Finite Group Databasebeta

← #14281877

Subgroups — #14281877

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#11752695C211yesmaximal, characteristic
2C5×#4833C211yesmaximal, characteristic, complemented
3#11746876C211yesmaximal, characteristic, complemented
4#11746305C211yesmaximal, characteristic, complemented
5C3×#64703C211yesmaximal, characteristic, complemented
6#11745845C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10601552—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C42×C5×D3C2211yescharacteristic
11C3×C4×D20C2211yescharacteristic
12#91456C411yescharacteristic
13#91452—21no—
14C4×#1201—21no—
15#91381C411yescharacteristic
16#91365C411yescharacteristic
17#91364C411yescharacteristic
18#91363—21no—
19#91357—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C4×C3⋊#168C2211yescharacteristic
22C5×(C2×D3)⋊C8—21no—
23C5×C8×Dic3—21no—
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26Dic3⋊#168—21no—
27(C2×D3)⋊#168—21no—
28#68169—51nomaximal, Hall
29#65813—31no—
30C5×#431—31no—
31#65214—31no—
32#64704—31no—
33#64704—31no—
34#64703—31no—
35#64703D311yescharacteristic, complemented
36C2×Dic30C2×C411yescharacteristic
37C2×C4×C5×D3C2×C411yescharacteristic
38C2×C4×C5×D3D411yescharacteristic
39C2×C4×C5×D3D411yescharacteristic
40C2×C3×D20C2×C411yescharacteristic
41C2×C3×C4×D5—21no—
42C2×#1201—21no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45C4⋊Dic15C2×C411yescharacteristic
46#6712—21no—
47C4×Dic15—21no—
48C2×C3⋊#168—21no—
49C4×C5×Dic3C2×C411yescharacteristic
50C4×C5×Dic3D411yescharacteristic
51C4×C5×Dic3D411yescharacteristic
52C2×C5×C3⋊C8—21no—
53C3×#685—21no—
54C3×C4⋊Dic5C2×C411yescharacteristic
55C2×C3×#168—21no—
56#6669—21no—
57#6668—21no—
58#6668—21no—
59(C2×D3)⋊Dic5—21no—
60#6665—21no—
61#6665—21no—
62#6665—21no—
63#5557—51no—
64#4833D511yescharacteristic, complemented
65#4685—51no—
66C3×D4⋊C8—51no—
67D4⋊(C3⋊C8)—51no—
68#4484—51no—
69#4456—51no—
70C2×C42×C5—31no—
71#4076—31no—
72#4075—61no—
73C4×C22⋊D5—61no—
74#4070—31no—
75#4022—61no—
76#4021—31no—
77C4×D20C2×D311yescharacteristic
78#4018—61no—
79#4016—31no—
80C4×Dic10—31no—
81C5×C4⋊C8—31no—
82C5×C4⋊C8C2×D311yescharacteristic
83C5×C22⋊C8—61no—
84C4×C5×C8—61no—
85C22⋊#168—61no—
86C4⋊#168—61no—
87C4×#168—31no—
88C4×#168C2×D311yescharacteristic
89#1482—151noSylow
90C22×C5×D3C22⋊C411yescharacteristic
91C22×C3×D5—21no—
92C2×C3×C4×C5C22×C411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×Dic15—21no—
96C2×Dic15—21no—
97Dic30—21no—
98Dic30—21no—
99C2×C5×Dic3C22⋊C411yescharacteristic
100C2×C5×Dic3C22⋊C411yescharacteristic
101C2×C5×Dic3C22⋊C411yescharacteristic
102C4×C5×D3—21no—
103C4×C5×D3—21no—
104C4×C5×D3—21no—
105C4×C5×D3—21no—
106C4×C5×D3—41no—
107C2×C3×Dic5—21no—
108C3×D20—21no—
109C3×D20—21no—
110C3×C4×D5—41no—
111C3×C4×D5—41no—
112#1201—42no—
113C3×C5×C8—41no—
114C3⋊#168—41no—
115C3×#168—41no—
116C5×C3⋊C8—41no—
117C3×C4×D4—51no—
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×D3C2×D511yescharacteristic
127C4×Dic6—51no—
128C3×C4⋊C8C2×D511yescharacteristic
129C3×C4×C8—51no—
130(C2×D3)⋊C8—21no—
131(C2×D3)⋊C8—101no—
