Finite Group Databasebeta

← #14417560

Subgroups — #14417560

Order 1920.

912 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
1C2×C3×D5×Q16C211yesmaximal, characteristic
2#11755140C212yesmaximal
3#11751285C211yesmaximal, characteristic, complemented
4C5×#5184C211yesmaximal, characteristic, complemented
5#11749263C212yesmaximal, complemented
6Dic3×#689C212yesmaximal, complemented
7#11749208C212yesmaximal
8#11747884C211yesmaximal, characteristic, complemented
9#11747870C211yesmaximal, characteristic, complemented
10#11747671C211yesmaximal, characteristic
11#11747646C211yesmaximal, characteristic
12#10611562—31nomaximal, Hall
13C2×C3×Q8×D5C2212yes—
14C2×C3×C5×Q16C2211yescharacteristic
15Q8×Dic15C2212yes—
16C5×Q8×Dic3C2212yes—
17C2×C3×#689C2212yes—
18C3×D5×Q16C418yescomplemented
19C2×C3×Dic20C2211yescharacteristic
20C2×C3×C8×D5C2211yescharacteristic
21#91358—22no—
22#91358C2212yes—
23#91357—22no—
24#91357C2211yescharacteristic
25#91331—22no—
26#91331C2212yes—
27Dic3×Dic10—22no—
28Dic3×Dic10C2212yes—
29C2×#6649C2211yescharacteristic
30#91119C2212yes—
31#91101C2211yescharacteristic
32#91099C2211yescharacteristic
33C5×#835C2212yes—
34C5×#817C2211yescharacteristic
35C5×#815C2211yescharacteristic
36#90988C2212yes—
37#90971C2212yes—
38#90970C2212yes—
39#90951C2211yescharacteristic
40Dic3×#168C2211yescharacteristic
41#83874—51nomaximal, Hall
42C2×D5×Q16D311yescharacteristic
43#65906—32no—
44C5×#441—31no—
45#65473—31no—
46C4×#689—32no—
47#65149—31no—
48#65142—31no—
49#65091—32no—
50#65079—32no—
51#65005—31no—
52#64997—31no—
53C2×C3×C5×Q8C2312yes—
54C3×Q8×D5—24no—
55C3×Q8×D5C2×C418yes—
56C2×C3×C4×D5—22no—
57C2×C3×C4×D5C2311yescharacteristic
58C2×C3×Dic10—22no—
59C2×C3×Dic10C2312yes—
60C3×C5×Q16C2×C414yes—
61C2×C3×C5×C8C2311yescharacteristic
62C4⋊Dic15—22no—
63C4⋊Dic15C2312yes—
64C4×Dic15—22no—
65C4×Dic15C2311yescharacteristic
66C2×C3⋊#168C2311yescharacteristic
67C5×C4⋊Dic3—22no—
68C5×C4⋊Dic3C2312yes—
69C4×C5×Dic3—22no—
70C4×C5×Dic3C2311yescharacteristic
71C2×C5×C3⋊C8C2311yescharacteristic
72C3×#689C2×C418yes—
73C2×C3×#168C2311yescharacteristic
74C3×Dic20C2×C414yes—
75C3×C8×D5C2×C414yes—
76#6668—22no—
77#6668—22no—
78#6668D412yes—
79#6665—22no—
80#6665D412yes—
81Dic3×Dic5—22no—
82Dic3×Dic5—22no—
83Dic3×Dic5—22no—
84#6649—22no—
85C22×C3×Q16—51no—
86#5812—52no—
87#5225—52no—
88#5184—51no—
89#5184—51no—
90#5184—51no—
91#5184D511yescharacteristic, complemented
92Dic3×Q16—52no—
93Dic3×Q16—52no—
