Finite Group Databasebeta

← #14290053

Subgroups — #14290053

Order 1920.

500 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C3×#65887C211yesmaximal, characteristic
2#11751108C211yesmaximal, characteristic, complemented
3#11747095C211yesmaximal, characteristic, complemented
4#11746890C211yesmaximal, characteristic, complemented
5C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#11745852C211yesmaximal, characteristic, complemented
7#11745841C211yesmaximal, characteristic, complemented
8#10598983—31nomaximal, Hall
9C2×C3×#709—21no—
10C3×C4×C5×D4C2211yescharacteristic
11#91758C2211yescharacteristic
12C3×#4086—21no—
13C3×#4076—21no—
14C3×#4039—21no—
15C3×#4030—22no—
16C3×#4020C2211yescharacteristic
17C3×C4×Dic10C2211yescharacteristic
18C2×#6662—21no—
19#91116—21no—
20#91091—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C4×C5×C3⋊C8C2211yescharacteristic
24#90974—21no—
25#90965—22no—
26#71920—51nomaximal, Hall
27#65887D311yescharacteristic
28#65296—31no—
29#65138—31no—
30#64983—31no—
31C5×D4⋊C8—31no—
32#64705—31no—
33#64676—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×Dic30—21no—
37C2×C3×C22⋊D5—22no—
38C2×C3×C22⋊D5—22no—
39C3×#709—42no—
40C3×#709—42no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C2×C3×D20D412yes—
44C2×C3×C4×D5—22no—
45C2×C3×Dic10D411yescharacteristic
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C5×C22⋊C4—21no—
48C3×C42×C5C2311yescharacteristic
49C4⋊Dic15—21no—
50C4⋊Dic15—21no—
51C2×C3⋊#168—21no—
52C2×C5×C3⋊C8—21no—
53C2×C5×C3⋊C8—21no—
54C3×#685—22no—
55C3×C4⋊Dic5D411yescharacteristic
56C3×#683—21no—
57C3×C4×Dic5—21no—
58#6662—42no—
59C3×#550—51no—
60#5070—51no—
61#5031—51no—
62#5007—51no—
63#4544—51no—
64#4535—51no—
65D4⋊(C3⋊C8)D511yescharacteristic, complemented
66C2×#709—21no—
67C4×C5×D4C2×D311yescharacteristic
68#4086—21no—
69#4076—21no—
70C2×Dic20—61no—
71#4039—21no—
72#4030—22no—
73#4020C2×D311yescharacteristic
74#4015—31no—
75C4×Dic10C2×D311yescharacteristic
76C5×C4⋊C8—31no—
77C4×C5×C8—31no—
78#3964—61no—
79#3953—62no—
80#3948—61no—
81#3939—61no—
82C4⋊#168—31no—
83#1641—151noSylow
84C23×C3×C5—21no—
85C22×C3×D5—22no—
86C3×C5×D4—21no—
87C3×C5×D4—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×Dic15—41no—
95Dic30—41no—
96Dic30—41no—
97C3×C22⋊D5—44no—
98C3×C22⋊D5—82no—
99C2×C3×Dic5—21no—
100C2×C3×Dic5—21no—
101C3×D20—42no—
102C3×D20—41no—
103C3×D20—41no—
104C3×D20—41no—
105C3×D20—41no—
106C3×C4×D5—44no—
107C3×Dic10—21no—
108C3×Dic10D812yes—
109C3⋊#168—41no—
110C5×C3⋊C8—41no—
111C5×C3⋊C8—41no—
112C2×C3×#41—101no—
113C3×#127—51no—
114C3×#127—101no—
115C3×#121—102no—
116C3×#121—101no—
117C3×C4×Q8—51no—
118C3×C4×D4—101no—
119C3×C4×D4C2×D511yescharacteristic
120C2×#216—101no—
121#869—51no—
122#832—102no—
123#832—101no—
124#810—101no—
125#807—101no—
126C4⋊(C3⋊C8)—51no—
127C4⋊(C3⋊C8)C2×D511yescharacteristic
128C4×C3⋊C8C2×D511yescharacteristic
129C2×C5×D4#6711yescharacteristic
130C22×C4×C5—21no—
131C2×C22⋊D5—22no—
132C2×C22⋊D5—22no—
