Finite Group Databasebeta

← #14288913

Subgroups — #14288913

Order 1920.

556 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 96 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×#66052C211yesmaximal, characteristic, complemented
2#11751174C211yesmaximal, characteristic, complemented
3#11747064C211yesmaximal, characteristic, complemented
4#11747028C211yesmaximal, characteristic, complemented
5C5×#4544C211yesmaximal, characteristic, complemented
6#11745840C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10599196—31nomaximal, Hall
9C2×C3×#711—21no—
10C3×C5×#127C2211yescharacteristic
11C2×#6715—22no—
12#91763C2211yescharacteristic
13C3×#4086—21no—
14C3×#4085—22no—
15C3×#4084—21no—
16C3×D4×Dic5—21no—
17C3×C4×D20C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19C2×#6658—21no—
20C2×#6653—21no—
21C4×C3⋊#168C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24#90968—21no—
25#90968—21no—
26#71918—51nomaximal, Hall
27#66052D311yescharacteristic, complemented
28#65362—31no—
29#65137—31no—
30#65132—31no—
31C5×#331—31no—
32#64704—31no—
33#64703—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4D412yes—
37C2×D60—21no—
38C2×D60—21no—
39C2×D60—21no—
40C2×C3×C22⋊D5—22no—
41C2×C3×C22⋊D5—22no—
42C22×C3×Dic5—22no—
43C3×#711—42no—
44C3×#711—42no—
45C2×C3×D20D411yescharacteristic
46C2×C3×C4×D5—21no—
47C2×C3×Dic10D411yescharacteristic
48C3×C42×C5C2311yescharacteristic
49#6715—44no—
50C2×C3⋊#168—21no—
51C2×C5×C3⋊C8—21no—
52C2×C5×C3⋊C8—21no—
53C3×C22⋊Dic5—22no—
54C3×#685—21no—
55C3×C4⋊Dic5D411yescharacteristic
56C3×C4⋊Dic5D411yescharacteristic
57C3×#683—21no—
58C3×C4×Dic5—21no—
59#6658—42no—
60#6653—42no—
61C3×#550—51no—
62#5073—51no—
63#5027—51no—
64#5015—51no—
65#4544D511yescharacteristic, complemented
66#4535—51no—
67D4⋊(C3⋊C8)—51no—
68C2×#711—21no—
69C5×#127C2×D311yescharacteristic
70#4086—21no—
71#4085—22no—
72#4084—21no—
73D4×Dic5—21no—
74C2×#686—62no—
75C2×D40—61no—
76C2×#677—61no—
77#4020—31no—
78C4×D20C2×D311yescharacteristic
79C4×Dic10C2×D311yescharacteristic
80C5×C4⋊C8—31no—
81C5×C4⋊C8—31no—
82#3953—61no—
83#3953—61no—
84C4×#168—31no—
85#1621—151noSylow
86C23×C3×C5—22no—
87C22×D15—41no—
88C22×C3×D5—21no—
89C3×C5×D4—42no—
90C3×C5×D4—41no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97D60—42no—
98D60—41no—
99D60—41no—
100D60—41no—
101D60—41no—
102C3×C22⋊D5—44no—
103C3×C22⋊D5—82no—
104C2×C3×Dic5—21no—
105C2×C3×Dic5—21no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—44no—
108C3×D20—21no—
109C3×D20—21no—
110C3×C4×D5—41no—
111C3×C4×D5—41no—
112C3×Dic10—21no—
113C3×Dic10D812yescomplemented
114C3⋊#168—22no—
115C5×C3⋊C8—41no—
116C5×C3⋊C8—41no—
117C2×C3×#41—101no—
118C3×#127—101no—
119C3×#127C2×D511yescharacteristic
120C3×#121—101no—
121C3×#121—102no—
122C3×C4×Q8—51no—
123C3×C4×D4—51no—
124C3×C4×D4—101no—
125C2×#215—101no—
126C2×#213—101no—
127C2×#213—102no—
128#874—51no—
129#809—101no—
130#809—101no—
131C4⋊(C3⋊C8)C2×D511yescharacteristic
132C4⋊(C3⋊C8)C2×D511yescharacteristic
133C4×C3⋊C8—51no—
134C2×C5×D4—21no—
135C2×C5×D4—21no—
136C2×C5×D4#6712yes—
137C2×C22⋊D5—22no—
138C2×C22⋊D5—22no—
139C22×Dic5—22no—
140#711—42no—
141#711—42no—
142C2×D20—61no—
