Finite Group Databasebeta

← #14295558

Subgroups — #14295558

Order 1920.

568 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
1C2×C3×#4131C211yesmaximal, characteristic
2#11752436C211yesmaximal, characteristic
3#11751988C212yesmaximal, complemented
4#11749172C211yesmaximal, characteristic
5#11746575C212yesmaximal, complemented
6#10603920—31nomaximal, Hall
7C2×C3×#711C2211yescharacteristic
8C2×#6762C2212yes—
9C2×C3×#704C411yescharacteristic, complemented
10C2×C3×#704C2211yescharacteristic
11C22×C3×#170C411yescharacteristic, complemented
12C22×C3×#170C2211yescharacteristic
13C3×#4131—22no—
14C3×#4131—22no—
15C2×C3×#700C411yescharacteristic, complemented
16C2×C3×D5⋊C8C411yescharacteristic, complemented
17#91528C2212yes—
18#91242C412yescomplemented
19#91234C412yescomplemented
20#91169—22no—
21Dic3×#170—22no—
22#91118C411yescharacteristic
23C5×#834C411yescharacteristic
24#90995C412yes—
25#72011—51nomaximal, Hall
26C2×#4131D311yescharacteristic
27#65777—31no—
28#65691—32no—
29#65029—31no—
30#64867—32no—
31C2×C3×C5×D4C2×C411yescharacteristic
32C2×C3×C22⋊D5C2×C411yescharacteristic
33C2×C3×C22⋊D5C2×C411yescharacteristic
34C22×C3×Dic5C2×C411yescharacteristic
35C22×C3×Dic5C2311yescharacteristic
36C3×#711—22no—
37C3×#711—22no—
38C2×C3×C4×D5C2×C411yescharacteristic
39C2×C3×Dic10C2×C411yescharacteristic
40#6762—22no—
41#6762C2×C414yes—
42C2×C3⋊#170—22no—
43C3×#704—22no—
44C3×#704—22no—
45C2×C3×#170—21no—
46C2×C3×#170—21no—
47C2×C3×#170C2×C411yescharacteristic
48C2×C3×#170C2×C411yescharacteristic
49C2×C3×#170C2×C411yescharacteristic
50C2×C3×#170C2×C411yescharacteristic
51C2×C3×#170D412yes—
52C2×C3×#170D412yes—
53C3×#700—22no—
54C3×D5⋊C8—21no—
55C3×D5⋊C8—21no—
56#6719C2×C412yes—
57C5×#217C2×C412yes—
58#6668—22no—
59Dic3×Dic5—22no—
60C2×C3×#131—51no—
61#5240—51no—
62#5237—51no—
63#5101—52no—
64#4556—52no—
65C2×#711C2×D311yescharacteristic
66C2×#704—32no—
67C2×#704Dic311yescharacteristic, complemented
68C2×#704C2×D311yescharacteristic
69C22×#170Dic311yescharacteristic, complemented
70C22×#170C2×D311yescharacteristic
71#4131—22no—
72#4131—22no—
73C2×#700Dic311yescharacteristic, complemented
74C2×D5⋊C8Dic311yescharacteristic, complemented
75#4023—32no—
76#4013—32no—
77#4005—32no—
78#4002—62no—
79C4×#170—62no—
80C5×#99—31no—
81#3966—31no—
82#3938—32no—
83#1757—151noSylow
84C23×C3×C5C4211yescharacteristic
85C23×C3×C5C22×C411yescharacteristic
86C22×C3×D5C4211yescharacteristic
87C3×C5×D4—22no—
88C2×C3×C4×C5C4211yescharacteristic
89C2×Dic15—22no—
90C2×C5×Dic3—22no—
91C3×C22⋊D5—22no—
92C3×C22⋊D5—22no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5C4211yescharacteristic
96C2×C3×Dic5C22×C411yescharacteristic
97C2×C3×Dic5C22×C411yescharacteristic
98C2×C3×Dic5C2×D412yes—
99C2×C3×Dic5#4112yes—
100C3×C4×D5—21no—
101C3×C4×D5—21no—
102C3×Dic10—22no—
103C3⋊#170—24no—
104C3×#170—21no—
105C3×#170—21no—
106C3×#170C22⋊C411yescharacteristic
107C3×#170C22⋊C411yescharacteristic
108C3×#170C22⋊C412yes—
109C2×C3×#41—51no—
110C3×#131—102no—
111C3×#131—102no—
112C2×C3×M16—51no—
113C2×C3×M16—51no—
114C2×C3×M16—51no—
115C22×C3×C8—51no—
116C22×C3×C8—51no—
117C22×C3×C8—51no—
118#926—52no—