133#709—42no—
134#709—42no—
135C2×D20—21no—
136C2×D20—21no—
137C2×D20#6712yes—
138C2×C4×D5—22no—
139C2×Dic10—61no—
140C2×Dic10#6711yescharacteristic
141C2×C5×C8—61no—
142C2×C5×C8—61no—
143C5×C4⋊C4#6711yescharacteristic
144C5×C22⋊C4—21no—
145C42×C5C22×D311yescharacteristic
146#685—22no—
147C4⋊Dic5—61no—
148C4⋊Dic5—61no—
149C4⋊Dic5#6711yescharacteristic
150#683—21no—
151C4×Dic5—21no—
152C2×#168—61no—
153Dic20—122no—
154#550—51no—
155#486—151no—
156#474—151no—
157#462—151no—
158#331—151no—
159Q8⋊C8—151no—
160D4⋊C8—31no—
161C22×C3×C5—41no—
162C22×C3×C5—41no—
163C22×C3×C5—41no—
164C22×C3×C5#12011yescharacteristic
165C2×C3×D5—42no—
166C2×C3×D5—42no—
167C2×C3×D5—42no—
168C3×C4×C5—21no—
169C3×C4×C5—41no—
170C3×C4×C5C2×D811yescharacteristic
171C3×C4×C5#13511yescharacteristic
172C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
173C3×C4×C5#13711yescharacteristic
174Dic15—81no—
175C3×Dic5—22no—
176C3×Dic5—41no—
177C3×#41—202no—
178C3×#41—202no—
179C2×C3×Q8—51no—
180C2×C3×D4—52no—
181C2×C3×D4—102no—
182C2×C3×D4—102no—
183C2×C3×D4—101no—
184C2×C3×D4—101no—
185C2×C3×D4D2011yescharacteristic
186C22×C3×C4—21no—
187C22×C3×C4—102no—
188C2×Dic6—101no—
189C3×C4⋊C4—51no—
190C3×C4⋊C4—101no—
191C3×C4⋊C4D2011yescharacteristic
192C3×C22⋊C4—21no—
193C3×C22⋊C4—102no—
194C3×C42—101no—
195C3×C42C22×D511yescharacteristic
196#216—202no—
197C4⋊Dic3—101no—
198C4⋊Dic3—101no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—101no—
202C23×C5—21no—
203C22×D5—22no—
204C5×D4—21no—
205C5×D4—21no—
206C2×C4×C5—21no—
207C2×C4×C5—41no—
208C2×C4×C5—41no—
209C2×C4×C5C2×#6711yescharacteristic
210C2×C4×C5C2×#6711yescharacteristic
211C2×C4×C5C2×#6711yescharacteristic
212C22⋊D5—44no—
213C22⋊D5—82no—
214C2×Dic5—21no—
215C2×Dic5—21no—
216C2×Dic5—121no—
217D20—42no—
218D20—41no—
219D20—41no—
220D20—41no—
221D20—41no—
222C4×D5—44no—
223Dic10—21no—
224Dic10—121no—
225Dic10—121no—
226Dic10#21312yes—
227C5×C8—121no—
228C5×C8—121no—
229#168—121no—
230C2×#41—101no—
231C2×Q16—301no—
232C4⋊Q8—151no—
233#127—51no—
234#127—101no—
235#121—102no—
236#121—101no—
237C4×Q8—51no—
238C4×D4—101no—
239C4×D4D3×D511yescharacteristic
240#107—301no—
241C4⋊C8—31no—
242C4⋊C8—151no—
243#103—301no—
244#102—302no—
245#102—301no—
246C4×C8—31no—
247C2×C3×C5—81no—
248C2×C3×C5#44711yescharacteristic
249C2×C3×C5#45211yescharacteristic
250C2×C3×C5#45511yescharacteristic
251C3×D5—82no—
252C23×C3—21no—
253C23×C3—102no—
254C3×Q8—52no—
255C3×Q8—101no—
256C3×D4—21no—
257C3×D4—21no—
258C3×D4—202no—
259C3×D4—204no—
260C3×D4—201no—
261C3×D4—201no—
262C3×D4—201no—
263C3×D4—201no—
264C3×D4—402no—
265C2×C3×C4—21no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—101no—
269C2×C3×C4—101no—
270C2×C3×C4—204no—
271C2×C3×C4C2×D2011yescharacteristic
272C2×C3×C4D4×D511yescharacteristic
273C2×C3×C4D4×D511yescharacteristic
274C2×Dic3—201no—
275Dic6—201no—
276Dic6—201no—
277C3⋊C8—41no—
278C3⋊C8—41no—
279C3⋊C8—201no—
280C22×C5—41no—
281C22×C5—41no—
282C22×C5—41no—
283C22×C5#95311yescharacteristic
