Subgroups — #23763554

Order 10112.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊(C₇₉⋊C₈)	C₂	1	6	yes	maximal
2	#376×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₇₉⋊C₈	C₂²	1	4	yes	—
4	C₄⋊(C₇₉⋊C₈)	—	2	12	no	—
5	C₂×C₄²×C₇₉	C₂²	1	3	yes	—
6	#95×C₇₉	C₄	1	4	yes	—
7	C₂×C₇₉⋊C₈	—	2	12	no	—
8	C₂²×C₄×C₇₉	C₂×C₄	1	6	yes	—
9	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
10	C₄²×C₇₉	D₄	1	6	yes	—
11	C₄²×C₇₉	Q₈	1	6	yes	—
12	C₂³×C₇₉	C₂²×C₄	1	1	yes	characteristic
13	C₂×C₄×C₇₉	—	2	12	no	—
14	C₂×C₄×C₇₉	C₄⋊C₄	1	12	yes	—
15	C₂×C₄×C₇₉	C₂×D₄	1	3	yes	—
16	C₂×C₄×C₇₉	C₂×Q₈	1	3	yes	—
17	C₇₉⋊C₈	—	4	4	no	—
18	C₂²×C₇₉	C₂×C₄⋊C₄	1	3	yes	—
19	C₂²×C₇₉	#131	1	4	yes	—
20	C₄×C₇₉	—	2	12	no	—
21	C₄×C₇₉	#127	1	1	yes	characteristic
22	C₄×C₇₉	C₄⋊Q₈	1	3	yes	—
23	C₂×C₇₉	#384	1	1	yes	characteristic
24	C₂×C₇₉	#424	1	6	yes	—
25	#1843	—	79	1	no	maximal, Sylow
26	C₇₉	#1843	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₄⋊C₈	—	79	6	no	—
28	#376	D₇₉	1	1	yes	characteristic
29	C₂²×C₈	—	79	4	no	—
30	C₂×C₄²	C₂×D₇₉	1	3	yes	—
31	C₄⋊C₈	—	158	12	no	—
32	#95	Dic₇₉	1	4	yes	—
33	C₂²×C₄	C₂×Dic₇₉	1	6	yes	—
34	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
35	C₂×C₈	—	158	12	no	—
36	C₄²	Dic₁₅₈	1	6	yes	—
37	C₄²	D₃₁₆	1	6	yes	—
38	C₂³	C₂²×Dic₇₉	1	1	yes	characteristic
39	C₂×C₄	—	2	12	no	—
40	C₂×C₄	C₄⋊Dic₇₉	1	12	yes	—
41	C₂×C₄	C₂×D₃₁₆	1	3	yes	—
42	C₂×C₄	C₂×Dic₁₅₈	1	3	yes	—
43	C₈	—	316	4	no	—
44	C₂²	C₂×C₄⋊Dic₇₉	1	3	yes	—
45	C₂²	#14579168	1	4	yes	—
46	C₄	—	2	12	no	—
47	C₄	#14579158	1	1	yes	characteristic
48	C₄	#14579161	1	3	yes	—
49	C₂	#19098433	1	1	yes	characteristic
50	C₂	#19098590	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₇₉
commutator, socle, prime radical	C₂³×C₇₉	C₂²×C₄
Fitting	#376×C₇₉	C₂
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	#376	D₇₉
hypocenter	C₇₉	#1843
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
26. C₇₉	#1843	semidirect