Finite Group Databasebeta

← #14415410

Subgroups — #14415410

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91929C212yesmaximal, complemented
2#11754330C211yesmaximal, characteristic
3C2×#91231C211yesmaximal, characteristic, complemented
4C3×#65758C211yesmaximal, characteristic, complemented
5#11752001C212yesmaximal, complemented
6#11751905C212yesmaximal, complemented
7#11751897C212yesmaximal, complemented
8#11751889C212yesmaximal, complemented
9#11751888C212yesmaximal, complemented
10#10617228—31nomaximal, Hall
11C2×#6782C2212yes—
12C22×C3⋊#170C2211yescharacteristic
13C22×C3⋊#170C2211yescharacteristic
14C2×C3×#704C2212yes—
15C2×#6740C2212yes—
16C2×#6739C2212yes—
17C2×#6738C2212yes—
18#91929—28no—
19C2×D3×#170C2212yes—
20#91819C411yescharacteristic
21C5×#930C411yescharacteristic
22C2×C3×C4×Dic5C2211yescharacteristic
23#91566C412yes—
24#91468C411yescharacteristic
25#91451C411yescharacteristic
26#91418C2211yescharacteristic
27Dic5×D12C2211yescharacteristic
28#91405C2212yes—
29#91350C412yes—
30#91231C2212yes—
31#91231C2212yes—
32C3×#4004C2212yes—
33C3×C4⋊#170C2211yescharacteristic
34C3×C4⋊#170C2211yescharacteristic
35#91171C2212yes—
36#91171C2212yes—
37(C2×D3)⋊#170C2212yes—
38(C2×D3)⋊#170C2212yes—
39#79042—51nomaximal, Hall
40C2×#4131—32no—
41#65930—31no—
42#65775—32no—
43#65773—32no—
44#65758D311yescharacteristic, complemented
45C2×#4002—31no—
46#65704—32no—
47#65694—32no—
48#65693—32no—
49C22×C3×C4×C5C2×C411yescharacteristic
50C2×#1220C2×C412yes—
51C2×D60C2×C411yescharacteristic
52C2×C5×#67C2×C412yes—
53C2×C5×D12C2×C411yescharacteristic
54C22×C3×Dic5C2×C411yescharacteristic
55C22×C3×Dic5C2311yescharacteristic
56C2×#1204C2×C412yes—
57C2×#1203C2×C412yes—
58C2×#1203C2×C412yes—
59C2×#1200C2312yes—
60#6782—24no—
61#6782—24no—
62C2×D3×Dic5C2312yes—
63C2×C3⋊#170—22no—
64C2×C3⋊#170D414yescomplemented
65C2×C3⋊#170C2312yes—
66C2×C3⋊#170C2312yes—
67C3×#704—24no—
68C2×C3×#170C2312yes—
69C2×C3×#170C2312yes—
70#6740—24no—
71#6739—24no—
72#6738—24no—
73D3×#170—24no—
74#6714C2×C412yes—
75C4⋊Dic15C2×C411yescharacteristic
76C5×(C2×D3)⋊C4C2×C412yes—
77C5×C4⋊Dic3C2×C411yescharacteristic
78C3×C4×Dic5C2×C411yescharacteristic
79C3×C4×Dic5C2×C411yescharacteristic
80C3×C4×Dic5C2311yescharacteristic
81C3×C4×Dic5C2311yescharacteristic
82#6668C2×C412yes—
83#6667C2×C412yes—
84(C2×D3)⋊Dic5C2×C412yes—
85C2×#907—52no—
86#5477—51no—
87C3×#423—51no—
88#5129—52no—
89C2×#803—51no—
90#4836—52no—
91#4836—52no—
92#4836—52no—
93#4836—52no—
94C2×#711—32no—
95C2×#704—32no—
96C2×#704C2×D312yes—
97C22×#170—31no—
98C22×#170—31no—
99C22×#170—32no—
100#4131—68no—
101C2×#700—32no—
102C2×D5⋊C8—32no—
103C5×#121—31no—
104#4086—31no—
105#4085—32no—
106D4×Dic5—31no—
107#4076—31no—
108C2×C4×Dic5C2×D311yescharacteristic
109#4039—31no—
110#4034—31no—
111#4031—32no—
112#4027—32no—
113C22⋊#170—32no—
114C22⋊#170—32no—
115#4004C2×D312yes—
116#4003—32no—
117#4003—32no—
118#4002—32no—
