Finite Group Databasebeta

← #13105244

Subgroups — #13105244

Order 1600.

658 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#87880C211yesmaximal, characteristic, complemented
2C2×#87870C211yesmaximal, characteristic, complemented
3#11717198C211yesmaximal, characteristic, complemented
4C5×#4030C211yesmaximal, characteristic, complemented
5C5×#4029C211yesmaximal, characteristic, complemented
6#11717091C211yesmaximal, characteristic, complemented
7#11717088C211yesmaximal, characteristic, complemented
8#11717087C211yesmaximal, characteristic, complemented
9#11717014C211yesmaximal, characteristic, complemented
10D5×C4⋊Dic5C211yesmaximal, characteristic, complemented
11#11717003C211yesmaximal, characteristic, complemented
12#11717002C211yesmaximal, characteristic, complemented
13#11716997C211yesmaximal, characteristic, complemented
14D5×#683C211yesmaximal, characteristic, complemented
15#11716958C211yesmaximal, characteristic, complemented
16C22×#1039C2211yescharacteristic
17C2×#6045C2211yescharacteristic
18C2×C5×C22⋊D5C2211yescharacteristic
19C2×C5×C22⋊D5C2211yescharacteristic
20C2×C5×C22⋊D5C2211yescharacteristic
21C2×C5×D20C2211yescharacteristic
22C2×C4×C5×D5C2211yescharacteristic
23C2×C4×C5×D5C2211yescharacteristic
24C2×#6039C2211yescharacteristic
25C2×#6037C2211yescharacteristic
26C2×#6037C2211yescharacteristic
27#87880—24no—
28C2×D5×Dic5C2211yescharacteristic
29C2×D5×Dic5C2211yescharacteristic
30C2×D5×Dic5C2211yescharacteristic
31C2×D5×Dic5C2211yescharacteristic
32C2×D5×Dic5C2211yescharacteristic
33#87870—24no—
34C52×C22⋊C4C2211yescharacteristic
35C22⋊#1039C2211yescharacteristic
36C4⋊#1039C2211yescharacteristic
37#87806C2211yescharacteristic
38#87806C2211yescharacteristic
39C5×C22⋊Dic5C2211yescharacteristic
40C5×#685C2211yescharacteristic
41C5×#685C2211yescharacteristic
42C5×C4⋊Dic5C2211yescharacteristic
43C5×#683C2211yescharacteristic
44C5×#683C2211yescharacteristic
45#87781C2211yescharacteristic
46#87780C2211yescharacteristic
47#87780C2211yescharacteristic
48#87780C2211yescharacteristic
49#87778C2211yescharacteristic
50#87778C2211yescharacteristic
51#87778C2211yescharacteristic
52Dic52C2211yescharacteristic
53#65989—51nomaximal
54#65945—51nomaximal
55C23×C52C2311yescharacteristic
56C22×C5×D5C2311yescharacteristic
57C22×C5×D5C2311yescharacteristic
58C22×C5×D5C2311yescharacteristic
59C2×C4×C52C2311yescharacteristic
60C2×C4×C52C2311yescharacteristic
61C2×#1039—22no—
62C2×#1039C2311yescharacteristic
63C2×#1039C2311yescharacteristic
64C2×#1039C2311yescharacteristic
65C2×#1039C2311yescharacteristic
66#6045—22no—
67C5×C22⋊D5—22no—
68C5×C22⋊D5—22no—
69C5×C22⋊D5—22no—
70C2×C5×Dic5C2311yescharacteristic
71C2×C5×Dic5C2311yescharacteristic
72C2×C5×Dic5C2311yescharacteristic
73C2×C5×Dic5C2311yescharacteristic
74C2×C5×Dic5C2311yescharacteristic
75C5×D20—22no—
76C4×C5×D5—22no—
77C4×C5×D5—22no—
78#6039—22no—
79#6037—22no—
80#6037D414yescomplemented
