Subgroups — #34176147

Order 20224.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇₉⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#23761600	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic
4	#19098389	—	2	1	no	—
5	C₇₉⋊C₆₄	—	2	1	no	—
6	C₂×D₁₆×C₇₉	—	2	1	no	—
7	D₃₂×C₇₉	—	2	1	no	—
8	D₃₂×C₇₉	C₄	1	2	yes	complemented
9	C₂×C₃₂×C₇₉	C₂²	1	1	yes	characteristic
10	#14579095	—	4	1	no	—
11	C₂×D₈×C₇₉	—	4	1	no	—
12	D₁₆×C₇₉	—	2	2	no	—
13	D₁₆×C₇₉	—	4	1	no	—
14	C₂×C₁₆×C₇₉	D₄	1	1	yes	characteristic
15	C₃₂×C₇₉	C₂×C₄	1	1	yes	characteristic
16	C₃₂×C₇₉	D₄	1	1	yes	characteristic
17	C₄⋊Dic₇₉	—	8	1	no	—
18	C₂×D₄×C₇₉	—	8	1	no	—
19	D₈×C₇₉	—	4	2	no	—
20	D₈×C₇₉	—	8	1	no	—
21	C₂×C₈×C₇₉	D₈	1	1	yes	characteristic
22	C₁₆×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₆×C₇₉	SD₁₆	1	1	yes	characteristic
24	C₂³×C₇₉	—	16	1	no	—
25	D₄×C₇₉	—	8	2	no	—
26	D₄×C₇₉	—	16	1	no	—
27	C₂×C₄×C₇₉	D₁₆	1	1	yes	characteristic
28	C₂×Dic₇₉	—	16	1	no	—
29	C₈×C₇₉	#102	1	1	yes	characteristic
30	C₈×C₇₉	SD₃₂	1	1	yes	characteristic
31	C₂²×C₇₉	—	16	2	no	—
32	C₂²×C₇₉	—	32	1	no	—
33	C₂²×C₇₉	—	32	1	no	—
34	C₂²×C₇₉	D₃₂	1	1	yes	characteristic
35	C₄×C₇₉	#357	1	1	yes	characteristic
36	C₄×C₇₉	SD₆₄	1	1	yes	characteristic
37	Dic₇₉	—	32	1	no	—
38	#7537	—	79	1	no	maximal, Sylow
39	C₂×C₇₉	—	32	2	no	—
40	C₂×C₇₉	#1415	1	1	yes	characteristic
41	C₂×C₇₉	D₆₄	1	1	yes	characteristic
42	C₂×C₇₉	SD₁₂₈	1	1	yes	characteristic
43	C₂×D₃₂	D₇₉	1	1	yes	characteristic
44	C₂×C₆₄	—	79	1	no	—
45	#1423	—	79	1	no	—
46	C₇₉	#7537	1	1	yes	characteristic, complemented, Sylow
47	C₂×D₁₆	—	2	1	no	—
48	D₃₂	—	2	1	no	—
49	D₃₂	Dic₇₉	1	2	yes	complemented
50	C₂×C₃₂	C₂×D₇₉	1	1	yes	characteristic
51	#366	—	158	1	no	—
52	C₆₄	—	158	1	no	—
53	C₂×D₈	—	4	1	no	—
54	D₁₆	—	2	2	no	—
55	D₁₆	—	4	1	no	—
56	C₂×C₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
57	#107	—	316	1	no	—
58	C₃₂	C₂×Dic₇₉	1	1	yes	characteristic
59	C₃₂	C₂²⋊D₇₉	1	1	yes	characteristic
60	C₂×D₄	—	8	1	no	—
61	D₈	—	4	2	no	—
62	D₈	—	8	1	no	—
63	C₂×C₈	#11929609	1	1	yes	characteristic
64	C₄⋊C₄	—	632	1	no	—
65	C₁₆	C₂²⋊Dic₇₉	1	1	yes	characteristic
66	C₁₆	#11929612	1	1	yes	characteristic
67	C₂³	—	16	1	no	—
68	D₄	—	8	2	no	—
69	D₄	—	16	1	no	—
70	C₂×C₄	—	1264	1	no	—
71	C₂×C₄	#14579102	1	1	yes	characteristic
72	C₈	#14579082	1	1	yes	characteristic
73	C₈	#14579105	1	1	yes	characteristic
74	C₂²	—	16	2	no	—
75	C₂²	—	32	1	no	—
76	C₂²	—	32	1	no	—
77	C₂²	#19098398	1	1	yes	characteristic
78	C₄	—	2528	1	no	—
79	C₄	#19098364	1	1	yes	characteristic
80	C₄	#19098401	1	1	yes	characteristic
81	C₂	—	32	2	no	—
82	C₂	#23761578	1	1	yes	characteristic
83	C₂	#23761612	1	1	yes	characteristic
84	C₂	#23761615	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19098398
commutator	C₃₂×C₇₉	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₇₉
Fitting, prime radical	C₂×D₃₂×C₇₉	C₂
socle	C₂²×C₇₉	D₃₂
cosocle	C₂×C₃₂×C₇₉	C₂²
hypercenter	C₂×D₃₂	D₇₉
hypocenter	C₇₉	#7537
LCS	G ▷ C₃₂×C₇₉ ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×D₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₇₉⋊C₆₄	C₂	semidirect
2. #23761600	C₂	semidirect
8. D₃₂×C₇₉	C₄	semidirect
46. C₇₉	#7537	semidirect
49. D₃₂	Dic₇₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇₉⋊C₆₄	2
#23761600	2
C₂×D₃₂×C₇₉	2
#7537	79