Finite Group Databasebeta

← #11753683

Subgroups — #11753683

Order 960.

588 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6773C211yesmaximal, characteristic, complemented
2C2×#6769C211yesmaximal, characteristic, complemented
3#91784C211yesmaximal, characteristic, complemented
4C5×#896C211yesmaximal, characteristic, complemented
5C3×#4042C211yesmaximal, characteristic, complemented
6#91461C211yesmaximal, characteristic, complemented
7#91459C211yesmaximal, characteristic, complemented
8#91459C211yesmaximal, characteristic, complemented
9#91454C211yesmaximal, characteristic, complemented
10#91448C211yesmaximal, characteristic, complemented
11#91424C211yesmaximal, characteristic, complemented
12#91420C211yesmaximal, characteristic, complemented
13#91420C211yesmaximal, characteristic, complemented
14#91411C211yesmaximal, characteristic, complemented
15#91404C211yesmaximal, characteristic, complemented
16#65963—31nomaximal, Hall
17C2×D60C2211yescharacteristic
18C2×D60C2211yescharacteristic
19C2×D60C2211yescharacteristic
20C2×C4×D15C2211yescharacteristic
21C2×C4×C5×D3C2211yescharacteristic
22C2×C5×Dic6C2211yescharacteristic
23C2×C3×C4×D5C2211yescharacteristic
24C2×C3×Dic10C2211yescharacteristic
25C2×#1203C2211yescharacteristic
26C2×#1203C2211yescharacteristic
27C2×#1203C2211yescharacteristic
28C2×#1202C2211yescharacteristic
29C2×#1202C2211yescharacteristic
30C2×#1202C2211yescharacteristic
31C2×#1201C2211yescharacteristic
32C2×#1200C2211yescharacteristic
33C2×#1200C2211yescharacteristic
34C2×#1200C2211yescharacteristic
35C2×#1200C2211yescharacteristic
36#6773—24no—
37#6769—24no—
38C3×C5×C4⋊C4C2211yescharacteristic
39#6714C2211yescharacteristic
40#6714C2211yescharacteristic
41C5×(C2×D3)⋊C4C2211yescharacteristic
42C5×(C2×D3)⋊C4C2211yescharacteristic
43C5×Dic3⋊C4C2211yescharacteristic
44C5×Dic3⋊C4C2211yescharacteristic
45C3×#685C2211yescharacteristic
46C3×#685C2211yescharacteristic
47C3×#683C2211yescharacteristic
48C3×#683C2211yescharacteristic
49Dic3⋊Dic5C2211yescharacteristic
50#6669C2211yescharacteristic
51#6668C2211yescharacteristic
52#6667C2211yescharacteristic
53#6667C2211yescharacteristic
54#5629—51nomaximal, Hall
55C2×#713—31no—
56C2×#709—31no—
57C5×C22⋊Q8—31no—
58#4092—31no—
59#4076—31no—
60#4042—31no—
61#4042D311yescharacteristic, complemented
62#4041—31no—
63#4041—31no—
64#4041—31no—
65D5×C4⋊C4—31no—
66#4030—31no—
67#4030—31no—
68#4030—31no—
69#4030—31no—
70C22×D15C2311yescharacteristic
71C22×D15C2311yescharacteristic
72C22×D15C2311yescharacteristic
73C22×C5×D3C2311yescharacteristic
74C22×C3×D5C2311yescharacteristic
75C2×C3×C4×C5C2311yescharacteristic
76C2×C3×C4×C5C2311yescharacteristic
77C2×C3×C4×C5C2311yescharacteristic
78C2×Dic15C2311yescharacteristic
79D60—22no—
80D60—22no—
81D60—41no—
82C4×D15—41no—
