Finite Group Databasebeta

← C3×#10604973 #14297020

Subgroups — C3×#10604973 #14297020

Order 1920.

1184 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Q8×D5C211yesmaximal, characteristic
2C2×C3×#4009C214yesmaximal, complemented
3C3×#65765C211yesmaximal, characteristic
4C3×D5⋊(C22⋊C8)C211yesmaximal, characteristic
5#10604973C311yesmaximal, characteristic, direct product factor, Hall
6C22×C3×C5×Q8C411yescharacteristic, complemented
7C2×C3×Q8×D5—28no—
8C2×C3×Q8×D5—21no—
9C2×C3×Q8×D5—21no—
10C2×C3×Q8×D5C412yescomplemented
11C2×C3×Q8×D5C2212yes—
12C22×C3×C4×D5—21no—
13C22×C3×C4×D5C2211yescharacteristic
14C22×C3×Dic10—21no—
15C22×C3×Dic10C411yescharacteristic, complemented
16C2×C3×C22⋊AGL(1,𝔽5)—21no—
17C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
18C2×C3×D5⋊C8C2212yes—
19C3×C22⋊#170—21no—
20C3×#4009—28no—
21C3×(C2×AGL(1,𝔽5))⋊C4—21no—
22C3×#4003—21no—
23C3×#1787—51nomaximal, Hall
24C22×Q8×D5C2×C311yescharacteristic
25C2×#4009C2×C314yescomplemented
26#65765C2×C311yescharacteristic
27D5⋊(C22⋊C8)C2×C311yescharacteristic
28C23×C3×D5D411yescharacteristic
29C22×C3×AGL(1,𝔽5)—22no—
30C2×C3×C5×Q8—24no—
31C2×C3×C5×Q8—21no—
32C2×C3×C5×Q8C2×C412yes—
33C22×C3×C4×C5—21no—
34C22×C3×C4×C5C2×C411yescharacteristic
35C22×C3×Dic5—21no—
36C22×C3×Dic5D411yescharacteristic
37C3×Q8×D5—28no—
38C3×Q8×D5—28no—
39C3×Q8×D5—24no—
40C3×Q8×D5—24no—
41C3×Q8×D5—24no—
42C3×Q8×D5D418yes—
43C2×C3×C4×D5—28no—
44C2×C3×C4×D5—22no—
45C2×C3×C4×D5—22no—
46C2×C3×C4×D5—24no—
47C2×C3×C4×D5C2×C411yescharacteristic
48C2×C3×C4×D5D411yescharacteristic
49C2×C3×C4×D5D411yescharacteristic
50C2×C3×C4×D5C2311yescharacteristic
51C2×C3×Dic10—28no—
52C2×C3×Dic10—21no—
53C2×C3×Dic10—22no—
54C2×C3×Dic10—22no—
55C2×C3×Dic10—24no—
56C2×C3×Dic10C2×C412yes—
57C3×C22⋊AGL(1,𝔽5)—42no—
58C2×C3×#170—22no—
59C3×C4⋊AGL(1,𝔽5)—24no—
60C3×D5⋊C8—24no—
61C23×C3×Q8—51no—
62C2×C3×#103—54no—
63C2×C3×C22⋊C8—51no—
64C3×#380—51no—
65C22×C5×Q8C3×C411yescharacteristic, complemented
66C2×Q8×D5—28no—
67C2×Q8×D5—21no—
68C2×Q8×D5—21no—
69C2×Q8×D5C3×C412yescomplemented
70C2×Q8×D5C22×C312yes—
71C22×C4×D5—21no—
72C22×C4×D5C22×C311yescharacteristic
73C22×Dic10—21no—
74C22×Dic10C3×C411yescharacteristic, complemented
75C2×C22⋊AGL(1,𝔽5)—21no—
76C2×C4⋊AGL(1,𝔽5)C22×C312yes—
77C2×D5⋊C8C22×C312yes—
78C22⋊#170—21no—
79#4009—28no—
80(C2×AGL(1,𝔽5))⋊C4—21no—
81#4003—21no—
82#1787—51noSylow
