Finite Group Databasebeta

← C2×#11753704 #14482779

Subgroups — C2×#11753704 #14482779

Order 1920.

3264 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6773C211yesmaximal, characteristic, complemented
2C22×#6769C211yesmaximal, characteristic, complemented
3C2×#91782C211yesmaximal, characteristic, complemented
4C2×C5×#897C211yesmaximal, characteristic, complemented
5C2×C3×#4043C211yesmaximal, characteristic, complemented
6C2×#91461C212yesmaximal, complemented
7C2×C4×#1201C211yesmaximal, characteristic, complemented
8C2×#91438C212yesmaximal, complemented
9C2×#91437C212yesmaximal, complemented
10C2×#91385C211yesmaximal, characteristic, complemented
11C2×#91356C212yesmaximal, complemented
12#11753704C2116yesmaximal, direct product factor
13C2×#65965—31nomaximal, Hall
14C22×D60C2211yescharacteristic
15C22×C4×D15C2212yes—
16C22×C4×C5×D3C2211yescharacteristic
17C22×C5×Dic6C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×C3×Dic10C2211yescharacteristic
20C22×#1203C2212yes—
21C22×#1202C2212yes—
22C22×#1201C2211yescharacteristic
23C22×#1200C2212yes—
24C22×#1200C2212yes—
25C2×#6773—28no—
26C2×#6773C2218yescomplemented
27C2×#6769—28no—
28C2×#6769C2218yescomplemented
29C2×C3×C5×C4⋊C4C2211yescharacteristic
30C2×#6714C2212yes—
31C2×C4×Dic15C2211yescharacteristic
32#91782C2218yescomplemented
33C2×C5×(C2×D3)⋊C4C2212yes—
34C2×C5×C4⋊Dic3C2212yes—
35C5×#897C2218yescomplemented
36C2×C3×#685C2212yes—
37C2×C3×C4⋊Dic5C2212yes—
38C3×#4043C2218yescomplemented
39C2×#6669C2211yescharacteristic
40C2×#6669C2212yes—
41C2×#6669C2212yes—
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44#91461C22116yescomplemented
45C4×#1201C2218yescomplemented
46#91438C22116yescomplemented
47#91437C22116yescomplemented
48#91385C2218yescomplemented
49#91356C22116yescomplemented
50C2×#5631—51nomaximal, Hall
51C22×#713—31no—
52C22×#709—31no—
53C2×C5×C22⋊Q8—31no—
54C2×#4090—31no—
55C2×C4×C22⋊D5—31no—
56#65965—316no—
57C2×#4043D311yescharacteristic, complemented
58C2×#4040—32no—
59C2×#4039—31no—
60C2×D5×C4⋊C4—32no—
61C2×#4030—32no—
62C2×#4029—32no—
63C23×D15C2312yes—
64C23×C5×D3C2311yescharacteristic
65C23×C3×D5C2311yescharacteristic
66C22×C3×C4×C5C2312yes—
67C22×C3×C4×C5C2311yescharacteristic
68C22×Dic15C2311yescharacteristic
69C22×Dic15C2311yescharacteristic
70C2×D60D418yescomplemented
71C2×D60C2314yes—
72C2×C4×D15—28no—
73C2×C4×D15C2318yes—
74C22×C5×Dic3C2311yescharacteristic
75C22×C5×Dic3C2312yes—
76C2×C4×C5×D3—24no—
77C2×C4×C5×D3C2314yes—
78C2×C5×Dic6—24no—
79C2×C5×Dic6C2314yes—