94#5106—51no—
95#5101—51no—
96C2×Q8×D5C2×D312yes—
97C2×C5×Q16C2×D311yescharacteristic
98C4×C5×Q8—32no—
99Q8×Dic5—32no—
100C2×#689C2×D312yes—
101D5×Q16Dic318yescomplemented
102C2×Dic20C2×D311yescharacteristic
103C2×#676—31no—
104C2×C8×D5C2×D311yescharacteristic
105#4038—32no—
106#4038—62no—
107#4033—32no—
108#4033—62no—
109#4018—31no—
110#4018—62no—
111C4×Dic10—32no—
112C4×Dic10—62no—
113C5×#106—31no—
114C5×#103—32no—
115C5×#97—31no—
116#3967—32no—
117#3949—31no—
118#3948—32no—
119#3947—31no—
120C8×Dic5—31no—
121#3942—32no—
122#3939—32no—
123C4×#168—31no—
124#2950—151noSylow
125C22×C3×D5C2×D411yescharacteristic
126C3×C5×Q8—22no—
127C3×C5×Q8C22×C414yes—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5C2411yescharacteristic
130C2×Dic15—22no—
131C2×Dic15C2×D412yes—
132C2×C5×Dic3—22no—
133C2×C5×Dic3C2×D412yes—
134C2×C3×Dic5—22no—
135C2×C3×Dic5C2×D411yescharacteristic
136C3×C4×D5—28no—
137C3×C4×D5C22×C412yes—
138C3×C4×D5#4112yes—
139C3×Dic10—22no—
140C3×Dic10—28no—
141C3×Dic10C22×C414yes—
142C3×C5×C8C22×C412yes—
143C3⋊#168—21no—
144C3×#168C22×C412yes—
145C5×C3⋊C8—21no—
146C22×C3×Q8—52no—
147C2×C3×Q16—52no—
148C2×C3×Q16—58no—
149C2×C3×Q16—51no—
150C2×C3×Q16C2×D511yescharacteristic
151C22×C3×C8—51no—
152Q8×Dic3—52no—
153Q8×Dic3—52no—
154Q8×Dic3—52no—
155Q8×Dic3—102no—
156Q8×Dic3—102no—
157Q8×Dic3C2×D512yes—
158#926—51no—
159#926—52no—
160#926—102no—
161#926—102no—
162C2×#208—51no—
163#835—52no—
164#835—52no—
165#835—52no—
166#835C2×D512yes—
167#818—52no—
168#817—51no—
169#817C2×D511yescharacteristic
170#815—51no—
171#815C2×D511yescharacteristic
172C8×Dic3—51no—
173C8×Dic3—51no—
174C2×C5×Q8C22×D312yes—
175Q8×D5—24no—
176Q8×D5C2×Dic318yes—
177C2×C4×D5—22no—
178C2×C4×D5C22×D311yescharacteristic
179C2×Dic10—22no—
180C2×Dic10C22×D312yes—
181C5×Q16C2×Dic314yes—
182C2×C5×C8—31no—
183C2×C5×C8C22×D311yescharacteristic
184C5×C4⋊C4—32no—
185C5×C4⋊C4—62no—
186C42×C5—31no—
187C42×C5—62no—
188#689C2×Dic318yes—
189#685—32no—
190#685—62no—
191C4⋊Dic5—32no—
192C4⋊Dic5—62no—
193#683—32no—
194#683—62no—
195#683—62no—
196C4×Dic5—31no—
197C4×Dic5—62no—
198C4×Dic5—62no—
199C4×Dic5—62no—
200C4×Dic5—62no—
201C2×#168—31no—
202C2×#168C22×D311yescharacteristic
203Dic20C2×Dic314yes—
204#676—62no—
205C8×D5C2×Dic314yes—
206C22×Q16—51no—
207#519—152no—
208#441—31no—
209#441—151no—
210#441—151no—
211#441—151no—
212C4×Q16—152no—
213C4×Q16—152no—
214#427—151no—
215#419—152no—
216#405—151no—
217C22×C3×C5C22×D411yescharacteristic