83C23×C3×C5C22⋊C411yescharacteristic
84C22×C3×D5—22no—
85C22×C3×D5—22no—
86C22×C3×D5C22⋊C411yescharacteristic
87C22×C3×D5SD1612yes—
88C22×C3×D5Q1612yes—
89C22×C3×D5C2×D411yescharacteristic
90C2×C3×AGL(1,𝔽5)—42no—
91C2×C3×AGL(1,𝔽5)—42no—
92C2×C3×AGL(1,𝔽5)—42no—
93C3×C5×Q8—24no—
94C3×C5×Q8—22no—
95C3×C5×Q8C22⋊C414yescomplemented
96C2×C3×C4×C5—24no—
97C2×C3×C4×C5—22no—
98C2×C3×C4×C5—22no—
99C2×C3×C4×C5C22⋊C411yescharacteristic
100C2×C3×C4×C5C22×C411yescharacteristic
101C2×C3×Dic5—24no—
102C2×C3×Dic5—22no—
103C2×C3×Dic5—22no—
104C2×C3×Dic5C22⋊C411yescharacteristic
105C2×C3×Dic5C2×D411yescharacteristic
106C3×C4×D5—28no—
107C3×C4×D5—28no—
108C3×C4×D5—22no—
109C3×C4×D5—22no—
110C3×C4×D5—22no—
111C3×C4×D5C2×D414yes—
112C3×Dic10—28no—
113C3×Dic10—24no—
114C3×Dic10—22no—
115C3×Dic10—28no—
116C3×Dic10C22⋊C414yescomplemented
117C3×#170—42no—
118C22×C3×Q8—52no—
119C22×C3×Q8—52no—
120C22×C3×Q8—51no—
121C22×C3×Q8—101no—
122C22×C3×Q8—101no—
123C22×C3×Q8—101no—
124C22×C3×Q8—108no—
125C22×C3×Q8AGL(1,𝔽5)11yescharacteristic, complemented
126C23×C3×C4—51no—
127C23×C3×C4—101no—
128C22×C3×C8—52no—
129C2×C3×C4⋊C4—52no—
130C2×C3×C22⋊C4—101no—
131C3×#103—108no—
132C3×C22⋊C8—101no—
133C3×C22⋊C8—101no—
134C3×#95—101no—
135C23×D5C3×D411yescharacteristic
136C22×AGL(1,𝔽5)—22no—
137C2×C5×Q8—24no—
138C2×C5×Q8—21no—
139C2×C5×Q8C2×C3×C412yes—
140C22×C4×C5—21no—
141C22×C4×C5C2×C3×C411yescharacteristic
142C22×Dic5—21no—
143C22×Dic5C3×D411yescharacteristic
144Q8×D5—28no—
145Q8×D5—28no—
146Q8×D5—24no—
147Q8×D5—24no—
148Q8×D5—24no—
149Q8×D5C3×D418yes—
150C2×C4×D5—28no—
151C2×C4×D5—22no—
152C2×C4×D5—22no—
153C2×C4×D5—24no—
154C2×C4×D5C2×C3×C411yescharacteristic
155C2×C4×D5C3×D411yescharacteristic
156C2×C4×D5C3×D411yescharacteristic
157C2×C4×D5C23×C311yescharacteristic
158C2×Dic10—28no—
159C2×Dic10—21no—
160C2×Dic10—22no—
161C2×Dic10—22no—
162C2×Dic10—24no—
163C2×Dic10C2×C3×C412yes—
164C22⋊AGL(1,𝔽5)—42no—
165C2×#170—22no—
166C4⋊AGL(1,𝔽5)—24no—
167D5⋊C8—24no—
168C23×Q8—51no—
169C2×#103—54no—
170C2×C22⋊C8—51no—
171#380—51no—
172C22×C3×C5—21no—
173C22×C3×C5—21no—
174C22×C3×C5#10312yescomplemented
175C22×C3×C5C2×C22⋊C411yescharacteristic
176C2×C3×D5—21no—
177C2×C3×D5—21no—
178C2×C3×D5—24no—
179C2×C3×D5—24no—
180C2×C3×D5#10312yescomplemented
181C2×C3×D5#12012yes—
182C2×C3×D5C2×SD1611yescharacteristic
183C2×C3×D5C2×Q1611yescharacteristic
184C2×C3×D5#13712yes—
185C3×AGL(1,𝔽5)—82no—