132Dic3⋊C8—101no—
133C8×Dic3—21no—
134C4⋊(C3⋊C8)C2×D511yescharacteristic
135C4×C3⋊C8—51no—
136C22×C4×C5—31no—
137C22×C4×C5—31no—
138C22×C4×C5—31no—
139C2×C22⋊D5—61no—
140C2×D20C4×D311yescharacteristic
141C2×C4×D5—21no—
142C2×Dic10—31no—
143C2×C5×C8—21no—
144C2×C5×C8—61no—
145C42×C5—31no—
146C42×C5—31no—
147C42×C5—31no—
148C42×C5C22×D311yescharacteristic
149C22⋊Dic5—61no—
150#685—21no—
151#685—61no—
152#685—61no—
153#685—61no—
154C4⋊Dic5—31no—
155C4⋊Dic5C4×D311yescharacteristic
156#683—61no—
157#683—61no—
158#683—61no—
159#683—61no—
160C4×Dic5—61no—
161C2×#168—21no—
162C2×#168—61no—
163#529—151no—
164#431—31no—
165#431—151no—
166Q8⋊C8—151no—
167Q8⋊C8—151no—
168D4⋊C8—51no—
169D4⋊C8—151no—
170C22×C3×C5C2×C22⋊C411yescharacteristic
171C2×C5×D3—21no—
172C2×C5×D3—21no—
173C2×C5×D3—21no—
174C2×C3×D5—41no—
175C2×C3×D5—41no—
176C2×C3×D5—41no—
177C3×C4×C5—21no—
178C3×C4×C5#13111yescharacteristic
179C3×C4×C5#13111yescharacteristic
180C3×C4×C5#13511yescharacteristic
181C3×C4×C5#13511yescharacteristic
182Dic15—41no—
183Dic15—41no—
184C3×Dic5—41no—
185C5×Dic3—21no—
186C5×Dic3—21no—
187C5×Dic3—21no—
188C2×C3×D4—51no—
189C22×C3×C4—101no—
190C2×#67—101no—
191C2×C4×D3C4×D511yescharacteristic
192C2×C4×D3D2011yescharacteristic
193C2×C4×D3C22⋊D511yescharacteristic
194C2×Dic6—51no—
195C2×C3×C8—21no—
196C2×C3×C8—101no—
197C3×C4⋊C4—51no—
198C3×C22⋊C4—101no—
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—101no—
210C4×Dic3C4×D511yescharacteristic
211C4×Dic3D2011yescharacteristic
212C4×Dic3C22⋊D511yescharacteristic
213C2×C3⋊C8—21no—
214C2×C3⋊C8—101no—
215C23×C5—31no—
216C22×D5—21no—
217C2×C4×C5—31no—
218C2×C4×C5—31no—
219C2×C4×C5—31no—
220C2×C4×C5—61no—
221C2×C4×C5—61no—
222C2×C4×C5—61no—
223C2×C4×C5—61no—
224C2×C4×C5—121no—
225C2×C4×C5C2×C4×D311yescharacteristic
226C2×C4×C5D3×D411yescharacteristic
227C2×C4×C5D3×D411yescharacteristic
228C22⋊D5—122no—
229C2×Dic5—21no—
230C2×Dic5—61no—
231C2×Dic5—61no—
232D20—21no—
233D20—21no—
234C4×D5—41no—
235C4×D5—41no—
236Dic10—61no—
237Dic10—61no—
238C5×C8—41no—
239C5×C8—121no—
240#168—41no—
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—51no—
250C4×D4—301no—
251#117—301no—
252C2×C42—31no—
253C4⋊C8—31no—
254C4⋊C8—301no—
255C4⋊C8D3×D511yescharacteristic
256C22⋊C8—61no—
257C22⋊C8—301no—
258C4×C8—51no—
259C4×C8—61no—
260C4×C8—151no—
261C2×C3×C5#40811yescharacteristic
262C2×C3×C5#41611yescharacteristic
263C2×C3×C5#42111yescharacteristic
264C3×D5—81no—
265C5×D3—41no—
266C23×C3—101no—
267C22×D3#68511yescharacteristic
268C3×D4—101no—
269C3×D4—101no—
270C2×C3×C4—101no—
271C2×C3×C4—201no—
272C2×C3×C4—201no—
273C2×C3×C4C2×C4×D511yescharacteristic
274C2×C3×C4C2×D2011yescharacteristic
275C2×C3×C4C2×C22⋊D511yescharacteristic
276#67—202no—
277C2×Dic3—101no—
278C2×Dic3—101no—
279C2×Dic3#68511yescharacteristic
280C2×Dic3#68511yescharacteristic
281C2×Dic3#68511yescharacteristic
282C4×D3—21no—
283C4×D3—21no—
284C4×D3—21no—
285C4×D3—21no—
286C4×D3—41no—
287Dic6—101no—
288Dic6—101no—
289C3×C8—41no—
290C3×C8—201no—
291C3⋊C8—41no—
292C3⋊C8—201no—
293C22×C5—61no—
294C22×C5—61no—
295C22×C5—61no—
