Finite Group Databasebeta

← #14290581

Subgroups — #14290581

Order 1920.

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

normal subgroups only

This group has 400 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#11751120C211yesmaximal, characteristic
3#11750952C211yesmaximal, characteristic, complemented
4#11750783C211yesmaximal, characteristic, complemented
5C3×C5×D4⋊C8C211yesmaximal, characteristic
6#11746307C211yesmaximal, characteristic, complemented
7#11746277C211yesmaximal, characteristic, complemented
8#10599002—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10#91825—21no—
11C2×#6716—21no—
12#91815—21no—
13#91813—21no—
14#91776—21no—
15#91768—22no—
16#91758C2211yescharacteristic
17#91758C2211yescharacteristic
18C4×Dic30C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C4×C5×C8C2211yescharacteristic
21#91102—22no—
22#91101—21no—
23#91100—21no—
24#91094—21no—
25C4⋊(C3⋊#168)C2211yescharacteristic
26#68209—51nomaximal, Hall
27#65876—31no—
28#65308—31no—
29#65140—31no—
30#64971—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—
46#6716—42no—
47C4⋊Dic15—21no—
48C4⋊Dic15—21no—
49C4⋊Dic15—21no—
50C4⋊Dic15D411yescharacteristic
51C4⋊Dic15D412yes—
52#6712—22no—
53#6712—21no—
54C4×Dic15—22no—
55C4×Dic15—21no—
56C2×C3⋊#168—21no—
57#5542—51no—
58#5019—51no—
59#4851—51no—
60#4682—51no—
61C3×D4⋊C8D511yescharacteristic
62#4486—51no—
63#4456—51no—
64C4×C5×D4C2×D311yescharacteristic
65#4082—61no—
66C2×#687—61no—
67#4072—61no—
68#4070—61no—
69#4033—61no—
70#4025—62no—
71#4015—31no—
72#4015—31no—
73C4×Dic10—31no—
74C5×C4⋊C8C2×D311yescharacteristic
75C4×C5×C8C2×D311yescharacteristic
76#3950—62no—
77#3949—61no—
78#3948—61no—
79#3942—61no—
80C4⋊#168—31no—
81#1650—151noSylow
82C23×C3×C5—21no—
83C3×C5×D4—21no—
84C3×C5×D4—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×Dic15—21no—
92C2×Dic15—21no—
93C2×Dic15—22no—
94C2×Dic15—41no—
95Dic30—21no—
96Dic30—21no—
97Dic30—41no—
98Dic30—41no—
99Dic30—41no—
100Dic30—41no—
101C3×C5×C8—22no—
102C3×C5×C8—41no—
103C3⋊#168—41no—
104C3×C4×D4C2×D511yescharacteristic
105#936—101no—
106C2×#214—101no—
107#926—101no—
108#924—101no—
109#887—101no—
110#879—102no—
111#869—51no—
112#869—51no—
113C4×Dic6—51no—
114C3×C4⋊C8C2×D511yescharacteristic
115C3×C4×C8C2×D511yescharacteristic
116#818—102no—
117#817—101no—
118#816—101no—
119#810—101no—
120C4⋊(C3⋊C8)—51no—
121C2×C5×D4D1211yescharacteristic
122C22×C4×C5—21no—
123C2×Dic10—31no—
124C2×Dic10—61no—
125C2×Dic10—61no—
126C2×C5×C8—21no—
127C2×C5×C8—21no—
128C5×C4⋊C4D1211yescharacteristic
129C5×C22⋊C4—21no—
130C42×C5C22×D311yescharacteristic
131C22⋊Dic5—62no—
132C22⋊Dic5—62no—
133#687—122no—
134C4⋊Dic5—31no—
135C4⋊Dic5—32no—
136C4⋊Dic5—61no—
137C4⋊Dic5—61no—
138C4⋊Dic5—61no—
139#683—62no—
140#683—61no—
141C4×Dic5—62no—
142C4×Dic5—61no—
143C2×#168—61no—
144#556—151no—
145#500—151no—
146#475—151no—
147#461—151no—
148#332—151no—
149Q8⋊C8—151no—
150D4⋊C8D1511yescharacteristic
151C22×C3×C5—41no—
152C22×C3×C5—41no—
153C22×C3×C5—41no—
154C22×C3×C5#12011yescharacteristic
155C3×C4×C5—21no—
156C3×C4×C5—41no—
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C3×C4×C5#13711yescharacteristic
161Dic15—42no—
162Dic15—41no—
163Dic15—41no—
164Dic15—81no—
165C2×C3×D4D2011yescharacteristic
166C22×C3×C4—21no—
167C2×Dic6—51no—
168C2×Dic6—101no—
169C2×Dic6—101no—
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C3×C4⋊C4D2011yescharacteristic
173C3×C22⋊C4—21no—
174C3×C42C22×D511yescharacteristic
175#217—102no—
176#217—102no—
177#214—202no—
178C4⋊Dic3—51no—
179C4⋊Dic3—52no—
180C4⋊Dic3—101no—
181C4⋊Dic3—101no—
182C4⋊Dic3—101no—
183Dic3⋊C4—102no—
184Dic3⋊C4—101no—
185C4×Dic3—102no—
186C4×Dic3—101no—
187C2×C3⋊C8—101no—
188C23×C5—21no—
189C5×D4—21no—
190C5×D4—21no—
191C2×C4×C5—21no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5C2×D1211yescharacteristic
