Finite Group Databasebeta

← #14414959

Subgroups — #14414959

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91796C211yesmaximal, characteristic, complemented
2#11754564C211yesmaximal, characteristic
3C22×D5×C3⋊C8C211yesmaximal, characteristic, complemented
4C5×#5119C211yesmaximal, characteristic, complemented
5C3×#65415C211yesmaximal, characteristic, complemented
6#11748350C211yesmaximal, characteristic, complemented
7#11748327C211yesmaximal, characteristic, complemented
8#11748047C214yesmaximal, complemented
9#11748043C214yesmaximal, complemented
10#10610804—31nomaximal, Hall
11C2×#6817C2211yescharacteristic
12C22×C3×C4×D5C2211yescharacteristic
13C2×C3×C5×M16C2211yescharacteristic
14C22×C3⋊#168C2211yescharacteristic
15#91796—24no—
16C2×#6705C2212yescomplemented
17C2×C8×D15C2212yescomplemented
18C5×#926C2211yescharacteristic
19C22×C5×C3⋊C8C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21#91564C412yes—
22#91546C412yes—
23#91450C412yes—
24C4×#1202C2214yes—
25#91360C412yes—
26C2×D5×C3⋊C8—24no—
27C2×D5×C3⋊C8C2212yes—
28C2×D5×C3⋊C8C2212yes—
29C5×Dic3⋊C8C2214yescomplemented
30C3×#3952C2214yes—
31#90957C2214yescomplemented
32#90953C2212yescomplemented
33Dic3×#168C2212yescomplemented
34#78626—51nomaximal, Hall
35C2×#4053—31no—
36C22×C8×D5—31no—
37#65858—31no—
38C5×#424—31no—
39#65415D311yescharacteristic, complemented
40#65399—31no—
41#65286—31no—
42#65125—34no—
43#65123—34no—
44C23×C3×D5C2×C411yescharacteristic
45C22×C3×C4×C5C2311yescharacteristic
46C2×#1220C2×C412yes—
47#6817—22no—
48#6817—22no—
49C2×D60C2×C411yescharacteristic
50C2×C4×D15C2312yes—
51C2×Dic30C2×C411yescharacteristic
52C22×C3×Dic5C2×C411yescharacteristic
53C2×C3×C4×D5—22no—
54C2×C3×C4×D5—22no—
55C2×C3×C4×D5C2×C412yes—
56C2×C3×C4×D5C2312yes—
57C2×#1202C2×C414yes—
58C3×C5×M16—22no—
59C2×C3×C5×C8C2312yes—
60C2×C3⋊#168D414yescomplemented
61C2×C3⋊#168C2311yescharacteristic
62C2×C3⋊#168C2311yescharacteristic
63#6705—24no—
64C8×D15—24no—
65C5×#217C2×C412yes—
66C5×C4⋊Dic3C2×C412yes—
67C4×C5×Dic3C2312yes—
68C2×C5×C3⋊C8—22no—
69C2×C5×C3⋊C8C2312yes—
70C3×#681—22no—
71C2×C3×#168C2312yes—
72Dic3⋊Dic5C2×C414yes—
73#6667C2×C414yes—
74#6665C2×C414yes—
75D5×C3⋊C8—24no—
76D5×C3⋊C8—24no—
77#5791—51no—
78C23×C3⋊C8—51no—
79C2×#907—51no—
80C3×#407—51no—
81#5129—51no—
82#5122—51no—
83#5119D511yescharacteristic, complemented
84#4730—54no—
85#67⋊C8—54no—
86C2×#709—31no—
87C22×C4×D5C2×D311yescharacteristic
88C2×C5×M16C2×D311yescharacteristic
89C22×C5×C8—31no—
90C5×#117—31no—
91C2×#681C2×D311yescharacteristic
92C22×#168—31no—
93#4053—64no—
94C2×#676—32no—
95C2×C8×D5—32no—
96C2×C8×D5—32no—
97C2×C8×D5—32no—
98C2×C8×D5—64no—
