Finite Group Databasebeta

← #14282473

Subgroups — #14282473

Order 1920.

460 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752695C211yesmaximal, characteristic
2C5×#4835C211yesmaximal, characteristic, complemented
3C4×D3×#168C211yesmaximal, characteristic, complemented
4#11746305C211yesmaximal, characteristic, complemented
5C3×#64703C211yesmaximal, characteristic, complemented
6#11745845C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10601593—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C42×C5×D3C2211yescharacteristic
11C3×C4×D20C2211yescharacteristic
12#91456C411yescharacteristic
13#91452—21no—
14C4×#1201—21no—
15#91381C411yescharacteristic
16#91365C411yescharacteristic
17#91364C411yescharacteristic
18#91363—21no—
19#91357—21no—
20C2×D3×#168—21no—
21C3×C5×C4⋊C8C2211yescharacteristic
22C4×C3⋊#168C2211yescharacteristic
23C5×(C2×D3)⋊C8—21no—
24C5×#815—21no—
25C5×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×#168C2211yescharacteristic
27Dic3×#168—21no—
28#68177—51nomaximal, Hall
29#65813—31no—
30C5×#432—31no—
31C2×C4×#168—31no—
32#64704—31no—
33#64704—31no—
34#64703—31no—
35#64703D311yescharacteristic, complemented
36C2×Dic30C2×C411yescharacteristic
37C2×C4×C5×D3C2×C411yescharacteristic
38C2×C4×C5×D3D411yescharacteristic
39C2×C4×C5×D3D411yescharacteristic
40C2×C3×D20C2×C411yescharacteristic
41C2×C3×C4×D5—21no—
42C2×#1201—21no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45C4⋊Dic15C2×C411yescharacteristic
46#6712—21no—
47C4×Dic15—21no—
48C2×C3⋊#168—21no—
49C4×C5×Dic3C2×C411yescharacteristic
50C4×C5×Dic3D411yescharacteristic
51C4×C5×Dic3D411yescharacteristic
52C2×C5×C3⋊C8—21no—
53C3×#685—21no—
54C3×C4⋊Dic5C2×C411yescharacteristic
55C2×C3×#168—21no—
56#6669—21no—
57#6668—21no—
58#6668—21no—
59(C2×D3)⋊Dic5—21no—
60#6665—21no—
61#6665—21no—
62#6665—21no—
63D3×#168—24no—
64#5557—51no—
65#4835D511yescharacteristic, complemented
66C4×D3×C8—51no—
67C3×D4⋊C8—51no—
68D4⋊(C3⋊C8)—51no—
69#4484—51no—
70#4456—51no—
71C2×C42×C5—31no—
72#4076—31no—
73#4075—61no—
74C4×C22⋊D5—61no—
75#4070—31no—
76C22×#168—61no—
77#4022—61no—
78#4021—31no—
79C4×D20C2×D311yescharacteristic
80#4018—61no—
81#4016—31no—
82C4×Dic10—31no—
83C5×C4⋊C8—31no—
84C5×C4⋊C8C2×D311yescharacteristic
85C5×C22⋊C8—61no—
86C5×#97—61no—
87C4×#168—31no—
88C4×#168—61no—
89C4×#168C2×D311yescharacteristic
90#1494—151noSylow
91C22×C5×D3C22⋊C411yescharacteristic
92C22×C3×D5—21no—
93C2×C3×C4×C5C22×C411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15—21no—
97C2×Dic15—21no—
98Dic30—21no—
99Dic30—21no—
100C2×C5×Dic3C22⋊C411yescharacteristic
101C2×C5×Dic3C22⋊C411yescharacteristic
102C2×C5×Dic3C22⋊C411yescharacteristic
103C4×C5×D3—22no—
104C4×C5×D3—21no—
105C4×C5×D3—21no—
106C4×C5×D3—21no—
107C4×C5×D3—21no—
108C2×C3×Dic5—21no—
109C3×D20—21no—
110C3×D20—21no—
111C3×C4×D5—41no—
112C3×C4×D5—41no—
113#1201—42no—
114C3×C5×C8—41no—
115C3⋊#168—22no—
116C3×#168—22no—
117C5×C3⋊C8—41no—
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×D3C2×D511yescharacteristic
