Finite Group Databasebeta

← C3×#10602703 #14289095

Subgroups — C3×#10602703 #14289095

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
2C3×#65377C211yesmaximal, characteristic, complemented
3C3×#65304C211yesmaximal, characteristic, complemented
4C3×#65304C211yesmaximal, characteristic, complemented
5C3×#64767C211yesmaximal, characteristic, complemented
6C3×D4⋊#168C211yesmaximal, characteristic, complemented
7C3×D4⋊#168C211yesmaximal, characteristic, complemented
8#10602703C311yesmaximal, characteristic, direct product factor, 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×C3×#686—21no—
18C2×C3×#686—21no—
19C3×#4020C2211yescharacteristic
20C3×#3941—21no—
21C3×#3941—21no—
22C3×#3941—22no—
23C3×C4⋊#168C2211yescharacteristic
24C3×C4⋊#168C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26C3×#1625—51nomaximal, Hall
27C5×#547C2×C311yescharacteristic, complemented
28#65377C2×C311yescharacteristic, complemented
29#65304C2×C311yescharacteristic, complemented
30#65304C2×C311yescharacteristic, complemented
31#64767C2×C311yescharacteristic, complemented
32D4⋊#168C2×C311yescharacteristic, complemented
33D4⋊#168C2×C311yescharacteristic, complemented
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×C3×D20—21no—
44C2×C3×D20—21no—
45C2×C3×D20—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
55C3×#686—42no—
56C3×#686—42no—
57C2×C3×#168—21no—
58C2×C3×#168—21no—
59C2×C3×#168—21no—
60C3×#547D511yescharacteristic, complemented
61C3×#486—51no—
62C3×#459—51no—
63C3×#459—51no—
64C3×#332—51no—
65C3×D4⋊C8—51no—
66C3×D4⋊C8—51no—
67C2×C5×#41—21no—
68C5×C4⋊Q8C22×C311yescharacteristic
69C5×#123—22no—
70C5×C22⋊Q8—21no—
71C5×#121—21no—
72C4×C5×D4C22×C311yescharacteristic
73C4×C5×D4C22×C311yescharacteristic
74C2×C5×C4⋊C4—21no—
75C2×#686—21no—
76C2×#686—21no—
77#4020C22×C311yescharacteristic
78#3941—21no—
79#3941—21no—
80#3941—22no—
81C4⋊#168C22×C311yescharacteristic
82C4⋊#168C22×C311yescharacteristic
83C4×#168C22×C311yescharacteristic
84#1625—51noSylow
85C23×C3×C5—21no—
86C23×C3×C5—21no—
87C22×C3×D5—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
106C3×D20—42no—
107C3×D20—41no—
108C3×D20—41no—
109C3×D20—41no—
110C3×D20—41no—
111C3×#168—41no—
112C3×#168—41no—
113C3×#168—41no—
114C2×C3×#41—21no—
115C2×C3×D8—101no—
116C2×C3×D8—101no—
117C3×C4⋊Q8C2×D511yescharacteristic
118C3×#127—51no—
119C3×#123—22no—
120C3×C22⋊Q8—21no—
121C3×#121—21no—
122C3×C4×D4C2×D511yescharacteristic
123C3×C4×D4C2×D511yescharacteristic
124C2×C3×C4⋊C4—21no—
125C3×C4⋊C8—51no—
126C3×C4⋊C8—51no—
127C3×#102—101no—
128C3×#102—101no—
129C3×#102—102no—
130C3×C4×C8—51no—
131C5×#41—42no—
132C5×#41—42no—
133C2×C5×Q8—21no—
134C2×C5×D4—22no—
135C2×C5×D4C3×D411yescharacteristic
136C2×C5×D4C3×D411yescharacteristic
137C22×C4×C5—22no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C2×D20—21no—
141C2×D20—21no—
142C2×D20—21no—
143C5×C4⋊C4—22no—
144C5×C4⋊C4—21no—
145C5×C4⋊C4C3×D411yescharacteristic
