Finite Group Databasebeta

← #14304713

Subgroups — #14304713

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
1#11751073C211yesmaximal, characteristic, complemented
2C2×C5×#809C211yesmaximal, characteristic
3#11748797C211yesmaximal, characteristic
4C2×#90967C211yesmaximal, characteristic
5C2×#90954C211yesmaximal, characteristic, complemented
6C3×#64749C211yesmaximal, characteristic, complemented
7#11745980C211yesmaximal, characteristic, complemented
8#10600981—31nomaximal, Hall
9C22×C5×D12C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×C4⋊Dic15C2211yescharacteristic
12C2×#6712—21no—
13C2×C4×Dic15C2211yescharacteristic
14C22×C5×C3⋊C8C2211yescharacteristic
15C2×C3×C4⋊Dic5C2211yescharacteristic
16C22×C3×#168C2211yescharacteristic
17C2×(C2×D3)⋊Dic5—21no—
18C2×(C2×D3)⋊Dic5—21no—
19#91115—21no—
20C5×#809—22no—
21#90967C414yescomplemented
22#90954—22no—
23#68856—51nomaximal, Hall
24C2×C5×#102—31no—
25#65510—31no—
26C2×#3964—31no—
27C2×#3947—31no—
28#65262—31no—
29#64771—31no—
30#64749D311yescharacteristic, complemented
31C23×C5×D3—21no—
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5C2311yescharacteristic
34C22×Dic15—21no—
35C22×Dic15D411yescharacteristic
36C22×Dic15D411yescharacteristic
37C2×C5×D12—21no—
38C2×C5×D12—21no—
39C2×C5×D12—21no—
40C2×C5×D12—21no—
41C2×C5×D12—21no—
42C2×C5×D12C2×C412yes—
43C22×C3×Dic5—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C4⋊Dic15—21no—
47C4⋊Dic15C2×C412yes—
48#6712—42no—
49C4×Dic15—21no—
50C4×Dic15—21no—
51C2×C5×C3⋊C8—21no—
52C2×C5×C3⋊C8—21no—
53C2×C5×C3⋊C8D412yes—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5—21no—
56C2×C3×#168—21no—
57C2×C3×#168—21no—
58C2×C3×#168C2×C412yes—
59(C2×D3)⋊Dic5—42no—
60(C2×D3)⋊Dic5—42no—
61C2×#821—51no—
62C2×#815—51no—
63#4988—51no—
64#4972—51no—
65C2×#809D511yescharacteristic
66C3×#340—51no—
67#4529—51no—
68C22×C5×D4—31no—
69C22×C5×C8—31no—
70C2×C5×C4⋊C4C2×D311yescharacteristic
71C2×C22⋊Dic5—61no—
72C2×C22⋊Dic5—61no—
73C2×C4⋊Dic5—31no—
74C2×C4⋊Dic5C2×D311yescharacteristic
75C2×#683—61no—
76C2×C4×Dic5—31no—
77C22×#168C2×D311yescharacteristic
78C5×#102—62no—
79#3964—34no—
80#3963—61no—
81#3947—62no—
82#1936—151noSylow
83C23×C3×C5C2×D411yescharacteristic
84C22×C5×D3—22no—
85C22×C5×D3—41no—
86C22×C5×D3—41no—
87C22×C5×D3—41no—
88C22×C5×D3—41no—
89C22×C5×D3—41no—
90C22×C5×D3—41no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5#4111yescharacteristic
97C2×C3×C4×C5#4111yescharacteristic
98C2×C3×C4×C5#4111yescharacteristic
99C2×C3×C4×C5#4111yescharacteristic
100C2×Dic15—22no—
101C2×Dic15—21no—
102C2×Dic15—21no—
103C2×Dic15—21no—
104C2×Dic15—21no—
105C2×Dic15—21no—
106C2×Dic15—21no—
107C2×Dic15—41no—
108C2×Dic15—41no—
109C5×D12—22no—
110C5×D12—22no—
111C5×D12—41no—
