Finite Group Databasebeta

← #14288659

Subgroups — #14288659

Order 1920.

416 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 78 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
1#11754483C211yesmaximal, characteristic
2C3×#65011C211yesmaximal, characteristic, complemented
3#11748622C211yesmaximal, characteristic, complemented
4#11748454C211yesmaximal, characteristic
5#11746291C211yesmaximal, characteristic
6C5×#4469C211yesmaximal, characteristic, complemented
7#11745960C211yesmaximal, characteristic, complemented
8#10598929—31nomaximal, Hall
9#91819C2211yescharacteristic
10C2×C5×Dic3⋊C4C2211yescharacteristic
11C2×C3×C4⋊Dic5C2211yescharacteristic
12C3×#4070C2211yescharacteristic
13#91556—21no—
14#91542—21no—
15#91433—21no—
16#91411—21no—
17#91345—21no—
18#91334—21no—
19C3×C5×C22⋊C8C2211yescharacteristic
20#91115C2211yescharacteristic
21C5×#830C2211yescharacteristic
22C3×#3950—21no—
23C3×#3948—21no—
24#90994—21no—
25#90994—21no—
26#90987—21no—
27#90968—21no—
28#71178—51nomaximal, Hall
29#65849—31no—
30#65275—31no—
31#65024—31no—
32#65011D311yescharacteristic, complemented
33C5×#324—31no—
34#64690—31no—
35#64687—31no—
36C22×C3×C4×C5C2311yescharacteristic
37C2×#1220—21no—
38C22×Dic15—21no—
39C2×D60D411yescharacteristic
40C22×C5×Dic3D411yescharacteristic
41C22×C5×Dic3D411yescharacteristic
42C22×C3×Dic5—21no—
43C2×C3×Dic10D411yescharacteristic
44C2×#1200—21no—
45C2×C3×C5×C8—21no—
46#6714—21no—
47C4⋊Dic15D411yescharacteristic
48C5×Dic3⋊C4—21no—
49C5×Dic3⋊C4—21no—
50C2×C5×C3⋊C8—21no—
51C3×C22⋊Dic5—21no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C3×#683—21no—
56#6669—21no—
57#6668—21no—
58#6668—21no—
59#6667—21no—
60#6667—21no—
61#6667—21no—
62Dic3×Dic5—21no—
63#5645—51no—
64C3×#484—51no—
65#4985—51no—
66#4968—51no—
67#4538—51no—
68#4470—51no—
69#4469D511yescharacteristic, complemented
70C2×C5×C4⋊C4—31no—
71#4076—31no—
72#4075—61no—
73C4×C22⋊D5—61no—
74C2×C4⋊Dic5C2×D311yescharacteristic
75#4070C2×D311yescharacteristic
76#4044—61no—
77#4042—61no—
78#4040—61no—
79#4035—61no—
80C5×C22⋊C8—31no—
81C5×C22⋊C8C2×D311yescharacteristic
82#3963—31no—
83#3963—61no—
84#3963—61no—
85#3953—61no—
86#3950—21no—
87#3949—61no—
88#3948—21no—
89#1615—151noSylow
90C23×C3×C5C2×D411yescharacteristic
91C22×D15—21no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95#1220—41no—
96#1220—41no—
97C2×Dic15—21no—
98C2×Dic15—41no—
99C2×Dic15—41no—
100C2×Dic15—41no—
101D60—41no—
102C2×C5×Dic3—21no—
103C2×C5×Dic3—21no—
104C2×C5×Dic3—21no—
105C2×C5×Dic3—21no—
106C2×C5×Dic3—41no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5—42no—
110C2×C3×Dic5—41no—
111C3×Dic10—41no—
112#1200—81no—
113C3×C5×C8—41no—
114C5×C3⋊C8—41no—
115C3×C22⋊Q8—51no—
116C2×C3×C4⋊C4—51no—
117#946—101no—
118#930—51no—
119C2×Dic3⋊C4C2×D511yescharacteristic
120#898—101no—
121#894—101no—
122#890—101no—
123#886—101no—
124#67⋊C4—101no—
125C3×#107—101no—
126C3×#103—101no—
127C3×C22⋊C8C2×D511yescharacteristic
128C3⋊#95—51no—
129C3⋊#95—101no—
130C3⋊#95—101no—
131#830C2×D511yescharacteristic
