Finite Group Databasebeta

← #14512996

Subgroups — #14512996

Order 1920.

530 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 59 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×#91948C211yesmaximal, characteristic, complemented
2C5×#5912C211yesmaximal, characteristic
3A4×#681C211yesmaximal, characteristic, complemented
4#11751576C212yesmaximal, complemented
5#11751573C212yesmaximal, complemented
6#10614656—31nomaximal, Hall
7C2×C4×C5×A4C2211yescharacteristic
8C2×A4⋊Dic5—21no—
9#91948—21no—
10#91948C2212yes—
11C5×GL(2,ℤ/4)—21no—
12C5×C4⋊S4C2211yescharacteristic
13C4×C5×S4—21no—
14C5×A4⋊Q8C2211yescharacteristic
15#91322—41nomaximal
16A4×#168C2212yes—
17#85444—51nomaximal, Hall
18C5×#525—31no—
19C2×#4097—31no—
20C2×#4070—31no—
21C22×#681D311yescharacteristic, complemented
22#65521—31no—
23#65341—32no—
24#65340—32no—
25#65331—32no—
26#65330—32no—
27#65293—31no—
28#65284—31no—
29C22×C5×A4D411yescharacteristic
30C2×C5×S4—21no—
31C2×Dic30—41no—
32C5×#235—41no—
33C4×C5×A4D411yescharacteristic
34C4×C5×A4C2311yescharacteristic
35A4⋊Dic5—22no—
36C5×SL(2,ℤ/4)—21no—
37C3×#681—41no—
38#6663—42no—
39#6659—42no—
40#5912D511yescharacteristic
41C2×A4⋊Q8—51no—
42A4×M16—51no—
43#5401—52no—
44#5398—52no—
45C2×C5×#41—31no—
46C23×C4×C5C2×D311yescharacteristic
47C22×Dic10—31no—
48C5×#123—61no—
49C5×C22⋊Q8—31no—
50C5×C22⋊Q8—31no—
51C5×#121—31no—
52C5×#121—31no—
53C5×#120—61no—
54C4×C5×D4—61no—
55C4×C5×D4—61no—
56C5×#117—31no—
57C2×C22⋊Dic5—61no—
58#4097—61no—
59#4097—62no—
60#4097—61no—
61C2×#689—32no—
62C2×#687—32no—
63C2×C4⋊Dic5—31no—
64#4070—32no—
65#4070—32no—
66#4070—61no—
67#4070—61no—
68C2×#683—61no—
69C2×#681—31no—
70C2×#681—31no—
71C2×#681—32no—
72C22×#168C2×D312yes—
73#3967—32no—
74#3964—32no—
75#3942—32no—
76#3942—32no—
77#3940—32no—
78#3939—32no—
79#3056—151noSylow
80C2×C5×A4—21no—
81C2×C5×A4C2×D411yescharacteristic
82C5×S4—41no—
83C2×C3×C4×C5—41no—
84C2×Dic15—81no—
85Dic30—42no—
86Dic30—81no—
87C5×#67—81no—
88C5×D12—41no—
89C4×C5×D3—81no—
90C5×Dic6—41no—
91C3×#168—42no—
92C2×C4×A4C2×D511yescharacteristic
93GL(2,ℤ/4)—21no—
94C2×SL(2,ℤ/4)—101no—
95C4⋊S4C2×D511yescharacteristic
96C4×S4—21no—
97A4⋊Q8—52no—
98A4⋊Q8—101no—
99A4⋊Q8C2×D511yescharacteristic
100#909—201no—
101C8×A4—52no—
102C24×C5D1211yescharacteristic
103C5×#41—61no—
104C5×#41—61no—
105C5×#41—61no—
106C5×#41—61no—
107C2×C5×Q8—31no—
108C2×C5×D4—31no—
109C2×C5×D4—61no—
110C2×C5×D4—61no—
111C2×C5×D4—61no—
112C22×C4×C5—31no—
113C22×C4×C5—31no—
114C22×C4×C5—31no—
115C22×C4×C5—31no—
116C22×C4×C5—61no—
117C22×C4×C5D1211yescharacteristic
118C22×C4×C5C22×D311yescharacteristic
119C22×Dic5—61no—
120C22×Dic5—61no—
121C2×Dic10—32no—
122C2×Dic10—61no—
123C2×Dic10—61no—
124C2×Dic10—61no—
125C2×Dic10—61no—
126C2×Dic10—61no—
127C5×C4⋊C4—31no—
128C5×C4⋊C4—31no—
129C5×C4⋊C4—61no—
130C5×C4⋊C4—61no—
131C5×C22⋊C4—61no—
132C5×C22⋊C4—61no—
133C5×C22⋊C4—61no—
134C5×C22⋊C4—61no—
135C5×C22⋊C4—61no—
