Finite Group Databasebeta

← #14299882

Subgroups — #14299882

Order 1920.

524 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5745C211yesmaximal, characteristic
2C3×#65413C211yesmaximal, characteristic, complemented
3#11748437C211yesmaximal, characteristic, complemented
4#11748424C211yesmaximal, characteristic
5C2×#90978C211yesmaximal, characteristic
6#11746376C211yesmaximal, characteristic, complemented
7#11745990C211yesmaximal, characteristic, complemented
8#10602821—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C5×#907—22no—
15C5×D3×M16—22no—
16C5×#901—22no—
17C2×C3×#681C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19C3×#3954—22no—
20#90983—22no—
21#90978—22no—
22#90978C412yescomplemented
23#90978C412yescomplemented
24#70735—51nomaximal, Hall
25C5×#568—31no—
26#65525—31no—
27C2×#3969—31no—
28#65413D311yescharacteristic, complemented
29#65407—31no—
30#64776—31no—
31#64775—31no—
32C22×C3×C4×C5C2311yescharacteristic
33C22×Dic15—21no—
34C2×C5×#67—21no—
35C5×#235—21no—
36C5×#235—21no—
37C5×#235C2×C412yes—
38C5×#235D412yes—
39C2×C5×D12Q811yescharacteristic
40C2×C4×C5×D3—21no—
41C2×C5×Dic6Q811yescharacteristic
42C3×C5×M16—21no—
43C3×C5×M16D412yes—
44C2×C3×C5×C8—21no—
45#6719—21no—
46C4⋊Dic15—21no—
47C4×Dic15—21no—
48C4×Dic15—21no—
49C4×Dic15C2×C411yescharacteristic
50C4×Dic15C2×C411yescharacteristic
51C5×#208—21no—
52C5×#208—21no—
53C2×C5×C3⋊C8D412yes—
54C5×ΓL(1,𝔽25)—24no—
55C5×D3×C8—24no—
56C3×#681—21no—
57C3×#681—21no—
58C3×#681—21no—
59C3×#681C2×C412yes—
60C2×C3×#168—21no—
61C2×C3×#168—21no—
62#5745D511yescharacteristic
63C3×#430—51no—
64#5139—51no—
65C2×#825—51no—
66#5118—51no—
67#4559—51no—
68#4555—51no—
69C2×C5×#41—31no—
70C5×#131—62no—
71C5×#131—62no—
72C2×C5×M16—31no—
73C2×C5×M16—62no—
74C2×C5×M16C2×D311yescharacteristic
75#4072—31no—
76C2×C4×Dic5—31no—
77C2×#681C2×D311yescharacteristic
78C2×#681C2×D311yescharacteristic
79#3969—32no—
80#3969—32no—
81#3969—62no—
82#3954—22no—
83#3946—62no—
84#1861—151noSylow
85C23×C3×C5#4111yescharacteristic
86C22×C5×D3—21no—
87C2×C3×C4×C5C22×C411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×Q811yescharacteristic
92C2×C3×C4×C5#4111yescharacteristic
93C2×Dic15—21no—
94C2×Dic15—21no—
95C2×Dic15—42no—
96C2×Dic15—41no—
97C5×#67—22no—
98C5×#67—22no—
99C2×C5×Dic3—21no—
100C5×D12—21no—
101C5×D12C4⋊C412yes—
102C4×C5×D3—22no—
103C4×C5×D3—22no—
104C5×Dic6—21no—
105C5×Dic6C4⋊C412yes—
106C3×C5×C8—22no—
107C3×#168—22no—
108C3×#168—41no—
109C5×C3⋊C8—22no—
110C2×#235C2×D511yescharacteristic
111C2×C3×M16—51no—
112C2×C3×M16—51no—
113C2×C3×M16C2×D511yescharacteristic
114#926—51no—
115C2×C4×Dic3—51no—
116C2×#208C2×D511yescharacteristic
117#907—22no—
118D3×M16—22no—
119#901—22no—
120C3×#108—102no—
121#825—52no—
122#825—52no—
123#825—102no—
124Dic3⋊C8—102no—
125C5×#41—32no—
126C5×#41—32no—
127C5×#41—61no—
128C5×#41—61no—
129C2×C5×Q8—31no—
130C2×C5×D4—31no—
131C2×C5×D4—61no—
132C22×C4×C5—61no—
133C22×C4×C5C22×D311yescharacteristic
