Finite Group Databasebeta

← C3×#10600419 #14300077

Subgroups — C3×#10600419 #14300077

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D20C211yesmaximal, characteristic
2C3×C5×#389C211yesmaximal, characteristic, complemented
3C2×C3×#3941C211yesmaximal, characteristic
4C2×C3×#3941C211yesmaximal, characteristic
5C2×C3×#3940C211yesmaximal, characteristic, complemented
6C3×#64749C211yesmaximal, characteristic, complemented
7C3×#64744C211yesmaximal, characteristic, complemented
8#10600419C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×D20C2211yescharacteristic
10C22×C3×C4×D5—21no—
11C2×C3×C5×C4⋊C4—21no—
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C2×C3×C42×C5C2211yescharacteristic
15C2×C3×#685—21no—
16C2×C3×C4⋊Dic5C2211yescharacteristic
17C22×C3×#168C2211yescharacteristic
18C22×C3×#168C2211yescharacteristic
19C3×C4×D20—22no—
20C3×C4×D20—22no—
21C3×C5×#95—21no—
22C3×#3941—22no—
23C3×#3941C414yescomplemented
24C3×#3940—22no—
25C3×#1864—51nomaximal, Hall
26C2×C4×D20C2×C311yescharacteristic
27C5×#389C2×C311yescharacteristic, complemented
28C2×#3941C2×C311yescharacteristic
29C2×#3941C2×C311yescharacteristic
30C2×#3940C2×C311yescharacteristic, complemented
31#64749C2×C311yescharacteristic, complemented
32#64744C2×C311yescharacteristic, complemented
33C23×C3×D5—21no—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5D411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C22×C3×Dic5—21no—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C2×C3×D20C2×C412yes—
44C2×C3×D20D412yes—
45C2×C3×D20Q812yes—
46C2×C3×C4×D5—24no—
47C2×C3×C4×D5—42no—
48C2×C3×C4×D5—42no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4—42no—
53C3×C5×C4⋊C4C2×C412yescomplemented
54C3×C42×C5—21no—
55C3×C42×C5—21no—
56C3×#685—24no—
57C3×C4⋊Dic5—21no—
58C3×C4⋊Dic5D412yes—
59C2×C3×#168—21no—
60C2×C3×#168—21no—
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63C2×C3×#168—21no—
64C2×C3×#168C2×C412yescomplemented
65C2×C3×C4×D4—51no—
66C2×C3×#106—51no—
67C2×C3×#102—51no—
68C2×C3×#102—51no—
69C3×#389D511yescharacteristic, complemented
70C3×#340—51no—
71C3×#336—51no—
72C22×D20C22×C311yescharacteristic
73C22×C4×D5—21no—
74C2×C5×C4⋊C4—21no—
75C2×C5×C4⋊C4C22×C311yescharacteristic
76C2×C5×C4⋊C4C22×C311yescharacteristic
77C2×C42×C5C22×C311yescharacteristic
78C2×#685—21no—
79C2×C4⋊Dic5C22×C311yescharacteristic
80C22×#168C22×C311yescharacteristic
81C22×#168C22×C311yescharacteristic
82C4×D20—22no—
83C4×D20—22no—
84C5×#95—21no—
85#3941—22no—
86#3941C3×C414yescomplemented
87#3940—22no—
88#1864—51noSylow
89C23×C3×C5C2×D411yescharacteristic
90C22×C3×D5—22no—
91C22×C3×D5—22no—
92C22×C3×D5—22no—
93C22×C3×D5—41no—
94C22×C3×D5—41no—
95C22×C3×D5—41no—
96C22×C3×D5—41no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—22no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5SD1612yes—
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×Q811yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×C3×Dic5—22no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5—41no—
118C3×D20—22no—
119C3×D20—22no—
120C3×D20—22no—
121C3×D20C4⋊C414yescomplemented
122C3×C4×D5—48no—
123C3×#168—22no—
124C3×#168—41no—
125C22×C3×D4—51no—
126C23×C3×C4—101no—
