Subgroups — #23763538

Order 10112.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098587	C₂	1	2	yes	maximal
2	#19098328	C₂	1	4	yes	maximal
3	C₂×C₄×C₈×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#11929608	C₂²	1	4	yes	—
5	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
6	C₂²×C₈×C₇₉	C₂²	1	2	yes	—
7	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₇₉	C₄	1	2	yes	—
9	C₄×C₈×C₇₉	C₄	1	2	yes	—
10	#11929608	—	2	8	no	—
11	C₂×C₇₉⋊C₈	—	2	4	no	—
12	C₂²×C₄×C₇₉	Q₈	1	2	yes	—
13	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
14	C₂×C₈×C₇₉	—	2	4	no	—
15	C₂×C₈×C₇₉	C₂×C₄	1	4	yes	—
16	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
18	C₄²×C₇₉	D₄	1	2	yes	—
19	C₂³×C₇₉	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₄×C₇₉	—	2	4	no	—
21	C₂×C₄×C₇₉	C₄⋊C₄	1	2	yes	—
22	C₂×C₄×C₇₉	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
25	C₂×C₄×C₇₉	#41	1	4	yes	—
26	C₈×C₇₉	—	2	4	no	—
27	C₇₉⋊C₈	—	4	4	no	—
28	C₂²×C₇₉	—	2	2	no	—
29	C₂²×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
30	C₂²×C₇₉	#125	1	2	yes	—
31	C₄×C₇₉	—	2	2	no	—
32	C₄×C₇₉	#108	1	4	yes	—
33	C₄×C₇₉	#117	1	2	yes	—
34	C₄×C₇₉	#124	1	2	yes	—
35	C₂×C₇₉	—	2	2	no	—
36	C₂×C₇₉	#382	1	1	yes	characteristic
37	C₂×C₇₉	C₂×#108	1	2	yes	—
38	#1837	—	79	1	no	maximal, Sylow
39	C₇₉	#1837	1	1	yes	characteristic, complemented, Sylow
40	#423	—	79	2	no	—
41	C₂×C₄×C₈	D₇₉	1	1	yes	characteristic
42	#341	—	79	4	no	—
43	C₂×M₁₆	—	79	4	no	—
44	C₂²×C₈	C₂×D₇₉	1	2	yes	—
45	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
46	C₄⋊C₈	—	158	4	no	—
47	C₄×C₈	Dic₇₉	1	2	yes	—
48	C₄×C₈	Dic₇₉	1	2	yes	—
49	C₂²×C₄	Dic₁₅₈	1	2	yes	—
50	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
51	M₁₆	—	158	8	no	—
52	C₂×C₈	—	2	4	no	—
53	C₂×C₈	—	158	4	no	—
54	C₂×C₈	C₂×Dic₇₉	1	4	yes	—
55	C₄²	D₃₁₆	1	2	yes	—
56	C₄²	C₂×Dic₇₉	1	1	yes	characteristic
57	C₄²	C₂×Dic₇₉	1	1	yes	characteristic
58	C₂³	C₂×Dic₁₅₈	1	1	yes	characteristic
59	C₂×C₄	—	2	4	no	—
60	C₂×C₄	C₄⋊Dic₇₉	1	2	yes	—
61	C₂×C₄	C₄⋊Dic₇₉	1	2	yes	—
62	C₂×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
63	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
64	C₂×C₄	#11929624	1	4	yes	—
65	C₈	—	2	4	no	—
66	C₈	—	316	4	no	—
67	C₂²	—	2	2	no	—
68	C₂²	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
69	C₂²	#14579153	1	2	yes	—
70	C₄	—	2	2	no	—
71	C₄	#14579097	1	4	yes	—
72	C₄	#14579120	1	2	yes	—
73	C₄	#14579149	1	2	yes	—
74	C₂	—	2	2	no	—
75	C₂	#19098429	1	1	yes	characteristic
76	C₂	C₂×#14579097	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₃₁₆
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	C₂×C₄×C₈×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₄⋊C₄
prime radical	C₂³×C₇₉	C₂×Q₈
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	C₂×C₄×C₈	D₇₉
hypocenter	C₇₉	#1837
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
39. C₇₉	#1837	semidirect