Finite Group Databasebeta

← #14290874

Subgroups — #14290874

Order 1920.

480 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 90 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#11752533C211yesmaximal, characteristic
2C3×#65135C211yesmaximal, characteristic, complemented
3#11747085C211yesmaximal, characteristic, complemented
4#11746947C211yesmaximal, characteristic, complemented
5#11746304C211yesmaximal, characteristic, complemented
6C5×#4482C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10599232—31nomaximal, Hall
9C2×#6766—21no—
10C4×D60C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×C4×D20C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14#91450—21no—
15#91413—22no—
16D5×C4⋊Dic3—21no—
17#91383—21no—
18C2×#6658—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×#3953—21no—
23C3×#3950—21no—
24#90986—22no—
25#90971—21no—
26#71111—51nomaximal, Hall
27#66060—31no—
28#65368—31no—
29#65135D311yescharacteristic, complemented
30#65130—31no—
31C5×#332—31no—
32#64703—31no—
33#64703—31no—
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×C5×Dic6—21no—
37C2×C3×D20D411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×C3×Dic10—21no—
40C2×#1202—22no—
41C2×D5×Dic3—22no—
42#6766—42no—
43#6766—42no—
44C2×C3×C5×C8—21no—
45C3×C42×C5C2311yescharacteristic
46#6714—21no—
47C4⋊Dic15D411yescharacteristic
48C2×C3⋊#168—21no—
49C5×C4⋊Dic3—21no—
50C5×C4⋊Dic3D412yes—
51C2×C5×C3⋊C8—21no—
52C3×#685—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5D411yescharacteristic
56#6668—22no—
57#6667—22no—
58#6658—42no—
59#5555—51no—
60C3×#474—51no—
61#5083—51no—
62#5080—51no—
63D4⋊(C3⋊C8)—51no—
64#4483—51no—
65#4482D511yescharacteristic, complemented
66C2×#713—61no—
67C5×C4⋊Q8—31no—
68#4092—61no—
69C2×#677—61no—
70#4041—61no—
71#4040—62no—
72D5×C4⋊C4—61no—
73C4×D20—31no—
74C4×D20C2×D311yescharacteristic
75#4015C2×D311yescharacteristic
76C5×C4⋊C8—31no—
77C5×C4⋊C8C2×D311yescharacteristic
78#3953—21no—
79#3950—21no—
80#3948—61no—
81#3940—62no—
82C4×#168—31no—
83#1654—151noSylow
84C22×D15—21no—
85C22×C3×D5—21no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—21no—
90D60—21no—
91D60—21no—
92C4×D15—41no—
93C4×D15—41no—
94C2×C5×Dic3—22no—
95C5×Dic6—41no—
96C5×Dic6—41no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—41no—
99C3×D20—21no—
100C3×D20SD1612yescomplemented
101C3×C4×D5—41no—
102C3×C4×D5—41no—
103C3×Dic10—41no—
104C3×Dic10—41no—
105#1202—44no—
106D5×Dic3—44no—
107C3×C5×C8—41no—
108C3⋊#168—22no—
109C5×C3⋊C8—41no—
110C2×#237—101no—
111C3×C4⋊Q8—51no—
112C3×C4×D4—51no—
113C2×#215—101no—
114#930—101no—
115C2×C4⋊Dic3—101no—
116#897—101no—
117#886—102no—
118C4×D12—51no—
119#869C2×D511yescharacteristic
120C3×#107—101no—
121C3×C4⋊C8C2×D511yescharacteristic
122C3×#102—101no—
123#835—101no—
124#808—102no—
125C4⋊(C3⋊C8)C2×D511yescharacteristic
126C4×C3⋊C8—51no—
127C2×C5×Q8—61no—
128#713—122no—
129#713—122no—