134C22×Dic5—61no—
135C5×M16—21no—
136C5×M16—64no—
137C5×M16—61no—
138C5×M16—61no—
139C5×M16#6712yes—
140C2×C5×C8—21no—
141C2×C5×C8—32no—
142C2×C5×C8—64no—
143C22⋊Dic5—61no—
144C4⋊Dic5—61no—
145C4×Dic5—31no—
146C4×Dic5—31no—
147C4×Dic5—61no—
148C4×Dic5—61no—
149#681—21no—
150#681—21no—
151#681—21no—
152#681C4×D312yes—
153C2×#168—21no—
154C2×#168—21no—
155#568—31no—
156#430—51no—
157#423—151no—
158#421—151no—
159C2×#104—151no—
160#344—151no—
161#339—151no—
162C22×C3×C5—41no—
163C22×C3×C5C4×D411yescharacteristic
164C22×C3×C5C22⋊Q811yescharacteristic
165C22×C3×C5#12311yescharacteristic
166C2×C5×D3—22no—
167C2×C5×D3—81no—
168C3×C4×C5C2×C4⋊C411yescharacteristic
169C3×C4×C5C4×D411yescharacteristic
170C3×C4×C5#12011yescharacteristic
171C3×C4×C5C22⋊Q811yescharacteristic
172Dic15—22no—
173Dic15—41no—
174Dic15—81no—
175C5×Dic3—22no—
176C22×C3×C4C22×D511yescharacteristic
177C2×#67—21no—
178C22×Dic3—101no—
179#235—21no—
180#235—21no—
181#235C4×D512yes—
182#235C22⋊D512yes—
183C2×D12Dic1011yescharacteristic
184C2×C4×D3—21no—
185C2×Dic6Dic1011yescharacteristic
186C3×M16—21no—
187C3×M16—52no—
188C3×M16—101no—
189C3×M16—101no—
190C3×M16—101no—
191C3×M16C22⋊D512yes—
192C2×C3×C8—21no—
193C2×C3×C8—101no—
194C2×C3×C8—101no—
195#217—101no—
196C4⋊Dic3—101no—
197C4×Dic3—51no—
198C4×Dic3—51no—
199C4×Dic3—101no—
200C4×Dic3—101no—
201#208—21no—
202#208—21no—
203C2×C3⋊C8C22⋊D512yes—
204ΓL(1,𝔽25)—24no—
205D3×C8—24no—
206C23×C5—61no—
207C23×C5#23911yescharacteristic
208C5×Q8—32no—
209C5×Q8—61no—
210C5×D4—32no—
211C5×D4—62no—
212C5×D4—62no—
213C5×D4—61no—
214C2×C4×C5—61no—
215C2×C4×C5—62no—
216C2×C4×C5—62no—
217C2×C4×C5C2×C4×D311yescharacteristic
218C2×C4×C5#23511yescharacteristic
219C2×C4×C5D3×D411yescharacteristic
220C2×C4×C5D3×D411yescharacteristic
221C2×C4×C5D3×Q811yescharacteristic
222C2×C4×C5C2×#6711yescharacteristic
223C2×Dic5—61no—
224C2×Dic5—61no—
225C2×Dic5—122no—
226C2×Dic5—121no—
227C5×C8—22no—
228C5×C8—62no—
229#168—22no—
230#168—41no—
231C2×#41—31no—
232#131—62no—
233#131—62no—
234C2×M16—31no—
235C2×M16—51no—
236C2×M16—51no—
237C2×M16—62no—
238C2×M16D3×D511yescharacteristic
239#117—151no—
240C2×C42—151no—
241#108—102no—
242C4⋊C8—302no—
243#104—152no—
244#104—152no—
245#104—302no—
246C2×C3×C5—21no—
247C2×C3×C5—21no—
248C2×C3×C5—21no—
249C2×C3×C5#38511yescharacteristic
250C5×D3—42no—
251C23×C3#70911yescharacteristic
252C22×D3—21no—
253C2×C3×C4C2×Dic1011yescharacteristic
254C2×C3×C4C2×C4×D511yescharacteristic
255C2×C3×C4#70911yescharacteristic
256C2×C3×C4C2×C22⋊D511yescharacteristic
257C2×C3×C4C2×C22⋊D511yescharacteristic
258C2×C3×C4C2×C22⋊D511yescharacteristic
259#67—22no—
260#67—22no—
261C2×Dic3—21no—
262C2×Dic3—101no—
263C2×Dic3—101no—
264C2×Dic3—202no—
265C2×Dic3—201no—
266D12—21no—
267D12#68312yes—
268C4×D3—22no—
269C4×D3—22no—
270Dic6—21no—
271Dic6#68312yes—
272C3×C8—22no—
273C3×C8—102no—
274C3×C8—201no—
275C3⋊C8—22no—
276C22×C5—41no—
277C22×C5—62no—
278C22×C5—241no—
279C22×C5#89311yescharacteristic
