Finite Group Databasebeta

← #14290380

Subgroups — #14290380

Order 1920.

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

normal subgroups only

This group has 480 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#11756314C211yesmaximal, characteristic
2C3×C5×#461C211yesmaximal, characteristic, complemented
3#11751188C211yesmaximal, characteristic, complemented
4#11751179C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
6#11746304C211yesmaximal, characteristic, complemented
7#11746303C211yesmaximal, characteristic, complemented
8#10601841—31nomaximal, Hall
9C2×#6819—21no—
10C2×C3×C5×SD16—21no—
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×C4×C5×D4C2211yescharacteristic
13#91819—21no—
14C2×C4⋊Dic15—21no—
15#91786—21no—
16#91775—22no—
17C4×D60C2211yescharacteristic
18#91758C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C5×#103—21no—
21#91093—21no—
22#91091—22no—
23#91091—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71048—51nomaximal, Hall
27#65889—31no—
28C5×#461D311yescharacteristic, complemented
29#65376—31no—
30#65367—31no—
31D4⋊#168—31no—
32#64703—31no—
33#64702—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4D411yescharacteristic
36C22×C3×C4×C5—21no—
37C2×#1220—22no—
38C22×Dic15—22no—
39#6819—42no—
40#6819—42no—
41C2×D60D411yescharacteristic
42C2×C4×D15—21no—
43C2×Dic30—21no—
44C3×C5×SD16—42no—
45C2×C3×C5×C8—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C22⋊C4—21no—
50C3×C42×C5C2311yescharacteristic
51#6714—22no—
52#6714—21no—
53C4⋊Dic15—22no—
54C4⋊Dic15—21no—
55C4⋊Dic15D412yes—
56C4⋊Dic15D411yescharacteristic
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59#5555—51no—
60C3×#461D511yescharacteristic, complemented
61#5087—51no—
62#5078—51no—
63D4⋊(C3⋊C8)—51no—
64#4483—51no—
65#4482—51no—
66C2×#711—61no—
67C2×C5×SD16—21no—
68C5×C4⋊Q8C2×D311yescharacteristic
69C4×C5×D4C2×D311yescharacteristic
70#4076—61no—
71C2×C4⋊Dic5—61no—
72#4043—61no—
73#4032—62no—
74C4×D20—31no—
75#4015—31no—
76C5×C4⋊C8C2×D311yescharacteristic
77C5×#103—21no—
78#3941—61no—
79#3939—62no—
80#3939—61no—
81C4⋊#168—31no—
82C4×#168—31no—
83#1647—151noSylow
84C23×C3×C5—21no—
85C22×D15—21no—
86C3×C5×Q8—41no—
87C3×C5×Q8—41no—
88C3×C5×D4—21no—
89C3×C5×D4D812yes—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—41no—
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—
98C2×Dic15—22no—
99C2×Dic15—21no—
100C2×Dic15—44no—
101D60—21no—
102D60—21no—
103C4×D15—41no—
104C4×D15—41no—
105Dic30—41no—
106Dic30—41no—
107C3×C5×C8—41no—
108C3⋊#168—22no—
109C3⋊#168—41no—
110C2×#237—101no—
111C2×C3×SD16—21no—
112C3×C4⋊Q8C2×D511yescharacteristic
113C3×C4×D4C2×D511yescharacteristic
114#930—101no—
115C2×C4⋊Dic3—101no—
116#897—101no—
117#886—102no—
118C4×D12—51no—
119#869—51no—
120C3×C4⋊C8C2×D511yescharacteristic
121C3×#103—21no—
122#809—101no—
123#807—102no—
124#807—101no—
125C4⋊(C3⋊C8)—51no—
126C4×C3⋊C8—51no—
127C2×C5×Q8—21no—
128C2×C5×D4#6711yescharacteristic
