Subgroups — #34176075

Order 20224.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23761611	C₂	1	1	yes	maximal, characteristic
2	#23761533	C₂	1	1	yes	maximal, characteristic
3	C₇₉×M₁₂₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇₉⋊C₃₂	C₄	1	1	yes	characteristic
5	C₁₆×Dic₇₉	C₄	1	1	yes	characteristic
6	C₇₉⋊C₆₄	C₄	1	2	yes	complemented
7	C₂×C₃₂×C₇₉	C₂²	1	1	yes	characteristic
8	C₆₄×C₇₉	C₄	1	2	yes	complemented
9	C₂×C₇₉⋊C₁₆	C₈	1	1	yes	characteristic
10	C₈×Dic₇₉	C₈	1	1	yes	characteristic
11	C₇₉⋊C₃₂	C₈	1	2	yes	—
12	C₂×C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
13	C₃₂×C₇₉	C₂×C₄	1	1	yes	characteristic
14	C₃₂×C₇₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₇₉⋊C₈	C₁₆	1	1	yes	characteristic
16	C₄×Dic₇₉	C₁₆	1	1	yes	characteristic
17	C₇₉⋊C₁₆	C₁₆	1	2	yes	—
18	C₂×C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
19	C₁₆×C₇₉	C₄²	1	1	yes	characteristic
20	C₁₆×C₇₉	C₂×C₈	1	1	yes	characteristic
21	C₂×C₄×C₇₉	C₂×C₁₆	1	1	yes	characteristic
22	C₂×Dic₇₉	—	2	1	no	—
23	C₈×C₇₉	C₄×C₈	1	1	yes	characteristic
24	C₈×C₇₉	C₂×C₁₆	1	1	yes	characteristic
25	C₇₉⋊C₈	—	2	1	no	—
26	C₂²×C₇₉	M₆₄	1	1	yes	characteristic
27	C₄×C₇₉	C₄×C₁₆	1	1	yes	characteristic
28	C₄×C₇₉	M₆₄	1	1	yes	characteristic
29	Dic₇₉	—	4	1	no	—
30	#7511	—	79	1	no	maximal, Sylow
31	C₂×C₇₉	—	2	1	no	—
32	C₂×C₇₉	#1397	1	1	yes	characteristic
33	M₁₂₈	—	79	1	no	—
34	M₁₂₈	D₇₉	1	1	yes	characteristic
35	#1397	—	79	1	no	—
36	C₇₉	#7511	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃₂	—	79	1	no	—
38	C₂×C₃₂	C₂×D₇₉	1	1	yes	characteristic
39	C₄×C₁₆	—	79	1	no	—
40	C₆₄	—	79	2	no	—
41	C₆₄	Dic₇₉	1	2	yes	complemented
42	C₂×C₁₆	—	79	1	no	—
43	C₂×C₁₆	C₄×D₇₉	1	1	yes	characteristic
44	C₄×C₈	—	79	1	no	—
45	C₃₂	—	79	2	no	—
46	C₃₂	C₄×D₇₉	1	1	yes	characteristic
47	C₃₂	C₂×Dic₇₉	1	1	yes	characteristic
48	C₂×C₈	—	79	1	no	—
49	C₂×C₈	C₈×D₇₉	1	1	yes	characteristic
50	C₄²	—	79	1	no	—
51	C₁₆	—	79	2	no	—
52	C₁₆	C₄×Dic₇₉	1	1	yes	characteristic
53	C₁₆	C₈×D₇₉	1	1	yes	characteristic
54	C₂×C₄	—	158	1	no	—
55	C₂×C₄	C₁₆×D₇₉	1	1	yes	characteristic
56	C₈	—	158	1	no	—
57	C₈	C₈×Dic₇₉	1	1	yes	characteristic
58	C₈	C₁₆×D₇₉	1	1	yes	characteristic
59	C₂²	#19098396	1	1	yes	characteristic
60	C₄	—	316	1	no	—
61	C₄	C₁₆×Dic₇₉	1	1	yes	characteristic
62	C₄	#19098396	1	1	yes	characteristic
63	C₂	—	2	1	no	—
64	C₂	#23761533	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₄×Dic₇₉
commutator	C₄×C₇₉	C₄×C₁₆
Frattini	C₂×C₃₂	C₂×D₇₉
Fitting	C₇₉×M₁₂₈	C₂
socle	C₂×C₇₉	#1397
prime radical	C₂²×C₇₉	M₆₄
cosocle	C₂×C₃₂×C₇₉	C₂²
hypercenter	M₁₂₈	D₇₉
hypocenter	C₇₉	#7511
LCS	G ▷ C₄×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₁₆ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
6. C₇₉⋊C₆₄	C₄	semidirect
8. C₆₄×C₇₉	C₄	semidirect
36. C₇₉	#7511	semidirect
41. C₆₄	Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23761611	2
#23761533	2
C₇₉×M₁₂₈	2
#7511	79