Finite Group Databasebeta

← #14303075

Subgroups — #14303075

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#11756575C211yesmaximal, characteristic
2#11756504C211yesmaximal, characteristic
3C2×C3×C5×#101C211yesmaximal, characteristic, complemented
4C2×#91120C211yesmaximal, characteristic, complemented
5#11751233C211yesmaximal, characteristic
6#11746380C211yesmaximal, characteristic, complemented
7#11746377C211yesmaximal, characteristic, complemented
8#10600917—31nomaximal, Hall
9C22×C3×C5×Q8C2211yescharacteristic
10C2×#6817C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×C3×C5×M16C2211yescharacteristic
13#91836—21no—
14#91835—22no—
15#91833—21no—
16#91818C414yes—
17#91815C2211yescharacteristic
18C2×#6710C2211yescharacteristic
19C2×#6710C2211yescharacteristic
20#91796—22no—
21M16×D15—22no—
22#91790—22no—
23C3×C5×#101—22no—
24#91120—22no—
25#91108—21no—
26#91107—21no—
27#70124—51nomaximal, Hall
28#66150—31no—
29#66079—31no—
30C2×C5×#101D311yescharacteristic, complemented
31C2×#3968—31no—
32#65421—31no—
33#64779—31no—
34#64776—31no—
35C2×C3×C5×Q8—21no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8—21no—
38C2×C3×C5×Q8—21no—
39C2×C3×C5×Q8—21no—
40C2×C3×C5×Q8—21no—
41C22×C3×C4×C5C2×C412yes—
42C22×C3×C4×C5C2311yescharacteristic
43C2×#1220C2×C412yes—
44#6817—21no—
45#6817—21no—
46#6817—21no—
47#6817—21no—
48C2×D60D411yescharacteristic
49C2×C4×D15D412yes—
50C2×Dic30D411yescharacteristic
51C3×C5×M16—21no—
52C3×C5×M16—21no—
53C3×C5×M16—21no—
54C3×C5×M16D412yes—
55C2×C3×C5×C8—21no—
56C2×C3×C5×C8—21no—
57#6719C2×C412yes—
58#6714—24no—
59C4⋊Dic15—21no—
60#6712—24no—
61C4×Dic15—21no—
62#6710—21no—
63#6710—21no—
64#6710—21no—
65#6710D412yes—
66C2×C3⋊#168—21no—
67C2×C3⋊#168—21no—
68#6705—24no—
69C8×D15—24no—
70#5816—51no—
71#5745—51no—
72C2×C3×#101D511yescharacteristic, complemented
73C2×#836—51no—
74#5132—51no—
75#4559—51no—
76#4556—51no—
77C22×C5×Q8C2×D311yescharacteristic
78C2×#709—31no—
79C2×C5×M16C2×D311yescharacteristic
80C2×C5×M16C2×D311yescharacteristic
81#4093—61no—
82#4092—62no—
83#4090—61no—
84#4075—34no—
85#4072—31no—
86C2×#681—31no—
87C2×#681—31no—
88#4053—62no—
89D5×M16—62no—
90#4047—62no—
91C5×#101—22no—
92#3968—62no—
93#3956—61no—
94#3955—61no—
95#1915—151noSylow
96C23×C3×C5C22×C411yescharacteristic
97C22×D15C22⋊C412yes—
98C3×C5×Q8—41no—
99C3×C5×Q8—41no—
100C3×C5×Q8—41no—
101C3×C5×Q8—41no—
102C2×C3×C4×C5—22no—
103C2×C3×C4×C5—22no—
104C2×C3×C4×C5—22no—
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111#1220—22no—
112#1220—22no—
113C2×Dic15—22no—
114C2×Dic15C22⋊C412yes—
115D60—21no—
116D60—21no—
117C4×D15—22no—
118C4×D15—22no—
119Dic30—21no—
120Dic30—21no—
121C3×C5×C8—22no—
122C3×C5×C8—41no—
123C3⋊#168—22no—
124C3⋊#168—41no—
125C22×C3×Q8C2×D511yescharacteristic
126C2×#235—51no—
127C2×C3×M16C2×D511yescharacteristic
128C2×C3×M16C2×D511yescharacteristic
129#947—101no—
130#946—102no—
131#944—101no—
132#929—54no—
133#926—51no—
134C2×#208—51no—
135C2×#208—51no—
136#907—102no—
137D3×M16—102no—
138#901—102no—
139C3×#101—22no—
140#836—102no—
141#824—101no—
