Finite Group Databasebeta

← C3×#10610939 #14413399

Subgroups — C3×#10610939 #14413399

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×M16C211yesmaximal, characteristic
2C3×D5×#117C211yesmaximal, characteristic
3C2×C3×#4038C211yesmaximal, characteristic
4C3×C5×#428C211yesmaximal, characteristic, complemented
5C3×#65410C211yesmaximal, characteristic, complemented
6C3×#65284C211yesmaximal, characteristic, complemented
7C3×#65253C211yesmaximal, characteristic, complemented
8C3×#65170C212yesmaximal, complemented
9C3×#65169C212yesmaximal, complemented
10C3×#65150C212yesmaximal, complemented
11C3×#65149C212yesmaximal, complemented
12#10610939C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C3×#685—21no—
18C3×#4072C2211yescharacteristic
19C2×C3×C4⋊Dic5C2211yescharacteristic
20C2×C3×C4×Dic5—21no—
21C2×C3×#681C2211yescharacteristic
22C3×D5×M16C418yescomplemented
23C2×C3×#676C2212yes—
24C2×C3×C8×D5C2212yes—
25C3×#4038—21no—
26C3×#4038—21no—
27C3×#4038C2211yescharacteristic
28C3×#4038C2211yescharacteristic
29C3×#4038C2212yes—
30C3×#4038C2212yes—
31C3×D5×C4⋊C4C2211yescharacteristic
32C3×D5×C4⋊C4C2211yescharacteristic
33C3×D5×C22⋊C4—21no—
34C3×#4023—21no—
35C3×#4018—21no—
36C3×C42×D5—21no—
37C3×C5×#107C2212yescomplemented
38C3×C5×#106C2212yescomplemented
39C3×#3950C2212yescomplemented
40C3×#3949C2212yescomplemented
41C3×#3940C2212yescomplemented
42C3×#3940C2212yescomplemented
43C3×#3939C2212yescomplemented
44C3×#3939C2212yescomplemented
45C3×#2911—51nomaximal, Hall
46C2×D5×M16C2×C311yescharacteristic
47D5×#117C2×C311yescharacteristic
48C2×#4038C2×C311yescharacteristic
49C5×#428C2×C311yescharacteristic, complemented
50#65410C2×C311yescharacteristic, complemented
51#65284C2×C311yescharacteristic, complemented
52#65253C2×C311yescharacteristic, complemented
53#65170C2×C312yescomplemented
54#65169C2×C312yescomplemented
55#65150C2×C312yescomplemented
56#65149C2×C312yescomplemented
57C23×C3×D5D411yescharacteristic
58C22×C3×C4×C5—21no—
59C22×C3×C4×C5C2311yescharacteristic
60C22×C3×Dic5—21no—
61C22×C3×Dic5D411yescharacteristic
62C2×C3×C4×D5—21no—
63C2×C3×C4×D5—21no—
64C2×C3×C4×D5C2×C414yes—
65C2×C3×C4×D5D411yescharacteristic
66C2×C3×C4×D5D411yescharacteristic
67C2×C3×C4×D5Q814yes—
68C2×C3×C4×D5C2311yescharacteristic
69C2×C3×C4×D5C2311yescharacteristic
70C3×C5×M16C2×C414yescomplemented
71C2×C3×C5×C8C2312yes—
72C3×C5×C4⋊C4—21no—
73C3×C5×C4⋊C4C2311yescharacteristic
74C3×C5×C4⋊C4C2312yes—
75C3×C5×C4⋊C4C2311yescharacteristic
76C3×C5×C22⋊C4—21no—
77C3×C42×C5—21no—
78C3×C22⋊Dic5—21no—
79C3×#685—21no—
80C3×#685—21no—
81C3×#685—22no—
82C3×#685—22no—
