Subgroups — C₂×C₂₅×#10587723 #41031239

Order 27300.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×#10587723	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₂₅×#63271	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₅×D₉₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂₅×#63271	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×#10587723	C₅	1	1	yes	maximal, characteristic
6	C₂₅×D₉₁	C₂×C₃	1	2	yes	complemented
7	C₂×C₇×C₁₃×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₂₅×D₁₃⋊C₃	—	7	1	no	maximal, Hall
9	C₅×#10587723	C₂×C₅	1	2	yes	—
10	C₂×C₅×#63271	C₂×C₅	1	1	yes	characteristic
11	C₇×C₁₃×C₂₅	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₂₅×AGL(1,𝔽₇)	—	13	1	no	maximal, Hall
13	C₂×C₂₅×C₁₃⋊C₃	—	7	1	no	—
14	C₂₅×D₁₃⋊C₃	—	7	2	no	—
15	C₂×C₅×D₉₁	C₃×C₅	1	1	yes	characteristic
16	C₅×#63271	C₂²×C₅	1	1	yes	characteristic
17	C₂×C₂₅×D₁₃	—	7	1	no	Hall
18	C₂×#10587723	C₂₅	1	1	yes	characteristic, direct product factor, Hall
19	C₂×ΓL(1,𝔽₈)×C₂₅	—	13	1	no	—
20	C₂₅×AGL(1,𝔽₇)	—	13	2	no	—
21	C₂₅×C₁₃⋊C₃	—	7	1	no	Hall
22	C₂×C₅×C₇×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic
23	C₅×D₉₁	C₂×C₃×C₅	1	2	yes	—
24	C₂×C₅×D₁₃⋊C₃	—	7	1	no	—
25	C₂×D₇×C₂₅	—	13	1	no	Hall
26	C₂×C₁₃×C₂₅	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
27	C₂₅×D₁₃	—	7	2	no	—
28	C₂×#63271	C₂×C₂₅	1	1	yes	characteristic, complemented
29	#10587723	C₂×C₂₅	1	2	yes	direct product factor
30	ΓL(1,𝔽₈)×C₂₅	—	13	1	no	Hall
31	C₅×C₇×C₁₃	C₂²×C₃×C₅	1	1	yes	characteristic
32	C₂×C₅×AGL(1,𝔽₇)	—	13	1	no	—
33	C₂×C₅×C₁₃⋊C₃	—	7	1	no	—
34	C₅×D₁₃⋊C₃	—	7	2	no	—
35	C₂×D₉₁	C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
36	C₂×C₇×C₂₅	D₁₃⋊C₃	1	1	yes	characteristic, complemented
37	D₇×C₂₅	—	13	2	no	—
38	C₁₃×C₂₅	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
39	C₂²×C₃×C₂₅	—	91	1	no	Hall
40	#63271	C₂²×C₂₅	1	1	yes	characteristic, complemented, Hall
41	C₂×C₅×D₁₃	—	7	1	no	—
42	C₂×C₅×ΓL(1,𝔽₈)	—	13	1	no	—
43	C₅×AGL(1,𝔽₇)	—	13	2	no	—
44	C₅×C₁₃⋊C₃	—	7	1	no	—
45	C₂×C₇×C₁₃	C₂×C₃×C₂₅	1	1	yes	characteristic, complemented
46	D₉₁	C₂×C₃×C₂₅	1	2	yes	complemented
47	C₇×C₂₅	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
48	C₂×D₁₃⋊C₃	—	7	1	no	Hall
49	C₂×C₃×C₂₅	—	91	2	no	—
50	C₂×C₃×C₂₅	—	91	1	no	—
51	C₂×C₅×D₇	—	13	1	no	—
52	C₂×C₅×C₁₃	C₅×AGL(1,𝔽₇)	1	1	yes	characteristic
53	C₅×D₁₃	—	7	2	no	—
54	C₅×ΓL(1,𝔽₈)	—	13	1	no	—
55	C₂²×C₂₅	—	91	1	no	Hall
56	C₇×C₁₃	C₂²×C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
57	C₂×AGL(1,𝔽₇)	—	13	1	no	Hall
58	C₂×C₁₃⋊C₃	—	7	1	no	—
59	D₁₃⋊C₃	—	7	2	no	—
60	C₃×C₂₅	—	91	1	no	Hall
61	C₂×C₅×C₇	C₅×D₁₃⋊C₃	1	1	yes	characteristic
62	C₅×D₇	—	13	2	no	—
63	C₅×C₁₃	C₂×C₅×AGL(1,𝔽₇)	1	1	yes	characteristic
64	C₂²×C₃×C₅	—	91	1	no	—
65	C₂×D₁₃	—	7	1	no	Hall
66	C₂×C₂₅	—	91	2	no	—
67	C₂×C₂₅	#10587723	1	1	yes	characteristic, direct product factor
68	C₂×ΓL(1,𝔽₈)	—	13	1	no	—
69	AGL(1,𝔽₇)	—	13	2	no	—
70	C₁₃⋊C₃	—	7	1	no	Hall
71	C₅×C₇	C₂×C₅×D₁₃⋊C₃	1	1	yes	characteristic
72	C₂×C₃×C₅	—	91	2	no	—
73	C₂×C₃×C₅	—	91	1	no	—
74	C₂×D₇	—	13	1	no	Hall
75	C₂×C₁₃	C₂₅×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
76	D₁₃	—	7	2	no	—
77	C₂₅	C₂×#10587723	1	1	yes	characteristic, direct product factor, Sylow
78	ΓL(1,𝔽₈)	—	13	1	no	Hall
79	C₂²×C₅	—	91	1	no	—
80	C₃×C₅	—	91	1	no	—
81	C₂×C₇	C₂₅×D₁₃⋊C₃	1	1	yes	characteristic, complemented
82	D₇	—	13	2	no	—
83	C₁₃	C₂×C₂₅×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
84	C₂²×C₃	—	91	1	no	Hall
85	C₂×C₅	—	91	2	no	—
86	C₂×C₅	C₅×#10587723	1	1	yes	characteristic
87	C₇	C₂×C₂₅×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	—	91	2	no	—
89	C₂×C₃	—	91	1	no	—
90	C₅	C₂×C₅×#10587723	1	1	yes	characteristic
91	C₂²	—	91	1	no	Sylow
92	C₃	—	91	1	no	Sylow
93	C₂	—	91	2	no	—
94	C₂	C₂₅×#10587723	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₅	#10587723
commutator, hypocenter	C₇×C₁₃	C₂²×C₃×C₂₅
Frattini	C₅	C₂×C₅×#10587723
Fitting	C₂×C₇×C₁₃×C₂₅	C₂×C₃
socle	C₂×C₅×C₇×C₁₃	C₂×C₃×C₅
prime radical	C₂×C₅×#10587723	C₅
cosocle	C₅×C₇×C₁₃	C₂²×C₃×C₅
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂×C₂₅

