Finite Group Databasebeta

← #14304744

Subgroups — #14304744

Order 1920.

568 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91087C211yesmaximal, characteristic, complemented
2C5×#4928C211yesmaximal, characteristic, complemented
3C3×#65228C211yesmaximal, characteristic
4C2×#90964C211yesmaximal, characteristic
5C2×#90964C211yesmaximal, characteristic
6#11745979C211yesmaximal, characteristic, complemented
7#11745979C211yesmaximal, characteristic, complemented
8#10600410—31nomaximal, Hall
9C22×C3×D20C2211yescharacteristic
10C2×C3×C42×C5C2211yescharacteristic
11C22×C3⋊#168C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C5×C4⋊Dic3C2211yescharacteristic
14C2×C5×C4⋊Dic3C2211yescharacteristic
15C2×C5×Dic3⋊C4—21no—
16C2×C3×#685—21no—
17C2×C3×#685—21no—
18C2×C3×C4⋊Dic5C2211yescharacteristic
19#91087—22no—
20C5×C3⋊#95—21no—
21#90964—22no—
22#90964C414yescomplemented
23#69645—51nomaximal, Hall
24C5×#389—31no—
25C2×#3941—31no—
26C2×#3941—31no—
27#65228D311yescharacteristic
28C2×#3935—31no—
29#64749—31no—
30#64749—31no—
31C23×C3×D5—21no—
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5D411yescharacteristic
34C22×C3×C4×C5C2311yescharacteristic
35C22×C5×Dic3—21no—
36C22×C5×Dic3—21no—
37C22×C3×Dic5—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C2×C3×D20C2×C412yes—
44C3×C42×C5—21no—
45C3×C42×C5—21no—
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C2×C3⋊#168—21no—
49C2×C3⋊#168—21no—
50C2×C3⋊#168C2×C412yes—
51C2×C3⋊#168D412yes—
52C5×C4⋊Dic3—21no—
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3—21no—
55C5×C4⋊Dic3C2×C412yes—
56C5×Dic3⋊C4—42no—
57C3×#685—42no—
58C3×#685—42no—
59C3×C4⋊Dic5—21no—
60C3×C4⋊Dic5—21no—
61C3×#390—51no—
62C2×#832—51no—
63C2×#832—51no—
64#4928D511yescharacteristic, complemented
65C2×#803—51no—
66#4529—51no—
67#4529—51no—
68C22×D20C2×D311yescharacteristic
69C2×C5×C4⋊C4—31no—
70C2×C5×C4⋊C4—31no—
71C2×C5×C4⋊C4—61no—
72C2×C42×C5C2×D311yescharacteristic
73C2×#685—21no—
74C2×#685—21no—
75C2×C4⋊Dic5C2×D311yescharacteristic
76C22×#168—31no—
77C22×#168—31no—
78C5×#95—61no—
79#3941—34no—
80#3941—62no—
81#3935—62no—
82#1936—151noSylow
83C23×C3×C5C2×D411yescharacteristic
84C22×C3×D5—22no—
85C22×C3×D5—41no—
86C22×C3×D5—41no—
87C22×C3×D5—41no—
88C22×C3×D5—41no—
89C22×C3×D5—41no—
90C22×C3×D5—41no—
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5#4111yescharacteristic
100C2×C3×C4×C5#4111yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C5×Dic3—22no—
104C2×C5×Dic3—41no—
105C2×C5×Dic3—41no—
106C2×C5×Dic3—41no—
107C2×C5×Dic3—41no—
108C2×C5×Dic3—41no—
109C2×C3×Dic5—41no—
110C2×C3×Dic5—41no—
111C2×C3×Dic5—41no—
112C3×D20—22no—
113C3×D20—22no—
114C3×D20—41no—
115C3×D20—41no—
116C3⋊#168—22no—
117C3⋊#168—22no—
118C22×C3×D4—51no—
119C2×C3×C4⋊C4—51no—
120C2×C3×C22⋊C4—101no—
121C2×C3×C22⋊C4—101no—