83C3×C4⋊Dic5—21no—
84C3×C4⋊Dic5C2311yescharacteristic
85C3×C4⋊Dic5C2312yes—
86C3×C4⋊Dic5C2311yescharacteristic
87C3×#683—21no—
88C3×#683—21no—
89C3×C4×Dic5—21no—
90C3×C4×Dic5—21no—
91C3×C4×Dic5—21no—
92C3×C4×Dic5—22no—
93C3×C4×Dic5—22no—
94C3×#681C2×C414yescomplemented
95C2×C3×#168C2312yes—
96C3×#676C2×C418yescomplemented
97C3×C8×D5C2×C418yescomplemented
98C22×C3×M16—51no—
99C2×C3×#117—51no—
100C2×C3×#117—51no—
101C3×#428—51no—
102C3×#428—51no—
103C3×#428—51no—
104C3×#428—52no—
105C3×#428—52no—
106C3×#428D511yescharacteristic, complemented
107C3×#427—52no—
108C3×#427—52no—
109C22×C4×D5C22×C311yescharacteristic
110C2×C5×M16C22×C311yescharacteristic
111C5×#117C22×C311yescharacteristic
112C2×C5×C4⋊C4C22×C311yescharacteristic
113C2×#685—21no—
114#4072C22×C311yescharacteristic
115C2×C4⋊Dic5C22×C311yescharacteristic
116C2×C4×Dic5—21no—
117C2×#681C22×C311yescharacteristic
118D5×M16C3×C418yescomplemented
119C2×#676C22×C312yes—
120C2×C8×D5C22×C312yes—
121#4038—21no—
122#4038—21no—
123#4038C22×C312yes—
124#4038C22×C312yes—
125#4038C22×C311yescharacteristic
126#4038C22×C311yescharacteristic
127D5×C4⋊C4C22×C311yescharacteristic
128D5×C4⋊C4C22×C311yescharacteristic
129D5×C22⋊C4—21no—
130#4023—21no—
131#4018—21no—
132C42×D5—21no—
133C5×#107C22×C312yescomplemented
134C5×#106C22×C312yescomplemented
135#3950C22×C312yescomplemented
136#3949C22×C312yescomplemented
137#3940C22×C312yescomplemented
138#3940C22×C312yescomplemented
139#3939C22×C312yescomplemented
140#3939C22×C312yescomplemented
141#2911—51noSylow
142C23×C3×C5C2×D411yescharacteristic
143C22×C3×D5—41no—
144C22×C3×D5—41no—
145C22×C3×D5C4⋊C414yes—
146C22×C3×D5C2×D411yescharacteristic
147C22×C3×D5C2×D411yescharacteristic
148C2×C3×C4×C5—22no—
149C2×C3×C4×C5—21no—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5—42no—
152C2×C3×C4×C5C22×C412yes—
153C2×C3×C4×C5C2×D411yescharacteristic
154C2×C3×C4×C5C2×Q812yes—
155C2×C3×C4×C5C2411yescharacteristic
156C2×C3×Dic5—21no—
157C2×C3×Dic5—21no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5—42no—
160C2×C3×Dic5C4⋊C414yes—
161C2×C3×Dic5C2×D411yescharacteristic
162C2×C3×Dic5C2×D411yescharacteristic
163C3×C4×D5—42no—
164C3×C4×D5—42no—
165C3×C4×D5C4⋊C414yes—
166C3×C4×D5C4⋊C414yes—
167C3×C4×D5C22×C412yes—
168C3×C4×D5C22×C412yes—
169C3×C4×D5C2×Q812yes—
170C3×C4×D5C2×Q812yes—
171C3×C5×C8C22×C414yes—
172C3×#168C22×C414yes—
173C23×C3×C4—51no—
174C2×C3×M16—51no—
175C2×C3×M16—58no—
176C2×C3×M16—52no—
177C2×C3×M16C2×D511yescharacteristic
178C22×C3×C8—52no—
179C3×#117—51no—
180C3×#117—51no—
181C3×#117—52no—
182C3×#117—51no—
183C3×#117—52no—