99#4043—32no—
100#4041—32no—
101#4032—32no—
102#4028—32no—
103C4×D20—34no—
104C5×C4⋊C8—34no—
105#3952—34no—
106#3952C2×D314yes—
107#3935—32no—
108C4×#168—32no—
109#2929—151noSylow
110C23×C3×C5C22×C411yescharacteristic
111C22×D15C22×C412yes—
112C22×C3×D5—22no—
113C22×C3×D5—24no—
114C22×C3×D5C22×C412yes—
115C2×C3×C4×C5C22×C411yescharacteristic
116C2×C3×C4×C5C2×D412yes—
117C2×C3×C4×C5#4112yes—
118C2×C3×C4×C5C2411yescharacteristic
119#1220—24no—
120C2×Dic15C22×C412yes—
121D60—22no—
122C4×D15—22no—
123C4×D15—22no—
124Dic30—22no—
125C2×C5×Dic3C22×C414yes—
126C2×C3×Dic5—22no—
127C2×C3×Dic5C22×C412yes—
128C3×C4×D5—24no—
129C3×C4×D5—22no—
130C3×C4×D5—22no—
131#1202—28no—
132C3×C5×C8—22no—
133C3⋊#168C2×D412yes—
134C3⋊#168C2×D412yes—
135C3×#168—22no—
136C5×C3⋊C8—22no—
137C23×C3×C4—51no—
138C2×#235—51no—
139C2×C3×M16—51no—
140C2×C3×M16C2×D511yescharacteristic
141#953—52no—
142#930—52no—
143#929—52no—
144C4×#67—54no—
145#926C2×D511yescharacteristic
146#924—52no—
147C22×C3⋊C8—51no—
148C22×C3⋊C8—52no—
149C22×C3⋊C8—52no—
150C22×C3⋊C8—104no—
151C22×C3⋊C8C2×D511yescharacteristic
152#907—104no—
153C2×ΓL(1,𝔽25)—52no—
154C2×D3×C8—52no—
155C3×C22⋊C8—54no—
156(C2×D3)⋊C8—54no—
157#815—52no—
158Dic3⋊C8C2×D514yescomplemented
159C8×Dic3—52no—
160C23×D5C4×D311yescharacteristic
161C22×C4×C5C22×D311yescharacteristic
162C2×C22⋊D5—32no—
163C22×Dic5C4×D311yescharacteristic
164#709—62no—
165#709—62no—
166C2×D20—34no—
167C2×D20—31no—
168C2×C4×D5—22no—
169C2×C4×D5—22no—
170C2×C4×D5—32no—
171C2×C4×D5C4×D312yes—
172C2×C4×D5C22×D312yes—
173C2×Dic10—31no—
174C5×M16—22no—
175C2×C5×C8—32no—
176C2×C5×C8—62no—
177C2×C5×C8C22×D312yes—
178C5×C4⋊C4—32no—
179C5×C22⋊C4—32no—
180C42×C5—32no—
181#685—34no—
182#685—34no—
183C4⋊Dic5—34no—
184#681—22no—
185C2×#168—34no—
186C2×#168—31no—
187C2×#168—31no—
188C2×#168C22×D312yes—
189#676—64no—
190C8×D5—64no—
191C8×D5—64no—
192C8×D5—64no—
193C2×#131—151no—
194C23×C8—151no—
195#525—151no—
196#435—154no—
197C8×D4—154no—
198#424—31no—
199#408—151no—
200#407—51no—
201#405—151no—
202C22×C3×C5—22no—
203C22×C3×C5C4×D412yes—
204C22×C3×C5C23×C411yescharacteristic
205C2×D15—22no—
206C2×D15—24no—
207C2×C3×D5—28no—
208C2×C3×D5—22no—
209C2×C3×D5—22no—
210C2×C3×D5#13114yescomplemented
211C3×C4×C5C4×D412yes—
212C3×C4×C5C22×D411yescharacteristic
213C3×C4×C5C2×#4111yescharacteristic
214Dic15—22no—
215C3×Dic5—22no—
216C5×Dic3—24no—
217C24×C3—51no—
218C22×C3×C4—51no—
219C22×C3×C4—52no—
220C22×C3×C4—52no—
221C22×C3×C4—102no—
222C22×C3×C4—102no—
223C22×C3×C4C22×D511yescharacteristic
224C2×#67—52no—
225C2×#67—54no—
226#235—102no—
227#235—102no—
228C2×D12—51no—
229C2×C4×D3—52no—
