Finite Group Databasebeta

← #14419346

Subgroups — #14419346

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11753517C211yesmaximal, characteristic
2#11752364C211yesmaximal, characteristic, complemented
3C3×#65702C211yesmaximal, characteristic, complemented
4#11751899C212yesmaximal, complemented
5#11751875C212yesmaximal, complemented
6C4×D3×#170C211yesmaximal, characteristic, complemented
7#11751807C211yesmaximal, characteristic, complemented
8#11751792C211yesmaximal, characteristic, complemented
9#11751769C212yesmaximal, complemented
10#11751767C212yesmaximal, complemented
11Dic6×#170C211yesmaximal, characteristic, complemented
12#10617265—31nomaximal, Hall
13C2×#6758C2212yes—
14C2×C3×D5⋊C8C2212yes—
15C2×D3×#170C2211yescharacteristic
16C2×D3×#170C2211yescharacteristic
17#91779C411yescharacteristic
18C5×#897C411yescharacteristic
19C3×#4039C2211yescharacteristic
20#91457C412yes—
21#91456C411yescharacteristic
22#91440C2212yes—
23C4×D3×Dic5C2211yescharacteristic
24#91368C411yescharacteristic
25#91361C412yes—
26#91358C2212yes—
27Dic5×Dic6C2211yescharacteristic
28#91232C2212yes—
29C4⋊(C3⋊#170)C2211yescharacteristic
30C4×C3⋊#170C2211yescharacteristic
31C3×#4003C2212yes—
32C3×C4⋊#170C2211yescharacteristic
33C3×C4×#170C2211yescharacteristic
34#91177C2212yes—
35Dic3⋊#170C2212yes—
36(C2×D3)⋊#170C2212yes—
37#91169C2212yes—
38#91169C2212yes—
39Dic3×#170C2212yes—
40Dic3×#170C2211yescharacteristic
41Dic3×#170C2211yescharacteristic
42#79401—51nomaximal, Hall
43#65958—31no—
44#65788—31no—
45Q8×#170—31no—
46#65759—31no—
47C2×C4×#170—31no—
48#65706—32no—
49#65705—31no—
50#65702D311yescharacteristic, complemented
51#65701—32no—
52#65693—32no—
53#65692—32no—
54C2×C4×C5×D3C2×C411yescharacteristic
55C2×C5×Dic6C2×C411yescharacteristic
56C2×C3×D20C2×C411yescharacteristic
57C2×C3×C4×D5C2312yes—
58C2×#1201C2×C412yes—
59C2×D3×Dic5C2×C411yescharacteristic
60C2×D3×Dic5C2311yescharacteristic
61C2×C3⋊#170C2311yescharacteristic
62C2×C3⋊#170C2312yes—
63C2×C3⋊#170C2311yescharacteristic
64#6758—24no—
65C2×C3×#170C2311yescharacteristic
66C2×C3×#170C2312yes—
67C2×C3×#170C2311yescharacteristic
68C3×D5⋊C8—24no—
69D3×#170—22no—
70D3×#170—22no—
71C3×C5×C4⋊C4C2×C411yescharacteristic
72C4⋊Dic15C2×C411yescharacteristic
73C4⋊Dic15C2×C412yes—
74#6712C2×C412yes—
75C4×Dic15C2×C411yescharacteristic
76C5×(C2×D3)⋊C4C2×C412yes—
77C5×C4⋊Dic3C2×C412yes—
78C3×#685C2×C412yes—
79C3×C4×Dic5C2311yescharacteristic
80Dic3⋊Dic5C2×C412yes—
81#6665C2×C412yes—
82#6665C2×C412yes—
83#6665C2×C412yes—
84Dic3×Dic5C2×C411yescharacteristic
85Dic3×Dic5C2311yescharacteristic
86Dic3×Dic5C2312yes—
87#5557—51no—
88C3×C8×D4—51no—
89C8×#67—52no—
90#5101—52no—
91#5012—51no—
92#4835—51no—
93#4831—51no—
94#4728—52no—
95#4720—52no—
96C4×D3×C8—51no—
97C8×Dic6—51no—
98C22×#170—31no—
99C22×#170—31no—
100C2×#700—32no—