146C5×C4⋊C4C3×D411yescharacteristic
147C5×C4⋊C4C3×D412yes—
148C5×C22⋊C4—22no—
149C5×C22⋊C4—21no—
150C5×C22⋊C4—21no—
151C42×C5C23×C311yescharacteristic
152#686—42no—
153#686—42no—
154C2×#168—21no—
155C2×#168—21no—
156C2×#168—21no—
157#547C3×D511yescharacteristic, complemented
158#486—51no—
159#459—51no—
160#459—51no—
161#332—51no—
162D4⋊C8—51no—
163D4⋊C8—51no—
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×C3×D5—81no—
172C2×C3×D5—81no—
173C2×C3×D5—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×D4—101no—
187C2×C3×D4—101no—
188C2×C3×D4—101no—
189C2×C3×D4C22⋊D511yescharacteristic
190C2×C3×D4C22⋊D511yescharacteristic
191C22×C3×C4—22no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C3×D8—202no—
195C3×D8—202no—
196C2×C3×C8—101no—
197C2×C3×C8—101no—
198C2×C3×C8—101no—
199C3×C4⋊C4—22no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4C22⋊D511yescharacteristic
202C3×C4⋊C4C22⋊D511yescharacteristic
203C3×C4⋊C4C22⋊D512yes—
204C3×C22⋊C4—22no—
205C3×C22⋊C4—21no—
206C3×C22⋊C4—21no—
207C3×C42C22×D511yescharacteristic
208C23×C5—21no—
209C23×C5—21no—
210C22×D5—41no—
211C5×Q8—41no—
212C5×Q8—41no—
213C5×D4—21no—
214C5×D4—21no—
215C5×D4—21no—
216C5×D4—44no—
217C5×D4C3×D812yescomplemented
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×C3×D411yescharacteristic
227C2×C4×C5C2×C3×D411yescharacteristic
228C2×C4×C5C2×C3×D411yescharacteristic
229D20—42no—
230D20—41no—
231D20—41no—
232D20—41no—
233D20—41no—
234#168—41no—
235#168—41no—
236#168—41no—
237C2×#41—21no—
238C2×D8—101no—
239C2×D8—101no—
240C4⋊Q8C2×C3×D511yescharacteristic
241#127—51no—
242#123—22no—
243C22⋊Q8—21no—
244#121—21no—
245C4×D4C2×C3×D511yescharacteristic
246C4×D4C2×C3×D511yescharacteristic
247C2×C4⋊C4—21no—
248C4⋊C8—51no—
249C4⋊C8—51no—
250#102—101no—
251#102—101no—
252#102—102no—
253C4×C8—51no—
254C2×C3×C5—42no—
255C2×C3×C5—81no—
256C2×C3×C5#44711yescharacteristic
257C2×C3×C5#44911yescharacteristic
258C2×C3×C5#45411yescharacteristic
259C3×D5—161no—
260C23×C3—21no—
261C23×C3—21no—
262C23×C3—201no—
263C3×Q8—41no—
264C3×Q8—41no—
265C3×D4—21no—
266C3×D4—21no—
267C3×D4—21no—
268C3×D4—44no—
269C3×D4—202no—
270C3×D4—201no—
271C3×D4—201no—
272C3×D4—201no—
273C3×D4—201no—
274C3×D4#68612yescomplemented
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—22no—
278C2×C3×C4—44no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4C2×C22⋊D511yescharacteristic
284C2×C3×C4C2×C22⋊D511yescharacteristic
285C2×C3×C4C2×C22⋊D511yescharacteristic
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×C5C3×#12011yescharacteristic
296C2×D5—81no—
297C2×D5—81no—
298C2×D5—81no—
299C4×C5—21no—
300C4×C5—41no—
301C4×C5—42no—
302C4×C5—41no—
303C4×C5C2×C3×D811yescharacteristic
304C4×C5C3×#13511yescharacteristic
305C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
306C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
307#41—42no—
308#41—42no—
309C2×Q8—21no—
310C2×D4—22no—
311C2×D4—101no—
