Finite Group Databasebeta

← #14322478

Subgroups — #14322478

Order 1920.

1568 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D15⋊Q8C211yesmaximal, characteristic
2C2×#91781C211yesmaximal, characteristic
3C2×#91386C211yesmaximal, characteristic
4C5×#4973C211yesmaximal, characteristic, complemented
5C3×#65263C211yesmaximal, characteristic, complemented
6#11748935C214yesmaximal, complemented
7#11748889C214yesmaximal
8#11748609C211yesmaximal, characteristic, complemented
9#11748589C211yesmaximal, characteristic, complemented
10#10608341—31nomaximal, Hall
11C22×C4×D15C2211yescharacteristic
12C22×C5×Dic6C2211yescharacteristic
13C22×C3×Dic10C2211yescharacteristic
14C22×#1204C2212yes—
15C22×#1200C2212yes—
16C2×D15⋊Q8—24no—
17C2×D15⋊Q8—24no—
18C2×D15⋊Q8C418yescomplemented
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×#6714C2212yes—
21C2×C4⋊Dic15C2211yescharacteristic
22C2×C4×Dic15C2212yes—
23#91781—24no—
24C2×C4×C5×Dic3C2211yescharacteristic
25C2×C3×C4×Dic5C2211yescharacteristic
26C2×#6669C2212yes—
27C2×#6667C2212yes—
28#91386—24no—
29C5×C3⋊#95C2214yes—
30C3×#3963C2214yes—
31#90994C2214yes—
32#90994C2214yes—
33#76610—51nomaximal, Hall
34C22×Q8×D5—31no—
35C2×#4038—31no—
36C2×#4018—31no—
37C5×#391—31no—
38#65519—31no—
39#65263D311yescharacteristic, complemented
40#65218—31no—
41#64953—34no—
42#64935—34no—
43C23×D15C2311yescharacteristic
44C22×C3×C4×C5C2312yes—
45C22×C3×C4×C5C2311yescharacteristic
46C22×Dic15C2312yes—
47C22×Dic15C2311yescharacteristic
48C2×C4×D15C2×C414yes—
49C2×C4×D15D414yes—
50C2×C4×D15D414yes—
51C22×C5×Dic3C2312yes—
52C22×C5×Dic3C2312yes—
53C2×C5×Dic6—22no—
54C2×C5×Dic6—22no—
55C2×C5×Dic6C2×C414yes—
56C22×C3×Dic5C2312yes—
57C22×C3×Dic5C2312yes—
58C2×C3×Dic10—22no—
59C2×C3×Dic10—22no—
60C2×C3×Dic10C2×C414yes—
61C2×#1204—24no—
62C2×#1204—24no—
63C2×#1204C2×C418yes—
64C2×#1200—24no—
65C2×#1200—24no—
66C2×#1200C2×C418yes—
67D15⋊Q8—232no—
68C3×C5×C4⋊C4—22no—
69#6714—24no—
70C4⋊Dic15—22no—
71C4×Dic15—24no—
72C4×C5×Dic3—22no—
73C3×C4×Dic5—22no—
74#6669—24no—
75#6667—24no—
76C22×D3×Q8—51no—
77C2×#892—51no—
78C2×#872—51no—
79C3×#391—51no—
80#5229—51no—
81#4973D511yescharacteristic, complemented
82#4929—51no—
83#4664—54no—
84#4646—54no—
85C22×C5×Q8—31no—
86C2×Q8×D5—38no—
87C2×Q8×D5—64no—
88C2×Q8×D5—64no—
89C22×C4×D5—31no—
90C22×C4×D5—32no—
91C22×Dic10—32no—
92C22×Dic10C2×D311yescharacteristic
93C2×C5×C4⋊C4C2×D311yescharacteristic
94C2×C42×C5—31no—
95C2×#685—32no—
96C2×#685—32no—
97C2×C4⋊Dic5—31no—
98C2×#683—32no—
99C2×C4×Dic5—32no—
100C2×C4×Dic5C2×D311yescharacteristic
101#4038—64no—
102#4018—64no—
103C5×#95—34no—
104#3963—34no—
105#3963—34no—
106#3963C2×D314yes—
107#2310—151noSylow
108C23×C3×C5C2411yescharacteristic
