Finite Group Databasebeta

← #14295519

Subgroups — #14295519

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×#91990C211yesmaximal, characteristic
2#11752436C211yesmaximal, characteristic
3#11752350C212yesmaximal, complemented
4C3×#65029C211yesmaximal, characteristic
5#11746738C212yesmaximal, complemented
6#10603920—31nomaximal, Hall
7C2×C3×#711C2211yescharacteristic
8C2×#6762C411yescharacteristic, complemented
9C2×#6762C2212yes—
10C2×#6762C2211yescharacteristic
11C22×C3⋊#170C411yescharacteristic, complemented
12C22×C3⋊#170C2211yescharacteristic
13#91990—22no—
14#91990—22no—
15C2×#6758C411yescharacteristic, complemented
16C2×D5⋊(C3⋊C8)C411yescharacteristic, complemented
17C3×#4023C2212yes—
18#91242C412yescomplemented
19#91234C412yescomplemented
20#91231—22no—
21C4×C3⋊#170—22no—
22C3×C5×#99C411yescharacteristic
23C3×#3966C411yescharacteristic
24C3×#3938C412yes—
25#70040—51nomaximal, Hall
26C2×#4131—31no—
27#65777—31no—
28#65691—32no—
29#65029D311yescharacteristic
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#6762—22no—
42#6762—22no—
43#6762C2×C414yes—
44C2×C3⋊#170—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—
53#6758—22no—
54D5⋊(C3⋊C8)—21no—
55D5⋊(C3⋊C8)—21no—
56C3×C5×C22⋊C4C2×C412yes—
57C3×C22⋊Dic5C2×C412yes—
58C3×#683—22no—
59C3×C4×Dic5—22no—
60C2×#948—51no—
61C3×#410—51no—
62#5237—51no—
63#4997—52no—
64#4533—52no—
65C2×#711C2×D311yescharacteristic
66C2×#704—31no—
67C2×#704—31no—
68C2×#704—32no—
69C22×#170—31no—
70C22×#170—31no—
71#4131—62no—
72#4131—62no—
73C2×#700—31no—
74C2×D5⋊C8—31no—
75#4023C2×D312yes—
76#4013—32no—
77#4005—32no—
78#4002—62no—
79C4×#170—62no—
80C5×#99Dic311yescharacteristic
81#3966Dic311yescharacteristic
82#3938Dic312yes—
83#1757—151noSylow
84C23×C3×C5C4211yescharacteristic
85C23×C3×C5C22×C411yescharacteristic
86C22×C3×D5C4211yescharacteristic
87C3×C5×D4—22no—
88C2×C3×C4×C5—22no—
89C2×C3×C4×C5C4211yescharacteristic
90C3×C22⋊D5—22no—
91C3×C22⋊D5—22no—
92C2×C3×Dic5—21no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—22no—
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—21no—
104C3⋊#170—21no—
105C3⋊#170—24no—
106C3⋊#170C22⋊C411yescharacteristic
107C3⋊#170C22⋊C411yescharacteristic
108C3⋊#170C22⋊C412yes—
109C2×C3×#41—51no—
110C3×#117—52no—
111#948—102no—
112#948—102no—
113C2×#208—51no—
114C2×#208—51no—
115C2×#208—51no—
116C2×#208—52no—
117C22×C3⋊C8—51no—
118C22×C3⋊C8—51no—
119C22×C3⋊C8—51no—
120C3×#99—51no—
121C3×#99—52no—
122C3×#99AGL(1,𝔽5)11yescharacteristic
123#836—52no—
124#833—52no—
125#803—102no—
126C4×C3⋊C8—102no—
127C2×C5×D4C2×Dic311yescharacteristic
128C2×C22⋊D5C4×D311yescharacteristic
129C2×C22⋊D5C2×Dic311yescharacteristic
130C22×Dic5C4×D311yescharacteristic
131C22×Dic5C22×D311yescharacteristic
132#711—22no—
133#711—22no—
134C2×C4×D5C4×D311yescharacteristic
135C2×Dic10C4×D311yescharacteristic
136#704—34no—
137#704—62no—
138#704—62no—
139#704—62no—
140C2×#170—31no—
141C2×#170—31no—
142C2×#170—32no—
143C2×#170—32no—
144C2×#170—31no—
145C2×#170—31no—
146C2×#170—61no—
147C2×#170—61no—
148C2×#170—62no—
149#700—62no—
150D5⋊C8—61no—
151D5⋊C8—61no—
152C5×C22⋊C4C2×Dic312yes—
153C22⋊Dic5C2×Dic312yes—
154#683—22no—
155C4×Dic5—22no—
156C2×#131—151no—
157#413—151no—
158#410—51no—
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—
169C3×C4×C5—42no—
170C3×Dic5—21no—
171C3×Dic5—42no—
172C3×Dic5C2×C22⋊C411yescharacteristic
173C3×Dic5#11711yescharacteristic
174C3×Dic5C4×D412yes—
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×C4⋊C4—102no—
185C3×C22⋊C4—52no—
186C3×C22⋊C4C2×AGL(1,𝔽5)12yes—
187C3×C42—102no—
188#208—54no—
189#208—102no—
190#208—102no—
191#208—102no—
192#208—102no—
193C2×C3⋊C8—52no—
194C2×C3⋊C8—52no—
195C2×C3⋊C8—51no—
196C2×C3⋊C8—51no—
197C2×C3⋊C8—51no—
198C2×C3⋊C8—51no—
199C2×C3⋊C8—101no—
200C2×C3⋊C8—101no—
201C2×C3⋊C8—101no—
202C2×C3⋊C8—101no—