296C22×C5D3×C22⋊C411yescharacteristic
297C2×D5—41no—
298C2×D5—41no—
299C2×D5—41no—
300C4×C5—21no—
301C4×C5—61no—
302C4×C5—61no—
303C4×C5—61no—
304C4×C5#90111yescharacteristic
305C4×C5#90711yescharacteristic
306C4×C5#91211yescharacteristic
307C4×C5#91611yescharacteristic
308Dic5—41no—
309Dic5—121no—
310Dic5—121no—
311C2×Q8—151no—
312C2×D4—51no—
313C2×D4—301no—
314C22×C4—31no—
315C22×C4—31no—
316C22×C4—31no—
317C22×C4—101no—
318C2×C8—21no—
319C2×C8—61no—
320C2×C8—101no—
321C2×C8—301no—
322C4⋊C4—51no—
323C4⋊C4—151no—
324C4⋊C4—301no—
325C4⋊C4—301no—
326C4⋊C4—301no—
327C4⋊C4—301no—
328C22⋊C4—101no—
329C22⋊C4—301no—
330C22⋊C4—301no—
331C22⋊C4—301no—
332C22⋊C4—301no—
333C42—31no—
334C42—31no—
335C42—31no—
336C42—301no—
337C42C2×D3×D511yescharacteristic
338C3×C5#148211yescharacteristic, complemented, Hall
339C22×C3—201no—
340C22×C3—201no—
341C22×C3—201no—
342C22×C3C2×#68511yescharacteristic
343C2×D3—21no—
344C2×D3—21no—
345C2×D3—21no—
346C3×C4—21no—
347C3×C4—201no—
348C3×C4#404711yescharacteristic
349C3×C4#404711yescharacteristic
350C3×C4#409611yescharacteristic
351C3×C4#409611yescharacteristic
352Dic3—21no—
353Dic3—21no—
354Dic3—21no—
355Dic3—201no—
356Dic3—201no—
357C2×C5—121no—
358C2×C5#472711yescharacteristic
359C2×C5#477211yescharacteristic
360C2×C5#482111yescharacteristic
361D5—81no—
362C23—31no—
363C23—101no—
364Q8—301no—
365Q8—301no—
366D4—101no—
367D4—101no—
368D4—602no—
369C2×C4—31no—
370C2×C4—31no—
371C2×C4—31no—
372C2×C4—61no—
373C2×C4—61no—
374C2×C4—61no—
375C2×C4—61no—
376C2×C4—101no—
377C2×C4—121no—
378C2×C4—201no—
379C2×C4—201no—
380C2×C4—301no—
381C2×C4—301no—
382C2×C4C4×D3×D511yescharacteristic
383C2×C4D3×D2011yescharacteristic
384C2×C4D3×C22⋊D511yescharacteristic
385C8—41no—
386C8—121no—
387C8—201no—
388C8—601no—
389C2×C3—401no—
390C2×C3#6529111yescharacteristic
391C2×C3#6539911yescharacteristic
392C2×C3#6542811yescharacteristic
393D3—41no—
394C5#6816911yescharacteristic, complemented, Sylow
395C22—61no—
396C22—61no—
397C22—61no—
398C22—201no—
399C22—201no—
400C22—201no—
401C22D3×#68511yescharacteristic
402C4—21no—
403C4—61no—
404C4—61no—
405C4—61no—
406C4—201no—
407C4—601no—
408C4—601no—
409C4#9126511yescharacteristic
410C4#9126711yescharacteristic
411C4#9149311yescharacteristic
412C4#9151711yescharacteristic
413C3#1060155211yescharacteristic, complemented, Sylow
414C2—121no—
415C2—401no—
416C2#1174750211yescharacteristic
417C2#1174813911yescharacteristic
418C2#1174823311yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91456C4
cosocleC3×C42×C5C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1482
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C5×#4833C2semidirect
3. #11746876C2semidirect
4. #11746305C2semidirect
5. C3×#64703C2semidirect
6. #11745845C2semidirect
7. #11745834C2semidirect
35. #64703D3semidirect
64. #4833D5semidirect
338. C3×C5#1482semidirect
394. C5#68169semidirect
413. C3#10601552semidirect

Maximal subgroups

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

subgroupindex
#117526952
C5×#48332
#117468762
#117463052
C3×#647032
#117458452
#117458342
#106015523
#681695