Finite Group Databasebeta

← #14298606

Subgroups — #14298606

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
1C3×#65856C211yesmaximal, characteristic
2#11748624C211yesmaximal, characteristic
3#11748353C211yesmaximal, characteristic
4#11746352C211yesmaximal, characteristic, complemented
5C5×#4531C211yesmaximal, characteristic, complemented
6#11745978C211yesmaximal, characteristic, complemented
7#11745977C211yesmaximal, characteristic, complemented
8#10599504—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C2×C3×C4×Dic5C2211yescharacteristic
16C3×#4039—21no—
17C3×#4033—21no—
18C3×#4027—22no—
19C3×#4018C412yescomplemented
20C3×C42×D5C412yescomplemented
21#90995—22no—
22#90961—21no—
23#90958—21no—
24#71644—51nomaximal, Hall
25#65856D311yescharacteristic
26#65421—31no—
27#65295—31no—
28C5×H(3,ℤ/4)—31no—
29#64775—31no—
30#64752—31no—
31#64751—31no—
32C22×C3×C4×C5C2311yescharacteristic
33C2×C3×C22⋊D5D412yes—
34C22×C3×Dic5—21no—
35C3×#709—21no—
36C3×#709—21no—
37C3×#709—21no—
38C3×#709—21no—
39C2×C3×D20D411yescharacteristic
40C2×C3×C4×D5—22no—
41C2×C3×C4×D5C2×C412yes—
42C2×C3×Dic10D411yescharacteristic
43C3×C5×C4⋊C4—21no—
44C3×C5×C22⋊C4—21no—
45C3×C42×C5C2×C412yes—
46#6719—21no—
47C4⋊Dic15—21no—
48C4×Dic15—21no—
49#6710—21no—
50#6710—21no—
51C2×C3⋊#168—21no—
52C5×#217—21no—
53C5×C4⋊Dic3—21no—
54C4×C5×Dic3—21no—
55C5×#208—21no—
56C5×#208—21no—
57C2×C5×C3⋊C8—21no—
58C3×#685—22no—
59C3×#683—22no—
60C3×C4×Dic5—21no—
61C3×C4×Dic5—22no—
62C3×C4×Dic5C2×C411yescharacteristic
63C3×C4×Dic5C2×C411yescharacteristic
64C3×C4×#41—51no—
65#5240—51no—
66#5237—51no—
67#4531—51no—
68#4531D511yescharacteristic, complemented
69#4523—51no—
70#4523—51no—
71C2×#709C2×D311yescharacteristic
72C2×C5×M16—31no—
73C5×#117—31no—
74C5×#117C2×D311yescharacteristic
75#4072—31no—
76C2×C4×Dic5C2×D311yescharacteristic
77C2×#681—31no—
78#4039—21no—
79#4033—21no—
80#4027—22no—
81#4018Dic312yescomplemented
82C42×D5Dic312yescomplemented
83#3956—61no—
84#3955—61no—
85#3938—62no—
86#1827—151noSylow
87C23×C3×C5C2×D411yescharacteristic
88C22×C3×D5C22⋊C412yes—
89C2×C3×C4×C5—22no—
90C2×C3×C4×C5C22×C411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5#4111yescharacteristic
93C2×C3×C4×C5#4111yescharacteristic
94C2×C3×C4×C5#4111yescharacteristic
95C2×C3×C4×C5#4111yescharacteristic
96C2×Dic15—41no—
97C2×C5×Dic3—41no—
98C3×C22⋊D5—22no—
99C3×C22⋊D5—22no—
100C2×C3×Dic5—21no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—42no—
103C2×C3×Dic5C22⋊C412yes—
104C3×D20—21no—
105C3×D20—21no—
106C3×C4×D5—22no—
107C3×C4×D5—22no—
108C3×C4×D5—44no—
109C3×Dic10—21no—
110C3×Dic10—21no—
111C3⋊#168—41no—
112C5×C3⋊C8—41no—
113C2×C3×#41—51no—
114C3×C4×Q8—101no—
115C3×C4×D4—102no—
116C3×C4×D4—101no—
117C3×#117—52no—
118C3×#117C2×D511yescharacteristic
119C2×C3×C42—51no—
120C2×C3×C42—52no—
121#926—51no—
122#926C2×D511yescharacteristic
123C2×#208—51no—
124C2×#208C2×D511yescharacteristic
125#836—101no—
126#834—102no—
127#833—101no—
128C22×C4×C5C22×D311yescharacteristic
129C2×C22⋊D5#6712yes—
130C22×Dic5—21no—
131#709—21no—
132#709—21no—
133#709—21no—
134#709—21no—
135C2×D20#6711yescharacteristic
136C2×C4×D5—22no—
137C2×C4×D5C2×Dic312yes—
