Finite Group Databasebeta

← #14417561

Subgroups — #14417561

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×Q16×D15C211yesmaximal, characteristic
2#11755124C212yesmaximal
3C5×#5184C211yesmaximal, characteristic, complemented
4C3×#65473C211yesmaximal, characteristic, complemented
5#11749257C212yesmaximal, complemented
6#11749244C212yesmaximal, complemented
7#11749218C212yesmaximal
8#11747876C211yesmaximal, characteristic, complemented
9#11747854C211yesmaximal, characteristic, complemented
10#11747687C211yesmaximal, characteristic
11#11747668C211yesmaximal, characteristic
12#10611562—31nomaximal, Hall
13C2×Q8×D15C2212yes—
14C2×C3×C5×Q16C2211yescharacteristic
15C2×#6718C2212yes—
16Q16×D15C418yescomplemented
17C2×Dic60C2211yescharacteristic
18C2×C8×D15C2211yescharacteristic
19C5×Q8×Dic3C2212yes—
20C3×Q8×Dic5C2212yes—
21#91386—22no—
22#91386C2211yescharacteristic
23#91347—22no—
24#91347C2212yes—
25#91340—22no—
26#91340C2212yes—
27#91333—22no—
28#91333C2212yes—
29C2×#6651C2211yescharacteristic
30C5×#835C2212yes—
31C5×#817C2211yescharacteristic
32C5×#815C2211yescharacteristic
33C3×#3967C2212yes—
34C3×#3949C2211yescharacteristic
35C3×#3947C2211yescharacteristic
36#90989C2212yes—
37#90975C2212yes—
38#90974C2212yes—
39Dic3×#168C2211yescharacteristic
40Dic5×C3⋊C8C2211yescharacteristic
41#79831—51nomaximal, Hall
42C2×D5×Q16—31no—
43#65906—32no—
44C5×#441—31no—
45#65473D311yescharacteristic, complemented
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—
54Q8×D15—24no—
55Q8×D15C2×C418yes—
56C2×C4×D15—22no—
57C2×C4×D15C2311yescharacteristic
58C2×Dic30—22no—
59C2×Dic30C2312yes—
60C3×C5×Q16C2×C414yes—
61C2×C3×C5×C8C2311yescharacteristic
62#6718C2×C418yes—
63C2×C3⋊#168C2311yescharacteristic
64Dic60C2×C414yes—
65C8×D15C2×C414yes—
66C5×C4⋊Dic3—22no—
67C5×C4⋊Dic3C2312yes—
68C4×C5×Dic3—22no—
69C4×C5×Dic3C2311yescharacteristic
70C2×C5×C3⋊C8C2311yescharacteristic
71C3×C4⋊Dic5—22no—
72C3×C4⋊Dic5C2312yes—
73C3×C4×Dic5—22no—
74C3×C4×Dic5C2311yescharacteristic
75C2×C3×#168C2311yescharacteristic
76#6669—22no—
77#6669—22no—
78#6669D412yes—
79#6667—22no—
80#6667D412yes—
81Dic3×Dic5—22no—
82Dic3×Dic5—22no—
83Dic3×Dic5—22no—
84#6651—22no—
85C2×D3×Q16—51no—
86#5572—52no—
87C3×#441—51no—
88#5184D511yescharacteristic, complemented
89C4×#216—52no—
90#4860—51no—
91#4853—51no—
92#4802—52no—
93#4790—52no—
94#4716—51no—
95#4708—51no—
96C2×Q8×D5—32no—
97C2×C5×Q16C2×D311yescharacteristic
98C4×C5×Q8—32no—
99Q8×Dic5C2×D312yes—
100C2×#689—32no—
101D5×Q16—38no—
102C2×Dic20—31no—
103C2×#676—31no—
104C2×C8×D5—31no—
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#3967C2×D312yes—
117#3949C2×D311yescharacteristic
118#3948—32no—
119#3947C2×D311yescharacteristic
120C8×Dic5—31no—
121#3942—32no—
122#3939—32no—
123C4×#168—31no—
124#2950—151noSylow
125C22×D15C2×D411yescharacteristic
126C3×C5×Q8—22no—
127C3×C5×Q8C22×C414yes—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5C2411yescharacteristic
130C2×Dic15—22no—
131C2×Dic15C2×D411yescharacteristic
132C4×D15—28no—
133C4×D15C22×C412yes—
