Finite Group Databasebeta

← #14290002

Subgroups — #14290002

Order 1920.

500 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 99 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#11756336C211yesmaximal, characteristic
2C3×C5×#462C211yesmaximal, characteristic, complemented
3#11751189C211yesmaximal, characteristic, complemented
4#11751188C211yesmaximal, characteristic, complemented
5#11746356C211yesmaximal, characteristic, complemented
6#11746306C211yesmaximal, characteristic, complemented
7#11746304C211yesmaximal, characteristic, complemented
8#10601854—31nomaximal, Hall
9C2×#6821—21no—
10C2×C3×C5×Q16—21no—
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×C4×C5×Q8C2211yescharacteristic
13#91784—22no—
14#91784—21no—
15#91763—21no—
16#91763C2211yescharacteristic
17C4×D60—21no—
18C4×D60C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C5×#103—21no—
21#91093—21no—
22#91093—22no—
23#91091—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71061—51nomaximal, Hall
27#65911—31no—
28C5×#462D311yescharacteristic, complemented
29#65377—31no—
30#65376—31no—
31Q8⋊#168—31no—
32#64705—31no—
33#64703—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D411yescharacteristic
36#6821—42no—
37#6821—42no—
38C2×D60—22no—
39C2×D60—21no—
40C2×D60—21no—
41C2×D60—22no—
42C2×D60D411yescharacteristic
43C2×D60D412yes—
44C2×C4×D15—22no—
45C2×C4×D15—21no—
46C3×C5×Q16—42no—
47C2×C3×C5×C8—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4D411yescharacteristic
52C3×C42×C5—21no—
53C3×C42×C5C2311yescharacteristic
54#6714—22no—
55#6714—21no—
56C4⋊Dic15D411yescharacteristic
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59#5577—51no—
60C3×#462D511yescharacteristic, complemented
61#5088—51no—
62#5087—51no—
63#4535—51no—
64#4485—51no—
65#4483—51no—
66C2×#713—61no—
67C2×C5×Q16—21no—
68C5×C4⋊Q8C2×D311yescharacteristic
69C4×C5×Q8C2×D311yescharacteristic
70#4041—62no—
71#4041—61no—
72#4020—31no—
73#4020—61no—
74C4×D20—31no—
75C4×D20—61no—
76C5×C4⋊C8C2×D311yescharacteristic
77C5×#103—21no—
78#3941—61no—
79#3941—62no—
80#3939—61no—
81C4⋊#168—31no—
82C4×#168—31no—
83#1641—151noSylow
84C22×D15—21no—
85C22×D15—22no—
86C3×C5×Q8—21no—
87C3×C5×Q8—41no—
88C3×C5×Q8—41no—
89C3×C5×Q8D812yes—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15—21no—
97D60—21no—
98D60—21no—
99D60—44no—
100D60—42no—
101D60—41no—
102D60—41no—
103D60—41no—
104D60—41no—
105D60—82no—
106C4×D15—44no—
107C4×D15—41no—
108C4×D15—41no—
109C3×C5×C8—41no—
110C3⋊#168—41no—
111C3⋊#168—41no—
112C2×#239—101no—
113C2×C3×Q16—21no—
114C3×C4⋊Q8C2×D511yescharacteristic
115C3×C4×Q8C2×D511yescharacteristic
116#895—102no—
117#895—101no—
118#874—51no—
119#874—101no—
120C4×D12—51no—
121C4×D12—101no—
122C3×C4⋊C8C2×D511yescharacteristic
123C3×#103—21no—
124#809—101no—
125#809—102no—
126#807—101no—
127C4⋊(C3⋊C8)—51no—
128C4×C3⋊C8—51no—
129C2×C5×Q8—21no—
130C2×C5×Q8#6711yescharacteristic
131#713—122no—
132#713—122no—
133C2×D20—31no—
134C2×D20—32no—
135C2×D20—62no—
