Finite Group Databasebeta

← #10608621

Subgroups — #10608621

Order 640.

696 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic5C211yesmaximal, characteristic, complemented
2C2×#4027C211yesmaximal, characteristic, complemented
3C2×#4027C211yesmaximal, characteristic, complemented
4C2×#4023C211yesmaximal, characteristic, complemented
5C5×#394C211yesmaximal, characteristic, complemented
6#65512C211yesmaximal, characteristic
7#65283C211yesmaximal, characteristic, complemented
8C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
9#65250C211yesmaximal, characteristic, complemented
10#65248C211yesmaximal, characteristic, complemented
11#65241C211yesmaximal, characteristic, complemented
12#65237C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
14#64955C211yesmaximal, characteristic, complemented
15#64946C211yesmaximal, characteristic, complemented
16C22×C5×D4C2211yescharacteristic
17C22×C22⋊D5C2211yescharacteristic
18C22×C22⋊D5C2211yescharacteristic
19C23×Dic5C2211yescharacteristic
20C23×Dic5C2211yescharacteristic
21C22×C4×D5C2211yescharacteristic
22C2×C5×C4⋊C4C2211yescharacteristic
23C2×C5×C22⋊C4C2211yescharacteristic
24C2×C5×C22⋊C4C2211yescharacteristic
25C2×C5×C22⋊C4C2211yescharacteristic
26C2×C5×C22⋊C4C2211yescharacteristic
27C2×C22⋊Dic5C2211yescharacteristic
28C2×C22⋊Dic5C2211yescharacteristic
29C2×C22⋊Dic5C2211yescharacteristic
30C2×C22⋊Dic5C2211yescharacteristic
31D4×Dic5—24no—
32C2×#685C2211yescharacteristic
33C2×#685C2211yescharacteristic
34C2×#685C2211yescharacteristic
35C2×#685C2211yescharacteristic
36C2×C4⋊Dic5C2211yescharacteristic
37C2×C4⋊Dic5C2211yescharacteristic
38C2×#683C2211yescharacteristic
39C2×#683C2211yescharacteristic
40C2×#683C2211yescharacteristic
41C2×#683C2211yescharacteristic
42C2×C4×Dic5C2211yescharacteristic
43C2×C4×Dic5C2211yescharacteristic
44C2×C4×Dic5C2211yescharacteristic
45C2×C4×Dic5C2211yescharacteristic
46#4027—24no—
47#4027—24no—
48#4023—24no—
49C5×#95C2211yescharacteristic
50#3963C2211yescharacteristic
51#3963C2211yescharacteristic
52#3963C2211yescharacteristic
53#3963C2211yescharacteristic
54#3963C2211yescharacteristic
55#2392—51nomaximal, Sylow
56C24×C5C2311yescharacteristic
57C24×C5C2311yescharacteristic
58C23×D5C2311yescharacteristic
59C2×C5×D4—22no—
60C2×C5×D4—22no—
61C2×C5×D4—22no—
62C22×C4×C5C2311yescharacteristic
63C22×C4×C5C2311yescharacteristic
64C22×C4×C5C2311yescharacteristic
65C22×C4×C5C2311yescharacteristic
66C22×C4×C5C2311yescharacteristic
67C2×C22⋊D5—22no—
68C2×C22⋊D5—22no—
69C2×C22⋊D5—22no—
70C2×C22⋊D5—22no—
71C2×C22⋊D5—22no—
72C2×C22⋊D5—22no—
73C22×Dic5—22no—
74C22×Dic5—22no—
75C22×Dic5—22no—
76C22×Dic5—22no—
77C22×Dic5—22no—
78C22×Dic5D414yescomplemented
79C22×Dic5C2311yescharacteristic
80C22×Dic5C2311yescharacteristic
81C22×Dic5C2311yescharacteristic
82C22×Dic5C2311yescharacteristic
83C22×Dic5C2311yescharacteristic
84C22×Dic5C2311yescharacteristic
85C22×Dic5C2311yescharacteristic
86C2×C4×D5—22no—
87C2×C4×D5—22no—
88C2×C4×D5—22no—
89C5×C4⋊C4—22no—
90C5×C22⋊C4—22no—
91C5×C22⋊C4—22no—
92C5×C22⋊C4—22no—
93C5×C22⋊C4—22no—
94C22⋊Dic5—22no—
95C22⋊Dic5—22no—
96C22⋊Dic5—22no—
97C22⋊Dic5—22no—
98#685—22no—
99#685—22no—
100#685—22no—
101#685—22no—
102C4⋊Dic5—22no—
103C4⋊Dic5—22no—
104#683—22no—
105#683—22no—
106#683—22no—
107#683—22no—
