Finite Group Databasebeta

← C3×#10599101 #14282753

Subgroups — C3×#10599101 #14282753

Order 1920.

476 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65958C211yesmaximal, characteristic
2C3×#65007C211yesmaximal, characteristic, complemented
3C3×#64937C211yesmaximal, characteristic, complemented
4C3×C5×#328C211yesmaximal, characteristic, complemented
5C3×#64758C211yesmaximal, characteristic, complemented
6C3×#64690C211yesmaximal, characteristic
7C3×#64671C211yesmaximal, characteristic
8#10599101C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C22⋊Q8C2211yescharacteristic
10C3×#4093C411yescharacteristic, complemented
11C3×Q8×Dic5C411yescharacteristic, complemented
12C3×#4076C2211yescharacteristic
13C2×C3×C4×Dic5—21no—
14C2×C3×C4×Dic5C2211yescharacteristic
15C3×#4044—21no—
16C3×#4039C411yescharacteristic, complemented
17C3×#4038—21no—
18C3×#4036C411yescharacteristic, complemented
19C3×#4032—21no—
20C3×#4027—21no—
21C3×C5×C22⋊C8C2211yescharacteristic
22C3×C5×#95C2211yescharacteristic
23C3×#3963—21no—
24C3×#3963C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26C3×#3946—21no—
27C3×C8×Dic5—21no—
28C3×#1500—51nomaximal, Hall
29#65958C2×C311yescharacteristic
30#65007C2×C311yescharacteristic, complemented
31#64937C2×C311yescharacteristic, complemented
32C5×#328C2×C311yescharacteristic, complemented
33#64758C2×C311yescharacteristic, complemented
34#64690C2×C311yescharacteristic
35#64671C2×C311yescharacteristic
36C2×C3×C5×Q8C2×C411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C2×C3×C22⋊D5—21no—
40C22×C3×Dic5—21no—
41C22×C3×Dic5D411yescharacteristic
42C22×C3×Dic5D411yescharacteristic
43C2×C3×D20C2×C411yescharacteristic
44C2×C3×C4×D5—21no—
45C2×C3×C5×C8—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4C2×C411yescharacteristic
48C3×C5×C22⋊C4—21no—
49C3×#685—21no—
50C3×#685—21no—
51C3×#685—21no—
52C3×#685—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5C2×C411yescharacteristic
56C3×#683—21no—
57C3×C4×Dic5—24no—
58C3×C4×Dic5—21no—
59C3×C4×Dic5C2×C411yescharacteristic
60C3×C4×Dic5C2×C411yescharacteristic
61C3×C4×Dic5D411yescharacteristic
62C3×C4×Dic5D411yescharacteristic
63C2×C3×#168—21no—
64C3×#529—51no—
65C3×#431—51no—
66C3×#376—51no—
67C3×#328—51no—
68C3×#328D511yescharacteristic, complemented
69C3×#327—51no—
70C3×#327—51no—
71C5×C22⋊Q8C22×C311yescharacteristic
72#4093C3×C411yescharacteristic, complemented
73Q8×Dic5C3×C411yescharacteristic, complemented
74#4076C22×C311yescharacteristic
75C2×C4×Dic5—21no—
76C2×C4×Dic5C22×C311yescharacteristic
77#4044—21no—
78#4039C3×C411yescharacteristic, complemented
79#4038—21no—
80#4036C3×C411yescharacteristic, complemented
81#4032—21no—
82#4027—21no—
83C5×C22⋊C8C22×C311yescharacteristic
84C5×#95C22×C311yescharacteristic
85#3963—21no—
