Finite Group Databasebeta

← #14419092

Subgroups — #14419092

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic5×#237C211yesmaximal, characteristic
2#11752433C211yesmaximal, characteristic, complemented
3C3×#65774C211yesmaximal, characteristic, complemented
4#11752039C212yesmaximal, complemented
5#11752035C212yesmaximal, complemented
6#11751994C212yesmaximal, complemented
7Dic3×#704C212yesmaximal, complemented
8C4×D3×#170C211yesmaximal, characteristic, complemented
9#11751792C211yesmaximal, characteristic, complemented
10#11751789C211yesmaximal, characteristic, complemented
11#11751754C211yesmaximal, characteristic, complemented
12#10617545—31nomaximal, Hall
13C2×C5×#237C411yescharacteristic
14C2×#6762C2212yes—
15C2×C3×#704C2212yes—
16C2×D3×#170C2211yescharacteristic
17C2×D3×#170C2211yescharacteristic
18D4×Dic15C411yescharacteristic
19C3×D4×Dic5C2211yescharacteristic
20#67⋊Dic5C412yes—
21Dic5×#67C2212yes—
22#91529C412yes—
23C2×Dic3×Dic5C2212yes—
24C4×D3×Dic5C2211yescharacteristic
25#91344C411yescharacteristic
26#91338C411yescharacteristic
27Dic5×Dic6C2211yescharacteristic
28#91241C2212yes—
29C4⋊(C3⋊#170)C2211yescharacteristic
30C4×C3⋊#170C2211yescharacteristic
31C3×C22⋊#170C2212yes—
32C3×C4⋊#170C2211yescharacteristic
33C3×C4×#170C2211yescharacteristic
34#91177C2212yes—
35#91177C2212yes—
36(C2×D3)⋊#170C2212yes—
37#91169C2212yes—
38#91169C2212yes—
39Dic3×#170C2211yescharacteristic
40Dic3×#170C2212yes—
41Dic3×#170C2211yescharacteristic
42#79517—51nomaximal, Hall
43#41×Dic5—31no—
44#65788—31no—
45#65788—31no—
46#65774—31no—
47#65774D311yescharacteristic, complemented
48#65773—32no—
49#65773—32no—
50#65754—32no—
51C4×#704—32no—
52#65748—31no—
53C2×C4×#170—31no—
54C2×C3×C5×D4C2×C411yescharacteristic
55C22×Dic15C2×C412yes—
56C2×C5×#67C2×C412yes—
57C22×C5×Dic3C2×C412yes—
58C5×#237—24no—
59C2×C4×C5×D3C2×C411yescharacteristic
60C2×C5×Dic6C2×C411yescharacteristic
61C22×C3×Dic5C2312yes—
62C2×D3×Dic5C2×C411yescharacteristic
63C2×D3×Dic5C2311yescharacteristic
64#6762—24no—
65C2×C3⋊#170C2311yescharacteristic
66C2×C3⋊#170C2312yes—
67C2×C3⋊#170C2311yescharacteristic
68C3×#704—24no—
69C2×C3×#170C2311yescharacteristic
70C2×C3×#170C2312yes—
71C2×C3×#170C2311yescharacteristic
72D3×#170—22no—
73D3×#170—22no—
74#6719C2×C412yes—
75C4⋊Dic15C2×C411yescharacteristic
76C4×Dic15C2×C411yescharacteristic
77C3×C22⋊Dic5C2×C412yes—
78C3×C4⋊Dic5C2×C411yescharacteristic
79C3×C4×Dic5C2311yescharacteristic
80Dic3⋊Dic5C2×C412yes—
81Dic3⋊Dic5C2×C412yes—
82(C2×D3)⋊Dic5C2×C412yes—
83Dic3×Dic5C2×C411yescharacteristic
84Dic3×Dic5C2×C412yes—
85Dic3×Dic5C2×C412yes—
86Dic3×Dic5C2311yescharacteristic
87Dic3×Dic5C2312yes—
88C4×#237—51no—
89C3×#436—51no—
90#5127—52no—
91Dic3×M16—52no—
92#5012—51no—
93#4833—51no—
94#4831—51no—
95#4728—52no—
96#4718—52no—
97C4×D3×C8—51no—
98#4679—51no—
99C2×C5×#41—31no—
100C2×#704—32no—
101C2×#704C2×D312yes—
102C22×#170—31no—
103C22×#170—31no—
104Q8×Dic5—31no—
105Q8×Dic5—31no—
