Finite Group Databasebeta

← C3×#10600941 #14313624

Subgroups — C3×#10600941 #14313624

Order 1920.

500 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66166C211yesmaximal, characteristic
2C3×C5×#413C211yesmaximal, characteristic, complemented
3C3×#65526C211yesmaximal, characteristic, complemented
4C3×#64698C212yesmaximal, complemented
5C3×#64697C212yesmaximal, complemented
6#10600941C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×#41C2211yescharacteristic
8C2×C3×#709C411yescharacteristic
9C2×C3×C5×M16—21no—
10C3×#4093C2211yescharacteristic
11C3×#4090C2211yescharacteristic
12C3×#4086C411yescharacteristic
13C3×#4085—21no—
14C3×#4085—21no—
15C3×#4082C411yescharacteristic
16C3×C4×C22⋊D5—21no—
17C3×C4×C22⋊D5—21no—
18C2×C3×C4×Dic5C411yescharacteristic
19C2×C3×#681—21no—
20C3×C5×#101C2212yes—
21C3×C5×#100—21no—
22C3×#3968C2212yes—
23C3×#3965—21no—
24C3×#2132—51nomaximal, Hall
25#66166C2×C311yescharacteristic
26C5×#413C2×C311yescharacteristic, complemented
27#65526C2×C311yescharacteristic, complemented
28#64698C2×C312yescomplemented
29#64697C2×C312yescomplemented
30C3×C5×#41—41no—
31C3×C5×#41—41no—
32C2×C3×C5×Q8C2311yescharacteristic
33C2×C3×C5×D4C2×C411yescharacteristic
34C2×C3×C5×D4D411yescharacteristic
35C2×C3×C5×D4D411yescharacteristic
36C22×C3×C4×C5C2×C411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C2×C3×C22⋊D5—21no—
40C2×C3×C22⋊D5—21no—
41C2×C3×C22⋊D5—21no—
42C22×C3×Dic5—21no—
43C3×#709—41no—
44C3×#709—41no—
45C2×C3×D20C2×C411yescharacteristic
46C2×C3×C4×D5—21no—
47C2×C3×Dic10C2×C411yescharacteristic
48C3×C5×M16—22no—
49C3×C5×M16—41no—
50C2×C3×C5×C8—41no—
51C3×C22⋊Dic5—21no—
52C3×C22⋊Dic5—21no—
53C3×#685—21no—
54C3×#685—21no—
55C3×#683—21no—
56C3×#683—21no—
57C3×C4×Dic5—21no—
58C3×C4×Dic5C2×C411yescharacteristic
59C3×C4×Dic5C2×C411yescharacteristic
60C3×#681—22no—
61C3×#681—41no—
62C2×C3×#168—41no—
63C3×#532—51no—
64C3×#413—51no—
65C3×#413D511yescharacteristic, complemented
66C3×#356—52no—
67C3×#355—52no—
68C2×C5×#41C22×C311yescharacteristic
69C2×#709C3×C411yescharacteristic
70C2×C5×M16—21no—
71#4093C22×C311yescharacteristic
72#4090C22×C311yescharacteristic
73#4086C3×C411yescharacteristic
74#4085—21no—
75#4085—21no—
76#4082C3×C411yescharacteristic
77C4×C22⋊D5—21no—
78C4×C22⋊D5—21no—
79C2×C4×Dic5C3×C411yescharacteristic
80C2×#681—21no—
81C5×#101C22×C312yes—
82C5×#100—21no—
83#3968C22×C312yes—
84#3965—21no—
85#2132—51noSylow
86C23×C3×C5C22⋊C411yescharacteristic
87C23×C3×C5C22⋊C411yescharacteristic
88C23×C3×C5C22⋊C411yescharacteristic
89C22×C3×D5—21no—
90C3×C5×Q8—41no—
91C3×C5×D4—41no—
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—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5C22⋊C411yescharacteristic
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C3×C22⋊D5—42no—
105C3×C22⋊D5—42no—
106C3×C22⋊D5—42no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—42no—
111C3×D20—41no—
112C3×C4×D5—41no—
113C3×C4×D5—41no—
114C3×Dic10—41no—
115C3×C5×C8—42no—
116C3×#168—42no—
117C2×C3×#41—51no—
118C2×C3×#41C2×D511yescharacteristic
119C2×C3×M16—21no—
120C2×C3×M16—101no—
121C3×C4⋊Q8—51no—
122C3×#127—51no—
123C3×#124—51no—
124C3×#124—51no—
125C3×#121—101no—
126C3×#121—101no—
127C3×C4×D4—101no—
128C3×C4×D4—101no—
129C2×C3×C42—51no—
130C3×#101—52no—
131C3×#101C2×D512yes—
132C3×#100—21no—
133C3×#100—101no—
134C5×#41—41no—
135C5×#41—41no—
136C2×C5×Q8C23×C311yescharacteristic
137C2×C5×D4C2×C3×C411yescharacteristic
138C2×C5×D4C3×D411yescharacteristic
139C2×C5×D4C3×D411yescharacteristic
140C22×C4×C5C2×C3×C411yescharacteristic
