Finite Group Databasebeta

← #14289106

Subgroups — #14289106

Order 1920.

512 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 90 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#11752533C211yesmaximal, characteristic, complemented
2#11751173C211yesmaximal, characteristic, complemented
3C5×#5070C211yesmaximal, characteristic, complemented
4C3×#65361C211yesmaximal, characteristic, complemented
5#11745858C211yesmaximal, characteristic, complemented
6#11745838C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic, complemented
8#10601989—31nomaximal, Hall
9C2×#6766—21no—
10C3×C5×#127C2211yescharacteristic
11C2×#6715—21no—
12C4×D60C2211yescharacteristic
13C5×#869C2211yescharacteristic
14C2×C3×#686—21no—
15C3×C4×D20C2211yescharacteristic
16#91450—21no—
17#91413—22no—
18D5×C4⋊Dic3—21no—
19#91383—21no—
20#91116—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×#832—22no—
23C4×C5×C3⋊C8C2211yescharacteristic
24C3×#3964—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71018—51nomaximal, Hall
27#66060—31no—
28C5×#486—31no—
29#65361—31no—
30#65361D311yescharacteristic, complemented
31#64767—31no—
32#64679—31no—
33#64679—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×D60D411yescharacteristic
38C2×C4×D15—21no—
39C2×C5×Dic6—21no—
40C2×C3×D20D411yescharacteristic
41C2×C3×C4×D5—21no—
42C2×#1202—22no—
43C2×D5×Dic3—22no—
44#6766—42no—
45#6766—42no—
46C3×C42×C5C2311yescharacteristic
47#6715—42no—
48#6714—21no—
49C4⋊Dic15D411yescharacteristic
50C2×C3⋊#168—21no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3D412yes—
53C2×C5×C3⋊C8—21no—
54C3×#686—42no—
55C3×#685—21no—
56C3×C4⋊Dic5D411yescharacteristic
57C2×C3×#168—21no—
58#6668—22no—
59#6667—22no—
60#5555—51no—
61C3×#459—51no—
62#5072—51no—
63#5070D511yescharacteristic, complemented
64D4⋊(C3⋊C8)—51no—
65#4483—51no—
66#4482—51no—
67C2×#713—61no—
68C5×C4⋊Q8—31no—
69C5×#127C2×D311yescharacteristic
70#4092—61no—
71C2×#686—21no—
72C2×#686—61no—
73#4041—61no—
74#4040—62no—
75D5×C4⋊C4—61no—
76C4×D20—31no—
77C4×D20C2×D311yescharacteristic
78C5×#102—62no—
79C4×C5×C8—31no—
80#3964—21no—
81#3964—61no—
82C4⋊#168—31no—
83C4⋊#168C2×D311yescharacteristic
84#1625—151noSylow
85C23×C3×C5—41no—
86C22×D15—21no—
87C22×C3×D5—21no—
88C3×C5×D4—42no—
89C3×C5×D4—41no—
90C3×C5×D4—41no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15—21no—
97D60—21no—
98D60—21no—
99C4×D15—41no—
100C4×D15—41no—
101C2×C5×Dic3—22no—
102C5×Dic6—41no—
103C5×Dic6—41no—
104C2×C3×Dic5—21no—
105C3×D20—21no—
106C3×D20D812yescomplemented
107C3×C4×D5—41no—
108C3×C4×D5—41no—
109#1202—44no—
110D5×Dic3—44no—
111C3⋊#168—41no—
112C3×#168—41no—
113C5×C3⋊C8—41no—
114C2×#237—101no—
115C2×C3×D8—101no—
116C3×#127C2×D511yescharacteristic
117C3×C4×D4—51no—
118C2×#213—101no—
119#930—101no—
120C2×C4⋊Dic3—101no—
121#897—101no—
122#886—102no—
123C4×D12—51no—
124#869C2×D511yescharacteristic
125C3×C4⋊C8—51no—
126C3×#102—101no—
127#832—22no—
128#832—101no—
129C4⋊(C3⋊C8)—51no—
130C4×C3⋊C8C2×D511yescharacteristic
131C2×C5×Q8—61no—
132C2×C5×D4—21no—
133C2×C5×D4—21no—
134C2×C5×D4—21no—
135#713—122no—
136#713—122no—
