristic
39C5×#487—31no—
40#65382—31no—
41#65370—31no—
42D5×#103—34no—
43#65081—34no—
44C4×C8×D5—31no—
45#64970—31no—
46C2×C3×C5×Q8C2312yes—
47C2×Dic30—21no—
48C2×C5×Dic6—21no—
49C3×Q8×D5—28no—
50C2×C3×C4×D5—22no—
51C2×C3×C4×D5D411yescharacteristic
52C2×C3×C4×D5D411yescharacteristic
53C2×C3×C4×D5C2311yescharacteristic
54C2×C3×Dic10—22no—
55C2×C3×Dic10C2312yes—
56C2×#1204—22no—
57C2×D5×Dic3—22no—
58D5×Dic6—44no—
59C3×C5×C4⋊C4—21no—
60C3×C5×C4⋊C4—21no—
61C3×C42×C5C2311yescharacteristic
62C4⋊Dic15—21no—
63C4⋊Dic15C2312yes—
64C2×C3⋊#168C2312yes—
65C5×C4⋊Dic3—21no—
66C5×C4⋊Dic3C2312yes—
67C2×C5×C3⋊C8C2312yes—
68C3×C4⋊Dic5—21no—
69C3×C4⋊Dic5—21no—
70C3×#683—22no—
71C3×#683—22no—
72C3×C4×Dic5D411yescharacteristic
73C3×C4×Dic5D411yescharacteristic
74C3×C4×Dic5C2311yescharacteristic
75#6668—22no—
76#6668—22no—
77D5×C3⋊C8—24no—
78C2×C3×C4⋊Q8—51no—
79C2×#869—51no—
80C2×#835—54no—
81#5079—51no—
82#5079—51no—
83#5079—54no—
84#5079—51no—
85#5079D511yescharacteristic, direct product factor
86C2×C4×C3⋊C8—51no—
87C2×Q8×D5—61no—
88C2×Q8×D5C2×D312yes—
89C5×C4⋊Q8—31no—
90C5×C4⋊Q8C2×D311yescharacteristic
91#4090—61no—
92#4090C2×D312yes—
93C2×C8×D5—32no—
94D5×C4⋊C4—21no—
95D5×C4⋊C4—21no—
96D5×C4⋊C4—32no—
97D5×C4⋊C4—61no—
98#4034—21no—
99#4034—21no—
100#4034—32no—
101#4034—61no—
102C42×D5C2×D311yescharacteristic
103#4015—31no—
104#4015C2×D311yescharacteristic
105C5×#103—34no—
106C4×C5×C8—31no—
107#3967—34no—
108#3948—34no—
109C8×Dic5—32no—
110#3942—34no—
111C4×#168—31no—
112C2×#487—151noSylow
113C22×C3×D5C2×D411yescharacteristic
114C3×C5×Q8—24no—
115C2×C3×C4×C5—22no—
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5C2411yescharacteristic
119C2×Dic15—22no—
120Dic30—42no—
121C2×C5×Dic3—22no—
122C5×Dic6—42no—
123C2×C3×Dic5—22no—
124C2×C3×Dic5C2×D411yescharacteristic
125C2×C3×Dic5C2×D411yescharacteristic
126C2×C3×Dic5C2×D411yescharacteristic
127C3×C4×D5—44no—
128C3×C4×D5SD1614yes—
129C3×C4×D5Q1614yes—
130C3×C4×D5#4114yes—
131C3×Dic10—24no—
132C3×Dic10—44no—
133#1204—44no—
134D5×Dic3—44no—
135C3⋊#168—22no—
136C5×C3⋊C8—22no—
137C22×C3×Q8—52no—
138C22×Dic6—101no—
139C3×C4⋊Q8—52no—
140C3×C4⋊Q8—51no—
141C3×C4⋊Q8—101no—
142C3×C4⋊Q8—101no—
143C3×C4⋊Q8C2×D511yescharacteristic
144C2×C3×C4⋊C4—101no—
145C2×C3×C4⋊C4—101no—
146C2×C3×C42—51no—
147C2×C4⋊Dic3—52no—
148C2×C4⋊Dic3—101no—
149C22×C3⋊C8—52no—
150#869—51no—
151#869—52no—
152#869—101no—
153#869—101no—
154#869C2×D511yescharacteristic
155#835—54no—
156#835—54no—
157#835—54no—
158#835C2×D514yes—
159C4×C3⋊C8—51no—
160C4×C3⋊C8—52no—
161C4×C3⋊C8C2×D511yescharacteristic
162C2×C5×Q8—61no—
163C2×C5×Q8C22×D312yes—
164Q8×D5—28no—
165Q8×D5—124no—
166C2×C4×D5—22no—
167C2×C4×D5—62no—
168C2×C4×D5#6711yescharacteristic
169C2×C4×D5#6711yescharacteristic
170C2×C4×D5C22×D311yescharacteristic
171C2×Dic10—22no—
172C2×Dic10—61no—
173C2×Dic10—62no—
174C2×Dic10C22×D312yes—
175C2×C5×C8—32no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—32no—