132#809—101no—
133#808—101no—
134C22×C4×C5—31no—
135C22×C4×C5—31no—
136C22×C4×C5C22×D311yescharacteristic
137C2×C22⋊D5—61no—
138C22×Dic5—21no—
139C22×Dic5—61no—
140C2×D20—31no—
141C2×C4×D5—61no—
142C2×Dic10#6711yescharacteristic
143C2×C5×C8—21no—
144C2×C5×C8—61no—
145C5×C4⋊C4—61no—
146C5×C4⋊C4—61no—
147C22⋊Dic5—21no—
148#685—61no—
149#685—61no—
150#685—61no—
151#685—61no—
152C4⋊Dic5—21no—
153C4⋊Dic5—21no—
154C4⋊Dic5—31no—
155C4⋊Dic5#6711yescharacteristic
156#683—21no—
157#683—61no—
158#683—61no—
159#683—61no—
160C4×Dic5—61no—
161#539—151no—
162#484—51no—
163#481—151no—
164#400—151no—
165#328—151no—
166#327—151no—
167#324—31no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5#12011yescharacteristic
171C22×C3×C5#13511yescharacteristic
172C22×C3×C5#13711yescharacteristic
173C2×D15—41no—
174C2×D15—41no—
175C2×D15—41no—
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178Dic15—41no—
179Dic15—81no—
180C3×Dic5—41no—
181C3×Dic5—41no—
182C3×Dic5—81no—
183C5×Dic3—41no—
184C5×Dic3—41no—
185C2×C3×Q8—51no—
186C22×C3×C4—101no—
187C22×C3×C4C22×D511yescharacteristic
188C2×#67—101no—
189C22×Dic3—101no—
190C22×Dic3D2011yescharacteristic
191C22×Dic3D2011yescharacteristic
192C2×D12—51no—
193C2×C4×D3—101no—
194C2×C3×C8—21no—
195C3×C4⋊C4—51no—
196C3×C4⋊C4—101no—
197C3×C4⋊C4—101no—
198C3×C4⋊C4—101no—
199C3×C22⋊C4—101no—
200(C2×D3)⋊C4—101no—
201(C2×D3)⋊C4—101no—
202(C2×D3)⋊C4—101no—
203(C2×D3)⋊C4—101no—
204C4⋊Dic3—51no—
205C4⋊Dic3—101no—
206C4⋊Dic3—101no—
207Dic3⋊C4—21no—
208Dic3⋊C4—21no—
209Dic3⋊C4—101no—
210C4×Dic3—101no—
211C2×C3⋊C8—21no—
212C23×C5D3×D411yescharacteristic
213C22×D5—61no—
214C2×C4×C5—41no—
215C2×C4×C5—61no—
216C2×C4×C5—61no—
217C2×C4×C5—61no—
218C2×C4×C5—61no—
219C2×C4×C5—121no—
220C2×C4×C5D3×D411yescharacteristic
221C2×C4×C5C2×#6711yescharacteristic
222C22⋊D5—121no—
223C22⋊D5—121no—
224C2×Dic5—21no—
225C2×Dic5—21no—
226C2×Dic5—42no—
227C2×Dic5—41no—
228C2×Dic5—61no—
229C2×Dic5—121no—
230C2×Dic5—121no—
231C2×Dic5—121no—
232D20—121no—
233C4×D5—241no—
234Dic10—41no—
235C5×C8—41no—
236C5×C8—121no—
237#126—301no—
238#125—301no—
239#123—301no—
240#123—301no—
241C22⋊Q8—51no—
242C22⋊Q8—301no—
243#121—151no—
244C4×D4—301no—
245C2×C4⋊C4—31no—
246C2×C4⋊C4—51no—
247#107—101no—
248#106—301no—
249#103—101no—
250#102—301no—
251C22⋊C8—31no—
252C22⋊C8D3×D511yescharacteristic
253#95—151no—
254#95—301no—
255#95—301no—
256C2×C3×C5—21no—
257C2×C3×C5—21no—
258C2×C3×C5#45211yescharacteristic
259C2×C3×C5#45411yescharacteristic
260C2×C3×C5#45811yescharacteristic
261D15—81no—
262C23×C3C2×D2011yescharacteristic
263C22×D3—101no—
264C3×Q8—201no—
265C2×C3×C4—41no—
266C2×C3×C4—101no—
267C2×C3×C4—101no—
268C2×C3×C4—202no—
269C2×C3×C4—201no—
270C2×C3×C4D4×D511yescharacteristic
271C2×C3×C4D4×D511yescharacteristic
272#67—201no—
273#67—201no—
274C2×Dic3—21no—
275C2×Dic3—21no—
276C2×Dic3—21no—
277C2×Dic3—21no—
278C2×Dic3—41no—
279C2×Dic3—101no—
280C2×Dic3—201no—
281C2×Dic3—201no—
282C2×Dic3—201no—
283D12—201no—
284C4×D3—401no—
285C3×C8—41no—
286C3⋊C8—41no—
287C22×C5—21no—
