Finite Group Databasebeta

← #14303090

Subgroups — #14303090

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#11754251C211yesmaximal, characteristic
2#11754120C211yesmaximal, characteristic
3C2×C5×#824C211yesmaximal, characteristic, complemented
4C3×#65421C211yesmaximal, characteristic
5C2×#90962C211yesmaximal, characteristic, complemented
6#11746377C211yesmaximal, characteristic, complemented
7#11745991C211yesmaximal, characteristic, complemented
8#10600917—31nomaximal, Hall
9C22×C5×Dic6C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91536C414yes—
17#91385—21no—
18#91368—21no—
19#91359—22no—
20#91284—22no—
21#91283—22no—
22D5×#208—22no—
23C5×#824—22no—
24C3×#3956—21no—
25C3×#3955—21no—
26#90962—22no—
27#70138—51nomaximal, Hall
28#66150—31no—
29#66079—31no—
30C2×C5×#101—31no—
31C2×#3968—31no—
32#65421D311yescharacteristic
33#64779—31no—
34#64776—31no—
35C22×C3×C4×C5C2311yescharacteristic
36C22×C5×Dic3C2×C412yes—
37C2×C5×Dic6—21no—
38C2×C5×Dic6—21no—
39C2×C5×Dic6—21no—
40C2×C5×Dic6—21no—
41C2×C5×Dic6—21no—
42C2×C5×Dic6—21no—
43C2×C3×C22⋊D5C2×C412yes—
44C3×#709—21no—
45C3×#709—21no—
46C3×#709—21no—
47C3×#709—21no—
48C2×C3×D20D411yescharacteristic
49C2×C3×C4×D5D412yes—
50C2×C3×Dic10D411yescharacteristic
51C3×C5×M16—21no—
52C3×C5×M16—21no—
53C2×C3×C5×C8—21no—
54#6719C2×C412yes—
55C4⋊Dic15—21no—
56C4×Dic15—21no—
57#6710—21no—
58#6710D412yes—
59C2×C3⋊#168—21no—
60C5×#208—21no—
61C5×#208D412yes—
62C2×C5×C3⋊C8—21no—
63C3×#681—21no—
64C3×#681—21no—
65C2×C3×#168—21no—
66#6669—24no—
67#6665—24no—
68#6649—24no—
69D5×C3⋊C8—24no—
70#5825—51no—
71#5819—51no—
72C3×#413—51no—
73C2×#824—51no—
74C2×#824D511yescharacteristic, complemented
75#4556—51no—
76#4556—51no—
77C22×C5×Q8—31no—
78C2×#709C2×D311yescharacteristic
79C2×C5×M16—31no—
80C2×C5×M16C2×D311yescharacteristic
81#4093—61no—
82#4092—62no—
83#4090—61no—
84#4075—34no—
85#4072—31no—
86C2×#681—31no—
87C2×#681C2×D311yescharacteristic
88#4053—62no—
89D5×M16—62no—
90#4047—62no—
91C5×#101—62no—
92#3968—62no—
93#3956—21no—
94#3955—21no—
95#1915—151noSylow
96C23×C3×C5C22×C411yescharacteristic
97C22×C3×D5C22⋊C412yes—
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C2×Dic15—22no—
105C2×C5×Dic3—22no—
106C2×C5×Dic3—22no—
107C2×C5×Dic3—22no—
108C5×Dic6—41no—
109C5×Dic6—41no—
110C5×Dic6—41no—
111C5×Dic6—41no—
112C3×C22⋊D5—22no—
113C3×C22⋊D5—22no—
114C2×C3×Dic5C22⋊C412yes—
115C3×D20—21no—
116C3×D20—21no—
117C3×C4×D5—22no—
118C3×C4×D5—22no—
119C3×Dic10—21no—
120C3×Dic10—21no—
121C3×C5×C8—41no—
122C3⋊#168—22no—
123C3×#168—41no—
124C5×C3⋊C8—22no—
125C2×C3×#41—51no—
126C22×Dic6C2×D511yescharacteristic
127C2×C3×M16—51no—
128C2×C3×M16C2×D511yescharacteristic
129#948—102no—
130#948—102no—
131#944—101no—
132#936—101no—
133#935—54no—
134#926—51no—
135#924—102no—
136C2×#208—51no—
137C2×#208—102no—
138C2×#208C2×D511yescharacteristic
139C3×#101—101no—
140C3×#100—101no—
141#824—22no—
142#824—102no—
143C2×C5×Q8—61no—
144C2×C5×Q8—61no—
145C2×C5×Q8—61no—
146C2×C5×Q8—61no—
147C2×C5×Q8—61no—
148C2×C5×Q8—61no—
149C22×C4×C5—32no—
150C22×C4×C5C22×D311yescharacteristic
151C2×C22⋊D5C4×D312yes—
