Finite Group Databasebeta

← #14298610

Subgroups — #14298610

Order 1920.

524 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic5×#235C211yesmaximal, characteristic
2C5×#5132C211yesmaximal, characteristic
3#11748625C211yesmaximal, characteristic
4#11746378C211yesmaximal, characteristic, complemented
5C3×#64775C211yesmaximal, characteristic, complemented
6#11745978C211yesmaximal, characteristic, complemented
7#11745970C211yesmaximal, characteristic, complemented
8#10600924—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11#91815C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C3×#4072C2211yescharacteristic
15C2×C3×C4×Dic5C2211yescharacteristic
16Dic5×#67—22no—
17Dic5×D12—21no—
18C4×D3×Dic5C412yescomplemented
19#91371C412yescomplemented
20Dic5×Dic6—21no—
21C5×#824—21no—
22C5×#823—21no—
23#90996—22no—
24#68737—51nomaximal, Hall
25#41×Dic5—31no—
26C5×#413—31no—
27#65529—31no—
28#64777—31no—
29#64777—31no—
30#64775—31no—
31#64775D311yescharacteristic, complemented
32C22×C3×C4×C5C2311yescharacteristic
33C2×C5×#67D412yes—
34C5×#235—21no—
35C5×#235—21no—
36C5×#235—21no—
37C5×#235—21no—
38C2×C5×D12D411yescharacteristic
39C2×C4×C5×D3C2×C412yes—
40C2×C5×Dic6D411yescharacteristic
41C22×C3×Dic5—21no—
42C2×D3×Dic5—22no—
43C3×C5×M16—21no—
44C3×C5×M16—21no—
45C2×C3×C5×C8—21no—
46#6719—21no—
47#6719—21no—
48C4⋊Dic15—21no—
49C4⋊Dic15—21no—
50C4×Dic15—21no—
51C4×Dic15C2×C412yes—
52C5×#208—21no—
53C5×#208—21no—
54C2×C5×C3⋊C8—21no—
55C3×C22⋊Dic5—21no—
56C3×C4⋊Dic5—21no—
57C3×C4×Dic5—21no—
58C3×C4×Dic5—21no—
59C3×C4×Dic5C2×C411yescharacteristic
60C3×C4×Dic5C2×C411yescharacteristic
61Dic3⋊Dic5—22no—
62(C2×D3)⋊Dic5—22no—
63Dic3×Dic5—22no—
64C4×#235—51no—
65#5132D511yescharacteristic
66#5006—51no—
67C3×#339—51no—
68#4557—51no—
69#4531—51no—
70#4523—51no—
71C2×C5×#41—31no—
72C2×C5×M16—31no—
73C2×C5×M16C2×D311yescharacteristic
74Q8×Dic5—61no—
75D4×Dic5—61no—
76D4×Dic5—62no—
77#4072—31no—
78#4072—32no—
79#4072—31no—
80#4072C2×D311yescharacteristic
81C2×C4×Dic5—32no—
82C2×C4×Dic5C2×D311yescharacteristic
83C5×#101—61no—
84C5×#100—61no—
85#3966—62no—
86#1827—151noSylow
87C23×C3×C5C2×D411yescharacteristic
88C22×C5×D3C22⋊C412yes—
89C2×C3×C4×C5C22×C411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5#4111yescharacteristic
92C2×C3×C4×C5#4111yescharacteristic
93C2×C3×C4×C5#4111yescharacteristic
94C2×C3×C4×C5#4111yescharacteristic
95C2×Dic15—22no—
96C2×Dic15—41no—
97C5×#67—22no—
98C5×#67—22no—
99C2×C5×Dic3C22⋊C412yes—
100C5×D12—21no—
101C5×D12—21no—
102C4×C5×D3—22no—
103C4×C5×D3—22no—
104C5×Dic6—21no—
105C5×Dic6—21no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—42no—
109C2×C3×Dic5—41no—
110D3×Dic5—44no—
111C3×C5×C8—41no—
112C5×C3⋊C8—41no—
113C2×#235C2×D511yescharacteristic
114C2×C3×M16C2×D511yescharacteristic
115C3×#117—51no—
116C2×C3×C42—51no—
117C4×#67—102no—
118#926—51no—
119#926—51no—
120C2×#208C2×D511yescharacteristic
121C4×D12—101no—
122#872—52no—
123C42×D3—52no—
124C4×Dic6—101no—
125#824—21no—
126#823—21no—
127#806—102no—
128C5×#41—61no—
129C5×#41—61no—
130C5×#41—61no—
131C5×#41—61no—
132C2×C5×Q8—31no—
133C2×C5×D4—32no—
134C2×C5×D4—31no—
135C22×C4×C5—32no—
