Finite Group Databasebeta

← C3×#10599925 #14316683

Subgroups — C3×#10599925 #14316683

Order 1920.

516 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65921C211yesmaximal, characteristic, complemented
2C3×#65321C211yesmaximal, characteristic
3C3×#65035C211yesmaximal, characteristic, complemented
4C3×#65031C211yesmaximal, characteristic, complemented
5C3×C5×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
6C3×#64696C211yesmaximal, characteristic, complemented
7C3×#64693C211yesmaximal, characteristic, complemented
8#10599925C311yesmaximal, characteristic, direct product factor, Hall
9C3×#4144C2211yescharacteristic
10C3×C5×#120C2211yescharacteristic
11C3×#4099—21no—
12C2×C3×C22⋊Dic5—21no—
13C3×#4082C2211yescharacteristic
14C3×#4081—21no—
15C3×#4081C2211yescharacteristic
16C3×D4×Dic5—21no—
17C3×#4055—21no—
18C3×#4032—21no—
19C3×#4025—21no—
20C3×#4024—21no—
21C3×#4023—21no—
22C3×C5×#100C2211yescharacteristic
23C3×C5×#99C2211yescharacteristic
24C3×#3966C2211yescharacteristic
25C3×#3957—21no—
26C3×#3938—21no—
27C3×#3938—21no—
28C3×#2197—51nomaximal, Hall
29#65921C2×C311yescharacteristic, complemented
30#65321C2×C311yescharacteristic
31#65035C2×C311yescharacteristic, complemented
32#65031C2×C311yescharacteristic, complemented
33C5×AΣL(1,𝔽16)C2×C311yescharacteristic, complemented
34#64696C2×C311yescharacteristic, complemented
35#64693C2×C311yescharacteristic, complemented
36C24×C3×C5D411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4C2311yescharacteristic
39C2×C3×C22⋊D5—21no—
40C2×C3×C22⋊D5—21no—
41C2×C3×C22⋊D5—41no—
42C22×C3×Dic5—21no—
43C22×C3×Dic5—21no—
44C22×C3×Dic5D411yescharacteristic, complemented
45C3×#711—41no—
46C3×D4×D5—41no—
47C3×#709—21no—
48C2×C3×Dic10D411yescharacteristic, complemented
49C3×C5×M16—21no—
50C3×C5×C22⋊C4—21no—
51C3×C5×C22⋊C4—21no—
52C3×C5×C22⋊C4D411yescharacteristic
53C3×C22⋊Dic5—21no—
54C3×C22⋊Dic5—21no—
55C3×C22⋊Dic5—21no—
56C3×C22⋊Dic5—21no—
57C3×C22⋊Dic5—21no—
58C3×C22⋊Dic5—21no—
59C3×C22⋊Dic5—41no—
60C3×C22⋊Dic5D411yescharacteristic, complemented
61C3×#685—41no—
62C3×C4⋊Dic5—21no—
63C3×C4⋊Dic5—41no—
64C3×#683—21no—
65C3×#683—21no—
66C3×#683—21no—
67C3×C4×Dic5—21no—
68C3×C4×Dic5D411yescharacteristic, complemented
69C3×Dic20—41no—
70C3×#677—41no—
71C3×#551—51no—
72C3×#458—51no—
73C3×B(4,𝔽2)—51no—
74C3×#455—51no—
75C3×#354—51no—
76C3×#352—51no—
77C3×AΣL(1,𝔽16)D511yescharacteristic, complemented
78#4144C22×C311yescharacteristic
79C5×#120C22×C311yescharacteristic
80#4099—21no—
81C2×C22⋊Dic5—21no—
82#4082C22×C311yescharacteristic
83#4081—21no—
84#4081C22×C311yescharacteristic
85D4×Dic5—21no—
86#4055—21no—
87#4032—21no—
88#4025—21no—
89#4024—21no—
90#4023—21no—
91C5×#100C22×C311yescharacteristic
92C5×#99C22×C311yescharacteristic
93#3966C22×C311yescharacteristic
94#3957—21no—
95#3938—21no—
96#3938—21no—
97#2197—51noSylow