136C2×D20—61no—
137C2×D20—61no—
138C2×D20—62no—
139C2×C4×D5—62no—
140C2×C4×D5—61no—
141C5×Q16—42no—
142C2×C5×C8—21no—
143C5×C4⋊C4—21no—
144C5×C4⋊C4—21no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4#6711yescharacteristic
147C42×C5—21no—
148C42×C5C22×D311yescharacteristic
149#685—62no—
150#685—61no—
151C4⋊Dic5—31no—
152C2×#168—61no—
153C2×#168—61no—
154#550—151no—
155#486—151no—
156#474—151no—
157#462D1511yescharacteristic, complemented
158#331—151no—
159Q8⋊C8—151no—
160D4⋊C8—151no—
161C22×C3×C5#12011yescharacteristic
162C2×D15—42no—
163C2×D15—41no—
164C2×D15—41no—
165C2×D15—42no—
166C2×D15—42no—
167C2×D15—41no—
168C3×C4×C5—22no—
169C3×C4×C5—21no—
170C3×C4×C5—41no—
171C3×C4×C5—81no—
172C3×C4×C5C2×D811yescharacteristic
173C3×C4×C5#13511yescharacteristic
174C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
175C3×C4×C5#13711yescharacteristic
176Dic15—41no—
177C2×C3×Q8—21no—
178C2×C3×Q8C22⋊D511yescharacteristic
179#239—202no—
180#239—202no—
181C2×D12—51no—
182C2×D12—52no—
183C2×D12—102no—
184C2×D12—101no—
185C2×D12—101no—
186C2×D12—102no—
187C2×C4×D3—102no—
188C2×C4×D3—101no—
189C3×Q16—42no—
190C2×C3×C8—21no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4C22⋊D511yescharacteristic
195C3×C42—21no—
196C3×C42C22×D511yescharacteristic
197(C2×D3)⋊C4—102no—
198(C2×D3)⋊C4—101no—
199C4⋊Dic3—51no—
200C2×C3⋊C8—101no—
201C2×C3⋊C8—101no—
202C22×D5—61no—
203C22×D5—62no—
204C5×Q8—21no—
205C5×Q8—41no—
206C5×Q8—41no—
207C5×Q8#21312yes—
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5—41no—
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5D3×D411yescharacteristic
213C2×C4×C5C2×#6711yescharacteristic
214C2×Dic5—61no—
215D20—61no—
216D20—61no—
217D20—122no—
218D20—124no—
219D20—121no—
220D20—121no—
221D20—121no—
222D20—121no—
223D20—242no—
224C4×D5—124no—
225C4×D5—121no—
226C4×D5—121no—
227C5×C8—41no—
228#168—121no—
229#168—121no—
230C2×#41—301no—
231C2×Q16—21no—
232C4⋊Q8C2×D1511yescharacteristic
233#127—151no—
234#127—301no—
235#121—302no—
236#121—301no—
237C4×Q8C2×D1511yescharacteristic
238C4×D4—151no—
239C4×D4—301no—
240#107—301no—
241C4⋊C8—151no—
242C4⋊C8C2×D1511yescharacteristic
243#103—21no—
244#102—301no—
245#102—302no—
246C4×C8—151no—
247C2×C3×C5#44711yescharacteristic
248C2×C3×C5#45211yescharacteristic
249C2×C3×C5#45511yescharacteristic
250D15—81no—
251D15—82no—
252C22×D3—101no—
253C22×D3—102no—
254C3×Q8—21no—
255C3×Q8—41no—
256C3×Q8—41no—
257C3×Q8#68612yes—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—41no—
261C2×C3×C4D4×D511yescharacteristic
262C2×C3×C4D4×D511yescharacteristic
263C2×C3×C4C2×C22⋊D511yescharacteristic
264C2×Dic3—101no—
265D12—101no—
266D12—101no—
267D12—202no—
268D12—204no—
269D12—201no—
270D12—201no—
271D12—201no—
272D12—201no—
273D12—402no—
274C4×D3—204no—
275C4×D3—201no—
276C4×D3—201no—
277C3×C8—41no—
278C3⋊C8—201no—
279C3⋊C8—201no—
280C22×C5#93711yescharacteristic
281C2×D5—121no—
282C2×D5—122no—
283C2×D5—122no—
284C2×D5—121no—
285C2×D5—122no—
