Finite Group Databasebeta

← C4×#91953 #14513729

Subgroups — C4×#91953 #14513729

Order 1920.

556 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C2×#91953C211yesmaximal, characteristic
2C2×C4×C5×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
3#11752139C211yesmaximal, characteristic, complemented
4#11752113C211yesmaximal, characteristic, complemented
5C4×C5⋊GL(2,𝔽3)C211yesmaximal, characteristic, complemented
6#11752107C211yesmaximal, characteristic, complemented
7C4×C5⋊#226C211yesmaximal, characteristic, complemented
8C4×#4088—31nomaximal, Hall
9C22×C5×SL(2,𝔽3)C2211yescharacteristic
10#91953C414yesdirect product factor
11C2×C5⋊GL(2,𝔽3)C2211yescharacteristic
12C2×C5⋊#226C2211yescharacteristic
13C4×#1220—41nomaximal
14C4×C5×SL(2,𝔽3)C2211yescharacteristic
15C4×C5×SL(2,𝔽3)C2211yescharacteristic
16#91184C2211yescharacteristic
17#91184C2211yescharacteristic
18C4×#983—51nomaximal, Hall
19C2×C4×C5×Q8D311yescharacteristic, complemented
20C2×#4088—31no—
21C4×#709—31no—
22#65514—31no—
23#65319—31no—
24#65319—31no—
25C4×#689—31no—
26C4×#689—31no—
27#65315—31no—
28#65315—31no—
29C4×#688—31no—
30C4×#688—31no—
31#65255—31no—
32#65253—31no—
33C4×#681—31no—
34C22×C3×C4×C5—41no—
35C2×#1220—41no—
36C2×C4×D15—41no—
37C2×C5×SL(2,𝔽3)C2×C412yescomplemented
38C2×C5×SL(2,𝔽3)C2311yescharacteristic
39C5⋊GL(2,𝔽3)C2×C412yescomplemented
40C5⋊#226C2×C412yescomplemented
41#6719—41no—
42#6714—41no—
43#6712—41no—
44C4×Dic15—41no—
45C2×#983—51no—
46C2×C4×SL(2,𝔽3)D511yescharacteristic, complemented
47#5420—51no—
48#5394—51no—
49C4×GL(2,𝔽3)—51no—
50#5388—51no—
51C4×#226—51no—
52C22×C5×Q8C2×D311yescharacteristic
53C2×#709—31no—
54C4×C5×Q8—31no—
55C4×C5×Q8—31no—
56C4×C5×Q8C2×D311yescharacteristic
57C4×C5×Q8C2×D311yescharacteristic
58C2×C5×C4⋊C4—31no—
59C2×C42×C5—31no—
60C2×#689—31no—
61C2×#689—31no—
62#4088—34no—
63#4088—34no—
64C2×#688—31no—
65C2×#688—31no—
66C4×C22⋊D5—61no—
67C4×C22⋊D5—61no—
68#4072—31no—
69C2×#681—31no—
70C2×#681—31no—
71C4×D20—31no—
72C4×D20—31no—
73#4018—61no—
74C42×D5—61no—
75C4×Dic10—31no—
76C4×Dic10—31no—
77#3967—31no—
78#3967—31no—
79#3967—31no—
80#3967—31no—
81#3942—31no—
82#3942—31no—
83#3941—31no—
84#3941—31no—
85#3940—31no—
86#3940—31no—
87#3939—31no—
88#3939—31no—
89#3935—31no—
90#3935—31no—
91C4×#168—31no—
92C4×#168—31no—
93C4×#137—151noSylow
94C23×C3×C5—41no—
95C22×D15—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—82no—
99#1220—44no—
100C2×Dic15—41no—
101C2×Dic15—41no—
102C2×Dic15—41no—
103C4×D15—82no—
104C5×SL(2,𝔽3)C22×C411yescharacteristic
105C22×SL(2,𝔽3)C2×D511yescharacteristic
106#983—54no—
107C2×GL(2,𝔽3)—51no—
108C2×#226—51no—
109C4×#67—201no—
110C4×SL(2,𝔽3)C2×D511yescharacteristic
111C4×SL(2,𝔽3)C2×D511yescharacteristic
112#859—51no—
113#859—51no—
114C2×C5×Q8—31no—
115C2×C5×Q8—32no—
116C2×C5×Q8C4×D312yescomplemented
117C2×C5×Q8C22×D311yescharacteristic
118C22×C4×C5—31no—
119C22×C4×C5—31no—
120C22×C4×C5S411yescharacteristic
121C2×C22⋊D5—61no—
122#709—34no—
123#709—62no—
124C2×D20—31no—
125C2×C4×D5—61no—
126C2×C4×D5—61no—
127C2×C4×D5—61no—
128C2×Dic10—31no—
129C5×C4⋊C4—31no—
