Finite Group Databasebeta

← C3×#10601161 #14309025

Subgroups — C3×#10601161 #14309025

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
2C2×C3×C5×#104C211yesmaximal, characteristic
3C3×#65529C211yesmaximal, characteristic
4C3×#65525C211yesmaximal, characteristic
5C3×#64779C211yesmaximal, characteristic, complemented
6C3×#64777C211yesmaximal, characteristic, complemented
7C3×#64743C211yesmaximal, characteristic, complemented
8#10601161C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12C3×#4072C2211yescharacteristic
13C3×#4072C2211yescharacteristic
14C3×#4072C2211yescharacteristic
15C3×#4070—22no—
16C2×C3×#681C2211yescharacteristic
17C3×#4016—21no—
18C3×#4015—21no—
19C3×C4×Dic10—22no—
20C3×C5×#104—21no—
21C3×C5×#104—21no—
22C3×#3969—22no—
23C3×#3966—22no—
24C3×#2031—51nomaximal, Hall
25#65804C2×C311yescharacteristic, complemented
26C2×C5×#104C2×C311yescharacteristic
27#65529C2×C311yescharacteristic
28#65525C2×C311yescharacteristic
29#64779C2×C311yescharacteristic, complemented
30#64777C2×C311yescharacteristic, complemented
31#64743C2×C311yescharacteristic, complemented
32C3×C5×#41—21no—
33C3×C5×#41—21no—
34C3×C5×#41—21no—
35C3×C5×#41—21no—
36C2×C3×C5×Q8Q811yescharacteristic, complemented
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4Q811yescharacteristic, complemented
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5C2311yescharacteristic
42C2×C3×Dic10—22no—
43C3×C5×M16—21no—
44C3×C5×M16—21no—
45C2×C3×C5×C8—21no—
46C3×C42×C5—21no—
47C3×C42×C5D411yescharacteristic
48C3×C42×C5D411yescharacteristic
49C3×C22⋊Dic5—21no—
50C3×C22⋊Dic5—21no—
51C3×C22⋊Dic5D412yes—
52C3×C4⋊Dic5—22no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5—21no—
56C3×#683—24no—
57C3×C4×Dic5—21no—
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×#104D511yescharacteristic
66C3×#410—51no—
67C3×#344—51no—
68C3×#339—51no—
69C3×H(3,ℤ/4)—51no—
70C2×C5×#41C22×C311yescharacteristic
71C2×C5×M16C22×C311yescharacteristic
72C2×C42×C5C22×C311yescharacteristic
73#4072C22×C311yescharacteristic
74#4072C22×C311yescharacteristic
75#4072C22×C311yescharacteristic
76#4070—22no—
77C2×#681C22×C311yescharacteristic
78#4016—21no—
79#4015—21no—
80C4×Dic10—22no—
81C5×#104—21no—
82C5×#104—21no—
83#3969—22no—
84#3966—22no—
85#2031—51noSylow
86C23×C3×C5—21no—
87C23×C3×C5C2×D411yescharacteristic
88C3×C5×Q8—21no—
89C3×C5×Q8—21no—
90C3×C5×D4—21no—
91C3×C5×D4—21no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—42no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×Q811yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C2×C3×Dic5—22no—
107C2×C3×Dic5—22no—
108C2×C3×Dic5—41no—
109C3×Dic10—44no—
110C3×C5×C8—41no—
111C3×#168—41no—
112C2×C3×#41C2×D511yescharacteristic
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×#117—51no—
122C2×C3×C42C2×D511yescharacteristic
123C3×#104—21no—
124C3×#104—21no—
125C3×#104—102no—
126C3×#99—102no—
127C5×#41—21no—
128C5×#41—21no—
129C5×#41—21no—
130C5×#41—21no—
131C2×C5×Q8C3×Q811yescharacteristic, complemented
132C2×C5×D4—21no—
133C2×C5×D4C3×Q811yescharacteristic, complemented
134C22×C4×C5—21no—
135C22×C4×C5—21no—
136C22×C4×C5C23×C311yescharacteristic
137C2×Dic10—22no—
138C5×M16—21no—
139C5×M16—21no—
140C2×C5×C8—21no—
141C42×C5—21no—
142C42×C5C3×D411yescharacteristic
