Finite Group Databasebeta

← #14288901

Subgroups — #14288901

Order 1920.

556 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 93 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#11756312C211yesmaximal, characteristic, complemented
2#11751116C211yesmaximal, characteristic, complemented
3#11750949C211yesmaximal, characteristic, complemented
4#11750796C211yesmaximal, characteristic, complemented
5C3×C5×D4⋊C8C211yesmaximal, characteristic, complemented
6#11746306C211yesmaximal, characteristic, complemented
7#11746277C211yesmaximal, characteristic, complemented
8#10598979—31nomaximal, Hall
9C2×#6817—21no—
10C3×C4×C5×D4C2211yescharacteristic
11#91829—21no—
12C2×#6715—21no—
13#91819—21no—
14C2×D120—22no—
15C2×#6706—21no—
16#91782—21no—
17#91773—22no—
18#91763C2211yescharacteristic
19#91763C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C4×C5×C8C2211yescharacteristic
23#91105—21no—
24#91093—21no—
25C4⋊(C3⋊#168)C2211yescharacteristic
26#68186—51nomaximal, Hall
27#65887—31no—
28#65304—31no—
29#65137—31no—
30#64984—31no—
31C5×D4⋊C8D311yescharacteristic, complemented
32#64705—31no—
33#64676—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×#1220—22no—
37C2×#1220—22no—
38#6817—42no—
39#6817—42no—
40C2×D60—21no—
41C2×D60—21no—
42C2×D60—21no—
43C2×D60—21no—
44C2×D60—21no—
45C2×D60D412yes—
46C2×C4×D15—22no—
47C2×Dic30D411yescharacteristic
48C2×C3×C5×C8—21no—
49C2×C3×C5×C8—21no—
50C3×C5×C4⋊C4D411yescharacteristic
51C3×C5×C22⋊C4—21no—
52C3×C42×C5C2311yescharacteristic
53#6715—42no—
54#6714—22no—
55C4⋊Dic15D411yescharacteristic
56#6712—21no—
57C4×Dic15—21no—
58C2×C3⋊#168—21no—
59D120—44no—
60#6706—42no—
61#5553—51no—
62#5015—51no—
63#4848—51no—
64#4695—51no—
65C3×D4⋊C8D511yescharacteristic, complemented
66#4485—51no—
67#4456—51no—
68C2×#709—61no—
69C4×C5×D4C2×D311yescharacteristic
70#4086—61no—
71C2×#686—61no—
72#4076—61no—
73C2×D40—62no—
74C2×#677—61no—
75#4039—61no—
76#4030—62no—
77#4020—31no—
78#4020—31no—
79C4×Dic10—31no—
80C5×C4⋊C8C2×D311yescharacteristic
81C4×C5×C8C2×D311yescharacteristic
82#3953—61no—
83#3941—61no—
84C4⋊#168—31no—
85#1621—151noSylow
86C23×C3×C5—21no—
87C22×D15—22no—
88C22×D15—41no—
89C3×C5×D4—21no—
90C3×C5×D4—21no—
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97#1220—44no—
98#1220—82no—
99C2×Dic15—21no—
100C2×Dic15—21no—
101D60—42no—
102D60—42no—
103D60—41no—
104D60—41no—
105D60—41no—
106D60—41no—
107D60—41no—
108D60—41no—
109D60—41no—
110D60—41no—
111C4×D15—44no—
112Dic30—21no—
113Dic30D812yescomplemented
114C3×C5×C8—22no—
115C3×C5×C8—41no—
116C3⋊#168—41no—
117C2×#235—101no—
118C3×C4×D4C2×D511yescharacteristic
119#940—101no—
120C2×#213—101no—
121#930—101no—
122C2×D24—102no—
123C2×#204—101no—
124#893—101no—
125#884—102no—
126#874—51no—
127#874—51no—
128C4×Dic6—51no—
129C3×C4⋊C8C2×D511yescharacteristic
130C3×C4×C8C2×D511yescharacteristic
131#821—101no—
132#809—101no—
133C4⋊(C3⋊C8)—51no—
134C2×C5×D4D1211yescharacteristic
135C22×C4×C5—21no—
136C2×C22⋊D5—62no—
137C2×C22⋊D5—62no—
138#709—122no—
139#709—122no—
140C2×D20—32no—
141C2×D20—61no—
142C2×D20—61no—
143C2×D20—61no—
144C2×D20—61no—
145C2×D20—61no—