134C4×D15#4112yes—
135Dic30—22no—
136Dic30—28no—
137Dic30C22×C414yes—
138C2×C5×Dic3—22no—
139C2×C5×Dic3C2×D412yes—
140C2×C3×Dic5—22no—
141C2×C3×Dic5C2×D412yes—
142C3×C5×C8C22×C412yes—
143C3⋊#168C22×C412yes—
144C3×#168—21no—
145C5×C3⋊C8—21no—
146C2×D3×Q8—52no—
147C2×C3×Q16C2×D511yescharacteristic
148C3×C4×Q8—52no—
149Q8×Dic3C2×D512yes—
150C2×#216—52no—
151D3×Q16—58no—
152C2×Dic12—51no—
153C2×ΓL(1,𝔽25)—51no—
154C2×D3×C8—51no—
155#892—52no—
156#892—102no—
157#887—52no—
158#887—102no—
159#872—51no—
160#872—102no—
161C4×Dic6—52no—
162C4×Dic6—102no—
163C3×#106—51no—
164C3×#103—52no—
165C3×#97—51no—
166#835C2×D512yes—
167#817C2×D511yescharacteristic
168#816—52no—
169#815C2×D511yescharacteristic
170C8×Dic3—51no—
171#810—52no—
172#807—52no—
173C4×C3⋊C8—51no—
174C2×C5×Q8C22×D312yes—
175Q8×D5—38no—
176Q8×D5—64no—
177C2×C4×D5—31no—
178C2×C4×D5—62no—
179C2×Dic10—32no—
180C2×Dic10—62no—
181C5×Q16C4×D314yes—
182C2×C5×C8—31no—
183C2×C5×C8C22×D311yescharacteristic
184C5×C4⋊C4—32no—
185C5×C4⋊C4—62no—
186C42×C5—31no—
187C42×C5—62no—
188#689—38no—
189#685—32no—
190#685—62no—
191C4⋊Dic5—22no—
192C4⋊Dic5C22×D312yes—
193#683—32no—
194#683—62no—
195#683—62no—
196C4×Dic5—22no—
197C4×Dic5—62no—
198C4×Dic5—62no—
199C4×Dic5—62no—
200C4×Dic5C22×D311yescharacteristic
201C2×#168—31no—
202C2×#168C22×D311yescharacteristic
203Dic20—34no—
204#676—62no—
205C8×D5—34no—
206C22×Q16—151no—
207#519—152no—
208#441—31no—
209#441—51no—
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×D15—22no—
219C2×D15C4×D412yes—
220C3×C4×C5—24no—
221C3×C4×C5C23×C411yescharacteristic
222C3×C4×C5C2×#4111yescharacteristic
223Dic15—24no—
224Dic15C4×D412yes—
225C3×Dic5—22no—
226C3×Dic5—42no—
227C5×Dic3—22no—
228C5×Dic3—42no—
229C2×C3×Q8C22×D512yes—
230D3×Q8—58no—
231D3×Q8—104no—
232C2×C4×D3—51no—
233C2×C4×D3—102no—
234C2×Dic6—52no—
235C2×Dic6—102no—
236C3×Q16C4×D514yes—
237C2×C3×C8—51no—
238C2×C3×C8C22×D511yescharacteristic
239C3×C4⋊C4—52no—
240C3×C4⋊C4—102no—
241C3×C42—51no—
242C3×C42—102no—
243#216—58no—
244(C2×D3)⋊C4—52no—
245(C2×D3)⋊C4—102no—
246C4⋊Dic3—22no—
247C4⋊Dic3C22×D512yes—
248Dic3⋊C4—52no—
249Dic3⋊C4—102no—
250Dic3⋊C4—102no—
251C4×Dic3—22no—
252C4×Dic3—102no—
253C4×Dic3—102no—
254C4×Dic3—102no—
255C4×Dic3C22×D511yescharacteristic
256C2×C3⋊C8—51no—
257C2×C3⋊C8C22×D511yescharacteristic
258Dic12—54no—
259ΓL(1,𝔽25)—102no—
260D3×C8—54no—
261C22×D5—31no—
262C5×Q8—22no—
263C5×Q8C2×C4×D314yes—
264C2×C4×C5—22no—
265C2×C4×C5—32no—
266C2×C4×C5—62no—
267C2×C4×C5C23×D311yescharacteristic
268C2×Dic5—22no—
269C2×Dic5—31no—
270C2×Dic5—62no—
271C2×Dic5D3×D412yes—
272C4×D5—32no—
273C4×D5—32no—
274C4×D5—68no—
275Dic10—34no—
276Dic10—68no—
277Dic10—62no—
278C5×C8—61no—
279C5×C8C2×C4×D312yes—
280#168—21no—
281#168—32no—
282C22×Q8—152no—
283C2×Q16—152no—
284C2×Q16—158no—
285C2×Q16—151no—
286C2×Q16D3×D511yescharacteristic
287C2×M16—151no—
288C22×C8—151no—
289C4×Q8—32no—
290C4×Q8—52no—
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—51no—
302#103—32no—
303#103—52no—
304#103—152no—
305#103—152no—
306#97—31no—
307#97—51no—
