Finite Group Databasebeta

← #14289225

Subgroups — #14289225

Order 1920.

500 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 95 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#11756486C211yesmaximal, characteristic, complemented
2#11751189C211yesmaximal, characteristic, complemented
3#11750949C211yesmaximal, characteristic, complemented
4#11750944C211yesmaximal, characteristic
5C3×C5×#332C211yesmaximal, characteristic, complemented
6#11746305C211yesmaximal, characteristic, complemented
7#11746304C211yesmaximal, characteristic, complemented
8#10599250—31nomaximal, Hall
9C2×Q8×D15—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11#91835—21no—
12C2×D120—21no—
13C2×#6706—21no—
14#91785—22no—
15#91782—21no—
16#91777—21no—
17#91763C2211yescharacteristic
18C4×D60C2211yescharacteristic
19C4×Dic30C2211yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22#91105—21no—
23#91105—21no—
24#91093—22no—
25C4×C3⋊#168C2211yescharacteristic
26#68457—51nomaximal, Hall
27#66061—31no—
28#65377—31no—
29#65137—31no—
30#65132—31no—
31C5×#332D311yescharacteristic, complemented
32#64704—31no—
33#64703—31no—
34C2×C3×C5×Q8—21no—
35Q8×D15—42no—
36Q8×D15—42no—
37C2×D60—21no—
38C2×D60—21no—
39C2×D60—21no—
40C2×D60D411yescharacteristic
41C2×C4×D15—22no—
42C2×C4×D15—21no—
43C2×Dic30—22no—
44C2×Dic30D411yescharacteristic
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4D412yes—
49C3×C42×C5C2311yescharacteristic
50#6714—22no—
51#6714—21no—
52C4⋊Dic15D411yescharacteristic
53C4⋊Dic15D411yescharacteristic
54#6712—22no—
55#6712—21no—
56C4×Dic15—21no—
57C2×C3⋊#168—21no—
58D120—42no—
59#6706—42no—
60#5727—51no—
61#5088—51no—
62#4848—51no—
63#4843—51no—
64C3×#332D511yescharacteristic, complemented
65#4484—51no—
66#4483—51no—
67C2×Q8×D5—61no—
68C5×C4⋊Q8C2×D311yescharacteristic
69#4092—61no—
70C2×D40—61no—
71C2×#677—61no—
72#4042—62no—
73#4039—61no—
74#4034—61no—
75#4020—31no—
76C4×D20—31no—
77C4×Dic10—31no—
78C5×C4⋊C8C2×D311yescharacteristic
79C5×C4⋊C8C2×D311yescharacteristic
80#3953—61no—
81#3953—61no—
82#3941—62no—
83C4×#168—31no—
84#1627—151noSylow
85C22×D15—21no—
86C22×D15—41no—
87C3×C5×Q8—41no—
88C3×C5×Q8—41no—
89C2×C3×C4×C5—22no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×Dic15—21no—
94C2×Dic15—21no—
95C2×Dic15—21no—
96D60—21no—
97D60—42no—
98D60—41no—
99D60—41no—
100D60—41no—
101D60—41no—
102D60SD1612yescomplemented
103C4×D15—44no—
104C4×D15—41no—
105C4×D15—41no—
106Dic30—21no—
107Dic30—44no—
108Dic30D812yescomplemented
109C3×C5×C8—41no—
110C3×C5×C8—41no—
111C3⋊#168—41no—
112C2×D3×Q8—101no—
113C3×C4⋊Q8C2×D511yescharacteristic
114#946—101no—
115C2×D24—101no—
116C2×#204—101no—
117#896—102no—
118#893—101no—
119#888—101no—
120#874—51no—
121C4×D12—51no—
122C4×Dic6—51no—
123C3×C4⋊C8C2×D511yescharacteristic
124C3×C4⋊C8C2×D511yescharacteristic
125#821—101no—
126#821—101no—
127#809—102no—
128C4×C3⋊C8—51no—
129C2×C5×Q8—21no—
130Q8×D5—122no—
131Q8×D5—122no—
132C2×D20—31no—
133C2×D20—61no—
134C2×D20—61no—
