Finite Group Databasebeta

← #14413478

Subgroups — #14413478

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
1C2×C3×#4053C211yesmaximal, characteristic
2#11754509C211yesmaximal, characteristic
3#11754499C211yesmaximal, characteristic
4#11751222C211yesmaximal, characteristic, complemented
5C5×#5121C211yesmaximal, characteristic, complemented
6#11748458C211yesmaximal, characteristic, complemented
7C2×#90985C211yesmaximal, characteristic, complemented
8#11747672C212yesmaximal, complemented
9#11747619C212yesmaximal, complemented
10#11747618C212yesmaximal, complemented
11D5×#817C212yesmaximal, complemented
12#10610940—31nomaximal, Hall
13C2×C3×#709C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15#91815C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C5×#926C2211yescharacteristic
18C2×C5×C4⋊Dic3C2211yescharacteristic
19C22×C3×#168C2211yescharacteristic
20C3×#4053C418yescomplemented
21C2×C3×#676C2212yes—
22C2×C3×C8×D5C2212yes—
23#91559—22no—
24Dic3×C22⋊D5—22no—
25#91434—21no—
26Dic3×D20—21no—
27D5×C4⋊Dic3C2212yes—
28D5×C4⋊Dic3C2212yes—
29#91358C2212yes—
30#91358C2212yes—
31#91331—21no—
32Dic3×Dic10—21no—
33#91102C2212yes—
34#91101C2212yes—
35C5×#818C2212yes—
36C5×#817C2212yes—
37#90988C2211yescharacteristic
38#90988C2211yescharacteristic
39#90985C2211yescharacteristic
40#90985C2212yes—
41#90985C2212yes—
42#90985C2211yescharacteristic
43#83784—51nomaximal, Hall
44C2×#4053D311yescharacteristic
45#65857—31no—
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×Dic15—21no—
57C22×C5×Dic3—21no—
58C2×C3×C22⋊D5D412yes—
59C3×#709C2×C414yes—
60C3×#709Q814yes—
61C2×C3×D20D411yescharacteristic
62C2×C3×C4×D5C2312yes—
63C2×C3×Dic10D411yescharacteristic
64C2×D5×Dic3—22no—
65C2×D5×Dic3—22no—
66C3×C5×M16C2×C414yescomplemented
67C2×C3×C5×C8C2312yes—
68#6719—21no—
69C4⋊Dic15—21no—
70C4⋊Dic15C2311yescharacteristic
71C4⋊Dic15C2312yes—
72C4⋊Dic15C2311yescharacteristic
73C4×Dic15—21no—
74C5×#217—21no—
75C5×C4⋊Dic3—21no—
76C5×C4⋊Dic3C2311yescharacteristic
77C5×C4⋊Dic3C2312yes—
78C5×C4⋊Dic3C2311yescharacteristic
79C4×C5×Dic3—21no—
80C2×C3×#168C2×C414yescomplemented
81C2×C3×#168C2311yescharacteristic
82C2×C3×#168C2311yescharacteristic
83C3×#676C2×C418yescomplemented
84C3×C8×D5C2×C418yescomplemented
85#6668—22no—
86#6668—22no—
87#6665—22no—
88#6665—22no—
89Dic3×Dic5—22no—
90Dic3×Dic5—22no—
91C2×C3×#131—51no—
92#5827—51no—
93#5827—51no—
94#5121—51no—
95#5121—52no—
96#5121—52no—
97#5121D511yescharacteristic, complemented
98#5106—51no—
99#5106—52no—
100C2×#817—51no—
101C2×#817—52no—
102C2×#709C2×D311yescharacteristic
103C2×C5×M16C2×D311yescharacteristic
104C5×#117—31no—
105C2×C5×C4⋊C4—31no—
106C4×C22⋊D5—62no—
107#4072—31no—
108C2×C4⋊Dic5—31no—