138C2×Dic10#6711yescharacteristic
139C5×M16—61no—
140C5×M16—61no—
141C2×C5×C8—61no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4—61no—
144C5×C22⋊C4—21no—
145C5×C22⋊C4—61no—
146C42×C5—61no—
147C42×C5C2×Dic312yes—
148C22⋊Dic5—61no—
149#685—22no—
150C4⋊Dic5—61no—
151#683—22no—
152C4×Dic5—21no—
153C4×Dic5—22no—
154C4×Dic5—61no—
155C4×Dic5C2×Dic311yescharacteristic
156C4×Dic5C2×Dic311yescharacteristic
157#681—61no—
158#681—61no—
159C2×#168—61no—
160C4×#41—51no—
161#413—151no—
162#410—151no—
163#339—151no—
164#339—151no—
165H(3,ℤ/4)—31no—
166H(3,ℤ/4)—151no—
167C22×C3×C5—41no—
168C22×C3×C5C2×C22⋊C411yescharacteristic
169C22×C3×C5#12311yescharacteristic
170C22×C3×C5#12311yescharacteristic
171C2×C3×D5—22no—
172C2×C3×D5—42no—
173C3×C4×C5—42no—
174C3×C4×C5#11711yescharacteristic
175C3×C4×C5#11711yescharacteristic
176C3×C4×C5#12311yescharacteristic
177C3×C4×C5#12311yescharacteristic
178Dic15—81no—
179C3×Dic5—22no—
180C3×Dic5—22no—
181C3×Dic5—41no—
182C5×Dic3—81no—
183C3×#41—101no—
184C3×#41—101no—
185C3×#41—101no—
186C3×#41—101no—
187C2×C3×Q8—51no—
188C2×C3×D4—52no—
189C2×C3×D4—51no—
190C22×C3×C4—52no—
191C22×C3×C4—102no—
192C22×C3×C4—101no—
193C22×C3×C4C22×D511yescharacteristic
194C3×C4⋊C4—21no—
195C3×C4⋊C4—102no—
196C3×C22⋊C4—21no—
197C3×C22⋊C4—102no—
198C3×C42—51no—
199C3×C42—51no—
200C3×C42—102no—
201C3×C42—101no—
202C3×C42C4×D512yes—
203#217—21no—
204#217—101no—
205C4⋊Dic3—21no—
206C4⋊Dic3—101no—
207C4×Dic3—21no—
208C4×Dic3—101no—
209#208—21no—
210#208—21no—
211#208—101no—
212#208—101no—
213C2×C3⋊C8—21no—
214C2×C3⋊C8—101no—
215C23×C5C2×#6711yescharacteristic
216C22×D5#21712yes—
217C2×C4×C5—22no—
218C2×C4×C5—121no—
219C2×C4×C5#23511yescharacteristic
220C2×C4×C5#23511yescharacteristic
221C2×C4×C5#23511yescharacteristic
222C2×C4×C5#23511yescharacteristic
223C2×C4×C5C22×Dic311yescharacteristic
224C2×C4×C5C2×#6711yescharacteristic
225C22⋊D5—22no—
226C22⋊D5—22no—
227C2×Dic5—21no—
228C2×Dic5—21no—
229C2×Dic5—42no—
230C2×Dic5—121no—
231C2×Dic5#21712yes—
232D20—21no—
233D20—21no—
234C4×D5—22no—
235C4×D5—22no—
236C4×D5—44no—
237Dic10—21no—
238Dic10—21no—
239C5×C8—121no—
240#168—121no—
241C2×#41—51no—
242C2×M16—31no—
243C2×M16—151no—
244C4×Q8—101no—
245C4×D4—102no—
246C4×D4—101no—
247#117—31no—
248#117—52no—
249#117—151no—
250#117D3×D511yescharacteristic
251C2×C42—51no—
252C2×C42—52no—
253#101—301no—
254#100—301no—
255#99—302no—
256C2×C3×C5—21no—
257C2×C3×C5—21no—
258C2×C3×C5—21no—
259C2×C3×C5#38111yescharacteristic
260C3×D5—42no—
261C23×C3—52no—
262C23×C3D4×D511yescharacteristic
263C3×Q8—101no—
264C3×Q8—101no—
265C3×D4—102no—
266C3×D4—102no—
267C3×D4—101no—
268C3×D4—101no—
269C2×C3×C4—22no—
270C2×C3×C4—52no—
271C2×C3×C4—101no—
272C2×C3×C4—102no—
273C2×C3×C4—102no—
274C2×C3×C4—101no—
275C2×C3×C4—204no—
276C2×C3×C4—202no—
277C2×C3×C4C2×C4×D511yescharacteristic
278C2×C3×C4#70911yescharacteristic
279C2×C3×C4#70911yescharacteristic
280C2×C3×C4D4×D511yescharacteristic
281C2×C3×C4#71111yescharacteristic
282C2×C3×C4#71311yescharacteristic
283C2×Dic3—41no—
284C2×Dic3—201no—
285C3⋊C8—41no—
286C3⋊C8—201no—
287C22×C5—41no—
288C22×C5#92911yescharacteristic
289C22×C5#92911yescharacteristic
