Finite Group Databasebeta

← #14417773

Subgroups — #14417773

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91277C211yesmaximal, characteristic
2#11752520C212yesmaximal, complemented
3#11750809C211yesmaximal, characteristic, complemented
4C5×#4716C211yesmaximal, characteristic, complemented
5C3×#65000C211yesmaximal, characteristic, complemented
6#11748142C212yesmaximal, complemented
7#11747888C211yesmaximal, characteristic, complemented
8#11747815C211yesmaximal, characteristic, complemented
9#11747735C212yesmaximal, complemented
10#11747632C211yesmaximal, characteristic, complemented
11C4×#6655C212yesmaximal, complemented
12#10611563—31nomaximal, Hall
13C2×#6766C2212yes—
14C2×#6705C2211yescharacteristic
15C2×C8×D15C2211yescharacteristic
16#91761C2211yescharacteristic
17C2×C5×Dic12C2211yescharacteristic
18C4×C5×Dic6C2212yes—
19C2×C3×D40C2211yescharacteristic
20C3×C4×D20C2212yes—
21#91444—22no—
22#91437C2212yes—
23#91434C2212yes—
24#91395—22no—
25#91393—22no—
26D5×Dic3⋊C4—22no—
27#91344C2212yes—
28C2×#6655C2212yes—
29#91277C418yescomplemented
30C3×C5×#97C2211yescharacteristic
31#91099C2211yescharacteristic
32C8×Dic15C2211yescharacteristic
33C4×C3⋊#168C2211yescharacteristic
34C5×#817C2211yescharacteristic
35C5×#816C2212yes—
36C3×#3953C2212yes—
37C3×#3949C2211yescharacteristic
38#90986C2212yes—
39#90972C2212yes—
40#90964C2212yes—
41#79868—51nomaximal, Hall
42C2×#4065—31no—
43#65908—32no—
44C5×#441—31no—
45#65473—31no—
46C4×#688—32no—
47#65158—31no—
48D5×#106—31no—
49#65092—32no—
50#65077—32no—
51#65000D311yescharacteristic, complemented
52#64997—31no—
53C2×C4×D15C2311yescharacteristic
54C2×C5×Dic6C2312yes—
55C2×C3×D20C2312yes—
56C2×C3×C4×D5—22no—
57C2×#1202—22no—
58C2×#1200—22no—
59C2×D5×Dic3—22no—
60C2×D5×Dic3—22no—
61#6766—24no—
62#6766C2×C418yescomplemented
63C2×C3×C5×C8C2311yescharacteristic
64C2×C3×C5×C8C2311yescharacteristic
65C3×C42×C5C2311yescharacteristic
66#6714D412yes—
67#6712D412yes—
68C4×Dic15C2311yescharacteristic
69C2×C3⋊#168C2311yescharacteristic
70C2×C3⋊#168C2311yescharacteristic
71#6705—22no—
72C8×D15C2×C414yescomplemented
73C5×C4⋊Dic3C2312yes—
74C5×Dic3⋊C4—22no—
75C4×C5×Dic3—22no—
76C5×Dic12C2×C414yescomplemented
77C3×#685—22no—
78C3×C4⋊Dic5C2312yes—
79C3×D40C2×C414yescomplemented
80Dic3⋊Dic5—22no—
81#6669—22no—
82#6665—22no—
83Dic3×Dic5—22no—
84#6655C2×C418yescomplemented
85C2×#912—51no—
86#5546—52no—
87C3×#442—51no—
88#5152—51no—
89C4×#214—52no—
90D3×#106—51no—
91#4853—51no—
92#4771—52no—
93#4758—52no—
94#4716D511yescharacteristic, complemented
95#4708—51no—
96C2×#713—32no—
97C2×C5×Q16—31no—
98C4×C5×Q8—32no—
99Q8×Dic5—32no—
