Subgroups — #13120942

Order 1664.

844 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88129	C₂	1	3	yes	maximal, complemented
2	C₂×#88128	C₂	1	3	yes	maximal, complemented
3	C₁₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
4	#11718332	C₂	1	8	yes	maximal, complemented
5	C₂²×D₅₂	C₂²	1	3	yes	—
6	C₂²×D₅₂	C₂²	1	12	yes	—
7	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₁₃	C₂²	1	3	yes	—
9	C₂×#6103	C₂²	1	12	yes	—
10	#88129	—	2	12	no	—
11	#88128	—	2	12	no	—
12	C₁₃×#95	C₂²	1	4	yes	—
13	C₂³×D₁₃	C₂³	1	6	yes	—
14	C₂²×C₄×C₁₃	C₂³	1	6	yes	—
15	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
16	C₂²×Dic₁₃	C₂³	1	2	yes	—
17	C₂×D₅₂	—	2	24	no	—
18	C₂×D₅₂	—	2	12	no	—
19	C₂×D₅₂	—	2	6	no	—
20	C₂×D₅₂	—	4	24	no	—
21	C₂×Dic₂₆	—	2	6	no	—
22	C₄²×C₁₃	D₄	1	12	yes	complemented
23	#6103	—	2	24	no	—
24	#2657	—	13	1	no	maximal, Sylow
25	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
26	C₂²×D₁₃	—	2	6	no	—
27	C₂²×D₁₃	—	2	12	no	—
28	C₂²×D₁₃	—	2	24	no	—
29	C₂×C₄×C₁₃	—	2	12	no	—
30	C₂×C₄×C₁₃	C₂×D₄	1	12	yes	—
31	C₂×C₄×C₁₃	C₂×D₄	1	6	yes	—
32	C₂×Dic₁₃	—	2	6	no	—
33	D₅₂	—	4	48	no	—
34	D₅₂	—	4	12	no	—
35	Dic₂₆	—	4	4	no	—
36	C₂×#127	—	13	3	no	—
37	C₂×#124	—	13	3	no	—
38	#392	—	13	8	no	—
39	#376	D₁₃	1	1	yes	characteristic, complemented
40	C₂²×C₁₃	C₂²×D₄	1	3	yes	—
41	C₂²×C₁₃	H(5,𝔽₂)	1	4	yes	—
42	C₂×D₁₃	—	4	6	no	—
43	C₂×D₁₃	—	4	24	no	—
44	C₂×D₁₃	—	4	12	no	—
45	C₄×C₁₃	—	2	12	no	—
46	C₄×C₁₃	#127	1	4	yes	—
47	Dic₁₃	—	4	2	no	—
48	C₂²×Q₈	—	13	1	no	—
49	C₂²×D₄	—	13	3	no	—
50	C₂²×D₄	—	13	12	no	—
51	#127	—	26	12	no	—
52	#124	—	26	12	no	—
53	C₂×C₂²⋊C₄	—	13	12	no	—
54	C₂×C₄²	C₂×D₁₃	1	3	yes	—
55	#95	C₂×D₁₃	1	4	yes	—
56	C₂×C₁₃	C₂×#127	1	1	yes	characteristic
57	C₂×C₁₃	#535	1	6	yes	—
58	D₁₃	—	8	6	no	—
59	C₂⁴	—	13	6	no	—
60	C₂×Q₈	—	26	6	no	—
61	C₂×D₄	—	26	6	no	—
62	C₂×D₄	—	26	24	no	—
63	C₂×D₄	—	26	12	no	—
64	C₂×D₄	—	52	24	no	—
65	C₂²×C₄	—	13	2	no	—
66	C₂²×C₄	C₂²×D₁₃	1	6	yes	—
67	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
68	C₂²⋊C₄	—	26	24	no	—
69	C₄²	D₅₂	1	12	yes	complemented
70	C₁₃	#2657	1	1	yes	characteristic, complemented, Sylow
71	C₂³	—	26	6	no	—
72	C₂³	—	26	12	no	—
73	C₂³	—	26	24	no	—
74	C₂³	C₂³×D₁₃	1	1	yes	characteristic
75	Q₈	—	52	4	no	—
76	D₄	—	52	48	no	—
77	D₄	—	52	12	no	—
78	C₂×C₄	—	2	12	no	—
79	C₂×C₄	—	26	6	no	—
80	C₂×C₄	C₂×D₅₂	1	12	yes	—
81	C₂×C₄	C₂×D₅₂	1	6	yes	—
82	C₂²	—	52	6	no	—
83	C₂²	—	52	24	no	—
84	C₂²	—	52	12	no	—
85	C₂²	C₂²×D₅₂	1	3	yes	—
86	C₂²	#88256	1	4	yes	—
87	C₄	—	2	12	no	—
88	C₄	—	52	2	no	—
89	C₄	#88128	1	4	yes	—
90	C₂	—	104	6	no	—
91	C₂	C₂×#88128	1	1	yes	characteristic
92	C₂	#11719230	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃
commutator, socle, cosocle	C₂³×C₁₃	C₂⁴
Fitting	C₁₃×#376	C₂
hypercenter	#376	D₁₃
hypocenter	C₁₃	#2657
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ #376

Complements

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

N	H ≅ G/N	type
1. C₂×#88129	C₂	semidirect
2. C₂×#88128	C₂	semidirect
3. C₁₃×#376	C₂	semidirect
4. #11718332	C₂	semidirect
22. C₄²×C₁₃	D₄	semidirect
39. #376	D₁₃	semidirect
69. C₄²	D₅₂	semidirect
70. C₁₃	#2657	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88129	2
C₂×#88128	2
C₁₃×#376	2
#11718332	2
#2657	13