290C22×C5C2×#21711yescharacteristic
291C2×D5—22no—
292C2×D5—42no—
293C4×C5—42no—
294C4×C5—241no—
295C4×C5#92611yescharacteristic
296C4×C5#92611yescharacteristic
297C4×C5#92911yescharacteristic
298C4×C5#92911yescharacteristic
299Dic5—22no—
300Dic5—22no—
301Dic5—41no—
302Dic5—241no—
303#41—101no—
304#41—101no—
305#41—101no—
306#41—101no—
307C2×Q8—51no—
308C2×D4—52no—
309C2×D4—51no—
310C22×C4—52no—
311C22×C4—102no—
312C22×C4—101no—
313C22×C4C2×D3×D511yescharacteristic
314M16—61no—
315M16—61no—
316M16—301no—
317M16—301no—
318C2×C8—61no—
319C2×C8—301no—
320C4⋊C4—21no—
321C4⋊C4—61no—
322C4⋊C4—102no—
323C4⋊C4—301no—
324C22⋊C4—21no—
325C22⋊C4—61no—
326C22⋊C4—102no—
327C22⋊C4—301no—
328C42—51no—
329C42—51no—
330C42—61no—
331C42—102no—
332C42—101no—
333C42—301no—
334C42D5×Dic312yes—
335C3×C5#182711yescharacteristic, complemented, Hall
336C22×C3—41no—
337C22×C3—102no—
338C22×C3—202no—
339C22×C3D5×C22⋊C411yescharacteristic
340C22×C3#402911yescharacteristic
341C22×C3#404011yescharacteristic
342C3×C4—42no—
343C3×C4—102no—
344C3×C4—102no—
345C3×C4—201no—
346C3×C4#401811yescharacteristic
347C3×C4#402911yescharacteristic
348C3×C4#403811yescharacteristic
349C3×C4#404011yescharacteristic
350Dic3—81no—
351Dic3—401no—
352C2×C5—21no—
353C2×C5—21no—
354C2×C5—21no—
355C2×C5#521111yescharacteristic
356D5—42no—
357C23—52no—
358C23D5×#6711yescharacteristic
359Q8—101no—
360Q8—101no—
361D4—102no—
362D4—102no—
363D4—101no—
364D4—101no—
365C2×C4—22no—
366C2×C4—52no—
367C2×C4—101no—
368C2×C4—102no—
369C2×C4—102no—
370C2×C4—101no—
371C2×C4—121no—
372C2×C4—204no—
373C2×C4—202no—
374C2×C4—601no—
375C2×C4#677111yescharacteristic
376C2×C4#677111yescharacteristic
377C2×C4#677211yescharacteristic
378C2×C4#677311yescharacteristic
379C2×C4C2×D5×Dic311yescharacteristic
380C2×C4D5×#6711yescharacteristic
381C8—121no—
382C8—601no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—202no—
387C2×C3#6495311yescharacteristic
388C5#7164411yescharacteristic, complemented, Sylow
389C22—41no—
390C22—102no—
391C22—202no—
392C22#9134811yescharacteristic
393C22#9144711yescharacteristic
394C22D5×#21711yescharacteristic
395C4—42no—
396C4—102no—
397C4—102no—
398C4—201no—
399C4—241no—
400C4—1201no—
401C4#9134811yescharacteristic
402C4#9135711yescharacteristic
403C4#9135811yescharacteristic
404C4#9144711yescharacteristic
405C3#1059950411yescharacteristic, complemented, Sylow
406C2—21no—
407C2—21no—
408C2—21no—
409C2—202no—
410C2#1174873711yescharacteristic
subgroupG/H
centerC4#91357
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#381
prime radicalC2×C3×#709C22
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1827
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #11746352C2semidirect
5. C5×#4531C2semidirect
6. #11745978C2semidirect
7. #11745977C2semidirect
19. C3×#4018C4semidirect
20. C3×C42×D5C4semidirect
68. #4531D5semidirect
81. #4018Dic3semidirect
82. C42×D5Dic3semidirect
335. C3×C5#1827semidirect
388. C5#71644semidirect
405. C3#10599504semidirect

Maximal subgroups

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

subgroupindex
C3×#658562
#117486242
#117483532
#117463522
C5×#45312
#117459782
#117459772
#105995043
#716445