Subgroups — #13123230

Order 1664.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#88194	C₂	1	12	yes	maximal, complemented
3	C₂×#88128	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄²×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₄×C₁₃	C₂²	1	6	yes	—
6	C₂²×C₂²⋊D₁₃	C₂²	1	16	yes	—
7	C₂²×D₅₂	C₂²	1	6	yes	—
8	C₁₃×#127	—	2	4	no	—
9	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	#88194	—	2	48	no	—
11	C₂×C₄×Dic₁₃	C₂²	1	6	yes	—
12	#88128	—	2	4	no	—
13	C₂⁴×C₁₃	C₂³	1	4	yes	—
14	C₂³×D₁₃	C₂³	1	4	yes	—
15	C₂×D₄×C₁₃	—	2	24	no	—
16	C₂×D₄×C₁₃	—	2	12	no	—
17	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
18	C₂×C₂²⋊D₁₃	—	2	96	no	—
19	C₂²×Dic₁₃	C₂³	1	4	yes	—
20	C₂×D₅₂	—	2	12	no	—
21	C₂×D₅₂	—	2	24	no	—
22	C₄²×C₁₃	D₄	1	4	yes	complemented
23	C₄×Dic₁₃	D₄	1	24	yes	complemented
24	#2867	—	13	1	no	maximal, Sylow
25	C₂³×C₁₃	—	2	24	no	—
26	C₂³×C₁₃	—	2	4	no	—
27	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
28	C₂²×D₁₃	—	2	4	no	—
29	C₂²×D₁₃	—	2	24	no	—
30	D₄×C₁₃	—	4	24	no	—
31	C₂×C₄×C₁₃	C₂×D₄	1	12	yes	—
32	C₂×C₄×C₁₃	C₂×D₄	1	6	yes	—
33	C₂²⋊D₁₃	—	4	64	no	—
34	C₂×Dic₁₃	C₂×D₄	1	24	yes	—
35	D₅₂	—	4	24	no	—
36	C₂×#127	—	13	12	no	—
37	C₂×#127	—	13	1	no	—
38	C₂×#127	D₁₃	1	1	yes	characteristic, complemented
39	C₄³	—	13	1	no	—
40	C₂²×C₁₃	—	4	16	no	—
41	C₂²×C₁₃	—	4	12	no	—
42	C₂²×C₁₃	C₂²×D₄	1	6	yes	—
43	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
44	C₂×D₁₃	—	4	12	no	—
45	C₂×D₁₃	—	4	16	no	—
46	C₄×C₁₃	#127	1	12	yes	complemented
47	Dic₁₃	#127	1	16	yes	complemented
48	C₂²×D₄	—	13	16	no	—
49	C₂²×D₄	—	13	6	no	—
50	C₂²×D₄	C₂×D₁₃	1	6	yes	—
51	#127	—	2	4	no	—
52	#127	—	26	48	no	—
53	#127	—	26	4	no	—
54	C₂×C₄²	—	13	6	no	—
55	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
56	C₂×C₁₃	—	8	4	no	—
57	C₂×C₁₃	C₂×#127	1	3	yes	—
58	C₂×C₁₃	C₂×#127	1	4	yes	—
59	D₁₃	—	8	4	no	—
60	C₂⁴	—	13	4	no	—
61	C₂⁴	C₂²×D₁₃	1	4	yes	—
62	C₂×D₄	—	2	24	no	—
63	C₂×D₄	—	2	12	no	—
64	C₂×D₄	—	26	96	no	—
65	C₂×D₄	—	26	24	no	—
66	C₂×D₄	—	26	12	no	—
67	C₂²×C₄	—	13	4	no	—
68	C₂²×C₄	C₂²×D₁₃	1	3	yes	—
69	C₄²	—	13	24	no	—
70	C₄²	C₂²⋊D₁₃	1	4	yes	complemented
71	C₁₃	#2867	1	1	yes	characteristic, complemented, Sylow
72	C₂³	—	2	24	no	—
73	C₂³	—	2	4	no	—
74	C₂³	—	26	24	no	—
75	C₂³	—	26	4	no	—
76	C₂³	C₂³×D₁₃	1	1	yes	characteristic
77	D₄	—	4	24	no	—
78	D₄	—	52	64	no	—
79	D₄	—	52	24	no	—
80	C₂×C₄	—	13	24	no	—
81	C₂×C₄	D₄×D₁₃	1	12	yes	—
82	C₂×C₄	C₂×C₂²⋊D₁₃	1	6	yes	—
83	C₂²	—	4	12	no	—
84	C₂²	—	4	16	no	—
85	C₂²	—	52	12	no	—
86	C₂²	—	52	16	no	—
87	C₂²	C₂×D₄×D₁₃	1	6	yes	—
88	C₂²	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
89	C₄	—	13	16	no	—
90	C₄	#88194	1	12	yes	complemented
91	C₂	—	8	4	no	—
92	C₂	—	104	4	no	—
93	C₂	D₁₃×#127	1	4	yes	—
94	C₂	C₂×#88194	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃
commutator, socle, cosocle	C₂³×C₁₃	C₂⁴
Fitting	C₂×C₁₃×#127	C₂
hypercenter	C₂×#127	D₁₃
hypocenter	C₁₃	#2867
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#127

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#127	C₂	semidirect
2. C₂×#88194	C₂	semidirect
3. C₂×#88128	C₂	semidirect
4. C₄²×Dic₁₃	C₂	semidirect
22. C₄²×C₁₃	D₄	semidirect
23. C₄×Dic₁₃	D₄	semidirect
38. C₂×#127	D₁₃	semidirect
46. C₄×C₁₃	#127	semidirect
47. Dic₁₃	#127	semidirect
70. C₄²	C₂²⋊D₁₃	semidirect
71. C₁₃	#2867	semidirect
90. C₄	#88194	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#127	2
C₂×#88194	2
C₂×#88128	2
C₄²×Dic₁₃	2
#2867	13