Finite Group Databasebeta

← #14297586

Subgroups — #14297586

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91405C211yesmaximal, characteristic
2#11752417C211yesmaximal, characteristic, complemented
3C3×#65758C211yesmaximal, characteristic, complemented
4C2×#91174C212yesmaximal
5#11746574C212yesmaximal, complemented
6#10604246—31nomaximal, Hall
7C22×#1203C2211yescharacteristic
8C22×#1200C411yescharacteristic
9C22×D3×Dic5C411yescharacteristic
10C2×#6762C2212yes—
11C2×C3×#704C2212yes—
12C2×#6714C411yescharacteristic
13C2×C5×(C2×D3)⋊C4C411yescharacteristic
14C2×C3×C4×Dic5C2211yescharacteristic
15C2×#6668C2211yescharacteristic
16#91405—21no—
17#91405—21no—
18#91405—21no—
19#91405—21no—
20#91233—21no—
21C4⋊(C3⋊#170)—21no—
22C3×#4004—21no—
23C3×C4⋊#170—21no—
24#91174—24no—
25#70527—51nomaximal, Hall
26C2×#4027—31no—
27C2×#4013—32no—
28#65758—31no—
29#65758D311yescharacteristic, complemented
30#64919—32no—
31C23×D15C2×C411yescharacteristic
32C23×C5×D3C2×C411yescharacteristic
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×Dic15C2×C411yescharacteristic
35C22×C5×Dic3C2×C411yescharacteristic
36C22×C3×Dic5C2×C411yescharacteristic
37C22×C3×Dic5C2311yescharacteristic
38C2×#1203—21no—
39C2×#1203—21no—
40C2×#1203—21no—
41C2×#1203—21no—
42C2×#1203D412yes—
43C2×#1203Q812yes—
44C2×#1200—21no—
45C2×#1200—21no—
46C2×#1200—42no—
47C2×D3×Dic5—21no—
48C2×D3×Dic5—21no—
49C2×D3×Dic5—42no—
50#6762—22no—
51#6762—22no—
52C2×C3⋊#170—22no—
53C3×#704—22no—
54C3×#704—22no—
55C2×C3×#170—22no—
56#6714—21no—
57#6714—21no—
58C5×(C2×D3)⋊C4—21no—
59C5×(C2×D3)⋊C4—21no—
60C3×C4×Dic5D411yescharacteristic
61C3×C4×Dic5D411yescharacteristic
62C3×C4×Dic5D411yescharacteristic
63C3×C4×Dic5D411yescharacteristic
64#6668—21no—
65#6668—21no—
66C2×C4×D12—51no—
67C3×#423—51no—
68C2×#823—52no—
69#4924—51no—
70#4554—52no—
71C22×C22⋊D5—31no—
72C23×Dic5—31no—
73C22×C4×D5—31no—
74C2×#704—32no—
75C2×#704C2×D312yes—
76C2×C5×C22⋊C4—31no—
77C2×#685—31no—
78C2×#683—31no—
79C2×C4×Dic5C2×D311yescharacteristic
80#4027—61no—
81#4027—61no—
82#4027—61no—
83#4027—61no—
84#4013—64no—
85#4004—21no—
86#4004—61no—
87C4⋊#170—21no—
88C4⋊#170—61no—
89#1800—151noSylow
90C23×C3×C5C22×C411yescharacteristic
91C22×D15—21no—
92C22×D15—21no—
93C22×D15—41no—
94C22×D15—41no—
95C22×D15C4⋊C412yes—
96C22×C5×D3—21no—
97C22×C5×D3—21no—
98C22×C5×D3—41no—
99C22×C5×D3—41no—
100C22×C5×D3C4⋊C412yes—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5C22⋊C411yescharacteristic
103C2×C3×C4×C5C22⋊C411yescharacteristic
104C2×Dic15—21no—
105C2×Dic15—41no—
106C2×C5×Dic3—21no—
107C2×C5×Dic3—41no—
108C2×C3×Dic5—22no—
109C2×C3×Dic5C22⋊C411yescharacteristic
110C2×C3×Dic5C22⋊C411yescharacteristic
111C2×C3×Dic5C2×D411yescharacteristic
112C2×C3×Dic5C2×D411yescharacteristic
113C2×C3×Dic5C2×D411yescharacteristic
114C2×C3×Dic5C2×Q811yescharacteristic
115C2×C3×Dic5#4111yescharacteristic