86#3963C22×C311yescharacteristic
87C22⋊#168C22×C311yescharacteristic
88#3946—21no—
89C8×Dic5—21no—
90#1500—51noSylow
91C23×C3×C5C2×D411yescharacteristic
92C22×C3×D5—21no—
93C3×C5×Q8—41no—
94C2×C3×C4×C5—22no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5C22×C411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C3×C22⋊D5—41no—
103C3×C22⋊D5—41no—
104C2×C3×Dic5—21no—
105C2×C3×Dic5—21no—
106C2×C3×Dic5—22no—
107C2×C3×Dic5—22no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5—41no—
110C2×C3×Dic5—41no—
111C2×C3×Dic5C22⋊C411yescharacteristic
112C2×C3×Dic5C22⋊C411yescharacteristic
113C2×C3×Dic5C22⋊C411yescharacteristic
114C2×C3×Dic5C22⋊C411yescharacteristic
115C3×D20—41no—
116C3×C4×D5—42no—
117C3×C5×C8—41no—
118C3×#168—41no—
119C3×#126—101no—
120C3×#125—51no—
121C3×#124—51no—
122C3×#123—101no—
123C3×C22⋊Q8C2×D511yescharacteristic
124C3×#121—51no—
125C3×C4×Q8—51no—
126C3×C4×D4—51no—
127C3×C4×D4—101no—
128C3×#117—101no—
129C2×C3×C42—51no—
130C2×C3×C42—101no—
131C3×C4⋊C8—101no—
132C3×C22⋊C8—51no—
133C3×C22⋊C8C2×D511yescharacteristic
134C3×C4×C8—101no—
135C3×#95—51no—
136C3×#95—101no—
137C3×#95C2×D511yescharacteristic
138C2×C5×Q8C2×C3×C411yescharacteristic
139C22×C4×C5—21no—
140C22×C4×C5C23×C311yescharacteristic
141C2×C22⋊D5—21no—
142C22×Dic5—21no—
143C22×Dic5C3×D411yescharacteristic
144C22×Dic5C3×D411yescharacteristic
145C2×D20C2×C3×C411yescharacteristic
146C2×C4×D5—21no—
147C2×C5×C8—21no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4C2×C3×C411yescharacteristic
150C5×C22⋊C4—21no—
151#685—21no—
152#685—21no—
153#685—21no—
154#685—21no—
155C4⋊Dic5—21no—
156C4⋊Dic5—21no—
157C4⋊Dic5C2×C3×C411yescharacteristic
158#683—21no—
159C4×Dic5—24no—
160C4×Dic5—21no—
161C4×Dic5C2×C3×C411yescharacteristic
162C4×Dic5C2×C3×C411yescharacteristic
163C4×Dic5C3×D411yescharacteristic
164C4×Dic5C3×D411yescharacteristic
165C2×#168—21no—
166#529—51no—
167#431—51no—
168#376—51no—
169#328—51no—
170#328C3×D511yescharacteristic, complemented
171#327—51no—
172#327—51no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5C2×C22⋊C411yescharacteristic
176C22×C3×C5#13511yescharacteristic
177C22×C3×C5#13511yescharacteristic
178C2×C3×D5—41no—
179C2×C3×D5—41no—
180C2×C3×D5—41no—
181C3×C4×C5—21no—
182C3×C4×C5—21no—
183C3×C4×C5—42no—
184C3×C4×C5—41no—
185C3×C4×C5—41no—
186C3×Dic5—21no—
187C3×Dic5—21no—
188C3×Dic5—21no—
189C3×Dic5—42no—
190C3×Dic5—41no—
191C3×Dic5#10412yes—
192C2×C3×Q8C4×D511yescharacteristic
193C2×C3×D4—51no—
194C2×C3×D4—101no—
195C22×C3×C4—21no—
196C22×C3×C4—51no—
197C22×C3×C4—51no—
198C22×C3×C4—101no—
199C22×C3×C4—101no—
200C22×C3×C4C22×D511yescharacteristic
201C2×C3×C8—21no—
202C2×C3×C8—101no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—51no—
205C3×C4⋊C4—101no—
206C3×C4⋊C4—101no—
207C3×C4⋊C4—101no—
208C3×C4⋊C4C4×D511yescharacteristic