184C3×#117—101no—
185C3×#117—101no—
186C3×#117—101no—
187C3×#117—101no—
188C3×#117C2×D511yescharacteristic
189C2×C3×C4⋊C4—51no—
190C2×C3×C4⋊C4—51no—
191C2×C3×C4⋊C4—51no—
192C2×C3×C4⋊C4C2×D511yescharacteristic
193C2×C3×C22⋊C4—101no—
194C2×C3×C22⋊C4—101no—
195C2×C3×C42—101no—
196C2×C3×C42—101no—
197C3×#107—52no—
198C3×#107—52no—
199C3×#107—52no—
200C3×#107C2×D512yescomplemented
201C3×#106—52no—
202C3×#106—52no—
203C3×#106—52no—
204C3×#106C2×D512yescomplemented
205C23×D5C3×D411yescharacteristic
206C22×C4×C5—21no—
207C22×C4×C5C23×C311yescharacteristic
208C22×Dic5—21no—
209C22×Dic5C3×D411yescharacteristic
210C2×C4×D5—21no—
211C2×C4×D5—21no—
212C2×C4×D5C2×C3×C414yes—
213C2×C4×D5C3×D411yescharacteristic
214C2×C4×D5C3×D411yescharacteristic
215C2×C4×D5C3×Q814yes—
216C2×C4×D5C23×C311yescharacteristic
217C2×C4×D5C23×C311yescharacteristic
218C5×M16C2×C3×C414yescomplemented
219C2×C5×C8C23×C312yes—
220C5×C4⋊C4—21no—
221C5×C4⋊C4C23×C312yes—
222C5×C4⋊C4C23×C311yescharacteristic
223C5×C4⋊C4C23×C311yescharacteristic
224C5×C22⋊C4—21no—
225C42×C5—21no—
226C22⋊Dic5—21no—
227#685—21no—
228#685—21no—
229#685—22no—
230#685—22no—
231C4⋊Dic5—21no—
232C4⋊Dic5C23×C311yescharacteristic
233C4⋊Dic5C23×C312yes—
234C4⋊Dic5C23×C311yescharacteristic
235#683—21no—
236#683—21no—
237C4×Dic5—21no—
238C4×Dic5—21no—
239C4×Dic5—21no—
240C4×Dic5—22no—
241C4×Dic5—22no—
242#681C2×C3×C414yescomplemented
243C2×#168C23×C312yes—
244#676C2×C3×C418yescomplemented
245C8×D5C2×C3×C418yescomplemented
246C22×M16—51no—
247C2×#117—51no—
248C2×#117—51no—
249#428—51no—
250#428—51no—
251#428—51no—
252#428—52no—
253#428—52no—
254#428C3×D511yescharacteristic, complemented
255#427—52no—
256#427—52no—
257C22×C3×C5—21no—
258C22×C3×C5—21no—
259C22×C3×C5C2×C4⋊C412yes—
260C22×C3×C5C22×D411yescharacteristic
261C2×C3×D5—21no—
262C2×C3×D5—21no—
263C2×C3×D5—21no—
264C2×C3×D5—21no—
265C2×C3×D5—44no—
266C2×C3×D5C2×C4⋊C412yes—
267C2×C3×D5C2×C4⋊C412yes—
268C3×C4×C5—41no—
269C3×C4×C5—41no—
270C3×C4×C5—42no—
271C3×C4×C5C2×C4⋊C412yes—
272C3×C4×C5C23×C411yescharacteristic
273C3×C4×C5C22×Q811yescharacteristic
274C3×Dic5—41no—
275C3×Dic5—41no—
276C3×Dic5—42no—
277C3×Dic5C2×C4⋊C412yes—
278C3×Dic5C2×C4⋊C412yes—
279C24×C3—51no—
280C22×C3×C4—21no—
281C22×C3×C4—51no—
282C22×C3×C4—54no—
283C22×C3×C4—51no—
284C22×C3×C4—51no—
285C22×C3×C4—54no—
286C22×C3×C4—51no—
287C22×C3×C4—51no—
288C22×C3×C4—101no—
289C22×C3×C4—101no—
290C22×C3×C4—101no—
291C22×C3×C4C22×D511yescharacteristic
292C3×M16—54no—
293C3×M16—58no—
294C3×M16C4×D514yescomplemented
295C2×C3×C8—52no—
296C2×C3×C8—58no—
297C2×C3×C8C22×D512yes—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—51no—