136C42×C5—61no—
137C22⋊Dic5—62no—
138C22⋊Dic5—62no—
139#689—62no—
140#689—62no—
141#687—62no—
142#687—62no—
143C4⋊Dic5—32no—
144C4⋊Dic5—61no—
145#683—62no—
146#683—62no—
147#681—31no—
148#681—32no—
149#681—61no—
150#681S411yescharacteristic, complemented
151C2×#168—32no—
152C2×#168—32no—
153C2×#137—151no—
154C22×M16—51no—
155#525—31no—
156C2×C22⋊Q8—151no—
157#470—152no—
158#468—152no—
159#467—152no—
160#465—152no—
161#428—151no—
162#419—151no—
163#417—151no—
164C22×C3×C5—41no—
165C2×C5×D3—81no—
166C5×A4#13711yescharacteristic, complemented
167C3×C4×C5—41no—
168C3×C4×C5—41no—
169Dic15—82no—
170C5×Dic3—81no—
171C22×A4C22⋊D511yescharacteristic
172C2×S4—21no—
173#235—41no—
174C2×Dic6—201no—
175C4×A4C22⋊D511yescharacteristic
176C4×A4C22×D511yescharacteristic
177SL(2,ℤ/4)—21no—
178SL(2,ℤ/4)—102no—
179C3×M16—201no—
180Dic12—202no—
181#204—202no—
182C23×C5—21no—
183C23×C5—31no—
184C23×C5—31no—
185C23×C5—61no—
186C23×C5—61no—
187C23×C5C2×D1211yescharacteristic
188C5×Q8—61no—
189C5×Q8—61no—
190C5×D4—61no—
191C5×D4—61no—
192C5×D4—121no—
193C5×D4—121no—
194C5×D4—122no—
195C5×D4—121no—
196C5×D4—121no—
197C2×C4×C5—31no—
198C2×C4×C5—31no—
199C2×C4×C5—31no—
200C2×C4×C5—31no—
201C2×C4×C5—31no—
202C2×C4×C5—31no—
203C2×C4×C5—31no—
204C2×C4×C5—61no—
205C2×C4×C5—61no—
206C2×C4×C5—61no—
207C2×C4×C5—61no—
208C2×C4×C5—121no—
209C2×C4×C5—121no—
210C2×C4×C5C2×S411yescharacteristic
211C2×Dic5—62no—
212C2×Dic5—62no—
213C2×Dic5—121no—
214C2×Dic5—122no—
215C2×Dic5—121no—
216Dic10—62no—
217Dic10—62no—
218Dic10—121no—
219Dic10—121no—
220#168—32no—
221#168C2×S412yes—
222C2×#41—31no—
223C22×Q8—151no—
224C23×C4D3×D511yescharacteristic
225#137—301no—
226#137—302no—
227#137—301no—
228C2×Q16—152no—
229C2×SD16—152no—
230C2×M16—151no—
231C2×M16—151no—
232C2×M16—152no—
233C22×C8—52no—
234#123—61no—
235C22⋊Q8—31no—
236C22⋊Q8—31no—
237C22⋊Q8—152no—
238C22⋊Q8—152no—
239C22⋊Q8—301no—
240C22⋊Q8—301no—
241#121—31no—
242#121—31no—
243#120—61no—
244C4×D4—61no—
245C4×D4—61no—
246#117—31no—
247C2×C4⋊C4—151no—
248C2×C4⋊C4—301no—
249C2×C22⋊C4—301no—
250#107—152no—
251#106—152no—
252#103—152no—
253#103—152no—
254#103—152no—
255#102—152no—
256C2×C3×C5—41no—
257C2×C3×C5—81no—
258C5×D3—161no—
259C2×A4—21no—
260C2×A4C2×C22⋊D511yescharacteristic
261S4—41no—
262C2×C3×C4—41no—
263#67—81no—
264C2×Dic3—401no—
265D12—41no—
266C4×D3—81no—
267Dic6—41no—
268Dic6—202no—
269Dic6—401no—
270C3×C8—202no—
271C22×C5—31no—
272C22×C5—31no—
273C22×C5—31no—
274C22×C5—61no—
275C22×C5—61no—
276C22×C5—61no—
277C22×C5—61no—
278C22×C5—121no—
279C22×C5—121no—
280C22×C5—121no—
281C22×C5#90911yescharacteristic, complemented
282C22×C5C4⋊S411yescharacteristic
283C4×C5—31no—
284C4×C5—31no—
285C4×C5—121no—
286C4×C5—121no—
287C4×C5—121no—
288C4×C5C4⋊S411yescharacteristic
289C4×C5C22×S411yescharacteristic
290Dic5—122no—
291Dic5—122no—
292C24#120311yescharacteristic
293#41—61no—
294#41—61no—
295#41—61no—
296#41—61no—
297C2×Q8—31no—
