Finite Group Databasebeta

← C3×#10599572 #14309028

Subgroups — C3×#10599572 #14309028

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×#65804C211yesmaximal, characteristic, complemented
2C3×#65428C211yesmaximal, characteristic
3C3×#65295C211yesmaximal, characteristic
4C2×C3×#3937C211yesmaximal, characteristic
5C3×C5×#339C211yesmaximal, characteristic, complemented
6C3×#64776C211yesmaximal, characteristic, complemented
7C3×#64751C211yesmaximal, characteristic, complemented
8#10599572C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×#709C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13C3×#4072C2211yescharacteristic
14C3×#4072C2211yescharacteristic
15C3×#4070—22no—
16C2×C3×#681C2211yescharacteristic
17C3×#4016—21no—
18C3×#4015—21no—
19C3×C4×Dic10—22no—
20C3×#3957—22no—
21C3×#3938—22no—
22C3×#3937—21no—
23C3×#3937—21no—
24C3×#2031—51nomaximal, Hall
25#65804C2×C311yescharacteristic, complemented
26#65428C2×C311yescharacteristic
27#65295C2×C311yescharacteristic
28C2×#3937C2×C311yescharacteristic
29C5×#339C2×C311yescharacteristic, complemented
30#64776C2×C311yescharacteristic, complemented
31#64751C2×C311yescharacteristic, complemented
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5C2311yescharacteristic
34C2×C3×C22⋊D5—21no—
35C3×#709—21no—
36C3×#709—21no—
37C3×#709—21no—
38C3×#709—21no—
39C2×C3×D20Q811yescharacteristic, complemented
40C2×C3×C4×D5—21no—
41C2×C3×Dic10—22no—
42C2×C3×Dic10Q811yescharacteristic, complemented
43C3×C5×M16—21no—
44C3×C5×M16—21no—
45C2×C3×C5×C8—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C22⋊C4—21no—
48C3×C42×C5—21no—
49C3×C42×C5—21no—
50C3×C42×C5D411yescharacteristic
51C3×C42×C5D411yescharacteristic
52C3×C22⋊Dic5—21no—
53C3×C22⋊Dic5D412yes—
54C3×C4⋊Dic5—22no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5—21no—
57C3×#683—24no—
58C3×C4×Dic5—21no—
59C3×C4×Dic5D412yes—
60C3×#681—21no—
61C3×#681—21no—
62C2×C3×#168—21no—
63C3×#533—51no—
64C3×#421—51no—
65C2×C3×#104—51no—
66C3×#410—51no—
67C3×#344—51no—
68C3×#339D511yescharacteristic, complemented
69C3×H(3,ℤ/4)—51no—
70C2×#709C22×C311yescharacteristic
71C2×C5×M16C22×C311yescharacteristic
72C5×#117C22×C311yescharacteristic
73C2×C42×C5C22×C311yescharacteristic
74#4072C22×C311yescharacteristic
75#4072C22×C311yescharacteristic
76#4070—22no—
77C2×#681C22×C311yescharacteristic
78#4016—21no—
79#4015—21no—
80C4×Dic10—22no—
81#3957—22no—
82#3938—22no—
83#3937—21no—
84#3937—21no—
85#2031—51noSylow
86C23×C3×C5C2×D411yescharacteristic
87C22×C3×D5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—42no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×Q811yescharacteristic
95C2×C3×C4×C5#4111yescharacteristic
96C2×C3×C4×C5#4111yescharacteristic
97C2×C3×C4×C5#4111yescharacteristic
98C3×C22⋊D5—41no—
99C3×C22⋊D5—41no—
100C2×C3×Dic5—22no—
101C2×C3×Dic5—22no—
102C2×C3×Dic5—21no—
103C3×D20—21no—
104C3×D20—21no—
105C3×C4×D5—41no—
106C3×C4×D5—41no—
107C3×Dic10—21no—
108C3×Dic10—21no—
109C3×Dic10—44no—
110C3×C5×C8—41no—
111C3×#168—41no—
112C2×C3×#41—51no—
113C2×C3×M16—51no—
114C2×C3×M16C2×D511yescharacteristic
115C3×C4⋊Q8—101no—
116C3×#125—101no—
117C3×C22⋊Q8—102no—
118C3×C4×Q8—102no—
119C3×#117—51no—
120C3×#117—51no—
121C3×#117C2×D511yescharacteristic
122C2×C3×C42C2×D511yescharacteristic
123C3×#104—102no—