141C22×C4×C5C3×D411yescharacteristic
142C22×C4×C5C3×D411yescharacteristic
143C2×C22⋊D5—21no—
144C2×C22⋊D5—21no—
145C2×C22⋊D5—21no—
146C22×Dic5—21no—
147#709—41no—
148#709—41no—
149C2×D20C2×C3×C411yescharacteristic
150C2×C4×D5—21no—
151C2×Dic10C2×C3×C411yescharacteristic
152C5×M16—22no—
153C5×M16—41no—
154C2×C5×C8—41no—
155C22⋊Dic5—21no—
156C22⋊Dic5—21no—
157#685—21no—
158#685—21no—
159#683—21no—
160#683—21no—
161C4×Dic5—21no—
162C4×Dic5C2×C3×C411yescharacteristic
163C4×Dic5C2×C3×C411yescharacteristic
164#681—22no—
165#681—41no—
166C2×#168—41no—
167#532—51no—
168#413—51no—
169#413C3×D511yescharacteristic, complemented
170#356—52no—
171#355—52no—
172C22×C3×C5—21no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5—41no—
176C22×C3×C5—41no—
177C22×C3×C5—41no—
178C22×C3×C5C2×C22⋊C411yescharacteristic
179C2×C3×D5—41no—
180C2×C3×D5—41no—
181C2×C3×D5—41no—
182C3×C4×C5—21no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5#9911yescharacteristic
186C3×C4×C5#9911yescharacteristic
187C3×Dic5—22no—
188C3×Dic5—41no—
189C3×Dic5—41no—
190C3×#41—41no—
191C3×#41—41no—
192C3×#41—201no—
193C3×#41—201no—
194C2×C3×Q8—51no—
195C2×C3×Q8C22×D511yescharacteristic
196C2×C3×D4—51no—
197C2×C3×D4—101no—
198C2×C3×D4—101no—
199C2×C3×D4—101no—
200C2×C3×D4C4×D511yescharacteristic
201C2×C3×D4D2011yescharacteristic
202C2×C3×D4C22⋊D511yescharacteristic
203C22×C3×C4—101no—
204C22×C3×C4—101no—
205C22×C3×C4C4×D511yescharacteristic
206C22×C3×C4D2011yescharacteristic
207C22×C3×C4C22⋊D511yescharacteristic
208C3×M16—22no—
209C3×M16—41no—
210C3×M16—102no—
211C3×M16—201no—
212C2×C3×C8—41no—
213C2×C3×C8—201no—
214C3×C4⋊C4—101no—
215C3×C4⋊C4—101no—
216C3×C22⋊C4—101no—
217C3×C22⋊C4—101no—
218C3×C22⋊C4—101no—
219C3×C22⋊C4—101no—
220C3×C42—51no—
221C3×C42—51no—
222C3×C42—101no—
223C23×C5C3×C22⋊C411yescharacteristic
224C23×C5C3×C22⋊C411yescharacteristic
225C23×C5C3×C22⋊C411yescharacteristic
226C22×D5—21no—
227C5×Q8—41no—
228C5×D4—41no—
229C5×D4—41no—
230C5×D4—41no—
231C2×C4×C5—21no—
232C2×C4×C5—21no—
233C2×C4×C5—21no—
234C2×C4×C5—21no—
235C2×C4×C5—21no—
236C2×C4×C5—21no—
237C2×C4×C5C3×C22⋊C411yescharacteristic
238C2×C4×C5C22×C3×C411yescharacteristic
239C2×C4×C5C2×C3×D411yescharacteristic
240C2×C4×C5C2×C3×D411yescharacteristic
241C22⋊D5—42no—
242C22⋊D5—42no—
243C22⋊D5—42no—
244C2×Dic5—21no—
245C2×Dic5—21no—
246C2×Dic5—21no—
247C2×Dic5—42no—
248D20—41no—
249C4×D5—41no—
250C4×D5—41no—
251Dic10—41no—
252C5×C8—42no—
253#168—42no—
254C2×#41—51no—
255C2×#41C2×C3×D511yescharacteristic
256C2×M16—21no—
257C2×M16—101no—
258C4⋊Q8—51no—
259#127—51no—
260#124—51no—
261#124—51no—
262#121—101no—
263#121—101no—
264C4×D4—101no—
265C4×D4—101no—
266C2×C42—51no—
267#101—52no—
268#101C2×C3×D512yes—
269#100—21no—
270#100—101no—
271C2×C3×C5—21no—
272C2×C3×C5—41no—
273C2×C3×C5—41no—
274C2×C3×C5—41no—
275C2×C3×C5C2×#9911yescharacteristic
276C3×D5—81no—
277C23×C3—101no—
278C23×C3#68511yescharacteristic
279C23×C3#68511yescharacteristic
280C23×C3#68511yescharacteristic
281C3×Q8—41no—
282C3×Q8—201no—
283C3×D4—41no—
284C3×D4—41no—
285C3×D4—41no—
286C3×D4—201no—
287C3×D4—202no—
288C3×D4—202no—
289C3×D4—202no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—101no—
297C2×C3×C4—101no—
298C2×C3×C4—101no—
299C2×C3×C4—202no—
300C2×C3×C4—201no—
301C2×C3×C4—201no—
302C2×C3×C4#68511yescharacteristic
303C2×C3×C4C2×C4×D511yescharacteristic
304C2×C3×C4C2×D2011yescharacteristic
305C2×C3×C4C2×C22⋊D511yescharacteristic
306C3×C8—42no—
307C3×C8—202no—
308C22×C5—21no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5—41no—
