Finite Group Databasebeta

← #14302955

Subgroups — #14302955

Order 1920.

628 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756275C211yesmaximal, characteristic, complemented
2#11754252C211yesmaximal, characteristic
3C3×#65294C211yesmaximal, characteristic
4#11748420C211yesmaximal, characteristic
5C2×#90963C211yesmaximal, characteristic, complemented
6C5×#4531C211yesmaximal, characteristic, complemented
7#11745971C211yesmaximal, characteristic, complemented
8#10599501—31nomaximal, Hall
9C22×Dic30C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12#91815C2211yescharacteristic
13#91776—22no—
14#91766—22no—
15C4×Dic30—22no—
16C5×#926C2211yescharacteristic
17C2×C5×#208C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19#91537—22no—
20#91389C412yescomplemented
21#91364C412yescomplemented
22#91360—22no—
23C3×#3937—22no—
24#90976—22no—
25#90963—22no—
26#70411—51nomaximal, Hall
27#65860—31no—
28#65850—31no—
29#65428—31no—
30C2×#3956—31no—
31#65294D311yescharacteristic
32C5×H(3,ℤ/4)—31no—
33#64751—31no—
34C22×C3×C4×C5C2311yescharacteristic
35C22×Dic15D412yes—
36C2×Dic30—21no—
37C2×Dic30—21no—
38C2×Dic30—21no—
39C2×Dic30—21no—
40C2×Dic30C2×C412yes—
41C2×Dic30D412yes—
42C2×C3×C22⋊D5—21no—
43C3×#709—21no—
44C3×#709—21no—
45C3×#709—21no—
46C3×#709—21no—
47C2×C3×D20C2×C411yescharacteristic
48C2×C3×C4×D5—21no—
49C2×C3×Dic10C2×C411yescharacteristic
50C3×C5×C4⋊C4—21no—
51C3×C5×C22⋊C4—21no—
52C3×C42×C5D412yes—
53#6719—21no—
54C4⋊Dic15—21no—
55#6712—24no—
56C4×Dic15—24no—
57C4×Dic15D412yes—
58C5×#217—21no—
59C5×C4⋊Dic3—21no—
60C4×C5×Dic3C2×C412yes—
61C5×#208—21no—
62C5×#208—21no—
63C2×C5×C3⋊C8—21no—
64C3×#681—21no—
65C3×#681—21no—
66C2×C3×#168—21no—
67Dic3⋊Dic5—24no—
68#6665—24no—
69#5825—51no—
70#5516—51no—
71C3×#421—51no—
72#5236—51no—
73C2×#824—51no—
74#4557—51no—
75#4531D511yescharacteristic, complemented
76C2×#709C2×D311yescharacteristic
77C22×Dic10—31no—
78C2×C5×M16—31no—
79C5×#117—31no—
80C5×#117C2×D311yescharacteristic
81#4072—31no—
82C2×#681C2×D311yescharacteristic
83#4043—62no—
84#4033—62no—
85#4032—62no—
86#4023—62no—
87#4021—32no—
88#4015—32no—
89C4×Dic10—62no—
90#3957—62no—
91#3956—62no—
92#3937—22no—
93#1912—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C3×D5—21no—
96C2×C3×C4×C5—22no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×Dic15—22no—
104C2×Dic15—22no—
105C2×Dic15—22no—
106C2×Dic15C22⋊C414yes—
107Dic30—22no—
108Dic30—22no—
109Dic30—22no—
110Dic30—22no—
111C2×C5×Dic3—22no—
112C3×C22⋊D5—41no—
113C3×C22⋊D5—41no—
114C2×C3×Dic5—21no—
115C3×D20—21no—
116C3×D20—21no—
117C3×C4×D5—41no—
118C3×C4×D5—41no—
119C3×Dic10—21no—
120C3×Dic10—21no—
121C3×#168—41no—
122C5×C3⋊C8—41no—
123C2×C3×#41—51no—
124C22×Dic6—51no—
125C2×C3×M16—51no—
126C3×#117C2×D511yescharacteristic
127#944—52no—
128#936—52no—
129#935—102no—
130#926—51no—
131#926C2×D511yescharacteristic
132#924—102no—
133C2×#208C2×D511yescharacteristic
134#887—102no—
135#877—102no—
136C4×Dic6—102no—
137C3×#104—102no—
138#837—102no—
139#824—102no—
140C22×C4×C5C22×D311yescharacteristic
141C2×C22⋊D5—21no—
142C22×Dic5—32no—
143#709—21no—
144#709—21no—
145#709—21no—
146#709—21no—
147C2×D20C4×D311yescharacteristic
148C2×C4×D5—21no—
149C2×Dic10—32no—
150C2×Dic10—32no—
