Finite Group Databasebeta

← C3×#10601150 #14306028

Subgroups — C3×#10601150 #14306028

Order 1920.

640 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66166C211yesmaximal, characteristic
2C2×C3×C5×#104C211yesmaximal, characteristic, complemented
3C2×C3×#3969C211yesmaximal, characteristic, complemented
4C2×C3×#3957C211yesmaximal, characteristic, complemented
5C3×#65407C211yesmaximal, characteristic, complemented
6C3×#65221C211yesmaximal, characteristic, complemented
7C2×C3×#3937C211yesmaximal, characteristic, complemented
8#10601150C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13C3×#4093C411yescharacteristic, complemented
14C3×#4090C411yescharacteristic, complemented
15C3×#4086C411yescharacteristic, complemented
16C3×#4085—22no—
17C3×#4082C411yescharacteristic, complemented
18C3×C4×C22⋊D5—22no—
19C2×C3×C4×Dic5C2211yescharacteristic
20C2×C3×C4×Dic5C2211yescharacteristic
21C2×C3×#681C2211yescharacteristic
22C3×C5×#104—22no—
23C3×#3969—22no—
24C3×#3963—22no—
25C3×#3957—22no—
26C3×#3946—22no—
27C3×#3937—22no—
28C3×#1963—51nomaximal, Hall
29#66166C2×C311yescharacteristic
30C2×C5×#104C2×C311yescharacteristic, complemented
31C2×#3969C2×C311yescharacteristic, complemented
32C2×#3957C2×C311yescharacteristic, complemented
33#65407C2×C311yescharacteristic, complemented
34#65221C2×C311yescharacteristic, complemented
35C2×#3937C2×C311yescharacteristic, complemented
36C3×C5×#41—21no—
37C3×C5×#41—21no—
38C3×C5×#41—21no—
39C3×C5×#41—21no—
40C2×C3×C5×Q8C2×C411yescharacteristic
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4C2×C411yescharacteristic
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5C2311yescharacteristic
46C2×C3×C22⋊D5—21no—
47C2×C3×C22⋊D5—22no—
48C22×C3×Dic5—21no—
49C22×C3×Dic5D412yes—
50C3×#709—21no—
51C3×#709—21no—
52C3×#709—21no—
53C3×#709—21no—
54C2×C3×D20C2×C411yescharacteristic
55C2×C3×C4×D5—21no—
56C2×C3×Dic10C2×C411yescharacteristic
57C3×C5×M16—21no—
58C3×C5×M16—21no—
59C2×C3×C5×C8—21no—
60C3×C42×C5—21no—
61C3×C42×C5D412yescomplemented
62C3×C22⋊Dic5—22no—
63C3×#685—22no—
64C3×#683—22no—
65C3×C4×Dic5—21no—
66C3×C4×Dic5C2×C411yescharacteristic
67C3×C4×Dic5C2×C411yescharacteristic
68C3×C4×Dic5D412yes—
69C3×C4×Dic5D412yescomplemented
70C3×#681—21no—
71C3×#681—21no—
72C2×C3×#168—21no—
73C3×#532—51no—
74C3×#423—51no—
75C2×C3×#104—51no—
76C2×C3×#104—51no—
77C2×C3×#104—51no—
78C2×C3×#104D511yescharacteristic, complemented
79C3×#376—51no—
80C2×C5×#41C22×C311yescharacteristic
81C2×#709C22×C311yescharacteristic
82C2×C5×M16C22×C311yescharacteristic
83C2×C42×C5C22×C311yescharacteristic
84#4093C3×C411yescharacteristic, complemented
85#4090C3×C411yescharacteristic, complemented
86#4086C3×C411yescharacteristic, complemented
87#4085—22no—
88#4082C3×C411yescharacteristic, complemented
89C4×C22⋊D5—22no—
90C2×C4×Dic5C22×C311yescharacteristic
91C2×C4×Dic5C22×C311yescharacteristic
92C2×#681C22×C311yescharacteristic
93C5×#104—22no—
94#3969—22no—
95#3963—22no—
96#3957—22no—
97#3946—22no—
98#3937—22no—
99#1963—51noSylow
100C23×C3×C5—21no—
101C23×C3×C5C2×D411yescharacteristic
102C22×C3×D5—21no—
103C3×C5×Q8—21no—
104C3×C5×Q8—21no—
105C3×C5×D4—21no—
106C3×C5×D4—21no—
107C3×C5×D4—41no—