116C2×C3×Dic5#4111yescharacteristic
117#1203—22no—
118#1203—22no—
119#1203—22no—
120#1203—22no—
121#1200—42no—
122#1200—42no—
123D3×Dic5—42no—
124D3×Dic5—42no—
125C3⋊#170—42no—
126C3×#170—42no—
127C22×D12—51no—
128C22×C4×D3—51no—
129C22×C4×D3—51no—
130C2×C3×M16—52no—
131C2×C3×C42—51no—
132C2×(C2×D3)⋊C4—51no—
133C2×(C2×D3)⋊C4AGL(1,𝔽5)11yescharacteristic
134C2×C4⋊Dic3—51no—
135C2×#208—52no—
136C4×D12—101no—
137C4×D12—101no—
138C4×D12—101no—
139C4×D12—101no—
140C3×C4⋊C8—101no—
141C3×C4⋊C8—101no—
142#823—104no—
143C4⋊(C3⋊C8)—101no—
144C4⋊(C3⋊C8)—101no—
145C24×C5—31no—
146C23×D5—31no—
147C22×C4×C5—31no—
148C22×C4×C5C4×D311yescharacteristic
149C2×C22⋊D5—32no—
150C2×C22⋊D5—32no—
151C2×C22⋊D5—61no—
152C2×C22⋊D5—61no—
153C2×C22⋊D5—61no—
154C2×C22⋊D5—61no—
155C22×Dic5—31no—
156C22×Dic5—61no—
157C22×Dic5—61no—
158C22×Dic5—122no—
159C22×Dic5C4×D311yescharacteristic
160C22×Dic5C22×D311yescharacteristic
161C2×C4×D5—61no—
162C2×C4×D5—61no—
163C2×C4×D5—122no—
164#704—22no—
165#704—22no—
166#704—62no—
167#704—62no—
168C2×#170—22no—
169C2×#170—62no—
170C5×C22⋊C4—61no—
171C5×C22⋊C4—61no—
172#685—61no—
173#685—61no—
174#683—61no—
175#683—61no—
176C4×Dic5D1211yescharacteristic
177C4×Dic5D1211yescharacteristic
178C4×Dic5#6711yescharacteristic
179C4×Dic5#6711yescharacteristic
180C2×C4×D4—151no—
181#423—51no—
182#423—151no—
183C2×#100—152no—
184#343—152no—
185C22×C3×C5—21no—
186C22×C3×C5—21no—
187C22×C3×C5C2×C22⋊C411yescharacteristic
188C22×C3×C5C2×C4⋊C411yescharacteristic
189C22×C3×C5#11711yescharacteristic
190C2×D15—22no—
191C2×D15—42no—
192C2×D15—41no—
193C2×D15—41no—
194C2×D15—42no—
195C2×C5×D3—22no—
196C2×C5×D3—42no—
197C2×C5×D3—41no—
198C2×C5×D3—41no—
199C2×C5×D3—42no—
200C3×C4×C5—21no—
201C3×C4×C5—21no—
202Dic15—41no—
203C3×Dic5—21no—
204C3×Dic5#10012yescomplemented
205C3×Dic5#12111yescharacteristic
206C3×Dic5#12111yescharacteristic
207C3×Dic5C22⋊Q811yescharacteristic
208C3×Dic5C22⋊Q811yescharacteristic
209C5×Dic3—41no—
210C23×D3—51no—
211C23×D3C2×AGL(1,𝔽5)11yescharacteristic
212C22×C3×C4—51no—
213C22×C3×C4—51no—
214C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
215C22×Dic3—51no—
216C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
217C2×D12—52no—
218C2×D12—52no—
219C2×D12—101no—
220C2×D12—101no—
221C2×D12—101no—
222C2×D12—101no—
223C2×C4×D3—101no—
224C2×C4×D3—101no—
225C2×C4×D3—101no—
226C2×C4×D3—101no—
227C2×C4×D3—202no—
228C2×C4×D3—202no—
229C3×M16—102no—
230C3×M16—102no—
231C2×C3×C8—102no—
232C3×C42—51no—
233C3×C42—51no—
234C3×C42—51no—
235C3×C42—51no—
236(C2×D3)⋊C4—21no—
237(C2×D3)⋊C4—21no—
238(C2×D3)⋊C4—101no—
239(C2×D3)⋊C4—101no—
240C4⋊Dic3—101no—
241C4⋊Dic3—101no—
242#208—102no—
243#208—102no—
244C2×C3⋊C8—102no—
245C23×C5—32no—
246C23×C5—61no—
247C23×C5—61no—
248C23×C5—121no—
249C23×C5—121no—
250C23×C5C2×C4×D311yescharacteristic
251C22×D5—32no—
252C22×D5—61no—
253C22×D5—61no—
254C22×D5—121no—
255C22×D5—121no—
