Subgroups — #380×C₂₅₇ #30656249

Order 16448.

234 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₂₅₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×C₂₅₇	C₂	1	2	yes	maximal, complemented
3	C₂×C₂²⋊C₄×C₂₅₇	C₂	1	2	yes	maximal
4	#95×C₂₅₇	C₂	1	2	yes	maximal, complemented
5	C₂⁴×C₂₅₇	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₂₅₇	—	2	4	no	—
7	C₂²×C₄×C₂₅₇	C₄	1	4	yes	complemented
8	C₂²×C₄×C₂₅₇	C₂²	1	4	yes	—
9	C₂²×C₄×C₂₅₇	C₂²	1	1	yes	characteristic
10	C₂²×C₄×C₂₅₇	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₂₅₇	—	2	4	no	—
12	C₂²⋊C₄×C₂₅₇	—	2	4	no	—
13	C₂³×C₂₅₇	—	2	2	no	—
14	C₂³×C₂₅₇	—	2	2	no	—
15	C₂³×C₂₅₇	C₂×C₄	1	2	yes	—
16	C₂³×C₂₅₇	D₄	1	2	yes	—
17	C₂³×C₂₅₇	Q₈	1	2	yes	—
18	C₂³×C₂₅₇	C₂³	1	1	yes	characteristic
19	C₂×C₄×C₂₅₇	—	2	2	no	—
20	C₂×C₄×C₂₅₇	—	2	8	no	—
21	C₂×C₄×C₂₅₇	—	2	4	no	—
22	C₂×C₄×C₂₅₇	—	2	4	no	—
23	C₂×C₄×C₂₅₇	—	2	4	no	—
24	C₂×C₄×C₂₅₇	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₂₅₇	C₂×C₄	1	2	yes	—
26	C₂×C₄×C₂₅₇	D₄	1	4	yes	—
27	C₂²×C₂₅₇	—	2	2	no	—
28	C₂²×C₂₅₇	—	2	2	no	—
29	C₂²×C₂₅₇	—	2	4	no	—
30	C₂²×C₂₅₇	—	2	4	no	—
31	C₂²×C₂₅₇	C₄⋊C₄	1	4	yes	complemented
32	C₂²×C₂₅₇	C₂²×C₄	1	1	yes	characteristic
33	C₂²×C₂₅₇	C₂×D₄	1	2	yes	—
34	C₂²×C₂₅₇	C₂×D₄	1	1	yes	characteristic
35	C₂²×C₂₅₇	C₂×Q₈	1	1	yes	characteristic
36	C₂²×C₂₅₇	#41	1	2	yes	—
37	C₄×C₂₅₇	—	2	2	no	—
38	C₄×C₂₅₇	—	4	4	no	—
39	C₄×C₂₅₇	C₂²⋊C₄	1	4	yes	complemented
40	C₂×C₂₅₇	—	2	4	no	—
41	C₂×C₂₅₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₂₅₇	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₂×C₂₅₇	#117	1	1	yes	characteristic
44	C₂×C₂₅₇	#121	1	2	yes	—
45	C₂×C₂₅₇	C₂²⋊Q₈	1	2	yes	—
46	C₂₅₇	#380	1	1	yes	characteristic, direct product factor, Sylow
47	#380	C₂₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂³×C₄	C₂×C₂₅₇	1	1	yes	characteristic
49	C₂×C₄⋊C₄	C₂×C₂₅₇	1	2	yes	complemented
50	C₂×C₂²⋊C₄	C₂×C₂₅₇	1	2	yes	—
51	#95	C₂×C₂₅₇	1	2	yes	complemented
52	C₂⁴	C₂²×C₂₅₇	1	1	yes	characteristic
53	C₂²×C₄	—	2	4	no	—
54	C₂²×C₄	C₄×C₂₅₇	1	4	yes	complemented
55	C₂²×C₄	C₂²×C₂₅₇	1	4	yes	—
56	C₂²×C₄	C₂²×C₂₅₇	1	1	yes	characteristic
57	C₂²×C₄	C₂²×C₂₅₇	1	1	yes	characteristic
58	C₄⋊C₄	—	2	4	no	—
59	C₂²⋊C₄	—	2	4	no	—
60	C₂³	—	2	2	no	—
61	C₂³	—	2	2	no	—
62	C₂³	C₂×C₄×C₂₅₇	1	2	yes	—
63	C₂³	D₄×C₂₅₇	1	2	yes	—
64	C₂³	Q₈×C₂₅₇	1	2	yes	—
65	C₂³	C₂³×C₂₅₇	1	1	yes	characteristic
66	C₂×C₄	—	2	2	no	—
67	C₂×C₄	—	2	8	no	—
68	C₂×C₄	—	2	4	no	—
69	C₂×C₄	—	2	4	no	—
70	C₂×C₄	—	2	4	no	—
71	C₂×C₄	C₂×C₄×C₂₅₇	1	2	yes	—
72	C₂×C₄	C₂×C₄×C₂₅₇	1	2	yes	—
73	C₂×C₄	D₄×C₂₅₇	1	4	yes	—
74	C₂²	—	2	2	no	—
75	C₂²	—	2	2	no	—
76	C₂²	—	2	4	no	—
77	C₂²	—	2	4	no	—
78	C₂²	C₄⋊C₄×C₂₅₇	1	4	yes	complemented
79	C₂²	C₂²×C₄×C₂₅₇	1	1	yes	characteristic
80	C₂²	C₂×D₄×C₂₅₇	1	2	yes	—
81	C₂²	C₂×D₄×C₂₅₇	1	1	yes	characteristic
82	C₂²	C₂×Q₈×C₂₅₇	1	1	yes	characteristic
83	C₂²	#41×C₂₅₇	1	2	yes	—
84	C₄	—	2	2	no	—
85	C₄	—	4	4	no	—
86	C₄	C₂²⋊C₄×C₂₅₇	1	4	yes	complemented
87	C₂	—	2	4	no	—
88	C₂	C₂×C₂²⋊C₄×C₂₅₇	1	1	yes	characteristic
89	C₂	C₂×C₄⋊C₄×C₂₅₇	1	1	yes	characteristic
90	C₂	#117×C₂₅₇	1	1	yes	characteristic
91	C₂	#121×C₂₅₇	1	2	yes	—
92	C₂	C₂²⋊Q₈×C₂₅₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₅₇	C₂³
commutator	C₂²	C₂²×C₄×C₂₅₇
Frattini, cosocle	C₂³	C₂³×C₂₅₇
prime radical	C₂⁴×C₂₅₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₅₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄⋊C₄×C₂₅₇	C₂	semidirect
4. #95×C₂₅₇	C₂	semidirect
7. C₂²×C₄×C₂₅₇	C₄	semidirect
31. C₂²×C₂₅₇	C₄⋊C₄	semidirect
39. C₄×C₂₅₇	C₂²⋊C₄	semidirect
46. C₂₅₇	#380	direct (N × H)
47. #380	C₂₅₇	direct (N × H)
49. C₂×C₄⋊C₄	C₂×C₂₅₇	semidirect
51. #95	C₂×C₂₅₇	semidirect
54. C₂²×C₄	C₄×C₂₅₇	semidirect
78. C₂²	C₄⋊C₄×C₂₅₇	semidirect
86. C₄	C₂²⋊C₄×C₂₅₇	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₂₅₇	2
C₂×C₄⋊C₄×C₂₅₇	2
C₂×C₂²⋊C₄×C₂₅₇	2
#95×C₂₅₇	2
#380	257

Subgroups — #380×C257 #30656249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #380×C₂₅₇ #30656249