Subgroups — C₂²×#87775 #13105927

Order 1600.

592 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×Dic₁₀	C₂	1	2	yes	maximal
2	C₂²×#6029	C₂	1	1	yes	maximal, characteristic
3	C₂×#87775	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₄×C₅²	C₂²	1	1	yes	characteristic
5	C₂²×C₅×Dic₅	—	2	2	no	—
6	C₂×C₅×Dic₁₀	—	2	6	no	—
7	C₂×C₅×Dic₁₀	C₂²	1	12	yes	—
8	C₂×#6029	C₂²	1	6	yes	—
9	#87775	C₂²	1	16	yes	direct product factor
10	C₂²×#689	—	5	2	no	maximal
11	C₂³×C₅²	D₄	1	1	yes	characteristic
12	C₂×C₄×C₅²	D₄	1	3	yes	—
13	C₂×C₄×C₅²	C₂³	1	3	yes	—
14	C₂×C₅×Dic₅	—	2	12	no	—
15	C₅×Dic₁₀	—	2	12	no	—
16	C₅×Dic₁₀	C₂³	1	8	yes	—
17	#6029	C₂³	1	4	yes	—
18	C₂²×C₅×Q₈	—	5	2	no	—
19	C₂²×Dic₁₀	D₅	1	2	yes	—
20	C₂×#689	—	5	24	no	—
21	C₂²×#168	—	5	2	no	—
22	C₂²×#168	—	10	2	no	—
23	C₂²×C₅²	Q₁₆	1	4	yes	complemented
24	C₂²×C₅²	C₂×D₄	1	3	yes	—
25	C₄×C₅²	C₂×D₄	1	3	yes	—
26	C₄×C₅²	C₂⁴	1	1	yes	characteristic
27	C₅×Dic₅	—	2	8	no	—
28	C₂×C₅×Q₈	—	5	12	no	—
29	C₂×C₅×Q₈	—	10	6	no	—
30	C₂²×C₄×C₅	—	2	2	no	—
31	C₂²×C₄×C₅	—	10	2	no	—
32	C₂²×C₄×C₅	C₂×D₅	1	2	yes	—
33	C₂²×Dic₅	—	2	2	no	—
34	C₂×Dic₁₀	—	2	6	no	—
35	C₂×Dic₁₀	C₂×D₅	1	12	yes	—
36	#689	—	5	32	no	—
37	C₂×#168	—	5	12	no	—
38	C₂×#168	—	10	12	no	—
39	C₂²×Q₁₆	—	25	1	no	Sylow
40	C₂×C₅²	C₂×Q₁₆	1	6	yes	complemented
41	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
42	C₂³×C₅	—	2	2	no	—
43	C₂³×C₅	C₂²⋊D₅	1	2	yes	—
44	C₅×Q₈	—	5	8	no	—
45	C₅×Q₈	—	10	12	no	—
46	C₂×C₄×C₅	—	2	6	no	—
47	C₂×C₄×C₅	—	2	6	no	—
48	C₂×C₄×C₅	—	10	12	no	—
49	C₂×C₄×C₅	C₂²⋊D₅	1	6	yes	—
50	C₂×C₄×C₅	C₂²×D₅	1	6	yes	—
51	C₂×Dic₅	—	2	12	no	—
52	Dic₁₀	—	2	12	no	—
53	Dic₁₀	C₂²×D₅	1	8	yes	—
54	#168	—	5	8	no	—
55	#168	—	10	8	no	—
56	C₂²×Q₈	—	5	2	no	—
57	C₂×Q₁₆	—	25	12	no	—
58	C₂²×C₈	—	25	1	no	—
59	C₅²	C₂²×Q₁₆	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₅	—	2	6	no	—
61	C₂²×C₅	—	2	8	no	—
62	C₂²×C₅	#689	1	8	yes	complemented
63	C₂²×C₅	C₂×C₂²⋊D₅	1	6	yes	—
64	C₄×C₅	—	2	6	no	—
65	C₄×C₅	—	2	2	no	—
66	C₄×C₅	—	10	8	no	—
67	C₄×C₅	C₂×C₂²⋊D₅	1	6	yes	—
68	C₄×C₅	C₂³×D₅	1	2	yes	—
69	Dic₅	—	2	8	no	—
70	C₂×Q₈	—	5	12	no	—
71	C₂×Q₈	—	10	6	no	—
72	C₂²×C₄	—	10	2	no	—
73	C₂²×C₄	D₅²	1	1	yes	characteristic
74	Q₁₆	—	25	16	no	—
75	C₂×C₈	—	25	6	no	—
76	C₂×C₅	—	2	12	no	—
77	C₂×C₅	—	2	2	no	—
78	C₂×C₅	C₂×#689	1	12	yes	complemented
79	C₂×C₅	C₂²×C₂²⋊D₅	1	2	yes	—
80	C₂³	#6037	1	1	yes	characteristic
81	Q₈	—	5	8	no	—
82	Q₈	—	10	12	no	—
83	C₂×C₄	—	10	12	no	—
84	C₂×C₄	#6037	1	3	yes	—
85	C₂×C₄	C₂×D₅²	1	3	yes	—
86	C₈	—	25	4	no	—
87	C₅	—	2	2	no	—
88	C₅	C₂²×#689	1	2	yes	complemented
89	C₂²	#87775	1	4	yes	direct product factor
90	C₂²	C₂×#6037	1	3	yes	—
91	C₄	—	10	8	no	—
92	C₄	C₂×#6037	1	3	yes	—
93	C₄	C₂²×D₅²	1	1	yes	characteristic
94	C₂	C₂×#87775	1	6	yes	direct product factor
95	C₂	C₂²×#6037	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#6037
commutator, cosocle	C₄×C₅²	C₂⁴
Frattini	C₄	C₂²×D₅²
Fitting	C₂²×C₄×C₅²	C₂²
socle, prime radical	C₂³×C₅²	D₄
hypercenter	C₂²×C₄	D₅²
hypocenter	C₅²	C₂²×Q₁₆
LCS	G ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
3. C₂×#87775	C₂	direct (N × H)
9. #87775	C₂²	direct (N × H)
23. C₂²×C₅²	Q₁₆	semidirect
40. C₂×C₅²	C₂×Q₁₆	semidirect
59. C₅²	C₂²×Q₁₆	semidirect
62. C₂²×C₅	#689	semidirect
78. C₂×C₅	C₂×#689	semidirect
88. C₅	C₂²×#689	semidirect
89. C₂²	#87775	direct (N × H)
94. C₂	C₂×#87775	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×C₅×Dic₁₀	2
C₂²×#6029	2
C₂×#87775	2
C₂²×#689	5

Subgroups — C22×#87775 #13105927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#87775 #13105927