Finite Group Databasebeta

← #14289361

Subgroups — #14289361

Order 1920.

628 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×D20C211yesmaximal, characteristic
2C5×#5008C211yesmaximal, characteristic, complemented
3#11747079C211yesmaximal, characteristic, complemented
4#11746880C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
6#11745852C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10601936—31nomaximal, Hall
9C2×C3×D4×D5—21no—
10C22×C3×D20—21no—
11C3×C4×C5×D4C2211yescharacteristic
12C5×#869C2211yescharacteristic, complemented
13C3×#4076—21no—
14C3×#4041—21no—
15C3×#4028—22no—
16C3×#4020C2211yescharacteristic
17C3×C4×D20C2211yescharacteristic
18C2×#6655—22no—
19C4⋊(C3⋊#168)C2211yescharacteristic, complemented
20C4×C3⋊#168C2211yescharacteristic, complemented
21C5×#832—21no—
22C5×#808—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
24#90986—21no—
25#90964—21no—
26#71907—51nomaximal, Hall
27D4×D20D311yescharacteristic
28C5×#476—31no—
29#65374—31no—
30#65373—31no—
31D4⋊#168—31no—
32#64705—31no—
33#64703—31no—
34C23×C3×D5—22no—
35C2×C3×C5×D4D411yescharacteristic
36C22×C3×C4×C5—21no—
37C2×C5×Dic6—21no—
38C2×C3×C22⋊D5—22no—
39C3×D4×D5—42no—
40C3×D4×D5—42no—
41C2×C3×D20—22no—
42C2×C3×D20—21no—
43C2×C3×D20—21no—
44C2×C3×D20—42no—
45C2×C3×D20—42no—
46C2×C3×D20D411yescharacteristic
47C2×C3×D20D412yes—
48C2×C3×C4×D5—21no—
49C3×C5×C4⋊C4D411yescharacteristic
50C3×C5×C22⋊C4—21no—
51C3×C42×C5C2311yescharacteristic
52C2×C3⋊#168—21no—
53C2×C3⋊#168—21no—
54C5×C4⋊Dic3—21no—
55C5×C4⋊Dic3—21no—
56C2×C5×C3⋊C8—21no—
57C3×#685—22no—
58C3×#685—21no—
59C3×C4⋊Dic5D411yescharacteristic
60#6655—44no—
61C3×D42—51no—
62#5076—51no—
63#5008—51no—
64#5008D511yescharacteristic, complemented
65#4544—51no—
66D4⋊(C3⋊C8)—51no—
67D4⋊(C3⋊C8)—51no—
68C2×D4×D5—21no—
69C22×D20—21no—
70C5×C4⋊Q8—31no—
71C4×C5×D4C2×D311yescharacteristic
72C2×#688—62no—
73#4076—21no—
74#4041—21no—
75#4028—22no—
76#4020C2×D311yescharacteristic
77C4×D20C2×D311yescharacteristic
78C5×#106—61no—
79C5×C4⋊C8—31no—
80C5×#102—61no—
81#3941—61no—
82#3940—61no—
83C4⋊#168—31no—
84C4×#168—31no—
85#1629—151noSylow
86C23×C3×C5—21no—
87C22×C3×D5—21no—
88C22×C3×D5—22no—
89C22×C3×D5—44no—
90C22×C3×D5—44no—
91C22×C3×D5—82no—
92C3×C5×D4—21no—
93C3×C5×D4SD1612yescomplemented
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C5×Dic3—41no—
101C5×Dic6—42no—
102C3×C22⋊D5—44no—
103C2×C3×Dic5—21no—
104C3×D20—21no—
105C3×D20—42no—
106C3×D20—44no—
107C3×D20—41no—
108C3×D20—41no—
109C3×D20—41no—
110C3×D20—41no—
111C3×D20SD1612yescomplemented
112C3×C4×D5—41no—
113C3×C4×D5—41no—
114C3⋊#168—22no—
115C3⋊#168—41no—
116C5×C3⋊C8—41no—
117C22×C3×D4—101no—
118C22×C3×D4—101no—
119C3×#127—51no—
120C3×#121—101no—
121C3×#121—101no—
122C3×#120—102no—
123C3×C4×D4—51no—
124C3×C4×D4C2×D511yescharacteristic
125C2×#214—102no—
126#869C2×D511yescharacteristic, complemented
127#832—21no—
128#832—101no—
129#808—21no—
130#808—101no—
131C4⋊(C3⋊C8)—51no—
132C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
133C4×C3⋊C8—51no—
134C23×D5—22no—
135C2×C5×Q8—61no—
136C2×C5×D4#6711yescharacteristic
137C22×C4×C5—21no—
138C2×C22⋊D5—22no—
139D4×D5—42no—
140D4×D5—42no—
141C2×D20—22no—
142C2×D20—21no—
143C2×D20—21no—
144C2×D20—42no—
145C2×D20—42no—
146C2×D20#6711yescharacteristic
147C2×D20#6712yes—
148C2×C4×D5—21no—
149C2×C5×C8—61no—
150C5×C4⋊C4—61no—