100C2×#688—32no—
101#4065—38no—
102C2×D40C2×D311yescharacteristic
103C2×#676—31no—
104C2×C8×D5—31no—
105#4039—32no—
106#4039—62no—
107D5×C4⋊C4—32no—
108D5×C4⋊C4—62no—
109C4×D20—62no—
110C4×D20C2×D312yes—
111#4018—31no—
112#4018—62no—
113C5×#106—31no—
114C5×#103—32no—
115C5×#97C2×D311yescharacteristic
116#3967—32no—
117#3953C2×D312yes—
118#3949C2×D311yescharacteristic
119#3947—31no—
120C8×Dic5—31no—
121#3941—32no—
122#3940—32no—
123C4×#168—31no—
124#2952—151noSylow
125C22×D15C2×D411yescharacteristic
126C22×C3×D5—22no—
127C2×C3×C4×C5C2×D412yes—
128C2×C3×C4×C5C2411yescharacteristic
129C2×Dic15C2×D412yes—
130C2×Dic15C2×D411yescharacteristic
131C4×D15C22×C412yes—
132C4×D15#4112yes—
133C2×C5×Dic3—22no—
134C2×C5×Dic3—22no—
135C5×Dic6—22no—
136C5×Dic6C22×C414yes—
137C2×C3×Dic5—22no—
138C3×D20—22no—
139C3×D20C22×C414yes—
140C3×C4×D5—82no—
141#1202—28no—
142#1200—82no—
143D5×Dic3—28no—
144D5×Dic3—82no—
145C3×C5×C8—21no—
146C3×C5×C8C22×C412yes—
147C3⋊#168—21no—
148C3⋊#168C22×C412yes—
149C2×#237—52no—
150C2×C3×D8—51no—
151C3×C4×D4—52no—
152D4×Dic3—52no—
153C2×#214—52no—
154C4×#67—102no—
155C2×Dic3⋊C4—102no—
156#912—58no—
157C2×Dic12C2×D511yescharacteristic
158C2×ΓL(1,𝔽25)—51no—
159C2×D3×C8—51no—
160D3×C4⋊C4—52no—
161#887—52no—
162#67⋊C4—102no—
163#877—102no—
164#872—51no—
165C4×Dic6C2×D512yes—
166C3×#106—51no—
167C3×#102—52no—
168C3×#97C2×D511yescharacteristic
169#832—52no—
170#817C2×D511yescharacteristic
171#816C2×D512yes—
172#815—51no—
173C8×Dic3—51no—
174#810—52no—
175#808—52no—
176C4×C3⋊C8—51no—
177C2×C5×Q8—32no—
178#713—38no—
179#713—64no—
180C2×D20—62no—
181C2×D20C22×D312yes—
182C2×C4×D5—22no—
183C2×C4×D5—31no—
184C2×C4×D5—62no—
185C2×C4×D5—62no—
186C2×C4×D5—62no—
187C5×Q16—34no—
188C2×C5×C8C22×D311yescharacteristic
189C2×C5×C8C22×D311yescharacteristic
190C5×C4⋊C4—32no—
191C5×C4⋊C4—62no—
192C42×C5—62no—
193C42×C5C22×D311yescharacteristic
194#688—38no—
195#685—22no—
196#685—32no—
197#685—62no—
198C4⋊Dic5—62no—
199C4⋊Dic5C22×D312yes—
200#683—32no—
201#683—62no—
202C4×Dic5—31no—
203C4×Dic5—62no—
204C2×#168—31no—
205C2×#168—31no—
206D40C4×D314yescomplemented
207#676—62no—
208C8×D5—34no—
209C2×#135—151no—
210#520—152no—
211#442—51no—
212#442—151no—
213#441—31no—
214#441—151no—
215C4×SD16—152no—
216C4×SD16—152no—
217C2×#106—151no—
218#417—152no—
219#405—151no—
220C22×C3×C5C22×D411yescharacteristic
221C2×D15—22no—
222C2×D15C4×D412yes—
223C2×C3×D5—24no—
224C2×C3×D5—42no—
225C2×C3×D5—42no—
226C3×C4×C5—22no—
227C3×C4×C5C23×C411yescharacteristic
228C3×C4×C5C2×#4111yescharacteristic
229Dic15—22no—
230Dic15C4×D412yes—
231C3×Dic5—42no—
232C5×Dic3—24no—
233C5×Dic3—42no—
234C2×C3×D4—52no—