300C3×C4⋊C4—52no—
301C3×C4⋊C4—51no—
302C3×C4⋊C4—101no—
303C3×C4⋊C4—101no—
304C3×C4⋊C4—101no—
305C3×C4⋊C4C22×D511yescharacteristic
306C3×C4⋊C4C22×D512yes—
307C3×C4⋊C4C22×D511yescharacteristic
308C3×C22⋊C4—21no—
309C3×C22⋊C4—101no—
310C3×C22⋊C4—101no—
311C3×C22⋊C4—102no—
312C3×C22⋊C4—102no—
313C3×C22⋊C4—101no—
314C3×C42—21no—
315C3×C42—101no—
316C3×C42—101no—
317C3×C42—102no—
318C3×C42—102no—
319C3×C42—101no—
320C23×C5C2×C3×D411yescharacteristic
321C22×D5—41no—
322C22×D5—41no—
323C22×D5C3×C4⋊C414yes—
324C22×D5C2×C3×D411yescharacteristic
325C22×D5C2×C3×D411yescharacteristic
326C2×C4×C5—22no—
327C2×C4×C5—21no—
328C2×C4×C5—21no—
329C2×C4×C5—42no—
330C2×C4×C5C22×C3×C412yes—
331C2×C4×C5C2×C3×D411yescharacteristic
332C2×C4×C5C2×C3×Q812yes—
333C2×C4×C5C24×C311yescharacteristic
334C2×Dic5—21no—
335C2×Dic5—21no—
336C2×Dic5—22no—
337C2×Dic5—42no—
338C2×Dic5C3×C4⋊C414yes—
339C2×Dic5C2×C3×D411yescharacteristic
340C2×Dic5C2×C3×D411yescharacteristic
341C4×D5—42no—
342C4×D5—42no—
343C4×D5C3×C4⋊C414yes—
344C4×D5C3×C4⋊C414yes—
345C4×D5C22×C3×C412yes—
346C4×D5C22×C3×C412yes—
347C4×D5C2×C3×Q812yes—
348C4×D5C2×C3×Q812yes—
349C5×C8C22×C3×C414yes—
350#168C22×C3×C414yes—
351C23×C4—51no—
352C2×M16—51no—
353C2×M16—58no—
354C2×M16—52no—
355C2×M16C2×C3×D511yescharacteristic
356C22×C8—52no—
357#117—51no—
358#117—51no—
359#117—52no—
360#117—51no—
361#117—52no—
362#117—101no—
363#117—101no—
364#117—101no—
365#117—101no—
366#117C2×C3×D511yescharacteristic
367C2×C4⋊C4—51no—
368C2×C4⋊C4—51no—
369C2×C4⋊C4—51no—
370C2×C4⋊C4C2×C3×D511yescharacteristic
371C2×C22⋊C4—101no—
372C2×C22⋊C4—101no—
373C2×C42—101no—
374C2×C42—101no—
375#107—52no—
376#107—52no—
377#107—52no—
378#107C2×C3×D512yescomplemented
379#106—52no—
380#106—52no—
381#106—52no—
382#106C2×C3×D512yescomplemented
383C2×C3×C5—22no—
384C2×C3×C5C22×C4⋊C411yescharacteristic
385C2×C3×C5#57511yescharacteristic
386C2×C3×C5#57511yescharacteristic
387C3×D5—22no—
388C3×D5—22no—
389C23×C3—51no—
390C23×C3—51no—
391C23×C3—54no—
392C23×C3—201no—
393C23×C3—201no—
394C23×C3D4×D511yescharacteristic
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—22no—
398C2×C3×C4—42no—
399C2×C3×C4—51no—
400C2×C3×C4—51no—
401C2×C3×C4—54no—
402C2×C3×C4—52no—
403C2×C3×C4—52no—
404C2×C3×C4—52no—
405C2×C3×C4—52no—
406C2×C3×C4—54no—
407C2×C3×C4—54no—
408C2×C3×C4—101no—
409C2×C3×C4—101no—
410C2×C3×C4—102no—
411C2×C3×C4—202no—
412C2×C3×C4—202no—
413C2×C3×C4—202no—
414C2×C3×C4C2×C4×D512yes—
415C2×C3×C4D4×D511yescharacteristic
416C2×C3×C4Q8×D512yes—
417C2×C3×C4C23×D511yescharacteristic
418C3×C8—54no—