143C42×C5C3×D411yescharacteristic
144C22⋊Dic5—21no—
145C22⋊Dic5—21no—
146C22⋊Dic5C3×D412yes—
147C4⋊Dic5—22no—
148C4⋊Dic5—21no—
149C4⋊Dic5—21no—
150C4⋊Dic5—21no—
151#683—24no—
152C4×Dic5—21no—
153C4×Dic5—21no—
154C4×Dic5C3×D412yes—
155#681—21no—
156#681—21no—
157C2×#168—21no—
158#533—51no—
159#421—51no—
160C2×#104C3×D511yescharacteristic
161#410—51no—
162#344—51no—
163#339—51no—
164H(3,ℤ/4)—51no—
165C22×C3×C5—41no—
166C22×C3×C5—41no—
167C22×C3×C5—81no—
168C22×C3×C5#12011yescharacteristic
169C22×C3×C5C22⋊Q811yescharacteristic
170C22×C3×C5#12411yescharacteristic
171C3×C4×C5—22no—
172C3×C4×C5—41no—
173C3×C4×C5—41no—
174C3×C4×C5C22⋊Q811yescharacteristic
175C3×C4×C5C22⋊Q811yescharacteristic
176C3×C4×C5#12411yescharacteristic
177C3×C4×C5#12411yescharacteristic
178C3×Dic5—42no—
179C3×Dic5—42no—
180C3×Dic5—81no—
181C3×#41—21no—
182C3×#41—21no—
183C3×#41—21no—
184C3×#41—21no—
185C2×C3×Q8—102no—
186C2×C3×Q8Dic1011yescharacteristic, complemented
187C2×C3×D4—21no—
188C2×C3×D4Dic1011yescharacteristic, complemented
189C22×C3×C4—21no—
190C22×C3×C4—21no—
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—104no—
199C3×C4⋊C4—102no—
200C3×C4⋊C4—101no—
201C3×C4⋊C4—101no—
202C3×C4⋊C4—101no—
203C3×C22⋊C4—52no—
204C3×C22⋊C4—101no—
205C3×C22⋊C4—101no—
206C3×C42—21no—
207C3×C42—52no—
208C3×C42—101no—
209C3×C42—101no—
210C3×C42C22⋊D511yescharacteristic
211C3×C42C22⋊D511yescharacteristic
212C23×C5—21no—
213C23×C5C2×C3×D411yescharacteristic
214C5×Q8—21no—
215C5×Q8—21no—
216C5×D4—21no—
217C5×D4—21no—
218C5×D4—41no—
219C5×D4—41no—
220C2×C4×C5—21no—
221C2×C4×C5—21no—
222C2×C4×C5—21no—
223C2×C4×C5—42no—
224C2×C4×C5—41no—
225C2×C4×C5—41no—
226C2×C4×C5C2×C3×D411yescharacteristic
227C2×C4×C5C2×C3×D411yescharacteristic
228C2×C4×C5C2×C3×Q811yescharacteristic
229C2×C4×C5C3×#4111yescharacteristic
230C2×C4×C5C3×#4111yescharacteristic
231C2×C4×C5C3×#4111yescharacteristic
232C2×Dic5—22no—
233C2×Dic5—22no—
234C2×Dic5—41no—
235Dic10—44no—
236C5×C8—41no—
237#168—41no—
238C2×#41C2×C3×D511yescharacteristic
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#117—51no—
248C2×C42C2×C3×D511yescharacteristic
249#104—21no—
250#104—21no—
251#104—102no—
252#99—102no—
253C2×C3×C5—21no—
254C2×C3×C5—21no—
255C2×C3×C5—21no—
256C2×C3×C5—81no—
257C2×C3×C5#39311yescharacteristic
258C23×C3—21no—
259C23×C3D4×D511yescharacteristic
260C3×Q8—21no—
261C3×Q8—21no—
262C3×Q8—204no—
263C3×D4—21no—
264C3×D4—21no—
265C3×D4—41no—
266C3×D4—41no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—42no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—102no—
274C2×C3×C4—102no—
275C2×C3×C4—201no—
276C2×C3×C4C2×Dic1011yescharacteristic
277C2×C3×C4#70911yescharacteristic
278C2×C3×C4D4×D511yescharacteristic
279C2×C3×C4#71111yescharacteristic
280C2×C3×C4#71111yescharacteristic
281C2×C3×C4C2×C22⋊D511yescharacteristic
282C3×C8—41no—
283C3×C8—201no—
284C22×C5—41no—
285C22×C5—41no—
286C22×C5—81no—
287C22×C5C3×#12011yescharacteristic
288C22×C5C3×C22⋊Q811yescharacteristic
289C22×C5C3×#12411yescharacteristic
290C4×C5—22no—
291C4×C5—41no—
292C4×C5—41no—
293C4×C5C3×C22⋊Q811yescharacteristic
294C4×C5C3×C22⋊Q811yescharacteristic
295C4×C5C3×#12411yescharacteristic
296C4×C5C3×#12411yescharacteristic
297Dic5—42no—
298Dic5—42no—
299Dic5—81no—
300#41—21no—
