Finite Group Databasebeta

← C3×#10604452 #14297774

Subgroups — C3×#10604452 #14297774

Order 1920.

584 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×Q8×D5C211yesmaximal, characteristic
2C2×C3×#4009C212yesmaximal
3C3×#65689C211yesmaximal, characteristic
4C3×D5⋊(C4⋊C8)C211yesmaximal, characteristic
5C3×#64874C212yesmaximal
6#10604452C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×Q8×D5C2211yescharacteristic
8C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
9C2×C3×D5⋊C8C2212yes—
10C3×C4×C5×Q8C411yescharacteristic, complemented
11C3×Q8×Dic5C411yescharacteristic, complemented
12C3×D5×C4⋊C4—21no—
13C3×D5×C4⋊C4C2211yescharacteristic
14C3×#4033—21no—
15C3×#4033C411yescharacteristic, complemented
16C3×C42×D5—21no—
17C3×C42×D5C2211yescharacteristic
18C3×C4×Dic10—21no—
19C3×C4×Dic10C411yescharacteristic, complemented
20C3×#4009—24no—
21C3×(C2×AGL(1,𝔽5))⋊C4—21no—
22C3×(C2×AGL(1,𝔽5))⋊C4—21no—
23C3×#4004—21no—
24C3×C4⋊#170—21no—
25C3×#1805—51nomaximal, Hall
26C4×Q8×D5C2×C311yescharacteristic
27C2×#4009C2×C312yes—
28#65689C2×C311yescharacteristic
29D5⋊(C4⋊C8)C2×C311yescharacteristic
30#64874C2×C312yes—
31C22×C3×AGL(1,𝔽5)—22no—
32C2×C3×C5×Q8C2×C411yescharacteristic
33C3×Q8×D5—21no—
34C3×Q8×D5—21no—
35C3×Q8×D5D412yes—
36C3×Q8×D5Q812yes—
37C2×C3×C4×D5—21no—
38C2×C3×C4×D5—21no—
39C2×C3×C4×D5D411yescharacteristic
40C2×C3×C4×D5D411yescharacteristic
41C2×C3×C4×D5C2311yescharacteristic
42C2×C3×Dic10—21no—
43C2×C3×Dic10C2×C411yescharacteristic
44C2×C3×#170—22no—
45C3×C4⋊AGL(1,𝔽5)—22no—
46C3×C4⋊AGL(1,𝔽5)—22no—
47C3×D5⋊C8—22no—
48C3×D5⋊C8—22no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4C2×C411yescharacteristic
51C3×C42×C5—21no—
52C3×C42×C5C2×C411yescharacteristic
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5C2×C411yescharacteristic
55C3×#683—21no—
56C3×#683—21no—
57C3×#683—21no—
58C3×C4×Dic5—21no—
59C3×C4×Dic5—21no—
60C3×C4×Dic5—21no—
61C3×C4×Dic5C2×C411yescharacteristic
62C3×C4×Dic5D411yescharacteristic
63C3×C4×Dic5D411yescharacteristic
64C2×C3×C4×Q8—51no—
65C2×C3×C4⋊C8—51no—
66C2×C3×#103—52no—
67C3×#382—51no—
68C3×#340—52no—
69C2×Q8×D5C22×C311yescharacteristic
70C2×C4⋊AGL(1,𝔽5)C22×C312yes—
71C2×D5⋊C8C22×C312yes—
72C4×C5×Q8C3×C411yescharacteristic, complemented
73Q8×Dic5C3×C411yescharacteristic, complemented
74D5×C4⋊C4—21no—
75D5×C4⋊C4C22×C311yescharacteristic
76#4033—21no—
77#4033C3×C411yescharacteristic, complemented
78C42×D5—21no—
79C42×D5C22×C311yescharacteristic
80C4×Dic10—21no—
81C4×Dic10C3×C411yescharacteristic, complemented
82#4009—24no—
83(C2×AGL(1,𝔽5))⋊C4—21no—
84(C2×AGL(1,𝔽5))⋊C4—21no—
85#4004—21no—
86C4⋊#170—21no—
87#1805—51noSylow
88C22×C3×D5C2×D411yescharacteristic
89C2×C3×AGL(1,𝔽5)—42no—
90C2×C3×AGL(1,𝔽5)—42no—
91C2×C3×AGL(1,𝔽5)—42no—
92C3×C5×Q8—21no—
93C3×C5×Q8C4⋊C412yes—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5C22⋊C411yescharacteristic
97C2×C3×C4×C5C22⋊C411yescharacteristic