127C22×C3×C8—51no—
128C22×C3×C8—51no—
129C3×C4×D4—102no—
130C3×C4×D4—102no—
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4—51no—
133C2×C3×C4⋊C4C2×D511yescharacteristic
134C2×C3×C4⋊C4C2×D511yescharacteristic
135C2×C3×C22⋊C4—101no—
136C2×C3×C42C2×D511yescharacteristic
137C3×#106—102no—
138C3×#102—54no—
139C3×#102—102no—
140C3×#95—21no—
141C23×D5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5C3×D411yescharacteristic
145C22×C4×C5C3×D411yescharacteristic
146C22×C4×C5C23×C311yescharacteristic
147C22×Dic5—21no—
148C2×D20—21no—
149C2×D20—21no—
150C2×D20—21no—
151C2×D20C2×C3×C412yes—
152C2×D20C3×D412yes—
153C2×D20C3×Q812yes—
154C2×C4×D5—24no—
155C2×C4×D5—42no—
156C2×C4×D5—42no—
157C5×C4⋊C4—21no—
158C5×C4⋊C4—21no—
159C5×C4⋊C4—21no—
160C5×C4⋊C4—42no—
161C5×C4⋊C4C2×C3×C412yescomplemented
162C42×C5—21no—
163C42×C5—21no—
164#685—24no—
165C4⋊Dic5—21no—
166C4⋊Dic5C3×D412yes—
167C2×#168—21no—
168C2×#168—21no—
169C2×#168—21no—
170C2×#168—21no—
171C2×#168—21no—
172C2×#168C2×C3×C412yescomplemented
173C2×C4×D4—51no—
174C2×#106—51no—
175C2×#102—51no—
176C2×#102—51no—
177#389C3×D511yescharacteristic, complemented
178#340—51no—
179#336—51no—
180C22×C3×C5C4×D411yescharacteristic
181C22×C3×C5#12011yescharacteristic
182C22×C3×C5C22⋊Q811yescharacteristic
183C22×C3×C5C2×SD1611yescharacteristic
184C22×C3×C5#13511yescharacteristic
185C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
186C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
187C2×C3×D5—24no—
188C2×C3×D5—42no—
189C2×C3×D5—42no—
190C2×C3×D5—42no—
191C2×C3×D5—42no—
192C2×C3×D5—42no—
193C2×C3×D5—42no—
194C3×C4×C5—22no—
195C3×C4×C5—42no—
196C3×C4×C5—41no—
197C3×C4×C5—81no—
198C3×C4×C5C2×C4⋊C411yescharacteristic
199C3×C4×C5C4×D411yescharacteristic
200C3×C4×C5C22⋊Q811yescharacteristic
201C3×C4×C5#12311yescharacteristic
202C3×Dic5—42no—
203C24×C3—101no—
204C2×C3×D4—52no—
205C2×C3×D4—52no—
206C2×C3×D4—52no—
207C2×C3×D4—101no—
208C2×C3×D4—101no—
209C2×C3×D4—101no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—104no—
213C22×C3×C4—101no—
214C22×C3×C4—202no—
215C22×C3×C4—202no—
216C22×C3×C4C22⋊D511yescharacteristic
217C22×C3×C4C22⋊D511yescharacteristic
218C22×C3×C4C22×D511yescharacteristic
219C2×C3×C8—52no—
220C2×C3×C8—101no—
221C2×C3×C8—101no—
222C2×C3×C8—101no—
223C2×C3×C8—101no—
224C2×C3×C8—101no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—42no—
229C3×C4⋊C4—52no—
230C3×C4⋊C4—101no—
231C3×C4⋊C4C4×D512yescomplemented
232C3×C22⋊C4—104no—
233C3×C42—21no—
234C3×C42—21no—
235C23×C5C2×C3×D411yescharacteristic
236C22×D5—22no—
237C22×D5—22no—
238C22×D5—22no—
239C22×D5—41no—
240C22×D5—41no—
241C22×D5—41no—
242C22×D5—41no—
243C2×C4×C5—21no—
244C2×C4×C5—21no—
245C2×C4×C5—22no—
246C2×C4×C5—21no—
247C2×C4×C5—21no—
248C2×C4×C5—21no—
249C2×C4×C5—41no—
250C2×C4×C5—41no—
251C2×C4×C5—41no—
252C2×C4×C5—41no—
253C2×C4×C5—41no—
254C2×C4×C5C3×SD1612yes—
255C2×C4×C5C22×C3×C411yescharacteristic
256C2×C4×C5C2×C3×D411yescharacteristic
257C2×C4×C5C2×C3×D411yescharacteristic
258C2×C4×C5C2×C3×Q811yescharacteristic
259C2×C4×C5C3×#4111yescharacteristic
260C2×C4×C5C3×#4111yescharacteristic
261C2×Dic5—22no—
262C2×Dic5—41no—
263C2×Dic5—41no—
264D20—22no—
265D20—22no—
266D20—22no—