106D4×Dic5—31no—
107D4×Dic5—32no—
108D4×Dic5—32no—
109D4×Dic5C2×D311yescharacteristic
110#4072—32no—
111#4072—31no—
112C2×C4×Dic5—32no—
113C2×C4×Dic5—31no—
114C22⋊#170—32no—
115C22⋊#170—32no—
116C22⋊#170C2×D312yes—
117#4004—32no—
118#4004—32no—
119#4002—32no—
120#4002—32no—
121C4⋊#170—31no—
122C4⋊#170C2×D311yescharacteristic
123C4×#170—31no—
124C4×#170—31no—
125C4×#170—32no—
126C4×#170—31no—
127C4×#170C2×D311yescharacteristic
128#2965—151noSylow
129C23×C3×C5C22×C412yes—
130C22×C5×D3C22×C411yescharacteristic
131C3×C5×D4—22no—
132C2×C3×C4×C5C22×C411yescharacteristic
133C2×Dic15—24no—
134C2×Dic15C22×C412yes—
135C2×Dic15C22×C411yescharacteristic
136C2×Dic15C22×C411yescharacteristic
137C5×#67—24no—
138C2×C5×Dic3—24no—
139C2×C5×Dic3C22×C412yes—
140C2×C5×Dic3C22×C411yescharacteristic
141C4×C5×D3M1614yescomplemented
142C5×Dic6—22no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5C22×C412yes—
146C2×C3×Dic5C22×C411yescharacteristic
147C2×C3×Dic5C2411yescharacteristic
148D3×Dic5—22no—
149D3×Dic5—21no—
150D3×Dic5—21no—
151C3⋊#170—21no—
152C3⋊#170—22no—
153C3⋊#170#4112yescomplemented
154C3×#170—21no—
155C3×#170—22no—
156C3×#170#4112yescomplemented
157C2×#237AGL(1,𝔽5)11yescharacteristic
158C2×C3×M16—52no—
159C3×C4×D4—51no—
160D4×Dic3—51no—
161C4×#67—52no—
162C2×C4×Dic3—52no—
163C2×#208—52no—
164C2×D3×C8—51no—
165C2×D3×C8—51no—
166#892—51no—
167#887—51no—
168#67⋊C4—52no—
169#877—52no—
170C42×D3—51no—
171C4×Dic6—51no—
172C3×C4⋊C8—51no—
173C3×C22⋊C8—52no—
174C3×C4×C8—51no—
175#830—52no—
176(C2×D3)⋊C8—52no—
177#815—52no—
178#815—52no—
179Dic3⋊C8—52no—
180Dic3⋊C8—52no—
181C8×Dic3—51no—
182C8×Dic3—51no—
183C8×Dic3—52no—
184C4⋊(C3⋊C8)—51no—
185C4×C3⋊C8—51no—
186C5×#41—64no—
187C2×C5×Q8—31no—
188C2×C5×D4—32no—
189C2×C5×D4C4×D311yescharacteristic
190C22×C4×C5—31no—
191C22×C4×C5—32no—
192C22×Dic5—32no—
193C22×Dic5—31no—
194C22×Dic5—31no—
195C22×Dic5C22×D312yes—
196#704—24no—
197#704—64no—
198C2×#170—31no—
199C2×#170—31no—
200C2×#170—32no—
201C2×#170—62no—
202C2×#170—62no—
203C2×#170C22×D311yescharacteristic
204C2×#170C22×D312yes—
205C2×#170C22×D311yescharacteristic
206C22⋊Dic5—32no—
207C22⋊Dic5—32no—
208C22⋊Dic5C4×D312yes—
209C4⋊Dic5—31no—
210C4⋊Dic5—32no—
211C4⋊Dic5—32no—
212C4⋊Dic5C4×D311yescharacteristic
213C4×Dic5—31no—
214C4×Dic5—32no—
215C4×Dic5—31no—
216C4×Dic5—32no—
217C4×Dic5—31no—
218C4×Dic5—32no—
219C4×Dic5C22×D311yescharacteristic
220C4×#41—151no—
221#446—151no—
222#446—151no—
223#436—51no—
224#436—151no—
225#435—152no—
226#435—152no—
227#431—152no—
228#431—151no—
229C4×M16—152no—
230C2×C4×C8—151no—
231C22×C3×C5—22no—
232C22×C3×C5—22no—
233C22×C3×C5—22no—
234C22×C3×C5C23×C411yescharacteristic
235C2×C5×D3—21no—
236C2×C5×D3—21no—
237C2×C5×D3C2×M1612yes—
238C3×C4×C5C2×M1612yes—
239Dic15—21no—
240Dic15—22no—
241Dic15#13112yes—
242C3×Dic5—22no—
243C3×Dic5—21no—
244C3×Dic5C2×#4111yescharacteristic
245C3×Dic5C2×#4111yescharacteristic
246C5×Dic3—22no—
247C5×Dic3C2×M1612yes—
