Finite Group Databasebeta

← #14289605

Subgroups — #14289605

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
2C5×#5008C211yesmaximal, characteristic, complemented
3#11747096C211yesmaximal, characteristic, complemented
4#11746885C211yesmaximal, characteristic, complemented
5C3×D4⋊#168C211yesmaximal, characteristic, complemented
6#11745863C211yesmaximal, characteristic, complemented
7#11745839C211yesmaximal, characteristic, complemented
8#10601938—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
17C5×#869C2211yescharacteristic
18C2×#6663—22no—
19C5×#832—21no—
20C5×#808—21no—
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24#90985—21no—
25#90969—21no—
26#68203—51nomaximal, Hall
27#65897—31no—
28C5×#476—31no—
29#65381—31no—
30#65373—31no—
31D4⋊#168D311yescharacteristic, complemented
32#64703—31no—
33#64701—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×#1220—22no—
37C2×D60D411yescharacteristic
38C2×C4×D15—21no—
39C2×Dic30D412yes—
40C2×C5×Dic6—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—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3—21no—
53C2×C5×C3⋊C8—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56#6663—44no—
57#5563—51no—
58#5008D511yescharacteristic, complemented
59#4842—51no—
60#4699—51no—
61C3×D4⋊C8—51no—
62#4481—51no—
63#4459—51no—
64C5×C4⋊Q8—31no—
65C4×C5×D4C2×D311yescharacteristic
66C2×#689—62no—
67#4084—61no—
68#4076—61no—
69#4072—61no—
70#4038—61no—
71#4031—62no—
72C4×D20—31no—
73#4015—31no—
74C5×#106—61no—
75C5×C4⋊C8—31no—
76C5×#102—61no—
77#3941—61no—
78#3940—61no—
79C4⋊#168C2×D311yescharacteristic
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×C5×Dic3—41no—
101C5×Dic6—42no—
102C3×#168—22no—
103C3×#168—41no—
104C5×C3⋊C8—41no—
105C3×C4×D4C2×D511yescharacteristic
106#938—101no—
107#930—101no—
108#926—101no—
109C2×Dic12—102no—
110#892—101no—
111#885—102no—
112C4×D12—51no—
113#869—51no—
114#869C2×D511yescharacteristic
115C3×C4⋊C8—51no—
116C3×C4×C8—51no—
117#832—21no—
118#821—101no—
119#817—101no—
120#808—21no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C2×C5×Q8—61no—
123C2×C5×D4D1211yescharacteristic
124C22×C4×C5—21no—
125C2×C22⋊D5—62no—
126C2×D20—31no—
127C2×C4×D5—61no—
128C2×Dic10—32no—
129C2×C5×C8—61no—
130C5×C4⋊C4—61no—
131C5×C4⋊C4—61no—
132C5×C4⋊C4D1211yescharacteristic
133C5×C22⋊C4—21no—
134C42×C5C22×D311yescharacteristic
135C22⋊Dic5—62no—
136#689—124no—
137#685—62no—
138#685—61no—
139C4⋊Dic5—31no—
140C4⋊Dic5—61no—
141C4⋊Dic5—61no—
142C4×Dic5—62no—
143C2×#168—21no—
144C2×#168—21no—
145#555—151no—
146#494—151no—
147#476—31no—
148#476—151no—
149#333—151no—
150D4⋊C8—51no—
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—
167C5×Dic3—81no—
168C2×C3×D4C22⋊D511yescharacteristic
169C22×C3×C4—21no—
170C2×#67—102no—
171C2×D12—51no—
172C2×C4×D3—101no—
173C2×Dic6—21no—
174C2×Dic6—52no—
175C2×C3×C8—101no—
176C2×C3×C8—101no—
177C3×C4⋊C4C22⋊D511yescharacteristic
178C3×C22⋊C4—21no—
179C3×C42C22×D511yescharacteristic
180#217—102no—
181(C2×D3)⋊C4—102no—
182(C2×D3)⋊C4—101no—
183C4⋊Dic3—21no—
184C4⋊Dic3—21no—
185C4⋊Dic3—51no—
186C4⋊Dic3—101no—
187C4⋊Dic3—101no—
188C4×Dic3—102no—
189C2×C3⋊C8—21no—
190Dic12—204no—
191C23×C5—21no—
192C22×D5—61no—
193C5×Q8—122no—
194C5×D4—21no—
195C5×D4—21no—
196C2×C4×C5—21no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5—121no—
200C2×C4×C5C2×D1211yescharacteristic
201C2×C4×C5D3×D411yescharacteristic
202C2×C4×C5D3×D411yescharacteristic
203C22⋊D5—242no—
204C2×Dic5—61no—
