Finite Group Databasebeta

← C3×#10602635 #14309016

Subgroups — C3×#10602635 #14309016

Order 1920.

488 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#533C211yesmaximal, characteristic, complemented
2C3×#65295C211yesmaximal, characteristic
3C3×#65294C211yesmaximal, characteristic
4C2×C3×#3937C211yesmaximal, characteristic
5C3×#64753C211yesmaximal, characteristic, complemented
6C3×#64751C211yesmaximal, characteristic, complemented
7C3×#64743C211yesmaximal, characteristic, complemented
8#10602635C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#709C2211yescharacteristic
10C3×C5×C4⋊Q8—21no—
11C3×C5×#125—21no—
12C3×C5×C22⋊Q8—22no—
13C3×C4×C5×Q8—22no—
14C3×C5×#117C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16C2×C3×C42×C5C2211yescharacteristic
17C3×#4072C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20C3×#3938—22no—
21C3×#3937—22no—
22C3×#3937—21no—
23C3×#3937—21no—
24C3×#2031—51nomaximal, Hall
25C5×#533C2×C311yescharacteristic, complemented
26#65295C2×C311yescharacteristic
27#65294C2×C311yescharacteristic
28C2×#3937C2×C311yescharacteristic
29#64753C2×C311yescharacteristic, complemented
30#64751C2×C311yescharacteristic, complemented
31#64743C2×C311yescharacteristic, complemented
32C2×C3×C5×Q8—22no—
33C22×C3×C4×C5—21no—
34C22×C3×C4×C5C2311yescharacteristic
35C2×C3×C22⋊D5—21no—
36C3×#709—21no—
37C3×#709—21no—
38C3×#709—21no—
39C3×#709—21no—
40C2×C3×D20Q811yescharacteristic, complemented
41C2×C3×C4×D5—21no—
42C2×C3×Dic10Q811yescharacteristic, complemented
43C3×C5×C4⋊C4—24no—
44C3×C5×C4⋊C4—22no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C22⋊C4—21no—
48C3×C5×C22⋊C4D412yes—
49C3×C42×C5—21no—
50C3×C42×C5—21no—
51C3×C42×C5D411yescharacteristic
52C3×C42×C5D411yescharacteristic
53C3×C42×C5D412yes—
54C3×C22⋊Dic5—21no—
55C3×C4⋊Dic5—21no—
56C3×C4×Dic5—21no—
57C3×#681—21no—
58C3×#681—21no—
59C3×#681—21no—
60C3×#681—21no—
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63C3×#533D511yescharacteristic, complemented
64C3×#421—51no—
65C2×C3×#104—51no—
66C3×#410—51no—
67C3×#344—51no—
68C3×#339—51no—
69C3×H(3,ℤ/4)—51no—
70C2×#709C22×C311yescharacteristic
71C5×C4⋊Q8—21no—
72C5×#125—21no—
73C5×C22⋊Q8—22no—
74C4×C5×Q8—22no—
75C5×#117C22×C311yescharacteristic
76C5×#117C22×C311yescharacteristic
77C2×C42×C5C22×C311yescharacteristic
78#4072C22×C311yescharacteristic
79C2×#681C22×C311yescharacteristic
80C2×#681C22×C311yescharacteristic
81#3938—22no—
82#3937—22no—
83#3937—21no—
84#3937—21no—
85#2031—51noSylow
86C23×C3×C5C2×D411yescharacteristic
87C22×C3×D5—21no—
88C3×C5×Q8—44no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—42no—
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×Q811yescharacteristic
97C2×C3×C4×C5#4111yescharacteristic
98C2×C3×C4×C5#4111yescharacteristic
99C2×C3×C4×C5#4111yescharacteristic
100C3×C22⋊D5—41no—
101C3×C22⋊D5—41no—
102C2×C3×Dic5—21no—
103C2×C3×Dic5—41no—
104C3×D20—21no—
105C3×D20—21no—
106C3×C4×D5—41no—
107C3×C4×D5—41no—
108C3×Dic10—21no—
109C3×Dic10—21no—
110C3×#168—41no—
111C3×#168—41no—
112C2×C3×#41—51no—
113C2×C3×M16—51no—
114C2×C3×M16—51no—
115C3×C4⋊Q8—21no—
116C3×#125—21no—
117C3×C22⋊Q8—22no—
118C3×C4×Q8—22no—
119C3×#117—51no—
120C3×#117C2×D511yescharacteristic
121C3×#117C2×D511yescharacteristic
122C2×C3×C42C2×D511yescharacteristic
123C3×#104—101no—
124C3×#104—101no—
125C3×#104—102no—
126C3×#99—102no—
127C2×C5×Q8—22no—
128C22×C4×C5—21no—
129C22×C4×C5C23×C311yescharacteristic
130C2×C22⋊D5—21no—
