Subgroups — #34174886

Order 20224.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23761318	C₂	1	1	yes	maximal, characteristic
2	#23761317	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#1312	C₂	1	1	yes	maximal, characteristic
4	C₄×C₇₉⋊C₁₆	C₄	1	2	yes	—
5	C₄×C₇₉⋊C₁₆	C₄	1	1	yes	characteristic
6	C₄×C₇₉⋊C₁₆	C₄	1	1	yes	characteristic
7	C₄×C₁₆×C₇₉	C₄	1	2	yes	—
8	C₈²×C₇₉	C₂²	1	1	yes	characteristic
9	C₂×C₇₉⋊C₁₆	—	2	2	no	—
10	C₂×C₇₉⋊C₁₆	C₈	1	2	yes	—
11	C₂×C₇₉⋊C₁₆	C₈	1	2	yes	—
12	C₂×C₁₆×C₇₉	—	2	2	no	—
13	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
14	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
15	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
16	C₇₉⋊C₁₆	—	2	2	no	—
17	C₇₉⋊C₁₆	—	4	2	no	—
18	C₇₉⋊C₁₆	C₁₆	1	4	yes	complemented
19	C₂×C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
20	C₂×C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
21	C₂×C₈×C₇₉	M₁₆	1	2	yes	—
22	C₂×C₈×C₇₉	M₁₆	1	2	yes	—
23	C₄²×C₇₉	C₄²	1	1	yes	characteristic
24	C₁₆×C₇₉	—	4	2	no	—
25	C₂×C₄×C₇₉	C₄×C₈	1	1	yes	characteristic
26	C₂×C₄×C₇₉	#97	1	1	yes	characteristic
27	C₂×C₄×C₇₉	#97	1	1	yes	characteristic
28	C₈×C₇₉	—	2	2	no	—
29	C₈×C₇₉	—	2	2	no	—
30	C₈×C₇₉	C₂×C₁₆	1	2	yes	—
31	C₈×C₇₉	M₃₂	1	2	yes	—
32	C₂²×C₇₉	#322	1	1	yes	characteristic
33	C₄×C₇₉	C₄×C₁₆	1	1	yes	characteristic
34	C₄×C₇₉	#346	1	1	yes	characteristic
35	C₄×C₇₉	#347	1	2	yes	—
36	C₄×C₇₉	#347	1	2	yes	—
37	#7053	—	79	1	no	maximal, Sylow
38	C₂×C₇₉	#1312	1	1	yes	characteristic
39	C₂×C₇₉	#1313	1	1	yes	characteristic
40	C₂×C₇₉	#1313	1	1	yes	characteristic
41	#1312	—	79	1	no	—
42	#1312	D₇₉	1	1	yes	characteristic
43	#1311	—	79	1	no	—
44	C₇₉	#7053	1	1	yes	characteristic, complemented, Sylow
45	C₄×C₁₆	—	79	1	no	—
46	C₄×C₁₆	—	79	1	no	—
47	C₄×C₁₆	—	79	2	no	—
48	C₄×C₁₆	Dic₇₉	1	2	yes	—
49	C₈²	C₂×D₇₉	1	1	yes	characteristic
50	C₂×C₁₆	—	2	2	no	—
51	C₂×C₁₆	—	79	2	no	—
52	C₂×C₁₆	—	79	2	no	—
53	C₂×C₁₆	—	158	2	no	—
54	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
55	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
56	C₄×C₈	C₂×Dic₇₉	1	1	yes	characteristic
57	C₂×C₈	C₈×D₇₉	1	1	yes	characteristic
58	C₂×C₈	C₈×D₇₉	1	1	yes	characteristic
59	C₂×C₈	#11929607	1	2	yes	—
60	C₂×C₈	#11929608	1	2	yes	—
61	C₄²	C₄×Dic₇₉	1	1	yes	characteristic
62	C₁₆	—	4	2	no	—
63	C₁₆	—	316	2	no	—
64	C₁₆	—	79	4	no	—
65	C₁₆	—	158	2	no	—
66	C₂×C₄	C₈×Dic₇₉	1	1	yes	characteristic
67	C₂×C₄	#14579071	1	1	yes	characteristic
68	C₂×C₄	#14579072	1	1	yes	characteristic
69	C₈	—	2	2	no	—
70	C₈	—	2	2	no	—
71	C₈	C₁₆×D₇₉	1	2	yes	—
72	C₈	#14579100	1	2	yes	—
73	C₂²	#19098285	1	1	yes	characteristic
74	C₄	C₁₆×Dic₇₉	1	1	yes	characteristic
75	C₄	#19098338	1	1	yes	characteristic
76	C₄	#19098340	1	2	yes	—
77	C₄	#19098341	1	2	yes	—
78	C₂	#23761319	1	1	yes	characteristic
79	C₂	#23761321	1	1	yes	characteristic
80	C₂	#23761322	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₄×Dic₇₉
commutator	C₄×C₇₉	C₄×C₁₆
Frattini	C₈²	C₂×D₇₉
Fitting	C₇₉×#1312	C₂
socle, prime radical	C₂²×C₇₉	#322
cosocle	C₈²×C₇₉	C₂²
hypercenter	#1312	D₇₉
hypocenter	C₇₉	#7053
LCS	G ▷ C₄×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄² ◁ #1312

Complements

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

N	H ≅ G/N	type
18. C₇₉⋊C₁₆	C₁₆	semidirect
44. C₇₉	#7053	semidirect

Maximal subgroups

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

subgroup	index
#23761318	2
#23761317	2
C₇₉×#1312	2
#7053	79