119#4002—32no—
120C4⋊#170C2×D311yescharacteristic
121C4⋊#170C2×D311yescharacteristic
122#2932—151noSylow
123C23×C3×C5C22×C411yescharacteristic
124C22×D15C22×C412yes—
125C22×C5×D3C22×C412yes—
126C2×C3×C4×C5—41no—
127C2×C3×C4×C5C22×C411yescharacteristic
128C2×C3×C4×C5C22×C411yescharacteristic
129#1220—24no—
130C2×Dic15C22×C412yes—
131D60—41no—
132C5×#67—24no—
133C2×C5×Dic3C22×C412yes—
134C5×D12—41no—
135C2×C3×Dic5—41no—
136C2×C3×Dic5C22×C411yescharacteristic
137C2×C3×Dic5C22×C411yescharacteristic
138C2×C3×Dic5C22×C411yescharacteristic
139C2×C3×Dic5C2×D412yes—
140C2×C3×Dic5#4112yes—
141C2×C3×Dic5C2411yescharacteristic
142#1204—24no—
143#1203—24no—
144#1203—42no—
145#1200—22no—
146#1200—22no—
147D3×Dic5—22no—
148D3×Dic5—22no—
149C3⋊#170—22no—
150C3⋊#170C2×D414yes—
151C3×#170—22no—
152C3×#170—22no—
153C2×#235—52no—
154C2×C3×M16—52no—
155C2×C3×C42—51no—
156#930—51no—
157#930—52no—
158#930AGL(1,𝔽5)11yescharacteristic
159C22×C3⋊C8—51no—
160C22×C3⋊C8—51no—
161#907—108no—
162C2×ΓL(1,𝔽25)—52no—
163C2×ΓL(1,𝔽25)—52no—
164C2×D3×C8—52no—
165C2×D3×C8—52no—
166#875—52no—
167#874—51no—
168C4×D12—51no—
169C4×D12—52no—
170C4×D12—51no—
171#869—51no—
172C3×C4⋊C8—51no—
173C3×C4⋊C8—51no—
174C3×C4⋊C8—52no—
175(C2×D3)⋊C8—52no—
176(C2×D3)⋊C8—52no—
177(C2×D3)⋊C8—52no—
178(C2×D3)⋊C8—52no—
179#803—52no—
180#803—52no—
181C2×C5×D4—32no—
182C2×C5×D4—31no—
183C22×C4×C5C4×D311yescharacteristic
184C2×C22⋊D5—32no—
185C2×C22⋊D5—32no—
186C2×C22⋊D5—32no—
187C22×Dic5—32no—
188C22×Dic5C4×D311yescharacteristic
189C22×Dic5C22×D311yescharacteristic
190#711—64no—
191#711—64no—
192C2×D20—31no—
193C2×C4×D5—32no—
194C2×Dic10—32no—
195#704—24no—
196#704—64no—
197C2×#170—34no—
198C2×#170—32no—
199C2×#170—32no—
200C2×#170—64no—
201C2×#170—62no—
202C2×#170C22×D312yes—
203C2×#170C22×D312yes—
204#700—64no—
205D5⋊C8—64no—
206C5×C4⋊C4—31no—
207C5×C22⋊C4—32no—
208C22⋊Dic5—32no—
209#685—32no—
210#685—32no—
211C4⋊Dic5—31no—
212#683—32no—
213C4×Dic5C4×D311yescharacteristic
214C4×Dic5C4×D311yescharacteristic
215C4×Dic5C22×D311yescharacteristic
216C4×Dic5C22×D311yescharacteristic
217C2×#131—152no—
218#532—151no—
219#435—152no—
220#435—152no—
221#435—152no—
222#435—152no—
223#423—51no—
224#408—152no—
225C2×#97—151no—
226C22×C3×C5—21no—
227C22×C3×C5—21no—
228C22×C3×C5C4×D412yes—
229C22×C3×C5C23×C411yescharacteristic
230C2×D15—22no—
231C2×D15—22no—
232C2×D15—22no—
233C2×C5×D3—22no—
234C2×C5×D3—22no—
235C2×C5×D3—22no—
236C3×C4×C5—21no—
237C3×C4×C5—21no—
238Dic15—22no—
239C3×Dic5—21no—
240C3×Dic5—21no—
241C3×Dic5C4×D412yes—
242C3×Dic5C22×D411yescharacteristic
243C3×Dic5C2×#4111yescharacteristic
244C5×Dic3—22no—
245C22×C3×C4—51no—
246C22×C3×C4—51no—
247C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
248C2×#67—52no—
249C2×#67C2×AGL(1,𝔽5)12yes—
250#235—104no—
251#235—104no—
252C2×D12—52no—
253C2×D12—52no—
254C2×D12—51no—
255C2×D12C2×AGL(1,𝔽5)11yescharacteristic
256C2×C4×D3—52no—
