Finite Group Databasebeta

← #14282475

Subgroups — #14282475

Order 1920.

460 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 100 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#11752501C211yesmaximal, characteristic
2#11750936C211yesmaximal, characteristic, complemented
3C4×#6648C211yesmaximal, characteristic, complemented
4C5×#4484C211yesmaximal, characteristic, complemented
5C3×#64703C211yesmaximal, characteristic, complemented
6#11745843C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic, complemented
8#10599034—31nomaximal, Hall
9C42×D15C2211yescharacteristic
10C4×C5×Dic6C2211yescharacteristic
11C3×C4×D20C2211yescharacteristic
12#91465C411yescharacteristic
13C4×#1202—21no—
14#91384C411yescharacteristic
15#91383C411yescharacteristic
16#91368C411yescharacteristic
17#91366—21no—
18#91357—21no—
19#91354—21no—
20C2×#6648—21no—
21C3×C5×C4⋊C8C2211yescharacteristic
22#91104—21no—
23#91099—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C5×C3⋊C8C2211yescharacteristic
26C3×C4×#168C2211yescharacteristic
27#90951—21no—
28#68177—51nomaximal, Hall
29#65914—31no—
30#65124—31no—
31C4×C8×D5—31no—
32C5×Q8⋊C8—31no—
33Q8⋊#168—31no—
34#64703D311yescharacteristic, complemented
35#64679—31no—
36C2×C4×D15C2×C411yescharacteristic
37C2×C4×D15D411yescharacteristic
38C2×C4×D15D411yescharacteristic
39C2×C5×Dic6C2×C411yescharacteristic
40C2×C3×D20C2×C411yescharacteristic
41C2×C3×C4×D5—21no—
42C2×#1202—21no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45C4×Dic15C2×C411yescharacteristic
46C4×Dic15D411yescharacteristic
47C4×Dic15D411yescharacteristic
48C2×C3⋊#168—21no—
49C5×C4⋊Dic3C2×C411yescharacteristic
50C5×Dic3⋊C4—21no—
51C4×C5×Dic3—21no—
52C2×C5×C3⋊C8—21no—
53C3×#685—21no—
54C3×C4⋊Dic5C2×C411yescharacteristic
55C2×C3×#168—21no—
56Dic3⋊Dic5—21no—
57#6668—21no—
58#6668—21no—
59#6667—21no—
60#6665—21no—
61#6665—21no—
62#6665—21no—
63#6648—24no—
64#5557—51no—
65#4835—51no—
66C4×D3×C8—51no—
67C3×D4⋊C8—51no—
68D4⋊(C3⋊C8)—51no—
69#4484D511yescharacteristic, complemented
70#4456—51no—
71C4×C5×Q8—31no—
72#4093—31no—
73#4092—31no—
74C2×C8×D5—61no—
75#4044—61no—
76#4041—31no—
77#4040—61no—
78#4036—31no—
79C4×D20—61no—
80C4×D20C2×D311yescharacteristic
81#4018—61no—
82C42×D5—31no—
83C5×C4⋊C8C2×D311yescharacteristic
84C4×C5×C8—31no—
85#3952—61no—
86#3947—61no—
87C8×Dic5—61no—
88C4⋊#168—31no—
89C4×#168C2×D311yescharacteristic
90#1494—151noSylow
91C22×D15C22⋊C411yescharacteristic
92C22×C3×D5—21no—
93C2×C3×C4×C5C22×C411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15C22⋊C411yescharacteristic
97C2×Dic15C22⋊C411yescharacteristic
98C2×Dic15C22⋊C411yescharacteristic
99C4×D15—22no—
100C4×D15—21no—
101C4×D15—21no—
102C4×D15—21no—
103C4×D15—21no—
104C2×C5×Dic3—21no—
105C2×C5×Dic3—21no—
106C5×Dic6—21no—
107C5×Dic6—21no—
108C2×C3×Dic5—21no—
109C3×D20—21no—
110C3×D20—21no—
111C3×C4×D5—41no—
112C3×C4×D5—41no—
113#1202—42no—
114C3×C5×C8—41no—
115C3⋊#168—41no—
116C3×#168—22no—
117C5×C3⋊C8—22no—
118C3×C4×D4—51no—
119#938—51no—
120#936—51no—
121C4×#67—101no—
122#926—101no—
123C2×D3×C8—101no—
124#897—51no—
125#890—51no—
126#883—101no—
127#879—101no—
128C42×D3—51no—
129C4×Dic6C2×D511yescharacteristic
130C3×C4⋊C8C2×D511yescharacteristic