280C22×C5#89411yescharacteristic
281C22×C5#94611yescharacteristic
282C4×C5—62no—
283C4×C5D3×C4⋊C411yescharacteristic
284C4×C5#89611yescharacteristic
285C4×C5C4×#6711yescharacteristic
286C4×C5#93711yescharacteristic
287Dic5—62no—
288Dic5—121no—
289Dic5—241no—
290#41—32no—
291#41—32no—
292#41—61no—
293#41—61no—
294C2×Q8—31no—
295C2×D4—31no—
296C2×D4—61no—
297C22×C4—61no—
298C22×C4—301no—
299C22×C4C2×D3×D511yescharacteristic
300M16—21no—
301M16—52no—
302M16—64no—
303M16—61no—
304M16—61no—
305M16—101no—
306M16—101no—
307M16—101no—
308M16#120112yes—
309C2×C8—21no—
310C2×C8—32no—
311C2×C8—64no—
312C2×C8—101no—
313C2×C8—101no—
314C4⋊C4—301no—
315C22⋊C4—301no—
316C42—151no—
317C42—151no—
318C42—301no—
319C42—301no—
320C3×C5#186111yescharacteristic, complemented, Hall
321C22×C3—41no—
322C22×C3#407011yescharacteristic
323C22×C3C4×C22⋊D511yescharacteristic
324C22×C3#407511yescharacteristic
325C2×D3—22no—
326C2×D3—81no—
327C3×C4C2×#68311yescharacteristic
328C3×C4#407011yescharacteristic
329C3×C4C4×C22⋊D511yescharacteristic
330C3×C4#409911yescharacteristic
331Dic3—22no—
332Dic3—102no—
333Dic3—201no—
334Dic3—401no—
335C2×C5—21no—
336C2×C5—21no—
337C2×C5—21no—
338C2×C5—122no—
339C2×C5#498911yescharacteristic
340C23—61no—
341C23#676911yescharacteristic
342Q8—32no—
343Q8—61no—
344D4—32no—
345D4—62no—
346D4—62no—
347D4—61no—
348C2×C4—61no—
349C2×C4—62no—
350C2×C4—62no—
351C2×C4—301no—
352C2×C4—301no—
353C2×C4—602no—
354C2×C4—601no—
355C2×C4D3×Dic1011yescharacteristic
356C2×C4#677111yescharacteristic
357C2×C4C4×D3×D511yescharacteristic
358C2×C4C2×#120111yescharacteristic
359C2×C4D3×C22⋊D511yescharacteristic
360C2×C4D3×C22⋊D511yescharacteristic
361C8—22no—
362C8—62no—
363C8—102no—
364C8—201no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3#6549911yescharacteristic
369D3—42no—
370C5#7073511yescharacteristic, complemented, Sylow
371C22—41no—
372C22—62no—
373C22—241no—
374C22#9135111yescharacteristic
375C22#9136911yescharacteristic
376C22#9144611yescharacteristic
377C4—62no—
378C4—302no—
379C4—601no—
380C4—1201no—
381C4#9135211yescharacteristic
382C4D3×#68311yescharacteristic
383C4C4×#120111yescharacteristic
384C4#9156811yescharacteristic
385C3#1060282111yescharacteristic, complemented, Sylow
386C2—21no—
387C2—21no—
388C2—21no—
389C2—122no—
390C2#1174871611yescharacteristic
subgroupG/H
centerC4#91568
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#385
prime radicalC2×C5×#235C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1861
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C3×#65413C2semidirect
3. #11748437C2semidirect
6. #11746376C2semidirect
7. #11745990C2semidirect
22. #90978C4semidirect
23. #90978C4semidirect
28. #65413D3semidirect
320. C3×C5#1861semidirect
370. C5#70735semidirect
385. C3#10602821semidirect

Maximal subgroups

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

subgroupindex
C5×#57452
C3×#654132
#117484372
#117484242
C2×#909782
#117463762
#117459902
#106028213
#707355