Finite Group Databasebeta

← #14289096

Subgroups — #14289096

Order 1920.

512 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#547C211yesmaximal, characteristic, complemented
2#11751189C211yesmaximal, characteristic, complemented
3#11751116C211yesmaximal, characteristic, complemented
4#11751116C211yesmaximal, characteristic, complemented
5#11746368C211yesmaximal, characteristic, complemented
6D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
7D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
8#10602703—31nomaximal, Hall
9C2×C3×C5×#41—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×#123—22no—
12C3×C5×C22⋊Q8—21no—
13C3×C5×#121—21no—
14C3×C4×C5×D4C2211yescharacteristic
15C3×C4×C5×D4C2211yescharacteristic
16C2×C3×C5×C4⋊C4—21no—
17C2×#6715—21no—
18C2×#6715—21no—
19#91763C2211yescharacteristic
20#91093—22no—
21#91093—21no—
22#91093—21no—
23C4⋊(C3⋊#168)C2211yescharacteristic
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71910—51nomaximal, Hall
27C5×#547D311yescharacteristic, complemented
28#65377—31no—
29#65304—31no—
30#65304—31no—
31#64767—31no—
32D4⋊#168—31no—
33D4⋊#168—31no—
34C3×C5×#41—42no—
35C3×C5×#41—42no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×D4—22no—
38C2×C3×C5×D4D411yescharacteristic
39C2×C3×C5×D4D411yescharacteristic
40C22×C3×C4×C5—22no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5—21no—
43C2×D60—21no—
44C2×D60—21no—
45C2×D60—21no—
46C3×C5×C4⋊C4—22no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C4⋊C4D411yescharacteristic
50C3×C5×C4⋊C4D412yes—
51C3×C5×C22⋊C4—22no—
52C3×C5×C22⋊C4—21no—
53C3×C5×C22⋊C4—21no—
54C3×C42×C5C2311yescharacteristic
55#6715—42no—
56#6715—42no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59C2×C3⋊#168—21no—
60C3×#547D511yescharacteristic, complemented
61#5088—51no—
62#5015—51no—
63#5015—51no—
64#4547—51no—
65D4⋊(C3⋊C8)—51no—
66D4⋊(C3⋊C8)—51no—
67C2×C5×#41—21no—
68C5×C4⋊Q8C2×D311yescharacteristic
69C5×#123—22no—
70C5×C22⋊Q8—21no—
71C5×#121—21no—
72C4×C5×D4C2×D311yescharacteristic
73C4×C5×D4C2×D311yescharacteristic
74C2×C5×C4⋊C4—21no—
75C2×#686—61no—
76C2×#686—61no—
77#4020—31no—
78#3941—61no—
79#3941—61no—
80#3941—62no—
81C4⋊#168—31no—
82C4⋊#168—31no—
83C4×#168—31no—
84#1625—151noSylow
85C23×C3×C5—21no—
86C23×C3×C5—21no—
87C22×D15—41no—
88C3×C5×Q8—41no—
89C3×C5×Q8—41no—
90C3×C5×D4—21no—
91C3×C5×D4—21no—
92C3×C5×D4—21no—
93C3×C5×D4—44no—
94C3×C5×D4D812yescomplemented
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—22no—
98C2×C3×C4×C5—44no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106D60—42no—
107D60—41no—
108D60—41no—
109D60—41no—
110D60—41no—
111C3⋊#168—41no—
112C3⋊#168—41no—
113C3⋊#168—41no—
114C2×C3×#41—21no—
115C3×C4⋊Q8C2×D511yescharacteristic
116C3×#123—22no—
117C3×C22⋊Q8—21no—
118C3×#121—21no—
119C3×C4×D4C2×D511yescharacteristic
120C3×C4×D4C2×D511yescharacteristic
121C2×C3×C4⋊C4—21no—
122C2×#213—101no—
123C2×#213—101no—
124#874—51no—
125#809—101no—
126#809—101no—
127#809—102no—
128C4⋊(C3⋊C8)—51no—
129C4⋊(C3⋊C8)—51no—
130C4×C3⋊C8—51no—
131C5×#41—42no—
132C5×#41—42no—
133C2×C5×Q8—21no—
134C2×C5×D4—22no—
135C2×C5×D4#6711yescharacteristic
136C2×C5×D4#6711yescharacteristic
137C22×C4×C5—22no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C2×D20—61no—