129C22×C4×C5—21no—
130C2×C22⋊D5—62no—
131C22×Dic5—62no—
132#711—122no—
133#711—122no—
134C2×D20—31no—
135C2×C4×D5—61no—
136C2×Dic10—61no—
137C5×SD16—42no—
138C2×C5×C8—21no—
139C5×C4⋊C4—21no—
140C5×C4⋊C4—21no—
141C5×C4⋊C4#6711yescharacteristic
142C5×C22⋊C4—21no—
143C42×C5C22×D311yescharacteristic
144#685—62no—
145#685—61no—
146C4⋊Dic5—32no—
147C4⋊Dic5—31no—
148C4⋊Dic5—62no—
149C4⋊Dic5—61no—
150C2×#168—61no—
151C2×#168—61no—
152#547—151no—
153#500—151no—
154#474—151no—
155#461D1511yescharacteristic, complemented
156#332—151no—
157D4⋊C8—151no—
158D4⋊C8—151no—
159C22×C3×C5—22no—
160C22×C3×C5—41no—
161C22×C3×C5—41no—
162C22×C3×C5#12011yescharacteristic
163C2×D15—41no—
164C2×D15—41no—
165C2×D15—41no—
166C3×C4×C5—21no—
167C3×C4×C5—41no—
168C3×C4×C5—81no—
169C3×C4×C5C2×D811yescharacteristic
170C3×C4×C5#13511yescharacteristic
171C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
172C3×C4×C5#13711yescharacteristic
173Dic15—42no—
174Dic15—41no—
175C2×C3×Q8—21no—
176C2×C3×D4C22⋊D511yescharacteristic
177C22×C3×C4—21no—
178C2×#67—102no—
179C22×Dic3—102no—
180#237—202no—
181#237—202no—
182C2×D12—51no—
183C2×C4×D3—101no—
184C2×Dic6—101no—
185C3×SD16—42no—
186C2×C3×C8—21no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4C22⋊D511yescharacteristic
190C3×C22⋊C4—21no—
191C3×C42C22×D511yescharacteristic
192(C2×D3)⋊C4—102no—
193(C2×D3)⋊C4—101no—
194C4⋊Dic3—52no—
195C4⋊Dic3—51no—
196C4⋊Dic3—102no—
197C4⋊Dic3—101no—
198C2×C3⋊C8—101no—
199C2×C3⋊C8—101no—
200C23×C5—21no—
201C22×D5—61no—
202C5×Q8—41no—
203C5×Q8—41no—
204C5×D4—21no—
205C5×D4#21312yes—
206C2×C4×C5—21no—
207C2×C4×C5—41no—
208C2×C4×C5—41no—
209C2×C4×C5—41no—
210C2×C4×C5D3×D411yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5C2×#6711yescharacteristic
213C22⋊D5—124no—
214C2×Dic5—62no—
215C2×Dic5—61no—
216C2×Dic5—124no—
217D20—61no—
218D20—61no—
219C4×D5—121no—
220C4×D5—121no—
221Dic10—121no—
222Dic10—121no—
223C5×C8—41no—
224#168—62no—
225#168—121no—
226C2×#41—301no—
227C2×SD16—21no—
228C4⋊Q8—151no—
229C4⋊Q8C2×D1511yescharacteristic
230#123—302no—
231C22⋊Q8—301no—
232#121—301no—
233C4×D4—151no—
234C4×D4C2×D1511yescharacteristic
235C2×C4⋊C4—301no—
236#107—301no—
237#107—302no—
238C4⋊C8—151no—
239C4⋊C8C2×D1511yescharacteristic
240#103—21no—
241#102—301no—
242C4×C8—151no—
243C2×C3×C5—42no—
244C2×C3×C5#44711yescharacteristic
245C2×C3×C5#45211yescharacteristic
246C2×C3×C5#45611yescharacteristic
247D15—81no—
248C23×C3—21no—
249C22×D3—101no—
250C3×Q8—41no—
251C3×Q8—41no—
252C3×D4—21no—
253C3×D4#68612yes—
254C2×C3×C4—21no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4C2×C22⋊D511yescharacteristic
261#67—204no—
262C2×Dic3—102no—
263C2×Dic3—101no—
264C2×Dic3—204no—
265D12—101no—
266D12—101no—
267C4×D3—201no—
268C4×D3—201no—
269Dic6—201no—
270Dic6—201no—
271C3×C8—41no—
272C3⋊C8—102no—
273C3⋊C8—201no—
274C22×C5—22no—
275C22×C5—41no—
276C22×C5—41no—
277C22×C5#93711yescharacteristic
278C2×D5—121no—
279C2×D5—121no—
280C2×D5—121no—
281C4×C5—21no—
