Finite Group Databasebeta

← #14295352

Subgroups — #14295352

Order 1920.

696 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#700C211yesmaximal, characteristic
2C2×#91232C211yesmaximal, characteristic
3C2×#91169C211yesmaximal, characteristic, complemented
4C2×Dic3×#170C211yesmaximal, characteristic, complemented
5#11748702C211yesmaximal, characteristic
6#11746570C211yesmaximal, characteristic, complemented
7#11746570C211yesmaximal, characteristic, complemented
8#10603777—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C22×C3⋊#170C2211yescharacteristic
11C22×C3⋊#170C2211yescharacteristic
12C22×C3×#170C2211yescharacteristic
13C22×C3×#170C2211yescharacteristic
14C2×C3×#700—22no—
15C2×C3×#700—22no—
16C2×C3×#700C414yescomplemented
17C2×#6665C411yescharacteristic
18C2×#6665C411yescharacteristic
19C2×Dic3×Dic5C2211yescharacteristic
20C2×Dic3×Dic5C2211yescharacteristic
21#91232C414yescomplemented
22#91169—22no—
23Dic3×#170—22no—
24#91115C411yescharacteristic
25C5×C3⋊#95C411yescharacteristic
26#71983—51nomaximal, Hall
27C22×#700D311yescharacteristic
28C2×#4003—31no—
29C2×#4002—31no—
30C2×C4×#170—31no—
31#64955—31no—
32#64918—31no—
33#64918—31no—
34C23×C3×D5C2×C411yescharacteristic
35C22×C3×C4×C5C2×C411yescharacteristic
36C22×Dic15C2×C411yescharacteristic
37C22×Dic15C2×C411yescharacteristic
38C22×C5×Dic3C2×C411yescharacteristic
39C22×C5×Dic3C2×C411yescharacteristic
40C22×C3×Dic5C2311yescharacteristic
41C2×C3×C4×D5—21no—
42C2×C3×C4×D5—21no—
43C2×C3×C4×D5—21no—
44C2×C3×C4×D5—21no—
45C2×C3×C4×D5C2×C412yes—
46C2×C3×C4×D5C2×C412yes—
47C2×C3⋊#170—21no—
48C2×C3⋊#170—21no—
49C2×C3⋊#170—21no—
50C2×C3⋊#170—21no—
51C2×C3⋊#170C2×C412yes—
52C2×C3⋊#170C2×C412yes—
53C2×C3×#170—21no—
54C2×C3×#170—21no—
55C2×C3×#170C2×C412yes—
56C2×C3×#170C2×C412yes—
57C2×C3×#170D412yes—
58C2×C3×#170D412yes—
59C3×#700—28no—
60#6665—22no—
61#6665—22no—
62Dic3×Dic5—21no—
63Dic3×Dic5—21no—
64Dic3×Dic5—21no—
65Dic3×Dic5—21no—
66C22×C3×M16—51no—
67C4×#217—51no—
68C2×#830—51no—
69C2×#815—51no—
70C2×C8×Dic3—51no—
71#4550—51no—
72#4550—51no—
73C22×C4×D5C2×D311yescharacteristic
74C22×#170—31no—
75C22×#170—31no—
76C22×#170C2×D311yescharacteristic
77C22×#170C2×D311yescharacteristic
78C2×#700—22no—
79C2×#700—22no—
80C2×#700Dic314yescomplemented
81C2×#685—31no—
82C2×#685—31no—
83C2×C4×Dic5—31no—
84C2×C4×Dic5—31no—
85#4003—34no—
86#4002—62no—
87C4×#170—62no—
88C5×#95—31no—
89#3963—31no—
90#1753—151noSylow
91C23×C3×C5C22×C411yescharacteristic
92C22×C3×D5—21no—
93C22×C3×D5—21no—
94C22×C3×D5—21no—
95C22×C3×D5—21no—
96C22×C3×D5—21no—
97C22×C3×D5—21no—
98C22×C3×D5C4212yes—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5C4212yes—
102C2×Dic15—21no—
103C2×Dic15—21no—
104C2×Dic15—21no—
105C2×Dic15—21no—
106C2×Dic15—21no—
107C2×Dic15M1612yescomplemented
108C2×C5×Dic3—21no—
109C2×C5×Dic3—21no—
110C2×C5×Dic3—21no—
111C2×C5×Dic3—21no—
112C2×C5×Dic3—21no—
113C2×C5×Dic3M1612yescomplemented
114C2×C3×Dic5C22×C411yescharacteristic
115C2×C3×Dic5C22×C411yescharacteristic
116C2×C3×Dic5C2×D411yescharacteristic
