Finite Group Databasebeta

← #14299877

Subgroups — #14299877

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
1#11754125C211yesmaximal, characteristic
2#11751225C211yesmaximal, characteristic, complemented
3C5×#5139C211yesmaximal, characteristic
4C3×#65407C211yesmaximal, characteristic, complemented
5C2×#90979C211yesmaximal, characteristic
6#11745988C211yesmaximal, characteristic, complemented
7#11745977C211yesmaximal, characteristic, complemented
8#10601191—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C3×C4×Dic5C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91288—22no—
17D3×#681—22no—
18#91286—22no—
19#91106—22no—
20C5×#825—22no—
21C3×#3946—22no—
22#90979C412yescomplemented
23#90979C412yescomplemented
24#70530—51nomaximal, Hall
25#66153—31no—
26C5×#421—31no—
27C2×#3969—31no—
28#65413—31no—
29#65407D311yescharacteristic, complemented
30#64753—31no—
31#64752—31no—
32C22×C3×C4×C5C2311yescharacteristic
33C2×C5×#67—21no—
34C5×#235—21no—
35C5×#235—21no—
36C5×#235C2×C412yes—
37C5×#235D412yes—
38C2×C5×D12Q811yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C5×Dic6Q811yescharacteristic
41C22×C3×Dic5—21no—
42C3×C5×M16—21no—
43C3×C5×M16—21no—
44C2×C3×C5×C8—21no—
45#6710—21no—
46#6710—21no—
47#6710C2×C412yes—
48#6710D412yes—
49C2×C3⋊#168—21no—
50C2×C3⋊#168—21no—
51C5×#217—21no—
52C5×C4⋊Dic3—21no—
53C4×C5×Dic3—21no—
54C3×C4×Dic5—21no—
55C3×C4×Dic5C2×C411yescharacteristic
56C3×C4×Dic5C2×C411yescharacteristic
57C3×#681—21no—
58C3×#681—21no—
59C2×C3×#168D412yes—
60#6650—24no—
61D3×#168—24no—
62#5745—51no—
63C3×#423—51no—
64#5139D511yescharacteristic
65#5124—51no—
66C2×#805—51no—
67#4556—51no—
68#4523—51no—
69C2×C5×#41—31no—
70C2×C5×M16C2×D311yescharacteristic
71C5×#117—31no—
72#4094—62no—
73#4094—62no—
74C2×C4×Dic5C2×D311yescharacteristic
75C2×#681—31no—
76C2×#681—31no—
77C2×#681—62no—
78C2×#681C2×D311yescharacteristic
79C5×#104—62no—
80#3969—32no—
81#3969—32no—
82#3954—62no—
83#3946—22no—
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
93C5×#67—22no—
94C5×#67—22no—
95C2×C5×Dic3—21no—
96C2×C5×Dic3—41no—
97C5×D12—21no—
98C5×D12C4⋊C412yes—
99C4×C5×D3—22no—
100C4×C5×D3—22no—
101C5×Dic6—21no—
102C5×Dic6C4⋊C412yes—
103C2×C3×Dic5—21no—
104C2×C3×Dic5—21no—
105C2×C3×Dic5—42no—
106C3×C5×C8—41no—
107C3⋊#168—22no—
108C3⋊#168—22no—
109C3×#168—22no—
110C2×#235C2×D511yescharacteristic
111C2×C3×M16—51no—
112C2×C3×M16C2×D511yescharacteristic
113C2×C3×C42—51no—
114#926C2×D511yescharacteristic
115C2×#208—51no—
116C2×#208—51no—
117#907—102no—
118D3×M16—102no—
119#901—102no—
120C3×C4⋊C8—102no—
121#825—22no—
122#822—102no—
123#805—52no—
124#805—52no—
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—21no—
135C5×M16—21no—
136C5×M16—21no—
137C2×C5×C8—21no—
138C5×C4⋊C4—61no—
139C5×C22⋊C4—61no—
140C42×C5—61no—
141C4×Dic5—21no—
142C4×Dic5C4×D311yescharacteristic
143C4×Dic5C4×D311yescharacteristic
144#681—21no—
145#681—21no—
146#681—32no—
147#681—32no—
148#681—64no—
149#681—61no—
150#681—61no—
151C2×#168—64no—
152C2×#168—61no—
153C2×#168—61no—
154C2×#168#6712yes—
155#568—151no—
156#430—151no—
157#423—51no—
158#421—31no—
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
172C3×Dic5—22no—
173C3×Dic5—41no—
174C5×Dic3—22no—
175C5×Dic3—81no—
176C22×C3×C4—101no—
177C22×C3×C4C22×D511yescharacteristic
178C2×#67—21no—
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—21no—
188C3×M16—101no—
189C3×M16—101no—
190C2×C3×C8—21no—
191C2×C3×C8—52no—
192C3×C42—51no—
193C3×C42—51no—
194C3×C42—101no—
195#217—21no—
196C4⋊Dic3—21no—
197C4×Dic3—21no—
198#208—52no—
199#208—52no—
200#208—101no—
201#208—101no—
202C2×C3⋊C8—101no—
203C2×C3⋊C8—101no—
204ΓL(1,𝔽25)—104no—
205D3×C8—104no—
206C23×C5—61no—
207C23×C5#23511yescharacteristic
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×C5—121no—
218C2×C4×C5C2×C4×D311yescharacteristic
219C2×C4×C5D3×D411yescharacteristic
220C2×C4×C5D3×D411yescharacteristic
221C2×C4×C5D3×Q811yescharacteristic