81D5×Dic5—22no—
82D5×Dic5—22no—
83D5×Dic5—22no—
84D5×Dic5—22no—
85D5×Dic5—22no—
86C2×#711—51no—
87C2×#711—51no—
88C2×#711—51no—
89C2×#709—51no—
90C5×#123—51no—
91C5×#121—51no—
92#4085—51no—
93#4084—51no—
94#4081—51no—
95#4081—51no—
96D4×Dic5—51no—
97C4×C22⋊D5—51no—
98C2×C4⋊Dic5—51no—
99C2×#683—51no—
100#4042—51no—
101#4040—51no—
102D5×C4⋊C4—51no—
103D5×C4⋊C4—51no—
104#4034—51no—
105#4034—51no—
106#4032—51no—
107#4030D511yescharacteristic, complemented
108#4029—51no—
109#4029—51no—
110#4029D511yescharacteristic, complemented
111#4027—51no—
112#4027—51no—
113#4024—51no—
114#4024—51no—
115#4024—51no—
116#4024—102no—
117C22×C52—21no—
118C22×C52—21no—
119C22×C52—21no—
120C22×C52C2411yescharacteristic
121C2×C5×D5—21no—
122C2×C5×D5—21no—
123C2×C5×D5—21no—
124C2×C5×D5—21no—
125C2×C5×D5—21no—
126C2×C5×D5—21no—
127C2×C5×D5—21no—
128C2×C5×D5C2×D412yes—
129C2×C5×D5C2×D412yes—
130C4×C52—21no—
131C4×C52—21no—
132#1039—21no—
133#1039—21no—
134#1039—21no—
135#1039C2×D412yes—
136C5×Dic5—21no—
137C5×Dic5—21no—
138C5×Dic5—21no—
139C5×Dic5—21no—
140C5×Dic5#4112yescomplemented
141C2×C5×D4—51no—
142C2×C5×D4—51no—
143C2×C5×D4—51no—
144C2×C5×D4—51no—
145C22×C4×C5—51no—
146C22×C4×C5—51no—
147C2×C22⋊D5—51no—
148C2×C22⋊D5—51no—
149C2×C22⋊D5—51no—
150C2×C22⋊D5—51no—
151C2×C22⋊D5C2×D511yescharacteristic
152C2×C22⋊D5C2×D511yescharacteristic
153C2×C22⋊D5C2×D511yescharacteristic
154C22×Dic5—51no—
155C22×Dic5—51no—
156C22×Dic5—51no—
157C22×Dic5—51no—
158C22×Dic5—51no—
159C22×Dic5—51no—
160C22×Dic5—51no—
161C22×Dic5—102no—
162#711—104no—
163#711—104no—
164#711—104no—
165#709—104no—
166C2×D20C2×D511yescharacteristic
167C2×C4×D5—51no—
168C2×C4×D5—51no—
169C2×C4×D5—51no—
170C2×C4×D5—51no—
171C2×C4×D5—51no—
172C2×C4×D5C2×D511yescharacteristic
173C2×C4×D5C2×D511yescharacteristic
174C2×Dic10—51no—
175C2×Dic10—51no—
176C2×Dic10—51no—
177C2×Dic10—51no—
178C2×Dic10—102no—
179C5×C4⋊C4—51no—
180C5×C4⋊C4—51no—
181C5×C4⋊C4—51no—
182C5×C22⋊C4—22no—
183C5×C22⋊C4—51no—
184C5×C22⋊C4—51no—
185C5×C22⋊C4—51no—
186C5×C22⋊C4C2×D511yescharacteristic
187C5×C22⋊C4C2×D511yescharacteristic
188C22⋊Dic5—51no—
189C22⋊Dic5—51no—
190C22⋊Dic5—51no—
191C22⋊Dic5—51no—
192C22⋊Dic5—51no—
193C22⋊Dic5—102no—
194C22⋊Dic5C2×D511yescharacteristic
195#685—51no—
196#685—51no—
197#685—51no—
198#685C2×D511yescharacteristic
199#685C2×D511yescharacteristic
200C4⋊Dic5—51no—
201C4⋊Dic5—51no—
202C4⋊Dic5—51no—
203C4⋊Dic5—51no—
204C4⋊Dic5—51no—
205C4⋊Dic5—102no—
206C4⋊Dic5C2×D511yescharacteristic
207#683—51no—
208#683—51no—
209#683—51no—
210#683—51no—
211#683—51no—
212#683—51no—
213#683—51no—
214#683—51no—
215#683—51no—
216#683—102no—
217#683—102no—
218#683C2×D511yescharacteristic
219#683C2×D511yescharacteristic
220C4×Dic5—51no—
221C4×Dic5—51no—
222#547—251noSylow
223C2×C52—41no—
224C2×C52C22×D411yescharacteristic
225C2×C52C2×#4111yescharacteristic
226C2×C522−1+411yescharacteristic
227C5×D5—22no—
228C5×D5—22no—