151C5×C4⋊C4—61no—
152C5×C4⋊C4#6711yescharacteristic
153C5×C22⋊C4—21no—
154C42×C5C22×D311yescharacteristic
155#688—124no—
156#685—22no—
157#685—21no—
158C4⋊Dic5#6711yescharacteristic
159C2×#168—61no—
160C2×#168—61no—
161D42—51no—
162#492—151no—
163#476—31no—
164#476—151no—
165#331—151no—
166D4⋊C8—151no—
167D4⋊C8—151no—
168C22×C3×C5—22no—
169C22×C3×C5—41no—
170C22×C3×C5—41no—
171C22×C3×C5#12011yescharacteristic
172C2×C3×D5—22no—
173C2×C3×D5—41no—
174C2×C3×D5—41no—
175C2×C3×D5—42no—
176C2×C3×D5—42no—
177C2×C3×D5—42no—
178C2×C3×D5—88no—
179C3×C4×C5—21no—
180C3×C4×C5—41no—
181C3×C4×C5C2×SD1611yescharacteristic
182C3×C4×C5C2×SD1611yescharacteristic
183C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
184C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
185C3×Dic5—41no—
186C5×Dic3—81no—
187C24×C3—102no—
188C2×C3×D4—51no—
189C2×C3×D4—52no—
190C2×C3×D4—102no—
191C2×C3×D4—102no—
192C2×C3×D4—101no—
193C2×C3×D4—101no—
194C2×C3×D4—202no—
195C2×C3×D4—202no—
196C2×C3×D4—202no—
197C2×C3×D4—202no—
198C2×C3×D4C22⋊D511yescharacteristic
199C22×C3×C4—21no—
200C22×C3×C4—101no—
201C2×Dic6—21no—
202C3×C4⋊C4—51no—
203C3×C4⋊C4C22⋊D511yescharacteristic
204C3×C22⋊C4—21no—
205C3×C22⋊C4—102no—
206C3×C22⋊C4—101no—
207C3×C42C22×D511yescharacteristic
208#214—204no—
209C4⋊Dic3—21no—
210C4⋊Dic3—21no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—101no—
213C2×C3⋊C8—101no—
214C23×C5—21no—
215C22×D5—21no—
216C22×D5—22no—
217C22×D5—44no—
218C22×D5—44no—
219C22×D5—82no—
220C5×Q8—122no—
221C5×D4—21no—
222C5×D4#21412yescomplemented
223C2×C4×C5—21no—
224C2×C4×C5—41no—
225C2×C4×C5—41no—
226C2×C4×C5—121no—
227C2×C4×C5C2×#6711yescharacteristic
228C2×C4×C5C2×#6711yescharacteristic
229C2×C4×C5C2×#6711yescharacteristic
230C22⋊D5—44no—
231C2×Dic5—21no—
232D20—21no—
233D20—42no—
234D20—44no—
235D20—41no—
236D20—41no—
237D20—41no—
238D20—41no—
239D20#21412yescomplemented
240C4×D5—41no—
241C4×D5—41no—
242C5×C8—121no—
243#168—62no—
244#168—121no—
245C22×D4—101no—
246C22×D4—101no—
247C2×SD16—302no—
248C4⋊Q8—31no—
249#127—51no—
250#121—101no—
251#121—101no—
252#120—102no—
253C4×D4—51no—
254C4×D4D3×D511yescharacteristic
255#106—61no—
256#106—301no—
257C4⋊C8—31no—
258C4⋊C8—151no—
259#102—61no—
260#102—301no—
261C4×C8—151no—
262C2×C3×C5—42no—
263C2×C3×C5#45011yescharacteristic
264C2×C3×C5#45011yescharacteristic
265C2×C3×C5#45311yescharacteristic
266C3×D5—42no—
267C3×D5—82no—
268C23×C3—21no—
269C23×C3—101no—
270C23×C3—102no—
271C23×C3—204no—
272C23×C3—204no—
273C23×C3—402no—
274C3×D4—21no—
275C3×D4—52no—
276C3×D4—101no—
277C3×D4—202no—
278C3×D4—204no—
279C3×D4—204no—
280C3×D4—201no—
281C3×D4—201no—
282C3×D4—201no—
283C3×D4—201no—
284C3×D4#68812yescomplemented
285C2×C3×C4—21no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—101no—
289C2×C3×C4—201no—
290C2×C3×C4—201no—
291C2×C3×C4D4×D511yescharacteristic
292C2×C3×C4D4×D511yescharacteristic
293C2×C3×C4C2×C22⋊D511yescharacteristic
294C2×Dic3—41no—
295Dic6—42no—
296C3⋊C8—41no—
297C3⋊C8—102no—
298C3⋊C8—201no—
299C22×C5—22no—
300C22×C5—41no—
301C22×C5—41no—
302C22×C5#95311yescharacteristic
303C2×D5—22no—
304C2×D5—41no—
305C2×D5—41no—
306C2×D5—42no—
307C2×D5—42no—
308C2×D5—42no—
309C2×D5—88no—
310C4×C5—21no—
311C4×C5—41no—
312C4×C5—241no—
313C4×C5#93211yescharacteristic
314C4×C5#93211yescharacteristic
315C4×C5C2×#21411yescharacteristic
316C4×C5C2×#21411yescharacteristic
