Subgroups — #23761558

Order 10112.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098953	C₂	1	1	yes	maximal, characteristic
2	#19098358	C₂	1	1	yes	maximal, characteristic, complemented
3	#355×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11929611	—	2	1	no	—
5	C₂×#11929609	—	2	1	no	—
6	#14579158	C₄	1	1	yes	characteristic, complemented
7	#14579076	—	2	1	no	—
8	#14579072	C₄	1	1	yes	characteristic, complemented
9	#124×C₇₉	C₂²	1	1	yes	characteristic
10	#101×C₇₉	—	2	1	no	—
11	C₂×D₃₁₆	—	2	1	no	—
12	C₂×D₃₁₆	—	4	1	no	—
13	#11929611	—	4	2	no	—
14	#11929609	—	4	2	no	—
15	C₂×C₇₉⋊C₈	—	2	1	no	—
16	C₂²⋊Dic₇₉	—	4	1	no	—
17	C₂×Q₈×C₇₉	D₄	1	1	yes	characteristic
18	C₂×D₄×C₇₉	D₄	1	1	yes	characteristic
19	M₁₆×C₇₉	—	4	1	no	—
20	C₂²⋊C₄×C₇₉	—	4	1	no	—
21	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₇₉	—	2	1	no	—
23	C₂²×D₇₉	—	4	1	no	—
24	Q₈×C₇₉	—	4	1	no	—
25	D₄×C₇₉	—	4	1	no	—
26	C₂×C₄×C₇₉	—	2	1	no	—
27	C₂×C₄×C₇₉	—	2	1	no	—
28	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×Dic₇₉	—	8	1	no	—
30	D₃₁₆	—	4	1	no	—
31	D₃₁₆	—	4	1	no	—
32	D₃₁₆	—	8	2	no	—
33	C₈×C₇₉	—	8	1	no	—
34	C₇₉⋊C₈	—	2	2	no	—
35	C₂²×C₇₉	—	4	1	no	—
36	C₂²×C₇₉	—	8	1	no	—
37	C₂²×C₇₉	#99	1	1	yes	characteristic
38	C₂×D₇₉	—	8	2	no	—
39	C₂×D₇₉	—	8	1	no	—
40	C₄×C₇₉	—	2	1	no	—
41	C₄×C₇₉	—	4	1	no	—
42	C₄×C₇₉	—	4	1	no	—
43	Dic₇₉	—	16	1	no	—
44	C₂×C₇₉	—	2	1	no	—
45	C₂×C₇₉	—	8	1	no	—
46	C₂×C₇₉	#353	1	1	yes	characteristic
47	D₇₉	—	16	1	no	—
48	#1406	—	79	1	no	maximal, Sylow
49	C₇₉	#1406	1	1	yes	characteristic, complemented, Sylow
50	#496	—	79	1	no	—
51	#355	D₇₉	1	1	yes	characteristic, complemented
52	#354	—	79	1	no	—
53	C₂×SD₁₆	—	158	1	no	—
54	C₂×D₈	—	158	1	no	—
55	#127	—	79	1	no	—
56	#124	C₂×D₇₉	1	1	yes	characteristic
57	#101	—	2	1	no	—
58	#99	—	158	1	no	—
59	#97	—	79	1	no	—
60	C₂×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
61	C₂×D₄	—	316	1	no	—
62	C₂×D₄	—	158	1	no	—
63	C₂×D₄	D₃₁₆	1	1	yes	characteristic
64	SD₁₆	—	316	2	no	—
65	D₈	—	316	2	no	—
66	M₁₆	—	4	1	no	—
67	C₂×C₈	—	158	1	no	—
68	C₂²⋊C₄	—	4	1	no	—
69	C₂²⋊C₄	—	316	1	no	—
70	C₄²	C₄×D₇₉	1	1	yes	characteristic
71	C₂³	—	2	1	no	—
72	C₂³	—	316	1	no	—
73	Q₈	—	4	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	316	1	no	—
76	D₄	—	316	1	no	—
77	D₄	—	632	2	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	—	632	1	no	—
81	C₂×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
82	C₈	—	8	1	no	—
83	C₈	—	158	2	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	8	1	no	—
86	C₂²	—	632	2	no	—
87	C₂²	—	632	1	no	—
88	C₂²	#14579075	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	4	1	no	—
92	C₄	—	1264	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	8	1	no	—
95	C₂	—	1264	1	no	—
96	C₂	#19098355	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19098355
commutator	C₄²×C₇₉	C₂×C₄
Frattini	#124	C₂×D₇₉
Fitting	#355×C₇₉	C₂
socle	C₂×C₇₉	#353
prime radical	#19098953	C₂
cosocle	#124×C₇₉	C₂²
hypercenter	#355	D₇₉
hypocenter	C₇₉	#1406
LCS	G ▷ C₄²×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #355

Complements

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

N	H ≅ G/N	type
2. #19098358	C₂	semidirect
3. #355×C₇₉	C₂	semidirect
6. #14579158	C₄	semidirect
8. #14579072	C₄	semidirect
49. C₇₉	#1406	semidirect
51. #355	D₇₉	semidirect