131C3×C4×C8—51no—
132(C2×D3)⋊C8—101no—
133#815—101no—
134C8×Dic3—101no—
135C4⋊(C3⋊C8)—51no—
136C4×C3⋊C8C2×D511yescharacteristic
137C2×C5×Q8—31no—
138C2×D20—61no—
139C2×D20C4×D311yescharacteristic
140C2×C4×D5—21no—
141C2×C4×D5—31no—
142C2×C4×D5—31no—
143C2×C4×D5—31no—
144C2×C5×C8—21no—
145C2×C5×C8—61no—
146C5×C4⋊C4—31no—
147C5×C4⋊C4—61no—
148C42×C5—61no—
149C42×C5C22×D311yescharacteristic
150#685—21no—
151#685—61no—
152#685—61no—
153#685—61no—
154#685—61no—
155C4⋊Dic5—61no—
156C4⋊Dic5C4×D311yescharacteristic
157#683—61no—
158#683—61no—
159C4×Dic5—31no—
160C4×Dic5—31no—
161C4×Dic5—31no—
162C2×#168—21no—
163C2×#168—61no—
164C8×D5—64no—
165#529—151no—
166#432—151no—
167C2×C4×C8—151no—
168Q8⋊C8—31no—
169Q8⋊C8—151no—
170D4⋊C8—51no—
171D4⋊C8—151no—
172C22×C3×C5C2×C22⋊C411yescharacteristic
173C2×D15—21no—
174C2×D15—21no—
175C2×D15#10412yes—
176C2×C3×D5—41no—
177C2×C3×D5—41no—
178C2×C3×D5—41no—
179C3×C4×C5—21no—
180C3×C4×C5#13111yescharacteristic
181C3×C4×C5#13111yescharacteristic
182C3×C4×C5#13511yescharacteristic
183C3×C4×C5#13511yescharacteristic
184Dic15—21no—
185Dic15—21no—
186Dic15—21no—
187C3×Dic5—41no—
188C5×Dic3—41no—
189C5×Dic3—41no—
190C2×C3×D4—51no—
191C22×C3×C4—101no—
192C2×#67—101no—
193C2×C4×D3—51no—
194C2×C4×D3—51no—
195C2×C4×D3—51no—
196C2×Dic6C4×D511yescharacteristic
197C2×C3×C8—21no—
198C2×C3×C8—101no—
199C3×C4⋊C4—51no—
200C3×C22⋊C4—101no—
201C3×C42C22×D511yescharacteristic
202#217—101no—
203#217—101no—
204#217—101no—
205(C2×D3)⋊C4—101no—
206C4⋊Dic3—101no—
207C4⋊Dic3—101no—
208C4⋊Dic3C4×D511yescharacteristic
209Dic3⋊C4—21no—
210Dic3⋊C4—101no—
211C4×Dic3—21no—
212C4×Dic3—51no—
213C4×Dic3—51no—
214C4×Dic3—51no—
215C2×C3⋊C8—21no—
216C2×C3⋊C8—101no—
217D3×C8—104no—
218C22×D5—21no—
219C22×D5—31no—
220C5×Q8—61no—
221C5×Q8—61no—
222C2×C4×C5—61no—
223C2×C4×C5—61no—
224C2×C4×C5C2×C4×D311yescharacteristic
225C2×C4×C5D3×D411yescharacteristic
226C2×C4×C5D3×D411yescharacteristic
227C2×Dic5—21no—
228C2×Dic5—31no—
229C2×Dic5—31no—
230C2×Dic5—31no—
231D20—21no—
232D20—21no—
233D20—122no—
234C4×D5—41no—
235C4×D5—41no—
236C4×D5—62no—
237C4×D5—61no—
238C4×D5—61no—
239C4×D5—61no—
240C4×D5—61no—
241C5×C8—41no—
242C5×C8—62no—
243#168—22no—
244#168—121no—
245C22×C8—301no—
246#126—301no—
247#125—151no—
248#124—151no—
249#123—301no—
250C22⋊Q8—151no—
251#121—151no—
252C4×Q8—31no—
253C4×D4—51no—
254C4×D4—301no—
255#117—301no—
256C2×C42—151no—
257C4⋊C8—151no—
258C4⋊C8D3×D511yescharacteristic
259C22⋊C8—301no—
260#97—301no—
261C4×C8—31no—
262C4×C8—51no—
263C4×C8—301no—
264C2×C3×C5#40811yescharacteristic
265C2×C3×C5#41611yescharacteristic
266C2×C3×C5C2×#10411yescharacteristic
267D15—22no—
268C3×D5—81no—
269C23×C3—101no—
270C22×D3—51no—
271C3×D4—101no—
272C3×D4—101no—
273C2×C3×C4—101no—
274C2×C3×C4—201no—
275C2×C3×C4—201no—
276C2×C3×C4C2×C4×D511yescharacteristic
277C2×C3×C4D4×D511yescharacteristic
278C2×C3×C4D4×D511yescharacteristic
279#67—202no—
280C2×Dic3—21no—
281C2×Dic3—21no—
282C2×Dic3—51no—
283C2×Dic3—51no—
284C2×Dic3—51no—
285C4×D3—102no—
286C4×D3—101no—
287C4×D3—101no—
288C4×D3—101no—
289C4×D3—101no—
290Dic6—21no—
291Dic6—21no—
292C3×C8—41no—
293C3×C8—102no—
294C3⋊C8—22no—
295C3⋊C8—201no—