209C3×C22⋊C4—21no—
210C3×C22⋊C4—101no—
211C3×C22⋊C4—101no—
212C3×C22⋊C4—101no—
213C3×C22⋊C4—101no—
214C3×C42—51no—
215C3×C42—51no—
216C3×C42—51no—
217C3×C42—51no—
218C3×C42—101no—
219C3×C42—104no—
220C23×C5C2×C3×D411yescharacteristic
221C22×D5—21no—
222C5×Q8—41no—
223C2×C4×C5—22no—
224C2×C4×C5—21no—
225C2×C4×C5—21no—
226C2×C4×C5—41no—
227C2×C4×C5—41no—
228C2×C4×C5—41no—
229C2×C4×C5C22×C3×C411yescharacteristic
230C2×C4×C5C2×C3×D411yescharacteristic
231C22⋊D5—41no—
232C22⋊D5—41no—
233C2×Dic5—21no—
234C2×Dic5—21no—
235C2×Dic5—22no—
236C2×Dic5—22no—
237C2×Dic5—21no—
238C2×Dic5—41no—
239C2×Dic5—41no—
240C2×Dic5C3×C22⋊C411yescharacteristic
241C2×Dic5C3×C22⋊C411yescharacteristic
242C2×Dic5C3×C22⋊C411yescharacteristic
243C2×Dic5C3×C22⋊C411yescharacteristic
244D20—41no—
245C4×D5—42no—
246C5×C8—41no—
247#168—41no—
248#126—101no—
249#125—51no—
250#124—51no—
251#123—101no—
252C22⋊Q8C2×C3×D511yescharacteristic
253#121—51no—
254C4×Q8—51no—
255C4×D4—51no—
256C4×D4—101no—
257#117—101no—
258C2×C42—51no—
259C2×C42—101no—
260C4⋊C8—101no—
261C22⋊C8—51no—
262C22⋊C8C2×C3×D511yescharacteristic
263C4×C8—101no—
264#95—51no—
265#95—101no—
266#95C2×C3×D511yescharacteristic
267C2×C3×C5—21no—
268C2×C3×C5—21no—
269C2×C3×C5#41011yescharacteristic
270C2×C3×C5#41611yescharacteristic
271C2×C3×C5C2×#10411yescharacteristic
272C3×D5—81no—
273C23×C3—101no—
274C23×C3D4×D511yescharacteristic
275C3×Q8—41no—
276C3×D4—201no—
277C3×D4—201no—
278C3×D4—201no—
279C2×C3×C4—22no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—51no—
286C2×C3×C4—51no—
287C2×C3×C4—51no—
288C2×C3×C4—51no—
289C2×C3×C4—102no—
290C2×C3×C4—101no—
291C2×C3×C4—101no—
292C2×C3×C4—102no—
293C2×C3×C4—101no—
294C2×C3×C4—202no—
295C2×C3×C4—201no—
296C2×C3×C4—201no—
297C2×C3×C4C2×C4×D511yescharacteristic
298C2×C3×C4D4×D511yescharacteristic
299C3×C8—41no—
300C3×C8—201no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5C2×C3×C22⋊C411yescharacteristic
304C22×C5C3×#13511yescharacteristic
305C22×C5C3×#13511yescharacteristic
306C2×D5—41no—
307C2×D5—41no—
308C2×D5—41no—
309C4×C5—21no—
310C4×C5—21no—
311C4×C5—42no—
312C4×C5—41no—
313C4×C5—41no—
314Dic5—21no—
315Dic5—21no—
316Dic5—21no—
317Dic5—42no—
318Dic5—41no—
319Dic5C3×#10412yes—
320C2×Q8C3×C4×D511yescharacteristic
321C2×D4—51no—
322C2×D4—101no—
323C22×C4—21no—
324C22×C4—51no—
325C22×C4—51no—
326C22×C4—101no—
327C22×C4—101no—
328C22×C4C22×C3×D511yescharacteristic
329C2×C8—21no—
330C2×C8—101no—
331C4⋊C4—21no—
332C4⋊C4—51no—
333C4⋊C4—101no—
334C4⋊C4—101no—
335C4⋊C4—101no—
336C4⋊C4C3×C4×D511yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—101no—
339C22⋊C4—101no—
340C22⋊C4—101no—
341C22⋊C4—101no—
342C42—51no—
343C42—51no—
344C42—51no—
345C42—51no—
346C42—101no—
347C42—104no—
348C3×C5#150011yescharacteristic, complemented, Hall