230C2×Dic6—51no—
231C3×M16—22no—
232C3×M16—102no—
233C2×C3×C8—52no—
234C2×C3×C8C22×D512yes—
235#217—54no—
236#217C4×D512yes—
237(C2×D3)⋊C4—54no—
238C4⋊Dic3C4×D512yes—
239Dic3⋊C4—54no—
240C4×Dic3C22×D512yes—
241C2×C3⋊C8—22no—
242C2×C3⋊C8—54no—
243C2×C3⋊C8—51no—
244C2×C3⋊C8—51no—
245C2×C3⋊C8—104no—
246C2×C3⋊C8—104no—
247C2×C3⋊C8C22×D512yes—
248ΓL(1,𝔽25)—104no—
249D3×C8—104no—
250C23×C5C2×C4×D311yescharacteristic
251C22×D5—22no—
252C22×D5—24no—
253C22×D5—32no—
254C22×D5C2×C4×D312yes—
255C2×C4×C5—34no—
256C2×C4×C5C2×C4×D311yescharacteristic
257C2×C4×C5D3×D412yes—
258C2×C4×C5#23712yes—
259C2×C4×C5C23×D311yescharacteristic
260C22⋊D5—64no—
261C2×Dic5—22no—
262C2×Dic5—32no—
263C2×Dic5C2×C4×D312yes—
264D20—68no—
265D20—62no—
266C4×D5—24no—
267C4×D5—22no—
268C4×D5—22no—
269C4×D5—62no—
270C4×D5—62no—
271Dic10—62no—
272C5×C8—22no—
273C5×C8—62no—
274#168—22no—
275#168—32no—
276#168—32no—
277C2×#41—151no—
278C23×C4—51no—
279#131—304no—
280C2×M16—51no—
281C2×M16—152no—
282C2×M16D3×D511yescharacteristic
283C22×C8—31no—
284C22×C8—152no—
285C22×C8—152no—
286C22×C8—151no—
287C22×C8—152no—
288C22×C8—304no—
289#123—152no—
290C22⋊Q8—152no—
291#121—152no—
292#120—152no—
293C4×D4—154no—
294#117—31no—
295C4⋊C8—34no—
296C22⋊C8—54no—
297C22⋊C8—154no—
298#97—152no—
299C4×C8—152no—
300C2×C3×C5—22no—
301C2×C3×C5C2×C4×D411yescharacteristic
302C2×C3×C5C2×#13112yes—
303D15—42no—
304C3×D5—24no—
305C23×C3—52no—
306C23×C3—104no—
307C23×C3—102no—
308C23×C3C2×C4×D511yescharacteristic
309C22×D3—52no—
310C2×C3×C4—52no—
311C2×C3×C4—102no—
312C2×C3×C4—102no—
313C2×C3×C4—102no—
314C2×C3×C4—104no—
315C2×C3×C4C2×C4×D511yescharacteristic
316C2×C3×C4D4×D512yes—
317C2×C3×C4#71312yes—
318C2×C3×C4C23×D511yescharacteristic
319#67—108no—
320#67—104no—
321C2×Dic3—52no—
322C2×Dic3C2×C4×D514yes—
323D12—102no—
324C4×D3—102no—
325C4×D3—102no—
326Dic6—102no—
327C3×C8—22no—
328C3×C8—102no—
329C3⋊C8—22no—
330C3⋊C8—52no—
331C3⋊C8—52no—
332C22×C5—22no—
333C22×C5#67⋊C412yes—
334C22×C5C22×C4×D311yescharacteristic
335C2×D5—28no—
336C2×D5—22no—
337C2×D5—22no—
338C2×D5—62no—
339C2×D5—64no—
340C2×D5#90714yescomplemented
341C4×C5—64no—
342C4×C5#67⋊C412yes—
343C4×C5C2×D3×D411yescharacteristic
344C4×C5C2×#23711yescharacteristic
345Dic5—22no—
346Dic5—62no—
347C24—51no—
348#41—302no—
349#41—302no—
350C2×Q8—151no—
351C2×D4—154no—
352C2×D4—152no—
353C2×D4—151no—
354C22×C4—51no—
355C22×C4—52no—
356C22×C4—52no—
357C22×C4—102no—
358C22×C4—102no—
359C22×C4—152no—
360C22×C4C2×D3×D511yescharacteristic
361M16—22no—
362M16—102no—
363M16—304no—
364C2×C8—32no—
365C2×C8—52no—
366C2×C8—62no—
367C2×C8—154no—
368C2×C8—151no—
369C2×C8—151no—
370C2×C8—304no—