130C5×C4⋊C4—31no—
131C5×C4⋊C4—61no—
132C42×C5—31no—
133C42×C5—31no—
134C42×C5—31no—
135C42×C5—31no—
136C22⋊Dic5—61no—
137#689—34no—
138#689—32no—
139#689—32no—
140#688—34no—
141#688—32no—
142#688—32no—
143#685—61no—
144#685—61no—
145C4⋊Dic5—31no—
146C4⋊Dic5—31no—
147#683—61no—
148#683—61no—
149C4×Dic5—61no—
150C4×Dic5—61no—
151C4×Dic5—61no—
152#681—34no—
153#681—62no—
154C2×#168—31no—
155C2×#168—31no—
156C2×#168—31no—
157C2×#168—31no—
158C2×#137—151no—
159C4×#41—151no—
160C2×C4×Q8D1511yescharacteristic, complemented
161#441—151no—
162#441—151no—
163#440—151no—
164#440—151no—
165C4×Q16—151no—
166C4×Q16—151no—
167C4×SD16—151no—
168C4×SD16—151no—
169#428—151no—
170#419—151no—
171#417—151no—
172C4×M16—151no—
173C22×C3×C5—42no—
174C22×C3×C5—41no—
175C22×C3×C5—81no—
176C22×C3×C5—81no—
177C2×D15—42no—
178C2×D15—81no—
179C2×D15—81no—
180C3×C4×C5—42no—
181C3×C4×C5—81no—
182Dic15—42no—
183Dic15—81no—
184Dic15—81no—
185C22×C3×C4—41no—
186C2×#67—201no—
187C2×C4×D3—201no—
188C2×SL(2,𝔽3)C4×D512yescomplemented
189C2×SL(2,𝔽3)C22×D511yescharacteristic
190GL(2,𝔽3)—52no—
191#226—52no—
192#217—201no—
193(C2×D3)⋊C4—201no—
194Dic3⋊C4—201no—
195C4×Dic3—201no—
196C23×C5C2×S411yescharacteristic
197C22×D5—61no—
198C5×Q8—32no—
199C5×Q8—31no—
200C5×Q8—61no—
201C5×Q8C2×C4×D311yescharacteristic
202C2×C4×C5—22no—
203C2×C4×C5—32no—
204C2×C4×C5—32no—
205C2×C4×C5—31no—
206C2×C4×C5—31no—
207C2×C4×C5—31no—
208C2×C4×C5—31no—
209C2×C4×C5—121no—
210C2×C4×C5C2×S411yescharacteristic
211C2×C4×C5C2×S411yescharacteristic
212C22⋊D5—64no—
213C2×Dic5—61no—
214C2×Dic5—61no—
215C2×Dic5—61no—
216D20—32no—
217D20—61no—
218C4×D5—64no—
219C4×D5—122no—
220C4×D5—122no—
221Dic10—32no—
222Dic10—61no—
223#168—32no—
224#168—32no—
225#168—61no—
226#168—61no—
227C2×#41—151no—
228C22×Q8C2×D1511yescharacteristic
229#137—154no—
230#137—154no—
231C2×Q16—151no—
232C2×Q16—151no—
233C2×SD16—151no—
234C2×SD16—151no—
235C2×M16—151no—
236C2×M16—151no—
237C4×Q8—31no—
238C4×Q8—31no—
239C4×Q8—151no—
240C4×Q8—151no—
241C4×Q8C2×D1511yescharacteristic
242C4×Q8C2×D1511yescharacteristic
243C4×D4—151no—
244C4×D4—151no—
245C4×D4—301no—
246C4×D4—301no—
247#117—151no—
248#117—301no—
249C2×C4⋊C4—31no—
250C2×C42—31no—
251C2×C42—301no—
252#107—151no—
253#107—151no—
254#106—151no—
255#106—151no—
256#103—151no—
257#103—151no—
258#103—151no—
259#103—151no—
260#103—151no—
261#103—151no—
262#102—151no—
263#102—151no—
264#97—151no—
265#97—151no—
266C4×C8—151no—
267C4×C8—151no—
268C2×C3×C5—41no—
269C2×C3×C5—41no—
270C2×C3×C5—41no—
271C2×C3×C5—82no—
272D15—82no—
273C23×C3—41no—
274C22×D3—201no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—82no—
278#67—204no—
279C2×Dic3—201no—
280C2×Dic3—201no—
281C2×Dic3—201no—
282C4×D3—402no—
283SL(2,𝔽3)C2×C4×D511yescharacteristic
284C22×C5—21no—
285C22×C5—21no—
286C22×C5C4×S412yes—
287C22×C5C22×S411yescharacteristic
288C2×D5—62no—
289C2×D5—121no—
290C2×D5—121no—
291C4×C5—21no—
292C4×C5—31no—
293C4×C5—31no—
294C4×C5—32no—
295C4×C5—61no—
296C4×C5—61no—
297C4×C5#98312yescomplemented
298Dic5—62no—
299Dic5—121no—
300Dic5—121no—
301#41—154no—
