Finite Group Databasebeta

← #14413477

Subgroups — #14413477

Order 1920.

952 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
1C3×#65857C211yesmaximal, characteristic
2#11754499C211yesmaximal, characteristic
3C2×#91284C211yesmaximal, characteristic
4#11751099C211yesmaximal, characteristic, complemented
5C5×#4995C211yesmaximal, characteristic, complemented
6#11748453C211yesmaximal, characteristic, complemented
7C2×#90986C211yesmaximal, characteristic, complemented
8#11747453C212yesmaximal, complemented
9#11747432C212yesmaximal, complemented
10D5×#808C212yesmaximal, complemented
11#11747188C212yesmaximal, complemented
12#10610940—31nomaximal, Hall
13C2×C3×#709C2211yescharacteristic
14C3×C5×#117C2211yescharacteristic
15#91815C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C2×C5×C4⋊Dic3C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C2×C3×C4⋊Dic5C2211yescharacteristic
20C3×#4038C2212yes—
21C3×D5×C4⋊C4C2212yes—
22C3×#4027—22no—
23C3×C4×D20—21no—
24C3×C4×Dic10—21no—
25Dic3×C22⋊D5—22no—
26#91434—21no—
27D5×C4⋊Dic3C2212yes—
28#91358C2212yes—
29#91331—21no—
30C2×#6649C2212yes—
31#91284C418yescomplemented
32C2×D5×C3⋊C8C2212yes—
33#91092C2211yescharacteristic
34#91092C2211yescharacteristic
35#91091C2211yescharacteristic
36#91091C2211yescharacteristic
37C5×#808C2212yes—
38C5×#807C2212yes—
39#90990C2212yes—
40#90987C2212yes—
41#90986C2212yes—
42#90986C2212yes—
43#82561—51nomaximal, Hall
44C2×#4053—31no—
45#65857D311yescharacteristic
46#65838—31no—
47C5×#428—31no—
48#65410—31no—
49#65287—31no—
50C2×#3940—31no—
51#65170—32no—
52#65169—32no—
53#65150—32no—
54D5×#106—32no—
55C22×C3×C4×C5C2311yescharacteristic
56C22×C5×Dic3—21no—
57C2×C3×C22⋊D5D412yes—
58C22×C3×Dic5—21no—
59C3×#709C2×C414yes—
60C3×#709Q814yes—
61C2×C3×D20D411yescharacteristic
62C2×C3×C4×D5—22no—
63C2×C3×C4×D5C2312yes—
64C2×C3×Dic10D411yescharacteristic
65C2×D5×Dic3—22no—
66C3×C5×C4⋊C4C2311yescharacteristic
67C3×C5×C4⋊C4C2311yescharacteristic
68C3×C5×C22⋊C4—21no—
69C3×C42×C5—21no—
70#6719—21no—
71C4⋊Dic15C2311yescharacteristic
72C4⋊Dic15C2311yescharacteristic
73C4×Dic15—21no—
74C2×C3⋊#168C2×C414yescomplemented
75C2×C3⋊#168C2311yescharacteristic
76C2×C3⋊#168C2311yescharacteristic
77C5×C4⋊Dic3—21no—
78C5×C4⋊Dic3C2312yes—
79C5×#208C2×C414yescomplemented
80C2×C5×C3⋊C8C2312yes—
81C3×#685—22no—
82C3×C4⋊Dic5—21no—
83C3×C4⋊Dic5C2312yes—
84C3×#683—22no—
85C3×C4×Dic5—22no—
86#6668—22no—
87#6665—22no—
88Dic3×Dic5—22no—
89#6649C2×C418yescomplemented
90D5×C3⋊C8C2×C418yescomplemented
91C3×#520—51no—
92#5827—51no—
93C2×#948—51no—
94#4998—51no—
95#4998—52no—
96#4995—52no—
97#4995D511yescharacteristic, complemented
98#4964—51no—
99#4964—52no—
100C2×#808—51no—
101C2×#808—52no—
102C2×#709C2×D311yescharacteristic
103C2×C5×M16—31no—
104C5×#117C2×D311yescharacteristic
105C2×C5×C4⋊C4—31no—
106C4×C22⋊D5—62no—
107#4072—31no—
108C2×C4⋊Dic5C2×D311yescharacteristic
109C22×#168—31no—
110#4053—38no—
111C2×#676—32no—
