Finite Group Databasebeta

← C3×#10600950 #14305799

Subgroups — C3×#10600950 #14305799

Order 1920.

872 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4086C211yesmaximal, characteristic
2C2×C3×C5×#102C211yesmaximal, characteristic, complemented
3C2×C3×#3964C211yesmaximal, characteristic, complemented
4C2×C3×#3953C211yesmaximal, characteristic, complemented
5C2×C3×C8×Dic5C211yesmaximal, characteristic, complemented
6C3×#65265C211yesmaximal, characteristic, complemented
7C2×C3×#3941C211yesmaximal, characteristic, complemented
8#10600950C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C3×C22⋊D5—22no—
11C22×C3×D20C2211yescharacteristic
12C22×C3×C5×C8C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C3×#4086—22no—
15C3×#4086C414yescomplemented
16C2×C3×C4⋊Dic5C2211yescharacteristic
17C2×C3×#683—22no—
18C2×C3×C4×Dic5C2211yescharacteristic
19C22×C3×#168C2211yescharacteristic
20C3×C5×#102—22no—
21C3×#3964—22no—
22C3×#3953—22no—
23C3×C8×Dic5—22no—
24C3×#3941—22no—
25C3×#1957—51nomaximal, Hall
26C2×#4086C2×C311yescharacteristic
27C2×C5×#102C2×C311yescharacteristic, complemented
28C2×#3964C2×C311yescharacteristic, complemented
29C2×#3953C2×C311yescharacteristic, complemented
30C2×C8×Dic5C2×C311yescharacteristic, complemented
31#65265C2×C311yescharacteristic, complemented
32C2×#3941C2×C311yescharacteristic, complemented
33C24×C3×C5—21no—
34C23×C3×D5—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4C2×C412yes—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5C2311yescharacteristic
43C2×C3×C22⋊D5—28no—
44C2×C3×C22⋊D5—44no—
45C2×C3×C22⋊D5—44no—
46C22×C3×Dic5—21no—
47C22×C3×Dic5D412yes—
48C2×C3×D20—21no—
49C2×C3×D20—21no—
50C2×C3×D20—21no—
51C2×C3×D20—21no—
52C2×C3×D20—21no—
53C2×C3×D20C2×C412yes—
54C2×C3×C5×C8—21no—
55C2×C3×C5×C8—21no—
56C2×C3×C5×C8D412yescomplemented
57C3×C5×C4⋊C4—21no—
58C3×C5×C4⋊C4—21no—
59C3×C4⋊Dic5—21no—
60C3×C4⋊Dic5—21no—
61C3×#683—44no—
62C3×C4×Dic5C2×C412yes—
63C3×C4×Dic5D412yes—
64C2×C3×#168—21no—
65C2×C3×#168—21no—
66C2×C3×#168D412yescomplemented
67C2×C3×#127—51no—
68C2×C3×#102—51no—
69C2×C3×#102—51no—
70C2×C3×#102—51no—
71C2×C3×#102D511yescharacteristic, complemented
72C2×C3×C4×C8—51no—
73C3×#384—51no—
74C22×C5×D4C22×C311yescharacteristic
75C22×C22⋊D5—22no—
76C22×D20C22×C311yescharacteristic
77C22×C5×C8C22×C311yescharacteristic
78C2×C5×C4⋊C4C22×C311yescharacteristic
79#4086—22no—
80#4086C3×C414yescomplemented
81C2×C4⋊Dic5C22×C311yescharacteristic
82C2×#683—22no—
83C2×C4×Dic5C22×C311yescharacteristic
84C22×#168C22×C311yescharacteristic
85C5×#102—22no—
86#3964—22no—
87#3953—22no—
88C8×Dic5—22no—
89#3941—22no—
90#1957—51noSylow
91C23×C3×C5—22no—
92C23×C3×C5—41no—
93C23×C3×C5—41no—
94C23×C3×C5—42no—
95C23×C3×C5—42no—
96C23×C3×C5C2×D411yescharacteristic
97C22×C3×D5—22no—
98C22×C3×D5—41no—
99C22×C3×D5—41no—
100C22×C3×D5—42no—
101C22×C3×D5—42no—
102C3×C5×D4—22no—
103C3×C5×D4—22no—
104C3×C5×D4—41no—
105C3×C5×D4—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—42no—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C3×C22⋊D5—416no—
