Subgroups — D₉₁⋊D₅₇ #35209168

Order 20748.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₃₉₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₇₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₉×D₉₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₉₁⋊D₁₉	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₉×D₉₁	D₃	1	1	yes	characteristic, complemented
7	C₁₃×D₁₃₃	—	3	1	no	—
8	C₇×D₂₄₇	—	3	1	no	—
9	D₁₃×D₅₇	—	7	1	no	maximal, Hall
10	C₇×C₁₃×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₇×D₅₇	—	13	1	no	maximal, Hall
12	D₇₄₁	D₇	1	1	yes	characteristic, complemented
13	C₁₃×D₅₇	—	7	1	no	—
14	C₃×C₁₉×D₁₃	—	7	1	no	—
15	D₂₁⋊D₁₃	—	19	1	no	maximal, Hall
16	D₁₃×D₁₉	—	21	1	no	Hall
17	D₃₉₉	D₁₃	1	1	yes	characteristic, complemented
18	C₇×D₅₇	—	13	1	no	—
19	C₃×D₇×C₁₉	—	13	1	no	—
20	C₃×C₁₃×C₁₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
21	C₁₃×D₂₁	—	19	1	no	—
22	C₇×D₃₉	—	19	1	no	—
23	C₃×D₉₁	D₁₉	1	1	yes	characteristic, complemented
24	D₇×D₁₉	—	39	1	no	Hall
25	D₂₄₇	—	3	1	no	—
26	C₁₃×D₁₉	—	21	1	no	—
27	C₁₉×D₁₃	—	7	1	no	—
28	C₃×C₇×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
29	D₇×D₁₃	—	57	1	no	Hall
30	C₃×C₇×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
31	D₁₃₃	—	3	1	no	—
32	C₇×D₁₉	—	39	1	no	—
33	D₇×C₁₉	—	13	1	no	—
34	C₁₃×C₁₉	D₃×D₇	1	1	yes	characteristic, complemented, Hall
35	C₂×D₅₇	—	91	1	no	Hall
36	D₉₁	D₅₇	1	1	yes	characteristic, complemented
37	C₇×D₁₃	—	57	1	no	—
38	C₁₃×D₇	—	57	1	no	—
39	D₃×D₁₃	—	133	1	no	Hall
40	C₇×C₁₉	D₃×D₁₃	1	1	yes	characteristic, complemented, Hall
41	C₂×C₃×C₁₉	—	91	1	no	—
42	D₅₇	—	7	1	no	—
43	D₅₇	—	13	1	no	—
44	C₇×C₁₃	C₂×D₅₇	1	1	yes	characteristic, complemented, Hall
45	D₃×D₇	—	247	1	no	Hall
46	D₃₉	—	19	1	no	—
47	C₃×D₁₃	—	7	1	no	—
48	D₃×C₁₃	—	133	1	no	—
49	C₂×D₁₉	—	273	1	no	Hall
50	C₃×C₁₉	D₇×D₁₃	1	1	yes	characteristic, complemented, Hall
51	C₂×D₁₃	—	399	1	no	Hall
52	D₂₁	—	19	1	no	—
53	C₃×D₇	—	13	1	no	—
54	D₃×C₇	—	247	1	no	—
55	C₃×C₁₃	D₇×D₁₉	1	1	yes	characteristic, complemented, Hall
56	C₂×C₁₉	—	91	1	no	—
57	D₁₉	—	21	1	no	—
58	D₁₉	—	39	1	no	—
59	C₂×D₇	—	741	1	no	Hall
60	C₂×C₁₃	—	399	1	no	—
61	D₁₃	—	7	1	no	—
62	D₁₃	—	57	1	no	—
63	C₃×C₇	D₁₃×D₁₉	1	1	yes	characteristic, complemented, Hall
64	C₁₉	D₂₁⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₇	—	741	1	no	—
66	D₇	—	13	1	no	—
67	D₇	—	57	1	no	—
68	C₁₃	D₇×D₅₇	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₃	—	1729	1	no	Hall
70	C₇	D₁₃×D₅₇	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	91	1	no	—
72	D₃	—	133	1	no	—
73	D₃	—	247	1	no	—
74	C₂²	—	5187	1	no	Sylow
75	C₃	D₉₁⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	91	1	no	—
77	C₂	—	399	1	no	—
78	C₂	—	741	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃×C₇×C₁₃×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₃₉₉	C₂	semidirect
2. C₇×D₇₄₁	C₂	semidirect
3. C₃×C₁₉×D₉₁	C₂	semidirect
5. C₃×C₇×C₁₃×C₁₉	C₂²	semidirect
6. C₁₉×D₉₁	D₃	semidirect
10. C₇×C₁₃×C₁₉	C₂×D₃	semidirect
12. D₇₄₁	D₇	semidirect
17. D₃₉₉	D₁₃	semidirect
20. C₃×C₁₃×C₁₉	C₂×D₇	semidirect
23. C₃×D₉₁	D₁₉	semidirect
28. C₃×C₇×C₁₉	C₂×D₁₃	semidirect
30. C₃×C₇×C₁₃	C₂×D₁₉	semidirect
34. C₁₃×C₁₉	D₃×D₇	semidirect
36. D₉₁	D₅₇	semidirect
40. C₇×C₁₉	D₃×D₁₃	semidirect
44. C₇×C₁₃	C₂×D₅₇	semidirect
50. C₃×C₁₉	D₇×D₁₃	semidirect
55. C₃×C₁₃	D₇×D₁₉	semidirect
63. C₃×C₇	D₁₃×D₁₉	semidirect
64. C₁₉	D₂₁⋊D₁₃	semidirect
68. C₁₃	D₇×D₅₇	semidirect
70. C₇	D₁₃×D₅₇	semidirect
75. C₃	D₉₁⋊D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×D₃₉₉	2
C₇×D₇₄₁	2
C₃×C₁₉×D₉₁	2
D₉₁⋊D₁₉	3
D₁₃×D₅₇	7
D₇×D₅₇	13
D₂₁⋊D₁₃	19

Subgroups — D91⋊D57 #35209168

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉₁⋊D₅₇ #35209168