Subgroups — #11926739

Order 1216.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#64525	C₂	1	2	yes	maximal, complemented
3	#10597320	C₂	1	1	yes	maximal, characteristic, complemented
4	#10597266	C₂	1	2	yes	maximal, complemented
5	C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₁₉	—	2	1	no	—
8	C₂×D₇₆	—	2	1	no	—
9	C₂×D₇₆	—	2	1	no	—
10	C₂×D₇₆	C₂²	1	2	yes	—
11	C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²⋊C₄×C₁₉	—	2	1	no	—
13	C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	#64525	—	2	4	no	—
15	C₂×C₁₉⋊C₈	C₂²	1	2	yes	—
16	C₂³×C₁₉	—	2	1	no	—
17	C₂²×D₁₉	—	2	2	no	—
18	D₄×C₁₉	—	2	1	no	—
19	D₄×C₁₉	D₄	1	2	yes	complemented
20	C₂×C₄×C₁₉	—	2	1	no	—
21	C₂×C₄×C₁₉	—	4	2	no	—
22	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	D₇₆	—	2	2	no	—
26	D₇₆	—	2	2	no	—
27	D₇₆	—	4	2	no	—
28	D₇₆	—	4	2	no	—
29	C₁₉⋊C₈	—	2	2	no	—
30	C₂²×C₁₉	—	2	2	no	—
31	C₂²×C₁₉	—	4	1	no	—
32	C₂²×C₁₉	—	4	1	no	—
33	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂×D₁₉	—	4	2	no	—
35	C₂×D₁₉	—	4	2	no	—
36	C₂×D₁₉	—	4	2	no	—
37	C₄×C₁₉	—	2	1	no	—
38	C₄×C₁₉	—	4	1	no	—
39	C₄×C₁₉	D₈	1	2	yes	complemented
40	C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₄×C₁₉	#41	1	1	yes	characteristic
42	#459	—	19	1	no	maximal, Sylow
43	C₂×C₁₉	—	4	2	no	—
44	C₂×C₁₉	#121	1	1	yes	characteristic
45	C₂×C₁₉	C₂×D₈	1	1	yes	characteristic
46	C₂×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
47	D₁₉	—	8	2	no	—
48	C₂×D₈	—	19	2	no	—
49	#127	—	19	1	no	—
50	C₄×D₄	D₁₉	1	1	yes	characteristic, complemented
51	C₄⋊C₈	—	19	1	no	—
52	#102	—	19	2	no	—
53	C₁₉	#459	1	1	yes	characteristic, complemented, Sylow
54	C₂×D₄	—	19	2	no	—
55	C₂×D₄	—	38	1	no	—
56	C₂×D₄	—	38	1	no	—
57	C₂×D₄	C₂×D₁₉	1	1	yes	characteristic
58	C₂²×C₄	—	2	1	no	—
59	D₈	—	38	4	no	—
60	C₂×C₈	—	19	2	no	—
61	C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
62	C₂²⋊C₄	—	2	1	no	—
63	C₄²	C₂×D₁₉	1	1	yes	characteristic
64	C₂³	—	2	1	no	—
65	C₂³	—	38	2	no	—
66	D₄	—	2	1	no	—
67	D₄	—	38	2	no	—
68	D₄	—	38	2	no	—
69	D₄	—	76	2	no	—
70	D₄	—	76	2	no	—
71	D₄	D₇₆	1	2	yes	complemented
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	4	2	no	—
74	C₂×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
75	C₂×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
76	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
77	C₈	—	38	2	no	—
78	C₂²	—	2	2	no	—
79	C₂²	—	4	1	no	—
80	C₂²	—	4	1	no	—
81	C₂²	—	76	2	no	—
82	C₂²	—	76	2	no	—
83	C₂²	—	76	2	no	—
84	C₂²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
85	C₄	—	2	1	no	—
86	C₄	—	4	1	no	—
87	C₄	#64525	1	2	yes	complemented
88	C₄	C₂×D₇₆	1	1	yes	characteristic
89	C₄	#64541	1	1	yes	characteristic
90	C₂	—	4	2	no	—
91	C₂	—	152	2	no	—
92	C₂	#10597376	1	1	yes	characteristic
93	C₂	C₂×#64525	1	1	yes	characteristic
94	C₂	#10597395	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₄×D₄×C₁₉	C₂
socle	C₂²×C₁₉	C₂×D₄
hypercenter	C₄×D₄	D₁₉
hypocenter	C₁₉	#459
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₄×D₄×C₁₉	C₂	semidirect
2. C₂×#64525	C₂	semidirect
3. #10597320	C₂	semidirect
4. #10597266	C₂	semidirect
5. C₄⋊(C₁₉⋊C₈)	C₂	semidirect
19. D₄×C₁₉	D₄	semidirect
39. C₄×C₁₉	D₈	semidirect
50. C₄×D₄	D₁₉	semidirect
53. C₁₉	#459	semidirect
71. D₄	D₇₆	semidirect
87. C₄	#64525	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₄×C₁₉	2
C₂×#64525	2
#10597320	2
#10597266	2
C₄⋊(C₁₉⋊C₈)	2
#459	19