131#709—21no—
132#709—21no—
133#709—21no—
134#709—21no—
135C2×D20C3×Q811yescharacteristic, complemented
136C2×C4×D5—21no—
137C2×Dic10C3×Q811yescharacteristic, complemented
138C5×C4⋊C4—24no—
139C5×C4⋊C4—22no—
140C5×C4⋊C4—21no—
141C5×C4⋊C4—21no—
142C5×C22⋊C4—21no—
143C5×C22⋊C4C3×D412yes—
144C42×C5—21no—
145C42×C5—21no—
146C42×C5C3×D411yescharacteristic
147C42×C5C3×D411yescharacteristic
148C42×C5C3×D412yes—
149C22⋊Dic5—21no—
150C4⋊Dic5—21no—
151C4×Dic5—21no—
152#681—21no—
153#681—21no—
154#681—21no—
155#681—21no—
156C2×#168—21no—
157C2×#168—21no—
158#533C3×D511yescharacteristic, complemented
159#421—51no—
160C2×#104—51no—
161#410—51no—
162#344—51no—
163#339—51no—
164H(3,ℤ/4)—51no—
165C22×C3×C5—41no—
166C22×C3×C5#12011yescharacteristic
167C22×C3×C5C22⋊Q811yescharacteristic
168C22×C3×C5#12411yescharacteristic
169C2×C3×D5—41no—
170C2×C3×D5—81no—
171C3×C4×C5—22no—
172C3×C4×C5—41no—
173C3×C4×C5—42no—
174C3×C4×C5—42no—
175C3×C4×C5C22⋊Q811yescharacteristic
176C3×C4×C5C22⋊Q811yescharacteristic
177C3×C4×C5#12411yescharacteristic
178C3×C4×C5#12411yescharacteristic
179C3×Dic5—41no—
180C3×Dic5—81no—
181C3×#41—101no—
182C3×#41—101no—
183C3×#41—101no—
184C3×#41—101no—
185C2×C3×Q8—22no—
186C2×C3×Q8—51no—
187C2×C3×D4—51no—
188C2×C3×D4—101no—
189C22×C3×C4—21no—
190C22×C3×C4—101no—
191C22×C3×C4C22×D511yescharacteristic
192C3×M16—101no—
193C3×M16—101no—
194C3×M16—101no—
195C3×M16—101no—
196C2×C3×C8—101no—
197C2×C3×C8—101no—
198C3×C4⋊C4—24no—
199C3×C4⋊C4—22no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—101no—
203C3×C22⋊C4—21no—
204C3×C22⋊C4—101no—
205C3×C22⋊C4C22⋊D512yes—
206C3×C42—21no—
207C3×C42—21no—
208C3×C42—101no—
209C3×C42C22⋊D511yescharacteristic
210C3×C42C22⋊D511yescharacteristic
211C3×C42C22⋊D512yes—
212C23×C5C2×C3×D411yescharacteristic
213C22×D5—21no—
214C5×Q8—44no—
215C2×C4×C5—21no—
216C2×C4×C5—21no—
217C2×C4×C5—22no—
218C2×C4×C5—22no—
219C2×C4×C5—42no—
220C2×C4×C5C2×C3×D411yescharacteristic
221C2×C4×C5C2×C3×D411yescharacteristic
222C2×C4×C5C2×C3×Q811yescharacteristic
223C2×C4×C5C3×#4111yescharacteristic
224C2×C4×C5C3×#4111yescharacteristic
225C2×C4×C5C3×#4111yescharacteristic
226C22⋊D5—41no—
227C22⋊D5—41no—
228C2×Dic5—21no—
229C2×Dic5—41no—
230D20—21no—
231D20—21no—
232C4×D5—41no—
233C4×D5—41no—
234Dic10—21no—
235Dic10—21no—
236#168—41no—
237#168—41no—
238C2×#41—51no—
239C2×M16—51no—
240C2×M16—51no—
241C4⋊Q8—21no—
242#125—21no—
243C22⋊Q8—22no—
244C4×Q8—22no—
245#117—51no—
246#117C2×C3×D511yescharacteristic
247#117C2×C3×D511yescharacteristic
248C2×C42C2×C3×D511yescharacteristic
249#104—101no—
250#104—101no—
251#104—102no—
252#99—102no—
253C2×C3×C5—21no—
254C2×C3×C5—21no—
255C2×C3×C5—21no—
256C2×C3×C5#39311yescharacteristic
257C3×D5—81no—
258C23×C3—101no—
259C23×C3C2×C22⋊D511yescharacteristic
260C3×Q8—44no—
261C3×Q8—101no—
262C3×Q8—101no—
263C3×D4—101no—
264C3×D4—101no—
265C3×D4—201no—
266C3×D4—201no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—42no—
272C2×C3×C4—101no—
273C2×C3×C4—201no—
274C2×C3×C4—201no—
275C2×C3×C4—201no—
276C2×C3×C4Q8×D511yescharacteristic
277C2×C3×C4#71311yescharacteristic
278C2×C3×C4#71311yescharacteristic
279C2×C3×C4#71311yescharacteristic
280C2×C3×C4C2×C22⋊D511yescharacteristic
281C2×C3×C4C2×C22⋊D511yescharacteristic
282C3×C8—201no—
283C3×C8—201no—
284C22×C5—41no—
285C22×C5C3×#12011yescharacteristic
286C22×C5C3×C22⋊Q811yescharacteristic
287C22×C5C3×#12411yescharacteristic
288C2×D5—41no—
289C2×D5—81no—