186C3×C4×C5—24no—
187C3×C4×C5—21no—
188C3×C4×C5C2×C22⋊C412yes—
189C3×Dic5—21no—
190C3×Dic5—24no—
191C3×Dic5#12012yes—
192C24×C3—51no—
193C2×C3×Q8—24no—
194C2×C3×Q8—21no—
195C2×C3×Q8—58no—
196C2×C3×Q8—52no—
197C2×C3×Q8—102no—
198C2×C3×Q8—102no—
199C2×C3×Q8—104no—
200C2×C3×Q8—108no—
201C2×C3×Q8—104no—
202C2×C3×Q8—104no—
203C2×C3×Q8—108no—
204C2×C3×Q8—108no—
205C2×C3×Q8—104no—
206C2×C3×Q8—101no—
207C2×C3×Q8C2×AGL(1,𝔽5)12yes—
208C22×C3×C4—21no—
209C22×C3×C4—51no—
210C22×C3×C4—51no—
211C22×C3×C4—51no—
212C22×C3×C4—51no—
213C22×C3×C4—51no—
214C22×C3×C4—104no—
215C22×C3×C4—102no—
216C22×C3×C4—102no—
217C22×C3×C4—108no—
218C22×C3×C4—101no—
219C22×C3×C4—102no—
220C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
221C2×C3×C8—102no—
222C2×C3×C8—104no—
223C3×C4⋊C4—104no—
224C3×C22⋊C4—202no—
225C23×C5C3×C22⋊C411yescharacteristic
226C22×D5—22no—
227C22×D5—22no—
228C22×D5C3×C22⋊C411yescharacteristic
229C22×D5C3×SD1612yes—
230C22×D5C3×Q1612yes—
231C22×D5C2×C3×D411yescharacteristic
232C2×AGL(1,𝔽5)—42no—
233C2×AGL(1,𝔽5)—42no—
234C2×AGL(1,𝔽5)—42no—
235C5×Q8—24no—
236C5×Q8—22no—
237C5×Q8C3×C22⋊C414yescomplemented
238C2×C4×C5—24no—
239C2×C4×C5—22no—
240C2×C4×C5—22no—
241C2×C4×C5C3×C22⋊C411yescharacteristic
242C2×C4×C5C22×C3×C411yescharacteristic
243C2×Dic5—24no—
244C2×Dic5—22no—
245C2×Dic5—22no—
246C2×Dic5C3×C22⋊C411yescharacteristic
247C2×Dic5C2×C3×D411yescharacteristic
248C4×D5—28no—
249C4×D5—28no—
250C4×D5—22no—
251C4×D5—22no—
252C4×D5—22no—
253C4×D5C2×C3×D414yes—
254Dic10—28no—
255Dic10—24no—
256Dic10—22no—
257Dic10—28no—
258Dic10C3×C22⋊C414yescomplemented
259#170—42no—
260C22×Q8—52no—
261C22×Q8—52no—
262C22×Q8—51no—
263C22×Q8—101no—
264C22×Q8—101no—
265C22×Q8—101no—
266C22×Q8—108no—
267C22×Q8C3×AGL(1,𝔽5)11yescharacteristic, complemented
268C23×C4—51no—
269C23×C4—101no—
270C22×C8—52no—
271C2×C4⋊C4—52no—
272C2×C22⋊C4—101no—
273#103—108no—
274C22⋊C8—101no—
275C22⋊C8—101no—
276#95—101no—
277C2×C3×C5—22no—
278C2×C3×C5#37911yescharacteristic
279C2×C3×C5C2×#10311yescharacteristic
280C2×C3×C5#41911yescharacteristic
281C3×D5—22no—
282C3×D5#44812yes—
283C3×D5#45112yes—
284C23×C3—51no—
285C23×C3—51no—
286C23×C3—52no—
287C23×C3—52no—
288C23×C3—102no—
289C23×C3—102no—
290C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
291C3×Q8—24no—
292C3×Q8—22no—
293C3×Q8—54no—
294C3×Q8—108no—
295C3×Q8—108no—
296C3×Q8—104no—
297C3×Q8—102no—