130C2×D20—31no—
131C2×D20—62no—
132C2×D20#6711yescharacteristic
133C2×C4×D5—21no—
134C2×C4×D5—62no—
135C2×C4×D5—61no—
136C2×Dic10—21no—
137C2×C5×C8—21no—
138C2×C5×C8—61no—
139C5×C4⋊C4—32no—
140C5×C4⋊C4—61no—
141C42×C5C22×D311yescharacteristic
142#685—21no—
143#685—62no—
144#685—61no—
145C4⋊Dic5—21no—
146C4⋊Dic5—21no—
147C4⋊Dic5—31no—
148C4⋊Dic5#6711yescharacteristic
149#683—62no—
150C2×#168—61no—
151#677—122no—
152#547—151no—
153#498—151no—
154#474—51no—
155#461—151no—
156#332—31no—
157D4⋊C8—151no—
158D4⋊C8—151no—
159C22×C3×C5#12011yescharacteristic
160C2×D15—41no—
161C2×D15—41no—
162C2×D15—41no—
163C2×C3×D5—22no—
164C2×C3×D5—41no—
165C2×C3×D5—41no—
166C3×C4×C5—21no—
167C3×C4×C5C2×SD1611yescharacteristic
168C3×C4×C5#13511yescharacteristic
169C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171Dic15—41no—
172C3×Dic5—41no—
173C3×Dic5—81no—
174C5×Dic3—42no—
175C2×C3×Q8—101no—
176C2×C3×D4—51no—
177C22×C3×C4—101no—
178C2×#67—102no—
179C22×Dic3—102no—
180#237—202no—
181#237—202no—
182C2×D12—51no—
183C2×C4×D3—101no—
184C2×Dic6—21no—
185C2×C3×C8—21no—
186C3×C4⋊C4—51no—
187C3×C4⋊C4—101no—
188C3×C4⋊C4—101no—
189C3×C22⋊C4—101no—
190C3×C42C22×D511yescharacteristic
191#215—202no—
192(C2×D3)⋊C4—102no—
193(C2×D3)⋊C4—101no—
194C4⋊Dic3—21no—
195C4⋊Dic3—51no—
196C4⋊Dic3—102no—
197C4⋊Dic3D2012yes—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—101no—
200C22×D5—21no—
201C22×D5—61no—
202C5×Q8—121no—
203C5×Q8—121no—
204C2×C4×C5—62no—
205C2×C4×C5D3×D411yescharacteristic
206C2×C4×C5D3×D411yescharacteristic
207C2×C4×C5C2×#6711yescharacteristic
208C2×Dic5—21no—
209C2×Dic5—41no—
210C2×Dic5—61no—
211D20—21no—
212D20—61no—
213D20—61no—
214D20—124no—
215D20#21512yescomplemented
216C4×D5—41no—
217C4×D5—41no—
218C4×D5—124no—
219C4×D5—121no—
220C4×D5—121no—
221Dic10—41no—
222Dic10—41no—
223C5×C8—41no—
224C5×C8—121no—
225#168—62no—
226C2×#41—301no—
227C2×SD16—301no—
228C4⋊Q8—31no—
229C4⋊Q8—51no—
230#123—302no—
231C22⋊Q8—301no—
232#121—301no—
233C4×D4—51no—
234C4×D4—151no—
235C2×C4⋊C4—301no—
236#107—101no—
237#106—302no—
238C4⋊C8—31no—
239C4⋊C8D3×D511yescharacteristic
240#103—301no—
241#102—101no—
242C4×C8—151no—
243C2×C3×C5#44911yescharacteristic
244C2×C3×C5#45011yescharacteristic
245C2×C3×C5#45611yescharacteristic
246D15—81no—
247C3×D5—42no—
248C23×C3—101no—
249C22×D3—101no—
250C3×Q8—201no—
251C3×Q8—201no—
252C3×D4—52no—
253C3×D4—101no—
254C2×C3×C4—101no—
255C2×C3×C4—201no—
256C2×C3×C4—201no—
257C2×C3×C4—201no—
258C2×C3×C4C2×D2011yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4D4×D511yescharacteristic
261#67—204no—
262C2×Dic3—22no—
263C2×Dic3—101no—
264C2×Dic3—204no—
265D12—101no—
266D12—101no—
267C4×D3—201no—
268C4×D3—201no—
269Dic6—41no—
270Dic6—41no—
271C3×C8—41no—
272C3⋊C8—41no—
273C3⋊C8—102no—
274C22×C5#93711yescharacteristic
275C2×D5—22no—
276C2×D5—41no—
277C2×D5—41no—
278C2×D5—121no—
279C2×D5—121no—
280C2×D5—121no—
281C4×C5—21no—