80C22×C3×Dic5C2311yescharacteristic
81C22×C3×Dic5C2312yes—
82C2×C3×C4×D5—24no—
83C2×C3×C4×D5C2314yes—
84C2×C3×Dic10—24no—
85C2×C3×Dic10C2314yes—
86C2×#1203—28no—
87C2×#1203C2318yes—
88C2×#1202—28no—
89C2×#1202C2318yes—
90C2×#1201—24no—
91C2×#1201C2314yes—
92C2×#1200—28no—
93C2×#1200—28no—
94C2×#1200C2318yes—
95C2×#1200C2318yes—
96#6773—232no—
97#6769—232no—
98C3×C5×C4⋊C4C2314yes—
99#6714C2318yes—
100C4×Dic15C2314yes—
101C5×(C2×D3)⋊C4C2318yes—
102C5×C4⋊Dic3C2318yes—
103C3×#685C2318yes—
104C3×C4⋊Dic5C2318yes—
105#6669C2314yes—
106#6669C2318yes—
107#6669C2318yes—
108(C2×D3)⋊Dic5C2314yes—
109#6665C2314yes—
110C22×#239—51no—
111C22×#235—51no—
112C2×C3×C22⋊Q8—51no—
113C2×#944—51no—
114C2×C4×#67—51no—
115#5631—516no—
116C2×#897D511yescharacteristic, complemented
117C2×#894—52no—
118C2×#893—51no—
119C2×D3×C4⋊C4—52no—
120C2×#884—52no—
121C2×#883—52no—
122C22×C5×Q8—31no—
123C23×C4×C5—31no—
124C22×C22⋊D5—31no—
125C22×C22⋊D5—32no—
126C2×#713—38no—
127C2×#713—68no—
128C2×#709—38no—
129C2×#709—68no—
130C22×D20—31no—
131C22×D20—32no—
132C22×C4×D5—32no—
133C22×C4×D5—32no—
134C22×C4×D5—32no—
135C22×C4×D5C2×D311yescharacteristic
136C22×Dic10C2×D311yescharacteristic
137C5×C22⋊Q8—38no—
138C2×C5×C4⋊C4—32no—
139C2×C5×C4⋊C4C2×D311yescharacteristic
140C2×C5×C22⋊C4—32no—
141C2×C22⋊Dic5—31no—
142#4090—38no—
143C4×C22⋊D5—38no—
144C2×#685—31no—
145C2×#685—32no—
146C2×#685C2×D312yes—
147C2×C4⋊Dic5C2×D312yes—
148C2×#683—32no—
149C2×#683—32no—
150C2×#683—31no—
151C2×C4×Dic5—31no—
152#4043C2×D318yescomplemented
153#4040—316no—
154#4039—38no—
155D5×C4⋊C4—316no—
156#4030—316no—
157#4029—316no—
158C2×#547—151noSylow
159C23×C3×C5C2411yescharacteristic
160C22×D15—24no—
161C22×D15—24no—
162C22×D15C2×D418yes—
163C22×D15C2414yes—
164C22×C5×D3—22no—
165C22×C5×D3—22no—
166C22×C5×D3—22no—
167C22×C5×D3C2412yes—
168C22×C3×D5—22no—
169C22×C3×D5—22no—
170C22×C3×D5—22no—
171C22×C3×D5C2412yes—
172C2×C3×C4×C5—24no—
173C2×C3×C4×C5C2×D414yes—
174C2×C3×C4×C5C2414yes—
175C2×C3×C4×C5C2412yes—
176C2×Dic15—22no—
177C2×Dic15#4114yescomplemented
178C2×Dic15C2412yes—
179C2×Dic15C2412yes—
180D60C2×D4116yescomplemented
181C4×D15—216no—
182C2×C5×Dic3—22no—
183C2×C5×Dic3—24no—
184C2×C5×Dic3C2412yes—
185C2×C5×Dic3C2414yes—
186C4×C5×D3—28no—
187C5×Dic6—28no—
188C2×C3×Dic5—22no—
189C2×C3×Dic5—24no—
190C2×C3×Dic5C2412yes—
191C2×C3×Dic5C2414yes—
192C3×C4×D5—28no—
193C3×Dic10—28no—
194#1203—216no—
195#1202—216no—
196#1201—28no—
197#1200—216no—
198#1200—216no—
199C22×C3×Q8—51no—
200C23×C3×C4—51no—
201C22×#67—51no—
202C22×#67—52no—
203C2×#239—58no—