101C2×D5⋊C8C2×D312yes—
102C5×C22⋊Q8—31no—
103#4093—31no—
104Q8×Dic5—31no—
105#4076—31no—
106C2×C4×Dic5—31no—
107#4044—32no—
108#4039C2×D311yescharacteristic
109#4038—32no—
110#4036—31no—
111#4032—32no—
112#4027—32no—
113C22⋊#170—32no—
114#4004—32no—
115#4003—32no—
116#4003C2×D312yes—
117#4002—32no—
118#4002—32no—
119C4⋊#170—32no—
120C4⋊#170—31no—
121C4⋊#170C2×D311yescharacteristic
122C4×#170—32no—
123C4×#170—31no—
124C4×#170—31no—
125C4×#170—31no—
126C4×#170C2×D311yescharacteristic
127#2966—151noSylow
128C22×C5×D3C22×C411yescharacteristic
129C22×C3×D5C22×C412yes—
130C2×C3×C4×C5C22×C412yes—
131C2×C3×C4×C5C22×C411yescharacteristic
132C2×Dic15C22×C411yescharacteristic
133C2×Dic15C22×C411yescharacteristic
134C2×Dic15C22×C412yes—
135C2×C5×Dic3C22×C411yescharacteristic
136C2×C5×Dic3C22×C412yes—
137C4×C5×D3—22no—
138C5×Dic6—22no—
139C2×C3×Dic5C22×C411yescharacteristic
140C2×C3×Dic5C2411yescharacteristic
141C3×D20—22no—
142C3×C4×D5—22no—
143C3×C4×D5—22no—
144#1201—24no—
145D3×Dic5—22no—
146D3×Dic5—21no—
147D3×Dic5—21no—
148C3⋊#170—21no—
149C3⋊#170—22no—
150C3⋊#170#4112yes—
151C3×#170—21no—
152C3×#170—22no—
153C3×#170#4112yes—
154C22×C3×C8—52no—
155C3×C4×D4—51no—
156#938—51no—
157#936—51no—
158C4×#67—52no—
159#926—52no—
160C2×#208—52no—
161C2×D3×C8—51no—
162C2×D3×C8—51no—
163#897AGL(1,𝔽5)11yescharacteristic
164#890—51no—
165#883—52no—
166#879—52no—
167C42×D3—51no—
168C4×Dic6—51no—
169C3×C4⋊C8—51no—
170C3×C22⋊C8—52no—
171C3×C4×C8—51no—
172#830—52no—
173(C2×D3)⋊C8—52no—
174#815—52no—
175#815—52no—
176Dic3⋊C8—52no—
177Dic3⋊C8—52no—
178C8×Dic3—52no—
179C8×Dic3—51no—
180C8×Dic3—51no—
181C4⋊(C3⋊C8)—51no—
182C4×C3⋊C8—51no—
183C2×C5×Q8—31no—
184C22×C4×C5—31no—
185C2×C22⋊D5—32no—
186C22×Dic5—31no—
187C22×Dic5—31no—
188C2×D20C4×D311yescharacteristic
189C2×C4×D5C22×D312yes—
190C2×#170—31no—
191C2×#170—32no—
192C2×#170—31no—
193C2×#170—62no—
194C2×#170—62no—
195C2×#170C22×D312yes—
196C2×#170C22×D311yescharacteristic
197C2×#170C22×D311yescharacteristic
198#700—64no—
199D5⋊C8—24no—
200C5×C4⋊C4—32no—
201C5×C4⋊C4C4×D311yescharacteristic
202C5×C22⋊C4—32no—
203#685—32no—
204#685—32no—
205#685—32no—
206#685C4×D312yes—
207C4⋊Dic5—32no—
208C4⋊Dic5—31no—
209C4⋊Dic5—32no—
210#683—32no—
211C4×Dic5—31no—
212C4×Dic5—31no—
213C4×Dic5—31no—
214C4×Dic5—32no—
215C4×Dic5C22×D311yescharacteristic
216#529—151no—
217#446—151no—
218C8×Q8—151no—
219#436—151no—
220#435—152no—
221C8×D4—51no—
222C8×D4—152no—
223#433—152no—
224#432—151no—
225#405—152no—
226C2×C4×C8—151no—
227C22×C3×C5C23×C411yescharacteristic
228C2×C5×D3—21no—
229C2×C5×D3—21no—
230C2×C5×D3#13112yes—
231C2×C3×D5—22no—
232C2×C3×D5—22no—
233C2×C3×D5—22no—
234C3×C4×C5—22no—
235C3×C4×C5#13112yes—
236Dic15—21no—
237Dic15—21no—
238Dic15—22no—
239C3×Dic5—21no—
240C3×Dic5C2×#4111yescharacteristic
241C3×Dic5C2×#4111yescharacteristic