312C2×D4—101no—
313C2×D4—101no—
314C2×D4C3×C22⋊D511yescharacteristic
315C2×D4C3×C22⋊D511yescharacteristic
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—21no—
319D8—202no—
320D8—202no—
321C2×C8—101no—
322C2×C8—101no—
323C2×C8—101no—
324C4⋊C4—22no—
325C4⋊C4—21no—
326C4⋊C4C3×C22⋊D511yescharacteristic
327C4⋊C4C3×C22⋊D511yescharacteristic
328C4⋊C4C3×C22⋊D512yes—
329C22⋊C4—22no—
330C22⋊C4—21no—
331C22⋊C4—21no—
332C42C22×C3×D511yescharacteristic
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—401no—
341C22×C3—401no—
342C22×C3—401no—
343C22×C3#409911yescharacteristic
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×C5C3×#44711yescharacteristic
355C2×C5C3×#44911yescharacteristic
356C2×C5C3×#45411yescharacteristic
357D5—161no—
358C23—21no—
359C23—21no—
360C23—201no—
361Q8—41no—
362Q8—41no—
363D4—21no—
364D4—21no—
365D4—21no—
366D4—44no—
367D4—202no—
368D4—201no—
369D4—201no—
370D4—201no—
371D4—201no—
372D4C3×#68612yescomplemented
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×C3×C22⋊D511yescharacteristic
382C2×C4C2×C3×C22⋊D511yescharacteristic
383C2×C4C2×C3×C22⋊D511yescharacteristic
384C8—201no—
385C8—201no—
386C8—201no—
387C2×C3—42no—
388C2×C3—81no—
389C2×C3—801no—
390C2×C3#6550611yescharacteristic
391C2×C3#6552711yescharacteristic
392C2×C3#6553411yescharacteristic
393C5C3×#162511yescharacteristic, complemented, Sylow
394C22—22no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—401no—
401C22—401no—
402C22—401no—
403C22C3×#409911yescharacteristic
404C4—21no—
405C4—41no—
406C4—42no—
407C4—41no—
408C4C2×C3×#68611yescharacteristic
409C4C3×#407811yescharacteristic
410C4C3×#409511yescharacteristic
411C4C3×#409611yescharacteristic
412C3#1060270311yescharacteristic, direct product factor, Sylow
413C2—42no—
414C2—81no—
415C2—801no—
416C2C3×#6550611yescharacteristic
417C2C3×#6552711yescharacteristic
418C2C3×#6553411yescharacteristic
subgroupG/H
centerC22×C3#4099
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#547C2
socleC22×C3×C5#120
hypercenterC3×#547D5
hypocenterC5C3×#1625
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#547

Complements

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

NH ≅ G/Ntype
1. C3×C5×#547C2semidirect
2. C3×#65377C2semidirect
3. C3×#65304C2semidirect
4. C3×#65304C2semidirect
5. C3×#64767C2semidirect
6. C3×D4⋊#168C2semidirect
7. C3×D4⋊#168C2semidirect
8. #10602703C3direct (N × H)
27. C5×#547C2×C3semidirect
28. #65377C2×C3semidirect
29. #65304C2×C3semidirect
30. #65304C2×C3semidirect
31. #64767C2×C3semidirect
32. D4⋊#168C2×C3semidirect
33. D4⋊#168C2×C3semidirect
60. C3×#547D5semidirect
94. C3×C5×D4D8semidirect
157. #547C3×D5semidirect
217. C5×D4C3×D8semidirect
274. C3×D4#686semidirect
333. C3×C5#1625semidirect
372. D4C3×#686semidirect
393. C5C3×#1625semidirect
412. C3#10602703direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5472
C3×#653772
C3×#653042
C3×#647672
C3×D4⋊#1682
#106027033
C3×#16255