98C2×C3×C4×C5C22×C411yescharacteristic
99C2×C3×Dic5—21no—
100C2×C3×Dic5—21no—
101C2×C3×Dic5C22⋊C411yescharacteristic
102C2×C3×Dic5C22⋊C411yescharacteristic
103C2×C3×Dic5C2×D411yescharacteristic
104C3×C4×D5—22no—
105C3×C4×D5—22no—
106C3×C4×D5—22no—
107C3×C4×D5—22no—
108C3×C4×D5—42no—
109C3×C4×D5C2×D411yescharacteristic
110C3×C4×D5C2×Q811yescharacteristic
111C3×C4×D5#4111yescharacteristic
112C3×C4×D5#4111yescharacteristic
113C3×Dic10—21no—
114C3×Dic10—22no—
115C3×Dic10—22no—
116C3×Dic10C4⋊C412yes—
117C3×#170—42no—
118C22×C3×Q8—51no—
119C22×C3×C8—52no—
120C3×C4×Q8—51no—
121C3×C4×Q8—51no—
122C3×C4×Q8—51no—
123C3×C4×Q8—101no—
124C3×C4×Q8—101no—
125C3×C4×Q8AGL(1,𝔽5)11yescharacteristic, complemented
126C2×C3×C4⋊C4—51no—
127C2×C3×C4⋊C4—52no—
128C2×C3×C4⋊C4—101no—
129C2×C3×C42—51no—
130C2×C3×C42—101no—
131C3×C4⋊C8—101no—
132C3×C4⋊C8—101no—
133C3×#103—104no—
134C3×#95—101no—
135C3×#95—101no—
136C22×AGL(1,𝔽5)—22no—
137C2×C5×Q8C2×C3×C411yescharacteristic
138Q8×D5—21no—
139Q8×D5—21no—
140Q8×D5C3×D412yes—
141Q8×D5C3×Q812yes—
142C2×C4×D5—21no—
143C2×C4×D5—21no—
144C2×C4×D5C3×D411yescharacteristic
145C2×C4×D5C3×D411yescharacteristic
146C2×C4×D5C23×C311yescharacteristic
147C2×Dic10—21no—
148C2×Dic10C2×C3×C411yescharacteristic
149C2×#170—22no—
150C4⋊AGL(1,𝔽5)—22no—
151C4⋊AGL(1,𝔽5)—22no—
152D5⋊C8—22no—
153D5⋊C8—22no—
154C5×C4⋊C4—21no—
155C5×C4⋊C4C2×C3×C411yescharacteristic
156C42×C5—21no—
157C42×C5C2×C3×C411yescharacteristic
158C4⋊Dic5—21no—
159C4⋊Dic5C2×C3×C411yescharacteristic
160#683—21no—
161#683—21no—
162#683—21no—
163C4×Dic5—21no—
164C4×Dic5—21no—
165C4×Dic5—21no—
166C4×Dic5C2×C3×C411yescharacteristic
167C4×Dic5C3×D411yescharacteristic
168C4×Dic5C3×D411yescharacteristic
169C2×C4×Q8—51no—
170C2×C4⋊C8—51no—
171C2×#103—52no—
172#382—51no—
173#340—52no—
174C22×C3×C5C2×C22⋊C411yescharacteristic
175C2×C3×D5#12111yescharacteristic
176C2×C3×D5C22⋊Q811yescharacteristic
177C2×C3×D5#13512yes—
178C2×C3×D5#13712yes—
179C3×AGL(1,𝔽5)—82no—
180C3×C4×C5—22no—
181C3×C4×C5—21no—
182C3×C4×C5—21no—
183C3×C4×C5—41no—
184C3×C4×C5C2×C4⋊C411yescharacteristic
185C3×C4×C5#11711yescharacteristic
186C3×Dic5—22no—
187C3×Dic5—21no—
188C3×Dic5—21no—
189C3×Dic5—41no—
190C3×Dic5#12111yescharacteristic
191C3×Dic5C22⋊Q811yescharacteristic
192C2×C3×Q8—52no—
193C2×C3×Q8—52no—
194C2×C3×Q8—51no—
195C2×C3×Q8—101no—
196C2×C3×Q8—101no—
197C2×C3×Q8—101no—
198C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
199C22×C3×C4—51no—
200C22×C3×C4—51no—
201C22×C3×C4—51no—
202C22×C3×C4—101no—
203C22×C3×C4—101no—
204C22×C3×C4—102no—
205C2×C3×C8—102no—
206C2×C3×C8—102no—
207C2×C3×C8—102no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—51no—
210C3×C4⋊C4—101no—
211C3×C4⋊C4—101no—
212C3×C4⋊C4—101no—
213C3×C4⋊C4—102no—
214C3×C4⋊C4—102no—
215C3×C4⋊C4—101no—
216C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
217C3×C42—21no—
218C3×C42—51no—
219C3×C42—51no—