152#709—21no—
153#709—21no—
154#709—21no—
155#709—21no—
156C2×D20#6711yescharacteristic
157C2×C4×D5D1212yes—
158C2×Dic10#6711yescharacteristic
159C5×M16—21no—
160C5×M16—21no—
161C5×M16—32no—
162C5×M16—61no—
163C2×C5×C8—21no—
164C2×C5×C8—61no—
165C22⋊Dic5—32no—
166#685—64no—
167C4⋊Dic5—61no—
168#683—64no—
169C4×Dic5—61no—
170#681—21no—
171#681—21no—
172#681—32no—
173#681—61no—
174C2×#168—21no—
175C2×#168—61no—
176#676—64no—
177C8×D5—64no—
178#568—151no—
179#536—151no—
180#413—51no—
181C2×#101—31no—
182C2×#101—151no—
183#344—151no—
184#344—151no—
185C22×C3×C5—41no—
186C22×C3×C5C2×C22⋊C411yescharacteristic
187C22×C3×C5C4×D411yescharacteristic
188C22×C3×C5C4×D411yescharacteristic
189C2×C3×D5—22no—
190C2×C3×D5—42no—
191C3×C4×C5#12011yescharacteristic
192C3×C4×C5#12111yescharacteristic
193C3×C4×C5#12111yescharacteristic
194C3×C4×C5#12311yescharacteristic
195Dic15—42no—
196C3×Dic5—22no—
197C5×Dic3—42no—
198C3×#41—101no—
199C3×#41—101no—
200C3×#41—101no—
201C3×#41—101no—
202C2×C3×Q8—51no—
203C2×C3×D4—52no—
204C2×C3×D4—51no—
205C22×C3×C4—52no—
206C22×C3×C4C22×D511yescharacteristic
207C22×Dic3C4×D512yes—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6—21no—
211C2×Dic6—21no—
212C2×Dic6—21no—
213C2×Dic6—21no—
214C3×M16—21no—
215C3×M16—21no—
216C3×M16—101no—
217C3×M16—101no—
218C2×C3×C8—21no—
219C2×C3×C8—101no—
220#217—52no—
221#217—104no—
222C4⋊Dic3—101no—
223Dic3⋊C4—104no—
224C4×Dic3—101no—
225#208—21no—
226#208—52no—
227#208—104no—
228#208—101no—
229#208C22⋊D512yes—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—104no—
232C2×C3⋊C8—101no—
233C23×C5C2×C4×D311yescharacteristic
234C22×D5(C2×D3)⋊C412yes—
235C5×Q8—121no—
236C5×Q8—121no—
237C5×Q8—121no—
238C5×Q8—121no—
239C2×C4×C5—62no—
240C2×C4×C5—62no—
241C2×C4×C5—62no—
242C2×C4×C5C2×D1211yescharacteristic
243C2×C4×C5D3×D411yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5#23711yescharacteristic
246C2×C4×C5#23711yescharacteristic
247C2×C4×C5C2×#6711yescharacteristic
248C22⋊D5—22no—
249C22⋊D5—22no—
250C2×Dic5—62no—
251C2×Dic5(C2×D3)⋊C412yes—
252D20—21no—
253D20—21no—
254C4×D5—22no—
255C4×D5—22no—
256Dic10—21no—
257Dic10—21no—
258C5×C8—41no—
259C5×C8—62no—
260#168—41no—
261#168—62no—
262C2×#41—51no—
263C22×Q8—31no—
264#131—302no—
265#131—302no—
266C2×M16—31no—
267C2×M16—51no—
268C2×M16—151no—
269C2×M16—302no—
270C2×M16D3×D511yescharacteristic
271C4⋊Q8—301no—
272#124—301no—
273#123—154no—
274C22⋊Q8—302no—
275#117—151no—
276#101—62no—
277#101—101no—
278#101—302no—
279#100—101no—
280C2×C3×C5—21no—
281C2×C3×C5—21no—
282C2×C3×C5—21no—
283C2×C3×C5#38611yescharacteristic
284C3×D5—42no—
285C23×C3—52no—
286C23×C3C2×C4×D511yescharacteristic
287C3×Q8—101no—
288C3×Q8—101no—
289C3×D4—102no—
290C3×D4—102no—
291C3×D4—101no—
292C3×D4—101no—
293C2×C3×C4—52no—
294C2×C3×C4—102no—
295C2×C3×C4—102no—
296C2×C3×C4#70911yescharacteristic
297C2×C3×C4D4×D511yescharacteristic
298C2×C3×C4D4×D511yescharacteristic
299C2×C3×C4D4×D511yescharacteristic
300C2×C3×C4#71111yescharacteristic
301C2×C3×C4C2×C22⋊D511yescharacteristic
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—22no—
305C2×Dic3—102no—
