Finite Group Databasebeta

← C3×#10600495 #14287757

Subgroups — C3×#10600495 #14287757

Order 1920.

544 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 98 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×#65849C211yesmaximal, characteristic, complemented
2C3×C5×#394C211yesmaximal, characteristic, complemented
3C3×#65507C211yesmaximal, characteristic, complemented
4C3×#65506C211yesmaximal, characteristic
5C3×#64748C211yesmaximal, characteristic, complemented
6C3×#64672C211yesmaximal, characteristic, complemented
7C3×#64671C211yesmaximal, characteristic, complemented
8#10600495C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×C3×C5×C22⋊C4—21no—
12C2×C3×C5×C22⋊C4—21no—
13C2×C3×#687—21no—
14C2×C3×#686—21no—
15C3×#4076C2211yescharacteristic
16C3×#4075—21no—
17C3×C4×C22⋊D5—21no—
18C3×#4070C2211yescharacteristic
19C3×#4044—21no—
20C3×#4042—21no—
21C3×#4040—21no—
22C3×#4035—21no—
23C3×C5×#95C2211yescharacteristic
24C3×#3964—21no—
25C3×#3964—21no—
26C3×C22⋊#168C2211yescharacteristic
27C3×C22⋊#168C2211yescharacteristic
28C3×#1597—51nomaximal, Hall
29#65849C2×C311yescharacteristic, complemented
30C5×#394C2×C311yescharacteristic, complemented
31#65507C2×C311yescharacteristic, complemented
32#65506C2×C311yescharacteristic
33#64748C2×C311yescharacteristic, complemented
34#64672C2×C311yescharacteristic, complemented
35#64671C2×C311yescharacteristic, complemented
36C24×C3×C5—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—42no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5D411yescharacteristic
42C22×C3×C4×C5D411yescharacteristic
43C22×C3×C4×C5C2311yescharacteristic
44C2×C3×C22⋊D5—21no—
45C2×C3×D20D411yescharacteristic
46C2×C3×C4×D5—21no—
47C2×C3×Dic10D411yescharacteristic
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C22⋊C4—42no—
51C3×C5×C22⋊C4—42no—
52C3×C22⋊Dic5—21no—
53C3×#687—42no—
54C3×#686—42no—
55C3×#685—21no—
56C3×#685—21no—
57C3×#685—21no—
58C3×#685—21no—
59C3×C4⋊Dic5D411yescharacteristic
60C3×C4⋊Dic5D411yescharacteristic
61C3×#683—21no—
62C3×#683—21no—
63C3×#683—21no—
64C3×#683—21no—
65C3×C4×Dic5—21no—
66C2×C3×#168—21no—
67C2×C3×#168—21no—
68C3×#539—51no—
69C3×#450—51no—
70C3×#447—51no—
71C3×#394D511yescharacteristic, complemented
72C3×#328—51no—
73C3×#327—51no—
74C3×#324—51no—
75C22×C5×D4C22×C311yescharacteristic
76C2×C5×C4⋊C4C22×C311yescharacteristic
77C2×C5×C22⋊C4—21no—
78C2×C5×C22⋊C4—21no—
79C2×#687—21no—
80C2×#686—21no—
81#4076C22×C311yescharacteristic
82#4075—21no—
83C4×C22⋊D5—21no—
84#4070C22×C311yescharacteristic
85#4044—21no—
86#4042—21no—
87#4040—21no—
88#4035—21no—
89C5×#95C22×C311yescharacteristic
90#3964—21no—
91#3964—21no—
92C22⋊#168C22×C311yescharacteristic
93C22⋊#168C22×C311yescharacteristic
94#1597—51noSylow
95C23×C3×C5—22no—
96C23×C3×C5—41no—
97C23×C3×C5—41no—
98C23×C3×C5—41no—
99C23×C3×C5—41no—