282C4×C5—41no—
283C4×C5—81no—
284C4×C5#91511yescharacteristic
285C4×C5#91611yescharacteristic
286C4×C5C2×#21311yescharacteristic
287C4×C5#94911yescharacteristic
288Dic5—122no—
289Dic5—121no—
290#41—602no—
291#41—602no—
292C2×Q8—21no—
293C2×Q8—301no—
294C2×D4—151no—
295C2×D4—302no—
296C2×D4#122011yescharacteristic
297C22×C4—21no—
298C22×C4—302no—
299C22×C4—301no—
300SD16—42no—
301C2×C8—21no—
302C2×C8—301no—
303C2×C8—301no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—151no—
307C4⋊C4—152no—
308C4⋊C4—302no—
309C4⋊C4—301no—
310C4⋊C4#122011yescharacteristic
311C22⋊C4—21no—
312C22⋊C4—302no—
313C22⋊C4—301no—
314C42C22×D1511yescharacteristic
315C3×C5#164711yescharacteristic, complemented, Hall
316C22×C3—22no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3#408311yescharacteristic
320C2×D3—201no—
321C2×D3—201no—
322C2×D3—201no—
323C3×C4—21no—
324C3×C4—41no—
325C3×C4—81no—
326C3×C4#406111yescharacteristic
327C3×C4#406211yescharacteristic
328C3×C4C2×#68611yescharacteristic
329C3×C4#409511yescharacteristic
330Dic3—202no—
331Dic3—201no—
332C2×C5—42no—
333C2×C5#503611yescharacteristic
334C2×C5#517311yescharacteristic
335C2×C5#520511yescharacteristic
336D5—241no—
337C23—21no—
338C23—301no—
339Q8—41no—
340Q8—41no—
341Q8—601no—
342Q8—601no—
343D4—21no—
344D4—301no—
345D4—301no—
346D4—604no—
347D4#671512yes—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—301no—
353C2×C4—302no—
354C2×C4—604no—
355C2×C4—601no—
356C2×C4—601no—
357C2×C4D4×D1511yescharacteristic
358C2×C4D4×D1511yescharacteristic
359C2×C4C2×#122011yescharacteristic
360C8—41no—
361C8—302no—
362C8—601no—
363C2×C3—42no—
364C2×C3#6532511yescharacteristic
365C2×C3#6546211yescharacteristic
366C2×C3#6549411yescharacteristic
367D3—401no—
368C5#7104811yescharacteristic, complemented, Sylow
369C22—22no—
370C22—41no—
371C22—41no—
372C22—601no—
373C22—601no—
374C22—601no—
375C22#9182611yescharacteristic
376C4—21no—
377C4—41no—
378C4—81no—
379C4—601no—
380C4—602no—
381C4#9180411yescharacteristic
382C4#9180511yescharacteristic
383C4C2×#671511yescharacteristic
384C4#9183811yescharacteristic
385C3#1060184111yescharacteristic, complemented, Sylow
386C2—42no—
387C2—1201no—
388C2#1175113711yescharacteristic
389C2#1175127411yescharacteristic
390C2#1175130611yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#461C2
socleC22×C3×C5#120
prime radical#11756314C2
hypercenter#461D15
hypocenterC3×C5#1647
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. C3×C5×#461C2semidirect
3. #11751188C2semidirect
4. #11751179C2semidirect
5. D4⋊(C3⋊#168)C2semidirect
6. #11746304C2semidirect
7. #11746303C2semidirect
28. C5×#461D3semidirect
60. C3×#461D5semidirect
155. #461D15semidirect
315. C3×C5#1647semidirect
368. C5#71048semidirect
385. C3#10601841semidirect

Maximal subgroups

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

subgroupindex
#117563142
C3×C5×#4612
#117511882
#117511792
D4⋊(C3⋊#168)2
#117463042
#117463032
#106018413
#710485