112C5×D12—41no—
113C2×C3×Dic5—41no—
114C2×C3×Dic5—41no—
115C2×C3×Dic5—41no—
116C3×#168—22no—
117C5×C3⋊C8—22no—
118C22×D12C2×D511yescharacteristic
119C22×C3×C8—51no—
120C2×C3×C4⋊C4—51no—
121C2×C3×C4⋊C4C2×D511yescharacteristic
122C2×(C2×D3)⋊C4—101no—
123C2×(C2×D3)⋊C4—101no—
124C2×C4⋊Dic3—51no—
125C2×Dic3⋊C4—101no—
126C2×C4×Dic3—51no—
127C22×C3⋊C8C2×D511yescharacteristic
128C3⋊#95—101no—
129#821—54no—
130#815—102no—
131#809—22no—
132C24×C5—61no—
133C2×C5×D4—32no—
134C2×C5×D4—61no—
135C2×C5×D4—61no—
136C2×C5×D4—61no—
137C2×C5×D4—61no—
138C2×C5×D4—61no—
139C22×C4×C5—21no—
140C22×C4×C5C22×D311yescharacteristic
141C22×Dic5—21no—
142C22×Dic5—31no—
143C22×Dic5—31no—
144C22×Dic5—61no—
145C2×C5×C8—32no—
146C2×C5×C8—61no—
147C2×C5×C8—61no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4—21no—
150C22⋊Dic5—122no—
151C22⋊Dic5—122no—
152C4⋊Dic5—21no—
153C4⋊Dic5—21no—
154C4⋊Dic5—32no—
155C4⋊Dic5—61no—
156#683—122no—
157C4×Dic5—61no—
158C4×Dic5—61no—
159C2×#168—21no—
160C2×#168—21no—
161C2×#168C4×D312yes—
162C2×#102—31no—
163C2×#102—151no—
164C2×#97—151no—
165#390—151no—
166#389—151no—
167#340—51no—
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×C5×D3—42no—
177C2×C5×D3—42no—
178C2×C5×D3—42no—
179C2×C5×D3—81no—
180C2×C5×D3—81no—
181C2×C5×D3—81no—
182C2×C5×D3—81no—
183C3×C4×C5—81no—
184C3×C4×C5#11711yescharacteristic
185C3×C4×C5C4×D411yescharacteristic
186C3×C4×C5#12311yescharacteristic
187C3×C4×C5#12611yescharacteristic
188Dic15—42no—
189Dic15—41no—
190Dic15—41no—
191C3×Dic5—81no—
192C23×D3—21no—
193C22×C3×C4—21no—
194C22×C3×C4—101no—
195C22×C3×C4C22×D511yescharacteristic
196C22×Dic3—51no—
197C22×Dic3—51no—
198C22×Dic3—101no—
199C2×D12—21no—
200C2×D12—21no—
201C2×D12—21no—
202C2×D12—21no—
203C2×D12—21no—
204C2×D12C4×D512yes—
205C2×C3×C8—52no—
206C2×C3×C8—101no—
207C2×C3×C8—101no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—101no—
211C3×C4⋊C4—101no—
212(C2×D3)⋊C4—202no—
213(C2×D3)⋊C4—202no—
214C4⋊Dic3—52no—
215C4⋊Dic3—101no—
216Dic3⋊C4—202no—
217C4×Dic3—101no—
218C4×Dic3—101no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8C22⋊D512yes—
222C23×C5—62no—
223C23×C5—121no—
224C23×C5—121no—
225C23×C5—121no—
226C23×C5—121no—
227C23×C5—121no—
228C23×C5—121no—
229C23×C5D3×D411yescharacteristic
230C5×D4—62no—
231C5×D4—62no—
232C5×D4—121no—
233C5×D4—121no—
234C2×C4×C5—41no—
235C2×C4×C5—41no—
236C2×C4×C5—41no—
237C2×C4×C5C2×C4×D311yescharacteristic
238C2×C4×C5#23511yescharacteristic
239C2×C4×C5#23511yescharacteristic
240C2×C4×C5D3×D411yescharacteristic
241C2×C4×C5#23711yescharacteristic
242C2×C4×C5#23911yescharacteristic
243C2×Dic5—41no—
244C2×Dic5—41no—
245C2×Dic5—41no—
246C2×Dic5—61no—
247C2×Dic5—61no—
248C2×Dic5—62no—
249C2×Dic5—61no—
250C2×Dic5—61no—
