Finite Group Databasebeta

← #14289002

Subgroups — #14289002

Order 1920.

472 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 88 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#11752654C211yesmaximal, characteristic, complemented
2C3×#65137C211yesmaximal, characteristic, complemented
3#11747079C211yesmaximal, characteristic, complemented
4#11747043C211yesmaximal, characteristic
5#11746304C211yesmaximal, characteristic, complemented
6C5×#4481C211yesmaximal, characteristic, complemented
7#11745840C211yesmaximal, characteristic, complemented
8#10599283—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C2×C3×#677—21no—
12C3×#4020C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14#91437—21no—
15#91424—22no—
16#91418—21no—
17#91390—21no—
18#91388—21no—
19C2×#6655—22no—
20C2×#6653—21no—
21C3×C5×C4⋊C8C2211yescharacteristic
22C4×C3⋊#168C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×#3953—21no—
25#90965—21no—
26#71028—51nomaximal, Hall
27#66064—31no—
28#65374—31no—
29#65137D311yescharacteristic, complemented
30#65132—31no—
31C5×#333—31no—
32#64704—31no—
33#64703—31no—
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×C5×Dic6D412yes—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×Dic10D411yescharacteristic
41C2×#1200—22no—
42C2×C3×C5×C8—21no—
43C3×C42×C5C2311yescharacteristic
44#6714—21no—
45C4⋊Dic15D411yescharacteristic
46C2×C3⋊#168—21no—
47C5×C4⋊Dic3—21no—
48C5×C4⋊Dic3—21no—
49C2×C5×C3⋊C8—21no—
50C3×C4⋊Dic5D411yescharacteristic
51C3×#683—21no—
52C3×C4×Dic5—21no—
53C3×#677—42no—
54Dic3⋊Dic5—22no—
55#6669—22no—
56#6667—22no—
57#6655—44no—
58#6653—42no—
59#5579—51no—
60C3×#460—51no—
61#5076—51no—
62#5072—51no—
63#4535—51no—
64#4483—51no—
65#4481D511yescharacteristic, complemented
66C5×C4⋊Q8—31no—
67#4092—62no—
68C2×#688—62no—
69C2×D40—61no—
70C2×#677—21no—
71#4043—61no—
72#4039—61no—
73D5×C4⋊C4—61no—
74#4036—61no—
75#4020C2×D311yescharacteristic
76C4×D20—31no—
77C4×Dic10C2×D311yescharacteristic
78C5×C4⋊C8—31no—
79C5×C4⋊C8C2×D311yescharacteristic
80#3953—21no—
81#3953—61no—
82C4×#168—31no—
83#1622—151noSylow
84C22×D15—21no—
85C22×C3×D5—41no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—21no—
90D60—21no—
91D60SD1612yescomplemented
92C4×D15—41no—
93C4×D15—41no—
94C2×C5×Dic3—22no—
95C5×Dic6—42no—
96C2×C3×Dic5—21no—
97C2×C3×Dic5—21no—
98C3×D20—42no—
99C3×D20—41no—
100C3×D20—41no—
101C3×D20—41no—
102C3×D20—41no—
103C3×Dic10—21no—
104C3×Dic10—21no—
105#1200—82no—
106C3×C5×C8—41no—
107C3⋊#168—22no—
108C5×C3⋊C8—41no—
109C2×C3×SD16—101no—
110C3×#127—51no—
111C3×C4×Q8—51no—
112#946—101no—
113C2×#214—102no—
114C2×#213—101no—
115#896—102no—
116D3×C4⋊C4—101no—
117C4×D12—51no—
118C4×D12—101no—
119#870—101no—
120#869C2×D511yescharacteristic
121C3×C4⋊C8C2×D511yescharacteristic
122C3×#102—101no—
123#832—101no—
124C4⋊(C3⋊C8)C2×D511yescharacteristic
125C4×C3⋊C8—51no—
126C2×C5×Q8—32no—
