Finite Group Databasebeta

← #11752829

Subgroups — #11752829

Order 960.

540 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6779C211yesmaximal, characteristic
2C2×D5×Dic6C211yesmaximal, characteristic, complemented
3#91774C211yesmaximal, characteristic, complemented
4C5×#878C211yesmaximal, characteristic, complemented
5C3×#4029C211yesmaximal, characteristic, complemented
6#91575C211yesmaximal, characteristic, complemented
7#91548C211yesmaximal, characteristic, complemented
8#91526C211yesmaximal, characteristic, complemented
9#91470C211yesmaximal, characteristic, complemented
10#91429C211yesmaximal, characteristic, complemented
11#91424C211yesmaximal, characteristic, complemented
12#91413C211yesmaximal, characteristic, complemented
13#91394C211yesmaximal, characteristic, complemented
14#91348C211yesmaximal, characteristic, complemented
15#91328C211yesmaximal, characteristic, complemented
16#65962—31nomaximal, Hall
17C2×#1220C2211yescharacteristic
18C2×Dic30C2211yescharacteristic
19C22×C5×Dic3C2211yescharacteristic
20C2×C5×Dic6C2211yescharacteristic
21C2×C3×C22⋊D5C2211yescharacteristic
22C2×C3×C4×D5C2211yescharacteristic
23C2×#1204C2211yescharacteristic
24C2×#1204C2211yescharacteristic
25C2×#1204C2211yescharacteristic
26C2×#1202C2211yescharacteristic
27C2×#1200C2211yescharacteristic
28#6779—24no—
29C2×D5×Dic3C2211yescharacteristic
30C2×D5×Dic3C2211yescharacteristic
31D5×Dic6—24no—
32C3×C5×C22⋊C4C2211yescharacteristic
33#6719C2211yescharacteristic
34#6714C2211yescharacteristic
35#6714C2211yescharacteristic
36C4×Dic15C2211yescharacteristic
37C5×#217C2211yescharacteristic
38C5×C4⋊Dic3C2211yescharacteristic
39C5×Dic3⋊C4C2211yescharacteristic
40C5×Dic3⋊C4C2211yescharacteristic
41C3×C22⋊Dic5C2211yescharacteristic
42C3×#685C2211yescharacteristic
43C3×C4⋊Dic5C2211yescharacteristic
44C3×#683C2211yescharacteristic
45Dic3⋊Dic5C2211yescharacteristic
46Dic3⋊Dic5C2211yescharacteristic
47#6669C2211yescharacteristic
48#6669C2211yescharacteristic
49#6668C2211yescharacteristic
50#6667C2211yescharacteristic
51#6667C2211yescharacteristic
52#6665C2211yescharacteristic
53Dic3×Dic5C2211yescharacteristic
54#5648—51nomaximal, Hall
55C2×Q8×D5—31no—
56C2×#709—31no—
57C5×C22⋊Q8—31no—
58#4092—31no—
59#4070—31no—
60#4043—31no—
61#4040—31no—
62#4040—31no—
63#4038—31no—
64#4034—31no—
65#4034—31no—
66#4031—31no—
67#4031—31no—
68#4029—31no—
69#4029D311yescharacteristic, complemented
70C23×C3×C5C2311yescharacteristic
71C22×D15C2311yescharacteristic
72C22×C3×D5C2311yescharacteristic
73C2×C3×C4×C5C2311yescharacteristic
74C2×C3×C4×C5C2311yescharacteristic
75#1220—22no—
76C2×Dic15C2311yescharacteristic