251C2×Dic5—61no—
252C2×Dic5—61no—
253C2×Dic5—121no—
254C2×Dic5—121no—
255C5×C8—62no—
256#168—22no—
257C22×D4—31no—
258C22×C8—31no—
259C22×C8—51no—
260C2×C4⋊C4—51no—
261C2×C4⋊C4—151no—
262C2×C4⋊C4—301no—
263C2×C4⋊C4D3×D511yescharacteristic
264C2×C22⋊C4—301no—
265C2×C22⋊C4—301no—
266C2×C42—151no—
267#102—62no—
268#102—154no—
269#97—302no—
270#95—301no—
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
278C5×D3—82no—
279C23×C3D4×D511yescharacteristic
280C22×D3—22no—
281C22×D3—41no—
282C22×D3—41no—
283C22×D3—41no—
284C22×D3—41no—
285C22×D3—41no—
286C22×D3—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—201no—
291C2×C3×C4—201no—
292C2×C3×C4—201no—
293C2×C3×C4C2×C4×D511yescharacteristic
294C2×C3×C4#70911yescharacteristic
295C2×C3×C4#71111yescharacteristic
296C2×C3×C4#71111yescharacteristic
297C2×C3×C4#71111yescharacteristic
298C2×C3×C4C2×C22⋊D511yescharacteristic
299C2×Dic3—102no—
300C2×Dic3—101no—
301C2×Dic3—101no—
302C2×Dic3—101no—
303C2×Dic3—101no—
304C2×Dic3—101no—
305C2×Dic3—101no—
306C2×Dic3—201no—
307C2×Dic3—201no—
308D12—22no—
309D12—22no—
310D12—41no—
311D12—41no—
312C3×C8—102no—
313C3⋊C8—22no—
314C22×C5—122no—
315C22×C5—122no—
316C22×C5—122no—
317C22×C5—241no—
318C22×C5—241no—
319C22×C5—241no—
320C22×C5—241no—
321C22×C5#88411yescharacteristic
322C22×C5#88511yescharacteristic
323C22×C5#89311yescharacteristic
324C22×C5#91111yescharacteristic
325C22×C5#91411yescharacteristic
326C22×C5#91411yescharacteristic
327C22×C5#91811yescharacteristic
328C4×C5—81no—
329C4×C5#87211yescharacteristic
330C4×C5#67⋊C411yescharacteristic
331C4×C5#89411yescharacteristic
332C4×C5#89811yescharacteristic
333Dic5—81no—
334Dic5—122no—
335Dic5—121no—
336Dic5—121no—
337C24—61no—
338C2×D4—32no—
339C2×D4—61no—
340C2×D4—61no—
341C2×D4—61no—
342C2×D4—61no—
343C2×D4—61no—
344C22×C4—21no—
345C22×C4—101no—
346C22×C4—151no—
347C22×C4—151no—
348C22×C4—301no—
349C22×C4C2×D3×D511yescharacteristic
350C2×C8—32no—
351C2×C8—52no—
352C2×C8—61no—
353C2×C8—61no—
354C2×C8—101no—
355C2×C8—101no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—101no—
359C4⋊C4—101no—
360C4⋊C4—152no—
361C4⋊C4—301no—
362C4⋊C4—602no—
363C22⋊C4—602no—
364C22⋊C4—602no—
365C42—301no—
366C42—301no—
367C3×C5#193611yescharacteristic, complemented, Hall
368C22×C3#402711yescharacteristic
369C22×C3#403111yescharacteristic
370C22×C3#405711yescharacteristic
371C22×C3#405711yescharacteristic
372C22×C3#406011yescharacteristic
373C22×C3#406111yescharacteristic
374C22×C3#408411yescharacteristic
375C2×D3—42no—
376C2×D3—42no—
377C2×D3—42no—
378C2×D3—81no—
379C2×D3—81no—
380C2×D3—81no—
381C2×D3—81no—
382C3×C4—81no—
383C3×C4—401no—
384C3×C4#402311yescharacteristic
385C3×C4#402511yescharacteristic
386C3×C4C4×C22⋊D511yescharacteristic