229C5×D5—41no—
230C23×C5—22no—
231C23×C5—51no—
232C23×C5—51no—
233C23×C5—51no—
234C23×C5C22×D511yescharacteristic
235C23×C5C22×D511yescharacteristic
236C22×D5C22×D511yescharacteristic
237C22×D5C22×D511yescharacteristic
238C22×D5C22×D511yescharacteristic
239C5×D4—102no—
240C5×D4—102no—
241C5×D4—102no—
242C5×D4—102no—
243C2×C4×C5—22no—
244C2×C4×C5—22no—
245C2×C4×C5—51no—
246C2×C4×C5—51no—
247C2×C4×C5—51no—
248C2×C4×C5—51no—
249C2×C4×C5—51no—
250C2×C4×C5—102no—
251C2×C4×C5—102no—
252C2×C4×C5C22×D511yescharacteristic
253C2×C4×C5C22×D511yescharacteristic
254C2×C4×C5C22×D511yescharacteristic
255C2×C4×C5C22×D511yescharacteristic
256C22⋊D5—22no—
257C22⋊D5—22no—
258C22⋊D5—22no—
259C22⋊D5—54no—
260C22⋊D5—54no—
261C22⋊D5—102no—
262C22⋊D5—102no—
263C2×Dic5—51no—
264C2×Dic5—51no—
265C2×Dic5—51no—
266C2×Dic5—51no—
267C2×Dic5—51no—
268C2×Dic5—51no—
269C2×Dic5—51no—
270C2×Dic5—51no—
271C2×Dic5—102no—
272C2×Dic5—102no—
273C2×Dic5—102no—
274C2×Dic5—102no—
275C2×Dic5—102no—
276C2×Dic5—102no—
277C2×Dic5—102no—
278C2×Dic5—102no—
279C2×Dic5—102no—
280C2×Dic5—102no—
281C2×Dic5—102no—
282C2×Dic5—204no—
283C2×Dic5C22×D511yescharacteristic
284C2×Dic5C22×D511yescharacteristic
285C2×Dic5C22×D511yescharacteristic
286C2×Dic5C22×D511yescharacteristic
287C2×Dic5C22×D511yescharacteristic
288D20—22no—
289C4×D5—22no—
290C4×D5—22no—
291C4×D5—102no—
292C4×D5—102no—
293C4×D5—102no—
294C4×D5—102no—
295C4×D5—102no—
296Dic10—102no—
297Dic10—102no—
298Dic10—102no—
299Dic10—102no—
300Dic10—204no—
301C2×#41—251no—
302C2×#41—251no—
303C4⋊Q8—251no—
304#123—51no—
305#123—251no—
306#123—251no—
307#123—251no—
308C22⋊Q8—251no—
309C22⋊Q8—251no—
310#121—51no—
311#121—251no—
312C4×D4—251no—
313C4×D4—251no—
314C2×C4⋊C4—251no—
315C2×C4⋊C4—251no—
316C52#54711yescharacteristic, complemented, Sylow
317C22×C5—24no—
318C22×C5—21no—
319C22×C5—21no—
320C22×C5—21no—
321C22×C5—21no—
322C22×C5—21no—
323C22×C5—21no—
324C22×C5—22no—
325C22×C5—42no—
326C22×C5—42no—
327C22×C5—52no—
328C22×C5—52no—
329C22×C5—101no—
330C22×C5—101no—
331C22×C5—101no—
332C22×C5—101no—
333C22×C5—101no—
334C22×C5—101no—
335C22×C5—101no—
336C22×C5C23×D511yescharacteristic
337C22×C5C23×D511yescharacteristic
338C2×D5—21no—
339C2×D5—21no—
340C2×D5—21no—
341C2×D5—21no—
342C2×D5—21no—
343C2×D5—21no—
344C2×D5—21no—
345C2×D5D4×D512yes—
346C2×D5D4×D512yes—
347C4×C5—21no—
348C4×C5—21no—
349C4×C5—21no—
350C4×C5—21no—
351C4×C5—42no—
352C4×C5—42no—
353C4×C5—52no—
354C4×C5—101no—
355C4×C5—101no—
356C4×C5—101no—
357C4×C5—101no—
358Dic5—21no—
359Dic5—21no—
360Dic5—21no—
361Dic5—21no—
362Dic5—52no—
363Dic5—52no—
364Dic5—104no—
365Dic5—101no—
366Dic5—101no—
367Dic5—101no—
368Dic5—101no—
369Dic5—101no—
370Dic5—101no—
371Dic5—202no—
372Dic5—202no—
373Dic5—202no—
374Dic5#71112yescomplemented
375#41—504no—
376#41—504no—
377C2×Q8—251no—
378C2×Q8—251no—
379C2×D4—51no—
380C2×D4—51no—
381C2×D4—51no—
382C2×D4—51no—
383C2×D4—251no—
384C2×D4—251no—
385C22×C4—51no—
