Finite Group Databasebeta

← #14303112

Subgroups — #14303112

Order 1920.

616 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756285C211yesmaximal, characteristic
2#11754130C211yesmaximal, characteristic
3C2×#90963C211yesmaximal, characteristic, complemented
4C2×#90963C211yesmaximal, characteristic, complemented
5#11748357C211yesmaximal, characteristic
6C5×#4533C211yesmaximal, characteristic, complemented
7C3×#64753C211yesmaximal, characteristic, complemented
8#10599834—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×Dic30C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12#91786—22no—
13#91775C414yes—
14#91764—21no—
15#91758—21no—
16C2×C5×#208C2211yescharacteristic
17C2×C5×#208C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20#91292—22no—
21#91291—22no—
22#91290—22no—
23#90963—21no—
24#90963—22no—
25#90963—22no—
26#90960—21no—
27#69041—51nomaximal, Hall
28#66079—31no—
29#65860—31no—
30C2×#3956—31no—
31C2×#3956—31no—
32#65421—31no—
33C5×#344—31no—
34#64753D311yescharacteristic, complemented
35C22×C3×C4×C5C2311yescharacteristic
36C2×#1220C2×C412yes—
37C22×Dic15C2×C412yes—
38#6817—21no—
39#6817—21no—
40#6817—21no—
41#6817—21no—
42C2×D60D411yescharacteristic
43C2×C4×D15D412yes—
44C2×Dic30—21no—
45C2×Dic30—21no—
46C2×Dic30—21no—
47C2×Dic30—21no—
48C2×Dic30—21no—
49C2×Dic30—21no—
50C2×Dic30D411yescharacteristic
51C3×C5×C4⋊C4—21no—
52C3×C5×C22⋊C4C2×C412yes—
53C3×C42×C5—21no—
54#6714—24no—
55C4⋊Dic15—24no—
56C5×#208—21no—
57C5×#208—21no—
58C5×#208—21no—
59C5×#208D412yes—
60C2×C5×C3⋊C8—21no—
61C2×C5×C3⋊C8—21no—
62C3×#681—21no—
63C3×#681—21no—
64C3×#681—21no—
65C3×#681D412yes—
66C2×C3×#168—21no—
67C2×C3×#168—21no—
68#6651—24no—
69#6648—24no—
70#5745—51no—
71#5526—51no—
72C2×#824—51no—
73C2×#824—51no—
74#5132—51no—
75C3×#344—51no—
76#4533D511yescharacteristic, complemented
77C2×#709—31no—
78C22×Dic10—31no—
79C2×C5×M16—31no—
80C2×C5×M16—31no—
81C5×#117C2×D311yescharacteristic
82C2×#681C2×D311yescharacteristic
83C2×#681C2×D311yescharacteristic
84#4053—62no—
85D5×M16—62no—
86#4047—62no—
87#4043—62no—
88#4032—34no—
89#4021—61no—
90#4015—61no—
91#3956—62no—
92#3956—61no—
93#3956—62no—
94#3955—61no—
95#1915—151noSylow
96C23×C3×C5C22×C411yescharacteristic
97C22×D15C22⋊C412yes—
98C2×C3×C4×C5—22no—
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105#1220—22no—
106#1220—22no—
107C2×Dic15—22no—
108C2×Dic15—22no—
109C2×Dic15—22no—
110C2×Dic15C22⋊C412yes—
111D60—21no—
112D60—21no—
113C4×D15—22no—
114C4×D15—22no—
115Dic30—21no—
116Dic30—21no—
117Dic30—41no—
118Dic30—41no—
119Dic30—41no—
120Dic30—41no—
121C3×#168—22no—
122C3×#168—41no—
123C5×C3⋊C8—22no—
124C5×C3⋊C8—41no—
125C2×#235—51no—
126C22×Dic6—51no—
127C2×C3×M16—51no—
128C2×C3×M16—51no—
129C3×#117C2×D511yescharacteristic
130C2×#208C2×D511yescharacteristic
131C2×#208C2×D511yescharacteristic
132#907—102no—
133D3×M16—102no—
134#901—102no—
135#897—102no—
136#886—54no—
137#875—101no—
138#869—101no—
139#824—102no—
140#824—101no—
141#824—102no—
142#823—101no—
143C22×C4×C5C22×D311yescharacteristic
144C2×C22⋊D5—32no—
145C22×Dic5—32no—
146#709—61no—
147#709—61no—
148#709—61no—
149#709—61no—