419C3×C8C2×C4×D514yes—
420C22×C5—21no—
421C22×C5—21no—
422C22×C5C2×C3×C4⋊C412yes—
423C22×C5C22×C3×D411yescharacteristic
424C2×D5—21no—
425C2×D5—21no—
426C2×D5—21no—
427C2×D5—21no—
428C2×D5—44no—
429C2×D5C2×C3×C4⋊C412yes—
430C2×D5C2×C3×C4⋊C412yes—
431C4×C5—41no—
432C4×C5—41no—
433C4×C5—42no—
434C4×C5C2×C3×C4⋊C412yes—
435C4×C5C23×C3×C411yescharacteristic
436C4×C5C22×C3×Q811yescharacteristic
437Dic5—41no—
438Dic5—41no—
439Dic5—42no—
440Dic5C2×C3×C4⋊C412yes—
441Dic5C2×C3×C4⋊C412yes—
442C24—51no—
443C22×C4—21no—
444C22×C4—51no—
445C22×C4—54no—
446C22×C4—51no—
447C22×C4—51no—
448C22×C4—54no—
449C22×C4—51no—
450C22×C4—51no—
451C22×C4—101no—
452C22×C4—101no—
453C22×C4—101no—
454C22×C4C22×C3×D511yescharacteristic
455M16—54no—
456M16—58no—
457M16C3×C4×D514yescomplemented
458C2×C8—52no—
459C2×C8—58no—
460C2×C8C22×C3×D512yes—
461C4⋊C4—21no—
462C4⋊C4—51no—
463C4⋊C4—52no—
464C4⋊C4—51no—
465C4⋊C4—101no—
466C4⋊C4—101no—
467C4⋊C4—101no—
468C4⋊C4C22×C3×D511yescharacteristic
469C4⋊C4C22×C3×D512yes—
470C4⋊C4C22×C3×D511yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—101no—
473C22⋊C4—101no—
474C22⋊C4—102no—
475C22⋊C4—102no—
476C22⋊C4—101no—
477C42—21no—
478C42—101no—
479C42—101no—
480C42—102no—
481C42—102no—
482C42—101no—
483C3×C5#291111yescharacteristic, complemented, Hall
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—52no—
487C22×C3—52no—
488C22×C3—101no—
489C22×C3—101no—
490C22×C3—101no—
491C22×C3—101no—
492C22×C3—204no—
493C22×C3D5×C4⋊C412yes—
494C22×C3C2×D4×D511yescharacteristic
495C3×C4—42no—
496C3×C4—41no—
497C3×C4—41no—
498C3×C4—52no—
499C3×C4—52no—
500C3×C4—201no—
501C3×C4—201no—
502C3×C4—202no—
503C3×C4D5×C4⋊C412yes—
504C3×C4C22×C4×D511yescharacteristic
505C3×C4C2×Q8×D511yescharacteristic
506C2×C5—22no—
507C2×C5C22×C3×C4⋊C411yescharacteristic
508C2×C5C3×#57511yescharacteristic
509C2×C5C3×#57511yescharacteristic
510D5—22no—
511D5—22no—
512C23—51no—
513C23—51no—
514C23—54no—
515C23—201no—
516C23—201no—
517C23C3×D4×D511yescharacteristic
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—42no—
522C2×C4—51no—
523C2×C4—51no—
524C2×C4—54no—
525C2×C4—52no—
526C2×C4—52no—
527C2×C4—52no—
528C2×C4—52no—
529C2×C4—54no—
530C2×C4—54no—
531C2×C4—101no—
532C2×C4—102no—
533C2×C4—101no—
534C2×C4—202no—
535C2×C4—202no—
536C2×C4—202no—
537C2×C4C2×C3×C4×D512yes—
538C2×C4C3×D4×D511yescharacteristic
539C2×C4C3×Q8×D512yes—
540C2×C4C23×C3×D511yescharacteristic
541C8—54no—
542C8C2×C3×C4×D514yes—
543C2×C3—22no—
544C2×C3—102no—
545C2×C3—102no—
546C2×C3C2×D5×C4⋊C411yescharacteristic
547C2×C3#6610711yescharacteristic
548C2×C3#6611111yescharacteristic
