Finite Group Databasebeta

← C3×#10604005 #14295921

Subgroups — C3×#10604005 #14295921

Order 1920.

600 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5⋊#131C211yesmaximal, characteristic
2C3×#65794C211yesmaximal, characteristic
3C3×#65728C211yesmaximal, characteristic, complemented
4C3×C4×D5⋊C8C211yesmaximal, characteristic, complemented
5C3×D5×#104C211yesmaximal, characteristic
6C3×#64901C211yesmaximal, characteristic, complemented
7C3×#64862C211yesmaximal, characteristic, complemented
8#10604005C311yesmaximal, characteristic, direct product factor, Hall
9C3×D5×#41C2211yescharacteristic
10C3×#4133C412yescomplemented
11C3×#4131—22no—
12C3×#4131C412yescomplemented
13C3×#4130C2211yescharacteristic
14C3×D5⋊M16—21no—
15C3×D5⋊M16C2211yescharacteristic
16C2×C3×D5⋊C8—21no—
17C2×C3×D5⋊C8C2211yescharacteristic
18C2×C3×D5⋊C8C2211yescharacteristic
19C3×D5×M16C2211yescharacteristic
20C3×C42×D5C2211yescharacteristic
21C3×#4009C412yescomplemented
22C3×#4007C412yescomplemented
23C3×C4×#170—22no—
24C3×#3992—21no—
25C3×C8×AGL(1,𝔽5)—21no—
26C3×C5×#104C411yescharacteristic, complemented
27C3×#3969C411yescharacteristic, complemented
28C3×#3957C411yescharacteristic, complemented
29C3×#3937C411yescharacteristic, complemented
30C3×#1764—51nomaximal, Hall
31D5⋊#131C2×C311yescharacteristic
32#65794C2×C311yescharacteristic
33#65728C2×C311yescharacteristic, complemented
34C4×D5⋊C8C2×C311yescharacteristic, complemented
35D5×#104C2×C311yescharacteristic
36#64901C2×C311yescharacteristic, complemented
37#64862C2×C311yescharacteristic, complemented
38C3×C5×#41C2×C411yescharacteristic
39C3×#713C2×C411yescharacteristic
40C3×Q8×D5C2×C411yescharacteristic
41C3×#711—21no—
42C3×#711C2×C411yescharacteristic
43C3×D4×D5—21no—
44C3×D4×D5C2×C411yescharacteristic
45C3×#709—21no—
46C3×#709C2×C411yescharacteristic
47C2×C3×C4×D5—21no—
48C2×C3×C4×D5—21no—
49C2×C3×C4×D5C2311yescharacteristic
50C3×C22⋊AGL(1,𝔽5)—21no—
51C3×#704—21no—
52C3×#704—22no—
53C2×C3×#170—21no—
54C2×C3×#170—22no—
55C2×C3×#170D412yes—
56C3×C4⋊AGL(1,𝔽5)C2×C412yes—
57C3×C4×AGL(1,𝔽5)—21no—
58C3×#700—22no—
59C3×#700C2×C412yes—
60C3×D5⋊C8—21no—
61C3×D5⋊C8—21no—
62C3×D5⋊C8—22no—
63C3×D5⋊C8C2×C412yes—
64C3×D5⋊C8C2×C412yes—
65C3×D5⋊C8D411yescharacteristic
66C3×D5⋊C8D411yescharacteristic
67C3×C5×M16C2×C411yescharacteristic
68C3×C42×C5C2×C411yescharacteristic
69C3×C4×Dic5—21no—
70C3×C4×Dic5C2×C411yescharacteristic
71C3×#681C2×C411yescharacteristic
72C3×#676—21no—
73C3×C8×D5—21no—
74C2×C3×#131—51no—
75C2×C3×#104—51no—
76C3×#416—51no—