98C23×C3×C5—21no—
99C23×C3×C5—41no—
100C23×C3×C5—42no—
101C23×C3×C5C2×D411yescharacteristic
102C23×C3×C5C2×D411yescharacteristic
103C22×C3×D5—21no—
104C22×C3×D5—21no—
105C3×C5×D4—41no—
106C3×C5×D4—42no—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5C2×D411yescharacteristic
110C3×C22⋊D5—41no—
111C3×C22⋊D5—41no—
112C3×C22⋊D5—41no—
113C3×C22⋊D5—82no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—21no—
117C2×C3×Dic5—21no—
118C2×C3×Dic5—21no—
119C2×C3×Dic5—21no—
120C2×C3×Dic5—42no—
121C2×C3×Dic5—41no—
122C2×C3×Dic5—41no—
123C2×C3×Dic5—81no—
124C3×D20—21no—
125C3×C4×D5—41no—
126C3×Dic10—21no—
127C3×Dic10—41no—
128C3×C5×C8—41no—
129C3×H(5,𝔽2)—51no—
130C3×#137—101no—
131C3×#126—101no—
132C3×#124—51no—
133C3×#123—51no—
134C3×#123—101no—
135C3×#123—101no—
136C3×C22⋊Q8—101no—
137C3×#120—101no—
138C3×#120C2×D511yescharacteristic
139C3×C4×D4—101no—
140C3×#117—101no—
141C2×C3×C22⋊C4—101no—
142C3×#104—101no—
143C3×#100C2×D511yescharacteristic
144C3×#99—51no—
145C3×#99—101no—
146C3×#99—101no—
147C3×#99C2×D511yescharacteristic
148C24×C5C3×D411yescharacteristic
149C2×C5×D4—21no—
150C2×C5×D4C23×C311yescharacteristic
151C2×C22⋊D5—21no—
152C2×C22⋊D5—21no—
153C2×C22⋊D5—41no—
154C22×Dic5—21no—
155C22×Dic5—21no—
156C22×Dic5C3×D411yescharacteristic, complemented
157#711—41no—
158D4×D5—41no—
159#709—21no—
160C2×Dic10C3×D411yescharacteristic, complemented
161C5×M16—21no—
162C5×C22⋊C4—21no—
163C5×C22⋊C4—21no—
164C5×C22⋊C4C3×D411yescharacteristic
165C22⋊Dic5—21no—
166C22⋊Dic5—21no—
167C22⋊Dic5—21no—
168C22⋊Dic5—21no—
169C22⋊Dic5—21no—
170C22⋊Dic5—21no—
171C22⋊Dic5—41no—
172C22⋊Dic5C3×D411yescharacteristic, complemented
173#685—41no—
174C4⋊Dic5—21no—
175C4⋊Dic5—41no—
176#683—21no—
177#683—21no—
178#683—21no—
179C4×Dic5—21no—
180C4×Dic5C3×D411yescharacteristic, complemented
181Dic20—41no—
182#677—41no—
183#551—51no—
184#458—51no—
185B(4,𝔽2)—51no—
186#455—51no—
187#354—51no—
188#352—51no—
189AΣL(1,𝔽16)C3×D511yescharacteristic, complemented
190C22×C3×C5—22no—
191C22×C3×C5—21no—
192C22×C3×C5—21no—
193C22×C3×C5—41no—
194C22×C3×C5—41no—
195C22×C3×C5—41no—
196C22×C3×C5—42no—
197C22×C3×C5—41no—
198C22×C3×C5—81no—
199C22×C3×C5#12011yescharacteristic
200C2×C3×D5—41no—
201C2×C3×D5—81no—
202C2×C3×D5—81no—
203C3×C4×C5—21no—
204C3×C4×C5—41no—
205C3×C4×C5—81no—
206C3×Dic5—41no—
207C3×Dic5—41no—
208C3×Dic5—41no—
209C3×Dic5—41no—
210C3×Dic5—41no—
211C3×Dic5—81no—
212C24×C3D2011yescharacteristic
213C3×#41—101no—
214C3×#41—201no—
215C2×C3×Q8—51no—
216C2×C3×D4—21no—
217C2×C3×D4—101no—
218C2×C3×D4—101no—
219C2×C3×D4—201no—
220C2×C3×D4—201no—
221C2×C3×D4C22×D511yescharacteristic
222C22×C3×C4—51no—
223C22×C3×C4—101no—
224C22×C3×C4—101no—
225C3×Q16—201no—
226C3×SD16—201no—
227C3×M16—21no—
228C3×C4⋊C4—101no—
229C3×C4⋊C4—101no—
230C3×C4⋊C4—101no—
231C3×C4⋊C4—101no—
232C3×C4⋊C4—201no—
233C3×C22⋊C4—21no—