204C2×#239—108no—
205C2×#235—58no—
206C2×#235—108no—
207C22×D12—51no—
208C22×D12—52no—
209C22×C4×D3—52no—
210C22×C4×D3—52no—
211C22×C4×D3—52no—
212C22×C4×D3C2×D511yescharacteristic
213C22×Dic6C2×D511yescharacteristic
214C3×C22⋊Q8—58no—
215C2×C3×C4⋊C4—52no—
216C2×C3×C4⋊C4C2×D511yescharacteristic
217C2×C3×C22⋊C4—52no—
218C2×#217—51no—
219#944—58no—
220C4×#67—58no—
221C2×(C2×D3)⋊C4—51no—
222C2×(C2×D3)⋊C4—52no—
223C2×(C2×D3)⋊C4C2×D512yes—
224C2×C4⋊Dic3C2×D512yes—
225C2×Dic3⋊C4—52no—
226C2×Dic3⋊C4—52no—
227C2×Dic3⋊C4—51no—
228C2×C4×Dic3—51no—
229#897C2×D518yescomplemented
230#894—516no—
231#893—58no—
232D3×C4⋊C4—516no—
233#884—516no—
234#883—516no—
235C24×C5—31no—
236C23×D5—32no—
237C23×D5C22×D311yescharacteristic
238C2×C5×Q8—34no—
239C2×C5×Q8—64no—
240C22×C4×C5—32no—
241C22×C4×C5—31no—
242C22×C4×C5—34no—
243C22×C4×C5—64no—
244C22×C4×C5C22×D312yes—
245C22×C4×C5C22×D311yescharacteristic
246C2×C22⋊D5—34no—
247C2×C22⋊D5—38no—
248C2×C22⋊D5—68no—
249C2×C22⋊D5—64no—
250C22×Dic5—31no—
251C22×Dic5—31no—
252C22×Dic5C22×D311yescharacteristic
253C22×Dic5C22×D312yes—
254#713—632no—
255#709—632no—
256C2×D20—38no—
257C2×D20—34no—
258C2×D20—38no—
259C2×D20—68no—
260C2×C4×D5—24no—
261C2×C4×D5—38no—
262C2×C4×D5—38no—
263C2×C4×D5—38no—
264C2×C4×D5—68no—
265C2×C4×D5—68no—
266C2×C4×D5—68no—
267C2×C4×D5C22×D314yes—
268C2×Dic10—24no—
269C2×Dic10C22×D314yes—
270C5×C4⋊C4—38no—
271C5×C4⋊C4C22×D314yes—
272C5×C22⋊C4—38no—
273C22⋊Dic5—34no—
274#685—34no—
275#685—38no—
276#685C22×D318yes—
277C4⋊Dic5C22×D318yes—
278#683—38no—
279#683—38no—
280#683—34no—
281C4×Dic5—34no—
282C22×#41—151no—
283C22×#41—151no—
284#547—1516no—
285C2×C4⋊Q8—151no—
286C2×#123—152no—
287C2×#123—152no—
288C2×C22⋊Q8—31no—
289C2×C22⋊Q8—51no—
290C2×#121—152no—
291C2×C4×D4—151no—
292C2×C4×D4—151no—
293C22×C4⋊C4—152no—
294C22×C3×C5C22×D412yes—
295C22×C3×C5C2×#4112yes—
296C22×C3×C52−1+412yes—
297C22×C3×C5C2511yescharacteristic
298C2×D15—216no—
299C2×D15—24no—
300C2×D15—24no—
301C2×D15C22×D418yes—
302C2×C5×D3—22no—
303C2×C5×D3—22no—
304C2×C5×D3—22no—
305C2×C5×D3—44no—
306C2×C3×D5—22no—
307C2×C3×D5—22no—
308C2×C3×D5—22no—
309C2×C3×D5—44no—
310C3×C4×C5—24no—
311C3×C4×C5C22×D414yes—
312Dic15—22no—
313Dic15C2×#4114yescomplemented
314C3×Dic5—22no—
315C3×Dic5—24no—
316C5×Dic3—22no—
317C5×Dic3—24no—
318C24×C3—51no—
319C23×D3—52no—
320C23×D3C22×D511yescharacteristic
321C2×C3×Q8—54no—
322C2×C3×Q8—104no—
323C22×C3×C4—52no—
324C22×C3×C4—51no—
325C22×C3×C4—54no—
326C22×C3×C4—104no—
327C22×C3×C4C22×D512yes—
328C22×C3×C4C22×D511yescharacteristic
