Subgroups — #23763007

Order 10112.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098940	C₂	1	1	yes	maximal, characteristic
2	#19098911	C₂	1	4	yes	maximal, complemented
3	C₈×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#494×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₆₃₂	—	2	2	no	—
6	#14579158	C₂²	1	2	yes	—
7	#14579081	—	2	8	no	—
8	C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
9	C₂×Q₁₆×C₇₉	—	2	2	no	—
10	C₄⋊Q₈×C₇₉	C₂²	1	2	yes	—
11	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
12	C₂×D₃₁₆	—	2	4	no	—
13	C₂×D₃₁₆	—	2	2	no	—
14	D₆₃₂	—	4	4	no	—
15	C₂×C₇₉⋊C₈	D₄	1	4	yes	—
16	C₂×Q₈×C₇₉	—	2	2	no	—
17	Q₁₆×C₇₉	—	4	4	no	—
18	C₂×C₈×C₇₉	D₄	1	2	yes	—
19	C₄⋊C₄×C₇₉	—	2	4	no	—
20	C₄²×C₇₉	C₂³	1	1	yes	characteristic
21	C₂²×D₇₉	—	4	2	no	—
22	Q₈×C₇₉	—	4	4	no	—
23	C₂×C₄×C₇₉	—	4	2	no	—
24	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
25	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
26	D₃₁₆	—	4	4	no	—
27	D₃₁₆	—	4	8	no	—
28	C₈×C₇₉	D₈	1	4	yes	—
29	C₇₉⋊C₈	—	2	4	no	—
30	C₂²×C₇₉	#127	1	1	yes	characteristic
31	C₂×D₇₉	—	8	2	no	—
32	C₂×D₇₉	—	8	4	no	—
33	C₄×C₇₉	—	8	2	no	—
34	C₄×C₇₉	C₂×D₈	1	2	yes	—
35	C₄×C₇₉	#135	1	4	yes	—
36	C₂×C₇₉	#493	1	1	yes	characteristic
37	C₂×C₇₉	#495	1	2	yes	—
38	D₇₉	—	16	2	no	—
39	#1709	—	79	1	no	maximal, Sylow
40	C₇₉	#1709	1	1	yes	characteristic, complemented, Sylow
41	#494	D₇₉	1	1	yes	characteristic, complemented
42	#493	—	79	1	no	—
43	#486	—	79	4	no	—
44	C₈²	—	79	1	no	—
45	C₂×Q₁₆	—	2	2	no	—
46	C₂×D₈	—	158	2	no	—
47	C₄⋊Q₈	C₂×D₇₉	1	2	yes	—
48	#127	—	79	2	no	—
49	#102	—	158	8	no	—
50	C₄×C₈	—	79	2	no	—
51	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
52	C₂×Q₈	—	2	2	no	—
53	C₂×D₄	—	158	4	no	—
54	C₂×D₄	—	158	2	no	—
55	Q₁₆	—	4	4	no	—
56	D₈	—	316	4	no	—
57	C₂×C₈	—	79	4	no	—
58	C₂×C₈	C₂²⋊D₇₉	1	2	yes	—
59	C₄⋊C₄	—	2	4	no	—
60	C₄²	C₂²×D₇₉	1	1	yes	characteristic
61	C₂³	—	316	2	no	—
62	Q₈	—	4	4	no	—
63	D₄	—	316	4	no	—
64	D₄	—	316	8	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	D₄×D₇₉	1	2	yes	—
67	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
68	C₈	—	158	4	no	—
69	C₈	#11929609	1	4	yes	—
70	C₂²	—	632	2	no	—
71	C₂²	—	632	4	no	—
72	C₂²	#14579157	1	1	yes	characteristic
73	C₄	—	8	2	no	—
74	C₄	C₂×#11929609	1	2	yes	—
75	C₄	#14579184	1	4	yes	—
76	C₂	—	1264	2	no	—
77	C₂	#19098939	1	1	yes	characteristic
78	C₂	#19098948	1	2	yes	—

	subgroup	G/H
center	C₂²	#14579157
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#494×C₇₉	C₂
socle	C₂²×C₇₉	#127
prime radical	#19098940	C₂
hypercenter	#494	D₇₉
hypocenter	C₇₉	#1709
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

Complements

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

N	H ≅ G/N	type
2. #19098911	C₂	semidirect
3. C₈×C₇₉⋊C₈	C₂	semidirect
4. #494×C₇₉	C₂	semidirect
40. C₇₉	#1709	semidirect
41. #494	D₇₉	semidirect