Finite Group Databasebeta

← #14411539

Subgroups — #14411539

Order 1920.

1112 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91266C212yesmaximal
2C4×#6771C211yesmaximal, characteristic
3#11750808C211yesmaximal, characteristic, complemented
4C5×#4707C211yesmaximal, characteristic, complemented
5C3×D5×#97C211yesmaximal, characteristic, complemented
6#11748055C212yesmaximal, complemented
7#11748054C212yesmaximal, complemented
8#11747645C212yesmaximal, complemented
9#11747003C211yesmaximal, characteristic, complemented
10#11746983C211yesmaximal, characteristic, complemented
11D3×#3935C211yesmaximal, characteristic, complemented
12#10610247—31nomaximal, Hall
13C2×#6771C2211yescharacteristic
14C2×#6705C2212yes—
15C42×D15C2211yescharacteristic
16C2×C5×ΓL(1,𝔽25)C2212yes—
17C42×C5×D3C2211yescharacteristic
18C2×C3×C8×D5C2212yes—
19C3×C42×D5C2211yescharacteristic
20C4×#1204C412yes—
21C4×#1203C412yes—
22C4×#1202C412yes—
23C4×#1201C412yes—
24#91386C2211yescharacteristic
25#91371C2211yescharacteristic
26#91357C2211yescharacteristic
27C2×#6649C2212yes—
28C2×#6648C2212yes—
29C2×D3×#168C2212yes—
30#91266C4116yescomplemented
31C3×C5×#97C2211yescharacteristic
32C8×Dic15C2212yes—
33#91087C2211yescharacteristic
34C5×C8×Dic3C2212yes—
35C5×#803C2211yescharacteristic
36C3×#3947C2212yes—
37C3×#3935C2211yescharacteristic
38#90954C2212yes—
39#90953C2212yes—
40Dic5×C3⋊C8C2212yes—
41#78486—51nomaximal, Hall
42C2×#4053—32no—
43C4×#709—31no—
44C4×C5×M16—31no—
45#65411—32no—
46C2×#3935—31no—
47#64996—31no—
48#64996—31no—
49D5×#97—31no—
50D5×#97D311yescharacteristic, complemented
51#64978—32no—
52#64978—32no—
53C2×C4×D15C2×C412yes—
54C2×C4×D15C2311yescharacteristic
55C2×C4×C5×D3C2×C412yes—
56C2×C4×C5×D3C2311yescharacteristic
57C2×C3×C4×D5C2×C412yes—
58C2×C3×C4×D5C2311yescharacteristic
59C2×#1204C2×C411yescharacteristic
60C2×#1203C2×C411yescharacteristic
61C2×#1202C2×C411yescharacteristic
62C2×#1201C2×C411yescharacteristic
63#6771C2×C418yes—
64C2×C3×C5×C8C2312yes—
65C3×C42×C5C2311yescharacteristic
66C4×Dic15C2×C412yes—
67C4×Dic15C2311yescharacteristic
68C2×C3⋊#168C2312yes—
69#6705C2×C418yescomplemented
70C4×C5×Dic3C2×C412yes—
71C4×C5×Dic3C2311yescharacteristic
72C2×C5×C3⋊C8C2312yes—
73C5×ΓL(1,𝔽25)C2×C418yescomplemented
74C3×C4×Dic5C2×C412yes—
75C3×C4×Dic5C2311yescharacteristic
76C2×C3×#168C2312yes—
77C3×C8×D5C2×C418yescomplemented
78Dic3⋊Dic5C2×C412yes—
79#6669C2×C412yes—
80#6668C2×C412yes—
81#6667C2×C412yes—
82(C2×D3)⋊Dic5C2×C412yes—
83#6665C2×C412yes—
84#6649C2×C418yescomplemented
85#6648C2×C418yescomplemented
86D3×#168C2×C418yescomplemented
87C2×#901—52no—
88C4×#235—51no—
89C2×C3×#97—51no—
90#5101—52no—
91C4×#208—51no—
92#4708—52no—
93#4708—52no—
94#4707—51no—
95#4707D511yescharacteristic, complemented
96D3×#97—51no—
97D3×#97—51no—
98C2×#709—31no—
99C2×C5×M16—32no—