108C4×Dic5—22no—
109C4×Dic5—22no—
110C4×Dic5—22no—
111C4×Dic5D414yescomplemented
112C2×C4×D4—51no—
113C2×C4×D4—51no—
114C2×C4×D4—51no—
115C2×#117—51no—
116#398—51no—
117#397—51no—
118#396—51no—
119#396—51no—
120#394—51no—
121#394—51no—
122#394D511yescharacteristic, complemented
123#392—51no—
124C4×C4⋊C4—51no—
125C4×C22⋊C4—51no—
126C4×C22⋊C4—51no—
127C23×C5—21no—
128C23×C5—21no—
129C23×C5—21no—
130C23×C5—21no—
131C23×C5—21no—
132C23×C5—21no—
133C23×C5—21no—
134C23×C5—21no—
135C23×C5—21no—
136C23×C5—21no—
137C23×C5—21no—
138C23×C5—21no—
139C23×C5C2×D412yes—
140C23×C5#4112yes—
141C23×C5C2411yescharacteristic
142C22×D5—21no—
143C22×D5—21no—
144C22×D5—21no—
145C22×D5—21no—
146C22×D5—21no—
147C22×D5—21no—
148C22×D5#4112yes—
149C5×D4—28no—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—21no—
156C2×C4×C5—21no—
157C2×C4×C5—21no—
158C2×C4×C5—21no—
159C2×C4×C5—21no—
160C2×C4×C5—21no—
161C2×C4×C5—21no—
162C2×C4×C5—21no—
163C2×C4×C5C2×D412yes—
164C2×C4×C5#4112yes—
165C22⋊D5—28no—
166C22⋊D5—28no—
167C2×Dic5—21no—
168C2×Dic5—21no—
169C2×Dic5—21no—
170C2×Dic5—21no—
171C2×Dic5—21no—
172C2×Dic5—21no—
173C2×Dic5—28no—
174C2×Dic5—21no—
175C2×Dic5—21no—
176C2×Dic5—21no—
177C2×Dic5—21no—
178C2×Dic5—21no—
179C2×Dic5—21no—
180C2×Dic5—21no—
181C2×Dic5—21no—
182C2×Dic5—21no—
183C2×Dic5—44no—
184C2×Dic5C2×D412yes—
185C2×Dic5C2×D412yes—
186C2×Dic5C2×D412yes—
187C2×Dic5C2×D412yes—
188C2×Dic5#4112yes—
189C2×Dic5#4112yes—
190C4×D5—44no—
191C22×D4—51no—
192C22×D4—51no—
193C22×D4C2×D511yescharacteristic
194C23×C4—51no—
195C23×C4—51no—
196C23×C4—51no—
197C4×D4—104no—
198C4×D4—104no—
199C4×D4—104no—
200#117—104no—
201C2×C4⋊C4—51no—
202C2×C4⋊C4—51no—
203C2×C4⋊C4—51no—
204C2×C4⋊C4—51no—
205C2×C4⋊C4—51no—
206C2×C4⋊C4—51no—
207C2×C4⋊C4C2×D511yescharacteristic
208C2×C22⋊C4—51no—
209C2×C22⋊C4—51no—
210C2×C22⋊C4—51no—
211C2×C22⋊C4—51no—
212C2×C22⋊C4—51no—
213C2×C22⋊C4—51no—
214C2×C22⋊C4—51no—
215C2×C22⋊C4—51no—
216C2×C22⋊C4C2×D511yescharacteristic
217C2×C22⋊C4C2×D511yescharacteristic
218C2×C22⋊C4C2×D511yescharacteristic
219C2×C22⋊C4C2×D511yescharacteristic
220C2×C42—51no—
221C2×C42—51no—
222C2×C42—51no—
223C2×C42—51no—
224#95—51no—
225#95—51no—
226#95—51no—
227#95—51no—
228#95—51no—
229#95C2×D511yescharacteristic
230C22×C5—22no—
231C22×C5—22no—
232C22×C5—22no—
233C22×C5—22no—
234C22×C5—22no—
235C22×C5—22no—
236C22×C5—41no—
237C22×C5—41no—
238C22×C5—41no—
239C22×C5—41no—
240C22×C5—41no—
241C22×C5—41no—
242C22×C5—41no—
243C22×C5—41no—
244C22×C5C22×D411yescharacteristic
245C22×C5C22×D411yescharacteristic
246C22×C5C2×#4111yescharacteristic
247C22×C5C2×#4111yescharacteristic
248C22×C5C2×#4111yescharacteristic
249C22×C5C2×#4111yescharacteristic
250C22×C5C2×#4111yescharacteristic
251C2×D5—22no—
252C2×D5—22no—
253C2×D5—22no—
254C2×D5—41no—
255C2×D5—41no—
256C2×D5—41no—
257C2×D5—41no—
258C4×C5—22no—
259C4×C5—22no—
260C4×C5—41no—
261C4×C5—41no—
262C4×C5—41no—
263Dic5—22no—
264Dic5—22no—
265Dic5—22no—
266Dic5—41no—
267Dic5—41no—
268Dic5—41no—
269Dic5#12114yes—
270C24—51no—
271C24C22×D511yescharacteristic
272C24C22×D511yescharacteristic
273C2×D4—22no—
274C2×D4—22no—
275C2×D4—22no—
276C2×D4—102no—
277C2×D4—102no—
278C2×D4—102no—
279C2×D4—102no—
280C2×D4—102no—
281C2×D4—102no—
282C22×C4—51no—
283C22×C4—54no—
284C22×C4—51no—
285C22×C4—51no—
286C22×C4—51no—