308C4×C8—151no—
309C4×C8—151no—
310C2×C3×C5C2×C4×D411yescharacteristic
311C2×C3×C5#57812yes—
312D15—22no—
313C22×D3—51no—
314C3×Q8—22no—
315C3×Q8C2×C4×D514yes—
316C2×C3×C4—22no—
317C2×C3×C4—52no—
318C2×C3×C4—102no—
319C2×C3×C4C23×D511yescharacteristic
320C2×Dic3—22no—
321C2×Dic3—51no—
322C2×Dic3—102no—
323C2×Dic3D4×D512yes—
324C4×D3—52no—
325C4×D3—52no—
326C4×D3—108no—
327Dic6—54no—
328Dic6—108no—
329Dic6—102no—
330C3×C8—101no—
331C3×C8C2×C4×D512yes—
332C3⋊C8—21no—
333C3⋊C8—52no—
334C22×C5C2×D3×D411yescharacteristic
335C2×D5—32no—
336C2×D5—62no—
337C4×C5—24no—
338C4×C5—62no—
339C4×C5—122no—
340C4×C5C22×C4×D311yescharacteristic
341C4×C5D3×#4111yescharacteristic
342Dic5—22no—
343Dic5—32no—
344Dic5—42no—
345Dic5—64no—
346C2×Q8—158no—
347C2×Q8—152no—
348C2×Q8—302no—
349C2×Q8—304no—
350C2×Q8C2×D3×D512yes—
351C22×C4—151no—
352C22×C4—302no—
353Q16—158no—
354Q16—154no—
355Q16#120014yes—
356M16—302no—
357C2×C8—31no—
358C2×C8—51no—
359C2×C8—151no—
360C2×C8—154no—
361C2×C8C2×D3×D511yescharacteristic
362C4⋊C4—32no—
363C4⋊C4—52no—
364C4⋊C4—62no—
365C4⋊C4—102no—
366C4⋊C4—152no—
367C4⋊C4—302no—
368C4⋊C4—302no—
369C22⋊C4—152no—
370C22⋊C4—302no—
371C42—31no—
372C42—51no—
373C42—62no—
374C42—102no—
375C42—302no—
376C42—302no—
377C42—302no—
378C3×C5#295011yescharacteristic, complemented, Hall
379C22×C3C2×D4×D511yescharacteristic
380C2×D3—52no—
381C2×D3—102no—
382C3×C4—24no—
383C3×C4—102no—
384C3×C4—202no—
385C3×C4C22×C4×D511yescharacteristic
386C3×C4D5×#4111yescharacteristic
387Dic3—22no—
388Dic3—42no—
389Dic3—52no—
390Dic3—104no—
391C2×C5C4×D3×D411yescharacteristic
392C2×C5#577912yes—
393D5—62no—
394C23—151no—
395Q8—22no—
396Q8—154no—
397Q8—308no—
398Q8—302no—
399Q8C2×#120014yes—
400C2×C4—22no—
401C2×C4—32no—
402C2×C4—52no—
403C2×C4—62no—
404C2×C4—102no—
405C2×C4—151no—
406C2×C4—152no—
407C2×C4—152no—
408C2×C4—308no—
409C2×C4—302no—
410C2×C4C22×D3×D511yescharacteristic
411C8—61no—
412C8—101no—
413C8—152no—
414C8C2×#120012yes—
415C2×C3C4×D4×D511yescharacteristic
416C2×C3#6611312yes—
417D3—102no—
418C5#7983111yescharacteristic, complemented, Sylow
419C22—152no—
420C22—302no—
421C22D3×D4×D511yescharacteristic
422C4—24no—
423C4—62no—
424C4—102no—
425C4—122no—
426C4—152no—
427C4—202no—
428C4—304no—
429C4#9202411yescharacteristic
430C4C22×#120011yescharacteristic
431C3#1061156211yescharacteristic, complemented, Sylow
432C2—302no—
433C2#1175411112yes—
434C2D4×#120011yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×Q16C22
socleC22×C3×C5C22×D4
prime radicalC22×D15C2×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. C5×#5184C2semidirect
4. C3×#65473C2semidirect
5. #11749257C2semidirect
6. #11749244C2semidirect
8. #11747876C2semidirect
9. #11747854C2semidirect
16. Q16×D15C4semidirect
45. #65473D3semidirect
88. #5184D5semidirect
378. C3×C5#2950semidirect
418. C5#79831semidirect
431. C3#10611562semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D152
#117551242
C5×#51842
C3×#654732
#117492572
#117492442
#117492182
#117478762
#117478542
#117476872
#117476682
#106115623
#798315