Subgroups — #23761617

Order 10112.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₂₆₄	C₂	1	1	yes	maximal, characteristic
2	C₇₉⋊C₆₄	C₂	1	1	yes	maximal, characteristic
3	Q₆₄×C₇₉	C₂	1	1	yes	maximal, characteristic
4	Dic₆₃₂	—	2	1	no	—
5	Q₃₂×C₇₉	—	2	1	no	—
6	C₃₂×C₇₉	C₂²	1	1	yes	characteristic
7	Dic₃₁₆	—	4	1	no	—
8	Q₁₆×C₇₉	—	4	1	no	—
9	C₁₆×C₇₉	D₄	1	1	yes	characteristic
10	Q₈×C₇₉	—	8	1	no	—
11	Dic₁₅₈	—	8	1	no	—
12	C₈×C₇₉	D₈	1	1	yes	characteristic
13	C₄×C₇₉	—	16	1	no	—
14	C₄×C₇₉	D₁₆	1	1	yes	characteristic
15	Dic₇₉	—	16	1	no	—
16	C₂×C₇₉	D₃₂	1	1	yes	characteristic
17	Q₁₂₈	—	79	1	no	maximal, Sylow
18	C₇₉	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	Q₆₄	—	79	1	no	—
20	Q₆₄	D₇₉	1	1	yes	characteristic
21	C₆₄	—	79	1	no	—
22	Q₃₂	—	2	1	no	—
23	Q₃₂	—	158	1	no	—
24	C₃₂	C₂×D₇₉	1	1	yes	characteristic
25	Q₁₆	—	4	1	no	—
26	Q₁₆	—	316	1	no	—
27	C₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
28	Q₈	—	8	1	no	—
29	Q₈	—	632	1	no	—
30	C₈	#11929609	1	1	yes	characteristic
31	C₄	—	16	1	no	—
32	C₄	—	1264	1	no	—
33	C₄	#14579102	1	1	yes	characteristic
34	C₂	#19098398	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₇₉	Q₁₂₈	semidirect