386C22×C4—51no—
387C22×C4—251no—
388C22×C4—251no—
389C22×C4—251no—
390C22×C4—251no—
391C22×C4—251no—
392C22×C4—251no—
393C4⋊C4—51no—
394C4⋊C4—51no—
395C4⋊C4—51no—
396C4⋊C4—251no—
397C4⋊C4—251no—
398C4⋊C4—251no—
399C4⋊C4—251no—
400C4⋊C4—251no—
401C4⋊C4—251no—
402C4⋊C4—251no—
403C22⋊C4—51no—
404C22⋊C4—51no—
405C22⋊C4—51no—
406C22⋊C4—251no—
407C22⋊C4—251no—
408C22⋊C4—251no—
409C22⋊C4—251no—
410C22⋊C4D5211yescharacteristic
411C42—251no—
412C2×C5—22no—
413C2×C5—22no—
414C2×C5—22no—
415C2×C5—44no—
416C2×C5—41no—
417C2×C5—41no—
418C2×C5—102no—
419C2×C5—102no—
420C2×C5—201no—
421C2×C5C2×D4×D511yescharacteristic
422C2×C5C2×D4×D511yescharacteristic
423C2×C5C2×#71111yescharacteristic
424C2×C5D5×#4111yescharacteristic
425C2×C5#415011yescharacteristic
426C2×C5#415011yescharacteristic
427D5—22no—
428D5—22no—
429D5—41no—
430C23—51no—
431C23—51no—
432C23—51no—
433C23C2×D5211yescharacteristic
434Q8—502no—
435Q8—502no—
436D4—102no—
437D4—102no—
438D4—102no—
439D4—102no—
440D4—254no—
441D4—502no—
442C2×C4—51no—
443C2×C4—51no—
444C2×C4—51no—
445C2×C4—51no—
446C2×C4—51no—
447C2×C4—102no—
448C2×C4—102no—
449C2×C4—251no—
450C2×C4—251no—
451C2×C4—251no—
452C2×C4—251no—
453C2×C4—502no—
454C2×C4—502no—
455C2×C4—502no—
456C2×C4—502no—
457C2×C4—502no—
458C2×C4—502no—
459C2×C4C2×D5211yescharacteristic
460C2×C4C2×D5211yescharacteristic
461C5—22no—
462C5#6594511yescharacteristic, complemented
463C5#6598911yescharacteristic, complemented
464C22—21no—
465C22—21no—
466C22—21no—
467C22—52no—
468C22—52no—
469C22—101no—
470C22—101no—
471C22—101no—
472C22—101no—
473C22—101no—
474C22—101no—
475C22—101no—
476C22C22×D5211yescharacteristic
477C4—21no—
478C4—21no—
479C4—52no—
480C4—101no—
481C4—101no—
482C4—101no—
483C4—101no—
484C4—252no—
485C4—501no—
486C4—501no—
487C4—501no—
488C2—41no—
489C2—102no—
490C2—102no—
491C2—201no—
492C2#1171746311yescharacteristic
493C2D4×D5211yescharacteristic
494C2D5×#71111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC52×C22⋊C4C22
hypercenterC22⋊C4D52
hypocenterC52#547
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#87880C2semidirect
2. C2×#87870C2semidirect
3. #11717198C2semidirect
4. C5×#4030C2semidirect
5. C5×#4029C2semidirect
6. #11717091C2semidirect
7. #11717088C2semidirect
8. #11717087C2semidirect
9. #11717014C2semidirect
10. D5×C4⋊Dic5C2semidirect
11. #11717003C2semidirect
12. #11717002C2semidirect
13. #11716997C2semidirect
14. D5×#683C2semidirect
15. #11716958C2semidirect
80. #6037D4semidirect
107. #4030D5semidirect
110. #4029D5semidirect
140. C5×Dic5#41semidirect
316. C52#547semidirect
374. Dic5#711semidirect
462. C5#65945semidirect
463. C5#65989semidirect

Maximal subgroups

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

subgroupindex
C2×#878802
C2×#878702
#117171982
C5×#40302
C5×#40292
#117170912
#117170882
#117170872
#117170142
D5×C4⋊Dic52
#117170032
#117170022
#117169972
D5×#6832
#117169582
#659895
#659455