Finite Group Databasebeta

← D5×#4977 #14319995

Subgroups — D5×#4977 #14319995

Order 1920.

1424 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×C4⋊C4C211yesmaximal, characteristic
2C2×D5×C4⋊Dic3C211yesmaximal, characteristic
3C2×C4×D5×Dic3C211yesmaximal, characteristic
4#11751078C211yesmaximal, characteristic, complemented
5C5×#4977C211yesmaximal, characteristic, complemented
6D5×C3⋊#95C214yesmaximal
7#11748642C214yesmaximal, complemented
8#11748623C211yesmaximal, characteristic, complemented
9#11748619C211yesmaximal, characteristic, complemented
10D5×#382—31nomaximal, Hall
11C22×C3×C4×D5C2212yes—
12C22×C3×C4×D5C2211yescharacteristic
13C22×D5×Dic3C2212yes—
14C22×D5×Dic3C2212yes—
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C4×Dic15C2211yescharacteristic
18C2×C5×C4⋊Dic3C2211yescharacteristic
19C2×C4×C5×Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic5C2211yescharacteristic
21C2×C3×#683C2212yes—
22C3×D5×C4⋊C4—24no—
23C2×#6668C2212yes—
24C2×Dic3×Dic5C2212yes—
25D5×C4⋊Dic3—24no—
26C4×D5×Dic3C418yescomplemented
27#91115C2214yes—
28C5×C3⋊#95C2214yes—
29#90994C2214yes—
30#90994C2214yes—
31C2×#4977—51nomaximal, Hall
32C2×D5×C4⋊C4—31no—
33C2×D5×C4⋊C4D311yescharacteristic
34C2×C42×D5—31no—
35C5×#382—31no—
36#65266—31no—
37#65266—31no—
38#65225—31no—
39D5×#95—34no—
40#64939—34no—
41C23×C3×D5C2311yescharacteristic
42C22×C3×C4×C5C2312yes—
43C22×C3×C4×C5C2311yescharacteristic
44C22×Dic15C2312yes—
45C22×Dic15C2312yes—
46C22×C5×Dic3C2312yes—
47C22×C5×Dic3C2312yes—
48C22×C3×Dic5C2312yes—
49C22×C3×Dic5C2311yescharacteristic
50C2×C3×C4×D5—24no—
51C2×C3×C4×D5—28no—
52C2×C3×C4×D5C2×C414yes—
53C2×C3×C4×D5D414yes—
54C2×C3×C4×D5Q814yes—
55C2×D5×Dic3—24no—
56C2×D5×Dic3—24no—
57C2×D5×Dic3—24no—
58C2×D5×Dic3—28no—
59C2×D5×Dic3C2×C418yes—
60C3×C5×C4⋊C4—22no—
61C4⋊Dic15—22no—
62C4×Dic15C2×C414yescomplemented
63C5×C4⋊Dic3—22no—
64C4×C5×Dic3C2×C414yescomplemented
65C3×C4⋊Dic5—22no—
66C3×#683—24no—
67#6668—24no—
68Dic3×Dic5C2×C418yescomplemented
69C22×C3×C4⋊C4—51no—
70C22×C4⋊Dic3—51no—
71C22×C4×Dic3—51no—
72C2×C3⋊#95—54no—
73#4977—51no—
74#4977—51no—
75#4977—51no—
76#4977—54no—
77#4977D511yescharacteristic, direct product factor
78C22×C4×D5—32no—
79C22×C4×D5—32no—
80C22×C4×D5C2×D312yes—
81C22×C4×D5C2×D311yescharacteristic
82C2×C5×C4⋊C4—31no—
83C2×C5×C4⋊C4C2×D311yescharacteristic
84C2×C42×C5—31no—
85C2×C4⋊Dic5—31no—
86C2×C4⋊Dic5C2×D311yescharacteristic
87C2×#683—32no—
88C2×#683C2×D312yes—
89C2×C4×Dic5—31no—
90C2×C4×Dic5—32no—
91D5×C4⋊C4—24no—
92D5×C4⋊C4—64no—
93C42×D5—38no—
94C5×#95—34no—
95#3963—34no—
96#3963—34no—
97#3963—34no—
98C2×#382—151noSylow
99C23×C3×C5C2411yescharacteristic
100C22×C3×D5C22×C412yes—