329C2×#67—54no—
330C2×#67—58no—
331C2×#67—108no—
332C2×#67—104no—
333C22×Dic3—51no—
334C22×Dic3—51no—
335C22×Dic3C22×D512yes—
336C22×Dic3C22×D511yescharacteristic
337#239—1032no—
338#235—1032no—
339C2×D12—58no—
340C2×D12—54no—
341C2×D12—58no—
342C2×D12—108no—
343C2×C4×D3—24no—
344C2×C4×D3—58no—
345C2×C4×D3—58no—
346C2×C4×D3—58no—
347C2×C4×D3—108no—
348C2×C4×D3—108no—
349C2×C4×D3—108no—
350C2×C4×D3C22×D514yes—
351C2×Dic6—24no—
352C2×Dic6C22×D514yes—
353C3×C4⋊C4—58no—
354C3×C4⋊C4C22×D514yes—
355C3×C22⋊C4—58no—
356#217—54no—
357(C2×D3)⋊C4—54no—
358(C2×D3)⋊C4—58no—
359(C2×D3)⋊C4C22×D518yes—
360C4⋊Dic3C22×D518yes—
361Dic3⋊C4—58no—
362Dic3⋊C4—58no—
363Dic3⋊C4—54no—
364C4×Dic3—54no—
365C23×C5—32no—
366C23×C5—62no—
367C23×C5—62no—
368C23×C5—62no—
369C23×C5C23×D311yescharacteristic
370C22×D5—22no—
371C22×D5—22no—
372C22×D5—22no—
373C22×D5—38no—
374C22×D5—34no—
375C22×D5—64no—
376C22×D5—64no—
377C22×D5C23×D312yes—
378C5×Q8—68no—
379C2×C4×C5—24no—
380C2×C4×C5—34no—
381C2×C4×C5—32no—
382C2×C4×C5—62no—
383C2×C4×C5—64no—
384C2×C4×C5—68no—
385C2×C4×C5D3×D414yes—
386C2×C4×C5C23×D314yes—
387C2×C4×C5C23×D312yes—
388C22⋊D5—616no—
389C22⋊D5—68no—
390C2×Dic5—24no—
391C2×Dic5—22no—
392C2×Dic5—34no—
393C2×Dic5—32no—
394C2×Dic5—32no—
395C2×Dic5—62no—
396C2×Dic5C23×D314yes—
397C2×Dic5C23×D312yes—
398D20—316no—
399D20—616no—
400C4×D5—28no—
401C4×D5—616no—
402C4×D5—616no—
403C4×D5—616no—
404Dic10—28no—
405C2×#41—158no—
406C2×#41—158no—
407C2×#41—308no—
408C2×#41—308no—
409C22×Q8—31no—
410C22×Q8—51no—
411C22×D4—152no—
412C22×D4—152no—
413C22×D4—151no—
414C22×D4—151no—
415C23×C4—31no—
416C23×C4—51no—
417C23×C4—152no—
418C23×C4—152no—
419C23×C4—152no—
420C4⋊Q8—158no—
421#123—1516no—
422#123—1516no—
423C22⋊Q8—38no—
424C22⋊Q8—58no—
425#121—1516no—
426C4×D4—158no—
427C4×D4—158no—
428C2×C4⋊C4—32no—
429C2×C4⋊C4—52no—
430C2×C4⋊C4—1516no—
431C2×C4⋊C4—151no—
432C2×C4⋊C4—152no—
433C2×C4⋊C4—152no—
434C2×C4⋊C4D3×D511yescharacteristic
435C2×C22⋊C4—32no—
436C2×C22⋊C4—52no—
437C2×C22⋊C4—151no—
438C2×C22⋊C4—151no—
439C2×C22⋊C4—152no—
440C2×C42—151no—
441C2×C3×C5#54714yescomplemented
442C2×C3×C5C23×D411yescharacteristic
443C2×C3×C5C22×#4111yescharacteristic
444C2×C3×C5C2×2−1+411yescharacteristic
445D15—28no—
446C3×D5—42no—
447C5×D3—42no—
448C23×C3—52no—
449C23×C3—102no—
450C23×C3—102no—
451C23×C3—102no—
452C23×C3C23×D511yescharacteristic
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—58no—
457C22×D3—54no—
458C22×D3—104no—
459C22×D3—104no—
460C22×D3C23×D512yes—
461C3×Q8—108no—
462C2×C3×C4—24no—
463C2×C3×C4—54no—