Complements

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

N	H ≅ G/N	type
1. C₂₅×#10587723	C₂	direct (N × H)
2. C₂×C₂₅×#63271	C₂	semidirect
3. C₂×C₂₅×D₉₁	C₃	semidirect
4. C₂₅×#63271	C₂²	semidirect
6. C₂₅×D₉₁	C₂×C₃	semidirect
7. C₂×C₇×C₁₃×C₂₅	C₂×C₃	semidirect
11. C₇×C₁₃×C₂₅	C₂²×C₃	semidirect
18. C₂×#10587723	C₂₅	direct (N × H)
26. C₂×C₁₃×C₂₅	AGL(1,𝔽₇)	semidirect
28. C₂×#63271	C₂×C₂₅	semidirect
29. #10587723	C₂×C₂₅	direct (N × H)
35. C₂×D₉₁	C₃×C₂₅	semidirect
36. C₂×C₇×C₂₅	D₁₃⋊C₃	semidirect
38. C₁₃×C₂₅	C₂×AGL(1,𝔽₇)	semidirect
40. #63271	C₂²×C₂₅	semidirect
45. C₂×C₇×C₁₃	C₂×C₃×C₂₅	semidirect
46. D₉₁	C₂×C₃×C₂₅	semidirect
47. C₇×C₂₅	C₂×D₁₃⋊C₃	semidirect
56. C₇×C₁₃	C₂²×C₃×C₂₅	semidirect
67. C₂×C₂₅	#10587723	direct (N × H)
75. C₂×C₁₃	C₂₅×AGL(1,𝔽₇)	semidirect
77. C₂₅	C₂×#10587723	direct (N × H)
81. C₂×C₇	C₂₅×D₁₃⋊C₃	semidirect
83. C₁₃	C₂×C₂₅×AGL(1,𝔽₇)	semidirect
87. C₇	C₂×C₂₅×D₁₃⋊C₃	semidirect
94. C₂	C₂₅×#10587723	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₅×#10587723	2
C₂×C₂₅×#63271	2
C₂×C₂₅×D₉₁	3
C₂×C₅×#10587723	5
C₂×C₂₅×D₁₃⋊C₃	7
C₂×C₂₅×AGL(1,𝔽₇)	13

Subgroups — C2×C25×#10587723 #41031239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₅×#10587723 #41031239