135C2×D20—61no—
136C2×C4×D5—62no—
137C2×C4×D5—61no—
138C2×Dic10—31no—
139C2×Dic10—62no—
140C2×C5×C8—21no—
141C2×C5×C8—21no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4D1212yes—
144C42×C5C22×D311yescharacteristic
145#685—62no—
146#685—61no—
147C4⋊Dic5—31no—
148C4⋊Dic5—31no—
149#683—62no—
150#683—61no—
151C4×Dic5—61no—
152C2×#168—61no—
153D40—122no—
154#677—122no—
155D4×Q8—151no—
156#486—151no—
157#460—151no—
158#459—151no—
159#332D1511yescharacteristic, complemented
160Q8⋊C8—151no—
161D4⋊C8—151no—
162C22×C3×C5#12011yescharacteristic
163C2×D15—22no—
164C2×D15—41no—
165C2×D15—41no—
166C2×D15—81no—
167C2×D15—81no—
168C2×D15—81no—
169C3×C4×C5—21no—
170C3×C4×C5—42no—
171C3×C4×C5C2×D811yescharacteristic
172C3×C4×C5C2×SD1611yescharacteristic
173C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
174C3×C4×C5#13711yescharacteristic
175Dic15—22no—
176Dic15—41no—
177Dic15—41no—
178C2×C3×Q8—21no—
179D3×Q8—202no—
180D3×Q8—202no—
181C2×D12—51no—
182C2×D12—101no—
183C2×D12—101no—
184C2×D12—101no—
185C2×C4×D3—102no—
186C2×C4×D3—101no—
187C2×Dic6—51no—
188C2×Dic6—102no—
189C2×C3×C8—21no—
190C2×C3×C8—21no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4D2012yes—
193C3×C42C22×D511yescharacteristic
194(C2×D3)⋊C4—102no—
195(C2×D3)⋊C4—101no—
196C4⋊Dic3—51no—
197C4⋊Dic3—51no—
198Dic3⋊C4—102no—
199Dic3⋊C4—101no—
200C4×Dic3—101no—
201C2×C3⋊C8—101no—
202D24—202no—
203#204—202no—
204C22×D5—61no—
205C22×D5—121no—
206C5×Q8—41no—
207C5×Q8—41no—
208C2×C4×C5—22no—
209C2×C4×C5C2×D1211yescharacteristic
210C2×C4×C5D3×D411yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C2×Dic5—61no—
213C2×Dic5—61no—
214C2×Dic5—61no—
215D20—32no—
216D20—61no—
217D20—122no—
218D20—121no—
219D20—121no—
220D20—121no—
221D20—121no—
222C4×D5—124no—
223C4×D5—121no—
224C4×D5—121no—
225Dic10—32no—
226Dic10—61no—
227Dic10—124no—
228C5×C8—41no—
229C5×C8—41no—
230#168—121no—
231C22×Q8—301no—
232C2×SD16—301no—
233C2×D8—301no—
234C4⋊Q8—301no—
235C4⋊Q8C2×D1511yescharacteristic
236#127—151no—
237C22⋊Q8—301no—
238C22⋊Q8—302no—
239C4×Q8—151no—
240C4×D4—151no—
241C4×D4—301no—
242C4⋊C8C2×D1511yescharacteristic
243C4⋊C8C2×D1511yescharacteristic
244#102—301no—
245#102—301no—
246#102—302no—
247C4×C8—151no—
248C2×C3×C5#44711yescharacteristic
249C2×C3×C5#44811yescharacteristic
250C2×C3×C5#45411yescharacteristic
251D15—42no—
252D15—161no—
253C22×D3—101no—
254C22×D3—201no—
255C3×Q8—41no—
256C3×Q8—41no—
257C2×C3×C4—22no—
258C2×C3×C4C2×D2011yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4D4×D511yescharacteristic
261C2×Dic3—101no—
262C2×Dic3—101no—
263C2×Dic3—101no—
264D12—52no—
265D12—101no—
266D12—202no—
267D12—201no—
268D12—201no—
269D12—201no—
270D12—201no—
271C4×D3—204no—
272C4×D3—201no—
273C4×D3—201no—
274Dic6—52no—
275Dic6—101no—
276Dic6—204no—
277C3×C8—41no—
278C3×C8—41no—
279C3⋊C8—201no—
280C22×C5#88211yescharacteristic
281C2×D5—62no—
282C2×D5—121no—
283C2×D5—121no—
284C2×D5—241no—
285C2×D5—241no—
286C2×D5—241no—
287C4×C5—21no—
288C4×C5—42no—