302#41—302no—
303C2×Q8—31no—
304C2×Q8—32no—
305C2×Q8—151no—
306C2×Q8C4×D1512yescomplemented
307C2×Q8C22×D1511yescharacteristic
308C2×D4—151no—
309C2×D4—301no—
310C22×C4—31no—
311C22×C4—31no—
312C22×C4—301no—
313C22×C4—301no—
314C22×C4—301no—
315C22×C4C5⋊S411yescharacteristic
316Q16—154no—
317Q16—152no—
318Q16—152no—
319SD16—154no—
320SD16—152no—
321SD16—152no—
322M16—154no—
323M16—302no—
324C2×C8—151no—
325C2×C8—151no—
326C2×C8—151no—
327C2×C8—151no—
328C4⋊C4—31no—
329C4⋊C4—31no—
330C4⋊C4—61no—
331C4⋊C4—151no—
332C4⋊C4—151no—
333C4⋊C4—301no—
334C4⋊C4—301no—
335C22⋊C4—301no—
336C22⋊C4—301no—
337C22⋊C4—301no—
338C42—31no—
339C42—31no—
340C42—31no—
341C42—31no—
342C42—301no—
343C42—301no—
344C42—301no—
345C3×C5—41noHall
346C22×C3—42no—
347C22×C3—41no—
348C22×C3—81no—
349C22×C3—81no—
350C2×D3—202no—
351C2×D3—401no—
352C2×D3—401no—
353C3×C4—42no—
354C3×C4—81no—
355Dic3—202no—
356Dic3—401no—
357Dic3—401no—
358C2×C5—22no—
359C2×C5C2×C4×S411yescharacteristic
360C2×C5C2×#98311yescharacteristic
361C2×C5#592311yescharacteristic
362D5—122no—
363C23—301no—
364C23C2×C5⋊S411yescharacteristic
365Q8—32no—
366Q8—31no—
367Q8—61no—
368Q8—152no—
369Q8—301no—
370Q8C2×C4×D1511yescharacteristic
371D4—152no—
372D4—301no—
373D4—304no—
374C2×C4—22no—
375C2×C4—32no—
376C2×C4—32no—
377C2×C4—31no—
378C2×C4—31no—
379C2×C4—31no—
380C2×C4—31no—
381C2×C4—121no—
382C2×C4—304no—
383C2×C4—301no—
384C2×C4—301no—
385C2×C4—301no—
386C2×C4—602no—
387C2×C4—602no—
388C2×C4C2×C5⋊S411yescharacteristic
389C2×C4C2×C5⋊S411yescharacteristic
390C8—152no—
391C8—152no—
392C8—301no—
393C8—301no—
394C2×C3—41no—
395C2×C3—41no—
396C2×C3—41no—
397C2×C3—82no—
398D3—402no—
399C5C4×#98311yescharacteristic, complemented, Sylow
400C22—21no—
401C22—21no—
402C22—302no—
403C22—601no—
404C22—601no—
405C22C4×C5⋊S412yes—
406C22C22×C5⋊S411yescharacteristic
407C4—21no—
408C4—31no—
409C4—31no—
410C4—32no—
411C4—61no—
412C4—61no—
413C4—302no—
414C4—601no—
415C4—601no—
416C4#9195312yesdirect product factor
417C3—41noSylow
418C2—22no—
419C2—602no—
420C2C2×C4×C5⋊S411yescharacteristic
421C2C2×#9195311yescharacteristic
422C2#1175690711yescharacteristic
subgroupG/H
centerC2×C4C2×C5⋊S4
commutator, hypocenterC5×SL(2,𝔽3)C22×C4
FrattiniC22C22×C5⋊S4
FittingC2×C4×C5×Q8D3
socleC22×C5C22×S4
prime radicalC2×#91953C2
cosocleC2×C5×SL(2,𝔽3)C23
hypercenterC22×C4C5⋊S4
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C5×SL(2,𝔽3)C2semidirect
3. #11752139C2semidirect
4. #11752113C2semidirect
5. C4×C5⋊GL(2,𝔽3)C2semidirect
6. #11752107C2semidirect
7. C4×C5⋊#226C2semidirect
10. #91953C4direct (N × H)
19. C2×C4×C5×Q8D3semidirect
37. C2×C5×SL(2,𝔽3)C2×C4semidirect
39. C5⋊GL(2,𝔽3)C2×C4semidirect
40. C5⋊#226C2×C4semidirect
46. C2×C4×SL(2,𝔽3)D5semidirect
116. C2×C5×Q8C4×D3semidirect
160. C2×C4×Q8D15semidirect
188. C2×SL(2,𝔽3)C4×D5semidirect
297. C4×C5#983semidirect
306. C2×Q8C4×D15semidirect
399. C5C4×#983semidirect
416. C4#91953direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#919532
C2×C4×C5×SL(2,𝔽3)2
#117521392
#117521132
C4×C5⋊GL(2,𝔽3)2
#117521072
C4×C5⋊#2262
C4×#40883
C4×#12204
C4×#9835