Subgroups — #19098402

Order 5056.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₆₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₂₆₄	C₂	1	1	yes	maximal, characteristic
3	C₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₃₁₆	—	2	1	no	—
5	D₆₃₂	—	2	1	no	—
6	C₁₆×C₇₉	C₂²	1	1	yes	characteristic
7	D₃₁₆	—	4	1	no	—
8	Dic₁₅₈	—	4	1	no	—
9	C₈×C₇₉	D₄	1	1	yes	characteristic
10	C₂×D₇₉	—	8	1	no	—
11	C₄×C₇₉	D₈	1	1	yes	characteristic
12	Dic₇₉	—	8	1	no	—
13	C₂×C₇₉	D₁₆	1	1	yes	characteristic
14	D₇₉	—	16	1	no	—
15	C₇₉	SD₆₄	1	1	yes	characteristic, complemented, Sylow
16	SD₆₄	—	79	1	no	maximal, Sylow
17	Q₃₂	—	79	1	no	—
18	D₁₆	—	79	1	no	—
19	C₃₂	D₇₉	1	1	yes	characteristic, complemented
20	Q₁₆	—	158	1	no	—
21	D₈	—	158	1	no	—
22	C₁₆	C₂×D₇₉	1	1	yes	characteristic
23	Q₈	—	316	1	no	—
24	D₄	—	316	1	no	—
25	C₈	D₃₁₆	1	1	yes	characteristic
26	C₂²	—	632	1	no	—
27	C₄	—	632	1	no	—
28	C₄	D₆₃₂	1	1	yes	characteristic
29	C₂	—	1264	1	no	—
30	C₂	D₁₂₆₄	1	1	yes	characteristic

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