150C2×D20—31no—
151C2×C4×D5—32no—
152C2×Dic10—31no—
153C2×Dic10—61no—
154C2×Dic10—61no—
155C2×Dic10—61no—
156C2×Dic10—61no—
157C2×Dic10—61no—
158C2×Dic10—61no—
159C5×M16—32no—
160C5×M16—61no—
161C5×M16—61no—
162C5×M16—61no—
163C2×C5×C8—61no—
164C2×C5×C8—61no—
165C5×C4⋊C4—21no—
166C5×C22⋊C4C4×D312yes—
167C42×C5—21no—
168#685—64no—
169C4⋊Dic5—64no—
170#681—21no—
171#681—21no—
172#681—21no—
173#681D1212yes—
174C2×#168—21no—
175C2×#168—21no—
176#676—64no—
177C8×D5—64no—
178#568—151no—
179#536—151no—
180#413—151no—
181C2×#101—151no—
182C2×#101—151no—
183#344—31no—
184#344—51no—
185C22×C3×C5—41no—
186C22×C3×C5C2×C22⋊C411yescharacteristic
187C22×C3×C5C4×D411yescharacteristic
188C22×C3×C5C4×D411yescharacteristic
189C2×D15—22no—
190C2×D15—42no—
191C3×C4×C5—42no—
192C3×C4×C5#12011yescharacteristic
193C3×C4×C5#12111yescharacteristic
194C3×C4×C5#12111yescharacteristic
195C3×C4×C5#12311yescharacteristic
196Dic15—22no—
197Dic15—42no—
198C22×C3×C4C22×D511yescharacteristic
199C2×#67—52no—
200C22×Dic3—52no—
201#235—101no—
202#235—101no—
203#235—101no—
204#235—101no—
205C2×D12—51no—
206C2×C4×D3—52no—
207C2×Dic6—51no—
208C2×Dic6—101no—
209C2×Dic6—101no—
210C2×Dic6—101no—
211C2×Dic6—101no—
212C2×Dic6—101no—
213C2×Dic6—101no—
214C3×M16—52no—
215C3×M16—101no—
216C3×M16—101no—
217C3×M16—101no—
218C2×C3×C8—101no—
219C2×C3×C8—101no—
220C3×C4⋊C4—21no—
221C3×C22⋊C4C4×D512yes—
222C3×C42—21no—
223(C2×D3)⋊C4—104no—
224C4⋊Dic3—104no—
225#208—21no—
226#208—21no—
227#208—21no—
228#208D2012yes—
229C2×C3⋊C8—21no—
230C2×C3⋊C8—21no—
231ΓL(1,𝔽25)—104no—
232D3×C8—104no—
233C23×C5C2×C4×D311yescharacteristic
234C22×D5—32no—
235C2×C4×C5—22no—
236C2×C4×C5C2×D1211yescharacteristic
237C2×C4×C5#23511yescharacteristic
238C2×C4×C5D3×D411yescharacteristic
239C2×C4×C5D3×D411yescharacteristic
240C2×C4×C5D3×D411yescharacteristic
241C2×C4×C5#23911yescharacteristic
242C22⋊D5—62no—
243C22⋊D5—62no—
244C2×Dic5—32no—
245C2×Dic5—62no—
246C2×Dic5—62no—
247C2×Dic5—62no—
248D20—61no—
249D20—61no—
250C4×D5—62no—
251C4×D5—62no—
252Dic10—61no—
253Dic10—61no—
254Dic10—121no—
255Dic10—121no—
256Dic10—121no—
257Dic10—121no—
258C5×C8—62no—
259C5×C8—121no—
260#168—22no—
261#168—41no—
262C2×#41—151no—
263C22×Q8—151no—
264#131—302no—
265#131—302no—
266C2×M16—31no—
267C2×M16—31no—
268C2×M16—51no—
269C2×M16—51no—
270C2×M16—302no—
271C4⋊Q8—301no—
272#124—301no—
273#123—154no—
274C22⋊Q8—302no—
275#117D3×D511yescharacteristic
276#101—302no—
277#101—302no—
278#101—301no—
279#100—301no—
280C2×C3×C5—21no—
281C2×C3×C5—21no—
282C2×C3×C5—21no—
283C2×C3×C5#38611yescharacteristic
284D15—42no—
285C23×C3C2×C4×D511yescharacteristic
286C22×D3—52no—
287C2×C3×C4—22no—
288C2×C3×C4C2×D2011yescharacteristic
289C2×C3×C4#70911yescharacteristic
290C2×C3×C4D4×D511yescharacteristic
291C2×C3×C4D4×D511yescharacteristic
292C2×C3×C4D4×D511yescharacteristic
293C2×C3×C4#71311yescharacteristic
294#67—102no—
295#67—102no—
296C2×Dic3—52no—
297C2×Dic3—102no—
298C2×Dic3—102no—
299C2×Dic3—102no—
300D12—101no—
301D12—101no—
302C4×D3—102no—
303C4×D3—102no—
304Dic6—101no—
305Dic6—101no—
306Dic6—201no—
307Dic6—201no—
308Dic6—201no—
309Dic6—201no—