100C2×C42×C5—31no—
101C4×C22⋊D5—32no—
102C4×C22⋊D5—32no—
103#4072—31no—
104C22×#168—32no—
105#4053—316no—
106C2×#676—32no—
107C2×#676—32no—
108C2×C8×D5—32no—
109C2×C8×D5C2×D312yes—
110C4×D20—32no—
111#4018—31no—
112#4018—31no—
113C42×D5—31no—
114C42×D5C2×D311yescharacteristic
115C4×Dic10—32no—
116C5×#97—31no—
117C5×#97C2×D311yescharacteristic
118C4×C5×C8—32no—
119#3947—32no—
120#3947C2×D312yes—
121C8×Dic5—32no—
122C8×Dic5—32no—
123#3935—31no—
124#3935—32no—
125#3935C2×D311yescharacteristic
126#2875—151noSylow
127C22×D15C22×C411yescharacteristic
128C22×C5×D3C22×C411yescharacteristic
129C22×C3×D5C22×C411yescharacteristic
130C2×C3×C4×C5C22×C412yes—
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15C22×C412yes—
133C2×Dic15C22×C411yescharacteristic
134C4×D15—42no—
135C4×D15C22×C414yes—
136C2×C5×Dic3C22×C412yes—
137C2×C5×Dic3C22×C411yescharacteristic
138C4×C5×D3—42no—
139C4×C5×D3C22×C414yes—
140C2×C3×Dic5C22×C412yes—
141C2×C3×Dic5C22×C411yescharacteristic
142C3×C4×D5—42no—
143C3×C4×D5C22×C414yes—
144#1204C4214yes—
145#1203C4214yes—
146#1202C4214yes—
147#1201C4214yes—
148C3×C5×C8C22×C414yes—
149C3⋊#168C22×C414yes—
150C3×#168C22×C414yes—
151C5×C3⋊C8C22×C414yes—
152C2×#235—51no—
153C22×C3×C8—52no—
154C2×C3×C42—51no—
155C4×#67—52no—
156C4×#67—52no—
157#926—51no—
158C2×#208—52no—
159#901—516no—
160C2×ΓL(1,𝔽25)—52no—
161C2×ΓL(1,𝔽25)C2×D512yes—
162C2×D3×C8—52no—
163C2×D3×C8—52no—
164C4×D12—52no—
165#872—51no—
166#872—51no—
167C42×D3—51no—
168C42×D3C2×D511yescharacteristic
169C4×Dic6—52no—
170C3×#97—52no—
171C3×#97—51no—
172C3×#97C2×D511yescharacteristic
173#815—52no—
174#815—52no—
175C8×Dic3—52no—
176C8×Dic3C2×D512yes—
177#803—51no—
178#803C2×D511yescharacteristic
179C4×C3⋊C8—52no—
180C22×C4×C5—31no—
181C22×C4×C5—32no—
182C2×C22⋊D5—31no—
183C2×C22⋊D5—31no—
184#709—38no—
185C2×D20—31no—
186C2×C4×D5—31no—
187C2×C4×D5—32no—
188C2×C4×D5C4×D312yes—
189C2×C4×D5C22×D311yescharacteristic
190C2×Dic10—31no—
191C5×M16—38no—
192C2×C5×C8—32no—
193C2×C5×C8C22×D312yes—
194C42×C5—32no—
195C42×C5—31no—
196C42×C5C22×D311yescharacteristic
197C22⋊Dic5—32no—
198#685—32no—
199#685—32no—
200C4⋊Dic5—32no—
201#683—32no—
202#683—32no—
203C4×Dic5—32no—
204C4×Dic5—31no—
205C4×Dic5C4×D312yes—
206C4×Dic5C22×D311yescharacteristic
207C2×#168—32no—
208C2×#168—38no—
209C2×#168C22×D312yes—
210#676—38no—
211#676—38no—
212C8×D5—38no—
213C8×D5C4×D318yescomplemented
214C2×#131—152no—
215C4×#41—151no—
216#405—152no—
217#405—152no—
218#405—152no—
219C4×M16—31no—
220C4×M16—151no—
221C4×M16—151no—
222C2×#97—51no—
223C2×#97—151no—
224C2×#97—151no—
225C22×C3×C5C23×C411yescharacteristic
226C2×D15—22no—
227C2×D15C2×C4212yes—
228C2×C5×D3—22no—
229C2×C5×D3C2×C4212yes—
230C2×C3×D5—22no—
231C2×C3×D5C2×C4212yes—
232C3×C4×C5—22no—
233C3×C4×C5C23×C412yes—
234Dic15—22no—
235Dic15C2×C4212yes—
236C3×Dic5—22no—