203C2×C3⋊C8—102no—
204C23×C5C4×Dic311yescharacteristic
205C23×C5C22×Dic311yescharacteristic
206C22×D5C4×Dic311yescharacteristic
207C5×D4—22no—
208C2×C4×C5—22no—
209C2×C4×C5C4×Dic311yescharacteristic
210C22⋊D5—22no—
211C22⋊D5—22no—
212C2×Dic5—21no—
213C2×Dic5—21no—
214C2×Dic5—22no—
215C2×Dic5C4×Dic311yescharacteristic
216C2×Dic5C2×C4×D311yescharacteristic
217C2×Dic5C2×C4×D311yescharacteristic
218C2×Dic5D3×D412yes—
219C2×Dic5#23712yes—
220C4×D5—21no—
221C4×D5—21no—
222Dic10—22no—
223#170—31no—
224#170—31no—
225#170—32no—
226#170—61no—
227#170—61no—
228#170—64no—
229C2×#41—51no—
230#131—302no—
231#131—302no—
232C2×M16—151no—
233C2×M16—151no—
234C2×M16—151no—
235C2×M16—152no—
236C22×C8—151no—
237C22×C8—151no—
238C22×C8—151no—
239#117—52no—
240#101—152no—
241#100—152no—
242#99—51no—
243#99—52no—
244#99ΓL(1,𝔽16)11yescharacteristic
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—22no—
260C2×C3×C4—51no—
261C2×C3×C4—51no—
262C2×C3×C4—52no—
263C2×C3×C4—52no—
264C2×C3×C4—51no—
265C2×C3×C4—101no—
266C2×C3×C4—101no—
267C2×C3×C4—101no—
268C2×C3×C4—101no—
269C2×C3×C4—102no—
270C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
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×C5D4×Dic312yes—
282C2×D5—21no—
283C2×D5—41no—
284C4×C5—21no—
285C4×C5—42no—
286Dic5—21no—
287Dic5—42no—
288Dic5#87711yescharacteristic
289Dic5D3×C22⋊C411yescharacteristic
290Dic5#67⋊C412yes—
291#41—102no—
292#41—102no—
293C2×Q8—51no—
294C2×D4—51no—
295C2×D4—51no—
296C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
297C22×C4—51no—
298C22×C4—51no—
299C22×C4—51no—
300M16—154no—
301M16—302no—
302M16—302no—
303M16—302no—
304M16—302no—
305C2×C8—152no—
306C2×C8—152no—
307C2×C8—151no—
308C2×C8—151no—
309C2×C8—151no—
310C2×C8—151no—
311C2×C8—301no—
312C2×C8—301no—
313C2×C8—301no—
314C2×C8—301no—
315C2×C8—302no—
316C4⋊C4—102no—
317C22⋊C4—52no—
318C22⋊C4C2×ΓL(1,𝔽16)12yes—
319C42—102no—
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—42no—
330C3×C4—51no—
331C3×C4—51no—
332C3×C4—52no—
333C3×C4—101no—
334C3×C4—202no—
335C2×C5—22no—
336C2×C5—21no—
337C2×C5—41no—
338C2×C5Dic3×C22⋊C411yescharacteristic
339D5—41no—
340C23—51no—
341C23C4×ΓL(1,𝔽16)11yescharacteristic
342C23C22×ΓL(1,𝔽16)11yescharacteristic
343Q8—102no—
344D4—22no—
345D4—102no—
346D4—102no—
347C2×C4—22no—
348C2×C4—51no—
349C2×C4—51no—
350C2×C4—52no—
351C2×C4—52no—
352C2×C4—51no—
353C2×C4—101no—
354C2×C4—101no—
355C2×C4—101no—
356C2×C4—101no—
357C2×C4—102no—
358C2×C4C4×ΓL(1,𝔽16)11yescharacteristic
359C8—151no—
360C8—151no—
361C8—152no—
362C8—301no—
363C8—301no—
364C8—304no—
365C2×C3—22no—
366C2×C3—21no—
367C2×C3—41no—
368C2×C3—201no—
369C2×C3C22⋊C4×AGL(1,𝔽5)11yescharacteristic
370C5#7004011yescharacteristic, complemented, Sylow
371C22—21no—
372C22—41no—
373C22—41no—
374C22—101no—
375C22—201no—
376C22C2×C4×ΓL(1,𝔽16)11yescharacteristic
377C22D4×ΓL(1,𝔽16)12yes—
378C4—21no—
379C4—42no—
380C4—51no—
381C4—52no—
382C4—51no—
383C4—101no—
384C4—202no—
385C3#1060392011yescharacteristic, complemented, Sylow
386C2—22no—
387C2—21no—
388C2—41no—
389C2—201no—
390C2C22⋊C4×ΓL(1,𝔽16)11yescharacteristic
subgroupG/H
centerC2C22⋊C4×ΓL(1,𝔽16)
commutatorC22×C3×C5C2×C42
FrattiniC23C22×ΓL(1,𝔽16)
FittingC3×C5×#99C4
socleC2×C3×C5C4×C22⋊C4
prime radicalC2×C3×#711C22
cosocleC22×C3×Dic5C23
hypercenter#99ΓL(1,𝔽16)
hypocenterC3×C5#1757
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
3. #11752350C2semidirect
5. #11746738C2semidirect
8. C2×#6762C4semidirect
11. C22×C3⋊#170C4semidirect
15. C2×#6758C4semidirect
16. C2×D5⋊(C3⋊C8)C4semidirect
18. #91242C4semidirect
19. #91234C4semidirect
320. C3×C5#1757semidirect
370. C5#70040semidirect
385. C3#10603920semidirect

Maximal subgroups

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

subgroupindex
C2×#919902
#117524362
#117523502
C3×#650292
#117467382
#106039203
#700405