108C3×C5×D4—41no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—22no—
111C2×C3×C4×C5—42no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5C22×C411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5#4111yescharacteristic
119C2×C3×C4×C5#4111yescharacteristic
120C3×C22⋊D5—44no—
121C3×C22⋊D5—41no—
122C3×C22⋊D5—41no—
123C2×C3×Dic5—21no—
124C2×C3×Dic5—22no—
125C2×C3×Dic5—42no—
126C2×C3×Dic5—42no—
127C2×C3×Dic5C22⋊C412yes—
128C2×C3×Dic5C22⋊C412yes—
129C3×D20—21no—
130C3×D20—21no—
131C3×C4×D5—41no—
132C3×C4×D5—41no—
133C3×Dic10—21no—
134C3×Dic10—21no—
135C3×C5×C8—41no—
136C3×#168—41no—
137C2×C3×#41—51no—
138C2×C3×#41C2×D511yescharacteristic
139C2×C3×M16—51no—
140C2×C3×M16C2×D511yescharacteristic
141C3×C4⋊Q8—51no—
142C3×#127—51no—
143C3×#124—51no—
144C3×#124—51no—
145C3×#121—102no—
146C3×C4×D4—102no—
147C2×C3×C42—51no—
148C2×C3×C42—51no—
149C2×C3×C42C2×D511yescharacteristic
150C3×C4⋊C8—102no—
151C3×#104—22no—
152C3×#104—102no—
153C3×#104—102no—
154C3×#104—102no—
155C3×#95—102no—
156C5×#41—21no—
157C5×#41—21no—
158C5×#41—21no—
159C5×#41—21no—
160C2×C5×Q8C2×C3×C411yescharacteristic
161C2×C5×D4—21no—
162C2×C5×D4C2×C3×C411yescharacteristic
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5C23×C311yescharacteristic
166C2×C22⋊D5—21no—
167C2×C22⋊D5—22no—
168C22×Dic5—21no—
169C22×Dic5C3×D412yes—
170#709—21no—
171#709—21no—
172#709—21no—
173#709—21no—
174C2×D20C2×C3×C411yescharacteristic
175C2×C4×D5—21no—
176C2×Dic10C2×C3×C411yescharacteristic
177C5×M16—21no—
178C5×M16—21no—
179C2×C5×C8—21no—
180C42×C5—21no—
181C42×C5C3×D412yescomplemented
182C22⋊Dic5—22no—
183#685—22no—
184#683—22no—
185C4×Dic5—21no—
186C4×Dic5C2×C3×C411yescharacteristic
187C4×Dic5C2×C3×C411yescharacteristic
188C4×Dic5C3×D412yes—
189C4×Dic5C3×D412yescomplemented
190#681—21no—
191#681—21no—
192C2×#168—21no—
193#532—51no—
194#423—51no—
195C2×#104—51no—
196C2×#104—51no—
197C2×#104—51no—
198C2×#104C3×D511yescharacteristic, complemented
199#376—51no—
200C22×C3×C5—22no—
201C22×C3×C5—41no—
202C22×C3×C5—42no—
203C22×C3×C5C2×C22⋊C411yescharacteristic
204C22×C3×C5#12111yescharacteristic
205C22×C3×C5#12111yescharacteristic
206C2×C3×D5—41no—
207C2×C3×D5—42no—
208C3×C4×C5—42no—
209C3×C4×C5—41no—
210C3×C4×C5C4×D411yescharacteristic
211C3×C4×C5C4×D411yescharacteristic
212C3×C4×C5#12411yescharacteristic
213C3×C4×C5#12711yescharacteristic
214C3×Dic5—22no—
215C3×Dic5—22no—
216C3×Dic5—42no—
217C3×Dic5—41no—
218C3×#41—21no—
219C3×#41—21no—
220C3×#41—21no—
221C3×#41—21no—
222C3×#41—101no—
223C3×#41—101no—
224C3×#41—101no—
225C3×#41—101no—
226C2×C3×Q8—51no—
227C2×C3×Q8C4×D511yescharacteristic
228C2×C3×D4—21no—
229C2×C3×D4—51no—
230C2×C3×D4—102no—
231C2×C3×D4—101no—
232C2×C3×D4C4×D511yescharacteristic
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—52no—
236C22×C3×C4—101no—
237C22×C3×C4—101no—
238C22×C3×C4C22×D511yescharacteristic
239C3×M16—21no—
240C3×M16—21no—
241C3×M16—101no—
242C3×M16—101no—
243C2×C3×C8—21no—
244C2×C3×C8—101no—
245C3×C4⋊C4—102no—
246C3×C22⋊C4—102no—
247C3×C22⋊C4—102no—
248C3×C42—21no—
249C3×C42—51no—
250C3×C42—51no—
251C3×C42—52no—
252C3×C42—52no—
253C3×C42—101no—
254C3×C42C22⋊D512yescomplemented
255C23×C5—21no—
256C23×C5C2×C3×D411yescharacteristic
