Finite Group Databasebeta

← #14281854

Subgroups — #14281854

Order 1920.

424 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756316C211yesmaximal, characteristic
2#11750934C211yesmaximal, characteristic, complemented
3#11750786C211yesmaximal, characteristic, complemented
4C3×C5×D4⋊C8C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
6#11746305C211yesmaximal, characteristic, complemented
7#11746277C211yesmaximal, characteristic, complemented
8#10598962—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10#91827C411yescharacteristic
11#91825C411yescharacteristic
12C4×#1220—21no—
13#91815—21no—
14#91786C411yescharacteristic
15#91779C411yescharacteristic
16#91772—21no—
17#91768—21no—
18C42×D15C2211yescharacteristic
19C4×Dic30C2211yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C4×C5×C8C2211yescharacteristic
22#91104—21no—
23#91104—21no—
24#91098—21no—
25C8×Dic15—21no—
26C4⋊(C3⋊#168)C2211yescharacteristic
27C4×C3⋊#168C2211yescharacteristic
28#68169—51nomaximal, Hall
29#65891—31no—
30#65122—31no—
31#64974—31no—
32C5×D4⋊C8D311yescharacteristic, complemented
33D4⋊#168—31no—
34#64704—31no—
35#64676—31no—
36C2×C3×C5×D4C2×C411yescharacteristic
37C22×C3×C4×C5—21no—
38C2×#1220—21no—
39C2×C4×D15C2×C411yescharacteristic
40C2×C4×D15D411yescharacteristic
41C2×C4×D15D411yescharacteristic
42C2×Dic30C2×C411yescharacteristic
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4C2×C411yescharacteristic
46C3×C5×C22⋊C4—21no—
47C3×C42×C5C2311yescharacteristic
48#6719—21no—
49#6719—21no—
50#6719—21no—
51#6714—21no—
52C4⋊Dic15—21no—
53C4⋊Dic15—21no—
54C4⋊Dic15C2×C411yescharacteristic
55#6712—21no—
56#6712—21no—
57C4×Dic15—21no—
58C4×Dic15C2×C411yescharacteristic
59C4×Dic15D411yescharacteristic
60C4×Dic15D411yescharacteristic
61C2×C3⋊#168—21no—
62C2×C3⋊#168—21no—
63#5557—51no—
64#4833—51no—
65#4685—51no—
66C3×D4⋊C8D511yescharacteristic, complemented
67D4⋊(C3⋊C8)—51no—
68#4484—51no—
69#4456—51no—
70C4×C5×D4C2×D311yescharacteristic
71#4084—31no—
72#4082—31no—
73C4×C22⋊D5—61no—
74#4072—61no—
75#4043—31no—
76#4036—31no—
77#4029—61no—
78#4025—61no—
79C42×D5—31no—
80C4×Dic10—31no—
81C5×C4⋊C8C2×D311yescharacteristic
82C4×C5×C8C2×D311yescharacteristic
83#3952—61no—
84#3952—61no—
85#3946—61no—
86C8×Dic5—61no—
87C4⋊#168—31no—
88C4×#168—31no—
89#1482—151noSylow
90C23×C3×C5—21no—
91C22×D15C22⋊C411yescharacteristic
92C3×C5×D4—21no—
93C3×C5×D4—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100#1220—42no—
101C2×Dic15—21no—
102C2×Dic15—21no—
103C2×Dic15C22⋊C411yescharacteristic
104C2×Dic15C22⋊C411yescharacteristic
105C2×Dic15C22⋊C411yescharacteristic
106C4×D15—21no—
107C4×D15—21no—
108C4×D15—21no—
109C4×D15—21no—
110C4×D15—41no—
111Dic30—21no—
112Dic30—21no—
113C3×C5×C8—41no—
114C3×C5×C8—41no—
115C3⋊#168—41no—
116C3⋊#168—41no—
117C3×C4×D4C2×D511yescharacteristic
118#938—51no—
119#936—51no—
120C4×#67—101no—
121#926—101no—
122#897—51no—
123#890—51no—
124#883—101no—
125#879—101no—
126C42×D3—51no—
127C4×Dic6—51no—
128C3×C4⋊C8C2×D511yescharacteristic
129C3×C4×C8C2×D511yescharacteristic
130(C2×D3)⋊C8—101no—
131(C2×D3)⋊C8—101no—
132Dic3⋊C8—101no—
133C8×Dic3—101no—
134C4⋊(C3⋊C8)—51no—
135C4×C3⋊C8—51no—
136C2×C5×D4C4×D311yescharacteristic