101C22×C3×D5C2×D412yes—
102C22×C3×D5C2×Q812yes—
103C22×C3×D5#4114yes—
104C22×C3×D5#4114yes—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—24no—
107C2×C3×C4×C5C22×C412yes—
108C2×C3×C4×C5C2×D412yes—
109C2×C3×C4×C5C2×Q812yes—
110C2×Dic15—22no—
111C2×Dic15—22no—
112C2×Dic15—22no—
113C2×Dic15—24no—
114C2×Dic15C22×C414yes—
115C2×C5×Dic3—22no—
116C2×C5×Dic3—22no—
117C2×C5×Dic3—22no—
118C2×C5×Dic3—24no—
119C2×C5×Dic3C22×C414yes—
120C2×C3×Dic5—22no—
121C2×C3×Dic5—24no—
122C2×C3×Dic5C22×C412yes—
123C2×C3×Dic5C2×D412yes—
124C2×C3×Dic5C2×Q812yes—
125C3×C4×D5—48no—
126C3×C4×D5C4⋊C4116yes—
127D5×Dic3—216no—
128D5×Dic3—48no—
129C23×C3×C4—51no—
130C23×C3×C4—52no—
131C23×Dic3—52no—
132C23×Dic3—52no—
133C2×C3×C4⋊C4—52no—
134C2×C3×C4⋊C4—51no—
135C2×C3×C4⋊C4—104no—
136C2×C3×C4⋊C4C2×D511yescharacteristic
137C2×C4⋊Dic3—51no—
138C2×C4⋊Dic3—52no—
139C2×C4⋊Dic3—104no—
140C2×C4⋊Dic3C2×D511yescharacteristic
141C2×C4×Dic3—51no—
142C2×C4×Dic3—52no—
143C2×C4×Dic3—58no—
144C2×C4×Dic3C2×D511yescharacteristic
145C3⋊#95—54no—
146C3⋊#95—54no—
147C3⋊#95—54no—
148C3⋊#95C2×D514yes—
149C23×D5C22×D311yescharacteristic
150C22×C4×C5—32no—
151C22×C4×C5—32no—
152C22×C4×C5C22×D312yes—
153C22×C4×C5C22×D311yescharacteristic
154C22×Dic5—32no—
155C22×Dic5—32no—
156C22×Dic5C22×D312yes—
157C22×Dic5C22×D311yescharacteristic
158C2×C4×D5—28no—
159C2×C4×D5—24no—
160C2×C4×D5—38no—
161C2×C4×D5—64no—
162C2×C4×D5—64no—
163C2×C4×D5—68no—
164C2×C4×D5—64no—
165C2×C4×D5Dic614yes—
166C2×C4×D5C4×D314yes—
167C2×C4×D5#6714yes—
168C5×C4⋊C4—22no—
169C5×C4⋊C4—62no—
170C42×C5—34no—
171C4⋊Dic5—22no—
172C4⋊Dic5—62no—
173#683—24no—
174#683—64no—
175C4×Dic5—34no—
176C4×Dic5—38no—
177C22×C4⋊C4—51no—
178C22×C4⋊C4—151no—
179C22×C42—151no—
180#382—31no—
181#382—154no—
182#382—151no—
183#382—151no—
184#382—151no—
185C2×#95—154no—
186C22×C3×C5C23×C411yescharacteristic
187C22×C3×C5C22×D411yescharacteristic
188C22×C3×C5C22×Q811yescharacteristic
189C22×C3×C5C2×#4112yes—
190C22×C3×C5C2×#4112yes—
191C2×C3×D5C2×C4⋊C414yes—
192C2×C3×D5#11718yes—
193C2×C3×D5#12414yes—
194C2×C3×D5#12414yes—
195C2×C3×D5#12518yes—
196C3×C4×C5—42no—
197C3×C4×C5C2×C4⋊C414yes—
198Dic15—24no—
199Dic15—42no—
200C3×Dic5—42no—
201C3×Dic5C2×C4⋊C414yes—
202C5×Dic3—24no—
203C5×Dic3—42no—
204C24×C3—51no—
205C22×C3×C4—51no—
206C22×C3×C4—54no—
207C22×C3×C4—54no—
208C22×C3×C4—54no—
209C22×C3×C4—52no—
210C22×C3×C4—104no—
211C22×C3×C4—108no—
212C22×C3×C4C22×D512yes—
213C22×C3×C4C22×D511yescharacteristic
214C22×Dic3—52no—
215C22×Dic3—58no—
216C22×Dic3—52no—
217C22×Dic3—104no—
218C22×Dic3—104no—
219C22×Dic3—104no—
220C22×Dic3—108no—
221C22×Dic3C22×D512yes—
222C22×Dic3C22×D512yes—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—104no—