257C2×C4×D3—52no—
258C2×Dic6—52no—
259C3×M16—104no—
260C2×C3×C8—52no—
261C2×C3×C8—52no—
262C3×C42—51no—
263C3×C42—51no—
264C3×C42—51no—
265C3×C42—51no—
266(C2×D3)⋊C4—52no—
267(C2×D3)⋊C4—52no—
268(C2×D3)⋊C4—52no—
269(C2×D3)⋊C4C2×AGL(1,𝔽5)12yes—
270C4⋊Dic3—51no—
271C4⋊Dic3—52no—
272C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
273C2×C3⋊C8—52no—
274C2×C3⋊C8—54no—
275C2×C3⋊C8—52no—
276C2×C3⋊C8—102no—
277ΓL(1,𝔽25)—104no—
278ΓL(1,𝔽25)—104no—
279D3×C8—104no—
280D3×C8—104no—
281C23×C5—32no—
282C23×C5C2×C4×D311yescharacteristic
283C22×D5—32no—
284C5×D4—64no—
285C5×D4—121no—
286C2×C4×C5—32no—
287C2×C4×C5—41no—
288C2×C4×C5C2×C4×D311yescharacteristic
289C2×C4×C5C2×C4×D311yescharacteristic
290C22⋊D5—64no—
291C22⋊D5—64no—
292C22⋊D5—122no—
293C2×Dic5—32no—
294C2×Dic5—41no—
295C2×Dic5—62no—
296C2×Dic5—62no—
297C2×Dic5C2×C4×D311yescharacteristic
298C2×Dic5C2×C4×D311yescharacteristic
299C2×Dic5C2×C4×D311yescharacteristic
300C2×Dic5D3×D412yes—
301C2×Dic5#23912yes—
302C2×Dic5C23×D311yescharacteristic
303D20—121no—
304C4×D5—62no—
305C4×D5—62no—
306Dic10—64no—
307#170—22no—
308#170—22no—
309#170—34no—
310#170—62no—
311C2×#41—152no—
312#131—308no—
313C2×M16—52no—
314C2×M16—152no—
315C2×M16—152no—
316C22×C8—152no—
317C22×C8—152no—
318C22×C8—151no—
319C22×C8—151no—
320C4⋊Q8—151no—
321#127—151no—
322#124—152no—
323#121—31no—
324#121—152no—
325#121—151no—
326C4×D4—152no—
327C4×D4—151no—
328C4×D4—151no—
329C2×C42—51no—
330C4⋊C8—51no—
331C4⋊C8—51no—
332C4⋊C8—52no—
333C22⋊C8—152no—
334C22⋊C8—152no—
335C22⋊C8—152no—
336C22⋊C8—152no—
337#97—152no—
338#97—152no—
339C2×C3×C5—22no—
340C2×C3×C5C2×C4×D411yescharacteristic
341C2×C3×C5#56811yescharacteristic
342C2×C3×C5#56811yescharacteristic
343D15—42no—
344C5×D3—42no—
345C23×C3C22×AGL(1,𝔽5)11yescharacteristic
346C22×D3—52no—
347C22×D3C22×AGL(1,𝔽5)12yes—
348C2×C3×C4—41no—
349C2×C3×C4—52no—
350C2×C3×C4—52no—
351C2×C3×C4—51no—
352C2×C3×C4—51no—
353C2×C3×C4—51no—
354C2×C3×C4—51no—
355C2×C3×C4—201no—
356C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
357C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
358#67—24no—
359#67—104no—
360C2×Dic3—52no—
361C2×Dic3C22×AGL(1,𝔽5)12yes—
362D12—41no—
363D12—104no—
364D12—201no—
365D12—202no—
366C4×D3—102no—
367C4×D3—102no—
368C4×D3—102no—
369C4×D3—102no—
370Dic6—104no—
371C3×C8—102no—
372C3×C8—102no—
373C3⋊C8—54no—
374C3⋊C8—102no—
375C22×C5—21no—
376C22×C5—21no—
377C22×C5—62no—
378C22×C5—62no—
379C22×C5—62no—
380C22×C5#89312yes—
381C22×C5C22×C4×D311yescharacteristic
382C2×D5—62no—
383C2×D5—62no—
384C2×D5—62no—
385C4×C5—21no—
386C4×C5—21no—
387C4×C5—62no—
388Dic5—21no—
389Dic5—21no—
390Dic5—62no—
391Dic5#89312yes—
392Dic5C2×D3×D411yescharacteristic
393Dic5C2×#23911yescharacteristic
394#41—304no—
395#41—304no—
396C2×Q8—152no—
397C2×D4—32no—
398C2×D4—31no—
399C2×D4—152no—
400C2×D4—152no—
401C2×D4—152no—
402C2×D4—151no—
403C22×C4—51no—
404C22×C4—51no—
405C22×C4—152no—
