Finite Group Databasebeta

← #14295967

Subgroups — #14295967

Order 1920.

600 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91284C211yesmaximal, characteristic
2#11751223C211yesmaximal, characteristic, complemented
3C2×C3×#3957C211yesmaximal, characteristic
4#11748365C211yesmaximal, characteristic
5C2×Dic5×C3⋊C8C211yesmaximal, characteristic, complemented
6C5×#4558C211yesmaximal, characteristic, complemented
7#11745978C211yesmaximal, characteristic, complemented
8#10599719—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11#91815C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C22×C5×C3⋊C8C2211yescharacteristic
15C2×C3×C4×Dic5C2211yescharacteristic
16C2×#6649—21no—
17#91284—22no—
18#91284C414yescomplemented
19C2×D5×C3⋊C8—21no—
20#91099—21no—
21C8×Dic15—21no—
22C3×#3957C414yescomplemented
23#90971C412yescomplemented
24#90965C412yescomplemented
25Dic5×C3⋊C8—22no—
26#70369—51nomaximal, Hall
27C2×#4053—31no—
28C2×#3957D311yescharacteristic
29#65411—31no—
30#65402—31no—
31C2×C8×Dic5—31no—
32C5×#341—31no—
33#64775—31no—
34C22×C3×C4×C5C2311yescharacteristic
35C2×C3×C22⋊D5—21no—
36C22×C3×Dic5—21no—
37C3×#709—21no—
38C3×#709—21no—
39C3×#709C2×C412yes—
40C3×#709C2×C412yes—
41C2×C3×D20C2×C411yescharacteristic
42C2×C3×C4×D5—21no—
43C2×C3×Dic10C2×C411yescharacteristic
44C3×C5×M16—21no—
45C3×C5×M16C2×C412yes—
46C2×C3×C5×C8—21no—
47#6719—21no—
48C4⋊Dic15C2×C412yes—
49C4×Dic15—21no—
50C2×C3⋊#168C2×C412yes—
51C2×C3⋊#168D412yes—
52C2×C3⋊#168D411yescharacteristic
53C2×C3⋊#168D411yescharacteristic
54C5×#208—21no—
55C5×#208C2×C412yes—
56C2×C5×C3⋊C8—21no—
57C2×C5×C3⋊C8—21no—
58C2×C5×C3⋊C8—21no—
59C2×C5×C3⋊C8C2×C412yes—
60C3×C4×Dic5—21no—
61C3×C4×Dic5C2×C412yes—
62#6649—24no—
63D5×C3⋊C8—24no—
64C2×#948—51no—
65C2×C3×#104—51no—
66#5233—51no—
67#5122—51no—
68C2×C4×C3⋊C8—51no—
69#4558D511yescharacteristic, complemented
70#4523—51no—
71C2×#709C2×D311yescharacteristic
72C2×C5×M16—31no—
73C2×C5×M16C2×D311yescharacteristic
74C22×C5×C8—31no—
75#4072—31no—
76C2×C4×Dic5C2×D311yescharacteristic
77C22×#168—31no—
78#4053—34no—
79#4053—62no—
80C2×#676—61no—
81C2×C8×D5—61no—
82#3957Dic314yescomplemented
83#3953—32no—
84#3948—32no—
85#3947—61no—
86C8×Dic5—62no—
87C8×Dic5—61no—
88#1764—151noSylow
89C23×C3×C5#4111yescharacteristic
90C22×C3×D5—21no—
91C2×C3×C4×C5C22×C411yescharacteristic
92C2×C3×C4×C5C22×C411yescharacteristic
93C2×C3×C4×C5C22×C411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5#4111yescharacteristic
97C2×Dic15—22no—
98C3×C22⋊D5—22no—
99C3×C22⋊D5—22no—
100C2×C3×Dic5—24no—
101C2×C3×Dic5—22no—
102C2×C3×Dic5—21no—
103C3×D20—21no—
104C3×D20C4212yes—
105C3×C4×D5—22no—
106C3×C4×D5—22no—
107C3×Dic10—21no—
108C3×Dic10C4212yes—
109C3×C5×C8—22no—
110C3⋊#168C22⋊C412yes—
111C3⋊#168C22⋊C412yes—
112C5×C3⋊C8—22no—
113C5×C3⋊C8—22no—
114C2×C3×#41—51no—
115C2×C3×M16C2×D511yescharacteristic
116C2×C3×C42—51no—
117#948—54no—
118#948—102no—
119#926—51no—
120C2×#208—101no—
121C2×#208C2×D511yescharacteristic
122C22×C3⋊C8—51no—
123C22×C3⋊C8—101no—
124C22×C3⋊C8C2×D511yescharacteristic
125C3×#104—54no—
126#835—52no—
127#832—52no—
128#815—101no—
129C8×Dic3—101no—
130C4×C3⋊C8—102no—
131C22×C4×C5C22×D311yescharacteristic