298C3×Q8C22⋊AGL(1,𝔽5)14yescomplemented
299C2×C3×C4—24no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—51no—
303C2×C3×C4—54no—
304C2×C3×C4—51no—
305C2×C3×C4—102no—
306C2×C3×C4—102no—
307C2×C3×C4—108no—
308C2×C3×C4—108no—
309C2×C3×C4—102no—
310C2×C3×C4—104no—
311C2×C3×C4—102no—
312C2×C3×C4—102no—
313C2×C3×C4—202no—
314C2×C3×C4—202no—
315C2×C3×C4—202no—
316C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
317C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
318C3×C8—202no—
319C22×C5—21no—
320C22×C5—21no—
321C22×C5C3×#10312yescomplemented
322C22×C5C2×C3×C22⋊C411yescharacteristic
323C2×D5—21no—
324C2×D5—21no—
325C2×D5—24no—
326C2×D5—24no—
327C2×D5C3×#10312yescomplemented
328C2×D5C3×#12012yes—
329C2×D5C2×C3×SD1611yescharacteristic
330C2×D5C2×C3×Q1611yescharacteristic
331C2×D5C3×#13712yes—
332AGL(1,𝔽5)—82no—
333C4×C5—24no—
334C4×C5—21no—
335C4×C5C2×C3×C22⋊C412yes—
336Dic5—21no—
337Dic5—24no—
338Dic5C3×#12012yes—
339C24—51no—
340C2×Q8—24no—
341C2×Q8—21no—
342C2×Q8—58no—
343C2×Q8—52no—
344C2×Q8—102no—
345C2×Q8—102no—
346C2×Q8—104no—
347C2×Q8—108no—
348C2×Q8—104no—
349C2×Q8—104no—
350C2×Q8—108no—
351C2×Q8—108no—
352C2×Q8—104no—
353C2×Q8—101no—
354C2×Q8C2×C3×AGL(1,𝔽5)12yes—
355C22×C4—21no—
356C22×C4—51no—
357C22×C4—51no—
358C22×C4—51no—
359C22×C4—51no—
360C22×C4—51no—
361C22×C4—104no—
362C22×C4—102no—
363C22×C4—102no—
364C22×C4—108no—
365C22×C4—101no—
366C22×C4—102no—
367C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
368C2×C8—102no—
369C2×C8—104no—
370C4⋊C4—104no—
371C22⋊C4—202no—
372C3×C5#178711yescharacteristic, complemented, Hall
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—52no—
376C22×C3—51no—
377C22×C3—51no—
378C22×C3—52no—
379C22×C3—52no—
380C22×C3—104no—
381C22×C3—104no—
382C22×C3—101no—
383C22×C3—101no—
384C22×C3#400912yescomplemented
385C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
386C3×C4—24no—
387C3×C4—21no—
388C3×C4—52no—
389C3×C4—101no—
390C3×C4—104no—
391C3×C4—402no—
392C3×C4C2×C22⋊AGL(1,𝔽5)12yes—
393C2×C5—22no—
394C2×C5C3×#37911yescharacteristic
395C2×C5C2×C3×#10311yescharacteristic
396C2×C5C3×#41911yescharacteristic
397D5—22no—
398D5C3×#44812yes—
399D5C3×#45112yes—
400C23—51no—
401C23—52no—
402C23—52no—
403C23—51no—
404C23—102no—
405C23—102no—
406C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
407Q8—24no—
408Q8—22no—
409Q8—54no—
410Q8—108no—
411Q8—108no—
412Q8—104no—
