Subgroups — C₂²×#87839 #13107697

Order 1600.

452 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6039	C₂	1	2	yes	maximal
2	C₂²×#6034	C₂	1	1	yes	maximal, characteristic
3	C₂×#87839	C₂	1	12	yes	maximal, direct product factor
4	C₂²×#1039	C₂²	1	1	yes	characteristic
5	C₂²×C₅×Dic₅	—	2	2	no	—
6	C₂×#6039	—	2	6	no	—
7	C₂×#6039	C₂²	1	12	yes	—
8	C₂×#6034	C₂²	1	6	yes	—
9	#87839	C₂²	1	16	yes	direct product factor
10	C₂³×C₅²	D₄	1	1	yes	characteristic
11	C₂×#1039	D₄	1	3	yes	—
12	C₂×#1039	C₂³	1	3	yes	—
13	C₂×C₅×Dic₅	—	2	12	no	—
14	#6039	—	2	12	no	—
15	#6039	C₂³	1	8	yes	—
16	#6034	C₂³	1	4	yes	—
17	C₂²×Dic₁₀	—	10	2	no	—
18	C₂²×#170	—	10	1	no	—
19	C₂²×C₅²	Q₁₆	1	4	yes	complemented
20	C₂²×C₅²	C₂×D₄	1	3	yes	—
21	#1039	C₂×D₄	1	3	yes	—
22	#1039	C₂⁴	1	1	yes	characteristic
23	C₅×Dic₅	—	2	8	no	—
24	C₂²×C₄×C₅	—	10	2	no	—
25	C₂²×Dic₅	—	2	2	no	—
26	C₂²×Dic₅	—	10	1	no	—
27	C₂²×Dic₅	—	10	2	no	—
28	C₂×Dic₁₀	—	10	12	no	—
29	C₂×Dic₁₀	—	10	12	no	—
30	C₂×#170	—	10	6	no	—
31	C₂²×Q₁₆	—	25	1	no	maximal, Sylow
32	C₂×C₅²	C₂×Q₁₆	1	6	yes	complemented
33	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
34	C₂³×C₅	—	2	2	no	—
35	C₂³×C₅	—	2	1	no	—
36	C₂×C₄×C₅	—	10	12	no	—
37	C₂×Dic₅	—	2	12	no	—
38	C₂×Dic₅	—	10	6	no	—
39	C₂×Dic₅	—	10	3	no	—
40	C₂×Dic₅	—	10	3	no	—
41	C₂×Dic₅	—	10	6	no	—
42	Dic₁₀	—	10	8	no	—
43	Dic₁₀	—	10	24	no	—
44	#170	—	10	4	no	—
45	C₂²×Q₈	—	25	2	no	—
46	C₂×Q₁₆	—	25	12	no	—
47	C₂²×C₈	—	25	1	no	—
48	C₅²	C₂²×Q₁₆	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₅	—	2	8	no	—
50	C₂²×C₅	—	2	4	no	—
51	C₂²×C₅	—	2	6	no	—
52	C₂²×C₅	—	2	3	no	—
53	C₄×C₅	—	10	8	no	—
54	Dic₅	—	2	8	no	—
55	Dic₅	—	10	6	no	—
56	Dic₅	—	10	3	no	—
57	Dic₅	—	10	1	no	—
58	Dic₅	—	10	2	no	—
59	C₂×Q₈	—	25	12	no	—
60	C₂×Q₈	—	50	6	no	—
61	C₂²×C₄	—	10	2	no	—
62	C₂²×C₄	—	25	1	no	—
63	Q₁₆	—	25	16	no	—
64	C₂×C₈	—	25	6	no	—
65	C₂×C₅	—	2	12	no	—
66	C₂×C₅	—	2	6	no	—
67	C₂×C₅	—	2	2	no	—
68	C₂×C₅	—	2	1	no	—
69	C₂³	D₅²⋊C₂	1	1	yes	characteristic
70	Q₈	—	25	8	no	—
71	Q₈	—	50	12	no	—
72	C₂×C₄	—	10	12	no	—
73	C₂×C₄	—	25	3	no	—
74	C₂×C₄	—	25	3	no	—
75	C₈	—	25	4	no	—
76	C₅	—	2	2	no	—
77	C₅	—	2	1	no	—
78	C₂²	#87839	1	4	yes	direct product factor
79	C₂²	C₂×D₅²⋊C₂	1	3	yes	—
80	C₄	—	10	8	no	—
81	C₄	—	25	1	no	—
82	C₄	—	25	3	no	—
83	C₂	C₂×#87839	1	6	yes	direct product factor
84	C₂	C₂²×D₅²⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³	D₅²⋊C₂
commutator, cosocle	#1039	C₂⁴
Frattini	C₂	C₂²×D₅²⋊C₂
Fitting, socle, prime radical	C₂³×C₅²	D₄
hypocenter	C₅²	C₂²×Q₁₆
LCS	G ▷ #1039 ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
3. C₂×#87839	C₂	direct (N × H)
9. #87839	C₂²	direct (N × H)
19. C₂²×C₅²	Q₁₆	semidirect
32. C₂×C₅²	C₂×Q₁₆	semidirect
48. C₅²	C₂²×Q₁₆	semidirect
78. C₂²	#87839	direct (N × H)
83. C₂	C₂×#87839	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#6039	2
C₂²×#6034	2
C₂×#87839	2
C₂²×Q₁₆	25

Subgroups — C22×#87839 #13107697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#87839 #13107697