Subgroups — #19098340

Order 5056.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14579101	C₂	1	1	yes	maximal, characteristic
2	#14579071	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇₉⋊C₈	C₄	1	1	yes	characteristic
5	C₄×Dic₇₉	C₄	1	1	yes	characteristic
6	C₇₉⋊C₁₆	C₄	1	2	yes	complemented
7	C₂×C₈×C₇₉	C₂²	1	1	yes	characteristic
8	C₁₆×C₇₉	C₄	1	2	yes	complemented
9	C₂×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
10	C₂×Dic₇₉	—	2	1	no	—
11	C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
12	C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
13	C₇₉⋊C₈	—	2	1	no	—
14	C₂²×C₇₉	M₁₆	1	1	yes	characteristic
15	C₄×C₇₉	C₄²	1	1	yes	characteristic
16	C₄×C₇₉	M₁₆	1	1	yes	characteristic
17	Dic₇₉	—	4	1	no	—
18	C₂×C₇₉	—	2	1	no	—
19	C₂×C₇₉	#97	1	1	yes	characteristic
20	C₇₉	#347	1	1	yes	characteristic, complemented, Sylow
21	#347	—	79	1	no	maximal, Sylow
22	M₃₂	—	79	1	no	—
23	M₃₂	D₇₉	1	1	yes	characteristic
24	#97	—	79	1	no	—
25	C₂×C₈	—	79	1	no	—
26	C₂×C₈	C₂×D₇₉	1	1	yes	characteristic
27	C₄²	—	79	1	no	—
28	C₁₆	—	79	2	no	—
29	C₁₆	Dic₇₉	1	2	yes	complemented
30	C₂×C₄	—	158	1	no	—
31	C₂×C₄	C₄×D₇₉	1	1	yes	characteristic
32	C₈	—	158	1	no	—
33	C₈	C₄×D₇₉	1	1	yes	characteristic
34	C₈	C₂×Dic₇₉	1	1	yes	characteristic
35	C₂²	#11929607	1	1	yes	characteristic
36	C₄	—	316	1	no	—
37	C₄	C₄×Dic₇₉	1	1	yes	characteristic
38	C₄	#11929607	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	#14579071	1	1	yes	characteristic

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