77C3×#405—51no—
78C2×C3×C4×C8—51no—
79C3×#341—51no—
80C3×#339—51no—
81D5×#41C22×C311yescharacteristic
82#4133C3×C412yescomplemented
83#4131—22no—
84#4131C3×C412yescomplemented
85#4130C22×C311yescharacteristic
86D5⋊M16—21no—
87D5⋊M16C22×C311yescharacteristic
88C2×D5⋊C8—21no—
89C2×D5⋊C8C22×C311yescharacteristic
90C2×D5⋊C8C22×C311yescharacteristic
91D5×M16C22×C311yescharacteristic
92C42×D5C22×C311yescharacteristic
93#4009C3×C412yescomplemented
94#4007C3×C412yescomplemented
95C4×#170—22no—
96#3992—21no—
97C8×AGL(1,𝔽5)—21no—
98C5×#104C3×C411yescharacteristic, complemented
99#3969C3×C411yescharacteristic, complemented
100#3957C3×C411yescharacteristic, complemented
101#3937C3×C411yescharacteristic, complemented
102#1764—51noSylow
103C22×C3×D5—21no—
104C22×C3×D5#4111yescharacteristic
105C2×C3×AGL(1,𝔽5)—22no—
106C3×C5×Q8C4211yescharacteristic
107C3×C5×D4—21no—
108C3×C5×D4C4211yescharacteristic
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5C22×C411yescharacteristic
112C3×C22⋊D5—21no—
113C3×C22⋊D5—21no—
114C3×C22⋊D5—21no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—21no—
117C2×C3×Dic5C2×D411yescharacteristic
118C3×D20—21no—
119C3×D20C4211yescharacteristic
120C3×C4×D5—24no—
121C3×C4×D5—21no—
122C3×C4×D5—21no—
123C3×C4×D5—21no—
124C3×C4×D5C22×C411yescharacteristic
125C3×C4×D5C22×C411yescharacteristic
126C3×C4×D5C2×D411yescharacteristic
127C3×C4×D5#4111yescharacteristic
128C3×Dic10—21no—
129C3×Dic10C4211yescharacteristic
130C3×#170—22no—
131C3×#170—22no—
132C3×#170C22⋊C412yes—
133C3×#170C22⋊C412yes—
134C3×C5×C8—21no—
135C3×#168—21no—
136C2×C3×#41—51no—
137C3×#131—52no—
138C3×#131—52no—
139C3×#131—102no—
140C2×C3×M16—51no—
141C2×C3×M16—51no—
142C2×C3×M16—101no—
143C22×C3×C8—51no—
144C22×C3×C8—51no—
145C22×C3×C8—101no—
146C3×#117—51no—
147C2×C3×C42—51no—
148C3×#104—51no—
149C3×#104—51no—
150C3×#104—51no—
151C3×#104AGL(1,𝔽5)11yescharacteristic, complemented
152C3×#103—52no—
153C3×#102—52no—
154C3×#97—101no—
155C3×C4×C8—101no—
156C3×C4×C8—102no—
157C5×#41C2×C3×C411yescharacteristic
158#713C2×C3×C411yescharacteristic
159Q8×D5C2×C3×C411yescharacteristic
160#711—21no—
161#711C2×C3×C411yescharacteristic
162D4×D5—21no—
163D4×D5C2×C3×C411yescharacteristic
164#709—21no—
165#709C2×C3×C411yescharacteristic
166C2×C4×D5—21no—
167C2×C4×D5—21no—
168C2×C4×D5C23×C311yescharacteristic
169C22⋊AGL(1,𝔽5)—21no—
170#704—21no—
171#704—22no—
172C2×#170—21no—
173C2×#170—22no—
174C2×#170C3×D412yes—
175C4⋊AGL(1,𝔽5)C2×C3×C412yes—
176C4×AGL(1,𝔽5)—21no—
177#700—22no—
178#700C2×C3×C412yes—