100C23×C3×C5—41no—
101C23×C3×C5—41no—
102C23×C3×C5C2×D411yescharacteristic
103C22×C3×D5—21no—
104C3×C5×D4—22no—
105C3×C5×D4—22no—
106C3×C5×D4—41no—
107C3×C5×D4—41no—
108C2×C3×C4×C5—21no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5—41no—
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5C2×D411yescharacteristic
119C3×C22⋊D5—41no—
120C3×C22⋊D5—41no—
121C2×C3×Dic5—21no—
122C2×C3×Dic5—21no—
123C2×C3×Dic5—21no—
124C3×D20—41no—
125C3×C4×D5—81no—
126C3×Dic10—41no—
127C3×#168—41no—
128C3×#168—41no—
129C22×C3×D4C2×D511yescharacteristic
130C2×C3×SD16—101no—
131C2×C3×D8—101no—
132C3×#126—101no—
133C3×#125—101no—
134C3×#123—101no—
135C3×#123—101no—
136C3×C22⋊Q8—51no—
137C3×C22⋊Q8—101no—
138C3×#121—51no—
139C3×C4×D4—101no—
140C2×C3×C4⋊C4C2×D511yescharacteristic
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—21no—
143C3×#102—101no—
144C3×#102—101no—
145C3×C22⋊C8—51no—
146C3×C22⋊C8—51no—
147C3×#95C2×D511yescharacteristic
148C24×C5—21no—
149C2×C5×D4—21no—
150C2×C5×D4—21no—
151C2×C5×D4—42no—
152C22×C4×C5—21no—
153C22×C4×C5C3×D411yescharacteristic
154C22×C4×C5C3×D411yescharacteristic
155C22×C4×C5C23×C311yescharacteristic
156C2×C22⋊D5—21no—
157C2×D20C3×D411yescharacteristic
158C2×C4×D5—21no—
159C2×Dic10C3×D411yescharacteristic
160C5×C4⋊C4—21no—
161C5×C4⋊C4—21no—
162C5×C22⋊C4—42no—
163C5×C22⋊C4—42no—
164C22⋊Dic5—21no—
165#687—42no—
166#686—42no—
167#685—21no—
168#685—21no—
169#685—21no—
170#685—21no—
171C4⋊Dic5C3×D411yescharacteristic
172C4⋊Dic5C3×D411yescharacteristic
173#683—21no—
174#683—21no—
175#683—21no—
176#683—21no—
177C4×Dic5—21no—
178C2×#168—21no—
179C2×#168—21no—
180#539—51no—
181#450—51no—
182#447—51no—
183#394C3×D511yescharacteristic, complemented
184#328—51no—
185#327—51no—
186#324—51no—
187C22×C3×C5—21no—
188C22×C3×C5—21no—
189C22×C3×C5—42no—
190C22×C3×C5—42no—
191C22×C3×C5—42no—
192C22×C3×C5—81no—
193C22×C3×C5—81no—
194C22×C3×C5—81no—
195C22×C3×C5—81no—
196C22×C3×C5#12011yescharacteristic
197C22×C3×C5#13511yescharacteristic
198C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
199C2×C3×D5—41no—
200C2×C3×D5—41no—
201C2×C3×D5—41no—
202C3×C4×C5—21no—
203C3×C4×C5—21no—
204C3×C4×C5—41no—
205C3×C4×C5—41no—
206C3×C4×C5—81no—
207C3×Dic5—41no—
208C3×Dic5—41no—
209C3×Dic5—41no—
210C24×C3—21no—
211C2×C3×Q8—51no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—42no—
215C2×C3×D4—51no—
216C2×C3×D4—101no—
217C22×C3×C4—21no—
218C22×C3×C4—101no—
219C22×C3×C4C22⋊D511yescharacteristic
220C22×C3×C4C22⋊D511yescharacteristic
221C22×C3×C4C22×D511yescharacteristic
222C3×SD16—202no—
223C3×D8—202no—
224C2×C3×C8—101no—
225C2×C3×C8—101no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—51no—
229C3×C4⋊C4—51no—
230C3×C4⋊C4—101no—
231C3×C4⋊C4—101no—
232C3×C4⋊C4—101no—
233C3×C4⋊C4—101no—
234C3×C22⋊C4—42no—
235C3×C22⋊C4—42no—
236C3×C22⋊C4—101no—