109C22×#168C2×D311yescharacteristic
110#4053Dic318yescomplemented
111C2×#676C2×D312yes—
112C2×C8×D5C2×D312yes—
113#4039—61no—
114#4038—32no—
115#4038—32no—
116D5×C4⋊C4—32no—
117D5×C4⋊C4—32no—
118#4033—61no—
119#4027—62no—
120C4×D20—61no—
121C4×Dic10—61no—
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×C5C22×C412yes—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×Q812yes—
138C2×C3×C4×C5C2411yescharacteristic
139C2×Dic15—21no—
140C2×Dic15—22no—
141C2×Dic15—21no—
142C2×Dic15—81no—
143C2×C5×Dic3—21no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—21no—
146C2×C5×Dic3—81no—
147C3×C22⋊D5C4⋊C418yes—
148C2×C3×Dic5C2×D412yes—
149C3×D20C4⋊C414yes—
150C3×C4×D5C22×C414yes—
151C3×C4×D5C2×Q814yes—
152C3×Dic10C4⋊C414yes—
153D5×Dic3—82no—
154D5×Dic3—82no—
155C3×C5×C8C22×C414yes—
156C3×#168C22×C412yes—
157C3×#168C22×C412yes—
158C2×C3×#41—51no—
159C3×#131—58no—
160C2×C3×M16—52no—
161C2×C3×M16C2×D511yescharacteristic
162C22×C3×C8—51no—
163C22×C3×C8—52no—
164Q8×Dic3—101no—
165Q8×Dic3—101no—
166D4×Dic3—101no—
167D4×Dic3—101no—
168D4×Dic3—102no—
169D4×Dic3—102no—
170#926—51no—
171#926—52no—
172#926—52no—
173#926C2×D511yescharacteristic
174C2×C4⋊Dic3—51no—
175C2×C4⋊Dic3—52no—
176C2×C4⋊Dic3—52no—
177C2×C4⋊Dic3C2×D511yescharacteristic
178#818—52no—
179#818—51no—
180#818—51no—
181#818C2×D512yes—
182#817—52no—
183#817—52no—
184#817—52no—
185#817—51no—
186#817—51no—
187#817C2×D512yes—
188C22×C4×C5—61no—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5D1212yes—
191C22×Dic5—61no—
192#709Dic614yes—
193#709C2×Dic314yes—
194C2×D20D1211yescharacteristic
195C2×C4×D5—62no—
196C2×C4×D5—62no—
197C2×C4×D5C22×D312yes—
198C2×Dic10D1211yescharacteristic
199C5×M16C2×Dic314yescomplemented
200C2×C5×C8C22×D312yes—
201C5×C4⋊C4—32no—
202C5×C4⋊C4—31no—
203C5×C4⋊C4—31no—
204C5×C4⋊C4—61no—
205C5×C22⋊C4—61no—
206C42×C5—61no—
207C22⋊Dic5—61no—
208#685—62no—
209#685—62no—
210C4⋊Dic5—31no—
211C4⋊Dic5—31no—
212C4⋊Dic5—32no—
213C4⋊Dic5—61no—
214#683—62no—
215#683—62no—
216C4×Dic5—61no—
217C4×Dic5—62no—
218C4×Dic5—62no—
219C2×#168C2×Dic314yescomplemented
220C2×#168C22×D311yescharacteristic
221C2×#168C22×D311yescharacteristic
222#676C2×Dic318yescomplemented
223C8×D5C2×Dic318yescomplemented
224C2×#131—51no—
225#520—151no—
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×C5C2×C4⋊C412yes—
243C3×C4×C5C23×C411yescharacteristic
244C3×C4×C5C22×Q811yescharacteristic
245Dic15—41no—
246Dic15—42no—
247Dic15—41no—
248C3×Dic5C2×C4⋊C414yes—
249C5×Dic3—41no—
250C5×Dic3—42no—
251C5×Dic3—41no—
252C3×#41—54no—
253C3×#41—54no—
254C2×C3×Q8—51no—
255C2×C3×D4—52no—
256C2×C3×D4—51no—
257C22×C3×C4—52no—
258C22×C3×C4C22×D511yescharacteristic
259C22×Dic3—21no—
260C22×Dic3—102no—
261C22×Dic3—102no—
262C22×Dic3—101no—