296C22×C5D3×C22⋊C411yescharacteristic
297C2×D5—32no—
298C2×D5—41no—
299C2×D5—41no—
300C2×D5—41no—
301C2×D5—61no—
302C2×D5—61no—
303C4×C5—21no—
304C4×C5—121no—
305C4×C5—121no—
306C4×C5#90111yescharacteristic
307C4×C5#90711yescharacteristic
308C4×C5#91211yescharacteristic
309C4×C5#91611yescharacteristic
310Dic5—41no—
311Dic5—61no—
312Dic5—61no—
313Dic5—61no—
314C2×Q8—31no—
315C2×D4—51no—
316C2×D4—301no—
317C22×C4—101no—
318C22×C4—151no—
319C22×C4—151no—
320C22×C4—151no—
321C2×C8—21no—
322C2×C8—61no—
323C2×C8—101no—
324C2×C8—304no—
325C2×C8—301no—
326C4⋊C4—31no—
327C4⋊C4—51no—
328C4⋊C4—61no—
329C4⋊C4—301no—
330C4⋊C4—301no—
331C4⋊C4—301no—
332C22⋊C4—101no—
333C22⋊C4—301no—
334C22⋊C4—301no—
335C22⋊C4—301no—
336C22⋊C4—301no—
337C42—61no—
338C42—151no—
339C42—151no—
340C42—151no—
341C42C2×D3×D511yescharacteristic
342C3×C5#149411yescharacteristic, complemented, Hall
343C22×C3—201no—
344C22×C3—201no—
345C22×C3—201no—
346C22×C3D5×C22⋊C411yescharacteristic
347C2×D3—52no—
348C2×D3—101no—
349C2×D3—101no—
350C3×C4—21no—
351C3×C4—201no—
352C3×C4#404711yescharacteristic
353C3×C4#405311yescharacteristic
354C3×C4#406211yescharacteristic
355C3×C4#406511yescharacteristic
356Dic3—41no—
357Dic3—41no—
358Dic3—101no—
359Dic3—101no—
360Dic3—101no—
361C2×C5#472711yescharacteristic
362C2×C5#477211yescharacteristic
363C2×C5D3×#10411yescharacteristic
364D5—62no—
365D5—81no—
366C23—101no—
367C23—151no—
368Q8—61no—
369Q8—61no—
370D4—101no—
371D4—101no—
372D4—602no—
373C2×C4—61no—
374C2×C4—61no—
375C2×C4—101no—
376C2×C4—151no—
377C2×C4—151no—
378C2×C4—151no—
379C2×C4—201no—
380C2×C4—201no—
381C2×C4—302no—
382C2×C4—301no—
383C2×C4—301no—
384C2×C4—301no—
385C2×C4—301no—
386C2×C4C4×D3×D511yescharacteristic
387C2×C4#677711yescharacteristic
388C2×C4#679011yescharacteristic
389C8—41no—
390C8—62no—
391C8—102no—
392C8—601no—
393C2×C3—401no—
394C2×C3#6501611yescharacteristic
395C2×C3#6509311yescharacteristic
396C2×C3D5×#10411yescharacteristic
397D3—102no—
398C5#6817711yescharacteristic, complemented, Sylow
399C22—152no—
400C22—201no—
401C22—201no—
402C22—201no—
403C22—301no—
404C22—301no—
405C22#9147311yescharacteristic
406C4—21no—
407C4—121no—
408C4—121no—
409C4—201no—
410C4—301no—
411C4—301no—
412C4—301no—
413C4#9126611yescharacteristic
414C4#9126711yescharacteristic
415C4#9149711yescharacteristic
416C4#9152111yescharacteristic
417C3#1059903411yescharacteristic, complemented, Sylow
418C2—302no—
419C2—401no—
420C2#1174750611yescharacteristic
421C2#1174814411yescharacteristic
422C2#1174823611yescharacteristic
subgroupG/H
centerC2×C4#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91465C4
cosocleC3×C42×C5C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1494
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11750936C2semidirect
3. C4×#6648C2semidirect
4. C5×#4484C2semidirect
5. C3×#64703C2semidirect
6. #11745843C2semidirect
7. #11745835C2semidirect
34. #64703D3semidirect
69. #4484D5semidirect
342. C3×C5#1494semidirect
398. C5#68177semidirect
417. C3#10599034semidirect

Maximal subgroups

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

subgroupindex
#117525012
#117509362
C4×#66482
C5×#44842
C3×#647032
#117458432
#117458352
#105990343
#681775