286C2×D5—121no—
287C4×C5—21no—
288C4×C5—22no—
289C4×C5—41no—
290C4×C5—81no—
291C4×C5#91811yescharacteristic
292C4×C5#91911yescharacteristic
293C4×C5C2×#21311yescharacteristic
294C4×C5#94911yescharacteristic
295Dic5—121no—
296#41—602no—
297#41—602no—
298C2×Q8—21no—
299C2×Q8#122011yescharacteristic
300C2×D4—151no—
301C2×D4—152no—
302C2×D4—302no—
303C2×D4—302no—
304C2×D4—301no—
305C2×D4—301no—
306C22×C4—302no—
307C22×C4—301no—
308Q16—42no—
309C2×C8—21no—
310C2×C8—301no—
311C2×C8—301no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—151no—
316C4⋊C4#122011yescharacteristic
317C22⋊C4—302no—
318C22⋊C4—301no—
319C42—21no—
320C42C22×D1511yescharacteristic
321C3×C5#164111yescharacteristic, complemented, Hall
322C22×C3#408311yescharacteristic
323C2×D3—202no—
324C2×D3—201no—
325C2×D3—201no—
326C2×D3—202no—
327C2×D3—202no—
328C2×D3—201no—
329C3×C4—22no—
330C3×C4—21no—
331C3×C4—41no—
332C3×C4—81no—
333C3×C4#406411yescharacteristic
334C3×C4#406511yescharacteristic
335C3×C4C2×#68611yescharacteristic
336C3×C4#409511yescharacteristic
337Dic3—201no—
338C2×C5#503611yescharacteristic
339C2×C5#518711yescharacteristic
340C2×C5#520211yescharacteristic
341D5—241no—
342D5—242no—
343C23—301no—
344C23—302no—
345Q8—21no—
346Q8—41no—
347Q8—41no—
348Q8#671512yes—
349D4—301no—
350D4—301no—
351D4—602no—
352D4—604no—
353D4—601no—
354D4—601no—
355D4—601no—
356D4—601no—
357D4—1202no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—301no—
362C2×C4—604no—
363C2×C4—601no—
364C2×C4—601no—
365C2×C4D4×D1511yescharacteristic
366C2×C4D4×D1511yescharacteristic
367C2×C4C2×#122011yescharacteristic
368C8—41no—
369C8—601no—
370C8—601no—
371C2×C3#6532511yescharacteristic
372C2×C3#6547611yescharacteristic
373C2×C3#6549111yescharacteristic
374D3—401no—
375D3—402no—
376C5#7106111yescharacteristic, complemented, Sylow
377C22—601no—
378C22—602no—
379C22—602no—
380C22—601no—
381C22—602no—
382C22—601no—
383C22#9182611yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—81no—
388C4—601no—
389C4#9180711yescharacteristic
390C4#9180811yescharacteristic
391C4C2×#671511yescharacteristic
392C4#9183811yescharacteristic
393C3#1060185411yescharacteristic, complemented, Sylow
394C2—1201no—
395C2—1202no—
396C2#1175113711yescharacteristic
397C2#1175128811yescharacteristic
398C2#1175130311yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#462C2
socleC22×C3×C5#120
prime radical#11756336C2
hypercenter#462D15
hypocenterC3×C5#1641
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. C3×C5×#462C2semidirect
3. #11751189C2semidirect
4. #11751188C2semidirect
5. #11746356C2semidirect
6. #11746306C2semidirect
7. #11746304C2semidirect
28. C5×#462D3semidirect
60. C3×#462D5semidirect
157. #462D15semidirect
321. C3×C5#1641semidirect
376. C5#71061semidirect
393. C3#10601854semidirect

Maximal subgroups

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

subgroupindex
#117563362
C3×C5×#4622
#117511892
#117511882
#117463562
#117463062
#117463042
#106018543
#710615