263C3×M16—58no—
264C3×M16C4×D514yescomplemented
265C2×C3×C8—54no—
266C2×C3×C8—51no—
267C2×C3×C8—51no—
268C2×C3×C8—58no—
269C2×C3×C8C22×D512yes—
270#217—21no—
271#217—102no—
272#217—102no—
273#217—101no—
274C4⋊Dic3—21no—
275C4⋊Dic3—51no—
276C4⋊Dic3—52no—
277C4⋊Dic3—51no—
278C4⋊Dic3—102no—
279C4⋊Dic3—102no—
280C4⋊Dic3—101no—
281C4⋊Dic3C22×D512yes—
282C4⋊Dic3C22×D511yescharacteristic
283C4⋊Dic3C22×D511yescharacteristic
284C4×Dic3—21no—
285C4×Dic3—102no—
286C4×Dic3—102no—
287C4×Dic3—101no—
288C23×C5C2×D1211yescharacteristic
289C22×D5C2×D1212yes—
290C2×C4×C5—61no—
291C2×C4×C5—62no—
292C2×C4×C5—61no—
293C2×C4×C5—241no—
294C2×C4×C5C2×Dic612yes—
295C2×C4×C5C2×D1211yescharacteristic
296C2×C4×C5C22×Dic312yes—
297C2×C4×C5C23×D311yescharacteristic
298C22⋊D5C4⋊Dic318yes—
299C2×Dic5—61no—
300C2×Dic5—61no—
301C2×Dic5—62no—
302C2×Dic5—241no—
303C2×Dic5C2×D1212yes—
304D20C4⋊Dic314yes—
305C4×D5—242no—
306C4×D5—242no—
307C4×D5C2×Dic614yes—
308C4×D5C22×Dic314yes—
309Dic10C4⋊Dic314yes—
310C5×C8C22×Dic314yes—
311#168C22×Dic312yes—
312#168C22×Dic312yes—
313C2×#41—51no—
314#131—58no—
315C2×M16—52no—
316C2×M16D3×D511yescharacteristic
317C22×C8—51no—
318C22×C8—52no—
319C4×Q8—301no—
320C4×Q8—301no—
321C4×D4—301no—
322C4×D4—302no—
323C4×D4—301no—
324C4×D4—302no—
325#117—31no—
326#117—152no—
327#117—152no—
328#117—151no—
329C2×C4⋊C4—31no—
330C2×C4⋊C4—152no—
331C2×C4⋊C4—152no—
332C2×C4⋊C4—151no—
333#107—32no—
334#107—151no—
335#107—151no—
336#107—152no—
337#106—32no—
338#106—151no—
339#106—152no—
340#106—152no—
341#106—151no—
342#106—152no—
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—52no—
354C2×C3×C4—54no—
355C2×C3×C4—54no—
356C2×C3×C4C2×C4×D512yes—
357C2×C3×C4D4×D511yescharacteristic
358C2×C3×C4Q8×D512yes—
359C2×C3×C4C23×D511yescharacteristic
360C2×Dic3—21no—
361C2×Dic3—21no—
362C2×Dic3—22no—
363C2×Dic3—81no—
364C2×Dic3—101no—
365C2×Dic3—101no—
366C2×Dic3—102no—
367C2×Dic3—402no—
368C2×Dic3—402no—
369C2×Dic3—401no—
370C3×C8—52no—
371C3×C8—52no—
372C3×C8C2×C4×D514yes—
373C22×C5—21no—
374C22×C5—21no—
375C22×C5C2×C4⋊Dic312yes—
376C22×C5C22×D1211yescharacteristic
377C2×D5—22no—
378C2×D5—22no—
379C2×D5C2×C4⋊Dic314yes—
380C4×C5—121no—
381C4×C5—122no—
382C4×C5—121no—
383C4×C5C2×C4⋊Dic312yes—
384C4×C5C22×Dic611yescharacteristic
385C4×C5C23×Dic311yescharacteristic
386Dic5—121no—
387Dic5—122no—
388Dic5—121no—
389Dic5C2×C4⋊Dic314yes—
390#41—54no—
391#41—54no—
392C2×Q8—51no—
393C2×D4—52no—
394C2×D4—51no—
395C22×C4—52no—
396C22×C4—61no—
397C22×C4—302no—
398C22×C4—302no—
399C22×C4—301no—
400C22×C4C2×D3×D511yescharacteristic
401M16—58no—
402M16D5×Dic314yescomplemented
403C2×C8—54no—
404C2×C8—51no—
405C2×C8—51no—
406C2×C8—58no—
407C2×C8C2×D3×D512yes—
408C4⋊C4—31no—
409C4⋊C4—32no—
