Subgroups — #23761559

Order 10112.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098958	C₂	1	1	yes	maximal, characteristic
2	#19098360	C₂	1	1	yes	maximal, characteristic
3	#354×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#11929614	—	2	1	no	—
5	C₂×#11929612	—	2	1	no	—
6	#14579161	C₄	1	1	yes	characteristic, complemented
7	#14579080	—	2	1	no	—
8	#14579072	C₄	1	1	yes	characteristic, complemented
9	#124×C₇₉	C₂²	1	1	yes	characteristic
10	#99×C₇₉	—	2	1	no	—
11	C₂×Dic₁₅₈	—	2	1	no	—
12	#11929614	—	4	2	no	—
13	#11929612	—	4	2	no	—
14	#11929608	—	4	1	no	—
15	C₂×C₇₉⋊C₈	—	2	1	no	—
16	C₄⋊Dic₇₉	—	4	1	no	—
17	C₂×Q₈×C₇₉	D₄	1	1	yes	characteristic
18	C₂×D₄×C₇₉	D₄	1	1	yes	characteristic
19	C₂²⋊C₄×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	Q₈×C₇₉	—	4	1	no	—
24	D₄×C₇₉	—	4	1	no	—
25	C₂×C₄×C₇₉	—	2	1	no	—
26	C₂×C₄×C₇₉	—	2	1	no	—
27	C₂×C₄×C₇₉	—	8	1	no	—
28	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×Dic₇₉	—	4	1	no	—
30	Dic₁₅₈	—	4	1	no	—
31	Dic₁₅₈	—	4	1	no	—
32	C₇₉⋊C₈	—	2	2	no	—
33	C₇₉⋊C₈	—	8	1	no	—
34	C₂²×C₇₉	—	4	1	no	—
35	C₂²×C₇₉	—	8	1	no	—
36	C₂²×C₇₉	#99	1	1	yes	characteristic
37	C₄×C₇₉	—	2	1	no	—
38	C₄×C₇₉	—	4	1	no	—
39	C₄×C₇₉	—	4	1	no	—
40	C₄×C₇₉	—	16	1	no	—
41	Dic₇₉	—	8	1	no	—
42	C₂×C₇₉	—	2	1	no	—
43	C₂×C₇₉	—	8	1	no	—
44	C₂×C₇₉	#353	1	1	yes	characteristic
45	#1407	—	79	1	no	maximal, Sylow
46	C₇₉	#1407	1	1	yes	characteristic, complemented, Sylow
47	#497	—	79	1	no	—
48	#355	—	79	1	no	—
49	#354	D₇₉	1	1	yes	characteristic
50	C₂×Q₁₆	—	158	1	no	—
51	C₂×SD₁₆	—	158	1	no	—
52	C₄⋊Q₈	—	79	1	no	—
53	#124	C₂×D₇₉	1	1	yes	characteristic
54	#101	—	158	1	no	—
55	#99	—	2	1	no	—
56	#97	—	79	1	no	—
57	C₂×Q₈	—	158	1	no	—
58	C₂×Q₈	D₃₁₆	1	1	yes	characteristic
59	C₂×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
60	Q₁₆	—	316	2	no	—
61	SD₁₆	—	316	2	no	—
62	M₁₆	—	316	1	no	—
63	C₂×C₈	—	158	1	no	—
64	C₄⋊C₄	—	316	1	no	—
65	C₂²⋊C₄	—	4	1	no	—
66	C₂²⋊C₄	—	4	1	no	—
67	C₄²	C₄×D₇₉	1	1	yes	characteristic
68	C₂³	—	2	1	no	—
69	Q₈	—	4	1	no	—
70	Q₈	—	316	1	no	—
71	Q₈	—	316	1	no	—
72	D₄	—	4	1	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	8	1	no	—
76	C₂×C₄	—	316	1	no	—
77	C₂×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
78	C₈	—	632	1	no	—
79	C₈	—	158	2	no	—
80	C₂²	—	4	1	no	—
81	C₂²	—	8	1	no	—
82	C₂²	#14579075	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	16	1	no	—
87	C₄	—	632	1	no	—
88	C₂	—	2	1	no	—
89	C₂	—	8	1	no	—
90	C₂	#19098355	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19098355
commutator	C₄²×C₇₉	C₂×C₄
Frattini	#124	C₂×D₇₉
Fitting	#354×C₇₉	C₂
socle	C₂×C₇₉	#353
prime radical	C₂×D₄×C₇₉	D₄
cosocle	#124×C₇₉	C₂²
hypercenter	#354	D₇₉
hypocenter	C₇₉	#1407
LCS	G ▷ C₄²×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #354

Complements

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

N	H ≅ G/N	type
6. #14579161	C₄	semidirect
8. #14579072	C₄	semidirect
46. C₇₉	#1407	semidirect