282C4×C5—122no—
283C4×C5#91111yescharacteristic
284C4×C5#91211yescharacteristic
285C4×C5C2×#21511yescharacteristic
286C4×C5#94911yescharacteristic
287Dic5—41no—
288Dic5—81no—
289Dic5—121no—
290#41—602no—
291#41—602no—
292C2×Q8—61no—
293C2×Q8—101no—
294C2×D4—51no—
295C2×D4—151no—
296C2×D4—302no—
297C22×C4—101no—
298C22×C4—302no—
299C22×C4—301no—
300SD16—602no—
301C2×C8—21no—
302C2×C8—61no—
303C2×C8—301no—
304C4⋊C4—32no—
305C4⋊C4—51no—
306C4⋊C4—61no—
307C4⋊C4—101no—
308C4⋊C4—101no—
309C4⋊C4—151no—
310C4⋊C4—302no—
311C22⋊C4—101no—
312C22⋊C4—302no—
313C22⋊C4—301no—
314C42C2×D3×D511yescharacteristic
315C3×C5#165411yescharacteristic, complemented, Hall
316C22×C3—102no—
317C22×C3—201no—
318C22×C3—201no—
319C22×C3#402811yescharacteristic
320C2×D3—201no—
321C2×D3—201no—
322C2×D3—201no—
323C3×C4—21no—
324C3×C4—201no—
325C3×C4—401no—
326C3×C4#405711yescharacteristic
327C3×C4D5×SD1611yescharacteristic
328C3×C4#406011yescharacteristic
329C3×C4#406511yescharacteristic
330Dic3—42no—
331Dic3—201no—
332C2×C5#504611yescharacteristic
333C2×C5#515811yescharacteristic
334C2×C5#520511yescharacteristic
335D5—42no—
336D5—241no—
337C23—101no—
338C23—301no—
339Q8—121no—
340Q8—121no—
341Q8—201no—
342Q8—201no—
343D4—52no—
344D4—101no—
345D4—301no—
346D4—301no—
347D4—604no—
348C2×C4—62no—
349C2×C4—101no—
350C2×C4—201no—
351C2×C4—201no—
352C2×C4—201no—
353C2×C4—301no—
354C2×C4—604no—
355C2×C4—601no—
356C2×C4—601no—
357C2×C4D3×D2011yescharacteristic
358C2×C4#677711yescharacteristic
359C2×C4D5×#6711yescharacteristic
360C8—41no—
361C8—121no—
362C8—302no—
363C2×C3—202no—
364C2×C3#6504111yescharacteristic
365C2×C3#6506511yescharacteristic
366C2×C3#6510011yescharacteristic
367D3—401no—
368C5#7111111yescharacteristic, complemented, Sylow
369C22—102no—
370C22—201no—
371C22—201no—
372C22—601no—
373C22—601no—
374C22—601no—
375C22#9147411yescharacteristic
376C4—21no—
377C4—122no—
378C4—201no—
379C4—401no—
380C4—601no—
381C4#9125811yescharacteristic
382C4#9127711yescharacteristic
383C4#9147811yescharacteristic
384C4D5×#21511yescharacteristic
385C3#1059923211yescharacteristic, complemented, Sylow
386C2—202no—
387C2—1201no—
388C2#1174748111yescharacteristic
389C2#1174815011yescharacteristic
390C2#1174825311yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#11752533C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1654
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#65135C2semidirect
3. #11747085C2semidirect
4. #11746947C2semidirect
5. #11746304C2semidirect
6. C5×#4482C2semidirect
7. #11745834C2semidirect
29. #65135D3semidirect
65. #4482D5semidirect
100. C3×D20SD16semidirect
215. D20#215semidirect
315. C3×C5#1654semidirect
368. C5#71111semidirect
385. C3#10599232semidirect

Maximal subgroups

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

subgroupindex
#117525332
C3×#651352
#117470852
#117469472
#117463042
C5×#44822
#117458342
#105992323
#711115