220C3×C42—51no—
221C3×C42—101no—
222C3×C42—101no—
223C3×C42—101no—
224C3×C42C2×AGL(1,𝔽5)11yescharacteristic
225C22×D5C2×C3×D411yescharacteristic
226C2×AGL(1,𝔽5)—42no—
227C2×AGL(1,𝔽5)—42no—
228C2×AGL(1,𝔽5)—42no—
229C5×Q8—21no—
230C5×Q8C3×C4⋊C412yes—
231C2×C4×C5—21no—
232C2×C4×C5—21no—
233C2×C4×C5C3×C22⋊C411yescharacteristic
234C2×C4×C5C3×C22⋊C411yescharacteristic
235C2×C4×C5C22×C3×C411yescharacteristic
236C2×Dic5—21no—
237C2×Dic5—21no—
238C2×Dic5C3×C22⋊C411yescharacteristic
239C2×Dic5C3×C22⋊C411yescharacteristic
240C2×Dic5C2×C3×D411yescharacteristic
241C4×D5—22no—
242C4×D5—22no—
243C4×D5—22no—
244C4×D5—22no—
245C4×D5—42no—
246C4×D5C2×C3×D411yescharacteristic
247C4×D5C2×C3×Q811yescharacteristic
248C4×D5C3×#4111yescharacteristic
249C4×D5C3×#4111yescharacteristic
250Dic10—21no—
251Dic10—22no—
252Dic10—22no—
253Dic10C3×C4⋊C412yes—
254#170—42no—
255C22×Q8—51no—
256C22×C8—52no—
257C4×Q8—51no—
258C4×Q8—51no—
259C4×Q8—51no—
260C4×Q8—101no—
261C4×Q8—101no—
262C4×Q8C3×AGL(1,𝔽5)11yescharacteristic, complemented
263C2×C4⋊C4—51no—
264C2×C4⋊C4—52no—
265C2×C4⋊C4—101no—
266C2×C42—51no—
267C2×C42—101no—
268C4⋊C8—101no—
269C4⋊C8—101no—
270#103—104no—
271#95—101no—
272#95—101no—
273C2×C3×C5#38011yescharacteristic
274C2×C3×C5#41611yescharacteristic
275C2×C3×C5#41911yescharacteristic
276C3×D5#46412yes—
277C3×D5#47912yes—
278C23×C3—51no—
279C3×Q8—21no—
280C3×Q8—52no—
281C3×Q8—102no—
282C3×Q8—102no—
283C3×Q8—101no—
284C3×Q8C4⋊AGL(1,𝔽5)12yes—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—51no—
288C2×C3×C4—51no—
289C2×C3×C4—51no—
290C2×C3×C4—51no—
291C2×C3×C4—51no—
292C2×C3×C4—51no—
293C2×C3×C4—51no—
294C2×C3×C4—102no—
295C2×C3×C4—102no—
296C2×C3×C4—102no—
297C2×C3×C4—102no—
298C2×C3×C4—101no—
299C2×C3×C4—101no—
300C2×C3×C4—202no—
301C2×C3×C4—202no—
302C2×C3×C4—202no—
303C2×C3×C4—202no—
304C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
305C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
306C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
307C3×C8—202no—
308C22×C5C2×C3×C22⋊C411yescharacteristic
309C2×D5C3×#12111yescharacteristic
310C2×D5C3×C22⋊Q811yescharacteristic
311C2×D5C3×#13512yes—
312C2×D5C3×#13712yes—
313AGL(1,𝔽5)—82no—
314C4×C5—22no—
315C4×C5—21no—
316C4×C5—21no—
317C4×C5—41no—
318C4×C5C2×C3×C4⋊C411yescharacteristic
319C4×C5C3×#11711yescharacteristic
320Dic5—22no—
321Dic5—21no—
322Dic5—21no—
323Dic5—41no—
324Dic5C3×#12111yescharacteristic
325Dic5C3×C22⋊Q811yescharacteristic
326C2×Q8—52no—
327C2×Q8—52no—
328C2×Q8—51no—
329C2×Q8—101no—
330C2×Q8—101no—
331C2×Q8—101no—
332C2×Q8C2×C3×AGL(1,𝔽5)11yescharacteristic
333C22×C4—51no—
334C22×C4—51no—
335C22×C4—51no—
336C22×C4—101no—
337C22×C4—101no—
338C22×C4—102no—
339C2×C8—102no—
340C2×C8—102no—
341C2×C8—102no—
342C4⋊C4—21no—
343C4⋊C4—51no—
344C4⋊C4—101no—
345C4⋊C4—101no—
346C4⋊C4—101no—
347C4⋊C4—102no—
348C4⋊C4—102no—
349C4⋊C4—101no—
350C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