117C2×C3×Dic5C2×D411yescharacteristic
118C2×C3×Dic5#4111yescharacteristic
119C2×C3×Dic5#4111yescharacteristic
120C3×C4×D5—22no—
121C3×C4×D5—22no—
122C3×C4×D5—22no—
123C3×C4×D5—22no—
124C3⋊#170—22no—
125C3⋊#170—22no—
126C3×#170—22no—
127C3×#170C22⋊C414yescomplemented
128C23×C3×C4—51no—
129C2×C3×M16—54no—
130C2×C3×M16—102no—
131C2×C3×M16—102no—
132C22×C3×C8—51no—
133C22×C3×C8—51no—
134C2×#217—51no—
135C2×#217—51no—
136C2×C4×Dic3—51no—
137C2×C4×Dic3—51no—
138C22×C3⋊C8—51no—
139C22×C3⋊C8—51no—
140C3⋊#95—51no—
141C3⋊#95AGL(1,𝔽5)11yescharacteristic
142#830—54no—
143#815—102no—
144C8×Dic3—102no—
145C23×D5C4×D311yescharacteristic
146C22×C4×C5—31no—
147C22×C4×C5—31no—
148C22×C4×C5C4×D311yescharacteristic
149C22×Dic5—31no—
150C22×Dic5—31no—
151C22×Dic5C22×D311yescharacteristic
152C2×C4×D5—21no—
153C2×C4×D5—21no—
154C2×C4×D5—21no—
155C2×C4×D5—21no—
156C2×C4×D5C4×D312yes—
157C2×C4×D5C2×Dic312yes—
158C2×#170—21no—
159C2×#170—21no—
160C2×#170—32no—
161C2×#170—32no—
162C2×#170—61no—
163C2×#170—61no—
164C2×#170—61no—
165C2×#170—61no—
166C2×#170C2×Dic312yes—
167C2×#170C2×Dic312yes—
168C2×#170#6712yes—
169C2×#170#6712yes—
170#700—28no—
171#685—62no—
172#685—62no—
173C4×Dic5—61no—
174C4×Dic5—61no—
175C4×Dic5—61no—
176C4×Dic5—61no—
177C22×M16—51no—
178C2×C22⋊C8—151no—
179C2×#97—151no—
180C2×C4×C8—151no—
181C4×C22⋊C4—151no—
182#336—151no—
183#336—151no—
184C22×C3×C5C2×C4211yescharacteristic
185C22×C3×C5C4×D411yescharacteristic
186C22×C3×C5C4×D411yescharacteristic
187C22×C3×C5C2×M1611yescharacteristic
188C22×C3×C5C2×M1611yescharacteristic
189C22×C3×C5#13111yescharacteristic
190C22×C3×C5#13111yescharacteristic
191C2×C3×D5—22no—
192C2×C3×D5—22no—
193C2×C3×D5—22no—
194C2×C3×D5—41no—
195C2×C3×D5—41no—
196C2×C3×D5—41no—
197C2×C3×D5—41no—
198C3×C4×C5—22no—
199Dic15—22no—
200Dic15—41no—
201C3×Dic5C2×C22⋊C411yescharacteristic
202C3×Dic5#11711yescharacteristic
203C3×Dic5C4×D411yescharacteristic
204C3×Dic5C4×D411yescharacteristic
205C5×Dic3—22no—
206C5×Dic3—41no—
207C24×C3—51no—
208C22×C3×C4—51no—
209C22×C3×C4—52no—
210C22×C3×C4—52no—
211C22×C3×C4—101no—
212C22×C3×C4—101no—
213C22×C3×C4—101no—
214C22×C3×C4—101no—
215C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
216C22×Dic3—51no—
217C22×Dic3—51no—
218C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
219C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
220C3×M16—108no—
221C2×C3×C8—52no—
222C2×C3×C8—52no—
223C2×C3×C8—52no—
224C2×C3×C8—52no—
225C2×C3×C8—101no—
226C2×C3×C8—101no—
227#217—102no—
228#217—102no—
229C4×Dic3—101no—
230C4×Dic3—101no—
231C4×Dic3—101no—
232C4×Dic3—101no—
233C2×C3⋊C8—52no—
234C2×C3⋊C8—52no—
235C2×C3⋊C8—101no—
236C2×C3⋊C8—101no—
237C2×C3⋊C8—101no—
238C2×C3⋊C8—101no—
239C23×C5C2×C4×D311yescharacteristic
240C22×D5—21no—
241C22×D5—21no—
242C22×D5—21no—
243C22×D5—21no—
244C22×D5—21no—
245C22×D5—21no—
246C22×D5C4×Dic312yes—
247C2×C4×C5—21no—
248C2×C4×C5—21no—
249C2×C4×C5—32no—
250C2×C4×C5—61no—
251C2×C4×C5—61no—
252C2×C4×C5—61no—
253C2×C4×C5—61no—
254C2×C4×C5—61no—
255C2×C4×C5C4×Dic312yes—
256C2×Dic5—32no—
257C2×Dic5—61no—
