Finite Group Databasebeta

← #14289136

Subgroups — #14289136

Order 1920.

512 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 96 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×#65885C211yesmaximal, characteristic, complemented
2C5×#5015C211yesmaximal, characteristic, complemented
3#11747026C211yesmaximal, characteristic, complemented
4#11746901C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
6#11745855C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10601805—31nomaximal, Hall
9C2×C3×#709—21no—
10C3×C4×C5×D4C2211yescharacteristic
11C2×C5×#213—21no—
12C5×#874C2211yescharacteristic
13C3×#4084—21no—
14C3×#4070—21no—
15C3×D5×C4⋊C4—21no—
16C3×#4029—22no—
17C3×C4×D20C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19C2×#6652—21no—
20C4⋊(C3⋊#168)C2211yescharacteristic
21C4×C3⋊#168C2211yescharacteristic
22C5×#809—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24#90966—22no—
25#90966—21no—
26#71910—51nomaximal, Hall
27#65885D311yescharacteristic, complemented
28C5×#459—31no—
29#65361—31no—
30#65359—31no—
31D4⋊#168—31no—
32#64706—31no—
33#64703—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C5×D12—21no—
39C2×C3×C22⋊D5—22no—
40C3×#709—42no—
41C3×#709—42no—
42C2×C3×D20D411yescharacteristic
43C2×C3×C4×D5—22no—
44C2×C3×C4×D5—21no—
45C2×C3×Dic10—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C5×C22⋊C4—21no—
48C3×C42×C5C2311yescharacteristic
49C2×C3⋊#168—21no—
50C2×C3⋊#168—21no—
51C5×#213—42no—
52C2×C5×C3⋊C8—21no—
53C3×C22⋊Dic5—22no—
54C3×#685—21no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5D412yes—
57C3×C4⋊Dic5D411yescharacteristic
58C3×#683—22no—
59#6652—42no—
60C3×#547—51no—
61#5088—51no—
62#5015—51no—
63#5015D511yescharacteristic, complemented
64#4547—51no—
65D4⋊(C3⋊C8)—51no—
66D4⋊(C3⋊C8)—51no—
67C2×#709—21no—
68C2×C5×D8—61no—
69C5×#127—31no—
70C4×C5×D4C2×D311yescharacteristic
71#4084—21no—
72C2×#686—61no—
73#4070—21no—
74D5×C4⋊C4—21no—
75#4029—22no—
76C4×D20C2×D311yescharacteristic
77#4015C2×D311yescharacteristic
78C5×C4⋊C8—31no—
79C5×#102—61no—
80#3964—62no—
81#3964—61no—
82C4⋊#168—31no—
83C4×#168—31no—
84#1625—151noSylow
85C23×C3×C5—21no—
86C22×C5×D3—41no—
87C22×C3×D5—21no—
88C3×C5×D4—21no—
89C3×C5×D4—21no—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C5×D12—42no—
97C5×D12—41no—
98C5×D12—41no—
99C5×D12—41no—
100C5×D12—41no—
101C3×C22⋊D5—44no—
102C2×C3×Dic5—21no—
103C2×C3×Dic5—22no—
104C3×D20—21no—
105C3×D20D812yescomplemented
106C3×C4×D5—44no—
107C3×C4×D5—41no—
108C3×C4×D5—41no—
109C3×Dic10—41no—
110C3×Dic10—41no—
111C3⋊#168—41no—
112C3⋊#168—41no—
113C5×C3⋊C8—41no—
114C2×C3×#41—101no—
115C3×C4⋊Q8—51no—
116C3×#123—102no—
117C3×C22⋊Q8—101no—
118C3×#121—101no—
119C3×C4×D4—51no—
120C3×C4×D4C2×D511yescharacteristic
121C2×C3×C4⋊C4—101no—
122C2×#213—21no—
123C2×#213—101no—
124#874C2×D511yescharacteristic
125#809—21no—
126#809—101no—
127#809—102no—
128C4⋊(C3⋊C8)—51no—
129C4⋊(C3⋊C8)C2×D511yescharacteristic
130C4×C3⋊C8—51no—
131C2×C5×D4—61no—
132C2×C5×D4—61no—
133C2×C5×D4—61no—
134C2×C5×D4#6711yescharacteristic
135C22×C4×C5—21no—
136C2×C22⋊D5—22no—
137#709—42no—
138#709—42no—
139C2×D20#6711yescharacteristic
