Finite Group Databasebeta

← #14289525

Subgroups — #14289525

Order 1920.

428 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 90 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#11752641C211yesmaximal, characteristic
2C5×#4842C211yesmaximal, characteristic
3#11747103C211yesmaximal, characteristic, complemented
4#11746963C211yesmaximal, characteristic, complemented
5#11746305C211yesmaximal, characteristic, complemented
6C3×#64701C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic
8#10601937—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C4×C5×D12C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91435—21no—
14D3×C4⋊Dic5—21no—
15#91410—22no—
16#91384—21no—
17#91365—21no—
18C2×#6661—22no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C5×#821—21no—
22C5×#817—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90988—21no—
25#90975—21no—
26#68492—51nomaximal, Hall
27#65877—31no—
28C5×#476—31no—
29#65381—31no—
30#65380—31no—
31D4⋊#168—31no—
32#64704—31no—
33#64701D311yescharacteristic, complemented
34C2×Dic30D411yescharacteristic
35C2×C5×D12D411yescharacteristic
36C2×C4×C5×D3—21no—
37C2×C5×Dic6—21no—
38C2×C3×Dic10D412yes—
39C2×D3×Dic5—22no—
40C2×C3×C5×C8—21no—
41C3×C42×C5C2311yescharacteristic
42C4⋊Dic15D411yescharacteristic
43#6712—21no—
44C4×Dic15—21no—
45C2×C3⋊#168—21no—
46C5×(C2×D3)⋊C4—21no—
47C5×C4⋊Dic3—21no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3D411yescharacteristic
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5—21no—
52C2×C3×#168—21no—
53Dic3⋊Dic5—22no—
54#6668—22no—
55(C2×D3)⋊Dic5—22no—
56#6661—44no—
57#5730—51no—
58#5092—51no—
59#4850—51no—
60#4842D511yescharacteristic
61C3×#333—51no—
62#4484—51no—
63#4483—51no—
64C5×C4⋊Q8—31no—
65C4×C5×D4—31no—
66C2×#689—62no—
67D4×Dic5—61no—
68C2×C4⋊Dic5—61no—
69#4070—61no—
70#4036—61no—
71#4024—62no—
72#4015C2×D311yescharacteristic
73C4×Dic10—31no—
74C5×#106—61no—
75C5×C4⋊C8C2×D311yescharacteristic
76C5×#102—61no—
77#3942—61no—
78#3939—61no—
79C4⋊#168C2×D311yescharacteristic
80C4×#168—31no—
81#1632—151noSylow
82C22×C5×D3—21no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—21no—
87C2×Dic15—21no—
88Dic30—21no—
89Dic30—21no—
90C2×C5×Dic3—21no—
91C2×C5×Dic3—41no—
92C5×D12—21no—
93C5×D12Q1612yescomplemented
94C4×C5×D3—41no—
95C4×C5×D3—41no—
96C5×Dic6—42no—
97C2×C3×Dic5—22no—
98C3×Dic10—42no—
99D3×Dic5—82no—
100C3×C5×C8—41no—
101C3⋊#168—22no—
102C3×#168—41no—
103C3×C4⋊Q8—51no—
104#946—102no—
105C2×#216—102no—
106#897—101no—
107#893—101no—
108D3×C4⋊C4—101no—
109#890—101no—
110C4×D12C2×D511yescharacteristic
111#869C2×D511yescharacteristic
112C4×Dic6—51no—
113C3×C4⋊C8—51no—
114C3×C4⋊C8C2×D511yescharacteristic
115#821—21no—
116#818—101no—
117#817—21no—
118#816—101no—
119C4×C3⋊C8—51no—
120C2×C5×Q8—61no—
121C2×C5×D4—31no—
122C22×C4×C5—61no—
123C22×Dic5—62no—
124C2×Dic10—31no—
125C2×Dic10D1212yes—
126C2×C5×C8—21no—
127C5×C4⋊C4—31no—
128C5×C4⋊C4—61no—
129C5×C4⋊C4—61no—
130C5×C22⋊C4—61no—
131C42×C5C22×D311yescharacteristic
132C22⋊Dic5—62no—
133#689—124no—
134C4⋊Dic5—21no—
135C4⋊Dic5—21no—
136C4⋊Dic5—31no—
137C4⋊Dic5—62no—
138#683—62no—
139#683—61no—
140C4×Dic5—61no—
141C2×#168—21no—
142C2×#168—61no—
143#554—151no—
144#494—151no—
145#477—151no—
146#476—31no—
147#333—51no—
148Q8⋊C8—151no—
149D4⋊C8—151no—
150C22×C3×C5#12011yescharacteristic
151C2×C5×D3—22no—
152C2×C5×D3—41no—
153C2×C5×D3—41no—
154C3×C4×C5—21no—
155C3×C4×C5C2×Q1611yescharacteristic
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13711yescharacteristic
158C3×C4×C5#13711yescharacteristic
159Dic15—41no—
160Dic15—41no—
161C3×Dic5—42no—
162C5×Dic3—41no—
163C5×Dic3—81no—
164C2×C3×Q8—52no—
165C2×D12C22⋊D511yescharacteristic
166C2×C4×D3—21no—
167C2×C4×D3—102no—
168C2×Dic6—21no—
169C2×Dic6—51no—
170C2×C3×C8—21no—
171C2×C3×C8—101no—
172C3×C4⋊C4—101no—
173C3×C4⋊C4—101no—
174C3×C42C22×D511yescharacteristic
175#216—204no—
176(C2×D3)⋊C4—21no—
177(C2×D3)⋊C4—102no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3—51no—
181C4⋊Dic3—102no—
