Subgroups — #11719621

Order 832.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#6129	C₂	1	1	yes	maximal, characteristic
2	C₂×#6122	C₂	1	4	yes	maximal, complemented
3	#88238	C₂	1	8	yes	maximal, complemented
4	D₁₃⋊M₁₆	C₂	1	2	yes	maximal, complemented
5	C₂×D₄×C₁₃	C₄	1	1	yes	characteristic
6	C₂×C₂²⋊D₁₃	C₄	1	2	yes	—
7	C₂²×Dic₁₃	C₂²	1	2	yes	—
8	#6129	C₄	1	4	yes	—
9	#6129	C₂²	1	4	yes	—
10	C₂×C₄×D₁₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₂₆	C₄	1	1	yes	characteristic
12	#6122	C₂²	1	4	yes	—
13	#6122	C₂²	1	8	yes	complemented
14	C₂×#1057	C₂²	1	8	yes	complemented
15	#6118	C₂²	1	4	yes	complemented
16	D₁₃⋊C₈	C₂²	1	4	yes	complemented
17	C₂³×C₁₃	C₂×C₄	1	2	yes	—
18	C₂²×D₁₃	C₂×C₄	1	1	yes	characteristic
19	D₄×C₁₃	C₂×C₄	1	4	yes	—
20	C₂×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂²⋊D₁₃	C₂×C₄	1	8	yes	—
22	C₂×Dic₁₃	C₂×C₄	1	2	yes	—
23	C₂×Dic₁₃	C₂×C₄	1	4	yes	—
24	C₂×Dic₁₃	C₂³	1	4	yes	—
25	C₂×Dic₁₃	C₂³	1	1	yes	characteristic
26	C₄×D₁₃	C₂×C₄	1	2	yes	—
27	C₄×D₁₃	C₂³	1	2	yes	—
28	Dic₂₆	C₂×C₄	1	4	yes	—
29	#1057	C₂³	1	8	yes	—
30	#568	—	13	1	no	maximal, Sylow
31	C₂²×C₁₃	—	4	2	no	—
32	C₂²×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₂²×C₁₃	C₂²×C₄	1	4	yes	—
34	C₂×D₁₃	—	4	1	no	—
35	C₂×D₁₃	C₂²×C₄	1	2	yes	—
36	C₄×C₁₃	C₂²×C₄	1	2	yes	—
37	Dic₁₃	C₂²×C₄	1	4	yes	—
38	Dic₁₃	C₂²×C₄	1	1	yes	characteristic
39	Dic₁₃	C₂⁴	1	1	yes	characteristic
40	C₂×#41	—	13	1	no	—
41	#131	—	13	8	no	—
42	C₂×M₁₆	—	13	2	no	—
43	C₂×M₁₆	—	13	4	no	—
44	C₂×C₁₃	—	2	1	no	—
45	C₂×C₁₃	—	2	4	no	—
46	C₂×C₁₃	C₂³×C₄	1	1	yes	characteristic
47	D₁₃	—	2	2	no	—
48	#41	—	13	4	no	—
49	#41	—	13	4	no	—
50	C₂×Q₈	—	13	1	no	—
51	C₂×D₄	—	13	2	no	—
52	C₂×D₄	#261	1	1	yes	characteristic
53	C₂²×C₄	—	13	2	no	—
54	C₂²×C₄	—	13	1	no	—
55	M₁₆	—	13	4	no	—
56	M₁₆	—	13	4	no	—
57	M₁₆	—	13	8	no	—
58	C₂×C₈	—	13	4	no	—
59	C₂×C₈	—	13	8	no	—
60	C₁₃	#568	1	1	yes	characteristic, complemented, Sylow
61	C₂³	—	13	1	no	—
62	C₂³	C₂×#261	1	2	yes	—
63	Q₈	—	13	4	no	—
64	D₄	—	13	8	no	—
65	D₄	C₂×#261	1	4	yes	—
66	C₂×C₄	—	13	4	no	—
67	C₂×C₄	—	13	1	no	—
68	C₂×C₄	—	13	2	no	—
69	C₂×C₄	—	13	4	no	—
70	C₂×C₄	—	13	2	no	—
71	C₂×C₄	—	13	2	no	—
72	C₂×C₄	C₂×#261	1	1	yes	characteristic
73	C₈	—	13	8	no	—
74	C₂²	—	4	2	no	—
75	C₂²	—	13	2	no	—
76	C₂²	—	52	1	no	—
77	C₂²	C₂²×#261	1	1	yes	characteristic
78	C₂²	C₂²×#261	1	4	yes	—
79	C₄	—	13	1	no	—
80	C₄	—	13	4	no	—
81	C₄	—	13	1	no	—
82	C₄	C₂²×#261	1	2	yes	—
83	C₂	—	2	1	no	—
84	C₂	—	2	4	no	—
85	C₂	—	26	2	no	—
86	C₂	C₂³×#261	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂³×#261
commutator, socle	C₂×C₁₃	C₂³×C₄
Fitting	C₂×D₄×C₁₃	C₄
prime radical	C₂×#6129	C₂
cosocle	Dic₁₃	C₂⁴
hypercenter	C₂×D₄	#261
hypocenter	C₁₃	#568
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×#6122	C₂	semidirect
3. #88238	C₂	semidirect
4. D₁₃⋊M₁₆	C₂	semidirect
13. #6122	C₂²	semidirect
14. C₂×#1057	C₂²	semidirect
15. #6118	C₂²	semidirect
16. D₁₃⋊C₈	C₂²	semidirect
60. C₁₃	#568	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#6129	2
C₂×#6122	2
#88238	2
D₁₃⋊M₁₆	2
#568	13