119C2×#208—52no—
120#836—52no—
121#834—51no—
122#834—52no—
123#834AGL(1,𝔽5)11yescharacteristic
124#833—52no—
125#815—102no—
126C8×Dic3—102no—
127C2×C5×D4C4×D311yescharacteristic
128C2×C22⋊D5C4×D311yescharacteristic
129C2×C22⋊D5C4×D311yescharacteristic
130C22×Dic5C2×Dic311yescharacteristic
131C22×Dic5C22×D311yescharacteristic
132#711—22no—
133#711—22no—
134C2×C4×D5C2×Dic311yescharacteristic
135C2×Dic10C4×D311yescharacteristic
136#704—22no—
137#704—22no—
138#704—34no—
139#704—62no—
140C2×#170—21no—
141C2×#170—21no—
142C2×#170—62no—
143C2×#170C2×Dic311yescharacteristic
144C2×#170C2×Dic311yescharacteristic
145C2×#170C2×Dic311yescharacteristic
146C2×#170C2×Dic311yescharacteristic
147C2×#170#6712yes—
148C2×#170#6712yes—
149#700—22no—
150D5⋊C8—21no—
151D5⋊C8—21no—
152C5×C22⋊C4—32no—
153C22⋊Dic5—32no—
154#683—62no—
155C4×Dic5—62no—
156C2×#131—51no—
157#413—151no—
158#410—151no—
159#405—152no—
160#344—152no—
161C22×C3×C5—21no—
162C22×C3×C5—41no—
163C22×C3×C5—41no—
164C22×C3×C5C2×C4211yescharacteristic
165C22×C3×C5C4×D412yes—
166C2×C3×D5—21no—
167C2×C3×D5—41no—
168C3×C4×C5—21no—
169Dic15—42no—
170C3×Dic5—21no—
171C3×Dic5C2×C22⋊C411yescharacteristic
172C3×Dic5#11711yescharacteristic
173C3×Dic5C4×D412yes—
174C5×Dic3—42no—
175C3×#41—102no—
176C3×#41—102no—
177C2×C3×Q8—51no—
178C2×C3×D4—51no—
179C2×C3×D4—51no—
180C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
181C22×C3×C4—51no—
182C22×C3×C4—51no—
183C22×C3×C4—51no—
184C3×M16—102no—
185C3×M16—102no—
186C3×M16—102no—
187C2×C3×C8—52no—
188C2×C3×C8—52no—
189C2×C3×C8—51no—
190C2×C3×C8—51no—
191C2×C3×C8—51no—
192C2×C3×C8—51no—
193C2×C3×C8—101no—
194C2×C3×C8—101no—
195C2×C3×C8—101no—
196C2×C3×C8—101no—
197#217—52no—
198#217C2×AGL(1,𝔽5)12yes—
199C4⋊Dic3—102no—
200C4×Dic3—102no—
201#208—54no—
202#208—102no—
203C2×C3⋊C8—102no—
204C23×C5C4×Dic311yescharacteristic
205C23×C5C2×C4×D311yescharacteristic
206C22×D5C4×Dic311yescharacteristic
207C5×D4—22no—
208C2×C4×C5—62no—
209C2×C4×C5C4×Dic311yescharacteristic
210C22⋊D5—22no—
211C22⋊D5—22no—
212C2×Dic5—21no—
213C2×Dic5—21no—
214C2×Dic5—62no—
215C2×Dic5C4×Dic311yescharacteristic
216C2×Dic5C2×C4×D311yescharacteristic
217C2×Dic5#23512yes—
218C2×Dic5C22×Dic311yescharacteristic
219C2×Dic5C2×#6712yes—
220C4×D5—21no—
221C4×D5—21no—
222Dic10—22no—
223#170—21no—
224#170—21no—
225#170—64no—
226#170#21711yescharacteristic
227#170#21711yescharacteristic
228#170#21712yes—
229C2×#41—51no—
230#131—102no—
231#131—102no—
232C2×M16—51no—
233C2×M16—51no—
234C2×M16—51no—
235C2×M16—152no—
236C22×C8—51no—
237C22×C8—51no—
238C22×C8—51no—
239#117—152no—
240#101—152no—
241#100—152no—
242#99—31no—
243#99—152no—
244#99—151no—
245#97—302no—
246C4×C8—302no—
247C2×C3×C5—22no—
248C2×C3×C5—21no—
249C2×C3×C5—41no—
250C2×C3×C5C4×C22⋊C411yescharacteristic
251C3×D5—41no—
252C23×C3—51no—
253C23×C3C4×AGL(1,𝔽5)11yescharacteristic
254C23×C3C22×AGL(1,𝔽5)11yescharacteristic
255C3×Q8—102no—
256C3×D4—22no—
257C3×D4—102no—
258C3×D4—102no—
259C2×C3×C4—51no—
260C2×C3×C4—51no—
261C2×C3×C4—52no—
262C2×C3×C4—52no—
263C2×C3×C4—51no—
264C2×C3×C4—101no—
265C2×C3×C4—101no—
266C2×C3×C4—101no—
267C2×C3×C4—101no—
268C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
