Finite Group Databasebeta

← #14289825

Subgroups — #14289825

Order 1920.

388 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 91 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
1#11756301C211yesmaximal, characteristic
2#11751109C211yesmaximal, characteristic
3#11750951C211yesmaximal, characteristic, complemented
4#11750782C211yesmaximal, characteristic, complemented
5C3×C5×D4⋊C8C211yesmaximal, characteristic
6#11746307C211yesmaximal, characteristic, complemented
7#11746277C211yesmaximal, characteristic, complemented
8#10598998—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10#91825—21no—
11#91815—21no—
12#91813—21no—
13#91776—21no—
14#91768—22no—
15#91758C2211yescharacteristic
16#91758C2211yescharacteristic
17C4×Dic30C2211yescharacteristic
18C3×C5×C4⋊C8C2211yescharacteristic
19C3×C4×C5×C8C2211yescharacteristic
20#91116—21no—
21#91102—21no—
22#91100—21no—
23#91100—22no—
24#91092—21no—
25C4⋊(C3⋊#168)C2211yescharacteristic
26#68205—51nomaximal, Hall
27#65876—31no—
28#65297—31no—
29#65139—31no—
30#64970—31no—
31C5×D4⋊C8D311yescharacteristic
32#64706—31no—
33#64676—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×Dic30—21no—
37C2×Dic30—21no—
38C2×Dic30D411yescharacteristic
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C5×C22⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44#6719—22no—
45#6719—22no—
46C4⋊Dic15—21no—
47C4⋊Dic15—21no—
48C4⋊Dic15—21no—
49C4⋊Dic15D411yescharacteristic
50C4⋊Dic15D412yes—
51#6712—22no—
52#6712—21no—
53C4×Dic15—22no—
54C4×Dic15—21no—
55C2×C3⋊#168—21no—
56#5542—51no—
57#5008—51no—
58#4850—51no—
59#4681—51no—
60C3×D4⋊C8D511yescharacteristic
61#4486—51no—
62#4456—51no—
63C4×C5×D4C2×D311yescharacteristic
64#4082—61no—
65#4072—61no—
66#4070—61no—
67#4033—61no—
68#4025—62no—
69#4015—31no—
70#4015—31no—
71C4×Dic10—31no—
72C5×C4⋊C8C2×D311yescharacteristic
73C4×C5×C8C2×D311yescharacteristic
74#3964—61no—
75#3950—61no—
76#3948—62no—
77#3948—61no—
78#3940—61no—
79C4⋊#168—31no—
80#1638—151noSylow
81C23×C3×C5—21no—
82C3×C5×D4—21no—
83C3×C5×D4—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—21no—
91C2×Dic15—21no—
92C2×Dic15—22no—
93C2×Dic15—41no—
94Dic30—21no—
95Dic30—21no—
96Dic30—41no—
97Dic30—41no—
98Dic30—42no—
99C3×C5×C8—41no—
100C3×C5×C8—41no—
101C3⋊#168—41no—
102C3×C4×D4C2×D511yescharacteristic
103#936—101no—
104#926—101no—
105#924—101no—
106#887—101no—
107#879—102no—
108#869—51no—
109#869—51no—
110C4×Dic6—51no—
111C3×C4⋊C8C2×D511yescharacteristic
112C3×C4×C8C2×D511yescharacteristic
113#832—101no—
114#818—101no—
115#816—102no—
116#816—101no—
117#808—101no—
118C4⋊(C3⋊C8)—51no—
119C2×C5×D4D1211yescharacteristic
120C22×C4×C5—21no—
121C2×Dic10—31no—
122C2×Dic10—61no—
123C2×Dic10—61no—
124C2×C5×C8—21no—
125C2×C5×C8—21no—
126C5×C4⋊C4D1211yescharacteristic
127C5×C22⋊C4—21no—
128C42×C5C22×D311yescharacteristic
129C22⋊Dic5—62no—
130C22⋊Dic5—62no—
131C4⋊Dic5—32no—
132C4⋊Dic5—31no—
133C4⋊Dic5—61no—
134C4⋊Dic5—61no—
135C4⋊Dic5—61no—
136#683—62no—
137#683—61no—
138C4×Dic5—62no—
139C4×Dic5—61no—
140C2×#168—61no—
141#556—151no—
142#487—151no—
143#477—151no—
144#476—151no—
145#332—151no—
146Q8⋊C8—151no—
147D4⋊C8D1511yescharacteristic
148C22×C3×C5—41no—
149C22×C3×C5—41no—
150C22×C3×C5—41no—
151C22×C3×C5#12011yescharacteristic
152C3×C4×C5—21no—
153C3×C4×C5—41no—
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13711yescharacteristic
157C3×C4×C5#13711yescharacteristic
158Dic15—41no—
159Dic15—42no—
160Dic15—41no—
161Dic15—81no—
162C2×C3×D4D2011yescharacteristic
163C22×C3×C4—21no—
164C2×Dic6—51no—
165C2×Dic6—101no—
166C2×Dic6—101no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C3×C4⋊C4D2011yescharacteristic
170C3×C22⋊C4—21no—
171C3×C42C22×D511yescharacteristic
172#217—102no—
173#217—102no—
174C4⋊Dic3—52no—
175C4⋊Dic3—51no—
176C4⋊Dic3—101no—
177C4⋊Dic3—101no—
178C4⋊Dic3—101no—
179Dic3⋊C4—102no—
180Dic3⋊C4—101no—
181C4×Dic3—102no—