317Dic5—41no—
318C24—102no—
319C2×Q8—61no—
320C2×D4—51no—
321C2×D4—52no—
322C2×D4—102no—
323C2×D4—102no—
324C2×D4—101no—
325C2×D4—101no—
326C2×D4—202no—
327C2×D4—202no—
328C2×D4—202no—
329C2×D4—202no—
330C2×D4#120111yescharacteristic
331C22×C4—21no—
332C22×C4—101no—
333SD16—604no—
334C2×C8—61no—
335C2×C8—301no—
336C2×C8—301no—
337C4⋊C4—51no—
338C4⋊C4—61no—
339C4⋊C4—61no—
340C4⋊C4#120111yescharacteristic
341C22⋊C4—21no—
342C22⋊C4—102no—
343C22⋊C4—101no—
344C42C2×D3×D511yescharacteristic
345C3×C5#162911yescharacteristic, complemented, Hall
346C22×C3—22no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3—102no—
350C22×C3—201no—
351C22×C3—201no—
352C22×C3—202no—
353C22×C3—202no—
354C22×C3—202no—
355C22×C3—408no—
356C22×C3#408311yescharacteristic
357C3×C4—21no—
358C3×C4—41no—
359C3×C4—201no—
360C3×C4D5×SD1611yescharacteristic
361C3×C4#406011yescharacteristic
362C3×C4C2×#68811yescharacteristic
363C3×C4#409511yescharacteristic
364Dic3—81no—
365C2×C5—42no—
366C2×C5#521811yescharacteristic
367C2×C5#521811yescharacteristic
368C2×C5#524111yescharacteristic
369D5—42no—
370D5—82no—
371C23—21no—
372C23—101no—
373C23—102no—
374C23—204no—
375C23—204no—
376C23—402no—
377Q8—122no—
378D4—21no—
379D4—52no—
380D4—101no—
381D4—202no—
382D4—204no—
383D4—204no—
384D4—201no—
385D4—201no—
386D4—201no—
387D4—201no—
388D4#665512yescomplemented
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—101no—
393C2×C4—121no—
394C2×C4—201no—
395C2×C4—201no—
396C2×C4C2×#120111yescharacteristic
397C2×C4D5×#6711yescharacteristic
398C2×C4D5×#6711yescharacteristic
399C8—121no—
400C8—302no—
401C8—601no—
402C2×C3—42no—
403C2×C3—202no—
404C2×C3—402no—
405C2×C3#6533511yescharacteristic
406C2×C3#6545811yescharacteristic
407C2×C3#6548711yescharacteristic
408C5#7190711yescharacteristic, complemented, Sylow
409C22—22no—
410C22—41no—
411C22—41no—
412C22—102no—
413C22—201no—
414C22—201no—
415C22—202no—
416C22—202no—
417C22—202no—
418C22—408no—
419C22#9156311yescharacteristic
420C4—21no—
421C4—41no—
422C4—201no—
423C4—241no—
424C4#9129811yescharacteristic
425C4C2×#665511yescharacteristic
426C4D5×#21411yescharacteristic
427C4#9149111yescharacteristic
428C3#1060193611yescharacteristic, complemented, Sylow
429C2—42no—
430C2—202no—
431C2—402no—
432C2#1174852711yescharacteristic
433C2#1174904411yescharacteristic
434C2#1174941711yescharacteristic
subgroupG/H
centerC22#91563
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radicalC3×D4×D20C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#1629
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C5×#5008C2semidirect
3. #11747079C2semidirect
4. #11746880C2semidirect
5. D4⋊(C3⋊#168)C2semidirect
6. #11745852C2semidirect
7. #11745834C2semidirect
12. C5×#869C22semidirect
19. C4⋊(C3⋊#168)C22semidirect
20. C4×C3⋊#168C22semidirect
23. C5×C4⋊(C3⋊C8)C22semidirect
64. #5008D5semidirect
93. C3×C5×D4SD16semidirect
111. C3×D20SD16semidirect
126. #869C2×D5semidirect
132. C4⋊(C3⋊C8)C2×D5semidirect
222. C5×D4#214semidirect
239. D20#214semidirect
284. C3×D4#688semidirect
345. C3×C5#1629semidirect
388. D4#6655semidirect
408. C5#71907semidirect
428. C3#10601936semidirect

Maximal subgroups

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

subgroupindex
C3×D4×D202
C5×#50082
#117470792
#117468802
D4⋊(C3⋊#168)2
#117458522
#117458342
#106019363
#719075