Subgroups — #23761614

Order 10112.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₅₂₈	C₂	1	1	yes	maximal, characteristic
2	C₇₉⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₆₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₂₆₄	—	2	1	no	—
5	Q₃₂×C₇₉	—	2	1	no	—
6	C₃₂×C₇₉	C₂²	1	1	yes	characteristic
7	D₆₃₂	—	4	1	no	—
8	Q₁₆×C₇₉	—	4	1	no	—
9	C₁₆×C₇₉	D₄	1	1	yes	characteristic
10	Q₈×C₇₉	—	8	1	no	—
11	D₃₁₆	—	8	1	no	—
12	C₈×C₇₉	D₈	1	1	yes	characteristic
13	C₂×D₇₉	—	16	1	no	—
14	C₄×C₇₉	—	16	1	no	—
15	C₄×C₇₉	D₁₆	1	1	yes	characteristic
16	C₂×C₇₉	D₃₂	1	1	yes	characteristic
17	D₇₉	—	32	1	no	—
18	SD₁₂₈	—	79	1	no	maximal, Sylow
19	C₇₉	SD₁₂₈	1	1	yes	characteristic, complemented, Sylow
20	Q₆₄	D₇₉	1	1	yes	characteristic, complemented
21	D₃₂	—	79	1	no	—
22	C₆₄	—	79	1	no	—
23	Q₃₂	—	2	1	no	—
24	D₁₆	—	158	1	no	—
25	C₃₂	C₂×D₇₉	1	1	yes	characteristic
26	Q₁₆	—	4	1	no	—
27	D₈	—	316	1	no	—
28	C₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
29	Q₈	—	8	1	no	—
30	D₄	—	632	1	no	—
31	C₈	#11929609	1	1	yes	characteristic
32	C₂²	—	1264	1	no	—
33	C₄	—	16	1	no	—
34	C₄	#14579102	1	1	yes	characteristic
35	C₂	—	2528	1	no	—
36	C₂	#19098398	1	1	yes	characteristic

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