205C2×Dic5—62no—
206D20—61no—
207D20—61no—
208C4×D5—121no—
209C4×D5—121no—
210Dic10—122no—
211C5×C8—121no—
212#168—22no—
213#168—41no—
214C2×Q16—302no—
215C4⋊Q8—31no—
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—61no—
225#106—301no—
226C4⋊C8—31no—
227C4⋊C8—51no—
228#102—61no—
229#102—301no—
230C4×C8—51no—
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×D4—21no—
239C3×D4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4D4×D511yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×C3×C4C2×C22⋊D511yescharacteristic
246#67—402no—
247C2×Dic3—41no—
248C2×Dic3—101no—
249C2×Dic3—102no—
250D12—101no—
251D12—101no—
252C4×D3—201no—
253C4×D3—201no—
254Dic6—42no—
255Dic6—202no—
256C3×C8—102no—
257C3×C8—201no—
258C3⋊C8—41no—
259C22×C5—41no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5#88211yescharacteristic
263C2×D5—121no—
264C2×D5—121no—
265C2×D5—121no—
266C4×C5—21no—
267C4×C5—41no—
268C4×C5—241no—
269C4×C5#90411yescharacteristic
270C4×C5#90911yescharacteristic
271C4×C5#91211yescharacteristic
272C4×C5#91511yescharacteristic
273Dic5—121no—
274Dic5—122no—
275C2×Q8—61no—
276C2×Q8—152no—
277C2×D4—151no—
278C2×D4—302no—
279C2×D4#120311yescharacteristic
280C22×C4—21no—
281C22×C4—301no—
282Q16—604no—
283C2×C8—61no—
284C2×C8—101no—
285C2×C8—101no—
286C4⋊C4—61no—
287C4⋊C4—61no—
288C4⋊C4—151no—
289C4⋊C4—301no—
290C4⋊C4—301no—
291C4⋊C4#120311yescharacteristic
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#408311yescharacteristic
303C2×D3—201no—
304C2×D3—201no—
305C2×D3—201no—
306C3×C4—21no—
307C3×C4—41no—
308C3×C4#406111yescharacteristic
309C3×C4#406211yescharacteristic
310C3×C4#408811yescharacteristic
311C3×C4#409611yescharacteristic
312Dic3—81no—
313Dic3—201no—
314Dic3—202no—
315C2×C5—81no—
316C2×C5#473311yescharacteristic
317C2×C5#478311yescharacteristic
318C2×C5#482211yescharacteristic
319D5—241no—
320C23—21no—
321C23—301no—
322Q8—122no—
323Q8—602no—
324D4—21no—
325D4—21no—
326D4—301no—
327D4—301no—
328D4—1202no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—121no—
333C2×C4—301no—
334C2×C4—302no—
335C2×C4—601no—
336C2×C4—601no—
337C2×C4C2×#120311yescharacteristic
338C2×C4#679011yescharacteristic
339C2×C4#679011yescharacteristic
340C8—102no—
341C8—121no—
342C8—201no—
343C2×C3—81no—
344C2×C3#6533611yescharacteristic
345C2×C3#6546211yescharacteristic
346C2×C3#6548711yescharacteristic
347D3—401no—
348C5#6820311yescharacteristic, complemented, Sylow
349C22—41no—
350C22—41no—
351C22—41no—
352C22—601no—
353C22—601no—
354C22—601no—
355C22#9157311yescharacteristic
356C4—21no—
357C4—41no—
358C4—241no—
359C4—602no—
360C4—601no—
361C4#9130311yescharacteristic
362C4#9132111yescharacteristic
363C4#9148811yescharacteristic
364C4#9149711yescharacteristic
365C3#1060193811yescharacteristic, complemented, Sylow
366C2—81no—
367C2—1201no—
368C2#1174856611yescharacteristic
369C2#1174906111yescharacteristic
370C2#1174942211yescharacteristic
subgroupG/H
centerC22#91573
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. C5×#5008C2semidirect
3. #11747096C2semidirect
4. #11746885C2semidirect
5. C3×D4⋊#168C2semidirect
6. #11745863C2semidirect
7. #11745839C2semidirect
31. D4⋊#168D3semidirect
58. #5008D5semidirect
298. C3×C5#1634semidirect
348. C5#68203semidirect
365. C3#10601938semidirect

Maximal subgroups

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

subgroupindex
#117563222
C5×#50082
#117470962
#117468852
C3×D4⋊#1682
#117458632
#117458392
#106019383
#682035