122C2×C3×C42C2×D511yescharacteristic
123C2×C4⋊Dic3C2×D511yescharacteristic
124C2×C4⋊Dic3C2×D511yescharacteristic
125C2×Dic3⋊C4—21no—
126C22×C3⋊C8—51no—
127C22×C3⋊C8—51no—
128#832—54no—
129#832—102no—
130C3⋊#95—21no—
131#803—102no—
132C23×D5—21no—
133C22×C4×C5—61no—
134C22×C4×C5—61no—
135C22×C4×C5#6711yescharacteristic
136C22×C4×C5#6711yescharacteristic
137C22×C4×C5C22×D311yescharacteristic
138C22×Dic5—21no—
139C2×D20—21no—
140C2×D20—21no—
141C2×D20—21no—
142C2×D20—21no—
143C2×D20—21no—
144C2×D20C4×D312yes—
145C5×C4⋊C4—32no—
146C5×C4⋊C4—61no—
147C5×C4⋊C4—61no—
148C5×C4⋊C4—61no—
149C5×C4⋊C4—122no—
150C42×C5—21no—
151C42×C5—21no—
152#685—42no—
153#685—42no—
154C4⋊Dic5—21no—
155C4⋊Dic5—21no—
156C2×#168—32no—
157C2×#168—32no—
158C2×#168—61no—
159C2×#168—61no—
160C2×#168—61no—
161C2×#168—61no—
162C2×#102—151no—
163C2×#102—151no—
164C2×#97—151no—
165#390—51no—
166#389—31no—
167#340—151no—
168#340—151no—
169C22×C3×C5C4×D411yescharacteristic
170C22×C3×C5#12111yescharacteristic
171C22×C3×C5#12411yescharacteristic
172C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
173C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
174C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
175C22×C3×C5#13711yescharacteristic
176C2×C3×D5—42no—
177C2×C3×D5—42no—
178C2×C3×D5—42no—
179C2×C3×D5—81no—
180C2×C3×D5—81no—
181C2×C3×D5—81no—
182C2×C3×D5—81no—
183C3×C4×C5—41no—
184C3×C4×C5—41no—
185C3×C4×C5#11711yescharacteristic
186C3×C4×C5C4×D411yescharacteristic
187C3×C4×C5#12311yescharacteristic
188C3×C4×C5#12611yescharacteristic
189C3×Dic5—81no—
190C5×Dic3—42no—
191C5×Dic3—81no—
192C24×C3—101no—
193C2×C3×D4—52no—
194C2×C3×D4—101no—
195C2×C3×D4—101no—
196C2×C3×D4—101no—
197C2×C3×D4—101no—
198C2×C3×D4—101no—
199C22×C3×C4—101no—
200C22×C3×C4C22⋊D511yescharacteristic
201C22×C3×C4C22⋊D511yescharacteristic
202C22×C3×C4C22×D511yescharacteristic
203C22×Dic3—21no—
204C22×Dic3—21no—
205C3×C4⋊C4—101no—
206C3×C4⋊C4—101no—
207C3×C22⋊C4—202no—
208C3×C22⋊C4—202no—
209C3×C42—21no—
210C3×C42—21no—
211C4⋊Dic3—21no—
212C4⋊Dic3—21no—
213C4⋊Dic3—21no—
214C4⋊Dic3C4×D512yes—
215Dic3⋊C4—42no—
216C2×C3⋊C8—52no—
217C2×C3⋊C8—52no—
218C2×C3⋊C8—101no—
219C2×C3⋊C8—101no—
220C2×C3⋊C8—101no—
221C2×C3⋊C8—101no—
222C23×C5C2×#6711yescharacteristic
223C22×D5—22no—
224C22×D5—41no—
225C22×D5—41no—
226C22×D5—41no—
227C22×D5—41no—
228C22×D5—41no—
229C22×D5—41no—
230C2×C4×C5—21no—
231C2×C4×C5—21no—
232C2×C4×C5—21no—
233C2×C4×C5—21no—
234C2×C4×C5—21no—
235C2×C4×C5—21no—
236C2×C4×C5—62no—
237C2×C4×C5—121no—
238C2×C4×C5—121no—
239C2×C4×C5—121no—
240C2×C4×C5—121no—
241C2×C4×C5—121no—
242C2×C4×C5C2×C4×D311yescharacteristic
243C2×C4×C5#23511yescharacteristic
244C2×C4×C5D3×D411yescharacteristic
245C2×C4×C5#23711yescharacteristic
246C2×C4×C5#23711yescharacteristic
247C2×C4×C5#23711yescharacteristic
248C2×Dic5—41no—