237C3×C22⋊C4—101no—
238C3×C22⋊C4—101no—
239C3×C22⋊C4—101no—
240C3×C22⋊C4—101no—
241C3×C42—101no—
242C23×C5—22no—
243C23×C5—41no—
244C23×C5—41no—
245C23×C5—41no—
246C23×C5—41no—
247C23×C5—41no—
248C23×C5—41no—
249C23×C5C2×C3×D411yescharacteristic
250C22×D5—21no—
251C5×D4—22no—
252C5×D4—22no—
253C5×D4—41no—
254C5×D4—41no—
255C2×C4×C5—21no—
256C2×C4×C5—21no—
257C2×C4×C5—21no—
258C2×C4×C5—21no—
259C2×C4×C5—41no—
260C2×C4×C5—41no—
261C2×C4×C5—41no—
262C2×C4×C5—41no—
263C2×C4×C5—41no—
264C2×C4×C5C2×C3×D411yescharacteristic
265C2×C4×C5C2×C3×D411yescharacteristic
266C22⋊D5—41no—
267C22⋊D5—41no—
268C2×Dic5—21no—
269C2×Dic5—21no—
270C2×Dic5—21no—
271D20—41no—
272C4×D5—81no—
273Dic10—41no—
274#168—41no—
275#168—41no—
276C22×D4C2×C3×D511yescharacteristic
277C2×SD16—101no—
278C2×D8—101no—
279#126—101no—
280#125—101no—
281#123—101no—
282#123—101no—
283C22⋊Q8—51no—
284C22⋊Q8—101no—
285#121—51no—
286C4×D4—101no—
287C2×C4⋊C4C2×C3×D511yescharacteristic
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290#102—101no—
291#102—101no—
292C22⋊C8—51no—
293C22⋊C8—51no—
294#95C2×C3×D511yescharacteristic
295C2×C3×C5—21no—
296C2×C3×C5—21no—
297C2×C3×C5—82no—
298C2×C3×C5#44911yescharacteristic
299C2×C3×C5#45411yescharacteristic
300C2×C3×C5B(4,𝔽2)11yescharacteristic
301C3×D5—81no—
302C23×C3—22no—
303C23×C3—41no—
304C23×C3—41no—
305C23×C3—41no—
306C23×C3—41no—
307C23×C3—41no—
308C23×C3—41no—
309C23×C3—101no—
310C23×C3C2×C22⋊D511yescharacteristic
311C3×Q8—201no—
312C3×D4—22no—
313C3×D4—22no—
314C3×D4—41no—
315C3×D4—41no—
316C3×D4—201no—
317C3×D4—201no—
318C3×D4—201no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—101no—
329C2×C3×C4—101no—
330C2×C3×C4—101no—
331C2×C3×C4—401no—
332C2×C3×C4D4×D511yescharacteristic
333C2×C3×C4D4×D511yescharacteristic
334C3×C8—201no—
335C3×C8—201no—
336C22×C5—21no—
337C22×C5—21no—
338C22×C5—42no—
339C22×C5—42no—
340C22×C5—42no—
341C22×C5—81no—
342C22×C5—81no—
343C22×C5—81no—
344C22×C5—81no—
345C22×C5C3×#12011yescharacteristic
346C22×C5C3×#13511yescharacteristic
347C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
348C2×D5—41no—
349C2×D5—41no—
350C2×D5—41no—
351C4×C5—21no—
352C4×C5—21no—
353C4×C5—41no—
354C4×C5—41no—
355C4×C5—81no—
356Dic5—41no—
357Dic5—41no—
358Dic5—41no—
359C24—21no—
360C2×Q8—51no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—42no—
364C2×D4—51no—
365C2×D4—101no—
366C22×C4—21no—
367C22×C4—101no—
368C22×C4C3×C22⋊D511yescharacteristic
369C22×C4C3×C22⋊D511yescharacteristic
370C22×C4C22×C3×D511yescharacteristic
371SD16—202no—
372D8—202no—
373C2×C8—101no—
374C2×C8—101no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—51no—
378C4⋊C4—51no—
379C4⋊C4—101no—
380C4⋊C4—101no—
381C4⋊C4—101no—
382C4⋊C4—101no—
383C22⋊C4—42no—
384C22⋊C4—42no—
385C22⋊C4—101no—
386C22⋊C4—101no—
387C22⋊C4—101no—
388C22⋊C4—101no—
389C22⋊C4—101no—