112C2×C8×D5—32no—
113#4039—61no—
114#4038—32no—
115#4038C2×D312yes—
116D5×C4⋊C4—32no—
117D5×C4⋊C4C2×D312yes—
118#4033—61no—
119#4027—22no—
120C4×D20—21no—
121C4×Dic10—21no—
122C5×#107—32no—
123C5×#106—32no—
124#3950—32no—
125#3949—32no—
126#3940—31no—
127#3940—31no—
128#3940—32no—
129#3940—32no—
130#3939—31no—
131#3939—31no—
132#2912—151noSylow
133C23×C3×C5C2×D411yescharacteristic
134C22×C3×D5C2×D412yes—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5C22×C412yes—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×Q812yes—
140C2×C3×C4×C5C2411yescharacteristic
141C2×Dic15—21no—
142C2×Dic15—21no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3—81no—
145C3×C22⋊D5C4⋊C418yes—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—81no—
148C2×C3×Dic5C2×D412yes—
149C3×D20C4⋊C414yes—
150C3×C4×D5—82no—
151C3×C4×D5C22×C414yes—
152C3×C4×D5C2×Q814yes—
153C3×Dic10C4⋊C414yes—
154D5×Dic3—82no—
155C3⋊#168C22×C412yes—
156C3⋊#168C22×C412yes—
157C5×C3⋊C8C22×C414yes—
158C2×C3×#41—51no—
159C3×C4×Q8—101no—
160C3×C4×D4—101no—
161C3×C4×D4—102no—
162C3×#117—52no—
163C3×#117C2×D511yescharacteristic
164C2×C3×C4⋊C4—51no—
165C2×C3×C4⋊C4—52no—
166#948—58no—
167Q8×Dic3—101no—
168D4×Dic3—101no—
169D4×Dic3—102no—
170#926—51no—
171#926—52no—
172C2×C4⋊Dic3—52no—
173C2×C4⋊Dic3C2×D511yescharacteristic
174C2×#208—52no—
175C2×#208C2×D511yescharacteristic
176C22×C3⋊C8—51no—
177C22×C3⋊C8—52no—
178#808—51no—
179#808—51no—
180#808—52no—
181#808—52no—
182#808—52no—
183#808C2×D512yes—
184#807—51no—
185#807—51no—
186#807—52no—
187#807C2×D512yes—
188C22×C4×C5—61no—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5#6712yes—
191C22×Dic5—21no—
192#709Dic614yes—
193#709C4×D314yes—
194C2×D20#6711yescharacteristic
195C2×C4×D5—22no—
196C2×C4×D5—62no—
197C2×C4×D5C22×D312yes—
198C2×Dic10#6711yescharacteristic
199C5×M16—34no—
200C2×C5×C8—32no—
201C5×C4⋊C4—32no—
202C5×C4⋊C4—61no—
203C5×C4⋊C4C22×D311yescharacteristic
204C5×C4⋊C4C22×D311yescharacteristic
205C5×C22⋊C4—21no—
206C42×C5—21no—
207C22⋊Dic5—61no—
208#685—22no—
209#685—62no—
210C4⋊Dic5—21no—
211C4⋊Dic5—31no—
212C4⋊Dic5—31no—
213C4⋊Dic5C22×D312yes—
214#683—22no—
215#683—62no—
216C4×Dic5—22no—
217C4×Dic5—61no—
218C4×Dic5—62no—
219C2×#168—34no—
220C2×#168—31no—
221C2×#168—31no—
222#676—38no—
223C8×D5—38no—
224C2×#131—151no—
225#520—51no—
226#520—151no—
227#428—31no—
228#428—152no—
229#428—152no—
230#428—151no—
231#427—152no—
232#427—151no—
233C2×#106—152no—
234C2×#106—151no—
235C22×C3×C5—21no—
236C22×C3×C5—21no—
237C22×C3×C5C2×C4⋊C412yes—
238C22×C3×C5C22×D411yescharacteristic
239C2×C3×D5—22no—
240C2×C3×D5—22no—
241C2×C3×D5C2×C4⋊C414yes—
242C3×C4×C5—41no—
243C3×C4×C5—41no—
244C3×C4×C5C2×C4⋊C412yes—
245C3×C4×C5C23×C411yescharacteristic
246C3×C4×C5C22×Q811yescharacteristic
247Dic15—41no—
248Dic15—41no—
249C3×Dic5—42no—
250C3×Dic5C2×C4⋊C414yes—
251C5×Dic3—42no—
252C3×#41—54no—
253C3×#41—54no—
254C2×C3×Q8—51no—
255C2×C3×D4—52no—
256C2×C3×D4—51no—
