Subgroups — #19098913

Order 5056.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14579161	C₂	1	1	yes	maximal, characteristic
2	#14579085	C₂	1	4	yes	maximal
3	C₄×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₅₈	—	2	1	no	—
6	C₂×C₇₉⋊C₈	C₂²	1	2	yes	—
7	C₄⋊Dic₇₉	—	2	1	no	—
8	C₄⋊Dic₇₉	C₂²	1	2	yes	—
9	C₂×Q₈×C₇₉	C₂²	1	2	yes	—
10	C₄⋊C₄×C₇₉	—	2	1	no	—
11	C₄⋊C₄×C₇₉	—	2	1	no	—
12	C₄²×C₇₉	C₂²	1	1	yes	characteristic
13	Q₈×C₇₉	—	2	4	no	—
14	C₂×C₄×C₇₉	—	2	2	no	—
15	C₂×C₄×C₇₉	D₄	1	1	yes	characteristic
16	C₂×C₄×C₇₉	D₄	1	1	yes	characteristic
17	C₂×C₄×C₇₉	C₂³	1	1	yes	characteristic
18	C₂×Dic₇₉	—	2	2	no	—
19	Dic₁₅₈	—	4	2	no	—
20	C₇₉⋊C₈	—	2	2	no	—
21	C₂²×C₇₉	C₂×D₄	1	1	yes	characteristic
22	C₄×C₇₉	—	4	2	no	—
23	C₄×C₇₉	SD₁₆	1	2	yes	—
24	C₄×C₇₉	Q₁₆	1	2	yes	—
25	C₄×C₇₉	#41	1	2	yes	—
26	Dic₇₉	—	4	2	no	—
27	C₂×C₇₉	#124	1	1	yes	characteristic
28	C₂×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
29	C₂×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
30	C₇₉	#487	1	1	yes	characteristic, complemented, Sylow
31	#487	—	79	1	no	maximal, Sylow
32	C₄⋊Q₈	—	79	1	no	—
33	C₄⋊Q₈	D₇₉	1	1	yes	characteristic
34	#103	—	79	4	no	—
35	C₄×C₈	—	79	1	no	—
36	C₂×Q₈	—	158	1	no	—
37	C₂×Q₈	C₂×D₇₉	1	2	yes	—
38	C₂×C₈	—	79	2	no	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	—	2	1	no	—
41	C₄⋊C₄	—	79	2	no	—
42	C₄⋊C₄	—	158	1	no	—
43	C₄²	C₂×D₇₉	1	1	yes	characteristic
44	Q₈	—	2	4	no	—
45	Q₈	—	316	2	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	158	2	no	—
48	C₂×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
49	C₂×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
50	C₂×C₄	C₂²×D₇₉	1	1	yes	characteristic
51	C₈	—	158	2	no	—
52	C₂²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	—	316	2	no	—
55	C₄	#11929611	1	2	yes	—
56	C₄	#11929614	1	2	yes	—
57	C₄	#11929623	1	2	yes	—
58	C₂	#14579148	1	1	yes	characteristic
59	C₂	C₂×#11929611	1	1	yes	characteristic
60	C₂	C₂×#11929614	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂³
Frattini	C₂×C₄	C₂²×D₇₉
Fitting	C₄⋊Q₈×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₄
hypercenter	C₄⋊Q₈	D₇₉
hypocenter	C₇₉	#487
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
30. C₇₉	#487	semidirect