Finite Group Databasebeta

← #14316144

Subgroups — #14316144

Order 1920.

460 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91271C211yesmaximal, characteristic, complemented
2C3×#65172C211yesmaximal, characteristic, complemented
3C2×#90940C211yesmaximal, characteristic, complemented
4C2×#90938C211yesmaximal, characteristic, complemented
5#11746312C211yesmaximal, characteristic, complemented
6C5×#4492C211yesmaximal, characteristic, complemented
7#11745879C211yesmaximal, characteristic, complemented
8#10600017—31nomaximal, Hall
9C2×#6773—21no—
10C2×D120C2211yescharacteristic
11C2×C5×Dic12C2211yescharacteristic
12C2×C3×D40C2211yescharacteristic
13C2×C3×C8×D5C2211yescharacteristic
14C3×#4041—21no—
15C2×#6660—21no—
16#91271—22no—
17#91271—22no—
18C3×C5×#107C2211yescharacteristic
19C2×C3⋊#672C2211yescharacteristic
20C2×C5×C3⋊C16C2211yescharacteristic
21C3×#3941—21no—
22#90940—22no—
23#90938—22no—
24#71076—51nomaximal, Hall
25C2×#4065—31no—
26C2×#3960—31no—
27C2×D80—31no—
28#65172D311yescharacteristic, complemented
29C5×#358—31no—
30#64727—31no—
31#64711—31no—
32C2×D60—21no—
33C2×C5×Dic6—21no—
34C2×C3×D20—21no—
35C2×C3×D20—41no—
36C2×C3×C4×D5D411yescharacteristic
37C2×#1202—41no—
38C2×#1200—41no—
39#6773—24no—
40#6773—42no—
41C2×C3×C5×C8C2311yescharacteristic
42C3×C5×C4⋊C4—21no—
43D120—21no—
44D120D412yescomplemented
45C5×Dic12—21no—
46C5×Dic12D412yescomplemented
47C3×#685—41no—
48C2×C3×#168D411yescharacteristic
49C3×D40—21no—
50C3×D40—21no—
51C3×C8×D5—21no—
52C3×C8×D5—21no—
53#6660—24no—
54C3⋊#672—21no—
55C5×C3⋊C16—21no—
56C2×#904—51no—
57C3×#466—51no—
58C2×#827—51no—
59C2×#826—51no—
60#4549—51no—
61#4492D511yescharacteristic, complemented
62#4491—51no—
63C2×#713—61no—
64C2×C5×Q16—31no—
65C2×#688—61no—
66#4065—62no—
67#4065—62no—
68C2×D40—31no—
69C2×D40C2×D311yescharacteristic
70C2×C8×D5C2×D311yescharacteristic
71#4041—21no—
72C2×C5×C16—31no—
73C5×#107C2×D311yescharacteristic
74#3960—62no—
75C2×#672—31no—
76#3941—21no—
77D80—62no—
78#2186—151noSylow
79C22×D15—41no—
80C22×C3×D5—41no—
81C22×C3×D5D811yescharacteristic
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5C2×D411yescharacteristic
84D60—22no—
85D60—41no—
86C2×C5×Dic3—41no—
87C5×Dic6—22no—
88C5×Dic6—41no—
89C2×C3×Dic5D811yescharacteristic
90C3×D20—41no—
91C3×D20—41no—
92C3×D20—82no—
93C3×C4×D5—21no—
94C3×C4×D5—21no—
95#1202—44no—
96#1200—44no—
97C3×C5×C8C2×D411yescharacteristic
98C3×C5×C8C2×D411yescharacteristic
99C3×#168—21no—
100C2×#235—101no—
101C2×C3×D8—51no—
102C22×C3×C8—51no—
103C3×#121—101no—
104C2×Dic12C2×D511yescharacteristic
105#904—102no—
106#904—102no—
107C2×D24—51no—
108C2×#204—101no—
109C3×#107C2×D511yescharacteristic
110C3×#102—101no—
111#827—102no—
112#826—102no—
113C2×C3⋊C16—51no—