124C3×#104—101no—
125C3×#104—101no—
126C3×#99—102no—
127C22×C4×C5—21no—
128C22×C4×C5C23×C311yescharacteristic
129C2×C22⋊D5—21no—
130#709—21no—
131#709—21no—
132#709—21no—
133#709—21no—
134C2×D20C3×Q811yescharacteristic, complemented
135C2×C4×D5—21no—
136C2×Dic10—22no—
137C2×Dic10C3×Q811yescharacteristic, complemented
138C5×M16—21no—
139C5×M16—21no—
140C2×C5×C8—21no—
141C5×C4⋊C4—21no—
142C5×C22⋊C4—21no—
143C42×C5—21no—
144C42×C5—21no—
145C42×C5C3×D411yescharacteristic
146C42×C5C3×D411yescharacteristic
147C22⋊Dic5—21no—
148C22⋊Dic5C3×D412yes—
149C4⋊Dic5—22no—
150C4⋊Dic5—21no—
151C4⋊Dic5—21no—
152#683—24no—
153C4×Dic5—21no—
154C4×Dic5C3×D412yes—
155#681—21no—
156#681—21no—
157C2×#168—21no—
158#533—51no—
159#421—51no—
160C2×#104—51no—
161#410—51no—
162#344—51no—
163#339C3×D511yescharacteristic, complemented
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—81no—
174C3×C4×C5C22⋊Q811yescharacteristic
175C3×C4×C5C22⋊Q811yescharacteristic
176C3×C4×C5#12411yescharacteristic
177C3×C4×C5#12411yescharacteristic
178C3×Dic5—42no—
179C3×Dic5—42no—
180C3×Dic5—41no—
181C3×#41—101no—
182C3×#41—101no—
183C3×#41—101no—
184C3×#41—101no—
185C2×C3×Q8—51no—
186C2×C3×Q8—102no—
187C2×C3×D4—51no—
188C2×C3×D4—101no—
189C22×C3×C4—21no—
190C22×C3×C4—101no—
191C22×C3×C4C22×D511yescharacteristic
192C3×M16—21no—
193C3×M16—21no—
194C3×M16—101no—
195C3×M16—101no—
196C2×C3×C8—21no—
197C2×C3×C8—101no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—104no—
200C3×C4⋊C4—102no—
201C3×C4⋊C4—101no—
202C3×C4⋊C4—101no—
203C3×C22⋊C4—21no—
204C3×C22⋊C4—52no—
205C3×C22⋊C4—101no—
206C3×C42—21no—
207C3×C42—21no—
208C3×C42—52no—
209C3×C42—101no—
210C3×C42D2011yescharacteristic
211C3×C42D2011yescharacteristic
212C23×C5C2×C3×D411yescharacteristic
213C22×D5—21no—
214C2×C4×C5—21no—
215C2×C4×C5—21no—
216C2×C4×C5—42no—
217C2×C4×C5—41no—
218C2×C4×C5C2×C3×D411yescharacteristic
219C2×C4×C5C2×C3×D411yescharacteristic
220C2×C4×C5C2×C3×Q811yescharacteristic
221C2×C4×C5C3×#4111yescharacteristic
222C2×C4×C5C3×#4111yescharacteristic
223C2×C4×C5C3×#4111yescharacteristic
224C22⋊D5—41no—
225C22⋊D5—41no—
226C2×Dic5—22no—
227C2×Dic5—22no—
228C2×Dic5—21no—
229D20—21no—
230D20—21no—
231C4×D5—41no—
232C4×D5—41no—
233Dic10—21no—
234Dic10—21no—
235Dic10—44no—
236C5×C8—41no—
237#168—41no—
238C2×#41—51no—
239C2×M16—51no—
240C2×M16C2×C3×D511yescharacteristic
241C4⋊Q8—101no—
242#125—101no—
243C22⋊Q8—102no—
244C4×Q8—102no—
245#117—51no—
246#117—51no—
247#117C2×C3×D511yescharacteristic
248C2×C42C2×C3×D511yescharacteristic
249#104—102no—
250#104—101no—
251#104—101no—
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×C3D4×D511yescharacteristic
260C3×Q8—101no—
261C3×Q8—101no—
262C3×Q8—204no—
263C3×D4—101no—
264C3×D4—101no—
265C3×D4—201no—
266C3×D4—201no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—42no—
270C2×C3×C4—41no—
271C2×C3×C4—102no—
272C2×C3×C4—102no—
273C2×C3×C4—101no—
274C2×C3×C4—201no—
275C2×C3×C4—201no—
276C2×C3×C4C2×D2011yescharacteristic
277C2×C3×C4#70911yescharacteristic
278C2×C3×C4#70911yescharacteristic
279C2×C3×C4D4×D511yescharacteristic
280C2×C3×C4#71111yescharacteristic
281C2×C3×C4Q8×D511yescharacteristic
282C3×C8—41no—
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—81no—
293C4×C5C3×C22⋊Q811yescharacteristic
294C4×C5C3×C22⋊Q811yescharacteristic
