Finite Group Databasebeta

← #14419310

Subgroups — #14419310

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752683C211yesmaximal, characteristic
2#11752342C211yesmaximal, characteristic, complemented
3C3×C4×D5⋊C8C211yesmaximal, characteristic, complemented
4#11751913C211yesmaximal, characteristic, complemented
5#11751909C212yesmaximal, complemented
6#11751875C212yesmaximal, complemented
7#11751868C212yesmaximal, complemented
8D12×#170C211yesmaximal, characteristic, complemented
9#11751798C212yesmaximal, complemented
10#11751789C211yesmaximal, characteristic, complemented
11Dic6×#170C211yesmaximal, characteristic, complemented
12#10617312—31nomaximal, Hall
13C2×C3×D5⋊C8C2211yescharacteristic
14C2×C3×D5⋊C8C2211yescharacteristic
15C2×#6739C2212yes—
16C2×D3×#170C2212yes—
17#91759C411yescharacteristic
18C5×#875C411yescharacteristic
19C3×C42×D5C2211yescharacteristic
20#91449C411yescharacteristic
21#91447C412yes—
22#91440C2212yes—
23Dic5×D12C2211yescharacteristic
24#91398C2212yes—
25#91372C412yes—
26#91359C411yescharacteristic
27Dic5×Dic6C2211yescharacteristic
28#91232C2212yes—
29#91231C2212yes—
30C4⋊(C3⋊#170)C2211yescharacteristic
31C4⋊(C3⋊#170)C2211yescharacteristic
32C3×C4×#170C2211yescharacteristic
33C3×C4×#170C2211yescharacteristic
34C3×C4×#170C2211yescharacteristic
35C3×C4×#170C2211yescharacteristic
36#91177C2212yes—
37Dic3⋊#170C2212yes—
38(C2×D3)⋊#170C2212yes—
39(C2×D3)⋊#170C2212yes—
40#91169C2212yes—
41Dic3×#170C2212yes—
42#78448—51nomaximal, Hall
43#66014—31no—
44#65788—31no—
45Q8×#170—31no—
46#65774—31no—
47D4×#170—31no—
48#65697—32no—
49#65694—32no—
50#65692—32no—
51#65691—32no—
52#65683—31no—
53C4×D5⋊C8D311yescharacteristic, complemented
54C2×C5×D12C2×C411yescharacteristic
55C2×C5×Dic6C2×C411yescharacteristic
56C2×C3×C4×D5C2×C411yescharacteristic
57C2×C3×C4×D5C2×C411yescharacteristic
58C2×C3×C4×D5C2311yescharacteristic
59C2×#1201C2×C412yes—
60C2×D3×Dic5C2312yes—
61C2×C3⋊#170C2312yes—
62C2×C3⋊#170C2312yes—
63C2×C3×#170C2311yescharacteristic
64C2×C3×#170C2311yescharacteristic
65C2×C3×#170C2311yescharacteristic
66C2×C3×#170C2311yescharacteristic
67C3×D5⋊C8—22no—
68C3×D5⋊C8—22no—
69#6739—24no—
70D3×#170—24no—
71C3×C42×C5C2×C411yescharacteristic
72C4⋊Dic15C2×C411yescharacteristic
73C4⋊Dic15C2×C411yescharacteristic
74#6712C2×C412yes—
75#6712C2×C412yes—
76C5×(C2×D3)⋊C4C2×C412yes—
77C5×(C2×D3)⋊C4C2×C412yes—
78C3×C4×Dic5C2×C411yescharacteristic
79C3×C4×Dic5C2311yescharacteristic
80C3×C4×Dic5C2311yescharacteristic
81Dic3⋊Dic5C2×C412yes—
82#6669C2×C412yes—
83(C2×D3)⋊Dic5C2×C412yes—
84(C2×D3)⋊Dic5C2×C412yes—
85#6665C2×C412yes—
86Dic3×Dic5C2312yes—
87#5479—51no—
88C2×C3×C4×C8—51no—
89#5111—52no—
90C8×#67—52no—
91#4926—51no—
92#4690—52no—
93#4689—52no—
94#4688—51no—
95C8×D12—51no—
96#4679—51no—
97C8×Dic6—51no—
98C2×#704—32no—
99C22×#170—32no—
100C2×D5⋊C8C2×D311yescharacteristic
101C2×D5⋊C8C2×D311yescharacteristic
102C5×#124—31no—
