Finite Group Databasebeta

← #14302928

Subgroups — #14302928

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#11756584C211yesmaximal, characteristic
2#11756275C211yesmaximal, characteristic, complemented
3C3×C5×#421C211yesmaximal, characteristic
4#11751337C211yesmaximal, characteristic
5C2×#91108C211yesmaximal, characteristic, complemented
6#11746378C211yesmaximal, characteristic, complemented
7#11746352C211yesmaximal, characteristic, complemented
8#10601204—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C22×Dic30C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13#91833C412yescomplemented
14#91825C412yescomplemented
15#91824—22no—
16#91815C2211yescharacteristic
17#91815C2211yescharacteristic
18#91813—22no—
19C2×#6710C2211yescharacteristic
20#91776—22no—
21#91766—22no—
22C4×Dic30—22no—
23C3×C5×#104—22no—
24#91121—22no—
25#91108—22no—
26#70411—51nomaximal, Hall
27#66159—31no—
28#65850—31no—
29C5×#421D311yescharacteristic
30#65525—31no—
31C2×#3956—31no—
32#64777—31no—
33#64751—31no—
34C3×C5×#41—21no—
35C3×C5×#41—21no—
36C3×C5×#41—21no—
37C3×C5×#41—21no—
38C2×C3×C5×Q8C2×C411yescharacteristic
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4C2×C411yescharacteristic
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5C2311yescharacteristic
43C22×Dic15D412yes—
44C2×Dic30—21no—
45C2×Dic30—21no—
46C2×Dic30—21no—
47C2×Dic30—21no—
48C2×Dic30C2×C412yes—
49C2×Dic30D412yes—
50C3×C5×M16—21no—
51C3×C5×M16—21no—
52C2×C3×C5×C8—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C22⋊C4—21no—
55C3×C42×C5D412yes—
56#6719—21no—
57#6719—21no—
58#6719—24no—
59C4⋊Dic15—21no—
60C4⋊Dic15—21no—
61#6712—24no—
62#6712—24no—
63C4×Dic15—24no—
64C4×Dic15C2×C412yes—
65C4×Dic15D412yes—
66#6710—21no—
67#6710—21no—
68C2×C3⋊#168—21no—
69#5825—51no—
70#5516—51no—
71C3×#421D511yescharacteristic
72#5236—51no—
73C2×#824—51no—
74#4557—51no—
75#4531—51no—
76C2×C5×#41C2×D311yescharacteristic
77C22×Dic10—31no—
78C2×C5×M16C2×D311yescharacteristic
79C5×#117C2×D311yescharacteristic
80#4090—32no—
81#4082—32no—
82#4081—62no—
83#4072—31no—
84#4072—31no—
85#4070—62no—
86C2×#681—31no—
87#4033—62no—
88#4023—62no—
89C4×Dic10—62no—
90C5×#104—22no—
91#3969—62no—
92#3956—62no—
93#1912—151noSylow
94C23×C3×C5—21no—
95C23×C3×C5C2×D411yescharacteristic
96C3×C5×Q8—21no—
97C3×C5×Q8—21no—
98C3×C5×D4—21no—
99C3×C5×D4—21no—
100C3×C5×D4—41no—
101C3×C5×D4—41no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—22no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5C22×C411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111C2×C3×C4×C5#4111yescharacteristic
112C2×Dic15—22no—
113C2×Dic15—22no—
114C2×Dic15—22no—
115C2×Dic15—22no—
116C2×Dic15C22⋊C414yes—
117Dic30—22no—
118Dic30—22no—
119Dic30—22no—
120Dic30—22no—
121C3×C5×C8—41no—
122C3⋊#168—41no—
123C2×C3×#41C2×D511yescharacteristic
124C22×Dic6—51no—
125C2×C3×M16C2×D511yescharacteristic
126C3×#117C2×D511yescharacteristic
127#944—52no—
128#936—52no—
129#935—102no—
130#926—51no—
131#926—51no—
132#924—102no—
133C2×#208—51no—
134#887—102no—
135#877—102no—
136C4×Dic6—102no—
137C3×#104—22no—
138#837—102no—
139#824—102no—
140C5×#41—21no—
141C5×#41—21no—
142C5×#41—21no—
143C5×#41—21no—
144C2×C5×Q8C4×D311yescharacteristic
145C2×C5×D4—21no—
146C2×C5×D4C4×D311yescharacteristic
147C22×C4×C5—21no—
