Subgroups — #1275×C₁₅₁ #34064607

Order 19328.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#431×C₁₅₁	C₂	1	2	yes	maximal
2	C₂×#97×C₁₅₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₁₅₁	C₄	1	2	yes	—
4	C₂×C₄²×C₁₅₁	C₂²	1	1	yes	characteristic
5	C₄⋊C₈×C₁₅₁	—	2	2	no	—
6	C₂²⋊C₈×C₁₅₁	—	2	2	no	—
7	#97×C₁₅₁	—	2	2	no	—
8	C₄×C₈×C₁₅₁	C₄	1	4	yes	—
9	C₂²×C₄×C₁₅₁	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄×C₁₅₁	D₄	1	1	yes	characteristic
11	C₂²×C₄×C₁₅₁	Q₈	1	1	yes	characteristic
12	C₂×C₈×C₁₅₁	—	2	2	no	—
13	C₂×C₈×C₁₅₁	—	2	2	no	—
14	C₂×C₈×C₁₅₁	—	2	4	no	—
15	C₂×C₈×C₁₅₁	C₈	1	4	yes	complemented
16	C₄²×C₁₅₁	C₂×C₄	1	2	yes	—
17	C₄²×C₁₅₁	D₄	1	2	yes	—
18	C₂³×C₁₅₁	C₄⋊C₄	1	1	yes	characteristic
19	C₂×C₄×C₁₅₁	—	4	1	no	—
20	C₂×C₄×C₁₅₁	—	4	1	no	—
21	C₂×C₄×C₁₅₁	C₄²	1	1	yes	characteristic
22	C₂×C₄×C₁₅₁	C₂²⋊C₄	1	2	yes	—
23	C₂×C₄×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₁₅₁	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₁₅₁	C₂×C₈	1	2	yes	—
26	C₂×C₄×C₁₅₁	M₁₆	1	2	yes	—
27	C₈×C₁₅₁	—	2	4	no	—
28	C₈×C₁₅₁	—	4	4	no	—
29	C₂²×C₁₅₁	—	2	1	no	—
30	C₂²×C₁₅₁	—	2	1	no	—
31	C₂²×C₁₅₁	#95	1	1	yes	characteristic
32	C₂²×C₁₅₁	C₄⋊C₈	1	2	yes	—
33	C₄×C₁₅₁	—	2	2	no	—
34	C₄×C₁₅₁	—	2	2	no	—
35	C₄×C₁₅₁	C₄×C₈	1	1	yes	characteristic
36	C₄×C₁₅₁	#97	1	1	yes	characteristic
37	C₄×C₁₅₁	C₂²⋊C₈	1	2	yes	—
38	C₂×C₁₅₁	—	2	2	no	—
39	C₂×C₁₅₁	#336	1	1	yes	characteristic
40	C₂×C₁₅₁	H(3,ℤ/4)	1	1	yes	characteristic
41	C₂×C₁₅₁	#338	1	1	yes	characteristic
42	C₁₅₁	#1275	1	1	yes	characteristic, direct product factor, Sylow
43	#1275	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	#431	C₂×C₁₅₁	1	2	yes	—
45	C₂×#97	C₂×C₁₅₁	1	1	yes	characteristic
46	C₂²×C₈	C₄×C₁₅₁	1	2	yes	—
47	C₂×C₄²	C₂²×C₁₅₁	1	1	yes	characteristic
48	C₄⋊C₈	—	2	2	no	—
49	C₂²⋊C₈	—	2	2	no	—
50	#97	—	2	2	no	—
51	C₄×C₈	C₄×C₁₅₁	1	4	yes	—
52	C₂²×C₄	C₂×C₄×C₁₅₁	1	1	yes	characteristic
53	C₂²×C₄	D₄×C₁₅₁	1	1	yes	characteristic
54	C₂²×C₄	Q₈×C₁₅₁	1	1	yes	characteristic
55	C₂×C₈	—	2	2	no	—
56	C₂×C₈	—	2	2	no	—
57	C₂×C₈	—	2	4	no	—
58	C₂×C₈	C₈×C₁₅₁	1	4	yes	complemented
59	C₄²	C₂×C₄×C₁₅₁	1	2	yes	—
60	C₄²	D₄×C₁₅₁	1	2	yes	—
61	C₂³	C₄⋊C₄×C₁₅₁	1	1	yes	characteristic
62	C₂×C₄	—	4	1	no	—
63	C₂×C₄	—	4	1	no	—
64	C₂×C₄	C₄²×C₁₅₁	1	1	yes	characteristic
65	C₂×C₄	C₂²⋊C₄×C₁₅₁	1	2	yes	—
66	C₂×C₄	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
67	C₂×C₄	C₄⋊C₄×C₁₅₁	1	2	yes	—
68	C₂×C₄	C₂×C₈×C₁₅₁	1	2	yes	—
69	C₂×C₄	M₁₆×C₁₅₁	1	2	yes	—
70	C₈	—	2	4	no	—
71	C₈	—	4	4	no	—
72	C₂²	—	2	1	no	—
73	C₂²	—	2	1	no	—
74	C₂²	#95×C₁₅₁	1	1	yes	characteristic
75	C₂²	C₄⋊C₈×C₁₅₁	1	2	yes	—
76	C₄	—	2	2	no	—
77	C₄	—	2	2	no	—
78	C₄	C₄×C₈×C₁₅₁	1	1	yes	characteristic
79	C₄	#97×C₁₅₁	1	1	yes	characteristic
80	C₄	C₂²⋊C₈×C₁₅₁	1	2	yes	—
81	C₂	—	2	2	no	—
82	C₂	#336×C₁₅₁	1	1	yes	characteristic
83	C₂	H(3,ℤ/4)×C₁₅₁	1	1	yes	characteristic
84	C₂	#338×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₅₁	C₄²
commutator	C₄	C₄×C₈×C₁₅₁
Frattini, cosocle	C₂×C₄²	C₂²×C₁₅₁
socle	C₂²×C₁₅₁	#95
prime radical	C₂³×C₁₅₁	C₄⋊C₄
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₂×C₈×C₁₅₁	C₈	semidirect
42. C₁₅₁	#1275	direct (N × H)
43. #1275	C₁₅₁	direct (N × H)
58. C₂×C₈	C₈×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
#431×C₁₅₁	2
C₂×#97×C₁₅₁	2
#1275	151

Subgroups — #1275×C151 #34064607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1275×C₁₅₁ #34064607