290C4×C5—22no—
291C4×C5—41no—
292C4×C5—42no—
293C4×C5—42no—
294C4×C5C3×C22⋊Q811yescharacteristic
295C4×C5C3×C22⋊Q811yescharacteristic
296C4×C5C3×#12411yescharacteristic
297C4×C5C3×#12411yescharacteristic
298Dic5—41no—
299Dic5—81no—
300#41—101no—
301#41—101no—
302#41—101no—
303#41—101no—
304C2×Q8—22no—
305C2×Q8—51no—
306C2×D4—51no—
307C2×D4—101no—
308C22×C4—21no—
309C22×C4—101no—
310C22×C4C22×C3×D511yescharacteristic
311M16—101no—
312M16—101no—
313M16—101no—
314M16—101no—
315C2×C8—101no—
316C2×C8—101no—
317C4⋊C4—24no—
318C4⋊C4—22no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—101no—
322C22⋊C4—21no—
323C22⋊C4—101no—
324C22⋊C4C3×C22⋊D512yes—
325C42—21no—
326C42—21no—
327C42—101no—
328C42C3×C22⋊D511yescharacteristic
329C42C3×C22⋊D511yescharacteristic
330C42C3×C22⋊D512yes—
331C3×C5#203111yescharacteristic, complemented, Hall
332C22×C3—41no—
333C22×C3—201no—
334C22×C3—401no—
335C22×C3#409211yescharacteristic
336C22×C3#409311yescharacteristic
337C22×C3#409911yescharacteristic
338C3×C4—22no—
339C3×C4—41no—
340C3×C4—42no—
341C3×C4—42no—
342C3×C4—201no—
343C3×C4—401no—
344C3×C4#409211yescharacteristic
345C3×C4#409211yescharacteristic
346C3×C4#409311yescharacteristic
347C3×C4#409311yescharacteristic
348C2×C5—21no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5C3×#39311yescharacteristic
352D5—81no—
353C23—101no—
354C23C2×C3×C22⋊D511yescharacteristic
355Q8—44no—
356Q8—101no—
357Q8—101no—
358D4—101no—
359D4—101no—
360D4—201no—
361D4—201no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—42no—
367C2×C4—101no—
368C2×C4—201no—
369C2×C4—201no—
370C2×C4—201no—
371C2×C4C3×Q8×D511yescharacteristic
372C2×C4C3×#71311yescharacteristic
373C2×C4C3×#71311yescharacteristic
374C2×C4C3×#71311yescharacteristic
375C2×C4C2×C3×C22⋊D511yescharacteristic
376C2×C4C2×C3×C22⋊D511yescharacteristic
377C8—201no—
378C8—201no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—401no—
383C2×C3#6552011yescharacteristic
384C5C3×#203111yescharacteristic, complemented, Sylow
385C22—41no—
386C22—201no—
387C22—401no—
388C22C3×#409211yescharacteristic
389C22C3×#409311yescharacteristic
390C22C3×#409911yescharacteristic
391C4—22no—
392C4—41no—
393C4—42no—
394C4—42no—
395C4—201no—
396C4—401no—
397C4C3×#409211yescharacteristic
398C4C3×#409211yescharacteristic
399C4C3×#409311yescharacteristic
400C4C3×#409311yescharacteristic
401C3#1060263511yescharacteristic, direct product factor, Sylow
402C2—21no—
403C2—21no—
404C2—21no—
405C2—401no—
406C2C3×#6552011yescharacteristic
subgroupG/H
centerC3×C4#4093
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#533C2
socleC2×C3×C5#393
prime radicalC2×C3×#709C22
hypercenterC3×#533D5
hypocenterC5C3×#2031
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#533

Complements

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

NH ≅ G/Ntype
1. C3×C5×#533C2semidirect
5. C3×#64753C2semidirect
6. C3×#64751C2semidirect
7. C3×#64743C2semidirect
8. #10602635C3direct (N × H)
25. C5×#533C2×C3semidirect
29. #64753C2×C3semidirect
30. #64751C2×C3semidirect
31. #64743C2×C3semidirect
40. C2×C3×D20Q8semidirect
42. C2×C3×Dic10Q8semidirect
63. C3×#533D5semidirect
135. C2×D20C3×Q8semidirect
137. C2×Dic10C3×Q8semidirect
158. #533C3×D5semidirect
331. C3×C5#2031semidirect
384. C5C3×#2031semidirect
401. C3#10602635direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5332
C3×#652952
C3×#652942
C2×C3×#39372
C3×#647532
C3×#647512
C3×#647432
#106026353
C3×#20315