269C2×Dic3—22no—
270C2×Dic3—102no—
271C3×C8—51no—
272C3×C8—51no—
273C3×C8—52no—
274C3×C8—101no—
275C3×C8—101no—
276C3⋊C8—104no—
277C22×C5—21no—
278C22×C5—41no—
279C22×C5—41no—
280C22×C5C2×C4×Dic311yescharacteristic
281C22×C5C4×#6712yes—
282C2×D5—21no—
283C2×D5—41no—
284C4×C5—21no—
285C4×C5—122no—
286Dic5—21no—
287Dic5—122no—
288Dic5#92611yescharacteristic
289Dic5C4×#6712yes—
290Dic5C2×#21711yescharacteristic
291#41—102no—
292#41—102no—
293C2×Q8—51no—
294C2×D4—51no—
295C2×D4—51no—
296C2×D4D3×AGL(1,𝔽5)11yescharacteristic
297C22×C4—51no—
298C22×C4—51no—
299C22×C4—51no—
300M16—102no—
301M16—102no—
302M16—102no—
303M16—154no—
304M16—302no—
305C2×C8—52no—
306C2×C8—52no—
307C2×C8—51no—
308C2×C8—51no—
309C2×C8—51no—
310C2×C8—51no—
311C2×C8—101no—
312C2×C8—101no—
313C2×C8—101no—
314C2×C8—101no—
315C2×C8—302no—
316C4⋊C4—302no—
317C22⋊C4—32no—
318C22⋊C4—152no—
319C42—302no—
320C3×C5#175711yescharacteristic, complemented, Hall
321C22×C3—21no—
322C22×C3—41no—
323C22×C3—41no—
324C22×C3—101no—
325C22×C3—201no—
326C22×C3C2×C4×AGL(1,𝔽5)11yescharacteristic
327C22×C3D4×AGL(1,𝔽5)12yes—
328C3×C4—21no—
329C3×C4—51no—
330C3×C4—51no—
331C3×C4—52no—
332C3×C4—101no—
333Dic3—42no—
334Dic3—202no—
335C2×C5—22no—
336C2×C5—21no—
337C2×C5—41no—
338C2×C5C4×#21711yescharacteristic
339D5—41no—
340C23—51no—
341C23Dic3×AGL(1,𝔽5)11yescharacteristic
342C23C2×D3×AGL(1,𝔽5)11yescharacteristic
343Q8—102no—
344D4—22no—
345D4—102no—
346D4—102no—
347C2×C4—51no—
348C2×C4—51no—
349C2×C4—52no—
350C2×C4—52no—
351C2×C4—51no—
352C2×C4—62no—
353C2×C4—101no—
354C2×C4—101no—
355C2×C4—101no—
356C2×C4—101no—
357C2×C4—302no—
358C2×C4Dic3×AGL(1,𝔽5)11yescharacteristic
359C8—51no—
360C8—51no—
361C8—52no—
362C8—101no—
363C8—101no—
364C8—304no—
365C2×C3—22no—
366C2×C3—21no—
367C2×C3—41no—
368C2×C3—201no—
369C2×C3C22⋊C4×AGL(1,𝔽5)11yescharacteristic
370C5#7201111yescharacteristic, complemented, Sylow
371C22—21no—
372C22—41no—
373C22—41no—
374C22—101no—
375C22—201no—
376C22C2×Dic3×AGL(1,𝔽5)11yescharacteristic
377C22AGL(1,𝔽5)×#6712yes—
378C4—21no—
379C4—51no—
380C4—52no—
381C4—51no—
382C4—101no—
383C4—122no—
384C4—602no—
385C3#1060392011yescharacteristic, complemented, Sylow
386C2—22no—
387C2—21no—
388C2—41no—
389C2—201no—
390C2AGL(1,𝔽5)×#21711yescharacteristic
subgroupG/H
centerC2AGL(1,𝔽5)×#217
commutatorC22×C3×C5C2×C42
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC2×C3×C5C4×C22⋊C4
prime radicalC2×C3×#711C22
cosocleC22×C3×Dic5C23
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#1757
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C23 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
3. #11751988C2semidirect
5. #11746575C2semidirect
9. C2×C3×#704C4semidirect
11. C22×C3×#170C4semidirect
15. C2×C3×#700C4semidirect
16. C2×C3×D5⋊C8C4semidirect
18. #91242C4semidirect
19. #91234C4semidirect
67. C2×#704Dic3semidirect
69. C22×#170Dic3semidirect
73. C2×#700Dic3semidirect
74. C2×D5⋊C8Dic3semidirect
320. C3×C5#1757semidirect
370. C5#72011semidirect
385. C3#10603920semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41312
#117524362
#117519882
#117491722
#117465752
#106039203
#720115