310C3×C8—102no—
311C3×C8—201no—
312C3⋊C8—22no—
313C3⋊C8—41no—
314C22×C5—41no—
315C22×C5C4×D1211yescharacteristic
316C22×C5D3×C22⋊C411yescharacteristic
317C22×C5#89311yescharacteristic
318C2×D5—62no—
319C2×D5—122no—
320C4×C5—42no—
321C4×C5#88211yescharacteristic
322C4×C5#88411yescharacteristic
323C4×C5#89411yescharacteristic
324C4×C5#89511yescharacteristic
325Dic5—62no—
326Dic5—122no—
327#41—301no—
328#41—301no—
329#41—301no—
330#41—301no—
331C2×Q8—151no—
332C2×Q8—301no—
333C2×Q8—301no—
334C2×Q8—301no—
335C2×Q8—301no—
336C2×Q8—301no—
337C2×Q8—301no—
338C2×D4—152no—
339C2×D4—151no—
340C22×C4—152no—
341C22×C4—152no—
342C22×C4C2×D3×D511yescharacteristic
343M16—32no—
344M16—52no—
345M16—61no—
346M16—61no—
347M16—61no—
348M16—101no—
349M16—101no—
350M16—101no—
351M16—304no—
352C2×C8—61no—
353C2×C8—61no—
354C2×C8—101no—
355C2×C8—101no—
356C2×C8—304no—
357C4⋊C4—21no—
358C4⋊C4—304no—
359C22⋊C4—304no—
360C22⋊C4#120012yes—
361C42—21no—
362C3×C5#191511yescharacteristic, complemented, Hall
363C22×C3—41no—
364C22×C3C4×D2011yescharacteristic
365C22×C3D5×C22⋊C411yescharacteristic
366C22×C3#403911yescharacteristic
367C2×D3—102no—
368C2×D3—202no—
369C3×C4—42no—
370C3×C4#402811yescharacteristic
371C3×C4#403011yescharacteristic
372C3×C4#404011yescharacteristic
373C3×C4#404111yescharacteristic
374Dic3—102no—
375Dic3—202no—
376C2×C5—21no—
377C2×C5—21no—
378C2×C5—21no—
379C2×C5#466511yescharacteristic
380D5—122no—
381C23—152no—
382C23C2×#120011yescharacteristic
383Q8—301no—
384Q8—301no—
385Q8—601no—
386Q8—601no—
387Q8—601no—
388Q8—601no—
389D4—302no—
390D4—302no—
391D4—301no—
392D4—301no—
393C2×C4—22no—
394C2×C4—152no—
395C2×C4—302no—
396C2×C4—302no—
397C2×C4—302no—
398C2×C4—302no—
399C2×C4—302no—
400C2×C4#676911yescharacteristic
401C2×C4#677311yescharacteristic
402C2×C4D5×D1211yescharacteristic
403C2×C4D3×D2011yescharacteristic
404C2×C4#679011yescharacteristic
405C2×C4#679011yescharacteristic
406C8—62no—
407C8—102no—
408C8—121no—
409C8—201no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3#6495411yescharacteristic
414D3—202no—
415C5#6904111yescharacteristic, complemented, Sylow
416C22—41no—
417C22—302no—
418C22—602no—
419C22#9141811yescharacteristic
420C22#9142811yescharacteristic
421C22#9156111yescharacteristic
422C4—42no—
423C4—302no—
424C4—602no—
425C4#9142011yescharacteristic
426C4#9143311yescharacteristic
427C4#9145911yescharacteristic
428C4#9147611yescharacteristic
429C3#1059983411yescharacteristic, complemented, Sylow
430C2—21no—
431C2—21no—
432C2—21no—
433C2—602no—
434C2#1174890411yescharacteristic
subgroupG/H
centerC2#11748904
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1915
LCSG ▷ C23×C3×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
3. C2×#90963C2semidirect
4. C2×#90963C2semidirect
6. C5×#4533C2semidirect
7. C3×#64753C2semidirect
34. #64753D3semidirect
76. #4533D5semidirect
362. C3×C5#1915semidirect
415. C5#69041semidirect
429. C3#10599834semidirect

Maximal subgroups

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

subgroupindex
#117562852
#117541302
C2×#909632
#117483572
C5×#45332
C3×#647532
#105998343
#690415