114C2×C3⋊C16C2×D511yescharacteristic
115C2×C5×Q8—61no—
116#713—64no—
117#713—122no—
118C2×D20—21no—
119C2×D20—41no—
120C2×D20—61no—
121C2×D20—121no—
122C2×C4×D5—121no—
123C2×C4×D5#6711yescharacteristic
124C5×Q16—32no—
125C5×Q16—61no—
126C2×C5×C8C22×D311yescharacteristic
127C5×C4⋊C4—21no—
128#688—64no—
129#685—41no—
130C2×#168#6711yescharacteristic
131D40—21no—
132D40—21no—
133D40—32no—
134D40—61no—
135C8×D5—21no—
136C8×D5—21no—
137C5×C16—61no—
138#672—61no—
139C2×#135—151no—
140C2×SD32—151no—
141C2×D16—151no—
142#466—51no—
143#358—31no—
144#357—151no—
145C22⋊C16—151no—
146C22×C3×C5C2×D811yescharacteristic
147C2×D15—42no—
148C2×D15—81no—
149C2×D15—81no—
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C2×C3×D5—21no—
153C2×C3×D5—81no—
154C2×C3×D5—81no—
155C2×C3×D5—81no—
156C3×C4×C5—81no—
157C3×C4×C5#12011yescharacteristic
158C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
159C3×Dic5—21no—
160C5×Dic3—42no—
161C2×C3×D4—101no—
162C2×C3×D4—201no—
163C22×C3×C4—51no—
164C2×#67—201no—
165#235—104no—
166#235—202no—
167C2×D12—101no—
168C2×C4×D3—201no—
169C2×Dic6—21no—
170C3×D8—101no—
171C3×D8—101no—
172C2×C3×C8—51no—
173C2×C3×C8—101no—
174C2×C3×C8—101no—
175C2×C3×C8C22×D511yescharacteristic
176C3×C4⋊C4—21no—
177C3×C22⋊C4—201no—
178Dic12—21no—
179Dic12D2012yescomplemented
180D24—52no—
181D24—101no—
182#204—104no—
183C3⋊C16—21no—
184C3⋊C16—101no—
185C22×D5—41no—
186C22×D5—121no—
187C22×D5#21311yescharacteristic
188C5×Q8—62no—
189C5×Q8—121no—
190C2×C4×C5—41no—
191C2×C4×C5—121no—
192C2×C4×C5C2×#6711yescharacteristic
193C2×Dic5#21311yescharacteristic
194D20—41no—
195D20—41no—
196D20—62no—
197D20—82no—
198D20—124no—
199D20—121no—
200C4×D5—21no—
201C4×D5—21no—
202C4×D5—124no—
203C5×C8D3×D411yescharacteristic
204C5×C8D3×D411yescharacteristic
205#168—21no—
206C2×#41—301no—
207#135—302no—
208#135—302no—
209C2×Q16—31no—
210C2×SD16—301no—
211C2×D8—51no—
212C2×D8—151no—
213C22×C8—51no—
214#121—101no—
215SD32—302no—
216D16—302no—
217C2×C16—31no—
218C2×C16—151no—
219#107D3×D511yescharacteristic
220#102—101no—
221C2×C3×C5#44711yescharacteristic
222C2×C3×C5#50811yescharacteristic
223C2×C3×C5#50911yescharacteristic
224D15—82no—
225C3×D5—41no—
226C3×D5—161no—
227C23×C3—51no—
228C23×C3—201no—
229C22×D3—201no—
230C3×D4—201no—
231C3×D4—201no—
232C3×D4—402no—
233C2×C3×C4—41no—
234C2×C3×C4—51no—
235C2×C3×C4—101no—
236C2×C3×C4—101no—
237C2×C3×C4D4×D511yescharacteristic
238#67—204no—
239C2×Dic3—41no—
240D12—102no—
241D12—201no—
242C4×D3—204no—
243Dic6—22no—
244Dic6—41no—
245C3×C8—101no—
246C3×C8C2×D2011yescharacteristic
247C3×C8D4×D511yescharacteristic
248C22×C5C2×#21311yescharacteristic
249C2×D5—21no—
250C2×D5—21no—
251C2×D5—21no—
252C2×D5—81no—
253C2×D5—81no—
254C2×D5—81no—
255C2×D5—122no—
256C2×D5—241no—