256C2×C4×C5—41no—
257C2×C4×C5—61no—
258C2×C4×C5—121no—
259C2×C4×C5(C2×D3)⋊C411yescharacteristic
260C2×C4×C5(C2×D3)⋊C411yescharacteristic
261C22⋊D5—62no—
262C22⋊D5—62no—
263C22⋊D5—62no—
264C22⋊D5—62no—
265C2×Dic5—22no—
266C2×Dic5—61no—
267C2×Dic5—122no—
268C2×Dic5—122no—
269C2×Dic5—121no—
270C2×Dic5(C2×D3)⋊C411yescharacteristic
271C2×Dic5(C2×D3)⋊C411yescharacteristic
272C2×Dic5C2×D1211yescharacteristic
273C2×Dic5D3×D411yescharacteristic
274C2×Dic5#23711yescharacteristic
275C2×Dic5D3×Q811yescharacteristic
276C2×Dic5#23911yescharacteristic
277C2×Dic5C2×#6711yescharacteristic
278C4×D5—122no—
279C4×D5—122no—
280#170—42no—
281#170—122no—
282C22×D4—151no—
283C23×C4—151no—
284C23×C4—151no—
285C2×M16—52no—
286C2×M16—152no—
287C4×D4—301no—
288C4×D4—301no—
289C4×D4—301no—
290C4×D4—301no—
291C2×C4⋊C4—151no—
292C2×C22⋊C4—31no—
293C2×C22⋊C4—151no—
294C2×C42—51no—
295C4⋊C8—101no—
296C4⋊C8—101no—
297C4⋊C8—301no—
298C4⋊C8—301no—
299#100—304no—
300C2×C3×C5—21no—
301C2×C3×C5—21no—
302C2×C3×C5#38011yescharacteristic
303C2×C3×C5C2×#10011yescharacteristic
304C2×C3×C5#41311yescharacteristic
305D15—42no—
306C5×D3—42no—
307C23×C3C22×AGL(1,𝔽5)11yescharacteristic
308C22×D3—21no—
309C22×D3—21no—
310C22×D3—41no—
311C22×D3—41no—
312C22×D3—52no—
313C22×D3—101no—
314C22×D3—101no—
315C22×D3—201no—
316C22×D3—201no—
317C22×D3C4⋊AGL(1,𝔽5)12yes—
318C2×C3×C4—41no—
319C2×C3×C4—51no—
320C2×C3×C4—51no—
321C2×C3×C4—51no—
322C2×C3×C4—51no—
323C2×C3×C4—51no—
324C2×C3×C4—51no—
325C2×C3×C4—51no—
326C2×C3×C4—51no—
327C2×C3×C4—102no—
328C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
329C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
330C2×Dic3—21no—
331C2×Dic3—41no—
332C2×Dic3—101no—
333C2×Dic3—201no—
334D12—102no—
335D12—102no—
336D12—102no—
337D12—102no—
338C4×D3—202no—
339C4×D3—202no—
340C4×D3—202no—
341C4×D3—202no—
342C3×C8—202no—
343C3⋊C8—202no—
344C22×C5—21no—
345C22×C5—21no—
346C22×C5—62no—
347C22×C5—122no—
348C22×C5—122no—
349C22×C5—121no—
350C22×C5—121no—
351C22×C5D3×C4⋊C411yescharacteristic
352C22×C5#89211yescharacteristic
353C22×C5C2×(C2×D3)⋊C411yescharacteristic
354C2×D5—62no—
355C2×D5—122no—
356C2×D5—121no—
357C2×D5—121no—
358C2×D5—122no—
359C4×C5—21no—
360C4×C5—21no—
361C4×C5—121no—
362Dic5—21no—
363Dic5—121no—
364Dic5#82312yescomplemented
365Dic5#89511yescharacteristic
366Dic5#89711yescharacteristic
367Dic5#93811yescharacteristic
368Dic5#94611yescharacteristic
369C24—31no—
370C24—151no—
371C2×D4—152no—
372C2×D4—152no—
373C2×D4—301no—
374C2×D4—301no—
375C2×D4—301no—
376C2×D4—301no—
377C22×C4—31no—
378C22×C4—51no—
379C22×C4—51no—
380C22×C4—151no—
381C22×C4—301no—
382C22×C4—301no—
383C22×C4—301no—
384C22×C4—301no—
385C22×C4—602no—
386C22×C4—602no—
387C22×C4D3×AGL(1,𝔽5)11yescharacteristic
388M16—102no—
389M16—102no—
390M16—302no—
391M16—302no—
392C2×C8—102no—
393C2×C8—302no—
394C4⋊C4—301no—
395C4⋊C4—301no—
396C22⋊C4—61no—