127C2×D20—21no—
128C2×D20—21no—
129C2×D20—21no—
130C2×D20—31no—
131C2×C4×D5—61no—
132C2×C4×D5—62no—
133C2×Dic10#6711yescharacteristic
134C2×C5×C8—21no—
135C2×C5×C8—61no—
136C5×C4⋊C4—61no—
137C5×C4⋊C4—61no—
138C42×C5C22×D311yescharacteristic
139#688—124no—
140#685—62no—
141#685—61no—
142C4⋊Dic5—31no—
143C4⋊Dic5—62no—
144C4⋊Dic5#6711yescharacteristic
145#683—21no—
146#683—62no—
147C4×Dic5—21no—
148C2×#168—61no—
149D40—122no—
150#677—42no—
151#554—151no—
152#492—151no—
153#460—51no—
154#459—151no—
155#333—31no—
156Q8⋊C8—151no—
157D4⋊C8—151no—
158C22×C3×C5#12011yescharacteristic
159C2×D15—22no—
160C2×D15—41no—
161C2×D15—41no—
162C2×C3×D5—81no—
163C2×C3×D5—81no—
164C2×C3×D5—81no—
165C3×C4×C5—21no—
166C3×C4×C5C2×SD1611yescharacteristic
167C3×C4×C5#13511yescharacteristic
168C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
169C3×C4×C5#13711yescharacteristic
170Dic15—41no—
171C3×Dic5—41no—
172C3×Dic5—41no—
173C5×Dic3—42no—
174C2×C3×Q8—51no—
175C2×C3×D4—101no—
176C2×C3×D4—101no—
177C2×C3×D4—101no—
178C2×D12—51no—
179C2×C4×D3—101no—
180C2×C4×D3—102no—
181C2×Dic6D2012yes—
182C3×SD16—202no—
183C2×C3×C8—21no—
184C3×C4⋊C4—51no—
185C3×C4⋊C4—101no—
186C3×C42—101no—
187C3×C42C22×D511yescharacteristic
188#214—204no—
189#213—202no—
190(C2×D3)⋊C4—102no—
191(C2×D3)⋊C4—101no—
192C4⋊Dic3—21no—
193C4⋊Dic3—21no—
194C4⋊Dic3—51no—
195Dic3⋊C4—102no—
196Dic3⋊C4—102no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—101no—
199C22×D5—41no—
200C22×D5—61no—
201C5×Q8—122no—
202C2×C4×C5—62no—
203C2×C4×C5D3×D411yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5C2×#6711yescharacteristic
206C2×Dic5—21no—
207C2×Dic5—21no—
208C2×Dic5—61no—
209D20—32no—
210D20—42no—
211D20—41no—
212D20—41no—
213D20—41no—
214D20—41no—
215D20—61no—
216C4×D5—121no—
217C4×D5—121no—
218C4×D5—242no—
219Dic10—21no—
220Dic10—21no—
221C5×C8—41no—
222C5×C8—121no—
223#168—62no—
224C2×SD16—101no—
225C2×SD16—302no—
226C2×D8—301no—
227C4⋊Q8—31no—
228#127—51no—
229#125—301no—
230C22⋊Q8—301no—
231C22⋊Q8—302no—
232C4×Q8—51no—
233C4×D4—151no—
234C4×D4—301no—
235C2×C4⋊C4—301no—
236C4⋊C8—31no—
237C4⋊C8D3×D511yescharacteristic
238#102—101no—
239#102—301no—
240C4×C8—151no—
241C2×C3×C5#44811yescharacteristic
242C2×C3×C5#44911yescharacteristic
243C2×C3×C5#45311yescharacteristic
244D15—42no—
245C3×D5—161no—
246C23×C3—201no—
247C22×D3—101no—
248C3×Q8—101no—
249C3×Q8—101no—
250C3×D4—202no—
251C3×D4—201no—
252C3×D4—201no—
253C3×D4—201no—
254C3×D4—201no—
255C2×C3×C4—101no—
256C2×C3×C4—101no—
257C2×C3×C4C2×D2011yescharacteristic
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260C2×Dic3—22no—
261C2×Dic3—101no—
262D12—52no—
263D12—101no—
264C4×D3—201no—
265C4×D3—201no—
266C4×D3—402no—
267Dic6—42no—
268C3×C8—41no—
269C3⋊C8—41no—
270C3⋊C8—102no—
271C22×C5#93711yescharacteristic
272C2×D5—62no—
273C2×D5—81no—
274C2×D5—81no—
275C2×D5—81no—
276C2×D5—121no—
277C2×D5—121no—
