Finite Group Databasebeta

← #14301599

Subgroups — #14301599

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4082C211yesmaximal, characteristic
2#11754188C211yesmaximal, characteristic, complemented
3#11751316C211yesmaximal, characteristic
4C5×#5215C211yesmaximal, characteristic
5C2×#90961C211yesmaximal, characteristic, complemented
6#11745978C211yesmaximal, characteristic, complemented
7#11745977C211yesmaximal, characteristic, complemented
8#10601118—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C3×Dic10C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C2×C3×C22⋊Dic5—22no—
16C3×#4082—22no—
17C3×#4082C414yescomplemented
18C2×C3×C4×Dic5C2211yescharacteristic
19#91528—22no—
20#91331—22no—
21Dic3×Dic10—22no—
22#91116—22no—
23C5×#832—22no—
24#90961—22no—
25#71724—51nomaximal, Hall
26C2×#4082D311yescharacteristic
27#65850—31no—
28C5×#418—31no—
29#65504—31no—
30C2×#3956—31no—
31#64775—31no—
32#64752—31no—
33C24×C3×C5—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4C2×C412yes—
40C22×C3×C4×C5C2311yescharacteristic
41C22×C3×Dic5—21no—
42C22×C3×Dic5D412yes—
43C2×C3×Dic10—21no—
44C2×C3×Dic10—21no—
45C2×C3×Dic10—21no—
46C2×C3×Dic10—21no—
47C2×C3×Dic10C2×C412yes—
48C2×C3×Dic10D412yes—
49#6719—21no—
50C4⋊Dic15D412yes—
51C4×Dic15—21no—
52#6710—21no—
53#6710—21no—
54C2×C3⋊#168—21no—
55C5×#217—21no—
56C5×C4⋊Dic3D412yes—
57C4×C5×Dic3—21no—
58C5×#208—21no—
59C5×#208—21no—
60C2×C5×C3⋊C8—21no—
61C3×C22⋊Dic5—28no—
62C3×C4×Dic5—21no—
63C3×C4×Dic5C2×C412yes—
64#6668—24no—
65Dic3×Dic5—24no—
66C2×C3×#124—51no—
67#5812—51no—
68C2×#836—51no—
69#5215—51no—
70#5215D511yescharacteristic
71#4523—51no—
72#4523—51no—
73C22×C5×D4C2×D311yescharacteristic
74C22×Dic10C2×D311yescharacteristic
75C2×C5×M16—31no—
76C5×#117—31no—
77C2×C22⋊Dic5—22no—
78#4082—22no—
79#4082Dic314yescomplemented
80#4072—31no—
81C2×C4×Dic5C2×D311yescharacteristic
82C2×#681—31no—
83#4033—62no—
84#4023—62no—
85C4×Dic10—62no—
86C5×#102—62no—
87#3964—62no—
88#3956—62no—
89#1888—151noSylow
90C23×C3×C5—22no—
91C23×C3×C5—44no—
92C23×C3×C5—41no—
93C23×C3×C5—41no—
94C23×C3×C5C2×D411yescharacteristic
95C3×C5×D4—22no—
96C3×C5×D4—22no—
97C3×C5×D4—41no—
98C3×C5×D4—41no—
99C2×C3×C4×C5C22×C411yescharacteristic
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
105C2×Dic15—22no—
106C2×C5×Dic3—22no—
107C2×C3×Dic5—22no—
108C2×C3×Dic5—22no—
109C2×C3×Dic5—22no—
110C2×C3×Dic5—42no—
111C2×C3×Dic5C22⋊C414yes—
112C3×Dic10—22no—
113C3×Dic10—22no—
114C3×Dic10—22no—
115C3×Dic10—22no—
116C3⋊#168—41no—
117C5×C3⋊C8—41no—
118C22×C3×Q8—51no—
119C22×C3×D4C2×D511yescharacteristic
120C3×#124—54no—
121C3×#124—102no—
122C2×C3×C22⋊C4—102no—
123C2×C3×C42—51no—
124Q8×Dic3—102no—
125Q8×Dic3—102no—
126#926—51no—
127#926—102no—
128#926C2×D511yescharacteristic
129C2×#208—51no—
130C2×#208C2×D511yescharacteristic
131#836—102no—
132#832—22no—
133#832—102no—
134C24×C5—21no—
135C2×C5×D4—21no—
136C2×C5×D4—21no—
137C2×C5×D4—21no—
138C2×C5×D4—21no—
139C2×C5×D4—21no—
140C2×C5×D4C2×Dic312yes—
141C22×C4×C5C22×D311yescharacteristic
142C22×Dic5—21no—
143C22×Dic5#6712yes—
144C2×Dic10—21no—
145C2×Dic10—21no—
146C2×Dic10—21no—
147C2×Dic10—21no—