406C22×C4—152no—
407C22×C4D3×AGL(1,𝔽5)11yescharacteristic
408M16—104no—
409M16—304no—
410M16—304no—
411C2×C8—52no—
412C2×C8—52no—
413C2×C8—152no—
414C2×C8—154no—
415C2×C8—152no—
416C2×C8—304no—
417C2×C8—304no—
418C2×C8—302no—
419C4⋊C4—31no—
420C4⋊C4—152no—
421C4⋊C4—151no—
422C22⋊C4—32no—
423C22⋊C4—152no—
424C22⋊C4—152no—
425C22⋊C4—152no—
426C42—51no—
427C42—51no—
428C42—51no—
429C42—51no—
430C3×C5#293211yescharacteristic, complemented, Hall
431C22×C3—21no—
432C22×C3—21no—
433C22×C3D4×AGL(1,𝔽5)12yes—
434C22×C3C23×AGL(1,𝔽5)11yescharacteristic
435C2×D3—22no—
436C2×D3—22no—
437C2×D3—22no—
438C2×D3—102no—
439C2×D3—102no—
440C2×D3—102no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—52no—
444C3×C4—51no—
445C3×C4—51no—
446C3×C4—101no—
447C3×C4—101no—
448Dic3—22no—
449Dic3—102no—
450C2×C5—22no—
451C2×C5—122no—
452C2×C5C2×#89311yescharacteristic
453C2×C5#574511yescharacteristic
454C2×C5#574511yescharacteristic
455D5—122no—
456C23—32no—
457C23—152no—
458C23C2×D3×AGL(1,𝔽5)11yescharacteristic
459Q8—304no—
460D4—64no—
461D4—121no—
462D4—304no—
463D4—304no—
464D4—601no—
465D4—602no—
466C2×C4—32no—
467C2×C4—41no—
468C2×C4—52no—
469C2×C4—52no—
470C2×C4—51no—
471C2×C4—51no—
472C2×C4—51no—
473C2×C4—51no—
474C2×C4—152no—
475C2×C4—201no—
476C2×C4—302no—
477C2×C4—302no—
478C2×C4—302no—
479C2×C4—302no—
480C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
481C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
482C8—102no—
483C8—102no—
484C8—154no—
485C8—302no—
486C2×C3—22no—
487C2×C3#6625611yescharacteristic
488C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
489C2×C3#6626411yescharacteristic
490D3—42no—
491D3—202no—
492C5#7904211yescharacteristic, complemented, Sylow
493C22—21no—
494C22—21no—
495C22—62no—
496C22—62no—
497C22—62no—
498C22—302no—
499C22—302no—
500C22—302no—
501C22#9192112yes—
502C22C22×D3×AGL(1,𝔽5)11yescharacteristic
503C4—21no—
504C4—21no—
505C4—51no—
506C4—51no—
507C4—52no—
508C4—62no—
509C4—101no—
510C4—101no—
511C4—302no—
512C3#1061722811yescharacteristic, complemented, Sylow
513C2—22no—
514C2—122no—
515C2—602no—
516C2#1175682311yescharacteristic
517C2C2×#9192111yescharacteristic
518C2#1175686311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radical#11754330C2
cosocleC2×C3×Dic5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2932
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#91929C2semidirect
3. C2×#91231C2semidirect
4. C3×#65758C2semidirect
5. #11752001C2semidirect
6. #11751905C2semidirect
7. #11751897C2semidirect
8. #11751889C2semidirect
9. #11751888C2semidirect
44. #65758D3semidirect
64. C2×C3⋊#170D4semidirect
430. C3×C5#2932semidirect
492. C5#79042semidirect
512. C3#10617228semidirect

Maximal subgroups

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

subgroupindex
C2×#919292
#117543302
C2×#912312
C3×#657582
#117520012
#117519052
#117518972
#117518892
#117518882
#106172283
#790425