103#4092—31no—
104Q8×Dic5—31no—
105#4084—31no—
106D4×Dic5—31no—
107#4029—32no—
108#4027—32no—
109#4025—32no—
110#4023—32no—
111C42×D5C2×D311yescharacteristic
112#4016—31no—
113C22⋊#170—32no—
114C22⋊#170—32no—
115#4004—32no—
116#4003—32no—
117#4002—32no—
118#4002—32no—
119C4⋊#170—32no—
120C4⋊#170—31no—
121C4⋊#170—31no—
122C4×#170—32no—
123C4×#170C2×D311yescharacteristic
124C4×#170C2×D311yescharacteristic
125C4×#170C2×D311yescharacteristic
126C4×#170C2×D311yescharacteristic
127#2966—151noSylow
128C22×C5×D3C22×C412yes—
129C22×C3×D5C22×C411yescharacteristic
130C2×C3×C4×C5C22×C411yescharacteristic
131C2×C3×C4×C5C22×C411yescharacteristic
132C2×C3×C4×C5C22×C411yescharacteristic
133C2×Dic15C22×C412yes—
134C2×Dic15C22×C412yes—
135C2×C5×Dic3C22×C412yes—
136C5×D12—22no—
137C5×Dic6—22no—
138C2×C3×Dic5C22×C411yescharacteristic
139C2×C3×Dic5C22×C411yescharacteristic
140C2×C3×Dic5C2411yescharacteristic
141C3×C4×D5—22no—
142C3×C4×D5—22no—
143C3×C4×D5—21no—
144C3×C4×D5—21no—
145#1201—24no—
146D3×Dic5—22no—
147D3×Dic5—22no—
148C3⋊#170—22no—
149C3⋊#170—22no—
150C3×#170—21no—
151C3×#170—21no—
152C3×#170#4112yes—
153C3×#170#4112yes—
154C22×C3×C8—51no—
155C22×C3×C8—51no—
156C2×C3×C42—51no—
157#930—51no—
158#929—52no—
159C4×#67—52no—
160#924—51no—
161C2×ΓL(1,𝔽25)—52no—
162C2×D3×C8—52no—
163#876—52no—
164#875AGL(1,𝔽5)11yescharacteristic
165C4×D12—51no—
166#872—52no—
167#870—51no—
168C4×Dic6—51no—
169C3×C4×C8—51no—
170C3×C4×C8—51no—
171C3×C4×C8—51no—
172C3×C4×C8—51no—
173#830—52no—
174(C2×D3)⋊C8—52no—
175(C2×D3)⋊C8—52no—
176#815—52no—
177Dic3⋊C8—52no—
178Dic3⋊C8—52no—
179C8×Dic3—52no—
180C4⋊(C3⋊C8)—51no—
181C4⋊(C3⋊C8)—51no—
182#803—52no—
183C2×C5×Q8—31no—
184C2×C5×D4—31no—
185C2×C22⋊D5—32no—
186C22×Dic5—32no—
187C2×C4×D5C4×D311yescharacteristic
188C2×C4×D5C4×D311yescharacteristic
189C2×C4×D5C22×D311yescharacteristic
190#704—64no—
191C2×#170—32no—
192C2×#170—32no—
193C2×#170—64no—
194C2×#170C22×D311yescharacteristic
195C2×#170C22×D311yescharacteristic
196C2×#170C22×D311yescharacteristic
197C2×#170C22×D311yescharacteristic
198D5⋊C8—22no—
199D5⋊C8—22no—
200C5×C22⋊C4—32no—
201C5×C22⋊C4—32no—
202C42×C5C4×D311yescharacteristic
203C22⋊Dic5—32no—
204C22⋊Dic5—32no—
205#685—32no—
206C4⋊Dic5—31no—
207C4⋊Dic5—31no—
208C4⋊Dic5—32no—
209#683—32no—
210#683—32no—
211#683—32no—
212C4×Dic5—32no—
213C4×Dic5C4×D311yescharacteristic
214C4×Dic5C22×D311yescharacteristic
215C4×Dic5C22×D311yescharacteristic
216#529—151no—
217#446—151no—
218C8×Q8—151no—
219#436—151no—
220#435—152no—
221C8×D4—151no—
222C8×D4—152no—
223#433—152no—
224#432—151no—
225#405—152no—
226C2×C4×C8—51no—
227C22×C3×C5C23×C411yescharacteristic
228C2×C5×D3—22no—
229C2×C5×D3—22no—
230C2×C5×D3—22no—
231C2×C3×D5—21no—
232C2×C3×D5—21no—
233C2×C3×D5#13112yes—
234C3×C4×C5—21no—
235C3×C4×C5—21no—
236C3×C4×C5#13112yes—
237Dic15—22no—
238Dic15—22no—
239C3×Dic5—21no—
240C3×Dic5—21no—
241C3×Dic5C2×#4111yescharacteristic