137C22×C4×C5—21no—
138C2×C22⋊D5—61no—
139C2×C4×D5—31no—
140C2×C4×D5—31no—
141C2×C4×D5—31no—
142C2×Dic10—31no—
143C2×C5×C8—21no—
144C2×C5×C8—21no—
145C5×C4⋊C4C4×D311yescharacteristic
146C5×C22⋊C4—21no—
147C42×C5C22×D311yescharacteristic
148C22⋊Dic5—61no—
149C22⋊Dic5—61no—
150C22⋊Dic5—61no—
151#685—61no—
152C4⋊Dic5—31no—
153C4⋊Dic5—61no—
154C4⋊Dic5—61no—
155#683—61no—
156#683—61no—
157C4×Dic5—31no—
158C4×Dic5—31no—
159C4×Dic5—31no—
160C4×Dic5—61no—
161C2×#168—61no—
162C2×#168—61no—
163#529—151no—
164#431—151no—
165#431—151no—
166Q8⋊C8—151no—
167Q8⋊C8—151no—
168D4⋊C8—151no—
169D4⋊C8D1511yescharacteristic, complemented
170C22×C3×C5—41no—
171C22×C3×C5—41no—
172C22×C3×C5—41no—
173C22×C3×C5C2×C22⋊C411yescharacteristic
174C2×D15—21no—
175C2×D15—21no—
176C2×D15—21no—
177C3×C4×C5—21no—
178C3×C4×C5—41no—
179C3×C4×C5#13111yescharacteristic
180C3×C4×C5#13111yescharacteristic
181C3×C4×C5#13511yescharacteristic
182C3×C4×C5#13511yescharacteristic
183Dic15—21no—
184Dic15—21no—
185Dic15—21no—
186Dic15—41no—
187Dic15—41no—
188C2×C3×D4C4×D511yescharacteristic
189C22×C3×C4—21no—
190C2×#67—101no—
191C2×C4×D3—51no—
192C2×C4×D3—51no—
193C2×C4×D3—51no—
194C2×Dic6—51no—
195C2×C3×C8—21no—
196C2×C3×C8—21no—
197C3×C4⋊C4C4×D511yescharacteristic
198C3×C22⋊C4—21no—
199C3×C42C22×D511yescharacteristic
200#217—101no—
201#217—101no—
202#217—101no—
203(C2×D3)⋊C4—101no—
204C4⋊Dic3—51no—
205C4⋊Dic3—101no—
206C4⋊Dic3—101no—
207Dic3⋊C4—101no—
208Dic3⋊C4—101no—
209C4×Dic3—51no—
210C4×Dic3—51no—
211C4×Dic3—51no—
212C4×Dic3—101no—
213C2×C3⋊C8—101no—
214C2×C3⋊C8—101no—
215C23×C5—21no—
216C22×D5—31no—
217C5×D4—21no—
218C5×D4—21no—
219C2×C4×C5—21no—
220C2×C4×C5—41no—
221C2×C4×C5—41no—
222C2×C4×C5C2×C4×D311yescharacteristic
223C2×C4×C5D3×D411yescharacteristic
224C2×C4×C5D3×D411yescharacteristic
225C22⋊D5—122no—
226C2×Dic5—31no—
227C2×Dic5—31no—
228C2×Dic5—31no—
229C2×Dic5—61no—
230C2×Dic5—61no—
231C4×D5—61no—
232C4×D5—61no—
233C4×D5—61no—
234C4×D5—61no—
235C4×D5—121no—
236Dic10—61no—
237Dic10—61no—
238C5×C8—41no—
239C5×C8—41no—
240#168—121no—
241#168—121no—
242#126—301no—
243#125—151no—
244#124—151no—
245#123—301no—
246C22⋊Q8—151no—
247#121—151no—
248C4×Q8—151no—
249C4×D4—301no—
250C4×D4C2×D1511yescharacteristic
251#117—301no—
252C2×C42—151no—
253C4⋊C8—151no—
254C4⋊C8—301no—
255C4⋊C8C2×D1511yescharacteristic
256C22⋊C8—301no—
257C22⋊C8—301no—
258C4×C8—151no—
259C4×C8—301no—
260C4×C8C2×D1511yescharacteristic
261C2×C3×C5—81no—
262C2×C3×C5#40811yescharacteristic
263C2×C3×C5#41611yescharacteristic
264C2×C3×C5#42111yescharacteristic
265D15—41no—
266C23×C3—21no—
267C22×D3—51no—
268C3×D4—21no—
269C3×D4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4C2×C4×D511yescharacteristic
274C2×C3×C4D4×D511yescharacteristic
275C2×C3×C4D4×D511yescharacteristic
276#67—202no—
277C2×Dic3—51no—
278C2×Dic3—51no—
279C2×Dic3—51no—
280C2×Dic3—101no—
281C2×Dic3—101no—
282C4×D3—101no—
283C4×D3—101no—
284C4×D3—101no—
285C4×D3—101no—
286C4×D3—201no—
287Dic6—101no—
288Dic6—101no—
289C3×C8—41no—
290C3×C8—41no—
291C3⋊C8—201no—
292C3⋊C8—201no—
293C22×C5—41no—
294C22×C5—41no—
295C22×C5—41no—
296C22×C5D3×C22⋊C411yescharacteristic
297C2×D5—61no—
298C2×D5—61no—