289C4×C5D3×D811yescharacteristic
290C4×C5D3×SD1611yescharacteristic
291C4×C5#91411yescharacteristic
292C4×C5#91811yescharacteristic
293Dic5—62no—
294Dic5—121no—
295Dic5—121no—
296C2×Q8—21no—
297C2×Q8—151no—
298C2×Q8—302no—
299C2×Q8—602no—
300C2×Q8—602no—
301C2×D4—151no—
302C2×D4—301no—
303C2×D4—301no—
304C2×D4—301no—
305C22×C4—302no—
306C22×C4—301no—
307SD16—602no—
308D8—602no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—301no—
312C4⋊C4—21no—
313C4⋊C4—151no—
314C4⋊C4—151no—
315C4⋊C4—302no—
316C4⋊C4—301no—
317C4⋊C4D6012yes—
318C22⋊C4—302no—
319C22⋊C4—301no—
320C42—301no—
321C42C22×D1511yescharacteristic
322C3×C5#162711yescharacteristic, complemented, Hall
323C22×C3#402811yescharacteristic
324C2×D3—102no—
325C2×D3—201no—
326C2×D3—201no—
327C2×D3—401no—
328C2×D3—401no—
329C2×D3—401no—
330C3×C4—21no—
331C3×C4—42no—
332C3×C4D5×D811yescharacteristic
333C3×C4D5×SD1611yescharacteristic
334C3×C4#406011yescharacteristic
335C3×C4#406411yescharacteristic
336Dic3—102no—
337Dic3—201no—
338Dic3—201no—
339C2×C5#475311yescharacteristic
340C2×C5#477311yescharacteristic
341C2×C5#480611yescharacteristic
342D5—122no—
343D5—481no—
344C23—301no—
345C23—601no—
346Q8—41no—
347Q8—41no—
348Q8—152no—
349Q8—301no—
350Q8—604no—
351D4—152no—
352D4—301no—
353D4—602no—
354D4—601no—
355D4—601no—
356D4—601no—
357D4—601no—
358C2×C4—22no—
359C2×C4—301no—
360C2×C4—301no—
361C2×C4—301no—
362C2×C4—604no—
363C2×C4—601no—
364C2×C4—601no—
365C2×C4C2×D6011yescharacteristic
366C2×C4D4×D1511yescharacteristic
367C2×C4D4×D1511yescharacteristic
368C8—41no—
369C8—41no—
370C8—601no—
371C2×C3#6504211yescharacteristic
372C2×C3#6506211yescharacteristic
373C2×C3#6509511yescharacteristic
374D3—202no—
375D3—801no—
376C5#6845711yescharacteristic, complemented, Sylow
377C22—302no—
378C22—601no—
379C22—601no—
380C22—1201no—
381C22—1201no—
382C22—1201no—
383C22#9177111yescharacteristic
384C4—21no—
385C4—42no—
386C4—302no—
387C4—601no—
388C4—601no—
389C4D8×D1511yescharacteristic
390C4SD16×D1511yescharacteristic
391C4#9180311yescharacteristic
392C4#9180711yescharacteristic
393C3#1059925011yescharacteristic, complemented, Sylow
394C2—602no—
395C2—2401no—
396C2#1175085411yescharacteristic
397C2#1175087411yescharacteristic
398C2#1175090711yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#332C2
socleC22×C3×C5#120
prime radical#11750944C2
hypercenter#332D15
hypocenterC3×C5#1627
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #11756486C2semidirect
2. #11751189C2semidirect
3. #11750949C2semidirect
5. C3×C5×#332C2semidirect
6. #11746305C2semidirect
7. #11746304C2semidirect
31. C5×#332D3semidirect
64. C3×#332D5semidirect
102. D60SD16semidirect
108. Dic30D8semidirect
159. #332D15semidirect
322. C3×C5#1627semidirect
376. C5#68457semidirect
393. C3#10599250semidirect

Maximal subgroups

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

subgroupindex
#117564862
#117511892
#117509492
#117509442
C3×C5×#3322
#117463052
#117463042
#105992503
#684575