Finite Group Databasebeta

← #14289072

Subgroups — #14289072

Order 1920.

480 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C5×#5563C211yesmaximal, characteristic, complemented
2C3×#65304C211yesmaximal, characteristic, complemented
3#11747079C211yesmaximal, characteristic, complemented
4#11747033C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
6#11745862C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic, complemented
8#10602720—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C5×#938—21no—
11C5×#930—21no—
12C5×#926—21no—
13C5×#892—21no—
14C5×#885—22no—
15C4×C5×D12C2211yescharacteristic
16C5×#869C2211yescharacteristic
17C2×C3×#686—21no—
18C3×#4020C2211yescharacteristic
19C2×#6655—22no—
20C2×#6652—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C4×C3⋊#168C2211yescharacteristic
23C3×#3941—21no—
24C3×C4⋊#168C2211yescharacteristic
25#90964—21no—
26#71017—51nomaximal, Hall
27C5×#555—31no—
28#65374—31no—
29#65304—31no—
30#65304D311yescharacteristic, complemented
31#64766—31no—
32D4⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×C5×#67—22no—
37C2×C5×D12D411yescharacteristic
38C2×C4×C5×D3—21no—
39C2×C5×Dic6D412yes—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C5×C22⋊C4—21no—
45C3×C42×C5C2311yescharacteristic
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C5×#217—22no—
49C5×(C2×D3)⋊C4—22no—
50C5×(C2×D3)⋊C4—21no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3—21no—
53C5×C4⋊Dic3D411yescharacteristic
54C4×C5×Dic3—22no—
55C3×#686—42no—
56C2×C3×#168—21no—
57#6655—44no—
58#6652—42no—
59#5563D511yescharacteristic, complemented
60C3×#459—51no—
61#5076—51no—
62#5072—51no—
63D4⋊(C3⋊C8)—51no—
64#4483—51no—
65#4481—51no—
66C5×C4⋊Q8—31no—
67C5×#124—62no—
68C5×#121—61no—
69C5×#121—61no—
70C4×C5×D4—31no—
71C4×C5×D4C2×D311yescharacteristic
72C5×#117—61no—
73C5×#117—61no—
74C2×#688—62no—
75C2×#686—21no—
76C2×#686—61no—
77#4020C2×D311yescharacteristic
78#3941—21no—
79#3941—61no—
80C4⋊#168—31no—
81C4⋊#168C2×D311yescharacteristic
82C4×#168—31no—
83#1624—151noSylow
84C23×C3×C5—21no—
85C22×C5×D3—21no—
86C22×C3×D5—41no—
87C3×C5×D4—21no—
88C3×C5×D4—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C5×#67—82no—
96C2×C5×Dic3—21no—
97C2×C5×Dic3—22no—
98C5×D12—21no—
99C5×D12—21no—
100C4×C5×D3—41no—
101C4×C5×D3—41no—
102C5×Dic6—42no—
103C3×D20—42no—
104C3×D20—41no—
105C3×D20—41no—
106C3×D20—41no—
107C3×D20—41no—
108C3⋊#168—22no—
109C3⋊#168—41no—
110C3×#168—41no—
111C2×C3×D8—101no—
112C3×#127—51no—
113C3×C4×D4C2×D511yescharacteristic
114#938—21no—
115C2×#214—102no—
116C2×#213—101no—
117#930—21no—
118#926—21no—
119#892—21no—
120#885—22no—
121C4×D12C2×D511yescharacteristic
122#869C2×D511yescharacteristic
123C3×C4⋊C8—51no—
124C3×#102—101no—
125#832—101no—
126C4⋊(C3⋊C8)—51no—
127C4×C3⋊C8—51no—
128C2×C5×Q8—32no—
129C2×C5×D4—31no—
130C2×C5×D4—62no—
131C2×C5×D4#6711yescharacteristic
132C22×C4×C5—21no—
133C22×C4×C5—61no—
134C2×D20—21no—
135C2×D20—21no—
136C2×D20—21no—
137C5×C4⋊C4—31no—
138C5×C4⋊C4—61no—