140C2×C4×D5—22no—
141C2×C4×D5—21no—
142C2×Dic10—21no—
143C5×D8—122no—
144C2×C5×C8—61no—
145C5×C4⋊C4#6711yescharacteristic
146C5×C22⋊C4—21no—
147C42×C5C22×D311yescharacteristic
148C22⋊Dic5—22no—
149#686—122no—
150#685—21no—
151C4⋊Dic5—21no—
152C4⋊Dic5#6712yes—
153C4⋊Dic5#6711yescharacteristic
154#683—22no—
155C2×#168—61no—
156C2×#168—61no—
157#547—51no—
158#486—151no—
159#459—31no—
160#459—151no—
161#332—151no—
162D4⋊C8—151no—
163D4⋊C8—151no—
164C22×C3×C5—41no—
165C22×C3×C5—41no—
166C22×C3×C5—41no—
167C22×C3×C5#12011yescharacteristic
168C2×C5×D3—81no—
169C2×C5×D3—81no—
170C2×C5×D3—81no—
171C2×C3×D5—22no—
172C2×C3×D5—41no—
173C2×C3×D5—41no—
174C3×C4×C5—21no—
175C3×C4×C5—41no—
176C3×C4×C5C2×D811yescharacteristic
177C3×C4×C5#13511yescharacteristic
178C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
179C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
180C3×Dic5—42no—
181C3×Dic5—41no—
182C3×#41—202no—
183C3×#41—202no—
184C2×C3×Q8—101no—
185C2×C3×D4—51no—
186C2×C3×D4—102no—
187C2×C3×D4C22⋊D511yescharacteristic
188C22×C3×C4—21no—
189C22×C3×C4—102no—
190C22×C3×C4—101no—
191C2×D12—21no—
192C2×D12—21no—
193C2×D12—21no—
194C3×C4⋊C4—51no—
195C3×C4⋊C4—52no—
196C3×C4⋊C4—102no—
197C3×C4⋊C4—101no—
198C3×C4⋊C4C22⋊D511yescharacteristic
199C3×C22⋊C4—21no—
200C3×C22⋊C4—102no—
201C3×C22⋊C4—101no—
202C3×C42C22×D511yescharacteristic
203#213—42no—
204#213—202no—
205C2×C3⋊C8—21no—
206C2×C3⋊C8—101no—
207C2×C3⋊C8—101no—
208C23×C5—21no—
209C23×C5—121no—
210C22×D5—21no—
211C5×D4—21no—
212C5×D4—21no—
213C5×D4—122no—
214C5×D4—121no—
215C5×D4—121no—
216C5×D4—121no—
217C5×D4—121no—
218C2×C4×C5—21no—
219C2×C4×C5—41no—
220C2×C4×C5—41no—
221C2×C4×C5C2×#6711yescharacteristic
222C2×C4×C5C2×#6711yescharacteristic
223C2×C4×C5C2×#6711yescharacteristic
224C22⋊D5—44no—
225C2×Dic5—21no—
226C2×Dic5—22no—
227D20—21no—
228D20#21312yescomplemented
229C4×D5—44no—
230C4×D5—41no—
231C4×D5—41no—
232Dic10—41no—
233Dic10—41no—
234C5×C8—121no—
235#168—121no—
236#168—121no—
237C2×#41—101no—
238C2×D8—61no—
239C2×D8—301no—
240C4⋊Q8—51no—
241#127—31no—
242#123—102no—
243C22⋊Q8—101no—
244#121—101no—
245C4×D4—51no—
246C4×D4D3×D511yescharacteristic
247C2×C4⋊C4—101no—
248C4⋊C8—31no—
249C4⋊C8—151no—
250#102—61no—
251#102—301no—
252#102—302no—
253C4×C8—151no—
254C2×C3×C5—81no—
255C2×C3×C5#44711yescharacteristic
256C2×C3×C5#44911yescharacteristic
257C2×C3×C5#45411yescharacteristic
258C3×D5—42no—
259C5×D3—161no—
260C23×C3—21no—
261C23×C3—101no—
262C22×D3—41no—
263C3×Q8—201no—
264C3×Q8—201no—
265C3×D4—21no—
266C3×D4—21no—
267C3×D4—52no—
268C3×D4—101no—
269C3×D4—204no—
270C2×C3×C4—21no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—101no—
274C2×C3×C4—102no—
275C2×C3×C4—204no—
276C2×C3×C4—201no—
277C2×C3×C4—201no—
278C2×C3×C4D4×D511yescharacteristic
279C2×C3×C4D4×D511yescharacteristic
280C2×C3×C4C2×C22⋊D511yescharacteristic
281D12—42no—
282D12—41no—
283D12—41no—
284D12—41no—
285D12—41no—
286C3⋊C8—41no—
287C3⋊C8—201no—
288C3⋊C8—201no—
289C22×C5—41no—
290C22×C5—41no—
291C22×C5—41no—
292C22×C5—241no—
293C22×C5—241no—
294C22×C5—241no—
295C22×C5#95311yescharacteristic
296C2×D5—22no—
297C2×D5—41no—
298C2×D5—41no—
