Finite Group Databasebeta

← #14289443

Subgroups — #14289443

Order 1920.

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

normal subgroups only

This group has 512 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#11756477C211yesmaximal, characteristic
2C5×#5076C211yesmaximal, characteristic, complemented
3#11746963C211yesmaximal, characteristic, complemented
4#11746885C211yesmaximal, characteristic, complemented
5C3×#64764C211yesmaximal, characteristic, complemented
6#11745844C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic, complemented
8#10602064—31nomaximal, Hall
9C2×#6819—21no—
10C3×C5×#127C2211yescharacteristic
11#91829—21no—
12#91828—22no—
13#91827—21no—
14D4×Dic15—21no—
15C4×D60C2211yescharacteristic
16C4×Dic30C2211yescharacteristic
17C2×C5×#214—22no—
18C5×#869C2211yescharacteristic
19C4×C5×C3⋊C8C2211yescharacteristic
20C3×C4⋊#168C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22#90988—21no—
23#90985—21no—
24#90975—21no—
25#90969—21no—
26#68405—51nomaximal, Hall
27#66052—31no—
28C5×#492—31no—
29#65380—31no—
30#65373—31no—
31#64764D311yescharacteristic, complemented
32#64679—31no—
33#64676—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4D412yes—
37C2×#1220—22no—
38C2×#1220—22no—
39C22×Dic15—22no—
40#6819—42no—
41#6819—42no—
42C2×D60D411yescharacteristic
43C2×C4×D15—21no—
44C2×Dic30D411yescharacteristic
45C2×C5×Dic6—21no—
46C3×C42×C5C2311yescharacteristic
47#6719—22no—
48#6714—21no—
49C4⋊Dic15D411yescharacteristic
50C4⋊Dic15D411yescharacteristic
51#6712—21no—
52C4×Dic15—21no—
53C5×#214—44no—
54C5×C4⋊Dic3—21no—
55C5×C4⋊Dic3—21no—
56C2×C5×C3⋊C8—21no—
57C2×C3×#168—21no—
58C2×C3×#168—21no—
59#5718—51no—
60#5076D511yescharacteristic, complemented
61#4850—51no—
62#4842—51no—
63C3×#331—51no—
64#4484—51no—
65#4483—51no—
66C2×#711—61no—
67C2×C5×SD16—62no—
68C5×C4⋊Q8—31no—
69C5×#127C2×D311yescharacteristic
70#4086—61no—
71#4085—62no—
72#4084—61no—
73D4×Dic5—61no—
74C4×D20—31no—
75C4×Dic10—31no—
76C4×C5×C8—31no—
77#3942—61no—
78#3941—61no—
79#3940—61no—
80#3939—61no—
81C4⋊#168C2×D311yescharacteristic
82C4⋊#168C2×D311yescharacteristic
83#1631—151noSylow
84C23×C3×C5—22no—
85C22×D15—21no—
86C3×C5×D4—42no—
87C3×C5×D4—41no—
88C3×C5×D4—41no—
89C3×C5×D4—41no—
90C3×C5×D4—41no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94#1220—44no—
95#1220—82no—
96C2×Dic15—21no—
97C2×Dic15—21no—
98C2×Dic15—21no—
99C2×Dic15—44no—
100D60—21no—
101D60—21no—
102C4×D15—41no—
103C4×D15—41no—
104Dic30—21no—
105Dic30SD1612yescomplemented
106C2×C5×Dic3—41no—
107C5×Dic6—42no—
108C3×#168—41no—
109C3×#168—41no—
110C5×C3⋊C8—22no—
111C2×#237—101no—
112C3×#127C2×D511yescharacteristic
113#940—101no—
114#939—102no—
115#938—101no—
116D4×Dic3—101no—
117C2×#214—22no—
118C4×D12—51no—
119#869C2×D511yescharacteristic
120C4×Dic6—51no—
121C3×C4⋊C8—51no—
122C3×C4⋊C8—51no—
123#821—101no—
124#818—101no—
125#817—101no—
126#816—101no—
127C4×C3⋊C8C2×D511yescharacteristic