139C5×C4⋊C4—61no—
140C5×C4⋊C4#6711yescharacteristic
141C5×C22⋊C4—21no—
142C5×C22⋊C4—62no—
143C5×C22⋊C4—62no—
144C5×C22⋊C4—61no—
145C42×C5—62no—
146C42×C5C22×D311yescharacteristic
147#688—124no—
148#686—42no—
149#686—122no—
150C2×#168—21no—
151C2×#168—61no—
152C2×#168—61no—
153#555—31no—
154#492—151no—
155#459—51no—
156#459—151no—
157#333—151no—
158D4⋊C8—151no—
159D4⋊C8—151no—
160C22×C3×C5—41no—
161C22×C3×C5—41no—
162C22×C3×C5—41no—
163C22×C3×C5#12011yescharacteristic
164C2×C5×D3—41no—
165C2×C5×D3—41no—
166C2×C5×D3—41no—
167C2×C3×D5—81no—
168C2×C3×D5—81no—
169C2×C3×D5—81no—
170C3×C4×C5—21no—
171C3×C4×C5—41no—
172C3×C4×C5#13511yescharacteristic
173C3×C4×C5#13511yescharacteristic
174C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
175C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
176C5×Dic3—41no—
177C5×Dic3—42no—
178C2×C3×D4—101no—
179C2×C3×D4—101no—
180C2×C3×D4—101no—
181C2×C3×D4C22⋊D511yescharacteristic
182C22×C3×C4—21no—
183C2×#67—22no—
184C2×D12C22⋊D511yescharacteristic
185C2×C4×D3—21no—
186C2×Dic6C22⋊D512yes—
187C3×D8—202no—
188C2×C3×C8—101no—
189C3×C4⋊C4C22⋊D511yescharacteristic
190C3×C22⋊C4—21no—
191C3×C42C22×D511yescharacteristic
192#217—22no—
193#214—204no—
194#213—202no—
195(C2×D3)⋊C4—22no—
196(C2×D3)⋊C4—21no—
197C4⋊Dic3—21no—
198C4⋊Dic3—21no—
199C4⋊Dic3C22⋊D511yescharacteristic
200C4×Dic3—22no—
201C2×C3⋊C8—101no—
202C2×C3⋊C8—101no—
203C23×C5—21no—
204C23×C5—61no—
205C22×D5—41no—
206C5×Q8—122no—
207C5×D4—21no—
208C5×D4—21no—
209C5×D4—61no—
210C5×D4—61no—
211C5×D4—242no—
212C2×C4×C5—21no—
213C2×C4×C5—41no—
214C2×C4×C5—41no—
215C2×C4×C5—61no—
216C2×C4×C5—62no—
217C2×C4×C5—121no—
218C2×C4×C5—121no—
219C2×C4×C5D3×D411yescharacteristic
220C2×C4×C5D3×D411yescharacteristic
221C2×C4×C5C2×#6711yescharacteristic
222D20—42no—
223D20—41no—
224D20—41no—
225D20—41no—
226D20—41no—
227#168—41no—
228#168—62no—
229#168—121no—
230C2×SD16—302no—
231C2×D8—101no—
232C2×D8—301no—
233C4⋊Q8—31no—
234#127—51no—
235#124—62no—
236#121—61no—
237#121—61no—
238C4×D4—31no—
239C4×D4D3×D511yescharacteristic
240#117—61no—
241#117—61no—
242C4⋊C8—51no—
243C4⋊C8—151no—
244#102—101no—
245#102—301no—
246C4×C8—151no—
247C2×C3×C5—81no—
248C2×C3×C5#44911yescharacteristic
249C2×C3×C5#44911yescharacteristic
250C2×C3×C5#45311yescharacteristic
251C3×D5—161no—
252C5×D3—81no—
253C23×C3—21no—
254C23×C3—201no—
255C22×D3—21no—
256C3×D4—21no—
257C3×D4—21no—
258C3×D4—202no—
259C3×D4—201no—
260C3×D4—201no—
261C3×D4—201no—
262C3×D4—201no—
263C2×C3×C4—21no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4C2×C22⋊D511yescharacteristic
267C2×C3×C4C2×C22⋊D511yescharacteristic
268C2×C3×C4C2×C22⋊D511yescharacteristic
269#67—82no—
270C2×Dic3—21no—
271C2×Dic3—22no—
272D12—21no—
273D12—21no—
274C4×D3—41no—
275C4×D3—41no—
276Dic6—42no—
277C3×C8—201no—
278C3⋊C8—102no—
279C3⋊C8—201no—
280C22×C5—41no—
281C22×C5—41no—
282C22×C5—41no—
283C22×C5—121no—
284C22×C5—121no—
285C22×C5—121no—
286C22×C5#93711yescharacteristic
287C2×D5—81no—
288C2×D5—81no—
289C2×D5—81no—