129C4×Dic6—51no—
130C3×C4⋊C8C2×D511yescharacteristic
131C3×C4×C8—51no—
132(C2×D3)⋊C8—21no—
133#815—21no—
134C8×Dic3—101no—
135C4⋊(C3⋊C8)C2×D511yescharacteristic
136C4×C3⋊C8—51no—
137C22×C4×C5—31no—
138C22×C4×C5—31no—
139C22×C4×C5—31no—
140C2×C22⋊D5—61no—
141C2×D20C4×D311yescharacteristic
142C2×C4×D5—21no—
143C2×Dic10—31no—
144C2×C5×C8—21no—
145C2×C5×C8—61no—
146C42×C5—31no—
147C42×C5—31no—
148C42×C5—31no—
149C42×C5C22×D311yescharacteristic
150C22⋊Dic5—61no—
151#685—21no—
152#685—61no—
153#685—61no—
154#685—61no—
155C4⋊Dic5—31no—
156C4⋊Dic5C4×D311yescharacteristic
157#683—61no—
158#683—61no—
159#683—61no—
160#683—61no—
161C4×Dic5—61no—
162C2×#168—21no—
163C2×#168—64no—
164C2×#168—61no—
165#529—151no—
166#432—31no—
167C2×C4×C8—151no—
168Q8⋊C8—151no—
169Q8⋊C8—151no—
170D4⋊C8—51no—
171D4⋊C8—151no—
172C22×C3×C5C2×C22⋊C411yescharacteristic
173C2×C5×D3—21no—
174C2×C5×D3—21no—
175C2×C5×D3#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—41no—
185Dic15—41no—
186C3×Dic5—41no—
187C5×Dic3—21no—
188C5×Dic3—21no—
189C5×Dic3—21no—
190C2×C3×D4—51no—
191C22×C3×C4—101no—
192C2×#67—101no—
193C2×C4×D3C4×D511yescharacteristic
194C2×C4×D3D2011yescharacteristic
195C2×C4×D3C22⋊D511yescharacteristic
196C2×Dic6—51no—
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—51no—
207C4⋊Dic3—101no—
208C4⋊Dic3—101no—
209Dic3⋊C4—101no—
210Dic3⋊C4—101no—
211C4×Dic3—101no—
212C4×Dic3C4×D511yescharacteristic
213C4×Dic3D2011yescharacteristic
214C4×Dic3C22⋊D511yescharacteristic
215C2×C3⋊C8—21no—
216C2×C3⋊C8—101no—
217D3×C8—104no—
218C23×C5—31no—
219C22×D5—21no—
220C2×C4×C5—31no—
221C2×C4×C5—31no—
222C2×C4×C5—31no—
223C2×C4×C5—62no—
224C2×C4×C5—61no—
225C2×C4×C5—61no—
226C2×C4×C5—61no—
227C2×C4×C5—61no—
228C2×C4×C5C2×C4×D311yescharacteristic
229C2×C4×C5D3×D411yescharacteristic
230C2×C4×C5D3×D411yescharacteristic
231C22⋊D5—122no—
232C2×Dic5—21no—
233C2×Dic5—61no—
234C2×Dic5—61no—
235D20—21no—
236D20—21no—
237C4×D5—41no—
238C4×D5—41no—
239Dic10—61no—
240Dic10—61no—
241C5×C8—41no—
242C5×C8—121no—
243#168—22no—
244#168—62no—
245C22×C8—301no—
246#126—301no—
247#125—151no—
248#124—151no—
249#123—301no—
250C22⋊Q8—151no—
251#121—151no—
252C4×Q8—151no—
253C4×D4—51no—
254C4×D4—301no—
255#117—301no—
256C2×C42—31no—
257C4⋊C8—31no—
258C4⋊C8D3×D511yescharacteristic
259C22⋊C8—61no—
260#97—61no—
261C4×C8—51no—
262C4×C8—151no—
263C4×C8—301no—
264C2×C3×C5#40811yescharacteristic
265C2×C3×C5#41611yescharacteristic
266C2×C3×C5C2×#10411yescharacteristic
267C3×D5—81no—
268C5×D3—22no—
269C23×C3—101no—
270C22×D3#68511yescharacteristic
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×C4C2×D2011yescharacteristic
278C2×C3×C4C2×C22⋊D511yescharacteristic
279#67—202no—
280C2×Dic3—101no—
281C2×Dic3—101no—
282C2×Dic3#68511yescharacteristic
283C2×Dic3#68511yescharacteristic
284C2×Dic3#68511yescharacteristic
285C4×D3—22no—
286C4×D3—21no—
287C4×D3—21no—
288C4×D3—21no—
289C4×D3—21no—
290Dic6—101no—
291Dic6—101no—
292C3×C8—41no—
293C3×C8—102no—
294C3⋊C8—41no—
295C3⋊C8—102no—