235C22×C3×C4—102no—
236C2×#67—102no—
237C22×Dic3—102no—
238C22×Dic3—102no—
239#237—58no—
240#237—104no—
241C2×C4×D3—51no—
242C2×C4×D3—102no—
243C2×Dic6C22×D512yes—
244C3×D8—54no—
245C2×C3×C8C22×D511yescharacteristic
246C2×C3×C8C22×D511yescharacteristic
247C3×C4⋊C4—52no—
248C3×C22⋊C4—102no—
249C3×C42C22×D511yescharacteristic
250#217—102no—
251#214—58no—
252(C2×D3)⋊C4—52no—
253C4⋊Dic3C22×D512yes—
254Dic3⋊C4—22no—
255Dic3⋊C4—52no—
256Dic3⋊C4—102no—
257Dic3⋊C4—102no—
258C4×Dic3—22no—
259C4×Dic3—51no—
260C4×Dic3—102no—
261C2×C3⋊C8—51no—
262C2×C3⋊C8—51no—
263Dic12C4×D514yescomplemented
264ΓL(1,𝔽25)—102no—
265D3×C8—54no—
266C22×D5—22no—
267C22×D5—31no—
268C5×Q8—34no—
269C5×Q8—62no—
270C2×C4×C5—62no—
271C2×C4×C5—62no—
272C2×C4×C5D3×D412yes—
273C2×C4×C5C23×D311yescharacteristic
274C2×Dic5—22no—
275C2×Dic5—31no—
276C2×Dic5—32no—
277D20—22no—
278D20—68no—
279D20C2×C4×D314yes—
280C4×D5—32no—
281C4×D5—32no—
282C4×D5—68no—
283C4×D5—82no—
284C4×D5—242no—
285C4×D5—242no—
286C5×C8—21no—
287C5×C8C2×C4×D312yes—
288#168—32no—
289#168—61no—
290C2×#41—152no—
291#135—158no—
292C2×Q16—31no—
293C2×SD16—152no—
294C2×D8—51no—
295C2×M16—151no—
296C22×C8—151no—
297C4×Q8—32no—
298C4×Q8—152no—
299C4×D4—52no—
300C4×D4—152no—
301C4×D4—302no—
302C4×D4—302no—
303#117—151no—
304#117—302no—
305C2×C4⋊C4—152no—
306C2×C4⋊C4—302no—
307#106—31no—
308#106—51no—
309#106—152no—
310#103—32no—
311#103—152no—
312#102—52no—
313#102—152no—
314#97—151no—
315#97D3×D511yescharacteristic
316C4×C8—151no—
317C4×C8—151no—
318C2×C3×C5C2×C4×D411yescharacteristic
319C2×C3×C5#57712yes—
320D15—22no—
321C3×D5—44no—
322C23×C3—102no—
323C22×D3—51no—
324C3×D4—54no—
325C3×D4—102no—
326C2×C3×C4—102no—
327C2×C3×C4—402no—
328C2×C3×C4D4×D512yes—
329C2×C3×C4C23×D511yescharacteristic
330#67—108no—
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—51no—
334C2×Dic3—52no—
335C2×Dic3—108no—
336C2×Dic3—402no—
337C4×D3—52no—
338C4×D3—52no—
339C4×D3—402no—
340Dic6—22no—
341Dic6C2×C4×D514yes—
342C3×C8—21no—
343C3×C8C2×C4×D512yes—
344C3⋊C8—52no—
345C3⋊C8—101no—
346C22×C5C2×D3×D411yescharacteristic
347C2×D5—24no—
348C2×D5—32no—
349C2×D5—42no—
350C2×D5—42no—
351C2×D5—62no—
352C4×C5—22no—
353C4×C5—64no—
354C4×C5—122no—
355C4×C5C22×C4×D311yescharacteristic
356C4×C5D3×#4111yescharacteristic
357Dic5—32no—
358Dic5—42no—
359Dic5—62no—
360#41—158no—
361#41—304no—
362C2×Q8—32no—
363C2×D4—52no—
364C2×D4—302no—
365C22×C4—102no—
366C22×C4—151no—
367C22×C4—302no—
368C22×C4—302no—
369C22×C4—302no—
370Q16—34no—
371SD16—158no—
372D8—54no—
373M16—302no—
374C2×C8—151no—
375C2×C8—154no—
376C2×C8—151no—
377C2×C8C2×D3×D511yescharacteristic