148C22×C4×C5C22×D311yescharacteristic
149C22×Dic5—32no—
150C2×Dic10—32no—
151C2×Dic10—32no—
152C2×Dic10—61no—
153C2×Dic10—61no—
154C2×Dic10—61no—
155C2×Dic10—61no—
156C5×M16—21no—
157C5×M16—21no—
158C2×C5×C8—21no—
159C5×C4⋊C4—21no—
160C5×C22⋊C4—21no—
161C42×C5#6712yes—
162C22⋊Dic5—64no—
163C22⋊Dic5—61no—
164C22⋊Dic5—61no—
165C4⋊Dic5—61no—
166C4⋊Dic5—61no—
167#683—64no—
168#683—64no—
169C4×Dic5—32no—
170C4×Dic5—32no—
171C4×Dic5—64no—
172#681—61no—
173#681—61no—
174C2×#168—61no—
175#536—151no—
176#519—151no—
177#421—151no—
178#421D1511yescharacteristic
179C2×#101—151no—
180H(3,ℤ/4)—151no—
181H(3,ℤ/4)—151no—
182C22×C3×C5—41no—
183C22×C3×C5—42no—
184C22×C3×C5—41no—
185C22×C3×C5C2×C22⋊C411yescharacteristic
186C22×C3×C5#12011yescharacteristic
187C22×C3×C5#12311yescharacteristic
188C3×C4×C5—42no—
189C3×C4×C5—41no—
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5C4×D411yescharacteristic
192C3×C4×C5#12111yescharacteristic
193C3×C4×C5#12111yescharacteristic
194Dic15—24no—
195Dic15—42no—
196Dic15—42no—
197C3×#41—21no—
198C3×#41—21no—
199C3×#41—21no—
200C3×#41—21no—
201C2×C3×Q8C4×D511yescharacteristic
202C2×C3×D4—21no—
203C2×C3×D4C4×D511yescharacteristic
204C22×C3×C4—21no—
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—21no—
214C3×M16—21no—
215C2×C3×C8—21no—
216C3×C4⋊C4—21no—
217C3×C22⋊C4—21no—
218C3×C42C22⋊D512yes—
219#217—104no—
220#217—101no—
221#217—101no—
222C4⋊Dic3—101no—
223C4⋊Dic3—101no—
224Dic3⋊C4—104no—
225Dic3⋊C4—104no—
226C4×Dic3—52no—
227C4×Dic3—52no—
228C4×Dic3—104no—
229#208—101no—
230#208—101no—
231C2×C3⋊C8—101no—
232C23×C5—21no—
233C23×C5D3×D411yescharacteristic
234C5×Q8—21no—
235C5×Q8—21no—
236C5×D4—21no—
237C5×D4—21no—
238C5×D4—41no—
239C5×D4—41no—
240C2×C4×C5—21no—
241C2×C4×C5—22no—
242C2×C4×C5—41no—
243C2×C4×C5—41no—
244C2×C4×C5C2×C4×D311yescharacteristic
245C2×C4×C5#23511yescharacteristic
246C2×C4×C5D3×D411yescharacteristic
247C2×C4×C5D3×D411yescharacteristic
248C2×C4×C5#23711yescharacteristic
249C2×C4×C5C2×#6711yescharacteristic
250C2×Dic5—34no—
251C2×Dic5—62no—
252C2×Dic5—62no—
253C2×Dic5—62no—
254C2×Dic5—62no—
255Dic10—62no—
256Dic10—62no—
257Dic10—62no—
258Dic10—62no—
259C5×C8—41no—
260#168—121no—
261C2×#41C2×D1511yescharacteristic
262C22×Q8—151no—
263C2×M16—151no—
264C2×M16C2×D1511yescharacteristic
265C4⋊Q8—152no—
266#124—152no—
267#123—302no—
268C22⋊Q8—302no—
269C4×Q8—302no—
270C4×Q8—302no—
271#117—151no—
272#117—151no—
273#117—302no—
274#117C2×D1511yescharacteristic
275#104—22no—
276#104—302no—
277#101—302no—
278C2×C3×C5—21no—
279C2×C3×C5—21no—
280C2×C3×C5—21no—
281C2×C3×C5—81no—
282C2×C3×C5#38611yescharacteristic
283C23×C3—21no—
284C23×C3D4×D511yescharacteristic
285C3×Q8—21no—
286C3×Q8—21no—
287C3×D4—21no—
288C3×D4—21no—
289C3×D4—41no—
290C3×D4—41no—
291C2×C3×C4—21no—
292C2×C3×C4—22no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4C2×C4×D511yescharacteristic
296C2×C3×C4#70911yescharacteristic
297C2×C3×C4D4×D511yescharacteristic
298C2×C3×C4D4×D511yescharacteristic
299C2×C3×C4#71111yescharacteristic
300C2×C3×C4C2×C22⋊D511yescharacteristic
301C2×Dic3—54no—
302C2×Dic3—102no—
303C2×Dic3—102no—
304C2×Dic3—102no—
305C2×Dic3—102no—
306Dic6—102no—
307Dic6—102no—
308Dic6—102no—
309Dic6—102no—
310C3×C8—41no—
311C3⋊C8—201no—
312C22×C5—41no—
313C22×C5—42no—
