Finite Group Databasebeta

← #14289608

Subgroups — #14289608

Order 1920.

436 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 88 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#11756322C211yesmaximal, characteristic
2C3×#65297C211yesmaximal, characteristic, complemented
3#11747100C211yesmaximal, characteristic, complemented
4#11746942C211yesmaximal, characteristic, complemented
5C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#11745863C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic, complemented
8#10598996—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10#91827—21no—
11#91819—21no—
12#91815—21no—
13#91781—21no—
14#91774—22no—
15C4×D60C2211yescharacteristic
16#91758C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C2×#6662—22no—
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C4×C5×C3⋊C8C2211yescharacteristic
21C3×#3964—21no—
22C3×#3940—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90987—21no—
25#90968—21no—
26#71145—51nomaximal, Hall
27#65897—31no—
28#65297D311yescharacteristic, complemented
29#65131—31no—
30#64988—31no—
31C5×D4⋊C8—31no—
32#64701—31no—
33#64679—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×#1220—22no—
37C2×D60D411yescharacteristic
38C2×C4×D15—21no—
39C2×Dic30D412yes—
40C2×C3×Dic10—21no—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C5×C22⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44#6719—22no—
45#6714—22no—
46#6714—21no—
47C4⋊Dic15—21no—
48C4⋊Dic15—21no—
49C4⋊Dic15D411yescharacteristic
50C4×Dic15—22no—
51C2×C5×C3⋊C8—21no—
52C2×C5×C3⋊C8—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C2×C3×#168—21no—
56#6662—44no—
57#5563—51no—
58C3×#476—51no—
59#5092—51no—
60#5084—51no—
61D4⋊(C3⋊C8)D511yescharacteristic, complemented
62#4483—51no—
63#4481—51no—
64C4×C5×D4C2×D311yescharacteristic
65#4084—61no—
66#4076—61no—
67#4072—61no—
68C2×Dic20—62no—
69#4038—61no—
70#4031—62no—
71C4×D20—31no—
72#4015—31no—
73#4015C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C4×C5×C8—31no—
76#3964—21no—
77#3953—61no—
78#3949—61no—
79#3940—21no—
80C4⋊#168C2×D311yescharacteristic
81#1634—151noSylow
82C23×C3×C5—21no—
83C22×D15—21no—
84C3×C5×D4—21no—
85C3×C5×D4—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92#1220—82no—
93C2×Dic15—21no—
94C2×Dic15—22no—
95D60—21no—
96D60—21no—
97C4×D15—41no—
98C4×D15—41no—
99Dic30—42no—
100C2×C3×Dic5—41no—
101C3×Dic10—42no—
102C3×#168—41no—
103C5×C3⋊C8—22no—
104C5×C3⋊C8—41no—
105C3×C4⋊Q8—51no—
106C3×C4×D4C2×D511yescharacteristic
107C2×#216—102no—
108#938—101no—
109#930—101no—
110#926—101no—
111#892—101no—
112#885—102no—
113C4×D12—51no—
114#869—51no—
115C3×#106—101no—
116C3×C4⋊C8—51no—
117C3×#102—101no—
118#809—101no—
119#808—101no—
120C4⋊(C3⋊C8)C2×D511yescharacteristic
121C4×C3⋊C8C2×D511yescharacteristic
122C2×C5×D4#6711yescharacteristic
123C22×C4×C5—21no—
124C2×C22⋊D5—62no—
125C2×D20—31no—
126C2×C4×D5—61no—
127C2×Dic10—21no—
128C2×Dic10—32no—
129C2×C5×C8—61no—
130C2×C5×C8—61no—
131C5×C4⋊C4#6711yescharacteristic
132C5×C22⋊C4—21no—
133C42×C5C22×D311yescharacteristic
134C22⋊Dic5—62no—
135#685—62no—
136#685—61no—
137C4⋊Dic5—21no—
138C4⋊Dic5—21no—
139C4⋊Dic5—31no—
140C4⋊Dic5—61no—
141C4⋊Dic5—61no—
142C4×Dic5—62no—
143C2×#168—21no—
144Dic20—124no—
145#555—151no—
146#494—151no—
147#476—51no—
148#476—151no—
149#333—151no—
150D4⋊C8—31no—
151D4⋊C8—151no—
152C22×C3×C5—41no—
153C22×C3×C5—41no—
154C22×C3×C5—41no—
155C22×C3×C5#12011yescharacteristic
156C2×D15—41no—
157C2×D15—41no—
158C2×D15—41no—
159C3×C4×C5—21no—
160C3×C4×C5—41no—
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C3×C4×C5#13711yescharacteristic
165Dic15—41no—
166Dic15—42no—
167C3×Dic5—81no—
168C2×C3×Q8—101no—
169C2×C3×D4D2011yescharacteristic
170C22×C3×C4—21no—
171C2×#67—102no—
172C2×D12—51no—
173C2×C4×D3—101no—
174C2×Dic6—52no—
175C2×C3×C8—101no—
176C3×C4⋊C4—101no—
177C3×C4⋊C4—101no—
178C3×C4⋊C4D2011yescharacteristic
179C3×C22⋊C4—21no—
180C3×C42C22×D511yescharacteristic
181#217—102no—
182#216—204no—
183(C2×D3)⋊C4—102no—
184(C2×D3)⋊C4—101no—
185C4⋊Dic3—51no—
186C4⋊Dic3—101no—
187C4⋊Dic3—101no—
188C4×Dic3—102no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C23×C5—21no—
192C22×D5—61no—
193C5×D4—21no—
194C5×D4—21no—