257C22×C3×C4—52no—
258C22×C3×C4—102no—
259C22×C3×C4—101no—
260C22×C3×C4C22×D511yescharacteristic
261C22×Dic3—21no—
262C22×Dic3—102no—
263C3×C4⋊C4—52no—
264C3×C4⋊C4—102no—
265C3×C4⋊C4—101no—
266C3×C4⋊C4C22×D511yescharacteristic
267C3×C4⋊C4C22×D511yescharacteristic
268C3×C22⋊C4—21no—
269C3×C22⋊C4—102no—
270C3×C42—21no—
271C3×C42—102no—
272#217—102no—
273#217—101no—
274C4⋊Dic3—21no—
275C4⋊Dic3—51no—
276C4⋊Dic3—51no—
277C4⋊Dic3—102no—
278C4⋊Dic3C22×D512yes—
279C4×Dic3—102no—
280C4×Dic3—101no—
281#208—58no—
282#208C4×D514yescomplemented
283C2×C3⋊C8—54no—
284C2×C3⋊C8—51no—
285C2×C3⋊C8—51no—
286C2×C3⋊C8—58no—
287C2×C3⋊C8C22×D512yes—
288C23×C5C2×#6711yescharacteristic
289C22×D5C2×#6712yes—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—62no—
293C2×C4×C5—241no—
294C2×C4×C5C2×Dic612yes—
295C2×C4×C5C2×C4×D312yes—
296C2×C4×C5C2×#6711yescharacteristic
297C2×C4×C5C23×D311yescharacteristic
298C22⋊D5Dic3⋊C418yes—
299C2×Dic5—22no—
300C2×Dic5—61no—
301C2×Dic5—61no—
302C2×Dic5—81no—
303C2×Dic5C2×#6712yes—
304D20Dic3⋊C414yes—
305C4×D5—82no—
306C4×D5—242no—
307C4×D5C2×Dic614yes—
308C4×D5C2×C4×D314yes—
309Dic10Dic3⋊C414yes—
310C5×C8—34no—
311#168—32no—
312#168—32no—
313C2×#41—51no—
314#131—158no—
315C2×M16—31no—
316C2×M16—152no—
317C22×C8—152no—
318C22×C8—151no—
319C4×Q8—101no—
320C4×Q8—301no—
321C4×D4—101no—
322C4×D4—102no—
323C4×D4—301no—
324C4×D4—302no—
325#117—52no—
326#117—152no—
327#117—151no—
328#117D3×D511yescharacteristic
329C2×C4⋊C4—31no—
330C2×C4⋊C4—51no—
331C2×C4⋊C4—52no—
332C2×C4⋊C4—152no—
333#107—32no—
334#107—152no—
335#107—151no—
336#107—151no—
337#106—32no—
338#106—152no—
339#106—152no—
340#106—152no—
341#106—151no—
342#106—151no—
343C2×C3×C5—22no—
344C2×C3×C5C22×C4⋊C411yescharacteristic
345C2×C3×C5#57711yescharacteristic
346C2×C3×C5#57711yescharacteristic
347C3×D5—24no—
348C23×C3—52no—
349C23×C3D4×D511yescharacteristic
350C3×Q8—54no—
351C3×D4—58no—
352C3×D4—54no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—52no—
356C2×C3×C4—54no—
357C2×C3×C4—54no—
358C2×C3×C4—102no—
359C2×C3×C4—402no—
360C2×C3×C4—401no—
361C2×C3×C4C2×C4×D512yes—
362C2×C3×C4D4×D511yescharacteristic
363C2×C3×C4Q8×D512yes—
364C2×C3×C4C23×D511yescharacteristic
365C2×Dic3—22no—
366C2×Dic3—81no—
367C2×Dic3—101no—
368C2×Dic3—101no—
369C2×Dic3—402no—
370C3⋊C8—52no—
371C3⋊C8—52no—
372C3⋊C8C2×C4×D514yes—
373C22×C5—21no—
374C22×C5—21no—
375C22×C5C2×Dic3⋊C412yes—
376C22×C5C22×#6711yescharacteristic
377C2×D5—22no—
378C2×D5—22no—
379C2×D5C2×Dic3⋊C414yes—
380C4×C5—41no—
381C4×C5—41no—
382C4×C5—122no—
383C4×C5C2×Dic3⋊C412yes—
384C4×C5C22×Dic611yescharacteristic
385C4×C5C22×C4×D311yescharacteristic
386Dic5—42no—
387Dic5—121no—
388Dic5—121no—
389Dic5C2×Dic3⋊C414yes—
390#41—54no—
391#41—54no—
392C2×Q8—51no—
393C2×D4—52no—
394C2×D4—51no—
395C22×C4—52no—
396C22×C4—61no—
397C22×C4—102no—
398C22×C4—101no—
399C22×C4—302no—
400C22×C4C2×D3×D511yescharacteristic
401M16—34no—
402M16—158no—