136C22×C4×C5C22×D311yescharacteristic
137C22×Dic5—21no—
138C22×Dic5—62no—
139C5×M16—21no—
140C5×M16—21no—
141C5×M16—61no—
142C5×M16—61no—
143C2×C5×C8—21no—
144C2×C5×C8—61no—
145C22⋊Dic5—21no—
146C22⋊Dic5—62no—
147C22⋊Dic5—61no—
148C22⋊Dic5—61no—
149C4⋊Dic5—21no—
150C4⋊Dic5—62no—
151C4⋊Dic5—61no—
152C4⋊Dic5—61no—
153C4×Dic5—21no—
154C4×Dic5—21no—
155C4×Dic5—32no—
156C4×Dic5—62no—
157C4×Dic5—61no—
158C4×Dic5C4×D311yescharacteristic
159C4×Dic5C4×D311yescharacteristic
160C4×#41—151no—
161#413—31no—
162#410—151no—
163#339—51no—
164#339—151no—
165H(3,ℤ/4)—151no—
166H(3,ℤ/4)—151no—
167C22×C3×C5—41no—
168C22×C3×C5C2×C22⋊C411yescharacteristic
169C22×C3×C5#12311yescharacteristic
170C22×C3×C5#12311yescharacteristic
171C2×C5×D3—22no—
172C2×C5×D3—42no—
173C3×C4×C5#11711yescharacteristic
174C3×C4×C5#11711yescharacteristic
175C3×C4×C5#12311yescharacteristic
176C3×C4×C5#12311yescharacteristic
177Dic15—42no—
178Dic15—81no—
179C3×Dic5—22no—
180C3×Dic5—41no—
181C3×Dic5—81no—
182C5×Dic3—22no—
183C22×C3×C4—101no—
184C22×C3×C4C22×D511yescharacteristic
185C2×#67D2012yes—
186#235—21no—
187#235—21no—
188#235—21no—
189#235—21no—
190C2×D12C22⋊D511yescharacteristic
191C2×C4×D3—102no—
192C2×C4×D3C4×D512yes—
193C2×Dic6C22⋊D511yescharacteristic
194C3×M16—21no—
195C3×M16—21no—
196C2×C3×C8—21no—
197C3×C4⋊C4—101no—
198C3×C22⋊C4—101no—
199C3×C42—51no—
200C3×C42—51no—
201C3×C42—101no—
202C3×C42—101no—
203#217—101no—
204#217—101no—
205(C2×D3)⋊C4—102no—
206C4⋊Dic3—101no—
207C4⋊Dic3—101no—
208Dic3⋊C4—102no—
209C4×Dic3—52no—
210C4×Dic3—102no—
211C4×Dic3—101no—
212#208—21no—
213#208—21no—
214C2×C3⋊C8—21no—
215C23×C5—32no—
216C23×C5D3×D411yescharacteristic
217C5×Q8—61no—
218C5×Q8—61no—
219C5×D4—62no—
220C5×D4—62no—
221C5×D4—61no—
222C5×D4—61no—
223C2×C4×C5—32no—
224C2×C4×C5—62no—
225C2×C4×C5—62no—
226C2×C4×C5C2×C4×D311yescharacteristic
227C2×C4×C5#23511yescharacteristic
228C2×C4×C5#23511yescharacteristic
229C2×C4×C5D3×D411yescharacteristic
230C2×C4×C5#23711yescharacteristic
231C2×C4×C5#23911yescharacteristic
232C2×Dic5—21no—
233C2×Dic5—21no—
234C2×Dic5—42no—
235C2×Dic5—41no—
236C2×Dic5—62no—
237C2×Dic5—124no—
238C2×Dic5—121no—
239C5×C8—41no—
240C5×C8—121no—
241C2×#41—31no—
242C2×M16—31no—
243C2×M16D3×D511yescharacteristic
244C4×Q8—301no—
245C4×D4—301no—
246C4×D4—302no—
247#117—51no—
248#117—152no—
249#117—151no—
250#117—151no—
251C2×C42—51no—
252C2×C42—152no—
253#101—61no—
254#100—61no—
255#99—302no—
256C2×C3×C5—21no—
257C2×C3×C5—21no—
258C2×C3×C5—21no—
259C2×C3×C5#38111yescharacteristic
260C5×D3—42no—
261C23×C3C2×D2011yescharacteristic
262C22×D3#68512yes—
263C2×C3×C4—101no—
264C2×C3×C4—101no—
265C2×C3×C4—202no—
266C2×C3×C4—201no—
267C2×C3×C4C2×C4×D511yescharacteristic
268C2×C3×C4#71111yescharacteristic
269C2×C3×C4#71111yescharacteristic
270C2×C3×C4#71111yescharacteristic
271C2×C3×C4#71111yescharacteristic
272C2×C3×C4C2×C22⋊D511yescharacteristic
273#67—22no—
274#67—22no—
275C2×Dic3—102no—
276C2×Dic3—201no—
277C2×Dic3#68512yes—
278D12—21no—
279D12—21no—
280C4×D3—22no—
281C4×D3—22no—
282C4×D3—204no—
283Dic6—21no—
284Dic6—21no—
285C3×C8—41no—
286C3⋊C8—41no—
287C22×C5—41no—
288C22×C5—62no—
289C22×C5—122no—
