Subgroups — #34176181

Order 20224.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₀₅₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₉⋊C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×D₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₅₂₈	—	2	1	no	—
5	D₃₂×C₇₉	—	2	1	no	—
6	C₆₄×C₇₉	C₂²	1	1	yes	characteristic
7	D₁₂₆₄	—	4	1	no	—
8	D₁₆×C₇₉	—	4	1	no	—
9	C₃₂×C₇₉	D₄	1	1	yes	characteristic
10	D₆₃₂	—	8	1	no	—
11	D₈×C₇₉	—	8	1	no	—
12	C₁₆×C₇₉	D₈	1	1	yes	characteristic
13	D₄×C₇₉	—	16	1	no	—
14	D₃₁₆	—	16	1	no	—
15	C₈×C₇₉	D₁₆	1	1	yes	characteristic
16	C₂²×C₇₉	—	32	1	no	—
17	C₂×D₇₉	—	32	1	no	—
18	C₄×C₇₉	D₃₂	1	1	yes	characteristic
19	D₁₂₈	—	79	1	no	maximal, Sylow
20	C₂×C₇₉	—	64	1	no	—
21	C₂×C₇₉	D₆₄	1	1	yes	characteristic
22	D₇₉	—	64	1	no	—
23	D₆₄	—	79	1	no	—
24	D₆₄	D₇₉	1	1	yes	characteristic, complemented
25	C₁₂₈	—	79	1	no	—
26	C₇₉	D₁₂₈	1	1	yes	characteristic, complemented, Sylow
27	D₃₂	—	2	1	no	—
28	D₃₂	—	158	1	no	—
29	C₆₄	C₂×D₇₉	1	1	yes	characteristic
30	D₁₆	—	4	1	no	—
31	D₁₆	—	316	1	no	—
32	C₃₂	C₂²⋊D₇₉	1	1	yes	characteristic
33	D₈	—	8	1	no	—
34	D₈	—	632	1	no	—
35	C₁₆	#11929609	1	1	yes	characteristic
36	D₄	—	16	1	no	—
37	D₄	—	1264	1	no	—
38	C₈	#14579102	1	1	yes	characteristic
39	C₂²	—	32	1	no	—
40	C₂²	—	2528	1	no	—
41	C₄	#19098398	1	1	yes	characteristic
42	C₂	—	64	1	no	—
43	C₂	—	5056	1	no	—
44	C₂	#23761612	1	1	yes	characteristic

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.