109C22×D15—22no—
110C22×D15—22no—
111C22×D15C22×C412yes—
112C22×D15C2×D412yes—
113C22×D15C2×D412yes—
114C2×C3×C4×C5—22no—
115C2×C3×C4×C5—24no—
116C2×C3×C4×C5C22×C412yes—
117C2×C3×C4×C5C2×D412yes—
118C2×C3×C4×C5C2×D412yes—
119C2×Dic15—22no—
120C2×Dic15—24no—
121C2×Dic15C22×C412yes—
122C2×Dic15C2×D412yes—
123C2×Dic15C2×D412yes—
124C4×D15C22⋊C4116yes—
125C2×C5×Dic3—22no—
126C2×C5×Dic3—22no—
127C2×C5×Dic3—22no—
128C2×C5×Dic3—22no—
129C2×C5×Dic3—22no—
130C2×C5×Dic3C22×C414yes—
131C5×Dic6—28no—
132C2×C3×Dic5—22no—
133C2×C3×Dic5—22no—
134C2×C3×Dic5—22no—
135C2×C3×Dic5—22no—
136C2×C3×Dic5—22no—
137C2×C3×Dic5C22×C414yes—
138C3×Dic10—28no—
139#1204—216no—
140#1200—216no—
141C22×C3×Q8—51no—
142C2×D3×Q8—58no—
143C2×D3×Q8—104no—
144C2×D3×Q8—104no—
145C22×C4×D3—51no—
146C22×C4×D3—52no—
147C22×Dic6—52no—
148C22×Dic6C2×D511yescharacteristic
149C2×C3×C4⋊C4C2×D511yescharacteristic
150C2×C3×C42—51no—
151C2×(C2×D3)⋊C4—52no—
152C2×(C2×D3)⋊C4—52no—
153C2×C4⋊Dic3—51no—
154C2×Dic3⋊C4—52no—
155C2×C4×Dic3—52no—
156C2×C4×Dic3C2×D511yescharacteristic
157#892—104no—
158#872—104no—
159C3×#95—54no—
160C3⋊#95—54no—
161C3⋊#95—54no—
162C3⋊#95C2×D514yes—
163C23×D5—31no—
164C2×C5×Q8—34no—
165C2×C5×Q8—62no—
166C2×C5×Q8—62no—
167C22×C4×C5—32no—
168C22×C4×C5—32no—
169C22×C4×C5C22×D312yes—
170C22×C4×C5C22×D311yescharacteristic
171C22×Dic5—31no—
172C22×Dic5—32no—
173C22×Dic5C22×D312yes—
174C22×Dic5C22×D312yes—
175Q8×D5—632no—
176C2×C4×D5—34no—
177C2×C4×D5—34no—
178C2×C4×D5—34no—
179C2×C4×D5—38no—
180C2×C4×D5—64no—
181C2×C4×D5—64no—
182C2×Dic10—22no—
183C2×Dic10—22no—
184C2×Dic10—38no—
185C2×Dic10—64no—
186C2×Dic10—64no—
187C2×Dic10C4×D314yes—
188C5×C4⋊C4—22no—
189C42×C5—62no—
190#685—64no—
191#685—64no—
192C4⋊Dic5—62no—
193#683—64no—
194C4×Dic5—22no—
195C4×Dic5—64no—
196C23×Q8—151no—
197C2×#117—151no—
198C2×#117—151no—
199#391—31no—
200#391—51no—
201#391—154no—
202#391—151no—
203#391—151no—
204#381—154no—
205C22×C3×C5C23×C411yescharacteristic
206C22×C3×C5C22×D411yescharacteristic
207C22×C3×C5C22×D411yescharacteristic
208C22×C3×C52−1+412yes—
209C22×C3×C52−1+412yes—
210C2×D15—24no—
211C2×D15—22no—
212C2×D15—24no—
213C2×D15—22no—
214C2×D15C2×C22⋊C414yes—
215C3×C4×C5—42no—
216C3×C4×C5C2×C22⋊C414yes—
217Dic15—42no—
218Dic15C2×C22⋊C414yes—
219C3×Dic5—24no—
220C3×Dic5—42no—
221C5×Dic3—24no—
222C5×Dic3—42no—
223C23×D3—51no—
224C2×C3×Q8—54no—
225C2×C3×Q8—102no—
226C2×C3×Q8—102no—
227C22×C3×C4—52no—
228C22×C3×C4—52no—
229C22×C3×C4C22×D512yes—
230C22×C3×C4C22×D511yescharacteristic
231C22×Dic3—51no—
232C22×Dic3—52no—
233C22×Dic3C22×D512yes—
234C22×Dic3C22×D512yes—
235D3×Q8—1032no—
236C2×C4×D3—54no—
237C2×C4×D3—54no—
238C2×C4×D3—54no—
239C2×C4×D3—58no—
240C2×C4×D3—104no—