77C2×Dic15C2311yescharacteristic
78C2×Dic15C2311yescharacteristic
79Dic30—22no—
80C2×C5×Dic3—22no—
81C2×C5×Dic3C2311yescharacteristic
82C2×C5×Dic3C2311yescharacteristic
83C2×C5×Dic3C2311yescharacteristic
84C2×C5×Dic3C2311yescharacteristic
85C5×Dic6—22no—
86C3×C22⋊D5—22no—
87C2×C3×Dic5C2311yescharacteristic
88C2×C3×Dic5C2311yescharacteristic
89C2×C3×Dic5C2311yescharacteristic
90C3×C4×D5—22no—
91#1204—22no—
92#1204—22no—
93#1204—22no—
94#1202—22no—
95#1200—22no—
96D5×Dic3—22no—
97D5×Dic3D414yes—
98C2×#237—51no—
99C22×Dic6—51no—
100C3×#123—51no—
101#935—51no—
102#929—51no—
103#896—51no—
104#896—51no—
105#888—51no—
106#888—51no—
107#886—51no—
108#885—51no—
109#885—51no—
110#878—51no—
111#878D511yescharacteristic, complemented
112#877—51no—
113C2×C5×Q8—31no—
114C22×C4×C5—31no—
115C2×C22⋊D5—31no—
116C2×C22⋊D5C2×D311yescharacteristic
117Q8×D5—64no—
118#709—64no—
119C2×D20—31no—
120C2×C4×D5—31no—
121C2×C4×D5—31no—
122C2×C4×D5—31no—
123C2×C4×D5C2×D311yescharacteristic
124C2×Dic10—31no—
125C2×Dic10—31no—
126C2×Dic10—31no—
127C2×Dic10—31no—
128C5×C4⋊C4—31no—
129C5×C4⋊C4—31no—
130C5×C4⋊C4—31no—
131C5×C22⋊C4—31no—
132C5×C22⋊C4C2×D311yescharacteristic
133C22⋊Dic5—31no—
134C22⋊Dic5C2×D311yescharacteristic
135#685—31no—
136#685—31no—
137#685—31no—
138#685—31no—
139#685—31no—
140#685C2×D311yescharacteristic
141C4⋊Dic5—31no—
142C4⋊Dic5—31no—
143C4⋊Dic5C2×D311yescharacteristic
144#683—31no—
145#683—31no—
146#683—31no—
147#683C2×D311yescharacteristic
148C4×Dic5—31no—
149C4×Dic5—31no—
150#536—151noSylow
151C22×C3×C5—21no—
152C22×C3×C5—21no—
153C22×C3×C5—21no—
154C22×C3×C5C2411yescharacteristic
155C2×D15—21no—
156C2×D15—21no—
157C2×D15—21no—
158C2×C3×D5—21no—
159C2×C3×D5—21no—
160C2×C3×D5C2×D412yes—
161C3×C4×C5—21no—
162C3×C4×C5—21no—
163Dic15—21no—
164Dic15—21no—
165Dic15C2×D412yes—
166C3×Dic5—21no—
167C3×Dic5—21no—
168C3×Dic5—21no—
169C5×Dic3—21no—
170C5×Dic3—21no—
171C5×Dic3—21no—
172C5×Dic3C2×D412yes—
173C2×C3×D4—51no—
174C22×C3×C4—51no—
175C2×#67—51no—
176C2×#67—51no—
177C22×Dic3—51no—
178C22×Dic3—51no—
179C22×Dic3C2×D511yescharacteristic
180#237—104no—
181C2×C4×D3—51no—
182C2×Dic6—51no—
183C2×Dic6—51no—
184C2×Dic6—51no—
185C2×Dic6—51no—
186C2×Dic6—104no—
187C2×Dic6C2×D511yescharacteristic
188C3×C4⋊C4—51no—
189C3×C4⋊C4—51no—
190C3×C22⋊C4—51no—
191C3×C22⋊C4—51no—
192C3×C22⋊C4C2×D511yescharacteristic
193#217—51no—
194#217—51no—
195#217C2×D511yescharacteristic
196(C2×D3)⋊C4—51no—
197(C2×D3)⋊C4—51no—
198(C2×D3)⋊C4—51no—
199(C2×D3)⋊C4—51no—
200C4⋊Dic3—51no—
201C4⋊Dic3C2×D511yescharacteristic
202Dic3⋊C4—51no—
203Dic3⋊C4—51no—
204Dic3⋊C4—51no—
205Dic3⋊C4—51no—