288C22×C5—21no—
289C22×C5#91811yescharacteristic
290C22×C5#91911yescharacteristic
291C22×C5#93711yescharacteristic
292C2×D5—121no—
293C2×D5—121no—
294C2×D5—121no—
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—121no—
298C4×C5—121no—
299Dic5—41no—
300Dic5—41no—
301Dic5—81no—
302Dic5—121no—
303Dic5—241no—
304C2×Q8—51no—
305C2×D4—151no—
306C2×D4—301no—
307C22×C4—31no—
308C22×C4—31no—
309C22×C4—101no—
310C22×C4—301no—
311C22×C4—301no—
312C22×C4C2×D3×D511yescharacteristic
313C2×C8—21no—
314C2×C8—61no—
315C4⋊C4—51no—
316C4⋊C4—61no—
317C4⋊C4—61no—
318C4⋊C4—101no—
319C4⋊C4—101no—
320C4⋊C4—101no—
321C4⋊C4—151no—
322C4⋊C4—301no—
323C4⋊C4—301no—
324C4⋊C4—301no—
325C22⋊C4—101no—
326C22⋊C4—301no—
327C22⋊C4—301no—
328C22⋊C4—301no—
329C22⋊C4—301no—
330C42—301no—
331C3×C5#161511yescharacteristic, complemented, Hall
332C22×C3—21no—
333C22×C3—21no—
334C22×C3#402811yescharacteristic
335C22×C3#405011yescharacteristic
336C22×C3#405511yescharacteristic
337C2×D3—201no—
338C2×D3—201no—
339C2×D3—201no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—201no—
343C3×C4—201no—
344C3×C4—401no—
345Dic3—41no—
346Dic3—41no—
347Dic3—201no—
348Dic3—401no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5#505311yescharacteristic
352C2×C5#518711yescharacteristic
353C2×C5#520111yescharacteristic
354D5—241no—
355C23—301no—
356C23D3×D2011yescharacteristic
357Q8—201no—
358D4—601no—
359D4—601no—
360D4—601no—
361C2×C4—41no—
362C2×C4—61no—
363C2×C4—61no—
364C2×C4—61no—
365C2×C4—61no—
366C2×C4—101no—
367C2×C4—101no—
368C2×C4—121no—
369C2×C4—202no—
370C2×C4—201no—
371C2×C4—301no—
372C2×C4—601no—
373C2×C4—601no—
374C2×C4—601no—
375C2×C4—1201no—
376C2×C4#677711yescharacteristic
377C2×C4D5×#6711yescharacteristic
378C8—41no—
379C8—121no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3#6502211yescharacteristic
383C2×C3#6503111yescharacteristic
384C2×C3#6504211yescharacteristic
385D3—401no—
386C5#7117811yescharacteristic, complemented, Sylow
387C22—21no—
388C22—21no—
389C22—601no—
390C22—601no—
391C22—601no—
392C22#9126311yescharacteristic
393C22#9127511yescharacteristic
394C22#9147411yescharacteristic
395C4—21no—
396C4—21no—
397C4—121no—
398C4—121no—
399C4—201no—
400C4—201no—
401C4—401no—
402C4—601no—
403C4—1201no—
404C3#1059892911yescharacteristic, complemented, Sylow
405C2—21no—
406C2—21no—
407C2—1201no—
408C2#1174713311yescharacteristic
409C2#1174815211yescharacteristic
410C2#1174825511yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5#120
prime radical#91819C22
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1615
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#65011C2semidirect
3. #11748622C2semidirect
6. C5×#4469C2semidirect
7. #11745960C2semidirect
32. #65011D3semidirect
69. #4469D5semidirect
331. C3×C5#1615semidirect
386. C5#71178semidirect
404. C3#10598929semidirect

Maximal subgroups

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

subgroupindex
#117544832
C3×#650112
#117486222
#117484542
#117462912
C5×#44692
#117459602
#105989293
#711785