222C2×C4×C5#23911yescharacteristic
223C2×C4×C5C2×#6711yescharacteristic
224C2×Dic5—21no—
225C2×Dic5—21no—
226C2×Dic5—42no—
227C5×C8—41no—
228#168—22no—
229#168—62no—
230#168—62no—
231C2×#41—31no—
232#131—302no—
233#131—302no—
234C2×M16—51no—
235C2×M16—151no—
236C2×M16—151no—
237C2×M16—302no—
238C2×M16D3×D511yescharacteristic
239#117—31no—
240C2×C42—51no—
241#108—302no—
242C4⋊C8—102no—
243#104—62no—
244#104—152no—
245#104—152no—
246C2×C3×C5—21no—
247C2×C3×C5—21no—
248C2×C3×C5—21no—
249C2×C3×C5#38511yescharacteristic
250C5×D3—42no—
251C23×C3#71111yescharacteristic
252C22×D3—21no—
253C2×C3×C4—101no—
254C2×C3×C4—101no—
255C2×C3×C4—202no—
256C2×C3×C4C2×Dic1011yescharacteristic
257C2×C3×C4C2×C4×D511yescharacteristic
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4#71111yescharacteristic
261C2×C3×C4C2×C22⋊D511yescharacteristic
262#67—22no—
263#67—22no—
264C2×Dic3—21no—
265C2×Dic3—41no—
266D12—21no—
267D12#68312yes—
268C4×D3—22no—
269C4×D3—22no—
270Dic6—21no—
271Dic6#68312yes—
272C3×C8—41no—
273C3×C8—102no—
274C3⋊C8—102no—
275C3⋊C8—102no—
276C22×C5—41no—
277C22×C5—62no—
278C22×C5—241no—
279C22×C5#89411yescharacteristic
280C22×C5#89611yescharacteristic
281C22×C5C4×#6711yescharacteristic
282C4×C5—62no—
283C4×C5—241no—
284C4×C5D3×C4⋊C411yescharacteristic
285C4×C5#89311yescharacteristic
286C4×C5#93711yescharacteristic
287C4×C5#94611yescharacteristic
288Dic5—22no—
289Dic5—41no—
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—101no—
299C22×C4C2×D3×D511yescharacteristic
300M16—21no—
301M16—21no—
302M16—101no—
303M16—101no—
304M16—152no—
305M16—152no—
306M16—304no—
307M16—301no—
308M16—301no—
309C2×C8—21no—
310C2×C8—52no—
311C2×C8—304no—
312C2×C8—301no—
313C2×C8—301no—
314C4⋊C4—61no—
315C22⋊C4—61no—
316C42—51no—
317C42—51no—
318C42—61no—
319C42—101no—
320C3×C5#186111yescharacteristic, complemented, Hall
321C22×C3—41no—
322C22×C3#402411yescharacteristic
323C22×C3#402711yescharacteristic
324C22×C3#408111yescharacteristic
325C2×D3—22no—
326C2×D3—81no—
327C3×C4—102no—
328C3×C4—201no—
329C3×C4#402411yescharacteristic
330C3×C4#402711yescharacteristic
331C3×C4C2×#68311yescharacteristic
332C3×C4#408311yescharacteristic
333Dic3—22no—
334Dic3—81no—
335C2×C5—21no—
336C2×C5—21no—
337C2×C5—21no—
338C2×C5—122no—
339C2×C5#498911yescharacteristic
340C23—61no—
341C23#677211yescharacteristic
342Q8—32no—
343Q8—61no—
344D4—32no—
345D4—62no—
346D4—62no—
347D4—61no—
348C2×C4—61no—
349C2×C4—62no—
350C2×C4—62no—
351C2×C4—101no—
352C2×C4—101no—
353C2×C4—121no—
354C2×C4—202no—
355C2×C4D3×Dic1011yescharacteristic
356C2×C4#676811yescharacteristic
357C2×C4C4×D3×D511yescharacteristic
358C2×C4D5×#6711yescharacteristic
359C2×C4D3×C22⋊D511yescharacteristic
360C2×C4#679011yescharacteristic
361C8—41no—
362C8—102no—
363C8—302no—
364C8—302no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3#6523511yescharacteristic
369D3—42no—
370C5#7053011yescharacteristic, complemented, Sylow
371C22—41no—
372C22—62no—
373C22—241no—
374C22#9142311yescharacteristic
375C22#9143211yescharacteristic
376C22#9144011yescharacteristic
377C4—62no—
378C4—102no—
379C4—201no—
380C4—241no—
381C4D3×#68311yescharacteristic
382C4#9140611yescharacteristic
383C4#9141011yescharacteristic
384C4#9157711yescharacteristic
385C3#1060119111yescharacteristic, complemented, Sylow
386C2—21no—
387C2—21no—
388C2—21no—
389C2—122no—
390C2#1174889211yescharacteristic
subgroupG/H
centerC4#91577
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. #11751225C2semidirect
4. C3×#65407C2semidirect
6. #11745988C2semidirect
7. #11745977C2semidirect
22. #90979C4semidirect
23. #90979C4semidirect
29. #65407D3semidirect
320. C3×C5#1861semidirect
370. C5#70530semidirect
385. C3#10601191semidirect

Maximal subgroups

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

subgroupindex
#117541252
#117512252
C5×#51392
C3×#654072
C2×#909792
#117459882
#117459772
#106011913
#705305