241C2×C4×D3—104no—
242C2×Dic6—22no—
243C2×Dic6—22no—
244C2×Dic6—58no—
245C2×Dic6—104no—
246C2×Dic6—104no—
247C2×Dic6C4×D514yes—
248C3×C4⋊C4—22no—
249C3×C42—102no—
250(C2×D3)⋊C4—104no—
251(C2×D3)⋊C4—104no—
252C4⋊Dic3—102no—
253Dic3⋊C4—104no—
254C4×Dic3—22no—
255C4×Dic3—104no—
256C23×C5C23×D311yescharacteristic
257C22×D5—32no—
258C22×D5—32no—
259C22×D5—32no—
260C22×D5—62no—
261C22×D5—62no—
262C5×Q8—68no—
263C2×C4×C5—22no—
264C2×C4×C5—24no—
265C2×C4×C5—34no—
266C2×C4×C5—62no—
267C2×C4×C5—62no—
268C2×C4×C5—62no—
269C2×C4×C5—62no—
270C2×C4×C5—62no—
271C2×C4×C5C2×C4×D312yes—
272C2×C4×C5D3×D412yes—
273C2×C4×C5D3×D412yes—
274C2×Dic5—22no—
275C2×Dic5—22no—
276C2×Dic5—22no—
277C2×Dic5—22no—
278C2×Dic5—22no—
279C2×Dic5—32no—
280C2×Dic5—32no—
281C2×Dic5—32no—
282C2×Dic5—62no—
283C2×Dic5—64no—
284C2×Dic5C2×C4×D314yes—
285C4×D5—316no—
286C4×D5—616no—
287Dic10—28no—
288Dic10—616no—
289C22×Q8—31no—
290C22×Q8—51no—
291C22×Q8—152no—
292C22×Q8—158no—
293C22×Q8—304no—
294C22×Q8—304no—
295C23×C4—152no—
296C23×C4—151no—
297#117—304no—
298#117—304no—
299C2×C4⋊C4—152no—
300C2×C4⋊C4—151no—
301C2×C4⋊C4D3×D511yescharacteristic
302C2×C22⋊C4—152no—
303C2×C22⋊C4—152no—
304C2×C42—31no—
305C2×C42—51no—
306C2×C42—152no—
307#95—34no—
308#95—54no—
309#95—154no—
310#95—154no—
311C2×C3×C5C22×C22⋊C411yescharacteristic
312C2×C3×C5#51912yes—
313C2×C3×C5#53611yescharacteristic
314C2×C3×C5#53612yes—
315C2×C3×C5#53611yescharacteristic
316D15—24no—
317C23×C3C23×D511yescharacteristic
318C22×D3—52no—
319C22×D3—52no—
320C22×D3—52no—
321C22×D3—102no—
322C22×D3—102no—
323C3×Q8—108no—
324C2×C3×C4—22no—
325C2×C3×C4—24no—
326C2×C3×C4—54no—
327C2×C3×C4—102no—
328C2×C3×C4—102no—
329C2×C3×C4—102no—
330C2×C3×C4—102no—
331C2×C3×C4—102no—
332C2×C3×C4C2×C4×D512yes—
333C2×C3×C4D4×D512yes—
334C2×C3×C4D4×D512yes—
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—52no—
341C2×Dic3—52no—
342C2×Dic3—52no—
343C2×Dic3—102no—
344C2×Dic3—104no—
345C2×Dic3C2×C4×D514yes—
346C4×D3—516no—
347C4×D3—1016no—
348Dic6—28no—
349Dic6—1016no—
350C22×C5C22×C4×D311yescharacteristic
351C22×C5C2×D3×D411yescharacteristic
352C22×C5C2×D3×D411yescharacteristic
353C22×C5#100712yes—
354C22×C5#101012yes—
355C2×D5—34no—
356C2×D5—62no—
357C2×D5—62no—
358C2×D5—64no—
359C2×D5—64no—
360C4×C5—42no—
361C4×C5—64no—
362C4×C5—122no—
363C4×C5D3×C22⋊C414yes—
364Dic5—24no—
365Dic5—34no—
366Dic5—42no—
367Dic5—122no—
368C24—151no—
369C2×Q8—34no—
370C2×Q8—54no—
371C2×Q8—62no—
372C2×Q8—62no—
373C2×Q8—102no—
374C2×Q8—102no—
375C2×Q8—158no—
376C2×Q8—304no—
377C2×Q8—304no—
378C2×Q8—3032no—
379C22×C4—32no—
380C22×C4—32no—
381C22×C4—52no—
382C22×C4—52no—
383C22×C4—158no—
384C22×C4—151no—
385C22×C4—154no—
386C22×C4—154no—
387C22×C4—154no—
