Subgroups — #23761604

Order 10112.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098393	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic
3	#14579097	—	2	2	no	—
4	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
5	C₃₂×C₇₉	C₄	1	2	yes	—
6	#11929608	—	4	2	no	—
7	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
8	C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₇₉	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
11	C₈×C₇₉	C₄⋊C₄	1	1	yes	characteristic
12	C₈×C₇₉	Q₁₆	1	1	yes	characteristic
13	C₇₉⋊C₈	—	8	2	no	—
14	C₂²×C₇₉	Q₃₂	1	1	yes	characteristic
15	C₄×C₇₉	#107	1	1	yes	characteristic
16	C₄×C₇₉	D₁₆	1	1	yes	characteristic
17	C₂×C₇₉	—	2	1	no	—
18	C₂×C₇₉	#366	1	1	yes	characteristic
19	#1425	—	79	1	no	maximal, Sylow
20	C₇₉	#1425	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃₂	D₇₉	1	1	yes	characteristic
22	#368	—	79	2	no	—
23	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
24	#108	—	158	2	no	—
25	C₃₂	Dic₇₉	1	2	yes	—
26	M₁₆	—	316	2	no	—
27	C₂×C₈	D₃₁₆	1	1	yes	characteristic
28	C₁₆	Dic₁₅₈	1	1	yes	characteristic
29	C₁₆	C₂×Dic₇₉	1	1	yes	characteristic
30	C₂×C₄	D₆₃₂	1	1	yes	characteristic
31	C₈	—	632	2	no	—
32	C₈	C₄⋊Dic₇₉	1	1	yes	characteristic
33	C₈	Dic₃₁₆	1	1	yes	characteristic
34	C₂²	Dic₆₃₂	1	1	yes	characteristic
35	C₄	#14579095	1	1	yes	characteristic
36	C₄	D₁₂₆₄	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#19098389	1	1	yes	characteristic

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

N	H ≅ G/N	type
20. C₇₉	#1425	semidirect