258C2×Dic5—61no—
259C2×Dic5—61no—
260C2×Dic5—61no—
261C2×Dic5—61no—
262C2×Dic5C2×C4×D311yescharacteristic
263C2×Dic5#23511yescharacteristic
264C2×Dic5#23511yescharacteristic
265C2×Dic5C22×Dic311yescharacteristic
266C2×Dic5C2×#6711yescharacteristic
267C2×Dic5C2×#6711yescharacteristic
268C4×D5—22no—
269C4×D5—22no—
270C4×D5—22no—
271C4×D5—22no—
272#170—22no—
273#170—62no—
274#170—62no—
275#170#21714yescomplemented
276C23×C4—51no—
277C2×M16—54no—
278C2×M16—102no—
279C2×M16—102no—
280C22×C8—51no—
281C22×C8—51no—
282C22×C8—151no—
283C22×C8—151no—
284C2×C22⋊C4—151no—
285C2×C22⋊C4—151no—
286C2×C42—151no—
287C2×C42—151no—
288C22⋊C8—154no—
289#97—302no—
290C4×C8—302no—
291#95—31no—
292#95—151no—
293C2×C3×C5C4×C22⋊C411yescharacteristic
294C2×C3×C5C4×M1611yescharacteristic
295C2×C3×C5#40511yescharacteristic
296C2×C3×C5#43511yescharacteristic
297C2×C3×C5#43511yescharacteristic
298C2×C3×C5#43611yescharacteristic
299C2×C3×C5#43611yescharacteristic
300C3×D5—42no—
301C23×C3—52no—
302C23×C3—101no—
303C23×C3—101no—
304C23×C3—101no—
305C23×C3—101no—
306C23×C3—101no—
307C23×C3—101no—
308C23×C3C22×AGL(1,𝔽5)11yescharacteristic
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—51no—
312C2×C3×C4—51no—
313C2×C3×C4—51no—
314C2×C3×C4—51no—
315C2×C3×C4—51no—
316C2×C3×C4—51no—
317C2×C3×C4—102no—
318C2×C3×C4—102no—
319C2×C3×C4—102no—
320C2×C3×C4—102no—
321C2×C3×C4C4×AGL(1,𝔽5)12yes—
322C2×Dic3—21no—
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—21no—
326C2×Dic3—21no—
327C2×Dic3—52no—
328C2×Dic3—101no—
329C2×Dic3—101no—
330C2×Dic3—101no—
331C2×Dic3—101no—
332C2×Dic3—101no—
333C2×Dic3#70012yescomplemented
334C3×C8—54no—
335C3×C8—102no—
336C3⋊C8—102no—
337C3⋊C8—102no—
338C22×C5D3×M1611yescharacteristic
339C22×C5D3×M1611yescharacteristic
340C22×C5#90711yescharacteristic
341C22×C5#90711yescharacteristic
342C22×C5C2×C4×Dic311yescharacteristic
343C22×C5C4×#6711yescharacteristic
344C22×C5C4×#6711yescharacteristic
345C2×D5—22no—
346C2×D5—22no—
347C2×D5—22no—
348C2×D5—41no—
349C2×D5—41no—
350C2×D5—41no—
351C2×D5—41no—
352C4×C5—22no—
353C4×C5—62no—
354C4×C5—121no—
355Dic5—62no—
356Dic5—121no—
357Dic5#92611yescharacteristic
358Dic5C4×#6711yescharacteristic
359Dic5C4×#6711yescharacteristic
360Dic5C2×#21711yescharacteristic
361C24—51no—
362C22×C4—31no—
363C22×C4—31no—
364C22×C4—51no—
365C22×C4—52no—
366C22×C4—52no—
367C22×C4—101no—
368C22×C4—101no—
369C22×C4—101no—
370C22×C4—101no—
371C22×C4—151no—
372C22×C4—151no—
373C22×C4D3×AGL(1,𝔽5)11yescharacteristic
374M16—108no—
375C2×C8—52no—
376C2×C8—52no—
377C2×C8—52no—
378C2×C8—52no—
379C2×C8—101no—
380C2×C8—101no—
381C2×C8—152no—
382C2×C8—152no—
383C2×C8—301no—
384C2×C8—301no—
385C2×C8—301no—
386C2×C8—301no—
387C22⋊C4—302no—
388C22⋊C4—302no—
389C42—301no—
390C42—301no—
391C42—301no—
392C42—301no—
393C3×C5#175311yescharacteristic, complemented, Hall
394C22×C3—102no—
395C22×C3—102no—
396C22×C3—102no—
397C22×C3—201no—
398C22×C3—201no—
399C22×C3—201no—
400C22×C3—201no—
401C22×C3C2×#70011yescharacteristic
402C22×C3D5⋊M1611yescharacteristic
403C22×C3C2×C4×AGL(1,𝔽5)11yescharacteristic