182C4⋊Dic3C22⋊D511yescharacteristic
183Dic3⋊C4—102no—
184Dic3⋊C4—101no—
185C4×Dic3—101no—
186C2×C3⋊C8—101no—
187C23×C5—61no—
188C5×Q8—122no—
189C5×D4—32no—
190C5×D4—61no—
191C2×C4×C5—61no—
192C2×C4×C5—121no—
193C2×C4×C5—121no—
194C2×C4×C5—121no—
195C2×C4×C5C2×D1211yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×Dic5—22no—
199C2×Dic5—61no—
200C2×Dic5—61no—
201C2×Dic5—242no—
202Dic10—42no—
203Dic10—61no—
204Dic10—61no—
205C5×C8—41no—
206#168—41no—
207#168—62no—
208C2×Q16—302no—
209C4⋊Q8—31no—
210C4⋊Q8—51no—
211#125—301no—
212C22⋊Q8—302no—
213C22⋊Q8—301no—
214C4×Q8—151no—
215C4×D4—31no—
216C4×D4—301no—
217C2×C4⋊C4—301no—
218#107—301no—
219#106—61no—
220C4⋊C8—51no—
221C4⋊C8D3×D511yescharacteristic
222#103—301no—
223#102—61no—
224C4×C8—151no—
225C2×C3×C5#45111yescharacteristic
226C2×C3×C5#45211yescharacteristic
227C2×C3×C5#45311yescharacteristic
228C5×D3—42no—
229C22×D3—21no—
230C3×Q8—202no—
231C2×C3×C4—102no—
232C2×C3×C4D4×D511yescharacteristic
233C2×C3×C4D4×D511yescharacteristic
234C2×C3×C4C2×C22⋊D511yescharacteristic
235C2×Dic3—21no—
236C2×Dic3—41no—
237C2×Dic3—101no—
238C2×Dic3—101no—
239D12—21no—
240D12#68912yescomplemented
241C4×D3—41no—
242C4×D3—41no—
243C4×D3—402no—
244Dic6—42no—
245Dic6—101no—
246Dic6—101no—
247C3×C8—41no—
248C3×C8—201no—
249C3⋊C8—102no—
250C22×C5—62no—
251C22×C5—121no—
252C22×C5—121no—
253C22×C5#88211yescharacteristic
254C4×C5—21no—
255C4×C5—121no—
256C4×C5—241no—
257C4×C5#91511yescharacteristic
258C4×C5#91611yescharacteristic
259C4×C5D3×Q1611yescharacteristic
260C4×C5#91811yescharacteristic
261Dic5—42no—
262Dic5—121no—
263Dic5—121no—
264C2×Q8—52no—
265C2×Q8—61no—
266C2×Q8—151no—
267C2×D4—31no—
268C22×C4—61no—
269C22×C4—302no—
270Q16—604no—
271C2×C8—21no—
272C2×C8—101no—
273C2×C8—301no—
274C4⋊C4—31no—
275C4⋊C4—61no—
276C4⋊C4—61no—
277C4⋊C4—101no—
278C4⋊C4—101no—
279C4⋊C4—151no—
280C4⋊C4—302no—
281C4⋊C4—302no—
282C4⋊C4—301no—
283C22⋊C4—61no—
284C22⋊C4—302no—
285C42—301no—
286C42C2×D3×D511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3#408311yescharacteristic
289C2×D3—22no—
290C2×D3—41no—
291C2×D3—41no—
292C3×C4—21no—
293C3×C4—202no—
294C3×C4#406111yescharacteristic
295C3×C4#406211yescharacteristic
296C3×C4C2×#68911yescharacteristic
297C3×C4#409711yescharacteristic
298Dic3—41no—
299Dic3—81no—
300Dic3—201no—
301Dic3—201no—
302C2×C5—122no—
303C2×C5#474711yescharacteristic
304C2×C5#480811yescharacteristic
305C2×C5#480911yescharacteristic
306C23—61no—
307Q8—122no—
308Q8—202no—
309Q8—301no—
310Q8—301no—
311D4—32no—
312D4—61no—
313C2×C4—61no—
314C2×C4—102no—
315C2×C4—121no—
316C2×C4—121no—
317C2×C4—121no—
318C2×C4—301no—
319C2×C4—301no—
320C2×C4—1202no—
321C2×C4D5×D1211yescharacteristic
322C2×C4#677711yescharacteristic
323C2×C4D3×C22⋊D511yescharacteristic
324C8—41no—
325C8—201no—
326C8—302no—
327C2×C3#6533911yescharacteristic
328C2×C3#6546211yescharacteristic
329C2×C3#6548711yescharacteristic
330D3—42no—
331C5#6849211yescharacteristic, complemented, Sylow
332C22—62no—
333C22—121no—
334C22—121no—
335C22#9147511yescharacteristic
336C4—21no—
337C4—121no—
338C4—202no—
339C4—241no—
340C4—601no—
341C4—601no—
342C4#9127611yescharacteristic
343C4#9128011yescharacteristic
344C4#9148611yescharacteristic
345C4D3×#68911yescharacteristic
346C3#1060193711yescharacteristic, complemented, Sylow
347C2—122no—
348C2#1174749511yescharacteristic
349C2#1174815811yescharacteristic
350C2#1174824611yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radicalC2×C5×D12D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1632
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #11747103C2semidirect
4. #11746963C2semidirect
5. #11746305C2semidirect
6. C3×#64701C2semidirect
33. #64701D3semidirect
93. C5×D12Q16semidirect
240. D12#689semidirect
287. C3×C5#1632semidirect
331. C5#68492semidirect
346. C3#10601937semidirect

Maximal subgroups

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

subgroupindex
#117526412
C5×#48422
#117471032
#117469632
#117463052
C3×#647012
#117458362
#106019373
#684925