128C2×C5×Q8—61no—
129C2×C5×D4—21no—
130C2×C5×D4—21no—
131C2×C5×D4D1212yes—
132C2×C22⋊D5—62no—
133C2×C22⋊D5—62no—
134C22×Dic5—62no—
135#711—122no—
136#711—122no—
137C2×D20—31no—
138C2×C4×D5—61no—
139C2×Dic10—31no—
140C5×SD16—124no—
141C2×C5×C8—61no—
142C5×C4⋊C4—61no—
143C5×C4⋊C4—61no—
144C42×C5C22×D311yescharacteristic
145C22⋊Dic5—62no—
146#685—61no—
147C4⋊Dic5—31no—
148C4⋊Dic5—31no—
149#683—61no—
150C4×Dic5—61no—
151C2×#168—21no—
152C2×#168—21no—
153#550—151no—
154#492—31no—
155#477—151no—
156#476—151no—
157#331—51no—
158Q8⋊C8—151no—
159D4⋊C8—151no—
160C22×C3×C5—42no—
161C22×C3×C5—42no—
162C22×C3×C5—42no—
163C22×C3×C5#12011yescharacteristic
164C2×D15—41no—
165C2×D15—41no—
166C2×D15—41no—
167C3×C4×C5—21no—
168C3×C4×C5C2×SD1611yescharacteristic
169C3×C4×C5#13511yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C3×C4×C5#13711yescharacteristic
172Dic15—22no—
173Dic15—41no—
174Dic15—41no—
175C5×Dic3—81no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4C22⋊D512yes—
179C2×#67—102no—
180C2×#67—102no—
181C22×Dic3—102no—
182#237—202no—
183#237—202no—
184C2×D12—51no—
185C2×C4×D3—101no—
186C2×Dic6—21no—
187C2×Dic6—51no—
188C2×C3×C8—101no—
189C2×C3×C8—101no—
190C3×C42C22×D511yescharacteristic
191#217—102no—
192#214—44no—
193(C2×D3)⋊C4—101no—
194C4⋊Dic3—21no—
195C4⋊Dic3—21no—
196C4⋊Dic3—51no—
197C4⋊Dic3—51no—
198Dic3⋊C4—101no—
199C4×Dic3—101no—
200C2×C3⋊C8—21no—
201C23×C5—22no—
202C22×D5—61no—
203C5×Q8—122no—
204C5×D4—42no—
205C5×D4—41no—
206C5×D4—41no—
207C5×D4—41no—
208C5×D4—41no—
209C2×C4×C5—121no—
210C2×C4×C5C2×D1211yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5D3×D411yescharacteristic
213C22⋊D5—124no—
214C22⋊D5—242no—
215C2×Dic5—61no—
216C2×Dic5—61no—
217C2×Dic5—61no—
218C2×Dic5—124no—
219D20—61no—
220D20—61no—
221C4×D5—121no—
222C4×D5—121no—
223Dic10—32no—
224Dic10—61no—
225C5×C8—62no—
226#168—41no—
227#168—41no—
228C2×#41—301no—
229C2×SD16—62no—
230C4⋊Q8—31no—
231#127—301no—
232#127D3×D511yescharacteristic
233#121—301no—
234#121—302no—
235C4×Q8—151no—
236C4×D4—151no—
237C4×D4—301no—
238#107—301no—
239#106—301no—
240C4⋊C8—51no—
241C4⋊C8—51no—
242#103—301no—
243#102—301no—
244C4×C8—31no—
245C2×C3×C5—82no—
246C2×C3×C5#45011yescharacteristic
247C2×C3×C5#45211yescharacteristic
248C2×C3×C5#45311yescharacteristic
249D15—81no—
250C23×C3—22no—
251C22×D3—101no—
252C3×D4—42no—
253C3×D4—41no—
254C3×D4—41no—
255C3×D4—41no—
256C3×D4—41no—
257C2×C3×C4D4×D511yescharacteristic
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4C2×C22⋊D511yescharacteristic
260#67—204no—
261#67—402no—
262C2×Dic3—41no—
263C2×Dic3—101no—
264C2×Dic3—101no—
265C2×Dic3—101no—
266C2×Dic3—204no—
267D12—101no—
268D12—101no—
269C4×D3—201no—
270C4×D3—201no—
271Dic6—42no—
272Dic6—52no—
273Dic6—101no—
274C3×C8—201no—
275C3×C8—201no—
276C3⋊C8—22no—
277C22×C5—42no—
278C22×C5—42no—
279C22×C5—42no—
280C22×C5#88211yescharacteristic
281C2×D5—121no—
282C2×D5—121no—
283C2×D5—121no—
284C4×C5—21no—