248C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
249C22×C3×C4—52no—
250C2×#67C2×AGL(1,𝔽5)12yes—
251C22×Dic3—52no—
252C22×Dic3C2×AGL(1,𝔽5)12yes—
253#237—24no—
254C2×C4×D3—51no—
255C2×C4×D3—51no—
256C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
257C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
258C3×M16—104no—
259C2×C3×C8—51no—
260C2×C3×C8—51no—
261C2×C3×C8—52no—
262C3×C4⋊C4—51no—
263C3×C22⋊C4—52no—
264C3×C42—51no—
265#217—52no—
266(C2×D3)⋊C4—52no—
267C4⋊Dic3—51no—
268Dic3⋊C4—52no—
269Dic3⋊C4—52no—
270C4×Dic3—51no—
271C4×Dic3—51no—
272C4×Dic3—52no—
273C4×Dic3—52no—
274C4×Dic3—51no—
275C4×Dic3—52no—
276#208—104no—
277C2×C3⋊C8—51no—
278C2×C3⋊C8—51no—
279C2×C3⋊C8—52no—
280D3×C8—102no—
281D3×C8—102no—
282C23×C5—31no—
283C23×C5C2×C4×D312yes—
284C5×Q8—62no—
285C5×D4—22no—
286C5×D4—64no—
287C2×C4×C5—31no—
288C2×C4×C5—34no—
289C2×C4×C5—32no—
290C2×C4×C5—64no—
291C2×C4×C5C2×C4×D311yescharacteristic
292C2×Dic5—22no—
293C2×Dic5—22no—
294C2×Dic5—31no—
295C2×Dic5—32no—
296C2×Dic5—31no—
297C2×Dic5—62no—
298C2×Dic5—64no—
299C2×Dic5—61no—
300C2×Dic5—61no—
301C2×Dic5C2×C4×D312yes—
302C2×Dic5C2×C4×D311yescharacteristic
303C2×Dic5C23×D311yescharacteristic
304#170—22no—
305#170—21no—
306#170—32no—
307#170—61no—
308#170—62no—
309#170#23712yescomplemented
310C2×#41—31no—
311C2×M16—52no—
312C2×M16—152no—
313C22×C8—151no—
314C22×C8—151no—
315C4×Q8—151no—
316C4×Q8—151no—
317C4×D4—51no—
318C4×D4—152no—
319C4×D4—152no—
320C4×D4—151no—
321#117—152no—
322#117—151no—
323C2×C42—151no—
324C2×C42—152no—
325C4⋊C8—51no—
326C4⋊C8—151no—
327C4⋊C8—152no—
328C4⋊C8—152no—
329C22⋊C8—52no—
330C22⋊C8—152no—
331C22⋊C8—152no—
332#97—152no—
333#97—152no—
334C4×C8—51no—
335C4×C8—151no—
336C4×C8—151no—
337C4×C8—151no—
338C4×C8—152no—
339C2×C3×C5—42no—
340C2×C3×C5C4×#4111yescharacteristic
341C2×C3×C5C22×M1611yescharacteristic
342C2×C3×C5C2×#13111yescharacteristic
343C5×D3—22no—
344C23×C3C22×AGL(1,𝔽5)12yes—
345C22×D3C22×AGL(1,𝔽5)11yescharacteristic
346C3×D4—22no—
347C2×C3×C4—51no—
348C2×C3×C4—52no—
349C2×C3×C4—51no—
350C2×C3×C4—102no—
351C2×C3×C4—102no—
352C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
353#67—24no—
354C2×Dic3—24no—
355C2×Dic3—51no—
356C2×Dic3—51no—
357C2×Dic3—52no—
358C2×Dic3—104no—
359C2×Dic3C22×AGL(1,𝔽5)12yes—
360C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
361C4×D3—102no—
362C4×D3—101no—
363C4×D3—101no—
364C4×D3#70414yescomplemented
365Dic6—22no—
366C3×C8—52no—
367C3×C8—101no—
368C3×C8—102no—
369C3⋊C8—52no—
370C3⋊C8—101no—
371C3⋊C8—102no—
372C22×C5—22no—
373C22×C5—22no—
374C22×C5—22no—
375C22×C5—32no—
376C22×C5—61no—
377C22×C5—61no—
378C22×C5C22×C4×D311yescharacteristic
379C4×C5—32no—
380C4×C5—62no—
381C4×C5D3×M1612yes—
382Dic5—21no—
383Dic5—22no—
384Dic5—32no—
385Dic5—62no—
386Dic5—61no—
387Dic5C2×#23711yescharacteristic
388Dic5D3×#4111yescharacteristic
389#41—64no—
390C2×Q8—31no—
391C2×D4—32no—
392C2×D4D3×AGL(1,𝔽5)11yescharacteristic
393C22×C4—31no—
394C22×C4—32no—
395C22×C4—52no—
