Finite Group Databasebeta

← #14290620

Subgroups — #14290620

Order 1920.

400 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 92 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×#65918C211yesmaximal, characteristic
2#11751121C211yesmaximal, characteristic, complemented
3#11747062C211yesmaximal, characteristic
4#11746960C211yesmaximal, characteristic, complemented
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745856C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic
8#10599043—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91758C2211yescharacteristic
11C3×#4092—21no—
12C3×#4044—22no—
13C3×#4038—21no—
14C3×#4021—21no—
15C3×C4×D20C2211yescharacteristic
16C3×#4015C2211yescharacteristic
17C3×C4×Dic10—21no—
18C2×#6657—21no—
19#91119—21no—
20#91092—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C4×C5×C3⋊C8C2211yescharacteristic
24#90990—22no—
25#90974—21no—
26#71933—51nomaximal, Hall
27#65918D311yescharacteristic
28#65309—31no—
29#65130—31no—
30#64971—31no—
31C5×Q8⋊C8—31no—
32#64702—31no—
33#64679—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×Dic30—21no—
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5—21no—
38C2×C3×Dic10—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4D411yescharacteristic
41C3×C42×C5—21no—
42C3×C42×C5C2311yescharacteristic
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45C2×C3⋊#168—21no—
46C2×C5×C3⋊C8—21no—
47C2×C5×C3⋊C8—21no—
48C3×#685—22no—
49C3×#685—22no—
50C3×#685—21no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5D411yescharacteristic
53C3×C4⋊Dic5D412yes—
54C3×#683—22no—
55C3×C4×Dic5—22no—
56#6657—42no—
57C3×#556—51no—
58#5078—51no—
59#5020—51no—
60#5019—51no—
61#4547—51no—
62#4535D511yescharacteristic, complemented
63D4⋊(C3⋊C8)—51no—
64C4×C5×Q8C2×D311yescharacteristic
65#4092—21no—
66C2×#677—61no—
67#4044—22no—
68#4038—21no—
69#4021—21no—
70C4×D20C2×D311yescharacteristic
71#4015—31no—
72#4015C2×D311yescharacteristic
73C4×Dic10—21no—
74C5×C4⋊C8—31no—
75C4×C5×C8—31no—
76#3967—61no—
77#3950—62no—
78#3948—61no—
79#3940—61no—
80C4⋊#168—31no—
81#1650—151noSylow
82C22×C3×D5—21no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—41no—
91Dic30—41no—
92Dic30—41no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—22no—
95C3×D20—21no—
96C3×D20—21no—
97C3×C4×D5—41no—
98C3×C4×D5—41no—
99C3×Dic10—41no—
100C3×Dic10—41no—
101C3⋊#168—41no—
102C5×C3⋊C8—22no—
103C5×C3⋊C8—41no—
104C3×C4⋊Q8—51no—
105C3×#126—102no—
106C3×#124—101no—
107C3×C22⋊Q8—101no—
108C3×C4×Q8—101no—
109C3×C4×Q8C2×D511yescharacteristic
110C3×C4×D4—51no—
111C3×#117—101no—
112C2×#214—101no—
113#869—51no—
114#835—101no—
115#810—101no—
116#808—101no—
117#807—102no—
118C4⋊(C3⋊C8)—51no—
119C4⋊(C3⋊C8)C2×D511yescharacteristic
120C4×C3⋊C8C2×D511yescharacteristic
121C2×C5×Q8#6711yescharacteristic
122C2×D20#6711yescharacteristic
123C2×C4×D5—21no—
124C2×Dic10—21no—
125C2×Dic10—61no—
126C2×C5×C8—61no—
127C2×C5×C8—61no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4#6711yescharacteristic
130C42×C5—21no—
131C42×C5C22×D311yescharacteristic
132#685—22no—
133#685—22no—
134#685—21no—
135C4⋊Dic5—21no—
136C4⋊Dic5—61no—
137C4⋊Dic5—61no—
138C4⋊Dic5#6711yescharacteristic
139C4⋊Dic5#6712yes—
140#683—22no—
141C4×Dic5—22no—
142C2×#168—61no—
143#677—122no—
144#556—51no—
145#500—151no—
146#475—151no—
147#461—151no—
148#332—151no—
149Q8⋊C8—31no—
150D4⋊C8—151no—
151C22×C3×C5#12011yescharacteristic
152C2×C3×D5—41no—
153C2×C3×D5—41no—
154C2×C3×D5—41no—
155C3×C4×C5—21no—
156C3×C4×C5—41no—
157C3×C4×C5—41no—
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
161C3×C4×C5#13711yescharacteristic
162Dic15—81no—
163C3×Dic5—42no—
164C3×Dic5—41no—
165C2×C3×Q8—101no—
166C2×C3×Q8D2011yescharacteristic
167C2×C3×D4—51no—
168C22×C3×C4—101no—
169C2×Dic6—101no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—52no—
172C3×C4⋊C4—51no—
173C3×C4⋊C4—102no—
174C3×C4⋊C4—101no—
175C3×C4⋊C4D2011yescharacteristic
176C3×C22⋊C4—102no—
177C3×C22⋊C4—102no—
178C3×C22⋊C4—101no—
179C3×C42—21no—
180C3×C42—102no—
181C3×C42C22×D511yescharacteristic