115C2×C3×Dic5—41no—
116C2×C3×Dic5—42no—
117C2×C3×Dic5C22⋊C414yes—
118C2×C3×Dic5D814yes—
119C2×C3×Dic5SD1614yes—
120C3×D20—22no—
121C3×D20—22no—
122C3×D20—41no—
123C3×D20—41no—
124C3×C5×C8—22no—
125C3×#168—22no—
126C22×C3×D4—51no—
127C22×C3×D4—102no—
128C22×C3×D4C2×D511yescharacteristic
129C22×C3×C8—51no—
130C22×C3×C8C2×D511yescharacteristic
131C3×#127—54no—
132C3×#127—102no—
133C2×C3×C4⋊C4—51no—
134C2×C3×C4⋊C4—102no—
135C2×C3×C4⋊C4C2×D511yescharacteristic
136C2×C3×C42—51no—
137C3×#102—22no—
138C3×#102—102no—
139C3×#102—102no—
140C3×#102—102no—
141C3×C4×C8—102no—
142C24×C5—21no—
143C23×D5—21no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4—21no—
147C2×C5×D4—21no—
148C2×C5×D4—21no—
149C2×C5×D4C2×C3×C412yes—
150C22×C4×C5—21no—
151C22×C4×C5C23×C311yescharacteristic
152C2×C22⋊D5—28no—
153C2×C22⋊D5—44no—
154C2×C22⋊D5—44no—
155C22×Dic5—21no—
156C22×Dic5C3×D412yes—
157C2×D20—21no—
158C2×D20—21no—
159C2×D20—21no—
160C2×D20—21no—
161C2×D20—21no—
162C2×D20C2×C3×C412yes—
163C2×C5×C8—21no—
164C2×C5×C8—21no—
165C2×C5×C8C3×D412yescomplemented
166C5×C4⋊C4—21no—
167C5×C4⋊C4—21no—
168C4⋊Dic5—21no—
169C4⋊Dic5—21no—
170#683—44no—
171C4×Dic5C2×C3×C412yes—
172C4×Dic5C3×D412yes—
173C2×#168—21no—
174C2×#168—21no—
175C2×#168C3×D412yescomplemented
176C2×#127—51no—
177C2×#102—51no—
178C2×#102—51no—
179C2×#102—51no—
180C2×#102C3×D511yescharacteristic, complemented
181C2×C4×C8—51no—
182#384—51no—
183C22×C3×C5—42no—
184C22×C3×C5—44no—
185C22×C3×C5—82no—
186C22×C3×C5—81no—
187C22×C3×C5—81no—
188C22×C3×C5C2×C22⋊C411yescharacteristic
189C22×C3×C5#12411yescharacteristic
190C22×C3×C5#12711yescharacteristic
191C22×C3×C5C2×D812yes—
192C22×C3×C5C2×SD1612yes—
193C2×C3×D5—42no—
194C2×C3×D5—44no—
195C2×C3×D5—82no—
196C2×C3×D5—81no—
197C2×C3×D5—81no—
198C3×C4×C5—81no—
199C3×C4×C5C4×D411yescharacteristic
200C3×C4×C5C4×D411yescharacteristic
201C3×C4×C5#12111yescharacteristic
202C3×C4×C5#12111yescharacteristic
203C3×Dic5—81no—
204C3×Dic5#10218yescomplemented
205C24×C3—21no—
206C24×C3—101no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—52no—
213C2×C3×D4—108no—
214C2×C3×D4—101no—
215C2×C3×D4—101no—
216C2×C3×D4—101no—
217C2×C3×D4—101no—
218C2×C3×D4—101no—
219C2×C3×D4—204no—
220C2×C3×D4—204no—
221C2×C3×D4C4×D512yes—
222C22×C3×C4—21no—
223C22×C3×C4—52no—
224C22×C3×C4—101no—
225C22×C3×C4C22×D511yescharacteristic
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8—52no—
229C2×C3×C8—101no—
230C2×C3×C8—101no—
231C2×C3×C8C22⋊D512yescomplemented
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—101no—
235C3×C4⋊C4—101no—
236C3×C4⋊C4—204no—
237C3×C42—52no—
238C3×C42—52no—
239C23×C5—22no—
240C23×C5—41no—
241C23×C5—41no—
242C23×C5—42no—
243C23×C5—42no—
244C23×C5C2×C3×D411yescharacteristic
245C22×D5—22no—
246C22×D5—41no—
247C22×D5—41no—
248C22×D5—42no—
249C22×D5—42no—
250C5×D4—22no—
251C5×D4—22no—
252C5×D4—41no—
253C5×D4—41no—
254C2×C4×C5—41no—
255C2×C4×C5—42no—
256C2×C4×C5C22×C3×C411yescharacteristic
257C2×C4×C5C2×C3×D411yescharacteristic
258C2×C4×C5C2×C3×D411yescharacteristic
259C2×C4×C5C2×C3×D411yescharacteristic