142#823—101no—
143C2×C5×Q8—21no—
144C2×C5×Q8—21no—
145C2×C5×Q8—21no—
146C2×C5×Q8—21no—
147C2×C5×Q8—21no—
148C2×C5×Q8—21no—
149C22×C4×C5C4×D312yes—
150C22×C4×C5C22×D311yescharacteristic
151C2×C22⋊D5—32no—
152#709—61no—
153#709—61no—
154#709—61no—
155#709—61no—
156C2×D20—31no—
157C2×C4×D5—32no—
158C2×Dic10—31no—
159C5×M16—21no—
160C5×M16—21no—
161C5×M16—21no—
162C5×M16#6712yes—
163C2×C5×C8—21no—
164C2×C5×C8—21no—
165C22⋊Dic5—32no—
166#685—64no—
167C4⋊Dic5—61no—
168#683—64no—
169C4×Dic5—61no—
170#681—32no—
171#681—61no—
172#681—61no—
173#681—61no—
174C2×#168—61no—
175C2×#168—61no—
176#676—64no—
177C8×D5—64no—
178#568—151no—
179#536—151no—
180#413—151no—
181C2×#101—151no—
182C2×#101D1511yescharacteristic, complemented
183#344—151no—
184#344—151no—
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—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C22×C3×C4C4×D512yes—
205C22×C3×C4C22×D511yescharacteristic
206C2×#67—52no—
207#235—101no—
208#235—101no—
209#235—101no—
210#235—101no—
211C2×D12—51no—
212C2×C4×D3—52no—
213C2×Dic6—51no—
214C3×M16—21no—
215C3×M16—21no—
216C3×M16—21no—
217C3×M16C22⋊D512yes—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220#217—52no—
221(C2×D3)⋊C4—104no—
222C4⋊Dic3—101no—
223Dic3⋊C4—104no—
224C4×Dic3—101no—
225#208—52no—
226#208—101no—
227#208—101no—
228#208—101no—
229C2×C3⋊C8—101no—
230C2×C3⋊C8—101no—
231ΓL(1,𝔽25)—104no—
232D3×C8—104no—
233C23×C5C2×C4×D311yescharacteristic
234C22×D5—32no—
235C5×Q8—41no—
236C5×Q8—41no—
237C5×Q8—41no—
238C5×Q8—41no—
239C2×C4×C5—22no—
240C2×C4×C5—22no—
241C2×C4×C5—22no—
242C2×C4×C5#23511yescharacteristic
243C2×C4×C5D3×D411yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5D3×D411yescharacteristic
246C2×C4×C5#23711yescharacteristic
247C2×C4×C5C2×#6711yescharacteristic
248C22⋊D5—62no—
249C22⋊D5—62no—
250C2×Dic5—32no—
251C2×Dic5—62no—
252D20—61no—
253D20—61no—
254C4×D5—62no—
255C4×D5—62no—
256Dic10—61no—
257Dic10—61no—
258C5×C8—22no—
259C5×C8—41no—
260#168—62no—
261#168—121no—
262C2×#41—151no—
263C22×Q8C2×D1511yescharacteristic
264#131—302no—
265#131—302no—
266C2×M16—151no—
267C2×M16—151no—
268C2×M16—302no—
269C2×M16C2×D1511yescharacteristic
270C2×M16C2×D1511yescharacteristic
271C4⋊Q8—301no—
272#124—301no—
273#123—154no—
274C22⋊Q8—302no—
275#117—151no—
276#101—22no—
277#101—301no—
278#101—302no—
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—
287C3×Q8—41no—
288C3×Q8—41no—
289C3×Q8—41no—
290C3×Q8—41no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4#70911yescharacteristic
295C2×C3×C4D4×D511yescharacteristic
296C2×C3×C4D4×D511yescharacteristic
297C2×C3×C4D4×D511yescharacteristic
298C2×C3×C4#71111yescharacteristic
299C2×C3×C4C2×C22⋊D511yescharacteristic
300#67—102no—
301#67—102no—
302C2×Dic3—52no—
303C2×Dic3—102no—
304D12—101no—
305D12—101no—
306C4×D3—102no—
307C4×D3—102no—
308Dic6—101no—
309Dic6—101no—
310C3×C8—22no—
311C3×C8—41no—
312C3⋊C8—102no—
313C3⋊C8—201no—
314C22×C5—41no—
315C22×C5D3×C22⋊C411yescharacteristic
316C22×C5#67⋊C411yescharacteristic
317C22×C5C4×#6711yescharacteristic