146C2×C4×D5—62no—
147C2×Dic10—31no—
148C2×C5×C8—21no—
149C2×C5×C8—21no—
150C5×C4⋊C4D1211yescharacteristic
151C5×C22⋊C4—21no—
152C42×C5C22×D311yescharacteristic
153#686—122no—
154#685—62no—
155C4⋊Dic5—31no—
156#683—61no—
157C4×Dic5—61no—
158C2×#168—61no—
159D40—124no—
160#677—122no—
161#550—151no—
162#493—151no—
163#460—151no—
164#459—151no—
165#331—151no—
166Q8⋊C8—151no—
167D4⋊C8D1511yescharacteristic, complemented
168C22×C3×C5—41no—
169C22×C3×C5—41no—
170C22×C3×C5—41no—
171C22×C3×C5#12011yescharacteristic
172C2×D15—42no—
173C2×D15—42no—
174C2×D15—42no—
175C2×D15—81no—
176C2×D15—81no—
177C2×D15—81no—
178C3×C4×C5—21no—
179C3×C4×C5—41no—
180C3×C4×C5C2×D811yescharacteristic
181C3×C4×C5#13511yescharacteristic
182C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
183C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
184Dic15—22no—
185Dic15—41no—
186C2×C3×D4D2011yescharacteristic
187C22×C3×C4—21no—
188C2×#67—102no—
189C2×#67—102no—
190#235—202no—
191#235—202no—
192C2×D12—52no—
193C2×D12—101no—
194C2×D12—101no—
195C2×D12—101no—
196C2×D12—101no—
197C2×D12—101no—
198C2×C4×D3—102no—
199C2×Dic6—51no—
200C2×C3×C8—21no—
201C2×C3×C8—21no—
202C3×C4⋊C4D2011yescharacteristic
203C3×C22⋊C4—21no—
204C3×C42C22×D511yescharacteristic
205#213—202no—
206(C2×D3)⋊C4—102no—
207C4⋊Dic3—51no—
208Dic3⋊C4—101no—
209C4×Dic3—101no—
210C2×C3⋊C8—101no—
211D24—204no—
212#204—202no—
213C23×C5—21no—
214C22×D5—62no—
215C22×D5—121no—
216C5×D4—21no—
217C5×D4—21no—
218C2×C4×C5—21no—
219C2×C4×C5—41no—
220C2×C4×C5—41no—
221C2×C4×C5C2×D1211yescharacteristic
222C2×C4×C5D3×D411yescharacteristic
223C2×C4×C5D3×D411yescharacteristic
224C22⋊D5—124no—
225C22⋊D5—242no—
226C2×Dic5—61no—
227C2×Dic5—61no—
228D20—122no—
229D20—122no—
230D20—121no—
231D20—121no—
232D20—121no—
233D20—121no—
234D20—121no—
235D20—121no—
236D20—121no—
237D20—121no—
238C4×D5—124no—
239Dic10—32no—
240Dic10—61no—
241C5×C8—22no—
242C5×C8—41no—
243#168—121no—
244C2×#41—301no—
245C2×SD16—301no—
246C2×D8—302no—
247C2×D8—301no—
248#127—151no—
249#127—151no—
250#127—301no—
251#121—302no—
252#121—301no—
253C4×Q8—151no—
254C4×D4—301no—
255C4×D4C2×D1511yescharacteristic
256C4⋊C8—151no—
257C4⋊C8C2×D1511yescharacteristic
258#102—301no—
259#102—301no—
260C4×C8C2×D1511yescharacteristic
261C2×C3×C5—81no—
262C2×C3×C5#44711yescharacteristic
263C2×C3×C5#44911yescharacteristic
264C2×C3×C5#45311yescharacteristic
265D15—82no—
266D15—161no—
267C23×C3—21no—
268C22×D3—102no—
269C22×D3—201no—
270C3×D4—21no—
271C3×D4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4C2×D2011yescharacteristic
276C2×C3×C4D4×D511yescharacteristic
277C2×C3×C4D4×D511yescharacteristic
278#67—204no—
279#67—402no—
280C2×Dic3—101no—
281C2×Dic3—101no—
282D12—202no—
283D12—202no—
284D12—201no—
285D12—201no—
286D12—201no—
287D12—201no—
288D12—201no—
289D12—201no—
290D12—201no—
291D12—201no—
292C4×D3—204no—
293Dic6—52no—
294Dic6—101no—
295C3×C8—22no—
296C3×C8—41no—
297C3⋊C8—201no—
298C22×C5—41no—
299C22×C5—41no—
300C22×C5—41no—
301C22×C5#88211yescharacteristic
302C2×D5—122no—
303C2×D5—122no—
304C2×D5—122no—
305C2×D5—241no—
306C2×D5—241no—
307C2×D5—241no—
308C4×C5—21no—
