Subgroups — #19098348

Order 5056.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14579167	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	M₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#11929624	C₄	1	1	yes	characteristic
5	#11929608	C₄	1	1	yes	characteristic
6	#11929607	—	2	1	no	—
7	C₈×D₇₉	—	2	1	no	—
8	C₇₉⋊C₁₆	—	2	1	no	—
9	C₂×C₈×C₇₉	C₂²	1	1	yes	characteristic
10	C₁₆×C₇₉	—	2	1	no	—
11	C₂×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
12	C₂²⋊D₇₉	—	2	1	no	—
13	D₃₁₆	C₈	1	1	yes	characteristic
14	C₄×D₇₉	—	2	1	no	—
15	Dic₁₅₈	C₈	1	1	yes	characteristic
16	C₈×C₇₉	D₄	1	1	yes	characteristic
17	C₈×C₇₉	D₄	1	1	yes	characteristic
18	C₇₉⋊C₈	—	2	1	no	—
19	C₂²×C₇₉	M₁₆	1	1	yes	characteristic
20	C₂×D₇₉	—	2	1	no	—
21	C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
23	Dic₇₉	—	2	1	no	—
24	C₂×C₇₉	—	2	1	no	—
25	C₂×C₇₉	C₂²⋊C₈	1	1	yes	characteristic
26	D₇₉	—	4	1	no	—
27	C₇₉	#350	1	1	yes	characteristic, complemented, Sylow
28	#350	—	79	1	no	maximal, Sylow
29	#131	—	79	1	no	—
30	M₃₂	D₇₉	1	1	yes	characteristic, complemented
31	C₂×C₁₆	—	79	1	no	—
32	#41	—	79	1	no	—
33	M₁₆	—	79	1	no	—
34	M₁₆	—	158	1	no	—
35	C₂×C₈	—	158	1	no	—
36	C₂×C₈	C₂×D₇₉	1	1	yes	characteristic
37	C₁₆	—	2	1	no	—
38	C₁₆	—	158	1	no	—
39	Q₈	—	79	1	no	—
40	D₄	—	79	1	no	—
41	D₄	—	158	1	no	—
42	C₂×C₄	—	158	1	no	—
43	C₂×C₄	C₄×D₇₉	1	1	yes	characteristic
44	C₈	—	158	1	no	—
45	C₈	D₃₁₆	1	1	yes	characteristic
46	C₈	C₂²⋊D₇₉	1	1	yes	characteristic
47	C₂²	—	158	1	no	—
48	C₂²	#11929607	1	1	yes	characteristic
49	C₄	—	158	1	no	—
50	C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
51	C₄	C₈×D₇₉	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	316	1	no	—
54	C₂	(C₂×D₇₉)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊D₇₉
commutator	C₄×C₇₉	C₂×C₈
Frattini	C₂×C₈	C₂×D₇₉
Fitting	M₃₂×C₇₉	C₂
socle	C₂×C₇₉	C₂²⋊C₈
hypercenter	M₃₂	D₇₉
hypocenter	C₇₉	#350
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×C₇₉⋊C₁₆	C₂	semidirect
3. M₃₂×C₇₉	C₂	semidirect
27. C₇₉	#350	semidirect
30. M₃₂	D₇₉	semidirect