403C2×C8—32no—
404C2×C8—158no—
405C2×C8—154no—
406C2×C8—151no—
407C2×C8—151no—
408C4⋊C4—32no—
409C4⋊C4—52no—
410C4⋊C4—61no—
411C4⋊C4—102no—
412C4⋊C4—101no—
413C4⋊C4—151no—
414C4⋊C4—151no—
415C4⋊C4—302no—
416C4⋊C4C2×D3×D511yescharacteristic
417C4⋊C4C2×D3×D511yescharacteristic
418C22⋊C4—21no—
419C22⋊C4—102no—
420C22⋊C4—302no—
421C22⋊C4—301no—
422C42—21no—
423C42—102no—
424C42—302no—
425C42—301no—
426C3×C5#291211yescharacteristic, complemented, Hall
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—54no—
430C22×C3—102no—
431C22×C3—102no—
432C22×C3D5×C4⋊C412yes—
433C22×C3C2×D4×D511yescharacteristic
434C3×C4—41no—
435C3×C4—41no—
436C3×C4—54no—
437C3×C4—202no—
438C3×C4D5×C4⋊C412yes—
439C3×C4C22×C4×D511yescharacteristic
440C3×C4C2×Q8×D511yescharacteristic
441Dic3—42no—
442Dic3—201no—
443Dic3—201no—
444C2×C5—22no—
445C2×C5C22×Dic3⋊C411yescharacteristic
446C2×C5#583611yescharacteristic
447C2×C5#583711yescharacteristic
448D5—24no—
449C23—52no—
450C23D5×#6711yescharacteristic
451Q8—54no—
452D4—58no—
453D4—54no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—52no—
457C2×C4—54no—
458C2×C4—54no—
459C2×C4—62no—
460C2×C4—102no—
461C2×C4—241no—
462C2×C4—301no—
463C2×C4—301no—
464C2×C4—402no—
465C2×C4—401no—
466C2×C4—1202no—
467C2×C4D5×Dic612yes—
468C2×C4C4×D3×D512yes—
469C2×C4D5×#6711yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—34no—
472C8—152no—
473C8—152no—
474C2×C3—22no—
475C2×C3—104no—
476C2×C3C2×D5×C4⋊C411yescharacteristic
477C2×C3#6610911yescharacteristic
478C2×C3#6611211yescharacteristic
479C5#8256111yescharacteristic, complemented, Sylow
480C22—21no—
481C22—21no—
482C22—54no—
483C22—102no—
484C22—102no—
485C22D5×Dic3⋊C412yes—
486C22C2×D5×#6711yescharacteristic
487C4—41no—
488C4—41no—
489C4—54no—
490C4—122no—
491C4—202no—
492C4—601no—
493C4—601no—
494C4D5×Dic3⋊C412yes—
495C4C2×D5×Dic611yescharacteristic
496C4C2×C4×D3×D511yescharacteristic
497C3#1061094011yescharacteristic, complemented, Sylow
498C2—22no—
499C2—104no—
500C2C2×D5×Dic3⋊C411yescharacteristic
501C2#1175531711yescharacteristic
502C2#1175533511yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#709C22
cosocleC2×C3×C4×C5C24
hypercenter#117D3×D5
hypocenterC3×C5#2912
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #11751099C2semidirect
5. C5×#4995C2semidirect
6. #11748453C2semidirect
7. C2×#90986C2semidirect
8. #11747453C2semidirect
9. #11747432C2semidirect
10. D5×#808C2semidirect
11. #11747188C2semidirect
31. #91284C4semidirect
74. C2×C3⋊#168C2×C4semidirect
79. C5×#208C2×C4semidirect
89. #6649C2×C4semidirect
90. D5×C3⋊C8C2×C4semidirect
97. #4995D5semidirect
282. #208C4×D5semidirect
426. C3×C5#2912semidirect
479. C5#82561semidirect
497. C3#10610940semidirect

Maximal subgroups

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

subgroupindex
C3×#658572
#117544992
C2×#912842
#117510992
C5×#49952
#117484532
C2×#909862
#117474532
#117474322
D5×#8082
#117471882
#106109403
#825615