296C22×C5—32no—
297C22×C5—61no—
298C22×C5—61no—
299C22×C5D3×C22⋊C411yescharacteristic
300C2×D5—41no—
301C2×D5—41no—
302C2×D5—41no—
303C4×C5—21no—
304C4×C5—61no—
305C4×C5—61no—
306C4×C5—61no—
307C4×C5#90111yescharacteristic
308C4×C5#90711yescharacteristic
309C4×C5#91211yescharacteristic
310C4×C5#91611yescharacteristic
311Dic5—41no—
312Dic5—121no—
313Dic5—121no—
314C2×Q8—151no—
315C2×D4—51no—
316C2×D4—301no—
317C22×C4—31no—
318C22×C4—31no—
319C22×C4—31no—
320C22×C4—101no—
321C2×C8—21no—
322C2×C8—61no—
323C2×C8—101no—
324C2×C8—304no—
325C2×C8—301no—
326C4⋊C4—51no—
327C4⋊C4—151no—
328C4⋊C4—301no—
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—31no—
338C42—31no—
339C42—31no—
340C42—301no—
341C42C2×D3×D511yescharacteristic
342C3×C5#149411yescharacteristic, complemented, Hall
343C22×C3—201no—
344C22×C3—201no—
345C22×C3—201no—
346C22×C3C2×#68511yescharacteristic
347C2×D3—21no—
348C2×D3—21no—
349C2×D3#395712yes—
350C3×C4—21no—
351C3×C4—201no—
352C3×C4#405311yescharacteristic
353C3×C4#405311yescharacteristic
354C3×C4#409611yescharacteristic
355C3×C4#409611yescharacteristic
356Dic3—21no—
357Dic3—21no—
358Dic3—21no—
359Dic3—201no—
360Dic3—201no—
361C2×C5—62no—
362C2×C5#472711yescharacteristic
363C2×C5#477211yescharacteristic
364C2×C5D3×#10411yescharacteristic
365D5—81no—
366C23—31no—
367C23—101no—
368Q8—301no—
369Q8—301no—
370D4—101no—
371D4—101no—
372D4—602no—
373C2×C4—31no—
374C2×C4—31no—
375C2×C4—31no—
376C2×C4—62no—
377C2×C4—61no—
378C2×C4—61no—
379C2×C4—61no—
380C2×C4—61no—
381C2×C4—101no—
382C2×C4—201no—
383C2×C4—201no—
384C2×C4—301no—
385C2×C4—301no—
386C2×C4C4×D3×D511yescharacteristic
387C2×C4D3×D2011yescharacteristic
388C2×C4D3×C22⋊D511yescharacteristic
389C8—41no—
390C8—102no—
391C8—121no—
392C8—302no—
393C2×C3—401no—
394C2×C3#6529111yescharacteristic
395C2×C3#6541811yescharacteristic
396C2×C3C2×#395711yescharacteristic
397D3—22no—
398C5#6817711yescharacteristic, complemented, Sylow
399C22—32no—
400C22—61no—
401C22—61no—
402C22—201no—
403C22—201no—
404C22—201no—
405C22D3×#68511yescharacteristic
406C4—21no—
407C4—61no—
408C4—61no—
409C4—61no—
410C4—201no—
411C4—601no—
412C4—601no—
413C4#9126611yescharacteristic
414C4#9126811yescharacteristic
415C4#9149311yescharacteristic
416C4#9151711yescharacteristic
417C3#1060159311yescharacteristic, complemented, Sylow
418C2—62no—
419C2—401no—
420C2#1174750211yescharacteristic
421C2#1174814011yescharacteristic
422C2D3×#395711yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91456C4
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. C5×#4835C2semidirect
3. C4×D3×#168C2semidirect
4. #11746305C2semidirect
5. C3×#64703C2semidirect
6. #11745845C2semidirect
7. #11745834C2semidirect
35. #64703D3semidirect
65. #4835D5semidirect
342. C3×C5#1494semidirect
398. C5#68177semidirect
417. C3#10601593semidirect

Maximal subgroups

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

subgroupindex
#117526952
C5×#48352
C4×D3×#1682
#117463052
C3×#647032
#117458452
#117458342
#106015933
#681775