Subgroups — #1295×C₂₆₉ #46806402

Order 34432.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#97×C₂₆₉	C₂	1	2	yes	maximal
2	#382×C₂₆₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₂₆₉	—	2	2	no	—
4	C₂×C₄⋊C₄×C₂₆₉	C₄	1	2	yes	—
5	C₂×C₄²×C₂₆₉	C₂²	1	1	yes	characteristic
6	#97×C₂₆₉	—	2	2	no	—
7	#97×C₂₆₉	C₄	1	4	yes	complemented
8	#95×C₂₆₉	—	2	2	no	—
9	C₂²×C₄×C₂₆₉	—	2	2	no	—
10	C₂²×C₄×C₂₆₉	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₄×C₂₆₉	D₄	1	2	yes	—
12	C₂×C₈×C₂₆₉	—	2	8	no	—
13	C₂×C₈×C₂₆₉	—	2	4	no	—
14	C₄⋊C₄×C₂₆₉	—	4	2	no	—
15	C₄²×C₂₆₉	C₂×C₄	1	2	yes	—
16	C₄²×C₂₆₉	D₄	1	1	yes	characteristic
17	C₄²×C₂₆₉	Q₈	1	1	yes	characteristic
18	C₂³×C₂₆₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₄×C₂₆₉	—	2	1	no	—
20	C₂×C₄×C₂₆₉	—	2	1	no	—
21	C₂×C₄×C₂₆₉	—	2	4	no	—
22	C₂×C₄×C₂₆₉	—	4	2	no	—
23	C₂×C₄×C₂₆₉	—	4	4	no	—
24	C₂×C₄×C₂₆₉	C₄²	1	1	yes	characteristic
25	C₂×C₄×C₂₆₉	C₂²⋊C₄	1	2	yes	—
26	C₂×C₄×C₂₆₉	C₄⋊C₄	1	2	yes	—
27	C₂×C₄×C₂₆₉	C₄⋊C₄	1	1	yes	characteristic
28	C₈×C₂₆₉	—	2	8	no	—
29	C₂²×C₂₆₉	#95	1	1	yes	characteristic
30	C₂²×C₂₆₉	#100	1	1	yes	characteristic
31	C₂²×C₂₆₉	#101	1	1	yes	characteristic
32	C₂²×C₂₆₉	#104	1	4	yes	—
33	C₄×C₂₆₉	—	2	2	no	—
34	C₄×C₂₆₉	—	2	2	no	—
35	C₄×C₂₆₉	—	2	1	no	—
36	C₄×C₂₆₉	—	2	1	no	—
37	C₄×C₂₆₉	—	8	2	no	—
38	C₂×C₂₆₉	#329	1	2	yes	—
39	C₂×C₂₆₉	#330	1	2	yes	—
40	C₂×C₂₆₉	#339	1	2	yes	—
41	C₂×C₂₆₉	#343	1	1	yes	characteristic
42	C₂₆₉	#1295	1	1	yes	characteristic, direct product factor, Sylow
43	#1295	C₂₆₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×#97	C₂×C₂₆₉	1	2	yes	—
45	#382	C₂×C₂₆₉	1	1	yes	characteristic
46	C₂²×C₈	—	2	2	no	—
47	C₂×C₄⋊C₄	C₄×C₂₆₉	1	2	yes	—
48	C₂×C₄²	C₂²×C₂₆₉	1	1	yes	characteristic
49	#97	—	2	2	no	—
50	#97	C₄×C₂₆₉	1	4	yes	complemented
51	#95	—	2	2	no	—
52	C₂²×C₄	—	2	2	no	—
53	C₂²×C₄	C₂×C₄×C₂₆₉	1	1	yes	characteristic
54	C₂²×C₄	D₄×C₂₆₉	1	2	yes	—
55	C₂×C₈	—	2	8	no	—
56	C₂×C₈	—	2	4	no	—
57	C₄⋊C₄	—	4	2	no	—
58	C₄²	C₂×C₄×C₂₆₉	1	2	yes	—
59	C₄²	D₄×C₂₆₉	1	1	yes	characteristic
60	C₄²	Q₈×C₂₆₉	1	1	yes	characteristic
61	C₂³	C₂²⋊C₄×C₂₆₉	1	1	yes	characteristic
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	—	4	4	no	—
67	C₂×C₄	C₄²×C₂₆₉	1	1	yes	characteristic
68	C₂×C₄	C₂²⋊C₄×C₂₆₉	1	2	yes	—
69	C₂×C₄	C₄⋊C₄×C₂₆₉	1	2	yes	—
70	C₂×C₄	C₄⋊C₄×C₂₆₉	1	1	yes	characteristic
71	C₈	—	2	8	no	—
72	C₂²	#95×C₂₆₉	1	1	yes	characteristic
73	C₂²	#100×C₂₆₉	1	1	yes	characteristic
74	C₂²	#101×C₂₆₉	1	1	yes	characteristic
75	C₂²	#104×C₂₆₉	1	4	yes	—
76	C₄	—	2	2	no	—
77	C₄	—	2	2	no	—
78	C₄	—	2	1	no	—
79	C₄	—	2	1	no	—
80	C₄	—	8	2	no	—
81	C₂	#329×C₂₆₉	1	2	yes	—
82	C₂	#330×C₂₆₉	1	2	yes	—
83	C₂	#339×C₂₆₉	1	2	yes	—
84	C₂	#343×C₂₆₉	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₆₉	C₂²⋊C₄
commutator	C₂×C₄	C₄²×C₂₆₉
Frattini, cosocle	C₂×C₄²	C₂²×C₂₆₉
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₆₉ ◁ C₂×C₄²×C₂₆₉ ◁ G

Complements

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

N	H ≅ G/N	type
7. #97×C₂₆₉	C₄	semidirect
42. C₂₆₉	#1295	direct (N × H)
43. #1295	C₂₆₉	direct (N × H)
50. #97	C₄×C₂₆₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#97×C₂₆₉	2
#382×C₂₆₉	2
#1295	269

Subgroups — #1295×C269 #46806402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1295×C₂₆₉ #46806402