237C3×Dic5C2×C4212yes—
238C5×Dic3—22no—
239C5×Dic3C2×C4212yes—
240C22×C3×C4—51no—
241C22×C3×C4—52no—
242C2×#67—51no—
243C2×#67—51no—
244#235—58no—
245C2×D12—51no—
246C2×C4×D3—51no—
247C2×C4×D3—52no—
248C2×C4×D3C4×D512yes—
249C2×C4×D3C22×D511yescharacteristic
250C2×Dic6—51no—
251C2×C3×C8—52no—
252C2×C3×C8—58no—
253C2×C3×C8C22×D512yes—
254C3×C42—52no—
255C3×C42—51no—
256C3×C42C22×D511yescharacteristic
257#217—52no—
258(C2×D3)⋊C4—52no—
259(C2×D3)⋊C4—52no—
260C4⋊Dic3—52no—
261Dic3⋊C4—52no—
262Dic3⋊C4—52no—
263C4×Dic3—52no—
264C4×Dic3—51no—
265C4×Dic3C4×D512yes—
266C4×Dic3C22×D511yescharacteristic
267#208—58no—
268C2×C3⋊C8—52no—
269C2×C3⋊C8C22×D512yes—
270ΓL(1,𝔽25)—58no—
271ΓL(1,𝔽25)C4×D518yescomplemented
272D3×C8—58no—
273D3×C8—58no—
274C23×C5—31no—
275C22×D5—31no—
276C22×D5C2×C4×D311yescharacteristic
277C2×C4×C5—31no—
278C2×C4×C5—34no—
279C2×C4×C5—32no—
280C2×C4×C5—122no—
281C2×C4×C5C2×C4×D312yes—
282C2×C4×C5C23×D311yescharacteristic
283C22⋊D5—34no—
284C22⋊D5—34no—
285C2×Dic5—31no—
286C2×Dic5—32no—
287C2×Dic5C2×C4×D312yes—
288C2×Dic5C2×C4×D311yescharacteristic
289D20—34no—
290C4×D5—34no—
291C4×D5—42no—
292C4×D5—122no—
293C4×D5C2×C4×D314yes—
294Dic10—34no—
295C5×C8—34no—
296C5×C8C2×C4×D314yes—
297#168—34no—
298#168C2×C4×D314yes—
299C2×#41—151no—
300#131—1516no—
301C2×M16—32no—
302C2×M16—152no—
303C2×M16—152no—
304C22×C8—52no—
305C22×C8—152no—
306C22×C8—152no—
307C4×Q8—152no—
308C4×D4—152no—
309C4×D4—152no—
310C4×D4—152no—
311#117—151no—
312#117—151no—
313#117—151no—
314C2×C42—31no—
315C2×C42—51no—
316C2×C42—151no—
317#97—31no—
318#97—52no—
319#97—51no—
320#97—152no—
321#97—152no—
322#97—151no—
323#97D3×D511yescharacteristic
324C4×C8—32no—
325C4×C8—152no—
326C4×C8—152no—
327C2×C3×C5C22×C4211yescharacteristic
328C2×C3×C5#56812yes—
329D15—22no—
330C3×D5—22no—
331C5×D3—22no—
332C23×C3—51no—
333C22×D3—51no—
334C22×D3C2×C4×D511yescharacteristic
335C2×C3×C4—51no—
336C2×C3×C4—54no—
337C2×C3×C4—52no—
338C2×C3×C4—202no—
339C2×C3×C4C2×C4×D512yes—
340C2×C3×C4C23×D511yescharacteristic
341#67—54no—
342#67—54no—
343C2×Dic3—51no—
344C2×Dic3—52no—
345C2×Dic3C2×C4×D512yes—
346C2×Dic3C2×C4×D511yescharacteristic
347D12—54no—
348C4×D3—42no—
349C4×D3—54no—
350C4×D3—202no—
351C4×D3C2×C4×D514yes—
352Dic6—54no—
353C3×C8—54no—
354C3×C8C2×C4×D514yes—
355C3⋊C8—54no—
356C3⋊C8C2×C4×D514yes—
357C22×C5—32no—
358C22×C5—62no—
359C22×C5C22×C4×D311yescharacteristic
360C2×D5—22no—
361C2×D5—32no—
362C2×D5—62no—
363C2×D5C42×D312yes—
364C4×C5—22no—
365C4×C5—32no—
366C4×C5—62no—
367C4×C5C22×C4×D312yes—
368Dic5—22no—
369Dic5—32no—
370Dic5—62no—
371Dic5C42×D312yes—
372#41—158no—
373C2×Q8—151no—
374C2×D4—151no—
375C2×D4—151no—
376C2×D4—151no—
377C22×C4—31no—
378C22×C4—32no—
379C22×C4—51no—
380C22×C4—52no—
381C22×C4—151no—
382C22×C4—152no—
383M16—38no—
384M16—158no—
385M16—158no—
386C2×C8—32no—
387C2×C8—52no—