378C2×C8C2×D3×D511yescharacteristic
379C4⋊C4—32no—
380C4⋊C4—52no—
381C4⋊C4—62no—
382C4⋊C4—152no—
383C4⋊C4—302no—
384C4⋊C4—302no—
385C22⋊C4—102no—
386C22⋊C4—152no—
387C22⋊C4—302no—
388C42—62no—
389C42—151no—
390C42—302no—
391C42C2×D3×D511yescharacteristic
392C3×C5#295211yescharacteristic, complemented, Hall
393C22×C3—104no—
394C22×C3—202no—
395C22×C3—202no—
396C22×C3C2×D4×D511yescharacteristic
397C2×D3—52no—
398C2×D3—102no—
399C3×C4—22no—
400C3×C4—202no—
401C3×C4C22×C4×D511yescharacteristic
402C3×C4D5×#4111yescharacteristic
403Dic3—24no—
404Dic3—42no—
405Dic3—52no—
406Dic3—102no—
407C2×C5C4×D3×D411yescharacteristic
408C2×C5#577512yes—
409D5—44no—
410D5—62no—
411C23—102no—
412C23—151no—
413Q8—34no—
414Q8—62no—
415D4—54no—
416D4—102no—
417D4—308no—
418C2×C4—62no—
419C2×C4—62no—
420C2×C4—102no—
421C2×C4—151no—
422C2×C4—152no—
423C2×C4—152no—
424C2×C4—152no—
425C2×C4—308no—
426C2×C4—402no—
427C2×C4—1202no—
428C2×C4—1202no—
429C2×C4#677712yes—
430C2×C4C22×D3×D511yescharacteristic
431C8—21no—
432C8—152no—
433C8—301no—
434C8C4×D3×D512yes—
435C2×C3—204no—
436C2×C3C4×D4×D511yescharacteristic
437C2×C3#6611212yes—
438D3—102no—
439C5#7986811yescharacteristic, complemented, Sylow
440C22—104no—
441C22—152no—
442C22—202no—
443C22—202no—
444C22—302no—
445C22C2×#677711yescharacteristic
446C4—22no—
447C4—64no—
448C4—122no—
449C4—152no—
450C4—202no—
451C4—302no—
452C4C2×C4×D3×D511yescharacteristic
453C4#9201611yescharacteristic
454C3#1061156311yescharacteristic, complemented, Sylow
455C2—204no—
456C2—302no—
457C2C4×#677711yescharacteristic
458C2#1175403712yes—
subgroupG/H
centerC22C2×#6777
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#97C22
socleC22×C3×C5C22×D4
prime radicalC2×#91277C2
cosocleC2×C3×C4×C5C24
hypercenter#97D3×D5
hypocenterC3×C5#2952
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #11752520C2semidirect
3. #11750809C2semidirect
4. C5×#4716C2semidirect
5. C3×#65000C2semidirect
6. #11748142C2semidirect
7. #11747888C2semidirect
8. #11747815C2semidirect
9. #11747735C2semidirect
10. #11747632C2semidirect
11. C4×#6655C2semidirect
29. #91277C4semidirect
51. #65000D3semidirect
62. #6766C2×C4semidirect
72. C8×D15C2×C4semidirect
76. C5×Dic12C2×C4semidirect
79. C3×D40C2×C4semidirect
84. #6655C2×C4semidirect
94. #4716D5semidirect
206. D40C4×D3semidirect
263. Dic12C4×D5semidirect
392. C3×C5#2952semidirect
439. C5#79868semidirect
454. C3#10611563semidirect

Maximal subgroups

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

subgroupindex
C2×#912772
#117525202
#117508092
C5×#47162
C3×#650002
#117481422
#117478882
#117478152
#117477352
#117476322
C4×#66552
#106115633
#798685