Finite Group Databasebeta

← #14309041

Subgroups — #14309041

Order 1920.

488 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756276C211yesmaximal, characteristic, complemented
2C3×#65294C211yesmaximal, characteristic
3#11748624C211yesmaximal, characteristic
4C2×#90976C211yesmaximal, characteristic
5C5×#4531C211yesmaximal, characteristic, complemented
6#11745991C211yesmaximal, characteristic, complemented
7#11745975C211yesmaximal, characteristic, complemented
8#10599507—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13#91779—21no—
14#91777—21no—
15#91767—22no—
16C4×Dic30—22no—
17C5×#926C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20C3×#3937—22no—
21#90995—22no—
22#90976—21no—
23#90976—21no—
24#70394—51nomaximal, Hall
25#65851—31no—
26C2×#3957—31no—
27#65295—31no—
28#65294D311yescharacteristic
29C5×H(3,ℤ/4)—31no—
30#64779—31no—
31#64752—31no—
32C22×C3×C4×C5C2311yescharacteristic
33C22×Dic15—21no—
34C2×Dic30—22no—
35C2×C3×C22⋊D5—21no—
36C3×#709—21no—
37C3×#709—21no—
38C3×#709—21no—
39C3×#709—21no—
40C2×C3×D20Q811yescharacteristic, complemented
41C2×C3×C4×D5—21no—
42C2×C3×Dic10Q811yescharacteristic, complemented
43C3×C5×C4⋊C4—21no—
44C3×C5×C22⋊C4—21no—
45C3×C42×C5D412yes—
46#6719D412yes—
47C4⋊Dic15—22no—
48C4⋊Dic15—21no—
49#6712—22no—
50#6712—22no—
51C4×Dic15—21no—
52C4×Dic15—21no—
53C4×Dic15D411yescharacteristic
54C4×Dic15D411yescharacteristic
55C5×#217—21no—
56C5×C4⋊Dic3—21no—
57C4×C5×Dic3—21no—
58C5×#208—21no—
59C5×#208—21no—
60C2×C5×C3⋊C8—21no—
61C3×#681—21no—
62C3×#681—21no—
63C2×C3×#168—21no—
64#5517—51no—
65C3×#421—51no—
66#5240—51no—
67C2×#837—51no—
68#4556—51no—
69#4555—51no—
70#4531D511yescharacteristic, complemented
71C2×#709C2×D311yescharacteristic
72C2×C5×M16—31no—
73C5×#117—31no—
74C5×#117C2×D311yescharacteristic
75#4072—31no—
76C2×C4×Dic5—31no—
77C2×#681C2×D311yescharacteristic
78#4036—61no—
79#4034—61no—
80#4024—62no—
81C4×Dic10—62no—
82#3957—61no—
83#3957—61no—
84#3938—62no—
85#3937—22no—
86#2031—151noSylow
87C23×C3×C5C2×D411yescharacteristic
88C22×C3×D5—21no—
89C2×C3×C4×C5—22no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×Q811yescharacteristic
93C2×C3×C4×C5#4111yescharacteristic
94C2×C3×C4×C5#4111yescharacteristic
95C2×C3×C4×C5#4111yescharacteristic
96C2×Dic15—21no—
97C2×Dic15—21no—
98C2×Dic15—22no—
99C2×Dic15—42no—
100Dic30—44no—
101C2×C5×Dic3—41no—
102C3×C22⋊D5—41no—
103C3×C22⋊D5—41no—
104C2×C3×Dic5—21no—
105C3×D20—21no—
106C3×D20—21no—
107C3×C4×D5—41no—
108C3×C4×D5—41no—
109C3×Dic10—21no—
110C3×Dic10—21no—
111C3×#168—41no—
112C5×C3⋊C8—41no—
113C2×C3×#41—51no—
114C2×C3×M16—51no—
115C3×#117C2×D511yescharacteristic
116#926—51no—
117#926C2×D511yescharacteristic
118C2×C4×Dic3—51no—
119C2×#208C2×D511yescharacteristic
120#890—101no—
121#888—101no—
122#878—102no—
123C4×Dic6—102no—
124C3×#104—102no—
125#837—101no—
126#837—101no—
127#834—102no—
128C22×C4×C5C22×D311yescharacteristic
129C2×C22⋊D5—21no—
130C22×Dic5—61no—
131#709—21no—
132#709—21no—
133#709—21no—
134#709—21no—
135C2×D20Dic611yescharacteristic, complemented
136C2×C4×D5—21no—
137C2×Dic10—62no—
138C2×Dic10Dic611yescharacteristic, complemented