249C2×Dic5—41no—
250C2×Dic5—41no—
251D20—22no—
252D20—22no—
253D20—41no—
254D20—41no—
255#168—62no—
256#168—62no—
257C22×D4—51no—
258C22×C8—151no—
259C22×C8—151no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—51no—
263C2×C4⋊C4—61no—
264C2×C22⋊C4—101no—
265C2×C22⋊C4—101no—
266C2×C42D3×D511yescharacteristic
267#102—154no—
268#102—302no—
269#97—302no—
270#95—61no—
271C2×C3×C5#38811yescharacteristic
272C2×C3×C5#44011yescharacteristic
273C2×C3×C5#44211yescharacteristic
274C2×C3×C5#46811yescharacteristic
275C2×C3×C5#46911yescharacteristic
276C2×C3×C5#48911yescharacteristic
277C2×C3×C5#49011yescharacteristic
278C3×D5—82no—
279C23×C3—102no—
280C23×C3—201no—
281C23×C3—201no—
282C23×C3—201no—
283C23×C3—201no—
284C23×C3—201no—
285C23×C3—201no—
286C23×C3C2×C22⋊D511yescharacteristic
287C3×D4—102no—
288C3×D4—102no—
289C3×D4—201no—
290C3×D4—201no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—201no—
298C2×C3×C4—201no—
299C2×C3×C4—201no—
300C2×C3×C4C2×C4×D511yescharacteristic
301C2×C3×C4#70911yescharacteristic
302C2×C3×C4D4×D511yescharacteristic
303C2×C3×C4#71111yescharacteristic
304C2×C3×C4#71311yescharacteristic
305C2×C3×C4#71311yescharacteristic
306C2×Dic3—22no—
307C2×Dic3—41no—
308C2×Dic3—41no—
309C2×Dic3—41no—
310C2×Dic3—41no—
311C2×Dic3—41no—
312C3⋊C8—102no—
313C3⋊C8—102no—
314C22×C5C4×#6711yescharacteristic
315C22×C5#93211yescharacteristic
316C22×C5#93211yescharacteristic
317C22×C5#93611yescharacteristic
318C22×C5#93911yescharacteristic
319C22×C5#94911yescharacteristic
320C22×C5#95111yescharacteristic
321C2×D5—42no—
322C2×D5—42no—
323C2×D5—42no—
324C2×D5—81no—
325C2×D5—81no—
326C2×D5—81no—
327C2×D5—81no—
328C4×C5—41no—
329C4×C5—41no—
330C4×C5—122no—
331C4×C5—241no—
332C4×C5#87711yescharacteristic
333C4×C5#87911yescharacteristic
334C4×C5#67⋊C411yescharacteristic
335C4×C5#88311yescharacteristic
336Dic5—81no—
337C24—101no—
338C2×D4—52no—
339C2×D4—101no—
340C2×D4—101no—
341C2×D4—101no—
342C2×D4—101no—
343C2×D4—101no—
344C22×C4—61no—
345C22×C4—61no—
346C22×C4—101no—
347C22×C4#120111yescharacteristic
348C22×C4#120111yescharacteristic
349C22×C4C2×D3×D511yescharacteristic
350C2×C8—152no—
351C2×C8—152no—
352C2×C8—301no—
353C2×C8—301no—
354C2×C8—301no—
355C2×C8—301no—
356C4⋊C4—32no—
357C4⋊C4—61no—
358C4⋊C4—61no—
359C4⋊C4—61no—
360C4⋊C4—101no—
361C4⋊C4—101no—
362C4⋊C4—122no—
363C22⋊C4—202no—
364C22⋊C4—202no—
365C42—21no—
366C42—21no—
367C3×C5#193611yescharacteristic, complemented, Hall
368C22×C3—202no—
369C22×C3—202no—
370C22×C3—202no—
371C22×C3—401no—
372C22×C3—401no—
373C22×C3—401no—
374C22×C3—401no—
375C22×C3C4×C22⋊D511yescharacteristic
376C22×C3#407811yescharacteristic
377C22×C3#408511yescharacteristic
378C22×C3#408811yescharacteristic
379C22×C3#409311yescharacteristic
380C22×C3#409511yescharacteristic
381C22×C3#409511yescharacteristic