314C22×C5—41no—
315C22×C5D3×C22⋊C411yescharacteristic
316C22×C5#88311yescharacteristic
317C22×C5#93711yescharacteristic
318C4×C5—42no—
319C4×C5—41no—
320C4×C5#67⋊C411yescharacteristic
321C4×C5#88411yescharacteristic
322C4×C5C4×#6711yescharacteristic
323C4×C5#93811yescharacteristic
324Dic5—64no—
325Dic5—122no—
326Dic5—122no—
327#41—21no—
328#41—21no—
329#41—21no—
330#41—21no—
331C2×Q8—152no—
332C2×Q8—152no—
333C2×Q8—301no—
334C2×Q8—301no—
335C2×Q8—301no—
336C2×Q8—301no—
337C2×Q8C4×D1511yescharacteristic
338C2×D4—21no—
339C2×D4C4×D1511yescharacteristic
340C22×C4—21no—
341C22×C4—152no—
342C22×C4C22×D1511yescharacteristic
343M16—21no—
344M16—21no—
345M16—301no—
346M16—301no—
347C2×C8—21no—
348C2×C8—301no—
349C4⋊C4—21no—
350C4⋊C4—304no—
351C4⋊C4—304no—
352C4⋊C4—301no—
353C4⋊C4—301no—
354C22⋊C4—21no—
355C22⋊C4—304no—
356C22⋊C4—301no—
357C22⋊C4—301no—
358C42—152no—
359C42—152no—
360C42—304no—
361C42#122012yes—
362C3×C5#191211yescharacteristic, complemented, Hall
363C22×C3—41no—
364C22×C3—42no—
365C22×C3—41no—
366C22×C3D5×C22⋊C411yescharacteristic
367C22×C3#402911yescharacteristic
368C22×C3#408311yescharacteristic
369C3×C4—42no—
370C3×C4—41no—
371C3×C4#402711yescharacteristic
372C3×C4#403011yescharacteristic
373C3×C4C4×C22⋊D511yescharacteristic
374C3×C4#408411yescharacteristic
375Dic3—104no—
376Dic3—202no—
377Dic3—202no—
378C2×C5—21no—
379C2×C5—21no—
380C2×C5—21no—
381C2×C5—81no—
382C2×C5#495611yescharacteristic
383C23—21no—
384C23D4×D1511yescharacteristic
385Q8—21no—
386Q8—21no—
387Q8—302no—
388Q8—302no—
389Q8—302no—
390Q8—302no—
391D4—21no—
392D4—21no—
393D4—41no—
394D4—41no—
395C2×C4—21no—
396C2×C4—22no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—154no—
400C2×C4—302no—
401C2×C4—302no—
402C2×C4—302no—
403C2×C4—302no—
404C2×C4C2×C4×D1511yescharacteristic
405C2×C4#681711yescharacteristic
406C2×C4D4×D1511yescharacteristic
407C2×C4D4×D1511yescharacteristic
408C2×C4#681911yescharacteristic
409C2×C4C2×#122011yescharacteristic
410C8—41no—
411C8—601no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—81no—
416C2×C3#6524511yescharacteristic
417C5#7041111yescharacteristic, complemented, Sylow
418C22—41no—
419C22—42no—
420C22—41no—
421C22C22⋊C4×D1511yescharacteristic
422C22#9177211yescharacteristic
423C22#9182611yescharacteristic
424C4—42no—
425C4—41no—
426C4—304no—
427C4—602no—
428C4—602no—
429C4#9177011yescharacteristic
430C4#9177311yescharacteristic
431C4C4×#122011yescharacteristic
432C4#9182711yescharacteristic
433C3#1060120411yescharacteristic, complemented, Sylow
434C2—21no—
435C2—21no—
436C2—21no—
437C2—81no—
438C2#1175105711yescharacteristic
subgroupG/H
centerC2#11751057
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#421C2
socleC2×C3×C5#386
prime radicalC2×C3×C5×#41C22
cosocleC22×C3×C4×C5C23
hypercenter#421D15
hypocenterC3×C5#1912
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #11756275C2semidirect
5. C2×#91108C2semidirect
6. #11746378C2semidirect
7. #11746352C2semidirect
13. #91833C4semidirect
14. #91825C4semidirect
362. C3×C5#1912semidirect
417. C5#70411semidirect
433. C3#10601204semidirect

Maximal subgroups

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

subgroupindex
#117565842
#117562752
C3×C5×#4212
#117513372
C2×#911082
#117463782
#117463522
#106012043
#704115