179C5×C4⋊C4—61no—
180C42×C5C22×D311yescharacteristic
181C4⋊Dic5—21no—
182C4⋊Dic5—21no—
183C4⋊Dic5—32no—
184C4⋊Dic5—61no—
185#683—22no—
186#683—22no—
187#683—62no—
188#683—62no—
189C4×Dic5#6711yescharacteristic
190C4×Dic5#6711yescharacteristic
191C4×Dic5C22×D311yescharacteristic
192C2×#168—32no—
193C8×D5—64no—
194C2×C4⋊Q8—51no—
195C2×C4⋊Q8—151no—
196#487—31no—
197#487—151no—
198#487—154no—
199#487—151no—
200#487—151no—
201C2×#103—154no—
202C2×C4×C8—151no—
203C22×C3×C5C22×D411yescharacteristic
204C2×C3×D5#12412yes—
205C2×C3×D5C2×SD1612yes—
206C2×C3×D5C2×Q1612yes—
207C3×C4×C5—42no—
208C3×C4×C5C2×SD1612yes—
209C3×C4×C5C2×Q1612yes—
210C3×C4×C5C2×#4112yes—
211Dic15—42no—
212C3×Dic5—42no—
213C3×Dic5#12412yes—
214C3×Dic5C2×SD1612yes—
215C3×Dic5C2×Q1612yes—
216C5×Dic3—42no—
217C2×C3×Q8—52no—
218C2×C3×Q8—102no—
219C2×C3×Q8—108no—
220C2×C3×Q8C22×D512yes—
221C22×C3×C4—51no—
222C22×C3×C4—51no—
223C22×C3×C4—51no—
224C22×C3×C4—102no—
225C22×Dic3—102no—
226C2×Dic6—21no—
227C2×Dic6—102no—
228C2×Dic6—101no—
229C2×Dic6—204no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—102no—
233C3×C4⋊C4—102no—
234C3×C4⋊C4—101no—
235C3×C4⋊C4—101no—
236C3×C42—51no—
237C3×C42—51no—
238C3×C42—51no—
239C3×C42C22×D511yescharacteristic
240C4⋊Dic3—21no—
241C4⋊Dic3—52no—
242C4⋊Dic3—102no—
243C4⋊Dic3—102no—
244C4⋊Dic3—101no—
245C4⋊Dic3C22×D512yes—
246C2×C3⋊C8—52no—
247C2×C3⋊C8—104no—
248C2×C3⋊C8C22×D512yes—
249C22×D5C2×#6711yescharacteristic
250C5×Q8—24no—
251C5×Q8—122no—
252C2×C4×C5—22no—
253C2×C4×C5—62no—
254C2×C4×C5C2×#6711yescharacteristic
255C2×C4×C5C2×#6711yescharacteristic
256C2×C4×C5C23×D311yescharacteristic
257C2×Dic5—22no—
258C2×Dic5—62no—
259C2×Dic5C2×#6711yescharacteristic
260C2×Dic5C2×#6711yescharacteristic
261C2×Dic5C2×#6711yescharacteristic
262C4×D5—44no—
263C4×D5—124no—
264C4×D5#21514yes—
265C4×D5#21614yes—
266C4×D5#23714yes—
267Dic10—24no—
268Dic10—44no—
269Dic10—122no—
270Dic10—124no—
271C5×C8—62no—
272#168—62no—
273C22×Q8—52no—
274C22×Q8—301no—
275C22×C8—152no—
276C4⋊Q8—31no—
277C4⋊Q8—52no—
278C4⋊Q8—51no—
279C4⋊Q8—101no—
280C4⋊Q8—101no—
281C4⋊Q8—152no—
282C4⋊Q8—151no—
283C4⋊Q8—301no—
284C4⋊Q8—301no—
285C4⋊Q8D3×D511yescharacteristic
286C2×C4⋊C4—101no—
287C2×C4⋊C4—101no—
288C2×C4⋊C4—152no—
289C2×C4⋊C4—301no—
290C2×C42—51no—
291#103—34no—
292#103—154no—
293#103—154no—
294#103—154no—
295C4×C8—31no—
296C4×C8—152no—
297C4×C8—151no—
298C2×C3×C5C2×#12411yescharacteristic
299C2×C3×C5C22×SD1611yescharacteristic
300C2×C3×C5C22×Q1611yescharacteristic
301C3×D5#48714yescomplemented
302C23×C3—51no—
303C3×Q8—24no—
304C3×Q8—104no—
305C3×Q8—204no—
306C2×C3×C4—22no—
307C2×C3×C4—51no—
308C2×C3×C4—51no—
309C2×C3×C4—51no—
310C2×C3×C4—54no—
311C2×C3×C4—54no—
312C2×C3×C4—54no—
313C2×C3×C4—102no—
314C2×C3×C4—204no—
315C2×C3×C4D4×D511yescharacteristic
316C2×C3×C4D4×D511yescharacteristic
317C2×C3×C4C23×D511yescharacteristic
318C2×Dic3—22no—
319C2×Dic3—102no—
320C2×Dic3—204no—