242C3×Dic5C2×#4111yescharacteristic
243C5×Dic3—22no—
244C22×C3×C4—51no—
245C22×C3×C4—51no—
246C22×C3×C4—51no—
247C2×#67—52no—
248C2×D12C2×AGL(1,𝔽5)11yescharacteristic
249C2×C4×D3—52no—
250C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
251C2×C3×C8—51no—
252C2×C3×C8—51no—
253C2×C3×C8—51no—
254C2×C3×C8—51no—
255C2×C3×C8—102no—
256C2×C3×C8—102no—
257C3×C42—51no—
258C3×C42—51no—
259C3×C42—51no—
260C3×C42C2×AGL(1,𝔽5)11yescharacteristic
261#217—52no—
262(C2×D3)⋊C4—52no—
263(C2×D3)⋊C4—52no—
264(C2×D3)⋊C4C2×AGL(1,𝔽5)12yes—
265(C2×D3)⋊C4C2×AGL(1,𝔽5)12yes—
266C4⋊Dic3—51no—
267C4⋊Dic3—51no—
268Dic3⋊C4—52no—
269Dic3⋊C4—52no—
270Dic3⋊C4—52no—
271Dic3⋊C4—52no—
272C4×Dic3—52no—
273C2×C3⋊C8—52no—
274C2×C3⋊C8—52no—
275ΓL(1,𝔽25)—104no—
276D3×C8—104no—
277C23×C5—32no—
278C22×D5C2×C4×D311yescharacteristic
279C5×Q8—62no—
280C5×D4—62no—
281C2×C4×C5—32no—
282C2×C4×C5C2×C4×D311yescharacteristic
283C2×C4×C5C2×C4×D311yescharacteristic
284C2×C4×C5C2×C4×D311yescharacteristic
285C22⋊D5—64no—
286C2×Dic5—32no—
287C2×Dic5—32no—
288C2×Dic5—62no—
289C2×Dic5—62no—
290C2×Dic5C2×C4×D311yescharacteristic
291C2×Dic5C2×C4×D311yescharacteristic
292C2×Dic5C23×D311yescharacteristic
293C4×D5—22no—
294C4×D5—22no—
295C4×D5—21no—
296C4×D5—21no—
297#170—21no—
298#170—21no—
299#170—62no—
300#170—62no—
301#170#23512yes—
302#170#23512yes—
303C2×M16—152no—
304C22×C8—51no—
305C22×C8—51no—
306C22×C8—152no—
307#126—152no—
308#125—151no—
309#124—31no—
310#123—152no—
311C22⋊Q8—151no—
312#121—151no—
313C4×Q8—151no—
314C4×D4—151no—
315C4×D4—152no—
316#117—152no—
317C2×C42—51no—
318C4⋊C8—151no—
319C4⋊C8—151no—
320C4⋊C8—152no—
321C4⋊C8—152no—
322C22⋊C8—152no—
323C22⋊C8—152no—
324C22⋊C8—152no—
325#97—152no—
326#97—152no—
327C4×C8—51no—
328C4×C8—51no—
329C4×C8—51no—
330C4×C8—51no—
331C4×C8—152no—
332C2×C3×C5C4×#4111yescharacteristic
333C2×C3×C5C2×#13111yescharacteristic
334C2×C3×C5C2×#13111yescharacteristic
335C3×D5—22no—
336C5×D3—42no—
337C23×C3—51no—
338C22×D3C22×AGL(1,𝔽5)12yes—
339C2×C3×C4—51no—
340C2×C3×C4—51no—
341C2×C3×C4—51no—
342C2×C3×C4—101no—
343C2×C3×C4—101no—
344C2×C3×C4—102no—
345C2×C3×C4—102no—
346C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
347C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
348C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
349#67—104no—
350C2×Dic3—52no—
351C2×Dic3—52no—
352C2×Dic3C22×AGL(1,𝔽5)12yes—
353D12—22no—
354C4×D3—102no—
355C4×D3—102no—
356Dic6—22no—
357C3×C8—52no—
358C3×C8—52no—
359C3×C8—101no—
360C3×C8—101no—
361C3⋊C8—102no—
362C3⋊C8—102no—
363C22×C5—62no—
364C22×C5—62no—
365C22×C5—62no—
366C22×C5C22×C4×D311yescharacteristic
367C2×D5—21no—
368C2×D5—21no—
369C2×D5#90112yes—
370C4×C5—21no—
371C4×C5—21no—
372C4×C5—62no—
373C4×C5#90112yes—
374Dic5—21no—
375Dic5—21no—
376Dic5—62no—
377Dic5—62no—
378Dic5C2×#23511yescharacteristic
379Dic5C2×#23511yescharacteristic
380C2×Q8—31no—
381C2×D4—31no—
382C2×D4—152no—
383C22×C4—51no—