132C2×C22⋊D5—21no—
133C22×Dic5—21no—
134#709—21no—
135#709—21no—
136#709C4×D312yes—
137#709C2×Dic312yes—
138C2×D20C4×D311yescharacteristic
139C2×C4×D5—21no—
140C2×Dic10C4×D311yescharacteristic
141C5×M16—21no—
142C5×M16—32no—
143C5×M16—61no—
144C5×M16C2×Dic312yes—
145C2×C5×C8—21no—
146C2×C5×C8—32no—
147C2×C5×C8—61no—
148C2×C5×C8—61no—
149C2×C5×C8—61no—
150C22⋊Dic5—61no—
151C4⋊Dic5—32no—
152C4×Dic5—21no—
153C4×Dic5—61no—
154C4×Dic5C2×Dic312yes—
155C2×#168—32no—
156C2×#168—31no—
157C2×#168—32no—
158C2×#168—31no—
159#676—64no—
160C8×D5—64no—
161C2×#131—151no—
162C2×#104—51no—
163#416—151no—
164#405—151no—
165C2×C4×C8—151no—
166#341—31no—
167#339—151no—
168C22×C3×C5—22no—
169C22×C3×C5#11711yescharacteristic
170C22×C3×C5C4×D411yescharacteristic
171C22×C3×C5C4×D411yescharacteristic
172C2×C3×D5—22no—
173C2×C3×D5—42no—
174C3×C4×C5C2×C4211yescharacteristic
175C3×C4×C5C2×C22⋊C411yescharacteristic
176C3×C4×C5C4×D411yescharacteristic
177C3×C4×C5C4×D411yescharacteristic
178Dic15—42no—
179C3×Dic5—24no—
180C3×Dic5—22no—
181C3×#41—52no—
182C3×#41—52no—
183C3×#41—101no—
184C3×#41—101no—
185C2×C3×Q8—51no—
186C2×C3×D4—51no—
187C2×C3×D4—101no—
188C22×C3×C4—101no—
189C22×C3×C4—101no—
190C22×C3×C4C22×D511yescharacteristic
191C3×M16—21no—
192C3×M16C4×D512yes—
193C2×C3×C8—21no—
194C3×C42—52no—
195C3×C42—101no—
196#217—101no—
197C4⋊Dic3—52no—
198C4×Dic3—101no—
199#208—21no—
200#208—104no—
201#208C4×D512yes—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—21no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—52no—
206C2×C3⋊C8—52no—
207C2×C3⋊C8—51no—
208C2×C3⋊C8—51no—
209C2×C3⋊C8—104no—
210C2×C3⋊C8C4×D512yes—
211C23×C5#23711yescharacteristic
212C22×D5—21no—
213C2×C4×C5C2×C4×D311yescharacteristic
214C2×C4×C5C2×C4×D311yescharacteristic
215C2×C4×C5D3×D411yescharacteristic
216C2×C4×C5D3×D411yescharacteristic
217C2×C4×C5#23711yescharacteristic
218C2×C4×C5C22×Dic311yescharacteristic
219C22⋊D5—22no—
220C22⋊D5—22no—
221C2×Dic5—24no—
222C2×Dic5—21no—
223C2×Dic5—22no—
224C2×Dic5—62no—
225D20—21no—
226D20C4×Dic312yes—
227C4×D5—22no—
228C4×D5—22no—
229Dic10—21no—
230Dic10C4×Dic312yes—
231C5×C8—22no—
232C5×C8—62no—
233C5×C8—62no—
234#168—32no—
235#168—32no—
236C2×#41—51no—
237#131—154no—
238#131—302no—
239C2×M16—31no—
240C2×M16—301no—
241C2×M16D3×D511yescharacteristic
242C22×C8—31no—
243C22×C8—151no—
244C22×C8—301no—
245#117—151no—
246C2×C42—51no—
247#104—54no—
248#103—152no—
249#102—152no—
250#97—301no—
251C4×C8—302no—
252C4×C8—301no—
253C2×C3×C5—21no—
254C2×C3×C5—21no—
255C2×C3×C5C4×C22⋊C411yescharacteristic
256C2×C3×C5#44312yes—
257C3×D5—42no—
258C23×C3—101no—
259C23×C3#71311yescharacteristic
260C3×Q8—52no—
261C3×Q8—101no—
262C3×D4—52no—
263C3×D4—102no—
264C3×D4—102no—
265C3×D4—101no—
266C2×C3×C4—104no—
267C2×C3×C4—102no—
268C2×C3×C4—101no—
269C2×C3×C4—102no—
270C2×C3×C4—102no—
271C2×C3×C4C2×C4×D511yescharacteristic
272C2×C3×C4C2×C4×D511yescharacteristic
273C2×C3×C4C2×C4×D511yescharacteristic
274C2×C3×C4D4×D511yescharacteristic
275C2×C3×C4D4×D511yescharacteristic
276C2×C3×C4#71111yescharacteristic
277C2×Dic3—102no—
278C3×C8—22no—
279C3⋊C8—22no—
280C3⋊C8—22no—
281C3⋊C8—52no—
282C3⋊C8—52no—
283C22×C5—22no—
