Subgroups — #11926484

Order 1216.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₉⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#95	C₂	1	1	yes	maximal, characteristic
4	C₁₉⋊#95	C₂	1	2	yes	maximal
5	C₁₉⋊#95	C₂	1	2	yes	maximal
6	C₂²×C₄×C₁₉	C₂²	1	2	yes	—
7	C₂²×C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×Dic₁₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₁₉	C₂²	1	2	yes	—
10	C₂²×Dic₁₉	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₉	—	2	2	no	—
12	Dic₁₉⋊C₄	—	2	2	no	—
13	C₂³×C₁₉	C₂³	1	1	yes	characteristic
14	C₂×C₄×C₁₉	—	2	2	no	—
15	C₂×C₄×C₁₉	—	2	2	no	—
16	C₂×C₄×C₁₉	—	2	2	no	—
17	C₂×C₄×C₁₉	—	2	2	no	—
18	C₂×C₄×C₁₉	D₄	1	2	yes	—
19	C₂×Dic₁₉	—	2	1	no	—
20	C₂×Dic₁₉	—	2	1	no	—
21	C₂×Dic₁₉	—	2	1	no	—
22	C₂×Dic₁₉	—	2	2	no	—
23	C₂×Dic₁₉	—	2	4	no	—
24	C₂×Dic₁₉	—	2	2	no	—
25	C₂×Dic₁₉	Q₈	1	2	yes	—
26	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
27	C₂²×C₁₉	C₂×Q₈	1	1	yes	characteristic
28	C₂²×C₁₉	#41	1	2	yes	—
29	C₂²×C₁₉	#41	1	1	yes	characteristic
30	C₂²×C₁₉	#41	1	2	yes	—
31	C₄×C₁₉	—	2	2	no	—
32	C₄×C₁₉	—	4	2	no	—
33	Dic₁₉	—	2	2	no	—
34	Dic₁₉	—	4	1	no	—
35	Dic₁₉	—	4	2	no	—
36	#400	—	19	1	no	maximal, Sylow
37	C₂×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
38	C₂×C₁₉	#123	1	1	yes	characteristic
39	C₂×C₁₉	#124	1	1	yes	characteristic
40	C₂×C₁₉	#125	1	2	yes	—
41	C₂×C₁₉	#126	1	2	yes	—
42	C₂×C₄⋊C₄	—	19	1	no	—
43	C₂×C₄⋊C₄	—	19	1	no	—
44	#95	—	19	2	no	—
45	#95	—	19	2	no	—
46	#95	D₁₉	1	1	yes	characteristic
47	C₁₉	#400	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₄	—	19	1	no	—
49	C₂²×C₄	—	19	2	no	—
50	C₂²×C₄	—	19	1	no	—
51	C₂²×C₄	C₂×D₁₉	1	2	yes	—
52	C₂²×C₄	C₂×D₁₉	1	1	yes	characteristic
53	C₄⋊C₄	—	38	2	no	—
54	C₄⋊C₄	—	38	2	no	—
55	C₂³	C₂²×D₁₉	1	1	yes	characteristic
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	19	2	no	—
61	C₂×C₄	—	38	1	no	—
62	C₂×C₄	—	38	1	no	—
63	C₂×C₄	—	38	2	no	—
64	C₂×C₄	—	38	1	no	—
65	C₂×C₄	—	38	4	no	—
66	C₂×C₄	—	38	2	no	—
67	C₂×C₄	D₇₆	1	2	yes	—
68	C₂²	C₂×D₇₆	1	1	yes	characteristic
69	C₂²	#64541	1	2	yes	—
70	C₂²	#64543	1	1	yes	characteristic
71	C₂²	#64543	1	2	yes	—
72	C₂²	Q₈×D₁₉	1	1	yes	characteristic
73	C₄	—	2	2	no	—
74	C₄	—	4	2	no	—
75	C₄	—	38	2	no	—
76	C₄	—	76	2	no	—
77	C₄	—	76	1	no	—
78	C₂	#10597321	1	1	yes	characteristic
79	C₂	#10597325	1	2	yes	—
80	C₂	#10597332	1	1	yes	characteristic
81	C₂	#10597335	1	2	yes	—
82	C₂	#10597343	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₉
commutator, socle, prime radical, cosocle	C₂³×C₁₉	C₂³
Fitting	C₁₉×#95	C₂
hypercenter	#95	D₁₉
hypocenter	C₁₉	#400
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
47. C₁₉	#400	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊Dic₁₉	2
C₂×Dic₁₉⋊C₄	2
C₁₉×#95	2
C₁₉⋊#95	2
#400	19