179D5⋊C8—21no—
180D5⋊C8—21no—
181D5⋊C8—22no—
182D5⋊C8C2×C3×C412yes—
183D5⋊C8C2×C3×C412yes—
184D5⋊C8C3×D411yescharacteristic
185D5⋊C8C3×D411yescharacteristic
186C5×M16C2×C3×C411yescharacteristic
187C42×C5C2×C3×C411yescharacteristic
188C4×Dic5—21no—
189C4×Dic5C2×C3×C411yescharacteristic
190#681C2×C3×C411yescharacteristic
191#676—21no—
192C8×D5—21no—
193C2×#131—51no—
194C2×#104—51no—
195#416—51no—
196#405—51no—
197C2×C4×C8—51no—
198#341—51no—
199#339—51no—
200C22×C3×C5—21no—
201C22×C3×C5C4×D411yescharacteristic
202C2×C3×D5—22no—
203C2×C3×D5—21no—
204C2×C3×D5—42no—
205C2×C3×D5#11711yescharacteristic
206C2×C3×D5C4×D411yescharacteristic
207C3×AGL(1,𝔽5)—42no—
208C3×C4×C5—22no—
209C3×C4×C5—21no—
210C3×C4×C5C2×C4211yescharacteristic
211C3×C4×C5C4×D411yescharacteristic
212C3×Dic5—22no—
213C3×Dic5—21no—
214C3×Dic5C2×C22⋊C411yescharacteristic
215C3×Dic5C4×D411yescharacteristic
216C3×#41—51no—
217C3×#41—51no—
218C3×#41—51no—
219C3×#41—101no—
220C3×#41—101no—
221C3×#41C2×AGL(1,𝔽5)11yescharacteristic
222C2×C3×Q8—51no—
223C2×C3×D4—51no—
224C2×C3×D4—101no—
225C22×C3×C4—51no—
226C22×C3×C4—101no—
227C22×C3×C4—101no—
228C3×M16—52no—
229C3×M16—51no—
230C3×M16—101no—
231C3×M16—102no—
232C3×M16—102no—
233C3×M16—101no—
234C3×M16C2×AGL(1,𝔽5)11yescharacteristic
235C2×C3×C8—51no—
236C2×C3×C8—52no—
237C2×C3×C8—51no—
238C2×C3×C8—52no—
239C2×C3×C8—52no—
240C2×C3×C8—101no—
241C2×C3×C8—102no—
242C2×C3×C8—102no—
243C2×C3×C8—101no—
244C2×C3×C8—101no—
245C2×C3×C8—101no—
246C3×C4⋊C4—52no—
247C3×C22⋊C4—101no—
248C3×C42—51no—
249C3×C42—101no—
250C3×C42—101no—
251C3×C42C2×AGL(1,𝔽5)11yescharacteristic
252C22×D5—21no—
253C22×D5C3×#4111yescharacteristic
254C2×AGL(1,𝔽5)—22no—
255C5×Q8C3×C4211yescharacteristic
256C5×D4—21no—
257C5×D4C3×C4211yescharacteristic
258C2×C4×C5—21no—
259C2×C4×C5—21no—
260C2×C4×C5C22×C3×C411yescharacteristic
261C22⋊D5—21no—
262C22⋊D5—21no—
263C22⋊D5—21no—
264C2×Dic5—21no—
265C2×Dic5—21no—
266C2×Dic5C2×C3×D411yescharacteristic
267D20—21no—
268D20C3×C4211yescharacteristic
269C4×D5—24no—
270C4×D5—21no—
271C4×D5—21no—
272C4×D5—21no—
273C4×D5C22×C3×C411yescharacteristic
274C4×D5C22×C3×C411yescharacteristic
275C4×D5C2×C3×D411yescharacteristic
276C4×D5C3×#4111yescharacteristic
277Dic10—21no—
278Dic10C3×C4211yescharacteristic
279#170—22no—
280#170—22no—
281#170C3×C22⋊C412yes—
282#170C3×C22⋊C412yes—
283C5×C8—21no—
284#168—21no—
285C2×#41—51no—
286#131—52no—
287#131—52no—
288#131—102no—
289C2×M16—51no—
290C2×M16—51no—
291C2×M16—101no—
292C22×C8—51no—
293C22×C8—51no—
294C22×C8—101no—
