Subgroups — #261×#401 #16791712

Order 3328.

1222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13130023	C₂	1	7	yes	maximal
2	#95×#261	C₂	1	7	yes	maximal
3	D₁₃×#401	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×#261	C₂²	1	7	yes	—
5	C₂×(C₂×#261)⋊C₄	C₂²	1	21	yes	—
6	C₁₃×#401	C₄	1	1	yes	characteristic, complemented
7	D₁₃×#95	C₂²	1	7	yes	—
8	C₁₃⋊#401	C₄	1	7	yes	complemented
9	C₂³×#261	C₂³	1	7	yes	—
10	C₂³×#261	C₂³	1	1	yes	characteristic
11	C₂²×C₄×D₁₃	C₂³	1	7	yes	—
12	C₂×C₄×#261	—	2	42	no	—
13	(C₂×#261)⋊C₄	—	2	42	no	—
14	C₁₃×#95	C₂×C₄	1	7	yes	—
15	#88071	C₂×C₄	1	21	yes	—
16	C₄×#401	—	13	1	no	maximal, Sylow
17	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
18	C₂²×#261	—	2	21	no	—
19	C₂²×#261	—	2	21	no	—
20	C₂²×#261	#41	1	14	yes	—
21	C₂²×#261	#41	1	14	yes	—
22	C₂²×C₄×C₁₃	C₂²×C₄	1	7	yes	—
23	C₂²×Dic₁₃	C₂²×C₄	1	7	yes	—
24	C₂×C₄×D₁₃	—	2	21	no	—
25	C₂×C₄×D₁₃	—	2	21	no	—
26	C₄×#261	—	4	28	no	—
27	C₂×#401	—	13	1	no	—
28	#1443	—	13	7	no	—
29	C₄×#95	—	13	7	no	—
30	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
31	C₂²×D₁₃	C₂×#41	1	7	yes	—
32	C₂²×D₁₃	C₂×#41	1	7	yes	—
33	C₂×#261	—	2	42	no	—
34	C₂×#261	—	4	7	no	—
35	C₂×#261	—	4	21	no	—
36	C₂×#261	#126	1	28	yes	—
37	C₂×C₄×C₁₃	—	2	21	no	—
38	C₂×Dic₁₃	—	2	21	no	—
39	C₄×D₁₃	—	4	7	no	—
40	C₄×D₁₃	—	4	21	no	—
41	C₂²×C₄²	—	13	7	no	—
42	#401	—	13	7	no	—
43	#401	#261	1	1	yes	characteristic, direct product factor
44	C₂×#95	—	13	7	no	—
45	C₂×#95	—	13	21	no	—
46	C₂²×C₁₃	C₄×#41	1	7	yes	—
47	C₂×D₁₃	C₂×#126	1	7	yes	—
48	C₂×D₁₃	#529	1	21	yes	—
49	#261	—	4	14	no	—
50	#261	#401	1	8	yes	direct product factor
51	C₄×C₁₃	—	4	7	no	—
52	Dic₁₃	—	4	7	no	—
53	C₂³×C₄	—	13	1	no	—
54	C₂³×C₄	—	13	7	no	—
55	C₂³×C₄	—	13	7	no	—
56	C₂×C₄²	—	26	42	no	—
57	#95	—	13	21	no	—
58	#95	—	26	42	no	—
59	#95	C₂×#261	1	7	yes	—
60	C₂×C₁₃	C₄×#126	1	7	yes	—
61	D₁₃	C₂×#401	1	1	yes	characteristic
62	D₁₃	#2401	1	7	yes	—
63	C₂⁴	—	13	1	no	—
64	C₂²×C₄	—	13	14	no	—
65	C₂²×C₄	—	13	14	no	—
66	C₂²×C₄	—	13	7	no	—
67	C₂²×C₄	—	26	21	no	—
68	C₂²×C₄	—	26	21	no	—
69	C₂²×C₄	—	26	21	no	—
70	C₂²×C₄	—	26	21	no	—
71	C₂²×C₄	C₂²×#261	1	7	yes	—
72	C₄²	—	52	28	no	—
73	C₁₃	C₄×#401	1	1	yes	characteristic, complemented, Sylow
74	C₂³	—	13	7	no	—
75	C₂³	—	13	7	no	—
76	C₂³	C₂³×#261	1	1	yes	characteristic
77	C₂×C₄	—	2	21	no	—
78	C₂×C₄	—	13	28	no	—
79	C₂×C₄	—	26	42	no	—
80	C₂×C₄	—	26	21	no	—
81	C₂×C₄	—	52	7	no	—
82	C₂×C₄	—	52	21	no	—
83	C₂×C₄	—	52	7	no	—
84	C₂×C₄	—	52	21	no	—
85	C₂²	—	13	7	no	—
86	C₂²	—	13	21	no	—
87	C₂²	#41×#261	1	7	yes	—
88	C₄	—	4	7	no	—
89	C₄	—	13	8	no	—
90	C₄	—	52	14	no	—
91	C₄	—	52	7	no	—
92	C₂	—	13	1	no	—
93	C₂	—	13	7	no	—
94	C₂	#126×#261	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×#261
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₁₃×#401	C₄
prime radical, cosocle	C₂³×D₁₃	C₂⁴
hypercenter	#401	#261
hypocenter	C₁₃	C₄×#401
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ #401

Complements

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

N	H ≅ G/N	type
6. C₁₃×#401	C₄	semidirect
8. C₁₃⋊#401	C₄	semidirect
43. #401	#261	direct (N × H)
50. #261	#401	direct (N × H)
73. C₁₃	C₄×#401	semidirect

Maximal subgroups

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

subgroup	index
#13130023	2
#95×#261	2
D₁₃×#401	2
C₄×#401	13