141C2×D20—61no—
142C2×D20—61no—
143C5×C4⋊C4—22no—
144C5×C4⋊C4—21no—
145C5×C4⋊C4#6711yescharacteristic
146C5×C4⋊C4#6711yescharacteristic
147C5×C4⋊C4#6712yes—
148C5×C22⋊C4—22no—
149C5×C22⋊C4—21no—
150C5×C22⋊C4—21no—
151C42×C5C22×D311yescharacteristic
152#686—122no—
153#686—122no—
154C2×#168—61no—
155C2×#168—61no—
156C2×#168—61no—
157#547D1511yescharacteristic, complemented
158#486—151no—
159#459—151no—
160#459—151no—
161#332—151no—
162D4⋊C8—151no—
163D4⋊C8—151no—
164C22×C3×C5—22no—
165C22×C3×C5—41no—
166C22×C3×C5—41no—
167C22×C3×C5—41no—
168C22×C3×C5—41no—
169C22×C3×C5—41no—
170C22×C3×C5#12011yescharacteristic
171C2×D15—81no—
172C2×D15—81no—
173C2×D15—81no—
174C3×C4×C5—21no—
175C3×C4×C5—41no—
176C3×C4×C5—42no—
177C3×C4×C5—41no—
178C3×C4×C5C2×D811yescharacteristic
179C3×C4×C5#13511yescharacteristic
180C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
181C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
182C3×#41—42no—
183C3×#41—42no—
184C2×C3×Q8—21no—
185C2×C3×D4—22no—
186C2×C3×D4C22⋊D511yescharacteristic
187C2×C3×D4C22⋊D511yescharacteristic
188C22×C3×C4—22no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C2×D12—101no—
192C2×D12—101no—
193C2×D12—101no—
194C3×C4⋊C4—22no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4C22⋊D511yescharacteristic
197C3×C4⋊C4C22⋊D511yescharacteristic
198C3×C4⋊C4C22⋊D512yes—
199C3×C22⋊C4—22no—
200C3×C22⋊C4—21no—
201C3×C22⋊C4—21no—
202C3×C42C22×D511yescharacteristic
203#213—202no—
204#213—202no—
205C2×C3⋊C8—101no—
206C2×C3⋊C8—101no—
207C2×C3⋊C8—101no—
208C23×C5—21no—
209C23×C5—21no—
210C22×D5—121no—
211C5×Q8—41no—
212C5×Q8—41no—
213C5×D4—21no—
214C5×D4—21no—
215C5×D4—21no—
216C5×D4—44no—
217C5×D4#21312yescomplemented
218C2×C4×C5—21no—
219C2×C4×C5—21no—
220C2×C4×C5—22no—
221C2×C4×C5—44no—
222C2×C4×C5—41no—
223C2×C4×C5—41no—
224C2×C4×C5—41no—
225C2×C4×C5—41no—
226C2×C4×C5C2×#6711yescharacteristic
227C2×C4×C5C2×#6711yescharacteristic
228C2×C4×C5C2×#6711yescharacteristic
229D20—122no—
230D20—121no—
231D20—121no—
232D20—121no—
233D20—121no—
234#168—121no—
235#168—121no—
236#168—121no—
237C2×#41—21no—
238C2×D8—301no—
239C2×D8—301no—
240C4⋊Q8C2×D1511yescharacteristic
241#127—151no—
242#123—22no—
243C22⋊Q8—21no—
244#121—21no—
245C4×D4C2×D1511yescharacteristic
246C4×D4C2×D1511yescharacteristic
247C2×C4⋊C4—21no—
248C4⋊C8—151no—
249C4⋊C8—151no—
250#102—301no—
251#102—301no—
252#102—302no—
253C4×C8—151no—
254C2×C3×C5—42no—
255C2×C3×C5—81no—
256C2×C3×C5#44711yescharacteristic
257C2×C3×C5#44911yescharacteristic
258C2×C3×C5#45411yescharacteristic
259D15—161no—
260C23×C3—21no—
261C23×C3—21no—
262C22×D3—201no—
263C3×Q8—41no—
264C3×Q8—41no—
265C3×D4—21no—
266C3×D4—21no—
267C3×D4—21no—
268C3×D4—44no—
269C3×D4#68612yescomplemented
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—22no—
273C2×C3×C4—44no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4C2×C22⋊D511yescharacteristic
279C2×C3×C4C2×C22⋊D511yescharacteristic
280C2×C3×C4C2×C22⋊D511yescharacteristic
281D12—202no—
282D12—201no—
283D12—201no—
284D12—201no—
285D12—201no—
286C3⋊C8—201no—
287C3⋊C8—201no—
288C3⋊C8—201no—
289C22×C5—22no—
290C22×C5—41no—
291C22×C5—41no—
292C22×C5—41no—
293C22×C5—41no—
294C22×C5—41no—
295C22×C5#95311yescharacteristic