301#41—21no—
302#41—21no—
303#41—21no—
304C2×Q8—102no—
305C2×Q8C3×Dic1011yescharacteristic, complemented
306C2×D4—21no—
307C2×D4C3×Dic1011yescharacteristic, complemented
308C22×C4—21no—
309C22×C4—21no—
310C22×C4C22×C3×D511yescharacteristic
311M16—21no—
312M16—21no—
313M16—101no—
314M16—101no—
315C2×C8—21no—
316C2×C8—101no—
317C4⋊C4—104no—
318C4⋊C4—102no—
319C4⋊C4—101no—
320C4⋊C4—101no—
321C4⋊C4—101no—
322C22⋊C4—52no—
323C22⋊C4—101no—
324C22⋊C4—101no—
325C42—21no—
326C42—52no—
327C42—101no—
328C42—101no—
329C42C3×C22⋊D511yescharacteristic
330C42C3×C22⋊D511yescharacteristic
331C3×C5#203111yescharacteristic, complemented, Hall
332C22×C3—41no—
333C22×C3—41no—
334C22×C3—81no—
335C22×C3#402411yescharacteristic
336C22×C3#403111yescharacteristic
337C22×C3#408311yescharacteristic
338C3×C4—22no—
339C3×C4—41no—
340C3×C4—41no—
341C3×C4—202no—
342C3×C4—202no—
343C3×C4—401no—
344C3×C4#402411yescharacteristic
345C3×C4#403111yescharacteristic
346C3×C4#407011yescharacteristic
347C3×C4#408211yescharacteristic
348C2×C5—21no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5—81no—
352C2×C5C3×#39311yescharacteristic
353C23—21no—
354C23C3×D4×D511yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—204no—
358D4—21no—
359D4—21no—
360D4—41no—
361D4—41no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—102no—
369C2×C4—102no—
370C2×C4—201no—
371C2×C4C2×C3×Dic1011yescharacteristic
372C2×C4C3×#70911yescharacteristic
373C2×C4C3×D4×D511yescharacteristic
374C2×C4C3×#71111yescharacteristic
375C2×C4C3×#71111yescharacteristic
376C2×C4C2×C3×C22⋊D511yescharacteristic
377C8—41no—
378C8—201no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—81no—
383C2×C3#6523611yescharacteristic
384C5C3×#203111yescharacteristic, complemented, Sylow
385C22—41no—
386C22—41no—
387C22—81no—
388C22C3×#402411yescharacteristic
389C22C3×#403111yescharacteristic
390C22C3×#408311yescharacteristic
391C4—22no—
392C4—41no—
393C4—41no—
394C4—202no—
395C4—202no—
396C4—401no—
397C4C3×#402411yescharacteristic
398C4C3×#403111yescharacteristic
399C4C3×#407011yescharacteristic
400C4C3×#408211yescharacteristic
401C3#1060116111yescharacteristic, direct product factor, Sylow
402C2—21no—
403C2—21no—
404C2—21no—
405C2—81no—
406C2C3×#6523611yescharacteristic
subgroupG/H
centerC3×C4#4031
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×#104C2
socleC2×C3×C5#393
prime radicalC2×C3×C5×#41C22
hypercenterC2×C3×#104D5
hypocenterC5C3×#2031
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#104

Complements

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

NH ≅ G/Ntype
1. C3×#65804C2semidirect
5. C3×#64779C2semidirect
6. C3×#64777C2semidirect
7. C3×#64743C2semidirect
8. #10601161C3direct (N × H)
25. #65804C2×C3semidirect
29. #64779C2×C3semidirect
30. #64777C2×C3semidirect
31. #64743C2×C3semidirect
36. C2×C3×C5×Q8Q8semidirect
38. C2×C3×C5×D4Q8semidirect
131. C2×C5×Q8C3×Q8semidirect
133. C2×C5×D4C3×Q8semidirect
186. C2×C3×Q8Dic10semidirect
188. C2×C3×D4Dic10semidirect
305. C2×Q8C3×Dic10semidirect
307. C2×D4C3×Dic10semidirect
331. C3×C5#2031semidirect
384. C5C3×#2031semidirect
401. C3#10601161direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658042
C2×C3×C5×#1042
C3×#655292
C3×#655252
C3×#647792
C3×#647772
C3×#647432
#106011613
C3×#20315