143C2×D20—61no—
144C2×D20—61no—
145C2×D20#6711yescharacteristic
146C2×C4×D5—21no—
147C2×Dic10#6711yescharacteristic
148C2×C5×C8—61no—
149C2×C5×C8—61no—
150C42×C5C22×D311yescharacteristic
151C22⋊Dic5—22no—
152#686—124no—
153#685—21no—
154C4⋊Dic5#6711yescharacteristic
155C4⋊Dic5#6711yescharacteristic
156#683—21no—
157C4×Dic5—21no—
158C2×#168—61no—
159D40—122no—
160#677—122no—
161#550—51no—
162#493—151no—
163#460—151no—
164#459—151no—
165#331—31no—
166Q8⋊C8—151no—
167D4⋊C8—151no—
168C22×C3×C5—42no—
169C22×C3×C5—42no—
170C22×C3×C5—42no—
171C22×C3×C5#12011yescharacteristic
172C2×D15—81no—
173C2×D15—81no—
174C2×D15—81no—
175C2×C3×D5—41no—
176C2×C3×D5—41no—
177C2×C3×D5—41no—
178C3×C4×C5—21no—
179C3×C4×C5C2×D811yescharacteristic
180C3×C4×C5#13511yescharacteristic
181C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
182C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
183C3×Dic5—22no—
184C3×Dic5—41no—
185C3×Dic5—41no—
186C3×#41—202no—
187C3×#41—202no—
188C2×C3×Q8—51no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—51no—
192C2×C3×D4—102no—
193C2×C3×D4—102no—
194C2×C3×D4D2012yes—
195C22×C3×C4—102no—
196C22×C3×C4—101no—
197C2×D12—101no—
198C2×D12—101no—
199C2×D12—101no—
200C3×C4⋊C4—51no—
201C3×C4⋊C4—51no—
202C3×C4⋊C4—101no—
203C3×C22⋊C4—102no—
204C3×C22⋊C4—101no—
205C3×C42—101no—
206C3×C42C22×D511yescharacteristic
207#215—202no—
208#213—202no—
209#213—204no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—101no—
213C23×C5—22no—
214C22×D5—21no—
215C22×D5—121no—
216C5×D4—42no—
217C5×D4—41no—
218C5×D4—41no—
219C5×D4—41no—
220C5×D4—41no—
221C2×C4×C5C2×#6711yescharacteristic
222C2×C4×C5C2×#6711yescharacteristic
223C2×C4×C5C2×#6711yescharacteristic
224C22⋊D5—44no—
225C22⋊D5—82no—
226C2×Dic5—21no—
227C2×Dic5—21no—
228C2×Dic5—21no—
229C2×Dic5—44no—
230D20—21no—
231D20—21no—
232D20—122no—
233D20—121no—
234D20—121no—
235D20—121no—
236D20—121no—
237C4×D5—41no—
238C4×D5—41no—
239Dic10—21no—
240Dic10#21312yescomplemented
241C5×C8—121no—
242C5×C8—121no—
243#168—62no—
244C2×#41—101no—
245C2×SD16—301no—
246C2×D8—301no—
247C2×D8—302no—
248#127—101no—
249#127—151no—
250#127D3×D511yescharacteristic
251#121—101no—
252#121—102no—
253C4×Q8—51no—
254C4×D4—51no—
255C4×D4—101no—
256C4⋊C8—31no—
257C4⋊C8—31no—
258#102—301no—
259#102—301no—
260C4×C8—151no—
261C2×C3×C5—82no—
262C2×C3×C5#44711yescharacteristic
263C2×C3×C5#44911yescharacteristic
264C2×C3×C5#45311yescharacteristic
265D15—161no—
266C3×D5—81no—
267C23×C3—22no—
268C23×C3—101no—
269C22×D3—201no—
270C3×Q8—52no—
271C3×Q8—101no—
272C3×D4—42no—
273C3×D4—41no—
274C3×D4—41no—
275C3×D4—41no—
276C3×D4—41no—
277C3×D4—101no—
278C3×D4—101no—
279C3×D4—204no—
280C3×D4—402no—
281C2×C3×C4—101no—
282C2×C3×C4—101no—
283C2×C3×C4—101no—
284C2×C3×C4—204no—
285C2×C3×C4—201no—
286C2×C3×C4—201no—
287C2×C3×C4C2×D2011yescharacteristic
288C2×C3×C4D4×D511yescharacteristic
289C2×C3×C4D4×D511yescharacteristic
290D12—202no—
291D12—201no—
292D12—201no—
293D12—201no—
294D12—201no—
295C3⋊C8—41no—
296C3⋊C8—41no—
297C3⋊C8—102no—
298C22×C5—42no—
299C22×C5—42no—
300C22×C5—42no—
301C22×C5#95311yescharacteristic
302C2×D5—41no—
303C2×D5—41no—
304C2×D5—41no—
305C2×D5—241no—