284C2×D5—42no—
285C2×D5—42no—
286C2×D5—42no—
287C4×C5—21no—
288C4×C5—41no—
289C4×C5C2×#21311yescharacteristic
290C4×C5#93211yescharacteristic
291C4×C5#95011yescharacteristic
292C4×C5#95111yescharacteristic
293Dic5—22no—
294Dic5—41no—
295Dic5—241no—
296#41—202no—
297#41—202no—
298C2×Q8—51no—
299C2×Q8—301no—
300C2×D4—52no—
301C2×D4—102no—
302C2×D4—102no—
303C2×D4—101no—
304C2×D4—101no—
305C2×D4#120211yescharacteristic
306C22×C4—21no—
307C22×C4—102no—
308Q16—602no—
309C2×C8—61no—
310C2×C8—61no—
311C2×C8—301no—
312C4⋊C4—51no—
313C4⋊C4—101no—
314C4⋊C4—301no—
315C4⋊C4—301no—
316C4⋊C4#120211yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—102no—
319C42—101no—
320C42C2×D3×D511yescharacteristic
321C3×C5#164111yescharacteristic, complemented, Hall
322C22×C3—41no—
323C22×C3—41no—
324C22×C3—41no—
325C22×C3—202no—
326C22×C3—202no—
327C22×C3—202no—
328C22×C3#402811yescharacteristic
329C3×C4—21no—
330C3×C4—41no—
331C3×C4—102no—
332C3×C4—201no—
333C3×C4#405011yescharacteristic
334C3×C4#405511yescharacteristic
335C3×C4D5×D811yescharacteristic
336C3×C4#406011yescharacteristic
337Dic3—401no—
338C2×C5—81no—
339C2×C5#521711yescharacteristic
340C2×C5#523911yescharacteristic
341C2×C5#524211yescharacteristic
342D5—82no—
343C23—21no—
344C23—102no—
345Q8—52no—
346Q8—101no—
347Q8—601no—
348Q8—601no—
349D4—21no—
350D4—21no—
351D4—202no—
352D4—204no—
353D4—201no—
354D4—201no—
355D4—201no—
356D4—201no—
357D4—402no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—101no—
362C2×C4—101no—
363C2×C4—204no—
364C2×C4—601no—
365C2×C4C2×#120211yescharacteristic
366C2×C4D5×#6711yescharacteristic
367C2×C4D5×#6711yescharacteristic
368C8—121no—
369C8—121no—
370C8—601no—
371C2×C3—81no—
372C2×C3—402no—
373C2×C3#6502211yescharacteristic
374C2×C3#6506211yescharacteristic
375C2×C3#6511411yescharacteristic
376C5#7192011yescharacteristic, complemented, Sylow
377C22—41no—
378C22—41no—
379C22—41no—
380C22—202no—
381C22—202no—
382C22—202no—
383C22#9156411yescharacteristic
384C4—21no—
385C4—41no—
386C4—102no—
387C4—201no—
388C4—1201no—
389C4#9131111yescharacteristic
390C4#9131311yescharacteristic
391C4D5×#21311yescharacteristic
392C4#9149111yescharacteristic
393C3#1059898311yescharacteristic, complemented, Sylow
394C2—81no—
395C2—402no—
396C2#1174853111yescharacteristic
397C2#1174902211yescharacteristic
398C2#1174946311yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radicalC3×#65887C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#1641
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. #11751108C2semidirect
3. #11747095C2semidirect
4. #11746890C2semidirect
5. C5×D4⋊(C3⋊C8)C2semidirect
6. #11745852C2semidirect
7. #11745841C2semidirect
65. D4⋊(C3⋊C8)D5semidirect
321. C3×C5#1641semidirect
376. C5#71920semidirect
393. C3#10598983semidirect

Maximal subgroups

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

subgroupindex
C3×#658872
#117511082
#117470952
#117468902
C5×D4⋊(C3⋊C8)2
#117458522
#117458412
#105989833
#719205