295#117—51no—
296C2×C42—51no—
297#104—51no—
298#104—51no—
299#104—51no—
300#104C3×AGL(1,𝔽5)11yescharacteristic, complemented
301#103—52no—
302#102—52no—
303#97—101no—
304C4×C8—102no—
305C4×C8—101no—
306C2×C3×C5—21no—
307C2×C3×C5—41no—
308C2×C3×C5C4×C22⋊C411yescharacteristic
309C3×D5—21no—
310C3×D5—41no—
311C3×D5#44312yes—
312C23×C3—51no—
313C23×C3—101no—
314C3×Q8—51no—
315C3×Q8—101no—
316C3×Q8C4×AGL(1,𝔽5)11yescharacteristic
317C3×D4—21no—
318C3×D4—51no—
319C3×D4—101no—
320C3×D4—101no—
321C3×D4—101no—
322C3×D4—101no—
323C3×D4C4×AGL(1,𝔽5)11yescharacteristic
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—51no—
327C2×C3×C4—51no—
328C2×C3×C4—51no—
329C2×C3×C4—51no—
330C2×C3×C4—51no—
331C2×C3×C4—101no—
332C2×C3×C4—101no—
333C2×C3×C4—104no—
334C2×C3×C4—101no—
335C2×C3×C4—101no—
336C2×C3×C4—101no—
337C2×C3×C4—102no—
338C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
339C3×C8—21no—
340C3×C8—52no—
341C3×C8—52no—
342C3×C8—102no—
343C3×C8—102no—
344C3×C8—101no—
345C22×C5—21no—
346C22×C5C3×C4×D411yescharacteristic
347C2×D5—22no—
348C2×D5—21no—
349C2×D5—42no—
350C2×D5C3×#11711yescharacteristic
351C2×D5C3×C4×D411yescharacteristic
352AGL(1,𝔽5)—42no—
353C4×C5—22no—
354C4×C5—21no—
355C4×C5C2×C3×C4211yescharacteristic
356C4×C5C3×C4×D411yescharacteristic
357Dic5—22no—
358Dic5—21no—
359Dic5C2×C3×C22⋊C411yescharacteristic
360Dic5C3×C4×D411yescharacteristic
361#41—51no—
362#41—51no—
363#41—51no—
364#41—101no—
365#41—101no—
366#41C2×C3×AGL(1,𝔽5)11yescharacteristic
367C2×Q8—51no—
368C2×D4—51no—
369C2×D4—101no—
370C22×C4—51no—
371C22×C4—101no—
372C22×C4—101no—
373M16—52no—
374M16—51no—
375M16—101no—
376M16—102no—
377M16—102no—
378M16—101no—
379M16C2×C3×AGL(1,𝔽5)11yescharacteristic
380C2×C8—51no—
381C2×C8—52no—
382C2×C8—51no—
383C2×C8—52no—
384C2×C8—52no—
385C2×C8—101no—
386C2×C8—102no—
387C2×C8—102no—
388C2×C8—101no—
389C2×C8—101no—
390C2×C8—101no—
391C4⋊C4—52no—
392C22⋊C4—101no—
393C42—51no—
394C42—101no—
395C42—101no—
396C42C2×C3×AGL(1,𝔽5)11yescharacteristic
397C3×C5#176411yescharacteristic, complemented, Hall
398C22×C3—21no—
399C22×C3—51no—
400C22×C3—51no—
401C22×C3—102no—
402C22×C3—101no—
403C22×C3—202no—
404C22×C3D4×AGL(1,𝔽5)11yescharacteristic
405C3×C4—22no—
406C3×C4—21no—
407C3×C4—51no—
408C3×C4—51no—
409C3×C4—102no—
410C3×C4—101no—
411C3×C4—202no—
412C3×C4C2×C4×AGL(1,𝔽5)11yescharacteristic
413C3×C4D4×AGL(1,𝔽5)11yescharacteristic
414C2×C5—21no—
415C2×C5—41no—
416C2×C5C3×C4×C22⋊C411yescharacteristic
417D5—21no—
418D5—41no—
419D5C3×#44312yes—
420C23—51no—
421C23—101no—