257C22×D5—21no—
258C5×Q8—21no—
259C5×Q8—21no—
260C5×D4—21no—
261C5×D4—21no—
262C5×D4—41no—
263C5×D4—41no—
264C2×C4×C5—21no—
265C2×C4×C5—22no—
266C2×C4×C5—42no—
267C2×C4×C5—41no—
268C2×C4×C5—41no—
269C2×C4×C5C22×C3×C411yescharacteristic
270C2×C4×C5C2×C3×D411yescharacteristic
271C2×C4×C5C2×C3×D411yescharacteristic
272C2×C4×C5C2×C3×D411yescharacteristic
273C2×C4×C5C3×#4111yescharacteristic
274C2×C4×C5C3×#4111yescharacteristic
275C22⋊D5—44no—
276C22⋊D5—41no—
277C22⋊D5—41no—
278C2×Dic5—21no—
279C2×Dic5—22no—
280C2×Dic5—42no—
281C2×Dic5—42no—
282C2×Dic5C3×C22⋊C412yes—
283C2×Dic5C3×C22⋊C412yes—
284D20—21no—
285D20—21no—
286C4×D5—41no—
287C4×D5—41no—
288Dic10—21no—
289Dic10—21no—
290C5×C8—41no—
291#168—41no—
292C2×#41—51no—
293C2×#41C2×C3×D511yescharacteristic
294C2×M16—51no—
295C2×M16C2×C3×D511yescharacteristic
296C4⋊Q8—51no—
297#127—51no—
298#124—51no—
299#124—51no—
300#121—102no—
301C4×D4—102no—
302C2×C42—51no—
303C2×C42—51no—
304C2×C42C2×C3×D511yescharacteristic
305C4⋊C8—102no—
306#104—22no—
307#104—102no—
308#104—102no—
309#104—102no—
310#95—102no—
311C2×C3×C5—21no—
312C2×C3×C5—21no—
313C2×C3×C5—81no—
314C2×C3×C5#39011yescharacteristic
315C2×C3×C5#42112yes—
316C3×D5—81no—
317C23×C3—21no—
318C23×C3—101no—
319C23×C3D4×D511yescharacteristic
320C3×Q8—21no—
321C3×Q8—21no—
322C3×Q8—101no—
323C3×Q8—101no—
324C3×D4—21no—
325C3×D4—21no—
326C3×D4—41no—
327C3×D4—41no—
328C3×D4—101no—
329C3×D4—101no—
330C3×D4—204no—
331C3×D4—201no—
332C3×D4—201no—
333C2×C3×C4—21no—
334C2×C3×C4—22no—
335C2×C3×C4—42no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—52no—
339C2×C3×C4—52no—
340C2×C3×C4—101no—
341C2×C3×C4—102no—
342C2×C3×C4—202no—
343C2×C3×C4—202no—
344C2×C3×C4—201no—
345C2×C3×C4—201no—
346C2×C3×C4C2×C4×D511yescharacteristic
347C2×C3×C4#70911yescharacteristic
348C2×C3×C4D4×D511yescharacteristic
349C2×C3×C4D4×D511yescharacteristic
350C2×C3×C4#71111yescharacteristic
351C2×C3×C4C2×C22⋊D511yescharacteristic
352C3×C8—41no—
353C3×C8—201no—
354C22×C5—22no—
355C22×C5—41no—
356C22×C5—42no—
357C22×C5C2×C3×C22⋊C411yescharacteristic
358C22×C5C3×#12111yescharacteristic
359C22×C5C3×#12111yescharacteristic
360C2×D5—41no—
361C2×D5—42no—
362C4×C5—42no—
363C4×C5—41no—
364C4×C5C3×C4×D411yescharacteristic
365C4×C5C3×C4×D411yescharacteristic
366C4×C5C3×#12411yescharacteristic
367C4×C5C3×#12711yescharacteristic
368Dic5—22no—
369Dic5—22no—
370Dic5—42no—
371Dic5—41no—
372#41—21no—
373#41—21no—
374#41—21no—
375#41—21no—
376#41—101no—
377#41—101no—
378#41—101no—
379#41—101no—
380C2×Q8—51no—
381C2×Q8C3×C4×D511yescharacteristic
382C2×D4—21no—
383C2×D4—51no—
384C2×D4—102no—
385C2×D4—101no—
386C2×D4C3×C4×D511yescharacteristic
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—52no—
390C22×C4—101no—
391C22×C4—101no—
392C22×C4C22×C3×D511yescharacteristic
393M16—21no—
394M16—21no—
395M16—101no—
396M16—101no—
397C2×C8—21no—
398C2×C8—101no—
399C4⋊C4—102no—
400C22⋊C4—102no—
401C22⋊C4—102no—
402C42—21no—
403C42—51no—
404C42—51no—
405C42—52no—
406C42—52no—
407C42—101no—
408C42C3×C22⋊D512yescomplemented
409C3×C5#196311yescharacteristic, complemented, Hall
410C22×C3—22no—
411C22×C3—42no—
412C22×C3—41no—
413C22×C3—202no—
414C22×C3—201no—
415C22×C3D5×C22⋊C411yescharacteristic