397C22⋊C4—61no—
398C22⋊C4—301no—
399C22⋊C4—301no—
400C42—51no—
401C42—51no—
402C42—51no—
403C42—51no—
404C3×C5#180011yescharacteristic, complemented, Hall
405C22×C3—21no—
406C22×C3—21no—
407C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
408C22×C3#413011yescharacteristic
409C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
410C2×D3—22no—
411C2×D3—42no—
412C2×D3—41no—
413C2×D3—41no—
414C2×D3—42no—
415C2×D3—102no—
416C2×D3—202no—
417C2×D3—201no—
418C2×D3—201no—
419C2×D3—202no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—51no—
423C3×C4—51no—
424C3×C4—51no—
425C3×C4—51no—
426C3×C4—52no—
427C3×C4—101no—
428Dic3—41no—
429Dic3—201no—
430C2×C5—21no—
431C2×C5—21no—
432C2×C5—122no—
433C2×C5#498711yescharacteristic
434C2×C5C2×#82311yescharacteristic
435C2×C5#513211yescharacteristic
436D5—122no—
437C23—32no—
438C23—61no—
439C23—61no—
440C23—121no—
441C23—121no—
442C23—152no—
443C23—301no—
444C23—301no—
445C23—601no—
446C23—601no—
447C23C2×D3×AGL(1,𝔽5)11yescharacteristic
448D4—302no—
449D4—302no—
450D4—302no—
451D4—302no—
452C2×C4—41no—
453C2×C4—51no—
454C2×C4—51no—
455C2×C4—51no—
456C2×C4—51no—
457C2×C4—51no—
458C2×C4—51no—
459C2×C4—51no—
460C2×C4—51no—
461C2×C4—61no—
462C2×C4—102no—
463C2×C4—121no—
464C2×C4—301no—
465C2×C4—602no—
466C2×C4—602no—
467C2×C4—602no—
468C2×C4—602no—
469C2×C4—601no—
470C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
471C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
472C8—202no—
473C8—602no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3#6576511yescharacteristic
477C2×C3#6577711yescharacteristic
478C2×C3D5⋊#10011yescharacteristic
479D3—42no—
480D3—202no—
481C5#7052711yescharacteristic, complemented, Sylow
482C22—21no—
483C22—21no—
484C22—62no—
485C22—122no—
486C22—122no—
487C22—121no—
488C22—121no—
489C22—302no—
490C22—602no—
491C22—602no—
492C22—601no—
493C22—601no—
494C22#9190711yescharacteristic
495C22D3×C4⋊AGL(1,𝔽5)11yescharacteristic
496C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
497C4—21no—
498C4—21no—
499C4—52no—
500C4—51no—
501C4—51no—
502C4—51no—
503C4—51no—
504C4—101no—
505C4—121no—
506C4—601no—
507C3#1060424611yescharacteristic, complemented, Sylow
508C2—21no—
509C2—21no—
510C2—122no—
511C2—602no—
512C2D5⋊#82311yescharacteristic
513C2#1175185511yescharacteristic
514C2#1175200811yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#1203C22
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1800
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #11752417C2semidirect
3. C3×#65758C2semidirect
5. #11746574C2semidirect
29. #65758D3semidirect
204. C3×Dic5#100semidirect
364. Dic5#823semidirect
404. C3×C5#1800semidirect
481. C5#70527semidirect
507. C3#10604246semidirect

Maximal subgroups

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

subgroupindex
C2×#914052
#117524172
C3×#657582
C2×#911742
#117465742
#106042463
#705275