422Q8—51no—
423Q8—101no—
424Q8C3×C4×AGL(1,𝔽5)11yescharacteristic
425D4—21no—
426D4—51no—
427D4—101no—
428D4—101no—
429D4—101no—
430D4—101no—
431D4C3×C4×AGL(1,𝔽5)11yescharacteristic
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—51no—
435C2×C4—51no—
436C2×C4—51no—
437C2×C4—51no—
438C2×C4—51no—
439C2×C4—101no—
440C2×C4—101no—
441C2×C4—104no—
442C2×C4—101no—
443C2×C4—101no—
444C2×C4—101no—
445C2×C4—102no—
446C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
447C8—21no—
448C8—52no—
449C8—52no—
450C8—102no—
451C8—102no—
452C8—101no—
453C2×C3—21no—
454C2×C3—41no—
455C2×C3—52no—
456C2×C3—101no—
457C2×C3—201no—
458C2×C3C22⋊C4×AGL(1,𝔽5)11yescharacteristic
459C5C3×#176411yescharacteristic, complemented, Sylow
460C22—21no—
461C22—51no—
462C22—51no—
463C22—102no—
464C22—101no—
465C22—202no—
466C22C3×D4×AGL(1,𝔽5)11yescharacteristic
467C4—22no—
468C4—21no—
469C4—51no—
470C4—51no—
471C4—102no—
472C4—101no—
473C4—202no—
474C4C2×C3×C4×AGL(1,𝔽5)11yescharacteristic
475C4C3×D4×AGL(1,𝔽5)11yescharacteristic
476C3#1060400511yescharacteristic, direct product factor, Sylow
477C2—21no—
478C2—41no—
479C2—52no—
480C2—101no—
481C2—201no—
482C2C3×C22⋊C4×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC3×C4D4×AGL(1,𝔽5)
commutatorC4×C5C2×C3×C42
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#104C4
socleC2×C3×C5C4×C22⋊C4
prime radicalC3×D5×#41C22
cosocleC2×C4×D5C23×C3
hypercenterC3×#104AGL(1,𝔽5)
hypocenterC5C3×#1764
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×#104

Complements

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

NH ≅ G/Ntype
3. C3×#65728C2semidirect
4. C3×C4×D5⋊C8C2semidirect
6. C3×#64901C2semidirect
7. C3×#64862C2semidirect
8. #10604005C3direct (N × H)
10. C3×#4133C4semidirect
12. C3×#4131C4semidirect
21. C3×#4009C4semidirect
22. C3×#4007C4semidirect
26. C3×C5×#104C4semidirect
27. C3×#3969C4semidirect
28. C3×#3957C4semidirect
29. C3×#3937C4semidirect
33. #65728C2×C3semidirect
34. C4×D5⋊C8C2×C3semidirect
36. #64901C2×C3semidirect
37. #64862C2×C3semidirect
82. #4133C3×C4semidirect
84. #4131C3×C4semidirect
93. #4009C3×C4semidirect
94. #4007C3×C4semidirect
98. C5×#104C3×C4semidirect
99. #3969C3×C4semidirect
100. #3957C3×C4semidirect
101. #3937C3×C4semidirect
151. C3×#104AGL(1,𝔽5)semidirect
300. #104C3×AGL(1,𝔽5)semidirect
397. C3×C5#1764semidirect
459. C5C3×#1764semidirect
476. C3#10604005direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5⋊#1312
C3×#657942
C3×#657282
C3×C4×D5⋊C82
C3×D5×#1042
C3×#649012
C3×#648622
#106040053
C3×#17645