413Q8—102no—
414Q8C3×C22⋊AGL(1,𝔽5)14yescomplemented
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—51no—
419C2×C4—54no—
420C2×C4—51no—
421C2×C4—102no—
422C2×C4—102no—
423C2×C4—108no—
424C2×C4—108no—
425C2×C4—102no—
426C2×C4—104no—
427C2×C4—102no—
428C2×C4—102no—
429C2×C4—202no—
430C2×C4—202no—
431C2×C4—202no—
432C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
433C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
434C8—202no—
435C2×C3—22no—
436C2×C3—52no—
437C2×C3—52no—
438C2×C3—102no—
439C2×C3C2×#400911yescharacteristic
440C2×C3#6578211yescharacteristic
441C2×C3#6580011yescharacteristic
442C5C3×#178711yescharacteristic, complemented, Sylow
443C22—21no—
444C22—21no—
445C22—51no—
446C22—51no—
447C22—52no—
448C22—52no—
449C22—52no—
450C22—104no—
451C22—104no—
452C22—101no—
453C22—101no—
454C22C3×#400912yescomplemented
455C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
456C4—24no—
457C4—21no—
458C4—52no—
459C4—101no—
460C4—104no—
461C4—402no—
462C4C2×C3×C22⋊AGL(1,𝔽5)12yes—
463C3#1060497311yescharacteristic, direct product factor, Sylow
464C2—22no—
465C2—52no—
466C2—52no—
467C2—102no—
468C2C2×C3×#400911yescharacteristic
469C2C3×#6578211yescharacteristic
470C2C3×#6580011yescharacteristic
subgroupG/H
centerC22×C3C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC22×C3×C5×Q8C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5D4
cosocleC2×C4×D5C23×C3
hypercenterC22×C3×Q8AGL(1,𝔽5)
hypocenterC5C3×#1787
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4009C2semidirect
5. #10604973C3direct (N × H)
6. C22×C3×C5×Q8C4semidirect
10. C2×C3×Q8×D5C4semidirect
15. C22×C3×Dic10C4semidirect
25. C2×#4009C2×C3semidirect
65. C22×C5×Q8C3×C4semidirect
69. C2×Q8×D5C3×C4semidirect
74. C22×Dic10C3×C4semidirect
95. C3×C5×Q8C22⋊C4semidirect
116. C3×Dic10C22⋊C4semidirect
125. C22×C3×Q8AGL(1,𝔽5)semidirect
174. C22×C3×C5#103semidirect
180. C2×C3×D5#103semidirect
237. C5×Q8C3×C22⋊C4semidirect
258. Dic10C3×C22⋊C4semidirect
267. C22×Q8C3×AGL(1,𝔽5)semidirect
298. C3×Q8C22⋊AGL(1,𝔽5)semidirect
321. C22×C5C3×#103semidirect
327. C2×D5C3×#103semidirect
372. C3×C5#1787semidirect
384. C22×C3#4009semidirect
414. Q8C3×C22⋊AGL(1,𝔽5)semidirect
442. C5C3×#1787semidirect
454. C22C3×#4009semidirect
463. C3#10604973direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×Q8×D52
C2×C3×#40092
C3×#657652
C3×D5⋊(C22⋊C8)2
#106049733
C3×#17875