182#214—202no—
183C4⋊Dic3—101no—
184C4⋊Dic3—101no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—101no—
188C22×D5—21no—
189C5×Q8—21no—
190C5×Q8—21no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5C2×#6711yescharacteristic
194C2×C4×C5C2×#6711yescharacteristic
195C2×C4×C5C2×#6711yescharacteristic
196C2×Dic5—21no—
197C2×Dic5—22no—
198C2×Dic5—121no—
199D20—21no—
200D20—21no—
201C4×D5—41no—
202C4×D5—41no—
203Dic10—41no—
204Dic10—41no—
205Dic10—121no—
206Dic10—121no—
207C5×C8—62no—
208C5×C8—121no—
209#168—121no—
210C2×SD16—301no—
211C4⋊Q8—51no—
212C4⋊Q8—151no—
213#126—102no—
214#124—101no—
215C22⋊Q8—101no—
216C4×Q8—101no—
217C4×Q8D3×D511yescharacteristic
218C4×D4—51no—
219#117—101no—
220#107—302no—
221#106—301no—
222C4⋊C8—31no—
223C4⋊C8—151no—
224#103—301no—
225#103—301no—
226C4×C8—31no—
227C2×C3×C5#44911yescharacteristic
228C2×C3×C5#45211yescharacteristic
229C2×C3×C5#45611yescharacteristic
230C3×D5—81no—
231C23×C3—101no—
232C3×Q8—21no—
233C3×Q8—21no—
234C3×Q8—201no—
235C3×Q8—201no—
236C3×D4—101no—
237C3×D4—101no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—101no—
241C2×C3×C4—102no—
242C2×C3×C4—201no—
243C2×C3×C4—201no—
244C2×C3×C4C2×D2011yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4D4×D511yescharacteristic
247C2×Dic3—201no—
248Dic6—201no—
249Dic6—201no—
250C3⋊C8—22no—
251C3⋊C8—41no—
252C3⋊C8—201no—
253C22×C5#95311yescharacteristic
254C2×D5—41no—
255C2×D5—41no—
256C2×D5—41no—
257C4×C5—21no—
258C4×C5—41no—
259C4×C5—41no—
260C4×C5#94911yescharacteristic
261C4×C5#95011yescharacteristic
262C4×C5#95011yescharacteristic
263C4×C5#95111yescharacteristic
264Dic5—42no—
265Dic5—41no—
266Dic5—241no—
267C2×Q8—101no—
268C2×Q8—301no—
269C2×Q8#120211yescharacteristic
270C2×D4—51no—
271C22×C4—101no—
272SD16—602no—
273C2×C8—61no—
274C2×C8—61no—
275C2×C8—301no—
276C4⋊C4—21no—
277C4⋊C4—51no—
278C4⋊C4—52no—
279C4⋊C4—102no—
280C4⋊C4—101no—
281C4⋊C4—301no—
282C4⋊C4—301no—
283C4⋊C4#120211yescharacteristic
284C22⋊C4—102no—
285C22⋊C4—102no—
286C22⋊C4—101no—
287C42—21no—
288C42—102no—
289C42C2×D3×D511yescharacteristic
290C3×C5#165011yescharacteristic, complemented, Hall
291C22×C3—201no—
292C22×C3—201no—
293C22×C3—201no—
294C22×C3#402811yescharacteristic
295C3×C4—21no—
296C3×C4—41no—
297C3×C4—41no—
298C3×C4—202no—
299C3×C4—201no—
300C3×C4#405011yescharacteristic
301C3×C4#405511yescharacteristic
302C3×C4#406011yescharacteristic
303C3×C4#406511yescharacteristic
304Dic3—401no—
305C2×C5#523811yescharacteristic
306C2×C5#523911yescharacteristic
307C2×C5#524611yescharacteristic
308D5—81no—
309C23—101no—
310Q8—21no—
311Q8—21no—
312Q8—201no—
313Q8—201no—
314Q8—601no—
315Q8—601no—
316D4—101no—
317D4—101no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—101no—
321C2×C4—102no—
322C2×C4—201no—
323C2×C4—201no—
324C2×C4—601no—
325C2×C4C2×#120211yescharacteristic
326C2×C4D5×#6711yescharacteristic
327C2×C4D5×#6711yescharacteristic
328C8—62no—
329C8—121no—
330C8—601no—
331C2×C3—401no—
332C2×C3#6502211yescharacteristic
333C2×C3#6510011yescharacteristic
334C2×C3#6511511yescharacteristic
335C5#7193311yescharacteristic, complemented, Sylow
336C22—201no—
337C22—201no—
338C22—201no—
339C22#9156411yescharacteristic
340C4—21no—
341C4—41no—
342C4—41no—
343C4—202no—
344C4—201no—
345C4—1201no—
346C4#9131111yescharacteristic
347C4#9131311yescharacteristic
348C4#9150211yescharacteristic
349C4#9151611yescharacteristic
350C3#1059904311yescharacteristic, complemented, Sylow
351C2—401no—
352C2#1174853111yescharacteristic
353C2#1174927211yescharacteristic
354C2#1174946411yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1650
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #11751121C2semidirect
4. #11746960C2semidirect
5. C5×#4535C2semidirect
6. #11745856C2semidirect
62. #4535D5semidirect
290. C3×C5#1650semidirect
335. C5#71933semidirect
350. C3#10599043semidirect

Maximal subgroups

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

subgroupindex
C3×#659182
#117511212
#117470622
#117469602
C5×#45352
#117458562
#117458352
#105990433
#719335