182C4×Dic3—101no—
183C2×C3⋊C8—101no—
184C23×C5—21no—
185C5×D4—21no—
186C5×D4—21no—
187C2×C4×C5—21no—
188C2×C4×C5—41no—
189C2×C4×C5—41no—
190C2×C4×C5C2×D1211yescharacteristic
191C2×C4×C5D3×D411yescharacteristic
192C2×C4×C5D3×D411yescharacteristic
193C2×Dic5—61no—
194C2×Dic5—61no—
195C2×Dic5—62no—
196C2×Dic5—121no—
197Dic10—61no—
198Dic10—61no—
199Dic10—121no—
200Dic10—121no—
201Dic10—122no—
202C5×C8—41no—
203C5×C8—41no—
204#168—121no—
205C4⋊Q8—151no—
206C4⋊Q8—151no—
207#126—302no—
208#124—301no—
209C22⋊Q8—301no—
210C4×Q8—151no—
211C4×Q8—301no—
212C4×D4C2×D1511yescharacteristic
213#117—301no—
214#107—301no—
215#106—301no—
216C4⋊C8—151no—
217C4⋊C8C2×D1511yescharacteristic
218#103—302no—
219#103—301no—
220#102—301no—
221C4×C8C2×D1511yescharacteristic
222C2×C3×C5—81no—
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45211yescharacteristic
225C2×C3×C5#45411yescharacteristic
226C23×C3—21no—
227C3×D4—21no—
228C3×D4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—41no—
231C2×C3×C4—41no—
232C2×C3×C4C2×D2011yescharacteristic
233C2×C3×C4D4×D511yescharacteristic
234C2×C3×C4D4×D511yescharacteristic
235C2×Dic3—101no—
236C2×Dic3—101no—
237C2×Dic3—102no—
238C2×Dic3—201no—
239Dic6—101no—
240Dic6—101no—
241Dic6—201no—
242Dic6—201no—
243Dic6—202no—
244C3×C8—41no—
245C3×C8—41no—
246C3⋊C8—201no—
247C22×C5—41no—
248C22×C5—41no—
249C22×C5—41no—
250C22×C5#88211yescharacteristic
251C4×C5—21no—
252C4×C5—41no—
253C4×C5#90411yescharacteristic
254C4×C5#90911yescharacteristic
255C4×C5#91211yescharacteristic
256C4×C5#91511yescharacteristic
257Dic5—122no—
258Dic5—121no—
259Dic5—121no—
260Dic5—241no—
261C2×Q8—151no—
262C2×Q8—301no—
263C2×Q8—301no—
264C2×D4D6011yescharacteristic
265C22×C4—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—301no—
269C4⋊C4—152no—
270C4⋊C4—151no—
271C4⋊C4—302no—
272C4⋊C4—301no—
273C4⋊C4—301no—
274C4⋊C4—301no—
275C4⋊C4—301no—
276C4⋊C4D6011yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—302no—
279C22⋊C4—302no—
280C42—302no—
281C42—301no—
282C42C22×D1511yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3#402811yescharacteristic
288C3×C4—21no—
289C3×C4—41no—
290C3×C4#405011yescharacteristic
291C3×C4#405511yescharacteristic
292C3×C4#405811yescharacteristic
293C3×C4#406111yescharacteristic
294Dic3—201no—
295Dic3—201no—
296Dic3—202no—
297Dic3—401no—
298C2×C5—81no—
299C2×C5#473311yescharacteristic
300C2×C5#478311yescharacteristic
301C2×C5#482711yescharacteristic
302C23—21no—
303Q8—301no—
304Q8—301no—
305Q8—602no—
306Q8—601no—
307Q8—601no—
308D4—21no—
309D4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—301no—
314C2×C4—302no—
315C2×C4—301no—
316C2×C4—601no—
317C2×C4C2×D6011yescharacteristic
318C2×C4D4×D1511yescharacteristic
319C2×C4D4×D1511yescharacteristic
320C8—41no—
321C8—41no—
322C8—601no—
323C2×C3—81no—
324C2×C3#6502211yescharacteristic
325C2×C3#6507211yescharacteristic
326C2×C3#6511611yescharacteristic
327C5#6820511yescharacteristic, complemented, Sylow
328C22—41no—
329C22—41no—
330C22—41no—
331C22#9177111yescharacteristic
332C4—21no—
333C4—41no—
334C4—601no—
335C4—602no—
336C4—601no—
337C4—1201no—
338C4#9179311yescharacteristic
339C4#9179811yescharacteristic
340C4#9180111yescharacteristic
341C4#9180411yescharacteristic
342C3#1059899811yescharacteristic, complemented, Sylow
343C2—81no—
344C2#1175083411yescharacteristic
345C2#1175088411yescharacteristic
346C2#1175092811yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterD4⋊C8D15
hypocenterC3×C5#1638
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
3. #11750951C2semidirect
4. #11750782C2semidirect
6. #11746307C2semidirect
7. #11746277C2semidirect
283. C3×C5#1638semidirect
327. C5#68205semidirect
342. C3#10598998semidirect

Maximal subgroups

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

subgroupindex
#117563012
#117511092
#117509512
#117507822
C3×C5×D4⋊C82
#117463072
#117462772
#105989983
#682055