416C22×C3#403011yescharacteristic
417C22×C3#408511yescharacteristic
418C3×C4—42no—
419C3×C4—41no—
420C3×C4—102no—
421C3×C4—102no—
422C3×C4—202no—
423C3×C4—201no—
424C3×C4#402711yescharacteristic
425C3×C4#403111yescharacteristic
426C3×C4C4×C22⋊D511yescharacteristic
427C3×C4#408611yescharacteristic
428C2×C5—21no—
429C2×C5—21no—
430C2×C5—81no—
431C2×C5C3×#39011yescharacteristic
432C2×C5C3×#42112yes—
433D5—81no—
434C23—21no—
435C23—101no—
436C23C3×D4×D511yescharacteristic
437Q8—21no—
438Q8—21no—
439Q8—101no—
440Q8—101no—
441D4—21no—
442D4—21no—
443D4—41no—
444D4—41no—
445D4—101no—
446D4—101no—
447D4—204no—
448D4—201no—
449D4—201no—
450C2×C4—22no—
451C2×C4—21no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—52no—
456C2×C4—52no—
457C2×C4—101no—
458C2×C4—102no—
459C2×C4—202no—
460C2×C4—202no—
461C2×C4—201no—
462C2×C4—201no—
463C2×C4C2×C3×C4×D511yescharacteristic
464C2×C4C3×#70911yescharacteristic
465C2×C4C3×D4×D511yescharacteristic
466C2×C4C3×D4×D511yescharacteristic
467C2×C4C3×#71111yescharacteristic
468C2×C4C2×C3×C22⋊D511yescharacteristic
469C8—41no—
470C8—201no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—81no—
474C2×C3—401no—
475C2×C3#6511012yes—
476C2×C3#6524611yescharacteristic
477C5C3×#196311yescharacteristic, complemented, Sylow
478C22—22no—
479C22—42no—
480C22—41no—
481C22—202no—
482C22—201no—
483C22C3×D5×C22⋊C411yescharacteristic
484C22C3×#403011yescharacteristic
485C22C3×#408511yescharacteristic
486C4—42no—
487C4—41no—
488C4—102no—
489C4—102no—
490C4—202no—
491C4—201no—
492C4C3×#402711yescharacteristic
493C4C3×#403111yescharacteristic
494C4C3×C4×C22⋊D511yescharacteristic
495C4C3×#408611yescharacteristic
496C3#1060115011yescharacteristic, direct product factor, Sylow
497C2—21no—
498C2—21no—
499C2—81no—
500C2—401no—
501C2C3×#6511012yes—
502C2C3×#6524611yescharacteristic
subgroupG/H
centerC2×C3×C4D4×D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C5×#104C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66166C2
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×#104D5
hypocenterC5C3×#1963
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#104

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#104C2semidirect
3. C2×C3×#3969C2semidirect
4. C2×C3×#3957C2semidirect
5. C3×#65407C2semidirect
6. C3×#65221C2semidirect
7. C2×C3×#3937C2semidirect
8. #10601150C3direct (N × H)
13. C3×#4093C4semidirect
14. C3×#4090C4semidirect
15. C3×#4086C4semidirect
17. C3×#4082C4semidirect
30. C2×C5×#104C2×C3semidirect
31. C2×#3969C2×C3semidirect
32. C2×#3957C2×C3semidirect
33. #65407C2×C3semidirect
34. #65221C2×C3semidirect
35. C2×#3937C2×C3semidirect
61. C3×C42×C5D4semidirect
69. C3×C4×Dic5D4semidirect
78. C2×C3×#104D5semidirect
84. #4093C3×C4semidirect
85. #4090C3×C4semidirect
86. #4086C3×C4semidirect
88. #4082C3×C4semidirect
181. C42×C5C3×D4semidirect
189. C4×Dic5C3×D4semidirect
198. C2×#104C3×D5semidirect
254. C3×C42C22⋊D5semidirect
408. C42C3×C22⋊D5semidirect
409. C3×C5#1963semidirect
477. C5C3×#1963semidirect
496. C3#10601150direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661662
C2×C3×C5×#1042
C2×C3×#39692
C2×C3×#39572
C3×#654072
C3×#652212
C2×C3×#39372
#106011503
C3×#19635