410C4⋊C4—31no—
411C4⋊C4—61no—
412C4⋊C4—152no—
413C4⋊C4—151no—
414C4⋊C4—151no—
415C4⋊C4—302no—
416C4⋊C4—302no—
417C4⋊C4—301no—
418C22⋊C4—61no—
419C22⋊C4—302no—
420C22⋊C4—302no—
421C22⋊C4—301no—
422C42—61no—
423C42—302no—
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—54no—
435C3×C4D5×C4⋊C412yes—
436C3×C4C22×C4×D511yescharacteristic
437C3×C4C2×Q8×D511yescharacteristic
438Dic3—41no—
439Dic3—42no—
440Dic3—41no—
441Dic3—201no—
442Dic3—201no—
443Dic3—202no—
444C2×C5—22no—
445C2×C5#575111yescharacteristic
446C2×C5#575111yescharacteristic
447C2×C5C22×C4⋊Dic311yescharacteristic
448D5—24no—
449C23—52no—
450C23D5×D1211yescharacteristic
451Q8—54no—
452D4—58no—
453D4—54no—
454C2×C4—52no—
455C2×C4—54no—
456C2×C4—54no—
457C2×C4—61no—
458C2×C4—61no—
459C2×C4—62no—
460C2×C4—241no—
461C2×C4—301no—
462C2×C4—301no—
463C2×C4—302no—
464C2×C4—1202no—
465C2×C4—1202no—
466C2×C4—1201no—
467C2×C4D5×Dic612yes—
468C2×C4D5×D1211yescharacteristic
469C2×C4C2×D5×Dic312yes—
470C2×C4C22×D3×D511yescharacteristic
471C8—52no—
472C8—52no—
473C8C2×D5×Dic314yes—
474C2×C3—22no—
475C2×C3—104no—
476C2×C3C2×D5×C4⋊C411yescharacteristic
477C2×C3#6610911yescharacteristic
478C2×C3#6611211yescharacteristic
479C5#8378411yescharacteristic, complemented, Sylow
480C22—21no—
481C22—21no—
482C22—54no—
483C22—102no—
484C22—102no—
485C22D5×C4⋊Dic312yes—
486C22C2×D5×D1211yescharacteristic
487C4—54no—
488C4—122no—
489C4—121no—
490C4—121no—
491C4—601no—
492C4—602no—
493C4—601no—
494C4D5×C4⋊Dic312yes—
495C4C2×D5×Dic611yescharacteristic
496C4C22×D5×Dic311yescharacteristic
497C3#1061094011yescharacteristic, complemented, Sylow
498C2—22no—
499C2—104no—
500C2#1175402311yescharacteristic
501C2#1175402511yescharacteristic
502C2C2×D5×C4⋊Dic311yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#709C22
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2912
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #11751222C2semidirect
5. C5×#5121C2semidirect
6. #11748458C2semidirect
7. C2×#90985C2semidirect
8. #11747672C2semidirect
9. #11747619C2semidirect
10. #11747618C2semidirect
11. D5×#817C2semidirect
20. C3×#4053C4semidirect
66. C3×C5×M16C2×C4semidirect
80. C2×C3×#168C2×C4semidirect
83. C3×#676C2×C4semidirect
84. C3×C8×D5C2×C4semidirect
97. #5121D5semidirect
110. #4053Dic3semidirect
199. C5×M16C2×Dic3semidirect
219. C2×#168C2×Dic3semidirect
222. #676C2×Dic3semidirect
223. C8×D5C2×Dic3semidirect
264. C3×M16C4×D5semidirect
402. M16D5×Dic3semidirect
426. C3×C5#2912semidirect
479. C5#83784semidirect
497. C3#10610940semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40532
#117545092
#117544992
#117512222
C5×#51212
#117484582
C2×#909852
#117476722
#117476192
#117476182
D5×#8172
#106109403
#837845