195C2×C4×C5D3×D411yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×Dic5—61no—
198C2×Dic5—61no—
199C2×Dic5—62no—
200C2×Dic5—121no—
201Dic10—61no—
202Dic10—61no—
203Dic10—121no—
204Dic10—121no—
205Dic10—121no—
206Dic10—121no—
207C5×C8—22no—
208C5×C8—41no—
209#168—121no—
210C2×SD16—301no—
211C4⋊Q8—151no—
212C4⋊Q8—151no—
213#126—302no—
214#124—301no—
215C22⋊Q8—301no—
216C4×Q8—151no—
217C4×Q8—301no—
218C4×D4C2×D1511yescharacteristic
219#117—301no—
220#107—302no—
221#106—301no—
222C4⋊C8—151no—
223C4⋊C8C2×D1511yescharacteristic
224#103—301no—
225#103—301no—
226C4×C8C2×D1511yescharacteristic
227C2×C3×C5—81no—
228C2×C3×C5#44911yescharacteristic
229C2×C3×C5#45211yescharacteristic
230C2×C3×C5#45611yescharacteristic
231C23×C3—21no—
232C3×D4—21no—
233C3×D4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—41no—
236C2×C3×C4—41no—
237C2×C3×C4C2×D2011yescharacteristic
238C2×C3×C4D4×D511yescharacteristic
239C2×C3×C4D4×D511yescharacteristic
240C2×Dic3—101no—
241C2×Dic3—101no—
242C2×Dic3—102no—
243C2×Dic3—201no—
244Dic6—101no—
245Dic6—101no—
246Dic6—201no—
247Dic6—201no—
248Dic6—201no—
249Dic6—201no—
250C3×C8—22no—
251C3×C8—41no—
252C3⋊C8—201no—
253C22×C5—41no—
254C22×C5—41no—
255C22×C5—41no—
256C22×C5#88211yescharacteristic
257C4×C5—21no—
258C4×C5—41no—
259C4×C5#90411yescharacteristic
260C4×C5#90811yescharacteristic
261C4×C5#91211yescharacteristic
262C4×C5#91511yescharacteristic
263Dic5—122no—
264Dic5—121no—
265Dic5—121no—
266Dic5—241no—
267C2×Q8—151no—
268C2×Q8—301no—
269C2×Q8—301no—
270C2×D4D6011yescharacteristic
271C22×C4—21no—
272SD16—602no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—301no—
276C4⋊C4—151no—
277C4⋊C4—152no—
278C4⋊C4—302no—
279C4⋊C4—301no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C4⋊C4—301no—
283C4⋊C4D6011yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—302no—
286C22⋊C4—302no—
287C42—302no—
288C42—301no—
289C42C22×D1511yescharacteristic
290C3×C5#165011yescharacteristic, complemented, Hall
291C22×C3—41no—
292C22×C3—41no—
293C22×C3—41no—
294C22×C3#402811yescharacteristic
295C3×C4—21no—
296C3×C4—41no—
297C3×C4#405011yescharacteristic
298C3×C4#405411yescharacteristic
299C3×C4#405811yescharacteristic
300C3×C4#406111yescharacteristic
301Dic3—201no—
302Dic3—201no—
303Dic3—202no—
304Dic3—401no—
305C2×C5—81no—
306C2×C5#473411yescharacteristic
307C2×C5#478311yescharacteristic
308C2×C5#482611yescharacteristic
309C23—21no—
310Q8—301no—
311Q8—301no—
312Q8—601no—
313Q8—601no—
314Q8—601no—
315Q8—601no—
316D4—21no—
317D4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—301no—
322C2×C4—302no—
323C2×C4—301no—
324C2×C4—601no—
325C2×C4C2×D6011yescharacteristic
326C2×C4D4×D1511yescharacteristic
327C2×C4D4×D1511yescharacteristic
328C8—22no—
329C8—41no—
330C8—601no—
331C2×C3—81no—
332C2×C3#6502311yescharacteristic
333C2×C3#6507211yescharacteristic
334C2×C3#6511511yescharacteristic
335C5#6820911yescharacteristic, complemented, Sylow
336C22—41no—
337C22—41no—
338C22—41no—
339C22#9177111yescharacteristic
340C4—21no—
341C4—41no—
342C4—601no—
343C4—602no—
344C4—601no—
345C4—1201no—
346C4#9179311yescharacteristic
347C4#9179711yescharacteristic
348C4#9180111yescharacteristic
349C4#9180411yescharacteristic
350C3#1059900211yescharacteristic, complemented, Sylow
351C2—81no—
352C2#1175083511yescharacteristic
353C2#1175088411yescharacteristic
354C2#1175092711yescharacteristic
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#1650
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. #11750952C2semidirect
4. #11750783C2semidirect
6. #11746307C2semidirect
7. #11746277C2semidirect
290. C3×C5#1650semidirect
335. C5#68209semidirect
350. C3#10599002semidirect

Maximal subgroups

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

subgroupindex
#117563012
#117511202
#117509522
#117507832
C3×C5×D4⋊C82
#117463072
#117462772
#105990023
#682095