234C3×C22⋊C4—21no—
235C3×C22⋊C4—51no—
236C3×C22⋊C4—101no—
237C3×C22⋊C4—101no—
238C3×C22⋊C4—101no—
239C3×C22⋊C4—101no—
240C3×C22⋊C4—101no—
241C3×C22⋊C4—101no—
242C3×C22⋊C4—201no—
243C3×C22⋊C4—201no—
244C3×C22⋊C4D2011yescharacteristic
245C3×C42—51no—
246C3×C42—101no—
247C23×C5—21no—
248C23×C5—41no—
249C23×C5—42no—
250C23×C5C2×C3×D411yescharacteristic
251C23×C5C2×C3×D411yescharacteristic
252C22×D5—21no—
253C22×D5—21no—
254C5×D4—41no—
255C5×D4—42no—
256C2×C4×C5—21no—
257C2×C4×C5—41no—
258C2×C4×C5C2×C3×D411yescharacteristic
259C22⋊D5—41no—
260C22⋊D5—41no—
261C22⋊D5—41no—
262C22⋊D5—82no—
263C2×Dic5—21no—
264C2×Dic5—21no—
265C2×Dic5—21no—
266C2×Dic5—21no—
267C2×Dic5—21no—
268C2×Dic5—21no—
269C2×Dic5—42no—
270C2×Dic5—41no—
271C2×Dic5—41no—
272C2×Dic5—81no—
273D20—21no—
274C4×D5—41no—
275Dic10—21no—
276Dic10—41no—
277C5×C8—41no—
278H(5,𝔽2)—51no—
279#137—101no—
280#126—101no—
281#124—51no—
282#123—51no—
283#123—101no—
284#123—101no—
285C22⋊Q8—101no—
286#120—101no—
287#120C2×C3×D511yescharacteristic
288C4×D4—101no—
289#117—101no—
290C2×C22⋊C4—101no—
291#104—101no—
292#100C2×C3×D511yescharacteristic
293#99—51no—
294#99—101no—
295#99—101no—
296#99C2×C3×D511yescharacteristic
297C2×C3×C5—21no—
298C2×C3×C5—41no—
299C2×C3×C5—41no—
300C2×C3×C5—42no—
301C2×C3×C5B(4,𝔽2)11yescharacteristic
302C3×D5—81no—
303C23×C3—21no—
304C23×C3—41no—
305C23×C3—42no—
306C23×C3—101no—
307C23×C3—101no—
308C23×C3C2×D2011yescharacteristic
309C23×C3D4×D511yescharacteristic
310C3×Q8—101no—
311C3×Q8—201no—
312C3×D4—41no—
313C3×D4—42no—
314C3×D4—101no—
315C3×D4—201no—
316C3×D4—201no—
317C3×D4—201no—
318C3×D4—402no—
319C2×C3×C4—21no—
320C2×C3×C4—41no—
321C2×C3×C4—101no—
322C2×C3×C4—101no—
323C2×C3×C4—101no—
324C2×C3×C4—101no—
325C2×C3×C4—101no—
326C2×C3×C4—101no—
327C2×C3×C4—201no—
328C2×C3×C4—202no—
329C2×C3×C4—201no—
330C2×C3×C4—201no—
331C2×C3×C4—401no—
332C2×C3×C4D4×D511yescharacteristic
333C3×C8—41no—
334C22×C5—22no—
335C22×C5—21no—
336C22×C5—21no—
337C22×C5—41no—
338C22×C5—41no—
339C22×C5—41no—
340C22×C5—42no—
341C22×C5—41no—
342C22×C5—81no—
343C22×C5C3×#12011yescharacteristic
344C2×D5—41no—
345C2×D5—81no—
346C2×D5—81no—
347C4×C5—21no—
348C4×C5—41no—
349C4×C5—81no—
350Dic5—41no—
351Dic5—41no—
352Dic5—41no—
353Dic5—41no—
354Dic5—41no—
355Dic5—81no—
356C24C3×D2011yescharacteristic
357#41—101no—
358#41—201no—
359C2×Q8—51no—
360C2×D4—21no—
361C2×D4—101no—
362C2×D4—101no—
363C2×D4—201no—
364C2×D4—201no—
365C2×D4C22×C3×D511yescharacteristic
366C22×C4—51no—
367C22×C4—101no—
368C22×C4—101no—
369Q16—201no—
370SD16—201no—
371M16—21no—
372C4⋊C4—101no—
373C4⋊C4—101no—
374C4⋊C4—101no—
375C4⋊C4—101no—
376C4⋊C4—201no—
377C22⋊C4—21no—
378C22⋊C4—21no—
379C22⋊C4—51no—
380C22⋊C4—101no—
381C22⋊C4—101no—
382C22⋊C4—101no—
383C22⋊C4—101no—
384C22⋊C4—101no—
385C22⋊C4—101no—
386C22⋊C4—201no—
387C22⋊C4—201no—
388C22⋊C4C3×D2011yescharacteristic