321Dic6—42no—
322Dic6—204no—
323Dic6—202no—
324C3⋊C8—22no—
325C3⋊C8—102no—
326C22×C5C22×#6711yescharacteristic
327C2×D5#93612yes—
328C2×D5C2×#21512yes—
329C2×D5C2×#21612yes—
330C4×C5—42no—
331C4×C5—122no—
332C4×C5C2×#21512yes—
333C4×C5C2×#21612yes—
334C4×C5C2×#23712yes—
335Dic5—42no—
336Dic5—122no—
337Dic5#93612yes—
338Dic5C2×#21512yes—
339Dic5C2×#21612yes—
340C2×Q8—52no—
341C2×Q8—61no—
342C2×Q8—102no—
343C2×Q8—108no—
344C2×Q8—302no—
345C2×Q8—301no—
346C2×Q8—604no—
347C2×Q8C2×D3×D512yes—
348C22×C4—51no—
349C22×C4—51no—
350C22×C4—51no—
351C22×C4—102no—
352C22×C4—302no—
353C2×C8—32no—
354C2×C8—152no—
355C2×C8—304no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—32no—
359C4⋊C4—61no—
360C4⋊C4—102no—
361C4⋊C4—102no—
362C4⋊C4—101no—
363C4⋊C4—101no—
364C4⋊C4—152no—
365C4⋊C4—302no—
366C4⋊C4—302no—
367C4⋊C4—301no—
368C42—51no—
369C42—51no—
370C42—51no—
371C42C2×D3×D511yescharacteristic
372C3×C5C2×#48711yescharacteristic, complemented, Hall
373C22×C3—52no—
374C22×C3—52no—
375C22×C3—52no—
376C22×C3C2×D4×D511yescharacteristic
377C3×C4—42no—
378C3×C4—52no—
379C3×C4—52no—
380C3×C4—52no—
381C3×C4—202no—
382C3×C4D5×SD1612yes—
383C3×C4D5×Q1612yes—
384C3×C4D5×#4112yes—
385Dic3—42no—
386Dic3—202no—
387C2×C5C2×#93611yescharacteristic
388C2×C5C22×#21511yescharacteristic
389C2×C5C22×#21611yescharacteristic
390D5#507914yesdirect product factor
391C23—51no—
392Q8—24no—
393Q8—104no—
394Q8—122no—
395Q8—204no—
396Q8—604no—
397Q8—602no—
398C2×C4—22no—
399C2×C4—51no—
400C2×C4—51no—
401C2×C4—51no—
402C2×C4—54no—
403C2×C4—54no—
404C2×C4—54no—
405C2×C4—62no—
406C2×C4—102no—
407C2×C4—204no—
408C2×C4—302no—
409C2×C4—604no—
410C2×C4D5×#6711yescharacteristic
411C2×C4D5×#6711yescharacteristic
412C2×C4C22×D3×D511yescharacteristic
413C8—62no—
414C8—302no—
415C2×C3—54no—
416C2×C3D5×#12411yescharacteristic
417C2×C3C2×D5×SD1611yescharacteristic
418C2×C3C2×D5×Q1611yescharacteristic
419C5C2×#507911yescharacteristic, complemented, Sylow
420C22—52no—
421C22—52no—
422C22—52no—
423C22C2×D5×#6711yescharacteristic
424C4—42no—
425C4—52no—
426C4—52no—
427C4—52no—
428C4—122no—
429C4—202no—
430C4—602no—
431C4D5×#21512yes—
432C4D5×#21612yes—
433C4D5×#23712yes—
434C3D5×#48711yescharacteristic, complemented, Sylow
435C2—54no—
436C2D5×#93611yescharacteristic
437C2C2×D5×#21511yescharacteristic
438C2C2×D5×#21611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5C2×#487
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #11751180C2semidirect
4. C5×#5079C2semidirect
5. #11749349C2semidirect
8. #11746924C2semidirect
9. #11746920C2semidirect
85. #5079D5direct (N × H)
301. C3×D5#487semidirect
372. C3×C5C2×#487semidirect
390. D5#5079direct (N × H)
419. C5C2×#5079semidirect
434. C3D5×#487semidirect

Maximal subgroups

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

subgroupindex
C3×D5×C4⋊Q82
D5×#8692
#117511802
C5×#50792
#117493492
D5×#8352
C4×D5×C3⋊C82
#117469242
#117469202
D5×#4873
C2×#50795