371C2×C8—304no—
372C2×C8—304no—
373C2×C8C2×D3×D512yes—
374C4⋊C4—32no—
375C4⋊C4—154no—
376C22⋊C4—32no—
377C22⋊C4—154no—
378C22⋊C4—154no—
379C42—32no—
380C3×C5#292911yescharacteristic, complemented, Hall
381C22×C3—22no—
382C22×C3—54no—
383C22×C3—108no—
384C22×C3—102no—
385C22×C3—102no—
386C22×C3#403912yes—
387C22×C3C22×C4×D511yescharacteristic
388C2×D3—104no—
389C2×D3—102no—
390C3×C4—102no—
391C3×C4#403912yes—
392C3×C4C2×D4×D511yescharacteristic
393C3×C4C2×#71311yescharacteristic
394Dic3—24no—
395Dic3—102no—
396C2×C5—22no—
397C2×C5C2×#67⋊C411yescharacteristic
398C2×C5C2×#90712yes—
399D5—24no—
400D5—122no—
401C23—52no—
402C23—104no—
403C23—102no—
404C23—152no—
405C23C4×D3×D511yescharacteristic
406Q8—302no—
407D4—308no—
408D4—304no—
409D4—302no—
410C2×C4—34no—
411C2×C4—52no—
412C2×C4—102no—
413C2×C4—104no—
414C2×C4—102no—
415C2×C4—102no—
416C2×C4—152no—
417C2×C4—302no—
418C2×C4—302no—
419C2×C4#676612yes—
420C2×C4C4×D3×D511yescharacteristic
421C2×C4#679012yes—
422C2×C4C22×D3×D511yescharacteristic
423C8—22no—
424C8—62no—
425C8—102no—
426C8—152no—
427C8—152no—
428C2×C3—22no—
429C2×C3—104no—
430C2×C3C2×#403911yescharacteristic
431C2×C3D5×#13112yes—
432D3—202no—
433C5#7862611yescharacteristic, complemented, Sylow
434C22—22no—
435C22—54no—
436C22—108no—
437C22—102no—
438C22—102no—
439C22—304no—
440C22—302no—
441C22#9139612yes—
442C22C2×C4×D3×D511yescharacteristic
443C4—64no—
444C4—102no—
445C4—302no—
446C4#9139612yes—
447C4C2×#676611yescharacteristic
448C4C2×#679011yescharacteristic
449C3#1061080411yescharacteristic, complemented, Sylow
450C2—22no—
451C2—104no—
452C2—602no—
453C2D5×#90712yes—
454C2C2×#9139611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×M16C22
prime radical#11754564C2
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2929
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#91796C2semidirect
3. C22×D5×C3⋊C8C2semidirect
4. C5×#5119C2semidirect
5. C3×#65415C2semidirect
6. #11748350C2semidirect
7. #11748327C2semidirect
8. #11748047C2semidirect
9. #11748043C2semidirect
16. C2×#6705C22semidirect
17. C2×C8×D15C22semidirect
29. C5×Dic3⋊C8C22semidirect
31. #90957C22semidirect
32. #90953C22semidirect
33. Dic3×#168C22semidirect
39. #65415D3semidirect
60. C2×C3⋊#168D4semidirect
83. #5119D5semidirect
158. Dic3⋊C8C2×D5semidirect
210. C2×C3×D5#131semidirect
340. C2×D5#907semidirect
380. C3×C5#2929semidirect
433. C5#78626semidirect
449. C3#10610804semidirect

Maximal subgroups

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

subgroupindex
C2×#917962
#117545642
C22×D5×C3⋊C82
C5×#51192
C3×#654152
#117483502
#117483272
#117480472
#117480432
#106108043
#786265