242C5×Dic3—22no—
243C5×Dic3—21no—
244C2×C3×D4—51no—
245C22×C3×C4—52no—
246C2×#67—52no—
247C2×C4×D3—51no—
248C2×C4×D3—51no—
249C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
250C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
251C2×C3×C8—51no—
252C2×C3×C8—51no—
253C2×C3×C8—52no—
254C2×C3×C8—104no—
255C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
256C3×C22⋊C4—52no—
257C3×C42—51no—
258#217—52no—
259#217—52no—
260#217—52no—
261(C2×D3)⋊C4C2×AGL(1,𝔽5)12yes—
262C4⋊Dic3—51no—
263C4⋊Dic3—52no—
264C4⋊Dic3C2×AGL(1,𝔽5)12yes—
265Dic3⋊C4—52no—
266Dic3⋊C4—52no—
267C4×Dic3—51no—
268C4×Dic3—51no—
269C4×Dic3—51no—
270C4×Dic3—52no—
271#208—104no—
272C2×C3⋊C8—51no—
273C2×C3⋊C8—51no—
274C2×C3⋊C8—52no—
275D3×C8—102no—
276D3×C8—102no—
277C23×C5—31no—
278C22×D5C2×C4×D312yes—
279C5×Q8—62no—
280C2×C4×C5—31no—
281C2×C4×C5—32no—
282C2×C4×C5—62no—
283C2×C4×C5C2×C4×D312yes—
284C2×C4×C5C2×C4×D311yescharacteristic
285C22⋊D5—64no—
286C2×Dic5—31no—
287C2×Dic5—31no—
288C2×Dic5—32no—
289C2×Dic5—62no—
290C2×Dic5—61no—
291C2×Dic5—61no—
292C2×Dic5C2×C4×D311yescharacteristic
293C2×Dic5C23×D311yescharacteristic
294D20—22no—
295C4×D5—22no—
296C4×D5—22no—
297#170—22no—
298#170—21no—
299#170—32no—
300#170—61no—
301#170—62no—
302#170#23712yes—
303C2×M16—152no—
304C22×C8—52no—
305C22×C8—151no—
306C22×C8—151no—
307#126—152no—
308#125—151no—
309#124—151no—
310#123—152no—
311C22⋊Q8—31no—
312#121—151no—
313C4×Q8—151no—
314C4×D4—51no—
315C4×D4—152no—
316#117—152no—
317C2×C42—151no—
318C4⋊C8—51no—
319C4⋊C8—151no—
320C4⋊C8—152no—
321C4⋊C8—152no—
322C22⋊C8—52no—
323C22⋊C8—152no—
324C22⋊C8—152no—
325#97—152no—
326#97—152no—
327C4×C8—51no—
328C4×C8—151no—
329C4×C8—151no—
330C4×C8—151no—
331C4×C8—152no—
332C2×C3×C5C4×#4111yescharacteristic
333C2×C3×C5C2×#13111yescharacteristic
334C2×C3×C5C2×#13111yescharacteristic
335C3×D5—42no—
336C5×D3—22no—
337C23×C3—52no—
338C22×D3C22×AGL(1,𝔽5)11yescharacteristic
339C3×D4—102no—
340C2×C3×C4—51no—
341C2×C3×C4—51no—
342C2×C3×C4—102no—
343C2×C3×C4—102no—
344C2×C3×C4C22×AGL(1,𝔽5)12yes—
345C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
346#67—104no—
347C2×Dic3—51no—
348C2×Dic3—51no—
349C2×Dic3—52no—
350C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
351C2×Dic3C22×AGL(1,𝔽5)12yes—
352C4×D3—22no—
353C4×D3—101no—
354C4×D3—101no—
355C4×D3—102no—
356Dic6—22no—
357C3×C8—52no—
358C3×C8—101no—
359C3×C8—102no—
360C3⋊C8—52no—
361C3⋊C8—101no—
362C3⋊C8—102no—
363C22×C5—32no—
364C22×C5—61no—
365C22×C5—61no—
366C22×C5C22×C4×D311yescharacteristic
367C2×D5—22no—
368C2×D5—22no—
369C2×D5—22no—
370C4×C5—22no—
371C4×C5—61no—
372C4×C5—62no—
373C4×C5#90112yes—
374Dic5—21no—
375Dic5—61no—
376Dic5—62no—
377Dic5—61no—
378Dic5C2×#23711yescharacteristic
379Dic5D3×#4111yescharacteristic
380C2×Q8—31no—
381C2×D4—51no—
382C2×D4—152no—
383C22×C4—31no—
384C22×C4—52no—