218C2×C3×D5—22no—
219C2×C3×D5C4×D412yes—
220C3×C4×C5—24no—
221C3×C4×C5C23×C411yescharacteristic
222C3×C4×C5C2×#4111yescharacteristic
223Dic15—22no—
224Dic15—42no—
225C3×Dic5—24no—
226C3×Dic5C4×D412yes—
227C5×Dic3—22no—
228C5×Dic3—42no—
229C2×C3×Q8—58no—
230C2×C3×Q8—52no—
231C2×C3×Q8—102no—
232C2×C3×Q8—104no—
233C2×C3×Q8C22×D512yes—
234C22×C3×C4—51no—
235C22×C3×C4—102no—
236C3×Q16—58no—
237C3×Q16—54no—
238C3×Q16C4×D514yes—
239C2×C3×C8—51no—
240C2×C3×C8—54no—
241C2×C3×C8C22×D511yescharacteristic
242#217—52no—
243#217—102no—
244C4⋊Dic3—22no—
245C4⋊Dic3—52no—
246C4⋊Dic3—52no—
247C4⋊Dic3—102no—
248C4⋊Dic3—102no—
249C4⋊Dic3—102no—
250C4⋊Dic3C22×D512yes—
251C4×Dic3—22no—
252C4×Dic3—51no—
253C4×Dic3—102no—
254C4×Dic3—102no—
255C4×Dic3—102no—
256C4×Dic3—102no—
257C4×Dic3C22×D511yescharacteristic
258#208—102no—
259C2×C3⋊C8—51no—
260C2×C3⋊C8C22×D511yescharacteristic
261C22×D5D3×D411yescharacteristic
262C5×Q8—22no—
263C5×Q8C22×Dic314yes—
264C2×C4×C5—22no—
265C2×C4×C5—32no—
266C2×C4×C5—62no—
267C2×C4×C5C23×D311yescharacteristic
268C2×Dic5—22no—
269C2×Dic5—32no—
270C2×Dic5—62no—
271C2×Dic5D3×D411yescharacteristic
272C4×D5—28no—
273C4×D5#23712yes—
274C4×D5C22×Dic312yes—
275Dic10—22no—
276Dic10—28no—
277Dic10C22×Dic314yes—
278C5×C8—61no—
279C5×C8C22×Dic312yes—
280#168—61no—
281#168C22×Dic312yes—
282C22×Q8—52no—
283C2×Q16—52no—
284C2×Q16—58no—
285C2×Q16—51no—
286C2×Q16D3×D511yescharacteristic
287C2×M16—151no—
288C22×C8—51no—
289C4×Q8—32no—
290C4×Q8—152no—
291C4×Q8—152no—
292C4×Q8—152no—
293C4×Q8—302no—
294C4×Q8—302no—
295#117—151no—
296#117—152no—
297#117—302no—
298#117—302no—
299#107—152no—
300#106—31no—
301#106—151no—
302#103—32no—
303#103—152no—
304#103—152no—
305#103—152no—
306#97—31no—
307#97—151no—
308C4×C8—151no—
309C4×C8—151no—
310C2×C3×C5C2×C4×D411yescharacteristic
311C2×C3×C5#57812yes—
312C3×D5—22no—
313C23×C3—51no—
314C3×Q8—22no—
315C3×Q8—54no—
316C3×Q8—108no—
317C3×Q8—102no—
318C3×Q8C2×C4×D514yes—
319C2×C3×C4—22no—
320C2×C3×C4—51no—
321C2×C3×C4—52no—
322C2×C3×C4—52no—
323C2×C3×C4—108no—
324C2×C3×C4—102no—
325C2×C3×C4C23×D511yescharacteristic
326C2×Dic3—22no—
327C2×Dic3—52no—
328C2×Dic3—102no—
329C2×Dic3D4×D512yes—
330C3×C8—52no—
331C3×C8C2×C4×D512yes—
332C3⋊C8—21no—
333C3⋊C8—101no—
334C22×C5C2×D3×D411yescharacteristic
335C2×D5—22no—
336C2×D5D4×Dic312yes—
337C4×C5—24no—
338C4×C5—62no—
339C4×C5—122no—
340C4×C5C2×#23711yescharacteristic
341C4×C5C23×Dic311yescharacteristic
342Dic5—24no—
