Subgroups — #34175953

Order 20224.

76 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	#23761476	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#1373	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇₉⋊C₃₂	C₄	1	1	yes	characteristic
5	C₂×C₇₉⋊C₃₂	C₄	1	1	yes	characteristic
6	#19098384	—	2	1	no	—
7	#364×C₇₉	—	2	1	no	—
8	C₄×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
9	#14579101	—	4	1	no	—
10	C₇₉⋊C₃₂	—	2	1	no	—
11	C₇₉⋊C₃₂	C₈	1	2	yes	—
12	M₃₂×C₇₉	—	4	1	no	—
13	C₂×C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₁₆×C₇₉	Q₈	1	1	yes	characteristic
15	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
16	C₇₉⋊C₁₆	—	8	1	no	—
17	C₂×C₈×C₇₉	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₈×C₇₉	D₈	1	1	yes	characteristic
19	C₄²×C₇₉	Q₁₆	1	1	yes	characteristic
20	C₁₆×C₇₉	—	2	1	no	—
21	C₁₆×C₇₉	—	8	1	no	—
22	C₁₆×C₇₉	C₂×C₈	1	1	yes	characteristic
23	C₁₆×C₇₉	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₇₉	—	2	1	no	—
25	C₂×C₄×C₇₉	#107	1	1	yes	characteristic
26	C₈×C₇₉	C₄⋊C₈	1	1	yes	characteristic
27	C₈×C₇₉	#108	1	1	yes	characteristic
28	C₈×C₇₉	SD₃₂	1	1	yes	characteristic
29	C₈×C₇₉	SD₃₂	1	1	yes	characteristic
30	C₂²×C₇₉	#368	1	1	yes	characteristic
31	C₄×C₇₉	—	4	1	no	—
32	C₄×C₇₉	#335	1	1	yes	characteristic
33	C₄×C₇₉	#367	1	1	yes	characteristic
34	#7464	—	79	1	no	maximal, Sylow
35	C₂×C₇₉	—	2	1	no	—
36	C₂×C₇₉	#1372	1	1	yes	characteristic
37	#1397	—	79	1	no	—
38	#1373	—	79	1	no	—
39	#1373	D₇₉	1	1	yes	characteristic
40	C₇₉	#7464	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃₂	—	79	1	no	—
42	C₂×C₃₂	—	79	1	no	—
43	#364	—	2	1	no	—
44	#364	—	158	1	no	—
45	C₄×C₁₆	C₂×D₇₉	1	1	yes	characteristic
46	M₃₂	—	4	1	no	—
47	M₃₂	—	316	1	no	—
48	C₂×C₁₆	Dic₁₅₈	1	1	yes	characteristic
49	C₂×C₁₆	C₄×D₇₉	1	1	yes	characteristic
50	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
51	C₃₂	—	79	2	no	—
52	C₃₂	—	158	1	no	—
53	C₂×C₈	Dic₇₉⋊C₄	1	1	yes	characteristic
54	C₂×C₈	#11929609	1	1	yes	characteristic
55	C₄²	#11929614	1	1	yes	characteristic
56	C₁₆	—	2	1	no	—
57	C₁₆	—	8	1	no	—
58	C₁₆	—	632	1	no	—
59	C₁₆	C₈×D₇₉	1	1	yes	characteristic
60	C₁₆	#11929607	1	1	yes	characteristic
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	#14579094	1	1	yes	characteristic
63	C₈	Dic₇₉⋊C₈	1	1	yes	characteristic
64	C₈	#14579096	1	1	yes	characteristic
65	C₈	#14579104	1	1	yes	characteristic
66	C₈	#14579105	1	1	yes	characteristic
67	C₂²	#19098392	1	1	yes	characteristic
68	C₄	—	4	1	no	—
69	C₄	#19098315	1	1	yes	characteristic
70	C₄	#19098390	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#23761473	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19098390
commutator	C₁₆×C₇₉	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₇₉
Fitting	C₇₉×#1373	C₂
socle	C₂×C₇₉	#1372
prime radical	C₂²×C₇₉	#368
cosocle	C₄×C₁₆×C₇₉	C₂²
hypercenter	#1373	D₇₉
hypocenter	C₇₉	#7464
LCS	G ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1373

Complements

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

N	H ≅ G/N	type
40. C₇₉	#7464	semidirect

Maximal subgroups

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

subgroup	index
#23761534	2
#23761476	2
C₇₉×#1373	2
#7464	79