299C2×D5—61no—
300C4×C5—21no—
301C4×C5—41no—
302C4×C5#90111yescharacteristic
303C4×C5#90711yescharacteristic
304C4×C5#91211yescharacteristic
305C4×C5#91611yescharacteristic
306Dic5—61no—
307Dic5—61no—
308Dic5—61no—
309Dic5—121no—
310Dic5—121no—
311C2×Q8—151no—
312C2×D4—301no—
313C2×D4C4×D1511yescharacteristic
314C22×C4—21no—
315C22×C4—151no—
316C22×C4—151no—
317C22×C4—151no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—301no—
321C2×C8—301no—
322C4⋊C4—151no—
323C4⋊C4—301no—
324C4⋊C4—301no—
325C4⋊C4—301no—
326C4⋊C4—301no—
327C4⋊C4C4×D1511yescharacteristic
328C22⋊C4—21no—
329C22⋊C4—301no—
330C22⋊C4—301no—
331C22⋊C4—301no—
332C22⋊C4—301no—
333C42—151no—
334C42—151no—
335C42—151no—
336C42—301no—
337C42C22×D1511yescharacteristic
338C3×C5#148211yescharacteristic, complemented, Hall
339C22×C3—41no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3D5×C22⋊C411yescharacteristic
343C2×D3—101no—
344C2×D3—101no—
345C2×D3—101no—
346C3×C4—21no—
347C3×C4—41no—
348C3×C4#404711yescharacteristic
349C3×C4#405311yescharacteristic
350C3×C4#405811yescharacteristic
351C3×C4#406211yescharacteristic
352Dic3—101no—
353Dic3—101no—
354Dic3—101no—
355Dic3—201no—
356Dic3—201no—
357C2×C5—81no—
358C2×C5#472711yescharacteristic
359C2×C5#477211yescharacteristic
360C2×C5#482111yescharacteristic
361D5—121no—
362C23—21no—
363C23—151no—
364Q8—301no—
365Q8—301no—
366D4—21no—
367D4—21no—
368D4—602no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—151no—
373C2×C4—151no—
374C2×C4—151no—
375C2×C4—301no—
376C2×C4—301no—
377C2×C4—301no—
378C2×C4—301no—
379C2×C4—301no—
380C2×C4—301no—
381C2×C4—601no—
382C2×C4C2×C4×D1511yescharacteristic
383C2×C4D4×D1511yescharacteristic
384C2×C4D4×D1511yescharacteristic
385C8—41no—
386C8—41no—
387C8—601no—
388C8—601no—
389C2×C3—81no—
390C2×C3#6501611yescharacteristic
391C2×C3#6506111yescharacteristic
392C2×C3#6511011yescharacteristic
393D3—201no—
394C5#6816911yescharacteristic, complemented, Sylow
395C22—41no—
396C22—41no—
397C22—41no—
398C22—301no—
399C22—301no—
400C22—301no—
401C22C22⋊C4×D1511yescharacteristic
402C4—21no—
403C4—41no—
404C4—301no—
405C4—301no—
406C4—301no—
407C4—601no—
408C4—601no—
409C4#9179011yescharacteristic
410C4#9179611yescharacteristic
411C4#9180111yescharacteristic
412C4#9180511yescharacteristic
413C3#1059896211yescharacteristic, complemented, Sylow
414C2—81no—
415C2—601no—
416C2#1175082811yescharacteristic
417C2#1175087311yescharacteristic
418C2#1175092211yescharacteristic
subgroupG/H
centerC2×C4D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5C2×C22⋊C4
prime radical#91827C4
cosocleC3×C42×C5C23
hypercenterD4⋊C8D15
hypocenterC3×C5#1482
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11750934C2semidirect
3. #11750786C2semidirect
4. C3×C5×D4⋊C8C2semidirect
5. D4⋊(C3⋊#168)C2semidirect
6. #11746305C2semidirect
7. #11746277C2semidirect
32. C5×D4⋊C8D3semidirect
66. C3×D4⋊C8D5semidirect
169. D4⋊C8D15semidirect
338. C3×C5#1482semidirect
394. C5#68169semidirect
413. C3#10598962semidirect

Maximal subgroups

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

subgroupindex
#117563162
#117509342
#117507862
C3×C5×D4⋊C82
D4⋊(C3⋊#168)2
#117463052
#117462772
#105989623
#681695