284C22×C5#87711yescharacteristic
285C22×C5#67⋊C411yescharacteristic
286C22×C5D4×Dic311yescharacteristic
287C2×D5—22no—
288C2×D5—42no—
289C4×C5D3×C22⋊C411yescharacteristic
290C4×C5#67⋊C411yescharacteristic
291C4×C5C2×C4×Dic311yescharacteristic
292C4×C5D4×Dic311yescharacteristic
293Dic5—24no—
294Dic5—22no—
295Dic5—122no—
296#41—52no—
297#41—52no—
298#41—101no—
299#41—101no—
300C2×Q8—51no—
301C2×D4—51no—
302C2×D4—101no—
303C22×C4—101no—
304C22×C4—101no—
305C22×C4C2×D3×D511yescharacteristic
306M16—21no—
307M16—32no—
308M16—61no—
309M16—304no—
310M16D5×Dic312yes—
311C2×C8—21no—
312C2×C8—32no—
313C2×C8—61no—
314C2×C8—61no—
315C2×C8—61no—
316C2×C8—152no—
317C2×C8—152no—
318C2×C8—151no—
319C2×C8—151no—
320C2×C8—304no—
321C4⋊C4—152no—
322C22⋊C4—301no—
323C42—52no—
324C42—101no—
325C42—301no—
326C3×C5#176411yescharacteristic, complemented, Hall
327C22×C3—22no—
328C22×C3—102no—
329C22×C3—202no—
330C22×C3#403811yescharacteristic
331C22×C3#403911yescharacteristic
332C22×C3#403911yescharacteristic
333C3×C4—104no—
334C3×C4—102no—
335C3×C4C42×D511yescharacteristic
336C3×C4D5×C22⋊C411yescharacteristic
337C3×C4#402711yescharacteristic
338C3×C4#402711yescharacteristic
339Dic3—202no—
340C2×C5—21no—
341C2×C5—21no—
342C2×C5#482412yes—
343C2×C5Dic3×C22⋊C411yescharacteristic
344D5—42no—
345C23—101no—
346C23#676611yescharacteristic
347Q8—52no—
348Q8—101no—
349D4—52no—
350D4—102no—
351D4—102no—
352D4—101no—
353C2×C4—104no—
354C2×C4—101no—
355C2×C4—102no—
356C2×C4—102no—
357C2×C4—102no—
358C2×C4—302no—
359C2×C4C4×D3×D511yescharacteristic
360C2×C4C4×D3×D511yescharacteristic
361C2×C4#677711yescharacteristic
362C2×C4C2×D5×Dic311yescharacteristic
363C2×C4#678011yescharacteristic
364C2×C4#679011yescharacteristic
365C8—22no—
366C8—62no—
367C8—62no—
368C8—152no—
369C8—152no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—202no—
373C2×C3#6495511yescharacteristic
374C2×C3#6518412yes—
375C5#7036911yescharacteristic, complemented, Sylow
376C22—22no—
377C22—102no—
378C22—202no—
379C22#9139411yescharacteristic
380C22#9139611yescharacteristic
381C22#9143411yescharacteristic
382C4—104no—
383C4—102no—
384C4—602no—
385C4C4×D5×Dic311yescharacteristic
386C4#9144211yescharacteristic
387C4#9147311yescharacteristic
388C4#9155911yescharacteristic
389C3#1059971911yescharacteristic, complemented, Sylow
390C2—21no—
391C2—21no—
392C2—202no—
393C2#1174817412yes—
394C2#1174888411yescharacteristic
subgroupG/H
centerC2×C4#6790
commutatorC3×C4×C5C2×C42
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C4×D4
prime radicalC2×C3×#709C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1764
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #11751223C2semidirect
5. C2×Dic5×C3⋊C8C2semidirect
6. C5×#4558C2semidirect
7. #11745978C2semidirect
18. #91284C4semidirect
22. C3×#3957C4semidirect
23. #90971C4semidirect
24. #90965C4semidirect
69. #4558D5semidirect
82. #3957Dic3semidirect
326. C3×C5#1764semidirect
375. C5#70369semidirect
389. C3#10599719semidirect

Maximal subgroups

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

subgroupindex
C2×#912842
#117512232
C2×C3×#39572
#117483652
C2×Dic5×C3⋊C82
C5×#45582
#117459782
#105997193
#703695