Subgroups — #34175603

Order 20224.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23761534	C₂	1	1	yes	maximal, characteristic
2	#23761316	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#1397	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇₉⋊C₃₂	C₄	1	2	yes	—
5	C₄×C₇₉⋊C₁₆	C₄	1	1	yes	characteristic
6	C₈×C₇₉⋊C₈	C₄	1	1	yes	characteristic
7	C₂×C₃₂×C₇₉	C₄	1	2	yes	—
8	C₄×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
9	C₂×C₇₉⋊C₁₆	C₈	1	2	yes	—
10	C₄×C₇₉⋊C₈	C₈	1	2	yes	—
11	C₇₉⋊C₃₂	—	2	2	no	—
12	C₂×C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
14	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
15	C₃₂×C₇₉	—	2	2	no	—
16	C₂×C₇₉⋊C₈	—	2	2	no	—
17	C₇₉⋊C₁₆	C₁₆	1	4	yes	—
18	C₂×C₈×C₇₉	C₄²	1	1	yes	characteristic
19	C₂×C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
20	C₄²×C₇₉	C₂×C₈	1	1	yes	characteristic
21	C₁₆×C₇₉	M₁₆	1	2	yes	—
22	C₁₆×C₇₉	M₁₆	1	2	yes	—
23	C₂×C₄×C₇₉	C₄×C₈	1	1	yes	characteristic
24	C₂×C₄×C₇₉	M₃₂	1	2	yes	—
25	C₈×C₇₉	#97	1	1	yes	characteristic
26	C₈×C₇₉	#97	1	1	yes	characteristic
27	C₈×C₇₉	C₂×C₁₆	1	2	yes	—
28	C₇₉⋊C₈	—	4	2	no	—
29	C₂²×C₇₉	#346	1	1	yes	characteristic
30	C₄×C₇₉	—	2	2	no	—
31	C₄×C₇₉	#322	1	1	yes	characteristic
32	C₄×C₇₉	C₄×C₁₆	1	1	yes	characteristic
33	#7332	—	79	1	no	maximal, Sylow
34	C₂×C₇₉	#1312	1	1	yes	characteristic
35	C₂×C₇₉	#1398	1	2	yes	—
36	#1397	—	79	1	no	—
37	#1397	D₇₉	1	1	yes	characteristic
38	#1311	—	79	1	no	—
39	C₇₉	#7332	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃₂	—	79	2	no	—
41	C₂×C₃₂	Dic₇₉	1	2	yes	—
42	C₄×C₁₆	—	79	1	no	—
43	C₄×C₁₆	C₂×D₇₉	1	1	yes	characteristic
44	C₈²	—	79	1	no	—
45	C₂×C₁₆	—	79	2	no	—
46	C₂×C₁₆	C₄×D₇₉	1	1	yes	characteristic
47	C₂×C₁₆	C₂×Dic₇₉	1	1	yes	characteristic
48	C₄×C₈	—	79	2	no	—
49	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
50	C₃₂	—	2	2	no	—
51	C₃₂	—	158	2	no	—
52	C₂×C₈	—	158	2	no	—
53	C₂×C₈	C₄×Dic₇₉	1	1	yes	characteristic
54	C₂×C₈	C₈×D₇₉	1	1	yes	characteristic
55	C₄²	C₈×D₇₉	1	1	yes	characteristic
56	C₁₆	—	79	4	no	—
57	C₁₆	#11929607	1	2	yes	—
58	C₁₆	#11929608	1	2	yes	—
59	C₂×C₄	C₈×Dic₇₉	1	1	yes	characteristic
60	C₂×C₄	#14579100	1	2	yes	—
61	C₈	—	316	2	no	—
62	C₈	#14579071	1	1	yes	characteristic
63	C₈	#14579072	1	1	yes	characteristic
64	C₈	C₁₆×D₇₉	1	2	yes	—
65	C₂²	#19098338	1	1	yes	characteristic
66	C₄	—	2	2	no	—
67	C₄	#19098285	1	1	yes	characteristic
68	C₄	C₁₆×Dic₇₉	1	1	yes	characteristic
69	C₂	#23761319	1	1	yes	characteristic
70	C₂	#23761535	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₄×Dic₇₉
commutator	C₄×C₇₉	C₄×C₁₆
Frattini	C₄×C₁₆	C₂×D₇₉
Fitting	C₇₉×#1397	C₂
socle, prime radical	C₂²×C₇₉	#346
cosocle	C₄×C₁₆×C₇₉	C₂²
hypercenter	#1397	D₇₉
hypocenter	C₇₉	#7332
LCS	G ▷ C₄×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ #1397

Complements

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

N	H ≅ G/N	type
39. C₇₉	#7332	semidirect

Maximal subgroups

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

subgroup	index
#23761534	2
#23761316	2
C₇₉×#1397	2
#7332	79