306Dic6—41no—
307Dic6—41no—
308Dic6—41no—
309Dic6—41no—
310C3×C8—41no—
311C3×C8—201no—
312C3⋊C8—22no—
313C3⋊C8—102no—
314C22×C5—41no—
315C22×C5#67⋊C411yescharacteristic
316C22×C5#67⋊C411yescharacteristic
317C22×C5C2×(C2×D3)⋊C411yescharacteristic
318C2×D5—22no—
319C2×D5—42no—
320C4×C5—122no—
321C4×C5#88211yescharacteristic
322C4×C5#88611yescharacteristic
323C4×C5#93911yescharacteristic
324C4×C5#93911yescharacteristic
325Dic5—22no—
326Dic5—122no—
327#41—101no—
328#41—101no—
329#41—101no—
330#41—101no—
331C2×Q8—51no—
332C2×Q8—61no—
333C2×Q8—61no—
334C2×Q8—61no—
335C2×Q8—61no—
336C2×Q8—61no—
337C2×Q8—61no—
338C2×D4—52no—
339C2×D4—51no—
340C22×C4—32no—
341C22×C4—52no—
342C22×C4C2×D3×D511yescharacteristic
343M16—21no—
344M16—21no—
345M16—32no—
346M16—61no—
347M16—101no—
348M16—101no—
349M16—152no—
350M16—304no—
351M16—301no—
352C2×C8—21no—
353C2×C8—61no—
354C2×C8—101no—
355C2×C8—304no—
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×C3—102no—
365C22×C3—202no—
366C22×C3D5×C22⋊C411yescharacteristic
367C22×C3#402711yescharacteristic
368C22×C3C4×C22⋊D511yescharacteristic
369C3×C4—102no—
370C3×C4#402911yescharacteristic
371C3×C4#403011yescharacteristic
372C3×C4#408311yescharacteristic
373C3×C4#408411yescharacteristic
374Dic3—42no—
375Dic3—202no—
376C2×C5—21no—
377C2×C5—21no—
378C2×C5—21no—
379C2×C5#495811yescharacteristic
380D5—42no—
381C23—52no—
382C23C4×D3×D511yescharacteristic
383Q8—101no—
384Q8—101no—
385Q8—121no—
386Q8—121no—
387Q8—121no—
388Q8—121no—
389D4—102no—
390D4—102no—
391D4—101no—
392D4—101no—
393C2×C4—52no—
394C2×C4—62no—
395C2×C4—62no—
396C2×C4—62no—
397C2×C4—102no—
398C2×C4—102no—
399C2×C4—302no—
400C2×C4#676511yescharacteristic
401C2×C4D5×D1211yescharacteristic
402C2×C4#677711yescharacteristic
403C2×C4#678011yescharacteristic
404C2×C4D5×#6711yescharacteristic
405C2×C4D3×C22⋊D511yescharacteristic
406C8—41no—
407C8—62no—
408C8—201no—
409C8—302no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—202no—
414C2×C3#6524511yescharacteristic
415C5#7013811yescharacteristic, complemented, Sylow
416C22—41no—
417C22—102no—
418C22—202no—
419C22#9144111yescharacteristic
420C22#9144211yescharacteristic
421C22D5×(C2×D3)⋊C411yescharacteristic
422C4—102no—
423C4—122no—
424C4—602no—
425C4#9140811yescharacteristic
426C4#9141411yescharacteristic
427C4#9147511yescharacteristic
428C4#9154911yescharacteristic
429C3#1060091711yescharacteristic, complemented, Sylow
430C2—21no—
431C2—21no—
432C2—21no—
433C2—202no—
434C2#1174890611yescharacteristic
subgroupG/H
centerC2#11748906
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radicalC2×C3×#709C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1915
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C2×C5×#824C2semidirect
5. C2×#90962C2semidirect
6. #11746377C2semidirect
7. #11745991C2semidirect
74. C2×#824D5semidirect
362. C3×C5#1915semidirect
415. C5#70138semidirect
429. C3#10600917semidirect

Maximal subgroups

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

subgroupindex
#117542512
#117541202
C2×C5×#8242
C3×#654212
C2×#909622
#117463772
#117459912
#106009173
#701385