343Dic5—62no—
344Dic5—122no—
345Dic5D4×Dic312yes—
346C2×Q8—58no—
347C2×Q8—52no—
348C2×Q8—102no—
349C2×Q8—104no—
350C2×Q8C2×D3×D512yes—
351C22×C4—51no—
352C22×C4—102no—
353Q16—58no—
354Q16—54no—
355Q16D5×Dic314yes—
356M16—302no—
357C2×C8—31no—
358C2×C8—51no—
359C2×C8—54no—
360C2×C8—151no—
361C2×C8C2×D3×D511yescharacteristic
362C4⋊C4—32no—
363C4⋊C4—62no—
364C4⋊C4—152no—
365C4⋊C4—152no—
366C4⋊C4—302no—
367C4⋊C4—302no—
368C4⋊C4—302no—
369C22⋊C4—152no—
370C22⋊C4—302no—
371C42—31no—
372C42—62no—
373C42—151no—
374C42—302no—
375C42—302no—
376C42—302no—
377C42—302no—
378C3×C5#295011yescharacteristic, complemented, Hall
379C22×C3—52no—
380C22×C3—102no—
381C22×C3C2×D4×D511yescharacteristic
382C3×C4—24no—
383C3×C4—52no—
384C3×C4—104no—
385C3×C4C22×C4×D511yescharacteristic
386C3×C4D5×#4111yescharacteristic
387Dic3—22no—
388Dic3—42no—
389Dic3—102no—
390Dic3—202no—
391C2×C5#576612yes—
392C2×C5C2×D4×Dic311yescharacteristic
393D5—22no—
394C23—51no—
395Q8—22no—
396Q8—54no—
397Q8—108no—
398Q8—102no—
399Q8C2×D5×Dic314yes—
400C2×C4—22no—
401C2×C4—32no—
402C2×C4—51no—
403C2×C4—52no—
404C2×C4—52no—
405C2×C4—62no—
406C2×C4—108no—
407C2×C4—102no—
408C2×C4—152no—
409C2×C4—302no—
410C2×C4C22×D3×D511yescharacteristic
411C8—52no—
412C8—61no—
413C8—301no—
414C8C2×D5×Dic312yes—
415C2×C3—102no—
416C2×C3C4×D4×D511yescharacteristic
417C2×C3#6611312yes—
418C5#8387411yescharacteristic, complemented, Sylow
419C22—52no—
420C22—102no—
421C22D3×D4×D511yescharacteristic
422C4—24no—
423C4—52no—
424C4—62no—
425C4—104no—
426C4—122no—
427C4—302no—
428C4—602no—
429C4D5×#23711yescharacteristic
430C4C22×D5×Dic311yescharacteristic
431C3#1061156211yescharacteristic, complemented, Sylow
432C2—102no—
433C2#1175410712yes—
434C2D4×D5×Dic311yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×Q16C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×D4
cosocleC2×C3×C4×C5C24
hypercenterC2×Q16D3×D5
hypocenterC3×C5#2950
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. #11751285C2semidirect
4. C5×#5184C2semidirect
5. #11749263C2semidirect
6. Dic3×#689C2semidirect
8. #11747884C2semidirect
9. #11747870C2semidirect
18. C3×D5×Q16C4semidirect
91. #5184D5semidirect
101. D5×Q16Dic3semidirect
378. C3×C5#2950semidirect
418. C5#83874semidirect
431. C3#10611562semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×Q162
#117551402
#117512852
C5×#51842
#117492632
Dic3×#6892
#117492082
#117478842
#117478702
#117476712
#117476462
#106115623
#838745