404C22×C3#413111yescharacteristic
405C22×C3D4×AGL(1,𝔽5)11yescharacteristic
406C22×C3D4×AGL(1,𝔽5)11yescharacteristic
407C22×C3#413311yescharacteristic
408C3×C4—22no—
409C3×C4—51no—
410C3×C4—51no—
411C3×C4—51no—
412C3×C4—51no—
413Dic3—22no—
414Dic3—41no—
415Dic3—102no—
416Dic3—201no—
417C2×C5Dic3×M1611yescharacteristic
418C2×C5#512211yescharacteristic
419C2×C5#512711yescharacteristic
420C2×C5#512711yescharacteristic
421C2×C5#512811yescharacteristic
422C2×C5#512811yescharacteristic
423C2×C5C4×#21711yescharacteristic
424D5—42no—
425C23—52no—
426C23—101no—
427C23—101no—
428C23—101no—
429C23—101no—
430C23—101no—
431C23—101no—
432C23C2×D3×AGL(1,𝔽5)11yescharacteristic
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—32no—
436C2×C4—51no—
437C2×C4—51no—
438C2×C4—51no—
439C2×C4—51no—
440C2×C4—51no—
441C2×C4—51no—
442C2×C4—61no—
443C2×C4—61no—
444C2×C4—61no—
445C2×C4—61no—
446C2×C4—61no—
447C2×C4—102no—
448C2×C4—102no—
449C2×C4—102no—
450C2×C4—102no—
451C2×C4—152no—
452C2×C4—301no—
453C2×C4—301no—
454C2×C4—301no—
455C2×C4—301no—
456C2×C4—301no—
457C2×C4Dic3×AGL(1,𝔽5)12yes—
458C8—54no—
459C8—102no—
460C8—302no—
461C8—302no—
462C2×C3—202no—
463C2×C3C4×#70011yescharacteristic
464C2×C3#6569311yescharacteristic
465C2×C3#6569511yescharacteristic
466C2×C3C22⋊C4×AGL(1,𝔽5)11yescharacteristic
467C2×C3#6570111yescharacteristic
468C2×C3#6570411yescharacteristic
469C2×C3#6570511yescharacteristic
470C5#7198311yescharacteristic, complemented, Sylow
471C22—102no—
472C22—102no—
473C22—102no—
474C22—201no—
475C22—201no—
476C22—201no—
477C22—201no—
478C22D3×#70011yescharacteristic
479C22#9191311yescharacteristic
480C22#9191511yescharacteristic
481C22#9191611yescharacteristic
482C22C2×Dic3×AGL(1,𝔽5)11yescharacteristic
483C22AGL(1,𝔽5)×#6711yescharacteristic
484C22AGL(1,𝔽5)×#6711yescharacteristic
485C4—22no—
486C4—51no—
487C4—51no—
488C4—51no—
489C4—51no—
490C4—62no—
491C4—121no—
492C4—302no—
493C4—601no—
494C3#1060377711yescharacteristic, complemented, Sylow
495C2—202no—
496C2#1175176311yescharacteristic
497C2Dic3×#70011yescharacteristic
498C2#1175178211yescharacteristic
499C2#1175188511yescharacteristic
500C2#1175188611yescharacteristic
501C2#1175191011yescharacteristic
502C2AGL(1,𝔽5)×#21711yescharacteristic
subgroupG/H
center, FrattiniC23C2×D3×AGL(1,𝔽5)
commutatorC22×C3×C5C2×C42
FittingC22×C3×C4×C5C2×C4
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C2×C4
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1753
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C2×#91169C2semidirect
4. C2×Dic3×#170C2semidirect
6. #11746570C2semidirect
7. #11746570C2semidirect
16. C2×C3×#700C4semidirect
21. #91232C4semidirect
80. C2×#700Dic3semidirect
107. C2×Dic15M16semidirect
113. C2×C5×Dic3M16semidirect
127. C3×#170C22⋊C4semidirect
275. #170#217semidirect
333. C2×Dic3#700semidirect
393. C3×C5#1753semidirect
470. C5#71983semidirect
494. C3#10603777semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#7002
C2×#912322
C2×#911692
C2×Dic3×#1702
#117487022
#117465702
#106037773
#719835