206Dic3⋊C4C2×D511yescharacteristic
207Dic3⋊C4C2×D511yescharacteristic
208C4×Dic3—51no—
209C4×Dic3—51no—
210C23×C5C22×D311yescharacteristic
211C22×D5—31no—
212C22×D5C22×D311yescharacteristic
213C5×Q8—62no—
214C2×C4×C5—31no—
215C2×C4×C5—31no—
216C2×C4×C5—31no—
217C2×C4×C5—31no—
218C2×C4×C5—62no—
219C2×C4×C5C22×D311yescharacteristic
220C2×C4×C5C22×D311yescharacteristic
221C22⋊D5—22no—
222C22⋊D5—62no—
223C2×Dic5—31no—
224C2×Dic5—31no—
225C2×Dic5—31no—
226C2×Dic5C22×D311yescharacteristic
227C2×Dic5C22×D311yescharacteristic
228C2×Dic5C22×D311yescharacteristic
229D20—62no—
230C4×D5—22no—
231C4×D5—34no—
232C4×D5—62no—
233C4×D5—62no—
234Dic10—62no—
235Dic10—62no—
236Dic10—62no—
237Dic10—62no—
238C2×#41—151no—
239C22×Q8—151no—
240C4⋊Q8—151no—
241C4⋊Q8—151no—
242#124—151no—
243#124—151no—
244#123—51no—
245#123—151no—
246#123—151no—
247#123—151no—
248C22⋊Q8—31no—
249C22⋊Q8—151no—
250C22⋊Q8—151no—
251C22⋊Q8—151no—
252#117—151no—
253C2×C3×C5—41no—
254C2×C3×C5C22×D411yescharacteristic
255C2×C3×C52−1+411yescharacteristic
256C2×C3×C52−1+411yescharacteristic
257D15—41no—
258C3×D5—22no—
259C23×C3—51no—
260C23×C3C22×D511yescharacteristic
261C22×D3—51no—
262C3×D4—102no—
263C2×C3×C4—51no—
264C2×C3×C4—51no—
265C2×C3×C4—51no—
266C2×C3×C4—102no—
267C2×C3×C4C22×D511yescharacteristic
268C2×C3×C4C22×D511yescharacteristic
269#67—102no—
270#67—102no—
271C2×Dic3—22no—
272C2×Dic3—51no—
273C2×Dic3—54no—
274C2×Dic3—51no—
275C2×Dic3—51no—
276C2×Dic3—102no—
277C2×Dic3C22×D511yescharacteristic
278C2×Dic3C22×D511yescharacteristic
279C2×Dic3C22×D511yescharacteristic
280C2×Dic3C22×D511yescharacteristic
281C4×D3—102no—
282Dic6—22no—
283Dic6—102no—
284Dic6—102no—
285Dic6—102no—
286Dic6—102no—
287C22×C5—21no—
288C22×C5—21no—
289C22×C5—21no—
290C22×C5C23×D311yescharacteristic
291C2×D5—21no—
292C2×D5—21no—
293C2×D5—61no—
294C2×D5—61no—
295C2×D5—61no—
296C2×D5D3×D412yes—
297C4×C5—21no—
298C4×C5—21no—
299C4×C5—32no—
300C4×C5—61no—
301C4×C5—61no—
302C4×C5—61no—
303Dic5—21no—
304Dic5—21no—
305Dic5—21no—
306Dic5—32no—
307Dic5—61no—
308Dic5—61no—
309#41—304no—
310C2×Q8—31no—
311C2×Q8—151no—
312C2×Q8—151no—
313C2×Q8—151no—
314C2×Q8—151no—
315C2×Q8—304no—
316C2×D4—51no—
317C2×D4—151no—
318C2×D4—151no—
319C22×C4—31no—
320C22×C4—51no—
321C22×C4—151no—
322C22×C4—151no—
323C22×C4—151no—
324C4⋊C4—31no—
325C4⋊C4—31no—
326C4⋊C4—31no—
327C4⋊C4—51no—
328C4⋊C4—51no—
329C4⋊C4—151no—
330C4⋊C4—151no—
331C4⋊C4—151no—
332C4⋊C4—151no—
333C4⋊C4—151no—
334C22⋊C4—31no—
335C22⋊C4—51no—
336C22⋊C4—51no—
337C22⋊C4—151no—
338C22⋊C4—151no—
339C22⋊C4—151no—
340C22⋊C4—151no—
341C22⋊C4—151no—
342C22⋊C4—151no—
343C22⋊C4D3×D511yescharacteristic