267D20C3×C4⋊C414yescomplemented
268C4×D5—48no—
269#168—22no—
270#168—41no—
271C22×D4—51no—
272C23×C4—101no—
273C22×C8—51no—
274C22×C8—51no—
275C4×D4—102no—
276C4×D4—102no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—51no—
279C2×C4⋊C4C2×C3×D511yescharacteristic
280C2×C4⋊C4C2×C3×D511yescharacteristic
281C2×C22⋊C4—101no—
282C2×C42C2×C3×D511yescharacteristic
283#106—102no—
284#102—54no—
285#102—102no—
286#95—21no—
287C2×C3×C5#38511yescharacteristic
288C2×C3×C5C4×SD1611yescharacteristic
289C2×C3×C5#44211yescharacteristic
290C2×C3×C5#44911yescharacteristic
291C2×C3×C5#45011yescharacteristic
292C2×C3×C5#47611yescharacteristic
293C2×C3×C5#47811yescharacteristic
294C3×D5—44no—
295C23×C3—102no—
296C23×C3—102no—
297C23×C3—102no—
298C23×C3—201no—
299C23×C3—201no—
300C23×C3—201no—
301C23×C3—201no—
302C23×C3C2×C22⋊D511yescharacteristic
303C3×D4—54no—
304C3×D4—102no—
305C3×D4—102no—
306C3×D4—102no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—22no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
318C2×C3×C4—102no—
319C2×C3×C4—208no—
320C2×C3×C4—201no—
321C2×C3×C4—201no—
322C2×C3×C4#68812yes—
323C2×C3×C4C2×C4×D511yescharacteristic
324C2×C3×C4#70911yescharacteristic
325C2×C3×C4D4×D511yescharacteristic
326C2×C3×C4D4×D511yescharacteristic
327C2×C3×C4Q8×D511yescharacteristic
328C2×C3×C4#71311yescharacteristic
329C3×C8—102no—
330C3×C8—201no—
331C22×C5C3×C4×D411yescharacteristic
332C22×C5C3×#12011yescharacteristic
333C22×C5C3×C22⋊Q811yescharacteristic
334C22×C5C2×C3×SD1611yescharacteristic
335C22×C5C3×#13511yescharacteristic
336C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
337C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
338C2×D5—24no—
339C2×D5—42no—
340C2×D5—42no—
341C2×D5—42no—
342C2×D5—42no—
343C2×D5—42no—
344C2×D5—42no—
345C4×C5—22no—
346C4×C5—42no—
347C4×C5—41no—
348C4×C5—81no—
349C4×C5C2×C3×C4⋊C411yescharacteristic
350C4×C5C3×C4×D411yescharacteristic
351C4×C5C3×C22⋊Q811yescharacteristic
352C4×C5C3×#12311yescharacteristic
353Dic5—42no—
354C24—101no—
355C2×D4—52no—
356C2×D4—52no—
357C2×D4—52no—
358C2×D4—101no—
359C2×D4—101no—
360C2×D4—101no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—104no—
364C22×C4—101no—
365C22×C4—202no—
366C22×C4—202no—
367C22×C4C3×C22⋊D511yescharacteristic
368C22×C4C3×C22⋊D511yescharacteristic
369C22×C4C22×C3×D511yescharacteristic
370C2×C8—52no—
371C2×C8—101no—
372C2×C8—101no—
373C2×C8—101no—
374C2×C8—101no—
375C2×C8—101no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—42no—
380C4⋊C4—52no—
381C4⋊C4—101no—
382C4⋊C4C3×C4×D512yescomplemented
383C22⋊C4—104no—
384C42—21no—
385C42—21no—
386C3×C5#186411yescharacteristic, complemented, Hall
387C22×C3—104no—
388C22×C3—202no—
389C22×C3—202no—
390C22×C3—202no—
391C22×C3—202no—
392C22×C3—202no—
393C22×C3—202no—
394C22×C3C4×C22⋊D511yescharacteristic
395C22×C3#407811yescharacteristic
396C22×C3#408311yescharacteristic
397C22×C3C2×#68811yescharacteristic
398C22×C3#409211yescharacteristic
399C22×C3#409511yescharacteristic
400C22×C3#409611yescharacteristic
401C3×C4—22no—
402C3×C4—42no—
403C3×C4—41no—
404C3×C4—81no—
405C3×C4—202no—
406C3×C4D5×C4⋊C411yescharacteristic
407C3×C4#403911yescharacteristic
408C3×C4#404011yescharacteristic
