Subgroups — #23761610

Order 10112.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₂×D₇₉	C₂	1	1	yes	maximal, characteristic
2	C₇₉⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×D₇₉	C₄	1	1	yes	characteristic
5	C₇₉⋊C₃₂	C₄	1	1	yes	characteristic
6	C₃₂×C₇₉	C₂²	1	1	yes	characteristic
7	C₈×D₇₉	C₈	1	1	yes	characteristic
8	C₇₉⋊C₁₆	C₈	1	1	yes	characteristic
9	C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
10	C₄×D₇₉	C₁₆	1	1	yes	characteristic
11	C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
12	C₇₉⋊C₈	C₁₆	1	1	yes	characteristic
13	C₂×D₇₉	C₃₂	1	1	yes	characteristic
14	C₄×C₇₉	C₂×C₁₆	1	1	yes	characteristic
15	Dic₇₉	C₃₂	1	1	yes	characteristic
16	C₂×C₇₉	C₂×C₃₂	1	1	yes	characteristic
17	D₇₉	—	2	1	no	—
18	M₁₂₈	—	79	1	no	maximal, Sylow
19	C₇₉	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃₂	—	79	1	no	—
21	C₆₄	—	79	1	no	—
22	C₆₄	D₇₉	1	1	yes	characteristic, complemented
23	C₂×C₁₆	—	79	1	no	—
24	C₃₂	—	79	1	no	—
25	C₃₂	C₂×D₇₉	1	1	yes	characteristic
26	C₂×C₈	—	79	1	no	—
27	C₁₆	—	79	1	no	—
28	C₁₆	C₄×D₇₉	1	1	yes	characteristic
29	C₂×C₄	—	79	1	no	—
30	C₈	—	79	1	no	—
31	C₈	C₈×D₇₉	1	1	yes	characteristic
32	C₂²	—	79	1	no	—
33	C₄	—	79	1	no	—
34	C₄	C₁₆×D₇₉	1	1	yes	characteristic
35	C₂	—	158	1	no	—
36	C₂	C₃₂×D₇₉	1	1	yes	characteristic

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