384C22×C4—51no—
385C22×C4—51no—
386C22×C4—152no—
387M16—304no—
388C2×C8—51no—
389C2×C8—51no—
390C2×C8—51no—
391C2×C8—51no—
392C2×C8—102no—
393C2×C8—102no—
394C2×C8—152no—
395C2×C8—152no—
396C2×C8—304no—
397C4⋊C4—152no—
398C4⋊C4—152no—
399C4⋊C4—152no—
400C4⋊C4—151no—
401C4⋊C4—152no—
402C4⋊C4—151no—
403C22⋊C4—32no—
404C22⋊C4—32no—
405C22⋊C4—152no—
406C22⋊C4—152no—
407C22⋊C4—152no—
408C42—51no—
409C42—51no—
410C42—51no—
411C42—152no—
412C42D3×AGL(1,𝔽5)11yescharacteristic
413C3×C5#296611yescharacteristic, complemented, Hall
414C22×C3—52no—
415C22×C3—101no—
416C22×C3—101no—
417C22×C3C23×AGL(1,𝔽5)11yescharacteristic
418C2×D3—22no—
419C2×D3—22no—
420C2×D3—22no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—51no—
424C3×C4—51no—
425C3×C4—101no—
426C3×C4—101no—
427C3×C4#413112yes—
428Dic3—22no—
429Dic3—102no—
430Dic3—102no—
431C2×C5—122no—
432C2×C5C4×#23511yescharacteristic
433C2×C5C2×#90111yescharacteristic
434C2×C5C2×#90111yescharacteristic
435D5—22no—
436C23—32no—
437C23—51no—
438Q8—62no—
439D4—62no—
440D4—304no—
441C2×C4—32no—
442C2×C4—51no—
443C2×C4—51no—
444C2×C4—51no—
445C2×C4—101no—
446C2×C4—101no—
447C2×C4—102no—
448C2×C4—102no—
449C2×C4—152no—
450C2×C4—152no—
451C2×C4—302no—
452C2×C4—302no—
453C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
454C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
455C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
456C8—52no—
457C8—52no—
458C8—101no—
459C8—101no—
460C8—302no—
461C8—302no—
462C2×C3—102no—
463C2×C3C2×#413111yescharacteristic
464C2×C3D5⋊#13111yescharacteristic
465C2×C3#41×AGL(1,𝔽5)11yescharacteristic
466D3—42no—
467C5#7844811yescharacteristic, complemented, Sylow
468C22—52no—
469C22—62no—
470C22—62no—
471C22—62no—
472C22—101no—
473C22—101no—
474C22C22×D3×AGL(1,𝔽5)11yescharacteristic
475C4—21no—
476C4—21no—
477C4—51no—
478C4—51no—
479C4—62no—
480C4—101no—
481C4—101no—
482C4—302no—
483C4—302no—
484C4#9191112yes—
485C3#1061731211yescharacteristic, complemented, Sylow
486C2—102no—
487C2—122no—
488C2C2×#9191111yescharacteristic
489C2D5⋊#90111yescharacteristic
490C2AGL(1,𝔽5)×#23511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C42×C5C2×C4
prime radical#91449C4
cosocleC2×C3×Dic5C24
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#2966
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #11752342C2semidirect
3. C3×C4×D5⋊C8C2semidirect
4. #11751913C2semidirect
5. #11751909C2semidirect
6. #11751875C2semidirect
7. #11751868C2semidirect
8. D12×#170C2semidirect
9. #11751798C2semidirect
10. #11751789C2semidirect
11. Dic6×#170C2semidirect
53. C4×D5⋊C8D3semidirect
413. C3×C5#2966semidirect
467. C5#78448semidirect
485. C3#10617312semidirect

Maximal subgroups

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

subgroupindex
#117526832
#117523422
C3×C4×D5⋊C82
#117519132
#117519092
#117518752
#117518682
D12×#1702
#117517982
#117517892
Dic6×#1702
#106173123
#784485