260C2×C4×C5C3×#4111yescharacteristic
261C2×C4×C5C3×#4111yescharacteristic
262C22⋊D5—416no—
263C2×Dic5—41no—
264C2×Dic5—42no—
265C2×Dic5C3×C22⋊C414yes—
266C2×Dic5C3×D814yes—
267C2×Dic5C3×SD1614yes—
268D20—22no—
269D20—22no—
270D20—41no—
271D20—41no—
272C5×C8—22no—
273#168—22no—
274C22×D4—51no—
275C22×D4—102no—
276C22×D4C2×C3×D511yescharacteristic
277C22×C8—51no—
278C22×C8C2×C3×D511yescharacteristic
279#127—54no—
280#127—102no—
281C2×C4⋊C4—51no—
282C2×C4⋊C4—102no—
283C2×C4⋊C4C2×C3×D511yescharacteristic
284C2×C42—51no—
285#102—22no—
286#102—102no—
287#102—102no—
288#102—102no—
289C4×C8—102no—
290C2×C3×C5—82no—
291C2×C3×C5#39011yescharacteristic
292C2×C3×C5C2×#10212yes—
293C2×C3×C5#48612yes—
294C2×C3×C5#49211yescharacteristic
295C2×C3×C5#49311yescharacteristic
296C3×D5—82no—
297C23×C3—22no—
298C23×C3—41no—
299C23×C3—42no—
300C23×C3—42no—
301C23×C3—41no—
302C23×C3—102no—
303C23×C3—201no—
304C23×C3—202no—
305C23×C3—202no—
306C23×C3—201no—
307C23×C3D4×D511yescharacteristic
308C3×D4—22no—
309C3×D4—22no—
310C3×D4—41no—
311C3×D4—41no—
312C3×D4—102no—
313C3×D4—102no—
314C3×D4—2016no—
315C3×D4—201no—
316C3×D4—201no—
317C2×C3×C4—42no—
318C2×C3×C4—41no—
319C2×C3×C4—54no—
320C2×C3×C4—54no—
321C2×C3×C4—54no—
322C2×C3×C4—202no—
323C2×C3×C4—201no—
324C2×C3×C4C2×C4×D511yescharacteristic
325C2×C3×C4#70911yescharacteristic
326C2×C3×C4D4×D511yescharacteristic
327C2×C3×C4D4×D511yescharacteristic
328C2×C3×C4#71111yescharacteristic
329C2×C3×C4C2×C22⋊D511yescharacteristic
330C3×C8—22no—
331C3×C8—102no—
332C22×C5—42no—
333C22×C5—44no—
334C22×C5—82no—
335C22×C5—81no—
336C22×C5—81no—
337C22×C5C2×C3×C22⋊C411yescharacteristic
338C22×C5C3×#12411yescharacteristic
339C22×C5C3×#12711yescharacteristic
340C22×C5C2×C3×D812yes—
341C22×C5C2×C3×SD1612yes—
342C2×D5—42no—
343C2×D5—44no—
344C2×D5—82no—
345C2×D5—81no—
346C2×D5—81no—
347C4×C5—81no—
348C4×C5C3×C4×D411yescharacteristic
349C4×C5C3×C4×D411yescharacteristic
350C4×C5C3×#12111yescharacteristic
351C4×C5C3×#12111yescharacteristic
352Dic5—81no—
353Dic5C3×#10218yescomplemented
354C24—21no—
355C24—101no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—52no—
362C2×D4—108no—
363C2×D4—101no—
364C2×D4—101no—
365C2×D4—101no—
366C2×D4—101no—
367C2×D4—101no—
368C2×D4—204no—
369C2×D4—204no—
370C2×D4C3×C4×D512yes—
371C22×C4—21no—
372C22×C4—52no—
373C22×C4—101no—
374C22×C4C22×C3×D511yescharacteristic
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—52no—
378C2×C8—101no—
379C2×C8—101no—
380C2×C8C3×C22⋊D512yescomplemented
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—101no—
384C4⋊C4—101no—
385C4⋊C4—204no—
386C42—52no—
387C42—52no—
388C3×C5#195711yescharacteristic, complemented, Hall
389C22×C3—44no—
390C22×C3—42no—
391C22×C3—82no—
392C22×C3—81no—
393C22×C3—81no—
394C22×C3—204no—
395C22×C3—202no—
396C22×C3—402no—
397C22×C3—401no—
398C22×C3—401no—
399C22×C3D5×C22⋊C411yescharacteristic
400C22×C3#403111yescharacteristic
401C22×C3D5×D812yes—
402C22×C3D5×SD1612yes—
403C22×C3#408611yescharacteristic
404C3×C4—58no—
405C3×C4—81no—
406C3×C4—401no—
407C3×C4#402711yescharacteristic