137C2×D20—31no—
138C2×D20—62no—
139C2×D20#6711yescharacteristic
140C2×C4×D5—21no—
141C2×C4×D5—62no—
142C2×C4×D5—61no—
143C2×C5×C8—61no—
144C5×C4⋊C4—32no—
145C5×C4⋊C4—61no—
146C42×C5C22×D311yescharacteristic
147#686—42no—
148#686—122no—
149#685—21no—
150#685—62no—
151#685—61no—
152C4⋊Dic5—31no—
153C4⋊Dic5#6711yescharacteristic
154#683—62no—
155C2×#168—21no—
156C2×#168—61no—
157#547—151no—
158#486—31no—
159#459—51no—
160#459—151no—
161#332—151no—
162D4⋊C8—151no—
163D4⋊C8—151no—
164C22×C3×C5—81no—
165C22×C3×C5—81no—
166C22×C3×C5—81no—
167C22×C3×C5#12011yescharacteristic
168C2×D15—41no—
169C2×D15—41no—
170C2×D15—41no—
171C2×C3×D5—22no—
172C2×C3×D5—41no—
173C2×C3×D5—41no—
174C3×C4×C5—21no—
175C3×C4×C5C2×D811yescharacteristic
176C3×C4×C5#13511yescharacteristic
177C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
178C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
179Dic15—41no—
180C3×Dic5—41no—
181C5×Dic3—42no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—51no—
186C22×C3×C4—101no—
187C2×#67—102no—
188C22×Dic3—102no—
189#237—202no—
190#237—202no—
191C2×D12—51no—
192C2×C4×D3—101no—
193C2×Dic6—21no—
194C3×D8—202no—
195C2×C3×C8—101no—
196C3×C4⋊C4—51no—
197C3×C22⋊C4—101no—
198C3×C42C22×D511yescharacteristic
199#213—202no—
200(C2×D3)⋊C4—102no—
201(C2×D3)⋊C4—101no—
202C4⋊Dic3—21no—
203C4⋊Dic3—51no—
204C4⋊Dic3—102no—
205C4⋊Dic3C22⋊D512yes—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—101no—
208C23×C5—41no—
209C22×D5—21no—
210C22×D5—61no—
211C5×Q8—121no—
212C5×Q8—121no—
213C5×D4—42no—
214C5×D4—41no—
215C5×D4—41no—
216C5×D4—41no—
217C5×D4—41no—
218C2×C4×C5—62no—
219C2×C4×C5D3×D411yescharacteristic
220C2×C4×C5D3×D411yescharacteristic
221C2×C4×C5C2×#6711yescharacteristic
222C2×Dic5—21no—
223C2×Dic5—61no—
224D20—21no—
225D20—61no—
226D20—61no—
227D20—124no—
228D20#21312yescomplemented
229C4×D5—41no—
230C4×D5—41no—
231C4×D5—124no—
232C4×D5—121no—
233C4×D5—121no—
234C5×C8—121no—
235#168—41no—
236#168—121no—
237C2×#41—301no—
238C2×D8—101no—
239C2×D8—301no—
240C4⋊Q8—31no—
241#127D3×D511yescharacteristic
242#123—302no—
243C22⋊Q8—301no—
244#121—301no—
245C4×D4—51no—
246C4×D4—151no—
247C2×C4⋊C4—301no—
248C4⋊C8—51no—
249C4⋊C8—151no—
250#102—62no—
251#102—101no—
252#102—301no—
253C4×C8—31no—
254C2×C3×C5—161no—
255C2×C3×C5#44711yescharacteristic
256C2×C3×C5#44911yescharacteristic
257C2×C3×C5#45411yescharacteristic
258D15—81no—
259C3×D5—42no—
260C23×C3—41no—
261C23×C3—101no—
262C22×D3—101no—
263C3×D4—42no—
264C3×D4—41no—
265C3×D4—41no—
266C3×D4—41no—
267C3×D4—41no—
268C3×D4—52no—
269C3×D4—101no—
270C2×C3×C4—101no—
271C2×C3×C4—201no—
272C2×C3×C4—201no—
273C2×C3×C4D4×D511yescharacteristic
274C2×C3×C4D4×D511yescharacteristic
275C2×C3×C4C2×C22⋊D511yescharacteristic
276#67—204no—
277C2×Dic3—22no—
278C2×Dic3—101no—
279C2×Dic3—204no—
280D12—101no—
281D12—101no—
282C4×D3—201no—
283C4×D3—201no—
284Dic6—41no—
285Dic6—41no—
286C3×C8—201no—
287C3⋊C8—41no—
288C3⋊C8—201no—
289C22×C5—81no—
290C22×C5—81no—
291C22×C5—81no—
292C22×C5#93711yescharacteristic
293C2×D5—22no—
294C2×D5—41no—
295C2×D5—41no—
296C2×D5—121no—