139C5×M16—61no—
140C5×M16—61no—
141C2×C5×C8—61no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4—61no—
144C5×C22⋊C4—21no—
145C5×C22⋊C4—61no—
146C42×C5—61no—
147C42×C5#6712yes—
148C22⋊Dic5—32no—
149C4⋊Dic5—62no—
150C4⋊Dic5—61no—
151#683—62no—
152#683—62no—
153C4×Dic5—31no—
154C4×Dic5—31no—
155C4×Dic5—61no—
156C4×Dic5—61no—
157#681—21no—
158#681—21no—
159C2×#168—21no—
160#533—151no—
161#421—51no—
162C2×#104—151no—
163#410—151no—
164#344—151no—
165#339—151no—
166H(3,ℤ/4)—31no—
167C22×C3×C5—41no—
168C22×C3×C5#12011yescharacteristic
169C22×C3×C5C22⋊Q811yescharacteristic
170C22×C3×C5#12411yescharacteristic
171C2×C3×D5—41no—
172C2×C3×D5—81no—
173C3×C4×C5—42no—
174C3×C4×C5C22⋊Q811yescharacteristic
175C3×C4×C5C22⋊Q811yescharacteristic
176C3×C4×C5#12411yescharacteristic
177C3×C4×C5#12411yescharacteristic
178Dic15—22no—
179Dic15—42no—
180Dic15—41no—
181C3×Dic5—41no—
182C5×Dic3—81no—
183C3×#41—101no—
184C3×#41—101no—
185C3×#41—101no—
186C3×#41—101no—
187C2×C3×Q8—51no—
188C2×C3×D4—51no—
189C2×C3×D4—101no—
190C22×C3×C4—101no—
191C22×C3×C4C22×D511yescharacteristic
192C22×Dic3—101no—
193C2×Dic6—102no—
194C3×M16—101no—
195C3×M16—101no—
196C2×C3×C8—101no—
197C3×C4⋊C4—21no—
198C3×C22⋊C4—21no—
199C3×C42D2012yes—
200#217—21no—
201#217—52no—
202C4⋊Dic3—21no—
203C4⋊Dic3—102no—
204C4⋊Dic3—101no—
205Dic3⋊C4—102no—
206Dic3⋊C4—102no—
207C4×Dic3—21no—
208C4×Dic3—51no—
209C4×Dic3—51no—
210C4×Dic3—101no—
211C4×Dic3—101no—
212#208—21no—
213#208—21no—
214C2×C3⋊C8—21no—
215C23×C5D3×D411yescharacteristic
216C22×D5—21no—
217C2×C4×C5—22no—
218C2×C4×C5—121no—
219C2×C4×C5C2×Dic611yescharacteristic
220C2×C4×C5#23511yescharacteristic
221C2×C4×C5D3×D411yescharacteristic
222C2×C4×C5#23711yescharacteristic
223C2×C4×C5#23711yescharacteristic
224C2×C4×C5C2×#6711yescharacteristic
225C22⋊D5—41no—
226C22⋊D5—41no—
227C2×Dic5—21no—
228C2×Dic5—61no—
229C2×Dic5—61no—
230C2×Dic5—62no—
231C2×Dic5—122no—
232D20—21no—
233D20—21no—
234C4×D5—41no—
235C4×D5—41no—
236Dic10—21no—
237Dic10—21no—
238Dic10—124no—
239C5×C8—121no—
240#168—41no—
241C2×#41—51no—
242C2×M16—31no—
243C2×M16—51no—
244C4⋊Q8—301no—
245#125—301no—
246C22⋊Q8—302no—
247C4×Q8—302no—
248#117—31no—
249#117—151no—
250#117D3×D511yescharacteristic
251C2×C42—151no—
252#104—102no—
253#104—301no—
254#104—301no—
255#99—302no—
256C2×C3×C5—21no—
257C2×C3×C5—21no—
258C2×C3×C5—21no—
259C2×C3×C5#39311yescharacteristic
260C3×D5—81no—
261C23×C3—101no—
262C23×C3D4×D511yescharacteristic
263C3×Q8—101no—
264C3×Q8—101no—
265C3×D4—101no—
266C3×D4—101no—
267C3×D4—201no—
268C3×D4—201no—
269C2×C3×C4—22no—
270C2×C3×C4—101no—
271C2×C3×C4—201no—
272C2×C3×C4—201no—
273C2×C3×C4C2×D2011yescharacteristic
274C2×C3×C4#70911yescharacteristic
275C2×C3×C4#70911yescharacteristic
276C2×C3×C4D4×D511yescharacteristic
277C2×C3×C4#71111yescharacteristic
278C2×C3×C4Q8×D511yescharacteristic
279C2×Dic3—41no—
280C2×Dic3—101no—
281C2×Dic3—101no—
282C2×Dic3—102no—
283C2×Dic3—202no—
284Dic6—204no—
285C3×C8—201no—
286C3⋊C8—41no—
287C22×C5—41no—
288C22×C5#87811yescharacteristic
289C22×C5#88511yescharacteristic
290C22×C5#93711yescharacteristic
291C2×D5—41no—