549C5C3×#291111yescharacteristic, complemented, Sylow
550C22—21no—
551C22—21no—
552C22—52no—
553C22—52no—
554C22—101no—
555C22—101no—
556C22—101no—
557C22—101no—
558C22—204no—
559C22C3×D5×C4⋊C412yes—
560C22C2×C3×D4×D511yescharacteristic
561C4—42no—
562C4—41no—
563C4—41no—
564C4—52no—
565C4—52no—
566C4—201no—
567C4—201no—
568C4—202no—
569C4C3×D5×C4⋊C412yes—
570C4C22×C3×C4×D511yescharacteristic
571C4C2×C3×Q8×D511yescharacteristic
572C3#1061093911yescharacteristic, direct product factor, Sylow
573C2—22no—
574C2—102no—
575C2—102no—
576C2C2×C3×D5×C4⋊C411yescharacteristic
577C2C3×#6610711yescharacteristic
578C2C3×#6611111yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#428C2
socleC22×C3×C5C22×D4
prime radicalC23×C3×D5D4
cosocleC2×C4×C5C24×C3
hypercenterC3×#428D5
hypocenterC5C3×#2911
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#428

Complements

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

NH ≅ G/Ntype
4. C3×C5×#428C2semidirect
5. C3×#65410C2semidirect
6. C3×#65284C2semidirect
7. C3×#65253C2semidirect
8. C3×#65170C2semidirect
9. C3×#65169C2semidirect
10. C3×#65150C2semidirect
11. C3×#65149C2semidirect
12. #10610939C3direct (N × H)
22. C3×D5×M16C4semidirect
37. C3×C5×#107C22semidirect
38. C3×C5×#106C22semidirect
39. C3×#3950C22semidirect
40. C3×#3949C22semidirect
41. C3×#3940C22semidirect
42. C3×#3940C22semidirect
43. C3×#3939C22semidirect
44. C3×#3939C22semidirect
49. C5×#428C2×C3semidirect
50. #65410C2×C3semidirect
51. #65284C2×C3semidirect
52. #65253C2×C3semidirect
53. #65170C2×C3semidirect
54. #65169C2×C3semidirect
55. #65150C2×C3semidirect
56. #65149C2×C3semidirect
70. C3×C5×M16C2×C4semidirect
94. C3×#681C2×C4semidirect
96. C3×#676C2×C4semidirect
97. C3×C8×D5C2×C4semidirect
106. C3×#428D5semidirect
118. D5×M16C3×C4semidirect
133. C5×#107C22×C3semidirect
134. C5×#106C22×C3semidirect
135. #3950C22×C3semidirect
136. #3949C22×C3semidirect
137. #3940C22×C3semidirect
138. #3940C22×C3semidirect
139. #3939C22×C3semidirect
140. #3939C22×C3semidirect
200. C3×#107C2×D5semidirect
204. C3×#106C2×D5semidirect
218. C5×M16C2×C3×C4semidirect
242. #681C2×C3×C4semidirect
244. #676C2×C3×C4semidirect
245. C8×D5C2×C3×C4semidirect
254. #428C3×D5semidirect
294. C3×M16C4×D5semidirect
378. #107C2×C3×D5semidirect
382. #106C2×C3×D5semidirect
457. M16C3×C4×D5semidirect
483. C3×C5#2911semidirect
549. C5C3×#2911semidirect
572. C3#10610939direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×M162
C3×D5×#1172
C2×C3×#40382
C3×C5×#4282
C3×#654102
C3×#652842
C3×#652532
C3×#651702
C3×#651692
C3×#651502
C3×#651492
#106109393
C3×#29115