83C2×C5×Dic3C2311yescharacteristic
84C2×C5×Dic3C2311yescharacteristic
85C2×C5×Dic3C2311yescharacteristic
86C4×C5×D3—22no—
87C5×Dic6—22no—
88C2×C3×Dic5C2311yescharacteristic
89C2×C3×Dic5C2311yescharacteristic
90C2×C3×Dic5C2311yescharacteristic
91C3×C4×D5—22no—
92C3×Dic10—22no—
93#1203—22no—
94#1203—22no—
95#1203—41no—
96#1202—22no—
97#1202—22no—
98#1202—41no—
99#1201—41no—
100#1200—22no—
101#1200—22no—
102#1200—41no—
103#1200D414yescomplemented
104C2×#239—51no—
105C2×#235—51no—
106C3×C22⋊Q8—51no—
107#946—51no—
108#930—51no—
109#896—51no—
110#896D511yescharacteristic, complemented
111#895—51no—
112#895—51no—
113#895—51no—
114D3×C4⋊C4—51no—
115#884—51no—
116#884—51no—
117#884—51no—
118#884—51no—
119C2×C5×Q8—31no—
120C22×C4×C5—31no—
121C2×C22⋊D5—31no—
122C2×C22⋊D5—31no—
123C2×C22⋊D5—31no—
124C2×C22⋊D5—31no—
125#713—64no—
126#709—64no—
127C2×D20—31no—
128C2×D20—31no—
129C2×D20—31no—
130C2×D20—31no—
131C2×D20—31no—
132C2×D20—31no—
133C2×C4×D5—31no—
134C2×C4×D5—31no—
135C2×C4×D5—31no—
136C2×C4×D5—31no—
137C2×C4×D5—31no—
138C2×C4×D5C2×D311yescharacteristic
139C2×Dic10C2×D311yescharacteristic
140C5×C4⋊C4—31no—
141C5×C4⋊C4—31no—
142C5×C4⋊C4C2×D311yescharacteristic
143C5×C22⋊C4—31no—
144C5×C22⋊C4—31no—
145#685—31no—
146#685—31no—
147#685—31no—
148#685—31no—
149#685C2×D311yescharacteristic
150#685C2×D311yescharacteristic
151C4⋊Dic5—31no—
152#683—31no—
153#683—31no—
154#683C2×D311yescharacteristic
155#683C2×D311yescharacteristic
156#537—151noSylow
157C22×C3×C5C2411yescharacteristic
158C2×D15—21no—
159C2×D15—21no—
160C2×D15—21no—
161C2×D15—21no—
162C2×D15—21no—
163C2×D15—21no—
164C2×D15—21no—
165C2×D15—21no—
166C2×D15C2×D412yes—
167C2×C5×D3—21no—
168C2×C5×D3—21no—
169C2×C5×D3—21no—
170C2×C3×D5—21no—
171C2×C3×D5—21no—
172C2×C3×D5—21no—
173C3×C4×C5—21no—
174C3×C4×C5—21no—
175C3×C4×C5—21no—
176Dic15—21no—
177C3×Dic5—21no—
178C3×Dic5—21no—
179C3×Dic5C2×D412yes—
180C5×Dic3—21no—
181C5×Dic3—21no—
182C5×Dic3C2×D412yes—
183C2×C3×Q8—51no—
184C22×C3×C4—51no—
185C2×#67—51no—
186C2×#67—51no—
187C2×#67—51no—
188C2×#67—51no—
189#239—104no—
190#235—104no—
191C2×D12—51no—
192C2×D12—51no—
193C2×D12—51no—
194C2×D12—51no—
195C2×D12—51no—
196C2×D12—51no—
197C2×C4×D3—51no—
198C2×C4×D3—51no—
199C2×C4×D3—51no—
200C2×C4×D3—51no—
201C2×C4×D3—51no—
202C2×C4×D3C2×D511yescharacteristic
203C2×Dic6C2×D511yescharacteristic
204C3×C4⋊C4—51no—
205C3×C4⋊C4—51no—
206C3×C4⋊C4C2×D511yescharacteristic
207C3×C22⋊C4—51no—
208C3×C22⋊C4—51no—
209(C2×D3)⋊C4—51no—
210(C2×D3)⋊C4—51no—
211(C2×D3)⋊C4—51no—
212(C2×D3)⋊C4—51no—
213(C2×D3)⋊C4C2×D511yescharacteristic
214(C2×D3)⋊C4C2×D511yescharacteristic
215C4⋊Dic3—51no—
216Dic3⋊C4—51no—
217Dic3⋊C4—51no—
218Dic3⋊C4C2×D511yescharacteristic
219Dic3⋊C4C2×D511yescharacteristic
220C23×C5—31no—
221C22×D5—31no—
222C22×D5—31no—