306C2×D5—241no—
307C2×D5—241no—
308C4×C5—21no—
309C4×C5C2×#21311yescharacteristic
310C4×C5#93211yescharacteristic
311C4×C5#94911yescharacteristic
312C4×C5#95011yescharacteristic
313Dic5—22no—
314Dic5—41no—
315Dic5—41no—
316#41—202no—
317#41—202no—
318C2×Q8—51no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—51no—
322C2×D4—102no—
323C2×D4—102no—
324C2×D4—301no—
325C2×D4—301no—
326C2×D4—301no—
327C2×D4#120212yes—
328C22×C4—102no—
329C22×C4—101no—
330SD16—602no—
331D8—602no—
332D8—604no—
333C2×C8—61no—
334C2×C8—61no—
335C2×C8—301no—
336C4⋊C4—51no—
337C4⋊C4—51no—
338C4⋊C4—101no—
339C22⋊C4—102no—
340C22⋊C4—101no—
341C42—101no—
342C42C2×D3×D511yescharacteristic
343C3×C5#162111yescharacteristic, complemented, Hall
344C22×C3—42no—
345C22×C3—42no—
346C22×C3—42no—
347C22×C3—201no—
348C22×C3—201no—
349C22×C3—201no—
350C22×C3#402811yescharacteristic
351C2×D3—401no—
352C2×D3—401no—
353C2×D3—401no—
354C3×C4—21no—
355C3×C4—102no—
356C3×C4—201no—
357C3×C4—201no—
358C3×C4D5×D811yescharacteristic
359C3×C4#405711yescharacteristic
360C3×C4#406011yescharacteristic
361C3×C4#406211yescharacteristic
362C2×C5—82no—
363C2×C5#521711yescharacteristic
364C2×C5#523811yescharacteristic
365C2×C5#524111yescharacteristic
366D5—81no—
367D5—481no—
368C23—22no—
369C23—101no—
370C23—601no—
371Q8—52no—
372Q8—101no—
373D4—42no—
374D4—41no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—101no—
379D4—101no—
380D4—204no—
381D4—402no—
382D4—602no—
383D4—601no—
384D4—601no—
385D4—601no—
386D4—601no—
387C2×C4—101no—
388C2×C4—101no—
389C2×C4—101no—
390C2×C4—204no—
391C2×C4—201no—
392C2×C4—201no—
393C2×C4C2×#120211yescharacteristic
394C2×C4D5×#6711yescharacteristic
395C2×C4D5×#6711yescharacteristic
396C8—121no—
397C8—121no—
398C8—302no—
399C2×C3—82no—
400C2×C3—401no—
401C2×C3#6503611yescharacteristic
402C2×C3#6506211yescharacteristic
403C2×C3#6507011yescharacteristic
404D3—801no—
405C5#7191811yescharacteristic, complemented, Sylow
406C22—42no—
407C22—42no—
408C22—42no—
409C22—201no—
410C22—201no—
411C22—201no—
412C22—1201no—
413C22—1201no—
414C22—1201no—
415C22#9156411yescharacteristic
416C4—21no—
417C4—102no—
418C4—201no—
419C4—201no—
420C4D5×#21311yescharacteristic
421C4#9147811yescharacteristic
422C4#9149111yescharacteristic
423C4#9149211yescharacteristic
424C3#1059919611yescharacteristic, complemented, Sylow
425C2—82no—
426C2—401no—
427C2—2401no—
428C2#1174902211yescharacteristic
429C2#1174902611yescharacteristic
430C2#1174913811yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5#120
hypercenter#127D3×D5
hypocenterC3×C5#1621
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#66052C2semidirect
2. #11751174C2semidirect
3. #11747064C2semidirect
4. #11747028C2semidirect
5. C5×#4544C2semidirect
6. #11745840C2semidirect
7. #11745834C2semidirect
27. #66052D3semidirect
65. #4544D5semidirect
113. C3×Dic10D8semidirect
240. Dic10#213semidirect
343. C3×C5#1621semidirect
405. C5#71918semidirect
424. C3#10599196semidirect

Maximal subgroups

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

subgroupindex
C3×#660522
#117511742
#117470642
#117470282
C5×#45442
#117458402
#117458342
#105991963
#719185