292C2×D5—81no—
293C4×C5—42no—
294C4×C5—241no—
295C4×C5#87811yescharacteristic
296C4×C5#88511yescharacteristic
297C4×C5#92411yescharacteristic
298C4×C5#93611yescharacteristic
299Dic5—41no—
300Dic5—62no—
301Dic5—122no—
302Dic5—121no—
303#41—101no—
304#41—101no—
305#41—101no—
306#41—101no—
307C2×Q8—51no—
308C2×Q8—302no—
309C2×D4—51no—
310C2×D4—101no—
311C22×C4—101no—
312C22×C4—301no—
313C22×C4C2×D3×D511yescharacteristic
314M16—61no—
315M16—61no—
316M16—101no—
317M16—101no—
318C2×C8—61no—
319C2×C8—101no—
320C4⋊C4—21no—
321C4⋊C4—61no—
322C4⋊C4—302no—
323C4⋊C4—302no—
324C4⋊C4—302no—
325C4⋊C4—301no—
326C22⋊C4—21no—
327C22⋊C4—61no—
328C22⋊C4—152no—
329C42—61no—
330C42—151no—
331C42—151no—
332C42—301no—
333C42—301no—
334C42#120212yes—
335C3×C5#203111yescharacteristic, complemented, Hall
336C22×C3—41no—
337C22×C3—201no—
338C22×C3—401no—
339C22×C3#402811yescharacteristic
340C22×C3#403111yescharacteristic
341C22×C3#404211yescharacteristic
342C3×C4—42no—
343C3×C4—201no—
344C3×C4#402111yescharacteristic
345C3×C4#403111yescharacteristic
346C3×C4#404211yescharacteristic
347C3×C4#404311yescharacteristic
348Dic3—81no—
349Dic3—102no—
350Dic3—202no—
351Dic3—201no—
352C2×C5—21no—
353C2×C5—21no—
354C2×C5—21no—
355C2×C5#494711yescharacteristic
356D5—81no—
357C23—101no—
358C23#679011yescharacteristic
359Q8—101no—
360Q8—101no—
361Q8—604no—
362D4—101no—
363D4—101no—
364D4—201no—
365D4—201no—
366C2×C4—22no—
367C2×C4—101no—
368C2×C4—121no—
369C2×C4—201no—
370C2×C4—201no—
371C2×C4—301no—
372C2×C4—301no—
373C2×C4—302no—
374C2×C4—602no—
375C2×C4D5×Dic611yescharacteristic
376C2×C4#676511yescharacteristic
377C2×C4#676511yescharacteristic
378C2×C4#677211yescharacteristic
379C2×C4C2×#120211yescharacteristic
380C2×C4#679011yescharacteristic
381C8—121no—
382C8—201no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—401no—
387C2×C3#6496211yescharacteristic
388C5#7039411yescharacteristic, complemented, Sylow
389C22—41no—
390C22—201no—
391C22—401no—
392C22#9143111yescharacteristic
393C22#9146211yescharacteristic
394C22#9157211yescharacteristic
395C4—42no—
396C4—201no—
397C4—241no—
398C4—302no—
399C4—601no—
400C4—602no—
401C4#9136011yescharacteristic
402C4#9136411yescharacteristic
403C4#9143111yescharacteristic
404C4#9146211yescharacteristic
405C3#1059950711yescharacteristic, complemented, Sylow
406C2—21no—
407C2—21no—
408C2—21no—
409C2—401no—
410C2#1174879311yescharacteristic
subgroupG/H
centerC4#91364
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#393
prime radicalC2×C3×#709C22
hypercenter#117D3×D5
hypocenterC3×C5#2031
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #11756276C2semidirect
5. C5×#4531C2semidirect
6. #11745991C2semidirect
7. #11745975C2semidirect
40. C2×C3×D20Q8semidirect
42. C2×C3×Dic10Q8semidirect
70. #4531D5semidirect
135. C2×D20Dic6semidirect
138. C2×Dic10Dic6semidirect
335. C3×C5#2031semidirect
388. C5#70394semidirect
405. C3#10599507semidirect

Maximal subgroups

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

subgroupindex
#117562762
C3×#652942
#117486242
C2×#909762
C5×#45312
#117459912
#117459752
#105995073
#703945