Subgroups — #19098388

Order 5056.

46 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	#14579095	C₂	1	1	yes	maximal, characteristic
3	#107×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₇₉	—	2	1	no	—
5	C₇₉⋊C₁₆	C₄	1	2	yes	complemented
6	C₂×C₈×C₇₉	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₇₉	—	2	1	no	—
8	C₂×C₄×C₇₉	—	4	1	no	—
9	C₂×C₄×C₇₉	D₄	1	1	yes	characteristic
10	C₂×Dic₇₉	—	4	1	no	—
11	C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
12	C₈×C₇₉	Q₈	1	1	yes	characteristic
13	C₂²×C₇₉	D₈	1	1	yes	characteristic
14	C₄×C₇₉	—	8	1	no	—
15	C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₇₉	Q₁₆	1	1	yes	characteristic
17	Dic₇₉	—	8	1	no	—
18	C₂×C₇₉	#107	1	1	yes	characteristic
19	C₂×C₇₉	D₁₆	1	1	yes	characteristic
20	C₂×C₇₉	Q₃₂	1	1	yes	characteristic
21	C₇₉	#366	1	1	yes	characteristic, complemented, Sylow
22	#366	—	79	1	no	maximal, Sylow
23	C₂×C₁₆	—	79	1	no	—
24	#107	—	79	1	no	—
25	#107	D₇₉	1	1	yes	characteristic
26	C₂×C₈	C₂×D₇₉	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₄⋊C₄	—	158	1	no	—
29	C₁₆	—	79	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	316	1	no	—
32	C₂×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
33	C₈	Dic₁₅₈	1	1	yes	characteristic
34	C₈	C₄×D₇₉	1	1	yes	characteristic
35	C₂²	#11929609	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	632	1	no	—
38	C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
39	C₄	#11929614	1	1	yes	characteristic
40	C₂	#14579094	1	1	yes	characteristic
41	C₂	#14579102	1	1	yes	characteristic
42	C₂	#14579107	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. C₇₉⋊C₁₆	C₄	semidirect
21. C₇₉	#366	semidirect