148C2×Dic10C2×Dic312yes—
149C2×Dic10#6712yes—
150C5×M16—61no—
151C5×M16—61no—
152C2×C5×C8—61no—
153C5×C4⋊C4—32no—
154C5×C22⋊C4—61no—
155C42×C5—61no—
156C22⋊Dic5—28no—
157C22⋊Dic5—61no—
158C4⋊Dic5—32no—
159#683—64no—
160C4×Dic5—21no—
161C4×Dic5—64no—
162C4×Dic5—61no—
163C4×Dic5C2×Dic312yes—
164#681—61no—
165#681—61no—
166C2×#168—61no—
167C2×#124—51no—
168#519—151no—
169#418—31no—
170#418—151no—
171C2×#101—151no—
172#339—151no—
173#339—151no—
174C22×C3×C5—22no—
175C22×C3×C5—44no—
176C22×C3×C5—42no—
177C22×C3×C5—82no—
178C22×C3×C5—82no—
179C22×C3×C5C2×C22⋊C411yescharacteristic
180C22×C3×C5#12011yescharacteristic
181C22×C3×C5#12311yescharacteristic
182C3×C4×C5C4×D411yescharacteristic
183C3×C4×C5C4×D411yescharacteristic
184C3×C4×C5#12111yescharacteristic
185C3×C4×C5#12111yescharacteristic
186Dic15—42no—
187C3×Dic5—24no—
188C3×Dic5—42no—
189C5×Dic3—42no—
190C24×C3—21no—
191C2×C3×Q8—52no—
192C2×C3×Q8—52no—
193C2×C3×Q8—101no—
194C2×C3×Q8—101no—
195C2×C3×Q8—101no—
196C2×C3×Q8—101no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4—21no—
201C2×C3×D4—21no—
202C2×C3×D4C4×D512yes—
203C22×C3×C4—52no—
204C22×C3×C4—101no—
205C22×C3×C4C22×D511yescharacteristic
206C3×C22⋊C4—108no—
207C3×C42—52no—
208C3×C42—101no—
209#217—21no—
210#217—101no—
211C4⋊Dic3—52no—
212C4⋊Dic3—104no—
213C4⋊Dic3C22⋊D512yes—
214C4×Dic3—21no—
215C4×Dic3—104no—
216C4×Dic3—101no—
217#208—21no—
218#208—21no—
219#208—101no—
220#208—101no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—101no—
223C23×C5—22no—
224C23×C5—44no—
225C23×C5—41no—
226C23×C5—41no—
227C23×C5C2×#6711yescharacteristic
228C5×D4—22no—
229C5×D4—22no—
230C5×D4—41no—
231C5×D4—41no—
232C2×C4×C5—62no—
233C2×C4×C5D3×D411yescharacteristic
234C2×C4×C5D3×D411yescharacteristic
235C2×C4×C5#23711yescharacteristic
236C2×C4×C5#23711yescharacteristic
237C2×C4×C5C22×Dic311yescharacteristic
238C2×C4×C5C2×#6711yescharacteristic
239C2×Dic5—22no—
240C2×Dic5—22no—
241C2×Dic5—22no—
242C2×Dic5—42no—
243C2×Dic5—62no—
244C2×Dic5#21714yes—
245Dic10—22no—
246Dic10—22no—
247Dic10—22no—
248Dic10—22no—
249C5×C8—121no—
250#168—121no—
251C22×Q8—51no—
252C22×D4D3×D511yescharacteristic
253C2×M16—31no—
254C2×M16—151no—
255#124—54no—
256#124—102no—
257C4×Q8—302no—
258C4×Q8—302no—
259#117—31no—
260#117—151no—
261#117—302no—
262C2×C22⋊C4—102no—
263C2×C42—51no—
264#102—62no—
265#102—302no—
266#101—302no—
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5—82no—
270C2×C3×C5#38611yescharacteristic
271C2×C3×C5#45412yes—
272C23×C3—22no—
273C23×C3—44no—
274C23×C3—41no—
275C23×C3—41no—
276C23×C3D4×D511yescharacteristic
277C3×Q8—102no—
278C3×Q8—102no—
279C3×Q8—102no—
280C3×Q8—102no—
281C3×D4—22no—
282C3×D4—22no—
283C3×D4—41no—
284C3×D4—41no—
285C2×C3×C4—54no—
286C2×C3×C4—102no—
287C2×C3×C4—102no—
288C2×C3×C4—102no—
289C2×C3×C4—202no—
290C2×C3×C4C2×C4×D511yescharacteristic
291C2×C3×C4#70911yescharacteristic
292C2×C3×C4D4×D511yescharacteristic
293C2×C3×C4D4×D511yescharacteristic
294C2×C3×C4#71111yescharacteristic
295C2×C3×C4C2×C22⋊D511yescharacteristic
296C2×Dic3—22no—
297C2×Dic3—102no—
298C3⋊C8—41no—
299C3⋊C8—201no—
300C22×C5—22no—
301C22×C5—44no—
302C22×C5—42no—
303C22×C5—82no—