409C3×C4#404211yescharacteristic
410C2×C5C3×#38511yescharacteristic
411C2×C5C3×C4×SD1611yescharacteristic
412C2×C5C3×#44211yescharacteristic
413C2×C5C3×#44911yescharacteristic
414C2×C5C3×#45011yescharacteristic
415C2×C5C3×#47611yescharacteristic
416C2×C5C3×#47811yescharacteristic
417D5—44no—
418C23—102no—
419C23—102no—
420C23—102no—
421C23—201no—
422C23—201no—
423C23—201no—
424C23—201no—
425C23C2×C3×C22⋊D511yescharacteristic
426D4—54no—
427D4—102no—
428D4—102no—
429D4—102no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—102no—
442C2×C4—208no—
443C2×C4—201no—
444C2×C4—201no—
445C2×C4C3×#68812yes—
446C2×C4C2×C3×C4×D511yescharacteristic
447C2×C4C3×#70911yescharacteristic
448C2×C4C3×D4×D511yescharacteristic
449C2×C4C3×D4×D511yescharacteristic
450C2×C4C3×Q8×D511yescharacteristic
451C2×C4C3×#71311yescharacteristic
452C8—102no—
453C8—201no—
454C2×C3—204no—
455C2×C3#6527811yescharacteristic
456C2×C3#6530311yescharacteristic
457C2×C3C4×#68811yescharacteristic
458C2×C3#6532611yescharacteristic
459C2×C3#6533511yescharacteristic
460C2×C3#6535511yescharacteristic
461C2×C3#6537311yescharacteristic
462C5C3×#186411yescharacteristic, complemented, Sylow
463C22—104no—
464C22—202no—
465C22—202no—
466C22—202no—
467C22—202no—
468C22—202no—
469C22—202no—
470C22C3×C4×C22⋊D511yescharacteristic
471C22C3×#407811yescharacteristic
472C22C3×#408311yescharacteristic
473C22C2×C3×#68811yescharacteristic
474C22C3×#409211yescharacteristic
475C22C3×#409511yescharacteristic
476C22C3×#409611yescharacteristic
477C4—22no—
478C4—42no—
479C4—41no—
480C4—81no—
481C4—202no—
482C4C3×D5×C4⋊C411yescharacteristic
483C4C3×#403911yescharacteristic
484C4C3×#404011yescharacteristic
485C4C3×#404211yescharacteristic
486C3#1060041911yescharacteristic, direct product factor, Sylow
487C2—204no—
488C2C3×#6527811yescharacteristic
489C2C3×#6530311yescharacteristic
490C2C3×C4×#68811yescharacteristic
491C2C3×#6532611yescharacteristic
492C2C3×#6533511yescharacteristic
493C2C3×#6535511yescharacteristic
494C2C3×#6537311yescharacteristic
subgroupG/H
centerC23×C3C2×C22⋊D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#389C2
socleC23×C3×C5C2×D4
prime radicalC22×C3×D20C22
cosocleC22×C4×C5C23×C3
hypercenterC3×#389D5
hypocenterC5C3×#1864
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C3×#389

Complements

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

NH ≅ G/Ntype
2. C3×C5×#389C2semidirect
5. C2×C3×#3940C2semidirect
6. C3×#64749C2semidirect
7. C3×#64744C2semidirect
8. #10600419C3direct (N × H)
23. C3×#3941C4semidirect
27. C5×#389C2×C3semidirect
30. C2×#3940C2×C3semidirect
31. #64749C2×C3semidirect
32. #64744C2×C3semidirect
53. C3×C5×C4⋊C4C2×C4semidirect
64. C2×C3×#168C2×C4semidirect
69. C3×#389D5semidirect
86. #3941C3×C4semidirect
121. C3×D20C4⋊C4semidirect
161. C5×C4⋊C4C2×C3×C4semidirect
172. C2×#168C2×C3×C4semidirect
177. #389C3×D5semidirect
231. C3×C4⋊C4C4×D5semidirect
267. D20C3×C4⋊C4semidirect
382. C4⋊C4C3×C4×D5semidirect
386. C3×C5#1864semidirect
462. C5C3×#1864semidirect
486. C3#10600419direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×D202
C3×C5×#3892
C2×C3×#39412
C2×C3×#39402
C3×#647492
C3×#647442
#106004193
C3×#18645