309C4×C5—41no—
310C4×C5#90411yescharacteristic
311C4×C5#90811yescharacteristic
312C4×C5D3×D811yescharacteristic
313C4×C5#91411yescharacteristic
314Dic5—62no—
315Dic5—121no—
316#41—602no—
317#41—602no—
318C2×Q8—151no—
319C2×D4—152no—
320C2×D4—302no—
321C2×D4—302no—
322C2×D4—301no—
323C2×D4—301no—
324C2×D4—301no—
325C2×D4—301no—
326C2×D4—301no—
327C2×D4D6011yescharacteristic
328C22×C4—21no—
329C22×C4—302no—
330SD16—602no—
331D8—604no—
332D8—602no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—301no—
336C4⋊C4—151no—
337C4⋊C4—301no—
338C4⋊C4D6011yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—302no—
341C42—301no—
342C42C22×D1511yescharacteristic
343C3×C5#162111yescharacteristic, complemented, Hall
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3#402811yescharacteristic
348C2×D3—202no—
349C2×D3—202no—
350C2×D3—202no—
351C2×D3—401no—
352C2×D3—401no—
353C2×D3—401no—
354C3×C4—21no—
355C3×C4—41no—
356C3×C4#405011yescharacteristic
357C3×C4#405411yescharacteristic
358C3×C4D5×D811yescharacteristic
359C3×C4#406011yescharacteristic
360Dic3—102no—
361Dic3—201no—
362C2×C5—81no—
363C2×C5#473411yescharacteristic
364C2×C5#477311yescharacteristic
365C2×C5#482211yescharacteristic
366D5—242no—
367D5—481no—
368C23—21no—
369C23—302no—
370C23—601no—
371Q8—152no—
372Q8—301no—
373D4—21no—
374D4—21no—
375D4—602no—
376D4—602no—
377D4—604no—
378D4—601no—
379D4—601no—
380D4—601no—
381D4—601no—
382D4—601no—
383D4—601no—
384D4—601no—
385D4—601no—
386D4—1202no—
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—301no—
391C2×C4—301no—
392C2×C4—604no—
393C2×C4C2×D6011yescharacteristic
394C2×C4D4×D1511yescharacteristic
395C2×C4D4×D1511yescharacteristic
396C8—22no—
397C8—41no—
398C8—601no—
399C2×C3—81no—
400C2×C3#6502311yescharacteristic
401C2×C3#6506211yescharacteristic
402C2×C3#6511111yescharacteristic
403D3—402no—
404D3—801no—
405C5#6818611yescharacteristic, complemented, Sylow
406C22—41no—
407C22—41no—
408C22—41no—
409C22—602no—
410C22—602no—
411C22—602no—
412C22—1201no—
413C22—1201no—
414C22—1201no—
415C22#9177111yescharacteristic
416C4—21no—
417C4—41no—
418C4—302no—
419C4—601no—
420C4#9179311yescharacteristic
421C4#9179711yescharacteristic
422C4D8×D1511yescharacteristic
423C4#9180311yescharacteristic
424C3#1059897911yescharacteristic, complemented, Sylow
425C2—81no—
426C2—1202no—
427C2—2401no—
428C2#1175083511yescharacteristic
429C2#1175087411yescharacteristic
430C2#1175092311yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5#120
hypercenterD4⋊C8D15
hypocenterC3×C5#1621
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #11756312C2semidirect
2. #11751116C2semidirect
3. #11750949C2semidirect
4. #11750796C2semidirect
5. C3×C5×D4⋊C8C2semidirect
6. #11746306C2semidirect
7. #11746277C2semidirect
31. C5×D4⋊C8D3semidirect
65. C3×D4⋊C8D5semidirect
113. Dic30D8semidirect
167. D4⋊C8D15semidirect
343. C3×C5#1621semidirect
405. C5#68186semidirect
424. C3#10598979semidirect

Maximal subgroups

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

subgroupindex
#117563122
#117511162
#117509492
#117507962
C3×C5×D4⋊C82
#117463062
#117462772
#105989793
#681865