298C2×Q8—152no—
299C2×Q8—301no—
300C2×Q8—301no—
301C2×Q8—301no—
302C2×Q8—301no—
303C2×Q8—301no—
304C2×D4—31no—
305C2×D4—61no—
306C2×D4—61no—
307C2×D4—61no—
308C22×C4—31no—
309C22×C4—31no—
310C22×C4—31no—
311C22×C4—31no—
312C22×C4—61no—
313C22×C4—301no—
314C22×C4—301no—
315C22×C4#120311yescharacteristic
316C22×C4C2×D3×D511yescharacteristic
317Q16—302no—
318Q16—302no—
319SD16—302no—
320SD16—302no—
321M16—51no—
322M16—152no—
323M16—151no—
324M16—301no—
325C2×C8—152no—
326C2×C8—152no—
327C4⋊C4—31no—
328C4⋊C4—31no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—152no—
332C4⋊C4—301no—
333C4⋊C4—302no—
334C4⋊C4—302no—
335C22⋊C4—61no—
336C22⋊C4—61no—
337C22⋊C4—61no—
338C22⋊C4—61no—
339C22⋊C4—61no—
340C22⋊C4—302no—
341C22⋊C4—302no—
342C42—61no—
343C3×C5—41noHall
344C22×C3—41no—
345C2×D3—81no—
346A4#409711yescharacteristic, complemented
347C3×C4—41no—
348C3×C4—41no—
349Dic3—81no—
350Dic3—402no—
351C2×C5—21no—
352C2×C5—31no—
353C2×C5—31no—
354C2×C5—61no—
355C2×C5—241no—
356C2×C5C2×C4⋊S411yescharacteristic
357C23—21no—
358C23—31no—
359C23—31no—
360C23—61no—
361C23—61no—
362C23C2×#120311yescharacteristic
363Q8—61no—
364Q8—61no—
365Q8—302no—
366Q8—302no—
367Q8—601no—
368Q8—601no—
369D4—61no—
370D4—61no—
371D4—121no—
372D4—121no—
373D4—122no—
374D4—121no—
375D4—121no—
376C2×C4—31no—
377C2×C4—31no—
378C2×C4—31no—
379C2×C4—31no—
380C2×C4—31no—
381C2×C4—31no—
382C2×C4—31no—
383C2×C4—61no—
384C2×C4—61no—
385C2×C4—61no—
386C2×C4—61no—
387C2×C4—121no—
388C2×C4—121no—
389C2×C4—302no—
390C2×C4—302no—
391C2×C4—601no—
392C2×C4—602no—
393C2×C4—601no—
394C2×C4D5×S411yescharacteristic
395C8—52no—
396C8—152no—
397C2×C3—41no—
398C2×C3—81no—
399D3—161no—
400C5#8544411yescharacteristic, complemented, Sylow
401C22—31no—
402C22—31no—
403C22—31no—
404C22—61no—
405C22—61no—
406C22—61no—
407C22—61no—
408C22—121no—
409C22—121no—
410C22—121no—
411C22#9132211yescharacteristic, complemented
412C22#9190211yescharacteristic
413C4—31no—
414C4—31no—
415C4—121no—
416C4—121no—
417C4—121no—
418C4—602no—
419C4—602no—
420C4#9190211yescharacteristic
421C4C2×D5×S411yescharacteristic
422C3—41noSylow
423C2—21no—
424C2—31no—
425C2—31no—
426C2—61no—
427C2—241no—
428C2C2×#9190211yescharacteristic
subgroupG/H
centerC2C2×#91902
commutator, cosocleC4×C5×A4C23
FrattiniC4C2×D5×S4
FittingC23×C4×C5C2×D3
socleC23×C5C2×D12
prime radicalC5×#5912C2
hypercenterC2×C4D5×S4
hypocenterC5×A4#137
LCSG ▷ C4×C5×A4 ▷ C2×C5×A4 ▷ C5×A4
UCSC1 ◁ C2 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#91948C2semidirect
3. A4×#681C2semidirect
4. #11751576C2semidirect
5. #11751573C2semidirect
21. C22×#681D3semidirect
150. #681S4semidirect
166. C5×A4#137semidirect
281. C22×C5#909semidirect
346. A4#4097semidirect
400. C5#85444semidirect
411. C22#91322semidirect

Maximal subgroups

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

subgroupindex
C2×#919482
C5×#59122
A4×#6812
#117515762
#117515732
#106146563
#913224
#854445