318C2×D5—62no—
319C2×D5—122no—
320C4×C5—42no—
321C4×C5#88311yescharacteristic
322C4×C5#88411yescharacteristic
323C4×C5#93711yescharacteristic
324C4×C5#93811yescharacteristic
325Dic5—62no—
326Dic5—122no—
327#41—301no—
328#41—301no—
329#41—301no—
330#41—301no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—151no—
338C2×D4—152no—
339C2×D4—151no—
340C22×C4—152no—
341C22×C4C4×D1512yes—
342C22×C4C22×D1511yescharacteristic
343M16—21no—
344M16—21no—
345M16—21no—
346M16—152no—
347M16—304no—
348M16—301no—
349M16—301no—
350M16—301no—
351M16#122012yes—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—304no—
355C2×C8—301no—
356C2×C8—301no—
357C4⋊C4—304no—
358C4⋊C4—301no—
359C22⋊C4—152no—
360C22⋊C4—304no—
361C42—301no—
362C3×C5#191511yescharacteristic, complemented, Hall
363C22×C3—41no—
364C22×C3D5×C22⋊C411yescharacteristic
365C22×C3#402711yescharacteristic
366C22×C3C4×C22⋊D511yescharacteristic
367C2×D3—102no—
368C2×D3—202no—
369C3×C4—42no—
370C3×C4#402911yescharacteristic
371C3×C4#403011yescharacteristic
372C3×C4#408311yescharacteristic
373C3×C4#408411yescharacteristic
374Dic3—102no—
375Dic3—202no—
376C2×C5—21no—
377C2×C5—21no—
378C2×C5—21no—
379C2×C5#495611yescharacteristic
380D5—122no—
381C23—152no—
382C23C2×C4×D1511yescharacteristic
383Q8—41no—
384Q8—41no—
385Q8—41no—
386Q8—41no—
387Q8—301no—
388Q8—301no—
389D4—302no—
390D4—302no—
391D4—301no—
392D4—301no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—152no—
397C2×C4—302no—
398C2×C4—302no—
399C2×C4—302no—
400C2×C4#681711yescharacteristic
401C2×C4D4×D1511yescharacteristic
402C2×C4D4×D1511yescharacteristic
403C2×C4D4×D1511yescharacteristic
404C2×C4#681911yescharacteristic
405C2×C4C2×#122011yescharacteristic
406C8—22no—
407C8—41no—
408C8—302no—
409C8—601no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3#6524511yescharacteristic
414D3—202no—
415C5#7012411yescharacteristic, complemented, Sylow
416C22—41no—
417C22—302no—
418C22—602no—
419C22C22⋊C4×D1511yescharacteristic
420C22#9177011yescharacteristic
421C22C4×#122011yescharacteristic
422C4—42no—
423C4—302no—
424C4—602no—
425C4#9177211yescharacteristic
426C4#9177311yescharacteristic
427C4#9182611yescharacteristic
428C4#9182711yescharacteristic
429C3#1060091711yescharacteristic, complemented, Sylow
430C2—21no—
431C2—21no—
432C2—21no—
433C2—602no—
434C2#1175105711yescharacteristic
subgroupG/H
centerC2#11751057
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#101C2
socleC2×C3×C5#386
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenterC2×#101D15
hypocenterC3×C5#1915
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
3. C2×C3×C5×#101C2semidirect
4. C2×#91120C2semidirect
6. #11746380C2semidirect
7. #11746377C2semidirect
30. C2×C5×#101D3semidirect
72. C2×C3×#101D5semidirect
182. C2×#101D15semidirect
362. C3×C5#1915semidirect
415. C5#70124semidirect
429. C3#10600917semidirect

Maximal subgroups

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

subgroupindex
#117565752
#117565042
C2×C3×C5×#1012
C2×#911202
#117512332
#117463802
#117463772
#106009173
#701245