389C42—51no—
390C42—101no—
391C3×C5#219711yescharacteristic, complemented, Hall
392C22×C3—22no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—42no—
399C22×C3—41no—
400C22×C3—81no—
401C22×C3—201no—
402C22×C3—401no—
403C22×C3—401no—
404C22×C3#402811yescharacteristic
405C3×C4—21no—
406C3×C4—41no—
407C3×C4—81no—
408C3×C4—201no—
409C3×C4—201no—
410C3×C4—201no—
411C3×C4—201no—
412C3×C4—201no—
413C3×C4—401no—
414C2×C5—21no—
415C2×C5—41no—
416C2×C5—41no—
417C2×C5—42no—
418C2×C5C3×B(4,𝔽2)11yescharacteristic
419D5—81no—
420C23—21no—
421C23—41no—
422C23—42no—
423C23—101no—
424C23—101no—
425C23C2×C3×D2011yescharacteristic
426C23C3×D4×D511yescharacteristic
427Q8—101no—
428Q8—201no—
429D4—41no—
430D4—42no—
431D4—101no—
432D4—201no—
433D4—201no—
434D4—201no—
435D4—402no—
436C2×C4—21no—
437C2×C4—41no—
438C2×C4—101no—
439C2×C4—101no—
440C2×C4—101no—
441C2×C4—101no—
442C2×C4—101no—
443C2×C4—101no—
444C2×C4—201no—
445C2×C4—202no—
446C2×C4—201no—
447C2×C4—201no—
448C2×C4—401no—
449C2×C4C3×D4×D511yescharacteristic
450C8—41no—
451C2×C3—21no—
452C2×C3—41no—
453C2×C3—41no—
454C2×C3—42no—
455C2×C3—401no—
456C2×C3#6503011yescharacteristic
457C5C3×#219711yescharacteristic, complemented, Sylow
458C22—22no—
459C22—21no—
460C22—21no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—42no—
465C22—41no—
466C22—81no—
467C22—201no—
468C22—401no—
469C22—401no—
470C22C3×#402811yescharacteristic
471C4—21no—
472C4—41no—
473C4—81no—
474C4—201no—
475C4—201no—
476C4—201no—
477C4—201no—
478C4—201no—
479C4—401no—
480C3#1059992511yescharacteristic, direct product factor, Sylow
481C2—21no—
482C2—41no—
483C2—41no—
484C2—42no—
485C2—401no—
486C2C3×#6503011yescharacteristic
subgroupG/H
centerC2×C3#65030
commutator, cosocleC2×C5×D4C23×C3
FrattiniC2×D4C22×C3×D5
FittingC3×C5×AΣL(1,𝔽16)C2
socleC2×C3×C5B(4,𝔽2)
prime radicalC3×#65321C2
hypercenterC3×AΣL(1,𝔽16)D5
hypocenterC5C3×#2197
LCSG ▷ C2×C5×D4 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
1. C3×#65921C2semidirect
3. C3×#65035C2semidirect
4. C3×#65031C2semidirect
5. C3×C5×AΣL(1,𝔽16)C2semidirect
6. C3×#64696C2semidirect
7. C3×#64693C2semidirect
8. #10599925C3direct (N × H)
29. #65921C2×C3semidirect
31. #65035C2×C3semidirect
32. #65031C2×C3semidirect
33. C5×AΣL(1,𝔽16)C2×C3semidirect
34. #64696C2×C3semidirect
35. #64693C2×C3semidirect
44. C22×C3×Dic5D4semidirect
48. C2×C3×Dic10D4semidirect
60. C3×C22⋊Dic5D4semidirect
68. C3×C4×Dic5D4semidirect
77. C3×AΣL(1,𝔽16)D5semidirect
156. C22×Dic5C3×D4semidirect
160. C2×Dic10C3×D4semidirect
172. C22⋊Dic5C3×D4semidirect
180. C4×Dic5C3×D4semidirect
189. AΣL(1,𝔽16)C3×D5semidirect
391. C3×C5#2197semidirect
457. C5C3×#2197semidirect
480. C3#10599925direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659212
C3×#653212
C3×#650352
C3×#650312
C3×C5×AΣL(1,𝔽16)2
C3×#646962
C3×#646932
#105999253
C3×#21975