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—201no—
352C22×C3—201no—
353C22×C3—201no—
354C22×C3D5×C22⋊C411yescharacteristic
355C22×C3#406211yescharacteristic
356C22×C3#406511yescharacteristic
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—42no—
360C3×C4—41no—
361C3×C4—41no—
362C3×C4—52no—
363C3×C4—101no—
364C3×C4—101no—
365C3×C4—101no—
366C3×C4—202no—
367C3×C4—201no—
368C2×C5—21no—
369C2×C5—21no—
370C2×C5C3×#41011yescharacteristic
371C2×C5C3×#41611yescharacteristic
372C2×C5C2×C3×#10411yescharacteristic
373D5—81no—
374C23—101no—
375C23C3×D4×D511yescharacteristic
376Q8—41no—
377D4—201no—
378D4—201no—
379D4—201no—
380C2×C4—22no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—51no—
387C2×C4—51no—
388C2×C4—51no—
389C2×C4—51no—
390C2×C4—102no—
391C2×C4—101no—
392C2×C4—101no—
393C2×C4—102no—
394C2×C4—101no—
395C2×C4—202no—
396C2×C4—201no—
397C2×C4—201no—
398C2×C4C2×C3×C4×D511yescharacteristic
399C2×C4C3×D4×D511yescharacteristic
400C8—41no—
401C8—201no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—401no—
405C2×C3#6502911yescharacteristic
406C2×C3#6509311yescharacteristic
407C2×C3D5×#10411yescharacteristic
408C5C3×#150011yescharacteristic, complemented, Sylow
409C22—21no—
410C22—21no—
411C22—201no—
412C22—201no—
413C22—201no—
414C22C3×D5×C22⋊C411yescharacteristic
415C22C3×#406211yescharacteristic
416C22C3×#406511yescharacteristic
417C4—21no—
418C4—21no—
419C4—42no—
420C4—41no—
421C4—41no—
422C4—52no—
423C4—101no—
424C4—101no—
425C4—101no—
426C4—202no—
427C4—201no—
428C3#1059910111yescharacteristic, direct product factor, Sylow
429C2—21no—
430C2—21no—
431C2—401no—
432C2C3×#6502911yescharacteristic
433C2C3×#6509311yescharacteristic
434C2C3×D5×#10411yescharacteristic
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#328C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#4076C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#328D5
hypocenterC5C3×#1500
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#328

Complements

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

NH ≅ G/Ntype
2. C3×#65007C2semidirect
3. C3×#64937C2semidirect
4. C3×C5×#328C2semidirect
5. C3×#64758C2semidirect
8. #10599101C3direct (N × H)
10. C3×#4093C4semidirect
11. C3×Q8×Dic5C4semidirect
16. C3×#4039C4semidirect
18. C3×#4036C4semidirect
30. #65007C2×C3semidirect
31. #64937C2×C3semidirect
32. C5×#328C2×C3semidirect
33. #64758C2×C3semidirect
68. C3×#328D5semidirect
72. #4093C3×C4semidirect
73. Q8×Dic5C3×C4semidirect
78. #4039C3×C4semidirect
80. #4036C3×C4semidirect
170. #328C3×D5semidirect
348. C3×C5#1500semidirect
408. C5C3×#1500semidirect
428. C3#10599101direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659582
C3×#650072
C3×#649372
C3×C5×#3282
C3×#647582
C3×#646902
C3×#646712
#105991013
C3×#15005