297C2×D5—121no—
298C2×D5—121no—
299C4×C5—21no—
300C4×C5—122no—
301C4×C5#91111yescharacteristic
302C4×C5#91211yescharacteristic
303C4×C5C2×#21311yescharacteristic
304C4×C5#94911yescharacteristic
305Dic5—41no—
306Dic5—121no—
307#41—602no—
308#41—602no—
309C2×Q8—61no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—51no—
314C2×D4—151no—
315C2×D4—302no—
316C22×C4—101no—
317C22×C4—302no—
318C22×C4—301no—
319D8—202no—
320D8—602no—
321C2×C8—61no—
322C2×C8—101no—
323C2×C8—301no—
324C4⋊C4—32no—
325C4⋊C4—51no—
326C4⋊C4—61no—
327C4⋊C4—151no—
328C4⋊C4—302no—
329C22⋊C4—101no—
330C22⋊C4—302no—
331C22⋊C4—301no—
332C42C2×D3×D511yescharacteristic
333C3×C5#162511yescharacteristic, complemented, Hall
334C22×C3—81no—
335C22×C3—81no—
336C22×C3—81no—
337C22×C3—102no—
338C22×C3—201no—
339C22×C3—201no—
340C22×C3#408311yescharacteristic
341C2×D3—201no—
342C2×D3—201no—
343C2×D3—201no—
344C3×C4—21no—
345C3×C4—201no—
346C3×C4D5×D811yescharacteristic
347C3×C4#405711yescharacteristic
348C3×C4#406011yescharacteristic
349C3×C4#406211yescharacteristic
350Dic3—42no—
351Dic3—201no—
352C2×C5—161no—
353C2×C5#503611yescharacteristic
354C2×C5#515811yescharacteristic
355C2×C5#520111yescharacteristic
356D5—42no—
357D5—241no—
358C23—41no—
359C23—101no—
360C23—301no—
361Q8—121no—
362Q8—121no—
363D4—42no—
364D4—41no—
365D4—41no—
366D4—41no—
367D4—41no—
368D4—52no—
369D4—101no—
370D4—301no—
371D4—301no—
372D4—604no—
373C2×C4—62no—
374C2×C4—101no—
375C2×C4—201no—
376C2×C4—201no—
377C2×C4—301no—
378C2×C4—604no—
379C2×C4—601no—
380C2×C4—601no—
381C2×C4D5×#6711yescharacteristic
382C2×C4D3×C22⋊D511yescharacteristic
383C2×C4#679011yescharacteristic
384C8—121no—
385C8—201no—
386C8—601no—
387C2×C3—161no—
388C2×C3—202no—
389C2×C3#6535111yescharacteristic
390C2×C3#6544511yescharacteristic
391C2×C3#6546111yescharacteristic
392D3—401no—
393C5#7101811yescharacteristic, complemented, Sylow
394C22—81no—
395C22—81no—
396C22—81no—
397C22—102no—
398C22—201no—
399C22—201no—
400C22—601no—
401C22—601no—
402C22—601no—
403C22#9157711yescharacteristic
404C4—21no—
405C4—122no—
406C4—201no—
407C4—601no—
408C4D5×#21311yescharacteristic
409C4#9147811yescharacteristic
410C4#9149711yescharacteristic
411C4#9149811yescharacteristic
412C3#1060198911yescharacteristic, complemented, Sylow
413C2—161no—
414C2—202no—
415C2—1201no—
416C2#1174915111yescharacteristic
417C2#1174915811yescharacteristic
418C2#1174916711yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5#120
hypercenter#127D3×D5
hypocenterC3×C5#1625
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. #11752533C2semidirect
2. #11751173C2semidirect
3. C5×#5070C2semidirect
4. C3×#65361C2semidirect
5. #11745858C2semidirect
6. #11745838C2semidirect
7. #11745835C2semidirect
30. #65361D3semidirect
63. #5070D5semidirect
106. C3×D20D8semidirect
228. D20#213semidirect
333. C3×C5#1625semidirect
393. C5#71018semidirect
412. C3#10601989semidirect

Maximal subgroups

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

subgroupindex
#117525332
#117511732
C5×#50702
C3×#653612
#117458582
#117458382
#117458352
#106019893
#710185