296C2×D5—241no—
297C2×D5—241no—
298C2×D5—241no—
299C4×C5—21no—
300C4×C5—41no—
301C4×C5—42no—
302C4×C5—41no—
303C4×C5C2×#21311yescharacteristic
304C4×C5#93211yescharacteristic
305C4×C5#94911yescharacteristic
306C4×C5#95011yescharacteristic
307#41—42no—
308#41—42no—
309C2×Q8—21no—
310C2×D4—22no—
311C2×D4—301no—
312C2×D4—301no—
313C2×D4—301no—
314C2×D4#122011yescharacteristic
315C2×D4#122011yescharacteristic
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—21no—
319D8—602no—
320D8—602no—
321C2×C8—301no—
322C2×C8—301no—
323C2×C8—301no—
324C4⋊C4—22no—
325C4⋊C4—21no—
326C4⋊C4#122011yescharacteristic
327C4⋊C4#122011yescharacteristic
328C4⋊C4#122012yes—
329C22⋊C4—22no—
330C22⋊C4—21no—
331C22⋊C4—21no—
332C42C22×D1511yescharacteristic
333C3×C5#162511yescharacteristic, complemented, Hall
334C22×C3—22no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3—41no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3#409911yescharacteristic
341C2×D3—401no—
342C2×D3—401no—
343C2×D3—401no—
344C3×C4—21no—
345C3×C4—41no—
346C3×C4—42no—
347C3×C4—41no—
348C3×C4C2×#68611yescharacteristic
349C3×C4#407811yescharacteristic
350C3×C4#409511yescharacteristic
351C3×C4#409611yescharacteristic
352C2×C5—42no—
353C2×C5—81no—
354C2×C5#521711yescharacteristic
355C2×C5#523811yescharacteristic
356C2×C5#524511yescharacteristic
357D5—481no—
358C23—21no—
359C23—21no—
360C23—601no—
361Q8—41no—
362Q8—41no—
363D4—21no—
364D4—21no—
365D4—21no—
366D4—44no—
367D4—602no—
368D4—601no—
369D4—601no—
370D4—601no—
371D4—601no—
372D4#671512yescomplemented
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—44no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4C2×#122011yescharacteristic
382C2×C4C2×#122011yescharacteristic
383C2×C4C2×#122011yescharacteristic
384C8—601no—
385C8—601no—
386C8—601no—
387C2×C3—42no—
388C2×C3—81no—
389C2×C3#6550611yescharacteristic
390C2×C3#6552711yescharacteristic
391C2×C3#6553411yescharacteristic
392D3—801no—
393C5#7191011yescharacteristic, complemented, Sylow
394C22—22no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—1201no—
401C22—1201no—
402C22—1201no—
403C22#9184211yescharacteristic
404C4—21no—
405C4—41no—
406C4—42no—
407C4—41no—
408C4C2×#671511yescharacteristic
409C4#9182111yescharacteristic
410C4#9183811yescharacteristic
411C4#9183911yescharacteristic
412C3#1060270311yescharacteristic, complemented, Sylow
413C2—42no—
414C2—81no—
415C2—2401no—
416C2#1175131811yescharacteristic
417C2#1175133911yescharacteristic
418C2#1175134611yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#547C2
socleC22×C3×C5#120
hypercenter#547D15
hypocenterC3×C5#1625
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C3×C5×#547C2semidirect
2. #11751189C2semidirect
3. #11751116C2semidirect
4. #11751116C2semidirect
5. #11746368C2semidirect
6. D4⋊(C3⋊#168)C2semidirect
7. D4⋊(C3⋊#168)C2semidirect
27. C5×#547D3semidirect
60. C3×#547D5semidirect
94. C3×C5×D4D8semidirect
157. #547D15semidirect
217. C5×D4#213semidirect
269. C3×D4#686semidirect
333. C3×C5#1625semidirect
372. D4#6715semidirect
393. C5#71910semidirect
412. C3#10602703semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5472
#117511892
#117511162
#117463682
D4⋊(C3⋊#168)2
#106027033
#719105