223C22×D5—31no—
224C22×D5C22×D311yescharacteristic
225C5×Q8—62no—
226C2×C4×C5—31no—
227C2×C4×C5—31no—
228C2×C4×C5—31no—
229C2×C4×C5—62no—
230C2×C4×C5C22×D311yescharacteristic
231C2×C4×C5C22×D311yescharacteristic
232C2×C4×C5C22×D311yescharacteristic
233C22⋊D5—62no—
234C22⋊D5—62no—
235C22⋊D5—121no—
236C22⋊D5—121no—
237C2×Dic5—31no—
238C2×Dic5C22×D311yescharacteristic
239C2×Dic5C22×D311yescharacteristic
240C2×Dic5C22×D311yescharacteristic
241D20—62no—
242D20—62no—
243D20—62no—
244D20—62no—
245D20—121no—
246D20—121no—
247C4×D5—22no—
248C4×D5—34no—
249C4×D5—62no—
250C4×D5—62no—
251C4×D5—121no—
252C4×D5—121no—
253Dic10—22no—
254C2×#41—151no—
255C2×#41—151no—
256C22⋊Q8—31no—
257C22⋊Q8—51no—
258C22⋊Q8—151no—
259C22⋊Q8—151no—
260#121—151no—
261#121—151no—
262#121—151no—
263#121—151no—
264#121—151no—
265#121—151no—
266#121—151no—
267#121—151no—
268C2×C4⋊C4—151no—
269C2×C3×C5C22×D411yescharacteristic
270C2×C3×C5H(5,𝔽2)11yescharacteristic
271C2×C3×C52−1+411yescharacteristic
272D15—22no—
273D15—41no—
274D15—41no—
275C3×D5—41no—
276C5×D3—41no—
277C23×C3—51no—
278C22×D3—51no—
279C22×D3—51no—
280C22×D3—51no—
281C22×D3C22×D511yescharacteristic
282C3×Q8—102no—
283C2×C3×C4—51no—
284C2×C3×C4—51no—
285C2×C3×C4—51no—
286C2×C3×C4—102no—
287C2×C3×C4C22×D511yescharacteristic
288C2×C3×C4C22×D511yescharacteristic
289C2×C3×C4C22×D511yescharacteristic
290#67—102no—
291#67—102no—
292#67—201no—
293#67—201no—
294C2×Dic3—51no—
295C2×Dic3C22×D511yescharacteristic
296C2×Dic3C22×D511yescharacteristic
297C2×Dic3C22×D511yescharacteristic
298D12—102no—
299D12—102no—
300D12—102no—
301D12—102no—
302D12—201no—
303D12—201no—
304C4×D3—22no—
305C4×D3—54no—
306C4×D3—102no—
307C4×D3—102no—
308C4×D3—201no—
309C4×D3—201no—
310Dic6—22no—
311C22×C5—61no—
312C22×C5—61no—
313C22×C5—61no—
314C22×C5C23×D311yescharacteristic
315C2×D5—21no—
316C2×D5—21no—
317C2×D5—21no—
318C2×D5—32no—
319C2×D5—61no—
320C2×D5—61no—
321C2×D5—61no—
322C2×D5—61no—
323C2×D5—61no—
324C2×D5—61no—
325C2×D5—61no—
326C2×D5—61no—
327C4×C5—21no—
328C4×C5—21no—
329C4×C5—21no—
330C4×C5—32no—
331C4×C5—61no—
332C4×C5—61no—
333Dic5—21no—
334Dic5—21no—
335Dic5—61no—
336Dic5D3×D412yes—
337#41—304no—
338#41—304no—
339C2×Q8—31no—
340C2×Q8—51no—
341C2×D4—151no—
342C2×D4—151no—
343C2×D4—151no—
344C2×D4—151no—
345C2×D4—151no—
346C2×D4—151no—
347C2×D4—151no—
348C2×D4—151no—
349C2×D4—151no—
350C2×D4—151no—
351C22×C4—31no—
352C22×C4—51no—
353C22×C4—151no—
354C22×C4—151no—
355C22×C4—151no—
356C22×C4—151no—
357C22×C4—151no—
358C4⋊C4—31no—
359C4⋊C4—31no—
360C4⋊C4—51no—
361C4⋊C4—51no—
362C4⋊C4—151no—
363C4⋊C4—151no—
364C4⋊C4—151no—
365C4⋊C4D3×D511yescharacteristic
366C22⋊C4—31no—
367C22⋊C4—31no—
368C22⋊C4—51no—
369C22⋊C4—51no—
370C22⋊C4—151no—
371C22⋊C4—151no—
372C22⋊C4—151no—
373C22⋊C4—151no—