290C22×C5D3×C22⋊C411yescharacteristic
291C22×C5#88311yescharacteristic
292C22×C5#89411yescharacteristic
293C4×C5—62no—
294C4×C5#87211yescharacteristic
295C4×C5#88311yescharacteristic
296C4×C5#89211yescharacteristic
297C4×C5#89411yescharacteristic
298Dic5—22no—
299Dic5—41no—
300Dic5—81no—
301Dic5—122no—
302Dic5—241no—
303#41—61no—
304#41—61no—
305#41—61no—
306#41—61no—
307C2×Q8—31no—
308C2×D4—32no—
309C2×D4—31no—
310C22×C4—32no—
311C22×C4—101no—
312C22×C4—302no—
313C22×C4C2×D3×D511yescharacteristic
314M16—21no—
315M16—21no—
316M16—61no—
317M16—61no—
318C2×C8—21no—
319C2×C8—61no—
320C4⋊C4—101no—
321C4⋊C4—302no—
322C4⋊C4—301no—
323C4⋊C4—301no—
324C22⋊C4—101no—
325C22⋊C4—302no—
326C22⋊C4—301no—
327C22⋊C4—301no—
328C42—51no—
329C42—51no—
330C42—101no—
331C42—101no—
332C42—152no—
333C42—302no—
334C42—301no—
335C3×C5#182711yescharacteristic, complemented, Hall
336C22×C3—41no—
337C22×C3#403211yescharacteristic
338C22×C3#403211yescharacteristic
339C22×C3C2×#68511yescharacteristic
340C2×D3—22no—
341C2×D3—42no—
342C3×C4—102no—
343C3×C4—201no—
344C3×C4—401no—
345C3×C4#402311yescharacteristic
346C3×C4#402311yescharacteristic
347C3×C4#408111yescharacteristic
348C3×C4#408111yescharacteristic
349Dic3—22no—
350Dic3—202no—
351Dic3—401no—
352C2×C5—21no—
353C2×C5—21no—
354C2×C5—21no—
355C2×C5—122no—
356C2×C5#466411yescharacteristic
357C23—32no—
358C23D3×D2011yescharacteristic
359Q8—61no—
360Q8—61no—
361D4—62no—
362D4—62no—
363D4—61no—
364D4—61no—
365C2×C4—32no—
366C2×C4—62no—
367C2×C4—62no—
368C2×C4—101no—
369C2×C4—101no—
370C2×C4—202no—
371C2×C4—201no—
372C2×C4—302no—
373C2×C4—604no—
374C2×C4—601no—
375C2×C4#676811yescharacteristic
376C2×C4#677211yescharacteristic
377C2×C4C4×D3×D511yescharacteristic
378C2×C4#678011yescharacteristic
379C2×C4#678211yescharacteristic
380C2×C4D3×C22⋊D511yescharacteristic
381C8—41no—
382C8—121no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3#6523211yescharacteristic
387D3—42no—
388C5#6873711yescharacteristic, complemented, Sylow
389C22—41no—
390C22—62no—
391C22—122no—
392C22#9142711yescharacteristic
393C22#9145711yescharacteristic
394C22D3×#68511yescharacteristic
395C4—62no—
396C4—102no—
397C4—201no—
398C4—401no—
399C4—602no—
400C4—1201no—
401C4#9139811yescharacteristic
402C4#9140011yescharacteristic
403C4#9142311yescharacteristic
404C4#9155511yescharacteristic
405C3#1060092411yescharacteristic, complemented, Sylow
406C2—21no—
407C2—21no—
408C2—21no—
409C2—122no—
410C2#1174888011yescharacteristic
subgroupG/H
centerC4#91400
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#381
prime radicalC2×C5×#235C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1827
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
4. #11746378C2semidirect
5. C3×#64775C2semidirect
6. #11745978C2semidirect
7. #11745970C2semidirect
18. C4×D3×Dic5C4semidirect
19. #91371C4semidirect
31. #64775D3semidirect
335. C3×C5#1827semidirect
388. C5#68737semidirect
405. C3#10600924semidirect

Maximal subgroups

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

subgroupindex
Dic5×#2352
C5×#51322
#117486252
#117463782
C3×#647752
#117459782
#117459702
#106009243
#687375