Subgroups — C₂×#11716364 #13098376

Order 1600.

219 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₂₅	C₂	1	1	yes	maximal, characteristic
3	C₂²×#6014	C₂	1	1	yes	maximal, characteristic
4	#11716364	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₄×C₂₅	C₂²	1	1	yes	characteristic
6	C₂²×Dic₂₅	C₄	1	2	yes	—
7	C₂×C₈×C₂₅	C₄	1	4	yes	complemented
8	C₂×C₈×C₂₅	C₂²	1	2	yes	—
9	C₄×Dic₂₅	C₄	1	2	yes	—
10	C₄×Dic₂₅	C₂²	1	2	yes	—
11	C₂×#6014	C₄	1	4	yes	complemented
12	C₂×#6014	C₂²	1	2	yes	—
13	C₂×#3947	—	5	1	no	maximal
14	C₂³×C₂₅	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₂₅	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₂₅	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₂₅	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
19	C₂×Dic₂₅	—	2	4	no	—
20	C₂×Dic₂₅	C₂×C₄	1	4	yes	—
21	C₈×C₂₅	C₂×C₄	1	4	yes	complemented
22	#6014	C₂×C₄	1	4	yes	complemented
23	C₂²×C₅×C₈	D₅	1	1	yes	characteristic
24	C₂×C₄×Dic₅	—	5	1	no	—
25	C₂²×#168	—	5	1	no	—
26	#3947	—	5	4	no	—
27	C₂²×C₂₅	C₄²	1	2	yes	—
28	C₂²×C₂₅	M₁₆	1	4	yes	—
29	C₂²×C₂₅	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₂₅	C₄²	1	2	yes	—
31	C₄×C₂₅	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₂₅	C₂²×C₄	1	1	yes	characteristic
33	Dic₂₅	—	2	4	no	—
34	C₂²×C₄×C₅	C₂×D₅	1	1	yes	characteristic
35	C₂²×Dic₅	—	5	2	no	—
36	C₂×C₅×C₈	Dic₅	1	4	yes	—
37	C₂×C₅×C₈	C₂×D₅	1	2	yes	—
38	C₄×Dic₅	—	5	2	no	—
39	C₄×Dic₅	—	5	2	no	—
40	C₂×#168	—	5	4	no	—
41	C₂×#168	—	5	2	no	—
42	C₂×#97	—	25	1	no	Sylow
43	C₂×C₂₅	#97	1	4	yes	complemented
44	C₂×C₂₅	C₂×C₄²	1	1	yes	characteristic
45	C₂×C₂₅	C₂×M₁₆	1	2	yes	—
46	C₂³×C₅	C₄×D₅	1	1	yes	characteristic
47	C₂×C₄×C₅	C₄×D₅	1	1	yes	characteristic
48	C₂×C₄×C₅	C₄×D₅	1	2	yes	—
49	C₂×C₄×C₅	C₂×Dic₅	1	2	yes	—
50	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
51	C₂×Dic₅	—	5	4	no	—
52	C₂×Dic₅	—	10	4	no	—
53	C₅×C₈	C₂×Dic₅	1	4	yes	—
54	#168	—	5	4	no	—
55	C₂²×C₈	—	25	1	no	—
56	C₂²×C₈	D₂₅	1	1	yes	characteristic
57	C₂×C₄²	—	25	1	no	—
58	#97	—	25	4	no	—
59	C₂₅	C₂×#97	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₅	#676	1	4	yes	—
61	C₂²×C₅	C₄×Dic₅	1	2	yes	—
62	C₂²×C₅	C₂×C₄×D₅	1	1	yes	characteristic
63	C₄×C₅	C₄×Dic₅	1	2	yes	—
64	C₄×C₅	C₂×C₄×D₅	1	1	yes	characteristic
65	C₄×C₅	C₂²×Dic₅	1	1	yes	characteristic
66	Dic₅	—	10	4	no	—
67	C₂²×C₄	—	25	2	no	—
68	C₂²×C₄	C₂×D₂₅	1	1	yes	characteristic
69	C₂×C₈	—	25	4	no	—
70	C₂×C₈	—	25	2	no	—
71	C₂×C₈	Dic₂₅	1	4	yes	complemented
72	C₂×C₈	C₂×D₂₅	1	2	yes	—
73	C₄²	—	25	2	no	—
74	C₄²	—	25	2	no	—
75	C₂×C₅	#3947	1	4	yes	—
76	C₂×C₅	C₂×#676	1	2	yes	—
77	C₂×C₅	C₂×C₄×Dic₅	1	1	yes	characteristic
78	C₂³	C₄×D₂₅	1	1	yes	characteristic
79	C₂×C₄	—	25	4	no	—
80	C₂×C₄	—	50	4	no	—
81	C₂×C₄	C₄×D₂₅	1	1	yes	characteristic
82	C₂×C₄	C₄×D₂₅	1	2	yes	—
83	C₂×C₄	C₂×Dic₂₅	1	2	yes	—
84	C₂×C₄	C₂²×D₂₅	1	1	yes	characteristic
85	C₈	—	25	4	no	—
86	C₈	C₂×Dic₂₅	1	4	yes	complemented
87	C₅	C₂×#3947	1	1	yes	characteristic
88	C₂²	#87712	1	4	yes	—
89	C₂²	C₄×Dic₂₅	1	2	yes	—
90	C₂²	C₂×C₄×D₂₅	1	1	yes	characteristic
91	C₄	—	50	4	no	—
92	C₄	C₄×Dic₂₅	1	2	yes	—
93	C₄	C₂×C₄×D₂₅	1	1	yes	characteristic
94	C₄	C₂²×Dic₂₅	1	1	yes	characteristic
95	C₂	#11716364	1	4	yes	direct product factor
96	C₂	C₂×#87712	1	2	yes	—
97	C₂	C₂×C₄×Dic₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₂₅
commutator	C₂×C₂₅	C₂×C₄²
Frattini	C₂×C₄×C₅	C₂²×D₅
Fitting	C₂²×C₈×C₂₅	C₂
socle, prime radical	C₂³×C₅	C₄×D₅
cosocle	C₂×C₄×C₂₅	C₂³
hypercenter	C₂²×C₈	D₂₅
hypocenter	C₂₅	C₂×#97
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. #11716364	C₂	direct (N × H)
7. C₂×C₈×C₂₅	C₄	semidirect
11. C₂×#6014	C₄	semidirect
21. C₈×C₂₅	C₂×C₄	semidirect
22. #6014	C₂×C₄	semidirect
43. C₂×C₂₅	#97	semidirect
59. C₂₅	C₂×#97	semidirect
71. C₂×C₈	Dic₂₅	semidirect
86. C₈	C₂×Dic₂₅	semidirect
95. C₂	#11716364	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×C₈×C₂₅	2
C₂×C₄×Dic₂₅	2
C₂²×#6014	2
#11716364	2
C₂×#3947	5

Subgroups — C2×#11716364 #13098376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11716364 #13098376