299C4×C5—21no—
300C4×C5—41no—
301C4×C5C2×#21311yescharacteristic
302C4×C5#93211yescharacteristic
303C4×C5#94911yescharacteristic
304C4×C5#95011yescharacteristic
305Dic5—42no—
306Dic5—41no—
307#41—202no—
308#41—202no—
309C2×Q8—101no—
310C2×D4—51no—
311C2×D4—61no—
312C2×D4—61no—
313C2×D4—61no—
314C2×D4—102no—
315C2×D4#120111yescharacteristic
316C22×C4—21no—
317C22×C4—102no—
318C22×C4—101no—
319D8—122no—
320D8—602no—
321C2×C8—61no—
322C2×C8—301no—
323C2×C8—301no—
324C4⋊C4—51no—
325C4⋊C4—52no—
326C4⋊C4—102no—
327C4⋊C4—101no—
328C4⋊C4#120111yescharacteristic
329C22⋊C4—21no—
330C22⋊C4—102no—
331C22⋊C4—101no—
332C42C2×D3×D511yescharacteristic
333C3×C5#162511yescharacteristic, complemented, Hall
334C22×C3—41no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3—102no—
338C22×C3—201no—
339C22×C3—201no—
340C22×C3#408311yescharacteristic
341C2×D3—81no—
342C2×D3—81no—
343C2×D3—81no—
344C3×C4—21no—
345C3×C4—41no—
346C3×C4—201no—
347C3×C4—202no—
348C3×C4D5×D811yescharacteristic
349C3×C4#405711yescharacteristic
350C3×C4#407811yescharacteristic
351C3×C4#409611yescharacteristic
352C2×C5—81no—
353C2×C5—481no—
354C2×C5#521711yescharacteristic
355C2×C5#523811yescharacteristic
356C2×C5#524511yescharacteristic
357D5—42no—
358C23—21no—
359C23—101no—
360C23—121no—
361Q8—201no—
362Q8—201no—
363D4—21no—
364D4—21no—
365D4—52no—
366D4—101no—
367D4—122no—
368D4—121no—
369D4—121no—
370D4—121no—
371D4—121no—
372D4—204no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—101no—
377C2×C4—102no—
378C2×C4—204no—
379C2×C4—201no—
380C2×C4—201no—
381C2×C4C2×#120111yescharacteristic
382C2×C4D5×#6711yescharacteristic
383C2×C4D5×#6711yescharacteristic
384C8—121no—
385C8—601no—
386C8—601no—
387C2×C3—81no—
388C2×C3—202no—
389C2×C3#6532611yescharacteristic
390C2×C3#6544511yescharacteristic
391C2×C3#6549011yescharacteristic
392D3—161no—
393C5#7191011yescharacteristic, complemented, Sylow
394C22—41no—
395C22—41no—
396C22—41no—
397C22—102no—
398C22—201no—
399C22—201no—
400C22—241no—
401C22—241no—
402C22—241no—
403C22#9156311yescharacteristic
404C4—21no—
405C4—41no—
406C4—202no—
407C4—201no—
408C4#9129711yescharacteristic
409C4#9129911yescharacteristic
410C4D5×#21311yescharacteristic
411C4#9148911yescharacteristic
412C3#1060180511yescharacteristic, complemented, Sylow
413C2—81no—
414C2—202no—
415C2—481no—
416C2#1174851111yescharacteristic
417C2#1174902111yescharacteristic
418C2#1174945611yescharacteristic
subgroupG/H
centerC22#91563
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
hypercenterC4×D4D3×D5
hypocenterC3×C5#1625
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
1. C3×#65885C2semidirect
2. C5×#5015C2semidirect
3. #11747026C2semidirect
4. #11746901C2semidirect
5. D4⋊(C3⋊#168)C2semidirect
6. #11745855C2semidirect
7. #11745834C2semidirect
27. #65885D3semidirect
63. #5015D5semidirect
105. C3×D20D8semidirect
228. D20#213semidirect
333. C3×C5#1625semidirect
393. C5#71910semidirect
412. C3#10601805semidirect

Maximal subgroups

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

subgroupindex
C3×#658852
C5×#50152
#117470262
#117469012
D4⋊(C3⋊#168)2
#117458552
#117458342
#106018053
#719105