257C2×D5—241no—
258C4×C5—81no—
259C4×C5—122no—
260C4×C5#93711yescharacteristic
261C4×C5#94911yescharacteristic
262Dic5—21no—
263#41—304no—
264#41—602no—
265C2×Q8—61no—
266C2×D4—101no—
267C2×D4—201no—
268C2×D4—301no—
269C2×D4—601no—
270C22×C4—51no—
271C22×C4—601no—
272Q16—32no—
273Q16—61no—
274SD16—304no—
275D8—101no—
276D8—101no—
277D8—152no—
278D8—301no—
279C2×C8—51no—
280C2×C8—101no—
281C2×C8—101no—
282C2×C8C2×D3×D511yescharacteristic
283C4⋊C4—21no—
284C22⋊C4—201no—
285C16—61no—
286C16—301no—
287C3×C5#218611yescharacteristic, complemented, Hall
288C22×C3—101no—
289C22×C3—101no—
290C22×C3—101no—
291C22×C3—401no—
292C22×C3—401no—
293C22×C3—401no—
294C22×C3D5×D811yescharacteristic
295C2×D3—202no—
296C2×D3—401no—
297C2×D3—401no—
298C3×C4—81no—
299C3×C4—101no—
300C3×C4#402811yescharacteristic
301C3×C4#406011yescharacteristic
302Dic3—42no—
303C2×C5#503611yescharacteristic
304C2×C5#514711yescharacteristic
305C2×C5#519411yescharacteristic
306D5—41no—
307D5—161no—
308D5—242no—
309C23—51no—
310C23—201no—
311C23—601no—
312Q8—62no—
313Q8—121no—
314D4—201no—
315D4—201no—
316D4—302no—
317D4—402no—
318D4—604no—
319D4—601no—
320C2×C4—41no—
321C2×C4—51no—
322C2×C4—101no—
323C2×C4—101no—
324C2×C4—121no—
325C2×C4—604no—
326C2×C4D5×#6711yescharacteristic
327C8—101no—
328C8D3×D2011yescharacteristic
329C8#677711yescharacteristic
330C2×C3—201no—
331C2×C3—801no—
332C2×C3#6506211yescharacteristic
333C2×C3#6520311yescharacteristic
334C2×C3#6520811yescharacteristic
335D3—402no—
336C5#7107611yescharacteristic, complemented, Sylow
337C22—101no—
338C22—101no—
339C22—101no—
340C22—401no—
341C22—401no—
342C22—401no—
343C22—602no—
344C22—1201no—
345C22—1201no—
346C22D5×#21311yescharacteristic
347C4—81no—
348C4—101no—
349C4—122no—
350C4#9147411yescharacteristic
351C4#9150211yescharacteristic
352C3#1060001711yescharacteristic, complemented, Sylow
353C2—201no—
354C2—801no—
355C2—1202no—
356C2#1174748011yescharacteristic
357C2#1174827811yescharacteristic
358C2#1174830311yescharacteristic
subgroupG/H
centerC22D5×#213
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C2×D8
hypercenter#107D3×D5
hypocenterC3×C5#2186
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
1. C2×#91271C2semidirect
2. C3×#65172C2semidirect
3. C2×#90940C2semidirect
4. C2×#90938C2semidirect
5. #11746312C2semidirect
6. C5×#4492C2semidirect
7. #11745879C2semidirect
28. #65172D3semidirect
44. D120D4semidirect
46. C5×Dic12D4semidirect
61. #4492D5semidirect
179. Dic12D20semidirect
287. C3×C5#2186semidirect
336. C5#71076semidirect
352. C3#10600017semidirect

Maximal subgroups

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

subgroupindex
C2×#912712
C3×#651722
C2×#909402
C2×#909382
#117463122
C5×#44922
#117458792
#106000173
#710765