285C4×C5—241no—
286C4×C5#91111yescharacteristic
287C4×C5#91211yescharacteristic
288C4×C5D3×SD1611yescharacteristic
289C4×C5#91511yescharacteristic
290Dic5—62no—
291Dic5—121no—
292Dic5—121no—
293#41—602no—
294#41—602no—
295C2×Q8—61no—
296C2×Q8—151no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—151no—
300C2×D4—302no—
301C2×D4—302no—
302C2×D4#120312yes—
303C22×C4—302no—
304C22×C4—301no—
305SD16—124no—
306C2×C8—61no—
307C2×C8—101no—
308C2×C8—101no—
309C4⋊C4—61no—
310C4⋊C4—61no—
311C4⋊C4—151no—
312C4⋊C4—151no—
313C4⋊C4—301no—
314C22⋊C4—302no—
315C22⋊C4—301no—
316C42—301no—
317C42C2×D3×D511yescharacteristic
318C3×C5#163111yescharacteristic, complemented, Hall
319C22×C3—42no—
320C22×C3—42no—
321C22×C3—42no—
322C22×C3#408311yescharacteristic
323C2×D3—201no—
324C2×D3—201no—
325C2×D3—201no—
326C3×C4—21no—
327C3×C4D5×SD1611yescharacteristic
328C3×C4#406011yescharacteristic
329C3×C4#406111yescharacteristic
330C3×C4#406211yescharacteristic
331Dic3—81no—
332Dic3—102no—
333Dic3—201no—
334Dic3—201no—
335C2×C5—82no—
336C2×C5#474711yescharacteristic
337C2×C5#477611yescharacteristic
338C2×C5#478311yescharacteristic
339D5—241no—
340C23—22no—
341C23—301no—
342Q8—122no—
343Q8—152no—
344Q8—301no—
345D4—42no—
346D4—41no—
347D4—41no—
348D4—41no—
349D4—41no—
350D4—301no—
351D4—301no—
352D4—604no—
353D4—1202no—
354C2×C4—121no—
355C2×C4—301no—
356C2×C4—301no—
357C2×C4—301no—
358C2×C4—604no—
359C2×C4—601no—
360C2×C4—601no—
361C2×C4C2×#120311yescharacteristic
362C2×C4#679011yescharacteristic
363C2×C4#679011yescharacteristic
364C8—62no—
365C8—201no—
366C8—201no—
367C2×C3—82no—
368C2×C3#6536611yescharacteristic
369C2×C3#6545811yescharacteristic
370C2×C3#6546211yescharacteristic
371D3—401no—
372C5#6840511yescharacteristic, complemented, Sylow
373C22—42no—
374C22—42no—
375C22—42no—
376C22—601no—
377C22—601no—
378C22—601no—
379C22#9157311yescharacteristic
380C4—21no—
381C4—241no—
382C4—302no—
383C4—601no—
384C4—601no—
385C4#9148711yescharacteristic
386C4#9148811yescharacteristic
387C4#9149711yescharacteristic
388C4#9149811yescharacteristic
389C3#1060206411yescharacteristic, complemented, Sylow
390C2—82no—
391C2—1201no—
392C2#1174906111yescharacteristic
393C2#1174906211yescharacteristic
394C2#1174914311yescharacteristic
subgroupG/H
centerC22#91573
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5#120
prime radical#11756477C2
hypercenter#127D3×D5
hypocenterC3×C5#1631
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. C5×#5076C2semidirect
3. #11746963C2semidirect
4. #11746885C2semidirect
5. C3×#64764C2semidirect
6. #11745844C2semidirect
7. #11745838C2semidirect
31. #64764D3semidirect
60. #5076D5semidirect
105. Dic30SD16semidirect
318. C3×C5#1631semidirect
372. C5#68405semidirect
389. C3#10602064semidirect

Maximal subgroups

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

subgroupindex
#117564772
C5×#50762
#117469632
#117468852
C3×#647642
#117458442
#117458382
#106020643
#684055