464C2×C3×C4—52no—
465C2×C3×C4—102no—
466C2×C3×C4—104no—
467C2×C3×C4—108no—
468C2×C3×C4D4×D514yes—
469C2×C3×C4C23×D514yes—
470C2×C3×C4C23×D512yes—
471#67—1016no—
472#67—108no—
473C2×Dic3—24no—
474C2×Dic3—22no—
475C2×Dic3—54no—
476C2×Dic3—52no—
477C2×Dic3—52no—
478C2×Dic3—102no—
479C2×Dic3C23×D514yes—
480C2×Dic3C23×D512yes—
481D12—516no—
482D12—1016no—
483C4×D3—28no—
484C4×D3—1016no—
485C4×D3—1016no—
486C4×D3—1016no—
487Dic6—28no—
488C22×C5—62no—
489C22×C5—62no—
490C22×C5—62no—
491C22×C5—124no—
492C22×C5C2×D3×D412yes—
493C22×C5#100712yes—
494C22×C5D3×#4112yes—
495C22×C5C24×D311yescharacteristic
496C2×D5—22no—
497C2×D5—22no—
498C2×D5—22no—
499C2×D5—38no—
500C2×D5—44no—
501C2×D5—64no—
502C2×D5—64no—
503C2×D5—616no—
504C4×C5—24no—
505C4×C5—62no—
506C4×C5—64no—
507C4×C5C2×D3×D414yes—
508Dic5—24no—
509Dic5—22no—
510Dic5—34no—
511Dic5—62no—
512C24—31no—
513C24—51no—
514C24—152no—
515#41—3032no—
516#41—3032no—
517C2×Q8—34no—
518C2×Q8—54no—
519C2×Q8—64no—
520C2×Q8—104no—
521C2×D4—158no—
522C2×D4—158no—
523C2×D4—154no—
524C2×D4—158no—
525C2×D4—154no—
526C2×D4—308no—
527C2×D4—308no—
528C2×D4—304no—
529C22×C4—32no—
530C22×C4—31no—
531C22×C4—34no—
532C22×C4—52no—
533C22×C4—51no—
534C22×C4—54no—
535C22×C4—64no—
536C22×C4—104no—
537C22×C4—158no—
538C22×C4—158no—
539C22×C4—151no—
540C22×C4—151no—
541C22×C4—158no—
542C22×C4—308no—
543C22×C4—308no—
544C22×C4—308no—
545C22×C4C2×D3×D512yes—
546C22×C4C2×D3×D511yescharacteristic
547C4⋊C4—38no—
548C4⋊C4—58no—
549C4⋊C4—154no—
550C4⋊C4—158no—
551C4⋊C4—158no—
552C4⋊C4C2×D3×D514yes—
553C22⋊C4—38no—
554C22⋊C4—58no—
555C22⋊C4—154no—
556C22⋊C4—154no—
557C22⋊C4—158no—
558C42—154no—
559C3×C5C2×#54711yescharacteristic, complemented, Hall
560C22×C3—102no—
561C22×C3—102no—
562C22×C3—102no—
563C22×C3—204no—
564C22×C3C2×D4×D512yes—
565C22×C3#414712yes—
566C22×C3D5×#4112yes—
567C22×C3C24×D511yescharacteristic
568C2×D3—22no—
569C2×D3—22no—
570C2×D3—22no—
571C2×D3—44no—
572C2×D3—58no—
573C2×D3—1016no—
574C2×D3—104no—
575C2×D3—104no—
576C3×C4—24no—
577C3×C4—102no—
578C3×C4—104no—
579C3×C4C2×D4×D514yes—
580Dic3—24no—
581Dic3—22no—
582Dic3—54no—
583Dic3—102no—
584C2×C5—122no—
585C2×C5#563114yescomplemented
586C2×C5C22×D3×D411yescharacteristic
587C2×C5C2×#100711yescharacteristic
588C2×C5C2×D3×#4111yescharacteristic
589D5—42no—
590D5—68no—
591C23—32no—
592C23—52no—
593C23—62no—
594C23—62no—
595C23—62no—
596C23—102no—
597C23—102no—
598C23—102no—
599C23—158no—
600C23—154no—
601C23—304no—
602C23—304no—
603C23C22×D3×D511yescharacteristic
604Q8—68no—
605Q8—108no—