396C22×C4—151no—
397C22×C4—151no—
398C22×C4—152no—
399M16—104no—
400M16—304no—
401C2×C8—51no—
402C2×C8—51no—
403C2×C8—52no—
404C2×C8—151no—
405C2×C8—151no—
406C2×C8—152no—
407C2×C8—302no—
408C2×C8—302no—
409C4⋊C4—51no—
410C4⋊C4—152no—
411C4⋊C4—152no—
412C4⋊C4—151no—
413C22⋊C4—52no—
414C22⋊C4—152no—
415C22⋊C4—152no—
416C42—51no—
417C42—151no—
418C42—152no—
419C42—151no—
420C42—152no—
421C42—152no—
422C42—151no—
423C3×C5#296511yescharacteristic, complemented, Hall
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—22no—
427C22×C3C23×AGL(1,𝔽5)11yescharacteristic
428C2×D3—21no—
429C2×D3—21no—
430C2×D3C2×#70412yes—
431C3×C4—51no—
432C3×C4—51no—
433C3×C4—101no—
434C3×C4—102no—
435C3×C4C2×#70412yes—
436Dic3—22no—
437Dic3—52no—
438Dic3—102no—
439Dic3—101no—
440Dic3C2×#70412yes—
441C2×C5—42no—
442C2×C5—62no—
443C2×C5C4×#23711yescharacteristic
444C2×C5C2×D3×M1611yescharacteristic
445C2×C5D3×#13111yescharacteristic
446C23—31no—
447C23C2×D3×AGL(1,𝔽5)12yes—
448Q8—62no—
449D4—22no—
450D4—64no—
451C2×C4—31no—
452C2×C4—34no—
453C2×C4—32no—
454C2×C4—51no—
455C2×C4—51no—
456C2×C4—52no—
457C2×C4—64no—
458C2×C4—102no—
459C2×C4—102no—
460C2×C4—151no—
461C2×C4—152no—
462C2×C4—151no—
463C2×C4—301no—
464C2×C4—301no—
465C2×C4—302no—
466C2×C4—304no—
467C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
468C8—52no—
469C8—101no—
470C8—102no—
471C8—152no—
472C8—301no—
473C8—302no—
474C2×C3—42no—
475C2×C3D5⋊#13111yescharacteristic
476C2×C3#41×AGL(1,𝔽5)11yescharacteristic
477C2×C3C22×#70411yescharacteristic
478D3—22no—
479C5#7951711yescharacteristic, complemented, Sylow
480C22—22no—
481C22—22no—
482C22—22no—
483C22—32no—
484C22—61no—
485C22—61no—
486C22C22×D3×AGL(1,𝔽5)11yescharacteristic
487C4—32no—
488C4—51no—
489C4—51no—
490C4—62no—
491C4—101no—
492C4—102no—
493C4—152no—
494C4—302no—
495C4—301no—
496C4D3×#70412yes—
497C3#1061754511yescharacteristic, complemented, Sylow
498C2—42no—
499C2—62no—
500C2#1175684011yescharacteristic
501C2AGL(1,𝔽5)×#23711yescharacteristic
502C2C2×D3×#70411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×D4C2×C4
prime radicalC2×C5×#237C4
cosocleC2×C3×Dic5C24
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#2965
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #11752433C2semidirect
3. C3×#65774C2semidirect
4. #11752039C2semidirect
5. #11752035C2semidirect
6. #11751994C2semidirect
7. Dic3×#704C2semidirect
8. C4×D3×#170C2semidirect
9. #11751792C2semidirect
10. #11751789C2semidirect
11. #11751754C2semidirect
47. #65774D3semidirect
141. C4×C5×D3M16semidirect
153. C3⋊#170#41semidirect
156. C3×#170#41semidirect
309. #170#237semidirect
364. C4×D3#704semidirect
423. C3×C5#2965semidirect
479. C5#79517semidirect
497. C3#10617545semidirect

Maximal subgroups

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

subgroupindex
Dic5×#2372
#117524332
C3×#657742
#117520392
#117520352
#117519942
Dic3×#7042
C4×D3×#1702
#117517922
#117517892
#117517542
#106175453
#795175