382C3×C4—41no—
383C3×C4—41no—
384C3×C4—401no—
385C3×C4#403811yescharacteristic
386C3×C4#403911yescharacteristic
387C3×C4#404011yescharacteristic
388C3×C4#404411yescharacteristic
389Dic3—42no—
390Dic3—81no—
391C2×C5#494511yescharacteristic
392C2×C5#501411yescharacteristic
393C2×C5#501811yescharacteristic
394C2×C5#503911yescharacteristic
395C2×C5#504211yescharacteristic
396C2×C5#505511yescharacteristic
397C2×C5#507111yescharacteristic
398D5—82no—
399C23—102no—
400C23—201no—
401C23—201no—
402C23—201no—
403C23—201no—
404C23—201no—
405C23—201no—
406C23C2×#120111yescharacteristic
407D4—102no—
408D4—102no—
409D4—201no—
410D4—201no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—62no—
418C2×C4—121no—
419C2×C4—121no—
420C2×C4—121no—
421C2×C4—121no—
422C2×C4—121no—
423C2×C4—201no—
424C2×C4—201no—
425C2×C4—201no—
426C2×C4#676611yescharacteristic
427C2×C4#676611yescharacteristic
428C2×C4#677111yescharacteristic
429C2×C4C4×D3×D511yescharacteristic
430C2×C4#678011yescharacteristic
431C2×C4#679011yescharacteristic
432C8—302no—
433C8—302no—
434C2×C3—402no—
435C2×C3#6527911yescharacteristic
436C2×C3#6530311yescharacteristic
437C2×C3#6531511yescharacteristic
438C2×C3#6532811yescharacteristic
439C2×C3#6533811yescharacteristic
440C2×C3#6535611yescharacteristic
441C2×C3#6537811yescharacteristic
442C5#6964511yescharacteristic, complemented, Sylow
443C22—202no—
444C22—202no—
445C22—202no—
446C22—401no—
447C22—401no—
448C22—401no—
449C22—401no—
450C22#9129811yescharacteristic
451C22#9129811yescharacteristic
452C22#9129911yescharacteristic
453C22#9130711yescharacteristic
454C22#9136811yescharacteristic
455C22C4×#120111yescharacteristic
456C22#9157111yescharacteristic
457C4—41no—
458C4—41no—
459C4—122no—
460C4—241no—
461C4—401no—
462C4#9135411yescharacteristic
463C4#9136611yescharacteristic
464C4#9139411yescharacteristic
465C4#9139611yescharacteristic
466C3#1060041011yescharacteristic, complemented, Sylow
467C2—402no—
468C2#1174689711yescharacteristic
469C2#1174689811yescharacteristic
470C2#1174702111yescharacteristic
471C2#1174704811yescharacteristic
472C2#1174852311yescharacteristic
473C2#1174854611yescharacteristic
474C2#1174870911yescharacteristic
subgroupG/H
centerC23C2×#1201
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C2×D4
prime radicalC22×C3×D20C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1936
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#91087C2semidirect
2. C5×#4928C2semidirect
6. #11745979C2semidirect
7. #11745979C2semidirect
22. #90964C4semidirect
64. #4928D5semidirect
367. C3×C5#1936semidirect
442. C5#69645semidirect
466. C3#10600410semidirect

Maximal subgroups

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

subgroupindex
C2×#910872
C5×#49282
C3×#652282
C2×#909642
#117459792
#106004103
#696455