606D4—1516no—
607D4—3016no—
608D4—3016no—
609D4—308no—
610C2×C4—24no—
611C2×C4—34no—
612C2×C4—32no—
613C2×C4—54no—
614C2×C4—52no—
615C2×C4—62no—
616C2×C4—64no—
617C2×C4—68no—
618C2×C4—102no—
619C2×C4—104no—
620C2×C4—108no—
621C2×C4—154no—
622C2×C4—152no—
623C2×C4—152no—
624C2×C4—3016no—
625C2×C4—3016no—
626C2×C4—3016no—
627C2×C4—302no—
628C2×C4#677714yes—
629C2×C4C22×D3×D514yes—
630C2×C4C22×D3×D512yes—
631C2×C3—202no—
632C2×C3#6596514yescomplemented
633C2×C3C22×D4×D511yescharacteristic
634C2×C3C2×#414711yescharacteristic
635C2×C3C2×D5×#4111yescharacteristic
636D3—42no—
637D3—108no—
638C5C2×#563111yescharacteristic, complemented, Sylow
639C22—62no—
640C22—62no—
641C22—62no—
642C22—102no—
643C22—102no—
644C22—102no—
645C22—124no—
646C22—158no—
647C22—204no—
648C22—304no—
649C22—3016no—
650C22—304no—
651C22C2×#677712yes—
652C22#9202412yes—
653C22#9202912yes—
654C22C23×D3×D511yescharacteristic
655C4—24no—
656C4—62no—
657C4—64no—
658C4—102no—
659C4—104no—
660C4—154no—
661C4—302no—
662C4C2×#677714yes—
663C3C2×#6596511yescharacteristic, complemented, Sylow
664C2—122no—
665C2—202no—
666C2—308no—
667C2#1175370414yesdirect product factor
668C2C22×#677711yescharacteristic
669C2C2×#9202411yescharacteristic
670C2C2×#9202911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#547
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6773C2semidirect
2. C22×#6769C2semidirect
3. C2×#91782C2semidirect
4. C2×C5×#897C2semidirect
5. C2×C3×#4043C2semidirect
6. C2×#91461C2semidirect
7. C2×C4×#1201C2semidirect
8. C2×#91438C2semidirect
9. C2×#91437C2semidirect
10. C2×#91385C2semidirect
11. C2×#91356C2semidirect
12. #11753704C2direct (N × H)
26. C2×#6773C22semidirect
28. C2×#6769C22semidirect
32. #91782C22semidirect
35. C5×#897C22semidirect
38. C3×#4043C22semidirect
44. #91461C22semidirect
45. C4×#1201C22semidirect
46. #91438C22semidirect
47. #91437C22semidirect
48. #91385C22semidirect
49. #91356C22semidirect
57. C2×#4043D3semidirect
70. C2×D60D4semidirect
116. C2×#897D5semidirect
152. #4043C2×D3semidirect
177. C2×Dic15#41semidirect
180. D60C2×D4semidirect
229. #897C2×D5semidirect
313. Dic15C2×#41semidirect
441. C2×C3×C5#547semidirect
559. C3×C5C2×#547semidirect
585. C2×C5#5631semidirect
632. C2×C3#65965semidirect
638. C5C2×#5631semidirect
663. C3C2×#65965semidirect
667. C2#11753704direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67732
C22×#67692
C2×#917822
C2×C5×#8972
C2×C3×#40432
C2×#914612
C2×C4×#12012
C2×#914382
C2×#914372
C2×#913852
C2×#913562
#117537042
C2×#659653
C2×#56315