Subgroups — #23763540

Order 10112.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098587	C₂	1	1	yes	maximal, characteristic
2	C₂×#14579072	C₂	1	1	yes	maximal, characteristic
3	#19098327	C₂	1	4	yes	maximal
4	#423×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#11929608	C₂²	1	2	yes	—
6	C₂²×C₇₉⋊C₈	C₂²	1	2	yes	—
7	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
8	#14579072	C₄	1	4	yes	—
9	C₂×M₁₆×C₇₉	C₂²	1	2	yes	—
10	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
11	C₄⋊C₈×C₇₉	—	2	2	no	—
12	#11929608	—	2	4	no	—
13	C₂×C₇₉⋊C₈	—	2	2	no	—
14	C₂×C₇₉⋊C₈	—	2	2	no	—
15	C₂×C₇₉⋊C₈	—	2	2	no	—
16	C₂×C₇₉⋊C₈	C₂×C₄	1	4	yes	—
17	C₂²×C₄×C₇₉	Q₈	1	2	yes	—
18	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
19	M₁₆×C₇₉	—	2	4	no	—
20	C₂×C₈×C₇₉	—	2	2	no	—
21	C₄²×C₇₉	C₂×C₄	1	2	yes	—
22	C₄²×C₇₉	D₄	1	2	yes	—
23	C₂³×C₇₉	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄×C₇₉	—	4	2	no	—
25	C₂×C₄×C₇₉	C₄⋊C₄	1	4	yes	—
26	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₇₉	#41	1	2	yes	—
29	C₂×C₄×C₇₉	#41	1	2	yes	—
30	C₈×C₇₉	—	4	2	no	—
31	C₇₉⋊C₈	—	2	4	no	—
32	C₇₉⋊C₈	—	4	2	no	—
33	C₂²×C₇₉	—	2	2	no	—
34	C₂²×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂²×C₇₉	#125	1	2	yes	—
36	C₄×C₇₉	—	2	4	no	—
37	C₄×C₇₉	#117	1	2	yes	—
38	C₄×C₇₉	#124	1	1	yes	characteristic
39	C₄×C₇₉	#124	1	1	yes	characteristic
40	C₂×C₇₉	—	2	2	no	—
41	C₂×C₇₉	#382	1	1	yes	characteristic
42	C₂×C₇₉	#430	1	2	yes	—
43	#1838	—	79	1	no	maximal, Sylow
44	C₇₉	#1838	1	1	yes	characteristic, complemented, Sylow
45	#423	—	79	1	no	—
46	#423	D₇₉	1	1	yes	characteristic
47	C₂×#97	—	79	1	no	—
48	#341	—	79	4	no	—
49	C₂×M₁₆	—	79	2	no	—
50	C₂×M₁₆	C₂×D₇₉	1	2	yes	—
51	C₂²×C₈	—	79	2	no	—
52	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
53	C₄⋊C₈	—	2	2	no	—
54	C₄⋊C₈	—	158	2	no	—
55	#97	—	79	4	no	—
56	C₂²×C₄	Dic₁₅₈	1	2	yes	—
57	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
58	M₁₆	—	2	4	no	—
59	M₁₆	—	158	4	no	—
60	C₂×C₈	—	2	2	no	—
61	C₂×C₈	—	79	4	no	—
62	C₂×C₈	—	158	2	no	—
63	C₂×C₈	—	158	2	no	—
64	C₂×C₈	—	158	2	no	—
65	C₄²	C₄×D₇₉	1	2	yes	—
66	C₄²	C₂²⋊D₇₉	1	2	yes	—
67	C₂³	C₂×Dic₁₅₈	1	1	yes	characteristic
68	C₂×C₄	—	4	2	no	—
69	C₂×C₄	Dic₇₉⋊C₄	1	4	yes	—
70	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
71	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
72	C₂×C₄	#11929623	1	2	yes	—
73	C₂×C₄	#11929625	1	2	yes	—
74	C₈	—	4	2	no	—
75	C₈	—	316	2	no	—
76	C₈	—	158	4	no	—
77	C₂²	—	2	2	no	—
78	C₂²	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
79	C₂²	#14579152	1	2	yes	—
80	C₄	—	2	4	no	—
81	C₄	#14579119	1	2	yes	—
82	C₄	#14579148	1	1	yes	characteristic
83	C₄	#14579150	1	1	yes	characteristic
84	C₂	—	2	2	no	—
85	C₂	#19098428	1	1	yes	characteristic
86	C₂	#19098611	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#423×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₄⋊C₄
prime radical	C₂³×C₇₉	C₂×Q₈
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	#423	D₇₉
hypocenter	C₇₉	#1838
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
44. C₇₉	#1838	semidirect