304C22×C5—82no—
305C22×C5#93511yescharacteristic
306C22×C5#93711yescharacteristic
307C22×C5C2×#21711yescharacteristic
308C4×C5—122no—
309C4×C5D4×Dic311yescharacteristic
310C4×C5D4×Dic311yescharacteristic
311C4×C5#93911yescharacteristic
312C4×C5#93911yescharacteristic
313Dic5—24no—
314Dic5—42no—
315Dic5—122no—
316C24—21no—
317C2×Q8—52no—
318C2×Q8—52no—
319C2×Q8—101no—
320C2×Q8—101no—
321C2×Q8—101no—
322C2×Q8—101no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4D5×Dic312yes—
329C22×C4—52no—
330C22×C4—101no—
331C22×C4C2×D3×D511yescharacteristic
332M16—61no—
333M16—61no—
334M16—301no—
335M16—301no—
336C2×C8—61no—
337C2×C8—301no—
338C4⋊C4—32no—
339C4⋊C4—152no—
340C4⋊C4—304no—
341C22⋊C4—61no—
342C22⋊C4—108no—
343C22⋊C4—301no—
344C42—52no—
345C42—61no—
346C42—101no—
347C42—304no—
348C42—301no—
349C3×C5#188811yescharacteristic, complemented, Hall
350C22×C3—22no—
351C22×C3—44no—
352C22×C3—42no—
353C22×C3—82no—
354C22×C3—82no—
355C22×C3D5×C22⋊C411yescharacteristic
356C22×C3#402911yescharacteristic
357C22×C3#408311yescharacteristic
358C3×C4—104no—
359C3×C4—202no—
360C3×C4#402711yescharacteristic
361C3×C4#403011yescharacteristic
362C3×C4C4×C22⋊D511yescharacteristic
363C3×C4#408411yescharacteristic
364Dic3—42no—
365Dic3—202no—
366C2×C5—21no—
367C2×C5—21no—
368C2×C5—82no—
369C2×C5#506212yes—
370C2×C5#522011yescharacteristic
371C23—22no—
372C23—44no—
373C23—41no—
374C23—41no—
375C23D5×#6711yescharacteristic
376Q8—102no—
377Q8—102no—
378Q8—102no—
379Q8—102no—
380D4—22no—
381D4—22no—
382D4—41no—
383D4—41no—
384C2×C4—54no—
385C2×C4—62no—
386C2×C4—102no—
387C2×C4—102no—
388C2×C4—102no—
389C2×C4—202no—
390C2×C4—302no—
391C2×C4C2×D5×Dic311yescharacteristic
392C2×C4#677911yescharacteristic
393C2×C4#678011yescharacteristic
394C2×C4D5×#6711yescharacteristic
395C2×C4D3×C22⋊D511yescharacteristic
396C2×C4#679011yescharacteristic
397C8—121no—
398C8—601no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—82no—
402C2×C3#6524511yescharacteristic
403C2×C3#6549012yes—
404C5#7172411yescharacteristic, complemented, Sylow
405C22—22no—
406C22—44no—
407C22—42no—
408C22—82no—
409C22—82no—
410C22D5×#21711yescharacteristic
411C22#9154811yescharacteristic
412C22#9157711yescharacteristic
413C4—104no—
414C4—122no—
415C4—202no—
416C4—602no—
417C4#9154911yescharacteristic
418C4#9155011yescharacteristic
419C4Dic3×C22⋊D511yescharacteristic
420C4#9155911yescharacteristic
421C3#1060111811yescharacteristic, complemented, Sylow
422C2—21no—
423C2—21no—
424C2—82no—
425C2#1174916812yes—
426C2#1174951811yescharacteristic
subgroupG/H
centerC22#91577
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC22×C3×C5×D4C22
socleC22×C3×C5#120
cosocleC22×C3×C4×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1888
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11754188C2semidirect
5. C2×#90961C2semidirect
6. #11745978C2semidirect
7. #11745977C2semidirect
17. C3×#4082C4semidirect
79. #4082Dic3semidirect
349. C3×C5#1888semidirect
404. C5#71724semidirect
421. C3#10601118semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40822
#117541882
#117513162
C5×#52152
C2×#909612
#117459782
#117459772
#106011183
#717245