Subgroups — #19098392

Order 5056.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#14579097	C₂	1	1	yes	maximal, characteristic
3	#108×C₇₉	C₂	1	1	yes	maximal, characteristic
4	#11929608	—	2	1	no	—
5	C₇₉⋊C₁₆	C₄	1	2	yes	—
6	M₁₆×C₇₉	—	2	1	no	—
7	C₂×C₈×C₇₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₇₉	D₄	1	1	yes	characteristic
9	C₈×C₇₉	—	4	1	no	—
10	C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
11	C₈×C₇₉	Q₈	1	1	yes	characteristic
12	C₇₉⋊C₈	—	4	1	no	—
13	C₂²×C₇₉	Q₁₆	1	1	yes	characteristic
14	C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₇₉	D₈	1	1	yes	characteristic
16	C₂×C₇₉	—	2	1	no	—
17	C₂×C₇₉	#107	1	1	yes	characteristic
18	C₇₉	#368	1	1	yes	characteristic, complemented, Sylow
19	#368	—	79	1	no	maximal, Sylow
20	C₂×C₁₆	—	79	1	no	—
21	#108	—	79	1	no	—
22	#108	D₇₉	1	1	yes	characteristic
23	M₁₆	—	2	1	no	—
24	M₁₆	—	158	1	no	—
25	C₂×C₈	C₂×D₇₉	1	1	yes	characteristic
26	C₁₆	—	79	2	no	—
27	C₂×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
28	C₈	—	4	1	no	—
29	C₈	—	316	1	no	—
30	C₈	Dic₁₅₈	1	1	yes	characteristic
31	C₈	C₄×D₇₉	1	1	yes	characteristic
32	C₂²	#11929614	1	1	yes	characteristic
33	C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
34	C₄	#11929609	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#14579094	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₇₉	#368	semidirect