151C2×Dic10—61no—
152C2×Dic10—61no—
153C2×Dic10—61no—
154C2×Dic10—61no—
155C2×Dic10C4×D311yescharacteristic
156C5×M16—61no—
157C5×M16—61no—
158C2×C5×C8—61no—
159C5×C4⋊C4—21no—
160C5×C4⋊C4—61no—
161C5×C22⋊C4—21no—
162C5×C22⋊C4—61no—
163C42×C5—32no—
164C42×C5#6712yes—
165C22⋊Dic5—61no—
166#685—64no—
167C4⋊Dic5—64no—
168C4⋊Dic5—61no—
169#683—64no—
170C4×Dic5—32no—
171C4×Dic5—64no—
172#681—21no—
173#681—21no—
174C2×#168—21no—
175#536—151no—
176#519—151no—
177#421—51no—
178#421—151no—
179C2×#101—151no—
180H(3,ℤ/4)—31no—
181H(3,ℤ/4)—151no—
182C22×C3×C5—41no—
183C22×C3×C5C2×C22⋊C411yescharacteristic
184C22×C3×C5#12011yescharacteristic
185C22×C3×C5#12311yescharacteristic
186C2×C3×D5—42no—
187C2×C3×D5—41no—
188C3×C4×C5—42no—
189C3×C4×C5C4×D411yescharacteristic
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5#12111yescharacteristic
192C3×C4×C5#12111yescharacteristic
193Dic15—24no—
194Dic15—42no—
195C3×Dic5—41no—
196C5×Dic3—42no—
197C3×#41—101no—
198C3×#41—101no—
199C3×#41—101no—
200C3×#41—101no—
201C2×C3×Q8—51no—
202C2×C3×D4—51no—
203C2×C3×D4—101no—
204C22×C3×C4—101no—
205C22×C3×C4C22×D511yescharacteristic
206C22×Dic3—52no—
207C2×Dic6—52no—
208C2×Dic6—52no—
209C2×Dic6—101no—
210C2×Dic6—101no—
211C2×Dic6—101no—
212C2×Dic6—101no—
213C3×M16—101no—
214C3×M16—101no—
215C2×C3×C8—101no—
216C3×C4⋊C4—21no—
217C3×C22⋊C4—21no—
218C3×C42D2012yes—
219#217—21no—
220#217—104no—
221#217—101no—
222C4⋊Dic3—21no—
223C4⋊Dic3—101no—
224Dic3⋊C4—104no—
225Dic3⋊C4—104no—
226C4×Dic3—52no—
227C4×Dic3—104no—
228C4×Dic3C4×D512yes—
229#208—21no—
230#208—21no—
231C2×C3⋊C8—21no—
232C23×C5D3×D411yescharacteristic
233C22×D5—21no—
234C2×C4×C5—22no—
235C2×C4×C5—62no—
236C2×C4×C5C2×C4×D311yescharacteristic
237C2×C4×C5#23511yescharacteristic
238C2×C4×C5D3×D411yescharacteristic
239C2×C4×C5D3×D411yescharacteristic
240C2×C4×C5#23711yescharacteristic
241C2×C4×C5C2×#6711yescharacteristic
242C22⋊D5—41no—
243C22⋊D5—41no—
244C2×Dic5—21no—
245C2×Dic5—34no—
246C2×Dic5—62no—
247C2×Dic5—62no—
248C2×Dic5—62no—
249D20—21no—
250D20—21no—
251C4×D5—41no—
252C4×D5—41no—
253Dic10—21no—
254Dic10—21no—
255Dic10—62no—
256Dic10—62no—
257Dic10—62no—
258Dic10—62no—
259C5×C8—121no—
260#168—41no—
261C2×#41—51no—
262C22×Q8—151no—
263C2×M16—31no—
264C2×M16—51no—
265C4⋊Q8—152no—
266#124—152no—
267#123—302no—
268C22⋊Q8—302no—
269C4×Q8—302no—
270C4×Q8—302no—
271#117—31no—
272#117—151no—
273#117—302no—
274#117D3×D511yescharacteristic
275#104—102no—
276#104—302no—
277#101—302no—
278C2×C3×C5—21no—
279C2×C3×C5—21no—
280C2×C3×C5—21no—
281C2×C3×C5#38611yescharacteristic
282C3×D5—81no—
283C23×C3—101no—
284C23×C3D4×D511yescharacteristic
285C3×Q8—101no—
286C3×Q8—101no—
287C3×D4—101no—
288C3×D4—101no—
289C3×D4—201no—
290C3×D4—201no—
291C2×C3×C4—22no—
292C2×C3×C4—101no—
293C2×C3×C4—201no—
294C2×C3×C4—201no—
295C2×C3×C4C2×C4×D511yescharacteristic
296C2×C3×C4C2×D2011yescharacteristic
297C2×C3×C4#70911yescharacteristic
298C2×C3×C4D4×D511yescharacteristic
299C2×C3×C4D4×D511yescharacteristic
300C2×C3×C4#71311yescharacteristic
301C2×Dic3—22no—
302C2×Dic3—54no—
303C2×Dic3—102no—
304C2×Dic3—102no—
305C2×Dic3—102no—
306Dic6—102no—
307Dic6—102no—
308Dic6—102no—
309Dic6—102no—
310C3×C8—201no—
311C3⋊C8—41no—
312C22×C5—41no—