295C4×C5C3×#12411yescharacteristic
296C4×C5C3×#12411yescharacteristic
297Dic5—42no—
298Dic5—42no—
299Dic5—41no—
300#41—101no—
301#41—101no—
302#41—101no—
303#41—101no—
304C2×Q8—51no—
305C2×Q8—102no—
306C2×D4—51no—
307C2×D4—101no—
308C22×C4—21no—
309C22×C4—101no—
310C22×C4C22×C3×D511yescharacteristic
311M16—21no—
312M16—21no—
313M16—101no—
314M16—101no—
315C2×C8—21no—
316C2×C8—101no—
317C4⋊C4—21no—
318C4⋊C4—104no—
319C4⋊C4—102no—
320C4⋊C4—101no—
321C4⋊C4—101no—
322C22⋊C4—21no—
323C22⋊C4—52no—
324C22⋊C4—101no—
325C42—21no—
326C42—21no—
327C42—52no—
328C42—101no—
329C42C3×D2011yescharacteristic
330C42C3×D2011yescharacteristic
331C3×C5#203111yescharacteristic, complemented, Hall
332C22×C3—41no—
333C22×C3—201no—
334C22×C3—401no—
335C22×C3#402811yescharacteristic
336C22×C3#403111yescharacteristic
337C22×C3#404211yescharacteristic
338C3×C4—22no—
339C3×C4—41no—
340C3×C4—81no—
341C3×C4—202no—
342C3×C4—202no—
343C3×C4—201no—
344C3×C4#402111yescharacteristic
345C3×C4#403111yescharacteristic
346C3×C4#404211yescharacteristic
347C3×C4#404311yescharacteristic
348C2×C5—21no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5C3×#39311yescharacteristic
352D5—81no—
353C23—101no—
354C23C3×D4×D511yescharacteristic
355Q8—101no—
356Q8—101no—
357Q8—204no—
358D4—101no—
359D4—101no—
360D4—201no—
361D4—201no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—102no—
367C2×C4—102no—
368C2×C4—101no—
369C2×C4—201no—
370C2×C4—201no—
371C2×C4C2×C3×D2011yescharacteristic
372C2×C4C3×#70911yescharacteristic
373C2×C4C3×#70911yescharacteristic
374C2×C4C3×D4×D511yescharacteristic
375C2×C4C3×#71111yescharacteristic
376C2×C4C3×Q8×D511yescharacteristic
377C8—41no—
378C8—201no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—401no—
383C2×C3#6496211yescharacteristic
384C5C3×#203111yescharacteristic, complemented, Sylow
385C22—41no—
386C22—201no—
387C22—401no—
388C22C3×#402811yescharacteristic
389C22C3×#403111yescharacteristic
390C22C3×#404211yescharacteristic
391C4—22no—
392C4—41no—
393C4—81no—
394C4—202no—
395C4—202no—
396C4—201no—
397C4C3×#402111yescharacteristic
398C4C3×#403111yescharacteristic
399C4C3×#404211yescharacteristic
400C4C3×#404311yescharacteristic
401C3#1059957211yescharacteristic, direct product factor, Sylow
402C2—21no—
403C2—21no—
404C2—21no—
405C2—401no—
406C2C3×#6496211yescharacteristic
subgroupG/H
centerC3×C4#4031
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#339C2
socleC2×C3×C5#393
prime radicalC2×C3×#709C22
hypercenterC3×#339D5
hypocenterC5C3×#2031
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#339

Complements

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

NH ≅ G/Ntype
1. C3×#65804C2semidirect
5. C3×C5×#339C2semidirect
6. C3×#64776C2semidirect
7. C3×#64751C2semidirect
8. #10599572C3direct (N × H)
25. #65804C2×C3semidirect
29. C5×#339C2×C3semidirect
30. #64776C2×C3semidirect
31. #64751C2×C3semidirect
39. C2×C3×D20Q8semidirect
42. C2×C3×Dic10Q8semidirect
68. C3×#339D5semidirect
134. C2×D20C3×Q8semidirect
137. C2×Dic10C3×Q8semidirect
163. #339C3×D5semidirect
331. C3×C5#2031semidirect
384. C5C3×#2031semidirect
401. C3#10599572direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658042
C3×#654282
C3×#652952
C2×C3×#39372
C3×C5×#3392
C3×#647762
C3×#647512
#105995723
C3×#20315