195C2×C4×C5—21no—
196C2×C4×C5—41no—
197C2×C4×C5—41no—
198C2×C4×C5D3×D411yescharacteristic
199C2×C4×C5D3×D411yescharacteristic
200C2×C4×C5C2×#6711yescharacteristic
201C22⋊D5—242no—
202C2×Dic5—41no—
203C2×Dic5—61no—
204C2×Dic5—62no—
205D20—61no—
206D20—61no—
207C4×D5—121no—
208C4×D5—121no—
209Dic10—42no—
210Dic10—122no—
211C5×C8—62no—
212C5×C8—121no—
213#168—41no—
214C2×Q16—302no—
215C4⋊Q8—51no—
216C4⋊Q8—151no—
217#124—302no—
218#121—301no—
219#121—301no—
220C4×D4—151no—
221C4×D4D3×D511yescharacteristic
222#117—301no—
223#117—301no—
224#106—101no—
225#106—301no—
226C4⋊C8—31no—
227C4⋊C8—51no—
228#102—101no—
229#102—301no—
230C4×C8—31no—
231C2×C3×C5—81no—
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45211yescharacteristic
234C2×C3×C5#45311yescharacteristic
235D15—81no—
236C23×C3—21no—
237C22×D3—101no—
238C3×Q8—202no—
239C3×D4—21no—
240C3×D4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—201no—
245C2×C3×C4C2×D2011yescharacteristic
246C2×C3×C4D4×D511yescharacteristic
247C2×C3×C4D4×D511yescharacteristic
248#67—402no—
249C2×Dic3—101no—
250C2×Dic3—102no—
251D12—101no—
252D12—101no—
253C4×D3—201no—
254C4×D3—201no—
255Dic6—202no—
256C3×C8—201no—
257C3⋊C8—22no—
258C3⋊C8—41no—
259C22×C5—41no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5#93711yescharacteristic
263C2×D5—121no—
264C2×D5—121no—
265C2×D5—121no—
266C4×C5—21no—
267C4×C5—41no—
268C4×C5#91511yescharacteristic
269C4×C5#91611yescharacteristic
270C4×C5#94211yescharacteristic
271C4×C5#95011yescharacteristic
272Dic5—81no—
273Dic5—122no—
274Dic5—121no—
275C2×Q8—101no—
276C2×Q8—152no—
277C2×D4—151no—
278C2×D4—302no—
279C2×D4#120211yescharacteristic
280C22×C4—21no—
281C22×C4—301no—
282Q16—604no—
283C2×C8—61no—
284C2×C8—61no—
285C2×C8—101no—
286C4⋊C4—101no—
287C4⋊C4—101no—
288C4⋊C4—151no—
289C4⋊C4—301no—
290C4⋊C4—301no—
291C4⋊C4#120211yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—302no—
294C22⋊C4—302no—
295C22⋊C4—301no—
296C42—302no—
297C42C2×D3×D511yescharacteristic
298C3×C5#163411yescharacteristic, complemented, Hall
299C22×C3—41no—
300C22×C3—41no—
301C22×C3—41no—
302C22×C3#402811yescharacteristic
303C2×D3—201no—
304C2×D3—201no—
305C2×D3—201no—
306C3×C4—21no—
307C3×C4—41no—
308C3×C4—401no—
309C3×C4#405011yescharacteristic
310C3×C4#405511yescharacteristic
311C3×C4#405811yescharacteristic
312C3×C4#406111yescharacteristic
313Dic3—202no—
314Dic3—201no—
315C2×C5—81no—
316C2×C5#504711yescharacteristic
317C2×C5#517311yescharacteristic
318C2×C5#519811yescharacteristic
319D5—241no—
320C23—21no—
321C23—301no—
322Q8—202no—
323Q8—602no—
324D4—21no—
325D4—21no—
326D4—301no—
327D4—301no—
328D4—1202no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—201no—
333C2×C4—301no—
334C2×C4—302no—
335C2×C4—601no—
336C2×C4—601no—
337C2×C4C2×#120211yescharacteristic
338C2×C4#679011yescharacteristic
339C2×C4#679011yescharacteristic
340C8—62no—
341C8—121no—
342C8—201no—
343C2×C3—81no—
344C2×C3#6502211yescharacteristic
345C2×C3#6507211yescharacteristic
346C2×C3#6511111yescharacteristic
347D3—401no—
348C5#7114511yescharacteristic, complemented, Sylow
349C22—41no—
350C22—41no—
351C22—41no—
352C22—601no—
353C22—601no—
354C22—601no—
355C22#9157211yescharacteristic
356C4—21no—
357C4—41no—
358C4—401no—
359C4—602no—
360C4—601no—
361C4#9131111yescharacteristic
362C4#9131511yescharacteristic
363C4#9148811yescharacteristic
364C4#9149911yescharacteristic
365C3#1059899611yescharacteristic, complemented, Sylow
366C2—81no—
367C2—1201no—
368C2#1174855211yescharacteristic
369C2#1174906311yescharacteristic
370C2#1174942111yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radical#11756322C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#1634
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#65297C2semidirect
3. #11747100C2semidirect
4. #11746942C2semidirect
5. C5×D4⋊(C3⋊C8)C2semidirect
6. #11745863C2semidirect
7. #11745838C2semidirect
28. #65297D3semidirect
61. D4⋊(C3⋊C8)D5semidirect
298. C3×C5#1634semidirect
348. C5#71145semidirect
365. C3#10598996semidirect

Maximal subgroups

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

subgroupindex
#117563222
C3×#652972
#117471002
#117469422
C5×D4⋊(C3⋊C8)2
#117458632
#117458382
#105989963
#711455