287C22×C4—51no—
288C22×C4—51no—
289C22×C4—51no—
290C22×C4—102no—
291C22×C4—102no—
292C22×C4—102no—
293C22×C4—102no—
294C22×C4—102no—
295C22×C4—102no—
296C22×C4—102no—
297C22×C4—102no—
298C22×C4C22×D511yescharacteristic
299C22×C4C22×D511yescharacteristic
300C22×C4C22×D511yescharacteristic
301C22×C4C22×D511yescharacteristic
302C22×C4C22×D511yescharacteristic
303C4⋊C4—22no—
304C4⋊C4—102no—
305C4⋊C4—102no—
306C4⋊C4—102no—
307C4⋊C4—102no—
308C4⋊C4—102no—
309C4⋊C4—102no—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—102no—
315C22⋊C4—102no—
316C22⋊C4—102no—
317C22⋊C4—102no—
318C22⋊C4—102no—
319C22⋊C4—102no—
320C22⋊C4—102no—
321C22⋊C4—102no—
322C42—54no—
323C42—102no—
324C42—102no—
325C42—102no—
326C2×C5—42no—
327C2×C5—42no—
328C2×C5C2×#12111yescharacteristic
329C2×C5#52511yescharacteristic
330C2×C5#52511yescharacteristic
331C2×C5#52511yescharacteristic
332C2×C5#52911yescharacteristic
333C2×C5#52911yescharacteristic
334C2×C5#53211yescharacteristic
335D5—42no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—52no—
349C23—101no—
350C23—101no—
351C23—101no—
352C23—101no—
353C23—101no—
354C23—101no—
355C23D4×D512yes—
356C23#71112yes—
357C23C23×D511yescharacteristic
358D4—28no—
359D4—108no—
360D4—108no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—52no—
375C2×C4—52no—
376C2×C4—52no—
377C2×C4—52no—
378C2×C4—52no—
379C2×C4—52no—
380C2×C4—108no—
381C2×C4—101no—
382C2×C4—101no—
383C2×C4—101no—
384C2×C4—101no—
385C2×C4—101no—
386C2×C4—101no—
387C2×C4—101no—
388C2×C4—101no—
389C2×C4—101no—
390C2×C4—101no—
391C2×C4—101no—
392C2×C4—101no—
393C2×C4—101no—
394C2×C4—101no—
395C2×C4—101no—
396C2×C4—204no—
397C2×C4—204no—
398C2×C4D4×D512yes—
399C2×C4#71112yes—
400C5#239211yescharacteristic, complemented, Sylow
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—102no—
416C22—102no—
417C22—102no—
418C22—201no—
419C22—201no—
420C22—201no—
421C22—201no—
422C22C2×D4×D511yescharacteristic
423C22C2×D4×D511yescharacteristic
424C22C2×#71111yescharacteristic
425C22C2×#71111yescharacteristic
426C22D5×#4111yescharacteristic
427C22D5×#4111yescharacteristic
428C22D5×#4111yescharacteristic
429C4—22no—
430C4—22no—
431C4—41no—
432C4—41no—
433C4—41no—
434C4—54no—
435C4—102no—
436C4—102no—
437C4—102no—
438C4—201no—
439C4—201no—
440C4—201no—
441C2—42no—
442C2—42no—
443C2—202no—
444C2#6592011yescharacteristic
445C2#6593011yescharacteristic
446C2D5×#12111yescharacteristic
447C2#6594011yescharacteristic
448C2#6598311yescharacteristic
449C2#6599011yescharacteristic
450C2#6601411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#394C2
prime radical#65512C2
hypercenter#394D5
hypocenterC5#2392
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic5C2semidirect
2. C2×#4027C2semidirect
3. C2×#4027C2semidirect
4. C2×#4023C2semidirect
5. C5×#394C2semidirect
7. #65283C2semidirect
8. C4⋊C4×Dic5C2semidirect
9. #65250C2semidirect
10. #65248C2semidirect
11. #65241C2semidirect
12. #65237C2semidirect
13. C22⋊C4×Dic5C2semidirect
14. #64955C2semidirect
15. #64946C2semidirect
78. C22×Dic5D4semidirect
111. C4×Dic5D4semidirect
122. #394D5semidirect
400. C5#2392semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic52
C2×#40272
C2×#40232
C5×#3942
#655122
#652832
C4⋊C4×Dic52
#652502
#652482
#652412
#652372
C22⋊C4×Dic52
#649552
#649462
#23925