290C4×C5—21no—
291C4×C5—41no—
292C4×C5—122no—
293C4×C5—121no—
294C4×C5#91111yescharacteristic
295C4×C5#91211yescharacteristic
296C4×C5#93211yescharacteristic
297C4×C5#95011yescharacteristic
298C2×Q8—32no—
299C2×D4—31no—
300C2×D4—62no—
301C2×D4—101no—
302C2×D4—101no—
303C2×D4—101no—
304C2×D4#120111yescharacteristic
305C22×C4—21no—
306C22×C4—61no—
307SD16—604no—
308D8—202no—
309D8—602no—
310C2×C8—101no—
311C2×C8—301no—
312C2×C8—301no—
313C4⋊C4—31no—
314C4⋊C4—61no—
315C4⋊C4—61no—
316C4⋊C4#120111yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—62no—
319C22⋊C4—62no—
320C22⋊C4—61no—
321C42—62no—
322C42C2×D3×D511yescharacteristic
323C3×C5#162411yescharacteristic, complemented, Hall
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—401no—
328C22×C3—401no—
329C22×C3—401no—
330C22×C3#409911yescharacteristic
331C2×D3—41no—
332C2×D3—41no—
333C2×D3—41no—
334C3×C4—21no—
335C3×C4—41no—
336C3×C4#409511yescharacteristic
337C3×C4#409511yescharacteristic
338C3×C4#409611yescharacteristic
339C3×C4#409611yescharacteristic
340Dic3—41no—
341Dic3—42no—
342C2×C5—81no—
343C2×C5—241no—
344C2×C5#503711yescharacteristic
345C2×C5#515811yescharacteristic
346C2×C5#519811yescharacteristic
347D5—161no—
348C23—21no—
349C23—61no—
350C23—201no—
351Q8—122no—
352D4—21no—
353D4—21no—
354D4—61no—
355D4—61no—
356D4—202no—
357D4—201no—
358D4—201no—
359D4—201no—
360D4—201no—
361D4—242no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—61no—
366C2×C4—62no—
367C2×C4—121no—
368C2×C4—121no—
369C2×C4C2×#120111yescharacteristic
370C2×C4D3×C22⋊D511yescharacteristic
371C2×C4D3×C22⋊D511yescharacteristic
372C8—201no—
373C8—302no—
374C8—601no—
375C2×C3—81no—
376C2×C3—801no—
377C2×C3#6552711yescharacteristic
378C2×C3#6552711yescharacteristic
379C2×C3#6553011yescharacteristic
380D3—81no—
381C5#7101711yescharacteristic, complemented, Sylow
382C22—41no—
383C22—41no—
384C22—41no—
385C22—121no—
386C22—121no—
387C22—121no—
388C22—401no—
389C22—401no—
390C22—401no—
391C22#9156811yescharacteristic
392C4—21no—
393C4—41no—
394C4—122no—
395C4—121no—
396C4#9129711yescharacteristic
397C4#9129811yescharacteristic
398C4#9148011yescharacteristic
399C4#9149311yescharacteristic
400C3#1060272011yescharacteristic, complemented, Sylow
401C2—81no—
402C2—241no—
403C2—801no—
404C2#1174851711yescharacteristic
405C2#1174903511yescharacteristic
406C2#1174941911yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
hypercenterC4×D4D3×D5
hypocenterC3×C5#1624
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C5×#5563C2semidirect
2. C3×#65304C2semidirect
3. #11747079C2semidirect
4. #11747033C2semidirect
5. D4⋊(C3⋊#168)C2semidirect
6. #11745862C2semidirect
7. #11745836C2semidirect
30. #65304D3semidirect
59. #5563D5semidirect
323. C3×C5#1624semidirect
381. C5#71017semidirect
400. C3#10602720semidirect

Maximal subgroups

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

subgroupindex
C5×#55632
C3×#653042
#117470792
#117470332
D4⋊(C3⋊#168)2
#117458622
#117458362
#106027203
#710175