408C3×C4#403011yescharacteristic
409C3×C4C4×C22⋊D511yescharacteristic
410C3×C4#408511yescharacteristic
411C2×C5—82no—
412C2×C5C3×#39011yescharacteristic
413C2×C5C2×C3×#10212yes—
414C2×C5C3×#48612yes—
415C2×C5C3×#49211yescharacteristic
416C2×C5C3×#49311yescharacteristic
417D5—82no—
418C23—22no—
419C23—41no—
420C23—41no—
421C23—42no—
422C23—42no—
423C23—102no—
424C23—201no—
425C23—201no—
426C23—202no—
427C23—202no—
428C23C3×D4×D511yescharacteristic
429D4—22no—
430D4—22no—
431D4—41no—
432D4—41no—
433D4—102no—
434D4—102no—
435D4—2016no—
436D4—201no—
437D4—201no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—54no—
441C2×C4—54no—
442C2×C4—54no—
443C2×C4—201no—
444C2×C4—202no—
445C2×C4C2×C3×C4×D511yescharacteristic
446C2×C4C3×#70911yescharacteristic
447C2×C4C3×D4×D511yescharacteristic
448C2×C4C3×D4×D511yescharacteristic
449C2×C4C3×#71111yescharacteristic
450C2×C4C2×C3×C22⋊D511yescharacteristic
451C8—22no—
452C8—102no—
453C2×C3—82no—
454C2×C3—402no—
455C2×C3#6504912yes—
456C2×C3D5×#10212yes—
457C2×C3#6524611yescharacteristic
458C2×C3#6544011yescharacteristic
459C2×C3#6546411yescharacteristic
460C5C3×#195711yescharacteristic, complemented, Sylow
461C22—44no—
462C22—42no—
463C22—82no—
464C22—81no—
465C22—81no—
466C22—204no—
467C22—202no—
468C22—402no—
469C22—401no—
470C22—401no—
471C22C3×D5×C22⋊C411yescharacteristic
472C22C3×#403111yescharacteristic
473C22C3×D5×D812yes—
474C22C3×D5×SD1612yes—
475C22C3×#408611yescharacteristic
476C4—58no—
477C4—81no—
478C4—401no—
479C4C3×#402711yescharacteristic
480C4C3×#403011yescharacteristic
481C4C3×C4×C22⋊D511yescharacteristic
482C4C3×#408511yescharacteristic
483C3#1060095011yescharacteristic, direct product factor, Sylow
484C2—82no—
485C2—402no—
486C2C3×#6504912yes—
487C2C3×D5×#10212yes—
488C2C3×#6524611yescharacteristic
489C2C3×#6544011yescharacteristic
490C2C3×#6546411yescharacteristic
subgroupG/H
centerC23×C3D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×#102C2
socleC23×C3×C5C2×D4
prime radicalC2×C3×#4086C2
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×#102D5
hypocenterC5C3×#1957
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#102C2semidirect
3. C2×C3×#3964C2semidirect
4. C2×C3×#3953C2semidirect
5. C2×C3×C8×Dic5C2semidirect
6. C3×#65265C2semidirect
7. C2×C3×#3941C2semidirect
8. #10600950C3direct (N × H)
15. C3×#4086C4semidirect
27. C2×C5×#102C2×C3semidirect
28. C2×#3964C2×C3semidirect
29. C2×#3953C2×C3semidirect
30. C2×C8×Dic5C2×C3semidirect
31. #65265C2×C3semidirect
32. C2×#3941C2×C3semidirect
56. C2×C3×C5×C8D4semidirect
66. C2×C3×#168D4semidirect
71. C2×C3×#102D5semidirect
80. #4086C3×C4semidirect
165. C2×C5×C8C3×D4semidirect
175. C2×#168C3×D4semidirect
180. C2×#102C3×D5semidirect
204. C3×Dic5#102semidirect
231. C2×C3×C8C22⋊D5semidirect
353. Dic5C3×#102semidirect
380. C2×C8C3×C22⋊D5semidirect
388. C3×C5#1957semidirect
460. C5C3×#1957semidirect
483. C3#10600950direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40862
C2×C3×C5×#1022
C2×C3×#39642
C2×C3×#39532
C2×C3×C8×Dic52
C3×#652652
C2×C3×#39412
#106009503
C3×#19575