351C42—21no—
352C42—51no—
353C42—51no—
354C42—51no—
355C42—101no—
356C42—101no—
357C42—101no—
358C42C2×C3×AGL(1,𝔽5)11yescharacteristic
359C3×C5#180511yescharacteristic, complemented, Hall
360C22×C3—52no—
361C22×C3—51no—
362C22×C3—51no—
363C22×C3—52no—
364C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
365C3×C4—21no—
366C3×C4—22no—
367C3×C4—21no—
368C3×C4—41no—
369C3×C4—51no—
370C3×C4—51no—
371C3×C4—101no—
372C3×C4—102no—
373C3×C4—101no—
374C3×C4—201no—
375C3×C4—402no—
376C3×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
377C3×C4#413011yescharacteristic
378C2×C5C3×#38011yescharacteristic
379C2×C5C3×#41611yescharacteristic
380C2×C5C3×#41911yescharacteristic
381D5C3×#46412yes—
382D5C3×#47912yes—
383C23—51no—
384Q8—21no—
385Q8—52no—
386Q8—102no—
387Q8—102no—
388Q8—101no—
389Q8C3×C4⋊AGL(1,𝔽5)12yes—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—51no—
393C2×C4—51no—
394C2×C4—51no—
395C2×C4—51no—
396C2×C4—51no—
397C2×C4—51no—
398C2×C4—51no—
399C2×C4—102no—
400C2×C4—102no—
401C2×C4—102no—
402C2×C4—102no—
403C2×C4—101no—
404C2×C4—101no—
405C2×C4—202no—
406C2×C4—202no—
407C2×C4—202no—
408C2×C4—202no—
409C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
410C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
411C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
412C8—202no—
413C2×C3—52no—
414C2×C3—52no—
415C2×C3#6576511yescharacteristic
416C2×C3#6578211yescharacteristic
417C2×C3#6579411yescharacteristic
418C5C3×#180511yescharacteristic, complemented, Sylow
419C22—51no—
420C22—51no—
421C22—52no—
422C22—52no—
423C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
424C4—22no—
425C4—21no—
426C4—21no—
427C4—41no—
428C4—51no—
429C4—51no—
430C4—102no—
431C4—101no—
432C4—101no—
433C4—201no—
434C4—402no—
435C4C2×C3×C4⋊AGL(1,𝔽5)11yescharacteristic
436C4C3×#413011yescharacteristic
437C3#1060445211yescharacteristic, direct product factor, Sylow
438C2—52no—
439C2—52no—
440C2C3×#6576511yescharacteristic
441C2C3×#6578211yescharacteristic
442C2C3×#6579411yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C4×C5×Q8C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C2×D4
cosocleC2×C4×D5C23×C3
hypercenterC3×C4×Q8AGL(1,𝔽5)
hypocenterC5C3×#1805
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×Q8

Complements

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

NH ≅ G/Ntype
6. #10604452C3direct (N × H)
10. C3×C4×C5×Q8C4semidirect
11. C3×Q8×Dic5C4semidirect
15. C3×#4033C4semidirect
19. C3×C4×Dic10C4semidirect
72. C4×C5×Q8C3×C4semidirect
73. Q8×Dic5C3×C4semidirect
77. #4033C3×C4semidirect
81. C4×Dic10C3×C4semidirect
125. C3×C4×Q8AGL(1,𝔽5)semidirect
262. C4×Q8C3×AGL(1,𝔽5)semidirect
359. C3×C5#1805semidirect
418. C5C3×#1805semidirect
437. C3#10604452direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4×Q8×D52
C2×C3×#40092
C3×#656892
C3×D5⋊(C4⋊C8)2
C3×#648742
#106044523
C3×#18055