313C22×C5D3×C22⋊C411yescharacteristic
314C22×C5#88311yescharacteristic
315C22×C5#93711yescharacteristic
316C2×D5—42no—
317C2×D5—41no—
318C4×C5—42no—
319C4×C5—122no—
320C4×C5#67⋊C411yescharacteristic
321C4×C5#88411yescharacteristic
322C4×C5C4×#6711yescharacteristic
323C4×C5#93811yescharacteristic
324Dic5—41no—
325Dic5—64no—
326Dic5—122no—
327#41—101no—
328#41—101no—
329#41—101no—
330#41—101no—
331C2×Q8—51no—
332C2×Q8—152no—
333C2×Q8—152no—
334C2×Q8—301no—
335C2×Q8—301no—
336C2×Q8—301no—
337C2×Q8—301no—
338C2×D4—51no—
339C2×D4—101no—
340C22×C4—101no—
341C22×C4—152no—
342C22×C4C2×D3×D511yescharacteristic
343M16—61no—
344M16—61no—
345M16—101no—
346M16—101no—
347C2×C8—61no—
348C2×C8—101no—
349C4⋊C4—21no—
350C4⋊C4—61no—
351C4⋊C4—304no—
352C4⋊C4—304no—
353C4⋊C4—301no—
354C22⋊C4—21no—
355C22⋊C4—61no—
356C22⋊C4—304no—
357C22⋊C4—301no—
358C42—32no—
359C42—152no—
360C42—304no—
361C42#120212yes—
362C3×C5#191211yescharacteristic, complemented, Hall
363C22×C3—41no—
364C22×C3—202no—
365C22×C3—201no—
366C22×C3D5×C22⋊C411yescharacteristic
367C22×C3#402811yescharacteristic
368C22×C3#404011yescharacteristic
369C3×C4—42no—
370C3×C4—201no—
371C3×C4C4×D2011yescharacteristic
372C3×C4#403011yescharacteristic
373C3×C4#403911yescharacteristic
374C3×C4#404111yescharacteristic
375Dic3—42no—
376Dic3—104no—
377Dic3—202no—
378C2×C5—21no—
379C2×C5—21no—
380C2×C5—21no—
381C2×C5#495611yescharacteristic
382D5—81no—
383C23—101no—
384C23#679011yescharacteristic
385Q8—101no—
386Q8—101no—
387Q8—302no—
388Q8—302no—
389Q8—302no—
390Q8—302no—
391D4—101no—
392D4—101no—
393D4—201no—
394D4—201no—
395C2×C4—22no—
396C2×C4—62no—
397C2×C4—101no—
398C2×C4—154no—
399C2×C4—201no—
400C2×C4—201no—
401C2×C4—302no—
402C2×C4—302no—
403C2×C4—302no—
404C2×C4#676611yescharacteristic
405C2×C4#677111yescharacteristic
406C2×C4C4×D3×D511yescharacteristic
407C2×C4#677711yescharacteristic
408C2×C4C2×#120211yescharacteristic
409C2×C4#679011yescharacteristic
410C8—121no—
411C8—201no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—401no—
416C2×C3#6495411yescharacteristic
417C5#7041111yescharacteristic, complemented, Sylow
418C22—41no—
419C22—202no—
420C22—201no—
421C22#9135411yescharacteristic
422C22#9147311yescharacteristic
423C22#9157211yescharacteristic
424C4—42no—
425C4—122no—
426C4—201no—
427C4—304no—
428C4—602no—
429C4#9139611yescharacteristic
430C4C4×#120211yescharacteristic
431C4#9146111yescharacteristic
432C4#9146511yescharacteristic
433C3#1059950111yescharacteristic, complemented, Sylow
434C2—21no—
435C2—21no—
436C2—21no—
437C2—401no—
438C2#1174891711yescharacteristic
subgroupG/H
centerC2#11748917
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radicalC2×C3×#709C22
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1912
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #11756275C2semidirect
5. C2×#90963C2semidirect
6. C5×#4531C2semidirect
7. #11745971C2semidirect
20. #91389C4semidirect
21. #91364C4semidirect
75. #4531D5semidirect
362. C3×C5#1912semidirect
417. C5#70411semidirect
433. C3#10599501semidirect

Maximal subgroups

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

subgroupindex
#117562752
#117542522
C3×#652942
#117484202
C2×#909632
C5×#45312
#117459712
#105995013
#704115