388C22×C4—152no—
389C22×C4—304no—
390C22×C4—304no—
391C22×C4C2×D3×D512yes—
392C22×C4C2×D3×D511yescharacteristic
393C4⋊C4—22no—
394C4⋊C4—304no—
395C4⋊C4—302no—
396C22⋊C4—304no—
397C22⋊C4—304no—
398C42—62no—
399C42—102no—
400C42—304no—
401C3×C5#231011yescharacteristic, complemented, Hall
402C22×C3C22×C4×D511yescharacteristic
403C22×C3C2×D4×D511yescharacteristic
404C22×C3C2×D4×D511yescharacteristic
405C22×C3#414712yes—
406C22×C3#415012yes—
407C2×D3—54no—
408C2×D3—102no—
409C2×D3—104no—
410C2×D3—104no—
411C2×D3—102no—
412C3×C4—42no—
413C3×C4—104no—
414C3×C4—202no—
415C3×C4D5×C22⋊C414yes—
416Dic3—24no—
417Dic3—42no—
418Dic3—54no—
419Dic3—202no—
420C2×C5C2×D3×C22⋊C411yescharacteristic
421C2×C5#557212yes—
422C2×C5#562812yes—
423C2×C5#567511yescharacteristic
424C2×C5#572411yescharacteristic
425D5—64no—
426C23—152no—
427C23—152no—
428C23—152no—
429C23—302no—
430C23—302no—
431C23C22×D3×D511yescharacteristic
432Q8—68no—
433Q8—108no—
434Q8—3016no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—34no—
438C2×C4—54no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—62no—
443C2×C4—62no—
444C2×C4—102no—
445C2×C4—102no—
446C2×C4—102no—
447C2×C4—102no—
448C2×C4—102no—
449C2×C4—152no—
450C2×C4—152no—
451C2×C4—152no—
452C2×C4—1516no—
453C2×C4—3016no—
454C2×C4—304no—
455C2×C4—302no—
456C2×C4C4×D3×D512yes—
457C2×C4#677712yes—
458C2×C4#679012yes—
459C2×C3C2×D5×C22⋊C411yescharacteristic
460C2×C3#6590612yes—
461C2×C3#6596212yes—
462C2×C3#6600911yescharacteristic
463C2×C3#6605811yescharacteristic
464D3—104no—
465C5#7661011yescharacteristic, complemented, Sylow
466C22—154no—
467C22—302no—
468C22—302no—
469C22—304no—
470C22—304no—
471C22C2×C4×D3×D511yescharacteristic
472C22C2×#677711yescharacteristic
473C22#9202012yes—
474C22#9202912yes—
475C22C2×#679011yescharacteristic
476C4—42no—
477C4—64no—
478C4—104no—
479C4—122no—
480C4—154no—
481C4—202no—
482C4—602no—
483C4#9147314yes—
484C3#1060834111yescharacteristic, complemented, Sylow
485C2—304no—
486C2#1175338112yes—
487C2#1175369712yes—
488C2C2×#9147311yescharacteristic
489C2#1175483211yescharacteristic
490C2#1175514611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2310
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. C5×#4973C2semidirect
5. C3×#65263C2semidirect
6. #11748935C2semidirect
8. #11748609C2semidirect
9. #11748589C2semidirect
18. C2×D15⋊Q8C4semidirect
39. #65263D3semidirect
81. #4973D5semidirect
401. C3×C5#2310semidirect
465. C5#76610semidirect
484. C3#10608341semidirect

Maximal subgroups

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

subgroupindex
C22×D15⋊Q82
C2×#917812
C2×#913862
C5×#49732
C3×#652632
#117489352
#117488892
#117486092
#117485892
#106083413
#766105