312C22×C5—41no—
313C22×C5—41no—
314C22×C5C2×C3×C22⋊C411yescharacteristic
315C2×D5—41no—
316C2×D5—41no—
317C2×D5—41no—
318C4×C5—21no—
319C4×C5—21no—
320C4×C5—21no—
321C4×C5C3×#9911yescharacteristic
322C4×C5C3×#9911yescharacteristic
323Dic5—22no—
324Dic5—41no—
325Dic5—41no—
326#41—41no—
327#41—41no—
328#41—201no—
329#41—201no—
330C2×Q8—51no—
331C2×Q8C22×C3×D511yescharacteristic
332C2×D4—51no—
333C2×D4—101no—
334C2×D4—101no—
335C2×D4—101no—
336C2×D4C3×C4×D511yescharacteristic
337C2×D4C3×D2011yescharacteristic
338C2×D4C3×C22⋊D511yescharacteristic
339C22×C4—101no—
340C22×C4—101no—
341C22×C4C3×C4×D511yescharacteristic
342C22×C4C3×D2011yescharacteristic
343C22×C4C3×C22⋊D511yescharacteristic
344M16—22no—
345M16—41no—
346M16—102no—
347M16—201no—
348C2×C8—41no—
349C2×C8—201no—
350C4⋊C4—101no—
351C4⋊C4—101no—
352C22⋊C4—101no—
353C22⋊C4—101no—
354C22⋊C4—101no—
355C22⋊C4—101no—
356C42—51no—
357C42—51no—
358C42—101no—
359C3×C5#213211yescharacteristic, complemented, Hall
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—41no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3—201no—
367C22×C3—201no—
368C22×C3—201no—
369C22×C3C2×#68511yescharacteristic
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—102no—
374C3×C4—201no—
375C3×C4—201no—
376C3×C4#393811yescharacteristic
377C3×C4#393811yescharacteristic
378C2×C5—21no—
379C2×C5—41no—
380C2×C5—41no—
381C2×C5—41no—
382C2×C5C2×C3×#9911yescharacteristic
383D5—81no—
384C23—101no—
385C23C3×#68511yescharacteristic
386C23C3×#68511yescharacteristic
387C23C3×#68511yescharacteristic
388Q8—41no—
389Q8—201no—
390D4—41no—
391D4—41no—
392D4—41no—
393D4—201no—
394D4—202no—
395D4—202no—
396D4—202no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—101no—
404C2×C4—101no—
405C2×C4—101no—
406C2×C4—202no—
407C2×C4—201no—
408C2×C4—201no—
409C2×C4C3×#68511yescharacteristic
410C2×C4C2×C3×C4×D511yescharacteristic
411C2×C4C2×C3×D2011yescharacteristic
412C2×C4C2×C3×C22⋊D511yescharacteristic
413C8—42no—
414C8—202no—
415C2×C3—21no—
416C2×C3—41no—
417C2×C3—41no—
418C2×C3—41no—
419C2×C3—401no—
420C2×C3C2×#393811yescharacteristic
421C5C3×#213211yescharacteristic, complemented, Sylow
422C22—21no—
423C22—21no—
424C22—21no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—201no—
429C22—201no—
430C22—201no—
431C22C2×C3×#68511yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—102no—
436C4—201no—
437C4—201no—
438C4C3×#393811yescharacteristic
439C4C3×#393811yescharacteristic
440C3#1060094111yescharacteristic, direct product factor, Sylow
441C2—21no—
442C2—41no—
443C2—41no—
444C2—41no—
445C2—401no—
446C2C2×C3×#393811yescharacteristic
subgroupG/H
centerC3×C4#3938
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×Q8C22×C3×D5
FittingC3×C5×#413C2
socleC2×C3×C5C2×#99
prime radicalC3×#66166C2
cosocleC2×C5×Q8C23×C3
hypercenterC3×#413D5
hypocenterC5C3×#2132
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C2×C3×#41 ◁ C3×#413

Complements

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

NH ≅ G/Ntype
2. C3×C5×#413C2semidirect
3. C3×#65526C2semidirect
4. C3×#64698C2semidirect
5. C3×#64697C2semidirect
6. #10600941C3direct (N × H)
26. C5×#413C2×C3semidirect
27. #65526C2×C3semidirect
28. #64698C2×C3semidirect
29. #64697C2×C3semidirect
65. C3×#413D5semidirect
169. #413C3×D5semidirect
359. C3×C5#2132semidirect
421. C5C3×#2132semidirect
440. C3#10600941direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661662
C3×C5×#4132
C3×#655262
C3×#646982
C3×#646972
#106009413
C3×#21325