390C42—101no—
391C3×C5#159711yescharacteristic, complemented, Hall
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—42no—
395C22×C3—42no—
396C22×C3—42no—
397C22×C3—81no—
398C22×C3—81no—
399C22×C3—81no—
400C22×C3—81no—
401C22×C3—201no—
402C22×C3—201no—
403C22×C3—201no—
404C22×C3#407811yescharacteristic
405C22×C3#408311yescharacteristic
406C22×C3#409611yescharacteristic
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—41no—
410C3×C4—41no—
411C3×C4—81no—
412C3×C4—201no—
413C3×C4—201no—
414C3×C4—201no—
415C2×C5—21no—
416C2×C5—21no—
417C2×C5—82no—
418C2×C5C3×#44911yescharacteristic
419C2×C5C3×#45411yescharacteristic
420C2×C5C3×B(4,𝔽2)11yescharacteristic
421D5—81no—
422C23—22no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—101no—
430C23C2×C3×C22⋊D511yescharacteristic
431Q8—201no—
432D4—22no—
433D4—22no—
434D4—41no—
435D4—41no—
436D4—201no—
437D4—201no—
438D4—201no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—101no—
449C2×C4—101no—
450C2×C4—101no—
451C2×C4—401no—
452C2×C4C3×D4×D511yescharacteristic
453C2×C4C3×D4×D511yescharacteristic
454C8—201no—
455C8—201no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—82no—
459C2×C3—401no—
460C2×C3#6532111yescharacteristic
461C2×C3#6532611yescharacteristic
462C2×C3#6535111yescharacteristic
463C5C3×#159711yescharacteristic, complemented, Sylow
464C22—21no—
465C22—21no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—201no—
474C22—201no—
475C22—201no—
476C22C3×#407811yescharacteristic
477C22C3×#408311yescharacteristic
478C22C3×#409611yescharacteristic
479C4—21no—
480C4—21no—
481C4—41no—
482C4—41no—
483C4—81no—
484C4—201no—
485C4—201no—
486C4—201no—
487C3#1060049511yescharacteristic, direct product factor, Sylow
488C2—21no—
489C2—21no—
490C2—82no—
491C2—401no—
492C2C3×#6532111yescharacteristic
493C2C3×#6532611yescharacteristic
494C2C3×#6535111yescharacteristic
subgroupG/H
centerC22×C3#4083
commutator, cosocleC22×C4×C5C23×C3
FrattiniC22×C4C22×C3×D5
FittingC3×C5×#394C2
socleC22×C3×C5#120
prime radicalC3×#65506C2
hypercenterC3×#394D5
hypocenterC5C3×#1597
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#394

Complements

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

NH ≅ G/Ntype
1. C3×#65849C2semidirect
2. C3×C5×#394C2semidirect
3. C3×#65507C2semidirect
5. C3×#64748C2semidirect
6. C3×#64672C2semidirect
7. C3×#64671C2semidirect
8. #10600495C3direct (N × H)
29. #65849C2×C3semidirect
30. C5×#394C2×C3semidirect
31. #65507C2×C3semidirect
33. #64748C2×C3semidirect
34. #64672C2×C3semidirect
35. #64671C2×C3semidirect
71. C3×#394D5semidirect
183. #394C3×D5semidirect
391. C3×C5#1597semidirect
463. C5C3×#1597semidirect
487. C3#10600495direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658492
C3×C5×#3942
C3×#655072
C3×#655062
C3×#647482
C3×#646722
C3×#646712
#106004953
C3×#15975