225C3×C4⋊C4—102no—
226C4⋊Dic3—22no—
227C4⋊Dic3—104no—
228C4⋊Dic3—102no—
229C4×Dic3—54no—
230C4×Dic3—58no—
231C4×Dic3C4×D514yescomplemented
232C23×C5C23×D311yescharacteristic
233C22×D5C2×Dic612yes—
234C22×D5C2×C4×D312yes—
235C22×D5#23714yes—
236C22×D5#23914yes—
237C22×D5C2×#6712yes—
238C2×C4×C5—24no—
239C2×C4×C5—22no—
240C2×C4×C5—34no—
241C2×C4×C5—62no—
242C2×C4×C5—62no—
243C2×C4×C5—64no—
244C2×C4×C5—62no—
245C2×C4×C5C2×Dic612yes—
246C2×C4×C5C2×C4×D312yes—
247C2×C4×C5C2×#6712yes—
248C2×Dic5—24no—
249C2×Dic5—22no—
250C2×Dic5—34no—
251C2×Dic5—62no—
252C2×Dic5—62no—
253C2×Dic5—64no—
254C2×Dic5—62no—
255C2×Dic5C2×Dic612yes—
256C2×Dic5C2×C4×D312yes—
257C2×Dic5C2×#6712yes—
258C4×D5—48no—
259C4×D5—616no—
260C4×D5—128no—
261C4×D5Dic3⋊C4116yes—
262C23×C4—51no—
263C23×C4—52no—
264C23×C4—152no—
265C23×C4—152no—
266C2×C4⋊C4—31no—
267C2×C4⋊C4—52no—
268C2×C4⋊C4—51no—
269C2×C4⋊C4—104no—
270C2×C4⋊C4—152no—
271C2×C4⋊C4—151no—
272C2×C4⋊C4—304no—
273C2×C4⋊C4D3×D511yescharacteristic
274C2×C42—31no—
275C2×C42—158no—
276C2×C42—152no—
277C2×C42—151no—
278#95—34no—
279#95—154no—
280#95—154no—
281#95—154no—
282C2×C3×C5C22×C4⋊C411yescharacteristic
283C2×C3×C5C2×#11712yes—
284C2×C3×C5C2×#12411yescharacteristic
285C2×C3×C5C2×#12411yescharacteristic
286C2×C3×C5C2×#12512yes—
287C3×D5#38218yescomplemented
288C23×C3—52no—
289C23×C3—52no—
290C23×C3—52no—
291C23×C3—54no—
292C23×C3—54no—
293C23×C3C23×D511yescharacteristic
294C2×C3×C4—22no—
295C2×C3×C4—24no—
296C2×C3×C4—52no—
297C2×C3×C4—52no—
298C2×C3×C4—52no—
299C2×C3×C4—516no—
300C2×C3×C4—102no—
301C2×C3×C4—104no—
302C2×C3×C4—208no—
303C2×C3×C4C2×C4×D512yes—
304C2×C3×C4D4×D512yes—
305C2×C3×C4Q8×D512yes—
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—24no—
310C2×Dic3—54no—
311C2×Dic3—1016no—
312C2×Dic3—102no—
313C2×Dic3—102no—
314C2×Dic3—102no—
315C2×Dic3—104no—
316C2×Dic3—208no—
317C2×Dic3C2×C4×D514yes—
318C22×C5C22×Dic611yescharacteristic
319C22×C5C22×C4×D311yescharacteristic
320C22×C5C2×#23712yes—
321C22×C5C2×#23912yes—
322C22×C5C22×#6711yescharacteristic
323C2×D5#89018yes—
324C2×D5#89218yes—
325C2×D5C2×Dic3⋊C414yes—
326C2×D5#93614yes—
327C2×D5#94714yes—
328C4×C5—42no—
329C4×C5—64no—
330C4×C5—122no—
331C4×C5C2×Dic3⋊C414yes—
332Dic5—42no—
333Dic5—64no—
334Dic5—122no—
335Dic5C2×Dic3⋊C414yes—
336C24—51no—
337C22×C4—32no—
338C22×C4—32no—
339C22×C4—51no—
340C22×C4—54no—
341C22×C4—54no—
342C22×C4—54no—
343C22×C4—52no—
344C22×C4—104no—
345C22×C4—108no—
346C22×C4—158no—
347C22×C4—152no—
348C22×C4—152no—
349C22×C4—304no—
350C22×C4—304no—
351C22×C4—304no—
352C22×C4—308no—
353C22×C4C2×D3×D512yes—
354C22×C4C2×D3×D511yescharacteristic
355C4⋊C4—22no—
356C4⋊C4—62no—