388C2×C8—58no—
389C2×C8—158no—
390C2×C8—158no—
391C2×C8—152no—
392C2×C8C2×D3×D512yes—
393C4⋊C4—152no—
394C4⋊C4—152no—
395C4⋊C4—152no—
396C22⋊C4—152no—
397C22⋊C4—152no—
398C22⋊C4—152no—
399C42—32no—
400C42—31no—
401C42—52no—
402C42—51no—
403C42—152no—
404C42—151no—
405C42C2×D3×D511yescharacteristic
406C3×C5#287511yescharacteristic, complemented, Hall
407C22×C3—52no—
408C22×C3—102no—
409C22×C3C22×C4×D511yescharacteristic
410C2×D3—22no—
411C2×D3—52no—
412C2×D3—102no—
413C2×D3C42×D512yes—
414C3×C4—22no—
415C3×C4—52no—
416C3×C4—102no—
417C3×C4C22×C4×D512yes—
418Dic3—22no—
419Dic3—52no—
420Dic3—102no—
421Dic3C42×D512yes—
422C2×C5—62no—
423C2×C5C2×C42×D311yescharacteristic
424C2×C5#574512yes—
425D5—22no—
426D5—62no—
427C23—31no—
428C23—51no—
429C23—151no—
430Q8—154no—
431D4—154no—
432D4—154no—
433D4—154no—
434C2×C4—31no—
435C2×C4—34no—
436C2×C4—32no—
437C2×C4—51no—
438C2×C4—54no—
439C2×C4—52no—
440C2×C4—122no—
441C2×C4—151no—
442C2×C4—154no—
443C2×C4—152no—
444C2×C4—202no—
445C2×C4—602no—
446C2×C4C4×D3×D512yes—
447C2×C4C22×D3×D511yescharacteristic
448C8—34no—
449C8—54no—
450C8—154no—
451C8C4×D3×D514yes—
452C2×C3—102no—
453C2×C3C2×C42×D511yescharacteristic
454C2×C3#6607912yes—
455D3—22no—
456D3—102no—
457C5#7848611yescharacteristic, complemented, Sylow
458C22—32no—
459C22—52no—
460C22—62no—
461C22—102no—
462C22—152no—
463C22—302no—
464C22C2×C4×D3×D511yescharacteristic
465C4—22no—
466C4—32no—
467C4—52no—
468C4—62no—
469C4—102no—
470C4—152no—
471C4—302no—
472C4C2×C4×D3×D512yes—
473C3#1061024711yescharacteristic, complemented, Sylow
474C2—62no—
475C2—102no—
476C2—302no—
477C2C42×D3×D511yescharacteristic
478C2#1175404112yes—
subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutatorC2×C3×C5C22×C42
FittingC3×C5×#97C22
socleC22×C3×C5C23×C4
prime radicalC2×#6771C22
cosocleC2×C3×C4×C5C24
hypercenter#97D3×D5
hypocenterC3×C5#2875
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ #97

Complements

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

NH ≅ G/Ntype
3. #11750808C2semidirect
4. C5×#4707C2semidirect
5. C3×D5×#97C2semidirect
6. #11748055C2semidirect
7. #11748054C2semidirect
8. #11747645C2semidirect
9. #11747003C2semidirect
10. #11746983C2semidirect
11. D3×#3935C2semidirect
30. #91266C4semidirect
50. D5×#97D3semidirect
69. #6705C2×C4semidirect
73. C5×ΓL(1,𝔽25)C2×C4semidirect
77. C3×C8×D5C2×C4semidirect
84. #6649C2×C4semidirect
85. #6648C2×C4semidirect
86. D3×#168C2×C4semidirect
95. #4707D5semidirect
213. C8×D5C4×D3semidirect
271. ΓL(1,𝔽25)C4×D5semidirect
406. C3×C5#2875semidirect
457. C5#78486semidirect
473. C3#10610247semidirect

Maximal subgroups

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

subgroupindex
C2×#912662
C4×#67712
#117508082
C5×#47072
C3×D5×#972
#117480552
#117480542
#117476452
#117470032
#117469832
D3×#39352
#106102473
#784865