385C22×C4—151no—
386C22×C4—151no—
387M16—304no—
388C2×C8—51no—
389C2×C8—51no—
390C2×C8—52no—
391C2×C8—104no—
392C2×C8—151no—
393C2×C8—151no—
394C2×C8—152no—
395C2×C8—302no—
396C2×C8—302no—
397C4⋊C4—32no—
398C4⋊C4—152no—
399C4⋊C4—152no—
400C4⋊C4—152no—
401C4⋊C4—151no—
402C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
403C22⋊C4—32no—
404C22⋊C4—52no—
405C22⋊C4—152no—
406C22⋊C4—152no—
407C22⋊C4—152no—
408C42—51no—
409C42—151no—
410C42—152no—
411C42—151no—
412C42—151no—
413C3×C5#296611yescharacteristic, complemented, Hall
414C22×C3—102no—
415C22×C3—102no—
416C22×C3—102no—
417C22×C3C23×AGL(1,𝔽5)11yescharacteristic
418C2×D3—21no—
419C2×D3—21no—
420C2×D3#413312yes—
421C3×C4—22no—
422C3×C4—51no—
423C3×C4—51no—
424C3×C4—101no—
425C3×C4#413112yes—
426Dic3—22no—
427Dic3—21no—
428Dic3—101no—
429Dic3—102no—
430Dic3—101no—
431C2×C5—62no—
432C2×C5C4×#23711yescharacteristic
433C2×C5C2×#90111yescharacteristic
434C2×C5D3×#13111yescharacteristic
435D5—42no—
436C23—31no—
437C23—52no—
438Q8—62no—
439D4—102no—
440D4—304no—
441C2×C4—31no—
442C2×C4—32no—
443C2×C4—51no—
444C2×C4—51no—
445C2×C4—62no—
446C2×C4—102no—
447C2×C4—102no—
448C2×C4—151no—
449C2×C4—151no—
450C2×C4—152no—
451C2×C4—301no—
452C2×C4—301no—
453C2×C4—302no—
454C2×C4C2×D3×AGL(1,𝔽5)12yes—
455C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
456C8—52no—
457C8—102no—
458C8—101no—
459C8—152no—
460C8—301no—
461C8—302no—
462C2×C3—202no—
463C2×C3C2×#413111yescharacteristic
464C2×C3C2×#413311yescharacteristic
465C2×C3#41×AGL(1,𝔽5)11yescharacteristic
466D3—22no—
467C5#7940111yescharacteristic, complemented, Sylow
468C22—32no—
469C22—61no—
470C22—61no—
471C22—102no—
472C22—102no—
473C22—102no—
474C22C22×D3×AGL(1,𝔽5)11yescharacteristic
475C4—22no—
476C4—51no—
477C4—51no—
478C4—61no—
479C4—62no—
480C4—101no—
481C4—301no—
482C4—301no—
483C4—302no—
484C4#9191112yes—
485C3#1061726511yescharacteristic, complemented, Sylow
486C2—62no—
487C2—202no—
488C2C2×#9191111yescharacteristic
489C2AGL(1,𝔽5)×#23711yescharacteristic
490C2D3×#413311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C4C2×C4
prime radical#91456C4
cosocleC2×C3×Dic5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2966
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11752364C2semidirect
3. C3×#65702C2semidirect
4. #11751899C2semidirect
5. #11751875C2semidirect
6. C4×D3×#170C2semidirect
7. #11751807C2semidirect
8. #11751792C2semidirect
9. #11751769C2semidirect
10. #11751767C2semidirect
11. Dic6×#170C2semidirect
50. #65702D3semidirect
413. C3×C5#2966semidirect
467. C5#79401semidirect
485. C3#10617265semidirect

Maximal subgroups

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

subgroupindex
#117535172
#117523642
C3×#657022
#117518992
#117518752
C4×D3×#1702
#117518072
#117517922
#117517692
#117517672
Dic6×#1702
#106172653
#794015