357C4⋊C4—104no—
358C4⋊C4—102no—
359C4⋊C4—304no—
360C4⋊C4—302no—
361C42—34no—
362C42—158no—
363C42—154no—
364C3×C5C2×#38211yescharacteristic, complemented, Hall
365C22×C3—54no—
366C22×C3—58no—
367C22×C3—54no—
368C22×C3—54no—
369C22×C3—58no—
370C22×C3C22×C4×D511yescharacteristic
371C22×C3C2×D4×D511yescharacteristic
372C22×C3C2×Q8×D511yescharacteristic
373C22×C3D5×#4112yes—
374C22×C3D5×#4112yes—
375C3×C4—42no—
376C3×C4—54no—
377C3×C4—202no—
378C3×C4D5×C4⋊C414yes—
379Dic3—24no—
380Dic3—42no—
381Dic3—104no—
382Dic3—202no—
383C2×C5C2×#89012yes—
384C2×C5C2×#89212yes—
385C2×C5C22×Dic3⋊C411yescharacteristic
386C2×C5C2×#93611yescharacteristic
387C2×C5C2×#94711yescharacteristic
388D5#497718yesdirect product factor
389C23—52no—
390C23—52no—
391C23—54no—
392C23—54no—
393C23—52no—
394C23C22×D3×D511yescharacteristic
395C2×C4—24no—
396C2×C4—22no—
397C2×C4—34no—
398C2×C4—52no—
399C2×C4—52no—
400C2×C4—52no—
401C2×C4—516no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—64no—
405C2×C4—62no—
406C2×C4—104no—
407C2×C4—102no—
408C2×C4—154no—
409C2×C4—208no—
410C2×C4—3016no—
411C2×C4—302no—
412C2×C4—302no—
413C2×C4—304no—
414C2×C4—302no—
415C2×C4—608no—
416C2×C4D5×Dic612yes—
417C2×C4C4×D3×D512yes—
418C2×C4D5×#6712yes—
419C2×C3—58no—
420C2×C3C2×D5×C4⋊C411yescharacteristic
421C2×C3D5×#11712yes—
422C2×C3D5×#12411yescharacteristic
423C2×C3D5×#12411yescharacteristic
424C2×C3D5×#12512yes—
425C5C2×#497711yescharacteristic, complemented, Sylow
426C22—54no—
427C22—58no—
428C22—54no—
429C22—54no—
430C22—58no—
431C22C2×D5×Dic611yescharacteristic
432C22C2×C4×D3×D511yescharacteristic
433C22D5×#23712yes—
434C22D5×#23912yes—
435C22C2×D5×#6711yescharacteristic
436C4—42no—
437C4—54no—
438C4—64no—
439C4—122no—
440C4—202no—
441C4—304no—
442C4—602no—
443C4D5×Dic3⋊C414yes—
444C3D5×#38211yescharacteristic, complemented, Sylow
445C2—58no—
446C2D5×#89012yes—
447C2D5×#89212yes—
448C2C2×D5×Dic3⋊C411yescharacteristic
449C2D5×#93611yescharacteristic
450C2D5×#94711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#382
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11751078C2semidirect
5. C5×#4977C2semidirect
7. #11748642C2semidirect
8. #11748623C2semidirect
9. #11748619C2semidirect
26. C4×D5×Dic3C4semidirect
62. C4×Dic15C2×C4semidirect
64. C4×C5×Dic3C2×C4semidirect
68. Dic3×Dic5C2×C4semidirect
77. #4977D5direct (N × H)
231. C4×Dic3C4×D5semidirect
287. C3×D5#382semidirect
364. C3×C5C2×#382semidirect
388. D5#4977direct (N × H)
425. C5C2×#4977semidirect
444. C3D5×#382semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×C4⋊C42
C2×D5×C4⋊Dic32
C2×C4×D5×Dic32
#117510782
C5×#49772
D5×C3⋊#952
#117486422
#117486232
#117486192
D5×#3823
C2×#49775