278C4×C5—21no—
279C4×C5—122no—
280C4×C5D3×SD1611yescharacteristic
281C4×C5#91511yescharacteristic
282C4×C5#93211yescharacteristic
283C4×C5#95011yescharacteristic
284Dic5—41no—
285Dic5—41no—
286Dic5—121no—
287C2×Q8—32no—
288C2×Q8—51no—
289C2×D4—101no—
290C2×D4—101no—
291C2×D4—101no—
292C2×D4—151no—
293C22×C4—302no—
294C22×C4—301no—
295SD16—202no—
296SD16—604no—
297D8—602no—
298C2×C8—21no—
299C2×C8—61no—
300C2×C8—301no—
301C4⋊C4—51no—
302C4⋊C4—61no—
303C4⋊C4—61no—
304C4⋊C4—101no—
305C4⋊C4—151no—
306C4⋊C4—302no—
307C4⋊C4—302no—
308C22⋊C4—302no—
309C22⋊C4—301no—
310C42—101no—
311C42C2×D3×D511yescharacteristic
312C3×C5#162211yescharacteristic, complemented, Hall
313C22×C3—401no—
314C22×C3—401no—
315C22×C3—401no—
316C22×C3#402811yescharacteristic
317C2×D3—102no—
318C2×D3—201no—
319C2×D3—201no—
320C3×C4—21no—
321C3×C4—201no—
322C3×C4—201no—
323C3×C4D5×SD1611yescharacteristic
324C3×C4#406011yescharacteristic
325C3×C4#406411yescharacteristic
326C3×C4#406511yescharacteristic
327Dic3—42no—
328Dic3—201no—
329C2×C5#503711yescharacteristic
330C2×C5#517011yescharacteristic
331C2×C5#519811yescharacteristic
332D5—122no—
333D5—161no—
334C23—201no—
335C23—301no—
336Q8—101no—
337Q8—101no—
338Q8—122no—
339D4—152no—
340D4—202no—
341D4—201no—
342D4—201no—
343D4—201no—
344D4—201no—
345D4—301no—
346C2×C4—62no—
347C2×C4—101no—
348C2×C4—101no—
349C2×C4—301no—
350C2×C4—601no—
351C2×C4—601no—
352C2×C4—1202no—
353C2×C4D3×D2011yescharacteristic
354C2×C4#677711yescharacteristic
355C2×C4D5×#6711yescharacteristic
356C8—41no—
357C8—121no—
358C8—302no—
359C2×C3—801no—
360C2×C3#6503611yescharacteristic
361C2×C3#6509511yescharacteristic
362C2×C3#6510011yescharacteristic
363D3—202no—
364C5#7102811yescharacteristic, complemented, Sylow
365C22—302no—
366C22—401no—
367C22—401no—
368C22—401no—
369C22—601no—
370C22—601no—
371C22#9147411yescharacteristic
372C4—21no—
373C4—122no—
374C4—201no—
375C4—201no—
376C4—601no—
377C4#9125511yescharacteristic
378C4#9127811yescharacteristic
379C4#9149111yescharacteristic
380C4#9151611yescharacteristic
381C3#1059928311yescharacteristic, complemented, Sylow
382C2—602no—
383C2—801no—
384C2#1174751211yescharacteristic
385C2#1174789111yescharacteristic
386C2#1174824311yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#11747043C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1622
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #11752654C2semidirect
2. C3×#65137C2semidirect
3. #11747079C2semidirect
5. #11746304C2semidirect
6. C5×#4481C2semidirect
7. #11745840C2semidirect
29. #65137D3semidirect
65. #4481D5semidirect
91. D60SD16semidirect
312. C3×C5#1622semidirect
364. C5#71028semidirect
381. C3#10599283semidirect

Maximal subgroups

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

subgroupindex
#117526542
C3×#651372
#117470792
#117470432
#117463042
C5×#44812
#117458402
#105992833
#710285