387C3×C4#408111yescharacteristic
388Dic3—202no—
389Dic3—201no—
390Dic3—201no—
391C2×C5—242no—
392C2×C5#466911yescharacteristic
393C2×C5#476411yescharacteristic
394C2×C5#478211yescharacteristic
395C2×C5#479411yescharacteristic
396C2×C5#481211yescharacteristic
397C2×C5#486911yescharacteristic
398C2×C5#488911yescharacteristic
399C23—62no—
400C23—121no—
401C23—121no—
402C23—121no—
403C23—121no—
404C23—121no—
405C23—121no—
406C23#679011yescharacteristic
407D4—62no—
408D4—62no—
409D4—121no—
410D4—121no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—201no—
415C2×C4—201no—
416C2×C4—201no—
417C2×C4—302no—
418C2×C4—301no—
419C2×C4—301no—
420C2×C4—301no—
421C2×C4—301no—
422C2×C4—301no—
423C2×C4—301no—
424C2×C4—601no—
425C2×C4—601no—
426C2×C4#676511yescharacteristic
427C2×C4#676811yescharacteristic
428C2×C4#677211yescharacteristic
429C2×C4C4×D3×D511yescharacteristic
430C2×C4#678211yescharacteristic
431C2×C4D3×C22⋊D511yescharacteristic
432C8—62no—
433C8—102no—
434C2×C3#6504611yescharacteristic
435C2×C3#6505311yescharacteristic
436C2×C3#6505411yescharacteristic
437C2×C3#6507411yescharacteristic
438C2×C3#6523311yescharacteristic
439C2×C3#6544811yescharacteristic
440C2×C3#6546311yescharacteristic
441D3—82no—
442C5#6885611yescharacteristic, complemented, Sylow
443C22—122no—
444C22—122no—
445C22—122no—
446C22—241no—
447C22—241no—
448C22—241no—
449C22—241no—
450C22#9140611yescharacteristic
451C22#9146211yescharacteristic
452C22#9148211yescharacteristic
453C22#9150011yescharacteristic
454C22#9150611yescharacteristic
455C22#9152411yescharacteristic
456C22#9155711yescharacteristic
457C4—81no—
458C4—401no—
459C4—602no—
460C4—601no—
461C4—601no—
462C4#9134111yescharacteristic
463C4#9139811yescharacteristic
464C4#9142311yescharacteristic
465C4#9144111yescharacteristic
466C3#1060098111yescharacteristic, complemented, Sylow
467C2—242no—
468C2#1174723511yescharacteristic
469C2#1174723611yescharacteristic
470C2#1174738811yescharacteristic
471C2#1174740911yescharacteristic
472C2#1174872011yescharacteristic
473C2#1174903911yescharacteristic
474C2#1174928511yescharacteristic
subgroupG/H
centerC23#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC22×C5×D12C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1936
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11751073C2semidirect
5. C2×#90954C2semidirect
6. C3×#64749C2semidirect
7. #11745980C2semidirect
21. #90967C4semidirect
30. #64749D3semidirect
367. C3×C5#1936semidirect
442. C5#68856semidirect
466. C3#10600981semidirect

Maximal subgroups

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

subgroupindex
#117510732
C2×C5×#8092
#117487972
C2×#909672
C2×#909542
C3×#647492
#117459802
#106009813
#688565