374C3×C5#53711yescharacteristic, complemented, Hall
375C22×C3—101no—
376C22×C3—101no—
377C22×C3—101no—
378C22×C3C23×D511yescharacteristic
379C2×D3—21no—
380C2×D3—21no—
381C2×D3—21no—
382C2×D3—52no—
383C2×D3—101no—
384C2×D3—101no—
385C2×D3—101no—
386C2×D3—101no—
387C2×D3—101no—
388C2×D3—101no—
389C2×D3—101no—
390C2×D3—101no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—52no—
395C3×C4—101no—
396C3×C4—101no—
397Dic3—21no—
398Dic3—21no—
399Dic3—101no—
400Dic3D4×D512yes—
401C2×C5—121no—
402C2×C5C2×D3×D411yescharacteristic
403C2×C5#100711yescharacteristic
404C2×C5#100911yescharacteristic
405D5—41no—
406D5—62no—
407D5—121no—
408D5—121no—
409C23—31no—
410C23—51no—
411C23—151no—
412C23—151no—
413C23—151no—
414Q8—62no—
415Q8—102no—
416D4—302no—
417D4—302no—
418D4—302no—
419D4—302no—
420D4—302no—
421D4—302no—
422D4—601no—
423D4—601no—
424D4—601no—
425D4—601no—
426C2×C4—31no—
427C2×C4—31no—
428C2×C4—31no—
429C2×C4—51no—
430C2×C4—51no—
431C2×C4—51no—
432C2×C4—62no—
433C2×C4—102no—
434C2×C4—154no—
435C2×C4—151no—
436C2×C4—302no—
437C2×C4—302no—
438C2×C4—601no—
439C2×C4—601no—
440C2×C4C2×D3×D511yescharacteristic
441C2×C4C2×D3×D511yescharacteristic
442C2×C4C2×D3×D511yescharacteristic
443C2×C3—201no—
444C2×C3C2×D4×D511yescharacteristic
445C2×C3#414711yescharacteristic
446C2×C3#414911yescharacteristic
447D3—41no—
448D3—102no—
449D3—201no—
450D3—201no—
451C5#562911yescharacteristic, complemented, Sylow
452C22—61no—
453C22—61no—
454C22—61no—
455C22—101no—
456C22—101no—
457C22—101no—
458C22—152no—
459C22—301no—
460C22—301no—
461C22—301no—
462C22—301no—
463C22—301no—
464C22—301no—
465C22—301no—
466C22—301no—
467C22C22×D3×D511yescharacteristic
468C4—21no—
469C4—21no—
470C4—21no—
471C4—32no—
472C4—52no—
473C4—61no—
474C4—61no—
475C4—101no—
476C4—101no—
477C4—301no—
478C3#6596311yescharacteristic, complemented, Sylow
479C2—121no—
480C2—201no—
481C2—302no—
482C2—601no—
483C2—601no—
484C2#9201911yescharacteristic
485C2D3×D4×D511yescharacteristic
486C2#9202911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#537
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#6773C2semidirect
2. C2×#6769C2semidirect
3. #91784C2semidirect
4. C5×#896C2semidirect
5. C3×#4042C2semidirect
6. #91461C2semidirect
7. #91459C2semidirect
8. #91459C2semidirect
9. #91454C2semidirect
10. #91448C2semidirect
11. #91424C2semidirect
12. #91420C2semidirect
13. #91420C2semidirect
14. #91411C2semidirect
15. #91404C2semidirect
61. #4042D3semidirect
103. #1200D4semidirect
110. #896D5semidirect
374. C3×C5#537semidirect
451. C5#5629semidirect
478. C3#65963semidirect

Maximal subgroups

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

subgroupindex
C2×#67732
C2×#67692
#917842
C5×#8962
C3×#40422
#914612
#914592
#914542
#914482
#914242
#914202
#914112
#914042
#659633
#56295