344C42—151no—
345C42—151no—
346C3×C5#53611yescharacteristic, complemented, Hall
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—52no—
351C22×C3—101no—
352C22×C3—101no—
353C22×C3C23×D511yescharacteristic
354C2×D3—101no—
355C2×D3—101no—
356C2×D3—101no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—101no—
360C3×C4—101no—
361C3×C4—101no—
362Dic3—21no—
363Dic3—21no—
364Dic3—21no—
365Dic3—52no—
366Dic3—101no—
367Dic3—101no—
368Dic3D4×D512yes—
369C2×C5—41no—
370C2×C5C2×D3×D411yescharacteristic
371C2×C5#101011yescharacteristic
372C2×C5#101011yescharacteristic
373D5—22no—
374D5—121no—
375C23—51no—
376C23—151no—
377C23C2×D3×D511yescharacteristic
378Q8—62no—
379Q8—302no—
380Q8—302no—
381Q8—302no—
382Q8—302no—
383D4—102no—
384D4—302no—
385D4—302no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—31no—
389C2×C4—31no—
390C2×C4—51no—
391C2×C4—51no—
392C2×C4—51no—
393C2×C4—62no—
394C2×C4—102no—
395C2×C4—154no—
396C2×C4—151no—
397C2×C4—151no—
398C2×C4—151no—
399C2×C4—302no—
400C2×C4—302no—
401C2×C4C2×D3×D511yescharacteristic
402C2×C4C2×D3×D511yescharacteristic
403C2×C3—41no—
404C2×C3—102no—
405C2×C3C2×D4×D511yescharacteristic
406C2×C3#414711yescharacteristic
407C2×C3#415011yescharacteristic
408D3—201no—
409C5#564811yescharacteristic, complemented, Sylow
410C22—21no—
411C22—21no—
412C22—21no—
413C22—52no—
414C22—101no—
415C22—101no—
416C22—301no—
417C22—301no—
418C22—301no—
419C22C22×D3×D511yescharacteristic
420C4—21no—
421C4—21no—
422C4—32no—
423C4—61no—
424C4—61no—
425C4—61no—
426C4—101no—
427C4—101no—
428C4—101no—
429C4—152no—
430C4—301no—
431C4—301no—
432C3#6596211yescharacteristic, complemented, Sylow
433C2—41no—
434C2—102no—
435C2—601no—
436C2#9200011yescharacteristic
437C2#9202011yescharacteristic
438C2D3×D4×D511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
prime radicalC2×#6779C2
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#536
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×D5×Dic6C2semidirect
3. #91774C2semidirect
4. C5×#878C2semidirect
5. C3×#4029C2semidirect
6. #91575C2semidirect
7. #91548C2semidirect
8. #91526C2semidirect
9. #91470C2semidirect
10. #91429C2semidirect
11. #91424C2semidirect
12. #91413C2semidirect
13. #91394C2semidirect
14. #91348C2semidirect
15. #91328C2semidirect
69. #4029D3semidirect
111. #878D5semidirect
346. C3×C5#536semidirect
409. C5#5648semidirect
432. C3#65962semidirect

Maximal subgroups

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

subgroupindex
C2×#67792
C2×D5×Dic62
#917742
C5×#8782
C3×#40292
#915752
#915482
#915262
#914702
#914292
#914242
#914132
#913942
#913482
#913282
#659623
#56485